Homogeneous Regions for Rainfall Distribution in the City of Rio De Janeiro Associated to the Risk of Natural Disasters

Understanding the occurrence of natural disasters in regions where the occurrence is high is very important, it is known that the occurrence of disasters associated with intense rains are a source of research in different locations around the globe, being important not only for increasing accuracy of weather forecasting models, but important information for civil defense, where lives can be saved. The increase in the occurrence of natural disasters related to extreme rainfalls has become a problem of large urban centers, such as the city of Rio de Janeiro (CRJ). Thus, the identication of homogeneous regions for rainfall distribution (HRRD) becomes essential to identify regions at risks of oods and mass movements. The aim of this research was to identify HRRD in CRJ associated to the risk of natural disasters. The identication of homogeneous regions was carried out with the use of monthly rainfall data from 14 pluviometric stations spatially distributed in the study area between 1997 and 2018. Rainfall data were submitted to descriptive statistical analysis, and subsequently to Cluster Analysis. Cluster analysis identied 4 homogeneous groups regarding annual rainfall distribution. The result showed relevance regarding physiographic aspects that characterize the rainfall dynamics in CRJ, highlighting areas favorable to the occurrence of natural disasters.


Introduction
Understand the spatial and temporal distribution of rainfall with the identi cation of Homogeneous Regions for Rainfall Distribution (HRRD) is fundamental mainly for cities that showed an increase in urbanization and changes in rainfall distribution, because rainfall is the most important triggering factor of natural hazards. Excess or scarcity of rainfall can be harmful due to the occurrence of droughts, oods, mass movements and even deaths. Floods are the most serious natural disasters in the world, which put more lives at risk and cause economic and social damage than any other natural phenomenon (Gigovic et al. 2017). A considerable increase in the risk of ooding in large cities is expected, mainly as a result of climate change, which could further aggravate the social impacts of disasters (Aznar-Crespo et al. 2021). Mass movements and landslides are natural hazards that threaten life (Mangeney, 2011).
replaced by urban buildings, which contributes to increasing air temperature, changing the rainfall regime and causing natural disasters (Gheno et al. 2012;. In this context, urban forests have bene cial effects on cities by reducing air temperature, mitigating the effect of urban heat island, acoustic softening, ltering air polluting particles, increasing water in ltration in the soil, reducing landslides and above all increasing rainfall (Dacanal et  For cities like Rio de Janeiro, where one of the world's largest urban forests is located, understanding the role of the forest in the characterization of the urban microclimate is fundamental, especially regarding the knowledge of spatial and temporal rainfall distribution. Rainfall is the fundamental meteorological element to de ne and characterize the climate of a region, being essential for the urban supply of large urban centers, such as CRJ and to de ne the most frequent natural disasters (Wanderley and Bunhak, 2016). Rainfall distribution in CRJ suffers signi cant variations due to its topography, as its development took place around three large massifs. CRJ massifs are continuously positioned, forming a triangle composed of the Tijuca massif (MTJ), in the central portion of the city, the Pedra Branca massif and the Gericinó massif.
MTJ is a geomorphological system located in the city of Rio de Janeiro, with rugged and varied relief (Dacanal et al. 2010). This massif consists of mountains and hills, with slopes facing the North at Jacarepaguá, the central portion of CRJ and the Atlantic Ocean, separating the Northern and Southern neighborhoods of the city. The in uence of MTJ in the microclimate of CRJ was already rati ed when MTJ initially contained a dense forest, which was strictly deforested for the purpose of supplying loggers, for charcoal production and later for coffee plantation. One of the consequences of this deforestation was one of the highest water de cits established in CRJ during the Empire period in Brazil.
Today, the major problem of rainfall distribution in MTJ and its surroundings is the increase in intense rainfall events, since this region has the highest rainfall totals and the highest occurrences of natural disasters in CRJ (D'orsi et al. 2016; Maia, 2012). These characteristics increase the number of natural disasters associated with rainfalls, and consequently the number of deaths. Disasters caused by rainfalls in CRJ show that destruction has been part of the city's daily life for centuries. Initial records have shown that back in 1575, Father José de Anchieta wrote a letter to another Jesuit with reports on the occurrence of heavy rains in the city. The occurrence of heavy rains of 1711, 1756, 1779, 1803, 1811 should also be highlighted, which destroyed part of Morro do Castelo, leaving victims, 1833, 1862, 1864, 1906, 1911, 1928 and 1966 with 250 deaths and 50 thousand homeless (Marzban and Sandgathe, 2006). However, the real in uence of MTJ on the rainfall distribution in the city of Rio de Janeiro has not been quanti ed due to the lack of studies in this area of the city, in particular the HRRD in CRJ. There are a range of methods available to identify rainfall homogeneous regions. These methods can be broadly classi ed into four, namely, geographical convenience, subjective partitioning, objective partitioning and multivariate analysis (Hosking and Wallis, 1997

