Transcript Hopson_predictabilityx

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)
Sources of Predictability
Model solutions to the streamflow forecasting problem…
Historical Data
SNOW-17 / SAC
Historical Simulation
SWE
SM
Q
Past
Future
1. Run hydrologic model up to the start of the forecast period
to estimate basin initial conditions;
Sources of Predictability
Model solutions to the streamflow forecasting problem…
Historical Data
SNOW-17 / SAC
Historical Simulation
Forecasts
SNOW-17 / SAC
SWE
SM
Q
Past Future
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.
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
• Model parameters: 16 calibrated
parameters
• Input data: basin average precipitation
(P) and Potential Evapotranspiration (PET)
• Output: Channel inflow (Q)
Rainfall
- Evapotranspiration
- Changes in soil moisture storage
= Runoff
Soil Tension and Free Water
Sacramento Model Structure
E T Demand
Precipitation Input
Px
Impervious
Area
ET
PCTIM
Pervious Area
Impervious Area
Upper Zone
EXCESS
ET
Direct Runoff
ADIMP
Surface
Runoff
Tension Water
Free Water
UZTW
UZFW
UZK
ET
Interflow
Percolation
Zperc. Rexp
Total
Channel
Inflow
RIVA
ET
1-PFREE
Distribution
Function
Streamflow
PFREE
Lower Zone
Tension Water
ET
LZTW
Free
P
Water
S
LZFP
LZFS
LZSK
Supplemental
Base flow
RSERV
Primary
Baseflow
LZPK
Total
Baseflow
Side
Subsurface
Discharge
Model Parameters
PXADJ
PEADJ
UZTWM
UZFWM
UZK
PCTIM
ADIMP
RIVA
ZPERC
REXP
LZTWM
LZFSM
LZFPM
LZSK
LZPK
PFREE
RSERV
SIDE
ET Demand
PE Adjust
Precipitation adjustment factor
ET-demand adjustment factor
Upper zone tension water capacity (mm)
Upper zone free water capacity (mm)
Fractional daily upper zone free water withdrawal rate
Minimum impervious area (decimal fraction)
Additional impervious area (decimal fraction)
Riparian vegetation area (decimal fraction)
Maximum percolation rate coefficient
Percolation equation exponent
Lower zone tension water capacity (mm)
Lower zone supplemental free water capacity (mm)
Lower zone primary free water capacity (mm)
Fractional daily supplemental withdrawal rate
Fractional daily primary withdrawal rate
Fraction of percolated water going directly to lower zone free water storage
Fraction of lower zone free water not transferable to lower zone tension water
Ratio of deep recharge to channel baseflow
Daily ET demand (mm/day)
PE adjustment factor for 16th of each month
State Variables
ADIMC
UZTWC
UZFWC
LZTWC
LZFSC
LZFPC
Tension water contents of the ADIMP area
(mm)
Upper zone tension water contents (mm)
Upper zone free water contents (mm)
Lower zone tension water contents (mm)
Lower zone free supplemental contents
(mm)
Lower zone free primary contents (mm)
How the SAC-SMA Model Works
Study site: Root River basin in MN
Root River basin
• 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
Study site: Pudding River basin in NW Oregon
• Drainage area: 1368 km2
• originates from the western edge of the
Cascade Mountains along a snowpacklimited 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 3036hr
DJ Seo
Snow Modeling and Data Assimilation (SMADA)
Testbed Basin – Animas River (includes Senator Beck Basin)
• Drainage area: 1792 km2
• Unit Hydrograph:
Length 30hrs, time-to-conc 12-18hr
Andy Wood and Stacie Bender
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
890-1300 mm annual rain
• Unit Hydrograph:
Length 31hrs, time to conc 5hr
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
æ
¶E
Eö
= a E ç1 ¶t
E¥ ÷ø
è
E small
E large
¶E
®0
¶t
Another options:
E = a + (1 - e-bt )c
Displacement / model drift errors: E ~ sqrt(t)
(Orrell et al 2001)
Probability/m
Error growth, but with relaxation to climatology
Error growth around climatological mean
Short-lead forecast
Longer-lead forecast
Climatological PDF
=> Use simple model
Probability/m
Precipitation [m]
Error growth of extremes
p f (t) = errstatic [1- w(t)]po (t) + w(t) qc
Where:
pf(t) = the forecast prec
errstatic = fixed multiplicative error
w(t) = error growth curve weight
po(t) = observed precip
qc = some climatological quantile
Errstatic = [0.5, 0.8, 1.0, 1.2, 1.5]
Precipitation [m]
qc = [.1, .25, .5, .75, .95] percentiles
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
Greens Bayou Precip forcing fields – Nov 17, 2003 tornado
Perturbed obs ppt
[mm/hr]
Perturbed fcst ppt
Perturbed soil
moisture (up to
initialization)
Q response [mm/hr]
All perturbed (including
soil moisture)
Note: high ppt with low sm (aqua)
Low ppt with high sm (green)