Add reference and explanation on Soil_Inertia1.m

src/+equations/Soil_Inertia1.m

@@ -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
 
     % % parameters
 
-    theta_s = theta_s0; % (saturated water content, m3/m3)
+    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)
+    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, ≈fss if no measured data)
+    lambda_qc = 7.7;  %(thermal conductivity of quartz, W/m.K, constant)
 
-    lambda_s = (lambda_qc^(QC)) * lambda_d^(1 - QC);
-    lambda_wtr = 0.57;   % (thermal conductivity of water, W/m.K, constant)
+    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