Contrasting impacts of net cloud radiative forcing on the surface temperature trends in India

The rise of spatial heterogeneity in surface temperature (T s ) over India cannot be explained by only the direct effect of enhanced greenhouse gas forcing. Here we propose an analytical framework to estimate the impact of the net cloud radiative forcing (CRF) trend on the observed T s trend for the duration of 2000–2019. The cloud sensitivity ( λcld ) estimated from the satellite observations vary in the range −0.180 to 0.241 K per W m−2 across the seven T s homogeneous zones in India. Net average (±1σ) CRFs over the Indian landmass during 2000–2019 in the shortwave and longwave are −15.5 ±11.3 and 12.4 ± 7.4 W m−2, −28.1 ± 22.4 and 24.6 ± 9.8 W m−2, −75.1 ± 20.4 and 55.0 ± 13.8 W m−2 and −23.3 ± 14.9 and 21.6 ± 14.8 W m−2, respectively for the winter (Dec-Feb), pre-monsoon (Mar–May), monsoon (Jun–Sep) and post-monsoon (Oct–Nov) seasons. We find that in some of the T s homogeneous regions, seasonal T s trends are suppressed, whereas in some other T s homogeneous regions, seasonal T s trends are accelerated by the net CRF. Our framework can be useful in studying the role of clouds in observed surface warming trends.


Introduction
Clouds perturb the Earth's radiation budget by inducing a cooling effect at the top-of-the-atmosphere (TOA) in shortwave (SW) and a warming effect in longwave (LW) depending on the type of cloud (high or low), liquid/ice content, etc. The net cloud radiative forcing (CRF) is governed by cloud macrophysical (i.e., cloud fraction, f c and cloud top temperature, T cld ) and microphysical (i.e., phase, effective radius and optical depth, τ c ) properties that show large spatial and temporal variations in the Indian subcontinent (Rajeevan and Srinivasan 2000, Rajeevan et al 2012, Saud et al 2016, Ali et al 2019, Kant et al 2019. The impact of net CRF at TOA in modulating the surface temperature (T s ) trend through cloud radiative feedback (Stephens 2005, Haugstad et al 2017 is poorly understood not only in the Indian subcontinent but also anywhere else in the world. This issue can be addressed using climate models, but they have large uncertainty (and discrepancy across models) in cloud radiative feedback estimates (Klein et al 2013, Yin andPorporato 2017). Net CRF variability is examined over the Indian subcontinent utilizing the ERBE (Earth Radiation Budget Experiment) data Srinivasan 2000, Patil andYadav 2005, Sathiyamoorthy et  The general finding from IMD data is that the Indian region is warming (Kothawale and Rupa Kumar 2005), and this can be attributed to human interference beyond any doubt (Dileepkumar et al 2018). However, the warming trends show regional variations across the seven T s homogeneous zones (see supplementary figure S1(a) (available online at stacks.iop.org/ERC/4/041005/mmedia for the zonation)-Western Himalaya (WH), East Coast (EC), West Coast (WC), Northwest (NW), Northeast (NE), North Central (NC) and Interior Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Peninsula (IP). These T s homogeneous zones are demarcated based on geographical, topographical, and climatological features to identify the regional patterns of temperature variation within India (Kothawale and Rupa Kumar 2005). Figure S1(b) shows the linear trend (°C/10yr) in annual maximum and minimum temperatures for all-India and homogeneous regions using data available from Kothawale and Rupa Kumar (2005) for the period 1971-2003. Both for maximum and minimum temperature, positive trends suggest increasing temperature for all-India as well as seven homogeneous regions. Also, the day and nighttime T s trends are different in the winter, pre-monsoon, monsoon, and post-monsoon seasons. In general, over twice of the global land area, the daytime T s has been increasing at a lower rate than the nighttime T s (Cox et al 2020), thereby suppressing the diurnal temperature range (Kothawale and Rupa Kumar 2005). Recently, Sanjay et al (2020) have observed that annual mean, maximum and minimum temperatures averaged over India as a whole show significant warming trends of 0.15°C, 0.15°C, and 0.13°C per decade, respectively, since 1986. Padma Kumari et al (2007) examined the T s trend in India in terms of solar insolation flux and greenhouse gas (GHG) forcing. They showed that despite a drastic decrease in surface-reaching solar radiation (referred to as solar dimming), maximum and minimum T s over India are increasing. But the change in increase in maximum T s is only marginal from the decade (1981-1990) to decade (1991-2000) under the present scenario of increasing greenhouse gas emissions. This is likely as a result of natural climate variability that modulates (either suppress or enhance) greenhouse gas warming. On the contrary, the increase in minimum T s has doubled, indicating an increasing greenhouse gas forcing (Padma Kumari et al 2007). Ross et al (2018) studied the T s trend in India in connection with aerosols and explained the warming and cooling patterns in the decadal mean temperature based on the presence of a large region of brownish haze that is found over most of the North Indian Ocean and South Asia, particularly in the winter and spring months. Sea surface temperature (SST) and associated winds are examined to understand the possible mechanism behind the trends and variability of temperature over the west coast of India (Revadekar et al 2016). According to this study, SST variability alters the strength of winds to cause anomalies in temperature over the west coast. Kothawale et al (2016) has investigated temperature trends over various Indian cities and hill stations in view of urbanization and industrialization. Gautam and Singh (2018) studied the impact of urbanization on low-laying clouds near ground (fog) over Indo-Gangetic plains and they found suppressed fog fraction, amidst increased fog occurrence over the Indo-Gangetic Plains. This direct impact of urbanization on cloudiness has its' effect on T s trend as well.
Various studies in the literature clearly indicate that the T s trend in the Indian region shows strong spatial heterogeneity across the seven T s homogeneous zones that cannot be explained in terms of only greenhouse gas forcing. The influence of clouds in the observed T s pattern is least understood in this regard. There exist very limited studies that examine the T s pattern in terms of net CRF at TOA for all T s homogeneous zones. This research gap forms the scope of the present study. Here we examine the role of net CRF on the observed T s trends in India using an analytical framework. We define a 'cloud sensitivity' ( cld l ) term that links the net CRF trend (expressed in the form of ΔCRF) to T s trend attributed to clouds (hereafter represented as T s cld D ). We estimate the mean seasonal day and nighttime cld l values and subsequently T s cld D for the homogeneous T s zones in India using satellite-based albedo and cloud products. In the next section, we first derive the conceptual framework, followed by the analysis, and subsequently, the results are discussed.

