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

Abstract

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.

Annexure I: Geomorphologic Parameters

• (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 (S_i), Gravelius index (G_i), circulatory ratio (R_c), elongation ratio(R_e), compactness coefficient (C_c), and Ruggedness number (R_N) are some of the important shape parameters, which are normally used to predict stream flow.

• i) The shape index (S_i) is defined as:

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

(8)

where W_L is the length of the watershed along main stream; W_w is the average width of the watershed; and W_A is the area of the watershed.

• ii) The Gravelius index (G_i) is given as:

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

(9)

where W_p is the perimeter of the watershed.

• iii) The circulatory ratio (R_c) is defined as:

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

(10)

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

• iv) The elongation ratio (R_e) is defined as:

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

(11)

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

• v) The compactness coefficient (C_c) is calculated as:

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

(12)

where C_c is the compactness coefficient [dimensionless].

• vi) The Ruggedness number (R_N) is defined as:

$$ {R}_N=\Delta H\ast {D}_d $$

(13)

• (b) Derived Parameters

Important derived parameters are; bifurcation ratio (B_r), stream length ratio (R_L), drainage density (D_d), and relief ratio (R_r).

• i) The bifurcation ratio (R_b) is given by:

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

(14)

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

• ii) The stream length ratio (R_L) is described as:

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

(15)

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

• iii) The drainage density (D_d) is expressed as:

$$ {D}_d=\frac{W_L}{W_A} $$

(16)

• iv) The relief ratio (R_r) is given by:

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

(17)