Global Sensitivity Analysis of environmental models:Convergence and validation

AbstractWe address two critical choices in Global Sensitivity Analysis (GSA): the choice of the sample size and of the threshold for the identification of insensitive input factors. Guidance to assist users with those two choices is still insufficient. We aim at filling this gap. Firstly, we define criteria to quantify the convergence of sensitivity indices, of ranking and of screening, based on a bootstrap approach. Secondly, we investigate the screening threshold with a quantitative validation procedure for screening results. We apply the proposed methodologies to three hydrological models with varying complexity utilizing three widely-used GSA methods (RSA, Morris, Sobol’). We demonstrate that convergence of screening and ranking can be reached before sensitivity estimates stabilize. Convergence dynamics appear to be case-dependent, which suggests that “fit-for-all” rules for sample sizes should not be used. Other modellers can easily adopt our criteria and procedures for a wide range of GSA methods and cases

Towards Application of StorAge Selection Functions in Large-Scale Catchments with Heterogeneous Travel Times and Subsurface Reactivity

StorAge Selection (SAS) functions describe how a catchment selectively removes water and solute of different ages via discharge, thus controlling transit time distributions (TTDs) and solute composition of discharge. Previous studies have successfully applied SAS functions in a spatially lumped approach to capture catchment-scale transport phenomena of (non-)conservative solutes. The lumped approach assumes that water and solutes within a water parcel of a specific age are well-mixed. While this assumption does not cause any changes in the age of water, the spatial heterogeneity of solute concentrations within this water parcel is lost. In addition, in large catchments, headwater sub-catchments and lowland sub-catchments could behave in different ways, e.g., the transit times (TTs) and reaction rates between headwater and lowland sub-catchment could be of different magnitudes. This, in turn, might not be sufficiently represented in a lumped approach of SAS functions. In this study, we applied the mHM-SAS model (Nguyen et al., 2020) with a semi-distributed approach of SAS functions. The nested mesoscale catchment (Selke catchment, Germany) with heterogeneous land use management practices, TTs, and subsurface reactivity was used as a case study. In addition to spatial variability, a functional relationship between the parameters of the SAS functions and storage dynamics was introduced to capture temporal dynamics of the selection preference for discharge. High frequency instream nitrate data were used to validate the proposed approach. Results show that the proposed approach can well represent nitrate export at both sub-catchment and catchment levels. The model reveals that catchment nitrate export is controlled by (1) the headwater sub-catchment with fast TTs and a high denitrification rate, and (2) the lowland sub-catchment with longer TTs and a low denitrification rate. In general, the proposed approach serves as a promising tool for understanding the interplay of transport and reaction times between different sub-catchments, which controls nitrate export in a mesoscale heterogeneous catchment

Disparate Seasonal Nitrate Export from Nested Heterogeneous Subcatchments Revealed with StorAge Selection Functions

Understanding catchment controls on catchment solute export is a prerequisite for water quality management. StorAge Selection (SAS) functions encapsulate essential information about catchment functioning in terms of discharge selection preference and solute export dynamics. However, they lack information on the spatial origin of solutes when applied at the catchment scale, thereby limiting our understanding of the internal (subcatchment) functioning. Here, we parameterized SAS functions in a spatially explicit way to understand the internal catchment responses and transport dynamics of reactive dissolved nitrate (N-NO<sub>3</sub>). The model was applied in a nested mesoscale catchment (457 km²), consisting of a mountainous partly forested, partly agricultural subcatchment, a middle-reach forested subcatchment, and a lowland agricultural subcatchment. The model captured flow and nitrate concentration dynamics not only at the catchment outlet but also at internal gauging stations. Results reveal disparate subsurface mixing dynamics and nitrate export among headwater and lowland subcatchments. The headwater subcatchment has high seasonal variation in subsurface mixing schemes and younger water in discharge, while the lowland subcatchment has less pronounced seasonality in subsurface mixing and much older water in discharge. Consequently, nitrate concentration in discharge from the headwater subcatchment shows strong seasonality, whereas that from the lowland subcatchment is stable in time. The temporally varying responses of headwater and lowland subcatchments alternates the dominant contribution to nitrate export in high and low-flow periods between subcatchments. Overall, our results demonstrate that the spatially explicit SAS modeling provides useful information about internal catchment functioning, helping to develop or evaluate spatial management practices

QUADICA: Water quality, discharge and catchment attributes for large-sample studies in Germany

Environmental data are the key to define and address water quality and quantity challenges at catchment scale. Here, we present the first large-sample water quality data set for 1386 German catchments covering a large range of hydroclimatic, topographic, geologic, land use and anthropogenic settings. QUADICA (water QUAlity, DIscharge and Catchment Attributes for large-sample studies in Germany) combines water quality with water quantity data, meteorological and nutrient forcing data, and catchment attributes. The data set comprises time series of riverine macronutrient concentrations (species of nitrogen, phosphorus and organic carbon) and diffuse nitrogen forcing data at catchment scale (nitrogen surplus, atmospheric deposition and fixation). Time series are generally aggregated to an annual basis; however, for 140 stations with long-term water quality and quantity data (more than 20 years), we additionally present monthly median discharge and nutrient concentrations, flow-normalized concentrations and corresponding mean fluxes as outputs from weighted regressions on time, discharge, and season (WRTDS). The catchment attributes include catchment nutrient inputs from point and diffuse sources and characteristics from topography, climate, land cover, lithology and soils. This comprehensive, freely available data collection can facilitate large-sample data-driven water quality assessments at catchment scale as well as mechanistic modeling studies

QUADICA: A large-sample data set of water quality, discharge and catchment attributes for Germany

Environmental data are critical for understanding and managing ecosystems, including mitigation of degraded water quality. Therefore, we provide the first large-sample water quality data set of riverine water quality combined with water quantity, meteorological and nutrient forcing data, and catchment attributes for Germany in a preprocessed and structured form. The QUADICA data set (water QUAlity, DIscharge and Catchment Attributes for large-sample studies in Germany) covers 1386 German and transboundary catchments with a large range of hydroclimatic, topographic, geologic, land use and anthropogenic settings. The data set comprises time series of riverine macronutrient concentrations (species of nitrogen, phosphorus and organic carbon), discharge, meteorological and diffuse nitrogen forcing data (nitrogen surplus, atmospheric deposition and fixation). The time series are generally aggregated to an annual basis; however, for 140 stations with long-term water quality and quantity data (more than 20 years), we additionally provide monthly median discharge and nutrient concentrations, flow-normalized concentrations and corresponding mean fluxes as outputs from weighted regressions on time, discharge, and season (WRTDS). The catchment attributes include catchment nutrient inputs from point and diffuse sources and characteristics from topography, hydroclimate, land cover, lithology and soils. QUADICA is a comprehensive, freely available, ready-to-use data set that facilitates large-sample data-driven water quality assessments at catchment scale as well as mechanistic modeling studies. We hope to stimulate the hydrological and water quality communities to provide similar data sets to create novel research opportunities, increase our understanding of catchment functioning, and ultimately improve water quality management