[2298] | 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, K. Mogensen, A. Weaver, M. Martin ... % 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 OBS branch is a diagnostic branch which reads in observation files (profile temperature and |
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[2349] | 16 | salinity, sea surface temperature, sea level anomaly and sea ice concentration) and calculates |
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[2298] | 17 | an interpolated model equivalent value at the observation location and nearest model timestep. |
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| 18 | This is code with was originally developed for use with NEMOVAR. |
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| 19 | |
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| 20 | In the case of temperature data from moored buoys (TAO, TRITON, PIRATA) which in the |
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| 21 | ENACT/ENSEMBLES data-base are available as daily averaged quantities the observation operator |
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| 22 | averages the model temperature fields over one day before interpolating them to the observation |
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| 23 | location. For SST and altimeter observations, a 2D horizontal interpolator is needed. For {\em in |
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| 24 | situ} profiles, a 1D vertical interpolator is needed in addition to the 2D interpolator. |
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| 25 | |
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| 26 | The resulting data is saved in a ``feedback'' file or files which can be used for model validation |
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| 27 | and verification and also to provide information for data assimilation. This code is controlled by |
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[2349] | 28 | the namelist \textit{nam\_obs}. To build with the OBS code active \key{diaobs} must be set. |
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[2298] | 29 | |
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| 30 | There is a brief description of all the namelist options provided. |
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| 31 | |
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[2349] | 32 | Missing information: description of \key{sp}, \key{datetime\_out} |
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[2298] | 33 | |
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[2349] | 34 | |
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[2298] | 35 | % ================================================================ |
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| 36 | % Example |
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| 37 | % ================================================================ |
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| 38 | \section{Running the observation operator code example} |
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| 39 | \label{OBS_example} |
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| 40 | |
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| 41 | This section describes an example of running the observation operator code using |
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| 42 | profile data which can be freely downloaded. This shows how to adapt an existing |
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| 43 | run and build of NEMO to run the observation operator. |
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| 44 | |
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[2349] | 45 | First compile NEMO with \key{diaobs} set. |
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[2298] | 46 | |
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[2414] | 47 | Next download some ENSEMBLES EN3 data from the \href{http://www.hadobs.org}{website}. |
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[2298] | 48 | You should choose observations which are valid for the period of your test run |
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| 49 | because the observation operator compares the model and observations for a |
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| 50 | matching date and time. |
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| 51 | |
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| 52 | You will need to add the following to the namelist to run the observation |
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[2349] | 53 | operator on this data - set the \np{enactfiles} namelist parameter to the observation |
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| 54 | file name you wish to use (or link in): |
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[2298] | 55 | |
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| 56 | %------------------------------------------namobs_example----------------------------------------------------- |
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| 57 | \namdisplay{namobs_example} |
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| 58 | %------------------------------------------------------------------------------------------------------------- |
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| 59 | |
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| 60 | The option \np{ln\_t3d} and \np{ln\_s3d} switch on the temperature and salinity profile |
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| 61 | observation operator code. \np{ln\_ena} switch turns on the reading on ENACT/ENSEMBLES type |
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| 62 | profile data. The filename of the ENACT/ENSEMBLES data is set with enactfiles. Not this can be |
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| 63 | array of multiple files. The observation operator code needs to convert from observation |
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| 64 | latitude and longitude to model grid point. This is done using the grid searching part of the |
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| 65 | code. Setting \np{ln\_grid\_global} means that the code distributes the observations evenly |
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| 66 | between processors in a round-robin. Alternatively each processor will work with observations |
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| 67 | located within the model subdomain. The grid searching can be expensive, particularly for large |
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| 68 | numbers of observations, setting \np{ln\_grid\_search\_lookup} allows the use of a lookup |
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| 69 | table. This will need to generated the first time if it does not exist in the run directory |
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| 70 | however once produced it will significantly speed up future grid searches. |
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| 71 | |
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| 72 | The next step is viewing and working with the data. The NEMOVAR system contains utilities to |
