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Given the high and increasing lightning incidence over the Southeast of Brazil and the various impacts that this phenomenon generates to society, there is a growing need in predicting its occurrence, in order to minimize its consequences. In this context, this work presents the development of a methodology for the projection of lightning in the State of São Paulo (Southeastern Brazil), using the HadGEM2-ES and CSIRO-Mk3.6 models in two IPCC climate change scenarios: RCP4.5 and RCP8.5. Since lightning is not an output variable of climate models, tests were carried out to evaluate the relationship between the observed data of oceanic and atmospheric fields, which are known as outputs of the models, and the lightning from the RINDAT and BrasilDAT detection networks. As result, a correlation of 0.84 was obtained. In the projections, it was verified that, while during a large portion of the current climate we observed events of lightning below the average, the future climate reveals the preponderance of anomalously above average events, both in the scenario of intermediate-low emissions (RCP4.5) and in the scenario of high emissions (RCP8.5), suggesting a change in the pattern of the lightning incidence in the State of São Paulo.

The State of São Paulo, in the Southeast of Brazil, has presented a history with high number of storms accompanied by lightning that causes several impacts to the society. These storms are associated with the climatic characteristics of the region, which has a large space-time variation in the lightning incidence, as well as a continuous process of urbanization, which intensifies the development of these storms [

Over the years, several studies using different methodologies [

Due to this, there is currently great concern regarding the increase in the lightning incidence, mainly due to the great power of destruction caused by this phenomenon that although much occurs inside the cloud, that is, without the contact with the surface of the Earth [

In addition, the lightning can cause fatalities, being the second major cause of death by meteorological phenomena on the planet, according to World statistics. In Brazil alone, there are around 130 deaths per year, according to data from a survey of lightning deaths between 2000 and 2009. In the last decade, 1321 people died of being struck by lightning, with a higher number of fatalities, the Southeast Region, with 29% of the total [

These data reveal the great importance of understanding the behavior of this phenomenon in the future climate. In the short-term forecast scale, studies have been developed, based on meteorological parameters and/or cloud microphysics [

In view of this, the present study proposes to contribute with the advance in the knowledge of the lightning incidence of the cloud-to-ground type (CG) in the State of São Paulo, by means of future climatic projections of the occurrence of this phenomenon.

The results obtained will serve as a basis for the construction and improvement of alert systems, in the short and long term for the State of São Paulo, thus allowing preventive measures to be taken to minimize the impacts caused by this phenomenon.

Associated with this information, the alert in relation to increase of the frequency of the extreme climatic events caused by the intensification of the global warming, divulged by the Intergovernmental Panel in Climate Change-IPCC [

Finally, one of the main justifications for this kind of evaluation is that studies of this nature for this phenomenon in this region are still very incipient. However, it is of great relevance to several sectors of interest and can be used as a subsidy for environmental interventions that minimize the impacts caused by the lightning incidence.

Given the fact that the lightning is not an output variable of the climatic models, to obtain the projections of this phenomenon, tests were carried out to evaluate the relationship between ocean-atmospheric variables, which are outputs of the models, and lightning, using observed data (Reanalysis by National Centers for Environmental Predictions/National Center for Atmospheric Research-NCEP/NCAR) for the period of greatest occurrence of the phenomenon, summer. This was done because, based on the knowledge of the mathematical function that describes the behavior of a dependent variable (explained or predicted) as a function of the dynamics of other independent variables (explanatory or predictive), it is possible to make future projections using model data.

The CG lightning data used in this work for the State of São Paulo, in the Southeast of Brazil (

Sixteen years of data were considered, corresponding to the austral summer period from 1999 to 2014, of which the 1999-2010 data are from the RINDAT network and the data from 2011-2014 are from the BrasilDAT network. For the studied period, RINDAT showed detection efficiency above 80% and Brazil DAT above 90% [

Several tests were performed using oceanic-atmospheric parameters such as sea surface temperature (SST), precipitation, air temperature, outgoing longwave radiation (OLR) and the omega difference between the tropospheric levels of 850 and 500 hPa, to verify which of these variables presented the best relation with the lightning. These tests were done for both simultaneous and lagged correlations.

The data of the atmospheric variables were selected in the area on the State of

São Paulo and for the SST. The SST selected areas correspond to the oceanic regions with the highest correlation values, comprising an area of 5˚ × 5˚ in the Pacific Ocean (Lat: 46˚S to 50˚S and Lon: 111˚W to 107˚W), South Atlantic (Lat: 57˚S to 61˚S and Lon: 50˚W to 46˚W), and Tropical Atlantic (Lat: 24˚S to 28˚S and Lon: 40˚W to 36˚W).

Despite the use of all these parameters in the tests, we tried to apply the regression model that used a small number of independent variables, given that the size of the data sample is not very extensive. Since when one sets a model for a small sample, the more predictors one chooses to use, closer to the perfection the prediction will be, which, counterintuitively, is actually a bad thing because we want to choose only one or two variables to make a good prediction so as not to rely on several sources of data and to properly determine the relationship between the parameters. Thus, one must reduce the number of independent variables or increase the sample size [

The results of these tests showed that the parameters that pointed to a higher degree of relation with the lightning were the SST of the South Atlantic Ocean and Omega. Therefore, these variables were used for future projections. The methodological procedures used to achieve such projections will be described in Subsection 2.2.

