| Products - Algorithms |
| |
Notation: |
| |
TB1: |
AMSU Channel 1 brightness temperature (23.8 GHz) |
| |
TB2: |
AMSU Channel 2 brightness temperature (31.4 GHz) |
| |
TB3: |
AMSU Channel 3 brightness temperature (50.3 GHz) |
| |
TB16: |
AMSU Channel 16 brightness temperature (89.0 GHz) |
| |
TB17: |
AMSU Channel 17 brightness temperature (150.0 GHz) |
| |
Ts: |
2-meter shelter air temperature over land or SST over ocean |
| |
W : |
scattering parameter |
| |
m : |
cosine of local zenith angle |
| |
t o: |
optical thickness for oxygen |
| |
t V: |
optical thickness for water vapor |
| |
t L: |
optical thickness for cloud liquid water |
| |
e : |
emissivity |
| Cloud Liquid Water (CLW) / Total Precipitation Water (TPW) (See the sample) |
| |
These are ocean algorithms for TPW and CLW. |
L = a0{ln[Ts - TB2] - a1ln[Ts - TB1] - a2}
V = b0{ln[Ts - TB2] - b1ln[Ts - TB1] - b2} |
| where, L is vertically integrated cloud liquid water (L = ò0¥rLdz); |
| V is vertically integrated water vapor (V = ò0¥rVdz); |
| a0 = -0.5k V23 / (k V23k L31 - k V31k L23) |
| a1 = k V31 / k V23 |
| a2 = -2.0(t o31 - a1t o23) / m + (1.0 - a1)ln(Ts) + ln(1.0 - e31) - a1ln(1.0 - e23) |
| b0 = 0.5k L23 / (k V23k L31 - k V31k L23) |
| b1 = k L31 / k L23 |
| b2 = -2.0(t o31 - b1t o23) / m + (1.0 - b1)ln(Ts) + ln(1.0 - e31) - b1ln(1.0 - e23) |
where, e is sea surface emissivity; k V is water vapor mass absorption coefficient; and k L is cloud liquid water mass absorption coefficient. Coefficient kV can be derived from the following relationship
|
| t V = k V V |
| There is a similar relationship for coefficient k L: |
| t L = k L L |
Using Rayleigh's approximation, one can express k L in terms of cloud layer temperature, TL, as |
| k L = aL + bL TL + cL TL2 |
Oxygen optical thickness is parameterized as a funciton of sea surface temperature through |
| t o = ao + bo Ts |
The following is a table of the parameters calculated at two AMSU-A channels. They are used in the water vapor and cloud liquid water algorithms. |
| |
23.8 GHz |
31.4 GHz |
| k V |
4.80423E-3 |
1.93241E-3 |
| k L: a1 |
1.18201E-1 |
1.98774E-1 |
| k L: b1 |
-3.48761E-3 |
-5.45692E-3 |
| k L: c1 |
5.01301E-5 |
7.18339E-5 |
| t o: ao |
3.21410E-2 |
5.34214E-2 |
| t o: bo |
-6.31860E-5 |
-1.04835E-4 |
|
| Sea Ice Concentration (See the sample) |
| |
Retrieved emissivity at 23.8 GHz (Channel 1) is |
| e = a + b TB1 + c TB2 + d TB3 |
| where a = 1.84 - 0.723 m ; b = -0.00088; c = 0.0066 + 0.0029 m ; d = -0.00926. |
| Emissivity of water is |
| ewater = 0.1824 + 0.9048 m - 0.6221 m 2 |
| Emissivity of ice is |
ì 0.93 if (TB1 - TB2) < 5 K
e ice = í 0.87 if 5 £ (TB1 - TB2) £ 10 K
î 0.83 if 10 < (TB1 - TB2) |
| Sea ice concentration (%) is computed from |
| sice = 100 (e - e water) / (eice - e water) |
Note:
