3.4.3   Mathematical Modelling for Runoff and NPS load Estimation
For estimation of runoff, the fundamental assumption of the model is that the amount of storm water runoff from any given land use is in direct proportion to rainfall. The quality of runoff is controlled by that fraction of the land use category that is characterized as impervious, and the coefficient of both pervious and impervious area. The governing equations are as follows:

Rj = [Cp + (Ci - Cp) IMPj] *I (1) ………………………(1)
Where,
Rj = Total average annual surface runoff from total land use j (m)
IMPj = Fractional impervious of Agriculture land use j
I = monthly precipitation (m)
Cp = Pervious area runoff coefficient
Ci = impervious area runoff coefficient
and
Qj = Rj Aj (2)           ……………………………… (2)
Where,
Qj = amount of runoff (m3/month) from a particular land use in Kharif and Rabi season
Aj = is the area of land use (m2)

The non – point source addressed in this study is the loading from agricultural area into surface runoff. Total Nitrogen and Total Phosphorus loading through surface runoff were estimated using the mathematical model such as the one Watershed Management Model (WMM, 1998) reported by and Shelly & Petrus (2004), which is based on the component of pervious and impervious area in different land use in watershed.

Nitrogen and Phosphorus Loading from agricultural areas:
Considering the Talukawise agricultural area obtained from classification of IRS _ P6 data and fertilizer requirement of each type of crop (Table no 4) (as reported in Handbook of Agriculture and Annual Report Diary of Punjabrao Deshmukh Agricultural University, Akola, Maharashtra), the amount of fertilizer used in Kharif and rabi season was estimated. Since, the actual nutrient requirement of the crop is reported to be 40 to 60% (Environmental Pollution – Land, B. Prasad, year ), the excess amount remains in the soil. Considering the average rate of 50% utilization by crop, the amount of fertilizer used was estimated for each Taluka.

Simulation of Pollutographs
Mathematical models for removal of pollutants from impervious areas are reported in the literature. The formulation is basically the same as the overland flow quality model that is based on following assumptions:

• The amount of pollutants removed by runoff water is proportional to the amount of pollutant remaining
• No pollutants decay due to chemical or biological degradation during the runoff process
• The amount of pollutant percolating into the soil is negligible

Based on the first assumption, the amount of pollutant removed at any time t is proportional to the amount of pollutant remaining is written as:

dP/dt = -kP    ……………………………(3)       
Where,
P = amount of pollutant remaining at time t
k= velocity of pollutant removal
t = time

Since, the runoff rate affects the pollutant removal, it is reported that k must be functionally dependent on runoff rate R (m/month). Assuming that k is directly proportional to R, we get k=Constant*R.

The value of constant is reported as 4.6 for removal of pollutants from streets and is verified for impervious surfaces by Sartoe and Boyd (5). It represents largest value for constant and a smaller value (constant < 4.6) suggests contribution from pervious areas. However, the value is site-specific, pollutant-specific and depends upon the watershed, soil type and other factors. Vales such as 0.16 for Ca and 2.0 for mercury are reported in the literature (ref: Donald E. Overton and Michael E. Meadows, 1976, Stormwater Modelling, ACADEMIC PRESS, N.York, San-Francisco, London). Considering the first order D.E., Total Nitrogen and Total Phosphorus loading into the surface runoff were estimated as:

Premoved = P0 (1-exp (-k*t))     ……………………….(4)

Estimation of k for Kharif and Rabi season

Since, most of the rainfall occurs in kharif season, the amount of runoff generated is
maxium in kharif season. Therefore, value of k= constant* R was estimated considering average runoff intensity in Kharif and rabi season. Value of constant was assumed to be 3.0 for N and 2 for Phosphorus. Considering the average runoff intensity for kharif and Rabi season in each Taluka, the seasonal value of k was estimated for kharif and Rabi.

Estimation of Pollutant Concentration in Runoff
Considering the nutrient load in terms of nutrient (N and P) remaining in the soil and considering that 20% of nutrient gets washed off with runoff from a particular area, the Event Mean Concentration of pollutant (Cj) in the runoff is estimated as:

Cj = Ti / Qj              …………………………………… (5)

Where,
Ti = Total loading of pollutant i on the surface runoff on the watershed (Kg / month)