This study gives a phenomenologically based stochastic
model of space -time rainfall. Specifically, two random variables
on the spatial rainfall, e.g. the cumulative rainfall
within a season and the maximum cumulative rainfall per rainfall
event within a season are considered. An approach is
given to determine the cumulative distribution function
(c.d.f.) of the cumulative rainfall per event, based on a
particular random structure of space -time rainfall. Then the
first two moments of the cumulative seasonal rainfall are
derived based on a stochastic dependence between the cumulative
rainfall per event and the number of rainfall events
within a season. This stochastic dependence is important in
the context of the spatial rainfall process. A theorem is
then proved on the rate of convergence of the exact c.d.f. of
the seasonal cumulative rainfall up to the ith year, i > 1,
to its limiting c.d.f. Use of the limiting c.d.f. of the
maximum cumulative rainfall per rainfall event up to the ith
year within a season is given in the context of determination
of the 'design rainfall'. Such information is useful in the
design of hydraulic structures.
Special mathematical applications of the general
theory are developed from a combination of empirical and phenomenological based assumptions. A numerical application
of this approach is demonstrated on the Atterbury watershed
in the Southwestern United States.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/620120 |
| Date | 06 1900 |
| Creators | Gupta, Vijay Kumar |
| Contributors | Department of Hydrology & Water Resources, The University of Arizona |
| Publisher | Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ) |
| Source Sets | University of Arizona |
| Language | en_US |
| Detected Language | English |
| Type | text, Technical Report |
| Source | Provided by the Department of Hydrology and Water Resources. |
| Rights | Copyright © Arizona Board of Regents |
| Relation | Technical Reports on Hydrology and Water Resources, No. 18 |
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