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Dynamic and Thermodynamic Impacts of Climate Change on Organized Convection in Alaska

Basile Poujol, Andreas Prein, Maria Molina, Caroline Muller

To cite this version:

Basile Poujol, Andreas Prein, Maria Molina, Caroline Muller. Dynamic and Thermodynamic Impacts of Climate Change on Organized Convection in Alaska. Climate Dynamics, Springer Verlag, In press.

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Dynamic and Thermodynamic Impacts of Climate Change on Organized Convection in Alaska

--Manuscript Draft--

Manuscript Number:

Full Title: Dynamic and Thermodynamic Impacts of Climate Change on Organized Convection in Alaska

Article Type: Original Article

Keywords: Convective systems; Moisture; CAPE; CIN; Sea ice loss; Convection-permitting modeling

Corresponding Author: Basile Poujol, B.Sc.

Département de Géosciences, Ecole Normale Supérieure, PSL Res. Univ., Paris 75005 Paris, FRANCE

Corresponding Author Secondary Information:

Corresponding Author's Institution: Département de Géosciences, Ecole Normale Supérieure, PSL Res. Univ., Paris Corresponding Author's Secondary

Institution:

First Author: Basile Poujol, B.Sc.

First Author Secondary Information:

Order of Authors: Basile Poujol, B.Sc.

Andreas F. Prein, Ph.D.

Maria Molina, Ph.D.

Caroline Muller, Ph.D.

Order of Authors Secondary Information:

Funding Information: National Science Foundation

(1852977) Not applicable

U.S. Army Corps of Engineers (Climate Preparedness and Resilience Program)

Not applicable

H2020 European Research Council

(805041) Dr Caroline Muller

Abstract: Convective storms can cause economic damage and harm to humans by producing flash floods, lightning and severe weather. While organized convection is well studied in the tropics and mid-latitudes, few studies have focused on the physics and climate change impacts of pan-Arctic convective systems.

 Using a convection-permitting model we showed in a predecessor study that organized convective storm frequency might triple by the end of the century in Alaska assuming a high emission scenario. The present study assesses the reasons for this rapid increase in organized convection by investigating dynamic and thermodynamic changes within future storms and their environments, in light of canonical existing theories for mid-latitude and tropical deep convection.

In a future climate, more moisture originates from Arctic marine basins increasing relative humidity over Alaska due to the loss of sea ice, which is in sharp contrast to lower-latitude land regions that are expected to become drier. This increase in relative humidity favors the onset of organized convection through more unstable

thermodynamic environments, increased low-level buoyancy, and weaker downdrafts.

Our confidence in these results is increased by showing that these changes can be analytically derived from basic physical laws. This suggests that organized

thunderstorms might become more frequent in other pan-Arctic continental regions

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Suggested Reviewers: David Romps

University of California Berkeley romps@berkeley.edu

Paul O'Gorman

Massachusetts Institute of Technology pog@mit.edu

Jan Haerter

Kobenhavns Universitet Niels Bohr Instituttet haerter@nbi.ku.dk

Christopher Moseley National Taipei University

christopher.moseley@mpimet.mpg.de Christopher Holloway

University of Reading c.e.holloway@reading.ac.uk

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Noname manuscript No.

(will be inserted by the editor)

Dynamic and Thermodynamic Impacts of Climate

1

Change on Organized Convection in Alaska

2

Basile Poujol · Andreas F. Prein ·

3

Maria J. Molina · Caroline Muller

4

5

Received: date / Accepted: date

6

Abstract Convective storms can cause economic damage and harm to humans by

7

producing flash floods, lightning and severe weather. While organized convection

8

is well studied in the tropics and mid-latitudes, few studies have focused on the

9

physics and climate change impacts of pan-Arctic convective systems.

10

Using a convection-permitting model we showed in a predecessor study that orga-

11

nized convective storm frequency might triple by the end of the century in Alaska

12

assuming a high emission scenario. The present study assesses the reasons for this

13

rapid increase in organized convection by investigating dynamic and thermody-

14

namic changes within future storms and their environments, in light of canonical

15

existing theories for mid-latitude and tropical deep convection.

16

In a future climate, more moisture originates from Arctic marine basins increas-

17

ing relative humidity over Alaska due to the loss of sea ice, which is in sharp

18

contrast to lower-latitude land regions that are expected to become drier. This in-

19

B.Poujol

D´ epartement de G´ eosciences, ´ Ecole Normale Sup´ erieure, PSL. Res. Univ., Paris, France E-mail: basile.poujol@ens.fr

A.F. Prein

National Center for Atmospheric Research, Boulder, CO USA M.J.Molina

National Center for Atmospheric Research, Boulder, CO USA C.Muller

CNRS, Laboratoire de M´ et´ eorologie Dynamique / Institut Pierre Simon Laplace, ´ Ecole Nor- male Sup´ erieure, Paris, France

Click here to view linked References

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crease in relative humidity favors the onset of organized convection through more

20

unstable thermodynamic environments, increased low-level buoyancy, and weaker

21

downdrafts. Our confidence in these results is increased by showing that these

22

changes can be analytically derived from basic physical laws. This suggests that

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organized thunderstorms might become more frequent in other pan-Arctic con-

24

tinental regions highlighting the uniqueness and vulnerability of these regions to

25

climate change.

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Keywords Convective systems · Moisture · CAPE · CIN · Sea ice loss ·

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Convection-permitting modeling

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1 Introduction

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Organized convective storms are a common feature of the climate system in con-

30

tinental regions, where they typically occur in the summer [Houze Jr, 2004]. They

31

are of particular importance since they can produce large amounts of precipita-

32

tion as well as severe hazards (e.g., hail, flash floods), and play an important

33

role in the hydrological cycle. The characteristics of these storms has been shown

34

to largely depend on dynamical and thermodynamic environments (e.g., [Geerts

35

et al., 2017]), which can be supportive for deep convection and for convective

36

organization.

37

Key ingredients for intense, deep convection to occur in the mid-latitudes are

38

usually a buoyant low level air mass, measured by convective available potential

39

energy (CAPE) [Moncrieff and Miller, 1976], a large amount of moisture usually

40

provided by local evaporation or by advection driven by a low-level jet from mar-

41

itime regions [Stensrud, 1996], and a forcing mechanism such as solar heating, or

42

vertical lifting. Moreover, low-level and tropospheric wind shear [Weisman and Ro-

43

tunno, 2004], dry environments [McCaul Jr et al., 2005], and large-scale potential

44

vorticity or uplift [Antonescu et al., 2013] have been shown to be associated with

45

the organization of storms. Finally, convective inhibition (CIN) can be important

46

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for the buildup of CAPE [Parker, 2002], although too much inhibition can prevent

47

convection initiation without sufficiently strong forcing.

