1 | % ================================================================ |
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2 | % Chapter observation operator (OBS) |
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3 | % ================================================================ |
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4 | \chapter{Observation and model comparison (OBS)} |
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5 | \label{OBS} |
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6 | |
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7 | Authors: D. Lea, M. Martin, K. Mogensen, A. Vidard, A. Weaver... % do we keep that ? |
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8 | |
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9 | \minitoc |
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10 | |
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11 | |
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12 | \newpage |
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13 | $\ $\newline % force a new line |
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14 | |
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15 | The observation and model comparison code (OBS) reads in observation files |
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16 | (profile temperature and salinity, sea surface temperature, sea level anomaly, |
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17 | sea ice concentration, and velocity) and calculates an interpolated model equivalent |
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18 | value at the observation location and nearest model timestep. The OBS code is |
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19 | called from \np{opa.F90} in order to initialise the model and to calculate the |
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20 | model equivalent values for observations on the 0th timestep. The code is then |
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21 | called again after each timestep from \np{step.F90}. The code was originally |
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22 | developed for use with NEMOVAR. |
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23 | |
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24 | For all data types a 2D horizontal interpolator is needed |
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25 | to interpolate the model fields to the observation location. |
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26 | For {\em in situ} profiles, a 1D vertical interpolator is needed in addition to |
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27 | provide model fields at the observation depths. Currently this only works in |
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28 | z-level model configurations, but is being developed to work with a |
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29 | generalised vertical coordinate system. |
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30 | Temperature data from moored buoys (TAO, TRITON, PIRATA) in the |
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31 | ENACT/ENSEMBLES data-base are available as daily averaged quantities. For this |
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32 | type of observation the |
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33 | observation operator will compare such observations to the model temperature |
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34 | fields averaged over one day. The relevant observation type may be specified in the namelist |
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35 | using \np{endailyavtypes}. Otherwise the model value from the nearest |
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36 | timestep to the observation time is used. |
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37 | |
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38 | The resulting data are saved in a ``feedback'' file (or files) which can be used |
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39 | for model validation and verification and also to provide information for data |
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40 | assimilation. This code is controlled by the namelist \textit{nam\_obs}. To |
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41 | build with the OBS code active \key{diaobs} must be set. |
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42 | |
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43 | Section~\ref{OBS_example} introduces a test example of the observation operator |
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44 | code including where to obtain data and how to setup the namelist. |
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45 | Section~\ref{OBS_details} introduces some more technical details of the |
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46 | different observation types used and also shows a more complete namelist. |
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47 | Finally section~\ref{OBS_theory} introduces some of the theoretical aspects of |
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48 | the observation operator including interpolation methods and running on multiple |
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49 | processors. |
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50 | |
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51 | % ================================================================ |
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52 | % Example |
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53 | % ================================================================ |
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54 | \section{Running the observation operator code example} |
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55 | \label{OBS_example} |
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56 | |
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57 | This section describes an example of running the observation operator code using |
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58 | profile data which can be freely downloaded. It shows how to adapt an |
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59 | existing run and build of NEMO to run the observation operator. |
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60 | |
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61 | \begin{enumerate} |
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62 | \item Compile NEMO with \key{diaobs} set. |
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63 | |
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64 | \item Download some ENSEMBLES EN3 data from |
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65 | \href{http://www.hadobs.org}{http://www.hadobs.org}. Choose observations which are |
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66 | valid for the period of your test run because the observation operator compares |
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67 | the model and observations for a matching date and time. |
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68 | |
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69 | \item Add the following to the NEMO namelist to run the observation |
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70 | operator on this data. Set the \np{enactfiles} namelist parameter to the |
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71 | observation file name (or link in to \np{profiles\_01\.nc}): |