Methodology
2.1. Analytical framework T s is influenced by various parameters, such as CRF, atmospheric circulation (C a ), GHGs (G), aerosols (A), and other factors (O). Mathematically it can be represented as The total differential change in T s can be expressed as Therefore, the total change in T s (over time) can be written as The climate sensitivity term (l) is defined as where RF is anthropogenic radiative forcing at the TOA.
Analogous to this concept, we define the cloud sensitivity ( Cld l ) term as Finally, the total change in T s can be rewritten in terms of various sensitivity terms as, Furthermore, T s D could be rewritten as, Evidently, equation (5)  which is the change in surface temperature, T s due to clouds only.
We carry out our analysis by conceiving a simple cloud-modified radiative heat flux budget model. We assume a single layer cloud as a radiation shield, covering a fraction of the domain, f c with cloud macrophysical properties, such as cloud emissivity ( c e ) and cloud top temperature, T cld . The entire cloud layer is assumed to be at a spatially homogeneous temperature, T cld . Thereafter, the alteration of radiation budget due to the presence of this single layer cloud is investigated, and subsequently T s Cld D is mathematically derived in terms of Cld l and ΔCRF. It has already been shown in equation (6) that T s Cld D can be expressed as the product of Cld l and ΔCRF, where Cld l (K per Wm −2 ) is interpreted as the T s trend attributed to the cloud radiative feedback per unit net CRF trend (ΔCRF). Positive (negative) Cld l implies an increment (decrease) in T s in response to an increase in net CRF at TOA. We derive Cld l using the conventional definition of net CRF (i.e., the sum of SW and LW CRF) at the TOA: Both CRF SW and CRF LW can be represented as: where  denotes the outgoing flux at the TOA and the subscripts' Clr' and 'All' represent 'clear-sky' and 'allsky' conditions. SW CRF can be expressed as where, c e and f c represent cloud emissivity and cloud fraction, respectively. The first term of the RHS of equation (11) denotes atmospheric emission from the cloud-free area. The second and third terms quantify emission from the atmosphere below the cloud layer that transmits through clouds and emission from clouds, respectively. The fourth term represents surface-emission that transmits through clouds, and the last term denotes the surface-emission from the cloud-free area. For our study, we consider a first-order approximation, where atmospheric temperature T a may be represented by T s using [Marshall and Plumb, 2008]: Putting equations (10), (11) in equation (8) (3) and (16), we get: increases in response to an increasing trend in T cld , while the response to f c trend can go either way depending on the zone and season.

