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Figure 14. December 2017: Hinton diagram for different variables over a 3 x 3 grid point neighbourhood showing the change in Ranked Probability Score (RPS) and Continuous Ranked Probability Score (CRPS) from using 4D-Var compared to 3D-Var. The triangle area indicates the magnitude of the change, with the largest triangle representing a change of 20%. An upward pointing triangle indicates an improvement compared to the reference and a downward triangle a degradation. A bold triangle border indicates significance at the 0.05 level measured using the Wilcoxon signed-rank test.

Figure 14 December 2017: Hinton diagram for different variables over a 3 x 3 grid point neighbourhood showing the change in Ranked Probability Score (RPS) and Continuous Ranked Probability Score (CRPS) from using 4D-Var compared to 3D-Var. The triangle area indicates the magnitude of the change, with the largest triangle representing a change of 20%. An upward pointing triangle indicates an improvement compared to the reference and a downward triangle a degradation. A bold triangle border indicates significance at the 0.05 level measured using the Wilcoxon signed-rank test.

Related Figures (24)

Figure 1. Response as a function of wave period of the high-pass filter used within the UKV 4D-Var J, term.
Figure 1. Response as a function of wave period of the high-pass filter used within the UKV 4D-Var J, term.
ge 2. Example of mean absolute pressure tendency for the PF model at the lowest model level throughout the 4D-Var time window for different combinations of the daptive grid (AG) and J, digital filter penalty.
ge 2. Example of mean absolute pressure tendency for the PF model at the lowest model level throughout the 4D-Var time window for different combinations of the daptive grid (AG) and J, digital filter penalty.
Figure 3. The UKV forecast model domain, showing regions with different grid resolutions. The unshaded central domain uses a 1.5 km grid spacing, the dark blue cprners use a 4 km spacing and the light blue regions use 1.5 km in one direction and 4 km in the other depending on the orientation.
Figure 3. The UKV forecast model domain, showing regions with different grid resolutions. The unshaded central domain uses a 1.5 km grid spacing, the dark blue cprners use a 4 km spacing and the light blue regions use 1.5 km in one direction and 4 km in the other depending on the orientation.
Figure 4. Schematic overview of 3H3D-Var. Numbers followed by apostrophe are referred to minutes. The first analysis window spans from T-90’ to T+90’ while the second analysis window spans from T+90’ to T+270’ relative to the first cycle’s nominal analysis time.
Figure 4. Schematic overview of 3H3D-Var. Numbers followed by apostrophe are referred to minutes. The first analysis window spans from T-90’ to T+90’ while the second analysis window spans from T+90’ to T+270’ relative to the first cycle’s nominal analysis time.
Figure 5. Schematic overview of hourly 4D-Var.
Figure 5. Schematic overview of hourly 4D-Var.
jews 8. Similar to Figure 6, but a histogram including just radar Doppler radial wind observations in 3H3D-Var and hourly 4D-Var. The histogram bar for less than 501 servations per cycle does not fit on the vertical scale of the graph for the 3H3D-Var case, so the corresponding bar height is written at the top left of the figure. Figure 7. Similar to Figure 6, but a histogram including just SEVIRI radiance observations.
jews 8. Similar to Figure 6, but a histogram including just radar Doppler radial wind observations in 3H3D-Var and hourly 4D-Var. The histogram bar for less than 501 servations per cycle does not fit on the vertical scale of the graph for the 3H3D-Var case, so the corresponding bar height is written at the top left of the figure. Figure 7. Similar to Figure 6, but a histogram including just SEVIRI radiance observations.
PH igure 6. Histogram of all types of observations assimilated in 3H3D-Var (blue) and hourly 4D-Var (red). The total rate of observations (of all types) assimilated per hour is used to allow direct comparison between the 3H3D-Var and hourly 4D-Var systems (with the number of observations per cycle divided by 3 in the three-hourly cycling stem). The numbers of observations per hour averaged over the full period are shown at the top of the figure for 3H3D-Var (blue) and hourly 4D-Var (red).
PH igure 6. Histogram of all types of observations assimilated in 3H3D-Var (blue) and hourly 4D-Var (red). The total rate of observations (of all types) assimilated per hour is used to allow direct comparison between the 3H3D-Var and hourly 4D-Var systems (with the number of observations per cycle divided by 3 in the three-hourly cycling stem). The numbers of observations per hour averaged over the full period are shown at the top of the figure for 3H3D-Var (blue) and hourly 4D-Var (red).
Figure 9. Similar to Figure 6, but a histogram including just pseudo-observations of relative humidity (RH) on model levels generated using GeoCloud in 3H3D-Var anc hourly 4D-Var.
Figure 9. Similar to Figure 6, but a histogram including just pseudo-observations of relative humidity (RH) on model levels generated using GeoCloud in 3H3D-Var anc hourly 4D-Var.
yigure 10. Similar to Figure 6, but a histogram including just infrared hyperspectral sounder radiance observations in 3H3D-Var and hourly 4D-Var. The histogram bars for less than 26 observations per cycle do not fit on the vertical scale of the graph, so the corresponding bar heights are written at the top left of the figure.
