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A study to determine the envelope curve of precipitation (case study: Semnan province).


Planners and design engineers of water resources would like estimates of probable maximum precipitation for the design of spillway capacities of dams which are to be located up-stream of large towns and industrial areas. In the case of such hydraulic structures no risks regarding their failure can be taken as their failure due to inadequate design would result in tremendous loss of life and destruction of valuable property. P.M.P is defined as the highest or the extreme rainfall which is possible over a given point or a specified area for a given duration. It is also defined as the greatest depth of precipitation for a given duration that is physically possible over a given point or an area. Probable expression emphasis that there is not any possibility of exact calculation for maximum precipitation because earth atmosphere physics has not been recognized clearly and climate data are very approximate. In other words, maximum elevation of precipitation in a basin for a specific time of rainfall and in a special period of year is called P.M.P. [1]. There are various methods for calculating P.M.P, one of which is the envelop curve method. In this method, all records of precipitation for a location are plotted on a log-log graph in which X axis indicate time and Y axis is precipitation and finally a line is drawn in a way that covers all observed precipitation events. Designing hydrologic structures needs to survey and analysis of meteorology data and applying these analysis can have an important rule on success of these projects and increasing their useful life [2]. For this reason use of envelop curve can help to reach to this goal. Rainfall in the form rain and snow are main sources of recharging surface and ground water. Direct measurement of precipitation by pluviometer, totalizer and pluviograph is done by ministry of energy and meteorological organization of country. In some cases research stations is established by some organizations for their researches temporarily.

Hershfield [4,5] by use of general formula of rotation and records of daily rain for more than 2600 formal stations among which, %90 of are located in U.S.A. offered equation PMP [??]P. K.SD for calculation of P.M.P. where:

P.M.P = Probable Maximum Precipitation, P = mean observed of Precipitation, SD = standard deviation of observed Precipitation and K = rotation coefficient. He obtained amount of this coefficient for calculation of P.M.P to be equal to 15. Hershfield also collected the informal records of rainfall in 1981 that was evaluated by personnel of rain gauge stations and by fitting envelop curve on them offered P = 422[T.sup.0.475] equation for that envelop curve where: P = Precipitation (mm) and T = time (hour) [7]. Kapus et al., [8] in a study in Halileh, near of Boshehr city, offered a graphical equation for evaluation of P.M.P and Precipitation events with 2 to 100 year return periods and 5 minute to 24 hours time bases. Konrad [7] obtained the relation between precipitation, topography and local characteristics for a mountain in south of U.S. Rakhecha [11] achieved to rainfall frequency zonation by use of hybrid guesser in Alabama. In recent decades, considering the importance of probable flood and its effects in designing dams weirs, a lot of efforts has been done for estimation of P.M.P. Tehran regional water organization with cooperation of Mahab Ghodss consulting engineering [12] in multipurpose storage dam of Taleghan project attained to point evaluation of P.M.P in statistic and synoptic methods by use of rainfall records and evaporation of water surface. Mahab Ghodss consulting engineering [6] analysed P.M.P for Boshehr, Esfahan, Arak and Hamadan provinces by non-mountainous method and also evaluated P.M.P for stations of Arak, Hamadan(airport & nozheh) for a 24-hour period. Jalilian [6] by use of rainfall records in north of Iran synoptic stations offered envelop curve for this location and also P = 100.415[T.sup.0.3647] equation was suggested for this location where: P = Precipitation (mm) and T = time (hour). Ghahraman and Sepaskhah [3] attained to evaluation of P.M.P in some climate samples in south of Iran.

Materials and Methods

2.1. Case Study:

Semnan is one of the 30 provinces of Iran. It is in the north of the country, and its center is Semnan. The province of Semnan covers an area of 96,816 square kilometers and stretches along the Alborz mountain range and borders to Dasht-e Kavir desert in its southern parts. Because of Semnan's geography condition, its climate is desert, semi desert and arid, and because of soil and water limitation, agriculture status is not suitable. Cities of the province include Semnan, Damghan, Shahrood and Garmsar.

