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FACULTY OF METEOROLOGY

ADVANCED PROFESSIONAL KNOWLEDGE COURSE(METEOROLOGY)

BOOK – 08/12

ANALYSIS & PROGNOSIS, NUMERICAL ANALYSIS & MME

PREPARED BY WG CDR RAHUL VERMA( A&P), WG CDR SHREYA PANDIT (NA) & (MME)

AUGUST 2015

NOTE: - READ THE STARTER KIT WHICH HAS BEEN SENT TO YOU. IN CASE OF DOUBTS YOU MAY CONTACT TRAINING COORDINATION OFFICER (TCO) ON TELE: 2367000/7314

NOTE: - It has been the endeavour of Faculty of Meteorology to update courseware with the latest Policies/ Orders/ Instructions. However the contents of this book are to be used as course material, and not to be quoted as authority at any stage. Officers may refer to the references quoted in the text for official use.

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INDEX: BOOK – 8/12

Subject Chapter Page No.

Analysis & Prognosis

4. PROGNOSIS OF CAT & MOUNTAIN WAVES 4 – 27

5. MOVEMENT OF TROPICAL CYCLONES 28 – 59

Numerical Analysis

2. MATRICES AND LINEAR SYSTEMS OF EQUATIONS 60 - 72

MME2. LASER CEILOMETER 73 – 76

3. WIND PROFILERS 77- 82

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AMENDMENT RECORDS

CHAPTER – 4

PROGNOSIS OF CAT & MOUNTAIN WAVES

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Date Amendment Page No. Authority

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Chapter objectives

After reading this chapter, you should be able to: -

Assimilate the meaning of turbulence and classification of turbulence according to the causes. Understand the Clear Air Turbulence (CAT) and different sources of turbulent energy in the high troposphere and the low stratosphere. Understand the different methods of forecasting of CAT. Understand the turbulence associated with mountains.

Structure

1. Introduction.

2. Classification of Turbulence.

3. Clear Air Turbulence (Characteristics & type).

4. Energetics.

5. Analysis & Forecasting of CAT.

6. Turbulence Associated with Mountains.

7. Conclusion.

Introduction

1. The turbulence could occur at low levels as will as high levels. The essential difference between low level and high level turbulence is related to the dissipative force and the production and growth of turbulence within a limited time scale. The dissipative force is quite strong in the low level and a steady state can be achieved for considerable period. Thus the character of turbulence can be described with parameters such as mixing length and diffusion coefficient. In the upper air, however, a parcel of air moves through a dynamic pattern quite rapidly and thus the time scale for growth is quite small.

2. The basic mechanism of CAT at high level is not unlike the turbulence generated by friction near ground level. For the generation of turbulence of this type marked changes of wind speed along vertical and fairly steep lapse rate are two essential conditions.

3. Air flow over mountainous terrain is more disturbed than over the plains. The flow pattern is complex. An understanding of the characteristics of the flow pattern and the extent, scale and degree of turbulence associated with it, is vital for the safety of aircraft flying over the terrain.4. When an air stream with suitable stability conditions and wind profile strikes a mountain range, the stream over and on the lee of the range forms a train of waves extending vertically to a great height and horizontally downwind to a considerable distance. The flow pattern is extremely complicated and is dependent on the shape,

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length and height of the range on the one hand and the lapse rate and wind gradient of the air stream, on the other.

Classification of Turbulence

5. Turbulence according to the causes can be classified as:

(a) Thermal or Convective. This type is caused by local vertical currents induced by insolation and unstable lapse rates or due to movement of cold air mass over warm surface at low levels and at high levels due to convection in a cirrus shield, due to the release of static or conditional instability in the high troposphere.

(b) Mechanical. This type is caused by strong winds over rough and uneven terrain.

(c) Frontal. This type is caused by lifting at cold fronts or squall lines.

(d) Wind Shear . This type is caused by strong vertical and horizontal wind shears. It is related to Reynold's stresses, Richardsons number, sloping baroclinic zones, jet streams, vertical motion and its horizontal derivatives and temperature changes.

(e) Mountain wave . This type is caused by the break up of vertical oscillations induced by strong flow across a ridge of mountains, during the interaction of stable baroclinic zones. Three factors static stability, wind flow across the ridge and slope of the mountain ridge, are important.

(f) Convective Cloud . This type is caused by thermal instability and eddies produced by the large shears between updraughts and downdraughts.

Clear Air Turbulence (CAT)

6. CAT can be defined as an imbalance in the atmosphere in which eddies and gravity waves are formed. In general the term CAT is used to denote turbulence at high level (3 km and above) outside Cb clouds. CAT can occur in cirrus clouds, haze layers or clear air.

7. Typical dimensions of areas of CAT are 30km long and 5 to 15 km across, between heights 4 km and 5 km with a thickness of the order of 300m to 500m, lasting from 30 minutes to three hours. However, U2 flights have noted CAT at 20km and X15s at still greater heights. Individual turbulent zones or patches often occur in close proximity to one another, both vertically and horizontally.

Types of CAT

8. CAT can be divided into three separate categories. The first is the most common type, namely, Wind Shear Turbulence. This is associated with strong vertical and horizontal wind shears. The second class of CAT is associated with mountain wave activity. The breakdown of the waves produces the greatest amount of turbulence of all types. Some measurements suggest that gust velocities in mountain waves exceed the design criteria of heavy multi-jet aircraft. The components of mountain wave CAT consist of three variables – two of them being

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atmospheric viz. wind and static stability and one orographic, viz. the slope of the ridge. The third type of CAT is convective. CAT is associated with clear or dry convective cells and also convection in a cirrus shield. This is caused by the release of static or conditional instability in the high troposphere. There is yet another type of CAT, referred to as trough turbulence. However, this can be considered as either shear or convective turbulence, depending on its position relative to the jet core since it is connected with the atmospheric variable associated with the trough.

Energetics

9. The main sources of turbulent energy in the high troposphere and the low stratosphere are:-

(a) Vertical Shear . This factor makes turbulent energy available through Reynold's stresses. This can produce turbulence at a rapid rate under low Richardson Numbers (low static stability).

(b) Horizontal Wind Gradient . Horizontal wind shear and diuence can create turbulence through Reynold's stresses. This by itself is not significant and whatever correlation has been found is believed to be due to a combination with other factors.

(c) Static Stability . Static instability by itself is probably an insignificant factor in the upper atmosphere, since in most cases light turbulence would dissipate the energy as quickly as it is generated. Static stability since it constitutes a strong turbulence sink during the growth of turbulence, however, is of considerable importance.

(d) Gravity waves . These waves can be strong enough to cause severe turbulence over mountainous regions. Again, this factor by itself may not normally constitute a source of strong turbulence though it contributes significantly in increasing the probability and perhaps the intensity of CAT (Panofsky, 1968). Gravity waves in combination with vertical shear, however, produces severe turbulence. Gravity waves themselves provide a significant source of energy and the inclination of streamlines associated with gravity waves combined with strong vertical shear permits violent turbulence to be attained due to local Reynold's stresses.

(e) Dynamic Instability . Strong anticyclonic shear and curvature are favourable for dynamic instability. Any region of decreasing negative relative vorticity will thus from an area susceptible to turbulence, particularly if associated with low Richardson Number. These can be located in the temperature or thickness field. Dynamic instability can act as a source of turbulent energy and can create mesoscale perturbations. These factors with strong vertical shear will tend to create intense shears locally and effective release of energy. Reduced static stability will allow the energy to appear in the vertical and horizontal whereas static stability will act as a turbulent energy sink, thus constituting a very favourable region for occurrence of turbulence.

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CAT Analysis

10. The main difficulty in the analysis of CAT zones is the scale of motion involved. Individual turbulent eddies or waves have a microscale structure. The size of eddies which cause aircraft bumpiness varies from 300 to 1000 metres, depending on the speed of the aircraft. The distance between radiosonde observations is extremely wide, of the order of hundreds of miles. The data based on these observations do not reveal the microstructure of the waves. Thus the structure of eddies and waves are missed on the chart.

11. Important CAT features are:-

(a) CAT is a predominantly a patchy phenomenon and its intensity is generally less than the turbulence encountered in thunderstorms.

(b) High level turbulence is frequently anisotropic with stronger horizontal gusts. The bump frequency is greater at higher levels than at lower levels.

(c) There is a strong association between jet stream and CAT.

(d) Over land, CAT occurs mostly on the cyclonic side of the jet stream, while over water , CAT is mostly encountered on the anticyclonic side.

(e) CAT is significantly more at the tropopause.

(f) Terrain has an additive influence on CAT.

Forecasting of CAT

12. The synoptic features generally associated with CAT are curved, meandering and strong jet streams and sloping stable baroclinic zone. Wind shear turbulence occurs in regions of cyclonic wind shear. According to Banon (1961) turbulence is more severe near the level of the maximum winds in the jet stream and decreases sharply at higher levels. According to Rieter (1963), CAT occurs in and near the regions of strong horizontal temperature gradients at 250hPa (which indicate the presence of a baroclinic stable zone). Cold air advection enhances the probability of CAT, as in the case of the stratospheric warm tongue and confluent regions of two jet streams near an upper trough. The other feature strongly associated with CAT is

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the isentrophic trough north of a strong jet stream. According to Endlich (1963) the turbulence in a sharp trough associated with a stable layer with strong shear, cold advection, and convergence of the normal component of the wind. In the case of a ridge, turbulence occurs in the thermally stable layer associated with the tropopause and above and to the left of the jet core. The stable layer is associated with strong warm advection and convergence of the normal component of the wind. He suggests the following analysis scheme for CAT:-

(a) Identify the location of progressive upper-air troughs, ridges and jet stream by utilizing 12 hour changes in wind velocity, height and temperature.

(b) Utilise the lapse rate in the 300 to 200 hPa layer to aid in jet stream analysis. Jet core lies along the southern edge of the largest gradient in lapse rate.

(c) Identify the tropopause, upper stable layers, layers of strong vertical shear and advection.

13. Other synoptic features which are associated with turbulence are Jet fingers deflected from the main Jet core and easterly portion of the jet maxima of middle and high latitudes.

14. Horizontal and Vertical Shear. For shear turbulence, Harrison (1959) considers four locations in respect of the jet stream:

(a) Left of jet stream

(b) Right of jet stream

(c) Between two jets

(d) Sub-tropical jet stream

15. He suggests the use of a critical value of horizontal shear 40 kt in 150 N miles as a parameter. The probability of occurrence of turbulence in the four types as related to synoptic trough and ridges is shown in the figure above. In cases of type (b) and (c) vertical shear of 6 kt/300 m may be substituted in the case of horizontal wind shear. In the case of (c) confluence seems to be an important factor. CAT occurrences also seem to be associated with large gradient of shear.

16. George's Method. George (1960) has developed the following method for CAT prognosis: -

(a) Obtain all data where vertical shear values exceed 5 kt/300 m and plot them.

(b) Draw vertical wind shear isotachs for intervals of 3 kt/300m beginning with vertical shear value of 6. Hatch the area enclosed by the two innermost

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isopleths to indicate the centre of the vertical wind shear.

(c) Draw isolines at 1.5 km intervals for the altitude of the base of the vertical shear and note the regions of significant gradients.

(d) Inspect the upper wind/constant pressure charts immediately above the altitude of the base of vertical shear layer to determine if horizontal shear exceeds 40 kt/200 km. Enclose this area with a red line.

(e) Note the areas where vertical and strong horizontal wind shears overlap. Forecast severe CAT in these regions for a depth of 1000 m below to 2000m above the shear layer.

17. Tropopause and Turbulence. Tropopause is a favourable region where gravity waves, in regions of strong vertical shear, may become unstable and cause turbulence. These regions of strong vertical shears may manifest themselves as positive vertical shear as the case of polar tropopause and negative vertical shear in the case of sub-tropical tropopause. CAT also occurs at the tropopause break or where the tropopause slope is maximum.

18. Vertical Velocity and Turbulence. Variation of vertical motion perpendi-cular to the streamline of the jet axis (w/n) has been suggested as a forecasting parameter. Downstream spreading of isotherms constitutes a favourable area which causes a negative w/n.

19. Temperature Change and Turbulence. A daily temperature change chart at 200hPa provides an easy tool for locating areas of turbulence, since CAT has been associated with temperature change of 3°C to 5°C/24 hour and to the gradient of temperature of over 5°C/3½° latitude.

20. Richardson's Number and Turbulence. CAT occurs in regions of vertical wind shear and large horizontal temperature gradient. There is also considerable observational evidence that CAT is associated with baroclinic layers in which the vertical shear is so strong as to overcome static stability. Reiter believes that CAT in these layers is due to gravity wave, which becomes unstable due to strong vertical shear. The dimensionless Richardson Number which takes into account both the vertical stability of the air and the shear is thus a convenient forecasting parameter. The Richardson Number is defined as:

Ri=

where z is height, V the wind velocity, potential temperature and g gravity. Both perturbation theory and energy considerations lead us to the conclusion that there exists a critical value of the Richardson number below which perturbations can grow and produce turbulence. Taylor found this critical value to be 0.25. Panofsky et al (1968) found this value to be near 0.5. It has, however, been shown by Philips (1967) that a layer with greater than critical Richardson number can be made unstable by a wave with considerable vertical amplitude. In spite of the difficulty of assigning a critical value to the Richardson number by which turbulence is generated, there is no doubt that this can be used qualitatively at least for the separation of areas of turbulence and no turbulence. Colson and Panofsky (1965), have devised an index of clear air turbulence defined by.

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I = ( V)2 (I - Ri / Ri critical)

Where Ri critical has been taken as 0.75. The severity of turbulence may be classified for different values of the index as below:

I >25 = Severe turbulenceI 0 to 25 = ModerateI 0 to - 25 = LightI >- 25 = Nil

The value on the right hand side can easily be evaluated from available radiosonde on which upper wind data have been plotted. For Calculation of Ri asuming linear variations, it can be written

Ri=

Where k2 =

, and can be obtained from T- gram; to obtain k a polar diagram is used. Once these values are obtained Ri can be obtained from two other nomograms. If constant value of 9.4 is assumed for / , Ri can be determined directly from table 2. For obtaining Ri for layers between the jet maximum wind level and a standard isobaric level a correction is to be applied. This value of Ri assuming to be 3400 A and Z = 3250m can be written as Ri = (Ris x 1)/3250,

where Ris is the value given in table 2. Table 1 and 3 gives the Ri-values for different values of + Ris. 1 is the thickness of the layer between the level of maximum wind and 300/200 hPa.

