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What Drives the Intensification of Mesoscale Convective Systems over the West African Sahel under Climate
Change?
Rory Fitzpatrick, Douglas Parker, John Marsham, David Rowell, Francoise Guichard, Chris Taylor, Kerry Cook, Edward Vizy, Lawrence Jackson, Declan
Finney, et al.
To cite this version:
Rory Fitzpatrick, Douglas Parker, John Marsham, David Rowell, Francoise Guichard, et al.. What Drives the Intensification of Mesoscale Convective Systems over the West African Sahel under Cli- mate Change?. Journal of Climate, American Meteorological Society, 2020, 33 (8), pp.3151-3172.
�10.1175/JCLI-D-19-0380.1�. �hal-03002887�
1
1
What drives the intensification of mesoscale convective systems over the West African Sahel under Climate Change?
Rory G. J. Fitzpatrick
1,5; Douglas J. Parker
1; John H. Marsham
1; David P. Rowell
2; Francoise M. Guichard
3; Chris M. Taylor
4; Kerry H. Cook
5; Edward K. Vizy
5; Lawrence S. Jackson
1; Declan Finney
1; Julia Crook
1; Rachel Stratton
2; Simon Tucker
21. Institute for Climate and Atmospheric Sciences (ICAS), University of Leeds, Leeds, United Kingdom
2. Met Office, Exeter, United Kingdom
3. Centre National de Recherches Météorologiques (CNRM) - France 4. Centre for Ecology and Hydrology, Wallingford, United Kingdom 5. Jackson School of Geosciences, Austin, USA
Corresponding authors address: Rory Fitzpatrick, Jackson School of Geosciences, University of Texas at Austin, Austin TX, USA
E-mail: [email protected]
1
Abstract 2
Extreme rainfall is expected to increase under climate change carrying potential socio- 3
economic risks. However, the magnitude of increase is uncertain. Over recent decades, 4
extreme storms over the West African Sahel have increased in frequency with increased 5
vertical wind shear shown to be a cause. Drier mid-levels, stronger cold pools, and 6
increased storm organization have also been observed. Global models do not capture 7
the potential effects of lower-to-mid-tropospheric wind shear or cold pools on storm 8
organization since they parametrize convection. Here we use the first convection- 9
permitting simulations of African climate change to understand how changes in 10
thermodynamics and storm dynamics affect future extreme Sahelian rainfall. The 11
model, which simulates warming associated with Regional Climate Pathway 8.5 until 12
the end of the 21st Century, projects a 28% increase of the extreme rain rate of MCSs.
13
The Sahel moisture change on average follows Clausius-Clapeyron scaling, but has 14
regional heterogeneity. Rain rates scale with the product of time-of-storm total column 15
water (TCW) and in-storm vertical velocity. Additionally, pre-storm wind shear and 16
convective available potential energy both modulate in-storm vertical velocity. Although 17
wind shear affects cloud-top temperatures within our model, it has no direct correlation 18
with precipitation rates. In our model, projected future increase in TCW is the primary 19
explanation for increased rain rates. Finally, although colder cold pools are modelled in 20
the future climate, we see no significant change in near-surface winds, highlighting 21
avenues for future research on convection-permitting modelling of storm dynamics.
22
23
24
1. Introduction 25
The socio-economic risks to vulnerable people across West Africa due to climate 26
change are manifold (USAID 2017). Of particular interest are projections of the 27
frequency and intensity of extreme precipitation events. Mesoscale convective 28
systems (MCSs) are responsible for the majority of annual rainfall over the Sahel 29
(Laurent et al., 1998; Laing et al., 1999; Fink and Reiner 2003); understanding future 30
change of these events is pivotal to ascertaining future risk associated to rainfall.
31
The purpose of this study is to understand the processes by which climate 32
change can affect MCS precipitation rates, particularly the 99
thpercentile of surface 33
precipitation rates from MCSs (hereafter termed the extreme precipitation rate), over 34
the West African Sahel. We use a state-of-the-art regional climate model without any 35
active convection parameterization scheme to understand how variability on the 36
synoptic-to-climate timescale may affect MCS extreme precipitation rates.
