Large scale evaluation of single storm and short/long term erosivity index models

A. KARAMI, M. HOMAEE, M. R. NEYSHABOURI, S. AFZALINIA, S. BASIRAT 207 Turk J Agric For 36 (2012) 207-216 © TÜBİTAK doi:10.3906/tar-1102-24 Large scale evaluation of single storm and short/long term erosivity index models Alidad KARAMI1,*, Mehdi HOMAEE1, Mohammad Reza NEYSHABOURI2, Sadegh AFZALINIA3, Sanaz BASIRAT4 1Department of Soil Science, Faculty of Agriculture, Tarbiat Modares University, P.O. Box: 14115-336, Tehran - IRAN 2Department of Soil Science, Faculty of Agriculture, University of Tabriz, P.O. Box: 51666-16471, Tabriz - IRAN 3Department of Agricultural Engineering Research, Fars Research Center for Agriculture and Natural Resources, P.O. Box: 73415-111, Shiraz - IRAN 4Department of Horticulture Science of Shiraz Branch, Islamic Azad University, P.O. Box: 71397-77669, Shiraz - IRAN Received: 12.02.2011 Abstract: Rainfall erosivity of the Revised Universal Soil Loss Equation (RUSLE) is infl uenced by the type, amount, and intensity of storm. In this research, rainfall data from 18 recording rain gauge stations were collected and analyzed. Further, their single storm, daily, monthly, and annual erosion indices were calculated and estimated by diff erent models. Duration of each rainfall was divided into 15 min intervals. Intensity and energy of each interval, maximum rainfall intensity of 30 min, total energy of each rainfall, and erosivity index of every single storm were calculated. Furthermore, Cooley’s model for single storm was evaluated and its coeffi cients were estimated. For daily rainfall erosion index prediction, Richardson’s model was assessed and its coeffi cients were also estimated. A new power model based on monthly rainfall was proposed in order to predict monthly rainfall erosion index. For the estimation of the annual rainfall erosion index, the Arnoldus model was evaluated and its coeffi cients were estimated. Th e coeffi cients for all equations were also determined using multiple regression. According to the calibrated Arnoldus model, an iso-rainfall erosion index map was drawn for the studied area consisting of 150 rain gauge information. Th e results indicated that models of Cooley, Richardson, Arnoldus, and the newly proposed model for monthly rainfall erosion index provide a reasonable agreement with the rainfall characteristics of the studied area. Key words: Rainfall erosivity, RUSLE, single storm Research Article * E-mail: alidad_karami@yahoo.com. Introduction Soil is the most important component of natural resources and is also the most eff ective factor in the economy of each region that is threatened by erosion. Assessments of soil erosion are needed to evaluate contaminant mobility (Johansen et al. 2003), conservation soil organic carbon (Breshears and Allen 2002), evaluation of runoff and hydrology (Beeson et al. 2001; Wilson et al. 2001; Johansen et al. 2003), and utilization of land management (Hastings et al. 2003). Based on the results of research conducted in Turkey, soil erosion is an important issue in this country (Bayramin et al. 2002; Yılmaz et al. 2005; Bayramin et al. 2006). Th erefore, assessment of factors causing soil erosion or controlling its severity is necessary. Large scale evaluation of single storm and short/long term erosivity index models 208 Kırnak (2002) reported that, according to the results of research conducted by Türkseven and Ayday (2000), the Universal Soil Loss Equation (USLE) model worked well in Turkey. Th e USLE was originally developed based on the information obtained from 10,000 fi eld plots to predict the long term average annual soil loss from some agricultural areas (Wischmeier and Smith 1965). It was later extended to cover the whole United States (Wischmeier and Smith 1978). RUSLE is extensively used to assess the degree of rill and interrill erosions. All parameters of this equation can be determined using regional conditions, relevant curves, and