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| 73 | plot the feedback files, convert and recombine the files which are available on request from |
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| 74 | the NEMOVAR team. |
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| 75 | |
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| 76 | \section{Technical details} |
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| 77 | \label{OBS_details} |
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| 78 | |
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| 79 | Here we show a more complete example namelist and also describe the observation files that may |
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| 80 | be used with the observation operator |
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| 81 | |
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| 82 | %------------------------------------------namobs-------------------------------------------------------- |
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| 83 | \namdisplay{namobs} |
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| 84 | %------------------------------------------------------------------------------------------------------------- |
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| 85 | |
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| 86 | This name list uses the "feedback" type observation file input format for profile, sea level |
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| 87 | anomaly and sea surface temperature data |
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| 88 | |
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| 89 | \subsection{Profile feedback type observation file header} |
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| 90 | |
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| 91 | \begin{alltt} |
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| 92 | \tiny |
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| 93 | \begin{verbatim} |
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| 94 | netcdf profiles_01 { |
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| 95 | dimensions: |
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| 96 | N_OBS = 603 ; |
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| 97 | N_LEVELS = 150 ; |
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| 98 | N_VARS = 2 ; |
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| 99 | N_QCF = 2 ; |
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| 100 | N_ENTRIES = 1 ; |
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| 101 | N_EXTRA = 1 ; |
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| 102 | STRINGNAM = 8 ; |
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| 103 | STRINGGRID = 1 ; |
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| 104 | STRINGWMO = 8 ; |
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| 105 | STRINGTYP = 4 ; |
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| 106 | STRINGJULD = 14 ; |
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| 107 | variables: |
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| 108 | char VARIABLES(N_VARS, STRINGNAM) ; |
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| 109 | VARIABLES:long_name = "List of variables in feedback files" ; |
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| 110 | char ENTRIES(N_ENTRIES, STRINGNAM) ; |
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| 111 | ENTRIES:long_name = "List of additional entries for each variable in feedback files" ; |
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| 112 | char EXTRA(N_EXTRA, STRINGNAM) ; |
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| 113 | EXTRA:long_name = "List of extra variables" ; |
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| 114 | char STATION_IDENTIFIER(N_OBS, STRINGWMO) ; |
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| 115 | STATION_IDENTIFIER:long_name = "Station identifier" ; |
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| 116 | char STATION_TYPE(N_OBS, STRINGTYP) ; |
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| 117 | STATION_TYPE:long_name = "Code instrument type" ; |
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| 118 | double LONGITUDE(N_OBS) ; |
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| 119 | LONGITUDE:long_name = "Longitude" ; |
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| 120 | LONGITUDE:units = "degrees_east" ; |
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| 121 | LONGITUDE:_Fillvalue = 99999.f ; |
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| 122 | double LATITUDE(N_OBS) ; |
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| 123 | LATITUDE:long_name = "Latitude" ; |
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| 124 | LATITUDE:units = "degrees_north" ; |
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| 125 | LATITUDE:_Fillvalue = 99999.f ; |
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| 126 | double DEPTH(N_OBS, N_LEVELS) ; |
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| 127 | DEPTH:long_name = "Depth" ; |
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| 128 | DEPTH:units = "metre" ; |
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| 129 | DEPTH:_Fillvalue = 99999.f ; |
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| 130 | int DEPTH_QC(N_OBS, N_LEVELS) ; |
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| 131 | DEPTH_QC:long_name = "Quality on depth" ; |
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| 132 | DEPTH_QC:Conventions = "q where q =[0,9]" ; |
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| 133 | DEPTH_QC:_Fillvalue = 0 ; |
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| 134 | int DEPTH_QC_FLAGS(N_OBS, N_LEVELS, N_QCF) ; |
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| 135 | DEPTH_QC_FLAGS:long_name = "Quality flags on depth" ; |
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| 136 | DEPTH_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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| 137 | double JULD(N_OBS) ; |
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| 138 | JULD:long_name = "Julian day" ; |
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| 139 | JULD:units = "days since JULD_REFERENCE" ; |
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| 140 | JULD:Conventions = "relative julian days with decimal part (as parts of day)" ; |
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| 141 | JULD:_Fillvalue = 99999.f ; |
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| 142 | char JULD_REFERENCE(STRINGJULD) ; |
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| 143 | JULD_REFERENCE:long_name = "Date of reference for julian days" ; |
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| 144 | JULD_REFERENCE:Conventions = "YYYYMMDDHHMMSS" ; |
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| 145 | int OBSERVATION_QC(N_OBS) ; |
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| 146 | OBSERVATION_QC:long_name = "Quality on observation" ; |
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| 147 | OBSERVATION_QC:Conventions = "q where q =[0,9]" ; |
