Behavior of IMERG precipitation extremes with temperature at different spatial resolution

The Clausius-Clapeyron equation determines how saturation vapor pressure increases with temperature, which is important in determining variations in extreme precipitation. Regionally, the scaling of C–C does not vary significantly, but the relationship with extreme precipitation does. In this study, the precipitation from Integrated Multisatellite Retrievals for Global Precipitation Measurement (IMERG) is tested for its accuracy in scaling extreme precipitation rates with temperature (termed scaling factor). We utilized the IMERG precipitation data across the Indian Sub-continent at 0.1° × 0.1°, 0.25° × 0.25° and 0.5° × 0.5° spatial resolution from 2001 to 2020 datasets. Our findings show that, there is a transition in Global Precipitation Measurement’s precipitation extremes estimations (95th percentile) around 30 °C over spatial resolution of 0.25° and 0.1° from C–C to sub C–C. This study also evaluates the sensitivity of C–C scaling in different regimes of India having homogeneous precipitation climatology. It is found that southeast India is highly sensitive to the spatial resolution, as it shows steep slopes in extreme precipitation rates at high dew point temperatures. This is the first study to evaluate the sensitivity of spatial resolution on C–C analysis as most of the previous studies have considered temporal variations.


Introduction
Clausius-Clapeyron (C-C) relationship governs the atmosphere's capacity to retain water, which increases by approximately 7% at the surface and 15% in the upper troposphere for every degree of warming (Trenberth et al 2003). The real air humidity increases concurrently with the assumed constant relative humidity (Ali et al 2021), causing more precipitation at higher temperatures (Schroeer and Kirchengast 2018). This increase in the amount of rain would worsen the risk of flash floods and landslides, which in turn would threaten social and economic infrastructures (Fadhel et al 2018, Nikumbh et al 2019, Fowler et al 2021a, Nanditha and Mishra 2022. Previous studies have tried to estimate the increase in precipitation intensity rate know as scaling factor (SF) with rising temperatures (e.g. Ali et al 2018, Vergara-Temprado et al 2021, Zhang et al 2019, Liu and Allan 2012, Joyce et al 2004. Many factors influence this rate, including precipitation length and type, sesonality, spatial resolution and large-scale circulations (Berg et al 2009, Panthou et al 2014, Pumo and Noto 2021, Fowler et al 2021a. The Clausius-Clapeyron (C-C) connection predicts a rise in atmospheric moisture content of around 6%-7%/ • C at the surface and 15%/ • C at the upper troposphere, which should lead to an increase in severe precipitation (Trenberth et al 2003, Allan et al 2022. This has been discovered in part via observations and model simulations (Liu et al 2020). Berg et al (2013) discovered that heavier precipitation, such as the 99th percentile of daily precipitation, seems to follow a super C-C rate (14%/C), but a lower percentile (75th) follows the ordinary C-C rate (7%/C). Such alterations in precipitation properties will have a major effect on the hydrological cycle. Chang et al (2016) argued that processes are adjusting for the mismatch between the 6%-7%/C increase in the intensity of individual precipitation events and the 1%-2% /C rise in the global average precipitation rate. These processes may be either (1) thermodynamic, impacting the redistribution of extra humidity within the precipitation system, or (2) dynamical, changing the cell structure of the precipitation system. Nevertheless, the identification of these mechanisms is sensitive to changes in physical characteristics such as the starting location, intensity, spatial extent, duration, and the trajectory of the precipitation system (Chang et al 2016), as well as the available moisture and region of interest. These compensatory processes are anticipated to influence the scale of future precipitation systems, particularly for the most intense precipitation occurrences. Majority of studies evaluate the impact of temporal resolution on C-C scaling (Hosseini-Moghari et al 2022). However, the influence of spatial resolution on variability of C-C scaling is not well known.
Due to different factors, including data access issues, such as the low number of observation sites, understanding the relationship between precipitation and temperature remains an open question in many places. One possible data source that could be used in this research is remotely sensed precipitation data (Le et al 2020, Ali et al 2021, Fowler et al 2021b. The Integrated Multisatellite Retrievals for Global (IMERG) (Huffman et al 2015a) precipitation measurement is one of the most reliable satellite-based precipitation products. The IMERG algorithm combines information from the Global Precipitation Measurement (GPM) satellite constellation to estimate precipitation over the majority of the earth's surface. Therefore, this characteristic of IMERG is explored to study the sensitivity of C-C scaling on spatial resolution of precipitation products. The algorithm of this merged product provides a global coverage at spatial resolution of 0.1 • × 0.1 • and a 30 min temporal resolution making it exclusive among all other precipitation products.
In order to address the critical question of impact of spatial resolution on C-C scaling rates, this study relies on the research questions as follows: (1) How is the spatial resolution of precipitation extremes from GPM constellation sensitive to surface temperature? During this analysis precipitation rates from IMERG were evaluated at three different spatial resolutions (0.1 • , 0.25 • , 0.5 • ) over the Indian subcontinent. For C-C relationships precipitation rates are evaluated with respect to dew point temperature (DPT). The DPT estimates used in this study stems from European Centre for Medium-Range Weather Forecasts Reanalysis (ECMWF) -Interim (ERA-Interim) (Dee et al 2011).

