Description of Precipitation Retrieval Algorithm For ADEOS II AMSRGuosheng Liu
Florida State University

1. Basic Concepts of the Algorithm
This algorithm is based on Liu and Curry (1992, 1996), in which the rainfall rate is calculated from thecombination of emission and scattering signatures. Beam-filling correction is embedded in the algorithm.
Radiative transfer model tests show that it is not sensitive to the height of freezing level. This algorithm wastested in GPCP AIP-1, AIP-3, WetNet PIP-2 and PIP-3. The algorithm can retrieve rainfall over both ocean andland although slightly different formulations are used for the different surface types.
The AMSR algorithm is built on the SSM/I algorithm with conversions from AMSR brightness temperatures toSSM/I brightness temperatures.
Ocean Algorithm:
In this updated version, the combination function is defined by Liu et al. (1995) as following:f = (1 −DD0) + 2 (1 −PCT
PCT 0)(1)

where D is the depolarization of 18.7 GHz and D0 is D at the threshold of rain onset; PCT is the polarization
corrected brightness temperature defined by (Spencer et al., 1989): PCT = 1.818T B89V - 0.818TB89H, and PCT 0 is
PCT at the threshold of rain onset. PCT and D for AMSR channels are then converted to SSM/I PCT and D by
the following equations:

PCTSSM / I = 2.2 + 0.996PCTAMSRDSSM / I = −0.14 + 0.903 * DAMSR(2)These equations are derived by radiative transfer simulations for various atmospheric and surface conditions.
Then rainfall rate are calculated based on the equations originally derived from SSM/I channels.
D0 and P0 are determined monthly for every 3° (latitude) x 6° (longitude) box based on 37 GHz depolarization andsea surface temperature, and are saved in a file as a look-up table. The relationship between f and rainfall rate isdetermined by radiative transfer calculation result with consideration of beam-filling effect, and can be expressedby

R = αf β(3)where α and β are spatial scale-dependent coefficients. The dependence of α and β on spatial scale is due to thespatial dependence of beam-filling effect. For SSM/I in which the spatial resolution of 19 GHz is ~ 50 km,α=10.6 and β=1.621. For AMSR and TMI, the spatial resolution for 19 GHz is about half of that in SSM/I. Thevalues for α and β are determined by an empirical equation based on radiative transfer model simulation and TMI
data: α=8.25, and β=1.88. Test results show that these coefficients produce satisfactory rain rates from TMI datawhen compared to TRMM PR rain rates and GPCP climatology. Detailed discussion is given in section 2 on thescale-dependent parameters, α and β.
Land Algorithm:The land portion of our algorithm uses 18.7 and 89 GHz brightness temperatures. It is expressed by

R = a ( DT B − DT B 0 )(4)

where a=0.2 is a coefficient derived from radiative transfer model simulations; DTB =TB18.7 -TB89.
convert DT B for AMSR to DT B for SSM/I by

DTBSSM / I = −0.6 + 0.9558DT BAMSR

Again, we first(5)

Then the rainfall algorithm originally developed for SSM/I is used.
DTB0 is DTB at the threshold of rain onset that is determined monthly for every 3° (latitude) x 6° (longitude) box
based on Liu and Curry (1992) and is saved in a file as a look-up table.
The algorithm is deterministic (non-iterative) and all threshold parameters (D0 , PCT 0 , and DTB0) are available as alook-up table. Therefore, the retrieval is extremely fast.
2. Determination of the Scale-Dependent Parameters
Results of earlier studies (e.g., Liu and Curry, 1992, Spencer et al., 1989) showed that the beam-filling effect tends
to make the R-T B relation closer to “linear” than that indicated by radiative transfer models assuming aplane-parallel rain layer. Liu and Curry (1992) tried to explain this behavior of R-T B relation. The determinationof α and β in this algorithm is based on this consideration. First, we assume the parameter β in (3) varies withspatial scale, x ( in km), asβ = β∞ − A[1 − exp( − Bx κ )],(6)

where β∞ =2.792 is β for plain parallel rain layer determined by our radiative transfer simulations. κ is anadjustable parameter used to vary the strength of scale dependence. For now we use κ=0.7 which seems to work
well for our algorithm for TMI and SSM/I data. A and B are determined as following. First, when scale, x,becomes infinite large, β is 1, implying that for infinitely large spatial resolution the R-T B relation is linear (notethe argument mentioned earlier). Then, it is determined that A = β∞ − 1 . The constant B is then determinedby applying (6) to our SSM/I algorithm used in Liu and Curry (1996), which gives βSSMI =10.6 for a scale of 50km.

