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This page contains descriptions of the MSPPS Day-2 science algorithms. These descriptions are provided by the algorithm developers, and they are updated as needed.
Click here to read an article about the ice water path algorithm. Click here to download an MS Word report on the sea ice algorithm. To download an MS Word summary of most of the AMSU algorithms and the references, click here.
Notations
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
to : optical thickness for oxygen
tV : optical thickness for water vapor
tL : optical thickness for cloud liquid water
e : emissivity
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); and
a0 = -0.5kV23 / (kV23kL31 - kV31kL23)
a1 = kV31 / kV23
a2 = -2.0(to31 - a1to23) / m + (1.0 - a1)ln(Ts) + ln(1.0 - e31) - a1ln(1.0 - e23)
b0 = 0.5kL23 / (kV23kL31 - kV31kL23)
b1 = kL31 / kL23
b2 = -2.0(to31 - b1to23) / m + (1.0 - b1)ln(Ts) + ln(1.0 - e31) - b1ln(1.0 - e23)
where e is sea surface emissivity; kV is water vapor mass absorption coefficient; and kL is cloud liquid water mass absorption coefficient. Coefficient kV can be derived from the following relationship
tV = kV V
There is a similar relationship for coefficient kL:
tL = kL L
Using Rayleigh's approximation, one can express kL in terms of cloud layer temperature, TL, as
kL = aL + bL TL + cL TL2
Oxygen optical thickness is parameterized as a funciton of sea surface temperature through
to = 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 | |
| kV | 4.80423E-3 | 1.93241E-3 |
| kL: a1 | 1.18201E-1 | 1.98774E-1 |
| kL: b1 | -3.48761E-3 | -5.45692E-3 |
| kL: c1 | 5.01301E-5 | 7.18339E-5 |
| to: ao | 3.21410E-2 | 5.34214E-2 |
| to: bo | -6.31860E-5 | -1.04835E-4 |
The Day-2 TPW algorithm (see above) suffered from a strong angular dependence,
where there was considerable drop off in retrieved TPW away from nadir. This was caused by sensor
performance differences from radiative transfer calculations and related to the asymmetry seen
at channels 1 and 2. In addition, there was an overall positive bias, primarily due to
contamination from cloud water. The only reliable means of adjusting the TPW algorithm is
through statistical matches between the AMSU values and those calcualted from radiosondes.
Two regression functions are applied to the original AMSU TPW to address these two issues.
To make effective corrections, data are grouped into three categories: no rain (CLW < 0.2 mm),
medium rain (0.2 mm <= CLW <= 0.8 mm), and high rain (CLW > 0.8 mm). TPW is corrected with
different functions for each satellite and each category. In addition, the corrected TPW in
the high rain category( CLW > 0.8mm ) is flagged by its negative value to signal the high
possibility of rain contamination.
by negative value in all high rain cases. The two correction functions are
W1 = a0 W0 + a1 μ2 + a2 μ + a3
and
W = a4log(W1) + a5W1 + a6
where W is corrected TPW; W0 is the original TPW retrieval;
μ = cos(θ),
where θ is local zenith angle; and the coefficients a0 to a6
are given in the following table for NOAA-15 to NOAA-17.*
| CLW < 0.2 mm | |||||||
| a0 | a1 | a2 | a3 | a4 | a5 | a6 | |
| NOAA-15 | 0.968 | -13.498 | 12.557 | -3.651 | -2.349 | 1.118 | 3.666 |
| NOAA-16 | 0.968 | -2.268 | -2.758 | 1.186 | -1.845 | 1.101 | 2.573 |
| NOAA-17 | 0.968 | -3.187 | 0.687 | -0.878 | -1.954 | 1.108 | 2.384 |
| 0.2 mm <= CLW <= 0.8 mm | |||||||
| a0 | a1 | a2 | a3 | a4 | a5 | a6 | |
| NOAA-15 | 0.968 | 18.06 | -28.616 | 8.072 | -1.867 | 1.090 | 2.737 |
| NOAA-16 | 0.968 | 44.700 | -73.142 | 26.082 | -2.699 | 1.116 | 4.455 |
| NOAA-17 | 0.968 | 24.458 | -36.919 | 10.055 | -1.245 | 1.054 | 2.019 |
| CLW > 0.8 mm** | |||||||
| a0 | a1 | a2 | a3 | a4 | a5 | a6 | |
| NOAA-15 | 0.968 | 39.174 | -78.037 | 32.203 | 4.908 | 0.990 | -18.865 |
| NOAA-16 | 0.968 | 35.984 | -79.406 | 35.999 | -3.907 | 1.203 | 3.959 |
| NOAA-17 | 0.968 | 21.945 | -48.974 | 20.692 | 49.842 | -0.022 | -142.165 |
*: Currently NOAA-18 and MetOp-A TPW are calculated using the same coefficients
as NOAA-16 pending matchup with radiosondes. These products are being monitored and are of
comparable qualiry as those of NOAA-15 to NOAA-7.
