TIME-VARYING SENSITIVITY ANALYSIS REVEALS IMPACTS OF WATERSHED MODEL CHOICE ON THE INFERENCE OF DOMINANT PROCESSES

Abstract

Lumped rainfall-runoff models are widely used for flow prediction, but a longrecognized need exists for diagnostic tools to identify appropriate model structures for a given application based on the dominant processes they are meant to represent. To this end, we develop a comprehensive exploration of dominant processes in the Hymod, HBV, and Sacramento Soil Moisture Accounting (SACSMA) model structures. Model controls are isolated using time-varying Sobol^′ sensitivity analysis for twelve MOPEX watersheds in the eastern United States over a ten-year period. Sensitivity indices are visualized along gradients of observed precipitation and flow characteristics to determine behavioral consistency between the three models. Results indicate that the models’ dominant processes strongly depend on time-varying hydroclimatic conditions. Parameters associated with surface processes such as evapotranspiration and runoff generally dominate under dry conditions, since high evaporative fluxes and small contributions from fast runoff are required for the models to properly simulate low flow conditions. Parameters associated with routing processes typically dominate under high flow conditions, when performance depends on the timing of flow events, even though these parameters might be associated with subsurface processes. Additionally, the models exhibit very different dominant processes relative to one another due to their contrasting mathematical formulations. These results emphasize the importance of scrutinizing how the formulation of a model shapes the scientific inferences drawn its behavior, particularly in applications such as predictions under change where the ability to infer dominant processes from a model is crucial.  

Table of Contents

List of Figures                                                                                                               viChapter 1Introduction                                                                                                             1Chapter 2Data and Models                                                                                                     6 2.1                        Watershed Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                            6 2.2                           Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                               6 Chapter 3Methods                                                                                                                  10 3.1                     Sobol^′ Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . .                       10 3.2    Model Evaluation Metrics and Timescales             . . . . . . . . . . . . . .               12 3.3         Sorting Time Periods to Create a Hydroclimatic Gradient . . . . . .           13 Chapter 4Results                                                                                                                     15 4.1                 Time-Varying Sensitivity Analysis . . . . . . . . . . . . . . . . . . .                   15 4.2                         Monthly RMSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                           17 4.3       Sensitivity across Hydrologic Conditions (Annual ROCE Metric) . .         19 4.4           Sensitivity Analysis of Grouped Model Components . . . . . . . . .             21 Chapter 5Discussion                                                                                                               25 5.1           Cross-Model Comparison of Dominant Processes . . . . . . . . . . .             25 5.2                Implications of Contrasting Behaviors . . . . . . . . . . . . . . . . .                 31  

