Improved modelling of a Prairie catchment using a progressive two-stage calibration strategy with in situ soil moisture and streamflow data

Dynamic contributing areas, various fill-and-spill mechanisms and cold-region processes make the hydrological modelling of the Prairies very challenging. Several models (from simple conceptual to advanced process-based) are available, but the focus has been largely in reproducing streamflow. Few studies have assimilated soil moisture and other hydrological fluxes for improved simulation, but the emphasis has been predominately on simulating contributing areas. However, previous research has shown that the contributing areas are dynamic, and can vary from one year to the next, depending on hydro-meteorological conditions. Therefore, the areas deemed non-contributing can also occasionally contribute to streamflow. In this study, we introduce a progressive two-stage calibration strategy to constrain soil moisture in non-contributing areas. We demonstrate that constraining soil moisture in non-contributing areas can result in improved hydrological simulations and more realistic process representations. The Nash–Sutcliffe efficiency (NSE) values for simulated soil moisture in contributing areas increased by 68% at 20 cm and 25% at 50 cm soil depths during validation when noncontributing areas were constrained. This further led to increases in NSE values in streamflow simulation during calibration (6%) and validation (12%). Our findings suggest that soil moisture in non-contributing areas should be properly constrained for improved modelling of Prairie catchments. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/). doi: 10.2166/nh.2020.109 ://iwaponline.com/hr/article-pdf/51/3/505/698273/nh0510505.pdf Sujata Budhathoki Prabin Rokaya (corresponding author) Karl-Erich Lindenschmidt Global Institute for Water Security, University of Saskatchewan, 11 Innovation Blvd., Saskatoon, SK S7N 3H5, Canada E-mail: prabin.rokaya@usask.ca


INTRODUCTION
The Prairie region covers approximately 900,000 km 2 and spans from north-central Iowa in the United States to central Alberta in Canada (Daniel & Staricka ).
Agriculture is a key land use of the region, and hence, the economic prosperity of the region is heavily dependent on water (Pomeroy et al. ). The general topography of the Prairies is a hummocky terrain that consists of millions of closed depressions known as 'prairie potholes' or simply In Canada, the Prairies are located in the provinces of Alberta, Saskatchewan and Manitoba. The Canadian Prairies have a cold and semiarid climate with seasonally frozen ground, and low-angled, undulating topography. Annual precipitation ranges from approximately 300-400 mm, and the majority of the region sees continuous snow cover and frozen soils during the 4-5 months of winter (Pomeroy et al. ). Non-contributing areas in the Prairies refer to closed watersheds around the potholes/ponds since under normal hydro-meteorological conditions, the water never reaches the receiving river systems (see Figure 1 for the map of non-contributing areas). Instead, the adjacent network of ponds receives the surface runoff from the noncontributing areas, which exchange water by a fill-and-spill mechanism and ultimately feed a terminal pond. Terminal ponds lose water to evaporation and, potentially, to a local ground water flow system (Daniel & Staricka ). However, connectivity in the non-contributing areas is dynamic, leading to variable contributions to nearby river systems, especially during extreme flood events. hydrological models at the time were able to satisfactorily simulate Prairie hydrology (Shook   Literature review also showed that the state variables from non-contributing areas are not generally considered in hydrological modelling studies, despite the fact that contributing areas in the Prairies are dynamic and can significantly vary from one year to another, which is a major motivation for this study. In this study, we present a progressive two-stage calibration method in which soil moisture in non-contributing areas is calibrated first against observed soil moisture. In the second stage, soil moisture and streamflow in contributing areas are calibrated while using calibrated parameters for non-contributing areas (obtained from the first stage). The modelling results show that constraining soil moisture information in noncontributing areas can result in improved hydrological simulation in a Prairie catchment.