**: TPW in this category is flagged by is negative value.
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 m2
Emissivity of ice is
| eice = | { | 0.93, if (TB1 - TB2) < 5 K 0.87, if 5 < (TB1 - TB2) < 10 K 0.83, if 10 < (TB1 -TB2) |
This is a land algorithm for surface temperature.
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)
These are land algorithms for emissivities at three AMSU channels.
ei = 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 ei is the land emissivity of Channel i, i = 1, 2, 3.
The following is a table of the coefficients used in the above equations.
| b0 | b1 | b2 | b3 | b4 | b5 | b6 | |
| e1 | -2.5404E-1 | 1.1326E-2 | -1.9479E-5 | -4.5763E-3 | 1.7833E-5 | 3.2324E-3 | -1.9056E-5 |
| e2 | -2.2606E-1 | 3.4481E-3 | -9.7185E-6 | 4.3299E-3 | 5.3281E-6 | 1.8668E-3 | -1.5369E-5 |
| e3 | 8.9494E-2 | -3.6615E-3 | -4.2390E-7 | 1.0636E-2 | -6.4559E-6 | -4.2449E-4 | -6.6878E-6 |
IWP is retrieved by using the following equations:
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 / WN
where De is the effective particle diameter; r the scattering parameter ratio of 89 GHz and 150 GHz; WN 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 rsi the the density of solid ice. The regression coefficients ai (i = 0, 1, 2, 3) and bi (i = 0, 1, 2) are listed in the table below.
Close examination of the Day-2 IWP algorithm, plus user feedback, revealed some weaknesses that have been addressed by this recent algorithm upgrade. Most notably was the unphysical IWP frequency distribution, which had "preferred" retrieval values rather than an expected lognormal distribution. In addition, the values over water appeared to be too high. Further refinement of the retrieval model and coefficients have led to the following changes:
| a0 | a1 | a2 | a3 | |
| -0.300323 | 4.30881 | -3.98255 | 2.78323 | |
| b0 | b1 | b2 | ||
| De ≤ 1 mm | -0.294459 | 1.38838 | -0.753624 | |
| De > 1 mm | -1.19301 | 2.08831 | -0.857469 | |
Click here to read an article about the Day-2 IWP algorithm.
For newly detected rain(NOAA-15, -16 or -17), a new IWP parameter is
estimated following the empirically established relationship:
IWP = 2.924929 - 0.018356*TB176 + 0.000026*TB1762 + 0.234554 * cos(ZA)
where ZA is local zenith angle.
Rain rate is computed based on an IWP and rain rate relation derived from the MM5 cloud model data.
RR = a0 + a1 IWP + a2 IWP2
where the coefficients a0 to a2 are given in the table below.
Thorough validation of the Day-2 rain rate algorithm revealed a strong positive bias over oceans and a weaker negative bias over land. In addition, a non-uniform distribution of rain rates existed due to the problems noted in the IWP algorithm (see above). Finally, the maximum allowed rain rate of 20 mm/hr was not realistic and was attributed to the relationship used to convert IWP to rain rate. The improved algorithm has incorporated the following changes:
| a0 | a1 | a2 | |
| CI = 1 or 2 | 0.321717 | 16.5043 | -3.3419 |
| CI = 3 | 0.08925 | 20.8194 | -2.9117 |
The new technique computes Ice Water Path(IWP) and Rain Rate (RR)
only ove coastal AMSU-A or AMSU-B Field of Views(FOVs), when the necessary
conditions for the existence of rain as determined by the esixiting AMSU
algorithm are not met, ie,. IWP(kg/m2), Cloud Liquid Water ClW(mm) and the
Effective Diameter De(mm) estimated by the existing algorithm are below
the threshold values, In this situation, nwe rain is detected when the following conditions are met:
TB89 - TB150 > 3.0K,
TB54L - TB176 > -6.0K, and
TB54L - TB180 > 0.0K
where TB refers to Brightness Temperature in Kelvin(K), and attached numbers 89,150,
176,180 and 54L indicate channel frequency at AMSU-B 89, 150, 183∓7,
183∓3, GHz and at limb-corrected AMSU-A 53.65 GHz respectively.
