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We start by analysing the time series of uncertainties of the relative humidity, air temperature and wind speed in Figure 1, Figure 2 and Figure 3, displayed for all the standard pressure levels. The uncertainties are displayed in different colours according to the different time window used for the calculation of the averages. The peaks of higher uncertainties are due to large values in the departure values. It is then interesting to compare uncertainties of different stations, which might fluctuate due to the accuracy of the reanalyses. We note that there is no neat dependency on the pressure levels, and most of the uncertainties are distributed around an average values. The estimates of uncertainties become smaller with time, as can be expected by the improved accuracy of the sensors used for upper air measurements.
We also note that the variance of the uncertainties decreases as the size of the time averaging window increases, since the values are less affected by statistical fluctuations of the values of the departures. This is emphasized by plotting first the 30 day averages and the 180 day averages at last.
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Figure 1: Time series for the relative humidity variable (dimensionless) for station Lindenberg. Colored lines correspond to the values of the uncertainties, and the corresponding scale is shown on the right y-axis. The gray shaded lines are the actual observation values and the corresponding scale is shown in the left y-axis . Only the series for pressure level greater than 250hPa are shown, since the measurements are not sufficiently accurate at higher elevation, except in the most recent years (2000s onward)....
We note that reanalyses information for observations before 1950 is available only from surface data only reanalysis (we used NOAA-20CRv3 reanalyses, Sivlinksy et al. 2019). While these have not assimilated upper air observations, we still could interpolate from the reanalysis fields to the observation locations to get offline departures from that reanalysis. While useful, these are not sufficient to calculate Desroziers diagnostics. One really needs to assimilate the upper air data to get both analysis and background departures and to fulfil the necessary conditions for valid Desroziers diagnostics.
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Figure 2: Time series for the air temperature variable (units K). Colored lines correspond to the values of the uncertainties, and the corresponding scale is shown on the right y-axis. The gray shaded lines are the actual observation values and the corresponding scale is shown in the left y-axis .
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However, Desroziers et al. (2005) showed Figure 3: Time series for the wind speed variable (units m/s). Colored lines correspond to the values of the uncertainties, and the corresponding scale is shown on the right y-axis. The gray shaded lines are the actual observation values and the corresponding scale is shown in the left y-axis .
In Figure 4, Figure 5 and Figure 6 we show the distributions of the uncertainty values, always for individual pressure levels, for the different variables. We find typical values of around 0.05 for the relative humidity, 0.6 K for the Temperature and around 1 m/s for the wind speed. We note that the uncertainty decreases in time, which is of course a good sign, with a different extent depending on the specific station considered. Finally, that the larger the time window considered, the narrower the distributions since the average uncertainty gets smaller.
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Figure 4: Histograms of uncertainty estimates for the variable relative humidity, for standard pressure levels equal or larger than 250 hPa for station Lindenberg. Color coding is the same as in Figs. 1-3 for the different averaging intervals.
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Figure 5: Histograms of uncertainty estimates for the variable air temperature, for each standard pressure level.
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Figure 6: Histograms of uncertainty estimates for the variable wind speed, for each standard pressure level.
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Figure 7: Contours of the uncertainties for the air temperature (left) and wind speed (right), for all the available standard pressure levels at station Lindenberg. 925 hPa was not a standard pressure level before the early 1980s, thus the visual artifact in the lower left corner of the panels.
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As we described in the previous section, we calculated the uncertainties for standard pressure levels, and referring the observation time stamps to four standardized hours: 00, 06, 12 and 18. In principle we should report the results for those specific times; however, we did not find any significant difference between daytime and night-time estimates (see Fig. 8). This justifies our choice to show combined values for the uncertainties at different times.
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Figure 8: Time series for the air temperature Desroziers' uncertainty, calculated at 00, 06, 12 and 18 hours, at station Lindenberg. After 2013 the data from Lindenberg are reported in BUFR format at actual launch time, which is rarely exactly at the hour. Thus there appear to be fewer values after 2013.
In Figure 9 we show a global overview of average uncertainties for the available stations in the database, calculated over periods 1970-1980 and 2000-2020, for the relative humidity, air temperature and wind speed, at a pressure level of 850 hPa. We can clearly see that the average values decrease for more recent observations for all the variables, and that also the number of stations which exhibit large uncertainties tend to decrease in more recent time periods. We also note a cluster of stations with quite large uncertainties in the temperature and wind speed over India. Those stations are well known for their limited accuracy.
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Figure 9: Overview of the average values of the Desroziers' uncertainty, calculated using a time window of 30 days, in the period 1970-1980 (left) and 2000-2020 (right), at 850 hPa pressure. Top panels show the uncertainties of the relative humidity, middle panels show the uncertainty of the air temperature, and bottom panels of the wind speed.
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This document has been produced in the context of the Copernicus Climate Change Service (C3S). The activities leading to these results have been contracted by the European Centre for Medium-Range Weather Forecasts, operator of C3S on behalf of the European Union (Delegation Agreement agreement signed on 11/11/2014 and Contribution Agreement signed on 22/07/2021). All information in this document is provided "as is" and no guarantee or warranty is given that the information is fit for any particular purpose. The users thereof use the information at their sole risk and liability. For the avoidance of all doubt , the European Commission and the European Centre for Medium - Range Weather Forecasts have no liability in respect of this document, which is merely representing the author's view. |
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