Table 1

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Table 2

Table 3

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21. CAT Index. Another Index relates the Laplacian of the horizondal wind shear and vertical derivative of the normal wind with the intensity of turbulence. The relationship is

I= 2(Horizontal wind shear) - 10 (thermal wind)Large negative values of this index are associated with severe CAT.

22. Surface Feature and CAT. CAT frequently occurs above the north and northwestern section of a developing low. The turbulence in such cases is primarily

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due to a geostrophic field in this region of the atmosphere.

23. Turbulence and Satellite. Satellite pictures help us to identify jet stream location and configuration. An inference regarding the height of the tropopause level is also possible from such data - thus it is possible to utilise such data for delineating areas of possible turbulence. It is also possible to identify mountain waves and areas of turbulence from the satellite cloud pictures, particularly when lenticular clouds are observed Lee waves can also be observed as parallel cloud.

24. Forecasting Aids. Some useful tools for forecasting CAT are:-

(a) The 300 hPa pressure level analysis and forecast wind field. These are also used to determine the current and forecast position of jet stream core.

(b) The forecast tropopause height and smoothed vertical wind shear fields. These are used to identify the regions where the tropopause is steeply sloped and to locate the height of jet cores.

(c) The 500 hPa pressure level analysis and forecast velocity and wind fields which are used to identify areas of cold air advection, region of possible cyclogenesis and the areas where components are normal to mountain ridges.(d) The 250 hPa and 200 hPa level analysis and forecast temperature fields, regions of strong isotherm packing and temperature trough.

(e) The current and forecast surface fronts and pressure centers which are inspected for signs of cyclogenesis and position of jet stream core.

(f) The current and forecast pressure gradient which is checked to identify areas of possible mountain waves activities.

(g) The current and forecast wind fields at the ridge top level in mountain regions which identify the areas of occurrence of mountain waves.

(h) The aircraft observation which are used to determine the relationship between CAT observation and existing synoptic scale parameter.

(j) Satellite photographs and NWP forecast which are used especially in data sparse area to identify upper air short waves, the jet stream core position, surface fronts centre and standing mountain wave’s clouds.

(k) Plotted radiosonde ascent which are used to locate area of strong vertical wind shear, stable layers and tropopause height.

25. CAT Forecasting Hints. Forecasting of CAT is still in the stage of evolution. The main difficulty in the analysis of CAT zones is the scale of motion involved. Individual turbulent eddies or waves have a micro-scale structure. The size of eddies which cause aircraft bumpiness varies from 300 to 1000 meters, depending on the speed of the aircraft. The distance between radiosonde observations is extremely wide, of the order of hundreds of miles. The data based on these observations do not reveal the microstructure of the waves. Thus the structure of eddies and waves are missed on the chart. The difficulties in this regard

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are enhanced due to its patchy nature and the fact that CAT zones appear to develop and dissipate with an irregular life cycle.

26. CAT can be expected in the regions where:-

(a) Vertical wind shear greater than 4 kt per 300 m.

(b) Horizontal temperature shears of 5oC per 150 km.

(c) Horizontal wind shears greater than 25 kt per 150 km (moderate CAT) and 50 kt per 150 km (severe CAT).

(d) Left or polar side of jet stream at all altitudes around the jet stream and just below the tropical tropopause.

(e) In the convergence zone of two jet streams.

(f) Inversions especially near and downwind of mountain ranges.

(g) Over sharp troughs.

(h) One can encounter CAT when flying from a slow moving air mass of about 10 to 20 kt into or near a jet stream with speed of well above 100 kt.

27. It is also found that CAT could be predicted over the areas and near the levels of large inversions (Table 4).

Inversion Criteria Type of CAT1.5°C/1000' No CAT

1.5°C/1000' to 2.5°C/1000' Light CAT2.5°C/1000' to 4.0°C/1000' Moderate CAT

4.5°C/1000' Severe CAT

Table 4

28. According to published material, horizontal and vertical temperature gradient are considered to be better indications of turbulence in the 50000-70000 ft range than any other routine parameters. It has been emphasised that this includes large lapse as well as large inversion rates. A suggested relation is given in Table 5. Table 6 shows the CAT occurrence with regard to different types of waves.

Temp Gradient Horizontal Vertical Turbulence

Small 1°C /25 nm 1.5 ° C/1000' Very light to smooth

Medium 1.5°C/25 nm to 1°C/12 nm

1.5°C to 2.5°C /1000' Light to moderate

Large 1.5 °C/1000' 1.5 ° C/1000' Moderate to Severe

Table 5

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Type of Wave Dimension TurbulenceLarge Wave Horizontal wave heights/ 1/2

wavelength4/3 Moderate or

SevereMedium Wave Horizontal wave heights/ 1/2

wavelength4/3 to 3/4 Light to

3/4 ModSmall Wave Horizontal wave heights/1/2

wavelength3/4 Light or Less

CAT

Table 6

29. CAT relies more on pilots' abilities to extract information from their weather charts and meteorological forecasts, the reports of other aircraft in the vicinity, and good old fashioned experience. Pilots noting the curling cloud formations would likely conclude CAT was in the vicinity.

30. Forecasting techniques used are basically extrapolation through association with synoptic features. Although one cannot see CAT visually, a close scrutiny of the weather charts or the forecast turbulence factor on the flight plan, could usually warn pilots of possible affected areas on the route. Most of the knowledge of CAT is based on actual reports from aircraft. Every forecaster should, therefore obtain post-flight debriefing whenever aviator encounters CAT.

31. Checklist for CAT. It would be apparent from above that our knowledge about CAT is still incomplete and forecasting methods depend upon high level wind and temperature features, terrain parameters and gravity waves. A Check list prepared by Clodman et al (1960) for forecasting turbulence is a convenient aid, and is given on the next page.

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32. Problems in CAT Forecasting. There are several notable problems with CAT forecasting:-

(a) It cannot always be foreseen so there is no warning.

(b) It is usually felt at its mildest in the flight deck and is generally more severe in the aft section.

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(e) It is common at high altitudes, where cruising airline suddenly enter turbulent areas.

33. To overcome the above mentioned inherent problems in CAT forecasting, it is always advisable for a field forecaster, specially posted in the valley to make maximum use of airborne reports & debriefs obtained from the aviators.

Cat Occurrence Over India

34. The incidence of CAT over India has been studied from a large number of reports from aircraft on routine as well as non-routine high level flights. Some of the more important results of the study are given below:-

(a) CAT frequency is highest from October to May over central and northern India and in July-August over southern India.

(b) Maximum incidence is from December to February, coinciding with the peak activity of the sub-tropical jet stream.

(c) Cat zones are usually of patchy nature. Average dimensions of distinct zones are 150km in the north-south direction and twice this in the east-west direction.

(d) Vertical extent of a CAT zone may be about 300 to 600 metres but in many cases CAT extends through a deep layer.

(e) Most of the encounters are of feeble/moderate CAT. In a few cases they are reported as severe. Severe CAT is restricted to the period December to May.

(f) Greatest chances of CAT are in a zone about 300km to the south of the sub-tropical jet stream axis.

(g) In Western Himalayas, CAT is most frequent in October when the sub-tropical jet stream makes its appearance over the area.

(h) In Eastern Himalayas, CAT is frequency is high in the mid-winter months.

(j) In south peninsula, Cat is associated with the easterly jet stream of the south west monsoon season.

Turbulence Associated with Mountains (Mountain Waves)

35. Though flights through mountain waves have often been reported to be remarkably smooth, violent turbulence can often occur in association with some waves. The transition can be quite and dangerous. The turbulence associated with airflow over mountains are turbulence in frictional layer,rotor zone ,waves and lee waves:-

(a) Turbulence in Frictional Layer. The terrain over the mountainous region being uneven gives rise to a variable depth of frictional layer and the

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variation and irregularity of the terrain gives rise to turbulent layer (sometimes indicated by stratocumulus formation). With extensive upslope, the turbulence region may be visible by the cloud fall or the fohn wall. The factors which determine the turbulence are same as that over a level country viz., stability, surface roughness speed of the wind. The forecast of turbulence for this region has be done subjectively. Apart from the frictional turbulence, there often develops on the leeside of a mountain a semi-organized mechacal turbulence, which is quite severe and dangerous. This is known as rotor streaming and arises when very strong winds with high static stability extends through a restricted vertical depth (no more than 1½ times the height of the hills). Turbulence can also occur when the wind directions varies markedly with height. A schematic diagram showing laminar, standing eddy wave and rotor streaming with schematic wind profiles is given alongwith.

(b) Rotor zone . Rotor zone or low cloud zone is often an integral part of the wave flow over moderate and large sized mountains. These zones lie below the crest of the lee waves, and the most vicious rotors form below the first lee wave crest, downstream of the mountain ridge. The zone, often indicated by rotor clouds which at times appear as large stationary rolls, and often appear as a line of cumulus or stratocumulus, give rise to the most severe turbulence and vertical accelerations over 7g have been encountered. These form in a line parallel and downwind to the mountain with the base near the level of the crest. Rotors also form when the wind changes directions.

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(c) Waves. The smooth wave clouds often, quite suddenly become ragged indicating sudden breakdown of smooth flow to vigourous turbulence. This breakdown is associated with the air stream characteristics when conditions are near critical for wave formation. Turbulence in waves are more

likely with a short wave length less than 2 km. The turbulence c a n not be predicted with reliability but the height at which the turbulence is likely to be encountered, where the wave amplitude is changing most rapidly with height; the turbulent layer is the region immediately above strong inversions where the wave

amplitude is changing most rapidly with height. It is interesting to note that onset of nocturnal cooling often favours the development of waves especially if the wind is not strong enough to prevent the marked increase in stability. Morning heating has opposite effect of inhibiting wave activity and sing a decrease in amplitude and increase in wave length before the disappearance of waves. For similar reasons waves have a greater frequency in winter.

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(d) Lee Waves . Two of the most important factors which characterise the formation of lee waves are static stability and wind profile. The most favourable conditions are :-

(i) The flow at and above the mountain top level is at right angles and approximately constant in direction.

(ii) The wind at mountain top level exceeds 25 kt.

(iii) There is a rapid increase in wind speed with altitude upto several km above the mountain top. Strong wave development takes place with stronger winds with a peak in the vertical wind profile somewhat above the mountain top level.

(iv) The existence of a stable layer at or a certain height above the mountain top with lesser stability aloft. Topography and stability characteristics play an important part in the evolution of these waves. Effects of these features are shown in schematic diagrams below:

36. Theoretical computation can be used to determine the formation of lee waves. The occurrence and properties of lee depend upon the parameter , which neglecting the rate of change of wind shear with height which is of a smaller order of magnitude, can be written in the form:

where g = acceleration due to gravity U = horizontal wind speed = potential temperature

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Z = height

S = static stability =

37. Two methods are given below:-

(a) In order to compute the - profile, Foldvik (1962) suggests a theoretical profile of the from

l = l o e-cz where c is a constant.

If the atmosphere is represented by two layers viz. 1000 to 700 hPa and 700 to 300 hPa, we can obtain an approximate profile for centred at 850 hPa and 500 hPa level. To evalute 850 and 500, take the smoothed sounding or ascertain the temperature lapse (T1000-T700)and(T700—T300)from air mass characteristics and enter them on the appropriate nomogram vide figure to obtain 850 against appropriate prevailing wind speeds. The method to obtain a smoothed sounding is shown.

The process of smoothing. The broken lines represent smoothed wind and temperature data from which the parameter is computed. It is seen from the smoothed temperature data that the corresponding stability will vary continuously with height

To obtain maximum vertical velocities (Casewell 1966) use is made of the-following formulae:(w1)max = Hu0 c1 (w2)max = Hu0c2 where c1 and c2 are defined by

(2.5 +0.7)c ( and

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CL1 3.2C =c2H the height of the mountain barrier u0 = the wind speed at the ridge height across the mountains c1 and c2, h1, h2 and L1, L2 are found from the graphs given below:

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h1, h2 represent heights at which the maximum vertical velocity occurs) L1 and L2 are corresponding wave length. No lee wave is forecast if u0 is less than 20 kt or blows at an angle greater than 30 degrees from the perpendicular to the ridge line. If the point on the graph lies above the pressure line t the level of tropopause, then no wave is to be forecast. If the height of the maximum vertical velocity is higher the level of the tropopause then the values are not reliable and marked waves are not expected. If there is a marked decrease of wind speed at any level marked change in the direction say more than 30o,

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L850 (kilometers-1)

Graphs Used to Obtain L1, h1 and C1

---------- Values of C1 -- -- -- -- Values of h1 (meter)------- Values of L1 (Kms) Level Of Tropopause (hPa)

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then wave activity is to be considered to have been suppressed at this level and above.

(b) Scorer (1953) suggests the following:

(i) Obtain an estimate of the wind temperature profiles of the air and plot them on a T- gram upto at least 400 hPa.

(ii) For each 100 hPa layer, obtain the thickness z and the difference in θ between the top and bottom of the layer in degrees °C.

(iii) From the figure below, read off values of (U )-1 multiply this by U1 the average wind speed in the layer (kt) and obtain -1 in km.

Waves are more likely if (i) -1 increases rapidly with height (ii) when in a layer near the ground (at least 200 hPa thick) -1 is considerably less than the layer above (at least 300 hPa thick) (iii) If -1 is very large near the ground with a thicker layer above in which it is small (with another layer in which it is large above that). -1 does not change much in the lowest 500 hPa, it may be necessary to continue the calculation upto 300 or 200 hPa. The lee waves have a maximum amplitude at the top of the layer in which -1 is small i.e. at the level where -1 begins to rise substantially with height. The wavelength will be less than 2 / in the upper layers and more than 2 / as measured in the lower layers. If the ridge is well defined and fairly narrow, the first lee wave is only 3/4 of wavelength from the ridge crest. If during the day, because of decrease in the lapse rate in the lower layers, -1 increases, the wave length also increases but as it cannot exceed 2 / as measured in the upper layers waves may become impossible, only to return in the evening with a slowly shortening wave length. In the figure, isopleths of /UL are shown -1 is given in miles when is given knots.

