Normalized Antecedent Precipitation Index Based Model for Prediction of Runoff from Un-Gauged Catchments


The ‘Normalized Antecedent Precipitation Index (NAPI)’ model developed based on water balance equation was found capable to predict runoff yields from ungauged catchment when its parameters estimated from the gauged catchment are updated using the linear relationship of geomorphologic parameters of an ungauged to that of the gauged catchment, and cumulative geomorphologic index (CGI). The CGI was developed by assigning a relative weight on each geomorphologic parameter multiplied by the ratio of characteristic value of that parameter of the ungauged and gauged catchment. Influence of land-use and land-cover (LULC) on the model’s parameters was also analyzed by developing an index for LULC. The NAPI model has three parameters and its mathematical structure has rational form and the parameters possessed resonance with curve number (CN) of the SCS (Soil Conservation Services) model. The NAPI model demonstrated ability to simulate rainfall-runoff events both as direct and inverse problem. Performances of the model to predictions of runoffs from ungauged catchments were also tested with the data of two observation sites of the Bina basin in Madhya Pradesh (India) considering the data of one site as the runoffs from the ungauged catchment. The results exhibited a close match between the computed and observed values when the model’s parameters were also updated by the index of LULC.

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Data Availability

Data used in the research work from different sources have duly been acknowledged.


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The authors thankfully acknowledge the use of data from the published sources of the Central Water Commission, Madhya Pradesh. The second and third authors duly acknowledge the permission granted by the Director of the respective Institute.


This research work didn’t require any additional fund except the salary wages of the authors.

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1st author has contributed to the development of the concept and carrying out the research work including preparation of the manuscript; the second author contributed to the analysis of geomorphological parameters, preparation of maps and GIS related works; and the third author contributed to the NAPI related analysis.

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Correspondence to Narayan C. Ghosh.

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Annexure I: Geomorphologic Parameters

Annexure I: Geomorphologic Parameters

  1. (a)

    Watershed Geometric and Shape Parameters

The watershed geometric variables include: area, width, perimeter, length, stream order, stream length, maximum and minimum heights; The size and the shape of a watershed are the basic geomorphologic parameters. The shape index (Si), Gravelius index (Gi), circulatory ratio (Rc), elongation ratio(Re), compactness coefficient (Cc), and Ruggedness number (RN) are some of the important shape parameters, which are normally used to predict stream flow.

  1. i)

    The shape index (Si) is defined as:

$$ {S}_i\kern1em =\kern1em \frac{W_L}{W_w}\kern1em =\kern1em \frac{{W_L}^2}{W_A} $$

where WL is the length of the watershed along main stream; Ww is the average width of the watershed; and WA is the area of the watershed.

  1. ii)

    The Gravelius index (Gi) is given as:

$$ {G}_i\kern1em =\kern1em 0.28\kern0.5em \frac{W_p}{0.5\kern1em {W}_A} $$

where Wp is the perimeter of the watershed.

  1. iii)

    The circulatory ratio (Rc) is defined as:

$$ {R}_c\kern1em =\kern1em \frac{W_A}{W_e} $$

We is the equivalent circle area having perimeter as that of the watershed.

  1. iv)

    The elongation ratio (Re) is defined as:

$$ {R}_e\kern1em =\kern1em \frac{D}{W_L} $$

D is the diameter of the circle having the same area of the watershed.

  1. v)

    The compactness coefficient (Cc) is calculated as:

$$ {C}_c=\frac{0.28\kern0.5em {W}_p}{\sqrt{W_A}} $$

where Cc is the compactness coefficient [dimensionless].

  1. vi)

    The Ruggedness number (RN) is defined as:

$$ {R}_N=\Delta H\ast {D}_d $$
  1. (b)

    Derived Parameters

Important derived parameters are; bifurcation ratio (Br), stream length ratio (RL), drainage density (Dd), and relief ratio (Rr).

  1. i)

    The bifurcation ratio (Rb) is given by:

$$ {R}_b\kern1em =\kern1em \frac{N_u}{N_{u+1}} $$

where Nu and Nu + 1 are the number of streams of order u and u + 1, respectively.

  1. ii)

    The stream length ratio (RL) is described as:

$$ {R}_L=\frac{\overline{L_u}}{\overline{L_{u-1}}} $$

Where \( \overline{L_u} \) and \( \overline{L_{u-1}} \) are the average length of stream of order u and u-1, respectively.

  1. iii)

    The drainage density (Dd) is expressed as:

$$ {D}_d=\frac{W_L}{W_A} $$
  1. iv)

    The relief ratio (Rr) is given by:

$$ {R}_r=\frac{\Delta H}{L} $$

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Ghosh, N.C., Jaiswal, R.K. & Ali, S. Normalized Antecedent Precipitation Index Based Model for Prediction of Runoff from Un-Gauged Catchments. Water Resour Manage (2021).

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  • NAPI model
  • Un-gauged catchment
  • Geomorphological index
  • SCS-CN
  • Field testing