Application of Gaussian Error Propagation Principles for Theoretical Assessment of Model Uncertainty in Simulated Soil Processes Caused by Thermal and Hydraulic Parameters

Statistical uncertainty in soil temperature and volumetric water content and related moisture and heat fluxes predicted by a state-of-the-art soil module [embedded in a numerical weather prediction (NWP) model] is analyzed by Gaussian error-propagation (GEP) principles. This kind of uncertainty results from the indispensable use of empirical soil parameters. Since for the same thermodynamic and hydrological surface forcing and mean empirical parameters a soil module always provides the same mean value and standard deviation, uncertainty is first theoretically analyzed using artificial data for a wide range of soil conditions. Second, NWP results obtained for Alaska during a July episode are elucidated in relation to the authors’ theoretical findings. It is shown that uncertainty in predicted soil temperature and volumetric water content is of minor importance except during phase transition. Then the freeze–thaw term dominates and leads to soil temperature and moisture uncertainties of more than 15.8 K and 0.212 m 3 m 3 in mineral soils. Heat-flux uncertainty is of the same order of magnitude as typical errors in soil-heat-flux measurements. Uncertainty in the pore-size distribution index dominates uncertainty for all state variables and soil fluxes under most conditions. Uncertainties in hydraulic parameters (saturated hydraulic conductivity, pore-size distribution index, porosity, saturated water potential) affect soil-temperature uncertainty more than those in thermal parameters (density and specific heat capacity of dry soil material). Based on a thermal conductivity approach alternatively used, it is demonstrated that GEP principles are indispensable for evaluating parameterized soil-transfer processes. Generally, statistical uncertainty decreases with depth. Close beneath the surface, the uncertainty in predicted soil temperature, volumetric water content, and soil-moisture and heat fluxes undergoes a diurnal cycle.

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