Skip to content
GitLab
Projects
Groups
Snippets
Help
Loading...
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in
Toggle navigation
M
MWSNotes
Project overview
Project overview
Details
Activity
Releases
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Issues
0
Issues
0
List
Boards
Labels
Service Desk
Milestones
Merge Requests
0
Merge Requests
0
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Operations
Operations
Environments
Analytics
Analytics
CI / CD
Repository
Value Stream
Wiki
Wiki
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
Jean-Pierre Auclair
MWSNotes
Commits
8fbed8ef
Commit
8fbed8ef
authored
Mar 09, 2017
by
Arthanor
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Data Assimilation Part 1
parent
92ce9f0f
Changes
1
Hide whitespace changes
Inline
Side-by-side
Showing
1 changed file
with
101 additions
and
1 deletion
+101
-1
README.md
README.md
+101
-1
No files found.
README.md
View file @
8fbed8ef
...
...
@@ -68,4 +68,104 @@ Olivier Asselin:
Nathan Grivault: UoAlberta w/ Paul Myers
-
Freshwater in the Arctic: Arctic -> Lower latitudes
-
Impact on circulation: Export vs Forcing
\ No newline at end of file
-
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:
<E_
?
>
= 0
<x_t>
= L
<x_t>
+ KH
<x_t>
<x_t>
= (L+KH)
<x_t>
--> L+KH = I --> L = I - KH
Plug back in:
x_a = (I-KH)x_b + Ky
= x_b + K (y - H x_b) <== Kalman filter equation
**
-Need to get K
-'best' K is the one that minimizes trace of A where A =
<E
^
a
E
^
a*
>
1 subtract x^t from both sides of
**
to get an eqn for E^a
2 A =
<E
^
a
E
^
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 =
\s
igma^2_b I and R =
\s
igma^2_o I
xa = xb + BH^t (HBH^t+R)^-1 (y - Hx^b)
xa = xb + (sigma^2_b)(y-xb)/(sigma^2_o + sigma^2_b)
**
*
IF
\s
igma^2_o >>
\s
igma^2_b => xa -> xb because sig/(sig+sig) -> 0
IF
\s
igma^2_b >>
\s
igma^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
\ No newline at end of file
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment