Break in precipitation – temperature scaling over India 1 predominantly explained by cloud-driven cooling

. Climate models predict an intensification of precipitation extremes as a result of a warmer and 14 moister atmosphere at the rate of 7%/K. However, observations in tropical regions show contrastingly 15 negative precipitation-temperature scaling at temperatures above 23° - 25°C. We use observations from 16 India and show that this negative scaling can be explained by the radiative effects of clouds on surface 17 temperatures. Cloud radiative cooling during precipitation events make observed temperatures co-vary 18 with precipitation, with wetter periods and heavier precipitation having a stronger cooling effect. We 19 remove this confounding effect of clouds from temperatures using a surface energy balance approach 20 constrained by thermodynamics. We then find a diametric change in precipitation scaling with rates 21 becoming positive and coming closer to the Clausius – Clapeyron scaling rate (7%/K). Our findings imply 22 that the intensification of precipitation extremes with warmer temperatures expected with global warming 23 is consistent with observations from tropical regions when the radiative effect of clouds on surface 24 temperatures and the resulting covariation with precipitation is accounted for. 25 subsets (summer and winter monsoon). Our findings indicate that seasonality does have an effect on observed scaling while the "clear-sky" scaling rates remains positive irrespective of the seasons (see Appendix C).


Introduction
Climate models and observed trends have shown precipitation extremes to increase at the global scale 28 with anthropogenic global warming (Fischer et al., 2013;Westra et al., 2013;Donat et al., 2016). This 29 increase is largely explained by the thermodynamic Clausius-Clapeyron (CC) equation, suggesting a 30 ≈7%/K increase in atmospheric moisture holding capacity per degree rise in temperature ("CC rate") 31 (Allen & Ingram, 2002). Extreme precipitation is expected to increase at a similar rate (Trenberth et al., 32 2003;Held & Soden., 2006;O'Gorman & Schneider, 2009), as also shown by convection-permitting 33 climate model projections (Kendon et al., 2014;Ban et al., 2015). Precipitation -temperature scaling 34 rates, estimated using statistical methods and observed records, are widely used as an indicator to 35 constrain this response (Lenderink et al., 2008;Wasko et al, 2014). 36 37 However, observed scaling rates show large heterogeneity globally, with significant deviations from the 38 CC rate (Westra et al., 2014;Schroeer & Kirchengast, 2018). Deviations are larger in the tropical regions 39 where scaling rates are mostly negative and precipitation extremes largely show a monotonic decrease or 40 a sudden drop (hook) in scaling at high temperatures (Utsumi et al., 2011). These deviations have been 41 studied and attributed to number of factors. Two primarily argued reasons include the moisture 42 availability limitation at high temperatures (Hardwick et al., 2010) and dependence of scaling estimates 43 on the wet event duration (Gao et al., 2018;Ghausi & Ghosh 2020;Visser et al., 2021). Cooling effects 44 of rainfall events have also questioned the use of surface air temperature as scaling variable (Bao et al., 45 2017). Other scaling variables like atmospheric air temperature (Golroudbary et al., 2019), sampling 46 temperatures before the start of storm (Visser et al., 2020), using measures of atmospheric moisture like 47 approach to view the earth system. Similar approach had also been used in (Kleidon & Renner, 2013;109 Kleidon et al., 2014;Dhara et al., 2016) and were found to very well capture the observed surface 110 temperatures, energy partitioning and climate sensitivities. 111 To do this, we conceptualize the surface atmosphere system as a heat engine, with warm Earth surface as 112 the heat source and cooler atmosphere being the sink (Figure 1). Heat and mass are transported within 113 this engine by the exchange of turbulent fluxes (J) between the surface and the atmosphere. The 114 differential radiative heating and cooling between the surface and the atmosphere maintains the 115 temperature difference and drives the vertical convective motion. The power (G) associated with the work 116 done by the heat engine required to sustain convective motion in form of vertical mixing and exchange 117 of turbulent fluxes can be derived simply using the first and second law of thermodynamics and can be 118 represented by the well-established Carnot limit as 119 = ( − ) .
