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Modeling Concepts June 2325, 2014 (9:0010:00, Monday morning)

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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)

Modeling  Concepts  

June  23-­‐25,  2014  (9:00-­‐10:00,  Monday  morning)  

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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  

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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  

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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  

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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  

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haps://archive.org/details/streamflowforeca914work  

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haps://archive.org/details/streamflowforeca914work  

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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  

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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  

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SNOW-­‐17  

All  processes  index  to  the  air  temperature  

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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)  

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Most  models  contain  elements  of  all  three  approaches  

model  

data-­‐driven  

conceptual  

physical  

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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    

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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  

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DHSVM  

hap://www.virtualriverbasins.ocean.washington.edu/file/DHSVM+Input+Layers-­‐Landcover%2C+Soils%2C+ElevaHon  

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Other  spaHal  organizaHons  

hap://www.hydro.washington.edu/Leaenmaier/Models/VIC  

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hap://www.hydro.washington.edu/Leaenmaier/Models/VIC  

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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  

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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  

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Parameters  and  forcings  

Parameter  Specify  the  shape  of  the  funcHon      

Forcings  Time-­‐varying  boundary  condiHons  

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Forcings  

IniHal  state  

Parameters  

Computer  code  

What  is  a  model?  

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Stages  of  a  model  simulaHon  

Spinup   SimulaHon  

Model  Ini.al  State   Model  State  

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Combining  models  and  observaHons  

•  Developing  parameterizaHons  •  SpecificaHon  of  model  parameters  •  Model  forcings  •  Model  evaluaHon  •  Data  assimilaHon  

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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.  

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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.  

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Develop  parameterizaHons  

Clark  et  al.,  2014  

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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.  

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Specify  model  parameters  

hap://www.virtualriverbasins.ocean.washington.edu/file/DHSVM+Input+Layers-­‐Landcover%2C+Soils%2C+ElevaHon  

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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.  

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Model  evaluaHon  

Clark  et  al.,  2014  

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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  

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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.  

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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.  

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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.  

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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.  

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Model  evaluaHon  frameworks  

Clark  et  al.,  2014  


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