1. Combining statistical and dynamical methods for hydrologic prediction
Andy Wood
Seminar
Land Surface Hydrology Research Group
Civil and Environmental Engineering
University of Washington
Dec 19, 2006

2. Outline Ensemble Forecast Calibration
Synoptic Scale Hydrologic Indices

3. The importance of Seasonal Hydrologic Forecasting
water management
hydropower
irrigation
flood control
water supply
fisheries
recreation
navigation
water quality
Aug
Dec
Apr
Reservoir Storage

4. How does one make a forecast of river flow?
Naïve forecast (“climatology”) – simply use historical averages
Persistence (of states or anomalies)
(Multiple) Regression Forecast
Traditional Predictors:
snowpack (SWE), accumulated precipitation, current or past river flow, measured over the drainage basin
More advanced predictors:
ENSO state indicators (Nino3.4, SOI)
Predictand: daily, monthly or seasonal streamflow at some lead time in the future.
Model-based approaches

5. Introduction: Hydrologic prediction and the NRCS
PNW
Snow water content on April 1
SNOTEL Network
McLean, D.A., 1948 Western Snow Conf.
April to August runoff

6. Results for Winter 2003-04: volume runoff forecasts
UPPER HUMBOLDT RIVER BASIN
Streamflow Forecasts - May 1, 2003
<==== Drier === Future Conditions === Wetter ====>
Forecast Pt
============ Chance of Exceeding * ===========
   Forecast
90%
70%
50% (Most Prob)
30%
10%
30 Yr Avg
   Period
(1000AF)
(% AVG.)
MARY'S R nr Deeth, Nv
APR-JUL
12.3      
18.7      
23      
59      
27      
34      
39      
MAY-JUL
4.5      
11.3      
16.0      
55      
21      
28      
29      
LAMOILLE CK nr Lamoille, Nv
13.7      
17.4      
20      
67      
26      
30      
11.6      
15.4      
18.0      
64      
24      
N F HUMBOLDT R at Devils Gate
5.1      
11.0      
15.0      
44      
19.0      
25      
1.7      
7.2      
50      
14.8      
22      

7. Introduction: Hydrologic prediction and ESP
NWS River Forecast Center (RFC) approach:
rainfall-runoff modeling
(i.e., NWS River Forecast System,
Anderson, 1973
offspring of Stanford Watershed Model, Crawford & Linsley, 1966)
Ensemble Streamflow Prediction (ESP)
used for shorter lead predictions;
~ used for longer lead predictions
Currently, some western RFCs and NRCS coordinate their seasonal forecasts, using mostly statistical methods.
ICs
Spin-up
Forecast
obs
recently observed
meteorological data
ensemble of met. data
to generate forecast
ESP forecast
hydrologic
state

8. Forecast Calibration: Hydrologic Simulation Uncertainty
Simulation error results from:
-- parameter uncertainty
-- forcing uncertainty
-- model physics/structure
Techniques for addressing each exist:
-- multi-algorithm approaches
-- calibration science
-- forcing preparation techniques
Other approaches for improving simulation:
-- data assimilation
-- multi-model approaches
-- bias-correction

9. Forecast Calibration: Effect of Uncertainty on ESP
Model-based ensemble forecasts contain both “hydrologic uncertainty” (associated with the input data, model parameters & physics) and future climate uncertainty.
ESP accounts mostly for the latter, but not the former, hence ESP forecasts have an inherent tendency to be overconfident.
One approach that can be used to correct this is called forecast calibration.

10. Forecast Calibration: Overconfidence example

11. Forecast Calibration: Approach
Following a technique suggested by John Schaake for 15-day temperature forecast ensembles:
1. use only forecast ensemble
means
2. correlate forecast means
with observations
3. reconstruct forecast
uncertainty
A hindcast dataset is needed
for training of the parameters.
Also:
- correlation
- mean and variance of
hindcasts and observations

12. Forecast Calibration: hindcast dataset

13. Forecast Calibration: Approach
Algorithm:
hindcast
long
term
mean
one
calibrated
forecast
mean
obs
long
term
mean
correlation,
obs &
hindcast
means
one
forecast
mean
obs
long
term
std. dev
hindcast
long
term
std. dev
correlation,
obs &
hindcast
means
obs
long
term
variance
calibrated
forecast
variance

14. Forecast Calibration: Results

15. Forecast Calibration: State Dependent Approach

16. Forecast Calibration: Raw ESP

17. Forecast Calibration: Results
calib w/ entire
hindcast
calib w/ sample
size N=35
bias-corr only

18. Forecast Calibration: Reliability Improved

19. Outline Ensemble Forecast Calibration
Synoptic Scale Hydrologic Indices

20. We are currently migrating the daily update methods
UW Real-time Daily Nowcast
SM, SWE
(RO)
½ degree VIC implementation
Free running since last June
Uses data feed from NOAA ACIS server
“Browsable” Archive, 1915-present
Another area of current research relates to the surface water monitor developed last year by A. Wood. This system, applied at coarse (1/2 degree) resolution over the entire CONUS, is completely automated (free-running) and updates every day. It’s just a prototype, demo project that have been unable to get funding to extend, and the main products are maps of current soil moisture & SWE, and an monthly archive that extends back to 1915, that also has SM & SWE maps.
Anyway, we are now adapting the daily update approach for use in the westwide forecast system, and should have the first basin (PNW) land surface conditions updating daily (at 1/8 degree) within the month. After that we’ll move on to other basins, and probably extend the 1/8 nowcast eastward to the Mississippi R.
We are currently migrating the daily update methods
to the west-wide forecast system (1/8 degree)

21. The challenge of changing observing systems
Meteorological stations that still report in real time today
1920s
1990s

22. Surface Water Monitor Archive
March 1997: La
Nina conditions bring the highest recorded snowfall to the PNW
July 2002: the western U.S. drought centers on Colorado

23. Surface Water Monitor Archive
August 1993: the highest recorded flow on the Mississippi R.
March 2002: Virginia experiences severe drought, many well failures

24. Water Year 2005

28. Land Surface Indices Can capture information from PC1 and PC2 using:
NDX1 ~ PC1 = CNTR
NDX2 ~ PC2 = NW-SW
Then PCs or NDXs can be
used in regression framework
to predict future flow,
e.g., summer runoff

29. Flow prediction results
can we use the modes of variability to predict summer streamflow?

30. Flow prediction results

31. Take away message
The dream of a purely physical modeling based prediction system is unlikely to be realized due to uncertainties in data, parameters, physics and so forth.
Statistical techniques can work hand in hand with dynamical ones to move prediction applications forward.

32. Forecast Calibration: ESP