From rainfed agriculture to stress-avoidance irrigation: I. A generalized irrigation scheme with stochastic soil moisture

With vast regions already experiencing water shortages, it is becoming imperative to manage sustainably the available water resources. As agriculture is by far the most important user of freshwater and the role of irrigation is projected to increase in face of climate change and increased food requirements, it is particularly important to develop simple, widely applicable models of irrigation water needs for short- and long-term water resource management. Such models should synthetically provide the key irrigation quantities (volumes, frequencies, etc.) for different irrigation schemes as a function of the main soil, crop, and climatic features, including rainfall unpredictability. Here we consider often-employed irrigation methods (e.g., surface and sprinkler irrigation systems, as well as modern micro-irrigation techniques) and describe them under a unified conceptual and theoretical framework, which includes rainfed agriculture and stress-avoidance irrigation as extreme cases. We obtain mostly analytical solutions for the stochastic steady state of soil moisture probability density function with random rainfall timing and amount, and compute water requirements as a function of climate, crop, and soil parameters. These results provide the necessary starting point for a full assessment of irrigation strategies, with reference to sustainability, productivity, and profitability, developed in a companion paper [Vico G, Porporato A. From rainfed agriculture to stress-avoidance irrigation: II. Sustainability, crop yield, and net profit. Adv Water Resour 2011;34(2):272-81].     

A unique value function for an optimal control problem of irrigation water intake from a reservoir harvesting flash floods

Operation of reservoirs is a fundamental issue in water resource management. We herein investigate well-posedness of an optimal control problem for irrigation water intake from a reservoir in an irrigation scheme, the water dynamics of which is modeled with stochastic differential equations. A prototype irrigation scheme is being developed in an arid region to harvest flash floods as a source of water. The Hamilton–Jacobi–Bellman (HJB) equation governing the value function is analyzed in the framework of viscosity solutions. The uniqueness of the value function, which is a viscosity solution to the HJB equation, is demonstrated with a mathematical proof of a comparison theorem. It is also shown that there exists such a viscosity solution. Then, an approximate value function is obtained as a numerical solution to the HJB equation. The optimal control strategy derived from the approximate value function is summarized in terms of rule curves to be presented to the operator of the irrigation scheme.     

Stochastic control of a micro-dam irrigation scheme for dry season farming

Micro-dams are expected to be feasible options for water resources development in semi-arid regions such as the Guinea savanna agro-ecological zone of West Africa. An optimal water management strategy in a micro-dam irrigation scheme supplying water from an existing reservoir to a potential command area is discussed in this paper based on the framework of stochastic control. Water intake facilities are assumed to consist of photovoltaic pumping system units and hoses. The knowledge of current states of the storage volume of the reservoir and the soil moisture in the command area is fed-back to the intake flow rate. A system of two stochastic differential equations is proposed as a model for the dynamics of the micro-dam irrigation scheme, so that temporally backward solution of the Hamilton–Jacobi–Bellman equation determines an optimal control, which represents the optimal water management strategy. A computational procedure using the finite element method is successfully implemented to provide comprehensive information on the optimal control. The results indicate that the water initially stored in the reservoir can support full irrigation for about 80 days under the optimal water management strategy, which is predominantly based on the demand-side principle. However, the volatility of the soil moisture in the command area must be reasonably small.     

Drought impacts on water quality and potential implications for agricultural production in the Maipo River Basin,Central Chile

ABSTRACT

Droughts can have serious negative impacts on the water quality needed for irrigated agriculture. The Metropolitan region of Chile is a relevant producer of high-value crops and is prone to droughts. Standardized Drought Indices were used to characterize meteorological and hydrological droughts for the period from 1985 to 2015. To understand the relationship between droughts and water quality, we evaluated the correlations between daily discharge and surface water quality observations. The threshold level method was used to compare physicochemical parameters during hydrological drought periods with the Chilean water quality thresholds for agricultural uses. A significant (p < 0.05) negative relationship between discharge and electrical conductivity and major ions was found in most of the basin. Hydrological stations located in irrigation districts exceeded the official thresholds for these parameters during hydrological drought periods seriously threatening irrigated agriculture of the region.     

