1

Response of the hydrological cycle in Asian monsoon systems to global warming 1

through the lens of water vapor wave activity analysis 2

3

Daokai Xue1, Jian Lu2, L. Ruby Leung2 4

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1School of Atmospheric Sciences, Nanjing University, Nanjing, China 62Atmospheric Sciences and Global Change Division, Pacific Northwest National 7Laboratory, Richland, WA, USA. 8

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Corresponding author: Jian Lu (jian.lu@pnnl.gov) 10

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Key Points: 12

• A contour-following analysis is applied to water vapor to portray the 13hydrological cycle and its future changes over the Asian monsoon regions. 14

• The hydrological cycling rate increases/decreases in the Indian/East Asian 15monsoons, although hydrological cycle increases in both regions. 16

• The line-integral transformation of wave activity analysis improves robustness 17of the climate change response of the hydrological cycle. 18

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2

Abstract 20

The column integrated water vapor (CWV)-based local wave activity (LWA) is 21

adapted to examine the response of the hydrological cycle and extreme of the Asian 22

summer monsoon in CMIP5 simulations under the RCP8.5 forcing scenario. A tight 23

linear relationship between CWV LWA (𝒜") and its sink (𝑃 − 𝐸"), which measures 24

the intensity of the local hydrological cycle and extremes, affords a simple scaling 25

framework for the hydrological cycle intensity in terms of the contributions from (i) 26

ratio of moisture participating in the hydrological cycle, (ii) stirring length scale, (iii) 27

background moisture gradient, and (iv) hydrological cycling rate (HCR). Future 28

moisture LWA over the broad Asian monsoon region shows a large increase (~35%), 29

attributable largely to the increase of the background moisture. The scaling analysis 30

reveals a distinct mix of the contributing factors for the increase in (𝑃 − 𝐸") 31

between East Asian and Indian monsoon regions, despite both experiencing sizable 32

increase of (𝑃 − 𝐸"). 33

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1. Introduction 44

It has been well established that anthropogenic climate warming can enhance the 45

hydrological cycle measured by the global mean precipitation [P], or equivalently the 46

global mean evaporation [E] (Allen and Ingram, 2002; Held and Soden 2006; Meehl 47

et al., 2007). If one defines the hydrological cycling rate (HCR) as ratio of the global 48

mean precipitation to the globally integrated water vapor [𝑃]/[𝑄], the HCR tends to 49

weaken in response to increasing greenhouse gas concentrations, because the rate of 50

the increase of [P] is not commensurate with that of [Q], as the latter follows roughly 51

the Clausius-Clapeyron relation at a rate of ~7% per Kelvin warming (Pall et al., 2007; 52

Santer et al., 2007; Trenberth et al., 2003). This mismatch has been well understood as 53

the result of the radiative response to climate warming; that is, the radiative properties 54

of the atmospheric compositions restrain the radiative cooling from changing as much 55

as the rate of the water vapor (e.g., Stephens and Hu, 2010; Pendergrass and 56

Hartmann, 2014 JC). However, these globally integrated properties, especially the 57

important notion of the weakening of the HCR, cannot be automatically carried over 58

to regional hydrological cycle, which is more important for understanding regional 59

climate impacts. 60

61

Lately, Lu et al. (2017; 2018) developed a contour following analysis of CWV-based 62

local wave activity (LWA) budget to extend the concept of hydrological cycle to 63

regional precipitation and hydrological extremes, with a particular application to 64

features like atmospheric rivers (e.g., Zhu and Newell, 1998; Ralph et al. 2006; 65

Neiman et al. 2011). The essence of the water vapor wave activity is that it allows 66

areal or line integration over regions or intervals districted by contours of CWV (𝑀), 67

which, despite constantly varying, serve as the boundary of moisture ‘reservoirs’ for 68

budget analysis together with its corresponding equivalent latitude (𝜙.) (illustrated in 69

Figure 1). The main advantage of the areal integration transformation is that the 70

advection of CWV by the rotational component of the moisture flux disappears 71

identically due to the Gauss divergence theorem, thus affording a simpler balance 72

