Changes in temporal variability of precipitation over land due to anthropogenic forcings

This study investigated the anthropogenic influence on the temporal variability of annual precipitation for the period 1950–2005 as simulated by the CMIP5 models. The temporal variability of both annual precipitation amount (PRCPTOT) and intensity (SDII) was first measured using a metric of statistical dispersion called the Gini coefficient. Comparing simulations driven by both anthropogenic and natural forcing (ALL) with simulations of natural forcing only (NAT), we quantified the anthropogenic contributions to the changes in temporal variability at global, continental and sub-continental scales as a relative difference of the respective Gini coefficients of ALL and NAT. Over the period of 1950–2005, our results indicate that anthropogenic forcing have resulted in decreased uniformity (i.e. increase in unevenness or disparity) in annual precipitation amount and intensity at global as well as continental scales. In addition, out of the 21 sub-continental regions considered, 14 (PRCPTOT) and 17 (SDII) regions showed significant anthropogenic influences. The human impacts are generally larger for SDII compared to PRCTOT, indicating that the temporal variability of precipitation intensity is generally more susceptible to anthropogenic influence than precipitation amount. The results highlight that anthropogenic activities have changed not only the trends but also the temporal variability of annual precipitation, which underscores the need to develop effective adaptation management practices to address the increased disparity.


Introduction
Understanding the anthropogenic contributions to climate change is an important aspect of climate science to advance our knowledge of the causes of the observed climatic trends and changes in extremes. Previous studies have established the anthropogenic influence on trends of climate variables, such as, precipitation , surface air temperature (Hegerl et al 1997, Zhang et al 2006, tropopause height (Santer et al 2003) and ocean heat content (Barnett et al 2005a(Barnett et al , 2005b, among others. Some studies have highlighted the influence of human activities on individual extreme events, such as California's drought (Williams et al 2015), England's flood risk (Pall et al 2011) and European heat waves (Stott et  well as the concurrence of multiple climate extremes (Min et al 2011, Angélil et al 2014, Fischer and Knutti 2015. Zhang et al (2013) and Zwiers et al (2011) identified the contribution of anthropogenic factors for intensification of precipitation extremes and prolonging return periods of daily temperature extremes.
Understanding the changes in annual precipitation is crucial for water resources planning to sustain agricultural, ecological and water infrastructure development in addition to protection of transport systems, homes and business infrastructure. Long term trends explain only one aspect of the changes occurring to annual precipitation. Combining the inter-annual and inter-decadal variability of precipitation and precipitation trends would give an overall picture of changes occurring in annual precipitation. Previous studies established some linkages between annual and interannual-to-decadal variability of precipitation over land and natural modes of variability of the coupled climate system, such as El Nino-Southern Oscillation (ENSO), Arctic Oscillation (AO), and North Atlantic Oscillation (NAO), through teleconnection (Gu and Adler 2004, Medvigy et al 2008, Small and Islam 2008, Garreaud et al 2013. Global warming induced by anthropogenic forcing may alter the variability of precipitation. Simple thermodynamical argument in addition to circulation Changes (Schaller et al 2016) for 'wet gets wetter, dry gets drier' (Held and Soden 2006) and 'warm gets drier' (Xie et al 2010) suggests an increase in spatial heterogeneity of precipitation, as the increase in atmospheric precipitable water with warmer temperatures enhances moisture convergence or divergence in climatologically wet or dry regions. A similar heuristic argument would also suggest an increase in precipitation temporal variability would indicate an enhanced moisture convergence or divergence during wet or dry years.