(2) 120 Detailed derivation about the same can be found in (Kleidon & Renner, 2013;Kleidon et al., 2014). Here 121 Ta and Ts are the representative temperatures of cold atmosphere and the hot surface respectively. 122 Both temperatures are inferred from their respective energy balances. The atmospheric temperature (Ta) 123 is assumed to be equal to the radiative temperature of atmosphere and is estimated using the outgoing 124 longwave radiation at top of atmosphere (Rl,toa) 125 (3) 126 Here, σ is the Stefan Boltzmann constant (σ = 5.67 x 10 -8 Wm -2 K -4 ). A correction of 15K was applied to 127 Using the surface energy balance (Eq. 1), we can then express the surface temperature in terms of net 134 solar absorption, downwelling longwave radiation and turbulent fluxes (J) as 135 (5) 136 The differential radiative heating and cooling between the surface and the atmosphere maintains the 137 temperature difference and drives the vertical convective motion. Thermodynamics sets a limit to this 138 conversion and thus constrains the amount of turbulent flux exchange. Less turbulent fluxes result in a 139 hotter surface (Eq. 5), which will increase the temperature difference between the surface and atmosphere. 140 This will subsequently increase the efficiency term in the generation rate, the second term on the right-141 hand side of Eq. (2). On the other hand, an increase in turbulent fluxes (J) increases the first term in the 142 generation rate of Eq. (2), but it will, in turn, reduce the surface temperature and temperature difference 143 between surface and atmosphere (Eq. 5). Thus, there exists a trade-off that sets the limit for the power to 144 maintain vertical energy and mass exchange between surface and the atmosphere. This limit is termed as 145 the maximum power limit and provides an additional constraint to surface energy balance partitioning 146 that we used here to infer surface temperatures. 147 Using Equations. (2), (3) and (5), the rate of work done (power) produced by the heat engine can be 148 expressed as a function of turbulent fluxes (J) as 149 Note that power G = 0 when J = 0 or when J = Rs + Rld -Rl,toa. Hence, there is a maximum Gmax = G 151 (Jmaxpower) for a value between 0 < Jmaxpower < Rs + Rld -Rl,toa . The optimum J that maximizes power was 152 calculated numerically. This flux was then used to determine the surface temperatures. 153 Surface temperatures were estimated using Eq. 7 for "all-sky" and "clear-sky" radiative conditions using 155 radiative forcing from the NASA -CERES datasets. We then refer to these two temperatures derived 156 using Eq. 7 as "all-sky" and "clear-sky" temperatures. obtained from the NASA -CERES (EBAF 4.1) dataset (Loeb et al., 2018;Kato et al., 2018) and NASA 162 CERES Syn1deg dataset (Doelling et al., 2013(Doelling et al., ,2016. These datasets are available for both "all-sky" as 163 well as "clear-sky" conditions at monthly and daily scale respectively with a 1° latitude x 1° longitude 164 spatial grid resolution and were used as a forcing in our energy balance model. We evaluated our model 165 using observations derived gridded temperature data from Indian Meteorological Department (IMD, 166 Rajeevan et al., 2008). To estimate the precipitation -temperature scaling, we used daily gridded 167 precipitation and temperature datasets with a spatial resolution of 1° latitude x 1° longitude from the 168 Indian Meteorological Department (IMD, Rajeevan et al., 2008) and 3 hourly gridded rainfall data from 169 NASA-TRMM_3B42 with a spatial resolution of 0.25° x 0.25°. We repeated the analysis using daily 170 gridded precipitation and temperature data from the APHRODITE (Asian Precipitation Highly Resolved 171 Observational Data Integration towards Evaluation) dataset, available at a spatial resolution of 0.

