Annex

Tables for forward model

The tables listed here are part of the forward model used in the multi parameter retrieval. The following Tables 7, 8, 9, 10 are reprinted from [Wentz and Meissner, 2000] with the corresponding formulae are described in Forward Model.

Note

For completeness, the tables also include the coefficients for 23.8 GHz and 89 GHz, which are not available on the CIMR satellite. These coefficients are not used in the retrieval.

Table 7 Coefficients for atmospheric model

Frequency GHz	6.9	10.7	18.7	23.8	36.5	89.0
\(b_0\)	2.3950e+02	2.3951e+02	2.4024e+02	2.4169e+02	2.3945e+02	2.4258e+02
\(b_1\)	2.1392e+00	2.2519e+00	2.9888e+00	3.1032e+00	2.5441e+00	3.0233e+00
\(b_2\)	-4.6060e-02	-4.4686e-02	-7.2593e-02	-8.1429e-02	-5.1284e-02	-7.4976e-02
\(b_3\)	4.5711e-04	3.9182e-04	8.1450e-04	9.9893e-04	4.5202e-04	8.8066e-04
\(b_4\)	-1.6840e-06	-1.2200e-06	-3.6070e-06	-4.8370e-06	-1.4360e-06	-4.0880e-06
\(b_5\)	5.0000e-01	5.4000e-01	6.1000e-01	2.0000e-01	5.8000e-01	6.2000e-01
\(b_6\)	-1.1000e-01	-1.2000e-01	-1.6000e-01	-2.0000e-01	-5.7000e-01	-5.7000e-01
\(b_7\)	-2.1000e-03	-3.4000e-03	-1.6900e-02	-5.2100e-02	-2.3800e-02	-8.0700e-02
\(a_{\text{O}1}\)	8.3400e-03	9.0800e-03	1.2150e-02	1.5750e-02	4.0060e-02	5.3350e-02
\(a_{\text{O}2}\)	-4.8000e-05	-4.7000e-05	-6.1000e-05	-8.7000e-05	-2.0000e-04	-1.1800e-04
\(a_{\text{V}1}\)	7.0000e-05	1.8000e-04	1.7300e-03	5.1400e-03	1.8800e-03	8.7800e-03
\(a_{\text{V}2}\)	0.0000e+00	0.0000e+00	-5.0000e-07	1.9000e-06	9.0000e-07	8.0000e-06

Table 8 Coefficients for Rayleigh absorption and Mie scattering

Frequency GHz	6.9	10.7	18.7	23.8	36.5	89.0
\(a_{L1}\)	7.8000e-03	1.8300e-02	5.5600e-02	8.9100e-02	2.0270e-01	9.6930e-01
\(a_{L2}\)	3.0300e-02	2.9800e-02	2.8800e-02	2.8100e-02	2.6100e-02	1.4600e-02
\(a_{L3}\)	7.0000e-04	2.7000e-03	1.1300e-02	1.8800e-02	4.2500e-02	1.5060e-01
\(a_{L4}\)	0.0000e+00	6.0000e-03	4.0000e-03	2.0000e-03	-2.0000e-03	-2.0000e-03
\(a_{L5}\)	1.2216e+00	1.1795e+00	1.0636e+00	1.0220e+00	9.5460e-01	7.9610e-01

Table 9 Coefficients for geometric optics

Frequency GHz	6.9	10.7	18.7	23.8	36.5	89.0
v-pol \(r_0\)	-2.7000e-04	-3.2000e-04	-4.9000e-04	-6.3000e-04	-1.0100e-03	-1.5300e-03
h-pol \(r_0\)	5.4000e-04	7.2000e-04	1.1300e-03	1.3900e-03	1.9100e-03	2.0200e-03
v-pol \(r_1\)	-2.1000e-05	-2.9000e-05	-5.3000e-05	-7.0000e-05	-1.0500e-04	-1.1600e-04
h-pol \(r_1\)	3.2000e-05	4.4000e-05	7.0000e-05	8.5000e-05	1.1200e-04	1.3000e-04
v-pol \(r_2\)	-2.1000e-05	-2.1000e-05	-2.1000e-05	-2.1000e-05	-2.1000e-05	-2.1000e-05
h-pol \(r_2\)	-2.5260e-05	-2.8940e-05	-3.6900e-05	-4.1950e-05	-5.4510e-05	-5.5000e-05
v-pol \(r_3\)	0.0000e+00	8.0000e-08	3.1000e-07	4.1000e-07	4.5000e-07	-9.0000e-07
h-pol \(r_3\)	0.0000e+00	-2.0000e-08	-1.2000e-07	-2.0000e-07	-3.6000e-07	-4.6000e-07

Table 10 Coefficients m1 and m2

Frequency GHz	6.9	10.7	18.7	23.8	36.5	89.0
v-pol \(m_1\)	2.0000e-04	2.0000e-04	1.4000e-03	1.7800e-03	2.5700e-03	2.6000e-03
h-pol \(m_1\)	2.0000e-03	2.0000e-03	2.9300e-03	3.0800e-03	3.2900e-03	3.3000e-03
v-pol \(m_2\)	6.9000e-03	6.9000e-03	7.3600e-03	7.3000e-03	7.0100e-03	7.0000e-03
h-pol \(m_2\)	6.0000e-03	6.0000e-03	6.5600e-03	6.6000e-03	6.6000e-03	6.6000e-03

Table 11 Coefficients ice emissivities

Frequency GHz	1.4	6.9	10.7	18.7	23.8	36.5	89.0
eps_FY_V	0.92	0.958	0.960	0.965	0.960	0.946	0.615
eps_FY_H	0.86	0.868	0.879	0.887	0.882	0.864	0.488
eps_MY_V	0.94	0.972	0.948	0.885	0.839	0.731	0.666
eps_MY_H	0.85	0.866	0.845	0.799	0.763	0.675	0.630

Table 12 Coefficients for the first year ice thickness sensitivity

Frequency GHz	6.9	10.7	18.7	23.8	36.5	89.0
b_v	157.94	163.49	175.182	185.914	206.668	242.019
c_v	8.957	8.524	7.734	7.474	7.668	2.804
b_h	74.221	78.405	90.601	99.897	128.36	175.158
c_h	11.894	11.645	10.165	9.129	8.986	5.686

Table 13 linear regression Coefficients for emitting layer temperature calculation for Winter

Frequency GHz	6.9	10.7	18.7	23.8	36.5	89.0
a_fyi	0.23	0.26	0.29	0.29	0.30	0.37
b_fyi	-5.5	-5.2	-5.0	-4.9	-4.9	-4.2
a_myi	0.27	0.34	0.42	0.43	0.45	0.49
b_myi	-11.5	-10.5	-9.5	-9.2	- 8.9	-8.4