A smoothed cap model for variably saturated soils and its robust numerical implementation

This paper deals with the numerical implementation of a cap model for unsaturated soils. It provides a brief review of existing cap model approaches, based on which an improved model formulated in terms of generalised effective stress and matric suction is derived and described in detail. Although the proposed model is a multisurface plasticity model, it can efficiently be implemented using only single‐surface projections because of the smoothness of the model, which is obtained by construction. Numerical algorithms are provided for these single‐surface stress projections, using a single‐equation approach whenever possible. The robustness of the utilised single‐equation approaches is enhanced by proposing problem‐fitted start‐up procedures based on investigations of the nonlinear projection equations. A comparison of the model response with extensive material test data is used to validate the model and to demonstrate the robust application of the approach to silty sands and low to medium plasticity clays. Copyright © 2015 John Wiley & Sons, Ltd.     

Integrating isolated and riparian wetland modules in the PHYSITEL/HYDROTEL modelling platform: model performance and diagnosis

Mathematical modelling is a well‐accepted framework to evaluate the effects of wetlands on stream flow and watershed hydrology in general. Although the integration of wetland modules into a distributed hydrological model represents a cost‐effective way to make this assessment, the added value brought by landscape‐specific modules to a model's ability to replicate basic hydrograph characteristics remains unclear. The objectives of this paper were the following: (i) to present the adaptation of PHYSITEL (a geographic information system) to parameterize isolated and riparian wetlands; (ii) to describe the integration of specific isolated wetland and riparian wetland modules into HYDROTEL, a distributed hydrological model; and (iii) to evaluate the performance of the updated modelling platform with respect to the capacity of replicating various hydrograph characteristics. To achieve this, two sets of simulations were performed (with and without wetland modules), and the added value was assessed at three river segments of the Becancour River watershed, Quebec, Canada, using six general goodness‐of‐fit indicators and 14 water flow criteria. A sensitivity analysis of the wetland module parameters was performed to characterize their impact on stream flows of the modelled watershed. Results of this study indicate the following: (i) integration of specific wetland modules can slightly increase the capacity of HYDROTEL to replicate basic hydrograph characteristics; and (ii) the updated modelling platform allows for the explicit assessment of the impact of wetlands (e.g. typology and location) on watershed hydrology. Copyright © 2015 John Wiley & Sons, Ltd.     

Watershed delineation using hydrographic features and a DEM in plain river network region

Watershed delineation is a required step when conducting any spatially distributed hydrological modelling. Automated approaches are often proposed to delineate a watershed based on a river network extracted from the digital elevation model (DEM) using the deterministic eight‐neighbour (D8) method. However, a realistic river network cannot be derived from conventional DEM processing methods for a large flat area with a complex network of rivers, lakes, reservoirs, and polders, referred to as a plain river network region (PRNR). In this study, a new approach, which uses both hydrographic features and DEM, has been developed to address the problems of watershed delineation in PRNR. It extracts the river nodes and determines the flow directions of the river network based on a vector‐based hydrographic feature data model. The river network, lakes, reservoirs, and polders are then used to modify the flow directions of grid cells determined by D8 approach. The watershed is eventually delineated into four types of catchments including lakes, reservoirs, polders, and overland catchments based on the flow direction matrix and the location of river nodes. Multiple flow directions of grid cells are represented using a multi‐direction encoding method, and multiple outflows of catchments are also reflected in the topology of catchments. The proposed approach is applied to the western Taihu watershed in China. Comparisons between the results obtained from the D8 approach, the ‘stream burning’ approach, and those from the proposed approach clearly demonstrate an improvement of the new approach over the conventional approaches. This approach will benefit the development of distributed hydrological models in PRNR for the consideration of different types and multiple inlets and outlets of catchments. Copyright © 2015 John Wiley & Sons, Ltd.     