Fuzzy chance-constrained linear fractional programming approach for optimal water allocation

A fuzzy chance-constrained linear fractional programming method was developed for agricultural water resources management under multiple uncertainties. This approach improved upon the previous programming methods, and could reflect the ratio objective function and multiple uncertainties expressed as probability distributions, fuzzy sets, and their combinations. The proposed approach is applied to an agricultural water resources management system where many crops are considered under different precipitation years. Through the scenarios analyses, the multiple alternatives are presented. The solutions show that it is applicable to practical problems to address the crop water allocation under the precipitation variation and sustainable development with ratio objective function of the benefit and the irrigation amount. It also provides bases for identifying desired agriculture water resources management plans with reasonable benefit and irrigation schedules under crops.     

Identification of wind stress on shallow water surfaces by optimal smoothing

Using the state space approach, an on-line filter procedure for combined wind stress identification and tidal flow forecasting is developed. The stochastic dynamic approach is based on the linear twodimensional shallow water equations. Using a finite difference scheme, a system representation of the model is obtained. To account for uncertainties, the system is embedded into a stochastic environment. By employing a Kalman filter, the on-line measurements of the water-level available can be used to identify and predict the shallow water flow. Because it takes a certain time before a fluctuation in the wind stress can be noticed in the water-level measurements, an optimal fixed-lag smoother is used to identify the stress.     

Optimal control of linear buildings under seismic excitations

Considerable effort has been devoted to develop optimal control methods for reducing structural response under seismic forces. In this study analytical solution of the linear regulator problem applied widely to the control of earthquake‐excited structures is obtained by using the sufficient conditions of optimality even though almost all of the optimal controls proposed previously for structural control are based on the necessary conditions of optimality. Since the resulting optimal closed–open‐loop control cannot be implemented for civil structures exposed to earthquake forces, the solution of the optimal closed–open‐loop control is carried out approximately based on the prediction of the seismic acceleration values in the near future. Upon obtaining the relation between the exact optimal solution and future values of seismic accelerations, it is shown numerically that the solution of the optimal closed–open‐loop control problem can be performed approximately by using only the first few predicted seismic acceleration values if a given norm criteria is satisfied. Calculated performance measures indicate that the suggested approximate solution is better than the closed‐loop control and as we predict the future values of the excitation more accurately, it will approach the optimal solution. Copyright © 2001 John Wiley & Sons, Ltd.     

Improving drought predictability in Arkansas using the ensemble PDSI forecast technique

Drought prediction is important for improved water resources management and agriculture planning. Although Arkansas has suffered severe droughts and economic loss in recent years, no significant study has been done. This study proposes a local nonparametric autoregressive model with designed stochastic residual-resampling approach to produce ensemble drought forecasts with associated confidence. The proposed model utilizes historical climate records, including drought indices, temperature, and precipitation to improve the quality of the short-term forecast of drought indices. Monthly forecasts of Palmer Drought Severity Index (PDSI) in Arkansas climate divisions show remarkable skills with 2–3 month lead-time based on selected performance measure such as, Normalized Root Mean Square Error (NRMSE) and the Kuiper Skill Score (KSS). Rank histograms also show that the model captures the natural variability very well in the produced drought forecasts. The incorporation of categorical long-term precipitation prediction significantly enhances the performance of the monthly drought forecasts.     

Risk assessment of agricultural irrigation water under interval functions

In recent years, water shortages and unreliable water supplies have been considered as major barriers to agricultural irrigation water management in China, which are threatening human health, impairing prospects for agriculture and jeopardizing survival of ecosystems. Therefore, effective and efficient risk assessment of agricultural irrigation water management is desired. In this study, an inexact full-infinite two-stage stochastic programming (IFTSP) method is developed. It incorporates the concepts of interval-parameter programming and full-infinite programming within a two-stage stochastic programming framework. IFTSP can explicitly address uncertainties presented as crisp intervals, probability distributions and functional intervals. The developed model is then applied to Zhangweinan river basin for demonstrating its applicability. Results from the case study indicate that compromise solutions have been obtained. They provide the desired agricultural irrigation water-supply schemes, which are related to a variety of tradeoffs between conflicting economic benefits and associated penalties attributed to the violation of predefined policies. The solutions can be used for generating decision alternatives and thus help decision makers to identify desired agricultural irrigation targets with maximized system benefit and minimized system-failure risk. Decision makers can adjust the existing agricultural irrigation patterns, and coordinate the conflict interactions among economic benefit, system efficiency, and agricultural irrigation under uncertainty.     