In the studies of Liu and Curry (1992), it is also found that when rainfall rate is as high as 50 mm/hr, the ratio
between observed TB and plane-parallel model generated TB should be close to 1. Based on this argument, wedetermine α by letting
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 R50  β AMSR  R50  β SSMI=  αAMSR  αSSMI (7)

where R50 =50 mm/h.
It is noted that the development of the parameters of α and β are based on the algorithm we developed for SSM/I.
Figure 1 shows the f-R relations derived from the aforementioned approach for different spatial resolutions. Forvery high resolution, we may believe the rainfall within the FOV is homogenous. For very low resolution, thef-R relation is assumed to be linear. Actual satellite measurements (AMSR, TMI, SSM/I) will have an f-Rrelation curve between the two extremes.

2.8

2.4

2
Homogeneous(Very Hi-Res)
TMI/

1.6

AMSR

SSM/I
1.2

Very Low-Res

0.8

SSMI
0.4

TMIlinear[low]Homo[high]005

101520253035

404550RAIN (mm/hr)

Fig. 1 Relations between f and rainfall rate for different spatial resolutions.

3. Validation -- Comparison with Other Datasets
Figure 2 shows the comparison of this algorithm using SSM/I data with GPCP satellite-raingauge combinedmonthly rainfall product (Huffman, et al., 1997) for the year of 1992. The two retrievals are generally agreed
with each other although some discrepancies can also be found; such our retrievals are general lower, particularly
for latitudes where precipitation peaks. This disagreement can partially be attributed to the low temporal
coverage of SSM/I data.
Figure 3 shows the comparison with TRMM TMI-PR combined (3B31) product and GPCP satellite-raingauge
combined product for 1998. Our retrievals seem to compare well with these products. We are still working on
this comparison for other years to investigate whether there are discrepancies for those years. Furtherinvestigation may lead modification of the tuning parameter, κ, given in (6). Figure 4 shows the comparison
with product derived from TRMM PR alone. The latitudinal variation of the two estimates agrees well although
our estimates are slightly larger than the PR estimates. It is noted that PR estimates are also smaller than TRMM
TMI and TRMM Combined products.

The following table lists the bias, correlation coefficient and rms difference when of our algorithm whencompared to TRMM combined and GPCP products. The statistics are calculated using 1998 monthly 5° x 5°
datasets.

Statistics When Compared to TRMM Combined and GPCP Data
Bias in %Correlation

rms Diff in %

GPCP

1%

0.78

69%

TRMM Combined

6%

0.82

61%

4. References
Huffman, G. J., R. F. Adler, P.A. Arkin, A. Chang, R. Ferraro, A. Gruber, J. Janowiak, R.J. Joyce, A. McNab, B.
Rudolf, U. Schneider, and P. Xie, 1997: The Global Precipitation Climatology Project (GPCP)
Combined Precipitation Data Set. Bull. Amer. Meteor. Soc., 78, 5-20.
Liu, G., and J. A. Curry, 1992: Retrieval of precipitation from satellite microwave measurements using bothemission and scattering. J. Geophys. Res., 97, 9959-9974.
Liu, G., and J. A. Curry, 1996: Large-scale cloud features during January 1993 in the North Atlantic Ocean asdetermined from SSM/I and SSM/T-2 observations. J. Geophys. Res., 101,7019-7032.
Liu, G., J. A. Curry and R. -S. Sheu, 1995: Classification of clouds over the western equatorial Pacific Ocean using
combined infrared and microwave satellite data. J. Geophys. Res., 100, 13,811-13,826.
Spencer, R. W., H. M. Goodman, and R. E. Hood, 1989: Precipitation retrieval over land and ocean with SSM/I:
Identification and characteristics of the scattering signal. J. Atmos. Oceanic Technol., 6, 254-273

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300-30-60-90012345678 012345678 01234567801234RAIN (mm/day)Fig. 2 Comparison with GPCP satellite-raingauge combined rainfall(blue).

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1 2 34 5RAIN (mm/day)Fig. 4 Comparison with TRMM Precipitation Radar (red) product for 1998.

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