38. Conditions favourable for Mountain Waves formation. The meteorological conditions required for the formation of MW are:-

(a) Marked stability in the lower layer with comparability low stability aloft.

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(b) Wind speed at the level of the summit exceeding a minimum which varies from 8 – 13 m/sec (15kt – 30 kt) depending upon the ridge generating the waves and either increasing or at least remaining constant upto the tropopause.

(c) Wind direction within 30° to the normal of the ridge not substantially changing in direction.

39. Forecasting Hints. Gulati gives these following hints to forecast Mountain Waves:-

(a) Determine whether standing waves are possible in airstreams under consideration . Scorer parameter 2 should be more at lower levels and less at higher levels.

(b) Check if the wind blowing is perpendicular across the ridge or not. Speed should be sufficient comparable to the height of the peak.

(c) Presence of Jet stream is favourable condition.

(d) Diurnal variation and seasonal variation to be kept in mind. Dusk is more favourable as stability sets in lower levels.

(e) It is been established that larger the mountain, stronger the waves necessary to produce maximum effect.

40. Mountain Waves over India .

(a) Mountain waves occur NE India during winter months with wave lengths 20 – 30km. Wave lengths of 5 – 10 km have also been observed.

(b) Over Western Ghats waves are observed during winter season with wave length 26 to 78.5 km. The vertical velocities were between 0.6 m/sec and 5.6 m/sec, the amplitude is found to increase with wave length.

(c) Western and central Himalayas are prone to mountain waves during monsoon and winter seasons with a systematic shift eastward during winter and a westward shift during monsoon. The observed wavelength are 15-22 km and the longest observed was 38 km.

(d) Jammu & Kashmir experiences maximum mountain waves during winter season and in the wake of a western disturbance or westerly wave.

(e) Severe Mountain Waves are possible over Sikkim during winter after the passage of a western disturbances.

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Check Assimilation

State true or false / Fill in the blanks1. (a) Turbulence is only low level phenomena.

(b) Wind shear turbulence is associated with strong vertical and horizontal wind shears.(c) Richardson number is dimensionless.(d) CAT occurs at the tropopause break or where the tropopause slope is minimum.(e) Rotor clouds are associated with severe turbulence.

2. (a) CAT can be defined as an imbalance in the atmosphere in which _________ and _____________________are found.(b) Typical dimensions of areas of CAT are ________ km long and ___________ to ____________ km(c) CAT occurs in region of ___________ wind shear and large _____________ temperature gradient.(d) Two of the most important factors which characterise the formation of Lee waves are ________________ and ________________.(e) CAT frequency is highest from _________ over Central and Northern India and _____________ over Southern India.

Conclusion

41. Forecasting of CAT is still in the stage of evolution. The difficulties in this regard are enhanced due to its patchy nature and the fact that CAT zones appear to develop and dissipate with an irregular life cycle. Most of our knowledge of CAT is based on actual reports from aircraft. CAT is generally associated with Jet stream and mostly occurs near the tropopause. Mountain barriers are responsible for the creation of Mountain Waves induced turbulence. Wind fields over mountainous terrains is disturbed than that over plain land. These disturbances are found over and to the lee side of the mountain extending upto stratosphere.

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Check Assimilation: The Key

State true or false / Fill in the blanks1. (a) False; Turbulence could occur at low level as well as high levels.

(b) True(c) True(d) False; Tropopause slope is maximum.(e True

2. (a) CAT can be defined as an imbalance in the atmosphere in which eddies and gravity waves are found.(b) Typical dimensions of areas of CAT are 30 km long and 5 to 15 km(c) CAT occurs in region of vertical wind shear and large horizontal temperature gradient.(d) Two of the most important factors which charecterise the formation of Lee waves are static stability and wind profile.(e) CAT frequency is highest from Oct To Nov over Central and Northern India and Jul to Aug over Southern India.

Bibliography

1. Meteorology Indian Weather and aids to forecasting - Training Notes , AFAC, Vol IV.

2. Manual of Meteorology for Air crew - IAP 3201.

3. WMO Tech Note - 38

4. An Index of CAT, QJRMS (1965) by Colson & Panofsky.

5. Forecasting Techniques of CAT including that associated with Mountain Waves –

WMO Tech Note 155.6. http:// www.ucar.du/research/society/turbulence.html

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CHAPTER - 5

MOVEMENT OF TROPICAL CYCLONE S

Chapter Objectives

After reading this chapter, you should be able to:-

Understand what causes a tropical cyclone to move. Understand some empirical techniques of forecasting movement of tropical cyclone. Understand statistical forecasting of tropical cyclone tracks. Understand recurvature of storms. Appreciate some latest forecasting techniques of tropical cyclone movement. Understand Tropical Cyclone intensity analysis. Conclusion.

Structure

1. Introduction.

2. What causes a Tropical Cyclone to move?

3. Empirical Techniques of Forecasting.

4. Statistical Track Prediction.

5. Recurvature of Storms.

6. Latest Techniques.

7. Tropical Cyclone Intensity Analysis Technique.

8. Conclusion.

Introduction

1. A tropical cyclone is defined as a non-frontal, synoptic-scale cyclone, developing over tropical or subtropical waters at any level and having a definitely organised circulation. Intense tropical cyclones are the most impressive phenomena of the tropical regions. The destructive potential of their high wind speeds, rainfall amounts, and storm tides is well known. In the areas struck by tropical cyclones, the resultant damage is often extensive, especially in developed coastal areas. A knowledge of their future movement is vital for safety of men and material.

2. In general, a tropical cyclone moves initially towards west or northwest in northern hemisphere. Its recurvature, towards northeast, some times occurs at about 20-30° N.

What causes a Tropical Cyclone to move

3. It has been proven that because a tropical cyclone has cyclonic vorticity throughout much of the troposphere, it will move towards the area of max ∂ζ / ∂t.

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Therefore, physical processes which cause the vorticity distribution to change to lead to a change in the movement of a tropical cyclone.

4. In particular, a tropical cyclone embedded in a non-quiescent environment will have an area of max ∂ζ / ∂t downstream of the direction of the environmental flow due to the advection of ζ. This is like an object flowing along a stream, being steered by the stream flow. The environmental flow is therefore often referred to as the steering flow and the component of motion due to this advective process is called steering.

5. Since ∂ζ / ∂t depend on other factors as well, steering only contributes to part of the motion of the tropical cyclone. However, in general, unless the environment is very weak, steering explains a very large part (> 80%) of the motion.In a weak environment, the advection and convergence of planetary vorticity becomes important. This is known as the β-effect. Consider the case in which the environmental flow is zero and the atmosphere is barotropic. Then, ∂ζ / ∂t is max to the west of the cyclone:

Physically, this is because β(= df/dy) is constant and the meridional component is max to the west of the cyclone. However, an increase in ζ to the west and a decrease to the east will induce a secondary circulation → northward motion. The combined effect therefore produces a northwestward motion. If the steering component is now added, the motion will depend on the direction of the steering flow:

Thus, a tropical cyclone will move in a direction and with a speed different from those of the steering flow. This deviation depends on the direction of the steering flow.

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Empirical Techniques of Forecasting, Movement of Tropical Cyclone

6. These arc those techniques which can be used without reference to regression equation or requirement of computer capabilities. Some of these techniques have been incorporated into statistical and dynamical models in countries possessing large computer facilities. Empirical techniques can be considered as falling into three general categories of which two or more are frequently used in combination to atrive at a forecast for the next 12 to 24 hrs. These categories are :

(a) Persistence

(b) Climatology

(c) Synoptic

7. Persistence forecasts. A persistence forecast assumes that the integrated effect of all forces which have steered the tropical cyclone during some past period will continue to predominate during some future period. In general, persistence is taken as the smoothed past 12 to 24 hrs motion of the tropical cyclone. The persistence forecast is then linear extrapolation of this motion for next 12 to 24 hrs. A higher order persistence forecast can be made by taking into account directional and speed changes during the past 24 hrs. Fig. 1 gives an example of first-order persistence forecast (uniform speed and direction). Fig. 2 illustrates a second order persistence forecast accounting for speed change, while Fig. 3 illustrates a second-order persistence forecast accounting for directional change.

Fig. 1

270/17.5KT 270/15KT 270/12.5KT 270/10KT

08 / 12Z24 HOUR

FORECAST

08 / 00Z12 HOUR

FORECAST

07 / 12ZCURRENTLOCATION

07 / 00ZPAST 12 HOUR

LOCATION


LOCATION

270/17.5KT 270/15KT 270/12.5KT 270/10KT

08 / 12Z24 HOUR

FORECAST

08 / 00Z12 HOUR

FORECAST



LOCATION


LOCATION

270/17.5KT 270/15KT 270/12.5KT 270/10KT

08 / 12Z24 HOUR

FORECAST

08 / 00Z12 HOUR

FORECAST



LOCATION


LOCATION

Fig. 2

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300 / 15KT

290 / 15KT

280 / 15KT270 / 15KT

21 / 00Z24 HOUR

FORECAST20 / 12Z

12 HOURFORECAST



LOCATION


LOCATION

300 / 15KT

290 / 15KT

280 / 15KT270 / 15KT

21 / 00Z24 HOUR

FORECAST20 / 12Z

12 HOURFORECAST



LOCATION


LOCATION

300 / 15KT

290 / 15KT

280 / 15KT270 / 15KT

21 / 00Z24 HOUR

FORECAST20 / 12Z

12 HOURFORECAST



LOCATION


LOCATION

Fig. 3

8. In addition to illustrating the persistence forecast, these figures also show the importance of maintaining the continuity of a tropical cyclone track unless there is strong evidence for a departure from previous. When a limited number of past centre locations are present, the forecast must be cautious of straight-line connections from fix to fix.. Experience at the National Hurricane Centre in the United States of America has revealed that the oscillatory motions of a tropical cyclone frequently seen on plots of land based radar observations and more recently in movie loops derived from geostationary satellites (Lawarence and Mayfield 1977), will usually lie within an envelope of the size 15-100 km (sheets 1972). This also happens to be the general range of positioning errors of tropical cyclones. Therefore, the smoothed track extension should weigh these factors in assessing whether it should be to the left, through, or to the right of the present location. Unless there is strong evidence to the contrary, every effort should be made to fit all position locations so as to minimise directional and speed changes. The main advantage of a persistence forecasts tend to be best where and when the climatological frequency of occurrence is high.

9. Climatological Forecasts. A climatological forecast makes use of the temporal and spatial repetitiveness of tropical cyclone tracks produced by the synoptic patterns which steer the cyclones. Depending on the sample size, the resultant direction and mean scalar speed of motion can be obtained for latitude squares as small as two and half degrees and time periods as short as five days. The climatological forecast moves the tropical cyclones in the resultant direction at the mean scalar speed for the given location (latitude and longitude) and time of year. If the cyclone moves to a position with different mean values during the desired forecast period, the forecast can be modified to take this into account. When bimodal tracks exist, the appropriate mode should be selected according to current storm motion.

10. The advantages and disadvantages of climatological forecasts are more readily apparent than in most other techniques. They perform best where and when the frequency of occurrence is high. They generally decrease in utility with increasing latitude and/or anomalous synoptic patterns. The recognition of this latter fact is an aid in itself. The tropical cyclone forecaster should always have a thorough knowledge of the regional climatology so that a distinction can readily be made between normal and anomalous situations.

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11. Persistence-Plus-Climatology Forecasts. This type of forecast was first described by Bell (1962) and has proved to be quite useful in many eastern hemisphere tropical cyclone forecast centres. It can be expressed as nP+mC where P and C stand for persistence and climatology and n and m are weighting factors. The frequently used method is called the 1/2 (P + C) rule because equal weight is given to both predictors. The persistence vector is obtained as the linear extrapolation of the smoothed past 12 hrs motion. .The climatology vector is based on the regional climatology for the current location and time of season of the tropical cyclone. The forecast position, usually for 24 hrs ahead, is the mid point connecting the two positions obtained from persistence and climatology when plotted on a Mercator chart. An example is shown in Fig. 4. Amadore (1972) has also modified the technique to give different weightings for obtaining latitude and longitude components separately for tropical cyclones east of the Philippines. However, similar attempts made at the Royal Observatory. Hong Kong, for the South China Sea area did not produce significantly improved results.

Fig. 4

12. The use of higher order persistence and climatology would be analogous to the examples given separately for persistence and climatological forecasts. The main advantage of either a first or second order equal weighting of persistence plus climatology is its ready availability. A forecast can be prepared as soon as the current position is available while other weightings and stratifications require some additional computations. The technique is also independent of the synoptic situation. Among the disadvantages are its decreasing utility at higher latitudes because of recurvature and insufficient climatology and the presence of bimodal direction in some areas.

13. Synoptic Techniques. There are two types of forecast which can be considered synoptic. The first is in the conventional sense of the simultaneous observation of pressure, temperature, moisture, wind and other meteorological parameters. The second is equally valid, in that it is an extension of a single simultaneous observation of the integrated effect of all the conventional data that is a satellite photograph. Neither type uses regression equation nor requires computer facilities. Different synoptic techniques are:

(a) Surface geostrophic steering(b) Upper air Steering

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(c) Thermal steering(d) The control-point method(e) The Fujiwhara effect

14. Surface Geostrophic Steering. The surface pressure map together with 24 hrs surface pressure changes (to eliminate large diurnal effects in the tropics) has been used by tropical cyclone forecast centres since the 1950s. It is still used in conjunction with more sophisticated techniques and observing systems to obtain the present motion so vital to the analog, statistical and dynamically techniques and to assess better the shorter range objective forecasts versus the current synoptic situation.

