Parameter identifiability, parameter estimation and parameter regionalisation for the Wageningen Lowland Runoff Simulator (WALRUS)

Abstract:

Introduction

Recently, we developed the Wageningen Lowland Runoff Simulator (WALRUS), a rainfall-runoff model for catchments with shallow groundwater. WALRUS is a new rainfall-runoff model which can fill the gap between complex, spatially distributed models which are often used in lowland catchments and simple, parametric models which have mostly been developed for mountainous catchments. WALRUS accounts explicitly for processes that are important in lowland areas, such as groundwater-unsaturated zone coupling, wetness-dependent flowroutes, groundwater-surface water feedbacks, and seepage and surface water supply (Brauer et al., 2013a, 2013b).

The model has been developed using experience and data from two Dutch catchments: one freely draining catchment and one polder with controlled water levels. When developing the model, special attention was paid to limiting the number of parameters and model complexity. The model performs well for these two experimental catchments, but the question now is whether it yields equally good results for catchments that were not involved in model development. The aim of this research project is to assess whether the degree of model complexity is appropriate for practical applications by investigating parameter identifiability for different catchments in The Netherlands. In addition, we evaluate several methods for parameter estimation in practical applications.

Model parameters

The structure and code of WALRUS are simple, which facilitates detailed investigation of the effect of parameters on all model variables. WALRUS contains only four parameters which require calibration. These parameters are intended to have a strong, qualitative relation with catchment characteristics. The parameter determining how the division between quick and slow flowroutes depends on catchment wetness is mainly related to field scale drainage density (drainpipes, macropores and soil cracks). The parameter determining the speed with which the groundwater table responds to changes in the unsaturated zone depends on soil type. The soil reservoir constant determining groundwater drainage or surface water infiltration depends on geology and drainage density (ditches and channels). The quickflow reservoir constant depends on slope.

Parameter estimation remains a challenge, even though only four parameters need calibration. The model structure contains three main feedbacks: between groundwater and surface water, between saturated and unsaturated zone and between catchment wetness and (quick/slow) flowroute division. These feedbacks are necessary to simulate the rainfall-runoff processes in lowland catchments adequately, but increase the risk of parameter dependence and equifinality.

Parameter regionalisation using catchment classification

In many Dutch catchments (and polders), discharge is not measured and therefore techniques to estimate parameters without calibration are necessary for application of WALRUS in ungauged catchments. The qualitative relations between catchment characteristics and model parameters suggest that parameter regionalisation could be an option.

As a first step towards parameter regionalisation, streamflow signatures have been computed for 17 gauged catchments from different landscape units in The Netherlands: eleven freely draining catchments and six polders. In five of the polders a pumping station forms the outlet of the catchment. In all six polders surface water is supplied and surface water levels are controlled. As streamflow indices, we computed and compared monthly mean discharges, flow duration curves, autocorrelation functions, baseflow indices and the relative contributions of the variance caused by fluctuations with event, seasonal and multi-year time scales. As an example, the obtained baseflow indices for the different streams (color) are plotted on an elevation map of The Netherlands (grayscale) in the accompanying Figure.

Based on the streamflow indices, the catchments could be divided into four clusters: (1) the slowly responding groundwater systems in the southeast of The Netherlands, (2) the faster responding freely draining catchments, (3) the nearly-flat freely draining catchments and polder catchments with limited influence of pumping stations on the discharge regime, and (4) the polders with a large influence of pumping stations in the west. The clusters can roughly be placed along a southeast-northwest gradient, which corresponds to a decrease in elevation, slope and soil permeability (sand and gravel in the south and east, and clay and peat in the north and west).

The next step is to calibrate WALRUS for each of these catchments and determine ranges of parameter values for each of these clusters. Water managers can use these parameter ranges to predict discharge with WALRUS, including bandwidths indicating the effect of parameter uncertainty.

Parameter regularisation

Because the model parameters have a physical connotation, it is possible to define reasonable ranges for model parameters, thereby reducing the number of options and the risk of equifinality. These first estimates of parameter values can be obtained from parameter regionalisation. For each parameter a probability distribution can be computed for different situations. When an a priori estimate of parameter values is used in the calibration procedure, optimal parameter values are found more quickly: it is computationally more robust to use a penalty for straining too far from the a priori value than to impose hard boundaries. In addition, the resulting model output (both discharge and internal model variables) is more realistic. Additionally, penalties on unrealistic behaviour in the model variables can be used during model calibration.

Conclusions

The model structure of WALRUS is simple and the number of parameters small. Therefore the role and effect of parameters on model output can be investigated in detail. A first step towards parameter regionalisation, we divided 17 Dutch catchments into four clusters with different streamflow regimes. These clusters could be qualitatively related to catchment characteristics, which is a promising beginning towards parameter estimation without calibration. Parameter regularisation using a priori parameter estimates (for example obtained with parameter regionalisation) would improve the applicability of WALRUS in catchments with a limited amount of data and should be incorporated in every systematic calibration procedure for WALRUS.