corresponding tables. However, the rainfall erosivity factor of RUSLE should be calculated from the rainfall pattern or from the long term continuous rain record information. Th e most common approach for estimating rainfall erosivity uses the interaction between the storm energy (E) (MJ ha–1) and the highest continuous 30 min rainfall intensity (I30) (mm h–1). Th e multiple products of these factors equal rainfall erosivity, noted as EI30. Th e parameter EI30 has been shown to be a better predictor of sediment yield than rainfall depth (Foster et al. 1982). Th e predictor is commonly used to model soil loss as well as sediment yield (Renard et al. 1997). Computation of the erosion index (EI), which is basic to the determination of the rainfall runoff erosivity factor R of the Revised Universal Soil Loss Equation (RUSLE), is tedious and time consuming and requires continuous records of rainfall intensity (Diodato 2004). Consequently, various researchers have introduced some models to calculate the rainfall erosivity index using the rainfall data that are available at rain gauge stations (Ateshian 1974; Wischmeier and Smith 1978). Bullock et al. (1990) stated that several years’ duration of rainfall intensity data are needed to calculate the R factor. Bagarello and D’Asarro (1994) found that the erosion index of a single storm is only related to the amount of rainfall, and derived an equation with power of 1.54 for the erosion index of the Mediterranean area. Th ey also developed a model for the erosion index in terms of rainfall amount and the maximum intensity of 30 min. Another rainfall erosion index model was presented for estimating erosion losses from individual rainfall events (Foster et al. 1981). Ateshian (1974) and Cooley (1980) developed 2 empirical equations for estimating EI30 from rainfall amounts for storms of diff erent types and durations. Hadda et al. (1991) expressed the relationship between rainfall erosion index (REI) and daily rainfall depth in the form of a model with random and deterministic components. Selker et al. (1990) also developed a model for the rainfall erosivity index based on daily rainfall. Th ey also evaluated another model for the erosivity index that has been developed based on the hourly precipitation. Richardson et al. (1983) developed a model to estimate the daily rainfall erosion index from daily rainfall amounts. Th eir model includes both deterministic and random components. Bullock et al. (1990) reported that the erosion index calculated by the Richardson model was more reliable than EI30 calculated by hourly data in southern Saskatchewan. Elsenbeer et al. (1993) reported that the Richardson model can properly predict the rainfall erosivity from daily rainfall amount. Posch and Rekolainen (1993) derived a power equation to estimate REI on daily rainfall because of a lack of continuous rainfall data in Finland. Th ey also reported that variation of REI was very small all over the country. Although the REI varied from station to station, the variation in coeffi cients at diff erent stations was negligible. Variation in REI was due to the rainfall intensity variation, which is a normal phenomenon. On the other hand, the slight variation in model coeffi cients indicated that the model had very good compatibility for the area of study to predict REI. Renard and Freimund (1994) developed a model to estimate monthly erosion index from average monthly rainfall. De Santos Loureio et al. (2001) estimated the EI30 index from monthly rainfall data for the south of Portugal. In the Mediterranean environment, 3 erosive periods were identifi ed. Th e fi rst period extends from July to October, the second erosive period has a duration of 2 months, from May to June, and the third erosive period extends from November to April, with values of erosivity 87.8 MJ mm ha−1 h−1, 0.10 Mg ha−1 month−1, and 17.5 MJ mm ha−1 h−1, respectively (López Vicente et al. 2008). A. KARAMI, M. HOMAEE, M. R. NEYSHABOURI, S. AFZALINIA, S. BASIRAT 