15. The main advantage of the surface geostrophic steering concept is that all forecast offices have surface pressure analysis and can use it when no other aids are available. The use of pressure or height changes in conjunction with the computation of present motion gives the forecast an added dimension beyond just. persistence. In addition, it can help prevent forecast errors based on misinterpretation of centre fix data which implies radical departures from the previous smoothed track. It also aids in determining critical track changes during landfall situations, an occurrence not normally picked up by analog, statistical or dynamical techniques.

16. The main disadvantage of using the geostrophic steering techniques is their sensitivity to inaccuracies in the surface and upper-air analyses which must be drawn over data-sparse areas. The sensitivity of the computations to the Coriolis effect at lower latitudes can lead to large forecast errors for small (one-hPa) analysis errors. While pressure and height changes help in determining directional and speed changes, their magnitudes and movement relative to the tropical cyclone make the timing of these changes rather difficult.

17. Upper Air Steering. The steering level is defined as the level in the upper air where the circulation of the cyclonic storm does not exist for practical purposes. It is believed that the undisturbed flow at that level steers the storm. There are two ways in which we can choose the steering level. It can be the level which has steered the storm during 24 hrs or it can be the mean flow throughout the depth of the storm.

18. Quite a few interesting results have been achieved by considering the undisturbed flow at 500 hPa as the basic steering current. The procedure of computing the undisturbed flow at 500 hPa consists in first computing graphically / numerically the perturbatical flow caused by the tropical storm in the basic flow at 500 hPa and then to subtract that is in from the 500 hPa actual flow.

19. The steering concept evolved because of the knowledge that tropical cyclones respond to the environmental flow in which they are embedded. Below is a summary of the major contribution in the past 30 years using this technique for prediction of storm tracks. The summary shows that there is at present no agreement on the best level to use for steering although the majority of authors use data from the surface to 500hpa.

Reference Method used and levels

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Riehl and Shafer 700 and 500hPa wind and changes the height of the base of the polar westerlies.

Simpson, Riehl and Burgner

Steering current of a zonal belt 50 wide extending 2.50 north and south and 450 east and west of the storm centre and vertically from sea level to 300hPa.

Gentry Jordan Winds at the top of the storm Surface to 300hPa extending over 80 latitude width centred on the storm.

Miller 500 to 200hPa integrated over a doughnut-sharped ring 2-60

from the centre of the storm.Miller and Moore Geostrophic wind components at 700, 500 and 300hPa levels

around the cyclone motion with equal merit.Tse 700hPa chart for height values at 100 radius north, east, south

and west of the cyclone centre.Chin Winds at 700 and 500hPa and 4-60 radius to the right of the

storm movement.Renard and Levings

Their study relates cyclone centre motion to surrounding geostrophic winds derived from smoothed isobaric height fields. 700hPa was established as the optimum steering level. A operational test in 1971 suggested 850hPa for forecast intervals beyond 36 hours.

20. Thermal Steering. The mean thermal patterns represented by the height differences between the 500hPa and 100 hPa levels, and at times 500 and 700 hPa levels often help in giving a clue to the movement of the cyclone. Areas of greater thickness represent warm areas and the storms often move towards the warmest area.

21. The Control-Point Method. The method for predicting the direction of movement of a tropical cyclone was described by Chin (1970) and has been used by the Hong Kong forecast centre for several years. It is based on a high correlation between the direction of movement of tropical cyclones and the wind direction at certain points in the middle troposphere. This direction is combined with the mean speed obtained from the 1/2 (P+C) technique to arrive at the 24 hours forecast location. The control point lies on a straight line perpendicular and to the right (left in the southern hemisphere) of the past 24 hour displacement vector passing through the cyclone centre.

22. In the fixed point method the point along the perpendicular from 3 to 8 of latitude at 700 hPa or 500 hPa which gives the smallest mean angular deviation from the cyclone’s subsequent 24 hour motion in the data sample is alvvays used as the control point. Experience at the Royal Observatory, Hong Kong has shown that a different fixed point is more desirable for typhoons (hurricanes) than for weaker tropical cyclones. Experience at Hong Kong also indicates that results could be improved by taking into account the size of the cyclone circulation to vary the control point. In this variable control point method the strength of the cyclone is no longer desired.

23. /\s described by Chin (1970), the normal pressure at the position where the tropical cyclone is located is obtained from the regional climatological atlas. Next, the distance from the tropical cyclones to this pressure on the current synoptic chart is measured along a straight-line perpendicular to the displacement vector. This distance is plotted against the optimum distance on the nomogram derived from the

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sample, it is then assumed that the extent of the circulation at 700 hPa or 500 hPa is the same as at the surface, and the wind direction at that point is used with the 1/2 (P+C) speed to obtain the 24 hour forecast location.

24. The advantage of the control point methods is their simplicity and the fact that they include some synoptic data beyond climatology and persistence. They are probably most useful south of the sub-tropical ridge. The accuracy of required streamline analysis at middle tropospheric levels may be a definite disadvantage in data sparse areas. Even satellite cloud motion vector are sparse at these levels. The techniques become inapplicable when the control points are located in the cols of the wind field. However this usually occurs during stationary or slow moving cyclone situation except when binary or tertiary systems are in the proximity. The techniques then have little forecast value.

25. The Fujiwhara Effect. Fujiwhara (1921) first noted the tendency for vortices in proximity to one another to rotate about a point located on a line joining their centres. If the cyclones are of equal size and intensity, this point will be midway between two centres. The two typhoons Kathy and Marie swung around each other during the period 15 to 19 August 1964 and merged into one typhoon on 20 August. During the merging process the circulation of typhoon Marie apparently weakend and dissipated while the circulation of typhoon Kathy was maintained.

Statistical Track Prediction

26. Statistical forecasting of tropical cyclone tracks come as an off-shoot of the steering concept, since certain parameters were compared quantitatively with the storm motion.

27. Riehl, Haggard and Sanborn used historical data to develop regression equations for forecasting the 24 hour meridional and zonal components of cyclone motion from the respective components of the geostrophic wind at 500 hPa, measured from a grid extended for 7.50 longitude east and west of the storm, and from 5° of latitude south to a boundary 5 to 10° of latitude north of the storm. The northern boundary of the grid varied with the predicted motion of the storm. The equations are:-

Cn = 0.8 + 1.2Gn for meridional storm motion

Cw= Gw for westward storm motion

Cw = O.9Gn +0.02 (Gw x Gw) for eastward storm motion

Gn and Gw are the corresponding 500 hPa geostrophic flow components. Units of Cn and Cw are respectively degrees latitude and degrees per day.

28. Veigas, Miller and Howe used storm statistics to prepare regression equations. The equations used the present and past 24 hour positions of the storm and selected surface pressure as the predictor. A similar technique was developed for the Pacific by Wang. He used geopotential heights of the 700 hPa level and the intensity and orientation of the major axis of the sub-tropical anticyclone as predictors. Later Veigas included the surface and 500 hPa pressure height to develop a new set of prediction equations. Arakawa developed a scheme similar to

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the earlier one of Veigas for typhoons with the inclusion of persistence as a predictor, 700 hPa height values were used as the primary predictors.

29. The technique developed by Miller and Moore uses a grid similar to that what used by Riehl, Haggard and Sanbom. For latitude initially < 27.5° N and latitude = 27.5° N, they gave the following equations:-

u = 0.42u+0.54Px -2.4v = 0.23v +0.65 Py + 2.3

For a latitude initial > 27.50 ) N.

u = 061u+0.48Px – 3.8v = 0.71v+0.40Py+3.0

where u and v are the mean 24 hour zonal and meridional speeds, Px and Py are respectively the average rate of storm motion in zonal and meridional directions for the 12 hours preceding the forecast time, and u and v are respectively the zonal and meridional geostrophic components computed from the grid area at the 700 hPa level. All speeds are in knots. The equations were developed for Atlantic hurricanes, but Erdei has recomputed the constants for use in the western Pacific for members of the team in the Joint -Typhoon Warning Centre at Guam.

30. Sanders and Burpee developed a barotropic hunicane track forecasting numerical model which gave much improved results. In his discussion of the major hypothesis of barotropic track forecasting Sanders stated that the motion of a tropical cyclone was principally governed by advection of mean vorticity in the air column containing the storms, which is taken to be the entire tropical troposphere. Operationally Sander's scheme (SAN'BAR) does provide significantly improved forecasts at 48 and 72 hours. The National Hurricane Centre and the NOAA research group are currently developing baroclinic primitive equation models for track prediction. The initial outlook is that these will be much superior to all previous numerical methods. They will also be able to predict storm precipitation.

Recurvature of storms

31. Prediction Method. The methods for the prediction of recurvature of a cyclone can be grouped as follows:-

(a) Steering concept(b) Isallobaric analysis(c) Winds and height field analysis(d) Statistical(e) Climatological

32. Steering Concept. Steering concept is that the tropical cyclones are vortices embedded in the basic flow and thus should move with the so called "steering current". Riehl and Shafer (1944) related the movement of hurricanes to the middle level (i.e. 700 & 500 hPa) wind and height. fields. Simpson (1946) showed that the best steering level of a tropical storm is determined by the height to which the storm s vertical circulation extends. Miller (1958) and Miller and Moore (1960) also found same results in their studies.

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33. Chakraborty and Basu (l957) have discussed some conditions over Indian regions. These are as follows:-

(a) At the time of recurvature the centre of storm is likely to be in the area covered by latitude 0° N and 18° N.

(b) If there is any well marked anticyclone in the upper air over Burma and neighbourhood it is likely to shift eastwards or southeastwards before recurvature of the storm over the bay.

(c) Before recurvature westward or northwestward movement of the storm is likely to be retarded considerably. It may gain speed after recurvature.

34. Bhatia and Ananthakrishnan (1958) conducting a similar study found that the latitudinal zone of origin as well as that of recurvature undergoes a periodic oscillation with northward or southward movement of storm.

35. Mathur (1975) found, winds at 9.0 km give good idea about the movement of storm.

36. Ramanathan (1971) related the movement of storms over Bay region to those over South China Sea region and classified them as given below:-

(a) Class A. Storms and depressions which have origin in SE Bay and which move more or less WNW wards are related to typhoons, storms or depressions which move WNW wards or have crossed Philippines. Along with this easterly 10-20 Kt appear between 600 - 500 hPa level over Madras.

(b) Class B. Storms and depressions which recurve in the vicinity of 15° N are related to the presence of no storm or depressions over China Sea and some times related to troughs in westerlies moving west wards affecting North of 30° N.

(c) Class C. Storms and depressions which move irregularly are related to two systems (either storm or depression), one north of 25° N tending to recurve and other south of 25°N moving westwards, simultaneously present in the Pacific.

37. Isallobaric Analysis. Chakraborty and Basu (1957) found that the maximum pressure fall need not necessarily be directed towards NE or east sufficiently in advance but the relative second degree variation of pressure with time towards NE or east should be significant. George and Sharma (1973) also made similar observations. They have tried to tackle the problem of lack of data over sea region. The central pressure of storm was obtained by Fletcher's formula, which gives a relation between maximum wind speed and peripheral and central pressure. Isobars were drawn for two consecutive days and were superimposed over each other to get P24P24 values at point of intersection of isobars of two dates. The direction of maximum Isallobaric gradient was obtained by grid technique. This gives the forecast direction of the storm.

38. Winds and Height Field Analysis. George (1975) investigating tropical cyclone movements and surrounding parameter relationships found that unlike the

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conventional forecasting techniques based on 850-500 hPa .level, the wind and height data for upper troposphere at large radii is far better indicator for cyclone recurvature. Twenty one pairs of Tropical Storm Tracks were selected from western North Pacific. Each pair included one storm that recurved and one that did not. The pairs were selected in a manner such that the earlier portion of each storm track was within 5° latitude of each other. A separation point (s) was selected. The s point is arbitrarily at the longitude where the storm track begins to deviate significantly from the non-recurving storm. Surrounding tropospheric flow pattern at 700 and 200 hPa of one to three days before separation was studied. The charts of various parameters of recurving (r) non recurving (nr) storms and the difference between them were prepared. He has considered following parameters:-

(a) Wind direction and speed.(b) Zonal wind difference (Um - Ur)(c) Meridional wind difference (Vm - Vr)(d) Height difference (Hm - Hr)(e) Temperature difference (Tm - Tr)(f) The zonal and meridional geostrophic wind components calculated from the contour gradient north to south and eaast to west across the storm centres.

39. From this study they concluded that a significant 200 hPa wind field difference between storms that recurve and those that do not, is the width and strength of the westerlies to the North of the storm at a distance of 10-12° lat radius to the North. At s-60 time period, non recurving storms do not have westerlies within 16° of their centre, while the recurving storms have the westerlies at 10° radius to the north. The height difference field at 200 hPa for s-60 time period and 18-20° radius to the north showed that the non-recurving storms have heights which are over 150 meters greater than the recurving storms. The height difference increases to over 200 meters at (S-36) and to over 300 meters at the (S-12) time period. At approximately 24-72 hrs prior to the separation point for a recurving storm, there is a large height gradient between storm and 200 radius to the north of the storm.

40. Statistical Methods. The statistical forecast approach numerically screens various meteorological parameters for the motion related correlation and then uses these correlations to develop regression prediction equations. Riehl (1956) developed one of the earlier objective schemes which gave regression equations and a prediction diagram for forecasting purposes. The different case studies in statistical methods are as follows:-

(a) Surendra Kumar and Kantiprasad (1973) gave an objective method for 24 hrs forecast of storm movement 0000 UTC surface position of the storm points E, W, N, S, were marked at a distance 7.50 from the centre of the storms. Values of contour heights Ze, Zw, Zn, Zs were obtained. The predictors Zλ = Zs-Ze and ZΦ = Zn-Zw were marked out. The other predictors used were persistence Px and Py, time of longitudinal and latitudinal movement during past 12 hrs. The subsequent 24hrs zonal and meridional displacement Yλ and YΦ of the storm from 000UTC of the data 0000 UTC of next day were taken as. Displacement towards East and North are considered to be positive. They found out the multiple regression equations on the basis of least squares to be:-

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Y = .163 Px + .080 Zλ + .020 -------------- (1)Y = .163 Py + .53 ZΦ + .621 -------------- (2)

with multiple correlation coefficients.