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| 148 | OBSERVATION_QC:_Fillvalue = 0 ; |
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| 149 | int OBSERVATION_QC_FLAGS(N_OBS, N_QCF) ; |
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| 150 | OBSERVATION_QC_FLAGS:long_name = "Quality flags on observation" ; |
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| 151 | OBSERVATION_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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| 152 | OBSERVATION_QC_FLAGS:_Fillvalue = 0 ; |
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| 153 | int POSITION_QC(N_OBS) ; |
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| 154 | POSITION_QC:long_name = "Quality on position (latitude and longitude)" ; |
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| 155 | POSITION_QC:Conventions = "q where q =[0,9]" ; |
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| 156 | POSITION_QC:_Fillvalue = 0 ; |
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| 157 | int POSITION_QC_FLAGS(N_OBS, N_QCF) ; |
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| 158 | POSITION_QC_FLAGS:long_name = "Quality flags on position" ; |
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| 159 | POSITION_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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| 160 | POSITION_QC_FLAGS:_Fillvalue = 0 ; |
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| 161 | int JULD_QC(N_OBS) ; |
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| 162 | JULD_QC:long_name = "Quality on date and time" ; |
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| 163 | JULD_QC:Conventions = "q where q =[0,9]" ; |
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| 164 | JULD_QC:_Fillvalue = 0 ; |
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| 165 | int JULD_QC_FLAGS(N_OBS, N_QCF) ; |
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| 166 | JULD_QC_FLAGS:long_name = "Quality flags on date and time" ; |
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| 167 | JULD_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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| 168 | JULD_QC_FLAGS:_Fillvalue = 0 ; |
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| 169 | int ORIGINAL_FILE_INDEX(N_OBS) ; |
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| 170 | ORIGINAL_FILE_INDEX:long_name = "Index in original data file" ; |
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| 171 | ORIGINAL_FILE_INDEX:_Fillvalue = -99999 ; |
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| 172 | float POTM_OBS(N_OBS, N_LEVELS) ; |
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| 173 | POTM_OBS:long_name = "Potential temperature" ; |
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| 174 | POTM_OBS:units = "Degrees Celsius" ; |
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| 175 | POTM_OBS:_Fillvalue = 99999.f ; |
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| 176 | float POTM_Hx(N_OBS, N_LEVELS) ; |
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| 177 | POTM_Hx:long_name = "Model interpolated potential temperature" ; |
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| 178 | POTM_Hx:units = "Degrees Celsius" ; |
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| 179 | POTM_Hx:_Fillvalue = 99999.f ; |
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| 180 | int POTM_QC(N_OBS) ; |
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| 181 | POTM_QC:long_name = "Quality on potential temperature" ; |
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| 182 | POTM_QC:Conventions = "q where q =[0,9]" ; |
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| 183 | POTM_QC:_Fillvalue = 0 ; |
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| 184 | int POTM_QC_FLAGS(N_OBS, N_QCF) ; |
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| 185 | POTM_QC_FLAGS:long_name = "Quality flags on potential temperature" ; |
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| 186 | POTM_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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| 187 | POTM_QC_FLAGS:_Fillvalue = 0 ; |
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| 188 | int POTM_LEVEL_QC(N_OBS, N_LEVELS) ; |
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| 189 | POTM_LEVEL_QC:long_name = "Quality for each level on potential temperature" ; |
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| 190 | POTM_LEVEL_QC:Conventions = "q where q =[0,9]" ; |
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| 191 | POTM_LEVEL_QC:_Fillvalue = 0 ; |
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| 192 | int POTM_LEVEL_QC_FLAGS(N_OBS, N_LEVELS, N_QCF) ; |
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| 193 | POTM_LEVEL_QC_FLAGS:long_name = "Quality flags for each level on potential temperature" ; |
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| 194 | POTM_LEVEL_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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| 195 | POTM_LEVEL_QC_FLAGS:_Fillvalue = 0 ; |
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| 196 | int POTM_IOBSI(N_OBS) ; |
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| 197 | POTM_IOBSI:long_name = "ORCA grid search I coordinate" ; |
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| 198 | int POTM_IOBSJ(N_OBS) ; |
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| 199 | POTM_IOBSJ:long_name = "ORCA grid search J coordinate" ; |
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| 200 | int POTM_IOBSK(N_OBS, N_LEVELS) ; |
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| 201 | POTM_IOBSK:long_name = "ORCA grid search K coordinate" ; |
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| 202 | char POTM_GRID(STRINGGRID) ; |
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| 203 | POTM_GRID:long_name = "ORCA grid search grid (T,U,V)" ; |
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| 204 | float PSAL_OBS(N_OBS, N_LEVELS) ; |
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| 205 | PSAL_OBS:long_name = "Practical salinity" ; |
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| 206 | PSAL_OBS:units = "PSU" ; |
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| 207 | PSAL_OBS:_Fillvalue = 99999.f ; |
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| 208 | float PSAL_Hx(N_OBS, N_LEVELS) ; |
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| 209 | PSAL_Hx:long_name = "Model interpolated practical salinity" ; |
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| 210 | PSAL_Hx:units = "PSU" ; |
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| 211 | PSAL_Hx:_Fillvalue = 99999.f ; |
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| 212 | int PSAL_QC(N_OBS) ; |
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| 213 | PSAL_QC:long_name = "Quality on practical salinity" ; |
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| 214 | PSAL_QC:Conventions = "q where q =[0,9]" ; |
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| 215 | PSAL_QC:_Fillvalue = 0 ; |
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| 216 | int PSAL_QC_FLAGS(N_OBS, N_QCF) ; |
