Abstract. Wetland systems are among the largest stores of carbon on the planet, most biologically diverse of all ecosystems, and dominant controls of the hydrologic cycle. However, their representation in land surface models (LSMs), which are the terrestrial lower boundary of Earth system models (ESMs) that inform climate actions, is limited. Here, we explore different possible parametrizations to represent wetland-groundwater-upland interactions with varying levels of system and computational complexity. We perform a series of numerical experiments that are informed by field observations from wetlands in the well-instrumented White Gull Creek in Saskatchewan, in the boreal region of North America. We show that the typical representation of wetlands in LSMs, which ignores interactions with groundwater and uplands, can be inadequate. We show that the optimal level of model complexity depends on the land cover, soil type, and the ultimate modelling purpose, being nowcasting and prediction, scenario analysis, or diagnostic learning.

Abstract. Wetland systems are among the largest stores of carbon on the planet, most biologically diverse of all ecosystems, and dominant controls of the hydrologic cycle. However, their representation in land surface models (LSMs), which are the terrestrial lower boundary of Earth system models (ESMs) that inform climate actions, is limited. Here, we explore different possible parametrizations to represent wetland-groundwater-upland interactions with varying levels of system and computational complexity. We perform a series of numerical experiments that are informed by field observations from wetlands in the well-instrumented White Gull Creek in Saskatchewan, in the boreal region of North America. We show that the typical representation of wetlands in LSMs, which ignores interactions with groundwater and uplands, can be inadequate. We show that the optimal level of model complexity depends on the land cover, soil type, and the ultimate modelling purpose, being nowcasting and prediction, scenario analysis, or diagnostic learning.

Abstract. A simple numerical solution procedure – namely the method of lines combined with an off-the-shelf ordinary differential equation (ODE) solver – was shown in previous work to provide efficient, mass-conservative solutions to the pressure-head form of Richards' equation. We implement such a solution in our model openRE. We developed a novel method to quantify the boundary fluxes that reduce water balance errors without negative impacts on model runtimes – the solver flux output method (SFOM). We compare this solution with alternatives, including the classic modified Picard iteration method and the Hydrus 1D model. We reproduce a set of benchmark solutions with all models. We find that Celia's solution has the best water balance, but it can incur significant truncation errors in the simulated boundary fluxes, depending on the time steps used. Our solution has comparable runtimes to Hydrus and better water balance performance (though both models have excellent water balance closure for all the problems we considered). Our solution can be implemented in an interpreted language, such as MATLAB or Python, making use of off-the-shelf ODE solvers. We evaluated alternative SciPy ODE solvers that are available in Python and make practical recommendations about the best way to implement them for Richards' equation. There are two advantages of our approach: (i) the code is concise, making it ideal for teaching purposes; and (ii) the method can be easily extended to represent alternative properties (e.g., novel ways to parameterize the K(ψ) relationship) and processes (e.g., it is straightforward to couple heat or solute transport), making it ideal for testing alternative hypotheses.

Abstract. A simple numerical solution procedure – namely the method of lines combined with an off-the-shelf ordinary differential equation (ODE) solver – was shown in previous work to provide efficient, mass-conservative solutions to the pressure-head form of Richards' equation. We implement such a solution in our model openRE. We developed a novel method to quantify the boundary fluxes that reduce water balance errors without negative impacts on model runtimes – the solver flux output method (SFOM). We compare this solution with alternatives, including the classic modified Picard iteration method and the Hydrus 1D model. We reproduce a set of benchmark solutions with all models. We find that Celia's solution has the best water balance, but it can incur significant truncation errors in the simulated boundary fluxes, depending on the time steps used. Our solution has comparable runtimes to Hydrus and better water balance performance (though both models have excellent water balance closure for all the problems we considered). Our solution can be implemented in an interpreted language, such as MATLAB or Python, making use of off-the-shelf ODE solvers. We evaluated alternative SciPy ODE solvers that are available in Python and make practical recommendations about the best way to implement them for Richards' equation. There are two advantages of our approach: (i) the code is concise, making it ideal for teaching purposes; and (ii) the method can be easily extended to represent alternative properties (e.g., novel ways to parameterize the K(ψ) relationship) and processes (e.g., it is straightforward to couple heat or solute transport), making it ideal for testing alternative hypotheses.