Ry, PxZλ. = .9Ry, PyZΦ = .72

This method was tested on a storm during 1971 and average error of 80 Nm was observed.

(b) Bansal and Datta (1974) divided storms into two periods:-

(i) The post monsoon(ii) The pre monsoon

For both categories separate regression equations were developed. Data from 1963 to 1970 was used. A total of 33 predictors were used. λ-12 , Φ-12, P-12 i.e. central latitude, longitude and central pressure of storm 12 hrs prior to chart time. Similarly . λ--24 , Φ-24 P-24, the values 24 hrs prior to chart time, (λ0 , Φ0) latitude and longitude of storm centre at chart time X1 , X2,………… X25 pressure values at all grid points at chart time. From these predictors regression equations have been derived for (λ12 , Φ12) and(λ24 , Φ24) at latitude and longitude 12 hrs and 24 hrs after the chart time.

41. Climatology - Persistence track Prediction. Climatology-Persistence of a storm track relies upon empirical relationships related to cyclone tracks of previous storms. Colon (1953) performed an extensive study of the climatology of hurricanes in the Caribbean sea region. Hope and Neuman (1971) expanded on this original work with the use of computer. They also developed technique for selecting analogs for existing Tropical storm from past tracks of all Atlantic tropical storm since 1886. Those storms that have similar characteristics are selected and identified so as to give help in predicting track of the storm. A similar scheme has been prepared by Jarrel and Somerwell (1970) for Pacific region.

42. From the above discussion of recurvature of storms some of the important conclusions drawn are listed below:-

(a) Storms generally recurve when they are between latitudes .10°N and 18° N.

(b) Before recurvature the speed of the storm reduces.

(c) Just above the level where circulation ceases to exist, the flow pattern determines the future track of the storm.

(d) Second degree variation of pressure gives the indication of future movement.

(e) Storms move toward the maximum Isallobaric gradient.

(f) The contour height changes at 700hPa and 200hPa give good indication of recurvature of the storms.

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(g) Width and strength of westerlies, at 200 hPa at a distance of 10° - 12° latitude radius to the North, is significant for recurvature of a storm. Non recurving storms do not have westerlies.

Latest Techniques

43. The other techniques in addition to the discussed above are:-

(a) Veigas Miller Technique. Veigas has prepared regression equations to forecast motion for several different periods extending to 36 hrs (and under some conditions, to 72hrs). The grid in this case extended as much as 40° of the longitude and as much as 30° of latitude. After picking the predictors which contributed most to reduction in variance, regression equations were prepared. This statistical method is originally meant for storms in the Atlantic. However, performance evaluations show that it is capable of giving reasonably good results in the Western North Pacific and the South China Sea, particularly after the introduction of 12 hrs persistence. For practical purposes, the modified equations are best presented in the form of a computation sheet. The sea level pressure values used are to be extracted from a corresponding analysed surface chart at each 5° grid point with the aid of a transparent grid overlay. The method is very stable with respect to surface pressure values, but sensitive to large errors in locating the storm centres (Gentry 1964). Large errors in the forecasts may be experienced just before and well after curvature. If the storm slows down abruptly, this method tends to predict false recurvature. The advantage of using 12 hrs persistence to replace 24hrs persistence in the original equations is twofold; the modification gives slightly better results and allows the first forecast to be made 12 hrs earlier. .

(b) Tse’s Technique. Tse (1966) used the 700hpa chart values of 100

radius for predicting next 24 hrs motion. The overall synoptic pattern at 700 hPa was then introduced as an additional criterion. Regression lines corresponding to a few easily recognised synoptic patterns were derived from the scatter diagrams of 700 hPa contour height differences versus lat / long displacements of storms. Nomograms were presented for operational utilisation of this technique. The technique was generally successful in predicting the direction of motion but forecast displacements were biased towards low side, particularly when typhoons accelerate after recurvature.

(c) Chin's Singular Point Technique. Chin (1970) showed that the direction of movement of a storm is closely related to the wind direction at a singular point at 700 hPa level. The distance of this singular point from the centre of the storm depends on the storms intensity. The point is located at a line perpendicular to and to the right of the storm track, formed by joining two successive 24 hrs positions. The point is located at a distance of 5° latitude from the typhoon centre along the perpendicular (4° for less intense cyclones). Direction of wind at this point is combined with the (half persistence + half climatological) speed to forecast the movement of the storm during next 12 hrs.

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(d) Grav's Steering Current Study. Gray and associates carried out an extensive study of the ten years data (1961-70) of the tropical storms in the Western North Pacific. Approximately 20,000 Rawin Sonde soundings and some 200 cyclonic storms were investigated. The mean composite sounding winds were examined in relation to cyclonic motion. This was clone at all levels in the atmosphere as well as for various radial distances from the cyclonic centre. Another unique feature of this study was that the data set was broken down into a group of subsets or stratifications based on certain characteristics of the cyclones. This was done on the hypothesis that if, indeed, there are certain steering relationships between the cyclone motion and the wind flow, then these relationships should be consistent regardless of different storm characteristics such as speed, direction of movement, intensity etc. The cyclones were stratified into 13 different categories. Using this approach, the composite study brought out a consistent relationship between the cyclonic motion and the sounding flow. It has been shown statistically that the tropical cyclone motion is directly related to the surroundings wind and height fields. Tropical storm direction seem to be very well related to the mean 1 - 7° radius at 500 hPa surrounding wind direction while the cyclone speed is best related to the 1 -7° radius at 700 hPa surrounding wind speed. Thus, it is seen that the surrounding flow dictates the storm motion very well regardless of storm, latitude, speed, direction, intensity and intensity change. The structure of the tropical storm such as the inner convective activity is not a primary factor in influencing storm movement. In the statistical average, it appears that variations in the inner eye wall and inner region cumulus convection do not make a significant contribution to the surrounding steering flow and cyclone motion.

Tropical Cyclone Intensity Analysis Technique

44. Step 1. Locate The Cloud System Center (CSC). The cloud system center is defined as the focal point of all the curved lines or bands of the cloud system. It can also be thought of as the point toward which the curved lines merge or spiral.

45. Procedure:-

(a) The CSC is located at the center of the eye or at the center of curvature of a partial eye wall when one of these features is observed.

(b) When the CSC is not obvious, locate the model expected CSC.

Draw a line along the "curved band axis" through the densest (coldest) portion of the band. The axis should roughly parallel the concave (inner) over-cast boundary of the band. Locate the model expected center location in relation the curved band. (See plus symbols in diagram in Step 2A.) The center is located near the inner (concave) edge of the band on the counterclockwise end (comma head) portion of the band. Locate tightly curved lines, merging lines, or CDO near the point where the center is expected to fall. The CSC is located at the center of curvature, near the point of mergence or at the center of the CDO (for CDO of _< 1 1/2° latitude in size). For large CDO’s, the center is sometimes defined by an arc of overshooting cloud tops or in an isolated cluster of convective tops. When not visible, use (c) below.

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(c) When features are not visible at the expected CSC, or when the curved band is not apparent, use the circle method. The method consists of first drawing lines following the cloud line curvature or curved boundaries that fall within the curve of the curved band axis, and then fitting circles to the lines with tightest curvature. The CSC is located at the center of the area common to the circles. For relatively circular embedded center patterns of >T3.5 intensity, fit a log 10° spiral overlay to the curved band axis to locate center.

(d) When a cloud minimum wedge is visible on the concave side of the band near its middle, the CSC is located at the midpoint of a line drawn between the deepest cloud minimum incursion of the wedge and the counterclockwise extremity of the curved band axis. This method is frequently used with EIR pictures. In EIR pictures, the center is often located in the tight gradient near the coldest part of the pattern.

(e) When the location of the CSC is unclear, or could be placed at different locations, use all the methods above along with an extrapolation from the past track positions in making the final decision.

(f) When more than one well-defined CSC is apparent, use the one defined by the strongest appearing, lowest level cloud lines that best fits the past track of the storm. When strong vertical shear is apparent, remember that the upper level (dense) clouds will not be centered directly over the low-level center, but will be displaced with the CSC on the tight temperature gradient (sharp boundary) side of the dense cloud pattern.

46. Step 1A. Initial Development. The earliest signs of tropical cyclone development are observed about 1 1/2 days before a disturbance reaches tropical storm strength. At this time, the disturbance is classified a T1. A T1 is first used when a cluster of deep layer convective clouds showing line or band curvature has the following three properties:-

(a) It has persisted for 12 hours or more.

(b) It has a cloud system center defined within an area having a diameter of 2 1/2° latitude or less which has persisted for 6 hours.

(c) It has an area of dense, cold (DG or colder) overcast* of >1 1/2° in extent that appears less than 2° from the center. The overcast may also appear in cumulonimbus lines the curve around the center. The cloud system center will be defined in one of the following ways:-

(i) Curved band, a dense (DG or colder) overcast band that shows some curvature around a relatively warm (cloud minimum) area. It should curve at least one-fifth the distance around a 10° log spiral. Cirrus, when visible, will indicate anticyclonic shear across the expected CSC. (See diagrams, Step 6, PT 1.5 pattern types.)

(ii) Curved cirrus lines indicating a center of curvature within or near a dense, cold (DG or colder) overcast. (See Figure 8, Step 6, PT 1.5b.)

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(iii) Curved low cloud lines showing a center of curvature within 2° of a cold (DG or colder) cloud mass. (See diagrams, Step 2B, DT 1.5 pattern.) In many cloud clusters that eventually develop, the northern boundaries show a straightening about 1 1/2 days prior to the T1 classifications. During the organizing stage of the T1 pattern, there may be extreme variability in the cloud pattern. In most developments at the T1 stage, strong upper-level horizontal anticyclonic shear will be indicated across the disturbance center when curved cirrus lines are present to reveal the shear. These upper level clouds may indicate patterns far more advanced than T1 at the time of the initial classification. These patterns do not involve deep tropospheric circulations at this time and will be short lived. This means that the Day-2 data T-number may at times be less the Day-1’s, but still development is indicated as long as the DT is 2 or more. There may also be times during the first two days of development when cirrus or convective clouds are almost absent, showing little pattern during the nighttime hours. This usually does not mean the storm is weakening. The rule is to never lower the T-number at night during the first 24 hours of development. A flat boundary rotating clockwise across the north side of the pattern throughout the period is a good sign of development. Note that a classification of T1 forecasts tropical storm

*The amount of cold overcast may decrease during the subsequent nighttime hours making it crucial that the analyst watch for the required amount of overcast when it occurs. Intensity (T2.5) 36 hours after the T1 observation only when the environment is expected to remain favorable. A minus symbol is used after the T1 to indicate a T1 pattern that is not expected to develop. (See step 11)

47. Step 2. Determine the Pattern Type that Best Describes Your Disturbance and Measure Cloud Features as Indicated. The manner in which the cloud system center is defined determines the pattern to be analyzed. The pattern types listed below are described on the following pages. When the cloud pattern being analyzed does not resemble one of the patterns, proceed to Step 3.

(a) Step 2A. "Curved Band" Pattern

(b) Step 2B. "Shear" Pattern

(c) Step 2C. "Eye" Pattern

(d) Step 2D. Central Dense Overcast (CDO) Pattern

(e) Step 2E. Embedded Center Pattern

48. General Analysis Rules:

(a) When short-interval pictures are available, use the average measurement of all of the pictures with well-defined features taken within the 3-hour period ending at analysis time.

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(b) When two or more T-number estimates are made from the same picture, use the estimate closest to the MET.

(c) When in doubt concerning ambiguous features, bias the analysis toward the MET.

49. Step 2A. Curved Band Pattern. The intensity estimate determined from this pattern type is derived by measuring the arc length of the curved band fitted to a 10° logarithm spiral overlay. (A circle will give the same answer most of the time.) The intensity values that relate to the curved band length are given in the analysis diagrams, Figure 1, 3. Curved band measurements may be used with both VIS and EIR pictures until an intensity of DT 4.5 is reached. For EIR patterns greater than DT3.5 use measurements from VIS diagram.

50. The spiral overlay is fitted to the curvature of the dense (cold) band by first drawing a line along the "curved band axis" and then fitting the spiral curve to the line drawn. The curved band axis is defined as the axis of the coldest overcast gray shade (most dense clouds) within the cloud band. The line should roughly parallel the overcast edge on the concave side of the band. When the band indicates two possible axes, use the one with tightest curvature. Cellular cold globs that do not fall in line with the curve of the comma band are ignored when drawing the line. Fit the spiral to the line drawn on the picture and measure the spiral arc length of the dense (cold) band that follows the spiral curve.

51. In EIR patterns (like those in Figure 6, Step 6, Row b), the cold comma band will often show warm breaks through its middle. These breaks will appear to be almost clear in the VIS picture, When this occurs, draw the comma axis as though it were continuous through the breaks paralleling the edge of the cloud minimum incursion into the concave side of the band. As the curved band pattern evolves it will usually be defined by the dark gray shade of the BD curve, but may at times appear defined in warmer or colder shades of gray. At times the boundaries of the band must be interpreted from its form in previous pictures.

52. During the first 2 days of development (T1 to T2), the amount of overall band curvature may change excessively, very little, or even decrease somewhat for short periods even though typical development is occurring. For this reason, the tendency should be to raise the T-number by one during the first 24 hours of development as long as the band remains curved enough for T2 and clear signs of weakening or rapid development are not apparent. It is also important to allow at least 24 hours to pass between a T2 and a T4 classification. Even though the coiling process has been observed to be faster than this at times, the surface pressure does not fall accordingly.

53. During the T2.5 or T3 stage, a tightly curved band < 1 1/4° diameter of curvature observed within the curve of the broad curved band can also be, used as an indicator of tropical storm intensity. This is evidence that the wall cloud is forming. This tight curvature at weak tropical storm intensity is often ragged in appearance but will have deep-layer convective cloudiness on nearly opposite sides of a system center.

54. Step 2B. Shear Patterns. Shear patterns appear in pre-hurricane stages of development when vertical shear prevents the cold clouds from bending around

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the cloud system center as they do in the curved band patterns. The pattern may also appear after the hurricane stage has weakened to a pre-hurricane pattern because of increasing vertical shear.

