A STOCHASTIC DYNAMIC PROGRAMMING MODEL FOR THE OPTIMUM OPERATION OF A MULTI-PURPOSE RESERVOIR1

ABSTRACT: The main objective of this paper is to present a stockastic dynamic programming model useful in determining the optimal operating policy of a single multipurpose surface reservoir. It is the unreliability of forecasting the amount of future streamflow which makes the problem of a reservoir operation a stochastic process. In this paper the stochastic nature of the streamflow is taken into account by considering the correlation between the streamflows of each pair of consecutive time intervals. This interdependence is used to calculate the probability of transition from a given state and stage to its succeeding ones. A dynamic programming model with a physical equation and a stochastic recursive equation is developed to find the optimum operational policy. For illustrative purposes, the model is applied to a real surface water reservoir system.     

ESTIMATED IMPACTS OF CLIMATE WARMING ON CALIFORNIA WATER AVAILABILITY UNDER TWELVE FUTURE CLIMATE SCENARIOS1

Spatially disaggregated estimates of over 131 stream‐flow, ground water, and reservoir evaporation monthly time series in California have been created for 12 different climate warming scenarios for a 72‐year period. Such disaggregated hydrologic estimates of multiple hydrologic cycle components are important for impact and adaptation studies of California's water system. A statewide trend of increased winter and spring runoff and decreased summer runoff is identified. Without operations modeling, approximate changes in water availability are estimated for each scenario. Even most scenarios with increased precipitation result in less available water because of the current storage systems' inability to catch increased winter streamflow in compensation for reduced summer runoff. The water availability changes are then compared with estimated changes in urban and agricultural water uses in California between now and 2100. The methods used in this study are relatively simple, but the results are qualitatively consistent with other studies focusing on the hydrologies of single basins or surface water alone.     

FOREST HYDROLOGY ISSUES FOR THE 21ST CENTURY: A CONSULTANT'S VIEWPOINT1

ABSTRACT: Forest hydrology should be a mature science with routine use of hydrological procedures to evaluate the effect of past, current and proposed harvesting practices on water resources. It is not. However, water users are pressuring forest managers to exercise their role in managing forested watersheds for water supply. Most forest managers are poorly equipped to carry out this role. Forestry schools need to ensure that their graduates, whether employed in forest management positions or as specialists in watershed management, understand that all forestry operations may affect instream or downstream water users. Specialists in forest hydrology should be fully aware of the following: (1) climate and watershed characteristics influence streamflow in separate ways; (2) forestry practices produce changes in water yield and quality, and that only these changes need to be evaluated to estimate their effects; (3) watershed storage is a critical factor in evaluating the effects of harvesting on streamflow; and (4) the effect of harvest on one watershed cannot be extrapolated to another without consideration of the processes affected. Research is needed to assist watershed managers in applying models to watersheds for which climate and streamflow data are insufficient. Research is also needed to incorporate climate, streamflow and other data for hydrological models into geographic information systems. Joint research projects are needed to develop physical relationships between stream channel characteristics of importance to fisheries biologists and streamflow characteristics affected by forest harvest.     

COMPARISON OF STOCHASTIC AND DETERMINISTIC DYNAMIC PROGRAMMING FOR RESERVOIR OPERATING RULE GENERATION1

ABSTRACT: Two dynamic programming models — one deterministic and one stochastic — that may be used to generate reservoir operating rules are compared. The deterministic model (DPR) consists of an algorithm that cycles through three components: a dynamic program, a regression analysis, and a simulation. In this model, the correlation between the general operating rules, defined by the regression analysis and evaluated in the simulation, and the optimal deterministic operation defined by the dynamic program is increased through an iterative process. The stochastic dynamic program (SDP) describes streamflows with a discrete lag-one Markov process. To test the usefulness of both models in generating reservoir operating rules, real-time reservoir operation simulation models are constructed for three hydrologically different sites. The rules generated by DPR and SDP are then applied in the operation simulation model and their performance is evaluated. For the test cases, the DPR generated rules are more effective in the operation of medium to very large reservoirs and the SDP generated rules are more effective for the operation of small reservoirs.     