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72 | \end{enumerate} |
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73 | |
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74 | %------------------------------------------namobs_example----------------------------------------------------- |
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75 | \namdisplay{namobs_example} |
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76 | %------------------------------------------------------------------------------------------------------------- |
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77 | |
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78 | The option \np{ln\_t3d} and \np{ln\_s3d} switch on the temperature and salinity |
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79 | profile observation operator code. The \np{ln\_ena} switch turns on the reading |
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80 | of ENACT/ENSEMBLES type profile data. The filename or array of filenames are |
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81 | specified using the \np{enactfiles} variable. The model grid points for a |
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82 | particular observation latitude and longitude are found using the grid |
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83 | searching part of the code. This can be expensive, particularly for large |
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84 | numbers of observations, setting \np{ln\_grid\_search\_lookup} allows the use of |
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85 | a lookup table which is saved into an ``xypos`` file (or files). This will need |
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86 | to be generated the first time if it does not exist in the run directory. |
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87 | However, once produced it will significantly speed up future grid searches. |
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88 | Setting \np{ln\_grid\_global} means that the code distributes the observations |
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89 | evenly between processors. Alternatively each processor will work with |
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90 | observations located within the model subdomain. |
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91 | |
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92 | The NEMOVAR system contains utilities to plot the feedback files, convert and |
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93 | recombine the files. These are available on request from the NEMOVAR team. |
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94 | |
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95 | \section{Technical details} |
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96 | \label{OBS_details} |
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97 | |
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98 | Here we show a more complete example namelist and also show the NetCDF headers |
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99 | of the observation |
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100 | files that may be used with the observation operator |
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101 | |
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102 | %------------------------------------------namobs-------------------------------------------------------- |
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103 | \namdisplay{namobs} |
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104 | %------------------------------------------------------------------------------------------------------------- |
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105 | |
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106 | This name list uses the "feedback" type observation file input format for |
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107 | profile, sea level anomaly and sea surface temperature data. All the |
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108 | observation files must be in NetCDF format. Some example headers (produced using |
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109 | \mbox{\textit{ncdump~-h}}) for profile |
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110 | data, sea level anomaly and sea surface temperature are in the following |
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111 | subsections. |
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112 | |
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113 | \subsection{Profile feedback type observation file header} |
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114 | |
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115 | \begin{alltt} |
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116 | \tiny |
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117 | \begin{verbatim} |
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118 | netcdf profiles_01 { |
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119 | dimensions: |
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120 | N_OBS = 603 ; |
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121 | N_LEVELS = 150 ; |
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122 | N_VARS = 2 ; |
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123 | N_QCF = 2 ; |
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124 | N_ENTRIES = 1 ; |
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125 | N_EXTRA = 1 ; |
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126 | STRINGNAM = 8 ; |
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127 | STRINGGRID = 1 ; |
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128 | STRINGWMO = 8 ; |
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129 | STRINGTYP = 4 ; |
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130 | STRINGJULD = 14 ; |
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131 | variables: |
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132 | char VARIABLES(N_VARS, STRINGNAM) ; |
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133 | VARIABLES:long_name = "List of variables in feedback files" ; |
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134 | char ENTRIES(N_ENTRIES, STRINGNAM) ; |
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135 | ENTRIES:long_name = "List of additional entries for each variable in feedback files" ; |
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136 | char EXTRA(N_EXTRA, STRINGNAM) ; |
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137 | EXTRA:long_name = "List of extra variables" ; |
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138 | char STATION_IDENTIFIER(N_OBS, STRINGWMO) ; |
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139 | STATION_IDENTIFIER:long_name = "Station identifier" ; |
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140 | char STATION_TYPE(N_OBS, STRINGTYP) ; |
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141 | STATION_TYPE:long_name = "Code instrument type" ; |
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142 | double LONGITUDE(N_OBS) ; |
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143 | LONGITUDE:long_name = "Longitude" ; |
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144 | LONGITUDE:units = "degrees_east" ; |
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145 | LONGITUDE:_Fillvalue = 99999.f ; |
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146 | double LATITUDE(N_OBS) ; |
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147 | LATITUDE:long_name = "Latitude" ; |
