5.4.3 SIGMA-B Model

The SIGMA B algorithm was developed by Sigma Consultand, Sweden and is used, if no real-time meteorological data are available. Therefore the known annual periodicity of influence o meteorological factors are utilized in order to retrieval accuracy. Starting again with equation:

Leads to the following retrieval algorithms for V(θ) and L(θ).

Calculation of Water Vapour SIGMA B Model

Calculated at zenith value with

• b_1, b_2, b_3, b_4: values from MODEL.TXT, calculated with a(f), b(f), c(f,θ,Z_0) from basic equation

• t [day]: Number of the day

• Z_0 [m]: Height in meter not km

• X_12 (θ=90): value determined by by sky noise temperatuer f1, f2

• X_12 (θ=90): value determined by by sky noise temperatuer f1, f2

The variable X_12 is found as

• f_1: 31,75GHz
• f_2: 23,8GHz or 21,3GHz
• r(f,90): zenith opacity af frequency f
• r_OX (f,θ=90): opacity caused by oxygen at frequency f

• r_OX (19): opacity caused by oxygen

• P_0 [mbar]: Pressure at Radiometer Site replaced by expression:

• T_0 [K]: Temperature fix at 285K

And again the calculation of r(f,90):

• With m(θ): correction for actual look angle

• And r(f,θ): opacity af frequency f and El θ

• T_eff (f,θ): effective medium temperature
• T_S (f,θ): Measured Sky Noise Temp
• T_C : Cosmic Temperature

• a_1 (f), a_2 (f): values from MODEL.TXT
• T_0 [K] : Temperatur fix at 285K
• m(θ): correction for actual look angle

Calculation of Liquid Water SIGMA B Model

Calculated at zenith value

• b_1, b_2, b_3, b_4, b_5: values from MODEL.TXT, calculated with a(f), b(f), c(f,θ,Z_0) from basic equation
• t [day]: Number of the day
• f_1: 31,75GHz
• f_2: 23,8GHz or 21,3GHz
• r(f,90): zenith opacity af frequency f
• Z_0 [m]: Height in meter not km

• With m(θ): correction for actual look angle

• And r(f,θ): opacity af frequency f and El θ

• T_eff (f,θ): effective medium temperature
• T_S (f,θ): Measured Sky Noise Temp
• T_C : Cosmic Temperature

• a_1 (f), a_2 (f): values from MODEL.TXT
• T_0 [K] : actual ground temperature