Cold regions provide water resources for half the global population yet face rapid change. Their hydrology is dominated by snow, ice and frozen soils, and climate warming is having profound effects. Hydrological models have a key role in predicting changing water resources but are challenged in cold regions. Ground-based data to quantify meteorological forcing and constrain model parameterization are limited, while hydrological processes are complex, often controlled by phase change energetics. River flows are impacted by poorly quantified human activities. This paper discusses the scientific and technical challenges of the large-scale modelling of cold region systems and reports recent modelling developments, focussing on MESH, the Canadian community hydrological land surface scheme. New cold region process representations include improved blowing snow transport and sublimation, lateral land-surface flow, prairie pothole pond storage dynamics, frozen ground infiltration and thermodynamics, and improved glacier modelling. New algorithms to represent water management include multistage reservoir operation. Parameterization has been supported by field observations and remotely sensed data; new methods for parameter identification have been used to evaluate model uncertainty and support regionalization. Additionally, MESH has been linked to broader decision-support frameworks, including river ice simulation and hydrological forecasting. The paper also reports various applications to the Saskatchewan and Mackenzie River basins in western Canada (0.4 and 1.8 million km2). These basins arise in glaciated mountain headwaters, are partly underlain by permafrost, and include remote and incompletely understood forested, wetland, agricultural and tundra ecoregions. These illustrate the current capabilities and limitations of cold region modelling, and the extraordinary challenges to prediction, including the need to overcoming biases in forcing data sets, which can have disproportionate effects on the simulated hydrology.

Using data from five long-term field sites measuring soil moisture, we show the limitations of using soil moisture observations alone to constrain modelled hydrological fluxes. We test a land surface model, Modélisation Environnementale communautaire-Surface Hydrology/Canadian Land Surface Scheme, with two configurations: one where the soil hydraulic properties are determined using a pedotransfer function (the texture-based calibration) and one where they are assigned directly (the hydraulic properties-based calibration). The hydraulic properties-based calibration outperforms the texture-based calibration in terms of reproducing changes in soil moisture storage within a 1.6 m deep profile at each site, but both perform reasonably well, especially in the summer months. When the models are constrained using observations of changes in soil moisture, the predicted hydrological fluxes are subject to very large uncertainties associated with equifinality. The uncertainty is larger for the hydraulic properties-based calibration, even though the performance was better. We argue that since the pedotransfer functions constrain the model parameters in the texture-based calibrations in an unrealistic way, the texture-based calibration underestimates the uncertainty in the fluxes. We recommend that reproducing observed cumulative changes in soil moisture storage should be considered a necessary but insufficient criterion of model success. Additional sources of information are needed to reduce uncertainties, and these could include improved estimation of the soil hydraulic properties and direct observations of fluxes, particularly evapotranspiration.

Abstract The intent of this paper is to encourage improved numerical implementation of land models. Our contributions in this paper are two-fold. First, we present a unified framework to formulate and implement land model equations. We separate the representation of physical processes from their numerical solution, enabling the use of established robust numerical methods to solve the model equations. Second, we introduce a set of synthetic test cases (the laugh tests) to evaluate the numerical implementation of land models. The test cases include storage and transmission of water in soils, lateral sub-surface flow, coupled hydrological and thermodynamic processes in snow, and cryosuction processes in soil. We consider synthetic test cases as “laugh tests” for land models because they provide the most rudimentary test of model capabilities. The laugh tests presented in this paper are all solved with the Structure for Unifying Multiple Modeling Alternatives model (SUMMA) implemented using the SUite of Nonlinear and DIfferential/Algebraic equation Solvers (SUNDIALS). The numerical simulations from SUMMA/SUNDIALS are compared against (1) solutions to the synthetic test cases from other models documented in the peer-reviewed literature; (2) analytical solutions; and (3) observations made in laboratory experiments. In all cases, the numerical simulations are similar to the benchmarks, building confidence in the numerical model implementation. We posit that some land models may have difficulty in solving these benchmark problems. Dedicating more effort to solving synthetic test cases is critical in order to build confidence in the numerical implementation of land models.