A major source of uncertainty in the simple arguments used to scale changes in precipitation variability with warming is that they ignore potential changes in interannual or decadal modes of variability with warming and the teleconnection pathways that linked such changes to precipitation over land. Recent studies found a projected increase in the frequency of extreme ENSO event under GHG forcing (Cai et al 2014, Capotondi 2015, but the projected changes in spatial structure and amplitude of ENSO (e.g. Vecchi and Wittenberg 2010) and the precipitation response in the tropics and extra-tropics (Meehl andTeng 2007, Seager et al 2012) remain largely uncertain. By decomposing the model projected precipitation response to a canonical ENSO pattern of sea surface temperature variability into changes in the mean state of precipitation and the historical as well as a future enhancement in precipitation response to the canonical ENSO pattern, Bonfils et al (2015) identified regions that will likely experience precipitation anomalies that are without precedent in the current climate. These studies have provided a strong motivation to investigate the changes in precipitation temporal variability due to anthropogenic forcing in the past and future.
Estimating the changes in temporal variability of precipitation is complicated by uncertainty in the model simulations as well as the metrics used to define variability and detect its changes. This study attempts to estimate the changes in temporal variability of precipitation due to human contributions as well as quantifying its uncertainty. We introduce an index based on the Gini coefficient to quantify the anthropogenic influence on temporal variability of annual precipitation amount and intensity. The Gini coefficient is a measure of statistical dispersion that has been widely used in the field of economics as a measure of income inequality (Ceriani and Verme 2011). Recently, the Gini coefficient has also been applied in climate science (Masaki et al 2014, Rajah et al 2014. Unlike other measures, the Gini coefficient is not sensitive to the scale and probability distribution of the data, making it robust and easy to interpret (Rajah et al 2014, Ceriani andVerme 2011). We estimated the human contribution to potential changes in temporal precipitation variability at global and continental scales and to the Giorgi climate division (Giorgi 2000). The remainder of the paper is structured as follows: data description is in section 2, methods in section 3, and the results are presented in section 4, with discussions and conclusions provided in section 5.

Data
We utilized 42 realizations from 15 CMIP5 GCM models (see supplementary table T1 available at stacks. iop.org/ERL/12/024009/mmedia) to obtain 'annual total precipitation (PRCPTOT)' and 'simple precipitation intensity index (SDII)' from the CLIMDEX archive hosted by Canadian Centre for Climate Modeling and Analysis for the attribution analysis. PRCPTOT is defined as the total amount of precipitation on wet days (days with precipitation >1 mm). SDII is the annual precipitation intensity, obtained by dividing the total amount of precipitation in a year by the number of wet days in a year. PRCPTOT and SDII calculated from model simulations for historical  and historicalNat  were used to estimate the anthropogenic contribution to temporal variability. The historical simulations were driven by both time-dependent anthropogenic (greenhouse gas concentrations, aerosols and ozone and land use) and natural (solar and volcanic) forcing, while the historicalNat simulations were run only with the time-dependent natural forcing, hence providing estimates of the Earth's climate without anthropogenic influences. To compare the historical simulations, we utilized the observed dataset of the same variables obtained from HADEX2 dataset (Donat et al 2013) of CLIMDEX archive.
As the spatial resolution of the simulated precipitation variables from the GCMs varies, we have interpolated all the data to a common grid of resolution 2°latitude Â 2°longitude using bilinear interpolation method. For temporal attribution, numerous studies (Zhang et al 2013, Westra et al 2013, Santer et al 2007 found that the signal-to-noise ratio of climate variables is enhanced by spatial averaging, resulting in a more statistically significant climate signal. Therefore, we used the spatial mean of the global land, continental land, and the Giorgi climate division (Giorgi and Francisco 2000) to obtain a single time series for each specific spatial unit.

Gini coefficient
The Gini coefficient has been recently applied to quantify uniformity in time series of climate variables (Masaki et al 2014, Rajah et al 2014 and computed according to equation (1).
In our context, y i indicates the PRCPTOT or SDII at a particular year i and n indicates the total number of years. The value of G theoretically varies between 0 and 1, with 0 corresponding to a complete uniformity (i.e. all the precipitation values are the same) and 1 corresponding to maximal non-uniformity or largest disparity (i.e. only a single annual precipitation amount is observed during the entire study period). So, smaller values of the Gini coefficient signify more uniformity in the temporal variation of precipitation. Figure 1 presents a pictorial derivation of the Gini coefficient. A brief discussion on comparison between Gini coefficient and traditional methods are provided in the supplementary information. Other methods like standard deviation and coefficient of variation are sensitive to scale and probability distribution of the data.