Loss Rates from Lake Powell and Their Impact on Management of the Colorado River

As demand for water in the southwestern United States increases and climate change potentially decreases the natural flows in the Colorado River system, there will be increased need to optimize the water supply. Lake Powell is a large reservoir with potentially high loss rates to bank storage and evaporation. Bank storage is estimated as a residual in the reservoir water balance. Estimates of local inflow contribute uncertainty to estimates of bank storage. Regression analyses of local inflow with gaged tributaries have improved the estimate of local inflow. Using a stochastic estimate of local inflow based on the standard error of the regression estimator and of gross evaporation based on observed variability at Lake Mead, a reservoir water balance was used to estimate that more than 14.8 billion cubic meters (Gm³) has been stored in the banks, with a 90% probability that the value is actually between 11.8 and 18.5 Gm³. Groundwater models developed by others, observed groundwater levels, and simple transmissivity calculations confirm these bank storage estimates. Assuming a constant bank storage fraction for simulations of the future may cause managers to underestimate the actual losses from the reservoir. Updated management regimes which account more accurately for bank storage and evaporation could save water that will otherwise be lost to the banks or evaporation.     

A Streamflow Forecasting Framework using Multiple Climate and Hydrological Models1

Abstract: Water resources planning and management efficacy is subject to capturing inherent uncertainties stemming from climatic and hydrological inputs and models. Streamflow forecasts, critical in reservoir operation and water allocation decision making, fundamentally contain uncertainties arising from assumed initial conditions, model structure, and modeled processes. Accounting for these propagating uncertainties remains a formidable challenge. Recent enhancements in climate forecasting skill and hydrological modeling serve as an impetus for further pursuing models and model combinations capable of delivering improved streamflow forecasts. However, little consideration has been given to methodologies that include coupling both multiple climate and multiple hydrological models, increasing the pool of streamflow forecast ensemble members and accounting for cumulative sources of uncertainty. The framework presented here proposes integration and offline coupling of global climate models (GCMs), multiple regional climate models, and numerous water balance models to improve streamflow forecasting through generation of ensemble forecasts. For demonstration purposes, the framework is imposed on the Jaguaribe basin in northeastern Brazil for a hindcast of 1974‐1996 monthly streamflow. The ECHAM 4.5 and the NCEP/MRF9 GCMs and regional models, including dynamical and statistical models, are integrated with the ABCD and Soil Moisture Accounting Procedure water balance models. Precipitation hindcasts from the GCMs are downscaled via the regional models and fed into the water balance models, producing streamflow hindcasts. Multi‐model ensemble combination techniques include pooling, linear regression weighting, and a kernel density estimator to evaluate streamflow hindcasts; the latter technique exhibits superior skill compared with any single coupled model ensemble hindcast.     

Probabilistic Flood Inundation Forecasting Using Rating Curve Libraries

One approach for performing uncertainty assessment in flood inundation modeling is to use an ensemble of models with different conceptualizations, parameters, and initial and boundary conditions that capture the factors contributing to uncertainty. However, the high computational expense of many hydraulic models renders their use impractical for ensemble forecasting. To address this challenge, we developed a rating curve library method for flood inundation forecasting. This method involves pre‐running a hydraulic model using multiple inflows and extracting rating curves, which prescribe a relation between streamflow and stage at various cross sections along a river reach. For a given streamflow, flood stage at each cross section is interpolated from the pre‐computed rating curve library to delineate flood inundation depths and extents at a lower computational cost. In this article, we describe the workflow for our rating curve library method and the Rating Curve based Automatic Flood Forecasting (RCAFF) software that automates this workflow. We also investigate the feasibility of using this method to transform ensemble streamflow forecasts into local, probabilistic flood inundation delineations for the Onion and Shoal Creeks in Austin, Texas. While our results show water surface elevations from RCAFF are comparable to those from the hydraulic models, the ensemble streamflow forecasts used as inputs to RCAFF are the largest source of uncertainty in predicting observed floods.     

The Sensitivity of California Water Resources to Climate Change Scenarios1

Abstract: Using the latest available General Circulation Model (GCM) results we present an assessment of climate change impacts on California hydrology and water resources. The approach considers the output of two GCMs, the PCM and the HadCM3, run under two different greenhouse gas (GHG) emission scenarios: the high emission A1fi and the low emission B1. The GCM output was statistically downscaled and used in the Variable Infiltration Capacity (VIC) macroscale distributed hydrologic model to derive inflows to major reservoirs in the California Central Valley. Historical inflows used as inputs to the water resources model CalSim II were modified to represent the climate change perturbed conditions for water supply deliveries, reliability, reservoir storage and changes to variables of environmental concern. Our results show greater negative impacts to California hydrology and water resources than previous assessments of climate change impacts in the region. These impacts, which translate into smaller streamflows, lower reservoir storage and decreased water supply deliveries and reliability, will be especially pronounced later in the 21st Century and south of the San Francisco bay Delta. The importance of considering how climate change impacts vary for different temporal, spatial, and institutional conditions in addition to the average impacts is also demonstrated.     

