Model Sensitivity and Uncertainty


A sensitivity analysis was completed to examine the response of changing selected model parameters to model results. The analysis was done by varying the value of the parameter of interest while holding all other model parameters constant. The Upper Klamath River model has a large number of parameters—enough that a formal sensitivity analysis was not performed on every parameter. The process of adjusting model parameters during calibration, in addition to the feedback from PEST runs, provided a general sense of parameter sensitivity. In addition, several formal sensitivity tests were performed to examine the effect of varying parameters by 20 percent (table 7). These parameters included the wind sheltering coefficient (WSC), light extinction coefficient for water and dissolved constituents (EXH2O), fraction of solar radiation absorbed at the water surface (BETA), blue-green algae maximum growth rate (AG), blue-green algae maximum respiration rate (AR), blue-green algae maximum mortality rate (AM), blue-green algae settling rate (AS), blue-green algae light saturation intensity (ASAT), blue-green algae upper temperature for the rising rate function (AT2), labile dissolved organic matter decay rate (LDOMDK), labile particulate organic matter decay rate (LPOMDK), particulate organic matter settling rate (POMS), ammonia nitrification rate (NH4DK), release rate of ammonia from the sediment (NH4R), denitrification rate (NO3DK), release rate of phosphorus from the sediment (PO4R), and the three reaeration coefficients.


Water temperature was relatively insensitive to many model parameters, including WSC, EXH2O, and BETA; water temperature was instead more strongly controlled by the temperature of the inflows and overall meteorological conditions. The EXH2O parameter did affect dissolved oxygen, blue-green algae, ammonia, and orthophosphorus concentrations, showing that algal production was often light limited in this system. As expected, blue-green algae concentrations also were sensitive to manipulation of rates of growth, mortality, and settling, with less sensitivity to the respiration rate and temperature factors. An increase in blue-green algae growth rates produced increases in dissolved oxygen and ammonia and a decrease in orthophosphorus. The effect of changes in WSC and two of the reaeration coefficients on dissolved-oxygen concentrations demonstrates the importance of reaeration to the overall oxygen budget.


Model sensitivity, coupled with calibration and testing, aids in considering model uncertainty. Models are abstractions of reality and model equations necessarily involve simplified representations of complex natural phenomenon. The type of uncertainty associated with simplified representations can be termed “structural uncertainty” and can be minimized, but not eliminated, by choosing a model that has well-tested algorithms for the most important water-quality processes. Experimental work to better understand the dynamics of the most important processes also can help to refine algorithms and reduce such uncertainty. Important processes in the Upper Klamath River include algal and organic matter dynamics, SOD, and reaeration. Another source of model uncertainty is associated with input data. Uncertainty was minimized in this study by directly measuring as many of the needed inputs and calibration data as possible, with high-quality field and laboratory procedures, and using supported assumptions for the estimation of other unmeasured inputs. Finally, the selection of model parameters can be another source of model uncertainty. The PEST optimization software in this study was used to help choose a parameter set that minimized the error between model output and measured calibration data. These values also were compared to ensure parameters were within the range of values reported in published literature. In sum, it is important to realize that all models exhibit uncertainty that cannot be wholly eliminated. The approach for this project was to (1) minimize uncertainty through well-developed physical, chemical, and biological model representations; (2) provide careful field data-collection efforts; and (3) perform intensive model calibration and testing.


First posted July 14, 2011