Study basin description
The Brightwater Creek (BWC) basin lies within the sub-

MESH-PDMROF model set-up
The MESH model was set up for the BWC basin with an outlet at Brightwater Creek near Kenaston (05HG002) (see Figure 3(a)). The drainage database was prepared using the Environment and Climate Change Canada's Green Kenue software (Canadian Hydraulics Centre ).
The digital elevation data for the model were obtained from the Geobase database at the scale of 1:50,000, and the land cover data were derived from the Commission for Environmental Cooperation (CEC) in 30 m resolution (http://cec.org/tools-and-resources/map-files/land-cover-2010-landsat-30 m). Within the MESH model, the CLASS was selected for the vertical exchange of water and energy within a grid cell, the PDMROF for lateral soil (sub-surface) and surface water movement and WATROUTE for routing streamflow in river channels.
In this study, the PDMROF module was used because it better represents the variable nature of contributing and non-contributing areas of the Prairies (Mengistu & Spence ). The PDMROF was specifically designed by Mekonnen et al. () to simulate the complex hydrological behaviour of the Prairies, by employing the concept of the probability density approach of Moore () to parsimoniously represent their runoff and storage processes. The basic equation is given as follows: indicates the actual storage capacity, C max is the maximum storage capacity and B represents a shape factor parameter.
The two parameters, C max and B, control the degree of spatial variability of the storage capacity across the basin.
The unit of C is 'm' and B is a unitless parameter.

Meteorological forcing data
The meteorological inputs for MESH include incoming shortwave radiation, incoming longwave radiation, precipitation, temperature, barometric pressure, specific humidity and wind speed. All of these inputs, except precipitation Soil moisture and streamflow data The soil moisture data were retrieved from the Brightwater

Constraining soil moisture in non-contributing areas
In the first step, soil moisture in non-contributing areas was for both 20 and 50 cm soil depths (see also Figure 4).

Simulation of soil moisture in contributing areas
In the second step, soil moisture in contributing areas along with streamflow was calibrated using calibrated parameters for non-contributing areas. Note that multi-objective Note that if the sum of sand and clay in each soil layer does not equal to 100%, then the remaining percentage is assumed to be silt.    However, previous studies have demonstrated that the contributing and non-contributing areas in the basin are dynamic and can affect the generation of total streamflow.
In this study, we presented a progressive two-stage model calibration strategy where soil moistures in non-contributing areas is constrained first, and then streamflow and soil moisture in contributing areas are subsequently calibrated.
The proposed approach of constraining the non-contributing area improved the hydrological model performance.  (Beven & Freer ); therefore, parametric uncertainty poses another key challenge in hydrological modelling. To address this issue, we adopted an ensemble modelling approach (using 99 optimal parameter sets) instead of a deterministic simulation based on one optimal parameter set.
Similarly, the choice of calibration period also affects the generated optimal parameters and hence, simulated streamflows.
It is possible to end up with different optimal parameter sets, depending on the time period to which the model is calibrated. We calibrated the model for the 2011-2014 period and validated it for the timeframe 2015-2018. The year 2011 was considered a spin-up period to minimize the effects of initial conditions on simulated results. Our logic was to use half of the study period for calibration and other half to assess the predictive ability of the calibrated model through temporal validation. We also ensured that both relatively dry (2012, 2013, 2016 and 2017) and wet (2011, 2014, 2015 and 2018) conditions are present during both calibration and validation periods. We also acknowledge that practically, it is not possible to avoid all possible errors associated with hydrological modelling, but we used a uniform set of forcing data, model structure, parameter range and observation data between two approaches (i.e. using progressive two-stage calibration vs. calibrating both contributing and non-contributing areas at once), so that the differences observed are due to methodology, not because of forcing data or other modelrelated errors.

CONCLUSION
This study presents a progressive two-stage model calibration strategy where soil moisture in non-contributing areas is constrained first, and then streamflow and soil moisture in contributing areas are subsequently calibrated.
Our results show that constraining soil moisture in noncontributing areas leads to improvement in hydrological process simulations (particularly during validation) and, therefore, greater confidence in hydrological modelling.
The NSE values in simulated soil moisture of contributing areas increased by 68% at 20 cm soil depth and by 25% at 50 cm soil depth during validation when soil moisture in the non-contributing area was constrained. Similarly, an average increase of 6% in calibration and 12% in validation in NSE values were obtained for streamflow simulation.
More importantly, the representation of dynamic variability in contributing areas was more realistic with the presented approach. The presented methodology is model and scaleindependent; therefore, it can be used with other models and replicated to other small Prairie catchments or upscaled to larger Prairie watersheds. Since, the economic prosperity of the Prairie region is heavily dependent on water, the findings of this study is expected to contribute to improved water management in the region.

ACKNOWLEDGEMENT
This research was financially supported by the Global Water Futures program. We thank Daniel Princz from