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| 217 | PSAL_QC_FLAGS:long_name = "Quality flags on practical salinity" ; |
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| 218 | PSAL_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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| 219 | PSAL_QC_FLAGS:_Fillvalue = 0 ; |
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| 220 | int PSAL_LEVEL_QC(N_OBS, N_LEVELS) ; |
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| 221 | PSAL_LEVEL_QC:long_name = "Quality for each level on practical salinity" ; |
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| 222 | PSAL_LEVEL_QC:Conventions = "q where q =[0,9]" ; |
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| 223 | PSAL_LEVEL_QC:_Fillvalue = 0 ; |
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| 224 | int PSAL_LEVEL_QC_FLAGS(N_OBS, N_LEVELS, N_QCF) ; |
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| 225 | PSAL_LEVEL_QC_FLAGS:long_name = "Quality flags for each level on practical salinity" ; |
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| 226 | PSAL_LEVEL_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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| 227 | PSAL_LEVEL_QC_FLAGS:_Fillvalue = 0 ; |
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| 228 | int PSAL_IOBSI(N_OBS) ; |
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| 229 | PSAL_IOBSI:long_name = "ORCA grid search I coordinate" ; |
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| 230 | int PSAL_IOBSJ(N_OBS) ; |
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| 231 | PSAL_IOBSJ:long_name = "ORCA grid search J coordinate" ; |
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| 232 | int PSAL_IOBSK(N_OBS, N_LEVELS) ; |
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| 233 | PSAL_IOBSK:long_name = "ORCA grid search K coordinate" ; |
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| 234 | char PSAL_GRID(STRINGGRID) ; |
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| 235 | PSAL_GRID:long_name = "ORCA grid search grid (T,U,V)" ; |
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| 236 | float TEMP(N_OBS, N_LEVELS) ; |
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| 237 | TEMP:long_name = "Insitu temperature" ; |
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| 238 | TEMP:units = "Degrees Celsius" ; |
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| 239 | TEMP:_Fillvalue = 99999.f ; |
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| 240 | |
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| 241 | // global attributes: |
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| 242 | :title = "NEMO observation operator output" ; |
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| 243 | :Convention = "NEMO unified observation operator output" ; |
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| 244 | } |
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| 245 | \end{verbatim} |
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| 246 | \end{alltt} |
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| 247 | |
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| 248 | \subsection{Sea level anomaly feedback type observation file header} |
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| 249 | |
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| 250 | \begin{alltt} |
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| 251 | \tiny |
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| 252 | \begin{verbatim} |
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| 253 | netcdf sla_01 { |
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| 254 | dimensions: |
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| 255 | N_OBS = 41301 ; |
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| 256 | N_LEVELS = 1 ; |
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| 257 | N_VARS = 1 ; |
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| 258 | N_QCF = 2 ; |
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| 259 | N_ENTRIES = 1 ; |
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| 260 | N_EXTRA = 1 ; |
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| 261 | STRINGNAM = 8 ; |
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| 262 | STRINGGRID = 1 ; |
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| 263 | STRINGWMO = 8 ; |
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| 264 | STRINGTYP = 4 ; |
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| 265 | STRINGJULD = 14 ; |
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| 266 | variables: |
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| 267 | char VARIABLES(N_VARS, STRINGNAM) ; |
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| 268 | VARIABLES:long_name = "List of variables in feedback files" ; |
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| 269 | char ENTRIES(N_ENTRIES, STRINGNAM) ; |
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| 270 | ENTRIES:long_name = "List of additional entries for each variable in feedback files" ; |
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| 271 | char EXTRA(N_EXTRA, STRINGNAM) ; |
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| 272 | EXTRA:long_name = "List of extra variables" ; |
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| 273 | char STATION_IDENTIFIER(N_OBS, STRINGWMO) ; |
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| 274 | STATION_IDENTIFIER:long_name = "Station identifier" ; |
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| 275 | char STATION_TYPE(N_OBS, STRINGTYP) ; |
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| 276 | STATION_TYPE:long_name = "Code instrument type" ; |
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| 277 | double LONGITUDE(N_OBS) ; |
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| 278 | LONGITUDE:long_name = "Longitude" ; |
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| 279 | LONGITUDE:units = "degrees_east" ; |
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| 280 | LONGITUDE:_Fillvalue = 99999.f ; |
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| 281 | double LATITUDE(N_OBS) ; |
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| 282 | LATITUDE:long_name = "Latitude" ; |
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| 283 | LATITUDE:units = "degrees_north" ; |
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| 284 | LATITUDE:_Fillvalue = 99999.f ; |
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| 285 | double DEPTH(N_OBS, N_LEVELS) ; |
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| 286 | DEPTH:long_name = "Depth" ; |
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| 287 | DEPTH:units = "metre" ; |
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| 288 | DEPTH:_Fillvalue = 99999.f ; |
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| 289 | int DEPTH_QC(N_OBS, N_LEVELS) ; |
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| 290 | DEPTH_QC:long_name = "Quality on depth" ; |
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| 291 | DEPTH_QC:Conventions = "q where q =[0,9]" ; |
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| 292 | DEPTH_QC:_Fillvalue = 0 ; |