4

among fewer terms and, more importantly, a tighter linear relationship between CWV 73

wave activity and its sink (denoted as 𝑃 − 𝐸 " ) with their regression slope 74

indicating the HCR. See Lu et al. (2018) and next section for further details about the 75

formulation of the CWV wave activity budget and the associated scaling framework. 76

77

Here, we extend the CWV activity analysis to summertime regional hydrological 78

cycle, with a focus on the Asian monsoon regions. We first establish the spatial 79

correspondence between the transformed quantity( 𝑃 − 𝐸 ") and the hydrological 80

extremes represented by the 99.9th percentile of 𝑃 − 𝐸, as such inference regarding 81

the former may be translated to the hydrological extremes. The scaling factors 82

associated with the former help to further discern the different characteristics between 83

Indian and East Asian monsoons. Further, it is found that even though the 84

hydrological extremes increase over both Indian and East Asian monsoon regions 85

under future warming, the HCR is strengthened for the former but weakened for the 86

latter. However, the exact dynamical underpinning behind this intriguing result can be 87

very complicated and beyond the scope of this study. 88

89

2. Data and Methods 90

2.1. Data 91

The datasets utilized in the study are the historical (1976-2005) and future (2070-2099) 92

simulations by 16 climate models from the Coupled Model Intercomparison Project 93

Phase 5 (CMIP5) (Taylor et al., 2012), the former being forced by the best estimates 94

of the historical forcings and the latter by the Representative Concentration Pathways 95

8.5 (RCP8.5) forcing scenario, respectively. The number of models chosen is solely 96

based on data availability. To compute the CWV wave activity and the related budget 97

terms, daily outputs of precipitation, evaporation, and specific humidity and wind at 98

all vertical levels are needed. To test the Clausius-Clapeyron scaling, daily 850hPa air 99

temperature is also used. 100

101

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2.2. Formulation of local CWV finite-amplitude wave activity budget 102

As the CWV wave activity is a relatively novel approach to understanding regional 103

hydrological cycle, it is necessary to recapitulate the concept and associated budget 104

equations. For any field (𝑚) such as CWV that decreases monotonically with latitude 105

in general, the equivalent latitudes of the field may be defined as 106

𝜙. 𝑀 = arcsin(1 − ( 𝑐𝑜𝑠𝜙𝑑𝜆𝑑𝜙>?@ )/2π), (1) 107

so that the area enclosed poleward of contour M equals that poleward of latitude 𝜙.. 108

Obviously, 𝑚 in the area due to the poleward intrusion of the M contour is always 109

larger than 𝑀 (see Fig.1). This way, a one-to-one relationship between 𝑀 and the 110

equivalent latitude 𝜙. is established. With the identification of the equivalent latitude, 111

a pair of line-integral transformations to 𝑚 (Huang and Nakamura, 2016; Chen et al., 112

2015; Lu et al., 2018) can be defined for each longitude 𝜆: 113

ℒD[𝑚 𝜆, 𝜙. ] ≡ G

HIJKL𝑚 𝜆, 𝜙 𝑐𝑜𝑠𝜙𝑑𝜙>?@,K?KL

, (2a) 114

ℒ"[𝑚 𝜆, 𝜙. ] ≡ G

HIJKL𝑚 𝜆, 𝜙 𝑐𝑜𝑠𝜙𝑑𝜙>M@,KMKL

. (2b) 115

These will be referred to as moist LWA 𝒜" and dry LWA 𝒜D for the moist 116

(blue+white area) and dry (orange area) intrusions, respectively, as illustrated in 117

Figure 1. Since only the moist extremes are the subject of interest in this study, we 118

will be only focusing on 𝒜" and the associated budget terms. Analogous to the 119

budget equation of CWV, the major sink/source term of the moist LWA 𝒜" is 120

𝑃 − 𝐸 ", which is the ℒ" transformation of 𝑃 − 𝐸. As demonstrated in Lu et al. 121

(2018) there exists a tighter linear relationship between 𝒜" and 𝑃 − 𝐸 " even at 122

model grid scale, compared to the relationship between 𝑃 − 𝐸 and CWV at a fixed 123

grid. Thus, an empirical linear relationship emerges in which: 124

𝑃 − 𝐸 "~𝒜OD𝒜PO

Q, (3) 125

where 𝜏 gives the time scale for the sink 𝑃 − 𝐸 " to dissipate the CWV LWA 126

towards the baseline state 𝒜H", which is illustrated in Figure 1 and can be interpreted 127

as the maximum background water vapor intrusions without incurring a phase change 128

