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1
Hydrologic EnsemblePrediction
Tom HamillNOAA Earth System Research Lab
NOAA Earth SystemResearch Laboratory
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Some motivations for hydrologic predictionFlood forecasting Hydropower, flood protection
Irrigation
Managing natural resources Recreation
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Topics
• Sources of hydrologic forecast skill• Past and present hydrologic prediction systems.• Future ensemble hydrologic prediction systems
and technological challenges– coupling with weather-climate ensembles.– data and hydrologic data assimilation issues.– hydrologic ensemble modeling issues.– verification issues.
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Sources of hydrologic forecast skill forvery small basins, very short leads
• Good weather forecast/nowcast/observations; satellite, radar observationscrucial for improving flash-flood predictions.
• Especially dry, moist, rain-on-snow, or fire-baked soils can exacerbateflooding.
Flash flood in Versilia andGarfagnana (Apuan Alps,
Tuscany, Italy) 19 June 1996J. Kerkmann (EUMETSAT)
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Hydrologic predictability, short leads
• Plots of forecast normalized spreadand ensemble mean.
• Synoptic scale events morepredictable than convective-dominated events.
• More predictability in complex terrain(not shown).
Normalized Spread Ensemble Mean
Case1
Case2
Case3
Case4
Ref: Walser and Schär, J. Hydrology, 2004
Ensemble forecasts for 4flooding events in Italy.
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Example: 1-2 day lead hydrologic forecastfor a basin in Northern Italy
Skill of hydrologic forecast tied to the skill of the precipitation/temperature forecasts. Here, allforecasts missed timing of rainfall event, so subsequent hydrologic forecasts missed event.
Reservoir regulation, hydrologic model may have also had effects.
Source: A meteo-hydrological prediction system based on a multi-model approach for ensemble precipitation forecasting. Tomasso Diomede et al, ARPA-SIM, Bologna, Italy.
Hydrologic model forced with multi-model weather ensemble data.
?
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Sources of hydrologic skill:medium basins, medium leads
• Modeling of the land state (snow, soil moisture), observedprecipitation, upstream river conditions can be important.
• Weather-climate forecasts may have beneficial impact, e.g., suddenwarming diminishing snowpack.
1-day2-day
3-day
4-day
5-day
6-day An n-day hydrologicforecast in this basinwith its 6-day transittime requires 6-ndays of observationsand n days offorecasts.
(Actually, commonlyeven longer than 6-ndays of observationsto spin up and tunehydrology model)
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Sources of hydrologic forecast skill:large basins, long leads
• Diminishing influence of weather and climate forecasts due to largeerrors at longer leads. Small signals from ENSO and such.
• Deviations from climatology largely tied to land state / snowpack.
Ref: Pulwarty and Redmond, BAMS, March 1997
Columbia RiverBasin
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Sources ofhydrologic
skill:long leads
Relationship of runoff at variousleads and parts of North Americato various climate patterns ofvariability.
There can be some enhancedpredictability of future runoff from the current states of thesepatterns.
Not all patterns, nor even all phases of a pattern, providepredictability.
From Maurer et al., Water ResourcesResearch, 2004, W09306.
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Sources of hydrologic forecast skill:snow-water equivalent deviations
• Contours: loadings associatedwith leading principal componentfor runoff in given area.
• Shaded area: grid cells withrelationships of runoff and thisPC.
• Conclusion: dry ground --> lowrunoff in spring season,snowy/wet ground, high runoff inspring season. Not surprising.
• Ref: Maurer et al. 2004.
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Sources of hydrologic forecast skill:snow-water equivalent
• Looking one season ahead,in western US, low springsnow cover --> low summerrunoff. However, high springsnow cover in central USRockies does not necessarilymean high summer runoff(presumably because themelting may have alreadyoccurred)
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Past and present hydrologicforecast systems
• Example 1: Regression method• Example 2: US flash-flood warning system.• Example 3: Ensemble streamflow prediction
in US for seasonal forecasts.• Example 4: Bangladesh medium-range
probabilistic flood forecast system.• Example 5: European short-range flood
forecast system for small-medium basins.
