Uncertainty Propagation of Regional Climate Model Precipitation Forecasts to Hydrologic Impact Assessment

Phaedon C. Kyriakidis Regional Climate Center, Lawrence Berkeley National Laboratory, Berkeley, California

Search for other papers by Phaedon C. Kyriakidis in
Current site
Google Scholar
PubMed
Close
,
Norman L. Miller Regional Climate Center, Lawrence Berkeley National Laboratory, Berkeley, California

Search for other papers by Norman L. Miller in
Current site
Google Scholar
PubMed
Close
, and
Jinwon Kim Regional Climate Center, Lawrence Berkeley National Laboratory, Berkeley, California

Search for other papers by Jinwon Kim in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

A Monte Carlo framework is adopted for propagating uncertainty in dynamically downscaled seasonal forecasts of area-averaged daily precipitation to associated streamflow response calculations. Daily precipitation is modeled as a mixture of two stochastic processes: a binary occurrence process and a continuous intensity process, both exhibiting serial correlation. The parameters of these processes (e.g., the proportion of wet days and the average wet-day precipitation intensity in a month) are derived from the forecast record. Parameter uncertainty is characterized via an empirical Bayesian model, whereby such parameters are modeled as random with a specific joint probability distribution. The hyperparameters specifying this probability distribution are derived from historical precipitation records at the study basin. Simulated parameter values are then generated using the Bayesian model, leading to alternative synthetic daily precipitation records simulated via the stochastic precipitation model. The set of such synthetic precipitation records is finally input to a physically based deterministic hydrologic model for propagating uncertainty in forecasted precipitation to hydrologic impact assessment studies.

The stochastic simulation approach is applied for generating an ensemble (set) of synthetic area-averaged daily precipitation records at the Hopland basin in the northern California Coast Range for the winter months (December through February: DJF) of 1997/98. The parameters of the stochastic precipitation model are derived from a seasonal precipitation forecast based on the Regional Climate System Model (RCSM), available at a 36-km2 grid spacing. The large-scale forcing input to RCSM for dynamical downscaling was a seasonal prediction of the University of California, Los Angeles, Atmospheric General Circulation Model. A semidistributed deterministic hydrologic model (“TOPMODEL”) is then used for calculating the streamflow response for each member of the area-averaged precipitation ensemble set. Uncertainty in the parameters of the stochastic precipitation model is finally propagated to associated streamflow response, by considering parameter values derived from historical (DJF 1958–92) area-averaged precipitation records at Hopland.

Current affiliation: Department of Geography, University of California, Santa Barbara, Santa Barbara, California.

Corresponding author address: Phaedon C. Kyriakidis, Dept. of Geography, University of California, Santa Barbara, Ellison Hall 3611, Santa Barbara, CA 93106-4060.

Email: phaedon@geog.ucsb.edu

Abstract

A Monte Carlo framework is adopted for propagating uncertainty in dynamically downscaled seasonal forecasts of area-averaged daily precipitation to associated streamflow response calculations. Daily precipitation is modeled as a mixture of two stochastic processes: a binary occurrence process and a continuous intensity process, both exhibiting serial correlation. The parameters of these processes (e.g., the proportion of wet days and the average wet-day precipitation intensity in a month) are derived from the forecast record. Parameter uncertainty is characterized via an empirical Bayesian model, whereby such parameters are modeled as random with a specific joint probability distribution. The hyperparameters specifying this probability distribution are derived from historical precipitation records at the study basin. Simulated parameter values are then generated using the Bayesian model, leading to alternative synthetic daily precipitation records simulated via the stochastic precipitation model. The set of such synthetic precipitation records is finally input to a physically based deterministic hydrologic model for propagating uncertainty in forecasted precipitation to hydrologic impact assessment studies.

The stochastic simulation approach is applied for generating an ensemble (set) of synthetic area-averaged daily precipitation records at the Hopland basin in the northern California Coast Range for the winter months (December through February: DJF) of 1997/98. The parameters of the stochastic precipitation model are derived from a seasonal precipitation forecast based on the Regional Climate System Model (RCSM), available at a 36-km2 grid spacing. The large-scale forcing input to RCSM for dynamical downscaling was a seasonal prediction of the University of California, Los Angeles, Atmospheric General Circulation Model. A semidistributed deterministic hydrologic model (“TOPMODEL”) is then used for calculating the streamflow response for each member of the area-averaged precipitation ensemble set. Uncertainty in the parameters of the stochastic precipitation model is finally propagated to associated streamflow response, by considering parameter values derived from historical (DJF 1958–92) area-averaged precipitation records at Hopland.