6

or sink, or alternatively, the background water vapor holding capacity in the face of 129

the disturbances. As such, only the 𝒜" −𝒜H" portion participates in the hydrological 130

cycle (blue areas in Fig.1) and is subject to the dissipation by 𝑃 − 𝐸 ". This leads to 131

the definition of participation ratio (PR) of LWA to the hydrological cycle: 𝒜OD𝒜P

O

𝒜O . It 132

is worth noting that as 𝑃 − 𝐸 " tends to emphasize the extreme values of 𝑃 − 𝐸, it 133

represents not only the mean but also the extremes of 𝑃 − 𝐸, as to be demonstrated 134

in Figure 2. 135

136

The definition of 𝒜" allows us to further scale it as −ST𝜂"T V@

VW, with 𝜂" 137

representing the scale of the poleward stirring or stretching of the 𝑀 contour (Fig.1) 138

and V@VW

the Lagrangian meridional gradient of CWV. The former reflects the dynamic 139

and the latter the thermodynamic factors in LWA 𝒜" (Lu et al., 2018). Making use 140

of the linear relationship (3), we can develop a scaling for the fractional change of the 141

ℒ"-transformed hydrological cycle: 142

X YDZ O

YDZ O ≈ X 𝒜O\𝒜P

O

𝒜O

𝒜O\𝒜PO

𝒜O + ^𝒜O

𝒜O +^Q\_

Q\_≈

X 𝒜O\𝒜PO

𝒜O

𝒜O\𝒜PO

𝒜O +

^ `a`b`a`b

+ TXcO

cO+ ^Q\_

Q\_. (4) 143

Thus, the fractional change of 𝑃 − 𝐸 " can be decomposed into the fractional 144

changes in PR, V@VW

, moisture stirring length scale (𝜂"), and HCR (𝜏DS). We will 145

examine each term in Eq. (4) that contributes to the fractional change of 𝑃 − 𝐸 " in 146

the Asian monsoon regions to lend some insights into the dynamic and 147

thermodynamic changes governing the changes in mean and extreme hydrological 148

cycle in these regions under warming. 149

150

3. Results 151

3.1 Correspondence between the wave activity sink and extreme precipitation 152

Figure 2a shows the multi-model mean historical summertime 𝑃 − 𝐸 " (contours) 153

and its change (shading) under RCP8.5 scenario forcing. The high loadings of the 154

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historical 𝑃 − 𝐸 " pick out the summer storm track regions in the ocean as well as 155

the Asian monsoon regions, such as the Indian subcontinent, Bay of Bengal, and the 156

eastern seaboard of Asia. Under climate warming, 𝑃 − 𝐸 " in these regions all 157

increases, reflecting a wet-get-wetter pattern of the response (e.g., Held and Soden, 158

2006). The corresponding summer mean and change of the 99.9th percentile of 𝑃 − 𝐸 159

(denoted by (𝑃 − 𝐸)ee.e, hereafter) are displayed in Figure 2b, from which one can 160

see immediately their spatial correspondence with the 𝑃 − 𝐸 " fields. The features 161

of 𝑃 − 𝐸 " are slightly displaced equatorward compared with those of (𝑃 − 𝐸)ee.e, 162

due to the fact that the computed wave activity and wave source are reported at the 163

equivalent latitude (𝜙.), which is always equatorward of the moist intrusion features 164

as illustrated in Fig. 1. The spatial correspondence between the seasonal means of 165

these two quantities at the grid points within (70°-170°E, 5°-35°N, marked by the 166

dashed blue box) are illustrated by their joint probability density distributions and 167

their regressions in Figure 2c. Within the boxed region, the 𝑃 − 𝐸 " are highly 168

spatially correlated with (𝑃 − 𝐸)ee.e with a correlation coefficient at 0.83 (Fig. 2c). 169

