MWR Rain Rate Retrieval Algorithm. Rosa Menzerotolo MSEE Thesis defense Aug. 29, 2010

Transcription

1 MWR Rain Rate Retrieval Algorithm Rosa Menzerotolo MSEE Thesis defense Aug. 29,

2 Outline Objective Theoretical Basis Algorithm Approach Geophysical Retrieval Results Conclusion Future Work 2

3 Thesis Objective To develop a rain retrieval algorithm for the Aquarius/SAC-D Microwave Radiometer (MWR) Algorithm approach Based upon both radiative transfer theory and statistical regression Tuned using empirical data from WindSat Algorithm validation using WindSat Environmental Data Record (EDR) To deliver an Algorithm Theoretical Basis Document (ATBD) to CONAE in December

4 Algorithm Theoretical Basis 4

5 Microwave Brightness is the sum of three components Radiometric Emissions are Non-coherent and their Powers Add

6 Microwave Ocean Apparent Temp (Tap) (single layer atmosphere approx) T ap = T BU + τ atmos ( T b + T ) scat T scat = ( 1 ε) ( T BD + τ atmos T ) BC T BU = (1 τ atmos ) T U T BD = (1 τ atmos ) T D T b = ocean surface emission = ε * SST τ atmos = Atmospheric loss (transmission coefficient) T BC = cosmic brightness = 2.7 K (1 -τ atmos ) = Atmospheric absorption (1 -ε) = ocean Fresnel power reflection coeff T U & T D = effective atmos phys temp (up/down)

7 Atmospheric Transmissivity Atmos optical depth (nepers) A atmos = TOA K dz 0 A atmos = A O + A V + A L Atmos transmissivity τ atmos = exp[ secθ (A O + A V + A L )] τ atmos = τ O τ V τ L K = Atmospheric absorption coefficient (nepers/km) Z = Atmos height (zenith direction) A atmos = atmospheric absorption (Optical depth) τ O = Transmissivity due to oxygen τ V = Transmissivity due to water vapor τ L = Transmissivity due to liquid water (cloud liquid water and rain) 7

8 WindSat Rain Rate Algorithm 8

9 Rational for using WindSat WindSat radiometer has measured brightness temperatures (T b ) to develop this algorithm MWR has three channels, which are a subset of WindSat MWR: 24 GHz H-pol & 37 GHz H- & V-pol Corresponding WindSat: 24 GHz & 37 GHz, H-pol & V-pol Similar incident angles WindSat: 53 MWR: 52 & 58 Also WindSat environmental data records (EDR) are available for algorithm tuning and validation 9

10 Rain Retrieval Algorithm Theoretical Basis The following journal papers were used: Wentz, F. J. and T. Meissner. Algorithm Theoretical Basis Document (ATBD), version 2: AMSR Ocean Algorithm. RSS Tech. Proposal A-1. Remote Sensing Systems, Santa Rosa, CA. (2000): 66 pp. Spencer, W. Roy and Wentz, Frank J. SSM/I Rain Retrievals within a Unified All-Weather Ocean Algorithm. Journal of the Atmospheric Sciences 55:9 (1998): The MWR 24 GHz H-pol & 37 GHz (V- & H-pol) are a subset of the AMSR radiometers channels 10

11 AMSR Tb Forward Model Wentz AMSR algorithm is based on the fundamental principles of radiative transfer and explicitly shows: The forward geophysical model function (GMF) defines relationships between radiometer measurements Tb 24h, Tb 24v, Tb 37h, Tb 37v and environmental inputs Surface wind speed, W Columnar water vapor, V Cloud liquid water, CLW Columnar rain rate, R Atmos phys temp, T atmos Sea surface temp, SST 11

12 Liquid Water Transmissivity Algorithm The retrieval algorithm is the inversion of the forward model Four equations (Tb 24v, Tb 24h, Tb 37v, Tb 37h ) Tb 24V = F 24V (W,V,τ L24, SST) Tb 24H = F 24H (W,V,τ L24, SST) Tb 37V = F 37V (W,V,τ L37, SST) Tb 37H = F 37H (W,V,τ L37, SST) where SST is known a priori and τ L is atmos transmissivity due to liquid water The simultaneous solution yields the four unknown parameters: (W,V,τ L24,τ L37 ) 12

13 Liquid Water Transmissivity Algorithm cont. Unfortunately, these four non-linear equations have coefficients that are themselves f(v, SST) Therefore, the complexity of the equations made the simultaneous solutions impractical using MatLab F = T U (τ V τ O T U ) τ L + (τ V τ O Ε SST) τ L + (τ V τ O (1 Ε) T D ) τ L (τ V 2 τ O 2 (1 Ε) T D ) τ L (τ 2 V τ 2 2 O (1 Ε) T D ) τ L T U = function(v, f ) T D = function(v, f ) τ V = function(v, f ) τ O = function(v, f ) Ε = function(w, f,θ i ) 13

