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 landuse and landcover (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 rainfallrunoff 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.
This is a preview of subscription content, access via your institution.
Data Availability
Data used in the research work from different sources have duly been acknowledged.
References
Ali S, Ghosh NC, Singh R (2010) Rainfallrunoff simulation using normalized antecedent precipitation index. Hydrol Sci Jour 55(2):266–274
ASCE Task Committee on Application of Artificial Neural Networks in Hydrology (2000) Artificial neural networks in hydrology. Ipreliminary concepts. J Hydrol Eng 5(2):115–123
Beeven KJ (1997) TOPMODEL: a critique. Hydrol Process 11(9):1069–1086
Beven KJ, Freer J (2001) Equifinality, data assimilation, and uncertainty estimation in mechanistic modeling of complex environmental systems using the GLUE methodology. J Hydrol 249:11–29
Binjolkar P, Keshari AK (2007) Estimating geomorphological parameters using GIS for Tilaiya reservoir catchment. Institution of Engineers (India) Journal 88:21–26
Bishop CM (1994) Artificial networks and their applications. Rev Sci Instrum 65:1803–1832
Boughton WC (1968) A mathematical catchment model for estimating runoff. J Hydrol (N.Z) 7(2):75–100
Burt TP, Slattery MC (2005) Land use and land cover effects on runoff processes: agricultural effects (in rainfallrunoff process). John Wiley and Sons Ltd. https://doi.org/10.1002/0470848944.hsa122
Chang, Hyungjoon, Thomas Kjeldsen, Neil McIntyre, and Hyosang Lee, (2018). Regionalization of a PDM model for catchment runoff in mountainous region of Korea. KSCE jour. Civil Engg. Springer . 2, pp 4699–4709, https://doi.org/10.1007/s1229501816297
Chiew FHS, Stewardson MJ, McMohon TA (1993) Comparison of six rainfallrunoff modeling approaches. J Hydrol 147:1–36
Descroix L, Nouvelot, Vauclin M (2002) Evaluation of an antecedent index to model runoff yield in the western Sierra Madre (northWest Mexico). J Hydrol 263:114–130
Dowson CW, Abrahat RJ (2007) Evaluation of two different methods for the antecedent precipitation index in neural network river stage forecasting. Geophys Res Abstract 9:07522
Endreny TE (2005) Land use and land cover effects on runoff processes: urban and suburban development (in rainfallrunoff process). John Wiley and Sons Ltd. https://doi.org/10.1002/0470848944.hsa123
Garg, S.K. (1987), Hydrology and Water Resources Engineering, 7th edition, Khanna Publishers, New Delhi
Gayathri K. Devi, B. P. Ganasri, and G. S. Dwarakish, (2015). Application of Remote Sensing in Satellite Oceanography : A Review. International Conference on Water Resources, Coastal and Ocean Engineering (ICWRCOE’15), Mangalore, India, 12–14 March 2015, Aquatic Procedia Volume 4. (ed. G. S. Dwarakish), Elsevier B.V., Curran Associates, Inc., pp 579–584
Gosain AK, Mani A, Dwivedi C (2009) Hydrological modelling literature review: report no.1. IndoNorwegian Institutional Cooperation Program 20092011
Grayson RB, Moore ID, McMohon TA (1992) Physically based hydrologic modeling2 is the concept realistic? Water Resour Res 28(10):2659–2666
Haan CT (1972) A water yield model for small watersheds. Water Resour Res 8(1):58–69
Hawkins, R.H. (1984), ‘A comparison of predicted and observed runoff curve numbers,’ Proc., Spec. Conf., Irrig. and Drain. Div., ASCE, New York, pp. 702–709.
Heggen RJ (2001) Normalized antecedent precipitation index. J Hydrol Eng ASCE 6(5):377–381
Hughes DA, Sani K (1994) A semidistributed, variable time interval model of catchment hydrology structure and parameter estimation procedure. J Hydrol 155:265–291