37
The multi-decadal drought afflicting the Sahel in the 1970s and 80s has been 38
followed by a so-called “recovery period” (Nicholson 2005; Hagos and Cook 2008;
39
Lebel and Ali 2009; Lodoun et al., 2013; Evan et al., 2015; Sanogo et al., 2015) 40
during which average annual rainfall has returned to near-long-term mean levels 41
(Lélé and Lamb 2010; their Fig. 1). However, the nature of intra-seasonal rainfall 42
variability has changed over the Sahel during recent decades, with an observed 43
increase in the frequency of very rainy MCSs separated by longer periods of little to 44
no rainfall (Panthou et al., 2014, Taylor et al., 2017). More intense rain events carry 45
increased risk of flooding, with observational studies suggesting that flood events 46
over the Sahel have become more frequent over the past decades (Panthou et al., 47
2014; Nka et al., 2015, Panthou et al., 2018; Tazen et al., 2018; Wilcox et al., 2018).
48
Intense but temporarily sparse rain events can also deteriorate soil quality through 49
nutrient run off (Panagos et al., 2017) . 50
Taylor et al. (2017) observe a threefold increase in the frequency of early- 51
evening MCSs with mean cloud-top temperature < -75 °C over the Sahel since the 52
1980s. This increase is associated with an intensification of midday wind shear in the 53
vertical pressure column, henceforth wind shear, calculated as the difference 54
between low-level south-westerly/westerly winds and mid-level easterly winds, as 55
well as a drying of the Saharan air layer. Cold pools, and organized squall lines have 56
also been observed to intensify over the same timeframe, although the presence of 57
drier mid-level air and stronger cold pools may be coincidental and not dynamically 58
linked (c.f., James and Markowski 2010).
59
On the storm timescale, Taylor et al., (2017) found that ambient wind shear 60
intensity is significantly correlated with the mean cloud-top temperature of MCSs, 61
with subsequent observational work suggesting that ambient wind shear strength 62
may also influence the maximum precipitation rates of storms (Supplementary Fig.
63
S1). These findings are consistent with previous studies highlighting the role of wind 64
shear in organizing convection (Browning and Ludlam 1962; Moncrieff 1978, 1981;
65
Thorpe et al., 1982; Dudhia et al., 1987; Nicholls et al., 1988; Rotunno et al., 1988;
66
Mapes 1993; Houze Jr. 1993; Tao et al., 1995; Ferrier et al., 1996; LeMone et al.
67
1998; Mohr and Thorncroft 2006; Alfaro 2017).
68
Cloud-resolving model (CRM) studies have suggested that other ambient and 69
storm-relative variables are more important than wind shear in controlling MCS 70
precipitation rates. Takemi (2007; 2010; 2014) find that the vertical distribution of 71
high CAPE in the lower troposphere controls mean MCS precipitation rates to a
72
greater extent than lower/mid-tropospheric shear. However, Takemi (2010) also 73
found an inverse relationship between lower-tropospheric temperature lapse rate 74
and the maximum precipitation intensity of MCSs (their Fig. 14b), implying that 75
increased CAPE could be negatively correlated with maximum precipitation rates. A 76
similar result is found in Lucas et al., (2000), where enhanced wind shear positively 77
impacts total precipitation from MCSs, but negatively impacts maximum precipitation 78
rates. These results imply that storm-related drivers can be shown to positively or 79
negatively impact MCS intensity depending on the definition of storm intensity. It is 80
for this reason we primarily focus on extreme precipitation rates.
81
Finally, variability in moisture and ascent rates within MCSs have previously 82
been identified as influential in MCS precipitation rate variability. Increased inflow of 83
moist, buoyant air, and vertical ascent within convective updrafts increase maximum 84
precipitation rates (Alfaro 2017), as does enhanced lower-tropospheric relative 85
humidity (Lucas et al., 2000). Takemi (2014) hypothesized that increased 86
precipitable water available to a developing MCS will be positively correlated with 87
maximum precipitation rates. This theory is not explicitly tested by the author.
88
Rising temperatures under global warming have the potential to intensify 89
many of the MCS intensity drivers discussed above. Amplified warming of the 90
Sahara (Cook and Vizy 2015; Vizy and Cook 2017) will increase the meridional 91
temperature gradient across West Africa, leading to enhanced lower-to-mid- 92
tropospheric wind shear over the Sahel, in part through the enhancement of the 93
African Easterly Jet (Cook 1999). It is posited that a greater future meridional 94
temperature gradient over West Africa will lead to heavier precipitating MCSs under 95
climate change due to the strong water vapor feedback over the region (Dong and 96
Sutton, 2015; Evan et al., 2015). Through the Clausius-Clapeyron relationship, it is
expected that increased warming over the Sahel will lead to an increase in total 98
column water (TCW); this relationship has been identified previously within the 99
model used in this study (Kendon et al., 2019). Over the tropics, Takemi (2012a,b) 100
also find an increase in lower-tropospheric CAPE under global warming. In our 101
analysis, we examine the magnitude by which the above-identified MCS intensity 102
drivers increase in a potential future climate, and their subsequent dynamic effect on 103
MCS precipitation rates.
