Future scenarios (2011-2040) of temporal and spatial changes in precipitation in the Paraitinga and Paraibuna watersheds, São Paulo, Brazil

The alteration of global climate regimes due to anthropic action and excessive emission of greenhouse gases has been widely researched because it alters the patterns of climatological normals, generating changes in temperatures and precipitation worldwide. This study aimed to analyze the spatial and temporal variability of precipitation in the Paraitinga and Paraibuna watersheds that together form the Paraibuna Dam, the main one of the Paraiba do Sul river watershed. This dam supplies the São Paulo Metropolitan Region by transporting water to the Cantareira System, the Rio de Janeiro Metropolitan Region by transporting water to the Guandu watershed, and the Paraiba Valley Metropolitan Region, one of the most industrialized in Brazil. To investigate future precipitation trends, past and future climate simulations were used from the HadCM3/Eta model using the SRES (Special Report Emission Scenarios) A1B, and precipitation analysis using Quantis techniques to determine extreme rainfall and drought periods. The results point to an increase in precipitation averages in the region, followed by a greater intensity of extreme rainfall, which may lead to a higher occurrence of natural disasters such as landslides.


INTRODUCTION
Technological modernization and the development of industrial activities resulting from the Industrial Revolution has accelerated the emission of greenhouse gases, which aggravates this natural phenomenon, changing climate regimes on a planetary scale (IPCC, 2019). One of the climatic elements that is influenced is precipitation, an element of fundamental importance for the existence and maintenance of life on Earth (TEIXEIRA, 2009).
In a study on climate change scenarios for South America, Chou et al., (2014) conducted simulations using two global models, HadGEM2-ES and MIROC5, considering two distinct RCP scenarios (4.5 and 8.5), regionalized by the Eta model. The data indicate that there will be a downward trend in precipitation totals at the end of the 21 st century for the Brazilian Center-South region in the areas that are occupied by the South Atlantic Convergence Zone. The data also suggest that there will be a downward trend in the frequency of occurrence of the SACZ and a reduction of the moisture transfer capacity of the Amazon with a respective decrease in precipitation production, allied to an increase of high-pressure zones in the southeast region. Lyra et al., (2017) analyzed climate change projections for the metropolitan regions of São Paulo, Rio de Janeiro and Santos by the end of the 21 st century using the HadGEM2-ES climate simulation model regionalized by the Eta model with a 5km resolution. They noted that there will be a trend of an average increase in temperature above the normal climate of up to 8°C for the 2017-2100 period, coupled with a considerable decrease in rainfall during the summer period, ranging from 3 to 6 mm/day -1 by the end of the century, followed by an increase in extreme rainfall in the mountainous areas of the region, although accompanied by a general decrease in precipitation rates. Such extreme event associations could impact the region's water reservoirs and affect water availability for human consumption and power generation.
In a study on climate change in the municipality of Taubate/SP, located in the Paraiba Valley region, Horikoshi and Fisch (2007) used climate simulation data from the HadCM3 model, using SRES A1 and B1 for the study area, which indicated a rise in temperature between 0.5° to 2.7°C by the end of the 21 st century. This was followed by an increase in average rainfall, with a tendency to decrease in the summer and increase in the winter, causing a trend of increasing water deficit for the region until the end of the century. Santos and Fisch (2016) when analyzing the future trend of precipitation and temperature for the municipality of Taubate/SP, using the HadCM3 simulation model, SRES A1B, indicate that by the end of the century there will be an increase in daily precipitation averages for all months. followed by an increase in total precipitation averages with a tendency to rain concentration in the rainy season and an increase in maximum rainfall occurrences, indicating a future with greater presence of extreme rainfall.
Considering the future trends of changes in climate behavior for the southeastern region of Brazil, specifically for the Paraiba do Sul watershed, which is located among the main and most economically developed regions of the country, this study aims to analyze the precipitation regime for the Paraitinga and Paraibuna watersheds, which form the Paraibuna dam, and

Climate Simulation
The precipitation data used in this study were generated from climate simulation data from the HadCM3 model, regionalized by the Eta model, which was developed by the British Meteorological System. Data were simulated considering the SRES (Special Report Emission Scenarios) A1B of IPCC in its fourth report (IPCC, 2007), with a resolution grid of 20x20km. This future scenario is compatible with the RCP (Representative Concentration Pathway) 4.5 of the IPCC in its fifth report (IPCC, 2013;SANTOS and FISCH, 2016). 4 Rodrigo Cesar da Silva et al. Two temporal cut-offs were considered, one from a past period  and the other from a future period . Daily rainfall values, monthly and annual averages, rainy season averages (from October to March) and summer period averages (DJF) were analyzed. The simulated precipitation values are homogeneous across the simulation grid area of 400 km 2 , differing in each simulation grid.