55. The intensity estimate determined from this pattern type is derived by (1) the way in which the cloud system center is defined and (2) the distance between the low cloud center and the dense, cold overcast. For shear patterns associated with tropical storm intensity (T2.5 to T3.5), the center will be defined by parallel, circularly curved low cloud lines with a diameter of about 1.5° latitude or less. They indicate a center either near the edge or under the edge of a dense, cold (DG or colder) overcast cloud mass (see patterns in Step 2B, Figures 1, 3. During the weaker stages of development (T1.5 + .5), the low cloud center will either be poorly defined in spiral lines within 1.25° of the cold overcast, circularly defined but some distance (>1.25° latitude) from the cold overcast clouds, or circularly defined near a small amount (<1 1/2° diameter) of dense overcast.

56. Step 2C. Eye Pattern. Eye patterns are analyzed in this step only when the eye falls near the point of the expected cloud system center, and after a T2 or greater pattern has been observed 24 hours prior to the current observation.

57. The eye is defined as one of the following:-

(a) A warm (dark) spot in a dense, cold (OW or colder) overcast. (When more than one dark spot appears near the CSC, use the center closest to the expected center location.)

(b) A point in a dense, cold (OW or colder) overcast centered within the curvature of a colder (denser) band that curves at least halfway around the point with a diameter of curvature of 1 1/2° latitude or less.

(c) A spiral band wrapped around a relative warm (dark) spot with a diameter of curvature of 1 1/2° latitude or less. The band must curve at least 1.0 the distance around the 10° log spiral curve. (See pattern labeled DT 4 in Figure 7, 2A).

58. The analysis of the eye pattern involves three computations: The eye number (E), the eye adjustment factor (Eye Adj), and the banding feature (BF) Eye Adj. number. The equation is: CF + BF = DT {data T-number), where CF = E no. + 1. EIR only (See 2. for VIS)

(a) E (eye) Number. To get the E or eye number, first determine the coldest gray shade that surrounds the relatively warm spot. Make certain that the minimum width of this gray shade meets the ""narrowest width" requirement shown in the diagram. When a spiral eye is defined, use the average width of the spiral band to determine the narrowest width criteria.

(b) Eye Adjustment Factor. The eye adjustment factor is determined by using the graph in Figure 10. The graph is a plot of eye temperatures versus the temperature of the coldest ring or spiral that completely encircles the eye. This provides an adjustment of +_0.5, +_1, or 0 to the "E" number. No plus adjustment can be made for large eyes (>_ 3/4° diameter within the surrounding gray shade) or elongated eyes. When no previous subtraction

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was made, .5 is subtracted for elongated eyes having E numbers of > 4.5. Elongated eyes are defined as those having a short axis of <2/3 the long axis within the surrounding gray shade.

(c) Banding Feature (BF). The BF addition is used with EIR pictures only when the T-number estimates without the BF is lower than the model expected T-number. It is defined only for patterns of CF4 or more that contain a clear-cut comma tail band that:-

(i) Curves 1/4 or more of the distance around the central features or comma head,

(ii) Is cold (MG or colder), and

(iii) Has a warm wedge (DG or warmer) between the tail and the central features that cuts at least halfway through the pattern for patterns a and b, Figure 11, and at least 2/3 the way for pattern c.

59. VIS only (See 1 above for EIR). The E (eye) number is obtained by measuring the distance the eye is embedded in dense overcast clouds. The embedded distance of the eye is measured outward from the center of the eye to the nearest outside edge of the dense overcast for small (<30nm) eyes. For large eyes, measure outward from the inner wall of the eye. When a banding-type eye is indicated, the arc length of the band around the eye and the average width of the band surrounding the eye are important to the intensity determination, as indicated in the diagram. See analysis diagram (Figure 7, 2C) for the relationships between E-number and embedded distance (eye in CDO), and for band width (banding eye).

60. The eye adjustment factor is determined by the definition, shape, and size of the eye. The eye is well defined by either its blackness or by a well-defined boundary. To be well defined, the eye should be dark or black. Remember that a very high or very low sun angle may reduce the eye definition unrealistically, and that high-resolution pictures may show a poorly defined eye that would not appear in the low-resolution pictures for which the technique was designed. A poorly defined eye is one that is barely visible. A ragged eye is one with a very uneven boundary with little circularity. VIS eye adjustment rules are as follows. (1) For poorly defined or ragged eyes, subtract 1/2 number for E numbers of < 4.5 and subtract 1 number when E > 5. When analyzing patterns with poorly defined eyes especially in high-resolution pictures, also check the CDO size. Use the estimate which is most consistent with the MET. (2) For large eyes, limit the maximum T-number to T6 for round, well-defined eye patterns, and to T5 or lower for all other large-eyed pat-terns. And, (3) the E-number may also be adjusted upward by either .5 or 1.0 when the eye is well-defined, circular and embedded in a very smooth, very dense appearing canopy. The addition is made only when the data T-number is lower than the MET and the storm’s past history gives an expected T-number of T-6 or more. The general rule for the eye adjustment factor is: When an adjustment is not clear-cut, use the guidance of the MET to make the final decision.

61. The BF adjustment is often an important factor when VIS pictures are used. It is defined as a dense, mostly overcast band that curves quasi-circularly at least 1/4 the distance around the central feature. Bands that curve evenly around an inner BF may also be counted. The amount of the BF term ranges from .5 to 2.5. It depends

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on the width of the band and the amount the band curves evenly around the central features, as shown in Figure 12. A BF term is not used for pre-hurricane patterns when the curved dense band concept in Step 2A is used. However, it is still needed for CDO patterns and all hurricane patterns when indicated. For banding eye patterns use the central coil (once around the eye) as the CF and add the BF as indicated. This pattern type is rarely used for DT of greater than 4.5.

62. Step 2D. CDO Patterns (VIS only). CDO patterns are defined when a dense, solid-looking mass of clouds covers the cloud system center and lies within the curve of the system’s comma band. Both its size and the sharpness of its boundary are important to the analysis. A well-defined CDO has an abrupt edge on at least one side of the cloud mass. An irregular CDO appears within the curve of the comma band but has ragged boundaries and uneven texture. Generally, well-defined CDO’s that measure about 1° latitude in their narrowest width are associated with tropical storm intensities while those measuring 2° latitude or more are associated with hurricanes. The size-CF number relationship is given in the analysis diagram, Figure 7. Examples of CDO’s are shown in Figure 8, Step 6b. For CDO patterns, the analysis equation is CF + BF = DT. Banding features (BF) are usually added to the CF term for CDO patterns. The BF’s are described above in 2C,2C.

63. Step 2E. Embedded Center Patterns (EIR only). Embedded center patterns are analyzed when the storm has had a previous history of a T3.5 or greater intensity and when the CSC is clearly indicated to be within a cold overcast (OW or colder). Curved cloud lines or bands within the cold overcast as well as the outer curved bands will indicate the location of the CSC within the overcast. A 10° logarithmic spiral can often be fitted to the system’s pattern to help locate the CSC in patterns of hurricane intensity. (See Step 2A for fitting spiral.)

64. The analysis of this pattern is similar to the eye pattern analysis except that no eye adjustment factor is added. Determine the coldest overcast in which the CSC is embedded the required distance. This yields the central feature number (CF). Then add a banding feature (BF) adjustment when indicated. The equation being CF + BF = DT.

65. Step 3. Central Cold Cover (CCC) Pattern. The CCC pattern is defined when a more or less round, cold overcast mass of clouds covers the storm center or comma head obscuring the expected signs of pattern evolution. The outer curved bands and lines usually weaken with the onset of CCC. When using VIS pictures, substitute the word "dense" for "cold." It is only rarely that the CCC pattern is used with VIS pictures since the CDO or curved lines are usually visible through the thin cirrus clouds. When the CCC persists (see rules in diagram, Step 3), development has been arrested until signs of development or weakening once again appear in the cloud features. Care should be exercised under the following conditions:-

(a) Do not confuse a CCC pattern with a very cold comma pattern. A very cold (usually white) pattern is indicated by a very cold (very smooth texture) comma tail and head with some indication of a wedge in between. Curved cirrus lines or boundaries usually appear around the cold pattern and not around the CCC pattern. The very cold pattern for T-numbers of T3 or less warrant an additional 1/2 number in intensity estimate and often indicates rapid growth.

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(b) Do not assume weakening in a CCC pattern when the comma tail begins to decrease in size. It is common to observe the tail decreasing in size at the onset of the CCC. Also the CCC often warms as the eye of the T4 pattern begins to be carved out by a warm incursion into the side of the cold over-cast. This signals the resumption of pattern evolution (intensification) even though some warming is evident.

66. Step 4. Determine The Trend Of The Past 24-Hour Intensity Change. The trend of the past 24-hour intensity change is determined qualitatively by comparing the cloud features of the current picture with those in the 24-hour old picture of the storm. In general, a disturbance has developed when its center appears better defined with no change in the relation to the dense clouds of the disturbance or is more involved with dense overcast clouds. More precise definitions for development, weakening or steady state changes are given below.

67. The storm has developed (D):

(a) Curved Band Pattern. Curved band coils farther around the CSC.

(b) CDO Pattern. CDO becomes larger or an increase in banding features is noted.

(c) Shear Pattern. CSC becomes more tightly defined in curved cloud lines or appears closer to the dense overcast.

(d) Eye Pattern. Eye is more embedded, more distinct (warmer), less ragged, or is surrounded by colder (smoother textured) clouds, or more banding features.

(e) No significant warming (darkening) of the cloud system is noted. By significant, it is meant that a change that is not diurnal (near sunset), which lasts for more than 3 hours, and is great enough to lower the T-number.) The storm has weakened (W):

68. The storm has weakened when its cloud pattern indicates a persistent trend opposite to those listed in (1)-(5) above. Watch in particular for pat-terns that become sheared out (elongated with time) or for patterns undergoing nondiurnal warming (lowering) of their cloud tops.

69. The storm has become steady state (S):

(a) When a central cold cover appears in a T3.5 or greater storm or has persisted for more than 12 hours in a weaker storm; or

(b) When the CSC’s relationship to the cold clouds has not changed significantly; or

(c) When there are conflicting indications of both development and weakening.

70. Step 5. The Model Expected T-Number (MET). The MET is determined by using the 24-hour old T-number, the D, S, or W decision in Step 4, and the past

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amount of intensity change of the storm. When the growth rate has not been established in the case of new developments or reversals in trend, assume a past rate of change of one T-number per day. Equations for determining the MET are given below.

MET = 24-hour old T-number + (.5 to 1.5) when D was determined.

MET = 24-hour old T-number - (.5 to 1.5) when M was determined.

MET = 24-hour old T-number when S was determined.

71. Rapid or slow past rates of change are established when two consecutive analyses showing rapid or slow pattern evaluation are observed at 6-hour or more intervals, or when one observation accompanied by signs of strong intensification or weakening is observed (see Step 10).

72. Step 6. The Pattern T-Number (PT). The pattern T-number is used primarily as an adjustment to the MET when an adjustment is indicated. The PT-number is determined by choosing the pat-tern that best matches your storm picture from either the model expected T number column or the column on either side of it. When the pattern being analyzed looks more like the pattern in the column to the right or left of the MET column, then raise or lower the MET .5 to determine the PT.

73. Step 7. Rules for Determining the T-Number. Use the data T-number (DT) when the cloud feature measurements are clear-cut. Use the pattern T-number (PT) when the DT is not clear and the pattern is understandable. When neither the DT or the PT is clear, use the Model Expected T-number (MET).

74. Step 8. Final T-Number. This step provides the constraints within which the final T-number must fall. In other words, when the T-number gotten from Step 7 does not fall within the stated limits, it must be adjusted to the limits. The constraints hold the final T-number change to 1.5 during the first 24 hours of development; to 2 numbers in 24 hours for T-numbers T2 to T4 (i.e. 1/2 number over a six hour period); and to 2.5 numbers over a 24 hour period for changes in storms of T4 or greater intensity (i.e. 1 number over a six hour period, 1 1/2 numbers in 12 hours, 2 in 18 hours, and 2.5 in 24 hours). In general for storms of hurricane intensity, the final T-number must be within one number of the model expected T-number (MET). The constraints are listed in the diagram. The rules also prohibit the lowering of the T-number at night during the first 48 hours of development because the diurnal changes in clouds often give deceptive indications of weakening at this time.

75 Step 9. Current Intensity (CI) Number. The CI number relates directly to the intensity of the storm. The empirical relationship between the CI number and the storm’s wind speed is shown in figure 13.

76. After each intensity analysis, the previous analyses of the storm should be reviewed in the light of the current data. When an error was made in the previous day’s analysis, correct the T-number to provide a more-accurate model-expected intensity. The correction may at times alter the current intensity analysis.

77. The CI number is the same as the T-number during the development stages of a tropical cyclone but is held higher than the T-number while a cyclone is

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weakening. This is done because a lag is observed between the time a storm pattern indicates weakening has begun and the time when the storm’s intensity decreases. In practice, the CI number is not lowered until the T-number has shown weakening for 12 hours or more. The CI number is then held one higher than the T-number as the storm weakens. (Hold the CI number 1/2 number higher when the T-number shows a 24-hour decrease of 1/2 number.) When redevelopment occurs, the CI number is not lowered even if the T-number is lower than the CI number. In this case, let the CI number remain the same until the T-number increases to the value of the CI number.

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Figure 5. EIR Analysis Diagram, Part 1.

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Figure 6. EIR Analysis Diagram, Part 2

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Figure 7. VIS Analysis Diagram, Part 1.

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Figure 8. VIS Analysis Diagram, Part 2.

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Figure 9. Analysis Worksheet

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Figure 10. Eye Adjustment Graph. Rules: (1) For large or elongated eyes, use values to the right of the diagonal line only; (2) for elongated eye patterns >4.5,

subtract .5 when no other subtraction was made.

Figure 11. EIR Banding Features. Add to the CF only when the DT is lower than the MET.

Figure 12. VIS Banding Features.