Estimation of precipitation -temperature scaling rates
180 Extreme precipitation events were scaled with observed, "all-sky" and "clear-sky" temperatures using 181 two widely adopted scaling approaches: The Binning Method (Lenderink et al., 2008) and Quantile 182 Regression (Wasko et al., 2014). For the binning method, we defined extreme precipitation events using 183 a threshold of 99th percentile precipitation contained at each grid cell. Precipitation -temperature pairs 184 were then divided into the increasing order of non-overlapping bins of 2 K width. Only those bins which 185 have at least 150 data points have been considered for the analysis (Utsumi et al., 2011). The median 186 value of each bin was then used to examine the variation of precipitation extremes with temperature. Bins 187 with temperature less than 3°C were discarded to remove the effects of freezing, thawing and snowfall. 188 To ensure that our results are not biased with the number of data points in each bin and bin sizes (which 189 may affect the nature of the scaling relationship), we further used the Quantile Regression method to 190 estimate the scaling rates. 191 Quantile regression estimates the conditional quantile of the dependent variable (in our case, 192 precipitation) over the given values of the independent variable (temperature). We first fitted a quantile 193 regression model between the logarithmic precipitation and temperature values at the target quantile of 194 Here Pi denotes the mean daily precipitation intensity and Ti is the daily mean temperature, and : ;; and 197 < ;; are the regression coefficients for the 99th quantile of precipitation. The slope coefficient < ;; is then 198 exponentially transformed to estimate the scaling rate ( < ). 199 The following methodology had been widely adopted to estimate the extreme precipitation -temperature 201 scaling in previous studies (Lenderink et al., 2008(Lenderink et al., , 2010Utsumi et al., 2011;Wasko et al., 2014;Schroeer 202 et al., 2018). 203

204
In this section, we first start by a quick evaluation of our thermodynamic approach by comparing the 205 estimated "all-sky" temperatures against observations. We then quantify the cloud radiative effects on 206 surface temperatures and check for its spatial consistency across regions. We then estimated precipitation 207 -temperature scaling rates by including and excluding the effect of clouds on surface temperatures. We 208 also used dew point temperature (a proxy measure for atmospheric moisture) as a scaling variable. Later, 209 we discuss our interpretation of scaling by excluding cloud effects from temperatures, its comparison with 210 the dew point scaling and its implications across regions. 211 3.1: Evaluating the modelled temperatures 214 "All-sky" temperatures were estimated using the daily observed radiative fluxes from CERES in 215 conjunction with surface energy partitioning constrained by maximum power (see Equation 7). We found 216 an extremely good agreement of these estimated temperatures when compared to surface temperature 217 observations over India with R 2 > 0.9 and RMSE < 1.5 K over most regions (Figure 2). This signifies that 218 our formulation strongly captures the surface temperature variation over India and thus validates our 219 approach. We then extend this for clear-sky conditions by forcing our model with "clear-sky" radiative 220 fluxes from CERES and estimating "clear-sky" temperatures. It is to note that "clear-sky" temperatures 221 are reconstructed temperatures estimated by removing the effect of clouds from radiative transfer. 222 3.2: Estimating the cloud radiative cooling 223 We used the difference between the "all-sky" and "clear-sky" temperatures as a measure to quantify the 224 effect of cloud-driven cooling during rainfall events. This cooling increases strongly with precipitation 225 across regions, resulting in a stronger reduction in surface temperature with greater precipitation (Figure 226 3a). This cooling is predominantly caused by the substantial reduction in absorbed solar radiation at the 227 surface for "all-sky" conditions compared to "clear-sky" conditions (Figure 3b). On the other hand, 228 changes in longwave radiation are comparatively small and largely remain insensitive to precipitation. 