Soil moisture model (2 layers)

Overview

This page details the TFN forcing transformation function named climateTransform_soilMoistureModels_2layer. It is identical to the one layer model climateTransform_soilModels but it has a second deeper soil store whereby the free-drainage from the upper store drains into the deeper store and the maximum ET from the deep store equal the PET minus the shallow store ET. Like the one layer soil model, the two layer and can be used to simulate land cover change. Below are the following sections explaining aspects of the model different or additional to the one layer model:

Soil Moisture Equation

The soil moisture model can be used to simulate one soil moisture profile or two parallel soil moisture profiles, which each represent different land cover types and can be used to simulate land cover change. Below is a diagram illustrating the one profile model (left) and the two parallel profile model; at the bottom of which is an equation showing how a flux from the two parallel deep stores are aggregated to a single flux.

Soil moisture model diagram

The single profile soil moisture model is defined by the following two ordinary differential equations (extension of Kavetski et al. 2006). The first equation is for the upper store and the second for the deeper store:

$\frac{dS}{dt} = P_{inf} \left(1 - \frac{S}{SMSC}\right)^\alpha - k_{sat} \left(\frac{S}{SMSC}\right)^\beta - PET \left(\frac{S}{SMSC}\right)^\gamma$

$\frac{dS_{deep}}{dt} = k_{sat} \left(\frac{S}{SMSC}\right)^\beta - k_{sat,deep} \left(\frac{S_{deep}}{SMSC_{deep}}\right)^{\beta_{deep}} - \left(PET-\left(\frac{S}{SMSC}\right)^\gamma\right) \left(\frac{S_{deep}}{SMSC_{deep}}\right)^\gamma$

The two layer model has a number of assumptions adopted:

evaporation can occur from the shallow and deep stores, but the evaporative potential from the deep store is reduced to account for evaporation from the shallow store.
The power term for the evaporation, γ, is assumed to be identical in each layer.
soil water can only drain from the shallow to the deep layer. The shallow layer cannot uptake water from the deep layer.

The equations contains two state variable and requires the input of two daily meteorological time series. For the two profile model, both profiles are simulated using the above equation. The only difference between the non-tree and tree profiles is that the soil moisture capacity of the shallow and deep stores can differ because the soil moisture capacity of the tree store is defined by separate parameters, SMSC_trees and SMSC_trees,deep. The table below details each of the equation variables that are addition to that of the one store model climateTransform_soilModels.

Equation Variable	Description
S_deep	The deep layer soil moisture at time t [L]. The units are those of the input precipitation. In solving the differential equation, the initial value equals SMSC_deep * S_{deep,initialfrac}. The solver also applies the constraint 0<=S_deep<=SMSC_deep, which when S_deep=SMSC_deep, precipitation produces saturated excess runoff.

Soil Moisture Model Parameters

The soil moisture equation requires at least the soil moisture capacity parameters, SMSC and SMSC_deep, to be calibrated. Like the parameters for the one store model climateTransform_soilModels, the other parameters can be either calibrated or fixed.

Note, the following deep layer parameters can be set to be identical to the corresponding shallow layer parameter value: SMSC_deep, SMSC_trees,deep, S_{initialfrac,deep}_, k_sat,deep, β_deep. To set these parameters to be identical to the shallow layer, input an initial value of NaN and to Fixed.

The table below details each parameter additional to the one store model climateTransform_soilModels. The table details the parameter physical range, the physical range when transformed to a scale amenable to efficient calibration (note, the transform was log10 and the transform range is only shown below for only those parameters that were transformed), transformed initial value and if it calibrated by default within the HydroSight GUI.

Param.	Description	Range (Transformed)	Default Value	Default Calibrated?
SMSC_deep	The deep layer maximum soil moisture capacity [L]	10<=SMSC_deep<=1000 (1<=SMSC_deep<=3)	2	Yes
SMSC_trees,deep	The deep layer maximum soil moisture capacity for the parallel soil model used to simulate trees [L]	10<=SMSC_{trees, deep}<=2000 (1<=SMSC_{trees, deep}<= 3.3010)	2	No
S_{initialfrac,deep}	The deep layer initial soil moisture [-], expressed as a fraction of SMSC.	S_{initialfrac,deep}<=1	0.5	No
k_{sat, deep}	The deep layer maximum vertical soil conductivity [L/T] (i.e as saturation)	10<=k_{sat, deep}<=10,000 (1<=k_{sat, deep}<=4)	1	Yes
β_deep	Power term controlling the drainage response of the deep layer soil moisture. A large transformed value (eg 2) simulates drainage to have a threshold-like response where drainage only occurs when the soil is wet.	1<=β_deep<=Inf 0<=β_deep<=Inf	0.5	Yes

Soil Moisture Fluxes

The table below details the soil state variable and fluxes that are addition to that of the one store model climateTransform_soilModels.

Each variable and fluxes can be used in the time-series modelling and each is listed within the HydroSight GUI. If the parallel soil model is used, then each of the following is also available for just the non-tree soil store (denoted by nontree extension) and the tree soil store (denoted by tree extension). Like the one store model climateTransform_soilModels, For the former the store or flux is multiplied by (1-f_interflow) * TreeFraction. For the latter, the store or flux is multiplied by f_interflow_ * TreeFraction

Soil Model Flux Data	Description
drainage_deep	Deep layer soil free drainage ranging from 0 to k_sat_deep at the end of the day.
drainage_bypassFlow_deep	Deep layer soil free drainage plus a parameter set fraction of runoff.
drainage_normalised_deep	Normalised deep layer soil free drainage (0 to 1) at the end of the day.
evap_soil_deep	Deep layer soil ET at the end of the day.
evap_soil_total	Sum of the top layer and deep deep layer soil ET at the end of the day.
infiltration	Daily total infiltration.
evap gw potential	Groundwater evaporative potential (PET - soil total ET).
SMS_deep	Deep layer soil moisture storage at the end of each day.