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148 | LATITUDE:units = "degrees_north" ; |
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149 | LATITUDE:_Fillvalue = 99999.f ; |
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150 | double DEPTH(N_OBS, N_LEVELS) ; |
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151 | DEPTH:long_name = "Depth" ; |
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152 | DEPTH:units = "metre" ; |
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153 | DEPTH:_Fillvalue = 99999.f ; |
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154 | int DEPTH_QC(N_OBS, N_LEVELS) ; |
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155 | DEPTH_QC:long_name = "Quality on depth" ; |
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156 | DEPTH_QC:Conventions = "q where q =[0,9]" ; |
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157 | DEPTH_QC:_Fillvalue = 0 ; |
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158 | int DEPTH_QC_FLAGS(N_OBS, N_LEVELS, N_QCF) ; |
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159 | DEPTH_QC_FLAGS:long_name = "Quality flags on depth" ; |
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160 | DEPTH_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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161 | double JULD(N_OBS) ; |
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162 | JULD:long_name = "Julian day" ; |
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163 | JULD:units = "days since JULD_REFERENCE" ; |
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164 | JULD:Conventions = "relative julian days with decimal part (as parts of day)" ; |
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165 | JULD:_Fillvalue = 99999.f ; |
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166 | char JULD_REFERENCE(STRINGJULD) ; |
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167 | JULD_REFERENCE:long_name = "Date of reference for julian days" ; |
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168 | JULD_REFERENCE:Conventions = "YYYYMMDDHHMMSS" ; |
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169 | int OBSERVATION_QC(N_OBS) ; |
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170 | OBSERVATION_QC:long_name = "Quality on observation" ; |
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171 | OBSERVATION_QC:Conventions = "q where q =[0,9]" ; |
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172 | OBSERVATION_QC:_Fillvalue = 0 ; |
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173 | int OBSERVATION_QC_FLAGS(N_OBS, N_QCF) ; |
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174 | OBSERVATION_QC_FLAGS:long_name = "Quality flags on observation" ; |
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175 | OBSERVATION_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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176 | OBSERVATION_QC_FLAGS:_Fillvalue = 0 ; |
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177 | int POSITION_QC(N_OBS) ; |
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178 | POSITION_QC:long_name = "Quality on position (latitude and longitude)" ; |
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179 | POSITION_QC:Conventions = "q where q =[0,9]" ; |
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180 | POSITION_QC:_Fillvalue = 0 ; |
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181 | int POSITION_QC_FLAGS(N_OBS, N_QCF) ; |
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182 | POSITION_QC_FLAGS:long_name = "Quality flags on position" ; |
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183 | POSITION_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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184 | POSITION_QC_FLAGS:_Fillvalue = 0 ; |
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185 | int JULD_QC(N_OBS) ; |
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186 | JULD_QC:long_name = "Quality on date and time" ; |
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187 | JULD_QC:Conventions = "q where q =[0,9]" ; |
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188 | JULD_QC:_Fillvalue = 0 ; |
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189 | int JULD_QC_FLAGS(N_OBS, N_QCF) ; |
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190 | JULD_QC_FLAGS:long_name = "Quality flags on date and time" ; |
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191 | JULD_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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192 | JULD_QC_FLAGS:_Fillvalue = 0 ; |
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193 | int ORIGINAL_FILE_INDEX(N_OBS) ; |
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194 | ORIGINAL_FILE_INDEX:long_name = "Index in original data file" ; |
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195 | ORIGINAL_FILE_INDEX:_Fillvalue = -99999 ; |
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196 | float POTM_OBS(N_OBS, N_LEVELS) ; |
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197 | POTM_OBS:long_name = "Potential temperature" ; |
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198 | POTM_OBS:units = "Degrees Celsius" ; |
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199 | POTM_OBS:_Fillvalue = 99999.f ; |
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200 | float POTM_Hx(N_OBS, N_LEVELS) ; |
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201 | POTM_Hx:long_name = "Model interpolated potential temperature" ; |
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202 | POTM_Hx:units = "Degrees Celsius" ; |
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203 | POTM_Hx:_Fillvalue = 99999.f ; |
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204 | int POTM_QC(N_OBS) ; |
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205 | POTM_QC:long_name = "Quality on potential temperature" ; |
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206 | POTM_QC:Conventions = "q where q =[0,9]" ; |
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207 | POTM_QC:_Fillvalue = 0 ; |
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208 | int POTM_QC_FLAGS(N_OBS, N_QCF) ; |
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209 | POTM_QC_FLAGS:long_name = "Quality flags on potential temperature" ; |
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210 | POTM_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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211 | POTM_QC_FLAGS:_Fillvalue = 0 ; |
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212 | int POTM_LEVEL_QC(N_OBS, N_LEVELS) ; |
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213 | POTM_LEVEL_QC:long_name = "Quality for each level on potential temperature" ; |
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214 | POTM_LEVEL_QC:Conventions = "q where q =[0,9]" ; |
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215 | POTM_LEVEL_QC:_Fillvalue = 0 ; |
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216 | int POTM_LEVEL_QC_FLAGS(N_OBS, N_LEVELS, N_QCF) ; |
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217 | POTM_LEVEL_QC_FLAGS:long_name = "Quality flags for each level on potential temperature" ; |
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218 | POTM_LEVEL_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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219 | POTM_LEVEL_QC_FLAGS:_Fillvalue = 0 ; |
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220 | int POTM_IOBSI(N_OBS) ; |
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221 | POTM_IOBSI:long_name = "ORCA grid search I coordinate" ; |
