Soil moisture model

Overview

This page details the TFN forcing transformation function named climateTransform_soilMoistureModels. It is a generalised vertically lumped 1-D soil moisture model. It is used to transform daily climate data for use in the transfer noise function groundwater time-series model, and can be used to simulate land cover change. Below are the following sections explaining the model:

Importantly, the soil moisture equation is a very simple water balance model. While it has been found to be effective in simulating groundwater level dynamics in Australia, it should not be relied upon to simulate runoff. Furthermore, the model does not currently account for irrigation - but which could be simulated by adding the irrigation depth to the precipitation input data..

Soil Moisture Model Equations

The soil moisture model consists of equations for a single storage vadose zone, two parallel vadose zones (for simulating vegetation land cover change) and a snow melt model.

Soil moisture storage

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

Soil moisture model diagram

The single store soil moisture model is defined by the following ordinary differential equation (adapted from Kavetski et al. 2006):

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

The equation contains one state variable and requires the input of two daily meteorological time series. For the two store model both stores are simulated using the above equation. The only difference between the non-tree and tree stores is that the soil moisture capacity of the two stores can differ because the soil moisture capacity of the tree store is defined by a separate parameters, SMSC_trees.

The figure below illustrates how the soil moisture ODE fluxes change with the relevant model parameters. Each plot is explained below:

top-left plot shows how the infiltration capacity varies with soil moisture, whereby when the soil is dry all of the precipitation infiltrates. Conversely, when the soil is saturated, none of the precipitation infiltrates and it all runs off. When α is greater than one the infiltration declines rapidly with soil moisture. This relationship can be reproduced using the Forcing Data tab and creating a scatter plot of infiltration_fracCapacity against SMS_pcnt.
top-right plot shows how the infiltration capacity varies with soil moisture and the ε parameter (i.e. the fraction of the soil moisture capacity below which all precip. infiltrates). When ε equals 0.5, all precipitation infiltrates until the soil is 50% full, after which runoff commences. This relationship can be reproduced as per the top-left plot.
bottom-left plot shows how recharge from out of the bottom of the soil layer varies with soil moisture (expressed as a fraction of the vertical conductivity, K_sat). When β equals 8, recharge only begins once the soil moisture is at ~60% capacity. This results in episodic recharge events, rather than a more continuous recharge rate. This relationship can be reproduced using the Forcing Data tab and creating a scatter plot of drainage against SMS_pcnt.
bottom-right plot shows how soil evapotranspiration changes with soil moisture . When γ equals one the ET increases linearly with soil moisture. When γ is less than one the ET persists at a more constant and higher level, which is conceptualised as the vegetation trying to maintain a constant rate of water usage. This relationship can be reproduced using the Forcing Data tab and creating a scatter plot of evap soil divided by PET against SMS_pcnt.

Soil model fluxes

Snow melt

As of HydroSight version 1.4.1.4, a snow melt model was added to the soil model. The snow accumulation, ω, is defined as a function of the daily temperature, T; a threshold temperature for melting, T_melt and a degree-day-melt rate, D:

$https://latex.codecogs.com/svg.image?\frac{\mathrm{d \omega } }{\mathrm{d} t} = \begin{cases} P,& \text{if } T\leq T_{melt}\\ D \left(T - T_{melt} \right),& \text{otherwise}\end{cases}$

Using this snow accumulation equation, the liquid water P_liquid is equal to the melted snow plus the precipitation (when T > T_melt):

$https://latex.codecogs.com/svg.image?P_{liquid} = \begin{cases} 0,& \text{if } T\leq T_{melt}\\ D \left(T - T_{melt} \right) + P,& \text{otherwise}\end{cases}$

Model Variables

The table below details each of the equation variables for the above ODE..

Equation Variable	Description
S	The soil moisture at time t [L]. The units are those of the input precipitation. In solving the differential equation, the initial value equals SMSC* S_initialfrac. The solver also applies the constraint 0<=S<=SMSC, which when S=_SMSC, precipitation produces saturated excess runoff.
t	Time [T]. The differential equation is solved in continuous time, but solutions are reported at the end of each day.
P_inf	The precipitation available for infiltration [L/T]. That is, the minimum of the daily precipitation rate and the maximum infiltration rate, k_inf. When P>k_inf, infiltration excess runoff occurs.
P	The daily precipitation rate [L/T]. This should be the precipitation at a location thought to be driving the aquifer recharge.
PET	The daily areal potential evapotranspiration rate [L/T]. This should be the PET at a location thought to be influencing the recharge.

Model Input Timeseries Data

The soil moisture models requires a minimum two input timeseries forcing data. If the soil model is used to simulate landcover change, then a third input timeseries is required. If snow accumulation and melt is included, then the daily mean temperature is also required.

All inputs should extend from years prior to the first groundwater level observation to at least the most recent water level observation (see Data Requirements for details). Below is a summary of the data types.

