Gregory King (ICM-CSIC) Marcos Portabella (ICM-CSIC) Correlating extremes in rain with extremes in wind & wind stress divergence Gregory King (ICM-CSIC) Marcos Portabella (ICM-CSIC) Wenming Lin (NUIST) Ad Stoffelen (KNMI) This work aims to improve the wind quality control of Rapidscat and HY-2A scatterometer.

Meteosat Second Generation (MSG) Rain Rates (Produced by KNMI) ASCAT Winds A & B Africa Africa South America Left: A histogram of all Tropical Atlantic MCSs identified in the 14 year TRMM dataset. Right: Histograms for the diurnal variation. ASCAT passes occur in the Tropical Atlantic between 06h00 and 13h00 (basically the second row). South America Atlantic ITCZ Collocations ASCAT winds at time t 0 at time t 0 + 50 minutes MSG snapshots start: t 0 - 2 hrs end: t 0 + 2 hrs sampling interval: 15 minutes Data MSG Rain Rate: 3 km pixels, snapshot every 15 minutes (daylight only) ASCAT-A&B 12.5 km WVCs Overlapping A&B swaths (Atlantic ITCZ)

h h < -0.1 Locations where velocity gradients are steep Animation MSG Rain (black pixels) Singularity Exponent (h = -0.1) contour (red) Singularity Exponent h If Animation does not play — just wave hands about what it should show. Historical —> The three figs happened to get plotted on the screen at the same time and indicated a correlation between SEs, DIV and storm tracks. The equations explain why SEs and DIV have similar pattern (large velocity gradient). Key Point (very large rain rate correlates with very large DIV) is emphasized/summarized in the Next Slide. DIV Locations where velocity gradients are steep h < -0.1

h Visually, rain rates / storm tracks appear well-correlated with DIV. Animation MSG Rain (black pixels) Singularity Exponent (h = -0.1) contour (red) Visually, rain rates / storm tracks appear well-correlated with DIV. In fact… Key Point: Very large rain rates correlate with very large DIV. The TASK: make the correlation quantitative. Singularity Exponent h * Continuing from previous slide —> Key Point and the task ahead. * The remainder of the talk explains how the correlation is made. * Emphasize that the methodology to be described is conceptually straightforward and can be applied to many geophysical datasets. DIV Locations where velocity gradients are steep h < -0.1

Preparing data for correlation 25km-by-25km area spanned by Computational Cell 25km-by-25km area spanned by 12.5km WVCs … i+1 Ui+1,j Ui+1,j+1 i Ui,j Ui,j+1 j j+1 O Producing datasets for correlation… * Calculation technique for DIV * Rationale to use RRmax. * Next slide will show the DIV probability distribution: P(DIV) At each grid point (i+1/2, j+1/2)… DIV — calculate using difference-then-average method. RRmax — the max rain rate in the area spanned by the computational cell. Rationale: RRmax is the most influential rain rate affecting the calculation of DIV

Statistical Approach DIV P(DIV) Probability Wind Divergence Normal Probability Plot P(DIV) Gaussian Fat Tails Log Probability Data falling on the red line follow a Gaussian distribution (Non-Gaussian) Wind Divergence Top Left fig shows P(DIV) and its fat tails. (Note these figs are for Wind DIV; in rest of slides we use Wind Stress DIV) * Top Right fig uses quantiles to compare P(DIV) with Gaussian. (Normal Probability Plot — a useful tool.) * The arrows from P(DIV) to DIV emphasize character of data contributing to the fat tails. * Defining a threshold value. The Normal Probability Plot helps select a value. (See next slide) Top Left fig: P(DIV) Top Right fig: quantiles of P(DIV) vs quantiles of Gaussian. The Fat Tails are due to large Extreme Events Top Left & Bot Left fig show Splitting of P(DIV) into three subsets. To split the data — Must define a threshold. Probability Plot aids in selecting a threshold value. DIV

BG - BackGround (Gaussian) XC - eXtreme Convergence Using statistics to define a threshold and partition the data into subsets Normal Probability Plot BG - BackGround (Gaussian) XC - eXtreme Convergence XD - eXtreme Divergence Note that Wind Stress DIV thresholds are +/- 0.18 x 10-5 Nm-3 (the 2nd% and 98th% levels) Thresholds at +/- 0.18 x 10-5 Nm-3 Nm-3 Nm-3 Wind Stress Div XC XD BG

Define Rain Rate partitions Rain rates follow a different kind of distribution. Must apply a different strategy. We use the UK Met Office (UKMO) classification… Rain rate distribution (one month of collocations) * Rain rates are not Gaussian-like, so must use a different strategy — UKMO. * Ask if anyone in the audience knows how UKMO came up with those values? XR LR - Light Rain MR - Moderate Rain XR - eXtreme Rain Seen by SCAT-1 Seen by SCAT-2 (50 minutes later) LR MR

Wind Stress Divergence Results Wind Stress Divergence Probability of XC given XR Scattergram of DIV vs RRmax Data from one collocation and using one MSG snapshot. DIV and Rain categories are indicated along top and side SCAT-1 * Scattergram shows nearly all the data in the fat tails fall in the (XC, XR) and (XD, XR) bins. The figs on right show the result of calculating probability of finding XC (XD) at time 0, given XR in the 25km x 25km neighbourhood at time tau, for tau = -5,..,0,..10). Next Slide shows these figs again. (XC, XR) (XD, XR) MSG snapshot index Probability of XD given XR The most extreme DIVs fall mainly in the XR bins — i.e., bins (XC,XR) and (XD,XR).

Most extreme rain occurs 30 minutes after extreme convergence Most extreme rain occurs at the time of extreme divergence Extreme rain falls fast, resulting in a rapid impact on the wind field (downdrafts), These results show that … Extreme rain generally appears 30 minutes after extreme convergence. Temporal scale of Moist Convection is determined by the slower updraft process.

coherent spatial clusters Different sizes and shapes Extremes fall into coherent spatial clusters Different sizes and shapes DIV Rain XC and XD Clusters XR clusters * An XC cluster is defined as a set of XC WVCs that share a side or corner (called an 8-neighbourhood). Similarly for XD and XR. Note that we do not study XR clusters in this work. Next Slide - Pool statistics from all clusters seen by SCAT-1 and examine how the distribution has changed when SCAT-2 looks at the same WVC areas.

One month of collocations Pooled statistics … One month of collocations Extreme Convergence Extreme Divergence Statistics of SCAT-1 WVCs labelled as Extreme DIV Histogram Pool statistics from all clusters seen by SCAT-1 and examine how the distribution has changed when SCAT-2 looks at the same WVC areas. DIV statistics 50 minutes later for those same WVC areas… (SCAT-2 WVCs) Wind Stress Divergence A dramatic change in the distribution after only 50 minutes!

Summary Extremes correlate with Extremes: Extreme DIV with Extreme Rain A methodology was developed that made correlation quantitative. Extreme values found in spatially coherent clusters — indicating dynamical structures. Key time scales associated with wind field / Mesoscale Convective System interaction were identified. Further Work More investigation of SCAT-1/SCAT-2 differences. Apply methodology to investigate Wind Curl / Wind Stress Curl and correlation with extreme rain. Investigate correlation between extremes in other collocated datasets.