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Regularized joint inverse estimation of extreme rainfall amounts in ungauged coastal basins of El Salvador

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Abstract

A regularized joint inverse procedure is presented and used to estimate the magnitude of extreme rainfall events in ungauged coastal river basins of El Salvador: Paz, Jiboa, Grande de San Miguel, and Goascoran. Since streamflow measurements reflect temporal and spatial rainfall information, peak-flow discharge is hypothesized to represent a similarity measure suitable for regionalization. To test this hypothesis, peak-flow discharge values determined from streamflow recurrence information (10-year, 25-year, and 100-year) collected outside the study basins are used to develop regional (country-wide) regression equations. Peak-flow discharge derived from these equations together with preferred spatial parameter relations as soft prior information are used to constrain the simultaneous calibration of 20 tributary basin models. The nonlinear range of uncertainty in estimated parameter values (1 curve number and 3 recurrent rainfall amounts for each model) is determined using an inverse calibration-constrained Monte Carlo approach. Cumulative probability distributions for rainfall amounts indicate differences among basins for a given return period and an increase in magnitude and range among basins with increasing return interval. Comparison of the estimated median rainfall amounts for all return periods were reasonable but larger (3.2–26%) than rainfall estimates computed using the frequency-duration (traditional) approach and individual rain gauge data. The observed 25-year recurrence rainfall amount at La Hachadura in the Paz River basin during Hurricane Mitch (1998) is similar in value to, but outside and slightly less than, the estimated rainfall confidence limits. The similarity in joint inverse and traditionally computed rainfall events, however, suggests that the rainfall observation may likely be due to under-catch and not model bias.

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Abbreviations

A :

Drainage area in km2

CN:

Runoff curve number for a tributary basin

d r :

Vector of preferred regional dissimilarity between tributary basin parameter values

d a :

Vector of actual regional dissimilarity between tributary basin parameter values

h :

Vector (n-dimensional) of observation values (recurrent peak-flow discharge values determined externally for areas regression equations)

h 0 :

Current model outputs

j :

Regularization observations

j 0 :

Initial set of regularization constraints (soft prior information)

I :

Identity matrix

I a :

Initial abstraction

Lt :

Lag time

L :

Hydraulic length of tributary basin

L :

Operator indicating regularization observations acting on parameter set p

M :

Operator that maps parameter space to the space of observations

M(p):

Vector of simulated recurrent tributary basin peak-flow discharge and rainfall values determined using a rainfall–runoff model

P :

Vector of parameter (rainfall–runoff curve numbers) and boundary condition (recurrent rainfall amounts) values being estimated

p 0 :

Current parameter values

p − p 0 :

Parameter upgrade vector

p j :

Rainfall–runoff parameter value in tributary basin j

p k :

Rainfall–runoff parameter value in tributary basin k

pri :

Prior information

P :

Rainfall in mm

q um :

Unit peak discharge (m3/s/km2/mm)

Q :

Diagonal weight matrix used in the measurement objective function

R :

Depth of runoff in mm

S :

Maximum potential difference between rainfall and runoff (tributary basin retention) in mm

S :

Relative weight matrix used in the regularization objective function

w ri :

Regularization weights

X :

Jacobian matrix of the operator M

X T :

Transpose of matrix X

Y :

Tributary basin slope

Z :

Jacobian matrix of the operator L

β2 :

Regularization weight factor

λ I :

A diagonal matrix (Marquardt lambda) added to enhance inverse stability

Φm :

The model-to-measurement misfit described by a least-squares measurement objective function

Φr :

The model-to-regularization misfit described by a least-squares regularization objective function

References

  • Bates B, Campbell E (2001) A Markov chain Monte Carlo scheme for parameter estimation and inference in conceptual rainfall-runoff modeling. Water Resour Res 37(4):937–947

    Article  Google Scholar 

  • Beven KJ, Binley AM (1992) The future of distributed models: model calibration and uncertainty prediction. Hydrol Process 6:279–298

    Article  Google Scholar 

  • Bicknell BR, Imhorr JC, Kittle JL, Donigan AS, Johanson RC (1997) Hydrologic simulation program-fortran, user’s manual for version 11. U.S. Environmental Protection Agency EPA/600/R-97/-90, 755 pp

  • Bloschl G, Sivapalan M (1995) Scale issues in hydrological modeling – a review. Hydrol Process 9(3–4):251–290

    Article  Google Scholar 

  • British Broadcasting Corporation (2000) Flood emergency in El Salvador. http://www.news.bbc.co.uk/1/hi/world/americas/914509.stm. Accessed 7 September 2007

  • Chow VT, Maidment DR, Mays LW (1988) Applied hydrology. McGraw-Hill, New York

  • Cooley RL, Naff RL (1990) Regression modeling of ground-water flow. US Geological Survey Technical Water Resources Investigation: Book 3, Chapter B4, 232 pp

  • Crone AJ, Baum RL, Lidke DJ, Sather DND, Bradley LA, Tarr AC (2001) Landslides induced by hurricane Mitch in El Salvador – an inventory and descriptions of selected features. US Geological Survey Open File Report, 01-144

  • Curtis S, Crawford TW, Lecce SA (2007) A comparison of TRMM to other basin-scale estimates of rainfall during the 1999 Hurricane Floyd flood. Nat Hazards 43:187–198

