function [er] = ersoil(f,T,mv); % Calculation of the complex relative permittivity of moist soil % for the REBEX-7 and REBEX-8 sites % using the Dobson et al, 1985, semi-empirical model. % Soil texture for R8: 16.1% sand, 55.0% silt, 28.9% clay. % exp(-iwt) time dependence, Imag(er) > 0. % Brian Hornbuckle, April 16, 2002. Modified April 13, 2006. % This function uses the function erwater.m % which caculates the complex relative permittivity of pure water % mv = volumetric water content of the soil, m^3 m^-3 % T = temperature, K % f = frequency, Hz S = 0.161; Silt = 0.550; C = 0.289; % -------- fitting parameters alpha = 0.65; beta = 1.09 - 0.11*S + 0.18*C; % ------------ soil solids epsilon_ss = 4.7; % relative permittivity of soil solids ro_ss = 2.65; % particle density (density of soil solids), g cm-3 % could possibly change this will real data, % but epsilon_ss was optimized for this value ro_bulk = 0.362*1.21 + 0.638*1.09; % LOW bulk density = 1.21 g cm-3, HIGH bulk density = 1.09 g cm-3 % 36.2% LOW areas, 63.8% HIGH areas v_phi = 1 - ro_bulk/ro_ss; % soil porosity, cm-3 cm-3 ss = (1 - v_phi)*epsilon_ss^alpha; % soil solids contribution % ---------- air a = (v_phi - mv)*1^alpha; % air contribution % ---------- free and bound water fwbw = mv.^beta.*erwater(T,f).^alpha; % free and bound water contribution % ------------------- er = (ss + a + fwbw).^(1/alpha);