Abstract The intent of this paper is to encourage improved numerical implementation of land models. Our contributions in this paper are two-fold. First, we present a unified framework to formulate and implement land model equations. We separate the representation of physical processes from their numerical solution, enabling the use of established robust numerical methods to solve the model equations. Second, we introduce a set of synthetic test cases (the laugh tests) to evaluate the numerical implementation of land models. The test cases include storage and transmission of water in soils, lateral sub-surface flow, coupled hydrological and thermodynamic processes in snow, and cryosuction processes in soil. We consider synthetic test cases as “laugh tests” for land models because they provide the most rudimentary test of model capabilities. The laugh tests presented in this paper are all solved with the Structure for Unifying Multiple Modeling Alternatives model (SUMMA) implemented using the SUite of Nonlinear and DIfferential/Algebraic equation Solvers (SUNDIALS). The numerical simulations from SUMMA/SUNDIALS are compared against (1) solutions to the synthetic test cases from other models documented in the peer-reviewed literature; (2) analytical solutions; and (3) observations made in laboratory experiments. In all cases, the numerical simulations are similar to the benchmarks, building confidence in the numerical model implementation. We posit that some land models may have difficulty in solving these benchmark problems. Dedicating more effort to solving synthetic test cases is critical in order to build confidence in the numerical implementation of land models.

Extensive wetland drainage has occurred across the Canadian Prairies, and drainage activities are ongoing in many areas (Dahl 1990; Watmough and Schmoll 2007; Bartzen et al. 2010; Dahl 2014; Prairi...

Extensive wetland drainage has occurred across the Canadian Prairies, and drainage activities are ongoing in many areas (Dahl 1990; Watmough and Schmoll 2007; Bartzen et al. 2010; Dahl 2014; Prairi...

Cold regions provide water resources for half the global population yet face rapid change. Their hydrology is dominated by snow, ice and frozen soils, and climate warming is having profound effects. Hydrological models have a key role in predicting changing water resources, but are challenged in cold regions. Ground-based data to quantify meteorological forcing and constrain model parameterization are limited, while hydrological processes are complex, often controlled by phase change energetics. River flows are impacted by poorly quantified human activities. This paper reports scientific developments over the past decade of MESH, the Canadian community hydrological land surface scheme. New cold region process representation includes improved blowing snow transport and sublimation, lateral land-surface flow, prairie pothole storage dynamics, frozen ground infiltration and thermodynamics, and improved glacier modelling. New algorithms to represent water management include multi-stage reservoir operation. Parameterization has been supported by field observations and remotely sensed data; new methods for parameter identification have been used to evaluate model uncertainty and support regionalization. Additionally, MESH has been linked to broader decision-support frameworks, including river ice simulation and hydrological forecasting. The paper also reports various applications to the Saskatchewan and Mackenzie River basins in western Canada (0.4 and 1.8 million km). These basins arise in glaciated mountain headwaters, are partly underlain by permafrost, and include remote and incompletely understood forested, wetland, agricultural and tundra ecoregions. This imposes extraordinary challenges to prediction, including the need to overcoming biases in forcing data sets, which can have disproportionate effects on the simulated hydrology.

Cold regions provide water resources for half the global population yet face rapid change. Their hydrology is dominated by snow, ice and frozen soils, and climate warming is having profound effects. Hydrological models have a key role in predicting changing water resources, but are challenged in cold regions. Ground-based data to quantify meteorological forcing and constrain model parameterization are limited, while hydrological processes are complex, often controlled by phase change energetics. River flows are impacted by poorly quantified human activities. This paper reports scientific developments over the past decade of MESH, the Canadian community hydrological land surface scheme. New cold region process representation includes improved blowing snow transport and sublimation, lateral land-surface flow, prairie pothole storage dynamics, frozen ground infiltration and thermodynamics, and improved glacier modelling. New algorithms to represent water management include multi-stage reservoir operation. Parameterization has been supported by field observations and remotely sensed data; new methods for parameter identification have been used to evaluate model uncertainty and support regionalization. Additionally, MESH has been linked to broader decision-support frameworks, including river ice simulation and hydrological forecasting. The paper also reports various applications to the Saskatchewan and Mackenzie River basins in western Canada (0.4 and 1.8 million km). These basins arise in glaciated mountain headwaters, are partly underlain by permafrost, and include remote and incompletely understood forested, wetland, agricultural and tundra ecoregions. This imposes extraordinary challenges to prediction, including the need to overcoming biases in forcing data sets, which can have disproportionate effects on the simulated hydrology.

