Water Resources Management

, Volume 7, Issue 2, pp 131–151 | Cite as

A real-time flood forecasting model based on maximum-entropy spectral analysis: II. Application

  • P. F. Krstanovic
  • V. P. Singh
Article

Abstract

The MESA-based model, developed in the first paper, for real-time flood forecasting was verified on five watersheds from different regions of the world. The sampling time interval and forecast lead time varied from several minutes to one day. The model was found to be superior to a state-space model for all events where it was difficult to obtain prior information about model parameters. The mathematical form of the model was found to be similar to a bivariate autoregressive (AR) model, and under certain conditions, these two models became equivalent.

Key words

Real-time flood forecasting maximum-entropy spectral analysis model verification 

Notation

Ak

parameter matrix of the bivariate AR model

B

backshift operator in time series analysis

eT

forecast error (vector) at timet = T

εt

uncorrelated random series (white noise)

Fk

forward extension matrix of the entropy model forkth lag

I

identity matrix

m

order of the entropy model

N

number of observations

P

order of the AR model

Qp

peak of the direct runoff hydrograph

R

correlation matrix

tp

time to peak of the direct runoff hydrograph

ν1

coefficient of variation

ν2

ratio of absolute error to the mean

\(\hat x_i\)

forecasted runoff

xi

observed runoff

\(\bar x_i\)

mean of the observed runoff

X−1

inverse ofX matrix

X*

transpose of theX matrix

Abbreviations

AIC

Akaike information criterion

AR

autoregressive (model)

AR(p)

autoregressive process of thepth order

ARIMA

autoregressive integrated moving average (model)

acf

autocorrelation function

ccf

cross-correlation function

FLT

forecast lead time

MESA

maximum entropy spectral analysis

MSE

mean square error

STI

sampling time interval

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akaike, H., 1876, Canonical correlation analysis of time series and the use of an information criterion, in R. Mehra, and D. G., Lainiotis (eds.),Advances and Case Studies in System Identification, Academic Press, New York, pp. 27–96.Google Scholar
  2. Bras, R. L. and Rodriguez-Iturbe, I., 1985,Random Functions and Hydrology, Addison-Wesley, Reading, Mass.Google Scholar
  3. Cooper, D. M. and Wood, E. F., 1982, Identification of multivariate time series and multivariate input-output models,Water Resour. Res. 18(4), 937–946.Google Scholar
  4. Gosain, A. K., 1984, Intercomparison of real-time highflow forecasting models for Yamuna catchment, unpublished PhD Dissertation, Indian Institute of Technology, Delhi, India.Google Scholar
  5. Priestley, M. B., 1989. System identification, Kalman filtering and stochastic control, in D. R. Brilinger and G. C. Tiao (eds.),Directions in Time Series, Institute of Mathematical Statistics, pp. 188–218.Google Scholar
  6. World Meteorological Organization (WMO), 1975, Intercomparison of conceptual models used in operational hydrologic forecasting, Operational Hydrology Report No. 7, Secretariat of WMO, Geneva, Switzerland.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • P. F. Krstanovic
    • 1
  • V. P. Singh
    • 2
  1. 1.H. T. Harvey & AssociatesAlvisoUSA
  2. 2.Water Resources Program, Department of Civil EngineeringLouisiana State UniversityBaton RougeUSA

Personalised recommendations