Chapter 1

Introduction

Watershed models are valuable tools for predicting streamflow, particularly where historical observations are available for calibration. However, selecting an appropriate model structure for a given application is a challenging task. In practice, hydrologic models are often selected according to perceptions of the system, data availability, and modeling objectives [1–4] , in addition to less objective criteria such as prior experience and ease-of-use. There remains a need for diagnostic methods to explore the effects of model formulations on performance and inform the processes of model selection, calibration, and interpretation [5] . This task is particularly vital for Predictions in Ungauged Basins (PUB) and Predictions Under Change (PUC) applications, where the absence of measured system behavior requires the assumption that dominant model processes across a range of hydrologic conditions match the actual dominant processes in the system [6–8] . This study compares the time-varying dominant processes within three widely used lumped watershed models across a gradient of hydrologic conditions to identify the controlling components of each model and determine the extent to which they behave consistently with one another and with our perceptions of the underlying watersheds. Many of the diagnostic methods applied to hydrologic models pursue the same goal: to evaluate the dynamic behavior of a model and its constituent processes with respect to the physical system. Nearly forty years ago, McCuen [9] noted that “the time-dependent nature of sensitivity should be considered in the formulation of hydrologic models”. The popularity of model diagnostics in water resources applications has been motivated by the idea that the consistency of modeled and observed behavior and process controls-rather than model optimality with respect to some measures of performance-should be the primary objective of environmental model identification [10] . Figure 1.1 shows an example of dynamic system behavior using hydrographs at the monthly scale for the Guadalupe (Texas) and Bluestone (West Virginia) Rivers, with colors superimposed to indicate whether streamflow, precipitation, and potential evapotranspiration fall above or below their respective medians in a given month. Each colored quadrant suggests different dominant processes based on the relationship between these three characteristics. For example, a month with low precipitation and high streamflow likely indicates a release from storage,i.e., a baseflow-dominated regime. If a model structure accurately represents real-world processes, we would expect its dominant processes to change accordingly in time. Using Figure 1.1 as motivation, a rigorous diagnostic method should explore process-level model behavior while accounting for spatial and temporal variability in hydrologic conditions. The recent history of hydrologic model diagnostics encompasses a variety of methods to address this need, including performance-based, top-down, and sensitivity analysis approaches. Performance-based diagnostic methods evaluate the suitability of a model for a particular application by comparing outputs of interest–typically, streamflow– to observations. Examples of such diagnostic methods include [11–16] , and [17] , in which rainfall-runoff models are evaluated based on their ability to reproduce streamflow observations across many watersheds. Such multi-catchment approaches identify geographic regions of poor performance and thus potentially point to structural inadequacies in the model. Performance-based diagnostic methods have been extended to include comparisons across models and multi-model frameworks,e.g., [18–28] , where optimal performance is used to choose between competing model structures on a per-watershed basis. In this regard, multi-model frameworks explore the effects of model structure on error and uncertainty. Performancebased approaches benefit from their practical focus on streamflow prediction, a common application area for lumped watershed models due to the widespread availability of flow data. One weakness of this approach is that optimal perfor-  Figure 1.1. Monthly hydrographs for the Guadalupe River (Texas) and Bluestone River (West Virginia). The eight superimposed colors indicate whether streamflow, precipitation, and potential evapotranspiration fall above or below their respective medians in a given month, as shown in the quadrants to the left. The blue, green, red, and yellow quadrants signify the relationship between streamflow and precipitation, while the dark and light shades of each color represent high and low potential evapotranspiration, respectively. Each color suggests a different dominant process in the physical system which a model should reproduce. For example, a month with low precipitation, high streamflow, and low PE (denoted by the light green color) likely indicates a release from storage, i.e., a baseflow-dominated regime. The frequent changes in these regimes highlight the need for time-varying, rather than static, sensitivity analysis. mance does not necessarily signify the proper representation of underlying system processes [25,29–31] . This issue can be improved by including multiple hydrologic measures of performance in addition to the typical statistical measures,e.g. [32–36] , but in general it is very difficult to infer process-level behavior from statistical metrics alone. Opportunities remain for novel diagnostic methods to evaluate models according to process-level behavior in addition to output performance [4,5,37] . Performance-based diagnostic methods to infer model controls on hydrologic response variables are inherently related to the top-down modeling approach, which employs performance measures and visual inspection to select the minimum model complexity needed to identify dominant controls [38–43] . The top-down lumped approach is most appropriate at the watershed scale, given that the alternative– a bottom-up compilation of continuum-scale processes–is highly prone to overparameterization at coarse spatial resolutions [44,45] . Top-down methods focus on identifying parsimonious model structures by gradually increasing complexity until performance no longer improves. Performance in this context could be measured using statistical residuals [41] , the fraction of old versus new water [42] , ensemble reliability [43] , or other model evaluation techniques. This approach typically uses streamflow to assess performance, but can also benefit from additional data such as observations of evaporation or groundwater fluxes–if available, these can provide excellent guidance as to which dominant processes should be included in a model and which processes can safely be excluded without degrading performance [46] . Such observations have been used in conjunction with streamflow data to isolate the shortcomings of a model structure and suggest appropriate complexity [6,47–50] . This approach provides valuable comparisons to the physical system, but it is difficult to generalize; for many watersheds, the only readily available data are streamflow, precipitation, and temperature. Our study therefore aims to develop a diagnostic approach that is generally applicable to systems in which data beyond these basic watershed-scale observations are not available, and which extends traditional performance measures to formally quantify controls on performance. While top-down approaches use variations in model complexity to identify dominant components and select appropriate formulations, sensitivity analysis is often applied to quantitatively attribute the variability in performance to individual parameters. Sensitivity-based methods reveal the practical importance of structural assumptions without relying on optimization, which can produce good statistical performance regardless of model structural errors when sufficient degrees of freedom are present. Sensitivity analysis has a long history of application in hydrological modelling, particularly for exploring identifiability and uncertainty within complex parameter spaces and interpreting model behavior in the context of the system being modeled [22,51–60] . In particular, the need to identify the effects of parameter interactions on model behavior is a long-standing issue in the field [61] . Two recent ideas based on sensitivity analysis will serve as the foundation for this study: first, that the controls on model performance will change across a hydroclimatic gradient [7] ; and second, that parameter sensitivities will change in time as real-world dominant processes change [22,56,62–66] . These extensions of sensitivity analysis approaches reveal model behavior at the level of constituent processes, which is a valuable starting point for this study. Our study contributes a comprehensive diagnostic analysis of the Hymod, HBV, and SAC-SMA lumped watershed models for twelve watersheds in the Eastern United States, combining the strengths of many of the diagnostic methods discussed above. Rather than measuring performance alone, we use Sobol^′ sensitivity analysis to identify which model components control performance under different conditions, constructing a rigorous foundation for model selection. The sensitivity analysis is temporally discretized and incorporates watersheds from multiple hydroclimates to visualize model behavior across a gradient of hydrologic variability. Additionally, the sensitivity of grouped model components is calculated to enable inter-model comparison of implied dominant processes, an analysis which is especially critical to identify appropriate representations in changing or ungauged systems. In summary, this study contributes a novel approach to understanding the effects of model structural assumptions on performance, with the goal of informing appropriate model selection and the inference of dominant processes from conceptual models. TIME-VARYING SENSITIVITY ANALYSIS REVEALS IMPACTS OF WATERSHED MODEL CHOICE ON THE INFERENCE OF DOMINANT PROCESSES