Lightning assimilation and correction factor

As explained in the result section most of the applied rainfall corrections described by Vicente et al. (1998, 2002) do not show clear improvements in this study case when compared satellite estimations to radar and accumulations from ACA rain gauges. A new alternative using lightning data is explored in this research in order to make use of valuable electrical discharge information from the base of the clouds.

-The first step involves the localization in time and space of every positive and negative lightning strike and to score satellite pixels with the number of electrical discharges. As a result of a qualitative study (not shown), a time lapse of 20 minutes around the satellite image UTC time seems to be appropriate to situate and add rays to the image pixels. Taking in account that Meteosat-7 image has a real-time delay of 10 10 minutes from to the UTC time over Spain; lightning hits are located and represented in a period of 20 minutes before the UTC satellite time as illustrated in figure 8.6. In this display the radar image at 0150 UTC is associated to the Meteosat image at 0200 UTC but electrical discharges are retrieved from 0140 to 0200 UTC and the time assigned to this lightning image is 0150 UTC. So that, each satellite infrared image every 30 minutes also processes a parallel image showing lightning hits with identical geographical settings.

- The second step has to do with the separation of radar rain rates associated to lightning or no lightning and how they correspond to satellite thermal band temperature (11.5 µm) also corrected by parallax. Averaged lightning (ALR) and no lightning rain rates (ANLR) versus infrared brightness temperature (TIR) are drawn in figure 8.5a by

two different symbols (triangles and boxes respectively) connected by lines. The average rain rate line (AR) obtained by using data from the whole calibration dataset, and used to determine the A-Ec curve (8.1) as described in the previous section, is also plotted in this graph. While the AR and ANLR plots are very similar, the ALR, however, provide much more rain and it is more dispersed for warmer temperatures with a maximum of 23 mm h-1 for 243 K.

-The third step is thought to increase the rain rate associated to lightning in function of the satellite temperature. Rainfall estimated from the A-Ec curve is first corrected by parallax and later should be multiplied by a correction coefficient, KL, on those points where electrical discharges are detected. The KL coefficient is calculated as illustrated in figure 8.5b. Firstly, the ALR points are divided by the AR ones each 2.5 K generating the Factor curve (FC). Secondly, a frequency curve of electrical discharges

called, number of discharges (ND) in function of TIR, also, each 2.5 K determines the

sections of the FC best supported by the lightning data as shown in graph 8.5b. With 6079 strikes from the coldest cloud tops accumulated in the 217-222 K section and not shown in this figure, to as much as 30 hits in the warmest from 246 K to the end is the kind of information that can be obtained the ND plot. The FC curve represents the ideal correction factor but in practice we have averaged it in finite segments based on nearly constant sections of ND curve as follows:

KL1 = 1.5 for TIR < 222.5 K with a Σ1(NDi) = 6079

KL2 = 2.6 for 222.5 K ≤ TIR < 230 K with a Σ2(NDi) = 1699

KL3 = 8.2 for 230 K ≤ TIR < 240 K with a Σ3(NDi) = 497

KL4 = 14.1 for TIR ≥ 240 K with a Σ4(NDi) = 108

where KLj is the correction factor derived from averaged sections of the FC curve and

Σj(NDi) is the total number of electrical discharges in each temperature interval. The

lengths of the Temperature interval have been selected from the coldest TIR in which

most of the lightning hits have been detected and where FC is closer to 1, to warmer TIR.

We have find empirically that the Σj(NDi) can be divided by an value of 3.5 in order to

select the approximate length of the next warmer interval of temperatures. This process continues until the number of discharges is nil.

-The fourth step diminishes the rain rate of those rain pixels not associated to lightning and therefore considered as stratiform rain pixels. This should be performed dynamically over the rain pixels that are surrounding the electrical ones as far as 15 pixels. The purpose of this process is to compensate the general tendency to increase the rain rate produced by the KL factor over the lightning pixels. The rain rate average in a stormy cloud area should stay unchanged after this stage. The mean rain rate decreases in stratiform rain pixels after this step, and for this case is around 10 %.

In summary, satellite rain pixels associated to lightning activity considered as convective are multiplied by the KL correction factor that depends on TIR, the rest of

rain pixels in the cloud considered as stratiform have a diminished rain rate in order to compensate for the increment produced by the KL factor. This process called ‘LG’ is applied as another correction factor to A-Ec and MCRR algorithms.

Figure 8.5. (a) Averaged lightning and no lightning rain rate points each 2.5 K. Plot using the boxes connected with lines: averaged rain (AR), as the previous figure. Triangles connected with lines: averaged lightning rain (ALR) from radar points associated to lightning pixels (1005 points). Circles connected with lines: averaged rain curve (ANLR) from radar points not associated to lightning pixels (16926 points). (b) Lightning correction factor figure. Total number of electrical discharges plotted by the line with triangles each 2.5 K (ND). The right axis represents the correction factor scale. It has no units because it is the averaged lightning rain points (ALR) divided by the averaged rain points (AR) each 2.5 K which generates the factor plot (FC) shown using black circles. The parameterized factor (KL) is the FC averages on limited sections taking in account a nearly constant number of accumulated discharges.

(a)

(b)