Improved spatial delineation of streambed properties and water fluxes using distributed temperature sensing

A new method was developed for analysing and delineating streambed water fluxes, flow conditions and hydraulic properties using coiled fibre‐optic distributed temperature sensing or closely spaced discrete temperature sensors. This method allows for a thorough treatment of the spatial information embedded in temperature data by creating a matrix visualization of all possible sensor pairs. Application of the method to a 5‐day field dataset reveals the complexity of shallow streambed thermal regimes. To understand how velocity estimates are affected by violations of assumptions of one‐dimensional, saturated, homogeneous flow and to aid in the interpretation of field observations, the method was also applied to temperature data generated by numerical models of common field conditions: horizontal layering, presence of lateral flow and variable streambed saturation. The results show that each condition creates a distinct signature visible in the triangular matrices. The matrices are used to perform a comparison of the behaviour of one‐dimensional analytical heat‐tracing models. The results show that the amplitude ratio‐based method of velocity calculation leads to the most reliable estimates. The minimum sensor spacing required to obtain reliable velocity estimates with discrete sensors is also investigated using field data. The developed method will aid future heat‐tracing studies by providing a technique for visualizing and comparing results from fibre‐optic distributed temperature sensing installations and testing the robustness of analytical heat‐tracing models. Copyright © 2016 John Wiley & Sons, Ltd.     

Calibration of paired watersheds: Utility of moving sums in presence of externalities

Historically, paired watershed studies have been used to quantify the hydrological effects of land use and management practices by concurrently monitoring 2 similar watersheds during calibration (pretreatment) and post‐treatment periods. This study characterizes seasonal water table and flow response to rainfall during the calibration period and tests a change detection technique of moving sums of recursive residuals (MOSUM) to select calibration periods for each control–treatment watershed pair when the regression coefficients for daily water table elevation were most stable to minimize regression model uncertainty. The control and treatment watersheds were 1 watershed of 3–4‐year‐old intensely managed loblolly pine (Pinus taeda L.) with natural understory, 1 watershed of 3–4‐year‐old loblolly pine intercropped with switchgrass (Panicum virgatum), 1 watershed of 14–15‐year‐old thinned loblolly pine with natural understory (control), and 1 watershed of switchgrass only. The study period spanned from 2009 to 2012. Silvicultural operational practices during this period acted as external factors, potentially shifting hydrologic calibration relationships between control and treatment watersheds. MOSUM results indicated significant changes in regression parameters due to silvicultural operations and were used to identify stable relationships for water table elevation. None of the calibration relationships developed using this method were significantly different from the classical calibration relationship based on published historical data. We attribute that to the similarity of historical and 2010–2012 leaf area index on control and treatment watersheds as moderated by the emergent vegetation. Although the MOSUM approach does not eliminate the need for true calibration data or replace the classic paired watershed approach, our results show that it may be an effective alternative approach when true data are unavailable, as it minimizes the impacts of external disturbances other than the treatment of interest.     

Short‐ and long‐term evapotranspiration rates at ecological restoration sites along a large river receiving rare flow events

Many large rivers around the world no longer flow to their deltas, due to ever greater water withdrawals and diversions for human needs. However, the importance of riparian ecosystems is drawing increasing recognition, leading to the allocation of environmental flows to restore river processes. Accurate estimates of riparian plant evapotranspiration (ET) are needed to understand how the riverine system responds to these rare events and achieve the goals of environmental flows. In 2014, historic environmental flows were released into the Lower Colorado River at Morelos Dam (Mexico); this once perennial but now dry reach is the final stretch to the mighty Colorado River Delta. One of the primary goals was to supply native vegetation restoration sites along the reach with water to help seedlings establish and boost groundwater levels to foster the planted saplings. Patterns in ET before, during, and after the flows are useful for evaluating whether this goal was met and understanding the role that ET plays in this now ephemeral river system. Here, diurnal fluctuations in groundwater levels and Moderate Resolution Imaging Spectroradiometer (MODIS) data were used to compare estimates of ET specifically at 3 native vegetation restoration sites during 2014 planned flow events, and MODIS data were used to evaluate long‐term (2002–2016) ET responses to restoration efforts at these sites. Overall, ET was generally 0–10 mm d^?1 across sites, and although daily ET values from groundwater data were highly variable, weekly averaged estimates were highly correlated with MODIS‐derived estimates at most sites. The influence of the 2014 flow events was not immediately apparent in the results, although the process of clearing vegetation and planting native vegetation at the restoration sites was clearly visible in the results.     

