1. Streamflow Predictability
Tom Hopson

2. Conduct Idealized Predictability Experiments
Document relative importance of uncertainties in basin initial conditions and weather and climate forecasts on streamflow
Account for how uncertainties depend on
type of forcing (e.g. precip vs. T)
forecast lead-time
Regions, spatial-, and temporal-scales
Potential implications for:
how to focus research efforts (e.g. improvements in hydrologic models vs data assimilation techniques)
observational network resources (e.g. SNOTEL vs raingauge)
anticipate future needs (e.g. changes in weather forecast skill, impacts of climate change)

3. Initial efforts Start with SAC lumped model and SNOW-17
(ignoring spatial variability)
Applied to different regions
Four basins currently
Drive with errors in:
initial soil moisture states (multiplicative)
SWE (multiplicative)
Observations (ppt – multiplicative; T – additive)
Forecasts with parameterized error growth
Place in context of climatological distributions of variables to try and generalize regional and seasonal implications (e.g. forecast error in T less important in August compared to April in snow-dominated basins)

4. Sources of Predictability
Model solutions to the streamflow forecasting problem…
Historical Data
SNOW-17 / SAC
Historical Simulation
SWE SM Q
Past
Future
Run hydrologic model up to the start of the forecast period to estimate basin initial conditions;

5. Sources of Predictability
Model solutions to the streamflow forecasting problem…
Historical Data
Forecasts
SNOW-17 / SAC
SNOW-17 / SAC
Historical Simulation
SWE SM Q
Past
Future
Run hydrologic model up to the start of the forecast period to estimate basin initial conditions;
Run hydrologic model into the future, using an ensemble of local-scale weather and climate forecasts.

6. Sacramento Soil Moisture Accounting (SAC-SMA) model
Physically based conceptual model
Two-layer model
Upper layer: surface and interception storages
Lower layer: deeper soil and ground water storages
Routing: linear reservoir model
Integrated with snow17 model
Rainfall
- Evapotranspiration
- Changes in soil moisture storage
= Runoff
Model parameters: 16 calibrated parameters
Input data: basin average precipitation (P) and Potential Evapotranspiration (PET)
Output: Channel inflow (Q)

7. Soil Tension and Free Water

8. Sacramento Model Structure
E T Demand
Precipitation Input Px
Impervious
Area
E T
PCTIM
ADIMP
Direct Runoff
Pervious Area
Impervious Area
Upper Zone
Surface Runoff
EXCESS
Tension Water
UZTW Free Water
UZFW
E T
UZK
Interflow
E T
Percolation
Zperc. Rexp
Total Channel Inflow
Distribution Function
E T
RIVA
Streamflow
1-PFREE
PFREE
Lower Zone
Free Water
Tension Water P S
LZTW LZFP LZFS
RSERV
LZSK
Supplemental
Base flow
E T
LZPK
Total Baseflow
Primary
Baseflow
Side
Subsurface Discharge

9. Model Parameters PXADJ Precipitation adjustment factor
PEADJ ET-demand adjustment factor
UZTWM Upper zone tension water capacity (mm)
UZFWM Upper zone free water capacity (mm)
UZK Fractional daily upper zone free water withdrawal rate
PCTIM Minimum impervious area (decimal fraction)
ADIMP Additional impervious area (decimal fraction)
RIVA Riparian vegetation area (decimal fraction)
ZPERC Maximum percolation rate coefficient
REXP Percolation equation exponent
LZTWM Lower zone tension water capacity (mm)
LZFSM Lower zone supplemental free water capacity (mm)
LZFPM Lower zone primary free water capacity (mm)
LZSK Fractional daily supplemental withdrawal rate
LZPK Fractional daily primary withdrawal rate
PFREE Fraction of percolated water going directly to lower zone free water storage
RSERV Fraction of lower zone free water not transferable to lower zone tension water
SIDE Ratio of deep recharge to channel baseflow
ET Demand Daily ET demand (mm/day)
PE Adjust PE adjustment factor for 16th of each month

10. State Variables ADIMC Tension water contents of the ADIMP area (mm)
UZTWC Upper zone tension water contents (mm)
UZFWC Upper zone free water contents (mm)
LZTWC Lower zone tension water contents (mm)
LZFSC Lower zone free supplemental contents (mm)
LZFPC Lower zone free primary contents (mm)

11. How the SAC-SMA Model Works

12. Study site: Root River basin in MN
Drainage area: km2
Largely agricultural (72%), USDA
Receives 29 to 33 inches of annual
precipitation
Unit Hydrograph:
Length 54hrs, time to conc 6-12hr

13. Study site: Pudding River basin in NW Oregon
Drainage area: km2
originates from the western edge of the
Cascade Mountains along a snowpack-limited ridgeline (sensitive to climate change); lower part agricultural
min/avg/max Q: 0.1 / 35 / 1,237 m3/s
Unit Hydrograph:
Length 114hrs, time-to-conc 30-36hr
DJ Seo

14. Snow Modeling and Data Assimilation (SMADA) Testbed Basin – Animas River (includes Senator Beck Basin)
Drainage area: km2
Unit Hydrograph:
Length 30hrs, time-to-conc 12-18hr
Andy Wood and Stacie Bender

15. Study site: Greens Bayou river basin in eastern Texas
Greens Bayou basin
Drainage area: 178 km2
Most of the basin is highly
developed
Humid subtropical climate
mm annual rain
Unit Hydrograph:
Length 31hrs, time to conc 5hr
DJ Seo

16. Forcing and state errors
Observed MAP – multiplicative
[0.5, 0.8, 1.0, 1.2, 1.5]
Soil moisture states (up to forecast initialization time) – multiplicative
Precipitation forecasts – error growth model

17. Forecast Error Growth models
Lorenz, 1982
Primarily IC error
E small
E large
Another options:
Displacement / model drift errors: E ~ sqrt(t)
(Orrell et al 2001)

18. Error growth, but with relaxation to climatology
Error growth around climatological mean
Short-lead forecast
Probability/m
Longer-lead forecast
Climatological PDF
=> Use simple model
Precipitation [m]
Where:
pf(t) = the forecast prec
errstatic = fixed multiplicative error
w(t) = error growth curve weight
po(t) = observed precip
qc = some climatological quantile
Error growth of extremes
Probability/m
Errstatic = [0.5, 0.8, 1.0, 1.2, 1.5]
qc = [.1, .25, .5, .75, .95] percentiles
Precipitation [m]

19. Rule of Thumb:
-- Weather forecast skill (RMS error) increases with spatial (and temporal) scale
=> accuracy of weather forecasts in flood forecasting increases for larger catchments (at the same lead-time)
-- Logarithmic increase

20. Greens Bayou Precip forcing fields – Nov 17, 2003 tornado
Perturbed soil moisture (up to initialization)
All perturbed (including soil moisture)
Perturbed obs ppt [mm/hr]
Perturbed fcst ppt
Q response [mm/hr]
Note: high ppt with low sm (aqua)
Low ppt with high sm (green)