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| 293 | int DEPTH_QC_FLAGS(N_OBS, N_LEVELS, N_QCF) ; |
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| 294 | DEPTH_QC_FLAGS:long_name = "Quality flags on depth" ; |
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| 295 | DEPTH_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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| 296 | double JULD(N_OBS) ; |
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| 297 | JULD:long_name = "Julian day" ; |
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| 298 | JULD:units = "days since JULD_REFERENCE" ; |
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| 299 | JULD:Conventions = "relative julian days with decimal part (as parts of day)" ; |
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| 300 | JULD:_Fillvalue = 99999.f ; |
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| 301 | char JULD_REFERENCE(STRINGJULD) ; |
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| 302 | JULD_REFERENCE:long_name = "Date of reference for julian days" ; |
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| 303 | JULD_REFERENCE:Conventions = "YYYYMMDDHHMMSS" ; |
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| 304 | int OBSERVATION_QC(N_OBS) ; |
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| 305 | OBSERVATION_QC:long_name = "Quality on observation" ; |
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| 306 | OBSERVATION_QC:Conventions = "q where q =[0,9]" ; |
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| 307 | OBSERVATION_QC:_Fillvalue = 0 ; |
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| 308 | int OBSERVATION_QC_FLAGS(N_OBS, N_QCF) ; |
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| 309 | OBSERVATION_QC_FLAGS:long_name = "Quality flags on observation" ; |
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| 310 | OBSERVATION_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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| 311 | OBSERVATION_QC_FLAGS:_Fillvalue = 0 ; |
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| 312 | int POSITION_QC(N_OBS) ; |
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| 313 | POSITION_QC:long_name = "Quality on position (latitude and longitude)" ; |
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| 314 | POSITION_QC:Conventions = "q where q =[0,9]" ; |
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| 315 | POSITION_QC:_Fillvalue = 0 ; |
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| 316 | int POSITION_QC_FLAGS(N_OBS, N_QCF) ; |
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| 317 | POSITION_QC_FLAGS:long_name = "Quality flags on position" ; |
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| 318 | POSITION_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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| 319 | POSITION_QC_FLAGS:_Fillvalue = 0 ; |
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| 320 | int JULD_QC(N_OBS) ; |
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| 321 | JULD_QC:long_name = "Quality on date and time" ; |
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| 322 | JULD_QC:Conventions = "q where q =[0,9]" ; |
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| 323 | JULD_QC:_Fillvalue = 0 ; |
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| 324 | int JULD_QC_FLAGS(N_OBS, N_QCF) ; |
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| 325 | JULD_QC_FLAGS:long_name = "Quality flags on date and time" ; |
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| 326 | JULD_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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| 327 | JULD_QC_FLAGS:_Fillvalue = 0 ; |
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| 328 | int ORIGINAL_FILE_INDEX(N_OBS) ; |
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| 329 | ORIGINAL_FILE_INDEX:long_name = "Index in original data file" ; |
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| 330 | ORIGINAL_FILE_INDEX:_Fillvalue = -99999 ; |
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| 331 | float SLA_OBS(N_OBS, N_LEVELS) ; |
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| 332 | SLA_OBS:long_name = "Sea level anomaly" ; |
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| 333 | SLA_OBS:units = "metre" ; |
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| 334 | SLA_OBS:_Fillvalue = 99999.f ; |
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| 335 | float SLA_Hx(N_OBS, N_LEVELS) ; |
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| 336 | SLA_Hx:long_name = "Model interpolated sea level anomaly" ; |
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| 337 | SLA_Hx:units = "metre" ; |
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| 338 | SLA_Hx:_Fillvalue = 99999.f ; |
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| 339 | int SLA_QC(N_OBS) ; |
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| 340 | SLA_QC:long_name = "Quality on sea level anomaly" ; |
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| 341 | SLA_QC:Conventions = "q where q =[0,9]" ; |
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| 342 | SLA_QC:_Fillvalue = 0 ; |
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| 343 | int SLA_QC_FLAGS(N_OBS, N_QCF) ; |
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| 344 | SLA_QC_FLAGS:long_name = "Quality flags on sea level anomaly" ; |
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| 345 | SLA_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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| 346 | SLA_QC_FLAGS:_Fillvalue = 0 ; |
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| 347 | int SLA_LEVEL_QC(N_OBS, N_LEVELS) ; |
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| 348 | SLA_LEVEL_QC:long_name = "Quality for each level on sea level anomaly" ; |
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| 349 | SLA_LEVEL_QC:Conventions = "q where q =[0,9]" ; |
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| 350 | SLA_LEVEL_QC:_Fillvalue = 0 ; |
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| 351 | int SLA_LEVEL_QC_FLAGS(N_OBS, N_LEVELS, N_QCF) ; |
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| 352 | SLA_LEVEL_QC_FLAGS:long_name = "Quality flags for each level on sea level anomaly" ; |
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| 353 | SLA_LEVEL_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
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| 354 | SLA_LEVEL_QC_FLAGS:_Fillvalue = 0 ; |
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| 355 | int SLA_IOBSI(N_OBS) ; |
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| 356 | SLA_IOBSI:long_name = "ORCA grid search I coordinate" ; |
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| 357 | int SLA_IOBSJ(N_OBS) ; |
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| 358 | SLA_IOBSJ:long_name = "ORCA grid search J coordinate" ; |
---|
| 359 | int SLA_IOBSK(N_OBS, N_LEVELS) ; |
---|
| 360 | SLA_IOBSK:long_name = "ORCA grid search K coordinate" ; |
---|
| 361 | char SLA_GRID(STRINGGRID) ; |
---|
| 362 | SLA_GRID:long_name = "ORCA grid search grid (T,U,V)" ; |
---|
| 363 | float MDT(N_OBS, N_LEVELS) ; |
---|
| 364 | MDT:long_name = "Mean Dynamic Topography" ; |
