^{1}

^{*}

^{2}

The Soil Conservation Service Curve Number (SCS-CN) is a well-established loss-rate model to estimate runoff. It combines watershed parameters and climatic factors in one entity curve number (
*CN*). The
*CN* exhibits an inherent seasonality beyond its spatial variability, which cannot be accounted for by the conventional methods. In the present study, an attempt has been made to determine the
*CN* for different months of monsoon season with an objective to evaluate the impact of monthly
*CN* on runoff estimation for Ozat catchment (Gujarat State, India). The standard
*CN* and month wise
*CN* were determined by three procedures, viz, the median, geometric mean and standard asymptotic fit using gauged rainfall and runoff. This study shows that the predictive capability of
*CN* determination methods can be improved by using monthly
*CN*. Refined Willmott’s index (d
_{r}) and mean absolute error (MAE) were used to assess and validate the performance of each method. The asymptotic fit
*CN *method with monthly
*CN* resulting d
_{r} from 0.46 to 0.49 and MAE from 1.13 mm to 1.18 mm was judged to be more consistent with the existing commonly used
*CN* methods in terms of runoff estimation for the study area.

The Natural Resources Conservation Service (NRCS) curve number (CN) procedure is widely used to estimate runoff resulting from rainfall. The primary reason for its wide applicability and acceptability lies in the fact that it accounts for major runoff-generating watershed characteristics, namely, soil type, land use/treatment, surface condition and antecedent moisture condition [

After the critical examination of the methodology, the SCS-CN method has gained much attention with respect to its modification and investigation. Subsequent studies (e.g. [

The objectives of this study were 1) to assess the applicability of CNs determination procedures including the median, geometric mean [

Ozat is a river flowing in western India in Gujarat state whose origin is near Visavadar and meets in Arebian Sea. Ozat catchment considered in this study geographically locates within the latitudes 21˚19'N to 21˚33'N and the longitudes 70˚39'E to 70˚56'E respectively as can be seen from toposheet no 41 K ( 10-11-14 and 15) of scale 1:50000. The gauge discharge site is located near Khambhaliya village at bridge of Junagadh to Visavadar Road 33 km away from Junagadh. Information about soil and land use have been gathered from maps of National Bureau of Soil Survey and Land use Planning (ICAR) (1994). Study area (sub-watershed) has been delineated from Survey of India (SOI) topographic sheet using AutoCAD (2010) Software in ^{2} comprises of about 20.08% ( 72.0542 km ^{2}) grass and open scrub land and remaining 79.92% area under arable land irrigated ( 286.7815 km ^{2}). The major crops grown in the catchment are Ground nut, wheat and Cotton.

The hydrological data daily rainfall (mm) and runoff (m^{3}/s) (1980 to 2010) and meteorological data daily maximum and minimum temperatures of Ozat catchment were collected from the State Water Data Centre, Gandhinagar. The information related to watershed characteristics, namely, physiography, number of streams of different orders, their length, slope and area contributing runoff to these streams were obtained from the topographic maps of the watershed.

Periodic insufficient rainfall pattern, limited water storage capacity of aquifer and natural water conservation are vital issues for this region. Water availability is a critical factor in this area and therefore accurate estimation of runoff is needed for water resources management, crop water use, farm irrigation scheduling, and environmental assessment.

One of the most commonly used methods to estimate the volume of surface runoff for a given rainfall event is the (SCS-CN) method [

where P is the total precipitation (mm), I_{a} is the initial abstraction before runoff (mm), F is the cumulative infiltration after runoff begins (mm), Q is direct runoff (mm), S is the potential maximum retention (mm), and λ is the initial abstraction (ratio) coefficient.

Small amount of rainfall events result in even smaller changes in runoff that can sometimes be difficult to discern in the discharge time series. To minimize uncertainty in the determination of the storm event discharge, storms events with P ≥ 5 mm have been considered to determine CN values in calibration period for this study. In validation period all events have been considered to measure performance of different procedures.

λ = 0.2 was assumed in original SCS-CN model. But, this assumption has often been questioned for its rationality and applicability, invoking a critical examination of the I_{a}-S relationship for practical applications [

The general runoff equation combination of Equation (1) and Equation (2) is shown in Equation (4):

The potential maximum retention S (mm) can vary in the range of 0 ≤ S ≤ ∞, and it directly linked to CN. Parameter S is mapped to the CN using Equation (4) as:

The CN depends on land use, hydrologic soil group, hydrologic condition, antecedent moisture condition (AMC) and it can vary from 0 to 100. Three AMCs were defined as dry (lower limit of moisture or upper limit of S), moderate (normal or average soil moisture condition), and wet (upper limit of moisture or lower limit of S), and denoted as AMC I, AMC II, and AMC III, respectively [

Normally variations in storm characteristics and surface conditions can responsible for variation in CN between events. Possible sources of CN variability may be the effect of the temporal and spatial variability of storm and watershed properties, the quality of the measured data, and the effect of antecedent rainfall and associated soil moisture. [