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(1) Regression models topredict streamflow
Columbia RiverBasin
Example: predicting April maximum streamflow from Columbia-basin average 31 March snow-water equivalent
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(2) Flash-flood warning system• A sample system
(here, the US RiverForecast System) forflash-flood guidance insmall basins.
ref: Ntkelos et al, J. Hydrometeorology, Oct. 2006
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(2) Flash-flood warning system• Using geographic
information systemdata, a hydrologicmodel, and a variety ofland-state conditions,tables of the time-averaged amount ofprecipitation needed tocause a flash flood aretabulated for a smallbasin/ For example, iftoday’s soil is wet andthere is more than 20mm/hour * 6 hours, thebasin will flood.
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(2) Flash-flood warning system
• Precipitation estimatedfrom radar scans iscompared with theestimatedprecipitation rates thatwill produce a flood todetermine whether awarning should beissued.
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Results used in statistical analysis to produceforecasts with probabilistic values
Multiple streamflow scenarios with historicmeteorological or forecast weather/climatic data
Time
Flow
Scenario 1
Saved model statesreflect current
conditions
Ensemble of time series of possiblescenarios, commonly weather in pastyears, or model forecasts
(3) US ensemble streamflow prediction(ESP) technique (medium to long leads)
Scenario 2
Scenario 3
©The COMET Program/Kevin Werner
Hydrologicforecast modelusing initialmodel state andatmosphericensemble
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(4) Bangladesh flood forecast system
Tom Hopson and Peter Webster’s ensemble-based flood forecast system using ECMWFforecast data. Bangladesh is very flat country,prone to flooding.
Ref: Hopson and Webster, 2008, in review.
black = observed, red=ensemble
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(5) Short-term flood forecasting with hydrologicmodel driven by local-area ensemble forecasts
• COSMO-LEPS limited-area ensemble driving hydrologic forecast model.
At the start of this floodevent, driving thehydrologic model with adeterministic forecastproduced non-recordflood forecasts. Some ofthe ensemble membersdid produce recordflooding, as was observed.
Verbunt et al., August 2007 J. Hydrometeorology
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Flow
Time
Deficiencies of many 1st-generationcoupled hydrologic forecast systems
Future
Now
Past
©The COMET Program
Soil moisture, snowcover, streamflow are notknown perfectly at alllocations. What is theiruncertainty? How do errorsspatially co-vary?
A hydrologic forecast model is runduring this time, keeping track ofstreamflow changes. Such models are farfrom perfect, sources of model error maynot be accounted for.
Ensembles of atmosphericinformation driving hydrologicsystem may be biased, maynot represent all sourcesof forecast uncertainty, maynot have needed spatial detailif supplied from numericalmodel(s). For long-leadsimulations, samples ofpast years may not representchanging climate.
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“HEPEX”
aninternational,cooperativeproject toadvance
ensemblehydrologicpredictions
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HEPEX’senvisioned
“EnsembleHydrologicalPredictionSystem”
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Use ensemblesof statistically adjusted
weather / climate forecaststo provide
samples of futureatmospheric states
Important properties:(1) appropriately skillful
at short leads(2) representative of this year’sclimate if forecasts extend to
longer leads(3) calibrated data has
biases removed, correctspatial covariances.
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Develop anensemble of initial
land / snow/ streamflowstates consistent with
the observational data,with appropriate spreadand error covariances.
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Input the weather-climateensembles and land / snow
/ streamflow ensemblesinto hydrologic forecastmodel(s), with multiple
parameters or stochasticformulations to accountfor model uncertainty.
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Statistically adjust thestreamflow forecasts,
mitigating the remainingbiases/spread issues, andtailoring the products to theformats most useful to the
customers.
27
Monitor the forecasts,monitor the users’ issues,
and refine the process.