Determination of dry years and daily extreme rainfall
For the determination of dry and very dry years, and extreme rainfall, the Quantis technique was used, which was initially developed by Pinkayan (1966) and widely used in other studies (XAVIER et al., 2007;MONTEIRO et al., 2012).
According to Xavier et al. (2002), the Quantis technique is a method based on a series of precipitation data (x), where the total precipitation in a given year is considered to be a random variable, and the Quantil (Qx) represents a percentage variation of precipitation (x) as a function of (Q).
According to Pinkayan (1966) the distribution of precipitation depends on physiographic factors and atmospheric circulation, with dry or rainy years occurring as a function of precipitation variability, reservoir water stock and moisture contained in the air. The precipitation distribution is defined by Equation 1; when F(x) is known for x1, x2, x3, x4 and x5, the Quantis are determined considering Table 1.

( ) = [ ≤ ]
(1) In this study the Quantis technique was used to determine dry and very dry years and to determine daily extreme rainfall by analyzing the variation of daily rainfall for the past period  and classifying both daily extreme rainfalls and annual precipitation averages for the future period . For an explanation of the practical application of functions in the Microsoft Excel Application, see Monteiro et. al. (2012).

Determination of consecutive days with and without precipitation
The determination of consecutive days with and without precipitation is useful for determining the trends of drought periods. To this end, the Microsoft Excel application was used following the methodology proposed in Figure 2. The functions used in the application, in the version in Portuguese, were SEERO, SE, E and CONT.SE.
From the application of the methodology shown in Figure 2, the following occurrences of rainfall were classified: i) number of days without precipitation between 5 and 9 days; ii) number of days without precipitation equal to or greater than 10 days.

Pearson's coefficient of variation applied to precipitation variability
Pearson's Coefficient of Variation is widely used in research because it is a technique for measuring the dispersion of data for a given sample and is used to describe the distribution of the data and its relationship between standard deviation and mean of a sample. The smaller the values of Pearson's Coefficient of Variation, the greater is the concentration of data around the sample mean (SILVESTRE, 2016), as observed in Equation 2.
Pearson's coefficient of variation was calculated for all rainfall simulation grids for the past  and future  periods and then compared between both periods to analyze within-period variability and its respective change between past and future periods.

Precipitation comparison between past and future periods
The total average rainfall for the past period  for the climate simulation grids was 1346.2mm, with irregular spatial distribution throughout the Paraitinga and Paraibuna watershed. The variation of the average precipitation was to 1663.0mm in the P10 grid, while the lowest average (979.8mm) was observed in grid P5, with variation between the maximum and minimum precipitation grids of 41.1%. The grids with the highest precipitation values were, respectively, P10, P2, P6 and P7, with these points located in the center and north of the Paraitinga and Paraibuna watershed, close to the border with the Paraiba do Sul watershed, in which these basins are inserted. The points with the lowest precipitation indices were observed, respectively, in grids P5, P8, P3 and P1, located in the south of the study area, demonstrating that the Mar Sierra mountain formation causes high average windward precipitation rates due to orographic rainfall in oceanfacing municipalities such as Ubatuba/SP, which has an average precipitation of 2517.5mm (INMET, 2019); this decreases the downwind precipitation values, as observed for grids P5, P8, P3 and P1. It is important to highlight that the average precipitation value for the study area in the past period of 1346.2mm is compatible with the results obtained by Fisch (1995) and the climatological normal values in the municipality of Taubate/SP, which has an average precipitation of 1360.9mm (INMET, 2019).
The average precipitation for the future period (2011-2040) is 1456.3mm, and the irregular distribution of precipitation is persistent for the analyzed period, demonstrating that the formation of the irregular relief, with the presence of mountains and hills (AB'SABER, 2003), generates a spatial irregularity in the distribution of precipitation, results that are similar to those obtained by Silva and Simões (2014). The simulation points with the highest precipitation values were, respectively, the grids P10, P2, P7 and P6, where the minimum average precipitation value was 1027.5mm and the maximum was 1856.5mm, with a variation of 44.6% between precipitation extremes, values that are similar to results from Santos and Fisch (2016).
The points with the lowest precipitation values for the study area were, respectively, the grids P5, P8, P3 and P1, indicating that both the maximum and the minimum precipitation points remained almost unchanged. This demonstrates that there is a trend of continuity in the irregularity of rainfall distribution in the Paraitinga and Paraibuna watershed, following the same trend observed in the past period.
Analyzing the precipitation periods seasonally, the average rainfall for the rainy season in the study area from October to March in the past period was 958.7mm, while in the future period it was 1024.5mm, showing an increase between the analyzed periods of 6.9%. In the summer period between December, January and February, the rainfall for the past period was 478.3mm, while in the future period it was 529.7mm, with an increase between the analyzed periods of 11.1%. This fact demonstrates that rainfall tends to be concentrated in the summer period (DJF), which has the highest average monthly precipitation values, as shown in Figure  3.