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222 | int POTM_IOBSJ(N_OBS) ; |
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223 | POTM_IOBSJ:long_name = "ORCA grid search J coordinate" ; |
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224 | int POTM_IOBSK(N_OBS, N_LEVELS) ; |
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225 | POTM_IOBSK:long_name = "ORCA grid search K coordinate" ; |
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226 | char POTM_GRID(STRINGGRID) ; |
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227 | POTM_GRID:long_name = "ORCA grid search grid (T,U,V)" ; |
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228 | float PSAL_OBS(N_OBS, N_LEVELS) ; |
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229 | PSAL_OBS:long_name = "Practical salinity" ; |
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230 | PSAL_OBS:units = "PSU" ; |
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231 | PSAL_OBS:_Fillvalue = 99999.f ; |
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232 | float PSAL_Hx(N_OBS, N_LEVELS) ; |
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233 | PSAL_Hx:long_name = "Model interpolated practical salinity" ; |
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234 | PSAL_Hx:units = "PSU" ; |
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235 | PSAL_Hx:_Fillvalue = 99999.f ; |
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236 | int PSAL_QC(N_OBS) ; |
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237 | PSAL_QC:long_name = "Quality on practical salinity" ; |
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238 | PSAL_QC:Conventions = "q where q =[0,9]" ; |
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239 | PSAL_QC:_Fillvalue = 0 ; |
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240 | int PSAL_QC_FLAGS(N_OBS, N_QCF) ; |
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241 | PSAL_QC_FLAGS:long_name = "Quality flags on practical salinity" ; |
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242 | PSAL_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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243 | PSAL_QC_FLAGS:_Fillvalue = 0 ; |
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244 | int PSAL_LEVEL_QC(N_OBS, N_LEVELS) ; |
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245 | PSAL_LEVEL_QC:long_name = "Quality for each level on practical salinity" ; |
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246 | PSAL_LEVEL_QC:Conventions = "q where q =[0,9]" ; |
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247 | PSAL_LEVEL_QC:_Fillvalue = 0 ; |
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248 | int PSAL_LEVEL_QC_FLAGS(N_OBS, N_LEVELS, N_QCF) ; |
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249 | PSAL_LEVEL_QC_FLAGS:long_name = "Quality flags for each level on practical salinity" ; |
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250 | PSAL_LEVEL_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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251 | PSAL_LEVEL_QC_FLAGS:_Fillvalue = 0 ; |
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252 | int PSAL_IOBSI(N_OBS) ; |
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253 | PSAL_IOBSI:long_name = "ORCA grid search I coordinate" ; |
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254 | int PSAL_IOBSJ(N_OBS) ; |
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255 | PSAL_IOBSJ:long_name = "ORCA grid search J coordinate" ; |
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256 | int PSAL_IOBSK(N_OBS, N_LEVELS) ; |
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257 | PSAL_IOBSK:long_name = "ORCA grid search K coordinate" ; |
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258 | char PSAL_GRID(STRINGGRID) ; |
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259 | PSAL_GRID:long_name = "ORCA grid search grid (T,U,V)" ; |
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260 | float TEMP(N_OBS, N_LEVELS) ; |
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261 | TEMP:long_name = "Insitu temperature" ; |
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262 | TEMP:units = "Degrees Celsius" ; |
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263 | TEMP:_Fillvalue = 99999.f ; |
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264 | |
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265 | // global attributes: |
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266 | :title = "NEMO observation operator output" ; |
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267 | :Convention = "NEMO unified observation operator output" ; |
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268 | } |
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269 | \end{verbatim} |
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270 | \end{alltt} |
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271 | |
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272 | \subsection{Sea level anomaly feedback type observation file header} |
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273 | |
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274 | \begin{alltt} |
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275 | \tiny |
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276 | \begin{verbatim} |
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277 | netcdf sla_01 { |
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278 | dimensions: |
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279 | N_OBS = 41301 ; |
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280 | N_LEVELS = 1 ; |
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281 | N_VARS = 1 ; |
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282 | N_QCF = 2 ; |
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283 | N_ENTRIES = 1 ; |
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284 | N_EXTRA = 1 ; |
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285 | STRINGNAM = 8 ; |
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286 | STRINGGRID = 1 ; |
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287 | STRINGWMO = 8 ; |
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288 | STRINGTYP = 4 ; |
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289 | STRINGJULD = 14 ; |
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290 | variables: |
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291 | char VARIABLES(N_VARS, STRINGNAM) ; |
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292 | VARIABLES:long_name = "List of variables in feedback files" ; |
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293 | char ENTRIES(N_ENTRIES, STRINGNAM) ; |
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294 | ENTRIES:long_name = "List of additional entries for each variable in feedback files" ; |
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295 | char EXTRA(N_EXTRA, STRINGNAM) ; |
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296 | EXTRA:long_name = "List of extra variables" ; |
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297 | char STATION_IDENTIFIER(N_OBS, STRINGWMO) ; |
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298 | STATION_IDENTIFIER:long_name = "Station identifier" ; |
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299 | char STATION_TYPE(N_OBS, STRINGTYP) ; |
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300 | STATION_TYPE:long_name = "Code instrument type" ; |
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301 | double LONGITUDE(N_OBS) ; |
