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1. Introduction

Scientific research in the field of hydrology is continually seeking to better understand, predict, and model the movement of water throughout the earth. This research is important in a plethora of applications with great importance to society. For instance: better prediction of floods and droughts can lead to better management of watersheds with respect to impacts to water supplies, agricultural land, critical infrastructure, etc. A better understanding of the fundamentals of the various aspects of the water cycle can help to predict the potential impacts of a variety of changes - namely direct human impacts and a changing climate.

The heterogeneous and variable nature of the earth continues to be a challenge to represent in hydrological models (Haghnegahdar, Tolson, Craig, & Paya, 2015). There is ongoing work in the field of hydrology related to the best method of representing a watershed in a model and the required level of complexity. With limited watershed characteristic information, validation data, meteorological measurements, computational resources, and time, it is critical that discretization methods provide sufficient results for the modelling purpose in an efficient manner (Haghnegahdar, Tolson, Craig, & Paya, 2015).

The hydrological model being used in this project is the MESH model (Modelisation Environmentale Communautaire (MEC) - Surface and Hydrology). MESH is a land-surface-hydrology model which couples a land-surface scheme (LSS), which represents the vertical movement of water and energy between the atmosphere and earth’s surface and subsurface, and a hydrologic model, which characterizes the movement of water horizontally over the land as well as through the soil (Changing Cold Regions Network, 2019a). MESH was developed by Environment and Climate Change Canada (ECCC) for the purposes of streamflow forecasting, building on the model WATCLASS, which coupled the CLASS and WATFLOOD models (Pietroniro et al., 2007). MESH has since been expanded and now allows the modeller to select from a number of LSSs as well as hydrological routing methods and alternative or additional process representations. The MESH model is continually under development by ECCC and by researchers at the Global Institute for Water Security (GIWS) at the University of Saskatchewan, with ongoing improvements to the code and hydrological process representations (University of Saskatchewan, 2019a).

This project builds on the work of H. Mkandla, a former MWS student (Mkandla 2017) which included a comprehensive background discussion on topics pertaining to the project. He included a general discussion of both the benefits and drawbacks of hydrological models, the difference between conceptual vs. physically-based models, and between lumped and distributed models. There are number of sources of error in the hydrological modelling process, which were also discussed in that paper, and include data uncertainty, measurement error, data quality, model parameter uncertainty, lack of data, and the model structure (Mkandla, 2017). A summary of the most common techniques used to deal with spatial variability in hydrological models was also discussed, as well as issues with scale variability between process understanding and representation, measurements, and modelling. Mkandla (2017) also introduced the recent improvements in data availability and computing power, which has subsequently lead to an increase in the feasible level of complexity in the models.

To avoid redundancy, this literature review presents an overview of recent publications using the MESH model, as well as work since 2017 related to the representation of spatial heterogeneity in hydrological models.

Recent Research using the MESH Model

A number of key studies have been conducted in recent years which evaluate and seek to improve the representation of various hydrological processes and factors in MESH. Of note is a comparison of different routing modules and baseflow algorthms by Abdelhamed et al (2018), incorporation of controlled reservoirs by Yassin et al. (2019), alternative runoff algorithms, PDMROF and LATFLOW, proposed by Mekonnen et al. (2014) and Hossain (2017), respectively, and the parameterization and initialization of organic matter and permafrost conditions by Elshamy et al. (2019)

Abdelhamed et al. (2018) tested two different routing modules in MESH (WF_R and RTE) and two baseflow algorithms (WATFLOOD and Luo et al., 2012) in the Upper Liard sub-basin in the Yukon. They found that the WATFLOOD algorithm out-performed the other baseflow algorithm, and that using RTE routing showed slighly better performance than WF_R. They also found that performance metrics improved when using a combined objective function compared to the Nash-Sutcliffe alone (Abdelhamed et al., 2018).

Yassin et al. (2019) developed a method for incorporating a reservoir operation model into the MESH model, called the dynamically zoned target release (DZTR) model. They found that this model improved streamflow prediction versus a no-reservoir case and as compared to other reservoir models, especially for reservoirs where the ratio of storage capacity to annual inflow volume is greater than 0.5 (Yassin et al., 2019). Anis, Razavi, & Wheater (2017) also tested the coupling of MESH with MODSIM-DSS, a tool for modelling water management, and found it improved the representation of water withdrawls from the Bow River, Canada, particularly for irrigation purposes.

Two alternatives to the CLASS and WATROF representations of runoff generation have been developed for the MESH model. PDMROF was developed by Mekonnen et al. (2014) to better represent the fill-and-spill process for prairie wetlands. The algorithm represents the spatial variation in pothole storage and resulting dynamic relationship between surface storage capacity and contributing area for direct runoff due using a probability density function. One drawback of the PDMROF algorithm is that it does not include interflow (Hossain et al., 2016). PDMROF was tested in a prairie basin in Saskatchewan, Canada by Mengistu and Spence (2016) and found to adequately represent the contributing area compared to contributing area mapping. LATFLOW, developed by Hosain (2017), incorporates principles from both WATROF and PDMROF by using the probability density function to represent variable surface storage capacity and contributing area, and the Richards’ equation to incorporate interflow (as in WATROF; Kouwen, 2014). The presentation by Hossain (2016) presents a clear conceptual representation of the difference between the CLASS, WATROF, PDMROF, and LATFLOW runoff algorithms.