---|
| 365 | MDT:units = "metre" ; |
---|
| 366 | MDT:_Fillvalue = 99999.f ; |
---|
| 367 | |
---|
| 368 | // global attributes: |
---|
| 369 | :title = "NEMO observation operator output" ; |
---|
| 370 | :Convention = "NEMO unified observation operator output" ; |
---|
| 371 | } |
---|
| 372 | \end{verbatim} |
---|
| 373 | \end{alltt} |
---|
| 374 | |
---|
| 375 | \subsection{Sea surface temperature feedback type observation file header} |
---|
| 376 | |
---|
| 377 | \begin{alltt} |
---|
| 378 | \tiny |
---|
| 379 | \begin{verbatim} |
---|
| 380 | netcdf sst_01 { |
---|
| 381 | dimensions: |
---|
| 382 | N_OBS = 33099 ; |
---|
| 383 | N_LEVELS = 1 ; |
---|
| 384 | N_VARS = 1 ; |
---|
| 385 | N_QCF = 2 ; |
---|
| 386 | N_ENTRIES = 1 ; |
---|
| 387 | STRINGNAM = 8 ; |
---|
| 388 | STRINGGRID = 1 ; |
---|
| 389 | STRINGWMO = 8 ; |
---|
| 390 | STRINGTYP = 4 ; |
---|
| 391 | STRINGJULD = 14 ; |
---|
| 392 | variables: |
---|
| 393 | char VARIABLES(N_VARS, STRINGNAM) ; |
---|
| 394 | VARIABLES:long_name = "List of variables in feedback files" ; |
---|
| 395 | char ENTRIES(N_ENTRIES, STRINGNAM) ; |
---|
| 396 | ENTRIES:long_name = "List of additional entries for each variable in feedback files" ; |
---|
| 397 | char STATION_IDENTIFIER(N_OBS, STRINGWMO) ; |
---|
| 398 | STATION_IDENTIFIER:long_name = "Station identifier" ; |
---|
| 399 | char STATION_TYPE(N_OBS, STRINGTYP) ; |
---|
| 400 | STATION_TYPE:long_name = "Code instrument type" ; |
---|
| 401 | double LONGITUDE(N_OBS) ; |
---|
| 402 | LONGITUDE:long_name = "Longitude" ; |
---|
| 403 | LONGITUDE:units = "degrees_east" ; |
---|
| 404 | LONGITUDE:_Fillvalue = 99999.f ; |
---|
| 405 | double LATITUDE(N_OBS) ; |
---|
| 406 | LATITUDE:long_name = "Latitude" ; |
---|
| 407 | LATITUDE:units = "degrees_north" ; |
---|
| 408 | LATITUDE:_Fillvalue = 99999.f ; |
---|
| 409 | double DEPTH(N_OBS, N_LEVELS) ; |
---|
| 410 | DEPTH:long_name = "Depth" ; |
---|
| 411 | DEPTH:units = "metre" ; |
---|
| 412 | DEPTH:_Fillvalue = 99999.f ; |
---|
| 413 | int DEPTH_QC(N_OBS, N_LEVELS) ; |
---|
| 414 | DEPTH_QC:long_name = "Quality on depth" ; |
---|
| 415 | DEPTH_QC:Conventions = "q where q =[0,9]" ; |
---|
| 416 | DEPTH_QC:_Fillvalue = 0 ; |
---|
| 417 | int DEPTH_QC_FLAGS(N_OBS, N_LEVELS, N_QCF) ; |
---|
| 418 | DEPTH_QC_FLAGS:long_name = "Quality flags on depth" ; |
---|
| 419 | DEPTH_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
---|
| 420 | double JULD(N_OBS) ; |
---|
| 421 | JULD:long_name = "Julian day" ; |
---|
| 422 | JULD:units = "days since JULD_REFERENCE" ; |
---|
| 423 | JULD:Conventions = "relative julian days with decimal part (as parts of day)" ; |
---|
| 424 | JULD:_Fillvalue = 99999.f ; |
---|
| 425 | char JULD_REFERENCE(STRINGJULD) ; |
---|
| 426 | JULD_REFERENCE:long_name = "Date of reference for julian days" ; |
---|
| 427 | JULD_REFERENCE:Conventions = "YYYYMMDDHHMMSS" ; |
---|
| 428 | int OBSERVATION_QC(N_OBS) ; |
---|
| 429 | OBSERVATION_QC:long_name = "Quality on observation" ; |
---|
| 430 | OBSERVATION_QC:Conventions = "q where q =[0,9]" ; |
---|
| 431 | OBSERVATION_QC:_Fillvalue = 0 ; |
---|
| 432 | int OBSERVATION_QC_FLAGS(N_OBS, N_QCF) ; |
---|
| 433 | OBSERVATION_QC_FLAGS:long_name = "Quality flags on observation" ; |
---|
| 434 | OBSERVATION_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
---|
| 435 | OBSERVATION_QC_FLAGS:_Fillvalue = 0 ; |
---|
| 436 | int POSITION_QC(N_OBS) ; |
---|
| 437 | POSITION_QC:long_name = "Quality on position (latitude and longitude)" ; |
---|
| 438 | POSITION_QC:Conventions = "q where q =[0,9]" ; |
---|
| 439 | POSITION_QC:_Fillvalue = 0 ; |
---|
| 440 | int POSITION_QC_FLAGS(N_OBS, N_QCF) ; |
---|
| 441 | POSITION_QC_FLAGS:long_name = "Quality flags on position" ; |
---|
| 442 | POSITION_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
---|
| 443 | POSITION_QC_FLAGS:_Fillvalue = 0 ; |
---|
| 444 | int JULD_QC(N_OBS) ; |
---|
| 445 | JULD_QC:long_name = "Quality on date and time" ; |
---|
| 446 | JULD_QC:Conventions = "q where q =[0,9]" ; |
---|
| 447 | JULD_QC:_Fillvalue = 0 ; |
---|
| 448 | int JULD_QC_FLAGS(N_OBS, N_QCF) ; |
---|
| 449 | JULD_QC_FLAGS:long_name = "Quality flags on date and time" ; |
---|
| 450 | JULD_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
---|
| 451 | JULD_QC_FLAGS:_Fillvalue = 0 ; |
---|
| 452 | int ORIGINAL_FILE_INDEX(N_OBS) ; |
---|
| 453 | ORIGINAL_FILE_INDEX:long_name = "Index in original data file" ; |
---|
| 454 | ORIGINAL_FILE_INDEX:_Fillvalue = -99999 ; |
---|
| 455 | float SST_OBS(N_OBS, N_LEVELS) ; |
---|
| 456 | SST_OBS:long_name = "Sea surface temperature" ; |
---|
| 457 | SST_OBS:units = "Degree centigrade" ; |
---|
| 458 | SST_OBS:_Fillvalue = 99999.f ; |
---|
| 459 | float SST_Hx(N_OBS, N_LEVELS) ; |
---|
| 460 | SST_Hx:long_name = "Model interpolated sea surface temperature" ; |
---|
| 461 | SST_Hx:units = "Degree centigrade" ; |
---|
| 462 | SST_Hx:_Fillvalue = 99999.f ; |
---|
| 463 | int SST_QC(N_OBS) ; |
---|
| 464 | SST_QC:long_name = "Quality on sea surface temperature" ; |
---|
| 465 | SST_QC:Conventions = "q where q =[0,9]" ; |
---|
| 466 | SST_QC:_Fillvalue = 0 ; |
---|
| 467 | int SST_QC_FLAGS(N_OBS, N_QCF) ; |
---|
| 468 | SST_QC_FLAGS:long_name = "Quality flags on sea surface temperature" ; |
---|
| 469 | SST_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
---|
| 470 | SST_QC_FLAGS:_Fillvalue = 0 ; |
---|
| 471 | int SST_LEVEL_QC(N_OBS, N_LEVELS) ; |
---|
| 472 | SST_LEVEL_QC:long_name = "Quality for each level on sea surface temperature" ; |
---|
| 473 | SST_LEVEL_QC:Conventions = "q where q =[0,9]" ; |
---|
| 474 | SST_LEVEL_QC:_Fillvalue = 0 ; |
---|
| 475 | int SST_LEVEL_QC_FLAGS(N_OBS, N_LEVELS, N_QCF) ; |
---|
| 476 | SST_LEVEL_QC_FLAGS:long_name = "Quality flags for each level on sea surface temperature" ; |
---|
| 477 | SST_LEVEL_QC_FLAGS:Conventions = "NEMOVAR flag conventions" ; |
---|
| 478 | SST_LEVEL_QC_FLAGS:_Fillvalue = 0 ; |
---|
| 479 | int SST_IOBSI(N_OBS) ; |
---|
| 480 | SST_IOBSI:long_name = "ORCA grid search I coordinate" ; |
---|
| 481 | int SST_IOBSJ(N_OBS) ; |
---|
| 482 | SST_IOBSJ:long_name = "ORCA grid search J coordinate" ; |
---|
| 483 | int SST_IOBSK(N_OBS, N_LEVELS) ; |
---|
| 484 | SST_IOBSK:long_name = "ORCA grid search K coordinate" ; |
---|
| 485 | char SST_GRID(STRINGGRID) ; |
---|
| 486 | SST_GRID:long_name = "ORCA grid search grid (T,U,V)" ; |
---|
| 487 | |
---|
| 488 | // global attributes: |
---|
| 489 | :title = "NEMO observation operator output" ; |
---|
| 490 | :Convention = "NEMO unified observation operator output" ; |
---|
| 491 | } |
---|
| 492 | \end{verbatim} |
---|
| 493 | \end{alltt} |
---|
| 494 | |
---|
| 495 | \section{Theoretical details} |
---|
| 496 | |
---|
| 497 | \subsection{Horizontal interpolation methods} |
---|
| 498 | |
---|
| 499 | Consider an observation point ${\rm P}$ with |
---|
| 500 | with longitude and latitude $({\lambda_{}}_{\rm P}, \phi_{\rm P})$ and the |
---|
| 501 | four nearest neighbouring model grid points ${\rm A}$, ${\rm B}$, ${\rm C}$ |
---|
| 502 | and ${\rm D}$ with longitude and latitude ($\lambda_{\rm A}$, $\phi_{\rm A}$), |
---|
| 503 | ($\lambda_{\rm B}$, $\phi_{\rm B}$) etc. |
---|
| 504 | All horizontal interpolation methods implemented in NEMO |
---|
| 505 | estimate the value of a model variable $x$ at point $P$ as |