104
Coarse-resolution models with convection parameterization schemes, which 105
do not account for the role of wind shear, can struggle to model Sahelian storms and 106
their intensities accurately (Marsham et al., 2013). Convection-permitting models at 107
~4 km horizontal resolution have been shown to realistically simulate present day 108
monsoon flow, cold pool outflows (Marsham et al., 2013), convergence (Birch et al.
109
2014a,b), the diurnal cycle of rainfall (Vizy and Cook 2018a,b), and agricultural 110
decision-maker relevant monsoon metrics (Garcia-Carreras et al. 2015). Future 111
climate simulations of the West African climate at convection-permitting resolutions 112
therefore provide an opportunity to better understand changes in MCS dynamics 113
under global warming.
114
Section 2 describes the model used in this paper, with Section 3 explaining the 115
methods employed. Sections 4-7 provide results: first, we identify climatological 116
changes in the West African Monsoon between the current and future CP4-A climate 117
runs, then we analyze future changes in distributions of MCS precipitation intensity 118
relative to the current climate and the potential causes at different times of the day.
119
Section 8 gives conclusions and recommendations for future work.
120
2. Data
121
Within the Future Climate for Africa (FCFA) program, the Improving Model 122
Processes for African Climate (IMPALA) project has produced two 10-year model 123
simulations for the African continent at the convection-permitting horizontal grid 124
spacing of ~4.4 km. These simulations are referred to hereafter as “Convection 125
Permitting for Africa” (CP4-A; Stratton et al., 2018; Kendon et al., 2019). The CP4-A 126
simulations project the changes in African climate for the end of the 21
stCentury with 127
~4 K sea-surface temperature (SST) warming and ~5 K mean near-surface 128
temperature increase over the continent (Kendon et al., 2019). The model has 80 129
vertical levels with finer vertical resolution within the tropopause and boundary layer.
130
We provide a brief overview of the model and its quality below.
131
CP4-A is a regional model spanning longitudes 24°W – 56°E, and latitudes 45°S 132
– 39°N. The model is forced by lateral boundary conditions from an atmosphere-only 133
version the UK Met Office Global Climate Model (GCM) with ~25 km horizontal grid 134
spacing, and with prescribed daily SSTs. Land surface properties are initialized using 135
the most recent JULES land surface scheme (Walters et al., 2019), and allowed to 136
evolve freely over time. CP4-A uses an applied moisture conservation scheme 137
(Aranami 2015) and a three-dimensional blended boundary layer scheme (Boutle et 138
al., 2014). The large-scale cloud scheme is described in Smith (1990), and has been 139
used in other convection-permitting versions of the Met Office Unified Model. The 140
cloud scheme diagnoses liquid cloud fraction and condensed water when the grid- 141
box mean relative humidity exceeds a critical value. Ice water content is determined 142
by the microphysics scheme, with cloud fractions then diagnosed as in Abel (2017).
143
Other parameterization schemes are documented in Stratton et al. (2018, their Table 144
2). Both CP4-A, and the driving GCM, use the Even Newer Dynamics for General 145
Atmospheric Modelling of the Environment (ENDGame) dynamical core (Wood et al.
146
2014). The ENDGame dynamical core has been shown previously to improve the 147
representation of key processes over West Africa, particularly the seasonal 148
progression of monsoon rains (Vellinga et al. 2016; Fitzpatrick et al. 2016 Appendix 149
B).
150
In each climate respectively, the same SSTs are prescribed for the driving GCM, 151
CP4-A, and the parameterized model. Current climate SSTs are provided from the 152
Reynolds daily observational dataset (Reynolds et al., 2007). Future climate SSTs 153
are calculated first by quantifying the climatological change in SST values simulated 154
between 1975–2005 and 2085–2115 from a GCM run using the Coupled Model 155
Inter-comparison Project phase 5 Regional Climate Pathway 8.5 (RCP8.5). This 156
climatological SST change was calculated monthly, interpolated both spatially and 157
temporally, and added to the current climate values to produce future SSTs.
