Modeling)Concepts) - University of...
Transcript of Modeling)Concepts) - University of...
![Page 1: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/1.jpg)
Modeling Concepts
June 23-‐25, 2014 (9:00-‐10:00, Monday morning)
![Page 2: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/2.jpg)
Model General: a model is anything used in any way to represent anything else
wikipedia
More specific to this class: A simplified or idealized descripHon or concepHon of a parHcular system, situaHon, or process, oJen in mathemaHcal terms, that is put forward as a basis for theoreHcal or empirical understanding, or for calculaHons, predicHons, etc.; a conceptual or mental representaHon of something
Oxford English DicHonary
![Page 3: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/3.jpg)
More specific to this class: A simplified or idealized descripHon or concep.on of a parHcular system, situaHon, or process, o/en in mathema.cal terms, that is put forward as a basis for theore.cal or empirical understanding, or for calcula.ons, predic.ons, etc.; a conceptual or mental representaHon of something
Oxford English DicHonary
“EssenHally, all models are wrong, but some are useful.”
-‐ George E. P. Box,
in his 1987 book on Empirical Model Building and Response Surfaces
![Page 4: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/4.jpg)
Why model? “There are two main aims of simulaHon models. The first is to explore the implicaHons of making certain assumpHons about the nature of the real world system; the second is to predict the behaviour of the real world system under a set of naturally-‐occurring circumstances.”
Beven, K., 1989: Changing ideas in hydrology — The case of physically-‐based models. J Hydrol, 105, 157-‐172, 10.1016/0022-‐1694(89)90101-‐7.
• Develop hypotheses -‐ which can be tested through observaHon and experimentaHon
• ExploraHon • PredicHon and forecasHng
![Page 5: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/5.jpg)
Types of models Data-‐driven
Infer relaHonships from observaHons, without aaempHng to describe the underlying causal processes examples – staHsHcal model – regression model of maximum snow accumulaHon
and summer streamflow – stochasHc Hme series model – weather generators – machine learning – predicHon of consumer preferences
![Page 6: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/6.jpg)
haps://archive.org/details/streamflowforeca914work
![Page 7: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/7.jpg)
haps://archive.org/details/streamflowforeca914work
![Page 8: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/8.jpg)
Types of models Conceptual
Represent causal relaHonships without necessarily reflecHng the underlying physical processes Examples – series of linear reservoirs to describe flow in a river – Budyko / Manabe bucket model to represent land surface hydrology
![Page 9: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/9.jpg)
SNOW-‐17 “SNOW-‐17 is a conceptual model. Most of the important physical processes that take place within a snow cover are explicitly included in the model, but only in a simplified form.” “SNOW-‐17 is an index model using air temperature as the sole index to determine the energy exchange across the snow-‐air interface. In addiHon to temperature, the only other input variable needed to run the model is precipitaHon.”
Snow Accumula.on and Abla.on Model – SNOW-‐17, Eric Anderson, 2006
hap://www.nws.noaa.gov/oh/hrl/nwsrfs/users_manual/part2/_pdf/22snow17.pdf
![Page 10: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/10.jpg)
SNOW-‐17
All processes index to the air temperature
![Page 11: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/11.jpg)
Types of models Physically-‐based (physically-‐mo.vated)
Represent causal relaHonships as much as possible through a direct descripHon of the underlying physical processes examples – ballisHcs model – Richards equaHon for variably saturated flow to describe transport in
the vadose zone – Saint-‐Venant equaHons for 1D transient open channel flow
DisHncHon between conceptual and physically-‐based is not always clear-‐cut and oJen a funcHon of scale (Hme, space)
![Page 12: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/12.jpg)
Most models contain elements of all three approaches
model
data-‐driven
conceptual
physical
![Page 13: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/13.jpg)
ParameterizaHons In many cases a full descripHon of the underlying physics is not possible: • incomplete process knowledge • trade-‐off between physical realism and computaHonal
demand (or number of realizaHons)
! Rather than describe the physical processes explicitly, we mimic the behavior of the system and its main causal relaHonships: parameteriza.on
Doesn’t solve all problems, in parHcular: • incomplete knowledge of the parameters
![Page 14: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/14.jpg)
SpaHal organizaHon
Lumped No explicit representaHon of space
Distributed Explicit representaHon of space
hap://chrs.web.uci.edu/research/hydrologic_predicHons/acHviHes07.html
SAC-‐SMA DHSVM
hap://www.hydro.washington.edu/Leaenmaier/Models/DHSVM
![Page 15: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/15.jpg)
DHSVM
hap://www.virtualriverbasins.ocean.washington.edu/file/DHSVM+Input+Layers-‐Landcover%2C+Soils%2C+ElevaHon
![Page 16: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/16.jpg)
Other spaHal organizaHons
hap://www.hydro.washington.edu/Leaenmaier/Models/VIC
![Page 17: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/17.jpg)
hap://www.hydro.washington.edu/Leaenmaier/Models/VIC
![Page 18: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/18.jpg)
States and fluxes State variables
– Represent storage (mass, energy, momentum, etc.) – Evolve over Hme: state at Hme t is a funcHon of states at previous
Hmes
Fluxes
– Represent exchange/transport – Rate of flow of a property per unit area – Only depend on quanHHes at Hme t
Rate of change of a state is associated with one or more fluxes different from zero
Model IniHal State
![Page 19: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/19.jpg)
PrognosHc and diagnosHc equaHons / variables
Prognos.c: EquaHon / variable at Hme t is dependent on values at previous Hmes
Diagnos.c:
EquaHon / variable at Hme t is dependent only on values at Hme t
![Page 20: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/20.jpg)
Parameters and forcings
Parameter Specify the shape of the funcHon
Forcings Time-‐varying boundary condiHons
![Page 21: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/21.jpg)
Forcings
IniHal state
Parameters
Computer code
What is a model?