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302 | LONGITUDE:long_name = "Longitude" ; |
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303 | LONGITUDE:units = "degrees_east" ; |
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304 | LONGITUDE:_Fillvalue = 99999.f ; |
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305 | double LATITUDE(N_OBS) ; |
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306 | LATITUDE:long_name = "Latitude" ; |
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307 | LATITUDE:units = "degrees_north" ; |
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308 | LATITUDE:_Fillvalue = 99999.f ; |
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309 | double DEPTH(N_OBS, N_LEVELS) ; |
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310 | DEPTH:long_name = "Depth" ; |
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311 | DEPTH:units = "metre" ; |
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312 | DEPTH:_Fillvalue = 99999.f ; |
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313 | int DEPTH_QC(N_OBS, N_LEVELS) ; |
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314 | DEPTH_QC:long_name = "Quality on depth" ; |
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315 | DEPTH_QC:Conventions = "q where q =[0,9]" ; |
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316 | DEPTH_QC:_Fillvalue = 0 ; |
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317 | int DEPTH_QC_FLAGS(N_OBS, N_LEVELS, N_QCF) ; |
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318 | DEPTH_QC_FLAGS:long_name = "Quality flags on depth" ; |
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319 | DEPTH_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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320 | double JULD(N_OBS) ; |
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321 | JULD:long_name = "Julian day" ; |
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322 | JULD:units = "days since JULD_REFERENCE" ; |
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323 | JULD:Conventions = "relative julian days with decimal part (as parts of day)" ; |
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324 | JULD:_Fillvalue = 99999.f ; |
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325 | char JULD_REFERENCE(STRINGJULD) ; |
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326 | JULD_REFERENCE:long_name = "Date of reference for julian days" ; |
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327 | JULD_REFERENCE:Conventions = "YYYYMMDDHHMMSS" ; |
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328 | int OBSERVATION_QC(N_OBS) ; |
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329 | OBSERVATION_QC:long_name = "Quality on observation" ; |
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330 | OBSERVATION_QC:Conventions = "q where q =[0,9]" ; |
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331 | OBSERVATION_QC:_Fillvalue = 0 ; |
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332 | int OBSERVATION_QC_FLAGS(N_OBS, N_QCF) ; |
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333 | OBSERVATION_QC_FLAGS:long_name = "Quality flags on observation" ; |
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334 | OBSERVATION_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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335 | OBSERVATION_QC_FLAGS:_Fillvalue = 0 ; |
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336 | int POSITION_QC(N_OBS) ; |
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337 | POSITION_QC:long_name = "Quality on position (latitude and longitude)" ; |
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338 | POSITION_QC:Conventions = "q where q =[0,9]" ; |
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339 | POSITION_QC:_Fillvalue = 0 ; |
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340 | int POSITION_QC_FLAGS(N_OBS, N_QCF) ; |
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341 | POSITION_QC_FLAGS:long_name = "Quality flags on position" ; |
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342 | POSITION_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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343 | POSITION_QC_FLAGS:_Fillvalue = 0 ; |
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344 | int JULD_QC(N_OBS) ; |
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345 | JULD_QC:long_name = "Quality on date and time" ; |
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346 | JULD_QC:Conventions = "q where q =[0,9]" ; |
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347 | JULD_QC:_Fillvalue = 0 ; |
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348 | int JULD_QC_FLAGS(N_OBS, N_QCF) ; |
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349 | JULD_QC_FLAGS:long_name = "Quality flags on date and time" ; |
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350 | JULD_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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351 | JULD_QC_FLAGS:_Fillvalue = 0 ; |
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352 | int ORIGINAL_FILE_INDEX(N_OBS) ; |
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353 | ORIGINAL_FILE_INDEX:long_name = "Index in original data file" ; |
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354 | ORIGINAL_FILE_INDEX:_Fillvalue = -99999 ; |
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355 | float SLA_OBS(N_OBS, N_LEVELS) ; |
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356 | SLA_OBS:long_name = "Sea level anomaly" ; |
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357 | SLA_OBS:units = "metre" ; |
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358 | SLA_OBS:_Fillvalue = 99999.f ; |
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359 | float SLA_Hx(N_OBS, N_LEVELS) ; |
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360 | SLA_Hx:long_name = "Model interpolated sea level anomaly" ; |
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361 | SLA_Hx:units = "metre" ; |
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362 | SLA_Hx:_Fillvalue = 99999.f ; |
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363 | int SLA_QC(N_OBS) ; |
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364 | SLA_QC:long_name = "Quality on sea level anomaly" ; |
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365 | SLA_QC:Conventions = "q where q =[0,9]" ; |
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366 | SLA_QC:_Fillvalue = 0 ; |
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367 | int SLA_QC_FLAGS(N_OBS, N_QCF) ; |
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368 | SLA_QC_FLAGS:long_name = "Quality flags on sea level anomaly" ; |
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369 | SLA_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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370 | SLA_QC_FLAGS:_Fillvalue = 0 ; |
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371 | int SLA_LEVEL_QC(N_OBS, N_LEVELS) ; |
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372 | SLA_LEVEL_QC:long_name = "Quality for each level on sea level anomaly" ; |
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373 | SLA_LEVEL_QC:Conventions = "q where q =[0,9]" ; |
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374 | SLA_LEVEL_QC:_Fillvalue = 0 ; |
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375 | int SLA_LEVEL_QC_FLAGS(N_OBS, N_LEVELS, N_QCF) ; |
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376 | SLA_LEVEL_QC_FLAGS:long_name = "Quality flags for each level on sea level anomaly" ; |