2.2. Data Source:

In this study, records of all synoptic stations of Semnan province were used [9] (table 1). The records of 24-hour rainfall were entered into written programs with [c.sup.++] and visual basic language for obtaining of maximum rainfall amount in other time bases from 24 hour to 8784 hour (one year), next output of these program that was 8 records for maximum rainfall in any time bases entered to excel software, then graph of these records drawn, as on this log-log graph X axis was time (hour) and Y axis was precipitation (mm), after that, a line that covered all of maximum precipitation drawn. In this way for all of synoptic stations in Semnan an envelop curve obtained, finally by use of all of records envelop curve of precipitation of Semnan province prepared.

2.3. Methodology:

When records of 24-hour precipitation were entered into the programs written in [c.sup.++] and visual basic language, these programs by use of corresponded algorithms, of these numbers will calculate the maximum precipitation of other time bases from 24 to 8784 hours. Then these records will be classified in descent way and for each time base 8 maximum records is offered, after that these records are entered into excel software and envelop curve for every station is obtained, finally for Semnan province by use of records of synoptic stations, precipitation envelop curve is drawn in excel software (fig 1 to 5). Equations of these curves for synoptic stations of Semnan province are as followed (equations 1 to 5).
Semnan province: (equation 1) P = 13.53[t.sup.0.3564]

Semnan city: (equation 2) P = 14.54[t.sup.0.326]

Garmsar city: (equation 3) P = 15.244[t.sup.0.2874]

Shahrod city: (equation 4) P = 13.53[t.sup.0.3564]

Damghan city: (equation 5) P = 8.845[t.sup.0.326]

Where: P = Precipitation (mm) and T = time (hour) correlation coefficient of all of these equations is more than %90 and level of significance of these equations is %1.






3. Results and Discussion

Because in envelop curve method all records are used and are easily and fast applicable by using computer softwares, it can be applied for designing hydraulic structures, in other hand the records of maximum precipitation that are obtained by P.M.P method may never happen but the records that are obtained in this method are records that has happened in the past, therefore, can be used for determining P.M.P with more confidence. Comparison of maximum observed precipitation of Semnan province and maximum observed precipitation of the world clearly shows that precipitation of Semnan is too less than maximum observed precipitation in the world and this difference in long time precipitation is obvious Clearly. However short time precipitations amount is less than world maximum too, in a way that maximum Observed Precipitation of Semnan province is between %1 to %3 of maximum observed precipitation in the world (table 4). This condition is because of special climate and geology status of this province and its location in mid latitude and its distance from the sea. In tables 2 and 3 the maximum observed precipitation of the world and Semnan are represented, respectively and in table 4, records of table 2 and 3 are compared with each other. Because of lack of short time and showery Precipitation records, envelop curve for time bases of less than 24 hours has not been evaluated but by use of equations 1 to 4 these records can be evaluated for various cities of Semnan province. For Semnan province the maximum evaluated precipitation for 60, 20 and 15 minutes is equal to 13.53, 9.14 and 8.25 mm, respectively (table 2).

Comparison of maximum observed precipitation of synoptic stations of Semnan province with each other also show that maximum observed precipitation in Shahrod city is more than other cities and in Semnan is more than Garmsar and Damghan.


[1.] Farokhzadeh, B., 1999. Evaluation of maximum precipitation in various time steps and their relations to some sample climates of Iran. Thesis of Master of Science, Faculty of Natural Resources, University of Tehran.

[2.] Ghanbarpor, M.A., A.R. Telvary, 2003. Rainfall temporal pattern of synoptic stations in north of Iran. Pagouhesh va sazandegi journal in natural resources, 59: 96-103.

[3.] Ghahraman, B.A., M. Sepaskhah, 1994. Determining of extreme values in south of Iran. Nivar review, scientific and technical journal of meteorological organization, 22: 24-37.

