Considering that past climate changes have significantly impacted groundwater resources, quantitative predictions of climate change effects on groundwater recharge may be valuable for effective management of future water resources. This study used 16 global climate models (GCMs) and three global warming scenarios to investigate changes in groundwater recharge rates for a 2050 climate relative to a 1990 climate in the US High Plains region. Groundwater recharge was modeled using the Soil-Vegetation-Atmosphere-Transfer model WAVES for a variety of soil and vegetation types representative of the High Plains. The median projection under a 2050 climate includes increased recharge in the Northern High Plains (+8%), a slight decrease in the Central High Plains (-3%) and a larger decrease in the Southern High Plains (-10%), amplifying the current spatial trend in recharge from north to south. There is considerable uncertainty in both the magnitude and direction of these changes in recharge projections. Predicted changes in recharge between dry and wet future climate scenarios encompass both an increase and decrease in recharge rates, with the magnitude of this range greater than 50% of current recharge. On a proportional basis, sensitivity of recharge to changes in rainfall indicates that areas with high current recharge rates are least sensitive to change in rainfall and vice versa. Sensitivity analyses indicate an amplification of change in recharge compared to change in rainfall, this amplification is in the range of 1 to 6 with an average of 2.5 to 3.5 depending upon the global warming scenario.
The objective of this paper is to analyze the improvement in the performance of the particle filter by including a resample-move step or by using a modified Gaussian particle filter. Specifically, the standard particle filter structure is altered by the inclusion of the Markov chain Monte Carlo move step. The second choice adopted in this study uses the moments of an ensemble Kalman filter analysis to define the importance density function within the Gaussian particle filter structure. Both variants of the standard particle filter are used in the assimilation of densely sampled discharge records into a conceptual rainfall-runoff model.
The results indicate that the inclusion of the resample-move step in the standard particle filter and the use of an optimal importance density function in the Gaussian particle filter improves the effectiveness of particle filters. Moreover, an optimization of the forecast ensemble used in this study, allowed for a better performance of the modified Gaussian particle filter compared to the particle filter with resample-move step.
The operation of large-scale water resources systems often involves several conflicting and non-commensurable objectives. The full characterization of tradeoffs among them is a necessary step to inform and support decisions in the absence of a unique optimal solution. In this context, the common approach is to consider many singleobjective problems, resulting from different combinations of the original problem objectives, each one solved using standard optimization methods based on mathematical programming. This scalarization process is computationally very demanding as it requires one optimization run for each trade-off and often results in very sparse and poorly informative representations of the Pareto frontier. More recently, bio-inspired methods have been applied to compute an approximation of the Pareto frontier in one single run. These methods allow to acceptably cover the full extent of the Pareto frontier with a reasonable computational effort. Yet, the quality of the policy obtained might be strongly dependent on the algorithm tuning and preconditioning. In this paper we propose a novel multiobjective Reinforcement Learning algorithm that combines the advantages of the above two approaches and alleviates some of their drawbacks. The proposed algorithm is an extension of fitted Q-iteration (FQI) that enables to learn the operating policies for all the linear combinations of preferences (weights) assigned to the objectives in a single training process. The key idea of multiobjective FQI (MOFQI) is to enlarge the continuous approximation of the value function, that is performed by singleobjective FQI over the state-decision space, also to the weight space. The approach is demonstrated on a real-world case study concerning the optimal operation of the HoaBinh reservoir on the Da river, Vietnam. MOFQI is compared with the reiterated use of FQI and a multiobjective parameterization-simulation-optimization (MOPSO) approach. Results show that MOFQI provides a continuous approximation of the Pareto front with comparable accuracy as the reiterated use of FQI. MOFQI outperforms MOPSO when no a priori knowledge on the operating policy shape is available, while produces slightly less accurate solutions when MOPSO can exploit such knowledge.
