Groundwater management: Waiting for a drought*

In this article we present a stylized model for optimal management of an unconfined groundwater resource when the threat of drought exists. The drought is modeled as a stochastic event that hits at an uncertain date and two benchmark management policies are investigated: (a) A policy of optimal dynamic management ignoring the threat of drought; and (b) an economically optimal policy that accounts for the threat of a drought. We show that the optimal predrought steady‐state equilibrium stock size of groundwater under policy b is larger than that under policy (a) Furthermore, we show that an increase in the probability of a drought gives rise to two counteracting effects: One in the direction of a larger predrought steady‐state equilibrium stock size (a recovery effect) and one in the direction of a lower predrought steady‐state equilibrium stock (an extinction effect). We find that the recovery effect dominates the extinction effect. Recommendations for Resource Managers: We analyze two groundwater extraction policies that can be used when a threat of drought exists: (a) Dynamic optimal management ignoring the threat of drought; and (b) dynamic optimal management taking the threat of drought into account. We show that the predrought steady‐state equilibrium stock size of water should be larger under the policy (b) than under policy (a). This conclusion has three implications for resource managers:

• Current groundwater management should take future extraction possibilities into account.

• A resource manager ought to take the threat of drought into account in groundwater management.

• A buffer stock of water should be built‐up before the drought to be drawn upon during the event.

     

Playing with models and optimization to overcome the tragedy of the commons in groundwater

Groundwater is the natural resource most extracted in the world. It supplies 50% of the total potable water requirements, 40% of the industry take, and 20% of agriculture groundwater is a strategic resource for every country. That common‐pool resources are highly susceptible to lead to a tragedy of the commons is a well‐known fact. We claim that a combination of groundwater modeling, optimization, and a game theoretical analysis may in fact avoid the tragedy. A groundwater model in MODFLOW from Zamora aquifer in Mexico was used as input of a basic but instructive, optimization problem: extract the greatest possible volume of water, but at the same time minimizing the drawdown and drawdown velocity. The solutions of the optimization problem were used to construct the payoffs of a hypothetical game among the aquifer users, the resource's administrator, and a resource protector entity. We show that the success of the optimal management program depends heavily on the information that the users have about the resource. Therefore, better decision‐making processes are a consequence of sustainability literacy. Particularly, water literacy could lead to the usage of water considering it as a part of an ecosystem and not only as a natural resource. Additionally, a new non‐classical equation for underground flow was derived, that may be specially important to understand and predict the groundwater flow in highly heterogeneous conditions as in karstic aquifers or fractured media. © 2013 Wiley Periodicals, Inc. Complexity 19: 9–21, 2013     

孔洞裂隙水二维流数值模拟的广义差分法

研究区地下水主要为玄武岩类孔洞裂隙水,水文地质模型概化为各向异性非均质,根据第四系玄武岩承压含水层中地下水的分布特征及流动规律,建立二维非稳定流数学模型,采用广义差分法对其求解.通过研究区井群对模型进行识别、验证.结果表明,计算模型与实际水文地质条件比较接近;计算水位与实测水位相吻合.为城市地下水可持续性管理提供科学理论依据.     

Groundwater response to tidal fluctuation in a sloping leaky aquifer system

The effect of tidal fluctuation on groundwater flow is an important issue from many aspects in coastal areas. This paper develops a new analytical solution to describe the groundwater fluctuation in a sloping coastal aquifer system which comprises an upper unconfined aquifer, a lower confined aquifer, and an aquitard in between. The solution is allowed to investigate the effects of bottom slope and leakage as well as aquifer parameters on head fluctuations in both unconfined and confined aquifers. The research result indicates that the effect of the bottom angle on the groundwater fluctuation and time lag is significant in the unconfined aquifer and not negligible if the leakage in the confined aquifer is large. In addition, the joint effects of aquifer parameters and bottom angle on groundwater fluctuation and time lag are also discussed.     