1. Sea ice concentration is set to be zero in the latitude band from -50o to 50o.
2. A cutoff value of 30% is applied in the sea ice concentration algorithm. |
| Land Surface Temperature (See the sample) |
| |
Ts = 2.9079 x 102 - (8.5059 x 10-1 - 1.9821 x 10-3 TB1) TB1 + (6.1433 x 10-1 - 2.3579 x 10-3 TB2) TB2
- (1.1493 - 5.4709 x 10-3 TB3) TB3 - 1.50 x 101 (m - 5.40 x 10-1) |
| Surface Emissivity (23.8 GHz/31.4 GHz/50.3 GHz) (See the sample) |
| |
Land algorithms for emissivities at three AMSU channels |
| e i = b0, i + b1, i TB1 + b2, i TB12 + b3, i TB2 + b4, i TB22 + b5, i TB3 + b6, i TB32, i = 1, 2, 3 |
| where e i is the land emissivity of Channel i, i = 1, 2, 3. |
| The following is a table of the coefficients used in the above equations. |
Coefficients Derived for AMSU Channel 1 ~ 3 Emissivity
| |
b0 |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
| e 1 |
-2.5404E-1 |
1.1326E-2 |
-1.9479E-5 |
-4.5763E-3 |
1.7833E-5 |
3.2324E-3 |
-1.9056E-5 |
| e 2 |
-2.2606E-1 |
3.4481E-3 |
-9.7185E-6 |
4.3299E-3 |
5.3281E-6 |
1.8668E-3 |
-1.5369E-5 |
| e 3 |
8.9494E-2 |
-3.6615E-3 |
-4.2390E-7 |
1.0636E-2 |
-6.4559E-6 |
-4.2449E-4 |
-6.6878E-6 |
|
| Ice Water Path (IWP) (See the sample) |
| |
De = a0 + a1 r + a2 r2 + a3 r 3 |
| WN = exp{b0 + b1 ln(De) + b2 [ln(De)]2} |
| IWP = m rice rsi De W / W N |
where De is the effective particle diameter; r the scattering parameter ratio of 89 GHz and 150 GHz; W N the normalized scattering parameter; W the scattering parameter estimated using brightness temperatures at cloud top and base; rice the ice density fractional ratio, rice = 1 is used in the current algorithm; and r si the the density of solid ice. The following is a list of the regression coefficients used in the above equations. |
|
a0 |
a1 |
a2 |
a3 |
| -0.24843 |
3.86726 |
-4.70782 |
4.67150 |
De £ 2 mm |
b0 |
b1 |
b2 |
|
| -1.74663 |
1.90711 |
-0.73029 |
|
De > 2 mm |
b0 |
b1 |
b2 |
|
| -1.58571 |
1.52230 |
-0.52437 |
|
|
| Precipitation Rate (PR) (See the sample) |
| |
Rain rate is computed based on an IWP and rain rate relation derived from the MM5 cloud model data. |
| PR = a0 + a1 IWP + a2 IWP2 |
| where a0 = 0.321717; a1 = 16.5043; and a2 = -3.3419. |
| Snow Cover (See the sample) |
| |
Snow cover is identified by the scattering of high frequency microwaves from ice particles and the fact that scattering reduces the high frequency brightness temperature measurements relatively to the lower frequency measurements. The following two scattering indices (W31.4 and W89.0) are used to represent the differences between the lowest frequency (AMSU-A, 23.8 GHz) and the higher frequency channels at 31.4 GHz (AMSU-A) and 89.0 GHz (AMSU-B). |
W31.4 = TB1 - TB2 - 2.0 |
W89.0 = TB1 - TB16 - 3.0 |
If W31.4 < 3 and TB1 £ 215 K, then the snow type glacial snow is designated. W89.0 is used to identify normal snow cover on land and coast. Snow cover is present if the scattering index W 89.0 ³ 1. On coast, the AMSU-A 89.0 GHz is used instead of AMSU-B to compute W89.0, to alleviate aliasing effects resulting from differences in resolution between AMSU-A and AMSU-B channels. There are also checks to eliminate false signatures of snow due to precipitation and cold deserts. |
| Snow Water Equivalent (SWE) |
| |
The retrieval of the Snow Water Equivalent (SWE) is based on the scattering index W 31.4, which represents the difference between the brightness temperature at the lowest frequency channel (23.8 GHz) and the brightness temperature at a higher frequency channel (31.4 GHz), i.e. |
W31.4 = TB1 - TB2 |
The SWE is computed for the snow-covered pixels (see snow cover algorithm ) by the following empirical relationship: |
SWE = K1 + K2 * W31.4 |
where K1 = 2.60 and K2 = 0.39 are empirically derived coefficients, and SWE is in cm. These coefficient values were derived from regional studies in the U.S. |
|
| |
|