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377 | SLA_LEVEL_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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378 | SLA_LEVEL_QC_FLAGS:_Fillvalue = 0 ; |
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379 | int SLA_IOBSI(N_OBS) ; |
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380 | SLA_IOBSI:long_name = "ORCA grid search I coordinate" ; |
---|
381 | int SLA_IOBSJ(N_OBS) ; |
---|
382 | SLA_IOBSJ:long_name = "ORCA grid search J coordinate" ; |
---|
383 | int SLA_IOBSK(N_OBS, N_LEVELS) ; |
---|
384 | SLA_IOBSK:long_name = "ORCA grid search K coordinate" ; |
---|
385 | char SLA_GRID(STRINGGRID) ; |
---|
386 | SLA_GRID:long_name = "ORCA grid search grid (T,U,V)" ; |
---|
387 | float MDT(N_OBS, N_LEVELS) ; |
---|
388 | MDT:long_name = "Mean Dynamic Topography" ; |
---|
389 | MDT:units = "metre" ; |
---|
390 | MDT:_Fillvalue = 99999.f ; |
---|
391 | |
---|
392 | // global attributes: |
---|
393 | :title = "NEMO observation operator output" ; |
---|
394 | :Convention = "NEMO unified observation operator output" ; |
---|
395 | } |
---|
396 | \end{verbatim} |
---|
397 | \end{alltt} |
---|
398 | |
---|
399 | The mean dynamic |
---|
400 | topography (MDT) must be provided in a separate file defined on the model grid |
---|
401 | called {\it slaReferenceLevel.nc}. The MDT is required in |
---|
402 | order to produce the model equivalent sea level anomaly from the model sea |
---|
403 | surface height. Below is an example header for this file (on the ORCA025 grid). |
---|
404 | |
---|
405 | \begin{alltt} |
---|
406 | \tiny |
---|
407 | \begin{verbatim} |
---|
408 | dimensions: |
---|
409 | x = 1442 ; |
---|
410 | y = 1021 ; |
---|
411 | variables: |
---|
412 | float nav_lon(y, x) ; |
---|
413 | nav_lon:units = "degrees_east" ; |
---|
414 | float nav_lat(y, x) ; |
---|
415 | nav_lat:units = "degrees_north" ; |
---|
416 | float sossheig(y, x) ; |
---|
417 | sossheig:_FillValue = -1.e+30f ; |
---|
418 | sossheig:coordinates = "nav_lon nav_lat" ; |
---|
419 | sossheig:long_name = "Mean Dynamic Topography" ; |
---|
420 | sossheig:units = "metres" ; |
---|
421 | sossheig:grid = "orca025T" ; |
---|
422 | \end{verbatim} |
---|
423 | \end{alltt} |
---|
424 | |
---|
425 | \subsection{Sea surface temperature feedback type observation file header} |
---|
426 | |
---|
427 | \begin{alltt} |
---|
428 | \tiny |
---|
429 | \begin{verbatim} |
---|
430 | netcdf sst_01 { |
---|
431 | dimensions: |
---|
432 | N_OBS = 33099 ; |
---|
433 | N_LEVELS = 1 ; |
---|
434 | N_VARS = 1 ; |
---|
435 | N_QCF = 2 ; |
---|
436 | N_ENTRIES = 1 ; |
---|
437 | STRINGNAM = 8 ; |
---|
438 | STRINGGRID = 1 ; |
---|
439 | STRINGWMO = 8 ; |
---|
440 | STRINGTYP = 4 ; |
---|
441 | STRINGJULD = 14 ; |
---|
442 | variables: |
---|
443 | char VARIABLES(N_VARS, STRINGNAM) ; |
---|
444 | VARIABLES:long_name = "List of variables in feedback files" ; |
---|
445 | char ENTRIES(N_ENTRIES, STRINGNAM) ; |
---|
446 | ENTRIES:long_name = "List of additional entries for each variable in feedback files" ; |
---|
447 | char STATION_IDENTIFIER(N_OBS, STRINGWMO) ; |
---|
448 | STATION_IDENTIFIER:long_name = "Station identifier" ; |
---|
449 | char STATION_TYPE(N_OBS, STRINGTYP) ; |
---|
450 | STATION_TYPE:long_name = "Code instrument type" ; |
---|
451 | double LONGITUDE(N_OBS) ; |
---|
452 | LONGITUDE:long_name = "Longitude" ; |
---|
453 | LONGITUDE:units = "degrees_east" ; |
---|
454 | LONGITUDE:_Fillvalue = 99999.f ; |
---|
455 | double LATITUDE(N_OBS) ; |
---|
456 | LATITUDE:long_name = "Latitude" ; |
---|
457 | LATITUDE:units = "degrees_north" ; |
---|
458 | LATITUDE:_Fillvalue = 99999.f ; |
---|
459 | double DEPTH(N_OBS, N_LEVELS) ; |
---|
460 | DEPTH:long_name = "Depth" ; |
---|
461 | DEPTH:units = "metre" ; |
---|
462 | DEPTH:_Fillvalue = 99999.f ; |
---|
463 | int DEPTH_QC(N_OBS, N_LEVELS) ; |
---|
464 | DEPTH_QC:long_name = "Quality on depth" ; |
---|
465 | DEPTH_QC:Conventions = "q where q =[0,9]" ; |
---|
466 | DEPTH_QC:_Fillvalue = 0 ; |
---|
467 | int DEPTH_QC_FLAGS(N_OBS, N_LEVELS, N_QCF) ; |
---|
468 | DEPTH_QC_FLAGS:long_name = "Quality flags on depth" ; |
---|
469 | DEPTH_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
---|
470 | double JULD(N_OBS) ; |
---|
471 | JULD:long_name = "Julian day" ; |
---|
472 | JULD:units = "days since JULD_REFERENCE" ; |
---|
473 | JULD:Conventions = "relative julian days with decimal part (as parts of day)" ; |
---|
474 | JULD:_Fillvalue = 99999.f ; |
---|
475 | char JULD_REFERENCE(STRINGJULD) ; |
---|
476 | JULD_REFERENCE:long_name = "Date of reference for julian days" ; |
---|
477 | JULD_REFERENCE:Conventions = "YYYYMMDDHHMMSS" ; |
---|
478 | int OBSERVATION_QC(N_OBS) ; |
---|
479 | OBSERVATION_QC:long_name = "Quality on observation" ; |
---|
480 | OBSERVATION_QC:Conventions = "q where q =[0,9]" ; |
---|
481 | OBSERVATION_QC:_Fillvalue = 0 ; |
---|
482 | int OBSERVATION_QC_FLAGS(N_OBS, N_QCF) ; |
---|
483 | OBSERVATION_QC_FLAGS:long_name = "Quality flags on observation" ; |
---|
484 | OBSERVATION_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
---|
485 | OBSERVATION_QC_FLAGS:_Fillvalue = 0 ; |
---|
486 | int POSITION_QC(N_OBS) ; |
---|
487 | POSITION_QC:long_name = "Quality on position (latitude and longitude)" ; |
---|
488 | POSITION_QC:Conventions = "q where q =[0,9]" ; |
---|
489 | POSITION_QC:_Fillvalue = 0 ; |
---|
490 | int POSITION_QC_FLAGS(N_OBS, N_QCF) ; |
---|
491 | POSITION_QC_FLAGS:long_name = "Quality flags on position" ; |
---|
492 | POSITION_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
---|
493 | POSITION_QC_FLAGS:_Fillvalue = 0 ; |
---|
494 | int JULD_QC(N_OBS) ; |
---|
495 | JULD_QC:long_name = "Quality on date and time" ; |
---|
496 | JULD_QC:Conventions = "q where q =[0,9]" ; |
---|
497 | JULD_QC:_Fillvalue = 0 ; |
---|
498 | int JULD_QC_FLAGS(N_OBS, N_QCF) ; |
---|
499 | JULD_QC_FLAGS:long_name = "Quality flags on date and time" ; |
---|
500 | JULD_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
---|
501 | JULD_QC_FLAGS:_Fillvalue = 0 ; |
---|
502 | int ORIGINAL_FILE_INDEX(N_OBS) ; |
---|
503 | ORIGINAL_FILE_INDEX:long_name = "Index in original data file" ; |
---|
504 | ORIGINAL_FILE_INDEX:_Fillvalue = -99999 ; |
---|
505 | float SST_OBS(N_OBS, N_LEVELS) ; |
---|
506 | SST_OBS:long_name = "Sea surface temperature" ; |
---|
507 | SST_OBS:units = "Degree centigrade" ; |
---|
508 | SST_OBS:_Fillvalue = 99999.f ; |
---|
509 | float SST_Hx(N_OBS, N_LEVELS) ; |
---|
510 | SST_Hx:long_name = "Model interpolated sea surface temperature" ; |
---|
511 | SST_Hx:units = "Degree centigrade" ; |
---|
512 | SST_Hx:_Fillvalue = 99999.f ; |
---|
513 | int SST_QC(N_OBS) ; |
---|
514 | SST_QC:long_name = "Quality on sea surface temperature" ; |
---|
515 | SST_QC:Conventions = "q where q =[0,9]" ; |
---|
516 | SST_QC:_Fillvalue = 0 ; |
---|
517 | int SST_QC_FLAGS(N_OBS, N_QCF) ; |
---|
518 | SST_QC_FLAGS:long_name = "Quality flags on sea surface temperature" ; |
---|
519 | SST_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
---|
520 | SST_QC_FLAGS:_Fillvalue = 0 ; |
---|
521 | int SST_LEVEL_QC(N_OBS, N_LEVELS) ; |
---|
522 | SST_LEVEL_QC:long_name = "Quality for each level on sea surface temperature" ; |
---|
523 | SST_LEVEL_QC:Conventions = "q where q =[0,9]" ; |
---|
524 | SST_LEVEL_QC:_Fillvalue = 0 ; |
---|
525 | int SST_LEVEL_QC_FLAGS(N_OBS, N_LEVELS, N_QCF) ; |
---|
526 | SST_LEVEL_QC_FLAGS:long_name = "Quality flags for each level on sea surface temperature" ; |
---|
527 | SST_LEVEL_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
---|
528 | SST_LEVEL_QC_FLAGS:_Fillvalue = 0 ; |
---|
529 | int SST_IOBSI(N_OBS) ; |
---|
530 | SST_IOBSI:long_name = "ORCA grid search I coordinate" ; |
---|
531 | int SST_IOBSJ(N_OBS) ; |