We also compared the Gini coefficient of the observed and simulated PRCPTOT and SDII to identify regions where there is an agreement (disagreement) in terms of their temporal variability (figure 2). The multi model ensemble mean of the Gini coefficient captures the variability of PRCPTOT in most regions. However, it underestimates the Gini coefficients in the Andes Mountain in South America and Himalayan mountains in Asia, while in the Middle East and India it is overestimated. Similarly, for SDII, better performance was observed in Europe, Western Asia, North America and South Africa. The models tend to overestimate the Gini coefficient in Middle Eastern Asia and western part of India. Due to limited precipitation data in many parts of Africa, Australia, the Amazon in South America and Greenland, we only showed the modeled variability in locations with observations for comparison. However, the supplementary figure S2 includes the coverage of all the land regions. To sum up, figures 2 and S2 show higher values of the Gini coefficient in most of the global arid regions. Overall, the good agreement between the Gini coefficients from observed and modeled annual precipitation variability in terms of both magnitude and intensity supports the use of the CMIP5 model outputs to quantify the anthropogenic contribution to changes in the temporal variability of PRCPTOT and SDII.

Relative anthropogenic index
A change between any two scenarios can be detected by evaluating their difference or the ratio of the corresponding model outputs. With this conceptual framework, several studies have evaluated the influence of greenhouse gases on tropical cyclone characteristics (Gualdi et al 2007) and tropospheric sulphate aerosol (Langner et al 1992). More recently, the fractional attributable risk (FAR) methodology (Stott et al 2004) based on the relative difference of probabilities was used to estimate the influence of anthropogenic forcing on heat waves (Pall et al 2011), climate extremes (Fischer andKnutti 2015, King et al 2015) and meteorological drought (Gudmundsson and Seneviratne 2016). This methodology quantifies the influence of anthropogenic forcing along with its statistical significance through bootstrapping. Likewise, we quantify the anthropogenic influence on temporal variability of precipitation via a change in the Gini coefficient. Here we define a Relative Anthropogenic Index (RAI) as the relative difference between the historical and HistoricalNat scenarios as follows: Where, G ALL and G NAT represent the Gini coefficients of the anthropogenic plus natural forcing (ALL) and natural forcing only (NAT) simulations, respectively. A positive RAI indicates a decrease in annual precipitation variability, whereas a negative RAI indicates an increase in variability due to anthropogenic forcing. In the context of resource management, a positive RAI value implies increased challenges in managing water resources and ecosystems, whereas a negative value indicates reduced variability so water resources are more manageable. Also, as the RAI is a relative difference metric, a higher difference indicates more influence in positive as well negative RAI values. . Pictorial explanation of the Gini coefficient for temporal variability: the annual precipitation amount is first ranked before being added cumulatively and converted to percentiles as shown by the red curve. The Gini value is then estimated as twice the area between the equality line (1 to 1 line) and the ranked distribution, depicted by the pink shaded area. Hence, the more pink an area is, the more the variability.
Environ. Res. Lett. 12 (2017) 024009 We calculated the RAI for a specified spatial unit by first spatially averaging the gridded Gini coefficients over the specified region for a particular scenario and realization. Therefore, each spatial unit has a single Gini value for each CMIP5 realization separately for the ALL and NAT scenarios. Then we estimated the RAI as explained by equation (2) by using the multi model ensemble means of 42 CMIP5 realizations. In order to estimate uncertainty in the RAI values, we used the Bootstrapping resampling procedure (Efron and Tibshirani 1994) to generate 10 000 sub-samples from the 42 CMIP5 realizations and ranked them to extract the 5th percentile and 95th percentile RAI values. A positive RAI median is statistically significant if its 5th percentile value is also positive. Similarly, for negative RAI median to be statistically significant, the 95th percentile value should also be negative (Fischer andKnutti 2015, King et al 2015). Hence, the RAI estimates the influence of anthropogenic forcings on the temporal variation along with its significance. To further aid the significance of RAI, a two sample t-test on the G ALL and G NAT resamples was performed and reported in the supplementary information.