For the projection of future climate scenarios, we used data from two robust CMIP5 models: HadGEM2-ES e CSIRO-Mk3.6. The Hadley Centre Global Environmental Model version 2-Earth System (HadGEM2-ES) from the UK Met Office Hadley Centre, is a general circulation model of the atmosphere coupled to an ocean model. It has an atmospheric component with horizontal resolution N96, that is, approximately 1.250˚ in latitude and 1.875˚ in longitude, with 38 vertical levels, whereas the oceanic component presents horizontal resolution of 1˚, increasing to 1/3˚ in the equator, and 40 vertical levels [

The CSIRO-Mk3.6 global climate model is an ocean-atmosphere coupled model of the Commonwealth Scientific and Industrial Research Organisation (CSIRO) of the Australia, with sea ice dynamics and a soil-canopy scheme that presents prescribed vegetation properties. The atmospheric component of the CSIRO-Mk3.6 model presents horizontal resolution (spectral T63) of approximately 1.875˚ in latitude and 1.875˚ in longitude, with 18 vertical levels.

The oceanic component is based on version 2.2 of the Modular Ocean Model (MOM2.2) described by [

To carry out climatic projections of lightning, the multiple linear regression technique was used to evaluate the relationship between a single predicted variable and two or more predictor variables and to carry out projections from this uncovered relationship [

Through this analysis, it is also possible to determine the individual weight that each variable has in the set of relations, obtaining as a final result, the contextualized product of all the partitions involved and the degree of relationship between the variables under analysis [

Thus, in this work the dependent variable consists of the CG lightning and the independent variables comprise SST in the South Atlantic Ocean and the omega variable. The combination of independent variables used together to predict the dependent variable is also known as the equation or regression model [

The dependent variable is represented by y, and the independent variables by_{0} is called the intercept or linear coefficient, and represents the value of the intersection of the regression line with the Y-axis. The terms _{ }are the angular coefficients, and the term ε, represents the residue or regression error.

With the result of the multiple correlation and with a view to the detailed and systematic examination of the results, their validation was performed through the application of the cross validation method. Details of this method can be found in [

In order to evaluate the performance of predictions of climate models, a direct comparison was made between observed data and simulated data (bias), as well as the mean square error (RMSE).

The bias (Medium Error-ME) is the most objective measure of the prediction of a numerical model, it reports if the simulation underestimated or overestimated the actual values. If the result has a negative value, it means that the model tends to underestimate the observed data, and if the value is positive, it means that the model tends to overestimate the observed data. This measure of error can be obtained from Equation (2):

where

Another way to verify the efficiency of the models is to use the mean square error (RMSE), which is given by the sum of the squares of the differences between the simulated and observed data, as presented in Equation (3):

The RMSE can assume any positive value, and has the same unit of measure of the series under study. Like bias, the closer its result is to zero, the greater the efficiency of the model in reproducing the actual data. In general, the RMSE is expressed as a percentage of the average of observations (relative errors). Thus, the RMSE (%) represents the ratio between the error values and the mean of the observations, multiplied by one hundred [

In order to perform the adjustment of the data of the models (removal of the systematic error of the data obtained by the simulations), a statistical method, adapted from [

wherein

This section presents the results obtained in the projections of CG lightning, for the State of São Paulo. The following equation presents the values obtained in the cross validation process, which aims to evaluate the stability of the relationship found. In this equation, L(t) represents the variation of lightning over time, O_{ }is omega and SA_{ }is the SST in South Atlantic Ocean.

For this analysis, the values of the variables were normalized to a unit value, in order to obtain the contribution of each member in the correlation equation. Thus, it was observed that among the variables in studies, the SST of the South Atlantic Ocean was the one that presented the greatest contribution in the correlation equation. This probably occurs because SST is a basic parameter for climatic anomalies [

The

Given the above, it became feasible to analyze future lightning projections using model data. However, to properly analyze the future dynamics of the lighting incidence, it is necessary to first examine the performance of these models in simulating the variables used. Therefore, the model prediction evaluations will be presented first, bias and RMSE will be quantified, and future projections will be performed using the RCP’s scenarios.

Thus, it was observed that for the South Atlantic SST, the CSIRO-Mk3.6 model presented a more satisfactory performance than the HadGEM2-ES, due to the greater approximation of the simulated data with the observed data. HadGEM2-ES tends to have higher SST in this region, which in a future climate could indicate the intensification of the lightning incidence on the State of São Paulo, given the relation between the SST of these regions and the lightning.

Similarly to SST, the omega variable was also better simulated by the CSIRO-Mk3.6 model, in both indices under analysis. The systematic error of HadGEM2-ES was −0.009 W∙m^{−2} whereas that of CSIRO-Mk3.6 was −0.006 W∙m^{−2}. The RMSE of the HadGEM2-ES was of 45.5%, and the CSIRO-Mk3.6 was of 20.5%. These results show that in the future climate the HadGEM2-ES will represent greater convection/cloudiness over the study area, which would also intensify the lightning incidence over São Paulo.

Through the analysis of these indices, it was possible to observe the preponderance of CSIRO-Mk3.6 in relation to HadGEM2-ES for the proximity of the reanalysis data in the simulations of the omega variable.

In the face of the evaluation of the systematic errors of the models, it was essential to correct them before generating future projections as such. Therefore, the