209 Wischmeier (1962) computed the annual erosion index for 1700 stations in the USA, and prepared isoerodent maps. Wischmeier and Smith (1978) computed the rainfall erosion index and they prepared an isopluvial map. Kinnell (2003) compared USLE with modifi ed USLE (USLEM) equations. Because the USLEM includes the product of runoff ratio and EI30 value as the event erosivity index, it is more effi cient in estimating soil loss. Th e relationship between annual rainfall and erosivity is similar only in certain years. Th is confi rms the extreme variability of rainfall patterns in Mediterranean areas (Le Bissonnais et al. 2002; Renschler and Harbur 2002). Ateshian (1974) used the 2 year, 6 h rainfall to estimate the annual rainfall erosion index. Diodato (2004) obtained a power equation (r2 = 0.867) involving the annual erosion index (EI30annual) in the Mediterranean part of Italy. Arnoldus (1977), using monthly and annual rainfall, calculated annual rainfall erosion index, and obtained satisfactory results for 164 stations in the USA and 14 stations in West Africa. Hussein (1986) delineated the isoerodent map for Iraq by applying the Arnoldus model (1977). In this map, the erosion index varied from 5 SI units in the South and South Western parts to 700 SI units in north Iraq. Sepaskhah (1994) used the Arnoldus model (1977) and provided the isoerodent map of Iran using the rainfall data from all weather stations in the country. According to this map, the values of erosion index ranged from 500 to 1900 SI units. Bayramin et al. (2006) computed rainfall erosivity using the Fournier index and reported that rainfall erosivity had high variation in Turkey. Th is study was aimed to the calculate rainfall erosion index for diff erent rain gauge stations in northwest Iran. Th e second objective was to develop and evaluate single storm, daily, monthly, and annual rainfall erosivity index models for estimating EI30 from the single storm, daily, monthly, and annual rainfall information. Further, it was aimed to prepare iso-rainfall erosion index map for the study area. Materials and methods Extensive data from 18 chart type rain gauge stations in the Uremia lake basin (northwest Iran) were collected to calculate EI30. Th ese data were obtained from diff erent weather stations located in the Uremia lake basin. Th e basin covers an area of 50,862 km2 and located at 44°, 14ʹ to 47°, 56ʹ east longitude and 35°, 40ʹ to 38°, 30ʹ north latitude. Its mean elevation from the sea level varies between 1270 and 3707 m. To calculate the rainfall erosion index, any storm with at least 12.7 mm or with the intensity of more than 24 mm h-1 during a period of 15 min was considered an erosive event. An interval longer than 6 h is necessary between 2 storms to consider it a distinct event (Wischmeier and Smith 1978). Any storm not meeting this condition was eliminated from the EI30 calculation process. Th erefore, the rainfall hyetographs were divided into 15-min periods and the intensities were calculated. Rainfall kinetic energy was obtained using equations 1 and 2 (Foster et al. 1981). ei = 0.119+0.0873log 10 i i ≤ 76 mm h-1 (1) ei = 0.283 i > 76 mm h-1 (2) where ei is kinetic energy of 1 unit of rainfall (MJ ha-1 per mm) and i is rainfall intensity (mm h-1). To calculate each interval energy, the values of ei were multiplied by the amounts of relevant interval rainfall. In order to run the computation process on a computer, a program in Quick Basic language (EI.bas) was written. In this program data from 18 weather stations consisting of 15 min rainfall, date of rainfall events, and beginning and ending time of a rainfall were used. It was assumed that the time interval between 2 consequent rainstorms was equal or less than 6 h, and the ending time of rainstorm and each year were designated in the input data. Th e output were the date of rainfall event, beginning time of rainfall, rainfall amount, duration of rainstorm, the