Comparative evaluation of models to estimate direct runoff volume from an agricultural watershed

ABSTRACT Generally, runoff records are the most important input data in water resource management; however, their availability is very limited especially in developing country as compared to rainfall records, especially under medium and small-scale catchments. In our study, we estimated runoff from ungauged agricultural watershed with the curve number method and empirical mathematical models were compared with SCS-CN. Empirical mathematical models (Inglis and De Souza Formula (IDS), Turc relationship (TR), Indian Irrigation Department (DII) model, Coutagine relationship (CR), Khosla method (KH), Justin Equation (JE), Lacey relationship (LR), and Indian Council of Agricultural Research (ICAR)) model were used to estimate annual runoff (in cm). It was found that IDS model has capability to simulate annual runoff as very close to Soil Conservation Service Curve Number (SCS-CN) model and has lowest Root Mean Square Error (RMSE) value as 7.75, and ranking of this model (based on K factor (value of 0.001) analysis) was topmost (or 1st) in comparison to other eight models. This study suggests that empirical mathematical model has potential for annual runoff estimation from ungauged watershed.

Simple empirical equation relates catchment characteristics and complicated physical models are available to estimate the catchment runoff . The application of conceptual hydrological model to generate runoff from ungauged watershed with limited data have been studied by researchers in past (Kaleris et al., 2015). Regional scale model can explain the variation of the model parameters with physiographic factors. These models did not fully capture the local scale process and variations. However, the certainty of the calibrated model parameters is high enough to simulate the hydrologic response of ungauged watershed . According to Wheater et al. (2008) and Devia et al. (2015), a hydrological model is a simplification of a real-world system, used mainly for the prediction of hydrological processes based on rainfall, drainage area (topography), soil properties, vegetation cover, and runoff model. It is defined as a set of equations that enable the estimation of runoff as a function of various parameters used for describing watershed characteristics.
The Universal Soil Loss Equation (USLE) is an empirical equation. The Revised Universal Soil Loss Equation (RUSLE) is a modification of USLE, especially for more complex situations of rill and inter-rill erosion in conservation planning and land uses. Both erosion-prone models calculate detachment capacity and soil loss. RUSLE model predicts soil degradation and sediment concentrations better using another soil erodibility factor (F-soil factor, based on soil texture). The soil conservation service-curve number (SCS-CN) method has been used widely (Bérod et al., 1999;Pandey & Dabral, 2004;Vaze et al., 2011). The SCS-CN method is simple, predictable, stable, and relies on only one parameter, namely the CN. The land use/ land cover (LULC) class can be integrated with the hydrologic soil groups (HSG) of the sub basin in GIS, and the weighted CN can be estimated. These estimated weighted CN for the entire area can be used to compute runoff. Moore and Clarke (1981) showed that a variety of distributions that can be easily incorporated into this type of model structure and they derive analytical equations for the response of different distributions. Hosking and Clarke (1990) extended the work of Moore and Clarke (1981), and reported that the model can be used to derive a relationship between the frequencies of storm rainfall and flow peak magnitude in an analytical form. The UK Institute of Hydrology has shown the model for long runs to derive flood frequencies (Dorum et al., 2010;Lamb, 1999). Recently many studies have applied machine learning and soft computing approaches to study the soil properties and erosion (Jahani et al., 2016;Singh et al., 2020;Mosaffaei et al., 2020;Rahmati et al., 2020).
The earth observation datasets integration within Geographical Information System (GIS) make watershed modeling easy and accurate (Balázs et al. 2018). The capabilities of these technologies have been successfully utilized by many researchers in rainfallrunoff modeling . Earth-observing satellite provides more reliable input parameters for hydrological modeling (Rawat & Singh, 2017;Maliqi & Singh, 2019). However, GIS processing has become a critical step in hydrologic modeling (Thakur et al., 2017), since it contributes to generate model parameter distribution in spatial manner.
Although researchers delineated several models, the satellite-based inputs in these models were not comparatively used and limited model performance was evaluated. Hence, objectives of work are as follows: (i) to estimate daily runoff using SCS-CN and (ii) to find an optimal empirical mathematical model with respect to SCS-CN for generating annual runoff of ungauged Jhagrabaria watershed using satellite data.