48

All of the above processes have complex interactions in the atmosphere and

49

convective storms themselves have a strong influence on the state of the tropo-

50

sphere [Emanuel et al., 1994]. Deep convection can occur in a statistical equilib-

51

rium with its environment, which is called the radiative-convective equilibrium in

52

the tropics [Held et al., 1993]. The accumulation of large amounts of CAPE that,

53

when released, can produce very intense organized storms is rare and concentrated

54

in specific regions, such as the U.S. Great Plains, South American Pampas and

55

Gran Chaco, Sahel, and Northern India [Zipser et al., 2006], although one can also

56

find large CAPE occasionally elsewhere. However, convection can also organize

57

only due to radiative and thermodynamic feedbacks, without any other mechani-

58

cal triggering when radiative-convective equilibrium is satisfied (see [Wing et al.,

59

2017] for a review).

60

Ingredients for deep, organized convection have been shown to change with

61

increasing surface temperature and moisture. In particular, atmospheric CAPE is

62

expected to increase significantly over continents and oceans in general circulation

63

models [Chen et al., 2020], high-resolution regional climate models [Rasmussen

64

et al., 2017], and idealized cloud-resolving models [Muller et al., 2011]. This in-

65

crease of CAPE is also expected from analytical models [Romps, 2016]. Changes in

66

other, no less important, factors affecting the generation and organization of con-

67

vection are more uncertain. Recent studies suggested that CIN might strengthen

68

over continents. Changes in CIN are affected by competing influences of increasing

69

temperature, increasing moisture, and decreasing relative humidity making robust

70

climate change assessments difficult [Chen et al., 2020]. Also, some studies pre-

71

dict a decrease in high wind shear occurrences under global warming [Diffenbaugh

72

et al., 2013], however large scale dynamical changes, such as a latitude shift of the

73

eddy-driven jets or changes in the frequency of extratropical cyclones are still very

74

uncertain today due to the large dispersion in the GCM results [Shepherd, 2014].

75

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Finally, regional dynamical changes, for example in moisture advection, play an

76

important role in future changes but are very dependent on location.

77

It is, nevertheless, largely acknowledged that future environments will be con-

78

ducive for more intense storms [Singh et al., 2017], producing heavier downpours

79

and larger amounts of precipitation [Westra et al., 2014], as the saturated atmo-

80

spheric moisture is increasing almost exponentially with temperature [Clausius,

81

1850]. How the frequency, size, speed and organization of these storms will re-

82

spond to climate change is still uncertain (see [Schumacher and Rasmussen, 2020]

83

for a review). For example, [Prein et al., 2017b] simulated decreases of convective

84

system frequency over the U.S. Great Plains, but increases in Southern Canada.

85

Also, current modeling capacities at climate timescales are able to reproduce the

86

known climatology of convective storms [Prein et al., 2017a] but fail to reproduce

87

their structure [Haberlie and Ashley, 2019].

88

Comparatively, little is known about the environments that support the for-

89

mation of convective storms in the high-latitude continental regions. We know

90

from observations that organized convective systems are present but rare in the

91

pan-Arctic [ Жукова et al., 2018, Punkka and Bister, 2015]. In a predecessor study

92

[Poujol et al., 2020] we showed that organized convective storms are projected to

93

triple by the end of the century in Alaska under a high emission scenario as a re-

94

sult of anthropogenic climate change. These results are supported by observational

95

studies in Siberia [Chernokulsky et al., 2011] that report a strong increase in the

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frequency of deep convective clouds during the period 1991-2010. The reasons for

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such increases are still unclear but likely result from changes in the dynamical and

98

thermodynamic environments.

99

Pan-Arctic land regions undergo a very strong annual cycle and a weaker diur-

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nal cycle than mid-latitude regions and are also affected by more weather variations

101

in summer. Pan-Arctic regions are also unique since they are heavily affected by

102

melting sea ice. The increased open ocean areas in future climates provide an ad-

103

ditional source of moisture [Bintanja and Selten, 2014], which causes Pan-Arctic

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climate change to be uniquely different from climate change in other parts of the

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globe. This study investigates the causes for the threefold increase of Alaskan or-

106

ganized convective storms presented in [Poujol et al., 2020] by analysing changes

107

in moisture advection patterns and changes in dynamic and thermodynamics of

108

convective systems and their environments.

109

In section 2, we present the data and the methods of this study. Section 3

110

presents the results, including an overview of climatological changes in Alaska re-

111

lated to organized convection (section 3.1), analysis of the origin of air masses

112

entering into the storms (section 3.2), changes in the thermodynamic storm en-

113

vironments (section 3.3), and small-scale storm dynamics (section 3.4), including

114

vertical motions and cold pools. Section 4 closes with discussion and a conclusion.

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2 Data and methods

116

2.1 Data

117

This study uses data from high-resolution climate simulations of Alaska presented

118

in [Monaghan et al., 2018] and [Newman et al., 2020]. The simulation domain

119

covers most of Alaska and parts of Northwestern Canada (figure 1a). We are

120

interested in convective storms in the Interior, Western and Northern Alaska. As

121

in [Poujol et al., 2020], we define continental Alaska as the five climate regions

122

shown in Figure 1a, which were defined by [Bieniek et al., 2012]. The North Slope

123

has an Arctic climate and convective storms are rarely observed in this region

124

[Grice and Comiskey, 1976]. It is delimited to the South by the Brooks range,

125

about 2000m high. The West Coast has more maritime conditions during the ice-

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free season and is subject to the influence of sub-polar cyclones and rare polar

127

lows [Perica et al., 2012]. Interior Alaska is bordered by the Brooks range to the

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North and the Alaska range to the South. These mountains isolate the region from

129

the Arctic and Pacific oceans. Therefore, it has a continental climate and this is

130

where convective activity is strongest [Grice and Comiskey, 1976, Reap, 1991]. A

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more detailed description of the domain can be found in [Poujol et al., 2020]. The

132

full description of the model parameters is available in [Monaghan et al., 2018].