maximum 15 and 30 min intensities, kinetic energy of unit rainfall, total kinetic energy of each storm (MJ ha-1), and the storm erosion index (MJ mm ha-1 h-1). Th e EI30 for an event is the product of E and the maximum 30 min intensity (EI30) for the event. Rainfall amount, duration of single storm, the maximum 30 min intensity, kinetic energy, and the single storm erosivity index all were calculated using the EI.bas program for all chart type rain gauge recorders in the study area. Calculating rainfall erosion index needs a lot of initial information and is a time consuming Large scale evaluation of single storm and short/long term erosivity index models 210 process; therefore, the Cooley, Richardson, Monthly, and Arnoldus models were examined for estimating the single storm, daily, monthly, and annual erosion index, respectively. Th e Equation 3 as the general form of Cooley’s model indicating the relationship between single storm erosion index and relevant storm amount and duration. (3) where EIS is single storm erosion index (MJ mm ha-1 h-1), P is rainfall amount (mm), D is duration of rainfall (h), and α, β, and γ are model regression coeffi cients. In order to evaluate Cooley’s model, EI30, P, and D for each storm event in all stations were calculated. For estimating the daily rainfall erosion index, the model suggested by Richardson et al. (1983) was also calibrated and evaluated. Th erefore, total erosive daily rainfall of 18 rain record stations in the Uremia Lake Basin was collected and their daily rainfall erosion indices were calculated by Equation 4 (Richardson et al. 1983) EID = aPb + ε (4) where EID is daily rainfall erosion index (MJ mm ha-1 h-1), P is daily rainfall amount (mm), a, and b are regression coeffi cients of Richardson’s model. aPb is the deterministic component and ε is the random component of the relationship. Th e ε parameter for a given observation is the diff erence between the observed EID and predicted EID, using the deterministic part of the model. Th is evaluation also involved comparison of the model parameters (a and b) and the rainfall erosion index reported by other researchers (Sepaskhah and Sarkhosh 2005). Th e parameters of EID and rainfall amount (P) were calculated for each day and each station since its establishment. Th e regression between EID and P gave the coeffi cients a, b, ε and their statistical characteristics. To determine the monthly rainfall erosion index, the model proposed by Sepaskhah and Sarkhosh (2005) was evaluated. Th ey estimated monthly EI30 values (MJ mm ha-1 h-1), based on relevant monthly maximum daily rainfall (mm) in southern Iran according to Equation 5 EIMS = (a + (bP24)2)2 (5) where EIMS is the monthly rainfall erosion index (MJ mm ha-1 h-1), P24 is the maximum 24 h rainfall at the relevant month (mm), a and b are regression coeffi cients of the model; the value of a coeffi cient is dependent on the elevation and the b coeffi cient value was constant and equal to 0.004. In this study, a new model was proposed and is explained by Equation 6 (6) where EIM is the monthly rainfall erosion index (MJ mm ha-1 h-1), PM is the monthly rainfall at the relevant month (mm), and a and b are regression coeffi cients of the model. In this study, for the evaluation of the proposed model, EIM and PM were calculated for each month in all stations since their establishment. For estimating the annual erosion index, the Arnoldus model was used in the form of Equation 7 (Arnoldus 1977) (7) where EIA is the average annual erosion index (metric units), Pi is the average monthly rainfall (mm), P is the average annual rainfall (mm), n is the number of rainy months, and a and b are regression coeffi cients of the model. Hussein (1986) calibrated the Arnoldus model in the metric system as shown in Equation 8: (8) A logarithmic regression was used to estimate the constant coeffi cients of this model. Constant coeffi cients and statistical characteristics of these models were provided