Identification of occurrence of dry and very dry years
For the determination of dry and very dry years Quantis techniques were used and the parameters were established according to Table 1. The precipitation of the past period was used to establish the parameters as observed in Table 2. The results show that for the past period , there were 2 years classified as very dry, 5 years as dry, 5 years as normal, 11 years as rainy and 7 years as very rainy. The data reveal that there is a higher tendency of occurrence of rainy and very rainy years (18 occurrences) in detriment to the occurrence of dry or very dry years (7 occurrences).
In the future period (2011-2040), 1 very dry year, 2 dry years, 6 normal years, 5 rainy years and 16 very rainy years were observed. The data show that for the future period there will be a tendency for more frequent occurrence of rainy and very rainy years (21 occurrences), that is, an increase of 16.6% of this type of occurrence, while the occurrence of dry and very dry years will decrease by -71.4%. These data indicate that in the future period, due to more frequent rainy and very rainy years, there will be a tendency for an increase in the occurrence of natural disasters related to landslides in the study area, as the local topography is marked by the presence of hills and mountains, a trend similar to the results obtained by Mendes et al., (2018). Average precipitation data per period can be seen in Table 3. Table 3. Precipitation values for each point (P1 … P12) by period.

Percent change in precipitation average
Average rainfall in the rainy season (mm) Percent change in average rainfall in the rainy season Average rainfall in the summer period (mm)

Determination of average extreme rainfall by simulation point.
For the determination of daily extreme rainfall, the Quantis method was used, a technique identical to that used for the determination of dry and very dry years. When applying the technique to daily rainfall, data were classified according to Table 4. When analyzing the intense rainfall data its occurrence is irregular along the Paraitinga and Paraibuna rivers watershed; however, it is directly related to the simulation grids where the highest precipitation rates occur in the study area. For the past period, the areas where there was the highest occurrence of intense and very intense rainfall were in the simulation grids P10 (40 occurrences), P2 and P6 (30 occurrences) and P4 (24 occurrences), whereas the highest points occurrence of mild and very mild precipitation were the grids P8 (8 occurrences), P5 (10 occurrences), P3 (12 occurrences) and P12 (15 occurrences). The data reveal that the relief areas of hills and mountains are those with the highest incidence of heavy rainfall, demonstrating that these areas are the most prone to natural disasters and landslides related to heavy rainfall.
The future period (2011-2040) of rainfall distribution in the basins of the Paraitinga and Paraibuna Rivers was uneven, with the highest intensity rainfall being distributed almost unchanged over the study area compared to the past period. The grids with the highest occurrences of intense and very intense rainfall were P10 (66 occurrences), P6 (45 occurrences), P2 (41 occurrences) and P7 (35 occurrences). The grids with the highest occurrences of mild and very mild rainfall were P8 (7 occurrences), P5 (13 occurrences), P3 (15 occurrences) and P1 (23 occurrences). In all precipitation simulation grids, there was an increase in the occurrence of intense rainfall, with an average growth of 41.9%, except for point P8, which had a decrease of -12.5%. The values obtained show that there will be an increase in the total of intense and very intense rains when compared to past and future periods, demonstrating that the frequency of occurrence of natural disasters and landslides will tend to increase in the region, mainly to the north of the study area, where there are hills and mountains with great slopes.
However, the maximum values of very intense precipitation do not show the occurrence of precipitation greater than 200.0 mm preceded by days with intense and very intense precipitation as occurred in São Luiz do Paraitinga/SP in 2010/01/01, which caused a great flood, destroying much of the historical and cultural heritage of the municipality (VERDE and SCHICCHI, 2013). The frequency of intense and very intense rainfall is shown in Table 5.