The phenomenon of freezing point depression in frozen soils results in the co-existence of ice and liquid water in soil pores at temperatures below 273.15 K (0°C), and is thought to have two causes: (a) capillary and adsorption effects, where the phase transition relationship is modified due to soil-air-water-ice interactions, and (b) solute effects, where the presence of salts lowers the freezing temperature. The soil freezing characteristic curve (SFC) characterizes the relationship between liquid water content and temperature in frozen soils. Most hydrological models represent the SFC using only capillary and adsorption effects with a relationship known as the Generalized Clapeyron Equation (GCE). In this study, we develop and test a salt exclusion model for characterizing the SFC, comparing this with the GCE-based model and a combined salt-GCE effect model. We test these models against measured SFCs in laboratory and field experiments with diverse soil textures and salinities. We consistently found that the GCE-based models under-predicted freezing-point depression. We were able to match the observations with the salt exclusion model and the combined model, suggesting that salinity is a dominant control on the SFC in real soils that always contain solutes. In modeling applications where the salinity is unknown, the soil bulk solute concentration can be treated as a single fitting parameter. Improved characterization of the SFC may result in improvements in coupled mass-heat transport models for simulating hydrological processes in cold regions, particularly the hydraulic properties of frozen soils and the hydraulic head in frozen soils that drives cryosuction.

The phenomenon of freezing point depression in frozen soils results in the co-existence of ice and liquid water in soil pores at temperatures below 273.15 K (0°C), and is thought to have two causes: (a) capillary and adsorption effects, where the phase transition relationship is modified due to soil-air-water-ice interactions, and (b) solute effects, where the presence of salts lowers the freezing temperature. The soil freezing characteristic curve (SFC) characterizes the relationship between liquid water content and temperature in frozen soils. Most hydrological models represent the SFC using only capillary and adsorption effects with a relationship known as the Generalized Clapeyron Equation (GCE). In this study, we develop and test a salt exclusion model for characterizing the SFC, comparing this with the GCE-based model and a combined salt-GCE effect model. We test these models against measured SFCs in laboratory and field experiments with diverse soil textures and salinities. We consistently found that the GCE-based models under-predicted freezing-point depression. We were able to match the observations with the salt exclusion model and the combined model, suggesting that salinity is a dominant control on the SFC in real soils that always contain solutes. In modeling applications where the salinity is unknown, the soil bulk solute concentration can be treated as a single fitting parameter. Improved characterization of the SFC may result in improvements in coupled mass-heat transport models for simulating hydrological processes in cold regions, particularly the hydraulic properties of frozen soils and the hydraulic head in frozen soils that drives cryosuction.

Abstract. The interior of western Canada, like many similar cold mid- to high-latitude regions worldwide, is undergoing extensive and rapid climate and environmental change, which may accelerate in the coming decades. Understanding and predicting changes in coupled climate–land–hydrological systems are crucial to society yet limited by lack of understanding of changes in cold-region process responses and interactions, along with their representation in most current-generation land-surface and hydrological models. It is essential to consider the underlying processes and base predictive models on the proper physics, especially under conditions of non-stationarity where the past is no longer a reliable guide to the future and system trajectories can be unexpected. These challenges were forefront in the recently completed Changing Cold Regions Network (CCRN), which assembled and focused a wide range of multi-disciplinary expertise to improve the understanding, diagnosis, and prediction of change over the cold interior of western Canada. CCRN advanced knowledge of fundamental cold-region ecological and hydrological processes through observation and experimentation across a network of highly instrumented research basins and other sites. Significant efforts were made to improve the functionality and process representation, based on this improved understanding, within the fine-scale Cold Regions Hydrological Modelling (CRHM) platform and the large-scale Modélisation Environmentale Communautaire (MEC) – Surface and Hydrology (MESH) model. These models were, and continue to be, applied under past and projected future climates and under current and expected future land and vegetation cover configurations to diagnose historical change and predict possible future hydrological responses. This second of two articles synthesizes the nature and understanding of cold-region processes and Earth system responses to future climate, as advanced by CCRN. These include changing precipitation and moisture feedbacks to the atmosphere; altered snow regimes, changing balance of snowfall and rainfall, and glacier loss; vegetation responses to climate and the loss of ecosystem resilience to wildfire and disturbance; thawing permafrost and its influence on landscapes and hydrology; groundwater storage and cycling and its connections to surface water; and stream and river discharge as influenced by the various drivers of hydrological change. Collective insights, expert elicitation, and model application are used to provide a synthesis of this change over the CCRN region for the late 21st century.