for all stations of the study area. EI D P S a= c b EI aPM Mb= ( )EI a P Pi A i n b 2 1 = = / 0.297( )EI P Pi , A i n 2 1 93 1 = = / A. KARAMI, M. HOMAEE, M. R. NEYSHABOURI, S. AFZALINIA, S. BASIRAT 211 Average values of the monthly and annual rainfall for 150 stations covering the entire study area, calculated Arnoldus model coeffi cients, and the geographical information were used to determine erosivity values of each station. Th en using the obtained information and the Uremia lake basin map information, the iso- rainfall erosion index was developed for the entire study area. Th e single storm erosivity index values (EIS) versus P, the amount of rainfall (mm), and D duration of rainfall (h) based on Cooley’s model were entered to SAS soft ware and the regression coeffi cients α, β, and γ and statistical characteristics of the model were calculated for each station. Th e same as single storm erosivity index, the daily, monthly, and annual rainfall erosivity model parameters entered to SAS soft ware, and statistical characteristics and their calibrated form were derived. Results Based on results shown in Table 1, the maximum average annual rainfall and the erosivity index were obtained from Saqqiz and Sarab stations, respectively. Duncan’s multiple range tests showed that there was a signifi cant diff erence between the average amount of rainfalls and erosivity indices at diff erent stations (Table 1). Th e calibrated form of each station and the suitable form of the total area study of Cooley’s, Richardson’s, and Arnoldus models as well as the proposed model for the single storm, daily, monthly, and annual rainfall erosion index are presented in Table 2. In the Cooley’s multiple linear regression, between EIS of each storm were taken as the dependent variable and P and D of the same storm as independent variables. Th e results indicated that regression coeffi cients α, β, and γ were not considerably varied among the stations. Calculations were performed to fi nd out if there is any internal correlation between the coeffi cients (α, β, and γ) using accessible parameters, such as the height of each station. It was found that the coeffi cients are not statistically correlated. Th e daily rainfall erosion index for each weather station located in the Uremia lake basin were calculated based on equations proposed by Foster et al. (1981) using the EI.bas soft ware. Th ere were 5800 days in which the rainfall was erosive. Because of the huge volume of data sets in this respect, it is impossible to show them in this article. Th e calibrated form of daily REI model (Richardson et al. 1983) is given in Table 2. As can be seen in Table 2, the a coeffi cient varied from 0.12 to 0.37, and b coeffi cient from 1.47 to 1.83 for diff erent study stations. Table 1. Th e geographical specifi cations of diff erent stations and means comparison of their annual rainfall and erosivity index Stations Longitude Latitude Annual rainfall (mm) EI Saqqiz 46°16ʹ 36°14ʹ 482.0 a 242.2 cd Ushnuvyeh 45°03ʹ 37°02ʹ 458.2 ab 294.7 bc Mahabad 45°43ʹ 36°46ʹ 407.7 b 232.2 d Naghadeh 45°23ʹ 36°58ʹ 350.3 c 203.3 de Qaleh Jouq 44°28ʹ 39°17ʹ 341.9 c 339.4 b Uremia 47°03ʹ 37°33ʹ 338.8 c 232.5 d Lighvan 46°26ʹ 37°50ʹ 331.3 c 323.0 b Maragheh 46°14ʹ 37°24ʹ 330.0 c 158.2 ef Nowruzlu 46°12ʹ 36°54ʹ 310.0 cd 156.0 ef Sarab 47°31ʹ 37°56ʹ 292.6 cde 399.2 a Shahindez 46°33ʹ 36°40ʹ 288.4 cde 174.4 ef Alishah 45°50ʹ 38°09ʹ 256.6 def 74.3 h Qaraziaaddin 45°01ʹ 38°53ʹ 253.5 def 151.2 ef Salmas 44°47ʹ 38°12ʹ 252.1 def 89.4 gh Malakan 46°07ʹ 37°08ʹ 243.0 ef 84.6 gh Azarshahr 54°57ʹ 37°47ʹ 239.6 ef 136.7 fg Tabriz 46°22ʹ 38°04ʹ 236.4 ef 162.6 ef Polnavaei 46°15ʹ 38°35ʹ 220.6 f 137.4 fg Large scale evaluation of single storm and short/long term erosivity index models 212 Table 2. Th e obtained form of single storm, daily, monthly and annual rainfall erosivity index model Stations Elev. Single storm Daily Monthly Annual Polnavaei 1050 Qaraziaaddin 1090 Qaleh Jouq 1285 Alishah 1330 