IbrahimBathis K, Ahmed SA (2016) Rainfallrunoff modeling of Doddahalla watershed– an application of HECHMS and SCSCN in ungauged agricultural watershed. Arabian Jour Geosc Springer 9(170). https://doi.org/10.1007/s1251701522282
Jain A, Indurthy P (2003) Comparative analysis of event based rainfallrunoff modeling techniques  deterministic, statistical and artificial neural networks. J Hydrol Eng 8(2):93–98
Jain MK, Kothyari UC (2000) Estimation of soil erosion and sediment yield using GIS. J Hydrol Sci 45(5):771–786
Jain MK, Mishra SK, Singh VP (2006) Evaluation of AMCdependent SCSCNbased models using watershed characteristics. Water Resour Managt 20:531–552
Knapp, H Vernon, Ali Durgunoglu, and Terry W Ortel (1991), A review of rainfallrunoff modeling for storm water management, USGS, Illinois State Water Survey, Hydrology Division, SWS Contract Report 516. http://www.isws.illinois.edu/ pubdoc/cr/iswscr516.pdf (download on 12th May, 2016)
Knudsen J, Thomsen A, Resfgaard JC (1986) WATBAL: a semidistributed physically based hydrological modeling system. Nord Hydrol 17(4–5):347–362
Marquardt DW (1963) An algorithm for least squares estimation of nonlinear parameters. J Soc Indust Applied Mat 11(2):431–441
Mclntyre N, AlQurashi A (2009) Performance of ten rainfallrunoff models applied to an arid catchment in Oman. Environmental Modeling and Software. Elsevier Science Publishers 24(6):726–788. https://doi.org/10.1016/J.ensoft.2008.11.001
Mclntyre N, Lee H, Wheater H (2005) Ensemble predictions of runoff in ungauged catchments. Water Resour Res 41(W12434). https://doi.org/10.1029/2005WR004289
Mishra SK, Jain MK, Pandey RP, Singh VP (2005) Catchment areabased evaluation of the AMCdependent SCSCNbased rainfall runoff models. Jour Hydrol Processes 19:2701–2718
Moore RJ (2007) The PDM rainfallrunoff model. Hydrology and Earth Sciences 11(1):483–499
Moradkhani, Hamid, and Soroosh Sorooshian (2009) General review of rainfallrunoff modeling: Model calibration, data assimilation, and uncertainty analysis. in book edited by S. Sosooshian et al, Hydrological Modelling and the Water Cycle. Springer Science Series, 1–24 pp.
MunozVillers LE, McDonnel JJ (2013) Land use change effects on runoff generation in a humid tropical montane cloud forest region. Hydrol Earth Syst Sci 17:3543–3560. https://doi.org/10.5194/hess1735432013
Nayak TR, Gupta SK, Galkate R (2015) GIS based mapping of groundwater fluctuations in Bina Basin. Aqutic Procedia, Elsevier 2:1469–1467
Ponce VM, Hawkins RH (1996) Runoff curve number: has it reached maturity. J Hydrol Eng 1(1):11–16
Razavi T, Coulibaly P (2016) Improving streamflow estimation in ungauged basins using a multimodelling approach. Hydrol Sci J 61(15) Taylor & Francis. https://doi.org/10.1080/02626667.2016.1154558
RodriguezIturbe I, GonzalezSanabria M (1982) A geomorphoclimatic theory of the instantaneous unit hydrograph. Water Resour Res 18(4):877–886
RodriguezIturbe I, Valdes JB (1979) The geomorphologic structure of hydrologic response. Water Resour Res 15(6):1409–1420
Schneider LE, McCuen RH (2005) Statistical guidelines for curve number generation, J. Irri. Drain Eng. ASCE 13(3):282–290
SCS (1956, 1993) Hydrologynational engineering handbook, supplement a, section 4, Chapter 10, Soil Conservation Service. United State Department of Agriculture (USDA), Washington, DC
Sorooshian S, Daun Q, Gupta VK (1993) Calibration of rainfallrunoff models: application of global optimization to the Sacramento soil moisture accounting model. Water Resour Res 29(4):1185–1194
Strahler AN (1957) Quantitative analysis of watershed geomorphology. Trans Am Geophys Union 38:913–920
Synder WM (1972) Fitting of distribution functions by nonlinear least squares. Water Resour Res 8(6):1423–1432
