Evaluating Ecohydrological Model Sensitivity to Input Variability with an Information-Theory-Based Approach
2. Materials and Methods
2.1. Multi-Layer Canopy Model and Forcing Data
- Air temperature (Ta) affects stomatal conductance of plant and evaporation from both soil and canopy. The Campbell 083E instrument located at the flux tower has a precision for measuring Ta of C.
- Wind speed (U) affects canopy evaporation and associated heat flux partitioning. The precision of the CSAT3 measurement instrument at the tower for U is m/s.
- Vapor pressure deficit (VPD) is the difference between saturation water vapor pressure (es) and actual water vapor pressure (ea). It is the measure of atmospheric desiccation strength  and indicates the atmospheric demand for water vapor. The ea is determined by a large number of drivers and is also related to Ta in that it is upper bounded by es.
- Shortwave radiation (Rg) is a principle driver of , vapor, and heat exchange available in the system which controls photosynthesis and leaf energy balance.
- Precipitation (PPT) is often zero at the 15-min resolution considered here, such that changing the precision of PPT would not have any effect for most time steps.
- Carbon dioxide concentration (Ca) is a model parameter and is constant.
- Air pressure (Pa) varies within a very small range, and the model is relatively unresponsive to fluctuations in Pa. In other words, quantizing Pa would not lead to measurable differences in model behavior relative to other inputs.
- Canopy structure is described by leaf area density (LAD) profiles and the total leaf area index (LAI). In the model, the LAI is independent of all other forcing conditions and is based on surveys of maize or soybean plants throughout each year. It typically increases monotonically through the growing season and does not vary on a sub-daily to daily timescale.
2.2. Information Theory to Manipulate Forcing Precision
2.2.2. Illustrative Example of Quantization: Air Temperature
2.2.3. Quantized Model Cases
2.3. Sensitivity Analysis
3.1. Effects of Quantizing Individual Forcing Variables
3.1.2. Quantizing Rg Only: Changing Energy Balance Precision
3.1.3. Quantizing Ta Only: Temporally Varying Responses to Quantization
3.2. Model Sensitivity to Combinations of Forcing Precisions
3.3. Forcing Complexity and Model Behaviors
- Quantized VPD (yellow asterisks in Figure 9) shows a horizontal pattern in the (, SMt) space, which means quantization decreases forcing data complexity, but different levels of quantization (between 2 and 5) do not affect model output for LE. This indicates that the modeled LE is somewhat responsive to a change away from the instrument precision of VPD but does not vary further as the precision VPD is decreased even more. In general, this forcing variable can be greatly simplified without changes in model sensitivity. Moreover, quantizing VPD leads to the lowest SMt indicating the lowest sensitivity at this time of day of Cases 1-3, for which a single variable is quantized.
- Quantized Ta (blue asterisks in Figure 9) similarly decreases forcing data complexity but results in different model behavior based on each level of quantization. For example, the scenario of Case 1 has the largest LE sensitivity among other individually quantized forcing variables at this time of day. This also translates to other quantized cases where Ta is quantized to levels (Case 4, 5, 7) that lead to higher model sensitivity.
- Finally, quantizing U (red asterisks in Figure 9) also influences both model behavior and forcing complexity. Quantization decreases forcing data complexity similarly, but model sensitivity is less than when Ta is quantized.
4. Discussion and Conclusions
- Energy balance constraints: When incoming solar radiation is quantized, sensible and latent heat fluxes shift to meet the energy balance with some gaps that can be attributed to other energy fluxes that are not analyzed here, specifically ground heat flux and longwave radiation. Canopy carbon fluxes respond more nonlinearly and depend on whether the quantization increases or decreases the apparent radiation.
- Temporal variability and dependence on system states: We next explored model effects of air temperature quantization for different growing season time windows. This highlighted the connection between model sensitivity to forcing precision and system states, such as wetness or vegetation conditions. For example, quantized air temperature most influences latent heat fluxes during a relatively hot and dry period at the end of the growing season. This connects to previous findings based on observed data that causal interactions in ecohydrologic systems vary seasonally and with wetness conditions .
- Joint effects of multiple forcing precisions: Finally, we quantized combinations of air temperature, vapor pressure deficit, and wind speed to different extents, and plotted model responses along a forcing complexity axis, where forcing complexity indicated the extent to which the joint entropy of the forcing variables was reduced. From this, we can determine which combinations of variables are “most compressible” in terms of their ability to reduce model forcing complexity and which lead to large changes in model behavior. For example, a quantization that leads to vary forcing complexity with a very small change in model behavior would indicate that the model is not sensitive to a particular input or combinations of inputs, and the model forcing or use of that input could be simplified in some way. On the other hand, this could also indicate that the model is not utilizing the full extent of available information in the forcing and could motivate other changes to the model structure. We saw a general trend in which simulated heat fluxes diverge more from the original model case as multiple variables were increasingly quantized, but there was a wide range of forcing complexities that led to the same model sensitivity. This illustrates that the effect of forcing precision varies depending on the degree of quantization (N) and the combination of variables involved. In other words, it is possible to determine a set of forcing variables that can be maximally simplified with minimal change in model behavior.
Data Availability Statement
Conflicts of Interest
|CINet||Critical Zone Interface Network|
|IMLCZO||Managed Landscape Critical Zone Observatory|
|RMSE||Root Mean Square Error|
|GSA||Global Sensitivity Analysis|
|SUMMA||Structure for Unifying Multiple Modeling Alternatives|
|JULES||Joint UK Land Environment Simulator|
|MMSE||Minimum Mean Square Error|
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|Input Variable||Unit||Stdev||Opt Bin Width|
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Farahani, M.A.; Vahid, A.; Goodwell, A.E. Evaluating Ecohydrological Model Sensitivity to Input Variability with an Information-Theory-Based Approach. Entropy 2022, 24, 994. https://doi.org/10.3390/e24070994
Farahani MA, Vahid A, Goodwell AE. Evaluating Ecohydrological Model Sensitivity to Input Variability with an Information-Theory-Based Approach. Entropy. 2022; 24(7):994. https://doi.org/10.3390/e24070994Chicago/Turabian Style
Farahani, Mozhgan A., Alireza Vahid, and Allison E. Goodwell. 2022. "Evaluating Ecohydrological Model Sensitivity to Input Variability with an Information-Theory-Based Approach" Entropy 24, no. 7: 994. https://doi.org/10.3390/e24070994