Azarshahr 1340 Mahabad 1344 Malakan 1350 Nowruzlu 1350 Uremia 1360 Salmas 1380 Shahindez 1395 Maragheh 1465 Tabriz 1470 Ushnuvyeh 1480 Saqqiz 1480 Naghadeh 1565 Sarab 1750 Lighvan 2200 average 0.14EI D P . . S 0 93 2 4 = 0.14EI D P . . S 0 91 2 4 = 0.15EI D P . . S 0 74 2 3 = 0.14EI D P . . S 0 78 2 3 = 0.14EI D P . . S 0 78 2 3 = 0.15EI D P . . S 0 81 2 3 = 0.15EI D P . . S 0 88 2 4 = 0.15EI D P . . S 0 98 2 4 = 0.14EI D P . . S 0 87 2 3 = 0.13EI D P . . S 0 81 2 3 = 0.15EI D P . . S 0 88 2 3 = 0.14EI D P . . S 0 81 2 3 = 0.15EI D P . . S 0 77 2 3 = 0.14EI D P . . S 0 87 2 3 = 0.15EI D P . . S 0 86 2 3 = 0.14EI D P . . S 0 90 2 4 = 0.16EI D P . . S 0 67 2 2 = 0.16EI D P . . S 0 62 2 2 = 0.15EI D P . . S 0 83 2 31 = 0.13EI P .D 1 77= 0.15EI P .M m1 47= 0.14EI P .M m1 49= 0.22EI P .M m1 42= 0.95EI P .M m0 9= 0.29EI P .M m1 28= 0.37EI P .M m1 26= 0.1EI P .M m1 64= 0.31EI P .M m1 3= 0.24EI P .M m1 33= 0.15EI P .M m0 46= 0.29EI P .M m1 31= 0.46EI P .M m1 16= 0.86EI P .M m1 19= 0.22EI P .M m1 33= 0.19EI P .M m1 41= 0.33EI P .M m1 25= 0.41EI P .M m1 38= 0.31EI P .M m1 46= 0.33EI P .M m1 28= 0.12EI P .D 1 81= 0.19EI P .D 1 71= 0.25EI P .D 1 47= 0.17EI P .D 1 64= 0.13EI P .D 1 71= 0.16EI P .D 1 70= 0.19EI P .D 1 63= 0.15EI P .D 1 63= 0.13EI P .D 1 72= 0.19EI P .D 1 62= 0.17EI P .D 1 63= 0.25EI P .D 1 74= 0.13EI P .D 1 64= 0.19EI P .D 1 59= 0.14EI P .D 1 67= 0.37EI P .D 1 51= 0.15EI P .D 1 83= 0.17EI P .D 1 68= 1.12( )EI P Pi . A i n 2 1 32 1 = = / 1.68( )EI P Pi . A i n 1 2 1 22= = / 1.12( )EI P Pi . A i n 1 2 1 45= = / 1.19( )EI P Pi . A i n 2 1 11 1 = = / 1.21( )EI P Pi . A i n 2 1 27 1 = = / 1.89( )EI P Pi . A i n 2 1 14 1 = = / 0.30( )EI P Pi . A i n 2 1 47 1 = = / 1.14( )EI P Pi . A i n 2 1 22 1 = = / 1.45( )EI P Pi . A i n 2 1 26 1 = = / 0.25( )EI P Pi . A i n 2 1 55 1 = = / 1.21( )EI P Pi . A i n 2 1 25 1 = = / 1.63( )EI P Pi . A i n 2 1 13 1 = = / 2.49( )EI P Pi . A i n 2 1 15 1 = = / 1.26( )EI P Pi . A i n 2 1 26 1 = = / 0.97( )EI P Pi . A i n 2 1 25 1 = = / 0.54( )EI P Pi . A i n 2 1 44 1 = = / 0.81( )EI P Pi . A i n 2 1 58 1 = = / 1.15( )EI P Pi . A i n 2 1 43 1 = = / 1.19( )EI P Pi . A i 2 1 31 1 12 = = / A. KARAMI, M. HOMAEE, M. R. NEYSHABOURI, S. AFZALINIA, S. BASIRAT 213 Th e relationship between EIM and monthly rainfall, based on the proposed model, was evaluated to attain a simple model for EIM. Th e obtained results showed that the coeffi cients of this model had a limited variation. In addition, there was no relationship between these coeffi cients and the available parameters of the stations. Coeffi cient a varied from 0.098 to 0.948 and coeffi cient b varied from 0.46 to 1.64. To estimate the annual rainfall erosion index for the study area, long term yearly and monthly rainfall data and the relevant yearly rainfall erosion index for 18 rain gauge stations were computed. Th ese data were used to evaluate the Arnoldus model (1977) as reported by Hussein, (1986) and its coeffi cients were computed using logarithmic regression SAS soft ware. For annual REI coeffi cient a varied from 0.25 to 2.49, and b ranged from 1.11 to 1.57. Th ese variations did not follow a specifi c trend and did not show any correlation with accessible factors. Th erefore, the mean values of 1.19 and 1.31 were adapted to a and b coeffi cients, respectively. For preparing the iso-rainfall erosion index of the Uremia lake basin, information from 150 rain gauge stations was used. Th e long term annual rainfall erosion index (EIA) was calculated for each station (using the calibrated Arnoldus model). By entering the data of geographic parameters of each station and relevant EIA in to the SDRMAP soft ware, the iso- rainfall erosion index of the basin was obtained. Aft erwards, the mentioned data were sent to the AUTOCAD soft ware using a digitizer, and the fi nal map with corrected boundaries was prepared. Iso-rainfall erosion index lines were depicted using geographic latitude, and longitude of each station, long term average of EIA, and SDRMAP