NEAREST NEIGHBOR REGRESSION ESTIMATORS IN RAINFALL-RUNOFF FORECASTING

Persistent Link:
http://hdl.handle.net/10150/282088
Title:
NEAREST NEIGHBOR REGRESSION ESTIMATORS IN RAINFALL-RUNOFF FORECASTING
Author:
Karlsson, Magnus Sven
Issue Date:
1985
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
The subject of this study is rainfall-runoff forecasting and flood warning. Denote by (X(t),Y(t)) a sequence of equally spaced bivariate random variables representing rainfall and runoff, respectively. A flood is said to occur at time period (n + 1) if Y(n + 1) > T where T is a fixed number. The main task of flood warning is that of deciding whether or not to issue a flood alarm for the time period n + 1 on the basis of the past observations of rainfall and runoff up to and including time n. With each decision, warning or no warning, there is a certain probability of an error (false alarm or no alarm). Using notions from classical decision theory, the optimal solution is the decision that minimizes Bayes risk. In Chapter 1 a more precise definition of flood warning will be given. A critical review (Chapter 2) of classical methods for forecasting used in hydrology reveals that these methods are not adequate for flood warning and similar types of decision problems unless certain Gaussian assumptions are satisfied. The purpose of this study is to investigate the application of a nonparametric technique referred to as the k-nearest neighbor (k-NN) methods to flood warning and least squares forecasting. The motivation of this method stems from recent results in statistics which extends nonparametric methods for inferring regression functions in a time series setting. Assuming that the rainfall-runoff process can be cast in the framework of Markov processes then, with some additional assumptions, the k-NN technique will provide estimates that converge with an optimal rate to the correct decision function. With this in mind, and assuming that our assumptions are valid, then we can claim that this method will, as the historical record grows, provide the best possible estimate in the sense that no other method can do better. A detailed description of the k-NN estmator is provided along with a scheme for calibration. In the final chapters, the forecasts of this new method are compared with the forecasts of several other methods commonly used in hydrology, on both real and simulated data.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Rain and rainfall -- Forecasting.; Flood forecasting.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Systems and Industrial Engineering
Degree Grantor:
University of Arizona
Advisor:
Yakowitz, Sidney

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleNEAREST NEIGHBOR REGRESSION ESTIMATORS IN RAINFALL-RUNOFF FORECASTINGen_US
dc.creatorKarlsson, Magnus Svenen_US
dc.contributor.authorKarlsson, Magnus Svenen_US
dc.date.issued1985en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThe subject of this study is rainfall-runoff forecasting and flood warning. Denote by (X(t),Y(t)) a sequence of equally spaced bivariate random variables representing rainfall and runoff, respectively. A flood is said to occur at time period (n + 1) if Y(n + 1) > T where T is a fixed number. The main task of flood warning is that of deciding whether or not to issue a flood alarm for the time period n + 1 on the basis of the past observations of rainfall and runoff up to and including time n. With each decision, warning or no warning, there is a certain probability of an error (false alarm or no alarm). Using notions from classical decision theory, the optimal solution is the decision that minimizes Bayes risk. In Chapter 1 a more precise definition of flood warning will be given. A critical review (Chapter 2) of classical methods for forecasting used in hydrology reveals that these methods are not adequate for flood warning and similar types of decision problems unless certain Gaussian assumptions are satisfied. The purpose of this study is to investigate the application of a nonparametric technique referred to as the k-nearest neighbor (k-NN) methods to flood warning and least squares forecasting. The motivation of this method stems from recent results in statistics which extends nonparametric methods for inferring regression functions in a time series setting. Assuming that the rainfall-runoff process can be cast in the framework of Markov processes then, with some additional assumptions, the k-NN technique will provide estimates that converge with an optimal rate to the correct decision function. With this in mind, and assuming that our assumptions are valid, then we can claim that this method will, as the historical record grows, provide the best possible estimate in the sense that no other method can do better. A detailed description of the k-NN estmator is provided along with a scheme for calibration. In the final chapters, the forecasts of this new method are compared with the forecasts of several other methods commonly used in hydrology, on both real and simulated data.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectRain and rainfall -- Forecasting.en_US
dc.subjectFlood forecasting.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineSystems and Industrial Engineeringen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorYakowitz, Sidneyen_US
dc.identifier.proquest8526315en_US
dc.identifier.oclc13819480en_US
dc.identifier.bibrecord.b1556700xen_US
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