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Probabilistic systems can be developedfor flash flood warnings, also
proposed revisionof the flash-floodwarning systemdiscussed earlier.
ref: Ntkelos et al, J. Hydrometeorology, Oct. 2006
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HEPEX idea, again.
Nice in concept.
(1) What is the state ofdevelopment of such a
system?
(2) What are thetechnological hurdlesin the way of making
these sorts of systemsreally well calibrated
and useful to decisionmakers?
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Generating calibratedweather-climate
ensembles
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Climate forecasts
Simple: pre-adjustment system
Weather forecasts
Historicaltemperatures
and precipitation
Pre-adjustment
system
Adjustedtemperatures
and precipitation
c/o Kevin Werner, NOAA/NWS, and COMET
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Pre-adjustment method
Time
Tem
pera
ture
Temperature Ensemble
Adjusted Temperature ensemblebased on a CPC “warm” probabilityshift.Additive adjustment
Time
Prec
ipita
tion
Precipitation Ensemble
Adjusted Precipitation ensemblebased on a CPC “wet” probabilityshiftMultiplicative adjustment
c/o Kevin Werner, NOAA/NWS, and COMETCoarse model-forecast data are not downscaled,i.e, adjusted to have correct space-time variability.
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Dealing with ensemble forecast deficiencies: analogs using reforecasts
On the left are old forecastssimilar to today’s ensemble-mean forecast. For feedingensemble streamflow model,form an ensemble from the accompanyinganalyzed weather on theright-hand side.
Hamill and Whitaker, Nov. 2006 MWR.
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Dealing with ensemble forecast deficiencies: analogs using reforecasts
On the left are old forecastssimilar to today’s ensemble-mean forecast. For feedingensemble streamflow model,form an ensemble from the accompanyinganalyzed weather on theright-hand side.
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Develop anensemble of initial
land / snow / soil moisture /streamflow statesconsistent with theobservational data,
with appropriate spreadand error covariances.
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Example: probabilistic quantitativeprecipitation estimation in complex terrain
• Would like to define a griddedensemble of possible precipitationanalyses in a region. This wouldprovide forcings for a land-surfaceanalysis.
• Ensemble should have the rightuncertainty (spread, spatialcovariances).
• Proposed solution:(1) Compute climatological CDF usingpast observations. Use this CDF todefine transformation to Gaussian
(2)Using today’s availableobservations (dots), estimateconditional CDF of precipitationthrough regression analysis.(3) Generate ensembles fromcorrelated random fields to samplefrom the gridded precipitation CDFs.
ref: Clark and Slater, Feb. 2006 J. Hydrometeorology. [more]
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• At each grid point, performweighted regression basedon factors such as distance,similarity in elevation.Precipitation data isconverted to normaldistributions.
• Shown here: observations,regression-estimated POP,and estimated normalizedprecipitation amount forthree different days, with theright-hand columnrepresenting the mean of theCDF in normalizedcoordinates appropriate toeach grid point. Not shown:an estimate of the analysiserror in Z-space.
From stations to POPsand normalized
precipitation amount.
Observations Estimated POP Estimated Precipitation in Z-space
Cas
e 1
Cas
e 2
Cas
e 3
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Generating ensembles from correlated random fieldsto sample from the gridded precipitation CDFs.
1. Construct spatially correlated fields of random numbers
2. Use the cumulative probability that corresponds to therandom deviate to extract values from the estimatedCDFs at each grid cell
Rel?
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Land-surface model and satellite datain hydrologic data assimilation
• Use of land-surface model (LSM), satellite datadesirable because in-situ measurementsrelatively rare.
• LSM: energy-balance model forced by observedtemperature, precipitation; predicts snow, soilmoisture
• Satellite: microwave data most commonly used;however, retrievals of soil moisture biased,complicated by estimates of surface emissivity.
• Here, CLSM (NASA catchment land-surfacemodel) and SMMR (microwave satelliteestimates) are compared against global soilmoisture databank (GSMDB). Different symbolsfor different locations. Note large bias of bothsatellite, LSM relative to observations.
