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README.md

MEOPAR Winter School in Environmental Modeling Notes

Participant intros

Jenna Joyce: UoOttawa w/ Jackie Dawson

  • Shipping in the Arctic (Corridors)
  • Corridors & Environment/Culturally significant areas coexistence

Ewelina Luczko: Baird & associates "where land meets water"

  • Coastal engineering - wave modeling
  • Wave energy generation in SWAN

Lindsay Chipman: UoColorado - Boulder

  • Cycling of O2 and C in permeable sediment
  • O2 flux from

Lei Ren: NUI Galway

  • Surface flow fields from CODAR & Model
  • Focus area: West Coast of Ireland

Russel Glazer: UoFlorida - Tallahassee

  • Saturation over ice & water in models
  • Cloud formation scheme

Blanche St-BĂ©at: ULaval - Qc

  • Food Webs: distinguish ecosystemsĂ©establish stability
  • Resilience vs Resistance: Wood house is better than hay or bricks?!

Feifei Sun: Andrea Scott student

  • Predict ice thickness from data
  • New assimilation methods

Dennis Monteban: Denmark university

  • Study of Fjord west of Greenland / Wave-Ice damping
  • Validated & Calibrated MIKE model

Ben Moore-Maley: UBC w/ Susan Allen

  • 3D modeling of Salish Sea @ 500m resolution
  • Wind driven circulation/interactions

Nancy Chen: DFO - St-John's

  • Satellite SSH anomaly -> water transport
  • Labrador & Scotian Shelf

Deborah Benkort: PhD Laval

  • Krill aggregation & dispersion in GSL/GSE
  • Effect of envt. on growth, distribution, reproduction

Becky Segal: MSc UVic

  • Permafrost thaw sumps work before
  • Ice prediction/obs and creating relevant products for communities

Charles Brunette: McGill with Bruno

  • Predictability using Lagrangian methods
  • Seasonal & Regional
  • Later formation -> Thinner ice -> Minimum ice extent

Onur Bora: Coastal engineer/PhD student in Istanbul

  • Hydrodynamics effects from shipping -> impact on sediment
  • Water cooling/intake system design

Olivier Asselin:

  • Figure out the atmosphere
  • Energy constant vs \lambda for different processes: 2 slopes for everything?!
  • CFD

Nathan Grivault: UoAlberta w/ Paul Myers

  • Freshwater in the Arctic: Arctic -> Lower latitudes
  • Impact on circulation: Export vs Forcing

Data Assimilation

Development of data assimilation

  • developped for weather forecasting (fast time scale, highly nonlinear)
  • applied for operational oceanography (slower time scales, poorly observed)
  • starting to be used in sea ice

Why?

  • Obtain an improved state that can be used to initialize a forecast
  • Obtain consistent states that can be used in process studies or hindcasting
  • To challenge models with data and vice versa, leading to improvements in models and/or observational methods (OSSEs)

Assimilation cycle

1 Observation 2 Assimilation system 3 Analysis 4 Forecast model 5 Background 6 Repeat

Note: Need really good observations otherwise they can contaminate runs

Components of a DA system

  • DA is a state estimation problem
  • Need a prognostic model to solve time evolution of the state
  • the state is all you need to characterize the system
  • prevent model drift

DA problem

given a mapping from a state to observations, try to get from observation to state for y = H(x), try to get x = H-1(y) but size(x) and size(y) don't match so it's not invertible

Best Linear Unbiased Estimator (BLUE)

x_a = L x_b + K y a: state estimate at a given time b: background (state of the model for a given time) y: obs for a given time

Best estimate minimizes analysis error. E_a = x_a - x_t E_b = x_b - x_t E_o = y - x_t

x_t + E_a = L(x_t + E_b) + K(E_o + H(x_t))

assume errors are unbiased: = 0

= L + KH = (L+KH) --> L+KH = I --> L = I - KH

Plug back in: x_a = (I-KH)x_b + Ky = x_b + K (y - H x_b)

-Need to get K -'best' K is the one that minimizes trace of A where A =

1 subtract xt from both sides of ** to get an eqn for Ea 2 A = 3 A(K+dK) - A(K) = A(dK) 4 Trace A(dK) = 0

-2[(I-KH)BHt + KR]dK = 0 for any dK => (I-KH)BHt + KR = 0 ==> BHt - KHBHt - KR =0 ===> K(HBHt + R) = BHt ====> K = BHt (HBHt+R)-1

Try H = I, ie you have 1 observation for every state variable Try B = \sigma2_b I and R = \sigma2_o I

xa = xb + BHt (HBHt+R)-1 (y - Hxb)

xa = xb + (sigma2_b)(y-xb)/(sigma2_o + sigma2_b)***

IF \sigma2_o >> \sigma2_b => xa -> xb because sig/(sig+sig) -> 0 IF \sigma2_b >> \sigma2_o => xa -> y because sig/(sig+sig) -> 1

If model is biased, need to include bias in *** and have a coupled error/bias data assimilation

Generally treat things as a minimization problem.

Getting B and R:

Error covariance matrices: B: Model error covariance matrix for the model: how state variables vary with each others R: Obs error covariance matrix

Innovations: y - Hxb

Correlated B&R act as low&high pass filters of innovations. Using ensembles to create error correlation function: Not bad but spurious noise at longer range. => Use localization.

Case studies

T&S from buoy in Labrador sea using EnOI -> Improved profiles Sea ice concentration from passive microwave

Look at innovations (PDF, Space-time distributions) to diagnose DA Can take a while for assimilation to kick in