Formación de callo

Let g(X, Y, d, m)be the parametrized gust from from MOGREPS-G (defined in equation 6.1) and|v|(x, y, d, m)the 10 metre wind speed from MOGREPS-UK, where X, Y, x, y are the spatial coordinates on the respective model grids, d is the day of the year and m is the ensemble member.

Firstly, for each MOGREPS-G grid box (33×33 km), the maximum of the 10m wind speeds from MOGREPS-UK within that larger grid box is computed.

g is output every 3 hours and is the maximum gust over this period, whereas|v|is output every hour.

Therefore, in order to compare the two quantities, the temporal resolution is matched. In order to do this, the maximum|v|over the same 3 hours window is taken.

The wind gusts are detected and verified in the time window 12-18 UTC for the summer 2015. Only this period was chosen since the main aim of this chapter is to provide a proof of the concept of the application of the methodology for the sea-breeze case. Also, this time window has been chosen since it is when the highest gusts tend to occur in the sum- mer period (see (Hewston and Dorling,2011, Fig. 7)), when atmospheric instability due to surface heating facilitates thermally driven mixing, which in turn leads to transfer of momentum downward resulting in surface gusts.

In this time window there are two 3-hour windows (12-15 UTC and 15-18 UTC). If the day is defined as convective (meaning that the convective rainfall accumulation from MOGREPS-G is non-zero), then the period with the highest rainfall accumulation is cho- sen. If the day is not convective, then the time window corresponding to the highest MOGREPS-G gust is selected.

Thus the following variable is defined:

MRW(X, Y, T, m):=max

x,y,t |v|(x, y, t, m) (6.2) g(X, Y, T, m) and MRW(X, Y, T, m) (maximum resolved wind) can now be compared for each MOGREPS-G grid box. In this study only forecasts initialized at 00UTC for MOGREPS- G (and 03 UTC for MOGREPS-UK) on the same day are analysed. This is because this study serves as a proof of the concept. The subdomain chosen for this analysis is repre- sented by the black box shown in figure (6.1).

Figure 6.2 shows the comparison between g and MRW for three different grid boxes, in the upper, centre and lower part of the subdomain considered in this study and repre- sented by the smaller grid boxes in figure 6.1. This domain was chosen since it has a low and uniform elevation above sea level. This is to exclude cases where skill might depend

FIGURE 6.1: UK orography map from MOGREPS-UK. The black bigger dashed box indicates the domain considered in this study and the blue dots the station observation used for verification, whereas the three small dashed boxes indicate the three grid boxes referred after as upper, central

and lower.

on orographic effects. However, only the upper left corner presents an higher elevation and later in the chapter it will be shown how this affects the skill of the convective-scale forecast relative to low resolution ones.

In order to quantify the differences between the convective and non-convective cases a

two dimensional Kolmogorov-Smirnoff (KS) test has been performed on the pair((gconv, MRWconv)

,(g, MRW))and a one dimensional KS test on the two frequency distributions of the dif- ferences with respect to the best fit line. Firstly, it can be noticed that there is a high positive correlation between the two variables. This is quantified by ρ, the Pearson cor- relation coefficient.

Also, it can be noticed that MRW < g in most of the cases. However, for the convective cases, MRW is higher and closer to g. This is quantified by calculating the difference between the convective and non-convective data from the line of best fit trough all the points. Looking at the frequency distributions of the differences in figure 6.2, it can be seen that the convective cases are more shifted towards negative values of the differences between the best fit line and the observed values.

The two dimensional KS test gives a p-value of 6.07·10−119, 1.54·10−131, 6.20·10−145for the upper, central and lower grid box respectively. The test on the frequency distribu- tions gives a p-value of 4.89·10−26, 4.48·10−15, 2.5·10−20for the the three grid boxes.

FIGURE6.2: First column shows g(X, Y, T, m)against MRW(X, Y, T, m)for a) upper, b) central and c) lower grid box within the spatial domain con- sidered. Red dots represent convective cases as defined by the convection parametrization, whereas blue dots are the no-convective cases. Horizon- tal and vertical dotted lines represent the 95th percentile of the two dis- tributions respectively. The solid line is the best linear fit through all the data, the dash-dotted line is the 1:1 line, ρ is the Pearson correlation co- efficient. The second column represent the frequency distribution of the differences between the best fit line and the data for convective (red) and

non-convective (blue) cases.

• There is high correlation between the MOGREPS-G parameter gust and the 10m wind speed from MOGREPS-UK.

• The convective cases are significantly different from the non-convective cases. In the next sections the implications of these preliminary conclusions are investigated in terms of the probabilistic forecasts. For instance the fact that there is an high correlation between the two forecast fields, does it imply that the two probabilistic forecasts are performing in a similar way ? In other words, is the gust parameter a good predictor of high wind speed occurrence ? Also, does the convective parameter add additional information with respect to the gust parameter alone ? These will be addressed in the next sections.

FIGURE6.3: a) kernel density estimation of the distribution of wind gust events(solid lines) and no events (dashed lines). Events are defined as the occurrence of exceeding the 95thpercentile of the distribution. The distri- butions are plotted against the gust parameter for all (black), convective (red) and non convective cases (blue). b) shows the respective probabili- ties, obtained by applying the Bayes’ formula which involves the ratio be- tween the solid and dotted lines of the panel a). Black crosses represent the MOGREPS-UK probability values against the ensemble mean of the gust

parameters, for each day of our period of evaluation.