Assessing crop yield and crop water productivity and optimizing irrigation scheduling of winter wheat and summer maize in the Haihe plain using SWAT model

Haihe plain is an important food production area in China, facing an increasing water shortage. The water used for agriculture accounts for about 70% of total water resources. Thus, it is critical to optimize the irrigation scheduling for saving water and increasing crop water productivity (CWP). This study first simulated crop yield and CWP for winter wheat and summer maize in historical scenario during 1961–2005 for Haihe plain using previously well‐established Soil and Water Assessment Tool model. Then, scenarios under historical irrigation (scenario 1) and sufficient irrigation (scenario 2) were, respectively, simulated both with sufficient fertilizer. The crop yield in scenario 2 was considered as the potential crop yield. The optimal irrigation scheduling with sufficient fertilizer (scenario 3) was explored by iteratively adjusting irrigation scheduling based on the scenario 1 and previous studies related to water stress on crop growth. Results showed that net irrigation amount was, respectively, reduced 23.1% and 18.8% in scenario 3 for winter wheat and summer maize when compared with scenario 1. The CWP was 12.1% and 8.2% higher with very slight change of crop yield. Using optimal irrigation scheduling could save 8.8 × 10⁸ m³ irrigation water and reduce about 16.3% groundwater over‐exploitation in winter wheat growth period. The corresponding yield was 18.5% and 12.9% less than potential yield for winter wheat and summer maize but using less irrigation water. Therefore, it could be considered that the optimal irrigation was reasonable, which provided beneficial suggestions for increasing efficiency of agricultural water use with sustainable crop yield in Haihe plain. Copyright © 2013 John Wiley & Sons, Ltd.     

A drought index for Rainfed agriculture: The Standardized Precipitation Crop Evapotranspiration Index (SPCEI)

A drought index is one of the main methods used for measuring drought and represents the basis of drought monitoring, early warning, and classification. On the basis of an analysis of the advantages and limitations of the Standardized Precipitation Evapotranspiration Index (SPEI), the Standardized Precipitation Crop Evapotranspiration Index (SPCEI), which is a drought index of rainfed agriculture, was constructed in this study. The applicable conditions of the SPCEI were then investigated, and the results showed that the SPCEI was suitable for dryland crops under non‐irrigated conditions in arid and semi‐arid areas. The difference between the SPEI and SPCEI is analysed. Compared with the SPEI, the SPCEI considers crop evapotranspiration and the crop growth stage and was found to be more suitable for monitoring agricultural drought. Qigihar, which is located in a semi‐arid area in western Heilongjiang Province, China, was then analysed as an example. The characteristics of the spatial and temporal variability of regional agricultural drought were analysed based on maize and soybean in dryland areas. The results for the different growth stages of maize and soybean showed that drought intensity is more serious in the initial stage in the middle part. In crop development, mid‐season and late season stage, the drought conditions gradually increased from north to south. The drought degree of the two crops at the initial stage gradually increased, and the drought degree at the crop development stage gradually decreased. The main reason is that precipitation gradually increases during the crop development stage.     

Single multipurpose reservoir design: a modified optimal control problem by chance-constrained programming

This paper presents a chance-constrained programming model for optimal control of a multipurpose reservoir and its modification to a model for single reservoir design. An algorithm is developed for solving complex stochastic problems of multipurpose reservoir planning and design. The complexity of the problem is resolved by a two-step algorithm: (1) transformation of chance constraints on the state and control variables is performed at the first step; and (2) the choice of optimum control or optimal reservoir storage is carried out in the second step. The method of iterative convolution is chosen for the first step, while linear programming is selected for the second step. The algorithm allows the use of random inflows and random demands together with other deterministic demands. The reservoir design problem is presented as a modified optimal control problem. The procedure is illustrated with an example of a hypothetical reservoir design problem with three different types of downstream releases (hydropower production, municipal water supply, and irrigation).     

Evaluation of water‐use policies for baseflow recovery during droughts in an agricultural intensive karst watershed: Case study of the lower Apalachicola–Chattahoochee–Flint River Basin,southeastern United States