ERA-interim dew point temperature
The ERA-Interim Dew Point Temperature data were downloaded from the ECMWF server (Dee et al 2011). In ERA-Interim, the dew point temperature is derived from the model's representation of atmospheric moisture content and temperature. The estimation process involves assimilating various observations, such as surface meteorological data, radiosonde measurements, satellite data, and atmospheric reanalysis products. These observations are used to initialize the model, which then simulates the atmospheric state over a specific time period. It is important to note that ERA-Interim provides gridded data on a global scale, typically at a horizontal resolution of 0.75 • latitude by 0.75 • longitude. The estimated dew point temperature values are available at different vertical levels of the atmosphere as well. Due to their high temporal resolution, these data are also short-term forecast data. The period of data used in this study is from 2001 to 2020. The original data at native grid resolution are regridded to different resolutions (0.1 • × 0.1 • , 0.25 • × 0.25 • , 0.5 • × 0.5 • ) using a bilinear interpolation technique.

GPM IMERG
TRMM's follow-up satellite precipitation program, GPM, can give worldwide rain and snow data every half-hour using microwave and infrared technology. The TRMM sensor package is expanded with GPM, which improves the ability to observe precipitation. The GPM core observatory is equipped with a dualfrequency radar i.e Ku and Ka bands compared to TRMM satellites' four high-frequency channels of microwave radiometer thereby enhancing the observation capability for light precipitation and solid precipitation (Huffman et al 2007;Huffman et al 2015b). As a result, the GPM mission can offer more precise light (<0.5 mm h −1 ) and solid precipitation data, which are the most common types in mid-and high-latitude regions. Beginning in March 2014, the IMERG algorithm produces three types of products (i.e. the Early with latency ∼6 h, late with latency ∼18 h, and Final runs with latency ∼4 months) at half-hourly and 0.1 • × 0.1 • resolutions. The IMERG Early and Late Runs are distinguished by the fact that the Early uses just forward propagation (essentially extrapolation), whilst the Late uses both forward and backward propagation (allowing interpolation). The monthly in situ gauge data is used in the final run GPM IMERG to create research level products. The GPM satellite provides highly accurate and detailed measurements of GPM precipitation across India. The GPM satellite data has enabled researcher to study different hydrological applications such as climate research, drought monitoring, flood forecasting, agricultural planning etc. (Prakash et al 2016  The uncertainty in satellite precipitation data stems from several factors, including spatial and temporal scales. A study by Maggioni et al (2022) has reported some of the key factors such as, instrumental uncertainty, sampling uncertainty, retrieval algorithm uncertainty, zonal and topographical effects, and ancillary data. It is important to note that efforts are made by scientists and researchers to quantify and minimize these uncertainties through data assimilation techniques, algorithm improvements, and inter-comparison studies. However, despite these efforts, uncertainties still exist in satellite. Similarly, the reanalysis products (such as ERA-Interim) also contain uncertainties. But the analysis in this study has low impact from this uncertainties, as we intercompare the estimates of precipitation at different grid resolutions. Therefore, the contribution from uncertainty will be equally reflected in analysis at individual grid resolutions.