229 To examine the spatial consistency in precipitation variability and associated cooling, we isolated extreme 230 daily precipitation days over each grid. Figure 4a shows the mean magnitude of daily extreme 231 precipitation events over India. Figure 4b shows the cloud-cooling associated with these days. This 232 cooling effect of clouds and precipitation shows a clear, systematic variation across India. The cooling 233 effect is greater where precipitation rates are high. In contrast, in the more arid regions in the northwest 234 of India, the cooling effect almost disappears with low precipitation rates. Figure 4c further shows the 235 mean "all-sky" temperature during these days. We find that the heaviest events occur at a relatively lower 236 temperature as a result of stronger cooling. Figure 4d shows the mean number of rainfall days per year. 237 More rainy days implies more cloudy conditions and thus a stronger cloud radiative cooling over that 238 region. Having quantified this effect of cloud radiative cooling and its systematic variation across regions, 239 we then estimate its impact on the precipitation -temperature scaling. 240 3.3 Impact on precipitation-temperature scaling 242 We performed a binning analysis (Lenderink et al., 2008) to understand the scaling of precipitation 243 extremes with temperature using observed temperatures as well as our estimated "clear-sky" and "all-sky" 244 temperatures. Precipitation events were isolated and binned into P-T pairs and the resulting scaling 245 relationships are shown in Figure 5. The scaling relationship using observed and "all-sky" temperatures 246 showed similar scaling behaviour (yellow and red lines in Figure 5a). Extreme precipitation increases 247 close to the CC rate up to a threshold of around 23° -24°C, above which the scaling becomes negative. 248 This break in scaling behaviour with observed temperatures is consistent with the findings of previous 249 studies (Hardwick et al., 2010;Ghausi & Ghosh, 2020) and is commonly referred in literature as "hook" 250 or "peak structure" (Wang et al., 2017;Gao et al., 2018). However, when precipitation extremes are scaled 251 with "clear-sky" temperatures that excludes the cloud-cooling effect, the resulting scaling relationship 252 does not show a breakdown and increases consistently, close to the CC rate over the whole temperature 253 range (blue line in Fig. 5a). Similar results were obtained when the scaling curves were reproduced for 254

station-based observations (See Appendix A). 255
Previous studies (Hardwick et al., 2010;Chan et al., 2015;Wang et al., 2017) have attributed the break 256 in precipitation-temperature scaling to a lack of moisture availability as relative humidity tends to 257 decrease at high temperatures. To account for this effect of moisture limitation, some studies used dew 258 point temperature, a measure of atmospheric humidity, as an alternative scaling variable (Wasko et al., 259 2018;Barbero et al., 2018). They showed that the breakdown and negative scaling disappear when scaled 260 with dew point temperatures (Zhang et al., 2019;Ali et al., 2021). To evaluate this interpretation and 261 compare it to ours, we used the dew point temperature from the ERA-5 reanalysis. We derived the extreme 262 precipitation scaling using this temperature (Figure 5b) and compared it to our "all-sky" and "clear-sky" 263 temperatures (Figure 5c The scaling of dew point temperatures with "clear-sky" temperatures is much more uniform and consistent 284 across the whole temperature range and does not show a breakdown or a super CC scaling in the 285 relationship. This is because the "clear-sky" temperatures reflect the radiative conditions, and not the 286 effects of atmospheric humidity or clouds. In contrast, observed temperatures and "all-sky" temperatures 287 co-vary with cloud effects, which in turn are linked to precipitation and humidity, thus resulting in less 288 clear scaling relationships that are less straightforward to interpret. This further implies that moisture 289 loading of the atmosphere primarily occurs during the non-precipitating periods that are more 290 representative of clear-sky radiative conditions. 291 The breakdown in scaling effect can thus be explained by the cooler temperatures associated with 292 precipitation events. This cooling shifts the precipitation extremes to lower temperature bins while the 293 high-temperature bins then correspond to more arid regions or to the drier pre-monsoon season 294 temperatures with lower values of precipitation extremes. We refer to this as a "bin-shifting" effect. The 295 cooling effect is proportional to the amount of precipitation (Fig. 3A) and hence, the heavier the 296 precipitation, the stronger the cooling and bin shifting becomes. When the cloud cooling effect is 297 removed, as in the case of "clear-sky" temperatures, extreme precipitation then shows a scaling that is 298 consistent with the CC rate. This bin shifting effect arising due to the presence of clouds also causes a 299 decrease in relative humidity at higher temperatures. This effect can be seen by the stronger increase in 300 dewpoint temperatures below 25°C, and the decline above this temperature (Figure 5c). The breakdown 301 in scaling is thus not directly related to changes in aridity or moisture availability, but rather to the 302 radiative effect of clouds on surface temperature. 