133

We use the Weather Research and Forecasting (WRF) model [Skamarock et al.,

134

2005] with a horizontal grid spacing of 4km, that enables convection to be explic-

135

itly represented by the model dynamical core. The convective parameterization is

136

off and the microphysical scheme of [Thompson et al., 2008] is used. Other pa-

137

rameterizations include the Noah-MP land surface scheme [Niu et al., 2011], the

138

Yonsei University (YSU) planetary boundary layer representation [Hong et al.,

139

2006], and the RRTMG radiation scheme [Iacono et al., 2008]. The simulation is

140

conducted over the period September 2002 - June 2016 and covers thirteen full

141

summer seasons, from 2003 to 2015.

142

Two simulations are produced. One control simulation is forced by the Euro-

143

pean Centre for Medium Range Weather Forecasting Interim Reanalysis (ERA-

144

Interim) [Dee et al., 2011] and one future climate run using the pseudo-global-

145

warming (PGW) technique [Sch¨ ar et al., 1996] under a high emission scenario

146

at the end of the century. The monthly differences of temperature, moisture,

147

geopotential and wind from the fifth Coupled Model Intercomparison Project

148

(CMIP5; [Taylor et al., 2012]) multi-model mean between a high emission sce-

149

nario (RCP8.5,2071-2100 [Riahi et al., 2011]) and historical climate (1976-2005)

150

are added to the six-hourly boundary conditions of ERA-Interim used in the con-

151

trol simulation. Therefore, the PGW simulation includes the thermodynamic signal

152

of climate change, but does not account for synoptic-scale dynamical changes ex-

153

cept for their monthly mean. However, small-scale dynamical changes that occur

154

within the domain are taken into account. See [Newman et al., 2020] for a more

155

detailed description of how the PGW technique is applied in these simulations.

156

Temperature and precipitation climatology of Alaska in the historical WRF

157

simulation were evaluated against reanalysis and meteorological stations data in

158

[Monaghan et al., 2018]. The model accurately represents interannual variability

159

and precipitation maxima. Also, hourly precipitation in the model was evaluated

160

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against precipitation stations hourly data and the model was found to produce a

161

correct annual cycle, and to have a diurnal cycle delayed by 0-3 hours depending

162

on the stations [Poujol et al., 2020]. This last study showed that the model is able

163

to reproduce correctly the distribution of CAPE and CIN as observed by weather

164

balloons in Fairbanks, and also showed that the model reasonably represents orga-

165

nized convective storms compared to the few radar and satellite observations that

166

are available.

167

2.2 Methods

168

2.2.1 Storm tracking

169

Hourly simulated precipitation is used to track organized convective storms. The

170

tracking algorithm is similar to the ones presented in [Davis et al., 2006] and

171

[Prein et al., 2017a]. Hourly accumulated precipitation is smoothed in space and

172

time, and then only precipitation exceeding 4mm/hr is selected. Next, storms are

173

defined as contiguous precipitation objects in the x-y-t three-dimensional space.

174

Therefore, if two storms split or merge, they will be accounted for one single storm.

175

See [Poujol et al., 2020] for a more detailed description of the algorithm. In [Poujol

176

et al., 2020], about 500 storms were found in the control simulation and 1500 in

177

the pseudo-global warming simulation. A description of the characteristics of these

178

storms, their geographical repartition, as well as their diurnal and annual cycles,

179

can be found in [Poujol et al., 2020]. Here we build on the results of our initial study

180

to understand the physical processes that are responsible for the rapid increase in

181

storm frequency under future climate conditions.

182

2.2.2 Air mass tracking

183

Backward air mass tracking was conducted using the NOAA Air Resources Lab-

184

oratory (ARL) Hybrid Single-Particle Lagrangian Integrated Trajectory model

185

(HYSPLIT; [Stein et al., 2015]) using this study’s WRF simulations converted to

186

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ARL-format. Backward air parcel trajectories were run for a time period of 10 days

187

and initiated from the latitude and longitude location of each convective storm’s

188

center of precipitation mass at its initiation time. HYSPLIT computes the origins

189

of air parcels by spatially and temporally interpolating 3D wind data. Trajectory

190

paths are sensitive to the exact release point of air parcels [Stohl, 1998], and there-

191

fore a 3D matrix of trajectories was initiated from each convective storm instead

192

of a singular trajectory (e.g., [Molina et al., 2020]). The 3D matrix dimensions

193

are 7x7x7, consisting of a total of 343 trajectories, with horizontal grid spacing of

194

1-km, centered at the storm’s center of mass location. The top layer of each 3D

195

matrix was the height of the planetary boundary layer (HPBL, calculated by the

196

model PBL scheme) and each 3D matrix layer was spaced at 0.05xHPBL (down-

197

wards). Various along-trajectory meteorological variables were output at hourly

198

intervals and binned onto a 50x50-km spatial grid spanning the study domain for

199

visualization, including relative humidity and parcel track density (or frequency),

200

computed as trajectory intersections with grid cells. The moisture uptake algo-

201

rithm [Sodemann et al., 2008] was also applied to trajectory output, in order to

202

quantify where air parcels acquired moisture that contributed to the organized

203

convective storms. The moisture uptake algorithm consists of various heuristics,

204

which track the changes in specific humidity occurring along the trajectory’s path.

205

Moisture uptakes were identified when the increases in specific humidity occured

206

below the HPBL and were not lost via precipitation prior to reaching the convec-

207

tive storm. Moisture uptake results were subsequently gridded onto the 50x50-km

208

domain and frequency weighted. Additional details regarding the 3D trajectory

209

matrices and the moisture uptake algorithm as used in this study are available in

210

[Molina and Allen, 2020] and [Molina et al., 2020].

211

2.2.3 Atmospheric soundings

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For the purpose of this study, one atmospheric sounding is calculated for each

213

tracked storm that initiates between 16:00 and 21:00 (local time) in the historical

214

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and in the PGW simulations. The sounding is calculated at 16:00. This specific

215

time is chosen because of constraints on the time when 3D data was output in the

216

simulations. Since CAPE and CIN are very variable with location, the following

217

technique is used: for each storm, a grid box of 200*200 km is centered on the cen-

218

ter of mass (hourly precipitation) of the storm at its initiation. Then, the direction

219

of the maximum gradient of equivalent potential temperature at 2 m height is cal-

220

culated, and all non-precipitating grid cells that are within +/- 20 degrees of the

221

maximum equivalent potential temperature gradient direction are selected. Next,

222

3-D temperature, dewpoint temperature and pressure are averaged over these grid-

223

cells providing an average inflow sounding for each storm. A similar approach has

224

been used to define the inflow area of MCSs by [Trier et al., 2014a, Trier et al.,

225

2014b, Prein et al., 2017b]. This sounding is then used to calculate characteris-

226

tic variables of the environment: convective available potential energy (CAPE),

227

convective inhibition (CIN), level of free convection (LFC), freezing level, surface

228

temperature and surface relative humidity (RH) for the storm inflow environment.

