This section covers the theoretical basis for the retrieval of liquid and solid precipitation from the AMSR-E radiometers. The algorithm is a Bayesian type algorithm, which searches an a priori database of potential rain profiles and retrieves a weighted average of these entries based upon an uncertainty weighted proximity of the observed Brightness Temperatures (Tb) to the simulated Brightness Temperatures corresponding to each rain profile. The a priori information is supplied by the TRMM radar/radiometer algorithm as detailed in Kummerow et al. (2010). The solution provides a mean rain rate as well as its uncertainty. The major sources of systematic errors in these algorithms are the quality of the a priori database, the estimate of the forward model uncertainty, and the ancillary information used to subset the a priori database.
Instantaneous Ocean Rainfall
The ocean algorithm uses a Bayesian approach in which the TRMM satellite is used to create an a priori database of observed cloud and precipitation profiles as described in Kummerow, et al. (2010). The profiles for the rain ocean procedure are grouped by SST and TPW. The individual pixels TPW and SST are used to retrieve a group of pixels from the database. If there are fewer than 1000 profile clusters found, the search radius is expanded. Once the database of representative profiles and Brightness Temperatures are generated, the algorithm uses a Bayesian inversion methodology in the following manner:
Pr(R) = probability that a profile R will be observed
Pr(Tb | R) = probability of observing the brightness temperature vector, Tb, given a specific rain profile R.
The first term on the right hand side of Equation 1 is derived from the a priori database of rain profiles established by the radar/radiometer observing systems. The second term on the right hand side is obtained from radiative transfer computations through the cloud model profiles. The formal solution to the above problem is presented in detail in Kummerow et al. (1996). In summary, the retrieval procedure composes a new hydrometeor profile by taking the weighted sum of structures in the cloud structure database that are radiometrically consistent with the observations. The weighting of each model profile in the compositing procedure is an exponential factor containing the mean square difference of the sensor observed brightness temperatures and a corresponding set of brightness temperatures obtained from radiative transfer calculations through the cloudy atmosphere represented by the model profile.
The retrieval algorithm thus generates a new cloud profile from the weighted sum of structures in the cloud structure database that are consistent with the observations. The retrieval solution is:
Rj = the vector of model profile values from the a priori database model
Tbo = set of observed brightness temperatures
Tbs(xj) = corresponding set of computed brightness temperatures from model profile Rj
O = observational error covariance matrices
S = model error covariance matrices
Ã‚ = normalization factor
The AMSR-E code searches a subset of profiles with coincident Sea Surface Temperature (SST) and Total Column Water Vapor (TCWV). TCWV is internally within the AMSR-E precipitation algorithm using an Optimal Estimation (OE) framework developed by Elsaesser and Kummerow (2008). The SST is obtained from Optimum Interpolation Sea Surface Temperatures constructed by combining observations from different platforms (satellites, ships, buoys) on a regular global grid. The satellite observations are from the AVHRR and AMSR-E instruments until 03 October 2011, and AVHRR only after that date. For more information, refer to Optimum Interpolation Sea Surface Temperature (OISST) Web page. For more information on the development of the OISST, see Reynolds, et al. 2006. The same OE-based TCWV and SST climatology is also attached to the a priori database to ensure consistency between the brightness temperatures.
Instantaneous Land Rainfall
Accurate rainfall retrievals over land are far more difficult than oceanic retrievals due to the large and variable emissivity of the land surface. Specifically, the high emissivity masks the emission signature that is related directly to the water content in the atmosphere. Instead, only the brightness temperature depression due to scattering in the upper portion of clouds is observable. The scattering increases with increasing frequencies. Consequently, brightness temperature depressions at the 89-GHz channel of AMSR-E contain the least ambiguous signal of scattering by ice and/or large raindrops.
A further complication that arises over land is the lack of consistent backgrounds against which to compare the brightness temperature depression. To alleviate the problem caused by the varying emissivity associated with changes in surface characteristics such as surface wetness, snow cover, vegetation, etc. A rain/no-rain temperature depression threshold is required to screen out false identification of rain. Additionally, snow and desert surfaces cause depressed brightness temperatures at high frequencies due to surface volume scattering and can be confused with the rain signature. If these surface types are not properly screened, they can be misinterpreted as ice scattering in clouds.
GPROF 2010 Version 2 utilizes a two-step process for rain rate retrieval for the AMSR-E algorithm: rain identification and rain rate determination.
Land Rain/No Rain Determination
The rain/no rain determination results from the application of screens applied to the data retrieved at the 89-GHz channel of AMSR-E. McCollum et al. (1999) developed a methodology that adopts the GPROF approach but uses spatial information from neighboring pixels to “fill-in” indeterminate areas. See Figure 2 for a comparison between the three screening methods: NESDIS (Ferraro 1997), GSCAT2 used in the GPROF algorithm, and the new screening method.
Figure 2. Comparison of Rainfall Rates (mm/h)
Land Rain Rate Determination
The AMSR-E precipitation team decided to use the same GPROF retrieval methodology as used for the ocean retrieval. Unlike the ocean component, however, the initial database of possible profiles was carefully selected to include only those profiles that fit the empirical relation given in Equation 3.
RR = rain rate in mm/hr
SIL = Scattering Index Land
The relationship of Equation 3 was reproduced by selecting 36 profiles fitting Equation 3 from the several thousand profiles in the GPROF database (McCollum et al. 1999).
Version 3 utilizes the GPROF 2010 Version 2 algorithm and Version 3 Level-2A Brightness Temperatures as input. Version 3 now includes both rain and solid precipitation rates and types, as well as ISO lineage metadata. See the AMSR-E Data Versions Web page for a summary of algorithm changes since the start of mission.
Quantifying errors in this data set is complicated, because it involves understanding the nature of precipitation. Uncertainties arise when the rain layer thickness is not well understood, or when inhomogeneous rainfall occurs below the resolution of the satellite. Another potential source of error is the non-precipitating component of clouds, which contribute to brightness temperatures. Scattering-based retrievals over land also present many uncertainties, most notably the lack of a consistent relationship between frozen rain aloft and liquid at lower altitudes. Quantifying the scattering by ice is especially problematic. Ambiguities occur in the data because microwave radiation is scattered not only by rainfall and associated ice, but by snow cover and dry land (Kummerow and Ferraro 2007 ).
A known error exists related to sun glint that results in missing Rain Rate values, and presents as gray ovals in the AE_Rain browse images. Sun glint is not a problem over land; however, the algorithm is using only geometry to determine sun glint causing missing values to exist over land. Sun glint is included in the algorithm because it affects the brightness temperatures out to the missing radius; however, a thorough investigation is yet to be completed. Preliminary investigations indicate that the bias could be up to 15 percent in the affected areas.