303 To demonstrate the implications of our interpretation for precipitation scaling across regions, we 304 estimated regression slopes of 99th percentile precipitation events for both sub-daily (TRMM) and daily 305 (IMD & APHRODITE) precipitation with the different temperatures using the Quantile Regression 306 method (Wasko et al., 2014). We found that extreme precipitation scaling was negative for both, observed 307 and "all-sky" temperatures over most regions (Figure 6) except for the Himalayan foothills in the North 308 of India. The scaling rates for sub-daily extremes were slightly higher than those estimated for daily 309 extremes but yet remains negative over most grids. When the cooling effect of clouds is removed by using 310 "clear-sky" temperatures, extreme precipitation scaling then shows a diametric change and scaling 311 estimates come close to CC rates over most of the regions. A similar diametric change in the scaling was 312 also obtained with the APHRODITE precipitation dataset (Appendix B). 313 We note that negative scaling was also found over few regions of South-central and south-east India with 314 "clear-sky" temperatures at both daily and sub-daily scales (Figure 6 c,f). To our understanding, this 315 negative scaling is largely due to the cyclonic activities originating from Bay of Bengal during winter 316 months and resulting in heavy rains over these regions. These cyclonic systems thus cause very high 317 rainfall at very low temperatures which causes negative scaling. More work is needed to be done to resolve 318 these systems in conventional scaling approach and remains an important area for future research. 319 The effect of seasonality on precipitation scaling was also checked by producing the scaling curves for 320 different seasonal subsets (summer and winter monsoon). Our findings indicate that seasonality does have 321 an effect on observed scaling while the "clear-sky" scaling rates remains positive irrespective of the The confounding effect between precipitation and temperature on observed scaling relationships 324 "apparent scaling" had also been argued by some recent studies (Bao et al. 2017;Visser et al., 2020). Our 325 results agree with these studies that the observed scaling relationships also reflect the impact of synoptic 326 conditions and cooling associated with precipitation events on temperature. However, we suggest that this 327 confounding effect is largely associated with cloud radiative effect, which is removed by our use of "clear-328 sky" temperatures as a scaling variable. We also address the arguments raised to resolve apparent scaling 329 using dew point temperature (Barbero et al., 2018). Our results confirm that precipitation extremes scale 330 well with dew point temperatures as a measure for atmospheric moisture, but that the break in scaling 331 actually originates from the scaling of dew point temperatures with observed temperatures. This response 332 of dew point temperature to warming is further affected by the presence of clouds and associated radiative 333 cooling. "Clear-sky" temperatures are independent of the co-variations arising from cloud effects and are 334 thus a better, more independent measure and scaling variable to understand the precipitation response to 335 climate warming. 336

337
We showed that the observed negative scaling of extreme precipitation in India arises mostly from the 338 cloud radiative cooling of surface temperatures. When this effect is removed, we get a positive scaling 339 consistent with the CC rate. Scaling rates estimated from observed temperatures are thus likely to 340 misrepresent the response of extreme precipitation to global warming, because the cooling effects of 341 clouds make precipitation and temperature covary with each other. When this effect is removed by 342 estimating surface temperatures for "clear-sky" conditions, the scaling relationships with moisture content 343 and precipitation become much clearer and confirm the CC scaling of extreme precipitation events with 344 warmer temperatures. This explains the apparent discrepancy between the observed negative scaling rates 345 over India and the projected increase in precipitation extremes by climate models. 346 It is also important to note that the goal of our study was not to compare the accuracy of scaling estimates 347 from different gridded and station-based datasets, but rather to identify and remove the physical effects 348 that causes uncertainties in this response. Our methodology to remove the cooling effect of clouds from 349 surface temperatures significantly improves the scaling estimate for daily precipitation scaling.