1. 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.

2. 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 minutes
MSG snapshots
start: t hrs
end: t 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)

3. 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

4. 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

5. 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

6. 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

7. 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 +/ x 10-5 Nm-3
(the 2nd% and 98th% levels)
Thresholds at
+/ x 10-5 Nm-3
Nm-3
Nm-3
Wind Stress Div XC XD BG

8. 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

9. 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).

10. 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.

11. 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.

12. 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!

13. 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.