Ref: Reichle et al., J. Hydrometeorology, 2004.
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Input the weather-climateensembles and land / snow
/ streamflow ensemblesinto hydrologic forecastmodel(s), with multiple
parameters or stochasticformulations to accountfor model uncertainty.
Note: in some systems,the hydrologic forecastmodel is simply some “routing” model. In
others it may be a complicated land-surfacemodel coupled with routing model. In the latter
case, forecast information from thehydrological forecast model will be input back
into the hydrologic data assimilator.
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Hydrologic forecast basics• Infiltration happens when the precipitation filters into the
ground; some of which may be recovered by plant roots andbe transpired. If enough infiltration then water may penetrateall the way down to the water table. The water table is thetop layer of saturated ground that can be found across theplanet. In places where the water table intercepts the landsurface, it is manifested as wetlands, lakes and rivers. Thewater found below the water table is called groundwater. Ifthere has not been any rainfall for several days the river flowsare sustained by drainage from the groundwater reservoir(baseflow); these flows will gradually decrease until thegroundwater levels drop below the land surface.
• Surface runoff is when precipitation moves along the surfaceof the ground when either the ground can no longer absorbthe water, or the ground cannot absorb the water fastenough. The water flows (via gravity) along the surface until itfinds its way into a stream, river, lake, or ocean. Surfacerunoff causes the stream to rise quickly after heavy rainsbecause it is the fastest way water can reach a river orstream, much faster than through infiltration.
• To be able to forecast the amount of water flowing through acertain point along a river, the forecaster breaks the flowdown into three components: (1) Baseflow: the amount ofwater coming from groundwater. (2) Runoff: the amount ofwater coming from surface runoff. (3) Routed Flow: theamount of water coming from upstream areas.
Ref: http://www.srh.noaa.gov/abrfc/fcstmethods.shtml
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Lumped vs distributed models• Lumped: usually empirically based.
– Watershed represented with uniform characteristics (Precip(avg), Slope(avg), Soils(avg), …)– Area runoff “signature” (unit hydrograph) and regression relationships commonly used– Predict flow distribution at watershed outlet– “When no spatial variability is taken into account and when the channel reach or reservoir is
considered as a black box, the routing procedure is referred to as lumped routing.”– Vertical transport: collection of slabs parameters controlling vertical water movement
• Distributed: usually “physically based”– Spatial variability within watershed accounted for (P(x,y), S(x,y), Soils(x,y), …)– Overland flow and channel routing represented with more spatial detail– Channel routing: translation of runoff hydrograph through channel reaches; route and combine
at junctions– Diffusion equations for vertical water transport– “Propagation of flood waves in a river channel is a gradually varied unsteady process, which is
governed by mass and momentum equations.” Numerical solutions use the kinematic waveand (sometimes) dynamic wave equations
Refs: http://www.nws.noaa.gov/oh/hrl/distmodel/victor.ppt andRamirez, J. A., 2000: Prediction and Modeling of Flood Hydrology and Hydraulics Chapter 11, Inland Flood Hazards: Human, Riparian, and Aquatic Communities
Lumped Distributed
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Lumped model• Would like to predict flow at downstream gauge based
on flow atmospheric drivers such as “precipitationexcess”
• “Unit hydrograph” commonly adjusted to provide basinresponse to a unit pulse of excess precipitation (nextslide)
• A river basin may be modeled as a collection of“lumped” sub-basins to obtain a semi-distributedmodel
downstream gauge
blue area: thewatershed: all properties in this area are treated as homogeneous
UH
1
2
3
UH1
UH2
UH3
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“Unit hydrograph”• A special hydrograph, called the unit
hydrograph, is used to estimate how muchwater will be put into a stream by excessrunoff. The unit hydrograph is based on thebasin receiving enough rain in excess ofinfiltration to make one unit (cm, inch) ofrunoff, uniform over the basin for specifiedtime period. The unit hydrograph shows howmuch of this inch of runoff will go into thestream in a specific amount of time.