158
Greenhouse gases are taken from the RCP8.5 scenario for 2100; however the same 159
ozone and aerosol climatology is used in both simulations. Future changes in 160
precipitation rates across West Africa between the two simulations can be attributed 161
to rising temperatures and increases in greenhouse gases.
162
CP4-A has no convection scheme of any kind, using just model dynamics to 163
explicitly represent convective clouds. We note the caveat that a model at 4.4 km 164
grid spacing with no convective parameterization scheme may not capture the 165
complexity of convective development simulated in higher resolution CRM studies, 166
as model resolution has been highlighted in the past as a key issue in correctly 167
simulating cloud processes (e.g. Lin et al., 2012). With that said, the decision to have 168
no active convection scheme allows for a clearer comparison between convection 169
permitting and parameterized models produced during IMPALA.
170
Kendon et al. (2019) find that CP4-A better recreates observed high precipitation 171
rates over Africa compared to the parameterized-convection counterpart model and 172
projects a larger future increase in intense precipitation rates (their Fig. 1). Berthou 173
et al. (2019) find that CP4-A accurately simulates the frequency of MCSs over the 174
AMMA-CATCH observational sites. Stratton et al. (2018) and Berthou et al. (2019) 175
also show that the seasonal transition of monsoon rains across West Africa is better 176
captured in CP4-A compared to its parameterized convection counterpart, as well as 177
a reduction of the persistent dry bias within CP4-A. However, (Crook et al., 2019) 178
highlight that CP4-A fails to simulate MCSs of comparable area to the largest ones 179
observed, or speeds comparable to the quickest systems.
180
Simulations at the temporal and spatial scale of CP4-A incur an extensive 181
computational expense. As such, there has been a need for compromise with 182
regards to model design and output. There exists only one model representation for 183
the current and future climates respectively. The authors stress that the findings of 184
this paper are based on a research model, with a particular set of boundary 185
conditions from one global model, and so cannot be taken as projections with a 186
certainty level attached, but rather as results from climate sensitivity study.
187
The authors also stress that the two, ten-year simulations are not considered as 188
historical and future climatologies. Decadal and multi-decadal variability of ambient 189
conditions across West Africa can influence our results. We explore the role of this 190
variability further in Section 6.1.
191
3. Methods 192
In this paper, we analyze the climatic drivers of changes in early-evening MCS 193
extreme precipitation rates (the 99
thpercentile of MCS precipitation rate) over the
194
Sahel. The calculation methods for extreme precipitation rate and other considered 195
MCS-relevant metrics are presented in Table 1. We define the Sahel as 15°W–15°E, 196
10–18°N (displayed in Fig. 3); the suitability of this region for both climates is 197
explored in Section 4.1. The codes employed in this paper are available at 198
http://doi.org/10.5281/zenodo.2560371 and http://doi.org/10.5281/zenodo.2560410.
199
MCSs are classified as any contiguous structure with an area of cold-cloud 200
(Outgoing Longwave Radiation [OLR] <= 167 Wm
-2) of at least 25,000 km
2simulated 201
during July-September. Extreme precipitation rates are therefore calculated across a 202
region of at least 250 km
2(~ 16 grid cells). MCS tracking is performed from storm 203
genesis to decay using the algorithm presented in Stein et al. (2015) by identifying 204
contiguous regions of cold cloud that partially overlap between hourly intervals.
205
Tracked storms are analyzed at 1800 UTC in Sections 5 and 6 as this is the time of 206
maximum modelled precipitation (see Section 4). Different times of MCS occurrence 207
have been evaluated in Section 7.
208
Tracking MCSs using OLR instead of precipitation allows for continuous 209
identification of large-scale organized systems even when MCS precipitation may be 210
spatially or temporarily intermittent (Klein et al., 2018; their Fig. 4a). We have 211
analyzed precipitation-tracked events, finding little difference in key results (not 212
shown). The choice of a fixed temporal analysis window means that MCSs may be 213
analyzed at times when they are not at their maximum intensity; however, we believe 214
that this decision is fair given the availability of data as well as the complementary 215
analysis in Sections 4 and 7.
216
In this paper, we set two further restrictions on MCSs identification with the following 217
rationales:
218
All MCSs have an extreme rain rate at 1800 UTC greater than 10 mm/hr. This 219
restriction excludes non-precipitating cold cloud structures. The threshold of 220
10 mm/hr is arbitrary. Different thresholds (between 5 – 30 mm/hr) were 221
analyzed, with little difference in results.
