It is widely acknowledged in scientific research that as our planet's climate warms, extreme precipitation events are becoming more intense and frequent (Trenberth, et al. 2003). This intensification is particularly evident at shorter timescales, such as hourly or daily precipitation (Drobinski, Bastien, et al. 2016, Lenderink and Meijgaard 2008, Panthou, et al. 2014, Drobinski, Silva, et al. 2018). The trend is concerning because extreme precipitation can lead to severe consequences like flooding and landslides. Therefore, it is crucial to investigate the complex relationship between precipitation and temperature.

Understanding the connection between temperature and precipitation.

To grasp this connection, it is necessary to understand a fundamental principle: temperature determines the moisture-holding capacity and relative humidity of the atmosphere (Trenberth, et al. 2003). In simpler terms, warmer air can hold more moisture. The rate at which moisture-holding capacity increases with temperature is approximately 7% per degree Celsius (7%/°C), as described by the Clausius-Clapeyron (CC) equation. Now, assuming that the relative humidity of the air remains constant, and that extreme precipitation is primarily driven by the actual water content in the atmosphere,  extreme precipitation, theoretically, should also increase at a rate of around 7%/°C.

Variations in Precipitation-temperature scaling

The relationship between extreme precipitation and temperature has captured the attention of many researchers worldwide. For instance, a pioneering study conducted in the Netherlands (Lenderink and Meijgaard 2008) analysed a 99-year record of hourly precipitation observations. They found that extreme precipitation rates (particularly at the 99th percentile and higher) scaled closely to the CC rate for temperatures below 12°C. However, as temperatures exceeded 12°C, the scaling rate doubled, surpassing the CC rate.
Subsequent research efforts have examined similar scaling relationships in various regions, including the Mediterranean (Drobinski, Bastien, et al. 2016, Peleg, et al. 2018), Asia (Ali, et al. 2021), North America (Ali, et al. 2021, Panthou, et al. 2014), and Australia (Ali, et al. 2021, Wasko, Sharma and Westra 2016). These studies have provided valuable insights into how precipitation responds to temperature changes in diverse climates and geographic settings.

The results of these analyses have also revealed that the relationship between precipitation and temperature varies significantly with local conditions, including climate and topography. This variability makes it challenging to draw sweeping conclusions at the global or continental scale (Westra, et al. 2014).

Global gridded datasets

The primary aim of this study is to answer the following question: How to assess the scaling relationship between precipitation and dew point temperature (i.e., the point at which air becomes saturated, forming dew) using high-resolution global gridded dataset?

While most studies have relied on observational data from weather stations (Ali, et al. 2021, Lenderink and Meijgaard 2008, Panthou, et al. 2014, Wasko, Sharma and Westra 2016), a few have employed global gridded datasets (Berg, et al. 2009, Drobinski, Silva, et al. 2018). These datasets usually offer broader spatial coverage at finer resolutions.

To address the limitations associated with ground-based observational data, including instrumentation constraints, limited spatial coverage and historical records, this report leverages global gridded products for dew point temperature and precipitation estimates.

Specifically, nine locations spanning the globe were selected here to evaluate precipitation scaling with dew point temperature (Td). Gridded data of Td at 2 m above Earth's surface from ERA5  (Hersbach, et al. 2018) was used. ERA5 is the fifth generation of atmospheric reanalysis from the Copernicus Climate Change Service (C3S) at European Centre for Medium-Range Weather Forecasts (ECMWF). It provides the evolution of climate and weather variables on an hourly basis at approximately 31 km × 31 km from 1950.

The precipitation rate data was sourced from bias-corrected Climate Prediction Center morphing technique (CMORPH-CRT) (Xie, Joyce, et al., Bias-corrected Climate Prediction Center (CPC) morphing technique (CMORPH) satellite precipitation estimates (CMORPH, version 1.0, CRT) 2017), a global satellite product offering high-resolution data at 30-minute intervals and a spatial resolution of approximately 8 km × 8 km. CMORPH-CRT data is available from 1998 and covers the region between 60°S and 60°N (as shown in Figure 1). To match the temporal resolution of the ERA5 Td data, CMORPH-CRT data was aggregated to hourly intervals.

The dataset of gridded Td and precipitation data was aggregated to achieve a uniform spatial extent of around 80 km × 80 km at each location. It covers a 22-year period from 1 January 1998 to 31 December  2019.

Methodology

One of the classic methods for evaluating this scaling relationship is the binning technique  (Lenderink and Meijgaard 2008). The estimation procedure can be summarised in four steps as follows:

1. Pair variables: for each hourly interval within the 80 km × 80 km extent, pair Td with its coincident maximum precipitation rate (Pmax);
2. Define bins: place all Pmax–Td pairs into 12 Td ranges (bins), with the number of pairs being the same and the mean Td being the representative Td for each bin;
3. Compute percentiles: within each bin, sort Pmax and identify the percentiles of interest (e.g., 50th, 90th, 99th and 99.9th);
4. Quantify scaling rates: fit data from these bins with a linear regression of log-transformed Pmax on Td, given by

Case studies: Results at all locations

Figure 2 presents the scaling rate estimates between the hourly Pmax and daily mean Td at the selected nine locations in Belgium, China, Italy, Germany, India, Australia, New Zealand, and the United States.
A majority of the locations exhibit positive scaling results, which are in rough agreement with the CC rate. However, it is essential to note that this positive scaling is not universal. The significant spatial heterogeneity of extreme precipitation scaling observed across locations with varying climate conditions underscores the localised effects on precipitation-temperature relations. Consequently, drawing a single overarching conclusion on a global scale becomes a challenging endeavour.

Discussion

While this study provides valuable insights, it is important to acknowledge potential limitations associated with the dataset used, particularly CMORPH-CRT precipitation estimates. Researchers have highlighted that CMORPH-CRT often overestimates precipitation compared to ground observations (Bruster-Flores, et al. 2019), especially over arid and semiarid regions (Guo, et al. 2015, Wei, et al. 2018). Additionally, the 22-year CMORPH-CRT hourly precipitation data at the nine locations selected for this study contains a significant proportion of missing values, which may impact the statistical robustness of scaling estimations.

To address these limitations, future research might explore alternative satellite-based precipitation products, such as gauge-blended CMORPH (CMORPH-BLD, with CMORPH standing for: Climate Prediction Center morphing technique, and BLD for its blended version), which combines gauge data with satellite estimates (Xie and Xiong 2011) and has demonstrated higher data quality as well as more stable performance than CMORPH-CRT (Sun, et al. 2016). Furthermore, if ground observations are available, pooling data from multiple adjacent stations within larger regions (Ali, et al. 2021) could reduce variability in scaling estimation, particularly on small spatial scales with limited sample sizes.

Conclusion

In this study, CMORPH-CRT and ERA5 global gridded products were employed to assess the scaling relationship between spatiotemporal properties of hourly (extreme) precipitation and daily dew point temperature at various locations across the globe. The results generally align with previous studies using similar methods and data, such as the one by Wasko, Parinussa and Sharma (2016). The significant spatial heterogeneity of scaling results at those locations also suggests the impacts of local factors, including climate conditions and the proximity to humidity sources (e.g., oceans). Despite potential dataset and methodology limitations, this research provides valuable insights into the application of high-resolution global gridded products for precipitation-temperature scaling analysis.

Nonetheless, further research is essential to utilize more reliable datasets (and statistical approaches) for a comprehensive understanding of the factors influencing precipitation-temperature scaling. Exploring how the spatial structure of precipitation varies with temperature, especially dew point temperature, remains an area of continued scientific interest.