ERAD 2012 - THE SEVENTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY

Comparison of measured cloud reflectivity at 95 GHZ

with reflectivity simulations from hydrometeor particle

size distributions.

E. Fontaine1, A. Schwarzenboeck

1, A. Protat

2,3, J. Delanoe

3, N. Viltard

3, R. Dupuy

1, W. Wobrock

1,

C. Duroure1, and C. Gourbeyre

1.

1 Laboratoire de Météorologie Physique, Clermont-Ferrand, France.

2 Center for Australian and Weather Climate Research, Melbourne, Australia. 3 Laboratoire ATmosphère, Milieux, Observations Spatiales, Velizy, France.

(Dated: 15 April 2012)

E. Fontaine

1. Introduction.

The presented study is performed within the Megha-Tropiques (MT) project. Megha-Tropiques is a French-Indian

satellite devoted to improve our knowledge on the understanding of the processes linked to the tropical convection. The

relevant instrument on the satellite for cloud studies is the MADRAS microwave imager with 9 frequencies (18,7 GHz to 157

GHz). Two aircraft measurement campaigns (MT1 over West Africa in 2010 and MT2 over the Indian Ocean in 2011) have

been performed with the French Falcon 20 in order to improve cloud microphysics parameterization and precipitation

retrievals from the satellite data. The presented study is using solely MT1 data. Onboard the French Falcon aircraft, the

French Doppler radar RASTA (Radar Aéroporté et Sol de Télédétection des propriétés nuAgeuses; with a frequency of

95GHz: Protat & Al, 2009), the Cloud Imaging Probe (CIP), the Precipitation Imaging Probe (PIP) and the 2D Stereo (2DS).

In situ CWC mass has not been measured directly. After image data processing two types of composite particle size

distributions (hereafter PSD) have been derived. The representation of PSD is given as a function of the equivalent diameter

of a disc corresponding to the crystal surface (hereafter Deq), the second type of PSD is presented as a function of the

maximum length of the particle (Dmax). Both PSDs are calculated for a 1 s and 10 s time resolution (PSD are handled in 10

µm bin resolution from 50µm to 6400µm).

Determining the mass of a particle is very difficult when its shape is not known. Baker and Lawson, (2006) presented a

relationship between particle mass and geometric parameters derived from 2D particle images. Schmitt and Heymsfield

(2010) showed that the fractal dimensions of aggregates are related with their mass.

The estimation of IWC in MCS systems over West Africa presented in this study is based on two slightly different

approaches of IWC retrieval from simultaneous analysis of in situ cloud particle imagery and radar reflectivity measured at

95GHz with the cloud Doppler radar RASTA.

2. Method used to retrieve the mass-diameter relationship.

The reflectivity at 95 GHz is usually calculated, assuming the mass of the ice particles. Thus, our purpose is to estimate the

mass-diameter relationship which produces the smallest deviations (equation 2) between the measured radar reflectivity

(Z95GHz) and the equivalent reflectivity (ZMie) calculated from the mass-diameter power law (equation 1). The diameter D

stands either for the equivalent or the maximum diameter. In the present study the maximum error (cf. equation 2) has been

set to 5%.

(eqn. 1)

(eqn. 2)

The equivalent reflectivity at 95 GHz can be calculated as shown in the equation 3, where Ki and Kw are the dielectric

constants for ice and water. The PSD is represented with n(D) and the Mie scattering effect is described by the function f(D).

However, this formula is difficult to implement, since the Mie scattering effect cannot be described by a simple equation.

Therefore, to calculate properly the equivalent reflectivity we use an algorithm, where the Mie theory is applied on a sphere

with a homogenous mixture of ice and air. The mixture is related to the mass-diameter law by the fact that the ice fraction is

proportional to the mass of the ice in the particle divided by its mass if the particle would only consist of ice.

(eqn. 3)

The calculation is performed in two different ways: Either we fix the β exponent to be equal to 2.1 (for example) or we

calculate the β exponent as a function of the exponent of an area-diameter relationship (to be derived from particle images) of

the crystals. Thus, either β is a constant, or it is a function of the 2D images recorded by the in situ imagers (2DS, CIP, PIP).