Similar spatial correlation is also found between them in the future climate 170

simulations under RCP8.5 forcing scenario, while the regression slope is somewhat 171

higher than the historical slope, implying that in the future 𝑃 − 𝐸 " may represent 172

lower percentile than the 99.9th. Given the spatial relationship between 𝑃 − 𝐸 " and 173

(𝑃 − 𝐸)ee.e, inference about the P − E " should have immediate bearing on the 174

hydrological extremes. 175

176

3.2 Future changes of hydrological extremes in the Asian monsoons 177

Building on the linear relationship between the moist LWA and P − E " 178

(exemplified in Fig. S1) and the related scaling (4), we are now able to examine the 179

contributing factors in the local hydrological extremes P − E " : moist wave 180

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activities (𝒜"), participation ratio ((𝒜" −𝒜H")/𝒜"), stirring scale (𝜂"), and the 181

resident time (𝜏). Figure 3 shows the summer climatological feature of each term 182

averaged over 16 CMIP5 models. Apparently, the spatial feature of P − E " 183

strongly resembles that of 𝒜" because of their strong linear relationship, with Asian 184

and west Pacific monsoon regions standing out as characteristic of larger 𝒜" and 185

P − E " (Figure 3a, 3b). The PR pattern reveals an intriguing distinction between 186

the rainfall in the tropical monsoons and that in the midlatitude storm track (Fig. 3c). 187

PR tends to be small in the former, implicative of the larger background water holding 188

capacity associated with warmer temperature so less moisture in the poleward 189

intrusions participates in precipitation. In contrast, PR is much larger (can be > 50%) 190

at the core of the storm track in the middle of the north Pacific, implicative of the 191

warmer origin of the air parcels in the poleward intrusions relative to the colder 192

background above the north Pacific, so more moisture in the storms participates in 193

precipitation. An important exception is the high PR over the Himalayas, which can 194

be attributed to the condensation caused by topographic lifting of air parcels. The 195

pattern of the poleward stirring scale 𝜂" also reveals a unique characteristic of the 196

east Asian monsoon: air parcels travel longer distances poleward before they 197

precipitate compared to the case of the south Asian monsoon (Fig. 3d). Meanwhile, 198

large P − E " in both tropical monsoonal regions and the midlatitude storm track 199

means a rather short resident time for the CWV (less than 4 days) (Fig.3e). In addition, 200

the same local wave activity analysis with ERA-I reanalysis data (Fig. S2) gives 201

similar climatological characteristics of each factor as in Figure 3. 202

203

Per equation (4), the fractional change of extreme precipitation measured by 204

P − E " under future warming can be attributed to that of PR, 𝒜" and local HCR. 205

Focusing on Asian monsoon regions (blue box in Fig.2), we find that both moist wave 206

activities 𝒜" and P − E " increase over the broad Asian monsoon region under 207

the RCP8.5 warming scenario with a modest inter-model consensus for the South 208

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Asian monsoon region and relatively higher consensus for the East Asian monsoon 209

region (Fig. 4ab). Intriguingly, the pattern of the increases in the ensemble mean 210

P − E " bears considerable resemblance to the most detectable climate change 211

pattern in summer rainfall (Srivastava and DelSole, 2014). The contribution of the 212

thermodynamic component (𝑑𝑀/𝑑𝑦) is relatively uniform over a broad range of 213

latitudes (~20%, Fig. 4f), while the dynamical factor (𝜂", Fig.4d) exhibits a 214

meridional dipole in its change, manifesting the poleward shift of the monsoon 215

circulation widespread in CMIP5 projections (e.g., Sandeep and Ajayamohan, 2015). 216

In particular, the negative change of 𝜂"over India and Indochina, though weak, is in 217

keeping with the weakening of the horizontal monsoon wind widely documented in 218

literatures (Ueda et al. 2006; Turner and Annamalai, 2012; Li et al. 2017; Sandeep et 219

al. 2017). PR decreases almost everywhere over south and east Asia (Fig. 4c), 220

meaning a greater proportion of the moisture not participating in the hydrological 221

cycle in the summer monsoon systems as climate warms. This is likely the result of 222

larger temperature increases over land and the oceans to its east (e.g., Kirtman and 223

Power, Near-term climate change: projections and predictability, IPCC report AR5) 224

relative to the temperature increase over the regions of the water vapor source (Mei et 225

al. 2015). On the other hand, HCR exhibits intriguing contrasting behavior between 226

