Introduction to stochastic programming

Wind speeds over the world’s oceans have increased over the past two decades, as have wave heights. Studies of climate change typically consider measurements or predictions of temperature over extended periods of time. Climate, however, is much more than temperature. Over the oceans, changes in wind speed and the surface gravity waves generated by such winds play an important role. We used a 23-year database of calibrated and validated satellite altimeter measurements to investigate global changes in oceanic wind speed and wave height over this period. We find a general global trend of increasing values of wind speed and, to a lesser degree, wave height, over this period. The rate of increase is greater for extreme events as compared to the mean condition.

https://researchbank.swinburne.edu.au/file/bca43746-6f16-4ad2-a4b7-27f8d8d60fed/1/PDF (Published version).pdf

Global trends in wind speed and wave height over the past 25 years

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Compass and Gyroscope: Integrating Science and Politics for the Environment

Data assimilation (DA) holds considerable potential for improving hydrologic predictions as demonstrated in numerous research studies. However, advances in hydrologic DA research have not been adequately or timely implemented in operational forecast systems to improve the skill of forecasts for better informed real-world decision making. This is due in part to a lack of mechanisms to properly quantify the uncertainty in observations and forecast models in real-time forecasting situations and to conduct the merging of data and models in a way that is adequately efficient and transparent to operational forecasters. The need for effective DA of useful hydrologic data into the forecast process has become increasingly recognized in recent years. This motivated a hydrologic DA workshop in Delft, the Netherlands in November 2010, which focused on advancing DA in operational hydrologic forecasting and water resources management. As an outcome of the workshop, this paper reviews, in relevant detail, the current status of DA applications in both hydrologic research and operational practices, and discusses the existing or potential hurdles and challenges in transitioning hydrologic DA research into cost-effective operational forecasting tools, as well as the potential pathways and newly emerging opportunities for overcoming these challenges. Several related aspects are discussed, including (1) theoretical or mathematical aspects in DA algorithms, (2) the estimation of different types of uncertainty, (3) new observations and their objective use in hydrologic DA, (4) the use of DA for real-time control of water resources systems, and (5) the development of community-based, generic DA tools for hydrologic applications. It is recommended that cost-effective transition of hydrologic DA from research to operations should be helped by developing community-based, generic modeling and DA tools or frameworks, and through fostering collaborative efforts among hydrologic modellers, DA developers, and operational forecasters.

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Advancing data assimilation in operational hydrologic forecasting: progresses, challenges, and emerging opportunities

Dynamic programming and stochastic control

Short-term optimal operation of water systems using ensemble forecasts

This article investigates the improvement of the operation of a four-reservoir system in the Seine River basin, France, by use of deterministic and ensemble weather forecasts and real-time control. In the current management, each reservoir is operated independently from the others and following prescribed rule-curves, designed to reduce floods and sustain low flows under the historical hydrological conditions. However, this management system is inefficient when inflows are significantly different from their seasonal average and may become even more inadequate to cope with the predicted increase in extreme events induced by climate change. In this work, a centralized real-time control system is developed to improve reservoirs operation by exploiting numerical weather forecasts that are becoming increasingly available. The proposed management system implements a well-established optimization technique, model predictive control (MPC), and its recently modified version that can incorporate uncertainti...

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Optimal Operation of the Multireservoir System in the Seine River Basin Using Deterministic and Ensemble Forecasts

Uncertainty of hydrological forecasts represents valuable information for water managers and hydrologists. This explains the popularity of probabilistic models, which provide the entire distribution of the hydrological forecast. Nevertheless, many existing hydrological models are deterministic and provide point estimates of the variable of interest. Often, the model residual error is assumed to be homoscedastic; however, practical evidence shows that the hypothesis usually does not hold. In this paper we propose a simple and effective method to quantify predictive uncertainty of deterministic hydrological models affected by heteroscedastic residual errors. It considers the error variance as a hydrological process separate from that of the hydrological forecast and therefore predictable by an independent model. The variance model is built up using time series of model residuals, and under some conditions on the same residuals, it is applicable to any deterministic model. Tools for regression analysis applied to the time series of residual errors, or better their absolute values, combined with physical considerations of the hydrological features of the system can help to identify the most suitable input to the variance model and the most parsimonious model structure, including dynamic structure if needed. The approach has been called dynamic uncertainty modeling by regression on absolute errors and is demonstrated by application to two test cases, both affected by heteroscedasticity but with very different dynamics of uncertainty. Modeling results and comparison with other approaches, i.e., a constant, a cyclostationary, and a static model of the variance, confirm the validity of the proposed method.

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Dynamic modeling of predictive uncertainty by regression on absolute errors

Open water systems are one of the most externally influenced systems due to their size and continuous exposure to uncertain meteorological forces. The control of systems under uncertainty is, in general, a challenging problem. In this paper, we use a stochastic programming approach to control a drainage system in which the weather forecast is modeled as a disturbance tree. Each branch of the tree corresponds to a possible disturbance realization and has a certain probability associated to it. A model predictive controller is used to optimize the expected value of the system variables taking into account the disturbance tree. This technique, tree-based model predictive control (TBMPC), is solved in a distributed fashion. In particular, we apply dual decomposition to get an optimization problem that can be solved by different agents in parallel. In addition, different possibilities are considered in order to reduce the communicational burden of the distributed algorithm without reducing the performance of the controller significantly. Finally, the performance of this technique is compared with others such as minmax or multiple MPC.

Distributed tree-based model predictive control on a drainage water system

This paper presents a new methodology to generate a tree from an ensemble. The reason to generate a tree is to use the ensemble in multistage stochastic programming. A correct tree structure is of critical importance because it strongly affects the performance of the optimization. A tree, in contrast to an ensemble, specifies when its trajectories diverge from each other.



A tree can be generated from the ensemble data by aggregating trajectories over time until the difference between them becomes such that they can no longer be assumed to be similar, at such a point, the tree branches.



The proposed method models the information flow: it takes into account which observations will become available, at which moment, and their level of uncertainty, i.e. their probability distributions (pdf). No conditions are imposed on those distributions.



The method is well suited to trajectories that are close to each other at the beginning of the forecasting horizon and spread out going on in time, as ensemble forecasts typically are. Copyright © 2012 John Wiley & Sons, Ltd.

Luciano Raso

Papers

Short-term optimal operation of water systems using ensemble forecasts

Optimal Operation of the Multireservoir System in the Seine River Basin Using Deterministic and Ensemble Forecasts

Dynamic modeling of predictive uncertainty by regression on absolute errors

Distributed tree-based model predictive control on a drainage water system

Tree structure generation from ensemble forecasts for real time control