Soil moisture model v2 (1 & 2 layers)
This page details the TFN forcing transformation functions named climateTransform_soilMoistureModels_v2 and climateTransform_soilMoistureModels_2layer_v2. Both are an extension of the original 1-layer and 2-layer models. All of the features of the original models are preserved in these version 2 models. However, the version 2 models also include a constraint on the average modelled soil evapotranspiration that results in more plausible estimates of recharge.
In the field rainfall is partitioned into the three major fluxes of evapotranspiration, runoff and recharge. In water-limited climates (temperate and arid), and over the long-term, the vast majority of rainfall is partitioned to evapotranspiration (i.e. about >85%), with the majority of the remaining rainfall going to runoff (about 10%). This leave only about 5% of rainfall going to recharge.
HydroSight simulates such partitioning of rainfall. However, if the soil moisture dynamics are insufficiently constrained by the calibration of the model to the observed head, then rainfall can be implausibly partitioned. Most commonly this results in the evapotranspiration being too low, leaving an implausible fraction of rainfall going to recharge. The version 2 soil models address this problem of implausibly high recharge by constraining the simulated average soil evapotranspiration to a plausible range.
The estimation of a plausible long-term average soil evapotranspiration (ET) required adoption of a relevant hydrological law. Few exist, but the Budyko curve (below) is a well established finding that explains the change in partitioning of rainfall to runoff and ET. The curve was derived by examining the long-term average rainfall and runoff of hundreds of catchments over a wide range of climate types (and assuming no long-term change in storage and zero recharge).
Figure 1: Schematic of the Budyko curve. The x-axis shows the aridity, here labeled as the dryness index (rainfall / potential ET), and the y-axis shows the evaporative index (actual ET / rainfall). Source: Creed et al. (2014).
Over the long-term the ET from a catchment cannot exceed the rainfall, as shown in Fig. 1 by the y-axis being constrained to <=1. Looking at the x-axis, catchments that have less rainfall than the PET are water limited with those with more rainfall than PET are energy limited.
The Budyko curve (Fig. 1) uses estimates of the rainfall (P), actual catchment ET (AET) and the potential ET (PET). Calibrating a model using a soil moisture module requires input of P and PET, and so the only unknown is the AET. The AET is, however, estimated from the soil model. Therefore, for any given model the x-axis value within Fiq. 1 is know for the site and for any particular model parameter set we can calculate the y-axis value. From this we can calculate how far away the model is from the average catchment dynamics (Fig. 1 dashed line) for the site's dryness index. However, knowing the distance from the average catchment dynamic is insufficient to decide if the model is acceptable.
Recently, the Budyko curve was extended from the dashed curve in Fig. 1 representing the average of hundreds of catchments to a probabilistic estimate (Fig. 2 and Greeve et al. (2015)). For any given dryness index, the probabilistic estimate provides a probability distribution of the possible long-term average evaporative index. When the dryness index is 3.5 (see Fig 2) the probability distribution is pushed close to an evaporative index of one and it has a narrow range. Conversely, when the dryness index is 1.5 the mode of the distribution reduces and the range increases.
Figure 2: Probabilistic Budyko curve. The x-axis shows the aridity, here labeled as the dryness index (rainfall / potential ET), and the y-axis shows the evaporative index (actual ET / rainfall). The bottom panel shows the distribution of the evaporative index for given values of the dryness index. Source: Greeve et al. (2015).
These evaporative index distributions now allow a HydroSight soil model ET to be probabilistically assessed. Specifically, HydroSight undertakes the following steps during the calibration to assess if a given parameter set is acceptable. If the parameter set not acceptable, then it is rejected, the outcome of which is that only parameter sets that produce a plausible soil ET are accepted:
- Calculate the daily soil evaporation for the given model parameters using the soil moisture model.
- Calculate the annual average modelled soil ET using the entire forcing record (up to the end of the calibrate date).
- Calculate the annual average rainfall and potential ET (PET) using the entire input forcing data (up to the end of the calibrate date).
- Estimate the dryness index using the average P and PET.
- Using the implemented Greeve et al. (2015) probabilistic Budyko curve, calculate the probability distribution of the evaporative index using the site dryness index.
- Convert the evaporative index distribution into a distribution of actual ET using the site average rainfall.
- Assess if the annual average modelled soil ET is within the 10th to 90th percentile of the distribution of actual ET. If not, reject the parameter set.
The outcome from the above steps is that the calibrated model produces a plausible estimate of average soil ET. More importantly, now that the major rainfall flux (i.e. ET) is more reliably estimated, the modelled mean runoff and recharge should also be more reliable.
Peterson and Fulton (2019) detailed the above approach and applied it to a groundwater supplied irrigation area in Victoria, Australia. They found that the approach significantly reduced the estimate of mean recharge (relative to version one soil models) and produced estimates that were in close agreement with independent estimates for the region.
Building models with the version 2 soil module is nearly identical to that for the version one models. No additional input data or parameters are required. Simply select either climateTransform_soilMoistureModels_v2 or climateTransform_soilMoistureModels_2layer_v2 from the list of forcing transform models.
That said, the constraint on the mean soil ET makes finding valid soil parameter sets slow. Trials have found that also calibrating the γ parameter significantly improves the calibration time, the fit to the observed hydrograph and the estimated recharge. This is because the parameter controls the fraction of PET available for soil evapotranspiration whereby a transformed value of less than one enables the model to increase the soil ET (for a given soil moisture fraction), resulting in a higher mean soil ET (see the plot here for details).