Indian monsoon (left magenta box in Fig. 4e) and other Asian monsoon regions, with 227

an intensification for the former (~ 10%) and a weakening for the latter (~ -12%). 228

This means it will take longer time to dissipate the moist wave activity in the warmer 229

future climate over East Asian monsoon region but less time over Indian monsoon 230

region, despite the fact that P − E " increases about the same (~20%) over the 231

Indian monsoon and the Southeast Asian monsoon regions. The underlying 232

mechanisms for the increase in P − E " in the two regions might differ given their 233

distinct change in HCR, a topic warranting further investigation. 234

235

To gain more confidence in the characteristics discussed above, we further check 𝒜",236

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P − E ", PR, and HCR averaged over Southeast Asian monsoon region (Fig. 5a) and 237

Indian monsoon region (Fig. 5b), respectively, in each of the 16 CMIP5 models. 238

Under the forcing of RCP8.5 scenario, all models simulate an increased moist wave 239

activity over Southeast Asian monsoon region and 13 out the 16 models capture an 240

increase in P − E " . Meanwhile, PR decreases in all except one models. The 241

response of the HCR is slightly less robust, still 80% of the models project a decrease 242

in HCR over the Southeast Asia. For Indian monsoon region, the responses in 𝒜",243

P − E ", PR, and HCR exhibit similar robustness, except that the sign of the HCR 244

response is opposite: 13 out of 16 models project an intensification of HCR (stars in 245

Fig.5b). The modest robustness across the models examined thus lends us some 246

confidence in the projected intensification of the hydrological extremes in Asian 247

monsoons under climate warming. 248

249 250

4. Conclusion and discussion 251

Local CWV finite-amplitude wave activity is utilized in this study to examine the 252

projected changes of hydrological cycle in the future global warming scenario of the 253

CMIP5 models. The geometrically transformed 𝑃 − 𝐸 is found to be spatially 254

correlated with the precipitation extremes especially over Asian monsoon regions, so 255

any insight gained on the response of the former may be translated into that on the 256

latter. Further, the tight temporal linear relationship between P − E " and moist 257

LWA offers a different perspective for interpreting the hydrological cycle in the 258

monsoon regions: monsoon rainfall can be thought of as the result of air parcels being 259

disturbed meridionally from their source regions (this is especially true for the East 260

Asian monsoon) with the moisture they carry condensing efficiently as quantified by 261

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the small moisture residence time. 262

263

Under the RCP 8.5 warming scenario, both Indian monsoon and the east and southeast 264

Asian monsoon regions will undergo a relatively robust intensification in the 265

hydrological cycle measured by P − E ". Although it is not new that both the mean 266

and the extremes of precipitation over the Asian monsoon region will intensify under 267

greenhouse gas forcing (e.g., Turner and Slingo, 2009; Turner and Annamalai, 2012; 268

Sooraj et al. 2015; Pfahl and O’Gorman, 2017), the current investigation based on the 269

line-integral transformation of the hydrological quantities results in somewhat better 270

consensus, even on the change of the circulation factor. In particular, the scaling of 271

P − E " reveals an increased rate of the local HCR over Indian subcontinent, in 272

stark contrast to the broad Asian monsoon region and the hydrological cycle in winter 273

season. As the enhanced HCR is related to a steeper characteristic slope of the air 274

parcel trajectory feeding into the monsoon system (see Scaling for HCR in the 275

Supporting Information), the HCR increase here seems to be in broad agreement with 276

the upward vertical velocity anomalies over India subcontinent seen in CMIP 277

projections, despite a general weakening of tropical circulation elsewhere (e.g., 278

Vecchi and Soden, 2007) and a weakening of the Indian monsoon circulation as 279

depicted by the weakening of the meridional tropospheric temperature gradient and 280

vertical wind shear (Mei et al. 2015). The better consensus on the geometrically 281

transformed hydrological quantities may be attributed to the fact that they weigh the 282

extreme values more than the non-extremes through the geometric transformation, 283

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therefore, they are more representative of the hydrological extremes than the median 284

values. For Asian monsoons, indeed, CMIP models seem to converge robustly on the 285

warming-induced increase in the extreme categories of monsoonal rainfall (Kitoh et al. 286

