All catchments

Figure 13 shows the CRPS skill score of the monthly streamflow forecasts generated at Stage 4. For most catchments, forecasts of monthly streamflow are only skilful at very short lead times. However, forecasts for some locations and months can be skilful out to a number of months.

Note that some strongly negative skill score values are present for the BRS catchment (Burdekin River above Sellheim in northern Queensland). These appear during very dry months. When climatology forecasts are used as reference, the denominator in Equation (18) for skill score calculation is very small when streamflow is regularly zero or close to zero. For this reason, skill scores can be highly sensitive to forecast errors and may be strongly negative when in fact forecasts are only slightly inferior to the reference forecasts. In practice, however, these negative skill score values should have little bearing on the use of the forecasts for water management.

Figure 14 shows the CRPS skill score of the cumulative streamflow forecasts generated at Stage 4. In general, forecasts of cumulative streamflow are much more skilful than streamflow of individual months.

More detailed results of the forecasts generated at the four stages for each of the 20 catchments are given in Appendices 1-4.

Figure 7: PIT uniform probability plots of monthly streamflow forecasts for the BRP catchment (1:1 solid line, theoretical uniform distribution; dashed lines, Kolmogorov 5% significance band; dots, PIT values of observed streamflow). Forecast target month and lead time are shown at the top of each panel.

Figure 8: Quantile plots of monthly streamflow forecasts for the BRP catchment (1:1 line, forecast median; dark blue vertical lines, forecast [0.25, 0.75] quantile range; light and dark blue vertical lines, forecast [0.05, 0.95] quantile range; red dots, observed streamflow). Forecast target month and lead time are shown at the top of each panel.

Figure 9: CRPS skill score of cumulative streamflow forecasts for the BRP catchment. The row shows forecast start month, and the column shows accumulation time in months. Forecast generation stage is shown at the top of each panel.

Figure 10: RMSEP skill score of cumulative streamflow forecasts for the BRP catchment. The row shows forecast start month, and the column shows accumulation time in months. Forecast generation stage is shown at the top of each panel.

Figure 11: PIT uniform probability plots of cumulative streamflow forecasts for the BRP catchment (1:1 solid line, theoretical uniform distribution; dashed lines, Kolmogorov 5% significance band; dots, PIT values of observed streamflow). Forecast start month and accumulation time are shown at the top of each panel.

Figure 12. Quantile plots of cumulative streamflow forecasts for the BRP catchment (1:1 line, forecast median; dark blue vertical lines, forecast [0.25, 0.75] quantile range; light and dark blue vertical lines, forecast [0.05, 0.95] quantile range; red dots, observed streamflow). Forecast start month and accumulation time are shown at the top of each panel.

Figure 13: CRPS skill score of monthly streamflow forecasts for 20 catchments. The row shows forecast target month, and the column shows lead time in months. Catchment name is at the top of each panel.

Figure 14: CRPS skill score of cumulative streamflow forecasts for 20 catchments. The row shows forecast start month, and the column shows accumulation time in months. Catchment name is at the top of each panel.

4 Conclusions

In this report, we present the FOGSS model for generating forecast guided stochastic scenarios. The model first generates rainfall forecasts statistically using seasonal climate model predictions of rainfall and sea surface temperature as predictors. The rainfall forecasts are then used as inputs to a monthly water balance model, followed by error updating and uncertainty quantification, to produce ensemble forecasts of monthly streamflow time series. The method extends the current forecast horizon of three months to when skilful forecasts can be obtained and transit the forecasts to stochastic scenarios as skill diminishes at longer lead times.

The model is used to generate cross validation forecasts out to 12 months for 20 catchments. For most catchments, forecasts of monthly streamflow are only skilful at very short lead times. However, forecasts for some locations and seasons can be skilful out to a number of months. Forecasts of cumulative streamflow are much more skilful than streamflow of individual months. As cumulative streamflow is more relevant to water planning, skilful forecasts of the cumulative streamflow are valuable.