229

2.2.4 CAPE and CIN definitions

230

In this study, CAPE (CIN) is defined as the accumulated positive (negative) buoy-

231

ant energy per unit mass from a parcel lifted adiabatically from a level z

0

until

232

its equilibrium level, through its level of free convection (LFC). These levels are

233

defined as the two tropospheric levels where the parcel has a zero buoyancy. There-

234

fore, CAPE and CIN are defined as follows:

235

CAPE = Z

zEL

zLF C

g · T

p

− T

env

T

env

dz (1)

and

236

CIN = Z

zLF C

z0

g · T

p

− T

env

T

env

dz (2)

where g is Earth’s gravity acceleration, T

p

and T

env

refer respectively to the parcel

237

and the environment temperature and z to height. In this study, most unstable

238

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Fig. 1 a: Mean 2 m above ground temperature in summer (May to August) in the control simulation. Contours and initial letters indicate the five subregions of interest: North Slope (NS), West Coast (WC), Central Interior (CI), Northeast Interior (NI) and Southeast Interior (SI). The three major ocean basins are also indicated: Gulf of Alaska (GoA), Bering Sea (BS) and Arctic Ocean (AO). b: Mean temperature change as a function of height averaged over the summer (May-August) except for the Arctic Ocean (months are indicated in the legend).

Triangles on the x-axis show mean temperature change at 2 m. To avoid statistical bias, change is shown on the model levels and mean pressure is given as an indicative vertical coordinate.

All changes are statistically significant at a 95% confidence level according to a two-tailed Student’s t-test [Student, 1908]. c-f: Colored contours show monthly changes in temperature and the sea ice edge (0.15 sea ice concentration) is shown for the control (solid contour) and PGW (dashed contour) simulations. Dotted areas indicate a significant temperature change at a 95% confidence level according to Student’s t-test.

CAPE (MUCAPE) and the associated CIN are used by default. This means that

239

the z

0

chosen is the one between 0 and 3000m above the surface that maximizes

240

CAPE. However, for easier calculations, the parcel is taken at the surface and

241

surface-based CAPE and CIN are used in the analytical model.

242

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2.2.5 Cold pool tracking

243

This study also focuses on cold pools, that are patches of negative buoyancy pro-

244

duced by the evaporation of intense precipitation in convective downdrafts. In this

245

study, cold pools are identified using the same algorithm that is used to track the

246

convective storms, which is described in [Poujol et al., 2020]. Instead of hourly

247

precipitation, hourly surface negative buoyancy is used which is defined as:

248

−b = −g · θ − hθi

hθi (3)

where g is the Earth’s gravity acceleration, θ is 2m potential temperature and

249

brackets stand for horizontal average over a 100*100km box. Cold pools are de-

250

tected using a negative buoyancy threshold of 0.1m · s

−2

, a smoothing radius of

251

0.5 grid points in space, no smoothing in time, and a minimum volume of 50 grid

252

points in space and time. These parameters have been chosen by visual check-

253

ing, ensuring that cold pools are selected that have sharp buoyancy gradients at

254

their edges, and to avoid the detection of low buoyancy regions produced by non-

255

convective atmospheric features such as fronts. For further information about how

256

the algorithm works, refer to [Davis et al., 2006].

257

The algorithm also detects temperature inversions in low topography regions,

258

as well as spurious cold pools close to the coast due to the land-sea temperature

259

contrast, and spurious cold pools in the mountains probably due to the altitude-

260

induced temperature contrast. The use of potential temperature mitigates but does

261

not completely solve this issue. To avoid the problem in the coastal regions, cold

262

pools are tracked only in the Central interior, Northeast Interior and Southeast

263

Interior subregions. Also, all the grid points where the frequency of occurrence

264

of cold pools exceeds 10 hours per year in the historical simulation are removed

265

from the analysis (this concerns 3.7% of grid points in the three subregions). These

266

points are mainly located in the Alaska range and the Brooks range, and also along

267

the Yukon river where temperature inversions are frequent. This led to removing

268

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70% of identified cold pools and we will show in section 3 that the remaining cold

269

pools are dominantly related to convective storms. After all these criteria were

270

applied, the remaining sample size is of 3275 cold pools in the control simulation.

271

3 Results

272

3.1 Climatological changes in Alaska

273

Figure 1 shows the mean summertime 2 m above ground temperature in Alaska,

274

as well as monthly changes in temperature and sea ice concentration in the simu-

275

lations. Mean temperature is warmest in interior Alaska where it reaches almost

276

15

C, whereas it is coldest in the North Slope that is surrounded by sea ice until

277

July under current climate conditions. Temperature is also much warmer over land

278

than over ocean.

279

Climate change is projected to homogeneously warm the continent and the

280

Pacific ocean by 3-4 K during summer. However, the warming over the other ocean

281

regions is much more complex due to the effects of sea ice loss. The massive

282

sea ice retreat observed in May in the Bering and Chukchi Seas has a strong

283

fingerprint on atmospheric warming, that persists over the summer months, likely

284

owing to the large ocean heat capacity. Similarly, the Arctic ocean experiences less

285

temperature change during months when there is no sea ice loss, whereas a very

286

strong temperature increase is observed in July and August due to the retreat of

287

sea ice. The very small warming in a small layer close to the surface when the

288

ocean is covered by sea ice might occur because that temperature is maintained at

289

the freezing point by the sea ice, and all additional energy goes to melting during

290

this season. One can also notice patches of intense warming in the Alaska range

291

that likely correspond to snow-albedo feedbacks.

292

The sea ice loss in the region induces a reduced temperature gradient between

293

land and ocean due to the larger warming over ocean than over land. According

294

to [Byrne and O’Gorman, 2018], relative humidity changes over land can be ap-

295

(16)

Fig. 2 a: Mean relative humidity in the summer (May to August) in the control simulation.