Study Area
The study analyzed the rainfall distribution in the MTJ region and its surroundings, located in the city of Rio de Janeiro. This region stands out in the city due to the large number of geological-geotechnical disasters (D'orsi et al. 2016

Database
For analysis, monthly rainfall totals from 14 pluviometric stations spatially distributed in the study area ( Fig. 1) between January 1997 and December 2018 were used. Rainfall data come from the "Alerta Rio" System (http://alertario.rio.rj.gov.br). Rainfall data were submitted to Cluster Analysis to identify HRRD in CRJ in order to identify regions at greater risk for the occurrence of natural disasters. Pluviometric stations selected for the study are located on MTJ and its surroundings, covering the windward region, close to the sea, in mountainous regions, in the leeward region and also in more continental lowland regions. Among stations used in the analysis, the Alta da Boa Vista station is the only one with information from April 2010. Although it has different interval from the others, the use of information collected by this station is essential, as it is located on MTJ, being the highest altitude station. The geographical information used in the analysis is shown in Table 1. Cluster Analysis In order to identify regions with rainfall distribution homogeneity, monthly data were submitted to an exploration and data description tool, called cluster analysis (Fig. 2). Cluster analysis is a Descriptive Statistics technique with the purpose of identifying homogeneous groups and / or subgroups, or clusters, in the distribution of the variable under study, that is, rainfall in relation to the in uence of the Tijuca massif and its vegetation cover. To group pluviometric data based on similarity measure, data were allocated into a multivariate matrix n x p, X = [Xij], i = 1, ..., n; j = 1, ..., p, which contains rainfall values observed in each station, where Xij is the rainfall value j in station i (Yussouf et al. 2004). Cluster analysis was performed using the Ward method, where the distance between clusters is quanti ed by the squared Euclidean distance (ED) (Eq. 1). The distance between clusters is de ned as the increase in the sum of squares of errors that would result from merging them into a single cluster (Ward, 1963). The Ward's method consists of a hierarchical grouping procedure, in which similarity is used to de ne clusters. where, x ik -is the value of the k variable for i observation; x jk -is the value of the k variable for j observation.
This method uses an attribute to group objects by similarity and dissimilarity measures. Dissimilarity was calculated for all pairs of stations, allowing comparison between them, by the dissimilarity measure presented between them, grouping them according to the lowest ED into equal groups Ward (1963). The ED is a numerical measure of dissimilarity of how different two data objects vary from 0 for objects are similar and ∞ for the objects are different.

