Comparison and estimation study of the best suitable empirical method for runoff in the Hoshangabad region

Water is one of the necessities for supporting the life and improvement of society. Water is an extremely valuable endowment of nature to humankind. The significant wellspring of water is precipitation and for a large portion of the hydrological models, precipitation is utilized as one of the principal components to gauge the spillover interaction. The precipitation overflow model is a numerical model portraying the precipitation spillover relations of a waterway bowl or watershed. Precipitation information is questionable and overflow is one of the significant hydrologic factors utilized in water assets the executives and arranging. Rainstorms create overflow and its event and amount are subject to the attributes of the precipitation occasion. In any case, there are numerous watersheds or catchments that are unchecked; Thus, exact formulae were valuable for assessing overflow volume. This paper depicts the assessment of overflow utilizing observational conditions like Khuzla’s equation, English and Desouza recipe, Indian Irrigation Department, and Khosla’s recipe. For this reason, the Hoshangabad area is chosen and the yearly precipitation information from 1981 to 2017 has been gathered. Furthermore, the appropriateness of the model has been assessed by contrasting the overflow information and one another. After comparing the result of annual runoff calculated by using those formulas, we can observe that in all the years values of the Khosla formula and Khuzla formula are showing similar results, but in the English and Duez formula the value of runoff is too high. The runoff values calculated from the English and Duez formulas are nearly 7 times the actual value obtained from the other three formulas. So, it is not acceptable for the Hoshangabad region.


Introduction
Water is one of the necessities for supporting the life and improvement of society.Water might be a valuable endowment of nature to humanity [1].The significant wellspring of water is precipitation and for a considerable lot of the hydrological models, precipitation [2] is utilized along with most components to gauge the spillover interaction.As the populace is expanding step by step the interest in water is expanding and because of industrialization, metropolitan advancement's further burden on accessible water is expanded [3].Thus, it is a significant issue or need to assess accessible water for ideal utilization of water for different purposes like homegrown, horticulture, and industrialization.Hydrological models are significant and important instruments for water and natural assets on the board [12].Hydrologic processes change both in existence.For a large portion of the hydrological models, one of the fundamental components included is a precipitation overflow process [14].A precipitation spillover model is a numerical model depicting the precipitation overflow relations of a catchment region, seepage bowl, or watershed [6].A water assets framework could likewise be nonlinear and multivariate and consequently, the factors included have complex interrelationships.The fundamental prerequisite in planning water projects is the assessment of spillover coming about because of precipitation [13].The connection between precipitation and overflow is reliant upon a few variables.To decide the precise amount of surface run-off in any bowl, understanding the mind-boggling connection between precipitation and run-off cycles of the bowl is significant [7].
Overflow is one of the significant hydrologic factors used in water assets the board and arranging [9].Many models have been created in the downpour stream examination.Reenactment of precipitation overflow might be a release-based way to deal with a foreseen downpour that enters the watershed.To understand this reason, different strategies, experimental conditions, and precipitation overflow models [11] are frequently utilized.Many models have been created in the downpour stream examination.Simulation of precipitation overflow is a release-based way to deal with a foreseen downpour that enters the watershed.To accomplish this reason, different techniques, observational conditions, and precipitation spillover models can be utilized [10].Previously, numerous observational formulae have been grown, yet taken in their pertinent just to the district where they were inferred.Present examination work has practical experience in assessing the spillover utilizing the best experimental strategy.
Hoshangabad, the city of vegetation is one of the extremely lovely and quiet urban areas of India with the least weakness to normal dangers like tremors, floods, landslides, and so on.Lately, inhabitants of this city find themselves helpless against metropolitan floods.Prior to the stormy season in Hoshangabad used to be charming to such an extent that individuals used to go on lengthy outings in the close by regions by street just to partake in the downpours.These days everybody needs to remain at home to remain protected during downpours to avoid or to battle issues.The floods occur because of regular factors, for example, heavy precipitation, high floods, and so on.Obstructing of channels or exacerbation of seepage channels, ill-advised land use, deforestation in headwater districts, and so forth, are human variables.Hoshangabad city has no huge history of metropolitan floods.However, from the most recent multi-decade the city has been confronting numerous circumstances of metropolitan flooding during the storm season.The uneven circulation of precipitation combined with thoughtless urbanization, infringement, and filling of normal waste channels and metropolitan lakes to involve the high-esteem metropolitan land for structures are the reasons for metropolitan flooding.Weakness is the fundamental built-in flood risk for the executives.The Hoshangabad region is the area that is very much affected by the flood due to the Narmada River [8].This region is ungauged, so the amount of flood is unpredictable.So, there is a requirement for any empirical equation for this region.Empirical equations are the equation that is used to find the runoff of any ungauged area.Therefore, we have taken four empirical equations (Khuzla's equation, English and Desouza recipe, Indian Irrigation department, and Khosla's recipe).Then the comparison study is carried out for the obtained result from the equations to find the bestsuited equation for this region.

Study Area
The Narmada basin, trimmed among Vindhya and Satpura ranges, reaches out over an area of 98,796 km 2 (38,145.3sq mi) and lies between east longitudes 72°32' to 81°45' and north scopes 21°20' to 23°45' lying on the northern limit of the Deccan level.The upper plain area of the Narmada River basin at the Hoshangabad sub-catchment is used for this study, which has a drainage area of 10,594 km 2 and coordinates lies between 22°46'N and 77°43'E.The length of the stream beneath this structure is eightytwo km.

