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The standard deviation (estimate of random error) is the quantitative measure of precision (Table 4). The targets for precision are applied to the standard deviation of O-B over a certain period for each of the observed variables (Table 6). Like trueness, precision will be assessed 6-hourly, daily and monthly. Also, the 5-day moving average (Alert) of daily calculated standard deviation of O-B (Table 9) will be calculated for all variables and compared to the respective prescribed threshold ( Table 6). This together with the performance indicator for Trueness will be used by the Evaluation function on their daily monitoring activities to determine the level of priority for stations showing accuracy/measurement uncertainty issues (see table in Annex2 of WDQMS Guidance Document).
Table 4 - Precision
Definition | Standard deviation (std) of O-B values over a defined period |
Calculation | For each observed variable, the std of all valid data is computed for every station. |
Valid data | Data not flagged as missing value (O-B is not NULL) |
Minimum required valid data | Daily: 2 valid values |
Math expression | , where Nj is number of valid data for variable j and the bar denotes the average as defined in Table 4. |
Both bias and standard deviation contribute to the overall measurement uncertainty. The root mean square error (rmse) is a common metric used to measure accuracy, and it is applied to upper-air observations in the WDQMS web tool (section 6.2) based on the quantitative information for the two vertical layers (average and standard deviation of O-B departures over Trop and Stra, see section 2.2) provided by the NWP reports (see Table 5).
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Table 5 - Root Mean Square Error (rmse)
Definition | rmse of O-B values over a layer |
Calculation | For each observed variable, the rmse is computed based on valid data for every station. |
Valid data | Bias and std not NULL. |
Minimum required valid data | 2 valid value. |
Math expression | where bias and std are the average and standard deviation of O-B departures over a vertical layer (Trop or Stra, in section 2.2) |
Note that quality indicators are applied only to the measured quantities whose O-B departures are available in the NWP monitoring reports, i.e. the ones whose model equivalent is available from the NWP assimilation system (see sections 2.1 and 2.2). Therefore, if the O-B departures are missing because the model background is not calculated in a particular NWP assimilation (e.g., DWD does not have O-B departures for the observations they do not use in assimilation) the quality indicator will not be calculated and the station will not show on the quality map. This explains why some stations appear in availability map, but not in the quality one.
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Whenever the WDQMS performance targets are revised, the targets defined in WMO RRR for the global NWP application area are taken into account. Table 7 contains the prescribed exceedance limits for the variables monitored by WDQMS as defined by WMO RRR.
Table 6 - Exceedance thresholds as defined in the Manual on GOS (WMO-No. 544), Volume II-Regional Aspects.
Variable | Trueness | Precision |
Surface pressure | 0.5hPa | 1.5hPa |
Geopotential height | 30m | 40m |
2m Temperature | 0.5K | - |
10m wind vector | 3.0m/s | 5.0m/s |
10m relative humidity | 10% | - |
Upper air temperature | 0.5K | 1.5K |
Upper air wind vector | 3.0m/s | 5.0m/s |
Upper air relative humidity | 10% | - |
Table 7 - Exceedance limits for the relevant surface and upper-air variables as defined by WMO RRR (https://www.wmo-sat.info/oscar/requirements)
Variable | Gold | Breakthrough | Threshold |
Surface pressure | 0.5hPa | 0.5hPa | 1hPa |
Geopotential height | 30m | 30m | 30m |
2m Temperature | 0.5K | 1.0K | 2.0K |
10m wind vector | 0.5m/s | 2.0m/s | 3.0m/s |
10m relative humidity | 2% | 5% | 10% |
Upper air temperature | 0.5K | 1.0K | 3.0 K |
Upper air wind vector | 1.0m/s | 3.0m/s | 5.0m/s |
Upper air relative humidity | 2% | 5% | 10% |