[4.] Hershfield, D.M., 1961. Estimating the Probable Maximum Precipitation. J. Hyd. Div., Am. Soc. Of Civil Eng., 87: Hy. 99-116.

[5.] Hershfield, D.M., 1981. The magnitude of the hydrological frequency factor in maximum rainfall estimation.Hydro.Sci.Bulletin, 26(2-6): 171-177.

[6.] Jalilian, H., 2007. Preparing the envelop curve of precipitation for Northern Iran. M.Sc. seminar, Faculty of Natural Resources, Univ. of Tehran, pp: 80.

[7.] Konrad, C., 1995. Maximum precipitation rates in the southern Blue Ridge mountains of the southeastern United States. Climate Research, 5: 159-166.

[8.] Kapus, U.J., M., Bleek and S.H. Blair, 1977. Rainfall frequencies for the Persian Gulf coast of Iran. Hydrological Sciences-Bulletin-des Sciences Hydrologiques, 23: 1-3/1978.

[9.] Meteorological organization of Iran, 2007. Precipitation records of Semnan province.

(10.) Mahdavi, M., 2005. Applied hydrology. Tehran university press., 1: 401.

[11.] Rakhecha, P.R., B.N. Mandal and A.K. Kulkarni, 1994. estimation of probable maximum precipitation for catchment in eastern by a generalized method .Theor. Appl. Climatol 1995, 51: 67-74.

12.] Tehran regional water organization and cooperation of Mahab Ghodss consulting engineering, 1986. Report of multipurpose storage dam of Taleghan project.

[13..] Tehran regional water organization and cooperation of Mahab Ghodss consulting engineering, 1987. Evaluation of P.M.P for 15 Khordad dam project.

Saleh Arekhi

Assistant Professor, Watershed Management Department, Agriculture College, Ilam University, Ilam, Iran.

Corresponding Author

Saleh Arekhi, Assistant Professor, Watershed Management Department, Agriculture College, Ilam University, Ilam, Iran.

Table 1: Synoptic stations of Semnan province.

No. Station Duration Longitude Latitude Elevation
 (degree) (degree) (m)

1 Semnan 1961-2005 53 33 35 35 1130.8
2 Shahrod 1961-2005 54 57 36 25 1345.3
3 Damghan 2000-2005 54 19 36 09 1154.5
4 Garmsar 1982-2005 52 16 35 12 825.2

Table 2: Maximum observed rains in various time bases in the world.

Location Precipitation (mm) Time

Bavaria (Germany) 126 8 min.
plumb point (Jamaica) 198 15 min.
Missouri (America) 305 42 min.
Shanghai (China) 401 1 hour
Modeo chaidung (China) 840 6 hour
Reunion islands 2467 2 day
Cherrapunji (India) 5003 7 day
Cherrapunji (India) 9300 1 month
Cherrapunji (India) 22454 6 month
Cherrapunji (India) 26461 1 year

Table 3: Maximum observed rains in various time bases in Semnan

Location Precipitation (mm) Time

Shahrod city 42 24 hour
Shahrod city 61 48 hour
Shahrod city 68.2 72hour
Semnan city 73 7 day
Semnan city 258 1 month
Shahrod city 283.2 6 month
Shahrod city 344.2 1 year

Table 4: Comparison of maximum observed rains in Semnan province and
the world.

Time Maximum observed rains Maximum observed
 in Semnan province (mm) rains in the
 world (mm)

2 day 61 2467
7 day 73 5003
1 month 258 9300
6 month 283.2 22454
1 year 344.2 26461

Time Ratio of maximum observed
 rains in Semnan province
 to maximum observed rains
 in the world (%)

2 day 2.5
7 day 1.5
1 month 2.78
6 month 1.26
1 year 1.3
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Title Annotation:Original Article
Author:Arekhi, Saleh
Publication:Advances in Environmental Biology
Article Type:Report
Geographic Code:7IRAN
Date:Jan 1, 2012
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