Occurrence of drought periods
To determine the frequency of drought, the frequency of occurrence was selected based on categories of 5 to 9 days without precipitation and 10 days or more without precipitation, comparing the past and future periods. The data show that in the past period there was an average of 296 occurrences of 5 to 9 days without precipitation and an average of 100 occurrences with 10 days or more without precipitation. The points P10, P2, P7 and P12 had the lowest occurrence of 5 to 9 days without precipitation, these being the grids with the highest precipitation in the study area, except for P12. For the occurrence of 10 days without precipitation, the grids with the lowest occurrence were P2, P4, P7 and P10, and for drought periods there was no relationship between total precipitation volumes and occurrence of days  For the future period, an average of 299 occurrences of 5 to 9 days without precipitation were observed, while there were 93 occurrences of 10 days or more without precipitation. This represents an increase of 1.2% in the occurrence of 5 to 9 days without precipitation and a -7.5% decrease for 10 days or more without precipitation compared to the past period. For the occurrence of 5 to 9 days without precipitation, the lowest number of occurrences were observed in the grids P10, P12, P7 and P2, and these grids are those with the greatest precipitation in the study area, except for P12. The occurrence of 10 days or more without precipitation occurred less frequently at points P2, P10, P4 and P7, behaving similarly to the past period where there was no relationship between the points of greatest precipitation and the occurrence of drought over 10 days or more without precipitation.
When comparing the past and future periods it is observed that there will be a tendency to maintain periods of 5 to 9 days without precipitation, while there will be a decrease in drought periods of 10 days or more without precipitation. This demonstrates that when relating the average total precipitation values and the occurrence of days of intense and very intense precipitation, there will be a tendency of concentration of extreme events in the rainy period for the future . Data on days without precipitation can be seen in Table 6.

Spatial variability of precipitation
The results for the Pearson's Coefficient of Variation analysis of the spatial variability of precipitation for each climate simulation point show that for the past period ) the greatest spatial variability is found in grids P5 (19.1%), P8 (18.4%), P3 (18.1%) and P1 (17.3 %), with these points being those with the lowest average precipitation. The grids with the least variability are found in grids P10 (13.6%), P2 (14.8%), P12 (15.2%) and P7 (15.4%), compatible with the points of greatest precipitation in the area, except grid P12. These results show that the grids with the highest rainfall have less variability, revealing that in these areas rainfall is homogeneous and more intense, explaining that the northern region of the study area is more susceptible to extreme weather events and natural disasters.  In the future period (2011-2040) the highest spatial variability of precipitation is found in grids P5 (21.2%), P3 (20.3%), P1 (20.2%) and P8 (20.1%), showing considerable variation in the indices compared to the past period ; however, the grids with the lowest rainfall persisted. The grids with the lowest precipitation variability are P10 (15.7), P12 (16.1%), P7 (17.4%) and P2 (17.6%), and those with the highest precipitation have the lowest spatial variability of precipitation, except grid P12, demonstrating the tendency to maintain the area of occurrence of natural disasters and extreme events in the northern region of the study area.
The comparison between past and future periods shows that at all points there will be an increase in spatial variability in precipitation as there is an increase in total precipitation averages for the analyzed periods, demonstrating that the highest precipitation values per grid are related to the lowest spatial variability of precipitation. These data are shown in Table 7. Table 7. Pearson's coefficient of variation for simulated precipitation points. 1961-1990 2011-2040 1961-1990

CONCLUSIONS
Analyzing the rainfall simulated by the HadCM3 model for the Paraitinga and Paraibuna River's watershed, considering the past  and future periods , it was observed that there will be an increase of precipitation, with a concentration of rainfall in the summer period (DJF). There will be an increase of 41.9% in intense and very intense rainfall 11 Future scenarios (2011-2040) of temporal and spatial … Rev. Ambient. Água vol. 7 (supplement) -Taubaté 2019 2017 compared to past and future periods, with more frequent rainfall occurring in the mountainous areas of the study area, indicating a tendency for increased natural disasters related to rainfall, especially those related to landslides, considering the topography of the region.
There will be a tendency for a decrease of 7.5% in drought periods of 10 days or more without precipitation, followed by an increase in spatial variability of precipitation when past and future periods are compared, indicating a trend in the summer of larger extreme events followed by natural disasters.