In order to characterize a falling particle in the atmosphere, Heymsfield and Miloshevich, (2003) and Mitchell (1996) use the

area and the aspect ratio Ar (which is the area of the particle projected normal to the flow ( ) divided by the area of a

circumscribing disc).

ERAD 2012 - THE SEVENTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY

(eqn. 4)

(eqn. 5)

In this study we consider that the diameter-area law is equal to ( ). The Diameter-area law could be explained as the

expected area (or mean area) for a given maximum length (Dmax). An example of a diameter-area law is given in figure 1

and has been calculated using all particle images in a time interval of 10 seconds for one arbitrary flight of the MT1

campaign. We can see that the relationship between the mean area and the maximum length is well fitted with a power law.

The diameter-area law shown in this figure has been calculated for 2D images recorded by the PIP probe in the size interval

1000µm and 6400µm. The calculated mean areas are represented by triangular symbols and the line corresponds to the fitted

power law. The line above and below the data points represents one standard deviation.

Figure 1. Example of relationship for crystal mean area as

a function of the maximum length for an ice crystal

population of more than 200 analyzed crystals within a time

period of 10 seconds. The particles have been recorded by

the PIP probe.

-30 -20 -10 0 10 20 300

0.01

0.02

0.03

0.04

DBz

reflectivity at (95GHz) vs and Temperature

-40

-30

-20

-10

0

°C

Figure 2. Scatter plot of the reflectivity versus α of the mass-

diameter law. Each point corresponds to 1 second of

measurement data of flights 15, 17, 18, 19, 20 of the MT1

campaign and its color represents the measured in situ

temperature.

3. Results.

In this first part of the results, we show findings obtained when fixing β equal to 2.1. In figure 2, the calculated coefficient

α of the power law is plotted as a function of the reflectivity measured by RASTA. The temperature measured in the

corresponding cloud volume is color coding the data points. We can see that there is some temperature dependency in this

figure. Low values of α are particularly found for low temperatures, which is of course the result of having chosen a constant

exponent β independently of the temperature and related to the clouds microphysics.

A reason to study area-diameter relationships from particle imagery is also to compare the in situ findings to the terminal

velocity of the hydrometeors deduced from the reflectivity measured by the radar RASTA. Since area-diameter relationship is

varying during a flight and since the area-diameter law of the particles is strongly influenced by the specific ice microphysics,

different relationships between the β exponent of the mass-diameter law and the σ exponent from the area-diameter law have

been tested. Figures 3 and 4 present the results obtained with the dataset from the MT1 campaign. The mass-diameter laws

are calculated for the flights 15, 17, 18, 19, 20 with a time integration of 10 seconds. The PSD used have been built as a

function of the equivalent diameter Deq and the area-diameter law has been calculated using the 2D images monitored with

the PIP probe. In figure 3 we can see the relationship between the condensed water content (equation 6; CWC) and the

measured reflectivity (Z95GHz). The data points are color coded with measured temperature. The resulting relationship is a

power low which is influenced by the temperature (equation 7). For a given reflectivity, CWC increases with decreasing

temperature. We can also conclude that a given CWC produces lowest reflectivities for lowest temperatures.

(eqn. 6)

(eqn. 7)

The subsequent relation in equation 8 resumes what is presented in figure 4. α is written as a power law of β and with Cm

and Am both depending upon temperature. Overall, β increases (for given α) with increasing temperature T, whereas α

increases with decreasing T (for given β).

(eqn. 8)

Finally figure 5 shows the impact on CWC retrievals when applying 6 different mass-diameter relationships. The figure is a

zoom of 15 minutes of calculations for one exemplary flight (flight number 19). It shows results obtained with 4 different

relationships between σ (from the area-diameter law) and β (from the mass-diameter law) calculated for PSD expressed in

ERAD 2012 - THE SEVENTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY

terms of the maximum length Dmax and the area-diameter law calculated from the PIP probe (maximal length between

1000µm to 6400µm). To these four curves are added two curves. In one of these two curves CWC is calculated for PSDs

expressed in terms of the equivalent diameter Deq with data from the PIP probe, whereas in the other curve CWC is

calculated for Dmax, however for CIP data (maximal length between 500µm to 1600µm) derived area-diameter relationships.