yigure 10. Similar to Figure 6, but a histogram including just infrared hyperspectral sounder radiance observations in 3H3D-Var and hourly 4D-Var. The histogram bars for less than 26 observations per cycle do not fit on the vertical scale of the graph, so the corresponding bar heights are written at the top left of the figure.
Figure 11. Similar to Figure 6, but a histogram including just microwave humidity sounding radiance observations in 3H3D-Var and hourly 4D-Var. The histogram bar ft ess than 101 observations per cycle does not fit on the vertical scale of the graph for the 4D-Var case, so the corresponding bar height is written at the top left of the figur
Figure 11. Similar to Figure 6, but a histogram including just microwave humidity sounding radiance observations in 3H3D-Var and hourly 4D-Var. The histogram bar ft ess than 101 observations per cycle does not fit on the vertical scale of the graph for the 4D-Var case, so the corresponding bar height is written at the top left of the figur
nani Figure 12. Similar to Figure 6, but a histogram including just radiosonde observations in 3H3D-Var and hourly 4D-Var. The histogram bars for 0 observations per cycle not fit on the vertical scale of the graph, so the corresponding bar heights are written at the top left of the figure.
nani Figure 12. Similar to Figure 6, but a histogram including just radiosonde observations in 3H3D-Var and hourly 4D-Var. The histogram bars for 0 observations per cycle not fit on the vertical scale of the graph, so the corresponding bar heights are written at the top left of the figure.
Figure 13. Similar to Figure 6, but a histogram including just surface, in-situ upper air and ground-based remote sensing (excluding radar Doppler wind) observations in 3H3D-Var and hourly 4D-Var.
Figure 13. Similar to Figure 6, but a histogram including just surface, in-situ upper air and ground-based remote sensing (excluding radar Doppler wind) observations in 3H3D-Var and hourly 4D-Var.
igure 15. December, 2017: Fraction Skill Score (FSS) for a forecast of hourly accumulated precipitation exceeding 1 mm at T+3 hours. The horizontal axis shows th size of the verification neighbourhood in grid-lengths. Hourly 3D-Var results in the blue curve, hourly 4D-Var in the red curve.
igure 15. December, 2017: Fraction Skill Score (FSS) for a forecast of hourly accumulated precipitation exceeding 1 mm at T+3 hours. The horizontal axis shows th size of the verification neighbourhood in grid-lengths. Hourly 3D-Var results in the blue curve, hourly 4D-Var in the red curve.
Figure 16. Same as Figure 15 for T+6 hours.
Figure 16. Same as Figure 15 for T+6 hours.
Figure 17. December 2017: Hinton diagram showing the change in Fractions Skill Score from using 4D-Var compared to 3D-Var for different hourly accumulatec precipitation thresholds over a 5 x 5 grid point neighbourhood. Apart from the different colour scheme, the format follows that of Figure 14.
Figure 17. December 2017: Hinton diagram showing the change in Fractions Skill Score from using 4D-Var compared to 3D-Var for different hourly accumulatec precipitation thresholds over a 5 x 5 grid point neighbourhood. Apart from the different colour scheme, the format follows that of Figure 14.
Figure 18. Hinton diagram for July 2017 following the format of Figure 14.
Figure 18. Hinton diagram for July 2017 following the format of Figure 14.
fer 19. July, 2017: FSS for a forecast of hourly accumulated precipitation exceeding 1 mm at T+3 hours. The horizontal axis shows the size of the verification nvighbourhood in grid-lengths. Hourly 3D-Var results in the blue curve, hourly 4D-Var in the red curve.
fer 19. July, 2017: FSS for a forecast of hourly accumulated precipitation exceeding 1 mm at T+3 hours. The horizontal axis shows the size of the verification nvighbourhood in grid-lengths. Hourly 3D-Var results in the blue curve, hourly 4D-Var in the red curve.
Figure 21. July 2017: Hinton diagram of FSS for hourly accumulated precipitation following the format of Figure 17. Figure 20. Same as Figure 19 for T+6 hours.
Figure 21. July 2017: Hinton diagram of FSS for hourly accumulated precipitation following the format of Figure 17. Figure 20. Same as Figure 19 for T+6 hours.
igure 22. Summer season. FSS for hourly accumulated precipitation as a function of forecast hour for UKV and STEPS at a scale of 51 grid-lengths. (a) 1 mm threshold x 3H3D-Var in June 2017, (b) 1 mm threshold for hourly 4D-Var in August 2018, (c) and (d) 90th percentile for 3H3D-Var and for hourly 4D-Var respectively.
igure 22. Summer season. FSS for hourly accumulated precipitation as a function of forecast hour for UKV and STEPS at a scale of 51 grid-lengths. (a) 1 mm threshold x 3H3D-Var in June 2017, (b) 1 mm threshold for hourly 4D-Var in August 2018, (c) and (d) 90th percentile for 3H3D-Var and for hourly 4D-Var respectively.
Figure 23. Winter season. Same format as Figure 22. (a, c) October 2017 for 3H3DVar, (b, d) November 2018 for 4D-Var.
Figure 23. Winter season. Same format as Figure 22. (a, c) October 2017 for 3H3DVar, (b, d) November 2018 for 4D-Var.
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Environmental ScienceOceanographyData AssimilationAtmospheric sciences
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