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Next: 8.1.2 Hydrographic constraints Up: 8.1 The ECCO state Previous: 8.1 The ECCO state   Contents

Subsections

8.1.1 Sea surface height from TOPEX/Poseidon and ERS-1/2 altimetry

Altimetric SSH contributions from T/P and ERS-1/2 are four-fold:

  1. an $ nYears$ time mean SSH misfit between model and T/P
  2. daily SSH anomaly misfits between T/P and model
  3. daily SSH anomaly misfits between ERS-1/2 and model
  4. daily absolute SSH misfit between T/P and model, weighted by the full geoid error covariance.

8.1.1.1 Input fields

 


       
field file name deccription unit
       
       
psbar psbarfile daily model mean SSH fields [m]
tpmean topexmeanfile $ nYears$ T/P mean [cm]
tpobs topexfile daily T/P SSH anomalies [cm]
erspobs ersfile daily ERS-1/2 SSH anomalies [cm]
wp geoid_errfile diagonal of geoid error covariance [m]
wtp, wers ssh_errfile rms of SSH anomalies [cm]
       

8.1.1.2 nYears time mean SSH misfit

  1. Compute $ nYears$ model mean spatial distribution

    $\displaystyle psmean(i,j)\, =\, \frac{1}{nDaysRec} \sum_{i=1}^{nDaysRec} psbar(i,j)$ (8.1)

  2. Compute global offset between $ nYears$ model and T/P mean:

    \begin{equation*}\begin{aligned}offset & = \, \overline{tpmean} \, - \, \overlin... ...j) \right\} \cdot cosphi(i,j) \cdot tpmeanmask(i,j) \end{aligned}\end{equation*}

  3. Misfits are computed w.r.t. global $ offset$ .
    First spatial distribution:

    \begin{equation*}\begin{aligned}cost\_ssh\_mean(i,j) & = \, \frac{1}{wp^2} \left... ...j) \, - \, tpmean(i,j) \, + \, offset \, \right\}^2 \end{aligned}\end{equation*}

    Finally, sum over all spatial entries:

    $\displaystyle \overline{cost\_ssh\_mean} \, = \, \sum_{i,j} cost\_ssh\_mean(i,j)$ (8.4)

8.1.1.3 Misfit of daily SSH anomalies

Computation is same for T/P and ERS-1/2. Here we write out computation for T/P.

  1. Compute difference in anomalies:

    \begin{equation*}\begin{aligned}cost\_ssh\_anom(i,j,t) & = \, \frac{1}{wtp^2} \l... ... \, \left[ \, tpobs(i,j,t) \, \right] \, \right\}^2 \end{aligned}\end{equation*}

    where $ t$ denotes time (day) index, and where it is assumed that $ nYears$ mean T/P spatial distribution $ tpmean(i,j)$ has already been removed from data $ tpobs(i,j)$ !

  2. Sum over all spatial points and all times

    \begin{equation*}\begin{aligned}\overline{cost\_ssh\_anom} & = \, \sum_{t} \sum_{i,j} cost\_ssh\_anom(i,j,t) \end{aligned}\end{equation*}

8.1.1.4 Flow chart 

cost_ssh
|
|- < compute nYears model mean >
|
|- < read nYears T/P mean >
|  CALL COST_READTOPEXMEAN
|
|- < compute global T/P vs. model offset >
|
|- < compute cost_hmean >
|  CALL COST_SSH_MEAN
|
|- < ... >

8.1.1.5 Weights and notes

  • All data are currently masked to zero where less than 13 depth levels, mimicing no contribution for depth less than 1000m.
  • $ cosphi$ term in weights is set to 1.
  • bad T/P and ERS-1/2 values are flagged $ \le \, -9990. $
  • T/P and ERS-1/2 data $ \le \, 1.\exp^{-8}$ cm are flagged as bad values
  • $ wp$ is read from geoid_errfile and $ 1/wp^2$ is pre-computed in ecco_cost_weights

8.1.1.5.1 $ wp$ for SSH mean misfit

 

$ 1/wp^2$ is pre-computed in ecco_cost_weights;
$ wp$ is read from geoid_errfile;

8.1.1.5.2 $ wtp$ and $ wers$ for SSH anomaly misfit

 

$ 1/wtp^2$ , $ 1/wers^2$ are pre-computed in ecco_cost_weights;

  • $ wtp$ , $ wers$ are read from single ssh_errfile
  • both are converted to meters and halved
    $ wtp \, \longrightarrow \, wtp \cdot 0.01 \cdot 0.5 $
  • ERS error is set to T/P error + 5cm
    $ wers \, = \, wtp \, + 0.5cm $

8.1.1.6 Cost diagnostics

  • Map out $ cost\_ssh\_mean(i,j) $
  • Map out $ cost\_ssh\_anom(i,j,t) $ averaged over 1 month, i.e.

    $\displaystyle \frac{1}{\text{monthly entries}} \sum_{t}^{monthly} cost\_ssh\_anom(i,j,t) $

  • sum over daily entries and plot daily average as function of time. i.e.

    $\displaystyle \frac{1}{\text{daily entries}} \sum_{i,j} cost\_ssh\_anom(i,j,t) $

next up previous contents
Next: 8.1.2 Hydrographic constraints Up: 8.1 The ECCO state Previous: 8.1 The ECCO state   Contents
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