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rainfall series in the region for required storm durations. Factors that in fluency calculations of PMP values
are rainfall, dew point, temperature, wind speed, temperature and pressure.
2.1. Physically or maximization method
2.1.1. Depth-Area-Duration
An important step probable maximum estimates is the analysis of major storms. This analysis includes;
collection precipitation data from various sources. The objective of the storm analysis was to obtain
Deph-Area-Duration (DAD) information upon which to base PMP estimates as well as generalized
relations for other areas or other basin with similar climate and topographic characteristics. The first step
in order to development of DAD relations requires that rainfall amounts to all areas in the storms. Then
point precipitation amounts interpolated by assigning a particular precipitation gauge to a region.
Estimation of spatial distribution of rainfall is one of the basic steps in PMP studies. In this study in order
to interpolation were used kriging methods.
2.1.2.Maximum of storms humidity and dew point factor
Storm maximization, it is assumed that rainfall can be determined from the product of an available
moisture and storm mechanism. After selection of storms and estimation of mean rainfall depth for each
sub-basin, it was necessary to estimate maximum humidity source in order to maximize selected
storms. Storm moisture maximization factor was determined using the surface dew point temperature,
in conjunction with an assumed saturated atmosphere above surface level. Surface dew point was
used as a measure of moisture potential for server storms because it is the critical factor for server
storm development in small areas. Maximum dew point for any location is chosen as the highest value
persisting for 12-hour duration. In this study recorded surface dew points 7 station could be considered
as representative of in flow humidity source. There fore, to calculate the maximum in flow humidity to
storm, it is needed to investigate maximum persisting 12-hour dew point duration for statistical period of
7 station and also dew point values of those station at storm event. For investigation of maximum
persisting 12-hour dew point duration in statistical period, the 10-day recorded data for each year were
Figure (1) Southwest basins of Iran
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extracted and then maximum persisting 12-hour dew point values for each 10-day period were
calculated with 50-year return period by using frequency analysis. Having used the mean monthly
pressure data recorded at each station were transferred to 1000 millibar pressure level such that they
can be compared at different elevations. The calculated dew point temperature at the 7 station during
all storm events and maximum 12-hour persisting condition were reduced to equivalent mean sea level
(Msl, i.e.1000 millibar air pressure) dew point temperatures, using figure 2.
Figure(2):Peseoud-adiabatic chart for dew point reducation to 1000 hpa at high zero
In next step, variation of 10-day maximum 12-hour duration dew point of each station with 50-year
return period (at level 1000 millibar) are used the corresponding typical curves were plotted and then by
reading points from those curves, the humidity coefficients were estimated. Mentioned curves are
shown in figure (2). Usually recorded dew points in stormy days of a 12-hour period, which have the
biggest values, are selected to investigate 12-hour duration dew point at the selected storms. Then the
smallest of these values during storm event were used as maximum persisting 12-hour duration of dew
point.
These values were also transferred to 1000 millibar level by using stations air pressures data during
storm event to become comparable with each other. Then, the humidity coefficient calculated by using
equation1 FM=Wm/Ws (1)
in this equation Wm is maximum precipitable water at 1000 to 200 millibar levels which can be obtained
on the basis of maximum 12-hour duration dew point with 50-year return period in a simultaneous
period with storm.
Ws= maximum perceptible water at 1000 to 200 millibar levels which can be obtained on the basis of
maximum 12-hour duration dew point in a simultaneous period with storm.
The relevant values of dew point temperature and humidity coefficients are presented in table (1) and
(2).
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Table (2) the Moisture and Wind Maximization Factors for Some Selected Storms
Maxim12hr
return
Maximum persisting12hr wind (knot)
Moisturefactor
Precipitablewater(mm)
Maximumpersisting 12hr
dew point in1000 mb level
(100 year returnperiod)
()
Precipitablewater(mm)
Maximumpersisting 12hr
dew pointsin 1000 mblevel (in thestorm time)
()
SynopticStation
StormsDate
18.01.2549.619.439.616.9Abadan
181.5855.620.935.115.7Ahvaz
221.2648.419.132.414.8Mahshar
181.2648.419.138.416.6Omidyeh
181.3453.620.44017Dezful
1.34
30Mar1998
Averag
e
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Table (1) the Moisture and Wind Maximization Factors for Some Selected Storms
Maximpersisting
wind (k
Moisturefactor
Precipitablewater(mm)
Maximumpersisting 12hr dew point in 1000 mb
level (100 year return period)()
Precipitablewater(mm)
Maximum persisting12hr dew points in 1000mb level (in the storm
time) ()
SynopticStation
StormsDate
18.01.262.022.052.020.1Abadan
211.3857.521.141.617.4Ahvaz
151.4358.021.240.417.1Bushehr
181.1856.520.94819Mahshar
171.5764.423.440.817.2Omidyeh
201.216121.850.419.6BushehrCoastal
211.564.422.442.817.7Aghajari
23-26Nov1994
1.35Average
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2.1.3. Wind maximization
Wind maximization is most commonly used in orographic regions. (WMO.332) the wind maximization
ratio is simply the ratio is simply the maximum average wind speed for some specific duration and
critical direction obtained from a long record of observations, e.g. 50 y, to the observed maximum
average wind speed for the same duration in the storm being maximized.
Maximum values of wind speed are obtained from maximum persisting 12h. wihd. In order to estimate
high wind speed used 50-y return period.
2.2. Statistical Method
Statistical Method for estimating probable maximum precipitation is used wherever sufficient
precipitation data are available, and particularly useful for making quick estimate, or where othermeteorological data, such as dew point and wind records, are lacking. The statistical method is used
mostly for making quick estimate for basins of no more than about 1000 km2, but has been used for
much larger areas (WMO, 332). This method requires data for annual maximum precipitation series in
the region for required storm durations. The statistical method developed by Hershfield (1961) and
modified (1965) is based on the general frequency equation 2 (chow 1961)
Xt = Xn+ KSn (2)
Where Xt is the precipitation for return period t; Xn and Sn are respectively the mean and standard
deviation of a series of n annual maximum: and K is a common statistical variable, which varies with the
different frequency distributions fitting extreme value hydrologic data. This method requires some
adjustment, such as adjustment Of mean of annual series (Xn), standard deviation of annual series (Sn)
for maximum observed precipitation. Such as adjustment of mean (Xn) and standard deviation (Sn) of
annual series for maximum observed precipitation and also adjustment of mean and standard deviation
of annual series for length of record.
Table (3)estimated probable maximum precipitation value
based on statistical (Hershfield) and physically methods
Station Statistical (Hershfilds) methods
Physically
(maximization of
storms) methodAbadan 236 92.5
Ahvaz 371 114.7
Mahshahr 362 137.3
Brojerd 277 98
Bushehr 637 145.3
Dezful 418 151.7
Masjed
soleiman516 144
Omidieh 407 93.9
yasoj 356 134.9
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y = -5E-06x6
+ 0.0004x5
- 0.0118x4
+ 0.1789x3
- 1.3036x2
+ 3.2302x + 21.247
R2
= 0.8364
15
16
17
18
19
20
21
22
23
24
25
26
1-Oct.
10 20
1-Nov. 10 20
1-Dec.
10 20
1-Jan. 10 20
1-Feb. 10 20
1-Mar.
10 20
1-Apr.
10 20
1-May 10 20
TIME(DAY) a
DEWPOINT(C)
y = -8E-06x6
+ 0.0007x5
- 0.0199x4
+ 0.2907x3
- 1.9959x2
+ 4.2433x + 27.461
R2
= 0.9711
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
1-Oct.
10 20
1-Nov.
10 20
1-Dec.
10 20
1-Jan.
10 20
1-Feb.
10 20
1-Mar.
10 20
1-Apr.
10 20
1-May 10 20
TIME(DAY) b
DEWPOINT(C)
y = -4E-06x6
+ 0.0004x5
- 0.0113x4
+ 0.1667x3
- 1.0181x2
+ 0.4534x + 31.376
R2 = 0.9162
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
3031
32
1-Oct.
10 20
1-Nov. 10 20
1-Dec.
10 20
1-Jan.
10 20
1-Feb.
10 20
1-Mar.
10 20
1-Apr. 10 20
1-May 10 20
TIME(DAY) C
DEWPOINT(C)
y = -4E-06x6
+ 0.0003x5
- 0.01x4
+ 0.1469x3
- 0.9727x2
+ 1.23x + 27.867
R2
= 0.9859
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
1-Oct.
10 20
1-Nov. 10 20
1-Dec.
10 20
1-Jan.
10 20
1-Feb.
10 20
1-Mar.
10 20
1-Apr. 10 20
1-May 10 20
TIME(DAY) d
DEWPOINT(C)
Figure (3): Maximum dew point envelope curves (a) in the Dezful station(b) Abadan (c) Ahvaz and (d) Bushehr station
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ConclusionsIn this study two techniques used for estimating PMP which incloude statistical and physically methods.Statistical method based on the transposition and maximization of historical precipitation (annual maximumprecipitation series) and physically method based on the maximization of the physical factors (dew pointand wind) that the precipitation evolution. Using statistical method of estimating PMP rather than physicallymethod showed larger values. Also application of the physically method will allow for the provision of PMPestimates for catchments in the southwest Of Iran from 1-5000 km2 in size and duration of 24,48,72,96,120and 144 hours, whereas statistical method used mostly for basins about 1000km2. We found that PMPestimates by statistical method are well comparable with values of obtained by the physical method fordifferent durations. Results also shows that limited transposition of statistical methods gives higherestimates, in comparisons with physical method.
References
Desa, M.N., Noriah,A.b.and Rakhecha,P.R.(2001) Probable maximum precipitation for 24h duration
over southest Asian Monsoon region-Selangor Malaysia. www.Elsevier.com/ocate/atmos.
Koutsoyiannis, D. (1999)A probabilistic view of Hershfield method estimating probable maximum
precipitation. Water resources research.4:1313-1322.
Loukas, A and quick, M.C.A. (1996) Spatial and temporal distribution of storm precipitation in
southwestern British Columbia; Journal of Hydrology, 174: 37-56
Kennedy, M.R. (1982) The estimation of probable maximum precipitation in Australia- past and
Current practice, proc. Workshop on spillway design, Melbourne, 1981. Awrc cont. 26-52
Bureau of Meteorology (1985) ' The estimation of probable maximum precipitation in Australia for
short small areas' Bulletin 51, august 1984, AGPS, Canberra.World Meteorological Organization (1986)' Manual for estimation of probable maximum
precipitation; second edition. Operational hydrology report No.1, WMO-No.32, and Geneva.
Burea of Meteorology (1994)' the estimation of probable maximum precipitation in Australia:
Generalized short-duration method. Bulletin 53, December 1994, AGPS, Canberra.
Corrigan, p. and J. L. Vogel (1999)' probable maximum precipitation for California- Calculation
procedure, Hydro meteorological report No.58.national weather service.
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