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Figure 13. The empirical relationship between the current intensity number (CI), the maximum mean wind speed (MWS), and the minimum sea level

pressure (MSLP) in tropical cyclones. The MSLP values for the NW Pacific were recommended in Shewchuck and Weir (1980).

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Check Assimilation

State true or false / Fill in the blanks1. (a) Empirical techniques can be used without reference to

regression equation or requirement of computer capabilities.(b) Thermal steering technique is a statistical track prediction technique.(c) Areas of greater thickness represent cold areas and storms often move towards the coldest area.(d) The direction of maximum isallobaric gradient gives the forecast direction of the storm.(e) The contour height changes at 700hPa and 200hPa give good indication of recurvature of the storms.

2. (a) A higher order persistence forecast of the future movement of Tropical cyclone can be made by taking into account _________ and _________changes during the past 24 hours.(b) Statistical forecasting of tropical cyclone tracks came as an off short of the__________, since certain parameters were compared quantitatively with the storm motion .(c) Upper air steering level which has steered the storm during 24 hours or it can be the __________throughout the depth of the storm.(d) Storms generally recurve when they are between latitude _______and _________.(e) Tse used the _______ chart values of _____ radius for predictions next 24 hours motion.

Conclusion

78. Forecasting the intensification of a Tropical vortex is an important and yet an unsolved aspect. Tropical vortex may or may not intensify into a tropical cyclone. Some vortices suddenly show rapid intensification and some other cortices cease to intensify even when these are out in the open ocean with nearly the same conditions which are known to be favourable for the intensification. Forecasting the movement of a tropical cyclone is as important as the forecasting of intensification of a tropical vortex. Still, climatology of storms and cyclones is one of the most useful guide for a forecaster. Persistence in the speed and direction of movement of storms is another factor to be considered by a forecaster.

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Check Assimilation: The Key

State true or false / Fill in the blanks1. (a) True.

(b) False; Synoptic technique.(c) False; Areas of greater thickness represent warm areas and storms often move towards the warmest area.(d) True.(e True.

2. (a) A higher order persistence forecast can be made by taking into account directional and speed changes during the past 24 hours.(b) Statistical forecasting of tropical cyclone tracks came as an off short of the steering concept, since certain parameters were compared quantitatively with the storm motion.(c) Upper air steering level which has steered the storm during 24 hours or it can be the mean flow throughout the depth of the storm.(d) Storm generally recurve when they are between latitude 10° N and 18° N(e) Tse used the 700hPa chart values of 10° radius for predictions next 24 hours motion.

Bibliography.

1. Meteorology Indian Weather and aids to forecasting - Training Notes , AFAC, Vol IV.

2. Tropical Meteorology – GC Asnani

3. The Central Point Method for prediction of tropical cyclone movement – Royal Observatory technical Note No.30, PC Chin (1970)

4. Tropical cyclone intensity analysis forecasting from Satellite imagery – MWR 103, VF Dvorak (1975).

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NUMERICAL ANALYSIS

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CHAPTER – 2

MATRICES AND LINEAR SYSTEMS OF EQUATIONS

Chapter Objectives.

After reading this chapter you should be able to understand basic ideas concerning Matrix operations and how to obtain solution for Linear Systems of Equation.

Structure

1. Introduction

2. Basic definitions of Matrix

3. Matrix Operations

4. Consistency of a Linear System of equations.

5. Solution of Linear Systems of Equations.

6. The Figure values problem.

7. Conclusion

Introduction

1. Matrices occur in a variety of problems of interest; for example, in the solution of linear algebraic systems, solution of ordinary and partial differential equations, and eigenvalue problems. The matrix notation is convenient and powerful in expressing basic relationships in fields like elasticity and electrical engineering. In this chapter, we introduce the matrices independently although they can be treated, more conveniently, through the theory of linear transformations. We assume that the reader is familiar with the concept of a determinant and its properties and we describe briefly some simple properties of matrices which will be used in the solution of linear algebraic systems to which some considerable attention will be given in the later sections. The theorems will be stated without proof.

Basic Definitions

2. A matrix is an array of mn elements arranged in m rows and n columns. Such a matrix: A is usually denoted by

(1.1)

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where a11, a12, . . . are called its elements and may be either real or complex. The matrix A is said to be of size (m X n).

If m = n, the matrix is said to be a square matrix of order n. Thus,

is a square matrix of order 3. We may also have single row or single column matrices. These are called vectors. Thus, [al1, a12, a13, . . . , a1n] is a single row matrix or a row vector, and is a single column matrix or a column vector

3. The elements aii in a square matrix form the principal diagonal (or main diagonal). Their sum a11 + a22 + . . . + amn is called the trace of A. If all the elements of a square matrix are zero, then the matrix is said to be a null matrix. Thus, if aij = 0 for i, j = 1, 2, . . . , n, then A is a null matrix of order n. On the other hand, if only the elements on the main diagonal are nonzero, then the matrix is said to be a diagonal matrix. For example,

is a diagonal matrix.

In particular, the diagonal matrix

in which all of the diagonal elements are equal to one, is called a unit matrix of order 3. Unit matrices are usually denoted by I

4. A square matrix is said to be an upper triangular matrix if aij = 0 for i > j, and a lower triangular matrix if aij = 0 for i < j. For example,

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is an upper triangular matrix, and

is a lower triangular matrix. Matrices of the type

are called tridiagonal matrices. A square matrix A in which aij = aji is said to be symmetric; if aij = -aji. It is said to be skew-symmetric. For example,

is a symmetric matrix, and

is a skew-symmetric matrix.

Every square matrix A is associated with a number called its determinant which is written as

The minor Mij of the element aij of IAI is that determinant of order (n - 1) obtained by deleting the the row and column containing aij. The cofactor Aij of aij is given by

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If I A I ≠0, then A is said to be a nonsingular matrix; otherwise, it is said to be singular. Thus,

Is singular since I A I=0

5. Matrix Operations

(a) Equality of Two Matrices

Two matrices are said to be equal if they are of the same size and if their corresponding elements are equal.

(b) Addition and Subtraction of Matrices

Two matrices of the same size can be added or subtracted by adding or subtracting their corresponding elements. Thus, if

and

Then A+B= and

(c) Multiplication of a Matrix by a Scalar

if then

then k is a scalar

(d) The following properties of matrices easily follow from the definitions:

(i) A + (B + C) = (A + B) + C(ii) A+B=B+A(iii) k (A + B) = kA + kB, k being a scalar.(iv) (k1 + k2) A = k1A + k2A, k1 and k2 being scalars.

(e) Multiplication of a Matrix by another Matrix

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Two matrices A and B can be multiplied only if the number of columns of A is equal to the number of rows of B. Thus if A and B are of sizes (2 X 3) and (3 x 2) respectively, then their product C, given by

C= AB

is defined, and will be of size (2x 2). The elements of C are obtained by the rule that the element Cij of C is equal to the sum of the products of the corresponding elements of the ith row of A by those of the jth column of B. In general, if A is of size (Ix m) and B is of size (m x n), i.e., if

Then the product C = AB is of size (Ix n) and its elements Cij are given by

Multiplication of matrices is, in general, not commutative, i.e., if A and B are two square matrices then AB may be different from BA, For example,

=

but=

which is a different matrix.

Example 1

If

Then

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lml2 l1

2m22 21

1m 12 11

a.a a.....

a a a aa a

A

lnl2 l1

2n22 21

1n 12 11

.b b.....

b b b b b

b

b

B

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If

Then

If

Then

This example shows that the product AB may be a null matrix but neither A nor B be null matrices.

Then AI=IA=A

which shows that the commulative law holds good in this case.

Transpose of a Matrix

6. The matrix obtained by interchanging the rows and columns of a square matrix A is defined as the transpose of A and is denoted by A'. Thus,

If

then

it is easy to see that if A is symmetric, then A=A’

Theorem 1 If C = A + B, then C' = A' + B'.

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Theorem 2 If A and B are two square matrices, then the transposes of the product AB is the product of the transposes taken in the reverse order, i.e., (AB)' = B'A'.

The Inverse of a Matrix

7. Let A be a nonsingular square matrix of order n. Let B be another square matrix of the same order such that

BA = I,

where I is the unit matrix of order n. Then B is said to be the inverse of A which is written as A-I so that

AA-I = A-1A = I

The following nine properties can be shown to hold on the inverse of a square matrix

(a) A-I exists if and only if I A I ≠ 0. If I AI = 0, A is said to be aSingular matrix.

(b) If A-I exists, it is unique.

(c) If AA-I exists, I AA-I I = I AI-1 = 1 I AI

(d) (A-I)-I = A.

(e) (AI)-I= (A-I)I.

(f) (AB)-I = B-IA-I.

(g) If A is a diagonal matrix with diagonal elements aii, then A-I is

also a diagonal matrix with diagonal elements For example,

If

Then

(h) I-1 =I

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(i) The inverse A-I, when it exists, can be computed as follows:

1.2

Where A11, AI2... are the cofactors of a11, a12, ... in the determinant of the transpose A' of A. The matrix on the right side of (1.2) is called the adjoint of A. This is not an efficient method for the computation of the inverse. A better method is the Gaussian elimination method For a nonsquare matrix also, it is possible to define an inverse,called the generalized inverse. However, in this book, we shall consider inverses for square matrices only.

Rank of a Matrix

8. Consider a square matrix of order n. Of the n rows and n columns, if there are at least k rows and k columns which must be deleted in order to obtain a nonvanishing determinant, then the order of the highest ordered nonvanishing determinant in A is given by r = n - k, and this number is defined as the rank of A and is written r(A). Hence, the rank of a matrix is equal to the order of the highest ordered non vanishing determinant in A. If follows, therefore, that for a nonsingular square matrix of order n, the rank is equal to n. To determine the rank of a matrix, we have to find the order of the highest ordered nonvanishing determinant. This method, although general, would be tedious when applied to matrices of higher order, for which the Gaussian elimination method.

Consistency of a Linear System of Equations

9. Consider the system of m linear equations in n unknowns:

.......... 1.3

The matrix is called the coefficient matrix, and the matrix defined by

is called the augmented matrix. If r (A) is the rank of A and r(A, b) that of (A, b) then the following theorem is proved in books on linear algebra (for example; see W.L. Ferrar's Algebra).

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Theorem 3. If r (A) < r(A, b), then the equations. defined by (1.3) are inconsistent and there will be no solution; if r(A) = r(A, b), the equations are consistent and there exists atleast one solution to the system (1.3).

Solution Of Linear Systems-Direct Methods

10. The solution of a linear system of equations can be accomplished by a numerical method which falls in one of two categories: direct or iterative methods. Amongst the direct methods, we will describe the elimination method by Gauss as also its modifications and the factorization method, and also the matrix inversion method. About the iterative types, we will describe only the Jacobi and Gauss-Seidel methods.

Matrix Inversion Method

11. We consider the system of n linear equations in n unknowns:

(1.4)

The system (1.4) can be written in the matrix form

AX= B, (1.5)

where

Let A be nonsingular so that A-I exists. Then, premultiplying both sides of (1.29) by A -

I, we obtainA-lAX = A-I B

i.e., X = A-I B (1.6)Since A-I A = I and IX = X.

If A-I is known, then the solution vector X can be found out from the above matrix relation. The Eigenvalue Problem

15. Let A be a square matrix of order n with elements aij. We wish to find acolumn vector X and a constant ג such that '

AX = ג X (1.7)

In equation (1.7), is ג called the eigenvalue and X is called the corresponding eigenvector.The matrix equati6n (1.7), when written out in full, represents a set of homogeneous linear equations:

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A nontrivial solution exists only when the coefficient determinant in (1.8)vanishes. Hence, we have:

This equation, called the characteristic equation of the matrix A, is a polynomial equation of degree n in ג, the polynomial being called the characteristic polynomial of A. If the roots of (1.8) be given by ג i (i = I, 2, . . ., n), then for each value of ג i, there exists a corresponding Xi such that

AXi = גiXi (1.10)

The eigenvaluesג i may be either distinct (i.e., all different) or repeated. The evaluation of eigenvectors in the case of the repeated roots is a much involved process and will not be attempted here.

16. The eigenvalues are obtained by solving the algebraic equation (1.8). This method is unsuitable for matrices, of higher order and better methods must be applied. For symmetric matrices, in particular, several methods are available, but these require advanced concepts from the theory of linear algebra and will therefore not be explored here.

Check Assimilation

State True or False/ Fill in the Blanks.1. A matrix is an array of mn elements arranged in m columns and n rows.

2. In matrix A of size (mxn) if m=n , the matrix is said to be square matrix of order n.

3. In upper triangular square matrix A all the elements below the diagonal of matrix A are zero.

4. A square matrix in which aij= aji is said to be Skew symmetric.

5. For square matrix A if A 0 then it is called as non singular matrix.

6. For square matrix A is denoted by ______.

7. A square matrix A is said to be orthogonal if _______= ______.

8. AA- = ____ = I

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9. (A- ) - = ________

10. If r(A) < r (A,b) then the linear system of equations are _______.

Conclusion

This chapter gives an overview of application of matrix operations for finding out solution of linear systems of equations.

Check Assimilation: The Key.

1. False m rows and n columns.

2. True

3. True

4. False. In skew symmetric Square Matrix A aij= -aji.

5. True

6. A

7. AA =I

8. A- A

9. A

10. Inconsistent

Bibliography

1. Introductory Methods of Numerical Analysis By SS Sastry.

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MME (PART - II)

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Chapter – 2

LASER CEILOMETER

Chapter Objectives

After reading this chapter you should be able to:-

Know the basic principle of a laser ceilometer. Know about the components of ceilometer Know about various system specifications

Structure

1. Introduction

2. Basic principle and system

3. System Specifications

Introduction

1. Laser Ceilometer is a general purpose cloud height sensor employing diode laser LIDAR (Light Detection and Ranging) technology for detection of clouds and other obstruction to vision, and accurate determination of cloud heights, cloud amount and vertical visibility. The heights of base of clouds from 15m to 7500m from the ground. The Laser ceilometer will be integrated with the Automatic Weather Stations.