---|
| 506 | a weighted linear combination of the values of the model |
---|
| 507 | variables at the grid points ${\rm A}$, ${\rm B}$ etc.: |
---|
| 508 | \begin{eqnarray} |
---|
| 509 | {x_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & |
---|
| 510 | \frac{1}{w} \left( {w_{}}_{\rm A} {x_{}}_{\rm A} + |
---|
| 511 | {w_{}}_{\rm B} {x_{}}_{\rm B} + |
---|
| 512 | {w_{}}_{\rm C} {x_{}}_{\rm C} + |
---|
| 513 | {w_{}}_{\rm D} {x_{}}_{\rm D} \right) |
---|
| 514 | \end{eqnarray} |
---|
| 515 | where ${w_{}}_{\rm A}$, ${w_{}}_{\rm B}$ etc. are the respective weights for the |
---|
| 516 | model field at points ${\rm A}$, ${\rm B}$ etc., and |
---|
| 517 | $w = {w_{}}_{\rm A} + {w_{}}_{\rm B} + {w_{}}_{\rm C} + {w_{}}_{\rm D}$. |
---|
| 518 | |
---|
| 519 | Four different possibilities are available for computing the weights. |
---|
| 520 | |
---|
| 521 | \begin{enumerate} |
---|
| 522 | |
---|
| 523 | \item[1.] {\bf Great-Circle distance-weighted interpolation.} The weights |
---|
| 524 | are computed as a function of the great-circle distance $s(P, \cdot)$ |
---|
| 525 | between $P$ and the model grid points $A$, $B$ etc. For example, |
---|
| 526 | the weight given to the field ${x_{}}_{\rm A}$ is specified as the |
---|
| 527 | product of the distances from ${\rm P}$ to the other points: |
---|
| 528 | \begin{eqnarray} |
---|
| 529 | {w_{}}_{\rm A} = s({\rm P}, {\rm B}) \, s({\rm P}, {\rm C}) \, s({\rm P}, {\rm D}) |
---|
| 530 | \nonumber |
---|
| 531 | \end{eqnarray} |
---|
| 532 | where |
---|
| 533 | \begin{eqnarray} |
---|
| 534 | s\left ({\rm P}, {\rm M} \right ) |
---|
| 535 | & \hspace{-2mm} = \hspace{-2mm} & |
---|
| 536 | \cos^{-1} \! \left\{ |
---|
| 537 | \sin {\phi_{}}_{\rm P} \sin {\phi_{}}_{\rm M} |
---|
| 538 | + \cos {\phi_{}}_{\rm P} \cos {\phi_{}}_{\rm M} |
---|
| 539 | \cos ({\lambda_{}}_{\rm M} - {\lambda_{}}_{\rm P}) |
---|
| 540 | \right\} |
---|
| 541 | \end{eqnarray} |
---|
| 542 | and $M$ corresponds to $B$, $C$ or $D$. |
---|
| 543 | A more stable form of the great-circle distance formula for |
---|
| 544 | small distances ($x$ near 1) involves the arcsine function |
---|
| 545 | ($e.g.$ see p.~101 of \citet{Daley_Barker_Bk01}: |
---|
| 546 | \begin{eqnarray} |
---|
| 547 | s\left( {\rm P}, {\rm M} \right) |
---|
| 548 | & \hspace{-2mm} = \hspace{-2mm} & |
---|
| 549 | \sin^{-1} \! \left\{ \sqrt{ 1 - x^2 } \right\} |
---|
| 550 | \nonumber |
---|
| 551 | \end{eqnarray} |
---|
| 552 | where |
---|
| 553 | \begin{eqnarray} |
---|
| 554 | x & \hspace{-2mm} = \hspace{-2mm} & |
---|
| 555 | {a_{}}_{\rm M} {a_{}}_{\rm P} + {b_{}}_{\rm M} {b_{}}_{\rm P} + {c_{}}_{\rm M} {c_{}}_{\rm P} |
---|
| 556 | \nonumber |
---|
| 557 | \end{eqnarray} |
---|
| 558 | and |
---|
| 559 | \begin{eqnarray} |
---|
| 560 | {a_{}}_{\rm M} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\rm M}, |
---|
| 561 | \nonumber \\ |
---|
| 562 | {a_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\rm P}, |
---|
| 563 | \nonumber \\ |
---|
| 564 | {b_{}}_{\rm M} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm M} \cos {\phi_{}}_{\rm M}, |
---|
| 565 | \nonumber \\ |
---|
| 566 | {b_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm P} \cos {\phi_{}}_{\rm P}, |
---|
| 567 | \nonumber \\ |
---|
| 568 | {c_{}}_{\rm M} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm M} \sin {\phi_{}}_{\rm M}, |
---|
| 569 | \nonumber \\ |
---|
| 570 | {c_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm P} \sin {\phi_{}}_{\rm P}. |
---|
| 571 | \nonumber |
---|
| 572 | \nonumber |
---|
| 573 | \end{eqnarray} |
---|
| 574 | |
---|
| 575 | \item[2.] {\bf Great-Circle distance-weighted interpolation with small angle |
---|
| 576 | approximation.} Similar to the previous interpolation but with the |
---|
| 577 | distance $s$ computed as |
---|
| 578 | \begin{eqnarray} |
---|
| 579 | s\left( {\rm P}, {\rm M} \right) |
---|
| 580 | & \hspace{-2mm} = \hspace{-2mm} & |
---|
| 581 | \sqrt{ \left( {\phi_{}}_{\rm M} - {\phi_{}}_{\rm P} \right)^{2} |
---|
| 582 | + \left( {\lambda_{}}_{\rm M} - {\lambda_{}}_{\rm P} \right)^{2} |
---|
| 583 | \cos^{2} {\phi_{}}_{\rm M} } |
---|
| 584 | \end{eqnarray} |
---|
| 585 | where $M$ corresponds to $A$, $B$, $C$ or $D$. |
---|
| 586 | |
---|
| 587 | \item[3.] {\bf Bilinear interpolation for a regular spaced grid.} The |
---|
| 588 | interpolation is split into two 1D interpolations in the longitude |
---|
| 589 | and latitude directions, respectively. |
---|
| 590 | |
---|
| 591 | \item[4.] {\bf Bilinear remapping interpolation for a general grid.} An |
---|
| 592 | iterative scheme that involves first mapping a quadrilateral cell |
---|
| 593 | into a cell with coordinates (0,0), (1,0), (0,1) and (1,1). This |
---|
| 594 | method is based on the SCRIP interpolation package \citep{Jones_MWR99,Jones_Bk01}. |
---|
| 595 | |
---|
| 596 | \end{enumerate} |
---|
| 597 | |
---|
| 598 | \subsection{Grid search} |
---|
| 599 | |
---|
| 600 | For many grids used by the NEMO model, such as the ORCA family, |
---|
| 601 | the horizontal grid coordinates $i$ and $j$ are not simple functions |
---|
| 602 | of latitude and longitude. Therefore, it is not always straightforward |
---|
| 603 | to determine the grid points surrounding any given observational position. |
---|
| 604 | Before the interpolation can be performed, a search |
---|
| 605 | algorithm is then required to determine the corner points of |
---|
| 606 | the quadrilateral cell in which the observation is located. |
---|
| 607 | This is the most difficult and time consuming part of the |
---|
| 608 | 2D interpolation procedure. |
---|
| 609 | A robust test for determining if an observation falls |
---|
| 610 | within a given quadrilateral cell is as follows. Let |
---|
| 611 | ${\rm P}({\lambda_{}}_{\rm P} ,{\phi_{}}_{\rm P} )$ denote the observation point, |
---|
| 612 | and let ${\rm A}({\lambda_{}}_{\rm A} ,{\phi_{}}_{\rm A} )$, |
---|
| 613 | ${\rm B}({\lambda_{}}_{\rm B} ,{\phi_{}}_{\rm B} )$, |
---|
| 614 | ${\rm C}({\lambda_{}}_{\rm C} ,{\phi_{}}_{\rm C} )$ |
---|
| 615 | and |
---|
| 616 | ${\rm D}({\lambda_{}}_{\rm D} ,{\phi_{}}_{\rm D} )$ denote |
---|
| 617 | the bottom left, bottom right, top left and top right |
---|
| 618 | corner points of the cell, respectively. |
---|
| 619 | To determine if P is inside |
---|
| 620 | the cell, we verify that the cross-products |
---|
| 621 | \begin{eqnarray} |
---|
| 622 | \begin{array}{lllll} |
---|
| 623 | {{\bf r}_{}}_{\rm PA} \times {{\bf r}_{}}_{\rm PC} |
---|
| 624 | & = & [({\lambda_{}}_{\rm A}\; -\; {\lambda_{}}_{\rm P} ) |
---|
| 625 | ({\phi_{}}_{\rm C} \; -\; {\phi_{}}_{\rm P} ) |
---|
| 626 | - ({\lambda_{}}_{\rm C}\; -\; {\lambda_{}}_{\rm P} ) |
---|
| 627 | ({\phi_{}}_{\rm A} \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\ |
---|
| 628 | {{\bf r}_{}}_{\rm PB} \times {{\bf r}_{}}_{\rm PA} |
---|
| 629 | & = & [({\lambda_{}}_{\rm B}\; -\; {\lambda_{}}_{\rm P} ) |
---|
| 630 | ({\phi_{}}_{\rm A} \; -\; {\phi_{}}_{\rm P} ) |
---|
| 631 | - ({\lambda_{}}_{\rm A}\; -\; {\lambda_{}}_{\rm P} ) |
---|
| 632 | ({\phi_{}}_{\rm B} \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\ |
---|
| 633 | {{\bf r}_{}}_{\rm PC} \times {{\bf r}_{}}_{\rm PD} |
---|
| 634 | & = & [({\lambda_{}}_{\rm C}\; -\; {\lambda_{}}_{\rm P} ) |
