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Next: 8.2 Profiles: transect and Up: 8.1 The ECCO state Previous: 8.1.1 Sea surface height   Contents

Subsections

8.1.2 Hydrographic constraints

Observation of temperature and salinity from various sources are used to constrain the model. These are:

  1. CTD obs. for $ T$ , $ S$ from various WOCE sections
  2. XBT obs. for $ T$
  3. Sea surface temperature (SST) and salinity (SSS) from Reynolds et al. (???)
  4. $ T$ , $ S$ from ARGO floats
  5. $ T$ , $ S$ from fields from Levitus (???)

8.1.2.1 Input fields

 


       
field file name deccription unit
       
       
tbar tbarfile monthly model mean pot. temperature [ $ ^{\circ }\mathrm {C}$ ]
sbar sbarfile monthly model mean salinity [ppt]
tdat tdatfile monthly mean Levitus pot. temperature [ $ ^{\circ }\mathrm {C}$ ]
sdat sdatfile monthly mean Levitus salinity [ppt]
ctdtobs ctdtfile monthly WOCE CTD pot. temperature [ $ ^{\circ }\mathrm {C}$ ]
ctdsobs ctdsfile monthly WOCE CTD salinity [ppt]
xbtobs xbtfile monthly XBT in-situ(!) temperature [ $ ^{\circ }\mathrm {C}$ ]
sstdat sstdatfile monthly Reynolds pot. SST [ $ ^{\circ }\mathrm {C}$ ]
sssdat sssdatfile monthly Reynolds SSS [ppt]
argotobs argotfile monthly ARGO in-situ(!) temperature [ $ ^{\circ }\mathrm {C}$ ]
argosobs argosfile monthly ARGO salinity [ppt]
wti, wsi data_errfile vert. stdev. profile for $ T$ , $ S$  
wtvar temperrfile spatially varying stdev. [ $ ^{\circ }\mathrm {C}$ ]
wsvar salterrfile spatially varying stdev. [ppt]
       

8.1.2.2 XBT data

\begin{equation*}\begin{aligned}cost\_xbt\_t(i,j,k) & = \, \left[ \, \frac{fac \... ...theta[xbtobs(\tau)] \right\}^2 \, \right](i,j,k) \\ \end{aligned}\end{equation*}

8.1.2.3 WOCE CTD data

\begin{equation*}\begin{aligned}cost\_ctd\_t(i,j,k) & = \, \left[ \, \frac{fac \... ... - \, ctdSobs(\tau) \right\}^2 \, \right](i,j,k) \\ \end{aligned}\end{equation*}

8.1.2.4 ARGO float data

\begin{equation*}\begin{aligned}cost\_argo\_t(i,j,k) & = \, \left[ \, \frac{fac ... ...- \, argoSobs(\tau) \right\}^2 \, \right](i,j,k) \\ \end{aligned}\end{equation*}

8.1.2.5 Reynolds sea surface T, S data

\begin{equation*}\begin{aligned}cost\_sst(i,j) & = \, \left[ \, wsst \sum_{\tau=... ... \, - \, sssDat(\tau) \right\}^2 \, \right](i,j) \\ \end{aligned}\end{equation*}

8.1.2.6 Levitus montly T, S climatological data

Model vs. data misfits are taken from $ nYears$ monthly model means vs. Levitus monthly data. The description below is for potential temperature. Procedure for salinity is fully analogous. Spatial indices $ (i,j,k)$ are omitted throughout.

  1. Compute $ nYears$ monthly model means for each month $ imon$ :

    $\displaystyle \overline{Tbar}(imon) \, = \, \frac{1}{nYears} \sum_{iyear=1}^{nYears} Tbar(iyear,imon) $

  2. Compute misfit:

    $\displaystyle cost\_theta(i,j,k) \, = \, \left[ \frac{fac \cdot ratio}{wti^2} ... ...2} \left\{ \overline{Tbar}(imon) \, - \, Tdat(imon) \right\}^2 \right] (i,j,k) $

8.1.2.7 Weights and notes

  • $ T2\theta$ is an operator mapping in-situ to potential temperatures
  • Latitudinal weight not used:

    $\displaystyle cosphi(i,j) \, = \, 1 $

  • $ fac \, = \, cosphi \cdot mask $
  • Spatially constant weights:
    1. Read standard deviation vertical profiles for $ T$ , $ S$
      $ {\tt data\_errfile} \, \longrightarrow \, wti(k), \,\, wsi(k) $
      $ {\tt data\_errfile} \, \longrightarrow \, ratio = 0.25 = \left( \frac{1}{2} \right)^2 $
    2. Take inverse squares:

      \begin{equation*} \begin{aligned} wtheta(k) & = \, \frac{ratio}{wti(k)^2} \\ wsalt(k) & = \, \frac{ratio}{wsi(k)^2} \\ \end{aligned}\end{equation*}

  • Spatially varying weights:
    1. Read standard deviation fields
      $ {\tt temperrfile} \, \longrightarrow \, wtvar(i,j,k) $
      $ {\tt salterrfile} \, \longrightarrow \, wsvar(i,j,k) $
    2. Weights are combination of spatially constant and varying parts:

      \begin{equation*} \begin{aligned} wtheta2(i,j,k) & = \, \frac{ratio} {wti(k)^2 \... ... \frac{ratio} {wsi(k)^2 \, + \,wsvar(i,j,k)^2 } \\ \end{aligned}\end{equation*}

  • Sea surface $ T$ , $ S$ weights:
    • SST: $ wsst \, = \, fac \cdot wtheta(1)$ : horizontally constant
    • SSS: $ wsss \, = \, fac \cdot wsalt2(i,j,1)$ : horizontally varying
    (Why this difference? I don't know.)

8.1.2.8 Diagnostics

  • Map out $ wtheta2(i,j,k)$ , $ wsalt2(i,j,k)$ .

next up previous contents
Next: 8.2 Profiles: transect and Up: 8.1 The ECCO state Previous: 8.1.1 Sea surface height   Contents
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