    Google Scholar 

  • deGroote-Hedlin C, Constable S (1990) Occam’s inversion to generate smooth, two-dimensional models from magnetotelluric data. Geophysics 55(12):1624–1631

    Article  Google Scholar 

  • Doherty J (2004) PEST: model-independent parameter estimation, version 5 of user manual. Watermark Numerical computing, Brisbane, Australia, 213 pp

  • Doherty J, Johnston JM (2003) Methodologies for calibration and predictive analysis of a watershed model. J Am Water Resour As 39(2):251–265

    Article  Google Scholar 

  • El Diario de Hoy (1999) Flooding in El Salvador (various articles October), http://www.osb.org/pab/ES%20Flooding%20F99.htm. Accessed 7 September 2007

  • Elliot J, Smith ME, Friedel MJ, Litke D (2005) Post-fire hydrologic hazards study for the 2002 Hayman, Coal Seam, and Missionary Ridge wildfires, Colorado. U.S. Geological Survey, Science Investigations Report 2004–5300, 125 pp

  • Erazo AM (2004) Regionalization de cauldales maximos y medios en El Salvador, Servicio Nacional de Estudios Territoriales. http://www.snet.gob.sv/page.php?id=197&p=131&search=maximos. Accessed 19 March 2006

  • Friedel MJ (2005) Coupled inverse modeling of vadose zone water, heat, and solute transport: calibration constraints, parameter nonuniqueness, and predictive uncertainty. J Hydrol 312(1–4):148–175

    Article  Google Scholar 

  • Friedel MJ (2006a) Predictive streamflow uncertainty in relation to calibration-constraint information, model complexity, and model bias. Int J River Basin Manage 4(1):1–15

    Google Scholar 

  • Friedel MJ (2006b) Reliability in estimating urban groundwater recharge through the vadose zone: managing sustainable development in arid and semiarid regions. In: Tellam JH, Rivett MO, Israfilov RG (eds) Urban groundwater management and sustainability. NATO Science Series, IV. Earth and Environmental Sciences, vol. 74. Springer, Dordrecht, The Netherlands, pp 169–182

  • Friedel MJ Probable flood predictions in ungauged coastal basins of El Salvador. J Hydrol Eng (in press)

  • Helin J, Haigh H, Marks F (1999) Rainfall characteristics of Hurricane Mitch. Nature 399:316–316

    Article  Google Scholar 

  • Hill M (1998) Methods and guidelines for effective model calibration. U.S. Geological Survey Water-Resources Investigations Report 98-4005, 90 pp

  • Hossain F, Katiyar N (2006) Improving flood forecasting in international river basins. EOS Trans (AGU) 87(5):49–50

    Google Scholar 

  • Kuczera G (1983) Improved parameter inference in catchment models. 1. Evaluating parameter uncertainty. Water Resour Res 19(5):1151–1172

    Article  Google Scholar 

  • Lakshmi V (2004) The role of satellite remote sensing in the prediction of ungauged basins. J Hydrol Proc 18:1029–1034

    Article  Google Scholar 

  • Lin G-F, Chen L-H, Kao S-C (2005) Development of regional design hyetographs. J Hydrol Proc 19:937–946

    Article  Google Scholar 

  • Merz R, Bloschl G (2004) Regionalization of catchment model parameters. J Hydrol 287:95–123

    Article  Google Scholar 

  • Rossman L (2005) SWMM – storm water management model user’s manual version 5. U.S. Environmental Protection Agency, EPA/600/R-05/040, 247 pp

  • Shiklomanov AI, Lammers RB, Vörösmarty CJ (2002) Widespread decline in hydrological monitoring threatens pan-arctic research. EOS Trans 83(2):16–17

    Google Scholar 

  • Siebert J (1999) Regionalization of parameters for a conceptual rainfall-runoff model. Agric Forest Meterol 98/99:279–293

    Article  Google Scholar 

  • Sivapalan M (2003) Prediction in ungauged basins: a grand challenge for theoretical hydrology. Hydrol Process 17(15):3163–3170

    Article  Google Scholar 

  • Soil Conservation Service (1985) National engineering handbook, Sect. 4. U.S. Department of Agriculture, Washington, DC

  • Stokstad E (1999) Scarcity of rain, stream gages threatens forecasts. Science 285:1199

    Article  Google Scholar 

  • U.S. Army Corps of Engineers (1998) HEC-1 flood hydrograph package user’s manual. U.S. Army Corps of Engineers Hydrologic Engineering Center, Davis, CA, version 4(1), 434 pp

  • Weaver JD, Gamble CR (1993) Flood frequency of streams in rural basins of Tennessee. U.S. Geological Survey Water-Resources Investigations Report 92-4165

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Acknowledgments

This work was carried out under the Earthquake Reconstruction Program administered by U.S. Agency for International Development, as part of technical assistance following the catastrophic earthquakes of January and February 2001 in El Salvador.

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  1. Crustal Imaging and Characterization Team, United States Geological Survey, Denver Federal Center, MS 964, Box 25046, Lakewood, CO, 80225, USA

    Michael J. Friedel

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Correspondence to Michael J. Friedel.

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Friedel, M.J. Regularized joint inverse estimation of extreme rainfall amounts in ungauged coastal basins of El Salvador. Nat Hazards 46, 15–34 (2008). https://doi.org/10.1007/s11069-007-9179-1

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