Implementing C-C theorem
This study has utilized the binning technique to evaluate precipitation sensitivity with temperature (Zhang et al 2017). Through this approach the precipitation-temperature relationship is investigated by evaluating pairs of DPT and precipitation during rainy days. A day is considered as rainy when precipitation is ⩾ 2.5 mm following guidelines of rainy day by India Meteorological Department (Pai et al 2014). During this process, the DPT and precipitation values are sorted in ascending order of DPT and then divided into 12 bins with an equal number of observations of DPT and precipitation in each. A similar approach of binning is followed by Herath et al (2018). Furthermore, the mean, 90th, 95th, and 99th percentile was computed for each bin. To avoid the impact of specific atmospheric influences on extremely low and very high DPT values, the first and final bins were not taken into account while computing the SF. The percentile vectors were then fitted with a linear model (equation (1) where E (DPT) represents mean DPT value in • C, P represents precipitation, α represents slope of linear regression, β denotes intercept and SF represents scaling.
To evaluate sensitivity of precipitation with temperature, we performed analysis over entire Indian subcontinent and over four different climatological regimes in India. The four spatial domains of climatological regimes are the southwest, southeast, central, and regions (Nair and Indu 2017) as shown in figure 1. The geographical regularity of rainfall was used to choose these locations. The rainy season lasts from June to September, with the exception of the southeast area. During JJAS, the southeast area receives less than 3 mm per day but receives more rainfall during the winter monsoon months of October, November, and December. The southwest area including the Western Ghats receives the most rainfall during the summer season, with an average of roughly 20 mm per day. During July and August, the central area of India receives a significant quantity of rainfall, ranging from 10 to 15 mm per day. It is unsurprising that the northwest area, which is mainly desert, receives the least amount of rainfall throughout the summer season, with a maximum value of roughly 5 mm day1. Except for the southeast area, rainfall in all regions diminishes dramatically during the summer monsoon's withdrawal phase in September. We evaluated the relationship between precipitation extremes and temperature over these regimes which are not studied by previous studies.
Depending on the kind of precipitation climatology, the extreme value has been chosen as the 90th, 95th, or 99th percentiles. For big nations like India with highly heterogeneous precipitation pattern this value fluctuates greatly. To address this challenge, we compute value of precipitation extreme for each grid cells. The extreme precipitation threshold index is produced by calculating the number of incidents in a year that have intensities greater than the given threshold.
The Clausius-Clapeyron equation describes the relationship between temperature and the saturation vapor pressure of water, which governs the maximum amount of moisture that the atmosphere can hold. According to this equation, the saturation vapor pressure increases exponentially with temperature, implying that a warmer atmosphere can hold more moisture. Consequently, under the assumption that other factors remain constant, extreme precipitation events should increase in intensity as temperatures rise.
However, in the specific case mentioned, the scaling of extreme precipitation with temperature is not following the super Clausius-Clapeyron rates. This discrepancy suggests that there are additional factors at play that influence the relationship between temperature and extreme precipitation at that spatial resolution.
The implied physical meaning of different Clausius-Clapeyron rates at various spatial resolutions is that the local factors and processes affecting extreme precipitation vary across different scales. Climate models and observational studies often operate at different spatial resolutions to capture the complex interactions between temperature, moisture, atmospheric dynamics, and topographic features.
At finer resolutions, localized effects such as topography, land use, and microscale processes become more pronounced. These factors can modify the relationship between temperature and extreme precipitation, leading to variations in the Clausius-Clapeyron rates. Consequently, the scaling of extreme precipitation with temperature may deviate from the expectations based solely on the Clausius-Clapeyron equation.
Understanding these variations and their physical meaning at different spatial resolutions is crucial for accurately assessing the impacts of climate change on extreme precipitation events. It requires considering regional and local factors that can either amplify or mitigate the effects of temperature changes on extreme precipitation.

Sensitivity of spatial resolution precipitation extremes from GPM constellation to surface temperature
In this study we evaluate the sensitivity of precipitation extreme events captured by GPM with DPT measurements at different spatial resolution. For this process, precipitation extreme events are identified for thresholds as discussed in section 2.3. Figure 2 shows the temporal variation in domain averaged values of 95th percentile for study region. It is evident from the results that, re-gridding of GPM data to lower resolution by weighted average technique leads to change in threshold values which affect the calculation of C-C scaling. This factor is not addressed in any of the previous studies pertaining to precipitation temperature relationship. We further try to quantify this change in C-C scaling due to change in spatial resolution.
In many regions of the world, there is an increasing intensification of precipitation extremes because of warming. However, changes in sensitivity of precipitation extremes to spatial resolution of monitoring grid are unknown due to a paucity of observed precipitation data from well spread gauges over vast areas of South Asia. To close this gap, we employed satellite-based GPM data. Further, by binning precipitation intensities with DPT at various geographical resolutions, we investigated the fluctuation of precipitation extremes with spatial resolutions. The results indicated that precipitation extremes at 99th percentile rapidly with temperature, with super C-C rates in all resolutions (figure 3) except 0.25 • over the entire Indian subcontinent. The scaling of the 99th percentile extreme precipitation with temperature not meeting the super Clausius-Clapeyron (C-C) rates at a particular resolution (in this case, 0.25 • ) suggests that the relationship between temperature and extreme precipitation is not consistent with the expectations based on the Clausius-Clapeyron equation.
The super C-C scaling rates of precipitation extremes have been related to substantial condensational heating, which promotes upward movements in clouds, resulting in enhanced moisture convergence and greater rain (Lenderink and van Meijgaard 2008). While for lower percentiles (95th and 90th) we observed decrease in precipitation extremes for 0.1 • and 0.25 • resolutions. On the other hand, there is an increase in precipitation extremes observed at higher DPT for 0.5 • resolution. For higher spatial resolutions, the scaling breakdown at the high-temperature threshold was likewise absent. We further evaluate this by performing analysis on precipitation climatologically regions (explained in section 2.3). Figure 4 shows the variation in precipitation extreme rates with respect to dew point temperature for four different climatological regimes (as indicated by boxes in figure 1) as discussed in section 2.3. The 99th percentile events have a rapid increase in precipitation rates at higher DPT. It is observed that the south-east domain shows highest sensitivity to change in spatial resolution, such that the 99th percentile has a steep rise in precipitation intensity at higher DPT. The central and north-west regions show least sensitivity to change in spatial resolution of precipitation and temperature data.

