#### 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 x^{t} from both sides of ** to get an eqn for E^{a}
2 A =
3 A(K+dK) - A(K) = A(dK)
4 Trace A(dK) = 0

-2[(I-KH)BH^{t} + KR]dK = 0 for any dK
=> (I-KH)BH^{t} + KR = 0
==> BH^{t} - KHBH^{t} - KR =0
===> K(HBH^{t} + R) = BH^{t}
====> K = BH^{t} (HBH^{t+R)-1}

Try H = I, ie you have 1 observation for every state variable
Try B = \sigma^{2_b} I and R = \sigma^{2_o} I

xa = xb + BH^{t} (HBH^{t+R)-1} (y - Hx^{b)}

xa = xb + (sigma^{2_b)(y-xb)/(sigma2_o} + sigma^{2_b)***}

IF \sigma^{2_o} >> \sigma^{2_b} => xa -> xb because sig/(sig+sig) -> 0
IF \sigma^{2_b} >> \sigma^{2_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