The CN values corresponding to the catchment soil types, land cover and land management conditions can be selected from the NEH-4 tables. The CN value of AMC II (CNII) was provided by the SCS-CN manual and the CN value of AMC I (CNI) and CN value of AMC III (CNIII) can be calculated by applying the [

In this study CNs were determined by three different methods using gauged rainfall and runoff. These methods include the median, geometric mean, and standard asymptotic fit. When rainfall-runoff data are available for a watershed, P and Q pairs are used directly to determine the potential retention S characterizing the watershed [

CN value can be directly calculated from rainfall-runoff data by substituting value of S in Equation (5) and rearranging it as:

The median CN was computed by finding the median of the CNs of selected events from the calibration period (1980-1994). The CNs for events were computed using Equation (6) and Equation (7). The median CN as calculated from rainfall and runoff depths associated with the daily runoff events appears to have been the source of the original handbook table values. This procedure has the benefits of simplicity, precedent, and consistency with existing tables. However, it requires long records (one observation per year) and is incapable of capturing short term or transient effects, such as a fire or changes in agronomic practices [

The geometric mean has been used to determine a watershed CN if the values calculated from rainfall and runoff measured for each event are log normally distributed [

where α = 254 mm ( 10 in ).

In standard asymptotic fit method (AFM), P and Q data are re-aligned on a rank-order basis, creating a new set of P:Q pairs (ordered P:Q data). This is done by rank ordering the rainfalls and runoff separately, and reassembling them as rank-ordered pairs. The Standard response was observed in Ozat catchment and to be described by the following:

Equation (9) has the algebraic structure of the Horton infiltration equation. In the standard response, the CN as a function of rainfall P (CN[P]) decreases to an asymptotic constant CN_{∞} with k (the fitting coefficient or rate constant in the units of 1/P) that describes the CN approach to the asymptotic constant CN_{∞}. Optimized values of CN_{∞} and k are obtained by fitting Equation (9) using least-squares procedure. The recent report to NRCS [

The mean monthly CNs of fifteen years period (1980-1994) were calculated using median method and geometric mean method. The highest values of CN were recorded in September month while the lowest values were recorded in the month of October. In (AFM) method, month wise optimized values of parameters CN_{∞} and k were computed using ordered P:Q data. CNs values were then determined by incorporating mean monthly rainfall amount of calibration period (1980-1994), CN_{∞} and k in Equation (9). Variations in CN with rainfall P for each month of monsoon season are presented in Figures 2-6 with parameters CN_{∞} and k values. _{∞} and k during monsoon season are also presented in

In stream flow separation, the most frequently used methods are filtering separation method and statistical method (Frequency-Duration analysis). In filtering separation method, base flow separates from the stream flow time series data by processing or filtering procedure. Although these methods don’t have any physical basis it aims at generating an objective, repeatable and easily automated index that can be related to the base flow response of the catchment [

where,

Q_{d} = direct flow part of the stream flow which is subjected to Q_{d} ≥ 0 for the time i in days;

Q_{T} = total flow (i.e. base flow + direct flow);

α = a coefficient with value 0.925;

β = a coefficient with value 0.5.

In this study, the performance of three CN determination procedures, viz, the median, geometric mean and standard asymptotic fit with standard CN and monthly CN are evaluated using two popular statistical criteria refined Willmott’s index (d_{r}) [

Month | Mean monthly rainfall in mm | Median | Geometric mean | AFM | ||
---|---|---|---|---|---|---|

CN | CN | CN | CN_{∞} | K in mm^{−1} | ||

λ = 0.05 | ||||||

June | 198 | 69.22 | 48.25 | 51.45 | 46.80 | 0.18 |

July | 295 | 67.45 | 61.75 | 66.42 | 65.88 | 0.21 |

August | 150 | 69.66 | 62.94 | 76.38 | 51.71 | 0.07 |

September | 86 | 71.2 | 66.94 | 85.87 | 64.09 | 0.09 |

October | 16 | 43.82 | 54.58 | 97.81 | 11.59 | 0.02 |

λ = 0.10 | ||||||

June | 198 | 80.41 | 63.53 | 66.59 | 55.79 | 0.11 |

July | 295 | 79.25 | 73.36 | 73.66 | 68.75 | 0.09 |

August | 150 | 77.83 | 74.16 | 83.08 | 58.32 | 0.05 |

September | 86 | 80.85 | 77.13 | 90.44 | 67.66 | 0.06 |

October | 16 | 55.11 | 69.55 | 98.42 | 15.42 | 0.02 |

λ = 0.20 | ||||||

June | 198 | 85.74 | 76.72 | 80.8 | 61.66 | 0.05 |

July | 295 | 86.10 | 82.90 | 84.08 | 65.75 | 0.03 |

August | 150 | 85.55 | 83.44 | 88.85 | 65.96 | 0.04 |

September | 86 | 88.65 | 85.41 | 93.95 | 72.19 | 0.04 |

October | 16 | 66.41 | 81.49 | 98.95 | 18.86 | 0.01 |

in the units of the data of interest. These statistical criteria are used to measure the agreement between predicted and observed values of event runoff in validation period (1995-2010). To check precision and correctness of the methods, (d_{r}) is applied. The MAE does not tell about degree of error but it is used for the quantitative analysis of residuals.