soft ware. Th e Figure shows the iso-rainfall erosion index of the Uremia lake basin based on the modifi ed Arnoldus model for the study area. Discussion Since rainfall intensity, duration, and frequency varied at diff erent spatiotemporal settings, there was no specifi c relation between rainfall erosion index and annual rainfall at diff erent stations (Table 1). Th ese variations have been refl ected in the coeffi cients of models developed for erosivity index (Table 2). Th erefore, for calculating the rainfall erosion index, an appropriate model should be used for each station depending on the available rainfall information. In this investigation, α coeffi cient was estimated to be in the range of 0.13 to 0.16 by evaluating Cooley’s model. Since the variation of the estimated values for α was very low, the average value of 0.15 was adopted for α in the general equation. Th e β coeffi cient varied between 2.23 and 2.39. Th e average value of 2.31 was then chosen. Th is was very close to the range of 1.5 to 2.2 that was reported by Ateshian (1974) and Cooley (1980). Th e range of γ coeffi cient varied from 0.63 to 0.98 with the average value of 0.83. Th erefore, values of 0.15, 2.31, and 0.83 can be applied for α, β, and γ coeffi cients in the derived model, respectively. Statistical characteristics of the derived model showed that it can be considered a reasonably good predicting model for calculating the single storm erosion index. Because R2 values varied from 0.990 to 0.996, the mean square of regression at all stations was also highly signifi cant (P < 0.01). Th erefore, the mean values of 0.15, 2.31, and 0.83, for α, β, and γ coeffi cients, respectively, are recommended for the general form of the Cooley’s model for the entire study area. Cooley (1980) tested his model for diff erent patterns of rainfall in the USA and introduced the coeffi cients of the models for each storm type. Since the type of storm of this area has not been determined, the variation of α, β and γ should be evaluated aft er determining the type of storms. Th e mean values of the ε in the Richardson’s model are very close to zero. However its standard deviation ranges from 0.24 to 0.56 and the values are almost normally distributed. Th e standard error of ε parameter varied from 0.01 to 0.40 and the mean R2 value was 0.85. Th e chi square (χ2) analysis indicated that the daily REI for all study stations were signifi cant at the confi dence level of 99%. Th e mean square of regression at all study stations was also highly signifi cant (P < 0.01). Th e result of regressions between a and b parameters with accessible parameters including elevation of each station showed that they were not statistically correlated. Th ese results resemble the fi ndings of Richardson et al. (1983) and Elsenbeer et al. (1993). Consequently, the Richardson equation Large scale evaluation of single storm and short/long term erosivity index models 214 Scale=1:2000000 Ormeie Saqqiz Mahabad Ushnuvyeh Miyandoab Takab Maragheh Ormeie lake Salmas Tabriz Mean annual iso erosion index lines Lake Island City Main river basin Legend Sarab Figure. Isorainfall erosivity index in the Uremia lake basin. A. KARAMI, M. HOMAEE, M. R. NEYSHABOURI, S. AFZALINIA, S. BASIRAT 215 can be recommended as an effi cient method to estimate the daily REI for the Uremia lake basin with 0.17 and 1.68 for the coeffi cients a and b, respectively. To estimate the monthly rainfall erosion index (EIMS), the model developed by Sepaskhah and Sarkhosh (2005) was also tested. In this model, the a parameter varied from 2.57 to 5.23 and b from 0.00077 to 0.013. It was also found that there was no correlation between these coeffi cients and the available parameters of the stations. Based on the results reported by Sepaskhah and Panahi (2007), the range of a coeffi cient varied from 0.33 to 10.57, and b coeffi cient from 0.001 to 0.23. However, in our study, these coeffi cients had remarkable variations within