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Add explanation of Soil_Inertia1.m #224

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Add explanation of Soil_Inertia1.m #224

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Add reference and explanation on Soil_Inertia1.m
EntingTang Mar 14, 2024
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Change the comment style of Soil_Inertia1.m to follow the best practice
EntingTang Mar 14, 2024
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Change the comment of Soil_inertial1.m to follow the best practice
EntingTang Mar 14, 2024
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Change the comment style of Soil_Inertia1.m to follow the best practice
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32 changes: 16 additions & 16 deletions src/+equations/Soil_Inertia1.m
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@@ -1,34 +1,34 @@
function [GAM] = Soil_Inertia1(SMC, theta_s0)
% soil inertia method by Murray and Verhoef (
% soil inertia method by Murray and Verhoef (2007), and the soil inertial (GAM) is used to calculate the soil heat flux
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@Crystal-szj Crystal-szj Mar 25, 2024 •
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% soil inertia method by Murray and Verhoef (2007), and the soil inertial (GAM) is used to calculate the soil heat flux
% soil inertia method by Murray and Verhoef (2007), and the soil inertial (GAM) is used to calculate the soil heat flux
% Input:
% SMC : soil moisture (m3 m-3)
% theta_s0 : saturated soil moisture (m3 m-3)
% Output:
% GAM : soil inertia (J m-2 K-1 s-0.5)
% Reference:
% Murray, T., Verhoef, A., 2007. Moving towards a more mechanistic approach in the determination of soil heat
% flux from remote measurements: I. A universal approach to calculate thermal inertia. Agricultural and Forest
% Meteorology 147, 80-87.


% % parameters

theta_s = theta_s0; % (saturated water content, m3/m3)
Sr = SMC / theta_s;

% fss = 0.58; %(sand fraction)
gamma_s = 0.27; % (soil texture dependent parameter)
dels = 1.33; % (shape parameter)
% fss = 0.58; % (sand fraction)
gamma_s = 0.27; % (soil texture dependent parameter; if fss>0.4, gamma_s=0.96 while fss=<0.4, gamma_s=0.27)
dels = 1.33; % (shape parameter, constant)

ke = exp(gamma_s * (1 - power(Sr, gamma_s - dels)));
ke = exp(gamma_s * (1 - power(Sr, gamma_s - dels))); % (Kersten number, Eq.(15))

phis = theta_s0; % (phis == theta_s)
lambda_d = -0.56 * phis + 0.51;
phis = theta_s0; % (porosity, phis=theta_s=theta_s0)
lambda_d = -0.56 * phis + 0.51; % (thermal conductivity for air-dry soil, Eq.(16))

QC = 0.20; % (quartz content)
lambda_qc = 7.7; % (thermal conductivity of quartz, constant)
QC = 0.20; % (quartz content, approximate to fss if no measured QC)
lambda_qc = 7.7; % (thermal conductivity of quartz, W/m.K, constant)

lambda_s = (lambda_qc^(QC)) * lambda_d^(1 - QC);
lambda_s = (lambda_qc^(QC)) * lambda_d^(1 - QC); % (thermal conductivity of the soil solids, Eq.(18))
lambda_wtr = 0.57; % (thermal conductivity of water, W/m.K, constant)

lambda_w = (lambda_s^(1 - phis)) * lambda_wtr^(phis);
lambda_w = (lambda_s^(1 - phis)) * lambda_wtr^(phis); % (thermal conductivity for saturated soil, Eq.(17))

lambdas = ke * (lambda_w - lambda_d) + lambda_d;
lambdas = ke * (lambda_w - lambda_d) + lambda_d; % Eq.(14)

Hcs = 2.0 * 10^6;
Hcw = 4.2 * 10^6;
Hcs = 2.0 * 10^6; % (heat capacity of solid soil minerals, J/m3.K)
Hcw = 4.2 * 10^6; % (heat capacity of water, J/m3.K)

Hc = (Hcw * SMC) + (1 - theta_s) * Hcs;
Hc = (Hcw * SMC) + (1 - theta_s) * Hcs; % Eq.(13)

GAM = sqrt(lambdas .* Hc);
GAM = sqrt(lambdas .* Hc); % Eq.(10)
end
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