---|
532 | SST_IOBSJ:long_name = "ORCA grid search J coordinate" ; |
---|
533 | int SST_IOBSK(N_OBS, N_LEVELS) ; |
---|
534 | SST_IOBSK:long_name = "ORCA grid search K coordinate" ; |
---|
535 | char SST_GRID(STRINGGRID) ; |
---|
536 | SST_GRID:long_name = "ORCA grid search grid (T,U,V)" ; |
---|
537 | |
---|
538 | // global attributes: |
---|
539 | :title = "NEMO observation operator output" ; |
---|
540 | :Convention = "NEMO unified observation operator output" ; |
---|
541 | } |
---|
542 | \end{verbatim} |
---|
543 | \end{alltt} |
---|
544 | |
---|
545 | \section{Theoretical details} |
---|
546 | \label{OBS_theory} |
---|
547 | |
---|
548 | \subsection{Horizontal interpolation methods} |
---|
549 | |
---|
550 | Consider an observation point ${\rm P}$ with |
---|
551 | with longitude and latitude $({\lambda_{}}_{\rm P}, \phi_{\rm P})$ and the |
---|
552 | four nearest neighbouring model grid points ${\rm A}$, ${\rm B}$, ${\rm C}$ |
---|
553 | and ${\rm D}$ with longitude and latitude ($\lambda_{\rm A}$, $\phi_{\rm A}$), |
---|
554 | ($\lambda_{\rm B}$, $\phi_{\rm B}$) etc. |
---|
555 | All horizontal interpolation methods implemented in NEMO |
---|
556 | estimate the value of a model variable $x$ at point $P$ as |
---|
557 | a weighted linear combination of the values of the model |
---|
558 | variables at the grid points ${\rm A}$, ${\rm B}$ etc.: |
---|
559 | \begin{eqnarray} |
---|
560 | {x_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & |
---|
561 | \frac{1}{w} \left( {w_{}}_{\rm A} {x_{}}_{\rm A} + |
---|
562 | {w_{}}_{\rm B} {x_{}}_{\rm B} + |
---|
563 | {w_{}}_{\rm C} {x_{}}_{\rm C} + |
---|
564 | {w_{}}_{\rm D} {x_{}}_{\rm D} \right) |
---|
565 | \end{eqnarray} |
---|
566 | where ${w_{}}_{\rm A}$, ${w_{}}_{\rm B}$ etc. are the respective weights for the |
---|
567 | model field at points ${\rm A}$, ${\rm B}$ etc., and |
---|
568 | $w = {w_{}}_{\rm A} + {w_{}}_{\rm B} + {w_{}}_{\rm C} + {w_{}}_{\rm D}$. |
---|
569 | |
---|
570 | Four different possibilities are available for computing the weights. |
---|
571 | |
---|
572 | \begin{enumerate} |
---|
573 | |
---|
574 | \item[1.] {\bf Great-Circle distance-weighted interpolation.} The weights |
---|
575 | are computed as a function of the great-circle distance $s(P, \cdot)$ |
---|
576 | between $P$ and the model grid points $A$, $B$ etc. For example, |
---|
577 | the weight given to the field ${x_{}}_{\rm A}$ is specified as the |
---|
578 | product of the distances from ${\rm P}$ to the other points: |
---|
579 | \begin{eqnarray} |
---|
580 | {w_{}}_{\rm A} = s({\rm P}, {\rm B}) \, s({\rm P}, {\rm C}) \, s({\rm P}, {\rm D}) |
---|
581 | \nonumber |
---|
582 | \end{eqnarray} |
---|
583 | where |
---|
584 | \begin{eqnarray} |
---|
585 | s\left ({\rm P}, {\rm M} \right ) |
---|
586 | & \hspace{-2mm} = \hspace{-2mm} & |
---|
587 | \cos^{-1} \! \left\{ |
---|
588 | \sin {\phi_{}}_{\rm P} \sin {\phi_{}}_{\rm M} |
---|
589 | + \cos {\phi_{}}_{\rm P} \cos {\phi_{}}_{\rm M} |
---|
590 | \cos ({\lambda_{}}_{\rm M} - {\lambda_{}}_{\rm P}) |
---|
591 | \right\} |
---|
592 | \end{eqnarray} |
---|
593 | and $M$ corresponds to $B$, $C$ or $D$. |
---|
594 | A more stable form of the great-circle distance formula for |
---|
595 | small distances ($x$ near 1) involves the arcsine function |
---|
596 | ($e.g.$ see p.~101 of \citet{Daley_Barker_Bk01}: |
---|
597 | \begin{eqnarray} |
---|
598 | s\left( {\rm P}, {\rm M} \right) |
---|
599 | & \hspace{-2mm} = \hspace{-2mm} & |
---|
600 | \sin^{-1} \! \left\{ \sqrt{ 1 - x^2 } \right\} |
---|
601 | \nonumber |
---|
602 | \end{eqnarray} |
---|
603 | where |
---|
604 | \begin{eqnarray} |
---|
605 | x & \hspace{-2mm} = \hspace{-2mm} & |
---|
606 | {a_{}}_{\rm M} {a_{}}_{\rm P} + {b_{}}_{\rm M} {b_{}}_{\rm P} + {c_{}}_{\rm M} {c_{}}_{\rm P} |
---|
607 | \nonumber |
---|
608 | \end{eqnarray} |
---|
609 | and |
---|
610 | \begin{eqnarray} |
---|
611 | {a_{}}_{\rm M} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\rm M}, |
---|
612 | \nonumber \\ |
---|
613 | {a_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\rm P}, |
---|
614 | \nonumber \\ |
---|
615 | {b_{}}_{\rm M} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm M} \cos {\phi_{}}_{\rm M}, |
---|
616 | \nonumber \\ |
---|
617 | {b_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm P} \cos {\phi_{}}_{\rm P}, |
---|
618 | \nonumber \\ |
---|
619 | {c_{}}_{\rm M} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm M} \sin {\phi_{}}_{\rm M}, |
---|
620 | \nonumber \\ |
---|
621 | {c_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm P} \sin {\phi_{}}_{\rm P}. |
---|
622 | \nonumber |
---|
623 | \nonumber |
---|
624 | \end{eqnarray} |
---|
625 | |
---|
626 | \item[2.] {\bf Great-Circle distance-weighted interpolation with small angle |
---|
627 | approximation.} Similar to the previous interpolation but with the |
---|
628 | distance $s$ computed as |
---|
629 | \begin{eqnarray} |
---|
630 | s\left( {\rm P}, {\rm M} \right) |
---|
631 | & \hspace{-2mm} = \hspace{-2mm} & |
---|
632 | \sqrt{ \left( {\phi_{}}_{\rm M} - {\phi_{}}_{\rm P} \right)^{2} |
---|
633 | + \left( {\lambda_{}}_{\rm M} - {\lambda_{}}_{\rm P} \right)^{2} |
---|
634 | \cos^{2} {\phi_{}}_{\rm M} } |
---|
635 | \end{eqnarray} |
---|
636 | where $M$ corresponds to $A$, $B$, $C$ or $D$. |
---|
637 | |
---|
638 | \item[3.] {\bf Bilinear interpolation for a regular spaced grid.} The |
---|
639 | interpolation is split into two 1D interpolations in the longitude |
---|
640 | and latitude directions, respectively. |
---|
641 | |
---|
642 | \item[4.] {\bf Bilinear remapping interpolation for a general grid.} An |
---|
643 | iterative scheme that involves first mapping a quadrilateral cell |
---|
644 | into a cell with coordinates (0,0), (1,0), (0,1) and (1,1). This |
---|
645 | method is based on the SCRIP interpolation package \citep{Jones_1998}. |
---|
646 | |
---|
647 | \end{enumerate} |
---|
648 | |
---|
649 | \subsection{Grid search} |
---|
650 | |
---|
651 | For many grids used by the NEMO model, such as the ORCA family, |
---|
652 | the horizontal grid coordinates $i$ and $j$ are not simple functions |
---|
653 | of latitude and longitude. Therefore, it is not always straightforward |
---|
654 | to determine the grid points surrounding any given observational position. |
---|
655 | Before the interpolation can be performed, a search |
---|
656 | algorithm is then required to determine the corner points of |
---|
657 | the quadrilateral cell in which the observation is located. |
---|
658 | This is the most difficult and time consuming part of the |
---|
659 | 2D interpolation procedure. |
---|
660 | A robust test for determining if an observation falls |
---|
661 | within a given quadrilateral cell is as follows. Let |
---|
662 | ${\rm P}({\lambda_{}}_{\rm P} ,{\phi_{}}_{\rm P} )$ denote the observation point, |
---|
663 | and let ${\rm A}({\lambda_{}}_{\rm A} ,{\phi_{}}_{\rm A} )$, |
---|
664 | ${\rm B}({\lambda_{}}_{\rm B} ,{\phi_{}}_{\rm B} )$, |
---|
665 | ${\rm C}({\lambda_{}}_{\rm C} ,{\phi_{}}_{\rm C} )$ |
---|
666 | and |
---|
667 | ${\rm D}({\lambda_{}}_{\rm D} ,{\phi_{}}_{\rm D} )$ denote |
---|
668 | the bottom left, bottom right, top left and top right |
---|
669 | corner points of the cell, respectively. |
---|
670 | To determine if P is inside |
---|
671 | the cell, we verify that the cross-products |
---|
672 | \begin{eqnarray} |
---|
673 | \begin{array}{lllll} |
---|
674 | {{\bf r}_{}}_{\rm PA} \times {{\bf r}_{}}_{\rm PC} |
---|
675 | & = & [({\lambda_{}}_{\rm A}\; -\; {\lambda_{}}_{\rm P} ) |
---|
676 | ({\phi_{}}_{\rm C} \; -\; {\phi_{}}_{\rm P} ) |
---|
677 | - ({\lambda_{}}_{\rm C}\; -\; {\lambda_{}}_{\rm P} ) |
---|