Current affiliation: Department of Geography, University of California, Santa Barbara, Santa Barbara, California.

Corresponding author address: Phaedon C. Kyriakidis, Dept. of Geography, University of California, Santa Barbara, Ellison Hall 3611, Santa Barbara, CA 93106-4060.

Email: phaedon@geog.ucsb.edu

Save
  • Abramovitz, M., and I. A. Stegun, 1972: Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables. 9th ed. Dover, 1046 pp.

  • Barnett, T., 1995: Monte Carlo climate forecasting. J. Climate,8, 1005–1022.

  • Beven, K. J., and M. Kirkby, 1979: A physically-based, variable contributing area model of basin hydrology. Hydrol. Sci. Bull.,24, 43–69.

    • Crossref
    • Export Citation
  • ——, and A. Binley, 1992: The future of distributed models: Model calibration and uncertainty prediction. Hydrol. Proc.,6, 279–298.

    • Crossref
    • Export Citation
  • Box, G. E. P., and G. C. Tiao, 1973: Bayesian Inference in Statistical Analysis. Addison-Wesley, 588 pp.

  • Bras, R. L., and I. Rodríguez-Iturbe, 1985: Random Functions and Hydrology. Addison-Wesley, 559 pp.

  • Caers, J. K., 2000: Adding local accuracy to direct sequential simulation. Math. Geol.,32, 815–850.

    • Crossref
    • Export Citation
  • Carlin, B. P., and T. A. Louis, 2000: Bayes and Empirical Bayes Methods for Data Analysis. 2d ed. Chapman and Hall/CRC, 400 pp.

    • Crossref
    • Export Citation
  • Chang, T. J., M. L. Kavvas, and J. W. Delleur, 1984: Daily precipitation modeling by discrete autoregressesive moving average processes. Water Resour. Res.,20, 565–580.

    • Crossref
    • Export Citation
  • Chebaane, M., J. D. Salas, and D. C. Boes, 1995: Product periodic autoregressive processes for modeling intermittent monthly streamflows. Water Resour. Res.,31, 1513–1518.

    • Crossref
    • Export Citation
  • Deutsch, C. V., and A. G. Journel, 1998: GSLIB: Geostatistical Software Library and User’s Guide. 2d ed. Oxford University Press, 368 pp.

  • Entekhabi, D., and Coauthors, 1999: An agenda for land surface hydrology research and a call for the second international hydrological decade. Bull. Amer. Meteor. Soc.,80, 2043–2058.

    • Crossref
    • Export Citation
  • Foufoula-Georgiou, E., and W. Krajewski, 1995: Recent advances in rainfall modeling, estimation, and forecasting. Reviews of Geophysics, U.S. National Report to International Union of Geodesy and Geophysics 1991–1994, American Geophysical Union, 1125–1137.

    • Crossref
    • Export Citation
  • Gelman, A., J. B. Carlin, H. S. Stern, and D. B. Rubin, 1995: Bayesian Data Analysis. Chapman and Hall/CRC, 526 pp.

    • Crossref
    • Export Citation
  • Journel, A. G., 1989: Short Course in Geology. Vol. 8, Fundamentals of Geostatistics in Five Lessons, American Geophysical Union, 40 pp.

  • ——, 1999: Conditioning geostatistical operations to nonlinear volume averages. Math. Geol.,31, 931–953.

  • Katz, R. W., and M. B. Parlange, 1995: Generalizations of chain-dependent processes: Application to hourly precipitation. Water Resour. Res.,31, 1331–1341.

    • Crossref
    • Export Citation
  • Kim, J., N. L. Miller, A. K. Guetter, and K. P. Georgakakos, 1998: River flow response to precipitation and snow budget in California during the 1994/95 winter. J. Climate,11, 2376–2386.