Experimental methods
Before numerous exact formulae were grown, yet these are relevant just to the locale where they were determined.Moreover, alerts should be taken in their application assuming the attributes of the area have been exposed to artificial aggravation (settlement, land use design change) [12].These are basically precipitation overflow associations with extra third or fourth boundaries to represent climatic or catchment attributes.A portion of the significant observational spillover assessment formulae used in different pieces of India are given below: 2.2.4.Khosla's Formula.Khosla (1960) examined the precipitation, overflow, and temperature information for different catchments in India and the USA to arrive at an exact connection between spillover and precipitation [4].The time span is required as a month.His relationship for month-tomonth overflow for the T > 4.5 ˚C is, R = P -L (5) where L = (0.48*T)At the same time for the T ≤ the loss may provisionally be assumed as an annual runoff of Σ R. Khosla's equation is in a roundabout way founded on the water-balance idea and the mean month-to-month catchment temperature is utilized to mirror the misfortunes because of evapotranspiration.The equation has been tried on various catchments in India and is found to offer genuinely great outcomes for the yearly respect to be utilized in primer examinations.Where, R = monthly runoff in mm and R ≥ 0; P =monthly rainfall in mm; L = monthly losses in mm; T = mean monthly temperature of the catchment in °C IOP Publishing doi:10.1088/1755-1315/1258/1/0120044

Input Data
Annual rainfall data from 1981 to 2017 has been taken for the Narmada River basin [8] at the Hoshangabad sub-catchment from the CWC Bhopal.The environment of the Hoshangabad region is portrayed by a sweltering summer and general dryness during the southwest rainstorm season.The year might be partitioned into four seasons.The cold season, December to February is trailed by the hot season from Spring to about the center of June.The period from the center of June to September is the southwest rainstorm season.October also, November structure the post-storm or change period.The ordinary precipitation of the Hoshangabad area is 1225.9mm.It gets the greatest precipitation during the southwest storm period.Around 92.8% of the yearly precipitation is recorded during rainstorm seasons and just 7.2 % of the yearly rainfalls occur during the October to May period.The excess water for groundwater re-energizing is accessible just during the southwest rainstorm time frame.Then the yearly annual average temperature was taken for this study.

Annual Runoff calculation
Annual Runoff is calculated using different formula and their values has been given as follows:   Here we have taken the rainfall data from 1981 to 2017 and runoff was calculated according to the formula given by Khuzla formula.The maximum rainfall was in the year 2006 about 1784.9 mm due to cyclonic activity near Madhya Pradesh.The minimum runoff was in 2008 about 850 mm.A graph has been drawn between the amount of rainfall and runoff and shown by the red and blue colors respectively.On the X axis, the year has been denoted and on the Y axis rainfall and runoff amount has been indicated.In Figure 8. Shows the comparison between the different runoffs calculated by using different empirical formulas.Therefore, we can say that the three formulas (Khuzla, Indian irrigation department, and Khosla) can be used for the calculation of runoff in that area and the English & Duez formula is not giving the proper result, so we must regret this formula in use.While comparing the runoff values with the rainfall, we have observed that in the English & Duez formula, the runoff value is varying very much with the rainfall values.

Conclusion
In the present study, we have used different empirical formulas for the calculation of runoff of Hoshangabad which is situated at the bank of the Narmada River in Madhya Pradesh from the years 1981 to 2017 are taken for this study.The daily data is taken from CWC Bhopal for the Hoshangabad

Figure 1 .Figure 2 .
Figure 1.Location of Hoshangabad sub-catchment (Source: Central Ground Water Board, Aquifer Mapping and Ground Water Management Plan of Hoshangabad District, Madhya Pradesh)

Figure 3 .
Shows the yearly variation of (a) rainfall from 1981 to 2017, and (b) temperature variation from 1981 to 2017.In this figure 3(a).We can see the variation in rainfall patterns from the year 1981 to 2017.The maximum rainfall attained in the year 2006 is 1800mm.In Figure 3(b).The variation in mean annual temperature has been shown.The minimum temperature was 25.3℃ in 1997 and the maximum temperature was 26.6℃ in the year 2002.

Figure 4 .
Figure 4. Graph of variation between annual rainfall and runoff calculated using the Khuzla formula

Figure 5 .
Figure 5. Graph of variation between annual rainfall and runoff calculated using English and Duez formula In Figure 5. Annual variation of rainfall and runoff calculated by the English and Duez formula has been shown.The annual runoff from 1981 to 2017 has been calculated by using the English and Duez formula.For this calculation formula given by two scientists English and Duez for the non-ghat region has been used since the Hoshangabad region comes under this geological region of India.A graph has been drawn between the amount of rainfall and runoff and shown by the red and blue colors respectively.On the X axis, the year has been denoted and on the Y axis rainfall and runoff amount has been indicated.The maximum runoff observed by this formula in the year 2006 is 12617 mm.The minimum rainfall was in 2008 about 2788 mm.

Figure 6 .
Figure 6.Graph of variation between annual rainfall and runoff calculated using Indian irrigation department formula

Figure 7 .
Figure 7. Graph of variation between annual rainfall and runoff calculated using Khosla Formula

Figure 8 .
Figure 8.Comparison between runoff calculated by different formulas 1. Khuzla Formula.The Khuzla proposed the condition to work out overflow utilizing Temperature

Table 1 .
Comparison table for calculated Annual runoff using different formulasAnnual runoff has been calculated and summarized in Table1.In this table year, the year-wise runoff from 1981 to 2017 has been given and their corresponding values of the different empirical equations are mentioned in the above table.