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- etkf_cor_cl
class etkf_cor_cl |
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class for Ensemble Transform Kalman Filter solver for correlated observations
See Feng et al., ACP 2009; Palmer et al., 2011.
Members:
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# control variables
1. nx:<int>: size of control variable
2. ne:<int>: size of perturbation ensemble
3. x:<array, (nx, ne)>: perturbation ensemble
4. x_mean:<array, (nx)>: mean value of control variable
5. xnorm:<float>: normalized factor
# model observation
6. y:<array, (nobs, ne)>: ensemble for model observation perturbation
7. ny:<int>: ny=nobs
8. y_mean:<array, (nobs)>: model observations for self.mean_x
9. sp_y: <array, (nobs, ne)>: sparse matrix of self.y
# observation errors
9. r:<array, (nobs, nobs)>: observation err covariance
10. sp_r:<array, (nobs,)>: sparse matrix of r
11. sp_b:<array, (nobs, nobs)>: background error covariance in obsevation space
sp_b=sp_y*sp_y^T
12. sp_r:<array, (nobs, nobs)>: sp_r=sp_r+
Functions
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1. __init__: initialization
2. reset: re-do initialization
3. get_posterior: get posterior
4. get_tm: get transform matrix
6. get_inc_m: get increment matrix
7. get_x_inc: get analysis increment
8. get_y_inc: get analysis increment in observation space
9. do_y_transform: transform maxtrix in y space
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Methods defined here:
- __init__(self, x_mean, y_mean, x, y, r, xref=1, xnorm=1.0)
- Initialization
Inputs:
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1. x_mean:<array, (nx)>: mean values of control variables x
2. Y_mean:<array, (ny)>: mean model observation values.
3. x: <array, (nx, ne)>: ensemble of x perturbations
4. y: <array, (nobs, ne)>: ensemble of model forecast perturbations. ny=nobs
5. r: <array, (nobs, nobs)>: observation error
6. xref:<float>: value used to scale mean_x
7. xnorm:<float>: value used to scale ensemble purbations
- get_inc_m(self, yobs)
- get the analysis increment matrix
Inputs:
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1. yobs:<array, (nobs)>: the observations
Returns:
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1. inc_m :<array, (ne,)>:increase matrix
Notes:
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1. inc_m=y^T*(R+Y*Y^t)^-0.5*dy
- get_posterior(self, yobs)
- calculate posterior from assimilation of observations
Inputs:
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1. yobs:<array, nobs>: observations
Returns:
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1. postprior:<array, nx>:
Notes:
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1. xa=xf+k*(yobs-f(x))=xf+dx*inc_m
- get_tm(self)
- the analysis increment on the variables
Returns:
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1. tm :<array, (ne, ne)>: matrix for posterior ensemble: x(f)=x(a)*tm
Notes:
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1. tm*tm=[1.0+(y^t*R^-1*y) ]
- get_x_inc(self, inc_m, x_in=None, mean_x_in=None)
- the analysis increment of control variables
Inputs:
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1. inc_m:<array, (ne)>: increment matrix
2. x_in:<array, (nx, ne)>: ensemble perturbations
3. mean_x_in:<array, (nx)>: mean value
Returns:
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1. xinc: <array, nx>: the x increments
- get_y_inc(self, y_in, inc_m, mean_y=None)
- the analysis increment on the variables
Inputs:
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1. y_in:<array, (new_ny, ne)>: the 'new' observation perturbation
2. inc_m :<array, (ne)>: increment matrix
Returns:
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1. yinc: <array, new_ny>: y increments from xinc
- get_y_transform(self, y_in, tm, mean_y=None)
- multiply y_in by tm
Inputs:
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1. y_in:<array>, (new_ny, ne)>: 'new' observation perturbations
2. tm :<array, (ne, ne)>: Transformation matrix
Returns:
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1. yt:<array, (new_ny, ne)>: yt=y_in*tm
- reset(self, x_mean, y_mean, x, y, r, xref=1.0, xnorm=1.0, do_debug=False)
- Re-Initialization
Inputs:
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1. x_mean:<array, (nx)>: mean values of control variables x
2. Y_mean:<array, (ny)>: mean model observation values.
3. x: <array, (nx, ne)>: ensemble of x perturbations
4. y: <array, (nobs, ne)>: ensemble of model forecast perturbations. ny=nobs
5. r: <array, (nobs, nobs)>: observation error
6. xref:<float>: value used to scale mean_x
7. xnorm:<float>: value used to scale ensemble purbations
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