• Linearity is assumed, so…(1) If, for instance, the runoff is somethingother than 1.0 cm, 0.1 cm for example, thenmultiply the unit hydrograph value by 0.1 tofind the amount of flow into the stream.(2) Two separate pulses of rain can bemodeled with the sum of two scaled unithydrographs.(3) Time scale can be tuned lumped basincharacteristics (size, slope, geometry).
SCS Dimensionless UHG Features
0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
T/Tpeak
Q/Q
peak
Flow ratios
Cum. Mass
http://www.weather.gov/iao/InternationalHydrologyCourseCD1/johnson/wmo_2003/lectures/6_uhg_theory.ppt
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Sacramento Soil Moisture AccountingModel (a “lumped” model)
Ref: National Weather Service River Forecast System Model Calibration briefing by F. Fiedler
Inputs: initial hydrologicconditions, mean arealprecipitation, temperature,potential evapotranspiration.
Outputs: estimatedevapotranspiration,channel inflow.
Lots of model parametersthat control aspects like thepercolation rate.
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Estimating lumped hydrologic modelparameters and their uncertainty
Common approach: Force hydrologic model with “observed”meteorological conditions and upstream gauge data, tunemodel parameters until resulting flow at downstream gaugereasonably fits observed flow.
Problems / challenges: (1) Uncertainties in observed meteorological data accountedfor? (2) Why should parameters be considered fixed? Shouldthey vary temporally, or spatially, or with the model state? (3) Many parameters may need to be estimated. How doesone simultaneously tune all of them? (4) “Regulated basins” -- without natural streamflows, howdo you calibrate?
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Estimating hydrologic modelparameter uncertainty
This process is repeatedmany times over in a Monte-Carlo process withdifferent starting guessesat the model parametersand slightly differentinitial soil moistures andstreamflow states.
After many years, theresult is a distribution ofparameter estimates.
Ref: Vrugt et al., June 2006J. Hydrometeorology
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Estimate uncertainty using multiple models?
rainq
soile
baseq
SOILR
wlt! fld!
sat!
GFLWR
surfq
GWATR
percq
rainq
impvq
baseq
wlt! fld!
sat!
IZONE
LAYR2
surfq
soile
LAYR1
rainq
PCTIM
ADIMP
impvq
aimpq
bpriq
bsecq
percq
wlt! fld!
sat!
intfq
ADIMC
UZTWC UZFWC
LZTWC
LZFS
C
LZFP
C
soilerain
q
impvq
baseq
percqwlt
!sat
!
intfq
IMPZR
RZONE
IFLWR
GFLWR
surfq
LZONE
soile
fld!
lzZ
uzZ
lzZ
uzZ
lzZ
uzZ
lzZ
uzZ
PRMS SACRAMENTO
ARNO/VICTOPMODEL
c/o
Mar
tyn
Cla
rk, N
IWA
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Distributed model example:basin in Oklahoma (central US)
Dynamical equations to model vertical water transport and flow downstream. Basin characteristics here estimated with data sources such as GIS data.Tuning may also be involved.
http://www.weather.gov/ohd/hrl/distmodel/distmod.htm
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Issues with distributed models(1) Despite conceptual appeal, distributed models are stillnot totally “physically based” -- still can require lots of ad-hocassumptions, codified in profusion of parameters.
(2) Estimating parameters and their uncertainty for eachsub-basin all that much more complex than for lumped model.There may not be enough observations …. parameterestimation subject to “statistical overfitting.”
(3) For ensemble applications, require not only high-resolutiondatabases, but also high-resolution quantification ofuncertainty. Lots more work to do it “right”
51
Statistically adjust thestreamflow forecasts,
mitigating the remainingbiases/spread issues, andtailoring the products to theformats most useful to the
customers.
52
Statistically adjusting streamflows:“quantile mapping”
• ensures that CDF ofcorrected forecastconsistent with CDFof observed.
• Many examples inhydrologic literature,here for basin inIowa.
(no bias correction)event bias correctionLOWESS regressionquantile mapping
Ref: Hashino et al., 2006, Hydrology and Earth System Sciences Discussions
53
Understanding and tailoring hydrologic productfor customers. Example: reservoir rule curves
• Large reservoir operatorslargely spill based on rulecurves, with different rulesto follow for dry, average,wet years.
• Represent compromisesbetween storage for users(water supply, hydropower)and anticipated streamflow.
• Radically differentstreamflow forecasts fromclimatology may causereservoir operator to followa different rule curve.
• Possible product: translateensemble streamflowforecasts into ensemblepool size forecasts.
Ref: “Flood control regional scalefacilities” briefing, US Army Corps of Engineers
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Monitor the forecasts,monitor the users’ issues,
and refine the process.
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Validation / verification• Challenges:
– (1) regulated basins. How to estimate unregulatedflow?
– (2) non-independent observations (today’s &tomorrow’s streamflows highly correlated, gauge hereand a bit upstream highly correlated)
• → long time series of forecasts to achieve large enoughsample
• → “reforecasts” very helpful.
• Many of the techniques used in atmosphericensemble verification are still useful (reliabilitydiagrams, skill scores, economic value, rankhistograms, etc.)
• A few interesting new verification/display ideas
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Display techniques
from ECMWF Nov 2007 workshop
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Conclusions
• Weather-climate forecast inputs should beuseful for probabilistic streamflow predictions.
• Must appropriately model errors from– Weather & climate forecasts– Estimates of land-surface initial conditions– Hydrologic models
• Need to better understand customers’decision problems and tailor products to behelpful in making useful decisions.
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Short-range system in Italy
[back]
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NOAA’s reforecast data set• “Reforecast” definition: a data set of retrospective numerical forecasts using the same model
as is used to generate real-time forecasts.
• Model: T62L28 NCEP GFS, circa 1998
• Initial States: NCEP-NCAR Reanalysis II plus 7 +/- bred modes.
• Duration: 15 days runs every day at 00Z from 19781101 to now.(http://www.cdc.noaa.gov/people/jeffrey.s.whitaker/refcst/week2).
• Data: Selected fields (winds, hgt, temp on 5 press levels, precip, t2m, u10m, v10m, pwat, prmsl,rh700, heating). NCEP/NCAR reanalysis verifying fields included (Web form to download athttp://www.cdc.noaa.gov/reforecast).
• Validation data for this study: North American Regional Reanalysis (NARR)analyzedprecipitation (Mesinger et al., BAMS, 2006)
• Real-time downscaled probabilistic precipitation forecasts:http://www.cdc.noaa.gov/reforecast/narr
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Flow
Time
(3) ESP Technique (continued)
Future
Now
PastLow chance of thislevel flow or higher
High chance of thislevel flow or higher
Medium chance ofthis level flow orhigher
©The COMET Program
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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
SurfaceRunoff
Interflow
Supplemental Base flow
Side SubsurfaceDischarge
LZSK
LZPK
Upper Zone
Lower Zone
EXCESS
UZK
RIVA
PCTIM
ADIMP
TotalChannelInflow
DistributionFunction Streamflow
TotalBaseflow
Ref: National Weather Service River Forecast System Model Calibration briefing by F. Fiedler
63
Sacramento modelcontributions to runoff
Impervious and Direct Runoff
Surface Runoff
Interflow
Supplemental Baseflow
Primary Baseflow
SAC-SMA Model
Evaporation
Precipitation
Upper Zone
Lower
Zone
Pervious Impervious
Ref: National Weather Service River Forecast System Model Calibration briefing by F. Fiedler
64
Verification : ReliabilityDiagrams
% per category 95% confidence zone
Janu
ary
July
Precip > 0.0 (Logistic) Precip. > 12.7mm Precip. > 25.4mm
28.5%
30.5% 2.84%
1.86% 0.27%
0.47%
• Conditional probability that an event occurred, per category
Clark and Slater (2006) – Journal of Hydrometeorology[Back]
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