222
All MCSs must have mean ambient (1200 UTC – 1600 UTC) precipitation 223
rate below 1 mm/hr across the region where each MCS is located at 1800 224
UTC. This restriction removes MCSs where the midday atmosphere is 225
perturbed by precipitation. Use of this restriction reduces the number of 226
MCSs analyzed (only 26% of current climate storms and 27% of future 227
climate storms pass this criterion). Evaluation of the vertical profile of 228
horizontal winds, and CAPE, in the environment preceding the arrival of an 229
MCS requires an atmosphere not disturbed by the potential effects of prior 230
storms. Complementary analysis for all MCSs regardless of this restriction 231
shows similar findings to those given here (not shown).
232
There are 1020 current climate MCSs and 553 future climate MCSs that meet 233
both criteria. The fact that CP4-A projects fewer Sahelian MCSs in the future climate 234
fits with prior analysis (c.f., Riede et al., 2016). Berthou et al., (revised), and Kendon 235
et al., (2019) additionally show that CP4-A simulates fewer Sahelian rain events in 236
the future regardless of storm size.
237
All metrics listed in Table 1 are calculated over the location where each MCS 238
is present at 1800 UTC. “Ambient” conditions (e.g., MU-CAPE) are evaluated at 239
1200 UTC consistent with Taylor et al. (2017), while “internal” storm characteristics 240
(such as minimum omega), are evaluated at 1800 UTC. Our choice of evaluation 241
times allow us to examine the influence of pre-storm environment and the internal
242
highlight that our measure of ambient wind shear does not use fixed pressure levels 244
to evaluate the low-level south-westerly and mid-level easterly ambient wind 245
circulations. Rather, our shear measure captures the maximum difference between 246
these two circulations across the lower to mid-atmosphere. We consider this 247
modification of importance given that changes in surface pressure and the potential 248
vertical displacement of the AEJ are not variables we wish to explicitly consider as 249
potential drivers of storm intensification changes.
250
In our analysis, we considered both zonal wind shear (i.e. maximum low-level 251
westerlies minus maximum mid-level easterlies) and wind shear magnitude (using 252
both the zonal and meridional horizontal winds) [Table 1]. We found little difference 253
in the influence of either metric on extreme precipitation rates. As such, we do not 254
show results for both metrics. Finally, due to an irreparable issue with CP4-A, 600 255
hPa model output is not available for the current climate storms in 1998 and some 256
storms in 1999.
257
258
4. Climatological differences in monsoon features over the Sahel.
259
For our analysis, a fixed geographical region has been selected for analysis 260
across climates. However, changes in extremes may arise from shifts of the summer 261
rain belt or other monsoon features. In this section, we consider whether the 262
latitudes 10–18°N offer a fair comparison of the West African Monsoon across 263
climates.
264
Figure 1 displays the zonally-averaged (across 15°W–15°E) latitudinal change 265
in measures of the monsoon state across climates. Mean daily precipitation 266
(indicative of the location of the monsoon rain belt) shows similar rainfall patterns
267
across climates with the maximum change in daily precipitation rate of 1 mm/day 268
(Fig. 1a). There is also evidence of a northwards shift of the northernmost extent of 269
monsoon rains. Proportionally, precipitation increases are greater farther north (~40 - 270
50% near 18°N). The ~1° northwards shift of monsoon rainfall limit across climates, 271
as well as the higher future precipitation rates over the Sahel, and a projected 272
reduction of precipitation rates near the Guinea Coast (5–7°N) is consistent with 273
previous studies (e.g., Vizy et al., 2013; Cook and Vizy 2015; Vizy and Cook 2017).
274
Mean midday zonal wind shear (Fig. 1b) increases predominantly due to 275
stronger low-level south-westerly flow across all latitudes of around 1-2 m/s or up to 276
40% (Figs. 1d-e) and a relatively smaller intensification of AEJ-level easterlies 277
across the northern Sahel of no more than 0.5 m/s (<5% across climates Fig. 1c).
278
There is a projected latitudinal broadening of the AEJ in the future, most pronounced 279
north of 13°N (Fig. 1c). However, the latitudinal position of peak zonal wind shear 280
and 650 hPa winds is the same in the current and future climate simulations.
281
Enhanced low level westerlies, indicative of the West African Westerly Jet diurnal 282
peaks (WAWJ, Pu and Cook 2010; 2012), and southerlies imply an enhanced 283
horizontal transport of moisture over the Sahel in the future.