Accurate estimates of water losses by evaporation from shallow water tables are important for hydrological, agricultural, and climatic purposes. An experiment was conducted in a weighing lysimeter to characterize the diurnal dynamics of evaporation under natural conditions. Sampling revealed a completely dry surface sand layer after five days of evaporation. Its thickness was < 1 cm early in the morning, increasing to reach 4-5 cm in the evening. This evidence points out fundamental limitations of the approaches that assume hydraulic connectivity from the water table up to the surface, as well as those that suppose monotonic drying when unsteady conditions prevail. The computed vapor phase diffusion rates from the apparent drying front based on Fick's law failed to reproduce the measured cumulative evaporation during the sampling day. We propose that two processes rule natural evaporation resulting from daily fluctuations of climatic variables: (i) evaporation of water, stored during nighttime due to redistribution and vapor condensation, directly into the atmosphere from the soil surface during the early morning hours, that could be simulated using a mass transfer approach, and (ii) subsurface evaporation limited by Fickian diffusion, afterwards. For the conditions prevailing during the sampling day, the amount of water stored at the vicinity of the soil surface was 0.3 mm and was depleted before 11.00 AM. Combining evaporation from the surface before 11.00 AM and subsurface evaporation limited by Fickian diffusion after that time, the agreement between the estimated and measured cumulative evaporation was significantly improved.
Identifying the sources of continental precipitation has received increasing attention in recent years. With the use of various numerical methods, sources of precipitation have been identified from local to global scales. In this paper we identify the oceanic sources based on an atmospheric backtracking analysis of continental precipitation. We find that the strongest source areas are located close to the continents. In general, we define an oceanic area as a significant source when on average more than 20% of the total evaporation, and at least 250 mm/year of evaporation ends up as continental precipitation. We grouped these identified source areas into 15 regions and performed a forward tracking analysis of oceanic evaporation. We identified the areas on the adjacent continents that receive this oceanic moisture and whether this is nearby or remote. Moreover, we showed how the oceanic sources vary over the year in time and space. Furthermore, we correlated sea surface temperatures in the 15 source regions and the Niño 3.4 region with precipitation on all continents. For South America, we found that the El Niño Southern Oscillation (altering wind patterns) has a larger effect on precipitation than local sea surface temperatures. For West Africa, however, we show that sea surface temperature in the source regions is strongly correlated with precipitation in the rainy season. In Australia, both local sea surface temperature as well as the Niño 3.4 region appears to have a big influence on precipitation. As such this research provides new insight in the ocean-atmosphere-land coupling, which can be useful for studying seasonal weather predictions as well as climate change impact.
This paper presents a combinatorial approach for improving spatial predictions. First, copulas are used to interpolate a spatially distributed point rainfall field to a uniform spatial grid. It is observed that results vary substantially depending on the parameters chosen for interpolation leading to the hypothesis that it may be advantageous to estimate copula parameters locally or to combine local and global copula predictions. It is found that by modifying the method of forecast combinations [Bates and Granger, 1969], prediction errors in the spatial interpolation of rainfall can be reduced. Although this method of combining predictions is applied in the context of rainfall interpolation using local and global copula predictions, it can be used on other spatial variables and interpolation methods.
Effective sampling of hydrogeological systems is essential in guiding groundwater management practices. Optimal sampling of groundwater systems has previously been formulated based on the assumption that heterogeneous subsurface properties can be modeled using a geostatistical approach. Therefore, the monitoring schemes have been developed to concurrently minimize the uncertainty in the spatial distribution of systems states and parameters, such as the hydraulic conductivity K and the hydraulic head H, and the uncertainty in the geostatistical model of system parameter using a single objective function that aggregates all objectives. However, it has been shown that the aggregation of possibly conflicting objective functions is sensitive to the adopted aggregation scheme, and may lead to distorted results. In addition, the uncertainties in geostatistical parameters affect the uncertainty in the spatial prediction of K and H according to a complex nonlinear relationship, which has often been ineffectively evaluated using a first order approximation. In this study, we propose a multi-objective optimization framework to assist the design of monitoring networks of K and H with the goal of optimizing their spatial predictions and estimating the geostatistical parameters of the K field. The framework stems from the combination of a data assimilation (DA) algorithm and a multi-objective evolutionary algorithm (MOEA). The DA algorithm is based on the Ensemble Kalman Filter (EnKF), a Monte Carlo-based Bayesian update scheme for nonlinear systems, which is employed to approximate the posterior uncertainty in K, H, and the geostatistical parameters of K obtained by collecting new measurements. Multiple MOEA experiments are used to investigate the tradeoff among design objectives and identify the corresponding monitoring schemes. The methodology is applied to design a sampling network for a shallow unconfined groundwater system located in Rocky Ford, Colorado. Results indicate that the effect of uncertainties associated with the geostatistical parameters on the spatial prediction might be significantly alleviated (by up to 80% of the prior uncertainty in K and by 90% of the prior uncertainty in H) by sampling evenly distributed measurements with a spatial measurement density of more than 1 observation per 60 m × 60 m grid-block. In addition, exploration of the interaction of objective functions indicates that the ability of head measurements to reduce the uncertainty associated with the correlation scale is comparable to the effect of hydraulic conductivity measurements.