BENEFITS OF TRANSFERRING STREAMFLOW PRIORITY FROM AGRICULTURAL TO NON-AGRICULTURAL USE1

ABSTRACT: In Virginia, as in many states, priority to streamflow is held by riparian landowners who are predominantly agricultural users. The streamfiow may also have a high potential value to non-agricultural users who do not have riparian rights. The potential benefits of transferring streamfiow priority rights from agricultural to non-agricultural use were evaluated using simulation for an eastern Virginia watershed. Lowering irrigators' priority to streamflow reduced crop yields and irrigated returns in some years because of inadequate water supplies. However, the transfer of priorities increased the likelihood that the urban reservoir would be able to withdraw water from the stream without interruption. As a result, priority trades reduced the size of reservoir needed to meet a given water requirement by municipal users. The resulting savings in reservoir construction and maintenance costs more than offset the losses to irrigators. Net savings could be achieved even if the reservoir were required to release water periodically to maintain a minimum level of instream flow. The conclusion is that the state should encourage trading of access to streamflow in order to increase the use efficiency of streamfiows. Alternative means by which the state can facilitate water exchanges are discussed.     

THE VALUE OF STREAMFLOW FORECASTING IN RESERVOIR OPERATION1

ABSTRACT: The value of streamflow forecasts in reservoir operation depends on a number of factors and may vary considerably. Assessment of forecast benefits is presented here for three specific systems. Statistical streamflow models of increasing forecasting ability are coupled with a recently developed stochastic control method in extensive simulation experiments. The performance of the system is statisticafly evaluated with regard to energy generation and flood and drought prevention. The results indicate that forecast benefits are system specific and may range from quite substantial to fairly minimal.     

RESERVOIR OPERATION ANI EVALUATION OF DOWNSTREAM FLOW AUGMENTATION1

ABSTRACT: Operation of a storage‐based reservoir modifies the downstream flow usually to a value higher than that of natural flow in dry season. This could be important for irrigation, water supply, or power production as it is like an additional downstream benefit without any additional investment. This study addresses the operation of two proposed reservoirs and the downstream flow augmentation at an irrigation project located at the outlet of the Gandaki River basin in Nepal. The optimal operating policies of the reservoirs were determined using a Stochastic Dynamic Programming (SDP) model considering the maximization of power production. The modified flows downstream of the reservoirs were simulated by a simulation model using the optimal operating policy (for power maximization) and a synthetic long‐term inflow series. Comparing the existing flow (flow in river without reservoir operation) and the modified flow (flow after reservoir operation) at the irrigation project, the additional amount of flow was calculated. The reliability analysis indicated that the supply of irrigation could be increased by 25 to 100 percent of the existing supply over the dry season (January to April) with a reliability of more than 80 percent.     

USE OF STREAMFLOW INCREASES FROM VEGETATION MANAGEMENT IN THE VERDE RIVER BASIN1

ABSTRACT: Although the effects of vegetation management on streamflow have been studied in many locations, the effects of augmented streamflow on downstream water users have not been carefully analyzed. This study examines the routing of streamflow increases that could be produced in the Verde River Basin of Arizona. Reservoir management and water routing to users in the Salt River Valley around Phoenix were carefully modeled. Simulation of water routing with and without vegetation modification indicates that, under current institutional conditions, less than one-half of the streamflow increase would reach consumptive users as surface water. Most of the remainder would accumulate in storage until a year of unusually heavy runoff, when it would add to reservoir spills. Under alternative scenarios, from 39 to 58 percent of the streamflow increase was delivered to consumptive users.     