Data and analysis
We analyze two different datasets to compute mean seasonal cld l in the day and nighttime (table 1) We perform all the analysis at 1°× 1°grid using daily level 3 MODIS and CERES data and present the statistics averaged over the seven T s homogeneous zones. All seasonal trends are calculated as linear regression for the period 2000-2019 (tables S1 and S2 in SI). Regarding equation (18b), ΔCRF is calculated from the linear trends of net CRF in each of the homogeneous zones separately for day and nighttime in each season. Finally, is calculated for each T s homogeneous zone using the proposed analytical framework and compared against the total changes in T s during the study period (used from Kothawale and Rupa Kumar 2005).

Results
The mean seasonal daytime and nighttime net CRFs in the T s homogeneous zones in India are shown in figure 1.
Three key features are noteworthy. LW CRF is positive in every season in every T s homogeneous zones because clouds partially absorb outgoing LW radiation causing net warming at the TOA. In the nighttime, cloudradiation interaction is limited to only LW, and hence the net CRF is always positive in the nighttime (in the absence of any SW cooling). The magnitude, however, depends on f c and T cld (mean seasonal values are given in SI table S1 and S2). Higher cloud tops (i.e., lower T cld ) and larger f c lead to larger LW CRF, which is evident in all homogeneous zones during the monsoon and in some of the T s zones in the other seasons that provide conducive conditions for cloud invigoration.
Secondly, in the daytime, clouds reflect solar radiation, causing cooling at the TOA, and hence the net CRF depends on the relative magnitudes of LW warming and SW cooling. In the monsoon, SW cooling is stronger than LW warming by the deep convective clouds (Saud et al 2016), and hence the net CRF is cooling in all the regions except EC. In other seasons, we observe a mixed signal. In the pre-monsoon season, most (five out of seven) of the T s regions have a net positive CRF in the daytime. In this season, SW cooling is at its minimum because of the low moisture content and low f c in most of the regions. In the NE region that is frequently affected by thunderstorms in this season, the SW cooling dominates over the LW warming. During the post-monsoon and winter season, SW cooling and LW warming are of almost similar magnitudes leading to near-zero net CRF. Thirdly, the diurnal variation in net CRF is the largest in the monsoon season because the SW cooling is the largest in this season due to the high frequency of convective clouds.
Next, we examine mean seasonal daytime and nighttime Cld l for the seven T s zones (figure 2). Positive Cld l values imply that T S Cld D would increase in response to an increase in net CRF and negative Cld l values imply that T S Cld D would decrease in response to an increase in net CRF. In the winter, all T s zones show a positive Cld l during daytime and a mixed sign during nighttime. In the regions (e.g., EC, NE, and NW) where the signs are opposite in the day and nighttime, either an increase or decrease in net CRF in both day and nighttime would enhance the diurnal temperature range (DTR). In the regions where Cld l is either positive (e.g., IP, WC, and WH in the winter) or negative (e.g., NC, NE, and WC in the pre-monsoon), an increase (decrease) in net CRF would accelerate (retard) or retard (accelerate) surface warming. In the pre-monsoon and post-monsoon seasons, all the regions show a similar pattern in Cld l during the daytime and nighttime. In the monsoon, all the regions except NC show the same sign for .
Cld l Larger Cld l values imply that the impact of net CRF would be larger in those regions (and seasons) due to even a smaller change in net CRF. We now discuss the mean (±standard deviation) seasonal changes in T s due to the net CRF trends in the seven T s homogeneous zones of India (figure 3). This is explained by the variations in Cld l in conjunction with the changes in net CRF (table 1). In the EC, negative T s Cld D during March-September implies that clouds have a net cooling effect on T s in both day and nighttime. However, this should not be interpreted in absolute terms Table 1. Mean seasonal λ cld (K per Wm −2 ) and ΔCRF (W m −2 year −1 ) during daytime (1st row) and nighttime (2nd row) in the seven T s homogeneous zones of India.