Elshamy et al. (2019) outlined an approach for parameterizing and initializing areas where permafrost is present yet data is sparse. They found that a soil column depth of 50 m with the soil layer thickness increasing with depth as defined by a scaled power law was most suitable for stabilization of initial soil temperature and moisture conditions during spin-up (Elshamy et al., 2019). Spin-up considered a number of permafrost metrics for one hydrologic year for several iterations, and found that a quasi steady state was reached after 50-100 cycles. They found that the depth and composition of organic soil types as well as the depth to bedrock (SDEP) were important parameters that affected the thermal profile of the subsurface (Elshamy et al., 2019).

Represenatation of Spatial Variability

Since 2017, there has been little advancement in published literature regarding methods of representing spatial heterogeneity. However, in Haghnegahdar, Tolson, Craig, & Paya (2015), a quantitative methodology was proposed to compare the relative performance of different watershed discretization schemes. The general methodology was to vary the sub-grid complexity based on the number of grouped response units (GRUs) where the GRUs are selected by landcover-only or landcover and soil type, calibrate the configurations for a set period constrained by a select number of time budgets, and validate in neighbouring ungauged sub-basins. They found that good performance in the calibration basins is not an indication of performance in ungauged basins, increased model complexity does not always improve calibration results especially when the calibration runtime is limited due to computational budget, and calibration to a sub-period (i.e 1 year instead of 3 years) may provide comparible results at a fraction of the computational time (Haghnegahdar, Tolson, Craig, & Paya, 2015).

Objectives

In 2017, a Master’s of Water Security student at the University of Saskatchewan completed a project which explored the effect of different representations of spatial heterogeneity in the White Gull Creek watershed in Saskatchewan using the MESH model (Mkandla, 2017).

The objectives of the current project are:

1) In the Baker Creek Watershed (NWT), replicate the methodology used by Mkandla (2017) in the Whitegull Creek Watershed (SK) to evaluate the effect of complexity in the representation of spatial heterogeneity in the MESH model on model performance; and 2) Take the work further and explore additional model configuration options to explore their effects on model performance.

Summary of the Mkandla Project

The purpose of the Mkandla project was to compare the model performance under a number of different representations of sub-grid spatial variability in the MESH model. The model configurations ranged from relatively simple - considering areal-averaged forcing data and model parameters - to more complex setups which considered distributed forcing data and parameters.

The MESH model was used, and configurations were arranged as shown in Table 1.1 below - with the complexity of the model increasing from configuration 1 through configuration 6. These configurations differed by utilizing a uniform forcing dataset (average of two datasets) vs distributing two different forcing datasets by the 2 ecodistrics in the basin, by implementing a uniform parameter set over 1 or 2 GRUs (i.e. whole watershed or by ecodistric), varying the parameters within each GRU by ecodistric, or by distributing the parameters based on landcover type in each ecodistrict. Table 1.1 below, adapted from Mkandla, 2017, shows the differences between the configurations and whether the configuration methodology was used for the modelling of the Baker Creek watershed.

Table 1.1 - Summary of model configurations for the Mkandla experiment (Mkandla, 2017) and comparison with the Baker Creek modelling scenarios {width=60%}

The model was calibrated using OSTRICH software (Matott, 2017) using the Dynamically-Dimensioned Search (DDS) algorithm, General-purpose Constrained Optimization Platform (GCOP), and the Nash-Sutcliffe Efficiency (NSE, Nash & Sutcliffe, 1970) as the response variable. One hundred calibration trials were run for each configuration with 1000 iterations for each trial (Mkandla, 2017).

The findings from the MESH modelling of the White Gull Creek watershed were:

  • As the model complexity increased from configuration 1 through 4, so did the model performance during calibration, with a slight decrease in performance for configuration 5 and 6.
  • The model performance during validation increased steadily from configuration 1 through 6.
  • In all configurations, the NSE of the validation period was lower than that of the calibration period.
    • Therefore, model performance during calibration was not necessarily an indication of performance during validation.
  • The range of NSE values of the calibration runs generally decreased as the model complexity increased, with the exception of configuration 4 and 6, which saw a larger spread between the 25th and 75th percentiles of NSE values compared to scenarios 3 and 5, respectively.
  • The NSE values during both the calibration and validation periods for the best calibration run for configuration 1 and 2 were identical, highlighting the issue of equifinality (meaning different parameter sets can provide equally good solutions).
  • As the number of GRUs in the model increased, so did the model run time.
  • Configurations with uniform forcing data resulted in better performance during calibration, while configurations with distributed forcing data resulted in better performance during calibration (all other factors held constant) with minimal to no increase in run time.
  • Parameter identifiability (defined as those below a threshold of 0.3) improved between configurations 1-3 and configurations 4-5, but degraded for configuration 6.
  • The parameters below the identifiable threshold of 0.3 included saturated surface soil conductivity for configurations 1-3, minimum leaf-area index (LAI) for broadleaf trees in configuration 3, and minimum LAI, stream channel properties, percent clay in some soil layers, and saturated surface soil conductivity for configurations 4 and 5. Additionally, there were about 5 identifiable parameters in configuration 6.

This project will seek to compare the results of the White Gull Creek modelling with thoses obtained by modelling the Baker Creek Watershed.