Originally published on October 26, 2011 at The Spout
If you have read the previous posts, you know that as opposed to my fellow contributors, my approach to water problems is from an engineering perspective. So one more time I intend to share with you an engineer's perspective through the application of statistics to solve water related problems.
The main topic that I intend to introduce to you today is called moment matching, but first I will explain why we use moment matching for planning and management of water resources. In order to plan the long-term operation of a hydropower reservoir - through utilizing approaches such as stochastic dynamic programming - operation engineers need to have access to the forecasts of future inflows into the reservoir. Clearly, a great deal of uncertainty is inevitable in forecasting future inflows and operations engineers have to consider the pertaining risks. One of the useful methods to managing uncertainties is generating multiple inflow scenarios. Usually inflow scenario trees, which consider the dependency of the inflow at a time step to the inflow at the previous time step, are the desirable structure. Generating multiple potential scenarios of future events through analyzing the available data from similar events in the past is a common approach in many areas of research with numerous practical applications. Similarly, there are several statistical methods to generate scenarios of the inflows into a reservoir through the use of recorded inflows in the past. One of these methods I have been working with recently is called moment matching. It is not always possible to detect the statistical distribution of an event, which is the basis of several inflow forecasting methods, with the available historical data. In these instances, moment matching could be a useful surrogate. As its name implies, moment matching is a method that generates scenarios that match the statistical moments of the historically recorded data. Which moments to include is up to the researchers and depends on the specific problem they are trying to solve. For the case of inflow scenarios, for instance, there some studies have used moment matching for generating scenarios that match the first four statistical moments (expected value, standard deviation, skewness, kurtosis) and also the correlation coefficients (could be serial, seasonal, or spatial correlation) between historical inflows. In 2003, Michael Kaut and his colleagues wrote a paper on developing an efficient algorithm for scenario generation with the use of moment matching. If you are interested in learning more, or if you think the algorithm could be of use to you, do not hesitate to visit Michael Kaut’s website for free access to a full source code of the algorithm.
M. H. (Ali) Alipour is a Ph.D. student and recipient of Trustee Doctoral Fellowship at the University of Central Florida (Orlando). His research includes water resources planning and management, hydrology, and ecohydraulics.