Arrows indicate mean wind at 850hPa in the control simulation. b: Mean relative humidity change (shadings) and mean change of 850hPa wind. Dotted areas indicate a significant relative humidity change at a 95% confidence level according to a two-tailed Student’s t-test [Student, 1908]. Wind changes are not statistically significant. c: Mean relative humidity profile in the five subregions of interest under current climate conditions averaged during the warm season (May-August) except for the Arctic Ocean as indicated in the legend. d: Mean change in relative humidity as a function of height in the subregions of interest. Dots on the right of the panel indicate a statistically significant change with 95% confidence according to Student’s t-test. In c and d, triangles on the x-axis show relative humidity and its change at 2 m.

proximated by assuming that changes of moist static energy over land and over

296

oceans are similar: ∆h

land

= ∆h

ocean

that is:

297

c

p

∆T

land

+ L

v

∆q

land

= c

p

∆T

ocean

+ L

v

∆q

ocean

(4)

(17)

Figure 2a, shows that summer-mean near surface relative humidity is already al-

298

most at saturation over the oceans in the current climate. It is, therefore, reason-

299

able to hypothesize that relative humidity stays constant over the ocean. Using the

300

climatological values of temperature in Interior Alaska and the Bering Sea (respec-

301

tively 15

C and 7

C), relative humidity in the same regions (respectively 0.6 and

302

1) and temperature changes in July (respectively +4

C and +4.5

C), this sim-

303

ple model predicts a 5 % increase in continental relative humidity in Alaska. This

304

theoretical value is close to what the model simulates (figure 2b), and therefore

305

the sea-ice albedo feedback and the subsequent land-sea contrast under warming

306

appear to be responsible for a moistening of Alaska in summer. This is unique in

307

high-latitude land regions since most continents experience drying with climate

308

change, mainly due to the land-sea warming contrast [Joshi et al., 2008, Byrne

309

and O’Gorman, 2018]. This moistening is constrained to the low atmospheric lev-

310

els and very small changes are observed above 800 hPa (about 1500 m above sea

311

level). Moreover, figure 2d shows that over land, relative humidity changes are

312

statistically significant only below 900 hPa. It is interesting to notice that whereas

313

the Arctic Ocean experiences little relative humidity changes at the surface at the

314

end of the summer, like the other ocean basins, it experiences strong moistening in

315

the lower layers in May-June when most of it is still frozen both in the historical

316

and PGW simulations (fig. 1b). It therefore behaves like a continent in the early

317

summer.

318

Finally, mean wind at 850 hPa is shown on figure 2a-b. In the Interior regions,

319

the mean circulation is weak which suggests that convective storms generally occur

320

in a barometric swamp. This is also supported by the low average movement speeds

321

of convective storms [Poujol et al., 2020]. However the West coast and the North

322

Slope are dominated by Southerly winds. These winds appear to become weaker

323

in a future climate. This result must be taken with caution, as the PGW scenario

324

only captures monthly changes of the synoptic circulation. Alaska moisture trans-

325

port is dominated by meridional circulations that shift between Northerlies and

326

(18)

Southerlies and moisture is mostly transported by transient eddies [Naakka et al.,

327

2019]. Furthermore, [Tachibana et al., 2019] showed that strong sea ice loss in the

328

Bering and Chukchi seas can generate a persistent positive geopotential height

329

anomaly in these regions, and affect large-scale circulation over North America.

330

In particular, this last effect could be an explanation for the observed weakening

331

of Southerlies. Note that no important changes in low-level vertical wind shear

332

occur between the two simulations, probably owing to the PGW methodology. As

333

shown on figure S1, climatological wind shear is weak in the region of interest

334

(about 5m/s for shallow wind shear and 9m/s for deep layer shear), two to three

335

times smaller than typical values in the U.S. Great Plains for example. Moreover,

336

changes in wind shear are non significant between the historical and the PGW

337

simulations. Also, no statistically significant changes in soil moisture content or

338

evaporation occur in the simulations, except in the North Slope where the soil

339

contains more water in a future climate, possibly due to permafrost thaw (not

340

shown).

341

Warming and moistening are the dominant simulated changes in the region.

342

The rest of this study investigates the effect of these changes on future organized

343

convective storms focusing on the reasons for their threefold increase in frequency

344

[Poujol et al., 2020].

345

3.2 Origin of the storm air masses

346

Backward tracking of the air masses entering into the storms has been performed

347

in order to better understand the synoptic-scale patterns associated with the con-

348

vective storms and the properties of the air masses feeding them. The tracking

349

framework is described in the Methods section.

350

To provide an example, figure 3 shows the results of this air mass tracking for

351

the convective storms occurring over the North Slope. Panel a shows the track

352

frequency of the parcels released from convective storms and tracked backwards.

353

The frequency is largest in the North Slope itself; however some tracks cover a

354

(19)

Fig. 3 Results of the backward tracking analysis for the parcels released in the North Slope’s convective storms. a: Normalized parcel track density on a coarse grid of the model domain.

c: Mean of monthly mean of relative humidity of the parcels. e: Normalized moisture uptake from the parcels. b,d,f: Same as a,c,e, but in the PGW simulation.

large part of the domain including the Gulf of Alaska, the Bering Sea, and the

355

Arctic Ocean. The mean parcel relative humidity, shown in panel b, is close to

356

the surface climatological relative humidity over land. However, over the ocean,

357

parcels have a much lower relative humidity than the surface climatology, which

358

is likely due to the fact that they are lifted.

359

Consistently, the moisture uptake (shown in panel c) is very local, which sug-

360

gests that the storms occur under weak dynamical forcing, as already suggested by

361

the climatological wind speed on figure 2a. This also shows that the recycling ratio

362

(20)

is high for these storms. However, this should be taken with caution, as the study

363

domain is small, and evaporation over marine areas is prohibited by a low-level

364

troposphere that is almost saturated (Fig. 2). Therefore, the fact that moisture

365

uptake is local does not necessarily mean that the air masses feeding the storms

366

do not carry temperature and moisture characteristics from marine basins outside

367

the study domain.

368

Under future climate conditions (panels d-f), much more air feeding the storms

369

comes from the Arctic Ocean, potentially owing to the strong warming of this area

370

due to the retreat of sea ice. The mean relative humidity of the parcels is increased

371

over the whole domain, but this increase is much more pronounced over the Arctic

372

Ocean. This is also visible in the moisture uptake from the Arctic Ocean, that

373

increases by 50% (when normalized by the increase in the number of storms). All

374

these changes suggest that melting sea ice in this region provides an additional

375

source of moisture for future convective storms.