14 Selected Rain Retrieval Approach 14

15 Water Vapor and Wind Speed Retrieval Statistical Regression to calculate Water Vapor Dependent Variables: T B24h, T B24v,T B37h,T B37v, SST V = function(t B 24 v,t B 24h,T B 37v,T B 37h,SST) Statistical Regression to calculate Wind Speed Dependent Variables: T B24h, T B24v,T B37h,T B37v, SST, V W = function(t B 24 v,t B 24h,T B 37v,T B 37h,SST,V ) When rain is present, wind speed regression produces negative values which are replaced by a priori estimate of wind speed = 6.5 m/s 15

16 Liquid Water Transmissivity Retrieval After solving for V & W sequentially, this yields three 2nd-order equations of a single variable: 2 T B 24 h = a 1 + b 1 τ L 24h + c 1 τ L 24h 2 T B 37v = a 2 + b 2 τ L 37v + c 2 τ L 37v 2 T B 37h = a 3 + b 3 τ L 37h + c 3 τ L 37h where the coefficients based on AMSR Tbs are a coeff = function(t U, f ) b coeff = function(τ O,τ V,T D,T U,SST,Ε, f ) c coeff = function(τ O,τ V,T D,T ex,ε, f ) 16

17 Rain Rate Retrieval Statistical regression used to estimate columnar rain rate (R) as a function of τ L24 & τ L37 (atmos transmissivity due to liquid water) Height and temperature of rain (Wentz 1998) H = function(sst) T L = (SST + 273)/2 (Kelvin) Rain statistical regression 3 rd order R = function(h,t L,τ L 24 h,τ L 37v,τ L 37h ) 17

18 Tuning WindSat Brightness Temperature Coefficients for liquid water transmissivity equations are based on AMSR Tb s Tuning is necessary to match WindSat and AMSR Tb s 18

19 Geophysical Model Function: F freq (W,V,τ L ) GMF = Model TBs from radiative transfer theory Using GMF s from Wentz (1997) : F freq (W,V,τ L ) = T BU + τ atmos [E SST + (1 E) (T BD + τ atmos T BC )] Where F(W,V,t) = modeled AMSR Tb s T BU = Upwelling Brightness Temperature (freq dependent) τ atmos = Atmospheric transmittance (freq dependent) E = Sea-surface emissivity (freq dependent) SST = Sea Surface Temperature T BD = Downwelling Brightness Temperature (freq dependent) T BC = Cosmic Background Radiometric Temperature (2.7 K) 19

20 Empirical Relationships (based on AMSR) Atmospheric components (τ atm,t BU,T BD,T U,T D ) τ atm = function(v,sst,τ L, f ) T U T D = function(v,sst, f ) T BU = (1 τ atm ) T U = function(v,sst, f,τ L ) T BD = (1 τ atm ) T D = function(v,sst, f,τ L ) Sea Surface components Emissivity ε = ε 0 + ε W ε 0 = function(sst, salinity, θ i, f ) ε W = function(w, f ) 20

21 AMSR and WindSat Tb Tuning AMSR T B = WindSat T B + = *WindSat T B

22 WindSat Retrieval results EDR = WindSat Environmental data record retrievals Water Vapor Wind Speed Rain Rate

23 Water Vapor Retrieval (Rain-Free) 23

24 Wind Speed Regression (Rain-free) 24

25 Water Vapor Comparison 25

26 Wind Speed Comparison 26

27 Rain Rate Comparison

28 Rain Rate Image Box 1 Box 2 28

29 Rain Rate Comparison - Box 1 29

30 Rain Rate Comparison - Box 2 30

31 Conclusion A semi-empirical rain rate retrieval algorithm has been developed for the WindSat satellite radiometer Algorithm implemented in MatLab Capable of processing satellite data (faster than real time) Geophysical Retrievals Water Vapor, Wind Speed, Atmos Transmissivity due to Liquid Water (24 GHz & 37 GHz), and Rain Rate Performed rain rate validation using independent WindSat data set (~ 2 million pixels) 31

32 Future Work Investigate using GDAS water vapor and wind speed to retrieve atmos transmissivity (due to liquid water) Simulate MWR Tb measurements at spatial resolution: IFOV = 40 x 60 km Retrieve atmos 24 GHz & 37 GHz Perform rain rate statistical regression Validate rain rate retrieval error using WindSat EDR s Develop MWR Rain Retrieval Algorithm Theoretical Basis Document (ATBD) Deliver to CONAE early Dec