the stations and, hence, application of this model is not reliable for our study area. Estimated EIM from the proposed model was evaluated using the chi square test and the mean square regression method. Results showed that the erosion index was highly signifi cant (P < 0.01) based on both tests. Tomas et al. (1990) developed a model to calculate EIM for USLE using daily rainfall. Th is model can calculate the EIM based on the relevant month and its maximum rainfall, and the diff erence between the maximum daily rainfall and rainfall of the corresponding month. Since the parameters of this equation had high variation at diff erent years, it was not evaluated in this study. Th e calibrated form of the Arnoldus model for the study area was obtained as . Th e values of annual rainfall erosion indices obtained for all 18 stations and tested by chi square were highly signifi cant (P < 0.01). According to the Figure, rainfall erosion indices varied from 65 to 618 SI unit, which were much lower than those reported by Wischmeier and Smith (1978) and Narain et al. (1994). Th erefore, there is little variation in the R factor across the basin and so the model will be more sensitive to other management factors. Conclusions Estimating the single storm erosion index model, similar to that proposed by Cooley’s model, was developed for the study area. Th e variation of coeffi cients of this equation was very low. Th erefore, the mean values of 0.15, 2.31, and 0.83 were recommended for the constant coeffi cients (α, β, and γ) of the general form of Cooley’s model. For daily rainfall erosivity estimation, a power function model was derived for the study area. Results of this investigation were the same as the results reported by Richardson et al. (1983) and Elsenbeer et al. (1993). Due to the compatibility of the Richardson model for the study area, it can be recommended as an effi cient model to estimate the daily rainfall erosivity index with the values of 0.17 and 1.68 for the coeffi cients a and b, respectively. For monthly rainfall erosivity estimation, a new simple power model in which the monthly EIM may be estimated from relevant monthly rainfall was proposed. Th e results showed that the coeffi cients of this model had a limited variation, and there was no relationship between these coeffi cients and the available parameters of the stations. Averages of 0.33 and 1.28 for intercept and b coeffi cients were obtained and recommended, respectively. For the annual rainfall erosivity estimation, the Arnoldus model was evaluated and calibrated for the study area. Averages of 1.19 and 1.31 are appropriate for the a and b coeffi cients. According to the Arnoldus model with calibrated coeffi cients, an annual iso-erosivity map was drawn for the study area. Th is map indicated that the annual rainfall erosivity indices varied from 65 to 618 SI units, which were much lower than those reported for other regions. Th erefore, there was a slight little variation in the R factor across the Uremia lake basin in such a way that the RUSLE model was more sensitive to the other management factors. 1.19( )EI P Pi . A i 2 1 31 1 12 = = / References Arnoldus HMJ (1977) Methodology used to determine the maximum potential average annual soil loss due to sheet and rill erosion in Morocco. In assessing soil degradation. FAO soil Bult 34. Food Agr Org United Nations, Rome, Italy. pp. 39-48. Ateshian JKH (1974) Estimation of rainfall erosion index. J Irrig Drain Div Proc ASAE 100(IR3): 293-307. Bagarello V, D’Asarro F (1994) Estimating single storm erosion index. Trans ASAE 37: 785-791. Large scale evaluation of single storm and short/long term erosivity index models 216 Arnoldus HMJ (1977) Methodology used to determine the maximum potential average annual soil loss due to sheet and rill erosion in Morocco. In assessing soil degradation. FAO soil Bult 34. Food Agr Org United Nations, Rome, Italy. pp. 39-48. 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