A STOCHASTIC MODEL TO EVALUATE RIPARIAN IRRIGATION EXPANSION IN THE EASTERN UNITED STATES1

ABSTRACT: Irrigation has expanded in parts of the eastern United States. In some areas, the adjoining surface (riparian) water is the most economical source of irrigation water. Expanded demand for riparian water may lead to conflict among irrigators and other streamflow users. Accurate information on the potential for and impacts of riparian irrigation expansion is needed to decide if control of such expansion is necessary. In this study, a stochastic economic model to evaluate the impacts of potential irrigation expansion is presented. The model considers the soil, location, and land use characteristics of individual sites, as well as weather and streamflow patterns. The application of the model to an eastern Virginia watershed indicates that, with maximum potential expansion, water availability becomes limited and yields will be reduced in some years. As a result, the expected net returns from irrigation and the probability of breaking even on the investment are reduced substantially. The results suggest the need to consider regulation of surface water allocation for irrigation development in riparian watersheds.     

REAPPRAISAL OF WATER SUPPLY RESOURCES IN DELAWARE RIVER BASIN USING SYNTHETIC HYDROLOGY1

ABSTRACT The 60's drought (1961 1966) which hit the Northeastern United States, had its center over the Delaware River Basin and caused water supply shortages to New York City, Philadelphia, and many other towns and industries in the Basin. Until this event occurred, the existing water supply sources and those planned for the future had been considered adequate, as they were designed for the worst drought of record (usually the 1930-31 drought). In view of this “change in hydrology,” the Delaware River Basin Commission authorized a study (DRBC Resolution 67-4) to re-evaluate the adequacy of existing and planned water supply sources of the Delaware River Basin and its Service Area (New York City and northern New Jersey). Synthetic hydrology is a tool which can be used to overcome many of the limitations of the traditional approach. By analyzing generated streamflow traces in this study, it has been determined that there is a definite relationship between the accumulated rainfall deficiency during the drought and the return periods associated with various durations of runoff in the drought. This indicated that generated traces can be used to standardize the hydrology over an area where the intensity of drought varied. This represented an important facet in the study, because it provided a means to equalize the effects of this drought over the study area, and gave the Delaware River Basin Commission more information so that it could better plan and manage its water resources equitably, not only for the people within the Basin, but for the New York City and northern New Jersey areas as well. Synthetic hydrology was used to determine yield-probability relationships for 50-year periods, and storage-yield-frequency relationships for existing and planned water-supply reservoirs. It was also used to determine yield-probability relationships for reservoir systems within the Basin. In the study, it was determined that monthly streamflow traces and uniform draft rates could be used in yield analysis because of the magnitude of the reservoirs and because seasonal variations of draft rate are small in the study area. Although it was found that with the streamflow generating models (first order Markov) in common use today, it is not possible to definitely determine the actual frequency of a very severe historic drought, it is possible to place a drought in perspective by using synthetic hydrology. The study showed that it is a useful tool in determining water availability over a basin and is useful in studying water management problems such as interbasin transfers, and reservoir systems operations.     

A COMPARISON OF STREAMFLOW GENERATION MODELS FOR RESERVOIR CAPACITY-YIELD ANALYSIS1

ABSTRACT: An analysis of four streamflow generation schemes for the use in the estimation of the required conservation storage for a single reservoir is presented. The comparison of the generating schemes should aid in the selection of an appropriate model type for the reservoir sizing problem. The streamflow generation models are compared using two criteria. The first comparison is between the statistics of the generated streamflow sequences and the corresponding statistics from the historical record. The second evaluation compares the median reservoir size determined by each model with the required storage based on the historical flow sequence. The results of a comparative analysis for monthly streamflow data for the Rzav River in Yugoslavia are presented and discussed. The results indicate that both evaluation criteria are required to discriminate between the various options.     

Filyos River Streamflow Reconstruction from Tree‐Ring Chronologies with Nonparametric Approaches

The article presents nonparametric methods based on K nearest neighbors (KNNs), modified KNNs, and local polynomial techniques to reconstruct streamflow ensembles from tree‐ring data in Filyos River region (Turkey). Three methods were tested using cross‐validation for the overlap period, 1963‐1997 for which the tree‐ring and streamflow data are available. It was found that for the study where the length of the overlap period was limited, a nonparametric method based on a local polynomial technique provides simulations that have a slightly better solution than the other methods. After verification using standard statistical techniques, these methods were utilized to develop streamflow reconstructions from tree‐ring data for the paleo‐hydrologic period (1657‐1963). These reconstructions of seasonal low and high flows were discussed with the obtained flood duration curve. They were also compared with the historical archives and other tree‐ring reconstructions data available in the same river. Overall, the utility and limitations of these methods and the resulting streamflow simulations were discussed to assess the long‐term discharge behavior of Filyos River and to evaluate water supply reliability.     