376

The results in the other subregions are similar. Supplementary figure S2 depicts

377

the results for storms over the Central Interior, which are representative of the

378

other subregions as well. The moisture uptake is mainly local and parcels come

379

from the three marine basins. In the future, no strong changes are observed except

380

for an increase of the relative humidity of the parcels over land and over ocean.

381

For easier comparison and understanding of the origin of air masses, parcel

382

frequency has been aggregated by ocean basin in figure 4a,c. Also, figure 4b,d

383

shows the repartition of the origin of parcels (i.e. the location of the parcel at the

384

end of the backward tracking within the study domain). Although parcel frequency

385

is highest over land, most parcels originate from marine basins. Air coming from

386

the Gulf of Alaska contributes most to storms (about 50% of the air mass origin),

387

which is not surprising given that it is the warmest ocean basin. However, more

388

parcels originate from the Arctic Ocean and the Bering Sea at the end of summer,

389

when these basins are ice-free. The two different approaches (parcel frequency or

390

(21)

Fig. 4 Origin of the air masses feeding the storms. a: For each subregion, and for the historical and PGW simulations, bars represent the aggregated track density of the parcels over land and the three ocean basins in May-June. b: Bars represent the distribution of the origin of air parcels, which is defined at the location of the parcel at the end of the backward trajectory.

c-d: As a-b but for July and August.

parcel origin) give similar results on the ranking of marine basins in moisture origin

391

for all subregions, and how they change in a future climate.

392

In a future climate, the proportion of air masses coming from the Bering Sea

393

and the Arctic Ocean increases for all the subregions except the West Coast,

394

especially in July-August. Generally, this increase occurs at the expense of the

395

proportion of air masses coming from the Gulf of Alaska. This means that in a

396

future climate the proportion of storms that are fed by Arctic air masses is larger.

397

Changes in the frequency of origin of air parcels can also be interpreted using

398

the bayesian probability theory. For a given subregion, let S be the event “A storm

399

occurs in the subregion” and O a random variable representing the origin of the

400

(22)

air mass. According to the Bayes’ formula [Bayes, 1763] :

401

P (O = x|S) = P (S|O = x)

P (S) × P (O = x) (5) where x is an arbitrary ocean basin. The left-hand side corresponds to the prob-

402

ability that an air mass feeding a storm comes from a given ocean basin, which

403

is shown in figure 4. It is equal to the probability that a storm occurs when the

404

low-level air mass comes from this basin normalized by the number of storms (left-

405

hand factor of the right-hand side), multiplied by the probability that the air mass

406

comes from this basin (right-hand factor). Since there are no changes in the dy-

407

namical day-to-day variability in the simulations, the last factor P (O = x) remains

408

almost constant between the simulations. (This assumption could be checked by

409

investigating the origin of the air masses on days when no convection occurs, how-

410

ever this was not done in this study due to computational constraints.) Therefore,

411

changes in the frequencies shown in figure 4 directly reflect changes in the normal-

412

ized probability that an air mass coming from a given oceanic basin is associated

413

with the triggering of a convective storm. Therefore, it stems from these proba-

414

bilistic considerations that air masses coming from the Bering Sea and the Arctic

415

Ocean are more likely to be associated with convective storm initiation in almost

416

all subregions in a future climate. (Note that this conclusion could not be drawn if

417

the simulations included changes in the dynamics.) This can be due to the strong

418

sea ice retreat, providing an additional source of moisture, as well as the amplified

419

warming and moistening of the atmosphere subsequent to sea ice loss in these

420

regions. The fact that this increased contribution from Arctic marine basins is

421

largest at the end of summer, when sea ice loss is the strongest, further supports

422

this hypothesis.

423

(23)

Fig. 5 Joint distribution of most unstable CAPE and CIN averaged over the West Coast (a,b)

and Central Interior(c,d) at 16:00PM local time (AKDT), from May to August. Marginal

distributions are shown in gray. a,c: Control simulation. b,d: PGW simulation. Note the

logarithmic scale of the colorbar and the marginal distributions. A Gaussian smoothing with

a radius of 1 is applied to the distributions. Stippling indicates a 95% confidence significant

change according to a monthly block bootstrap test.

(24)

3.3 Changes in the thermodynamic convective environments

424

3.3.1 CAPE and CIN climatology

425

Figure 5 depicts the joint distribution of horizontally averaged most unstable

426

CAPE and CIN in the afternoon (16:00 local time) over two representative sub-

427

regions. Environments favorable to deep and organized convection are rare in the

428

current climate simulation. Subregion-averaged CAPE is usually below 100J/kg,

429

which is usually insufficient for organized convective storms to develop [Kirkpatrick

430

et al., 2011]. Indeed, as it will be shown later, the storms that we track in this

431

study tend to develop in environments with CAPE values ranging from 200 to

432

600J/kg and CIN values below 15J/kg. Such CAPE values are in the tail of the

433

current climate distribution causing these storms to be rare: in the current climate

434

simulation, they have a recurrence period of once per year South of the Yukon river

435

and longer in the Northern part of Alaska [Poujol et al., 2020]. The tail of the dis-

436

tribution extends towards much higher values of CAPE in the PGW simulation,

437

however CIN changes differ across subregions.

438

In the West Coast, the tail is extended towards high-CAPE and high-CIN

439

environments, similarly to what has been simulated in the U.S. Great Plains [Ras-

440

mussen et al., 2017]. This will likely favor more intense and organized systems,

441

however more energy will be necessary to trigger deep convection. In contrast, in

442

the Central Interior, the distribution is extending towards high-CAPE and low-

443

CIN environments. These environments are extremely favorable for organized, deep

444

convection, as an increased amount of energy is available for deep convection and

445

can be easily released.

446

The Northeast and Southeast Interior subregions show a behaviour very similar

447

to the Central Interior whereas the North Slope experiences changes in-between

448

the West Coast and the Interior with increases in high-CAPE and moderate-

449

CIN environments. In any case, the increase is much larger in the tail of the

450

(25)

distribution. For example, environments with CAPE> 300J/kg and CIN> −5J/kg

451

in the Central Interior region are five folding in the future simulations.

452

3.3.2 Storm inflow soundings and mathematical model

453

In order to explain these large changes in thermodynamic environments, a simple

454

model is used that simulates the effect of changes in surface temperature and

455

relative humidity in some key features of the environment. This is based on an

456

analytical model developed by [Romps, 2016].

