Matlab Soil Hydrologic Model
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The aim of this work was to develop, test, and apply a model suitable for the simulation of soil water content (SWC) pattern in Hyytiälä, Finland.
Integrating soil-atmosphere and plant systems provides a holistic understanding of biosphere-atmosphere interactions and feedback, emphasizing that the soil is the interface between the atmosphere and the plant system, playing a critical role in regulating water movement and storage (Silva & Lambers 2021). For that reason, in a detailed soil-atmosphere-plant systems analysis, parameters such as precipitation, snow, evaporation, and transpiration are directly linked with infiltration, runoff, percolation, and soil structure.
The present work is focused on developing a soil-hydrology model mainly based on and dialoguing with Neilson's (1995) model.
Materials and Methods
The model is descriptive and functional;
It was elaborated in MATLAB software;
The data used were daily measured between 1999 and 2001;
Were considered in the model:
Snowpack and snowmelt;
Saturated and unsaturated soil scenarios;
Three soil layers (50 cm depth in total).
Model inputs (daily data):
Precipitation
Air temperature
Evapotranspiration values.
Due to the high number of parameters (26), the calibration method chosen was fminsearch.
Model evaluation: Root Mean Square Error (RMSE), and the Coefficient of Determination (R²).
A sensitivity analysis was made for the drivers, considering the IPCC RCP6 scenario.
Snowpack/snowmelt extension
Precipitation values were split into snow, rain, and snow with rain, based on Neilson (1995).
The precipitation below -5ºC was considered as snow, thus added to the snowpack.
If precipitation occurs in temperatures above 0°C, it was assumed to be rain.
If precipitation occurs in temperatures in between were considered a mix between rain and snow.
Saturated/unsaturated soil scenarios
The soil water content (SWC) in the soil pack, was calculated as a weighted average of the SWC of the layers, per day.
The maximum value was considered as the maximum soil water content possible (Θmax);
The minimum value is the matrix potential (Θmp);
The field capacity (Θfc) per layer was based on Gao (2016);
The values between the Θmax and Θfc belong to the saturated scenario, for each soil layer;
The values between Θfc and Θmp belong to the unsaturated scenario, for each soil layer.
Since Neilson (1995) used different coefficient (k) values for each layer according to saturated/unsaturated scenarios, this was also considered in the proposed model.
Soil layers
The groundwater recharge was calculated for each layer and then combined into one soil pack, according to the layer's depth:
First layer: 10 cm;
Second layer: 10 cm;
Third layer: 30 cm.
Sensitivity Analysis
For the sensitivity analysis, the validated year 2001 was considered, and it was adopted the RCP6 scenario setup of seasons (boreal winter and boreal summer), temperature, and precipitation ranges (minimum and maximum). These inputs were altered accordingly with each range value in the model and the first step was to analyze temperature and precipitation model sensitivity separately. In sequence, both altered inputs were analyzed together.
Result
Calibration
RMSE = 18.89 mm
R² = 50%
Validation
RMSE = 22.78 mm
R² = 62%
Overall, the model tends to underestimate the values of water in the soil.
Additionally, it is responsive to changes in rainfall regime - in extreme precipitation events, as occurred in September 2021, the model diverges the most from the observed data. The same pattern happened in the calibration, where an extreme precipitation event also occurred in September 1999.
Result - Sensitivity Analysis
Temperature
The results have shown that temperature is not an important driver when analyzing the sensitivity of the model.
Although changing the temperature values significantly, the correlation between the scenario and the validated output of the model is high.
Model performance:
Tmin
R² = 0.98
RMSE = 1.7 mm
Tmax
R² = 0.97
RSME = 2.6 mm
Precipitation
The results have shown that precipitation is also not a sensitive driver in the model.
This also indicates that the correlation between validated and modelled scenario outputs remains high.
Model performance:
Pmin
R² = 0.94
RMSE = 5.3 mm
Pmax
R² = 0.91
RMSE = 4.6 mm
IPCC RCP6 scenario
Once the model is not sensitive regarding the drivers of precipitation and temperature in the first place, when applied the analysis of RCP6, considering both at the same time, the same result was obtained.
The minimum temperature presented slight variations and the minimum precipitation, although also slight, was the one with a clear difference in some points over the time series when compared to the modelled (validated) output.
Discussion
The validation result showed an “absence of water” in the system overall, and an amplified absence in specific seasons. This could be caused by a miscalculation of the layer depth, which influences the amount of water available in the system as well as the water percolation between the layers.
In the model, the amount of water available remained roughly 90 mm on average during the analyzed period, and this average is important to understand the sensitivity of the model to extreme precipitation events, such as the ones found in 1999, and 2001. These extreme precipitation events caused a peak in the validated and modelled scenario output, where a slight increase in precipitation represents a greater percentage of the amount of water in the system.
In that sense, the model was not capable of properly representing similar patterns of the observed data regarding the amount of water available and events with increasing precipitation. Furthermore, the lack of total understanding of the processes leads to uncertainties in the model.
For solving the issue of lack of water in the system, a better understanding of ΔΘ equation for each layer is needed, mainly regarding runoff, and adopting more detailed data such as 30-minute or hourly data.
Another way of improving the model could be by making a proportional distribution of evapotranspiration values according to different layers. In ΔΘ equations the evapotranspiration is been reduced in all of them, reducing the SWC overall, however, this input is an important source of SWC variation.
Conclusion
It is possible to say that the model can be improved in different factors.
A better understanding of how evapotranspiration affects each of the layers, and how soil moisture varies layer by layer would lead to better accuracy.
As expected, the model showed low sensitivity to the temperature driver (both positive and negative variations), Also, related to precipitation, it showed higher sensitivity to negative variations, which may be linked to the soil composition (sandier).
When simulating under the conditions presented by the RCP6.0 scenario, the model does not show significant changes because the scenario considers temperature and precipitation increases, precisely those changes that the model is not sensitive to.
In general, we can say that the model is able to assimilate the behavior of the variation of the amount of water in the soil in Hyytiälä, considering the inputs adopted.
Variables - their meanings and units
Variables - their meanings and units
Parameters - meanings, values, and units
Parameters - meanings, values, and units
Equations
Equations
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