Study area and data
The Jhagrabaria watershed is located in the Allahabad district of state Uttar Pradesh, India (Figure 1). Geologically the area consists of Upper Vindhayan formation consist of mainly sandstone and shale. The elevation is ranging from 85 to 192 m above mean sea level with nearly flat to gently undulated topography and small occasional hillocks. The upland area is covered with loam, except in the south-western part of tehsil Karchhana, where the soil is a mixture of clay and marsh. The area has semi-tropical climate as summer and the winter. The area receives about 91% of the total annual rainfall due to southwest monsoon from June to September. The relative humidity is high during the monsoon month (Rawat & Singh, 2017).

Datasets used
LANDSAT7 ETM+ (path/row: 231/67) was acquired on June 27, 2006 (Table 1). The image was converted to apparent reflectance through an image-based calibration method. Atmospheric correction was performed using Fast Line-of-sight Atmospheric Analysis of Hypercubes (FLAASH) algorithm. Image was geometrically rectified using ground control points collected from Survey of India (SOI) topographic sheets using nearest-neighborhood resampling technique and a root-mean-square error with less than one pixel was obtained during the geometric rectification. Land use/ land cover (LULC), viz. barren land, fallow land, vegetation, and water bodies/wetlands were identified in the field and their coordinates were recorded with a handheld global positioning system (GPS) device (Garmin eTrexH). The maximum likelihood classifier is a simple and easy to use classification algorithm, in which a pixel with the maximum likelihood is classified into the corresponding class Lu et al., 2004). Afterward window 3 × 3 size majority filter was applied to remove the "salt and pepper" noise from classified image.
The need of satellite-estimated precipitation arises because of the non-availability or poorly distributed ground rainfall data. For the work, the daily precipitation data were downloaded from ftp://ftpprd.ncep.noaa. gov/pub/cpc/fews/S.Asia/.
Resolution of rainfall estimates are of 0. The soil map of the Shankargarh block was collected from Soil Survey Department, Allahabad, U.P., India. The map was scanned and then registered with the help of geo-referenced Survey of India (SOI) topographical sheet no. 63 G/11 and 63 G/12, respectively. The registered soil maps were digitized and different soil attributes were assigned to the different soil groups in digital format. In present study, CN map is generated with help of LULC and HSG map, CNII is the CN for normal condition, CNI is the CN for dry condition, CNIII is the CN for wet condition and CN is assigned based on Section 2C-5 -Iowa Storm water Management 2C-5 Manual (2C-5 NRCS TR-55 Methodology) (2008).

LST role in models
LST data sets are important because five models (TR, CR, KH, JE, and ICAR) out of eight (KH, IDS, DII, TR, CR, ICAR, JE, and LR) models required LST as input data, to predict runoff. Average function was applied to calculate monthly and annual LST. In TR temperature is part of denominator, and it is also under square root function therefore its effective yield will be small, over all denominator will be a small quantity which gives a little fraction of annual rainfall, net result will come as high runoff from TR. In CR temperature is also part of denominator, and it does not has any constrain (like square root function); thus, a good yield will apply in denominator which gives small fraction of annual rainfall, resulting in the overestimation of runoff. KH model reveals a low annual runoff because a major part is subtracted from annual rainfall (T/3.74 (in °C)), and will be a big quantity). From JE model, in denominator temperature has multiple factor of 1.8 additional 32 which will give large number at dominator; therefore, a small yield in JE; Thus, this model have better result from other models being temperature-dependent (TR, CR, KH, and ICAR). ICAR model reveals that temperature is part of denominator and it is also multiplied by another factor which gives a big yield in denominator; therefore, a * TM Band 6 was acquired at 120-meter resolution, but products are resampled to 30-meter pixels. * ETM+ Band 6 is acquired at 60-meter resolution, but products are resampled to 30-meter pixels.
less net annual runoff from ICAR. ICAR may be good for a regional area because it is directly dependent on area, slope and other factors that dominate at regional scale. Hence, annual runoff fluctuates if annual mean surface temperature slightly varies because all equations are directly linked to surface temperature.

Runoff estimation
The SCS-CN method was developed to estimate surface runoff from small agricultural watersheds (USDA-SCS, 1967). The soils have been classified into four hydrologic groups namely A, B, C, and D (USDA, 1986), based on infiltration, soil classification, and other criteria (soil's surface condition (infiltration rate) and its horizon (transmission rate). Land use and management types have been used in the preparation of hydrological soil-cover complex, which has been utilized in estimating direct runoff. Antecedent Moisture Condition (AMC) is an indicator of watershed wetness and availability of soil moisture storage prior to a storm (Rawat & Singh, 2017). SCS has developed a guide for adjusting CN according to AMC based on total rainfall in the 5 day period preceding a storm. Three levels of AMC as: AMC-I (dry), AMC-II (normal), and AMC-III (wet) conditions. The seasonal rainfall limits for these three antecedent moisture conditions (Table 2). Many hydrologists have discussed relationships of precipitation and annual surface runoff with the assumption that physical characteristics of the watershed are constant (Castiglioni et al., 2010). The brief information about the empirical models applied in this study is presented in Tables 3-4.