Results
For global land analysis, the Gini coefficients are calculated separately for the ALL and NAT scenarios over all the land regions as mentioned in section 3.1 for all the 42 GCM realizations and averaged spatially. Then through the process of bootstrapping, we randomly selected GCM models with repetition from the pool of 42 GCM models considered and computed their ensemble means. This process was repeated 10 000 times to obtain 10 000 spatially averaged Gini coefficients that represent the inter-model variability.
The probability distributions of the globally averaged bootstrap resampled Gini coefficients derived from the multi-model ensemble global land means were plotted in figure 3 (top panel). This represents the inter-model GCM spread of the estimated global land averaged Gini coefficients. The RAI was then computed for all the resampled (shown in the top panel) Gini coefficients and from its distribution the median and 95th percentile values were determined as shown in figure 3 (bottom panel). We used the median RAI value obtained from this bootstrapped distribution as our best estimate in all our discussions. There is an increase in RAI for PRCPTOT (0.11) and SDII (0.14), which indicates higher temporal variability due to anthropogenic contributions at global scale. This result indicates a statistically significant (95% confidence) increase in non-uniformity of PRCPTOT and SDII by 11% and 14%, respectively due to anthropogenic forcings. Figure 4 shows the best RAI (i.e. median value) estimates at continental scale along with their 95% and  Figure 4. The temporal RAI estimates of PRCPTOT (red) and SDII (blue) calculated from spatially averaged over continents. In the figure, the median (solid dot) represents best estimates derived based on bootstrapping procedure.
Environ. Res. Lett. 12 (2017) 024009 5% limits. The RAI values for all continents except Australia (AUS) are significantly greater than zero for both PRCPTOTand SDII. Europe (EU), Asia (AS) and North America (NA) register higher temporal variability of SDII and PRCPTOT respectively due to anthropogenic forcing in comparison to all other continents. Furthermore, all continents exhibit small differences in anthropogenic influence on temporal variability between PRCPTOT and SDII with the exception of Europe (EU). Australia (AUS) does not exhibit a statistically significant change in temporal variability of both PRCPTOT and SDII. The best estimate RAI value for the African (AF), Asian (AS) and North American (NA) and South American (SA) continents indicates that asymmetry has increased in SDII and PRCPTOT due to anthropogenic forcing by a factor of 0.04, 0.1, 0.1 and 0.08 (4%, 10%, 10%, 8% increase) respectively. Figure 5 shows the best RAI estimates in the Giorgi regions along with their uncertainty range at 95% and 5% limits. Among all the Giorgi climate divisions, the GRL region located in North America exhibits higher anthropogenic influence on the variability of both PRCPTOT and SDII. The NEU region located in the European continent exhibits the largest difference of anthropogenic influence on the variability between PRCPTOT and SDII. However, EAF, SAF, SAH, SAS and WNA exhibit statistically insignificant anthropogenic influence on PRCPTOT. Similarly, for SDII, the regions of ENA, WNA and SSA exhibit insignificant anthropogenic influence. Overall, larger RAI values for SDII compared to PRCPTOT indicate that the temporal variability of precipitation intensity is more susceptible to anthropogenic disturbances than precipitation amounts. The African continent has more number of regions with insignificant anthropogenic induced non-uniformity. Both regions located in Europe show an average RAI value of 0.11 and 0.7 for SDII and PRCPTOT, respectively, indicating that Europe may have higher anthropogenic induced  Figure 5. The best temporal RAI estimates calculated based on the bootstrapping procedure for PRCPTOT (mm/year) and SDII (mm/day) over sub-continental Giorgi regions. The inserted figure represents the uncertainty range (5th to 95th percentile) of RAI and the solid dot represents best estimate (i.e. median value). Only the RAI estimates of the significant regions are shown.