    • Crossref
    • Export Citation
  • ——, ——, J. D. Farrara, and S.-Y. Hong, 2000: A seasonal precipitation and stream flow hindcast and prediction study for the 1997/98 winter season using a dynamic downscaling system. J. Hydrometeor.,1, 311–329.

    • Crossref
    • Export Citation
  • Kitanidis, P. K., 1986: Parameter uncertainty in estimation of spatial functions: Bayesian analysis. Water Resour. Res.,22, 499–507.

    • Crossref
    • Export Citation
  • Krzysztofowicz, R., 1998: Probabilistic hydrometeorological forecasts: Toward a new era in operational forecasting. Bull. Amer. Meteor. Soc.79, 243–251.

    • Crossref
    • Export Citation
  • ——, 1999: Bayesian theory for probabilistic forecasting via deterministic hydrologic model. Water Resour. Res.,35, 2739–2750.

    • Crossref
    • Export Citation
  • Lettenmaier, D. P., 1994: Application of stochastic modeling in climate change impact assessment. Stochastic and Statistical Methods in Hydrology and Environmental Engineering, K. W. Hipel et al., Eds., Time Series Analysis in Hydrology and Environmental Engineering, Vol. 3, Kluwer Academic, 3–17.

    • Crossref
    • Export Citation
  • Leung, L. R., M. S. Wigmosta, S. J. Ghan, D. J. Epstein, and L. W. Vail, 1996: Application of a subgrid orographic precipitation/surface hydrology scheme to a mountain watershed. J. Geophys. Res.,101, 12 803–12 817.

    • Crossref
    • Export Citation
  • ——, A. F. Hamlet, D. P. Lettenmaier, and A. Kumar, 1999: Simulations of the ENSO hydroclimate signals in the Pacific Northwest Columbia River basin. Bull. Amer. Meteor. Soc.,80, 2313–2329.

    • Crossref
    • Export Citation
  • Mardia, K. V., J. T. Kent, and J. M. Bibby, 1979: Multivariate Analysis. Academic Press, 518 pp.

  • Miller, N. L., and J. Kim, 1996: Numerical prediction of precipitation and river flow over the Russian River watershed during the January 1995 California storms. Bull. Amer. Meteor. Soc.,77, 101–105.

    • Crossref
    • Export Citation
  • ——, ——, R. K. Hartman, and J. D. Farrara, 1999: Downscaled climate and streamflow study of the southwestern United States. J. Amer. Water Resour. Assoc.,35, 1525–1538.

    • Crossref
    • Export Citation
  • Ripley, B., 1987: Stochastic Simulation. John Wiley and Sons, 256 pp.

    • Crossref
    • Export Citation
  • Salas, J. D., 1993: Analysis and modeling of hydrologic time series. Handbook of Hydrology, D. R. Maidment, Ed., McGraw-Hill, 19.1–19.71.

  • Tanner, M. A., 1996: Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions. Springer-Verlag, 207 pp.

    • Crossref
    • Export Citation
  • Valdés, J. B., I. Rodríguez-Iturbe, and G. J., Vicens, 1977: Bayesian generation of synthetic streamflows, 2: The multivariate case. Water Resour. Res.,13, 291–295.

    • Crossref
    • Export Citation
  • Valencia, R. D., and J. C. Schaake, 1973: Dissaggregation processes in stochastic hydrology. Water Resour. Res.,9, 580–585.

    • Crossref
    • Export Citation
  • Wilby, R. L., T. M. Wigley, D. Conway, P. D. Jones, B. C. Hewitson, J. Main, and D. S. Wilks, 1998: Statistical downscaling of general circulation model output: A comparison of methods. Water Resour. Res.,34, 2995–3008.

    • Crossref
    • Export Citation
  • Wilks, D. S., 1992: Adapting stochastic weather generation algorithms for climate change studies. Climatic Change,22, 67–84.

    • Crossref
    • Export Citation
  • ——, 1995: Statistical Methods in the Atmospheric Sciences. Academic Press, 467 pp.

  • Woolhiser, D. A., 1992: Modeling daily precipitation—progress and problems. Statistics in Environmental and Earth Sciences, A. T. Walden and P. Guttorp, Eds., Edward Arnold, 71–89.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 244 36 5
PDF Downloads 91 18 1