Stochastic Modeling: Difference between revisions
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“A stochastic process is one in which there is a chance component in each successive event and ordinarily some degree of correlation between successive events. Modeling of a stochastic process involves the use of the ‘Monte Carlo’ method of adding a random (chance) component to a corelated component in order to construct each new event. The correlated component can be related, not only to preceding events of the same series, but also to concurrent and preceding events of series of related phenomena.<ref name="EM 1110-2-1415">[[Hydrologic Frequency Analysis (EM 1110-2-1415) | EM 1110-2-1415 Hydrologic Frequency Analysis, USACE, 1993]]</ref> | “A stochastic process is one in which there is a chance component in each successive event and ordinarily some degree of correlation between successive events. Modeling of a stochastic process involves the use of the ‘Monte Carlo’ method of adding a random (chance) component to a corelated component in order to construct each new event. The correlated component can be related, not only to preceding events of the same series, but also to concurrent and preceding events of series of related phenomena.<ref name="EM 1110-2-1415">[[Hydrologic Frequency Analysis (EM 1110-2-1415) | EM 1110-2-1415 Hydrologic Frequency Analysis, USACE, 1993]]</ref> | ||
“Work in stochastic hydrology has related primarily to annual and monthly streamflows, but the results often apply to other hydrologic quantities such as precipitation and temperatures. Some work on daily streamflow simulation has been done.<ref name="EM 1110-2-1415" /> | “Work in stochastic [[hydrology]] has related primarily to annual and monthly [[streamflows]], but the results often apply to other hydrologic quantities such as [[precipitation]] and temperatures. Some work on daily streamflow simulation has been done.<ref name="EM 1110-2-1415" /> | ||
“Hydrologic records are usually shorter than 10 years in length, and most of the mare shorter than 25 years. Even in the case of the longest records, the most extreme drought or flood event can be far different from the next most extreme event. There is often serious question as to whether to extreme event is representative of the period of record. The severity of a long drought can be changed drastically by adding or subtracting 1 year of its duration. In order that some estimate of the likelihood of more severe sequences can be made, the stochastic process can be simulated, and long sequences of events can be generated. If the generation is done correctly, the hypothetical sequence would have as equal likelihood of occurrence in the future as did the observed record.<ref name="EM 1110-2-1415" /> | “Hydrologic records are usually shorter than 10 years in length, and most of the mare shorter than 25 years. Even in the case of the longest records, the most extreme drought or flood event can be far different from the next most extreme event. There is often serious question as to whether to extreme event is representative of the period of record. The severity of a long drought can be changed drastically by adding or subtracting 1 year of its duration. In order that some estimate of the likelihood of more severe sequences can be made, the stochastic process can be simulated, and long sequences of events can be generated. If the generation is done correctly, the hypothetical sequence would have as equal likelihood of occurrence in the future as did the observed record.<ref name="EM 1110-2-1415" /> | ||
Revision as of 06:23, 18 November 2022
“A stochastic process is one in which there is a chance component in each successive event and ordinarily some degree of correlation between successive events. Modeling of a stochastic process involves the use of the ‘Monte Carlo’ method of adding a random (chance) component to a corelated component in order to construct each new event. The correlated component can be related, not only to preceding events of the same series, but also to concurrent and preceding events of series of related phenomena.[1]
“Work in stochastic hydrology has related primarily to annual and monthly streamflows, but the results often apply to other hydrologic quantities such as precipitation and temperatures. Some work on daily streamflow simulation has been done.[1]
“Hydrologic records are usually shorter than 10 years in length, and most of the mare shorter than 25 years. Even in the case of the longest records, the most extreme drought or flood event can be far different from the next most extreme event. There is often serious question as to whether to extreme event is representative of the period of record. The severity of a long drought can be changed drastically by adding or subtracting 1 year of its duration. In order that some estimate of the likelihood of more severe sequences can be made, the stochastic process can be simulated, and long sequences of events can be generated. If the generation is done correctly, the hypothetical sequence would have as equal likelihood of occurrence in the future as did the observed record.[1]
“The design of water resource projects is commonly based on assumed recurrence of past hydrologic events. By generating a number of hydrologic sequences, each of a specified desired length, it is possible to create a much broader base for hydrologic design. While it is not possible to create information that is not already in the record, it is possible to use the information more systematically and more effectively. In selecting the number and length of hydrologic sequences to be generated, it is usually considered that 10 to 20 sequences would be adequate and that their length should correspond to the period of project amortization.[1]
“It must be recognized that the more hydrologic events that are generated, the more chance that an extreme event or combination of events will be exceeded. Consequently, it is not logical that a design be based on the most extreme generated event, but rather on some consideration of the total consequences that would prevail for a given design if all generated events should occur. The more events that are generated, the less proportional weight each event is given. If a design if tested on 10 sequences of hydrologic events, for example, the benefits and costs associated with each sequence would be divided by 10 and added in order to obtain the ‘expected’ net benefits”.[1]
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Revision ID: 4524
Revision Date: 11/18/2022