Analysis of snowpack dynamics during the spring melt season for a sub‐alpine site using point measurements and numerical modeling

Snowpack dynamics through October 2014–June 2017 were described for a forested, sub‐alpine field site in southeastern Wyoming. Point measurements of wetness and density were combined with numerical modeling and continuous time series of snow depth, snow temperature, and snowpack outflow to identify 5 major classes of distinct snowpack conditions. Class (i) is characterized by no snowpack outflow and variable average snowpack temperature and density. Class (ii) is characterized by short durations of liquid water in the upper snowpack, snowpack outflow values of 0.0008–0.005 cm hr^?1, an increase in snowpack temperature, and average snow density between 0.25–0.35 g cm^?3. Class (iii) is characterized by a partially saturated wetness profile, snowpack outflow values of 0.005–0.25 cm hr^?1, snowpack temperature near 0 °C, and average snow density between 0.25–0.40 g cm^?3. Class (iv) is characterized by strong diurnal snowpack outflow pattern with values as high as 0.75 cm hr^?1, stable snowpack temperature near 0 °C, and stable average snow density between 0.35–0.45 g cm^?3. Class (v) occurs intermittently between Classes (ii)–(iv) and displays low snowpack outflow values between 0.0008–0.04 cm hr^?1, a slight decrease in temperature relative to the preceding class, and similar densities to the preceding class. Numerical modeling of snowpack properties with SNOWPACK using both the Storage Threshold scheme and Richards' equation was used to quantify the effect of snowpack capillarity on predictions of snowpack outflow and other snowpack properties. Results indicate that both simulations are able to predict snow depth, snow temperature, and snow density reasonably well with little difference between the 2 water transport schemes. Richards' equation more accurately simulates the timing of snowpack outflow over the Storage Threshold scheme, especially early in the melt season and at diurnal timescales.     

Efficient DEM‐based overland flow routing using integrated recursive algorithms

Two primary concerns in performing watershed overland flow routing are the numerical instability and computational efficiency. The stability of executing an explicit scheme has to be maintained by observing the Courant–Friedrich–Lewy criterion, which is adopted to confirm that the numerical marching speed is larger than the wave celerity. Moreover, there is another criterion of time step devised in previous studies to avoid back‐and‐forth refluxing between adjacent grids. The situation of refluxing usually occurs on flat regions. In light of this, the selection of a small time increment to honor both restrictions simultaneously is believed to decrease the computational efficiency in performing overland flow routing. This study aims at creating a robust algorithm to relax both restrictions. The proposed algorithm was first implemented on a one‐dimensional overland plane to evaluate the accuracy of the numerical result by comparing it with an analytical solution. Then, the algorithm was further applied to a watershed for 2D runoff simulations. The results show that the proposed integrated algorithm can provide an accurate runoff simulation and achieve satisfactory performance in terms of computational speed.     

An analytical study on three‐dimensional versus two‐dimensional water table‐induced flow patterns in a Tóthian basin

Although it has been increasingly acknowledged that groundwater flow pattern is complicated in the three‐dimensional (3‐D) domain, two‐dimensional (2‐D) water table‐induced flow models are still widely used to delineate basin‐scale groundwater circulation. However, the validity of 2‐D cross‐sectional flow field induced by water table has been seldom examined. Here, we derive the analytical solution of 3‐D water table‐induced hydraulic head in a Tóthian basin and then examine the validity of 2‐D cross‐sectional models by comparing the flow fields of selected cross sections calculated by the 2‐D cross‐sectional model with those by the 3‐D model, which represents the “true” cases. For cross sections in the recharge or discharge area of the 3‐D basin, even if head difference is not significant, the 2‐D cross‐sectional models result in flow patterns absolutely different from the true ones. For the cross section following the principal direction of groundwater flow, although 2‐D cross‐sectional models would overestimate the penetrating depth of local flow systems and underestimate the recharge/discharge flux, the flow pattern from the cross‐sectional model is similar to the true one and could be close enough to the true one by adjusting the decay exponent and anisotropy ratio of permeability. Consequently, to determine whether a 2‐D cross‐sectional model is applicable, a comparison of hydraulic head difference between 2‐D and 3‐D solutions is not enough. Instead, the similarity of flow pattern should be considered to determine whether a cross‐sectional model is applicable. This study improves understanding of groundwater flow induced by more natural water table undulations in the 3‐D domain and the limitations of 2‐D models accounting for cross‐sectional water table undulation only.