457

The main hypothesis is that the environment profile obeys a Radiative-Convective

458

equilibrium (RCE), i.e. the profile of temperature is a balance between the radia-

459

tive transfers of energy in the atmosphere, and the mixing and latent heating

460

provided by convection. Although this is obviously not true in winter or in the

461

transition season in continental regions, it is a reasonable assumption in summer.

462

In particular, [Grice and Comiskey, 1976] noticed that deep convection occurs

463

nearly every day in Alaska in June and July and that most Alaskan thunder-

464

storms are of the air-mass type (i.e., they are triggered by solar forcing and are

465

not associated with a large-scale forcing). This is further confirmed by the fact

466

that the moisture uptake of these storms is very local as discussed in the pre-

467

vious section. This is a good indicator for the relevance of the RCE assumption.

468

Moreover, [Zhang, 2002] observed that changes in CAPE resulting from convection

469

and from large scale processes are almost in equilibrium in the free troposphere,

470

and disequilibrium mainly results from changes in the properties of the boundary

471

layer. Although this result is too weak to state that RCE is satisfied, it supports

472

the hypothesis that the free tropospheric temperature profile might result from an

473

equilibrium between convection and large scale processes even in Alaska.

474

Here we use the RCE model for qualitative comparison and discussion of the

475

physical reasons for changes seen in the simulation. It is not intended to (and

476

does not) reproduce quantitatively the results of the simulation, but it allows

477

to qualitatively assess the dependency of key environmental variables, such as

478

(26)

CAPE and CIN, on surface temperature, specific humidity and relative humidity.

479

We mainly use this model to establish causal relationships, that cannot be solely

480

inferred from one control and one future simulation.

481

As shown by [Romps, 2016], RCE can be expressed by the conservation of

482

environmental moist static energy defined as:

483

h

e

= c

p

T + gz + L

v

q

1 + a (6)

where a is a parameter regulating the environment lapse rate between a dry adi-

484

abatic (a = ∞) and moist adiabatic (a = 0). Here the parameter a was taken

485

equal to 1. The tropopause temperature is assumed constant at T

F AT

= 238 K

486

[Hartmann and Larson, 2002]. Differently from [Romps, 2016], where the parcel

487

is assumed to be saturated from the surface, we add a new variable which is rel-

488

ative humidity in the boundary layer. We therefore add the possibility to have

489

a lifted condensation level, and CIN. Therefore, the model only depends on two

490

parameters that are surface temperature and surface relative humidity. Although

491

it is extremely simple, it accounts for the changes in the atmospheric lapse rate

492

that are visible in figure 1b. This enables the calculation of several thermodynamic

493

variables by lifting the surface parcel into its environment. Analytical expressions

494

can be obtained through some relatively weak assumptions:

495

– Moist static energy of the parcel is conserved during its ascent (undilute plume)

496

– Saturated moisture depends exponentially on temperature q

(T) = q

s

exp((T −

497

T

s

)/T

c

)

498

– Relative moisture variations are large compared to relative temperature varia-

499

tions

500

– Virtual effects are neglected

501

– Atmospheric heat capacity, gravity acceleration and latent heat of vaporization

502

are taken constant

503

– Specific humidity and mixing ratio are taken equal

504

(27)

All variables are defined in the appendix. Notably q

refers to saturated mixing

505

ratio, T

s

refers to surface temperature, T

c

refers to a typical scaling temperature

506

for the Clausius-Clapeyron law (here fixed to 23K) and T

0

is some reference tem-

507

perature. This provides the following expression for CAPE, that is identical to

508

the expression of [Romps, 2016] if the surface is assumed to be the level of free

509

convection (LFC):

510

CAPE = a 1 + a L

v

q

(T

LF C

) T

0

(T

LF C

− T

F AT

− T

c

) (7)

(Refer to [Romps, 2016], sec.4 for the detailed calculation.) The expression of the

511

LFC temperature T

LF C

can be found in the appendix (equation 27) and depends

512

both on surface temperature and surface relative humidity. However, moisture

513

increases much faster than temperature, at the Clausius-Clapeyron rate (hereafter

514

CC scaling) [Clausius, 1850]. Therefore, CAPE increases should experience a CC

515

scaling with the temperature increases of the level of free convection. CAPE also

516

increases with surface relative humidity through the dependence of T

LF C

on RH ;

517

the moister RH, the lower and thus the warmer the LF C. The same model gives

518

the following formula for CIN:

519

CIN = Lq

s

T

c

T

0

f(RH, a) (8)

where f is always negative, and |f| decreases with relative humidity and with a.

520

The analytical formula for function f can be found in the appendix (equation 30).

521

This suggests that under constant relative humidity, CIN should also scale with

522

surface atmospheric moisture and therefore experience CC scaling. However, one

523

should bear in mind that f has a logarithmic and therefore somewhat sensitive

524

dependence on RH.

525

To verify and quantify this, the 1D RCE model is tested for usual summer

526

conditions in central Alaska (T

s

= 18

C and RH = 0.7) as shown on figure

527

6a. The assumptions for analytical calculations are relaxed for a more precise

528

(28)

20 10 0 10 20 30 Temperature [°C]

300

400

500 600 700 800 900 1000

Pressure [hPa]

a

0.4 0.2 0.0 0.2 0.4

Buoyancy [m/s2]

b

0.10 0.05 0.00 0.05 0.10 Buoyancy [m/s2]

c

West Coast Central Interior North Slope Northeast Interior Southeast Interior

Historical PGW

Control profile

Increased T, constant RH Increased T, increased RH

Fig. 6 a: Application of the Romps 2016 model with an atmospheric sounding determined from a surface temperature of 18

C and a surface relative humidity of 0.7 (solid). Dashed lines correspond to the model with increased surface temperature (+3K) and same relative humidity, dotted lines to the model with increased surface temperature (+3K) and increased surface relative humidity (+4%). CAPE and CIN are shaded for the control sounding and the sounding with increased surface temperature and no change in relative humidity. b: Buoyancy of the parcel in the different model experiments. c: Mean buoyancy for a parcel elevated from the surface in the storm environments, for different subregions (all storms have equal weights).