Todini E (1988) Rainfallrunoff modeling: Past, present and future. J Hydrol 100(1–3):341–352. https://doi.org/10.1016/00221694(88)/901916
USEPA (2017). An overview of rainfallrunoff model types. Report no.: EPA/600/R14/152, September, 2017. 28p
Valdes JB, Fiallo Y, RodreguezIturbe I (1979) A rainfallrunoff analysis of the gomorphologic IUH. Water Resour Res 15(6):1421–1434
Vaze J, Jordan P, Beecham R, Frost A, Summerell G (2011) Guidelines for rainfallrunoff modelling: towards best practice model application, eWater Cooperative Research Centre, Innovation Centre, Building 22, University drive south. Bruce ACT 2617
Viessman W, Lewis GL (1996) Introduction to hydrology, fourth edn. Publishers, NY, Harper Collins College
Wheater HS (2002) Progress in and prospects for fluvial flood modeling. Philos Trans R Soc London, Ser A 360(1796):1409–1431
Wilcon B, Rawls W, Brakensiek L, Wright R (1990) Predicting runoff from rangeland catchments: a comparison of two models. Water Resour Res 26:2401–2410
Zelazinski J (1986) Application of the geomorphological instantaneous unit hydrograph theory to development of forecasting models in Poland. Hydrol Sci J 31(2):263–270
Zhang GP, Savenije HHG (2005) Rainfallrunoff modelling in a catchment with a complex groundwater flow system: application of the representative elementary watershed (REW) approach. Hydrol Earth Syst Sci 9:243–261 http://www.copernicus.org/EGU/hess/hess/9/243/hess9243.pdf
Acknowledgements
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.
Funding
This research work didn’t require any additional fund except the salary wages of the authors.
Author information
Affiliations
Contributions
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.
Corresponding author
Ethics declarations
Ethical Approval
The work presented in this manuscript is research outputs; therefore, there is no need for any ethics approval.
Consent to Participate
The second and third author have duly acknowledged their respective head of the Institution for granting permission to carry out the research work; while the first author himself is the head of the Institution.
Consent to Publish
All authors have duly consented to publish this manuscript.
Competing Interests
There were no competing interest involved with this research work and its outputs.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Annexure I: Geomorphologic Parameters
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:
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:
where W_{p} is the perimeter of the watershed.

iii)
The circulatory ratio (R_{c}) is defined as:
W_{e} is the equivalent circle area having perimeter as that of the watershed.

iv)
The elongation ratio (R_{e}) is defined as:
D is the diameter of the circle having the same area of the watershed.

v)
The compactness coefficient (C_{c}) is calculated as:
where C_{c} is the compactness coefficient [dimensionless].

vi)
The Ruggedness number (R_{N}) is defined as:

(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:
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:
Where \( \overline{L_u} \) and \( \overline{L_{u1}} \) are the average length of stream of order u and u1, respectively.

iii)
The drainage density (D_{d}) is expressed as:

iv)
The relief ratio (R_{r}) is given by:
Rights and permissions
About this article
Cite this article
Ghosh, N.C., Jaiswal, R.K. & Ali, S. Normalized Antecedent Precipitation Index Based Model for Prediction of Runoff from UnGauged Catchments. Water Resour Manage (2021). https://doi.org/10.1007/s1126902102775w
Received:
Accepted:
Published:
Keywords
 NAPI model
 Ungauged catchment
 Geomorphological index
 SCSCN
 Field testing