MULTIOBJECTWE OPTIMIZATION OF RESERVOIR SYSTEMS OPERATION1

ABSTRACT: Development of optimal operational policies for large-scale reservoir systems is often complicated by a multiplicity of conflicting project uses and purposes. A wide range of multiobjective optimization methods are available for appraising tradeoffs between conificting objectives. The purpose of this study is to provide guidance as to those methods which are best suited to dealing with the challenging large-scale, nonlinear, dynamic, and stochastic characteristics of multireservoir system operations. As a case study, the selected methodologies are applied to the Han River Reservoir System in Korea for four principal project objectives: water supply and low flow augmentation; annual hydropower production, reliable energy generation, and minimization of risk of violating firm water supply requirements. Additional objectives such as flood control are also considered, but are imposed as fixed constraints.     

Urban Streamflow Response to Imported Water and Water Conservation Policies in Los Angeles,California

Los Angeles has a long history of importing water; however, drought, climate change, and environmental mitigation have forced the City to focus on developing more local water sources (target of 50% local supply by 2035). This study aims to improve understanding of water cycling in Los Angeles, including the impacts of imported water and water conservation policies. We evaluate the influence of local water restrictions on discharge records for 12 years in the Ballona Creek (urban) and Topanga Creek (natural) watersheds. Results show imported water has significantly altered the timing and volume of streamflow in the urban Ballona watershed, resulting in runoff ratios above one (more streamflow than precipitation). Further analysis comparing pre‐ vs. during‐mandatory water conservation periods shows there is a significant decrease in dry season streamflow during‐conservation in Ballona, indicating that prior to conservation efforts, heavy irrigation and other outdoor water use practices were contributing to streamflow. The difference between summer streamflow pre‐ vs. during‐conservation is enough to serve 160,000 customers in Los Angeles. If Los Angeles returns to more watering days, educating the public on proper irrigation rates is critical for ensuring efficient irrigation and conserving water; however, if water restrictions remain in place, the City must take the new flow volumes into account for complying with water quality standards in the region.     

THE POTENTIAL FOR INCREASING STREAMFLOW FROM SIERRA NEVADA WATERSHEDS1

The Sierra Nevada produces over 50 percent of California's water. Improvement of water yields from the Sierra Nevada through watershed management has long been suggested as a means of augmenting the state's water supply. Vegetation and snowpack management can increase runoff from small watersheds by reducing losses due to evapotranspiration, snow interception by canopy, and snow evaporation. Small clearcuts or group selection cuts creating openings less than half a hectare, with the narrow dimension from south to north, appear to be ideal for both increasing and delaying water delivery in the red fir-lodgepole pine and mixed-conifer types of the Sierra west slope. Such openings can have up to 40 percent more snow-water equivalent than does uncut forest. However, the water yield increase drops to 1/2-2 percent of current yield for an entire management unit, due to the small number of openings that can be cut at one time, physical and management constraints, and multiple use/sustained yield guidelines. As a rough forecast, water production from National Forest land in the Sierra Nevada can probably be increased by about 1 percent (0.6 cm) under intensive forest watershed management. Given the state of reservoir storage and water use in California, delaying streamflow is perhaps the greatest contribution watershed management can make to meeting future water demands.     

A COMPARISON OF SOME DYNAMIC,LINEAR AND POLICY ITERATION METHODS FOR RESERVOIR OPERATION1

Within the past few years, a number of papers have been published in which stochastic mathematical programming models, incorporating first order Markov chains, have been used to derive alternative sequential operating policies for a multiple purpose reservoir. This paper attempts to review and compare three such mathematical modeling and solution techniques, namely dynamic programming, policy iteration, and linear programming. It is assumed that the flows into the reservoir are serially correlated stochastic quantities. The design parameters are assumed fixed, i.e., the reservoir capacity and the storage and release targets, if any, are predetermined. The models are discrete since the continuous variables of time, volume, and flow are approximated by discrete units. The problem is to derive an optimal operating policy. Such a policy defines the reservoir release as a function of the current storage volume and inflow. The form of the solution and some of the advantages, limitations and computational efficiencies of each of the models and their algorithms are compared using a simplified numerical example.