Streamflow Predictability

Tom Hopson

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)

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)

Historical Simulation

Q

SWE

SM

Historical Data

Past Future

SNOW-17 / SAC

Sources of Predictability

1. Run hydrologic model up to the start of the forecast period to estimate basin initial conditions;

Model solutions to the streamflow forecasting problem…

Historical Simulation

Q

SWE

SM

Historical Data Forecasts

Past Future

SNOW-17 / SAC SNOW-17 / SAC

1. Run hydrologic model up to the start of the forecast period to estimate basin initial conditions;

2. Run hydrologic model into the future, using an ensemble of local-scale weather and climate forecasts.

Sources of PredictabilityModel solutions to the streamflow forecasting problem…

• 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

Sacramento Soil Moisture Accounting (SAC-SMA) 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)

Soil Tension and Free Water

Sacramento Model StructureE T Demand

Impervious Area

E T

E T

E T

E T

Precipitation Input

Px

Pervious Area

E T

Impervious Area

Tension Water

UZTW Free Water

UZFW

PercolationZperc. Rexp

1-PFREE PFREE

Free WaterTension Water P S

LZTW LZFP LZFS

RSERV

Primary Baseflow

Direct Runoff

Surface Runoff

Interflow

Supplemental Base flow

Side Subsurface Discharge

LZSK

LZPK

Upper Zone

Lower Zone

EXCESS

UZK

RIVA

PCTIM

ADIMP

Total Channel Inflow

Distribution Function Streamflow

Total Baseflow

Model ParametersPXADJ Precipitation adjustment factorPEADJ ET-demand adjustment factorUZTWM Upper zone tension water capacity (mm)UZFWM Upper zone free water capacity (mm)UZK Fractional daily upper zone free water withdrawal ratePCTIM Minimum impervious area (decimal fraction)ADIMP Additional impervious area (decimal fraction)RIVA Riparian vegetation area (decimal fraction)ZPERC Maximum percolation rate coefficientREXP Percolation equation exponentLZTWM 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 rateLZPK Fractional daily primary withdrawal ratePFREE Fraction of percolated water going directly to lower zone free water storageRSERV Fraction of lower zone free water not transferable to lower zone tension waterSIDE Ratio of deep recharge to channel baseflowET Demand Daily ET demand (mm/day)PE Adjust PE adjustment factor for 16th of each month

State VariablesADIMC 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)

How the SAC-SMA Model Works

Study site: Root River basin in MN

• Drainage area: 1593 km2

• Largely agricultural (72%), USDA• Receives 29 to 33 inches of annual precipitation• Unit Hydrograph:

Length 54hrs, time to conc 6-12hr

Root River basin

Study site: Pudding River basin in NW Oregon

• Drainage area: 1368 km2

• originates from the western edge of theCascade 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

Snow Modeling and Data Assimilation (SMADA) Testbed Basin – Animas River (includes Senator Beck Basin)

Andy Wood and Stacie Bender

• Drainage area: 1792 km2

• Unit Hydrograph: Length 30hrs, time-to-conc 12-18hr

Study site: Greens Bayou river basin in eastern Texas

• Drainage area: 178 km2

• Most of the basin is highlydeveloped

• Humid subtropical climate890-1300 mm annual rain

• Unit Hydrograph: Length 31hrs, time to conc 5hr

Greens Bayou basin

DJ Seo

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– [0.5, 0.8, 1.0, 1.2, 1.5]

• Precipitation forecasts – error growth model

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)

Error growth, but with relaxation to climatologyPr

obab

ility

/m

Precipitation [m]

Error growth around climatological mean

Prob

abili

ty/m

Precipitation [m]

Error growth of extremes

Short-lead forecast

Longer-lead forecast

Climatological PDF

=> Use simple model

Where: pf(t) = the forecast precerrstatic = fixed multiplicative errorw(t) = error growth curve weightpo(t) = observed precipqc = some climatological quantile

Errstatic = [0.5, 0.8, 1.0, 1.2, 1.5]

qc = [.1, .25, .5, .75, .95] percentiles

-- 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

Rule of Thumb:

Greens Bayou Precip forcing fields – Nov 17, 2003 tornado

Perturbed obs ppt [mm/hr] Perturbed fcst ppt

All perturbed (including soil moisture)

Q response [mm/hr]

Perturbed soil moisture (up to initialization)

Note: high ppt with low sm (aqua)Low ppt with high sm (green)