284
Mean 850 hPa temperature (Fig. 1f) indicate a future increase in the 285
meridional temperature gradient across West Africa, with temperatures increasing 286
over the Sahara (6–7 K) more than over the Guinea Coast (5–6 K). This increased 287
meridional temperature gradient is consistent with the enhanced zonal wind shear 288
across the Sahel via their co-dependence due to the thermal wind balance (Fig. 1b;
289
Cook 1999; Parker et al. 2005; Cook and Vizy 2015). Specific humidity (Fig. 1g) is 290
much greater across the entire West African region in the future climate, with the 291
difference between the two climates maximized at ~12°N. We see little (< 3%)
change in lower-tropospheric relative humidity between climates across the Sahel 293
(Fig. 1h). Increased low-level southerly winds across the Guinea Coast, coupled with 294
higher specific humidity is associated with an increase in TCW over the Sahel (Fig.
295
1i). The location of maximum TCW does not change across climates (9–10°N), but 296
the greatest absolute increase occurs within the Sahel (~12–13°N).
297
The latitudinal pattern of each variable considered in Fig. 1 is consistent 298
across climates. We conclude that the region 10–18°N is a fair region over which to 299
consider MCSs in both climates.
300
Figure 2 shows the diurnal cycle of CP4-A precipitation (Fig. 2a) and lower-to- 301
mid-tropospheric wind shear magnitude (Fig. 2b), averaged over our analysis region.
302
In both climates, the maximum precipitation rate occurs during the late afternoon and 303
is minimized around 11 UTC. Precipitation increases at all times of day with climate 304
change, but percentage wise, the greatest increases occur prior to 1200 UTC. CP4- 305
A has a bias towards too much midday precipitation across the Sahel, however the 306
model is improved over parameterized counterpart models (Berthou et al., 2019).
307
Hourly rainfall rates increase by less than 20% in the future climate for all times after 308
1400 UTC. Kendon et al. (2019) show fewer short-lived evening storms in the future 309
climate within CP4-A, potentially explaining the relatively small absolute/percentage 310
increase in precipitation across the afternoon and evening period.
311
Observed wind shear in the lower-to-mid-troposphere is maximized overnight, 312
since this is the time of strongest south-westerly monsoon flow (Parker et al., 2005).
313
The diurnal cycle of zonal wind shear is consistent across climates within our 314
observation region (Fig. 2b). We see an increase throughout the day in the 315
percentage change of zonal wind shear across climates with a peak increase
316
occurring at 2100 UTC (~ 40%). The larger percentage increase at 1500 - 2100 UTC 317
is due in part to these times corresponding to the diurnal minimum in shear values.
318
Absolute increases in zonal wind shear range between about 3.5 m/s (at 1500 UTC) 319
and 4.8 m/s (at 2100 UTC) [Supplementary Figure S2]. Spatial changes in zonal 320
wind shear calculated between set levels (925 and 600 hPa) are provided in 321
Supplementary Fig. S3 and highlight that zonal wind shear increases more, in 322
absolute terms, within the eastern Sahel.
323
We decide that using 1800 UTC as our storm reference time is fair as 1800 324
UTC is shortly after the time of maximum area-averaged precipitation in both 325
climates and aligns with available instantaneous data for wind speed and 326
temperature. However, there exist regions where overnight rainfall provides the 327
majority of local precipitation over the Sahel (Mathon et al. 2002; Vizy and Cook 328
2018a). Drivers of MCS extreme precipitation rates at 0000 UTC and 0600 UTC 329
storms are discussed in Section 7.
330
We next consider changes in TCW and their relationship to near-surface 331
temperature changes across climates and compared them to the expected rate of 332
change in TCW per unit warming from the Clausius-Clapeyron relationship (i.e. 7%
333
per K warming). We use the differential rate of TCW change per Kelvin, r, expressed 334
as a percentage change, from O’Gorman and Muller (2010; their equation 2, our Fig.
335
3a):
336
r=100 x
log (1+ r∆)∆T
(1)
337
Where ΔT is the mean 1.5 meter temperature difference across climates, and r
Δis 338
the fractional rate of TCW change per Kelvin, calculated as:
339
𝑟
∆=
𝑇𝐶𝑊𝑓𝑢𝑡𝑢𝑟𝑒𝑇𝐶𝑊−𝑇𝐶𝑊𝑐𝑢𝑟𝑟𝑒𝑛𝑡𝑐𝑢𝑟𝑟𝑒𝑛𝑡