Results And Discussion
Homogeneous groups Cluster analysis identi ed 4 homogeneous groups regarding annual rainfall distribution associated to the risk of natural disasters, for stations located in MTJ and its surroundings (Fig. 3). Regionalization on the basis of the properties of hydro-meteorological data helps in identifying the regions re ecting the similar characteristics which could be useful in designing hydrological structures as well as planning and management of water resources of the region (Goyal et al., 2019). Clustering result showed relevance to the physiographic aspects that characterize the rainfall dynamics in CRJ. Local orography is a key modulator of the spatiotemporal connections and substantially enhances the probability of cooccurrence of extreme precipitation events even for distant locations (Mastrantonas et al. 2021). The dendrogram shows groups that were formed, where each group gathers rainfall stations that have the greatest similarity in the rainfall distribution behavior. The graphic representation of the dendrogram is characterized by the agglutination of stations that show similar rainfall distribution in CRJ, indicated by stations that make up each group. The dissimilarity obtained for clusters was small or close to zero, indicating that the groups and / or subgroups formed have similarities in the rainfall distribution behavior.
Proximity matrix of the Euclidean distance between the stations of each group can be seen in Table 2.
The results found show that stations with shorter Euclidean distance show greater similarity, with dissimilarity being the degree of distance between the stations.  shows that the annual rainfall distribution behaved with greater similarity for these stations. Vidigal and Jardim Botânico stations were a subgroup due to the greater rainfall distribution similarity, which can be observed in Table 3. Min -minimum value, Max -maximum value, SD -standard deviation, CV-coe ent of variation.
The statistical analysis for stations that compose Group-I shows that Vidigal and Jardim Botânico stations present rainfall distribution similar to the other stations in the group. Thus, the lowest dissimilarity was observed for these two stations, with ED of 0.65, being the lowest trunk height of Group-I. This proximity can also be observed by statistical parameters available in Table 3, with maximum, total, average, variance, standard deviation, median and the closest coe cient of variation. The greatest dissimilarity presented by Group-I was observed for Rocinha station, which is a result of the higher rainfall values measured in that station. This dissimilarity is a result of the higher altitude of the station and its position to the windward side of MTJ, which makes this station to present the highest total rainfalls in the group. In this station, ED was 1.53 for Vidigal station, 1. Group-I stations is due to the proximity of stations to the coast, making stations to be positioned to the windward of the Tijuca massif slope, facing the ocean. This slope is in uenced by ocean currents, the effect of sea breeze, showing forest cover around it (Fig. 4). These characteristics make neighborhoods that compose Group-I to have great potential for the occurrence of natural disasters.
The physical and geographic locations of Group-I stations, mainly Rocinha and Vidigal stations, commonly present natural disasters due to rainfalls. Considering that the Rocinha station presented, in this analysis, the second highest total rainfall in the city of Rio de Janeiro. An example is the case of mass movement and deaths that occurred in February 2019, in Rocinha. In Vidigal, in the same rainfall event, more than 40 houses were interdicted for presenting risk of landslides. As expected in the case of rainfall, those classes with high precipitation were more susceptible. Water is one of the most important causative factors in landslide occurrence. The increasing of some variables, such as pore water pressure, swelling of some clay minerals, and increasing the weight of unstable earth mass, which can cause a landslide, depend on the in ltrated water. In addition, water is a lubricant factor on a sliding surface that facilitates landslide occurrence (Varnes, 1984).
In addition to the orographic effect that occurs in CRJ, rainfall distribution is in uenced by meteorological  Group-II (dark blue in the dendrogram) is composed only of one cluster, consisting of the Alto da Boa Vista station. This station has the highest dissimilarity values compared to all other stations, with values ranging from (2.24 for Vidigal) to (3.08 for Santa Tereza) and close to Group-I due to their common geographical and rainfall characteristics. Alto da Boa station was grouped in this way due to the fact that it presents attributes such as proximity to the ocean, to the windward side of the slope facing the ocean, great availability of forest cover and, above all, higher altitude among analyzed stations, which favors the effect of orography on rainfall formation. These characteristics make this station to present the highest minimum, maximum, average and total values of the city. The altitude of this station is a very important factor for the higher total rainfall values observed. This factor allows the formation of orographic rains on a local scale, which combined with macro and mesoscale systems, such as the entry of FS from the polar region, and with spring and summer convective systems, provide rainfalls in the region under analysis.
The systems that cause rainfalls in CRJ, in general moving from South to North and the presence of the topography force humid air to rise to the windward side of massifs. The rising air cools and condenses, forming clouds and rain, which produce maximum rains to the windward side of slopes, as observed in stations such as Rocinha and Tijuca. After reducing humidity, air comes down in slopes, being compressed and heated, thus inhibiting the formation of clouds and consequently reducing rainfall to the leeward side of massifs, explaining the lower totals in Group-IV. The Alto da Boa Vista station, located on the margin of TNP, is the one that best represents the importance of the presence of an urban forest in the city of Rio de Janeiro (Kong et al. 2015). The Tijuca forest is rich in biodiversity, located in a densely populated area in CRJ, which plays an important role in the city's microclimate, as observed in this analysis, providing the TNP station with average annual total rainfall greater than 2,000 mm year − 1 .
However, in the last decade, the urban forest of Tijuca has been suffering due to urban expansion, irregular occupation of forest areas and the cutting down of trees. This occupation makes society more vulnerable to natural disasters, which commonly occur in the study region, such as landslides and tree falls. The vulnerability is an important factor in determining overall vulnerability to ood hazards In Fig. 6 it is noteworthy that between the months of April to June this was the only season among all to maintain high levels of rainfall and still obtain a slight increase in rainfall (173.5 mm to 181.7 mm), while the other stations obtained a decrease in the same period.