Performance evaluation
Model's performance was evaluated using statistical parameters.

Ranking of empirical mathematical models
Factor K was estimated to provide proper weight (Rawat and Singh, 2018) to selected statistical index (all used statistical test) as: where, K is factor, i is n th statistical index and W is weight for particular statistical index. Lowest rating model will be on first rank and vice-versa.

Land use/land cover (LULC)
LULC affects the infiltration, erosion, and evapotranspiration hence, it is an important characteristic of runoff process. Overall 90% accuracy of classified LULC map was achieved. The area of barren land (36.91 km 2 ), fallow land (36.62 km 2 ), and vegetation (74.71 km 2 ) ( Figure 2). The fallow and barren land together have the highest area as 48.99% whereas vegetation area is 47.81%. The area exposed for erosion offer high rate of water erosion. Several studies have demonstrated the role of LULC in hydrologic modeling and runoff estimation (Adham et al., 2014;Tedela et al., 2012;Kumar et al., 2018).
Where, P is annual precipitation (cm), and R is annual runoff (cm) Praveen Kumar et al. (2016) 4 Turc relationship (TR) Relationship for watersheds with the area less than 300 km 2 based on achieved results from doing a study on 254 watersheds in various climatic and weather conditions R ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi 0: Where, P is annual precipitation (cm), R is annual runoff (cm), T is mean annual temperature (°C) and D is annual flow shortage. Khosravi et al. (2013) 5

Coutagine relationship (CR) Presented a general relationship
Where, P is annual precipitation (cm), R is annual runoff (cm), is coefficient and recommended as:-λ ¼ 1  (6) Where, P is annual precipitation (cm), R is annual runoff (cm) and T is mean annual temperature (° C).
Where, R is annual runoff (cm), P is mean annual precipitation (cm), T is Mean annual temperature (°C), S is mean slope of watershed, H is elevations of watershed, A is the watershed area R is mean annual runoff (cm), P is Mean annual precipitation (cm), F z is Parameter of rainfall duration and physiographic properties, Values of Fz coefficient are given in Table 4.

Soil map and hydrological soil group
The soil of the Jhgarbaria watershed is of Devra clay soil, Jarkhori sandy loam, Lohgara silty loam, Newaria loamy and stony land (Figure 3(a)). The watershed is mainly dominated by Newaria loam (58.26 km 2 or 38.82%), Devra clay soils (31.92 km 2 or 21.27%) and Jarkhori sandy loam soils (27.99 km 2 or 18.65%). Presence of sand fraction in large quantities under entire watershed makes it vulnerable to soil erosion. The stoniness of the land (14.63 km 2 or 9.75%) will act as barrier to store water however leading to generate higher amount of runoff (Castiglioni et al., 2010;Fathzadeh, 2008).The initial infiltration and transmission of surface water into an aquifer system is a function of soil type and its texture. From soil classes, further Hydrologic Soil Group (HSG) (Figure 3(b)) map of study area was developed with guidelines given by Chow et al. (1988).

Rainfall (2003-2014)
The daily rainfall data of 12 years are illustrated in Figure 4(a-c