![Page 22: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/22.jpg)
Stages of a model simulaHon
Spinup SimulaHon
Model Ini.al State Model State
![Page 23: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/23.jpg)
Combining models and observaHons
• Developing parameterizaHons • SpecificaHon of model parameters • Model forcings • Model evaluaHon • Data assimilaHon
![Page 24: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/24.jpg)
Develop parameterizaHons
Storck, P., D. P. Leaenmaier, and S. M. Bolton, 2002: Measurement of snow intercepHon and canopy effects on snow accumulaHon and melt in a mountainous mariHme climate, Oregon, United States. Water Resour Res, 38, 10.1029/2002wr001281.
![Page 25: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/25.jpg)
Develop parameterizaHons
Storck, P., D. P. Leaenmaier, and S. M. Bolton, 2002: Measurement of snow intercepHon and canopy effects on snow accumulaHon and melt in a mountainous mariHme climate, Oregon, United States. Water Resour Res, 38, 10.1029/2002wr001281.
![Page 26: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/26.jpg)
Develop parameterizaHons
Clark et al., 2014
![Page 27: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/27.jpg)
Develop parameterizaHons
U.S. Army Corps of Engineers, 1956: Snow hydrology; summary report of the snow inves?ga?ons. North Pacific Division, Corps of Engineers, U.S. Army, 437 pp.
![Page 28: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/28.jpg)
Specify model parameters
hap://www.virtualriverbasins.ocean.washington.edu/file/DHSVM+Input+Layers-‐Landcover%2C+Soils%2C+ElevaHon
![Page 29: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/29.jpg)
Model forcings
Livneh, B., E. A. Rosenberg, C. Lin, B. Nijssen, V. Mishra, K. M. Andreadis, E. P. Maurer, and D. P. Leaenmaier, 2014: A long-‐term hydrologically based dataset of land surface fluxes and states for the conterminous United States: Update and extensions (vol 26, pg 9384, 2013). J Climate, 27, 477-‐486, 10.1175/jcli-‐d-‐13-‐00697.1.
![Page 30: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/30.jpg)
Model evaluaHon
Clark et al., 2014
![Page 31: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/31.jpg)
Model uncertainty
• model input errors (precipitaHon, LW) • model parameter errors (e.g. the albedo-‐age decay etc.) • model structural errors One way of evaluaHng uncertainty is to use a large number of models / model implementaHons:
Ensembles
![Page 32: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/32.jpg)
Data assimilaHon Update model state based on observaHons
Slater, A. G., and M. P. Clark, 2006: Snow data assimilaHon via an ensemble Kalman filter. Journal of Hydrometeorology, 7, 478-‐493, 10.1175/jhm505.1
(upper) Examples of model control simulaHons and (lower) assimilaHon runs using the ensemble square root Kalman filter, with updates every 5 days (5-‐D). The ensemble of model simulaHons is given in light gray, and truth is given in the thick dark line, an the mean of the assimilated SWE is given by the dark squares complete with one standard deviaHon shown in the thin dark lines. Periods shown are from 29 September to 31 July of respecHve water years.
![Page 33: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/33.jpg)
Model intercomparison studies
Nijssen, B., and Coauthors, 2003: SimulaHon of high laHtude hydrological processes in the Torne–Kalix basin: PILPS Phase 2(e): 2: Comparison of model results with observaHons. Global Planet Change, 38, 31-‐53, 10.1016/s0921-‐8181(03)00004-‐3.
PILPS-‐2e: Project for Intercomparison of Land-‐surface ParameterizaHon Schemes (PILPS) Bowling et al. 2003.
![Page 34: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/34.jpg)
Model intercomparison studies
Nijssen, B., and Coauthors, 2003: SimulaHon of high laHtude hydrological processes in the Torne–Kalix basin: PILPS Phase 2(e): 2: Comparison of model results with observaHons. Global Planet Change, 38, 31-‐53, 10.1016/s0921-‐8181(03)00004-‐3.
![Page 35: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/35.jpg)
Model intercomparison studies All models parHcipaHng in PILPS Phase 2(e) capture the broad dynamics of snowmelt and runoff, but large differences in snow accumulaHon and ablaHon, turbulent heat fluxes, and streamflow exist. One of the difficulHes in interpreHng the results from the PILPS Phase 2(e) experiments is the complexity of the current generaHon of land-‐surface schemes. Even in an experiment where meteorological forcings and many of the land-‐surface characterisHcs were prescribed, the remaining number of degrees of freedom is large. Because of the nonlinearity of many of the land-‐surface processes, small differences in model parameters and in model parameteriza.ons can lead to large differences in model outcomes …
Nijssen, B., and Coauthors, 2003: SimulaHon of high laHtude hydrological processes in the Torne–
Kalix basin: PILPS Phase 2(e): 2: Comparison of model results with observaHons. Global Planet Change, 38, 31-‐53, 10.1016/s0921-‐8181(03)00004-‐3.
![Page 36: Modeling)Concepts) - University of Washingtondepts.washington.edu/.../Nijssen_ModelingConcepts.pdf · Dataassimilaon) Update)model)state)based)on)observaons))) Slater,)A.)G.,)and)M.)P.)Clark,)2006:)Snow)dataassimilaon)viaan)ensemble)](https://reader034.fdocuments.in/reader034/viewer/2022042320/5f0a43097e708231d42acbf9/html5/thumbnails/36.jpg)
Model evaluaHon frameworks
Clark et al., 2014