Environ. Res. Lett. 12 (2017) 024009 non-uniformity among all the continents. Asia and North America have also exhibited more number of regions with significant anthropogenic induced changes in temporal variability.
From a physical perspective, warming in the historical period could lead to an increase in total precipitation due to an increased water holding capacity in the atmosphere. For example, climate models projected an increase of global mean precipitation by about 2% per degree warming in the future (Held and Soden 2006). Regionally, precipitation changes are more variable. The difference in the Gini coefficient between the ALL forcing and NAT forcing simulations could potentially reflect the trends in response to warming in the ALL forcing simulations. To investigate if a larger magnitude of trend increases the Gini value, we calculated the linear trends of the multi-model ensemble mean for PRCPTOT and SDII in all 42 historical realizations for the period 1951 to 2005. The linear trend magnitude calculated using the absolute value of Sen's slope (Sen 1968) and its correlation with the Gini coefficient are shown in supplementary figure  S3. The coefficient of determination (R 2 ) between the linear trend magnitudes and the Gini coefficients is 0.0058 and 0.0067 for PRCTOT and SDII, respectively. These results indicate that statistically there is no linear relation between the magnitude of long-term linear trends and the Gini coefficients, suggesting that the differences in the Gini coefficients between the ALL forcing and NAT forcing simulations are not solely reflecting annual precipitation trends, but also changes in the interannual and/or interdecadal variability in annual precipitation and precipitation intensity.

Discussion and conclusions
Recognizing that anthropogenic forcing could have a significant influence on the temporal variability of precipitation amounts (PRCPTOT) and intensity (SDII), this study used the Gini coefficient to detect changes in the temporal variability of annual precipitation. By comparing CMIP5 simulations with ALL and NAT forcing, we found a clear signal indicating a significant anthropogenic influence on the temporal variability of PRCPTOT and SDII at global scale. The same is true at continental scale except for the Australian continent, where natural variability induced by various teleconnections (Risbey et al 2009, King et al 2014 is more dominant. Despite the lack of a signal in temporal variability, the decrease in Australian precipitation has been attributed to anthropogenic forcing (Timbal et al 2006 andDelworth andZeng 2014), consistent with the understanding that processes influence the trend and variability of PRCPTOT and SDII could be very different.
Out of the 21 Giorgi regions, we found 14 (PRCPTOT) and 17 (SDII) regions showing significant anthropogenic influences. The human impacts are generally larger for SDII compared to PRCTOT. This indicates that at regional scale, the temporal variability of precipitation intensity is generally more susceptible to anthropogenic influence than precipitation amount. Areas with higher precipitation magnitude (such as: SEA, AMZ and WAF) and low precipitation magnitude (such as: SAH, CAS) have both witnessed an increase in non-uniformity in temporal variability of annual precipitation due to anthropogenic forcing. Regions with statistically insignificant anthropogenic influence on PRCPTOT are mostly monsoon-dominated regions that exhibit higher natural variability related to ENSO and other modes of variability Ding 2008, Lee andWang 2014). This may be reflecting uncertainties in model simulations of interannual and decadal modes of variability as well as how they respond to anthropogenic forcing, opposing influence of circulation and moisture changes on precipitation variability, or the precipitation variability changes due to anthropogenic influences have not emerged due to small signal-to-noise ratios in the historical period. This highlights the need for further investigation on changes in precipitation temporal variability as anthropogenic forcing continues to increase in the future.
Overall our results indicate that anthropogenic emissions have not only influenced the trends of annual precipitation , but their influence can be detected on the temporal variability of annual precipitation amount as well as intensity. Both PRCPTOT and SDII have significant implications for the net primary production of terrestrial ecosystems (Estiarte et al 2016) and agricultural yields (Thornton et al 2014). Hence an increased temporal variability in PRCPTOT and SDII would increase the complexity in formulating policy for water resources planning and management.