Land surface temperature (LST)
The 8-days LST was plotted ( Figure 5(a-c)) and maximum temperature variation (32.8 to 41.3°C) was noted during 14-April-2010 to 25-Jun-2010 (335 th to 344 th 8-days). Figure 5(d) shows monthly LST and reveal that average monthly LST eight times cross 35°C limit line during different month of different years, and maximum monthly average LST was noted for during June-2010 as 37.3°C. Due to average function all peak values (in 8-days LST data sets, Figure 5(c)) all value range from 14.5 to 37.28°C, while monthly average mean value is noted as 25.3°C. Figure 5(e), represents annual LST, maximum LST 26.1°C was estimated in the year 2010 and minimum was 24.3°C in the year 2013. Hence, the maximum variation was only 1.8° C in 11 years. Figure 6(a-c) shows destitution of CNn at special extent and corresponding histogram showing destitution of CN n at pixel wise (n = I, II, and III) in images. Runoff calculation from SCS model mainly relied on CN value, which is a function of AMC, slope, soil type, and land use. The CN value reflects the possible runoff generation (Rawat & Singh, 2017). Under the same rainfall condition, low value of CN reflect that the land has a high possibility of water-holding capacity. While high value of CN, precipitation can be held by the land at a small extent. Therefore, any class LULC with high value of CN can generate a high amount of runoff which will cause of flood peak. In SCS model, AMC condition has influence on CN values that's why CN and AMC conditions are two major factors that can affect the runoff analysis in SCS modeling. Figure 7(a) represents a seasonal trend, the variability in runoff except high runoff during 05-September-07 (90.11 mm, because of high rainfall 118 mm), 05-October-2013 was noted as highest runoff (91 mm) due to highest rainfall (120 mm) during end of monsoon year of 2013. This was special month (October) of last ten years (2003 to 2012) when more rainfall in short time period (near about 135 mm within two days) and in year 2010 less runoff. Figure 7(b) represents monthly monsoon runoff during 2003 to 2014 and showed highest runoff (96 mm and 60.5% of total rainfall (159 mm)) during September-2007, because in August-2007 high amount of rainfall (309 mm) was received (total 16 days rainfall) but only 22% of total rainfall was converted into runoff, it comes as large amount of runoff (60.5% runoff) in next month (September) by 159 mm rainfall. Similarly, for high runoff (55.9% of total rainfall) during June-2005 (because high amount of rainfall receives in last days of previous month (22, 23, 25, 26, 27 29, and 30 May-2005). Figure 7(b) reveals that during year 2013 October rainfall also produces high runoff 51.9% of 293 mm rainfall, this October's runoff is given key information that a large amount of rainfall after September becomes as runoff because of surface saturation condition. Figure 7(c) graphical representation of annual runoff with rainfall and explain rainfall and runoff yield of 12 months.

Runoff from surface runoff model
Annual runoff was estimated by eight different surface runoff models (KHM, IDS, TR, CR, KH, ICAR, LR and JE). Table 5  describes the comparative runoff results of these models. These eight models were independent of LULC classes, soil categories, and AMC type. These models are only based on annual rainfall and annual temperature. From Table 5, we can easily distinguished two categories, (i) predicted annual runoff was overestimated (CR and KH) and (ii) predicted annual runoff was underestimated (IDS, TR, and ICAR).
Predicted runoff of CR model was always overestimated (because in each year the predicted runoff was more than the actual precipitation, like runoff of year 2013 is 34.72% of annual rainfall), therefore, in first screening this model can be discarded. In the same way, KH model also predicted high annual runoff. However, CR and IDS, the remaining models' runoff predictions are under the acceptable limit (based on % of annual rainfall).

Statistical performance evaluation
Comparative results of runoff estimation are obtained through statistical tests (    models have limited potential to estimate surface runoff. Significant difference was found among model with respect to SCS-CN (except IDS). Ghazavi and Abasali (2003) did not consider Coutagine method and corrected Langbin method, as suitable method in arid regions. Khosroshahi (1991) has mentioned that the estimation by ICAR is more than observed value; it is more obvious in the agricultural watersheds of more than 200 km 2 . Also, Fathzadeh (2008)

Conclusion
Runoff estimation of ungauged watershed is a challenge for hydrologists. Discharge value of ungauged catchments is important for hydrological planning and designing of various hydraulic structures. Precise knowledge about the runoff will help in better management of water resources of the local region. It is difficult to estimate the runoff more accurately from ungauged watershed with coarse resolution satellite data due to high uncertainty. SCS-CN model requires input of LULC, soil data, and rainfallthat can be obtained from satellite hence it easily provides the runoff estimation at macro level. Still there is need of some other simple alternate model for estimating annual runoff from ungauged agricultural watershed. That can provide runoff estimate close to SCS-CN model. In this context present study reveals that Inglis & De Souza (IDS) model is a simple and good alternative of SCS-CN model. It can serve the purpose of runoff estimation from ungauged watershed. IDS model required input of annual rainfall data. This can be generated from automatic weather station or satellite-based freely available data. The major drawback of all the empirical models except SCS-CN is estimation of runoff on annual basis. Still these models provide reliable information about the runoff. This information can be utilized by the planners and policy makers for management and designing purposes.