时变垂向入渗影响下河渠-潜水非稳定渗流模型的解及应用

在河渠边界控制下的半无限含水层中,对时变垂向入渗影响下的潜水非稳定渗流模型,利用Boussinesq第一线性化方法,通过Laplace变换并结合卷积原理,导出模型的解析解．根据不同水文地质条件下解的数学特征,建立相应的含水层参数求解方法;在此基础上,建立计算河渠与含水层之间水量交换的公式,以及计算潜水蒸发强度的递推公式．以安徽淮北平原某河流-潜水含水层系统为例,阐述上述方法的计算过程与步骤．     

Centralized and decentralized management of groundwater with multiple users

In this work, we investigate two groundwater inventory management schemes with multiple users in a dynamic game-theoretic structure: (i) under the centralized management scheme, users are allowed to pump water from a common aquifer with the supervision of a social planner, and (ii) under the decentralized management scheme, each user is allowed to pump water from a common aquifer making usage decisions individually in a non-cooperative fashion. This work is motivated by the work of Saak and Peterson [14], which considers a model with two identical users sharing a common aquifer over a two-period planning horizon. In our work, the model and results of Saak and Peterson [14] are generalized in several directions. We first build on and extend their work to the case of n non-identical users distributed over a common aquifer region. Furthermore, we consider two different geometric configurations overlying the aquifer, namely, the strip and the ring configurations. In each configuration, general analytical results of the optimal groundwater usage are obtained and numerical examples are discussed for both centralized and decentralized problems.     

A 3D hydrodynamic numerical model of the Río de la Plata and Montevideo’s coastal zone

The 3D hydrodynamic numerical model MOHID was applied in the Río de la Plata and Montevideo coastal zone in order to represent the main dynamics and to study its complex circulation pattern. The hydrodynamic model was calibrated and validated considering the following main forces: fresh water flow, astronomical and meteorological tides in the oceanic boundary, and wind acting on the water surface. A series of water levels measured at six coastal stations and vertical profiles of current velocity measured at four different locations in the estuarine zone of the Río de la Plata were used for calibrating and validating the hydrodynamic model. The calibration process was carried out in two steps. First the astronomical waves propagation was calibrated comparing harmonic constants of observed and computed sea surface elevation data. Next, both the astronomical and meteorological wave propagation was calibrated. Direct comparison of scatter plot and root-mean square errors of model results and field data were used when evaluating the calibration quality. The calibrated model shows good agreement with the measured water surface level in the entire domain with mean error values being minor than 20% of the measured data and correlation factors higher than 0.74. Also, the intensity and velocity direction observed in the currents data are well represented by the model in both bottom and surface levels with errors similar to 30% of the currents data components. Using the 3D calibrated model the bottom and surface residual circulation for a four month period of time was analyzed.     

A multi-objective optimal allocation model for irrigation water resources under multiple uncertainties

This paper proposed a multi-objective optimal water resources allocation model under multiple uncertainties. The proposed model integrated the chance-constrained programming, semi-infinite programming and integer programming into an interval linear programming. Then, the developed model is applied to irrigation water resources optimal allocation system in Minqin’s irrigation areas, Gansu Province, China. In this study, the irrigation areas’ economic benefits, social benefits and ecological benefits are regarded as the optimal objective functions. As a result, the optimal irrigation water resources allocation plans of different water types (surface water and groundwater) under different hydrological years (wet year, normal year and dry year) and probabilities are obtained. The proposed multi-objective model is unique by considering water-saving measures, irrigation water quality impact factors and the dynamic changes of groundwater exploitable quantity in the irrigation water resources optimal allocation system under uncertain environment. The obtained results are valuable for supporting the adjustment of the existing irrigation patterns and identify a desired water-allocation plan for irrigation under multiple uncertainties.     

Modeling the drainage and groundwater table above the collecting pipe through 2D groundwater models

In order to understand the effects of the landfill operation on groundwater flow behavior, 2D horizontal groundwater simulation model was carried out. The model saved the memory of computer and time consumption comparing with 3D groundwater flow model. However, the most difficulty is the assignment of collecting pipe boundary in the study site. Therefore, 2D vertical model was applied to calculate the change of groundwater table above the collecting pipe. This paper paid attention to examine the validation of the assignment of the collecting pipe boundary by applying the results of 2D vertical model. 2D horizontal model was coupled with the recharge model to solve the partial differential equation of groundwater flow. Finite difference method and iterative successive over relaxation were applied. The drainage volume of leachate collection was summed up in the whole landfill site and compared with the average volume of treated waste water. The study demonstrated that the results of 2D vertical model validated and can be applied to 2D horizontal groundwater flow simulation.     