Performance of GPM precipitation data in capturing extreme events in different climatologically regions
The region-dependent sensitivity of the relationship between precipitation and dew point temperature over India can be influenced by changes in spatial resolution. Spatial resolution refers to the level of detail or the size of grid cells used to represent the Earth's surface in climate models or observations. When examining the relationship between precipitation and dew point temperature at different spatial resolutions, several physical insights can be considered. Such as topographical features, India's diverse topography, including mountains, plains, and coastal regions, plays a crucial role in influencing the spatial distribution of precipitation and dew point temperature. At higher spatial resolutions, finer details of topographical features are better captured, leading to improved representation of local climatic processes such as orographic precipitation and coastal influences. This can lead to a more accurate depiction of the relationship between precipitation and dew point temperature in mountainous or coastal regions. The impact due to topographic features will be more prominent over south-west region as it encompasses Western Ghats (hilly terrain). However, the GPM precipitation estimates is less sensitive to precipitation extreme with DPT over the region. Another process affecting relationship between precipitation and DPT is convective processes. Convective processes, responsible for a significant portion of India's rainfall, are influenced by small-scale atmospheric features that may not be accurately captured at coarser spatial resolutions. Fine spatial resolutions allow for better representation of convective processes, which are sensitive to small changes in dew point temperature, leading to an improved understanding of the precipitation-DPT relationship in regions dominated by convective rainfall such as South-East region in figure 4. Furthermore, mesoscale circulations also impact the relationship between precipitation-DPT. Mesoscale atmospheric circulations, such as sea and land breezes, can influence the distribution of moisture and temperature at smaller scales. At higher spatial resolutions, these features can be better resolved, leading to improved representation of mesoscale circulations and their impact on the relationship between precipitation and dew point temperature in specific regions. In summary, finer spatial resolutions in datasets can provide more detailed representations of local-scale processes and features, leading to improved understanding and characterization of the relationship between precipitation and dew point temperature in different regions of India. However, it is essential to strike a balance between computational resources and the need for higher resolution, as finer grids can increase computational demands significantly.

Conclusion
In this study, we utilized GPM Mission datasets to evaluate performance in scaling precipitation extremes with the temperature at three different spatial resolution over India. The spatial resolutions considered in this study are 0.1 • , 0.25 • , and 0.50 • . This helps us to understand how Clausius-Clapeyron (C-C) scaling is affected by spatial resolution of data used to compute them. This is the first study to evaluate the impact of spatial resolution on C-C scaling of extreme precipitation events. There is a transition in GPM's precipitation extremes estimations (95th percentile) around 30 • C over spatial resolution of 0.25 • and 0.1 • from C-C to sub C-C. Therefore, this study shows that the C-C scaling studies are subjected to the spatial resolution of monitoring satellites. The findings of this study show that the GPM precipitation product has a lot of potential as a replacement for in situ data when it comes to scaling precipitation extremes at different spatial resolutions.
This study further evaluates the sensitivity of C-C scaling analysis of extreme precipitation events from different zones of India at different spatial resolution. It is found that the central and north India which has precipitation during summer monsoon season (June, July, August and September) are least sensitive to the spatial resolution during C-C analysis. While southeast India is highly sensitive the spatial resolution, as it shows steep slope in extreme precipitation rates at high dew point temperatures. We have considered precipitation estimates from GPM available at a highest spatial resolution of 0.1 • , availability of high-resolution data (<1 KM) can help us to understand the process further. Finally, different remotely sensed precipitation products, such as the PERSIANN family, CMORPH, and GSMaP (Global Satellite Mapping of Precipitation; Kubota et al 2007), are accessible at higher spatial resolution Comparison and integration of various products to obtain high-resolution precipitation data might lead to a more complete understanding, which is left to future research.
There is evidence that the rising temperatures are linked to the rise in precipitation extremes over the past 50 years. Their spatial-temporal properties are probably going to change as the climate changes. Thermodynamic increases in water vapor with warming are an important mechanism for intensifying extreme rainfall, although dynamical factors also cause extreme precipitation. To correctly comprehend the observed trends and get accurate future estimates, it is necessary to consider the increasing spatial extent of the underlying physical mechanisms of extreme rainfall events, which are size-dependent.

Data availability statement
No new data were created or analyzed in this study.