The results of these 6 curves are rather similar and somewhat independent of the relationship between σ and β,

independent of the probe used for the area-diameter relationship and thus, the range of the particles used to calculate that

relationship, and independently of the parameters (Dmax or Deq) of 2D images used to classified the particles to build up the

PSD.

-10 0 10 20 3010

-2

10-1

100

101

DBz

g/m

3

CWC vs RASTA vs Temperature

-40

-30

-20

-10

0

°C

Figure 3. Scatter plot of the CWC versus the reflectivity at

95 GHz measured by RASTA. Each point corresponds to 10

seconds of measurement data of flights 15, 17, 18, 19, 20 of

MT1 and its color shows the in-situ temperature.

1 2 310

-3

10-2

10-1

vs vs Temperature

-40

-30

-20

-10

0

°C

Figure 4. Scatter plot of α versus β from the mass-diameter

law m=αDβ. Each point corresponds to 10 seconds of

measurement data of flights 15, 17, 18, 19, 20 of MT1 and

its color shows the temperature in-situ.

4. Conclusion.

To resume figures 3, 4, 5, we can state that the mass-diameter relationship is significantly influenced by the temperature.

CWC calculated from the RASTA radar reflectivities using the Mie theory and applying different relationships for the mass-

diameter relation, the results are approximately the same, if all m(D) relations have been constraint by the radar reflectivities.

In fact, for any given value of β, α can be calculated to fit to the function given in equation 8. It is important to give the

variations of the area-diameter law to the mass-diameter law. It seems that the area-diameter law is influenced by the

temperature and some further parameters. More studies have to be performed in order to understand how the area-diameter

law varies in clouds, and what are the most significant physical parameters controlling the calculation of the area-diameter

law.

11:15 11:30

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

time

g/m

3

Comparaison de l'IWC restituer à partir de lois Masse-Diamètre différentes: Vol 19

= +1 PIP Dmax

= (+1).(0,5.-0,062) PIP Dmax

= 2. -1,2 PIP Dmax

= 2. -1,2 CIP Dmax

= 2,25. -1,5 CIP Dmax

= 2,25. -1,5 PIP Deq

Figure 5: CWC calculations for 6 different mass-diameter relationships, all laws have been constraint by the radar

reflectivities.

Acknowledgements

The authors are particularly grateful to CNES for funding the aircraft measurement campaigns within the Megha-Tropiques

project. We would like to thank SAFIRE for operating the French Falcon 20 research aircraft during the two campaigns.

ERAD 2012 - THE SEVENTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY

References

Baker, B., Lawson, R.P., 2006: Improvement in Determination of Ice Water Content from Two-Dimensional Particle Imagery. Part I:

Image-to-Mass Relationships. Journal of Applied Meteorology and Climatology 45, 1282–1290.

Heymsfield, A.J., Miloshevich, L.M., 2003: Parameterizations for the Cross-Sectional Area and Extinction of Cirrus and Stratiform Ice

Cloud Particles. Journal of the Atmospheric Sciences 60, 936–956.

Lawson, R.P., Baker, B.A., 2006: Improvement in Determination of Ice Water Content from Two-Dimensional Particle Imagery. Part II:

Applications to Collected Data. Journal of Applied Meteorology and Climatology 45, 1291–1303.

Mitchell, D.L., 1996: Use of Mass- and Area-Dimensional Power Laws for Determining Precipitation Particle Terminal Velocities. J.

Atmos. Sci. 53, 1710–1723.

Protat A, Bouniol D, Delanoë J, May PT, Plana-Fattori A, Hasson A, O'Connor E, Görsdorf U, Heymsfield AJ. 2009: Assessment of

CloudSat reflectivity measurements and ice cloud properties using ground-based and airborne cloud radar observations. J. Atmos. Oceanic

Technol. 26: 1717–1741.

Schmitt, C.G., Heymsfield, A.J., 2010: The Dimensional Characteristics of Ice Crystal Aggregates from Fractal Geometry. Journal of the

Atmospheric Sciences 67, 1605–1616.