Forecasts of monthly streamflow and cumulative streamflow are both shown to be statistically reliable in probability distributions. This indicates that the FoGSS model adequately represents the rainfall forecast uncertainty, hydrological uncertainty (other than rainfall forecast uncertainty), persistence in streamflow, and uncertainty propagation from the start of the forecasts out to 12 months. This is a significant achievement.

5 References

Clark, M.P., Gangopadhyay, S., Hay, L., Rajagopalan, B. and Wilby, R., 2004. The Schaake shuffle: a method for reconstructing space–time variability in forecasted precipitation and temperature fields. Journal of Hydrometeorology, 5: 243–262.

Jolliffe, I.T. and Stephenson, D.B., 2003. Forecast verification : a practitioner's guide in atmospheric science.

J. Wiley, Chichester, 240 pp.

Jones, D.A., Wang, W. and Fawcett, R., 2009. High-quality spatial climate data-sets for Australia. Australian Meteorological and Oceanographic Journal, 58(4): 233-248.

Li, M., Wang, Q.J. and Bennett, J., 2013. Accounting for seasonal dependence in hydrological model errors and prediction uncertainty. Water Resources Research, 49(9): 5913-5929.

Li, M., Q. J. Wang, J. Bennett, and D. E. Robertson (2014), A strategy to overcome adverse effects of autoregressive updating of streamflow predictions, submitted to Hydrology and Earth System Sciences.

Matheson, J.E. and Winkler, R.L., 1976. Scoring rules for continuous probability distributions. Management Science, 22(10): 1087-1096.

Raupach, M.R. et al., 2008. Australian Water Availability Project. CSIRO Marine and Atmospheric Research, Canberra, Australia.

Schepen, A. and Wang, Q., 2014a. Ensemble forecasts of monthly catchment rainfall out to long lead times by post-processing coupled general circulation model output. Journal of Hydrology, In Press.

Schepen, A. and Wang, Q.J., 2014b. Model averaging methods to merge operational statistical and dynamic seasonal streamflow forecasts in Australia. In Preparation.

Schepen, A. and Wang, Q.J., 2014c. Twelve month out forecasts of catchment rainfall by post-processing ECMWF System 4 and POAMA M2.4 forecasts, CSIRO Water for a Healthy Country Flagship, Melbourne, Australia.

Wang, Q. et al., 2011. Monthly versus daily water balance models in simulating monthly runoff. Journal of Hydrology, 404(3): 166-175.

Wang, Q.J. and Robertson, D.E., 2011. Multisite probabilistic forecasting of seasonal flows for streams with zero value occurrences. Water Resour. Res., 47: W02546.

Wang, Q.J., Robertson, D.E. and Chiew, F.H.S., 2009. A Bayesian joint probability modeling approach for seasonal forecasting of streamflows at multiple sites. Water Resour. Res., 45.

Wang, Q.J., Schepen, A. and Robertson, D.E., 2012. Merging Seasonal Rainfall Forecasts from Multiple Statistical Models through Bayesian Model Averaging. Journal of Climate, 25(16): 5524-5537.

Log-sinh transform paper

List of Appendices

Appendix A: Stage 1 forecast performance Appendix B: Stage 2 forecast performance Appendix C: Stage 3 forecast performance Appendix D: Stage 4 forecast performance

CONTACT US t 1300 363 400 +61 3 9545 2176 e [email protected] w www.csiro.au

YOUR CSIRO

Australia is founding its future on science and innovation. Its national science agency, CSIRO, is a powerhouse of ideas, technologies and skills for building prosperity, growth, health and sustainability. It serves governments, industries, business and communities across the nation.

FOR FURTHER INFORMATION CSIRO Land and Water Q. J. Wang

t +61 3 9252 6319 e [email protected]

w www.csiro.au/Organisation-Structure/Flagships/Water-for-a-Healthy-Country-Flagship.aspx