678 | ({\phi_{}}_{\rm A} \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\ |
---|
679 | {{\bf r}_{}}_{\rm PB} \times {{\bf r}_{}}_{\rm PA} |
---|
680 | & = & [({\lambda_{}}_{\rm B}\; -\; {\lambda_{}}_{\rm P} ) |
---|
681 | ({\phi_{}}_{\rm A} \; -\; {\phi_{}}_{\rm P} ) |
---|
682 | - ({\lambda_{}}_{\rm A}\; -\; {\lambda_{}}_{\rm P} ) |
---|
683 | ({\phi_{}}_{\rm B} \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\ |
---|
684 | {{\bf r}_{}}_{\rm PC} \times {{\bf r}_{}}_{\rm PD} |
---|
685 | & = & [({\lambda_{}}_{\rm C}\; -\; {\lambda_{}}_{\rm P} ) |
---|
686 | ({\phi_{}}_{\rm D} \; -\; {\phi_{}}_{\rm P} ) |
---|
687 | - ({\lambda_{}}_{\rm D}\; -\; {\lambda_{}}_{\rm P} ) |
---|
688 | ({\phi_{}}_{\rm C} \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\ |
---|
689 | {{\bf r}_{}}_{\rm PD} \times {{\bf r}_{}}_{\rm PB} |
---|
690 | & = & [({\lambda_{}}_{\rm D}\; -\; {\lambda_{}}_{\rm P} ) |
---|
691 | ({\phi_{}}_{\rm B} \; -\; {\phi_{}}_{\rm P} ) |
---|
692 | - ({\lambda_{}}_{\rm B}\; -\; {\lambda_{}}_{\rm P} ) |
---|
693 | ({\phi_{}}_{\rm D} \; - \; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\ |
---|
694 | \end{array} |
---|
695 | \label{eq:cross} |
---|
696 | \end{eqnarray} |
---|
697 | point in the opposite direction to the unit normal |
---|
698 | $\widehat{\bf k}$ (i.e., that the coefficients of |
---|
699 | $\widehat{\bf k}$ are negative), |
---|
700 | where ${{\bf r}_{}}_{\rm PA}$, ${{\bf r}_{}}_{\rm PB}$, |
---|
701 | etc. correspond to the vectors between points P and A, |
---|
702 | P and B, etc.. The method used is |
---|
703 | similar to the method used in |
---|
704 | the SCRIP interpolation package \citep{Jones_1998}. |
---|
705 | |
---|
706 | In order to speed up the grid search, there is the possibility to construct |
---|
707 | a lookup table for a user specified resolution. This lookup |
---|
708 | table contains the lower and upper bounds on the $i$ and $j$ indices |
---|
709 | to be searched for on a regular grid. For each observation position, |
---|
710 | the closest point on the regular grid of this position is computed and |
---|
711 | the $i$ and $j$ ranges of this point searched to determine the precise |
---|
712 | four points surrounding the observation. |
---|
713 | |
---|
714 | \subsection{Parallel aspects of horizontal interpolation} |
---|
715 | |
---|
716 | For horizontal interpolation, there is the basic problem that the |
---|
717 | observations are unevenly distributed on the globe. In numerical |
---|
718 | models, it is common to divide the model grid into subgrids (or |
---|
719 | domains) where each subgrid is executed on a single processing element |
---|
720 | with explicit message passing for exchange of information along the |
---|
721 | domain boundaries when running on a massively parallel processor (MPP) |
---|
722 | system. This approach is used by \NEMO. |
---|
723 | |
---|
724 | For observations there is no natural distribution since the |
---|
725 | observations are not equally distributed on the globe. |
---|
726 | Two options have been made available: 1) geographical distribution; |
---|
727 | and 2) round-robin. |
---|
728 | |
---|
729 | \subsubsection{Geographical distribution of observations among processors} |
---|
730 | |
---|
731 | %>>>>>>>>>>>>>>>>>>>>>>>>>>>> |
---|
732 | \begin{figure} \begin{center} |
---|
733 | \includegraphics[width=10cm,height=12cm,angle=-90.]{./TexFiles/Figures/Fig_ASM_obsdist_local} |
---|
734 | \caption{ \label{fig:obslocal} |
---|
735 | Example of the distribution of observations with the geographical distribution of observational data.} |
---|
736 | \end{center} \end{figure} |
---|
737 | %>>>>>>>>>>>>>>>>>>>>>>>>>>>> |
---|
738 | |
---|
739 | This is the simplest option in which the observations are distributed according |
---|
740 | to the domain of the grid-point parallelization. Figure~\ref{fig:obslocal} |
---|
741 | shows an example of the distribution of the {\em in situ} data on processors |
---|
742 | with a different colour for each observation |
---|
743 | on a given processor for a 4 $\times$ 2 decomposition with ORCA2. |
---|
744 | The grid-point domain decomposition is clearly visible on the plot. |
---|
745 | |
---|
746 | The advantage of this approach is that all |
---|
747 | information needed for horizontal interpolation is available without |
---|
748 | any MPP communication. Of course, this is under the assumption that |
---|
749 | we are only using a $2 \times 2$ grid-point stencil for the interpolation |
---|
750 | (e.g., bilinear interpolation). For higher order interpolation schemes this |
---|
751 | is no longer valid. A disadvantage with the above scheme is that the number of |
---|
752 | observations on each processor can be very different. If the cost of |
---|
753 | the actual interpolation is expensive relative to the communication of |
---|
754 | data needed for interpolation, this could lead to load imbalance. |
---|
755 | |
---|
756 | \subsubsection{Round-robin distribution of observations among processors} |
---|
757 | |
---|
758 | %>>>>>>>>>>>>>>>>>>>>>>>>>>>> |
---|
759 | \begin{figure} \begin{center} |
---|
760 | \includegraphics[width=10cm,height=12cm,angle=-90.]{./TexFiles/Figures/Fig_ASM_obsdist_global} |
---|
761 | \caption{ \label{fig:obsglobal} |
---|
762 | Example of the distribution of observations with the round-robin distribution of observational data.} |
---|
763 | \end{center} \end{figure} |
---|
764 | %>>>>>>>>>>>>>>>>>>>>>>>>>>>> |
---|
765 | |
---|
766 | An alternative approach is to distribute the observations equally |
---|
767 | among processors and use message passing in order to retrieve |
---|
768 | the stencil for interpolation. The simplest distribution of the observations |
---|
769 | is to distribute them using a round-robin scheme. Figure~\ref{fig:obsglobal} |
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770 | shows the distribution of the {\em in situ} data on processors for the |
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771 | round-robin distribution of observations with a different colour for |
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772 | each observation on a given processor for a 4 $\times$ 2 decomposition |
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773 | with ORCA2 for the same input data as in Fig.~\ref{fig:obslocal}. |
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774 | The observations are now clearly randomly distributed on the globe. |
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775 | In order to be able to perform horizontal interpolation in this case, |
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776 | a subroutine has been developed that retrieves any grid points in the |
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777 | global space. |
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778 | |
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779 | \subsection{Vertical interpolation operator} |
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780 | |
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781 | The vertical interpolation is achieved using either a cubic spline or |
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782 | linear interpolation. For the cubic spline, the top and |
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783 | bottom boundary conditions for the second derivative of the |
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784 | interpolating polynomial in the spline are set to zero. |
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785 | At the bottom boundary, this is done using the land-ocean mask. |
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