---|
| 635 | ({\phi_{}}_{\rm D} \; -\; {\phi_{}}_{\rm P} ) |
---|
| 636 | - ({\lambda_{}}_{\rm D}\; -\; {\lambda_{}}_{\rm P} ) |
---|
| 637 | ({\phi_{}}_{\rm C} \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\ |
---|
| 638 | {{\bf r}_{}}_{\rm PD} \times {{\bf r}_{}}_{\rm PB} |
---|
| 639 | & = & [({\lambda_{}}_{\rm D}\; -\; {\lambda_{}}_{\rm P} ) |
---|
| 640 | ({\phi_{}}_{\rm B} \; -\; {\phi_{}}_{\rm P} ) |
---|
| 641 | - ({\lambda_{}}_{\rm B}\; -\; {\lambda_{}}_{\rm P} ) |
---|
| 642 | ({\phi_{}}_{\rm D} \; - \; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\ |
---|
| 643 | \end{array} |
---|
| 644 | \label{eq:cross} |
---|
| 645 | \end{eqnarray} |
---|
| 646 | point in the opposite direction to the unit normal |
---|
| 647 | $\widehat{\bf k}$ (i.e., that the coefficients of |
---|
| 648 | $\widehat{\bf k}$ are negative), |
---|
| 649 | where ${{\bf r}_{}}_{\rm PA}$, ${{\bf r}_{}}_{\rm PB}$, |
---|
| 650 | etc. correspond to the vectors between points P and A, |
---|
| 651 | P and B, etc.. The method used is |
---|
| 652 | similar to the method used in |
---|
| 653 | the Scripp interpolation package \citep{Jones_Bk01}. |
---|
| 654 | |
---|
| 655 | In order to speed up the grid search, there is the possibility to construct |
---|
| 656 | a lookup table for a user specified resolution. This lookup |
---|
| 657 | table contains the lower and upper bounds on the $i$ and $j$ indices |
---|
| 658 | to be searched for on a regular grid. For each observation position, |
---|
| 659 | the closest point on the regular grid of this position is computed and |
---|
| 660 | the $i$ and $j$ ranges of this point searched to determine the precise |
---|
| 661 | four points surrounding the observation. |
---|
| 662 | |
---|
| 663 | \subsection{Parallel aspects of horizontal interpolation} |
---|
| 664 | |
---|
| 665 | For horizontal interpolation, there is the basic problem that the |
---|
| 666 | observations are unevenly distributed on the globe. In numerical |
---|
| 667 | models, it is common to divide the model grid into subgrids (or |
---|
| 668 | domains) where each subgrid is executed on a single processing element |
---|
| 669 | with explicit message passing for exchange of information along the |
---|
| 670 | domain boundaries when running on a massively parallel processor (MPP) |
---|
| 671 | system. This approach is used by the \NEMO. |
---|
| 672 | |
---|
| 673 | For observations there is no natural distribution since the |
---|
| 674 | observations are not equally distributed on the globe. |
---|
| 675 | Two options have been made available: 1) geographical distribution; |
---|
| 676 | and 2) round-robin. |
---|
| 677 | |
---|
| 678 | \subsubsection{Geographical distribution of observations among processors} |
---|
| 679 | |
---|
[2376] | 680 | %>>>>>>>>>>>>>>>>>>>>>>>>>>>> |
---|
| 681 | \begin{figure} \begin{center} |
---|
[2298] | 682 | \includegraphics[width=10cm,height=12cm,angle=-90.]{./TexFiles/Figures/Fig_ASM_obsdist_local} |
---|
[2376] | 683 | \caption{ \label{fig:obslocal} |
---|
| 684 | Example of the distribution of observations with the geographical distribution of observational data.} |
---|
| 685 | \end{center} \end{figure} |
---|
| 686 | %>>>>>>>>>>>>>>>>>>>>>>>>>>>> |
---|
[2298] | 687 | |
---|
| 688 | This is the simplest option in which the observations are distributed according |
---|
| 689 | to the domain of the grid-point parallelization. Figure~\ref{fig:obslocal} |
---|
| 690 | shows an example of the distribution of the {\em in situ} data on processors |
---|
| 691 | with a different colour for each observation |
---|
| 692 | on a given processor for a 4 $\times$ 2 decomposition with ORCA2. |
---|
| 693 | The grid-point domain decomposition is clearly visible on the plot. |
---|
| 694 | |
---|
| 695 | The advantage of this approach is that all |
---|
| 696 | information needed for horizontal interpolation is available without |
---|
| 697 | any MPP communication. Of course, this is under the assumption that |
---|
| 698 | we are only using a $2 \times 2$ grid-point stencil for the interpolation |
---|
| 699 | (e.g., bilinear interpolation). For higher order interpolation schemes this |
---|
| 700 | is no longer valid. A disadvantage with the above scheme is that the number of |
---|
| 701 | observations on each processor can be very different. If the cost of |
---|
| 702 | the actual interpolation is expensive relative to the communication of |
---|
| 703 | data needed for interpolation, this could lead to load imbalance. |
---|
| 704 | |
---|
| 705 | \subsubsection{Round-robin distribution of observations among processors} |
---|
| 706 | |
---|
[2376] | 707 | %>>>>>>>>>>>>>>>>>>>>>>>>>>>> |
---|
| 708 | \begin{figure} \begin{center} |
---|
[2298] | 709 | \includegraphics[width=10cm,height=12cm,angle=-90.]{./TexFiles/Figures/Fig_ASM_obsdist_global} |
---|
[2376] | 710 | \caption{ \label{fig:obsglobal} |
---|
| 711 | Example of the distribution of observations with the round-robin distribution of observational data.} |
---|
| 712 | \end{center} \end{figure} |
---|
| 713 | %>>>>>>>>>>>>>>>>>>>>>>>>>>>> |
---|
[2298] | 714 | |
---|
| 715 | An alternative approach is to distribute the observations equally |
---|
| 716 | among processors and use message passing in order to retrieve |
---|
| 717 | the stencil for interpolation. The simplest distribution of the observations |
---|
| 718 | is to distribute them using a round-robin scheme. Figure~\ref{fig:obsglobal} |
---|
| 719 | shows the distribution of the {\em in situ} data on processors for the |
---|
| 720 | round-robin distribution of observations with a different colour for |
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| 721 | each observation on a given processor for a 4 $\times$ 2 decomposition |
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| 722 | with ORCA2 for the same input data as in Fig.~\ref{fig:obslocal}. |
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| 723 | The observations are now clearly randomly distributed on the globe. |
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| 724 | In order to be able to perform horizontal interpolation in this case, |
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| 725 | a subroutine has been developed that retrieves any grid points in the |
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| 726 | global space. |
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| 727 | |
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| 728 | \subsection{Vertical interpolation operator} |
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| 729 | |
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| 730 | The vertical interpolation is achieved using either a cubic spline or |
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| 731 | linear interpolation. For the cubic spline, the top and |
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| 732 | bottom boundary conditions for the second derivative of the |
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| 733 | interpolating polynomial in the spline are set to zero. |
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| 734 | At the bottom boundary, this is done using the land-ocean mask. |
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