Buoyancy driven hydrodynamic instabilities of a miscible reactive interface in a homogeneous porous medium is examined. A bimolecular chemical reaction (A+B → C) is triggered at the interface between two reactant solutions A and B resulting in a chemical product solution C with different density and the viscosity from those of the reactants. The effects of the chemical reaction and a transverse flow parallel to the initial interface between the reactants are numerically analyzed. It was found that as a result of the transverse flow, fingers with sharp concentration gradients tend to develop and advance fast downward leading to higher rates of chemical production. Furthermore, a detailed analysis of the finger growth and the effects of buoyancy, transverse flow and chemical reaction allowed to reach a physical interpretation of the trends observed. Finally, a special tuning of the transverse velocity is proposed to ensure maximum or minimum chemical production applicable to subsurface flows.
In lowland karst areas of Ireland topographic depressions which get intermittently flooded on an annual cycle via groundwater sources are termed turloughs. These are sites of high ecological interest as they have communities and substrate characteristic of wetlands. The flooding in many turlough basins is due to insufficient capacity of the underground karst system to take increased flows following excessive precipitation events, causing the conduit-type network to surcharge. Continuous water level measurements have been taken in five linked turloughs in the lowland karst area of south Galway over a three year period. These water level fluctuations, in conjunction with river inputs and precipitation, were then used to elucidate the hydrogeological controls forming the hydraulic system beneath the ground. A model of the karst network has been developed using a pipe network model with the turloughs represented as ponds. The contribution to the karst network from diffuse flow through the epikarst via the matrix and fracture flow has also been modelled using a combination of an infiltration module and network of permeable pipes. The final model was calibrated against two separate hydrological years and in general provided a good simulation for all of the turloughs water levels particularly for the year with one main filling event. The model also accurately picked up the tidal response observed in these turloughs at shallow depths. The model has been used to predict the groundwater discharge to the coast via the main spring which had not heretofore been possible to measure, being below the sea level.
 The examination of hypoxia in the hypolimnion of large lakes traditionally focuses on the assessment of its spatial and temporal extent and its effect on water quality. In Lake Erie, hypoxia typically occurs between July and October in the central basin; however, there is considerable interannual variability both spatially and temporally. The processes driving this interannual variability as well as the small-scale time variation in oxygen depletion (e.g., −0.7 to +0.3 mg L−1 d−1) were examined in a field study conducted in the western part of the central basin of Lake Erie in 2008 and 2009. Data were obtained from a spatial array of moorings as well as sampling cruises that examined the physical and biological conditions needed to investigate the dynamics of the oxygen depletion and create a vertical oxygen budget. The flux of oxygen through the thermocline to the hypolimnion was a significant source of oxygen equivalent to ∼18% of the total oxygen depletion in the hypolimnion over the stratified period. The total oxygen depletion in the hypolimnion was due to equivalent amounts of hypolimnetic oxygen demand due to respiration in the water column and flux of oxygen to the bottom due to sediment oxygen demand. This latter finding was strongly dependent on hypolimnion thickness in Lake Erie, which also appeared to be an important parameter driving the rate of oxygen depletion by controlling the vertical volumetric fluxes and hence the competition between vertical flux and community respiration in the hypolimnion of shallow lakes.
 A generalized Boussinesq equation, the porous medium equation, was analyzed for a semi-infinite initially dry unconfined aquifer. The boundary conditions were a power-law head condition at the inlet boundary and a zero-head condition at infinity. Quadratic and cubic polynomial approximate solutions to the equation were derived. These approximate solutions replicate known exact solutions of the Boussinesq and porous medium equations. The approximate solutions were also compared to numerical solutions of the generalized Boussinesq equation computed using a method of Shampine. It was found that the solutions are easy to use and they have sufficient accuracy to be useful in practical applications, such as when the hydraulic conductivity is a power-law function of elevation.
