Post on 21-Jun-2020
Modeling Concepts
June 23-‐25, 2014 (9:00-‐10:00, Monday morning)
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
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
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
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
haps://archive.org/details/streamflowforeca914work
haps://archive.org/details/streamflowforeca914work
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
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
SNOW-‐17
All processes index to the air temperature
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)
Most models contain elements of all three approaches
model
data-‐driven
conceptual
physical
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
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
DHSVM
hap://www.virtualriverbasins.ocean.washington.edu/file/DHSVM+Input+Layers-‐Landcover%2C+Soils%2C+ElevaHon
Other spaHal organizaHons
hap://www.hydro.washington.edu/Leaenmaier/Models/VIC
hap://www.hydro.washington.edu/Leaenmaier/Models/VIC
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
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
Parameters and forcings
Parameter Specify the shape of the funcHon
Forcings Time-‐varying boundary condiHons
Forcings
IniHal state
Parameters
Computer code
What is a model?
Stages of a model simulaHon
Spinup SimulaHon
Model Ini.al State Model State
Combining models and observaHons
• Developing parameterizaHons • SpecificaHon of model parameters • Model forcings • Model evaluaHon • Data assimilaHon
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.
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.
Develop parameterizaHons
Clark et al., 2014
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.
Specify model parameters
hap://www.virtualriverbasins.ocean.washington.edu/file/DHSVM+Input+Layers-‐Landcover%2C+Soils%2C+ElevaHon
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.
Model evaluaHon
Clark et al., 2014
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
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.
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.
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.
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.
Model evaluaHon frameworks
Clark et al., 2014