عنوان مقاله [English]
Probable maximum precipitation (PMP) is a theoretical concept that is widely used by hydrologists to arrive at estimates for probable maximum flood (PMF) which is applicable to the risk evaluation of hydraulic structures such as dams and to review the adequacy of their spillway capacities. The PMP indicates the greatest amount of precipitation that is meteorologically possible for an area at a particular time with a given duration. There are the various methods to estimate PMP based on the different intended durations.
Material and Methods
In the present investigation using the annual maximum 24-h precipitation data series of 36 synoptic stations in 4 southwestern basins of Iran, the PMP values have been calculated based on the statistical (Hershfield-1 and Desa methods) and synoptical/physical methods.
The derived results from both methods statistically are compared together and to the mean precipitation values as well as the observational maximum 24-h precipitation values. Furthermore, the values are considered spatially over the country to find out the geographic distribution of the PMP ranges. The Hershfield method is a statistical method for estimating the PMP for small areas that has been developed by Hershfield (1965) based on a general frequency equation given by Chow (1951).The method considers the annual rainfall series of a raingauge or an area and can be used at any place where there is sufficient rainfall data and in particular to make estimates when other meteorological data such as dew point, wind etc are lacking.
In the present investigation the annual maximum 24-h precipitation data series of 36 synoptic stations through a period of 22 years (1989-2010) over the Southwestern basins, have been provided from IRIMO. The selection of the stations was based on their geographic position and complete time-length of their data series over the study period of 22 years.
Then, all data series have been arranged into a database center in Excel and GIS software. As aforementioned, The PMP values have been calculated based on the Hershfield-1 and Desa methods.
the results showed that the PMP values derived from Hershfield-1 method were extremely higher/deviated comparing to the long term mean values as well as the observational maximum 24-h precipitation. The ratio of PMP helshfield-1 to the long term mean values was up to 265%, and to the maximum 24-h precipitation has been estimated about 4.66, in the southern stations with low rainfall.
Whiles the Desa method estimated the PMP values more closer to the recorded maximum precipitation data, as obtained ratio for PMP of Desa to the long term mean values was about 119% and to the maximum 24-h precipitation has been estimated about 2.19.
By the way, the coefficients of variation and SKEW-test affirmed the highest variability of maximum 24-h precipitation in the southern stations, as therein the CVs and SKEW-test results were obtained more than 40% and 0.65 respectively. So the PMP values could be unreliable over such southern stations with low and irregular rainfall.
Coefficient of variations derived from PMP values of Hershfield-1 and Desa illustrated also a range of 24-72% and 22-67% respectively. As it is found the PMP values of Hershfield-1 could have more variability comparing to the outputs of Desa method. This difference is originated from Km (frequency coefficient) calculations which are various for each of two PMP estimation methods, as in the Desa calculation method, the highest event of maximum 24-h precipitation is ignored, hence the Km equation resulted a lower coefficient in contrast to what derived from Km calculation in the Hershfield-1 method. In the Physical method the storm happened in 16-17 November 1994 is selected as an example. For this method we applied the humidity factor to maximize the precipitation. The derived PMP through physical method illustrated the lowest PMP values comparing to the statistical methods showing a PMP range from 24 to 134mm respectively at Ahvaz and Masjedsolyman stations.
In the next step the maps of the estimated PMP by both two statistical methods, and the observed maximum 24-h precipitation data, have been drawn through ArcGIS software and using the Kriging interpolation method. The maps illustrated the highest ranges of PMP and maximum 24-h precipitation over the center of the Karoon basin and southern areas of Jarahi basin. But, the northern basins of Marzi-gharbi and Karkheh have showed the lowest ranges.