 In subsurface aquifers, dispersion of contaminant, or tracer, is mainly driven by spatial fluctuations in the flow field caused by heterogeneity of the hydraulic conductivity. Measurements of conductivity, however, are usually sparse. To assess the resulting uncertainty in the transport of tracers, Monte Carlo (MC) methods are usually applied, where the transport statistics are sampled over a large number of probable hydraulic conductivity realizations. In this paper, an alternative method is described that provides accurate transport statistics at a computational expense that is 3 orders of magnitude lower than conventional MC. The new method is applicable for conductivity fields with multivariate Gaussian characterization involving conductivity measurements for both small and high log-conductivity variances. The new method is validated against MC for different dispersion scenarios, where the region of interest spans tens of log-conductivity correlation lengths.
 The influence of uncertainty in land surface temperature, air temperature, and wind speed on the estimation of sensible heat flux is analyzed using a Bayesian inference technique applied to the Surface Energy Balance System (SEBS) model. The Bayesian approach allows for an explicit quantification of the uncertainties in input variables: a source of error generally ignored in surface heat flux estimation. An application using field measurements from the Soil Moisture Experiment 2002 is presented. The spatial variability of selected input meteorological variables in a multitower site is used to formulate the prior estimates for the sampling uncertainties, and the likelihood function is formulated assuming Gaussian errors in the SEBS model. Land surface temperature, air temperature, and wind speed were estimated by sampling their posterior distribution using a Markov chain Monte Carlo algorithm. Results verify that Bayesian-inferred air temperature and wind speed were generally consistent with those observed at the towers, suggesting that local observations of these variables were spatially representative. Uncertainties in the land surface temperature appear to have the strongest effect on the estimated sensible heat flux, with Bayesian-inferred values differing by up to ±5°C from the observed data. These differences suggest that the footprint of the in situ measured land surface temperature is not representative of the larger-scale variability. As such, these measurements should be used with caution in the calculation of surface heat fluxes and highlight the importance of capturing the spatial variability in the land surface temperature: particularly, for remote sensing retrieval algorithms that use this variable for flux estimation.
 This paper presents a semianalytical method to solve the multispecies reactive solute transport equation coupled with a sequential first-order reaction network under spatially or temporally varying flow velocities and dispersion coefficients. This method employs the generalized integral transform technique and general linear transformation method by Clement (2001) to transform the set of coupled multispecies reactive transport equations into a set of independent uncoupled equations and to solve these independent equations for spatially or temporally varying flow velocities and dispersion coefficients, as well as for a temporally varying inlet concentration. The proposed semianalytical solution is compared against previously published analytical solutions of Srinivasan and Clement (2008b) and van Genuchten (1985). An example is used to show application of the solution to a hypothetical multilayered medium. The solution of proposed approach is also compared with a numerical solution using the 2DFATMIC (Two-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals Model). Three scenarios are illustrated to show the capabilities of the proposed semianalytical method to deal with aquifer heterogeneity and transient situations. We also show a practical implementation of the solution to an actual field, single-well push-pull test example designed to obtain the concentration distribution of reactants consumed and products formed at the end of the injection phase.
 This article introduces a robust method for characterizing fractured reservoirs using tracer and flow-rate data. The flow-rate data are used to infer the interwell connectivity matrix, which describes how injected fluids are divided between producers in the reservoir. The tracer data are used to find a function called the tracer kernel for each injector-producer connection. The tracer kernel describes the volume and dispersive properties of the interwell flow path. A combination of parametric and nonparametric regression methods was developed to estimate the tracer kernels in situations where data are collected at variable flow rate or variable-injected concentration conditions. This characterization method was developed to describe enhanced geothermal systems, although it works well in general for characterizing incompressible flow in fractured reservoirs (e.g., geothermal, carbon sequestration, radioactive waste and waterfloods of oil fields) where transverse dispersivity can be considered negligible and production takes place at constant bottomhole pressure conditions. The inferred metrics can be used to sketch informative field maps and predict tracer breakthrough curves at variable flow-rate conditions.
We study dispersion in heterogeneous porous media for solutes evolving from point-like and extended source distributions in d = 2 and d = 3 spatial dimensions. The impact of heterogeneity on the dispersion behavior is captured by a stochastic modeling approach that represents the spatially fluctuating flow velocity as a spatial random field. We focus here on the sample to sample fluctuations of the dispersion coefficients about their ensemble mean. For finite source sizes, the definition of dispersion coefficients in single realizations is not unique. We consider dispersion measures that describe the extension of the solute distribution, as well as dispersion coefficients that quantify the solute spreading relative to injection points of the partial plumes that constitute the solute distribution. While the ensemble averages of these dispersion quantities may be identical, their fluctuation behavior is found to be different. Using a perturbation approach in the fluctuations of the random flow field, we derive explicit expressions for the temporal evolution of the variances of the dispersion coefficients between realizations. Their evolution is governed by the typical dispersion time over the characteristic heterogeneity scale and the dimensions of the source distribution. We find that the dispersion variance decreases towards zero with time in d = 3 spatial dimensions, while in d = 2 it converges towards a finite long time value that is independent of the source dimensions.