2013; Sooraj et a. 2015; Pfahl and O’Gorman, 2017; Lau et al. 2017). 287

288

Last, we must admit that although the wave activity based scaling can help shed some 289

fresh light on the thermodynamic and circulation factors in the hydrological cycle of 290

the monsoon systems, the approach is fundamentally diagnostic. Asian monsoons are 291

among the most complicated sub-systems of our climate system, involving complex 292

interplay among factors like the shape and properties of land, topography, elevated 293

heating, convection, moisture sources, and the nonlinear fluid dynamics of the ocean 294

and atmosphere. It remains a grand challenge to understand and predict how monsoon 295

would behave under any form of external climate forcings. 296

297

Acknowledgement 298

This work is supported by the U.S. Department of Energy Office of Science Biological and 299

Environmental Research (BER) as part of the Regional and Global Climate Modeling 300

Program. The Pacific Northwest National Laboratory is operated for the Department of 301

Energy by Battelle Memorial Institute under contract DE-AC05- 76RL01830. The authors 302

also acknowledge the World Climate Research Programme’s Working Group on Coupled 303

Modeling, which is responsible for CMIP, and we thank the climate modeling groups for 304

producing and making available their model output. We are also grateful to Jesse Norris for 305

confirming the positive circulation contribution to the precipitation extremes over Indian 306

monsoon region. 307

308

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441

Figure 1 Schematic for the concepts of CWV LWA and its sink 𝑷 − 𝑬". The solid 442wavy line denotes an isoline of CWV (M), and the dash line corresponds to the 443equivalent latitude of M. The northward (southward) intrusion of the M contour is 444associated with a moist (dry) anomaly, i.e., 𝒎 > 𝑴 (𝒎 < 𝑴), and the meridional 445line integral of which gives the local moist wave activity (𝓐") and dry wave 446activity (𝓐D), respectively. The white areas carved out by the magenta lines 447corresponds to the parts of LWA not participating the hydrological cycle, representing 448a concept of CWV holding capacity in the face of the meridional disturbances. 449450451452453454455456457458459460461462463464465466467468469470471472473474475

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476Figure 2 The climatology (contours) and the change (shaded) under the RCP8.5 477

forcing scenario of a) P − E " and b) (𝑃 − 𝐸)ee.e. The black points denote more 478

than 80% agreement among 15 CMIP5 models. c) is two-dimensional probability 479

density distribution of area averaged P − E " and (𝑃 − 𝐸)ee.e over the Asian 480

monsoon region demarcated by the dashed box in a) for historical simulations. d) is 481the same as c), but for the RCP8.5 simulations. The linear regression slopes are shown 482in solid lines in both c) and d).483484485486

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487

Figure 3 Climatological distribution of summertime a) P − E "; b) 𝒜"; c) 488

participation ratio (𝒜" −𝒜H")/(𝒜"); d) stirring scale 𝜂"; and e) residence time 𝜏 489

based on the ensemble average of each quantity over 16 CMIP5 models. 490491

492493494495496497498499500501502503504505506

19

507

Figure 4 The fractional change of P − E " and those in its scaling factors: 508

a) P − E "; b) 𝒜"; c) (𝒜" −𝒜H")/(𝒜"); d) 𝜂"; e) hydrological rate (𝜏DS); and f) 509

the Lagrangian gradient of CWV (𝑑𝑀/𝑑𝑦) with the inter-model spread expressed in 510gray shading. In panels a)-e), the corresponding background climatology of each is 511displayed as contours and the dots indicate regions where >80% of the models 512agreement on the sign of the change. 513514515516517518519520521522523524525526527

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528

Figure 5 The fractional change of P − E " , 𝒜" , (𝒜" −𝒜H")/(𝒜") and 𝜏 529

averaged over a) Southeast Asian monsoon and b) Indian monsoon regions under the 530RCP8.5 forcing scenario for each of the 16 CMIP5 models. The two domains for the 531regional average are marked by the magenta boxes in Fig.4 e). Filled (open) circle 532denotes fractional increase (decrease) with the magnitude of the change indicated by 533the legend. 534