2. The Laser Ceilometer will be installed at the runway end and the data will be transferred by radio transmitter of AWS to the Met Section. The equipment is equipped with a microcomputer, which has the necessary algorithm to check, process and finally transmit the data. The equipment will have autonomous round the clock operation without participation of any attendant.

Principle and systems.

3. The instrument is based on the principle of measurement of transit time using LIDAR to estimate the height of cloud base above the ground. The instrument consists of an optically critical transmitter and the receiver module and a display unit. The transmitter is a pulse injection laser diode (preferably GaAs type).

4. The system consists of a transreceiver (TR), digital indicator and associated control circuits. The cloud height sensor shall be Lidar type. It comprises of internal heaters and blower to keep the lenses free from condensation and accumulation of dirt. The sensor is equipped with a solar shutter to prevent direct irradiation of electro-optical components. The system measures:

(a) Cloud amount and heights of base of at least three layers of clouds are automatically measured, displayed, transmitted and made available to all

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users in the station and on LAN/WAN through central data acquisition computer in Met Section.

(b) System would be in conformity to all ICAO and WMO requirements for reporting data on height of base of clouds, cloud amount and vertical visibility

for aviation purpose.

System Specifications

5. Essential System Specifications for the Laser Ceilometer are as follows:

TRANSMITTER SYSTEM

Transmission source: Pulsed diodes (preferably GaAs laser type).

(b) Peak power: The laser output power should be sufficient to cover the entire detection range up to 7500 m.

(c) Pulse duration: 100 ns or less.

(d) Pulse repetition frequency:

1 KHz or more

(e) Wavelength of laser emission:

Infra-red (preferably 905-915nm range)

(f) Eye safety: Completely eye safe conforming to WHO Health Standard (with documentary proof).

(g) Optical system: Suitable to project vertically a beam of laser line with provision for easy adjustment of exact verticality.

RECEIVER SYSTEM

(a) Receiver collection

Avalanche photodiode with suitable optics and gain control

(b) Measuring range

0 – 7.5 km or better

(c) Accuracy Better than 1% up to 3000 m and 2% above 3000 m.

(d) Resolution 10 m or better

(e) Selectivity The attenuation on account of precipitation should not affect the detection of base of low clouds.

Detection of base of low cloud height should be possible under rainy and foggy conditions.

Detection of base of low cloud height should be possible under rainy and foggy conditions.

(f) Acquisition time 15 seconds for 7.5 km range

(g) Solar shutter Provision of built-in solar shutter/optical filter to protect the transmitter and receiver from direct sun light under clear sky

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conditions.

(h) Output data Height of base of at least three layers of clouds with thickness (in m/feet).

Vertical visibility (m/feet).

Sky Condition, Sky Coverage reported as SKC, FEW, SCT, BKN, OVC.

Check Assimilation1. The instrument is based on the principle of measurement of transit time using -

______________ to estimate the cloud base .

2. The _________________ is a pulse injection laser diode

3. Pulse repetition frequency of the instrument discussed here is __________ or more.

4. Resolution of the system discussed here is _______m or better.

5. Wavelength of laser emission is _____________

Check Assimilation: The Key1. The instrument is based on the principle of

measurement of transit time using LIDAR to estimate the height of cloud base above the ground

2. The transmitter is a pulse injection laser diode

3. Pulse repetition frequency of the instrument discussed here is 1 KHz or more

4. Resolutionof the system discussed here is 10 m or better

5. Wavelength of laser emission is Infra-red.

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Chapter – 3

WIND PROFILERS

Chapter Objectives

After reading this chapter you should be able to:-

Appreciate the dwar backs of conventional wind profiling methods. Understand the need for a electromagnetic profiler Understand the working principle of a Doppler wind profiler.

Structure

1. Introduction

2. Conventional method – Drawbacks

3. Doppler Radar wind profilers

4. Working Principle of Doppler wind profiler

5. Conclusion

Introduction

1. The wind measurement in the lowest few tens or even hundreds of meters are usually obtained by anemometers mounted at various heights on instrumented towers. Such towers yield wind profiles continuously in time, but at discrete heights from the ground. A conventional method of wind profiling to higher altitudes consists of releasing a balloon and tracking its movement with either manually or with the use of radar.

2. The radar performs three-dimensional tracking, providing both height and wind velocity information which is utilized for plotting the wind profile. The balloon method of profiling is routinely carried out around the globe by meteorological agencies. Balloon data have extensive meteorological applications including those in support of aerospace activities. From the point of view of aviation management, however, wind profiling by balloon tracking has some serious drawbacks. These are as follows:

(a) The method is very slow. Since the balloon drifts in the atmosphere only by natural air currents and buoyancy forces, it rises slowly to its operational ceiling, requiring a time interval of the order of one or two hours for a profiling operation.

(b) The wind profiles are obtained only along the flight path of the balloon, on which the operating personnel have no control. Depending on the local winds, the balloon may drift large distances away from the vertical at the launch point, and there is a great deal of uncertainty in ensuring that profiling

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is done over a small area of interest such as an airport area or a given flight corridor. Indeed, balloon profiling presents a paradox. The balloon will rise nearly straight upward and thus provide a vertical profile only when the atmosphere is calm, i.e. has very little wind shear. On the other hand, when there is significant shear, and hence profiling would be of interest, the balloon would drift and yield a profile far away from the vertical.

(c) Each balloon launch is a discrete operation in time. Since a single profiling may take an hour or more, balloon launches are separated by even longer intervals. Routine meteorological balloon launches are normally carried out twice a day from any given location. The launches may be made somewhat more frequent for dedicated aviation support such as from airport sites, but still the launch frequency would not be commensurate with the needs of modern aviation operations.

Radar wind profilers

3. Electromagnetic wind profilers provide a more modern method of obtaining the vertical profile of wind velocities. These profilers are essentially Doppler radars that are configured and optimised to receive echo returns from layers of air above their location and process the signal to derive their velocity parameters as functions of height. General purpose Doppler weather radar is capable of providing wind profiles when operated in the velocity-azimuth display (VAD) mode. However, since such general weather radars are designed and operated to perform a variety of functions, they are operated in the VAD mode only occasionally. It is, of course, possible to dedicate Doppler weather radar for wind profiling alone, but such use would amount to only a partial utilization of the radar's capabilities, and represent a costly solution to the profiling problem. The modern special-purpose electromagnetic wind profilers are also Doppler radars, but these are far less versatile, and consequently simpler, less costly and often smaller in size than the multifunction Doppler weather radars.

4. Since profiling is required to be done in all weather conditions, electromagnetic profilers are designed to operate satisfactorily with clear-air echoes from the atmospheric layers. Clear-air radar echoes are primarily caused by small-scale fluctuations in the atmospheric refractive index, which in turn arise from in homogeneities or irregularities in the local temperature and water vapour concentration. Further, the spatial scale of such fluctuations which contributes most to the echo power is one that corresponds to a half of the radar wavelength. Electromagnetic profilers typically utilize frequencies in the VHF and UHF bands in preference to microwave frequencies since the longer wavelengths provide stronger echo returns from the refractive index fluctuations associated with relatively large eddies that are in the inertial sub range, and hence do not dissipate rapidly. Centimeter scale eddies, which are efficient scatterers at microwave frequencies, decay rapidly after their creation due to viscous dissipation of energy.

5. Hydrometeoric scatterers such as raindrops are not considered to be good atmospheric tracers for profiling purposes even though they return strong echoes and hence can greatly reduce the transmitted power and/or sensitivity requirements of profiling radars. This is because hydrometeors are not present at all altitudes at all times. Further, since radar profilers 'look' essentially in a vertically upward direction, the considerable fall velocity of hydrometeors introduces additional Doppler shift

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which affects the accuracy of wind estimates (Wuertz et al., 1988). The use of the longer wavelengths in the VHF /UHF bands significantly reduces echoes from hydrometeors, but the velocity estimates may still be perceptibly affected by strong precipitation.

Working Principle of wind profiler

6. In an idealized profiling scenario the atmosphere may be assumed to be horizontally layered, with each layer moving at a different velocity in general. In such a case, profiling radar looking vertically upwards would not sense any mean Doppler shift since the beam axis is normal to the layer velocities. To be able to sense the horizontal velocities in the atmospheric layers through a Doppler shift, the beam should be tilted away from the vertical by a finite angle. A tilt of the order of 10 or 15 degrees is considered adequate for radar profiling. A larger tilt would, of course, provide a higher Doppler shift for a given horizontal wind speed and thus result in improved sensitivity for the measurement of low speeds. However, a large tilt angle would take the beam far away from the vertical, especially at high altitudes, and the wind velocities measured along the beam may not accurately represent the profile along the vertical. Further, for a given highest altitude of profiling, the slant range from the radar increases with the tilt angle, which would demand larger transmitted power on the part of the profiler.

7. If the wind velocity vector is horizontal and lies in the vertical plane through the profiler beam axis in its tilted position, the radial component v r of the velocity along the beam axis is

vr = v sin β

where v is the wind speed and β is the beam tilt angle. Then, from the Doppler shift equation 1 of chapter 1 , the Doppler shift of the echo relative to the transmitted signal, as a function of height, is given by the relation

fd (h) = - (2/) v(h) sin ,

where is the wavelength of the radar. The velocity profile v(h) can be readily deduced from the measured values of the Doppler frequency at each height (i.e. at the corresponding slant ranges).

8. In general the horizontal velocity vector will not lie in the vertical plane through the inclined beam. The profiler will then measure only the projection of the velocity vector on the vertical plane, which is the wind velocity component along the azimuth direction of the oblique beam. To obtain the vector velocity itself, its components along two beam positions must be measured such that the two beams do not lie on a common vertical plane. Preferred beam positions are along orthogonal directions in azimuth because they would measure the orthogonal components of the horizontal wind velocity vector.

9. Although a two-oblique-beam configuration is adequate for wind vector profiling under the assumption of horizontal wind velocity at all altitudes, such an assumption is not necessarily true in nature, with local winds at all but the layer immediately in contact with the ground often having significant vertical components. In such cases, the angle of the velocity vector with respect to the horizontal plane must be algebraically added to the tilt angle , and the two-beam profiler can yield

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significantly erroneous wind profiles. To estimate or eliminate the third (i.e. vertical) component, a third beam position would be necessary. The so-called tripod configuration may have three beams arranged along the vertices of an equilateral triangle. Alternatively, one of the beams may be vertical, with the other two tilting at equal angles along orthogonal directions in azimuth.

10. Wind profiling with the minimum configuration consisting of three beam positions is not very accurate. Since the different beam positions observe wind components at spatially separated points, the separation being as much as a few kilometers at high altitudes, non uniformities in wind fields can cause significant errors in the estimation of wind velocities. Such errors can be compensated to a certain extent by using more beam positions than the minimum of three necessary to estimate the wind components under ideal conditions. Proper signal processing and data averaging schemes can minimize the effects of noise and random wind fluctuations, as well as wind field non uniformities, on profiling accuracy (May and Strauch, 1989).

11. A common beam configuration for radar wind profiling employs five beams. Here, a vertical beam position is surrounded by four tilted beams in the manner of a cross. Such a configuration provides a degree of redundancy of information which permits more accurate profiling by averaging the common velocity components sensed by each pair of opposite beams. In each orthogonal plane there are three beams, which may be considered as two pairs with a common beam position. Each pair of beams provides an independent estimate of the wind velocity component in the plane, and averaging the two values would serve to reduce the statistical

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uncertainty associated with the estimates. The difference of the winds sensed by the two beam pairs in each plane would indicate the variation of the corresponding wind component across the baseline of the beam configuration, but such differential wind estimates have a high noise component.

12. The use of a few fixed beam positions for profiling obviates the need for a fully steerable antenna. This is a great advantage which substantially simplifies the profiler system, leading to significant cost saving. The advantage is particularly great in the case of large-sized profilers operating at relatively low frequencies. In particular, if array antennas are used, the generation of a few fixed beam positions greatly simplifies the phase shifter network and its control apparatus.

13. The diverse and often conflicting requirements of electromagnetic profilers in terms of operating frequency, antenna size, altitude coverage, etc. have led to the development of different types of pro filers, many of which can provide useful data of direct use for aviation (Frisch et ai, 1986; Strauch et ai, 1989a). A versatile profiler is the tropospheric wind profiler, which is a clear-air radar operating at 404.37 MHz, and is conveniently referred to as a 405 MHz profiler. This device can observe wind profiles up to a height of -17 km, covering the entire troposphere and the lower reaches of the stratosphere. It has a phased-array antenna producing a 60 conical beam; and has five discrete beam positions comprising one vertical beam and four north-south-east-west beams tilted at 150 with respect to the vertical. It is capable of automatic and continuous operation, and can generate wind profiles every hour with a height resolution of ~1500 ft (500 m) and velocity measurement accuracy of 1 m/s for horizontal wind components.

Check Assimilation 1. One of the disadvantages of the balloon method of wind profiling is the large

time interval required for a profiling operation.

2. Conventional radars operated in a vertical azimuth display mode can be used as a wind profiler.

3. Refractive index fluctuations associated with relatively small eddies are used as tracers in wind profilers. (large)

4. Horzontal velocities in the atmospheric layers can be traced Through Doppler shift by vertical beams of the radar.

Conclusion

14. While profiler networks can improve air traffic routing and en route flight efficiency by providing wide-area profile patterns, individual profilers can greatly aid local aviation operations such as in terminal areas. Very useful information about vertical wind shear and wind shifts in support of aircraft approach, landing and takeoff operations in terminal areas may be obtained from a single wind profiler suitably located within the airport area. A profiler for such an application does not have to cover as much altitude as a tropospheric profiler, but needs to 'see' only up to a maximum height of the order of 4-6 km, which is the ceiling of most terminal area operations. A profiler observing up to such heights is called a lower tropospheric wind profiler.

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Check Assimilation The Key1. True.2. False:

Doppler radars operated in a vertical azimuth display mode can be used as a wind profiler.

3. False:Refractive index fluctuations associated with relatively Large eddies are used as tracers in wind profilers.

4. False:Horzontal velocities in the atmospheric layers can be traced Through Doppler shift by radar beams tilted away from the vertical.

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