Residual errors of hydrological models are usually both heteroscedastic and autocorrelated. However, only a few studies have attempted to explicitly include these two statistical properties into the residual error model and jointly infer them with the hydrological model parameters. This technical note shows that applying autoregressive error models to raw heteroscedastic residuals, as done in some recent studies, can lead to unstable error models with poor predictive performance. This instability can be avoided by applying the autoregressive process to standardized residuals. The theoretical analysis is supported by empirical findings in three hydrologically distinct catchments. The case studies also highlight strong interactions between the parameters of autoregressive residual error models and the water balance parameters of the hydrological model.
We investigated the effect of the Three Gorges Project and other dams on the load of phosphorus (P) to the middle and lower Yangtze River (MLY) and discussed the alteration of P on the ecosystem of the MLY. We collected data for continuous flow and sediment over the past 60 years and observed the concentrations of total P (TP) and particulate P (PP) in the pool reaches of the Three Gorges Reservoir (TGR), both before and after the impoundment in 2003. As a result, we obtained highly positive correlations between P and sediment and revealed two changes that were caused by the impoundments: 1) the sediment load to the MLY decreases by 91% and the river becomes almost clear; and 2) the loads of TP and PP to the MLY are sequestered by 77% and 83.5% annually and 75% and 92% in dry seasons, respectively. Because P was the limiting nutrient for bioactivity in the MLY before 2003, such significant reductions, along with the many other consequences of the dams, will not only further reduce the bio-availability of P but also increase the existing high ratio of nitrogen (N) to P. Therefore, it is quite possible to alter the nutrient regime and reduce the aquatic primary productivity of the MLY. Given that many large dams with huge reservoirs are under construction or planned upstream and elsewhere, studies focused on the long term effects of sediment and P reduction deserve a high priority for the protection of lowland rivers and aquatic ecosystems.
The ability to monitor the carbon dioxide (CO2) that has been injected underground is important to large-scale implementation of Carbon Capture and Sequestration. The focus of this study is to understand how flow processes during CO2 injection impact the pressure observed at a nearby monitoring well. In particular, we are interested in how the reservoir structure (layering and anisotropy) and CO2 plume migration influence the pressure transients at different depths. For a multilayered geologic model, four basic combinations of homogeneity/heterogeneity and isotropy/anisotropy conditions are examined. Numerical simulations using TOUGH2 show different CO2 plume migration and large pressure buildups in the storage reservoir and the seal for each scenario. Pressure buildups normalized to the pressure buildup at the depth of injection are diagnostic of the approximate height of the CO2 plume and provide information on the reservoir structure. Vertical pressure gradients normalized to the initial hydrostatic pressure gradient are diagnostic of reservoir structure soon after the start of injection. Over time, they provide information on the height of the CO2 plume. The diagnostic features in the pressure response are evident long before the CO2 arrives at the monitoring well and can be attributed to buoyancy induced and gravity segregated aqueous flows caused by the advancing CO2 plume. The identified diagnostics will aid in the ultimate goal, which is to develop a monitoring technique based on multilevel pressure measurements.
Surface microtopography affects overland flow, infiltration, soil erosion, pollutant transport, and other fundamental hydrologic and environmental processes across scales. Under the influence of surface depressions, overland flow essentially features a series of progressive puddle-to-puddle (P2P) filling, spilling, merging, and splitting processes. The objectives of this study are to characterize puddles and their hierarchical relationships and model the microtopography-controlled P2P processes. We proposed a new modeling framework for simulating the P2P overland flow dynamics through cell-to-cell (C2C) and P2P routing for a set of puddle-based units (PBUs) in a well-delineated, cascaded P2P drainage system. Testing of the P2P model demonstrated its potential to improve overland flow modeling and hydrologic connectivity analysis by explicitly incorporating the hydrologic roles of depressions and quantifying the real microtopography-controlled P2P dynamics.