Buoyancy is shown as a function of model level, and mean pressure is used as an indicative coordinate.

calculation of the parcel trajectory (virtual effects and full Clausius-Clapeyron

529

law are taken into account). This provides a CAPE of 529 J/kg. The warming

530

of 3 K indeed causes an increase in CAPE and CIN (i.e. more negative CIN),

531

similarly to the results of [Rasmussen et al., 2017]. These increases are close to

532

the Clausius-Clapeyron scaling (+30 % for CAPE and 23 % for CIN), as expected

533

from the analytical equations. However, increasing relative humidity by 4% (dotted

534

line) increases CAPE by 29 % and decreases CIN by 28 % compared to the control

535

sounding. This leads to an eventual increase in CAPE by 68 % and a decrease

536

in CIN by 12 %. In the end, warming and moistening both impact CAPE, while

537

moistening dominates the CIN response.

538

(29)

The buoyancy profile of these changes is shown in figure 6b. It appears that

539

the increase in CAPE generated by warming alone (and subsequent lapse rate ad-

540

justment) results in an increase in buoyancy at high levels only (compare solid and

541

dashed lines), mainly owing to the increase in tropopause height. This is consis-

542

tent with the results of [Seeley and Romps, 2015, Singh and O’Gorman, 2013] and

543

[Parker, 2002] who noticed that CAPE is essentially modulated by the depth of

544

the layer of positive buoyancy. One can even see that buoyancy slightly decreases

545

in the lower troposphere compared to the control parcel. Conversely, moistening

546

produces an increase of buoyancy that is almost constant through the tropospheric

547

column (compare dashed and dotted lines). Therefore, these characteristic and dif-

548

ferent signatures support the hypothesis that moistening strongly enhances CAPE

549

increase in the simulations.

550

Figure 6c shows that buoyancy increases through the whole troposphere in the

551

Interior regions in the WRF simulations, whereas in the West Coast it increases

552

mainly in the upper troposphere. This suggests that the influence of surface moist-

553

ening on atmospheric instability mainly arises in the interior regions and is consis-

554

tent with the CAPE/CIN distribution extending toward strong CIN environments

555

in the West Coast (the temperature effect dominates) and weak CIN environ-

556

ments in the Interior (the surface moistening effect dominates) (figure 5). It is also

557

consistent with the larger low-level moistening of the Interior region compared to

558

the West Coast (figure 2b). In the North Slope, a decrease in buoyancy is found,

559

but the small number of storms in the control simulation (58) likely makes the

560

historical composite buoyancy profile not very robust.

561

The fact that buoyancy increases across the whole troposphere due to surface

562

moistening is of particular interest. Indeed, this implies that storms are affected

563

by the changing thermodynamic environment even during their early develop-

564

ment stages since buoyancy already increases at low levels. This could support

565

the onset of convective organization and convective updrafts to be more vigorous.

566

Conversely, in the case of a warming without increases in relative humidity, deep

567

(30)

convection will only be affected by buoyancy increases once it has reached the

568

upper troposphere, which is likely a storm that is close to or already mature. The

569

impact on convective organization would therefore be much smaller. The impact

570

of the vertical distribution of buoyancy can be considerable, as [Kirkpatrick et al.,

571

2011] found that in storms of moderate CAPE (like most of the storms considered

572

in this study), the maximum updraft speed can vary by a factor of 6 depending

573

on the vertical distribution of buoyancy. In their set of simulations, lowering the

574

altitude of maximum buoyancy could make the difference between a short-lived

575

and a persistent convective storm, without changing CAPE. This could be one of

576

the reasons why we find a threefolding of organized convective storm frequency in

577

Alaska under future climate conditions.

578

Several variables from the analytical models are shown in figure 7, together with

579

the joint and marginal distributions of these variables for storm environments in

580

the historical and PGW simulations. The model results do not follow the analytical

581

curves very well. This is due to the incompleteness and imperfectness of the RCE

582

model, but also to the fact that storms occur under a very broad range of surface

583

relative humidities, ranging from 0.3 to 1. The relative humidity of the RCE model

584

does not correspond to the surface relative humidity of the environments but the

585

analytical model is provided for qualitative comparison only.

586

Panel a shows the distribution of temperature and CAPE. The storms occur

587

under a broad range of surface temperature and CAPE values. The largest values

588

of CAPE roughly follow the changes in CAPE from the analytical model. As a

589

result, in the PGW simulation, where the temperature range extends to larger

590

values, high CAPE values increase following a Clausius-Clapeyron scaling.

591

Changes in CIN (panel b) also show that extreme CIN values follow the temper-

592

ature relationship. Mean CIN binned by temperature is similar in the two climates,

593

however more storms have extremely low values of CIN in the PGW simulation,

594

as it is visible in the marginal distribution. Given the shape of the theoretical

595

curves, it is likely attributable to the increase in surface relative humidity. This

596

(31)

10 15 20 25 30 0

200 400 600 800 1000 1200 1400

CAPE [J/kg]

RH = 0.6 RH = 0.65 RH = 0.7 RH = 0.75 RH = 0.8 RH = 0.85 RH = 0.9 RH = 0.95 RH = 1.0

a

10 15 20 25 30

200 175 150 125 100 75 50 25 0

CIN [J/kg] RH = 0.65 RH = 0.7

RH = 0.75 RH = 0.8 RH = 0.85 RH = 0.9 RH = 0.95 RH = 1.0

b

10 15 20 25 30

Temperature [°C]

0 1000 2000 3000 4000 5000 6000 7000 8000

Freezing level [m]

c RH = 0.3 RH = 0.4 RH = 0.5 RH = 0.6 RH = 0.7 RH = 0.8 RH = 0.9 RH = 1.0

10 15 20 25 30

Temperature [°C]

0 1000 2000 3000 4000 5000

Level of free convection [m]

d RH = 0.65 RH = 0.7 RH = 0.75 RH = 0.8 RH = 0.85 RH = 0.9 RH = 0.95 RH = 1.0

Fig. 7 Scatter plot of temperature and a: CAPE, b: CIN, c: freezing level height, d: LFC

height. Each point represents the environment of one storm in the control (blue points) and

PGW (red points) simulation. Solid blue and red lines respectively correspond to the centroids

of blue and red points binned by temperature with bin edges defined as the 10th,30th,50th,70th

and 90th percentiles of the temperature distribution. Solid gray lines show the relationship

expected from the analytical RCE model, for different values of surface relative humidity (line

color) as indicated in the legends. Marginal plots correspond to a normalized kernel density

estimation of the blue and red points. Note that the legend is different on panel c compared

to other panels.

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