The d_{r} is applied to quantify the degree to which values of observed runoff are captured by the models. The range of d_{r} is from −1.0 to 1.0. A d_{r} of 1.0 indicates perfect agreement between model and observation, and a d_{r} of −1.0 indicates either lack of agreement between the model and observation or insufficient variation in observations to adequately test the model.

MAE is error measure used to represent the average difference between model predicted and observed values. It is important to include absolute error measures MAE in a model evaluation because it provides an estimate of model error in the units of the variable. The MAE provides a more robust measure of average model error than the root mean square error (RMSE), since it is not influenced by extreme outliers [

All the three procedures with standard CN and monthly CN values, considered for the present study, have been applied to estimate runoff for the Ozat catchment. The resulting values of d_{r}, and MAE are presented in

With standard CN values | ||||||
---|---|---|---|---|---|---|

Median CN | Geometric mean CN | AFM CN | ||||

λ | d_{r} | MAE in mm | d_{r} | MAE in mm | d_{r} | MAE in mm |

0.05 | 0.27 | 1.47 | 0.37 | 1.24 | 0.47 | 1.18 |

0.10 | 0.15 | 1.68 | 0.27 | 1.44 | 0.48 | 1.16 |

0.20 | 0.04 | 1.89 | 0.14 | 1. 8 | 0.49 | 1.13 |

With monthly CN values | ||||||

Median CN | Geometric mean CN | AFM CN | ||||

λ | d_{r} | MAE in mm | d_{r} | MAE in mm | d_{r} | MAE in mm |

0.05 | 0.29 | 1.41 | 0.40 | 1.18 | 0.47 | 1.16 |

0.10 | 0.15 | 1.70 | 0.29 | 1.38 | 0.46 | 1.17 |

0.20 | 0.02 | 1.92 | 0.15 | 1.65 | 0.48 | 1.13 |

The median, geometric mean and standard asymptotic fit procedures are applied with standard CN and monthly CN on the data set of Ozat catchment. The data set of 15 years (1980-1994) was used to determine standard CN and monthly CN for each procedure and the data set of 16 years (1995-2010) was used for validation. The results of the performances of these methods are presented in

It is evident from _{∞} are increased while optimized values of parameter k are decreased with increment in λ. CN_{∞} values exhibited inverse relationship with k values. The highest value of CN_{∞} is estimated in September month within range of 64.09 to 72.19 while lowest value is found in the month of October within range of 11.59 to 15.42. The values of k decrease from 0.21 to 0.01 with increment in the λ from 0.05 to 0.20, it is also evident that a value of k is the lowest in the month of October.

The AFM procedure is provided comparatively more realistic results with d_{r} = 0.49 and MAE = 1.13 mm for λ = 0.20. As compare to AFM method, other two methods are shown poor performance in goodness of fit criteria and produced the results with marginally larger errors. Substantial improvement in error estimate is noticed while using monthly CN values replacing standard CN values. For λ = 0.05, all three methods had a good performance in predicting the daily runoff with monthly CN values for the study area. These results are in good agreement to the previous studies.

The median, geometric mean and asymptotic fit procedures for CN determination are applied and evaluated with standard CN values and monthly CN values to estimate runoff for Ozat catchment of India.

The following conclusions can be drawn from this study:

1) The performance of the SCS-CN method is improved on application of monthly CN.

2) The CN values increase with increment in λ from 0.05 to 0.20.

3) The CN values computed from median procedure are higher than CN values computed from geometric mean procedure.

4) All the methods perform well with λ = 0.05 for Ozat catchment.

5) The highest CN values are found in the month of September and the lowest CN values are found in the month of October for median and geometric mean methods.

6) Asymptotic CN parameters (CN_{∞}) increase with λ and attain the highest value in September.

7) Inverse relationship is observed between λ and fitting parameter k.

8) The lowest values of parameters CN_{∞} and k are found in October.

Considering above all the results, we conclude that the relatively best performance is observed by the AFM method with higher d_{r} values and lower MAE values. This study shows that the predictive capability of CN determination methods can be improved by the use of monthly CN values replacing standard CN values for the Ozat catchment.

The authors express sincere thanks to State Water Data Centre, Gandhinagar, for providing daily rainfall and runoff data of Khambhaliya Gauge Discharge Site and Divisional Office Junagadh (Irrigation Department), Gujarat for supplying us different maps of the study area.