Digital Earth Emissivity Information System (DEEIS) - JCSDA Algorithm

Physical Basis of Surface Emissivity Calculation from Satellite Observations

Satellite microwave measurements of brightness temperatures for a non-scattering atmosphere can be expressed as follows:

With

where T_B is the brightness temperatures at satellite height, e is the surface emissivity, T_s is the surface temperature, t the optical depth, z the atmospheric transmittance, m the cosine of the satellite local zenith angle; T_u and T_d are the brightness temperatures associated with upwelling and downwelling radiations, respectively. Variables z, T_u, and T_d can be obtained from the absorption model for given atmospheric profiles of temperature and water vapor.

For window channels, the atmospheric transmittance is near unity under clear conditions and high for non-precipitating conditions so that T_u and T_d are small. This implies that satellite microwave measurements are strongly characterized by surface emissivity. However, although the atmospheric corrections are small for window channels, they still need to be accounted for. Using (1), the emissivity is given by:

Since the radiation at the AMSU frequencies emanates from a thin surface layer, with penetration depths on the order of the wavelength, Eqs. (1) and (2) involve an “effective” emissivity over the depth of penetration and within the field of view of the satellite instrument.

SSMI Algorithm

Training Data Set

Direct microwave emissivity measurements are not available over various land surface conditions. Thus, the "truth" emissivity is also derived from SSM/I measurements of brightness temperatures. In doing so, the contributions to SSMI measurements from the atmospheric emission and surface temperature are first removed using an emission-based radiative transfer equation:

where ε_i is the land emissivity at the i-th channel; T_s is the surface temperature; the parameters; T_biu and T_bid are the upwelling and downwelling brightness temperature, respectively; and τ_i the atmospheric transmittance. The parameters τ_i, T_biu, and T_bid can be computed directly from the GDAS temperature and moisture profiles. This approach is similar to that used by Jones and Vonder Haar (1997) and by Prigent et al. (1997), except that the GDAS data are used to calculate T_s, T_biu, and T_bid . Note that SSMI pixels under rainy regions are removed using the screening algorithm developed by Ferraro et al. (1998). The emissivity is calculated from Eq. (1) is referred to the "truth" emissivity.

According to our analyses, the errors in various source terms in Eq. (1) (e.g., surface temperature, brightness temperature and transmittance) result in the errors in derived emissivity. In particular, one percent of error in the surface temperature would result in less than one percent error in land emissivity. The error due to water vapor results in the largest error in emissivity at 22V that is located at the water vapor absorption line. Prigent et al. (1997) estimated the range of these errors: with a typical value of 0.6 K the radiometric noise in measured brightness temperature will induce only small uncertainties on the emissivity retrieval using Eq. (1); with a value of 4 K in the surface temperature, the uncertainty is about 0.024; with a uncertainty of 30 % in moisture profile, the uncertainty in emissivity distributes between 0.001 and 0.02 at both 19.35, and 37.0 GHz and 0.005 and 0.1 at both 22.235 and 85.5 GHz. It is believed that our training data set of the emissivity may contain similar uncertainty.

Regression Algorithm Formula

With the multiple regression method, land emissivity at an SSM/I channel is predicted using seven channel SSM/I brightness temperatures as

where a_o, a_1i and a_2i (i=1~7) are the regression coefficients. This formula is applied to the prediction of the emissivity at all seven SSMI channels with a different set of coefficients as shown in Table 1 (Yan and Weng 2002).

Table 1: Coefficients used in Eq. (2) for calculating the emissivity at seven SSM/I channels

	ε1	ε2	ε3	ε4	ε5	ε6	ε7
a0	-1.20E-01	-1.45E-01	-1.02E-01	-2.16E-01	-2.08E-01	-2.31E-01	-2.63E-01
a11	5.57E-03	8.55E-04	-3.00E-03	-1.05E-03	-2.01E-03	-4.99E-03	-6.45E-03
a12	2.98E-06	5.46E-06	1.93E-05	7.75E-06	1.07E-05	2.30E-05	3.02E-05
a13	7.05E-01	1.15E-02	9.81E-03	7.21E-03	7.05E-03	9.97E-03	1.08E-02
a14	-1.44E-05	-1.57E-05	-2.21E-05	-1.44E-05	-1.45E-05	-2.21E-05	-2.49E-05
a15	-3.59E-03	-3.57E-03	1.54E-03	-3.98E-03	-3.20E-03	-3.19E-03	-2.28E-03
a16	-9.27E-06	-9.88E-06	-1.87E-05	-8.78E-06	-1.10E-05	-1.92E-05	-2.55E-05
a17	2.63E-03	2.25E-03	2.33E-03	9.97E-03	4.85E-03	5.86E-03	4.15E-03
a21	1.17E-06	9.04E-07	1.84E-06	-4.00E-06	-3.37E-06	-4.48E-06	-1.13E-06
a22	-3.78E-03	-3.19E-03	-3.83E-03	-3.96E-03	1.39E-03	-4.40E-03	-3.04E-03
a23	7.37E-06	7.23E-06	9.78E-06	7.09E-06	6.08E-06	1.02E-05	9.00E-06
a24	7.06E-03	5.16E-03	9.56E-03	7.85E-03	5.85E-03	1.24E-02	1.05E-02
a25	-1.66E-05	-1.15E-05	-2.18E-05	-1.88E-05	-1.36E-05	-1.73E-05	-2.35E-05
a26	-7.09E-03	-5.02E-03	-8.43E-03	-7.60E-03	-5.58E-03	-6.78E-03	-4.34E-03
a27	1.40E-05	8.35E-06	1.59E-05	1.56E-05	1.02E-05	1.23E-05	1.73E-05

Statistical Results of Emissivity Errors

With Eq. (2) and the coefficients given in Table 1, the emissivity at seven SSM/I channels can be rieved over various land conditions.

Note that the outliers of some SSM/I pixels away from 1:1 line may be related to the snow conditions here the algorithm may overestimate the emissivity. The predicted noises are also produced by the presence of clouds that cannot be detected from SSM/I brightness temperatures. Figure 1 is a comparison between the emissivity predicted using Eq. (2) and the truth using Eq. (1). It is found that the standard deviation is about 0.02 at 19.35 and 37 GHz and about 0.03 at 22.235 and 85.5 GHz, and the errors are larger at 22.235 and 85.5 GHz due to stronger water vapor absorption. At 85.5 GHz, cloud liquid water produces additional errors.

Fig. 1: The emissivity retrieved using Eq. (2) compared with those from more accurate retrievals using Eq. (1) at (a) 19V, (b) 19H, (c) 22V, (d) 37V, (e) 37H, (f) 85V, and (g) 85H.

AMSU Algorithm