Input Timeseries Name	Description	Required?
precip	Daily precipitation, ideally in units of mm/day.	Yes
et	Daily areal potential evapotranspiration, ideally in units of mm/day	Yes
T	Daily mean temperature, ideally in units of degree celsius	No
TreeFraction	A normalised valued (i.e. between zero and one) where zero denotes that the land type being simulated does not exists and one denotes that the land type being simulated is fully established. This input is only required if simulate landcover change	No

Model Parameters

The soil moisture can have a variable number of parameters to calibrate, with the minimum being only the parameter SMSC must be calibrated. The other parameters can be fixed (i.e. not calibrated) or calibrated. This allows considerable flexibility in the complexity of the soil model. For example, fixing α to 0 simulates all precipitation < k_inf as being infiltrated. Alternatively, fixing α to 1 simulates infiltration as a function of catchment wetness so that as the catchment wets up, infiltration declines. This flexibility allows the user to explore hypothesis for the vadose zone mechanisms driving the observed groundwater level dynamics.

The soil moisture model also has parameters which do not appear in the above differential equation but do control the calculation of the fluxes from the model (denote by * in the table below). For example, the free-drainage may occur by soil matrix flow and preferential flow of runoff re-routed to recharge.

The length units of all parameters are equal to that of the input precipitation and the time units are days. The parameter ranges have been developed for units of mm.

The table below details each parameter able to be controlled by the user, its 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	The maximum soil moisture capacity [L]	10<=SMSC<=1000 (1<=SMSC<=3)	2	Yes
SMSC_trees	The maximum soil moisture capacity for the parallel soil model used to simulate trees [L]	10<=SMSC_trees<=2000 (1<=SMSC<= 3.3010)	2	No
f_{tree area}^*	The fraction of the parallel soil model used to simulate trees that contributes to the catchment total flux. This fraction can be conceptualised as the fraction of the catchment that has trees, with one minus the fraction can be conceptualised as the fraction not having trees. [L]	0<=f_{tree area}<=1	0.5	No
S_initialfrac	The initial soil moisture [-], expressed as a fraction of SMSC.	S_initialfrac<=1	0.5	No
k_inf	The maximum daily infiltration rate [L/T].	10<k_inf<=Inf	Inf	No
k_sat	The maximum vertical soil conductivity [L/T] (i.e as saturation)	10<=k_sat<=10,000 (1<=k_sat<=4)	1	Yes
f_bypass^*	Fraction of runoff that goes to bypass drainage.	0<=f_bypass<=1	0	No
f_interflow^*	Fraction of free drainage going to interflow.	0<=f_interflow<=1	0	No
α	Power term controlling the fraction of precipitation available for infiltration, which is conceptualised as the catchment wetness. A value of zero causes all precipitation to be available for infiltration.	0<=α<=Inf	0	No
β	Power term controlling the drainage response of the soil to 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<=Inf 0<=β<=Inf	0.5	Yes
γ	Power term controlling the fraction of PET available for soil evapotranspiration. A transformed value of zero produces a linear relationship between PET and model soil ET.	0.01<=γ<=100 -2<=γ<=2	0	No
ε	Fraction of SMSC, below which all precip. infiltrates. Requires α>0. Improves runoff estimation by allowing all precip. to infiltrate whenthe soil moisture is below ε*SMSC	0<=ε<=1	0	No
D	Snow melt degree-day melt factor (unit of mm/degree/day). Require input temperature data.	0<=D<=2	Inf	No
T_melt	Threshold temperature for snow melt (degree Cy). Requires input temperature data.	-5<=T_melt<=5	Inf	No

Soil Moisture Fluxes

The following table soil state variable and fluxes can be used in the time-series modelling and each is listed within the HydroSight GUI. Those fluxes that are generally appropriate to use with the weighting functions are also denoted below, though all of the fluxes below could be used and all are available during graphical examination of the model forcing data.

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). 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	Used with weighting Function?
drainage	Soil free drainage ranging from 0 to k_sat at the end of the day.	Yes
drainage bypass flow	Free drainage plus a parameter set fraction of runoff.	Yes
evap soil	Estimated soil ET at the end of the day.	No
infiltration	Daily total infiltration.	No
evap gw potential	Groundwater evaporative potential (PET - soil ET).	Yes
interflow	Unsaturated interlow estimated as f_interflow * drainage. By default this flux is zero.	No
runoff	Total daily runoff estimated as precipitation - infiltration + interflow.	No
SMS	Soil moisture storage at the end of each day.	No
SMS_pcnt	Soil moisture fraction (SMS/SMSC) at the end of each day.	No
effectivePrecip	Precipitation limited by the maximum infiltration rate, k_inf.	No
infiltration	Soil infiltration.	No
infiltration_fracCapacity	Maximum infiltration capacity given α and ε.	No
snow	Snow accumulated at the end of the day (as mm rainfall).	No
melt	Melted snow at the end of the day (as mm rainfall).	No
liquidWater	Rainfall plus melted snow at the end of the day.	Yes
mass_balance_error	Soil model mass balance error derived from numerical integration of sub-daily soil fluxes.	No

Simulating Land Cover Types

As outlined above, the parallel soil moisture model can be used to simulate the impacts from different vegetation; for example, trees and pastures. This is achieved by simulating a soil store for up to two land types and then weighting required flux from each soil model by an input time series of the fraction of the second land type.

A challenge with the input time series of land cover is, however, that while the fraction of, say, land data clearing over time may be known the fraction of the catchment area cleared that influences a bore hydrograph is unknown. To address this, the modelling also include a parameter f_{tree area} for the fraction of the second land cover (notationally trees) that is influencing the observed water level.