Dec-Feb
Mar-May Jun-Sep Oct-Nov   (as a decrease in T s ); rather it means that in the absence of clouds, the observed rate of increase in T s in this region would have been higher. A similar impact is observed in the winter during nighttime. During the daytime in the winter and day and nighttime in the post-monsoon, the impact is reversed (i.e., T s rising trend is accelerated due to cloud feedback). Generally, T s increases at a faster rate during the nighttime than during the daytime (Davy et al 2017) due to global warming leading to a reduction in DTR. In the IP, throughout the year, clouds suppress the T s warming trend in both day and nighttime with a larger impact during nighttime in ON and DJF and daytime in the premonsoon and monsoon. These results imply that the DTR would increase in ON and DJF and decrease in the other two seasons due to cloud feedback if the current trends continue. A similar impact is observed in the WH except for the nighttime in the post-monsoon and the WC except in the pre-monsoon. In the NW, the cloud feedback is least as the region is dry and has the lowest f c (tables S1 in SI). In this and the other two (NC and NE) homogeneous zones, T s

Discussions and conclusions
Our proposed analytical framework to estimate the impact of net CRF trend on T s trend utilizes observed data and therefore can be universally applicable. We note that the observed T s trends is a manifestation of all the driving factors (including clouds), but here we quantify the roles of clouds only. Similar frameworks can be developed to understand the roles of other driving factors on the observed T s trend following the same philosophy.
We discuss a few key issues that are important for the proper interpretation of the results. First, we note that the Terra spacecraft crosses the Indian region at 10:30 AM and 10:30 PM, and so the cloud and albedo measurements and T s measurements do not coincide temporally. We feel that the temporal difference would not alter our broad conclusions. Second, we assume that the impact within a T s homogenous zone is unperturbed by the changes in net CRF in the adjacent region. Third, the trends used in cloud properties used in our analytical framework may be impacted by the uncertainty in cloud retrieval. For example, MODIS f c may be over-estimated in the cumulus-dominated regions (Dutta et al 2020, Zhao andDi Girolamo 2006) due to the resolution effect. Without any 'true' f c estimates, it is difficult to quantify such uncertainty. Fourth, f c responds to global warming through feedback processes as a function of cloud optical depth and T cld (Zhou et al 2013). To estimate cld l in our framework, we consider the rate of change of f c and T cld (equation 18a). Therefore, any changes in f c and T cld due to the feedback are already incorporated into the framework. Finally, we analyze 20-year data that may not be sufficient for detecting significant trends in all the parameters considered here. However, based on our analytical framework, the parameters without significant trends have a minimal impact on .
Cld l Comparing the estimates of changes in T s attributed to cloud net CRF with the changes in T s in the last 20 years, we interpret that in the regions where T s Cld D is negative, the T s would have increased at a higher rate had there been no influence of cloud radiative forcing. On the other hand, the regions where T s Cld D is positive, it accelerates the observed warming trend. We identified these regions in India and discussed the patterns in this work. Our results can be compared with climate model simulations with and without cloud radiative feedback for robust interpretation of the impacts of net CRF on surface temperature trends over India. The framework relies on the observed data that are available globally, and hence the framework can be applied universally. Finally, we note that a similar analysis is required to separate the role of other key factors like GHG forcing, aerosols, urbanization and natural climatic variability, which also impact the surface temperature trends (as discussed at the beginning of the framework).
The key conclusions of this study are as follows: 1. In the nighttime, the net CRF is positive in every season in every T s homogeneous zone in India with the largest LW CRF observed during the monsoon due to higher cloud tops (i.e. lower T cld ) and larger f c. In the daytime, net CRF shows a dual pattern depending on the relative strengths of SW cooling and LW warming.
2. The cloud sensitivity can be either a negative or a positive in India and varies in the range -0.180 K to +0.241 K per W m −2 net CRF.
3. Clouds are found to have a dual impact on the surface warming trends by suppressing the trends in regions where the cloud sensitivity and net CRF show opposing trends and accelerating the trends in regions where the cloud sensitivity and net CRF show similar trends.