Abstract. The interior of western Canada, like many similar cold mid- to high-latitude regions worldwide, is undergoing extensive and rapid climate and environmental change, which may accelerate in the coming decades. Understanding and predicting changes in coupled climate–land–hydrological systems are crucial to society yet limited by lack of understanding of changes in cold-region process responses and interactions, along with their representation in most current-generation land-surface and hydrological models. It is essential to consider the underlying processes and base predictive models on the proper physics, especially under conditions of non-stationarity where the past is no longer a reliable guide to the future and system trajectories can be unexpected. These challenges were forefront in the recently completed Changing Cold Regions Network (CCRN), which assembled and focused a wide range of multi-disciplinary expertise to improve the understanding, diagnosis, and prediction of change over the cold interior of western Canada. CCRN advanced knowledge of fundamental cold-region ecological and hydrological processes through observation and experimentation across a network of highly instrumented research basins and other sites. Significant efforts were made to improve the functionality and process representation, based on this improved understanding, within the fine-scale Cold Regions Hydrological Modelling (CRHM) platform and the large-scale Modélisation Environmentale Communautaire (MEC) – Surface and Hydrology (MESH) model. These models were, and continue to be, applied under past and projected future climates and under current and expected future land and vegetation cover configurations to diagnose historical change and predict possible future hydrological responses. This second of two articles synthesizes the nature and understanding of cold-region processes and Earth system responses to future climate, as advanced by CCRN. These include changing precipitation and moisture feedbacks to the atmosphere; altered snow regimes, changing balance of snowfall and rainfall, and glacier loss; vegetation responses to climate and the loss of ecosystem resilience to wildfire and disturbance; thawing permafrost and its influence on landscapes and hydrology; groundwater storage and cycling and its connections to surface water; and stream and river discharge as influenced by the various drivers of hydrological change. Collective insights, expert elicitation, and model application are used to provide a synthesis of this change over the CCRN region for the late 21st century.

Abstract. Shallow groundwater in the Prairie Pothole Region (PPR) is predominantly recharged by snowmelt in the spring and supplies water for evapotranspiration through the summer and fall. This two-way exchange is underrepresented in current land surface models. Furthermore, the impacts of climate change on the groundwater recharge rates are uncertain. In this paper, we use a coupled land–groundwater model to investigate the hydrological cycle of shallow groundwater in the PPR and study its response to climate change at the end of the 21st century. The results show that the model does a reasonably good job of simulating the timing of recharge. The mean water table depth (WTD) is well simulated, except for the fact that the model predicts a deep WTD in northwestern Alberta. The most significant change under future climate conditions occurs in the winter, when warmer temperatures change the rain/snow partitioning, delaying the time for snow accumulation/soil freezing while advancing early melting/thawing. Such changes lead to an earlier start to a longer recharge season but with lower recharge rates. Different signals are shown in the eastern and western PPR in the future summer, with reduced precipitation and drier soils in the east but little change in the west. The annual recharge increased by 25 % and 50 % in the eastern and western PPR, respectively. Additionally, we found that the mean and seasonal variation of the simulated WTD are sensitive to soil properties; thus, fine-scale soil information is needed to improve groundwater simulation on the regional scale.

The exchanges of water, energy and carbon between the land surface and the atmosphere are tightly coupled, so that errors in simulating evapotranspiration lead to errors in simulating both the water and carbon balances. Areas with seasonally frozen soils present a particular challenge due to the snowmelt‐dominated hydrology and the impact of soil freezing on the soil hydraulic properties and plant root water uptake. Land surface schemes that have been applied in high latitudes often have reported problems with simulating the snowpack and runoff. Models applied at the Boreal Ecosystem Research and Monitoring Sites in central Saskatchewan have consistently over‐predicted evapotranspiration as compared with flux tower estimates. We assessed the performance of two Canadian land surface schemes (CLASS and CLASS‐CTEM) for simulating point‐scale evapotranspiration at an instrumented jack pine sandy upland site in the southern edge of the boreal forest in Saskatchewan, Canada. Consistent with past reported results, these models over‐predicted evapotranspiration, as compared with flux tower observations, but only in the spring period. Looking systematically at soil properties and vegetation characteristics, we found that the dominant control on evapotranspiration within these models was the canopy conductance. However, the problem of excessive spring ET could not be solved satisfactorily by changing the soil or vegetation parameters. The model overestimation of spring ET coincided with the overestimation of spring soil liquid water content. Improved algorithms for the infiltration of snowmelt into frozen soils and plant‐water uptake during the snowmelt and soil thaw periods may be key to addressing the biases in spring ET.