垂直与水平渗透作用下潜水非稳定渗流运动规律

对河渠边界控制的半无限含水层,建立垂向入渗与河渠水平渗透共同作用下的潜水非稳定渗流模型;利用Boussinesq第一线性化方法,通过Laplace变换,给出模型的解析解. 证明相关经典公式与模型特定解之间的转换关系,分析经典公式适用范围．根据模型解,逐一定量研究下述变量,如垂向入渗强度、河渠水位变动幅度、含水层结构参数如给水度和导压系数、计算点与边界之间的距离,对渗流过程的影响．这些变量的变化,对潜水位获最大上升速度的时间产生延迟效应;论证一些变量间产生等效延迟效应的条件．根据解的数学特征,讨论其对应的物理意义和潜水位变动规律．     

Neural network modeling of hydrological systems: A review of implementation techniques

This paper presents a review of procedural steps and implementation techniques used in the development of artificial intelligence models, generally referred to as artificial neural networks (ANNs), within the water resources domain. It focusses on identifying different areas wherein ANNs have found application thereby elucidating its advantages and disadvantages as well as various challenges encountered in its use. Results from this review provide useful insights into how the performance of ANNs can be improved and potential areas of application that are yet to be explored in hydrological modeling. Recommendations for Resource Managers

• Development of integrated and hybrid artificial intelligent tools is critical to achieving improved forecasts in hydrological modeling studies.

• Further research into comprehending the internal mechanisms of neural networks is required to obtain a practical meaning of each network component deployed to solve real‐world problems.

• More robust optimization techniques and tools like differential evolution, particle swarm optimization and deep neural nets, are yet to be fully explored in the water resources analysis, and should be given more attention to enhance neural networks aptitude for modeling complex and nonlinear hydrological processes.

     

城市地下水资源可持续开发利用模型研究

根据地下水可持续开发利用原则,运用系统分析方法建立了地下水可持续开发利用模型,首先,运用有限元分析法对地下水运动偏微分方程进行离散,导出了地下水运动的数值方程,使得地下水运动方程能够与系统分析方法相结合建立城市地下水可持续开发利用模型;然后,以地下水位下降最小为目标函数,以各井的出水能力及时段内的需水量作为约束条件,建立了城市地下水优化利用模型,为城市地下水资源可持续开发利用提供新的规划管理方法.     

A decision tool for optimal irrigated crop planning and water resources sustainability

In the present study, the conjunctive use policies of surface and ground water resources are developed for minimizing water shortage in an irrigation district subject to constraints on groundwater withdrawals and crop planning capacities. An integrated soil water balance algorithm is coupled to a non-linear optimization model in order to carry out water allocation planning in complex deficit agricultural water resources systems based on an economic efficiency criterion. Various options of conjunctive use water resources along with current and proposed cropping patterns have been explored by Koohdasht Irrigation District (KID), a semi-arid region in I.R. Iran. The analysis provides various scenarios, which can help managers in decision-making for the optimum allocation plans of water resources within the irrigation area. The results reveal that the proposed model, as a decision tool for optimal irrigated crop planning and water resources sustainability, may be used for maximizing the overall net benefits and global water productivity of an irrigation district considering an allowable annual recharge of groundwater. Findings indicate the importance of the conjunctive water management modeling, which can be easily implemented and would enhance the overall benefits from cropping activities in the study area.     

Modelling the impact of wind stress and river discharge on Danshuei River plume

A three-dimensional, time-dependent, baroclinic, hydrodynamic and salinity model, UnTRIM, was performed and applied to the Danshuei River estuarine system and adjacent coastal sea in northern Taiwan. The model forcing functions consist of tidal elevations along the open boundaries and freshwater inflows from the main stream and major tributaries in the Danshuei River estuarine system. The bottom friction coefficient was adjusted to achieve model calibration and verification in model simulations of barotropic and baroclinic flows. The turbulent diffusivities were ascertained through comparison of simulated salinity time series with observations. The model simulation results are in qualitative agreement with the available field data.     

地下水与社会经济的协调发展分析模型及其应用

在我国北方水资源短缺的许多地区,发展用水主要是靠加大地下水超采量来维持的,即通过牺牲后备资源和生态环境,地下水资源对国民经济发展做出了重要贡献.但随着地下水资源的枯竭,可能对区域社会经济带来一定影响.为评价这种影响,提出了一个协调发展模型,简单实用,能够反映客观实际.并在海河流域的典型区域进行了实际应用,结果表明许多地区的地下水环境状况相当不容乐观,在发展经济的同时,也应当注意生态环境的保护.     

THE ROLE OF GROUNDWATER‐DEPENDENT ECOSYSTEMS IN GROUNDWATER MANAGEMENT

Ecosystems provide a wide range of services essential for a proper environmental, economic, and social performance. While the estimated global value of ecosystem services in 2014 is very significant, the annual loss of ecosystem services value is alarming. Our paper focuses on groundwater‐dependent ecosystems (GDEs), some very important to society, which are under threat due to groundwater overexploitation. Considering the ecosystem health/status function is essential for sound groundwater regulation policy. The paper assesses the conjunctive management of groundwater and GDEs both in theory and in a relevant case study, using a certain type of an ecosystem health function. The theoretical results demonstrate how the change in the slope values of a general ecosystem health function affects the optimal groundwater management policy. The analysis also suggests a change in groundwater management strategies as a function of the value of the ecosystem. The theoretical findings are corroborated with data from an aquifer in Spain and its associated GDE—the Tablas de Daimiel Wetland. The paper highlights theoretically and empirically the necessity for a better understanding of GDEs behavior. It calls for groundwater regulation to protect these resources.     