The lower Apalachicola–Chattahoochee–Flint River Basin in the Southeast United States represents a major agricultural area underlain by the highly productive karstic Upper Floridan aquifer (UFA). During El Niño Southern Oscillation‐induced droughts, intense groundwater withdrawal for irrigation lowers streamflow in the Flint River due to its hydraulic connectivity with the UFA and threatens the habitat of the federally listed and endangered aquatic biota. This study assessed the compounding hydrologic effects of increased irrigation pumping during drought years (2010–2012) on stream–aquifer water exchange (stream–aquifer flux) between the Flint River and UFA using the United States Geological Survey modular finite element groundwater flow model. Principal component and K‐means clustering analyses were used to identify critical stream reaches and tributaries that are adversely affected by irrigation pumping. Additionally, the effectiveness of possible water restriction scenarios on stream–aquifer flux was also analysed. Moreover, a cost–benefit analysis of acreage buyout procedure was conducted for various water restriction scenarios. Results indicate that increased groundwater withdrawal in Water Year 2011 decreased baseflow in the lower Apalachicola–Chattahoochee–Flint River Basin, particularly, in Spring Creek, where irrigation pumping during April, June, and July changed the creek condition from a gaining to losing stream. Results from sensitivity analysis and simulated water restrictions suggest that reducing pumping in selected sensitive areas is more effective in streamflow recovery (approximately 78%) than is reducing irrigation intensity by a prescribed percentage of current pumping rates, such as 15% or 30%, throughout the basin. Moreover, analysis of acreage buyout indicates that restrictions on irrigation withdrawal can have significant impacts on stream–aquifer flux in the Basin, especially in critical watersheds such as Spring and Ichawaynochaway Creeks. The proposed procedure for ranking of stream reaches (sensitivity analysis) in this study can be replicated in other study areas/models. This study provides useful information to policymakers for devising alternate irrigation water withdrawal policies during droughts for maintaining flow levels in the study area.     

Optimal estimation of irrigation schedule – An example of quantifying human interferences to hydrologic processes

Reliable records of water use for irrigation are often lacking. This presents a difficulty for a qualified water use and water availability assessment. Quantification of the hydrologic cycle processes in regions of intensive agricultural practice requires irrigation as an input to hydrologic models. This paper presents a coupled forward-inverse framework to estimate irrigation schedule using remote-sensed data and data assimilation and optimization techniques. Irrigation schedule is treated as an unknown input to a hydro-agronomic simulation model. Remote-sensed data is used to assess actual crop evapotranspiration, which is used as the “observation” of the computed crop evapotranspiration from the simulation model. To handle the impact of model and observation error and the unknown biased error with irrigation inputs, a coupled forward-inverse approach is proposed, implemented and tested. The coupled approach is realized by an integrated ensemble Kalman filter (EnKF) and genetic algorithm (GA). The result from a case study demonstrates that the forward and inverse procedures in the coupled framework are complementary to each other. Further analysis is provided on the impact of model and observation errors on the non-uniqueness problem with inverse modeling and on the exactness of irrigation estimates.     

Integration of surface water with groundwater resources aided by numerical modelling

ABSTRACT

The possibility was studied of a gradual extension of the irrigable area of the Tarlac Irrigation System, located in the alluvial plain of Luzon Island (Philippines). The extension would be made by integrating groundwater with surface water supplied from a reservoir already designed. Aquifer exploitation was studied adopting the criterion that groundwater is a very expensive resource to be turned to only in severe drought years. The objectives of the study were twofold: (a) planning the distribution of the wells (to be drilled during the various stages of the irrigation system development) so as to minimize the pumping cost; (b) establishing a policy for the well management in conjunction with the reservoir operation. Different schemes of the combined system management were analysed on the basis of the climatic and hydrological regime over the period 1950–1972. For this period the monthly water requirements for the different crops and the monthly values of aquifer recharge were computed. The economic analyses were performed using present prices of agricultural products and power together with several different hypotheses about future prices. A finite element model of the semiconfined aquifer was postulated and calibrated; the importance of the return flow from irrigation was also tested. Simulations of exploitation schemes provided a detailed forecast of the aquifer response to the irrigation demands.     

Drought hotspot analysis and risk assessment using probabilistic drought monitoring and severity–duration–frequency analysis

Drought hotspot identification requires continuous drought monitoring and spatial risk assessment. The present study analysed drought events in the agriculture‐dominated mid‐Mahanadi River Basin in Odisha, India, using crop water stress as a drought indicator. This drought index incorporated different factors that affect crop water deficit such as the cropping pattern, soil characteristics, and surface soil moisture. The drought monitoring framework utilized a relevance vector machine model‐based classification that provided the uncertainty associated with drought categorization. Using the proposed framework, drought hotspots are identified in the study region and compared with indices based on precipitation and soil moisture. Further, a bivariate copula is employed to model the agricultural drought characteristics and develop the drought severity–duration–frequency (S–D–F) relationships. The drought hotspot maps and S–D–F curves are developed for different locations in the region. These provided useful information on the site‐specific drought patterns and the characteristics of the devastating droughts of 2002 and 2012, characterized by an average drought duration of 7 months at several locations. The site‐specific risk of short‐ and long‐term agricultural droughts are then investigated using the conditional copula. The results suggest that the conditional return periods and the S–D–F curves are valuable tools to assess the spatial variability of drought risk in the region.     