In additon, the following filters remove confusion due to snow, ice and clouds, i.e.
instances meeting following conditions are filtered out as "non-rain":
TB53.4L < 244.5K and TB53L - TB182 < 15.0K, or
TB176 < 260K, or
TB180 > 256K
where TB182 indicate TB in K at AMSU-B 183∓1 GHz frequency.
The above applies to the NOAA-15 and -16 satellites. Foe the NOAA-17 satellite,
a new rain detection technique was developed due to the missig AMSU-A 53.6 GHz channel.
New rain is detected when the following conditions are met:
TB89 - TB150 > 3.0K,
TB182 - TB176 > -15.0K, and
TB182 - TB180 > 0.0K
In addition, the following filters remove confusion due to snow, ice and clouds. i.e.
instances meeting following conditions are filtered out as "non-rain":
TB176 > 255K or TB180 > 250K
For newly detected rain(NOAA-15, -16 or -17), a new IWP parameter is estimated following
the empirically established relationship:
IWP = 2.924929 - 0.018356*TB176 + 0.000026*TB1762 + 0.234554 * cos(ZA)
where ZA is local zenith angle. RR is estimated using the existing RR-IWP relationships.
The day-2 RR algorithm tends to generate much less rain coverage over ocean than other algorithms based on emission technique and also present an unrealistic frequency distribution due to inability to retrieve rain that has little or no ice(scattering approach) and with cross-scan characteristics of the instruments(different footprints for different local zenith angles).
The correction scheme is carried out in two steps. The first one to correct the systematic bias
is performed using a Gaussian PDF with meand and standard deviation depending on local zenith angle(LZA),
latitude(LAT) and surface type(ocean and land). This process is carried out fitting a polynomial equation
to the empirical data according to the following equation:
F(LZA,LAT) = A0 + A1*LZA + A2*LZA2 + A3*LAT + A4*LZA*LAT + A5*LAT2
where LZA is the absolute value of Local Zenith Angle and LAT is the absolute value of latitude.
| A0 | A1 | A2 | A3 | A4 | A5 | |
|---|---|---|---|---|---|---|
| μ - ocean | 8.4353 | -0.0603 | -0.0005 | -0.0337 | 0.0008 | 0.0009 |
| σ - ocean | 3.6702 | -0.0173 | -0.0003 | -0.0142 | 0.0004 | -0.0005 |
| μ - land | 4.1652 | -0.0373 | -0.0002 | -0.0129 | 0.0005 | -0.0004 |
| σ - land | 3.2898 | -0.0154 | -0.0004 | 0.0009 | 0.0003 | 0.0000 |
In the second stpe, Cloud Liquid Water(CLW) is proposed as a porxy for retrieving
rainfall over the ocean according with the following equation:
a1 + a2*CLW ( if CLW < 0.4mm and RR is indeterminate or RR == 0 )
RR
0 ( if CLW < 0.4mm and RR is indeterminate )
where a1 and a2 depends on "convective index" (see above).
In the case of land, because it's not possible to get CLW, mean values of rainfall rates are used to fill indeterminate according to the "convective index"
| Ocean | Land | ||
|---|---|---|---|
| a1 | a2 | a3 | |
| CI=1 | 1.93 | 0.57 | 1.97 |
| CI=2 | 4.17 | 2.04 | 5.95 |
| CI=3 | 7.81 | 4.91 | 10.95 |
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 W89.0 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.
The retrieval of the Snow Water Equivalent (SWE) is based on the scattering index W31.4, 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.