Excess pore water pressure due to ground surface erosion

The Laplace transform is applied to solve the groundwater flow equation with a boundary that is initially fixed but that starts to move at a constant rate after some fixed time. This problem arises in the study of pore water pressures due to erosional unloading where the aquifer lies underneath an unsaturated zone. We derive an analytic solution and examine the predicted pressure profiles and boundary fluxes. We calculate the negative pore water pressure in the aquifer induced by the initial erosion of the unsaturated zone and subsequent erosion of the aquifer.     

Optimal threshold density in a stochastic resource management model with pulse intervention

Human activities and agricultural practices are having huge impacts on the development of fishery and land resources through different ways. To model such systems that involve harvesting, an impulsive model of natural resources with a stochastic noise perturbation element is formulated to study the relationship between (a) the maximal expectation of biomass after harvesting or fishing events and (b) the minimal expectation of pest biomass and the number of times pesticide is applied. Using a detailed analytical treatment, time estimation, and numerical demonstrations, we establish that the proposed mechanism is capable of maximizing fish populations at the end of a fishing season and minimizing pest numbers after a crop harvesting season once the intensity of the noise is relatively small. Investigations of the effects of different parameters reveal that theoretical predictions from the new stochastic model accord with those from the deterministic case. Recommendations for Resource Managers

• Various measures can be implemented to manage natural resources, such as adjusting fishing quantity and intensity to maximize fish population.
• In the natural environment, population growth is inevitably affected by the environment noise. So it is important to understand the noise effect to maintain sustainability of resources.
• Investigated methods are useful to converse resources and can be widely applied to control pests.

     

Oxygen dynamics in coastal and lagoon ecosystems

Aquatic systems with a high trophic level (for example some coastal lagoons connected with sea, estuaries, and the neighbourhood) can be affected by some dystrophic phenomena. The instability of these ecosystems greatly depends on the nutrients availability and on the meteorological and climatic conditions. The variation of these factors can produce fast evolution of dystrophic phenomena into anoxis crises: that is the depletion of oxygen in the water column that, starting from localized areas, can interest all the basin. Due to these modifications, great changes can be observed in the composition of the biotic community. These processes may be described by a reaction-diffusion system based on the following biological hypotheses:

• 1.(i) the primary production is assumed to be constant (in particular of macrophytes),
• 2.(ii) the model consists of the balance equations of some chemical species, in the water column and in the sediment at the bottom of the water,
• 3.(iii) a simplified formalization of reaction kinetics.

The model presented can be used to evaluate the influence of environmental factors, such as temperature, wind, and lighting on the level of oxygen, and it is described by a system of semilinear partial differential equations of parabolic type.A numerical study, based on the semidiscrete Galerkin Method with finite elements, is proposed. The present approach uses an iterative process of successive approximations which splits the system in three independent systems of linear equations. Finally, some results of numerical simulation of oxygen consumption, with reference to the lagoon of Orbetello (Tuscany, Italy), are presented and discussed.     

FEATURES OF BIOECONOMICS MODELS FOR THE OPTIMAL MANAGEMENT OF A FISHERY EXPLOITED BY TWO DIFFERENT FLEETS

ABSTRACT. After the extension of the Exclusive Economic Zone, in 1977, to 200 miles, most fish stocks came under jurisdiction of the adjacent coastal states. This development opened prospects of effective management of the open sea fisheries. Coastal states have the right to plan out the operation of so-called by Clarke and Munro “distant water fishing nations” from their Exclusive Economic Zone. Under some arrangements, a foreign fleet is allowed to harvest the resource in the Exclusive Economic Zone area. Clarke and Munro, in [1987] and [1991], focus on the issue of optimum terms and conditions of access and, in doing so, built a multiobjective model. The main goal of the present work is the development of a more general model including more variables and parameters related to the presence of a domestic fleet as well as a distant water fishing nation. The main difficulty resides in sharing the harvesting between the two fleets. The study responds to the realistic problemof coastal states who own enough resource stocks to allow harvesting by several kinds of fleets. Two optimal scenarios are developed, in each of them a solution is given.