Catchment scale hydrology of an irrigated cropping system under soil conservation practices

Soil erosion by water is a pressing environmental problem caused and suffered by agriculture in Mediterranean environments. Soil conservation practices can contribute to alleviating this problem. The aim of this study is to gain more profound knowledge of the effects of conservation practices on soil losses by linking crop management and soil status to runoff and sediment losses measured at the outlet of a catchment during seven years. The catchment has 27.42 ha and is located in a commercial farm in southern Spain, where a package of soil conservation practices is an essential component of the farming system. The catchment is devoted to irrigated annual crops with maize–cotton–wheat as the primary rotation. Mean annual rainfall‐induced runoff coefficient was 0.14 and mean annual soil loss was 2.4 Mg ha^?1 y^?1. Irrigation contributed to 40% of the crop water supply, but the amount of runoff and sediment yield that it generated was negligible. A Principal Components Analysis showed that total soil loss is determined by the magnitude of the event (rainfall and runoff depths, duration) and by factors related to the aggressiveness of the events (rainfall intensity and preceding soil moisture). A third component showed the importance of crop coverage to reduce sediment losses. Cover crops grown during autumn and early winter and crop residues protecting the soil surface enhanced soil conservation notably. The role of irrigation to facilitate growing cover crops in Mediterranean environments is discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

Stochastic management of pump-and-treat strategies using surrogate functions

Typical pump-and-treat (PAT) optimization problems involve design of pumping schemes, while minimizing cost and meeting a set of constraints. Due to scarcity of information about the hydrogeological system, stochastic modeling approaches can be used to assess tradeoffs between optimality and reliability. Using a stochastic approach, the constrained, single-objective problem may be turned into a multiobjective problem by substituting constraint inequalities with an additional objective function (OF) that accounts for the reliability of the PAT process. In this work, two approaches are analyzed: in one case, the additional OF consists of the probability of failure of a given remediation policy; in another, the OF additional is represented by the recourse, namely the penalty cost induced by the violation of constraints. In order to overcome the overwhelming computational cost required by stochastic simulation, surrogate forms of the OFs are introduced. In the test case under investigation, such functions are estimated by a kriging interpolation of the OF over a series of data points obtained from stochastic simulations of flow and transport, and calibrated against stochastic optimization solutions. The analysis of the two approaches for addressing the tradeoff of cost vs. reliability indicates that recourse accounts not only for the frequency of constraint violations, as the probability of failure does, but also for the intensity with which these occur. Ultimately, the recourse method allows considering less restrictive policies, although these may be highly sensitive to the choice of penalty functions.     

Integrated Hydrologic Modeling to Untangle the Impacts of Water Management During Drought

Over the past century, groundwater levels in California's San Joaquin Valley have dropped by more than 30 m in some areas mostly due to excessive groundwater extraction used to irrigate agricultural lands and sustain a growing population. Between 2012 and 2015, California experienced the worst drought in its recorded history, depleting surface water supplies and further exacerbating groundwater depletion in the region. Due to a lack of groundwater regulation, exact quantities of extracted groundwater in California are unknown and hard to quantify. Recent adoption of the Sustainable Groundwater Management Act has intensified efforts to identify sustainable groundwater use. However, understanding sustainable use in a highly productive agricultural system with an extremely complex surface water allocation system, variable groundwater use, and spatially extensive and diverse irrigation practices is no easy task. Using an integrated hydrologic model coupled with a land surface model, we evaluated how water management activities, specifically a suite of irrigation and groundwater pumping scenarios, impact surface water–groundwater fluxes and storage components and how those activities and the relationships between them change during drought. Results showed that groundwater pumping volume had the most significant impact on long-term water storage changes. A comparison with total water storage anomaly (TWSA) estimates from NASA's Gravity Recover and Climate Experiment (GRACE) provided some insight regarding which combinations of pumping and irrigation matched the GRACE TWSA estimates, lending credibility to these scenarios. In addition, the majority of long-term water storage changes during the recent drought occurred in groundwater storage in the deeper subsurface.