Soil moisture model
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. Below are the following sections:
The soil moisture model is defined by the following ordinary differential equation (adapted from Kavetski et al. 2006):
The equation contains one state variable and requires the input of two daily meteorological time series. The table below details each of the equation variables.
| 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* Sinitialfrac. 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. |
| Pinf | The precipitation available for infiltration [L/T]. That is, the minimum of the daily precipitation rate and the maximum infiltration rate, kinf. When P>kinf, 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. |
The soil moisture equation requires six parameters but 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<kinf 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 |
| Sinitialfrac | The initial soil moisture [-], expressed as a fraction of SMSC. | Sinitialfrac<=1 | 0.5 | No |
| kinf | The maximum daily infiltration rate [L/T]. | 10<kinf<=Inf | Inf | No |
| ksat | The maximum vertical soil conductivity [L/T] (i.e as saturation) | 10<=ksat<=10,000 (1<=ksat<=4) |
1 | Yes |
| fbypass | Fraction of runoff that goes to bypass drainage. | 0<=fbypass<=1 | 0 | No |
| finterflow | Fraction of free drainage going to interflow. | 0<=finterflow<=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 |
The following soil fluxes/data can be used in the time-series modelling.
| Soil Model Flux/Data | Description |
| Drainage | soil free drainage ranging (0 to k_sat) at the end of the day. |
| Drainage bypass flow | Free drainage plus a parameter set fraction of runoff. |
| Drainage normalised | Normalised free drainage (0 to 1) at the end of the day. |
| Soil evaporation | Estimated soil ET at the end of the day. |
| Infiltration | Daily total infiltration rate. |
| Groundwater evaporative potential | Groundwater evaporative potential (PET - soil ET). |
| Runoff | Total daily runoff. |
| SMS | soil moisture storage at the end of each day. |
The soil moisture model can also be used to simulate the impacts from different vegetation; for example, trees and pastures. This is achieved by simulating a soil store for upto 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 challange 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 'treeArea_frac' for the fraction of the second land cover (notially trees) that is influencing the bore.