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.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Data Availability

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

References

  1. Ali S, Ghosh NC, Singh R (2010) Rainfall-runoff simulation using normalized antecedent precipitation index. Hydrol Sci Jour 55(2):266–274

    Article  Google Scholar 

  2. ASCE- Task Committee on Application of Artificial Neural Networks in Hydrology (2000) Artificial neural networks in hydrology. I-preliminary concepts. J Hydrol Eng 5(2):115–123

    Article  Google Scholar 

  3. Beeven KJ (1997) TOPMODEL: a critique. Hydrol Process 11(9):1069–1086

    Article  Google Scholar 

  4. 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

    Article  Google Scholar 

  5. Binjolkar P, Keshari AK (2007) Estimating geomorphological parameters using GIS for Tilaiya reservoir catchment. Institution of Engineers (India) Journal 88:21–26

    Google Scholar 

  6. Bishop CM (1994) Artificial networks and their applications. Rev Sci Instrum 65:1803–1832

    Article  Google Scholar 

  7. Boughton WC (1968) A mathematical catchment model for estimating runoff. J Hydrol (N.Z) 7(2):75–100

    Google Scholar 

  8. Burt TP, Slattery MC (2005) Land use and land cover effects on runoff processes: agricultural effects (in rainfall-runoff process). John Wiley and Sons Ltd. https://doi.org/10.1002/0470848944.hsa122

  9. 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/s12295-018-1629-7

  10. Chiew FHS, Stewardson MJ, McMohon TA (1993) Comparison of six rainfall-runoff modeling approaches. J Hydrol 147:1–36

    Article  Google Scholar 

  11. Descroix L, Nouvelot, Vauclin M (2002) Evaluation of an antecedent index to model runoff yield in the western Sierra Madre (north-West Mexico). J Hydrol 263:114–130

    Article  Google Scholar 

  12. 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

    Google Scholar 

  13. Endreny TE (2005) Land use and land cover effects on runoff processes: urban and suburban development (in rainfall-runoff process). John Wiley and Sons Ltd. https://doi.org/10.1002/0470848944.hsa123

  14. Garg, S.K. (1987), Hydrology and Water Resources Engineering, 7th edition, Khanna Publishers, New Delhi

  15. 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

  16. Gosain AK, Mani A, Dwivedi C (2009) Hydrological modelling literature review: report no.1. Indo-Norwegian Institutional Cooperation Program 2009-2011

  17. Grayson RB, Moore ID, McMohon TA (1992) Physically based hydrologic modeling-2 is the concept realistic? Water Resour Res 28(10):2659–2666

    Article  Google Scholar 

  18. Haan CT (1972) A water yield model for small watersheds. Water Resour Res 8(1):58–69

    Article  Google Scholar 

  19. 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.

  20. Heggen RJ (2001) Normalized antecedent precipitation index. J Hydrol Eng ASCE 6(5):377–381

    Article  Google Scholar 

  21. Hughes DA, Sani K (1994) A semi-distributed, variable time interval model of catchment hydrology- structure and parameter estimation procedure. J Hydrol 155:265–291

    Article  Google Scholar 

  22. Ibrahim-Bathis K, Ahmed SA (2016) Rainfall-runoff modeling of Doddahalla watershed– an application of HEC-HMS and SCS-CN in ungauged agricultural watershed. Arabian Jour Geosc Springer 9(170). https://doi.org/10.1007/s12517-015-2228-2

  23. Jain A, Indurthy P (2003) Comparative analysis of event based rainfall-runoff modeling techniques - deterministic, statistical and artificial neural networks. J Hydrol Eng 8(2):93–98

    Article  Google Scholar 

  24. Jain MK, Kothyari UC (2000) Estimation of soil erosion and sediment yield using GIS. J Hydrol Sci 45(5):771–786

    Article  Google Scholar 

  25. Jain MK, Mishra SK, Singh VP (2006) Evaluation of AMC-dependent SCS-CN-based models using watershed characteristics. Water Resour Managt 20:531–552

    Article  Google Scholar 

  26. Knapp, H Vernon, Ali Durgunoglu, and Terry W Ortel (1991), A review of rainfall-runoff modeling for storm water management, USGS, Illinois State Water Survey, Hydrology Division, SWS Contract Report 516. http://www.isws.illinois.edu/ pubdoc/cr/iswscr-516.pdf (download on 12th May, 2016)

  27. Knudsen J, Thomsen A, Resfgaard JC (1986) WATBAL: a semi-distributed physically based hydrological modeling system. Nord Hydrol 17(4–5):347–362

    Article  Google Scholar 

  28. Marquardt DW (1963) An algorithm for least squares estimation of nonlinear parameters. J Soc Indust Applied Mat 11(2):431–441

    Article  Google Scholar 

  29. Mclntyre N, Al-Qurashi A (2009) Performance of ten rainfall-runoff 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

    Article  Google Scholar 

  30. 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

  31. Mishra SK, Jain MK, Pandey RP, Singh VP (2005) Catchment area-based evaluation of the AMC-dependent SCS-CN-based rainfall- runoff models. Jour Hydrol Processes 19:2701–2718

    Article  Google Scholar 

  32. Moore RJ (2007) The PDM rainfall-runoff model. Hydrology and Earth Sciences 11(1):483–499

    Article  Google Scholar 

  33. Moradkhani, Hamid, and Soroosh Sorooshian (2009) General review of rainfall-runoff 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.

  34. Munoz-Villers 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/hess-17-3543-2013

    Article  Google Scholar 

  35. Nayak TR, Gupta SK, Galkate R (2015) GIS based mapping of groundwater fluctuations in Bina Basin. Aqutic Procedia, Elsevier 2:1469–1467

    Article  Google Scholar 

  36. Ponce VM, Hawkins RH (1996) Runoff curve number: has it reached maturity. J Hydrol Eng 1(1):11–16

    Article  Google Scholar 

  37. Razavi T, Coulibaly P (2016) Improving streamflow estimation in ungauged basins using a multi-modelling approach. Hydrol Sci J 61(15) Taylor & Francis. https://doi.org/10.1080/02626667.2016.1154558

  38. Rodriguez-Iturbe I, Gonzalez-Sanabria M (1982) A geomorphoclimatic theory of the instantaneous unit hydrograph. Water Resour Res 18(4):877–886

    Article  Google Scholar 

  39. Rodriguez-Iturbe I, Valdes JB (1979) The geomorphologic structure of hydrologic response. Water Resour Res 15(6):1409–1420

    Article  Google Scholar 

  40. Schneider LE, McCuen RH (2005) Statistical guidelines for curve number generation, J. Irri. Drain Eng. ASCE 13(3):282–290

    Google Scholar 

  41. SCS (1956, 1993) Hydrology-national engineering handbook, supplement a, section 4, Chapter 10, Soil Conservation Service. United State Department of Agriculture (USDA), Washington, DC

  42. Sorooshian S, Daun Q, Gupta VK (1993) Calibration of rainfall-runoff models: application of global optimization to the Sacramento soil moisture accounting model. Water Resour Res 29(4):1185–1194

    Article  Google Scholar 

  43. Strahler AN (1957) Quantitative analysis of watershed geomorphology. Trans Am Geophys Union 38:913–920

    Article  Google Scholar 

  44. Synder WM (1972) Fitting of distribution functions by nonlinear least squares. Water Resour Res 8(6):1423–1432

    Article  Google Scholar 

  45. Todini E (1988) Rainfall-runoff modeling: Past, present and future. J Hydrol 100(1–3):341–352. https://doi.org/10.1016/0022-1694(88)/90191-6

    Article  Google Scholar 

  46. US-EPA (2017). An overview of rainfall-runoff model types. Report no.: EPA/600/R-14/152, September, 2017. 28p

  47. Valdes JB, Fiallo Y, Rodreguez-Iturbe I (1979) A rainfall-runoff analysis of the gomorphologic IUH. Water Resour Res 15(6):1421–1434

    Article  Google Scholar 

  48. Vaze J, Jordan P, Beecham R, Frost A, Summerell G (2011) Guidelines for rainfall-runoff modelling: towards best practice model application, eWater Cooperative Research Centre, Innovation Centre, Building 22, University drive south. Bruce ACT 2617

  49. Viessman W, Lewis GL (1996) Introduction to hydrology, fourth edn. Publishers, NY, Harper Collins College

  50. Wheater HS (2002) Progress in and prospects for fluvial flood modeling. Philos Trans R Soc London, Ser A 360(1796):1409–1431

    Article  Google Scholar 

  51. 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

    Article  Google Scholar 

  52. 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

    Article  Google Scholar 

  53. Zhang GP, Savenije HHG (2005) Rainfall-runoff 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/hess-9-243.pdf

    Article  Google Scholar 

Download references

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

Authors

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

Correspondence to Narayan C. Ghosh.

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

  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:

$$ {S}_i\kern1em =\kern1em \frac{W_L}{W_w}\kern1em =\kern1em \frac{{W_L}^2}{W_A} $$
(8)

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:

$$ {G}_i\kern1em =\kern1em 0.28\kern0.5em \frac{W_p}{0.5\kern1em {W}_A} $$
(9)

where Wp is the perimeter of the watershed.

  1. iii)

    The circulatory ratio (Rc) is defined as:

$$ {R}_c\kern1em =\kern1em \frac{W_A}{W_e} $$
(10)

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

  1. iv)

    The elongation ratio (Re) is defined as:

$$ {R}_e\kern1em =\kern1em \frac{D}{W_L} $$
(11)

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

  1. v)

    The compactness coefficient (Cc) is calculated as:

$$ {C}_c=\frac{0.28\kern0.5em {W}_p}{\sqrt{W_A}} $$
(12)

where Cc is the compactness coefficient [dimensionless].

  1. vi)

    The Ruggedness number (RN) is defined as:

$$ {R}_N=\Delta H\ast {D}_d $$
(13)
  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:

$$ {R}_b\kern1em =\kern1em \frac{N_u}{N_{u+1}} $$
(14)

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:

$$ {R}_L=\frac{\overline{L_u}}{\overline{L_{u-1}}} $$
(15)

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:

$$ {D}_d=\frac{W_L}{W_A} $$
(16)
  1. iv)

    The relief ratio (Rr) is given by:

$$ {R}_r=\frac{\Delta H}{L} $$
(17)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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). https://doi.org/10.1007/s11269-021-02775-w

Download citation

Keywords

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