Group-III (purple color in the dendrogram) was composed of Tijuca, Santa Tereza, Copacabana and Grajaú stations. This cluster is formed by two subgroups, one consisting of Tijuca and Santa Tereza stations and the other consisting of Copacabana and Grajaú stations. Subgroup composed of Tijuca and Santa Tereza stations should be highlighted. Rainfall distribution in these stations showed close minimum, total and average values. Thus, the dissimilarity presented by these stations was the lowest in the group, showing greater correlation than the others in rainfall distribution similarity, with ED value of (0.63). The rainfall distribution characteristic in Tijuca and Santa Tereza stations is due to the fact that these stations are located in regions of adequate forest cover in their surroundings and altitude higher than 150 meters to the leeward side of MTJ. Associated with these characteristics, stations are located in the vicinity of the Guanabara Bay, which favors greater in uence of humidity not only from the ocean. The statistics of stations that compose Group-III prove this classi cation and seems to be analogous to that presented (Ward, 1963;Serra, 1970;Machao et al. 2010).
The Tijuca and Santa Tereza neighborhoods stand out with disasters associated with rainfalls due to the irregular occupation of hills and slums. There is a strong correlation between the slope degree and the landslide occurrence so that the weights are increased with a greater degree of the slope apart from the slope above fty degrees (Varnes, 1984). Thus, landslide deaths are common, such as the three deaths at Stations of the other subgroup-III, Copacabana and Grajaú, presented the lowest minimum, total and average rainfall values, with values close to one another. However, distant variance, standard deviation and coe cient of variation values were observed. Thus, ED value among stations was 0.884. Resulting from higher trunk height, it indicates lower similarity in rainfall distribution when compared to Tijuca and Santa Tereza stations. In the case of Copacabana and Grajaú stations, the rainfall distribution behavior is somehow different between stations. This is due to the fact that the Grajaú station is located in a region that still has a remaining forest cover, has forest reserve in balance with local constructions. In addition, its geographical position is closer to MTJ, the Grajaú station is thus in uenced by the available humidity of the forest and the orographic factor in the formation of rains. The Copacabana station is the most distant from MTJ regarding stations that compose Group-III. Thus, the orographic effect on the rainfall distribution in that station is not observed. In addition, concrete buildings in the neighborhood are associated with one of the highest demographic density in the city of Rio de Janeiro. These characteristics make this station to present the lowest total rainfall of Group-III stations. However, ooding is often observed on the streets of the Copacabana neighborhood, as well as tree The topographic effect that causes orographic rains in Group-IV stations located to the windward side of the slope, has not been veri ed. Thus, rainfall distribution in these stations is due to macro and mesoscale synoptic systems, making maximum and minimum totals similar in these stations. This characteristic enables observing the lowest rainfall totals in stations under analysis. Group-IV stations are located in an area of great density, where there is practically no forest cover and greater distance from the Tijuca massif. These characteristics prevent the passage of humid winds from the Atlantic Ocean, causing low relative humidity and the appearance of heat islands. In addition, the location of stations away from the coast is a relevant attribute for the lower in uence of the sea breeze. These characteristics con rm the lower annual rainfall totals observed in these stations. In these neighborhoods, the greatest problems caused by rainfalls are oods due to the over ow of rivers. The unplanned urbanization especially in developing countries and wide climate changes through global warming increase the risk of natural hazards. Landslide e Floods phenomenon are an important worldwide natural hazard.
The behavior of rainfall distributions for the stations that make up Group-IV behave very similarly and very close to each other throughout the year, being the most similar of all groups (Fig. 8).
The results of HRRD can be used by governments to identify critical areas of natural disasters, with the objective of developing actions that mitigate the impacts of the rainfall. These actions can be preventive measures with direct actions in neighborhoods such as: reforestation, infrastructure works, garbage collection, mapping of risk areas, rain forecasting and monitoring system, implementation of an operations center, audible warning sirens, weather radars. These actions can make CRJ more resilient, to heavy rainfall and natural disasters such as oods and landslides, mainly due to large daily rainfall totals. Figure 9 shows the highest total rainfall values at Alto da Boa Vista stations during January and Rocinha To Brazil precipitation extremes show heterogeneous signals for most of the country. In Northeast Brazil, there are changes towards a drier climate, especially in summer and autumn. In the Southern region, the climate is becoming wetter, with a reduction in consecutive dry days, especially in spring. For the other regions, there is no strong clear change sign, but both positive and negative precipitation extreme trends, without statistical signi cance, mostly in Southeast Region where is it located CRJ (Regoto et al. 2021).

Conclusions
In this study, four homogeneous groups were identi ed due to rainfall distribution in the city of Rio de Janeiro regarding the risk of natural disasters. It was veri ed that the orography of the Tijuca massif is a determining factor for the grouping of stations and in the homogeneity of rainfalls in the city of Rio de Janeiro, with the highest rainfall totals being observed in higher altitude stations.
The grouping of stations into clusters was also due to the vegetal coverage rate and the proximity of stations to the Atlantic Ocean and Guanabara Bay. Stations located to the windward side of the massif, far from water bodies, have the lowest rainfall totals in the city of Rio de Janeiro.
Neighborhoods that compose Group-I and Group-II, and some that compose Group-III, are the most vulnerable to natural disasters due to greater rainfall and irregular occupation of hills and slopes. Figure 1 Geographical locations of the rainfall stations in the city of Rio de Janeiro. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.

Figure 2
Cluster analysis and identi cation of homogeneous groups for 14 pluviometric stations in the city of Rio de Janeiro.

Figure 3
Dendrogram with the division of homogeneous groups.

Figure 4
Homogeneous precipitation groups. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.
Page 20/22  Monthly average rainfall for the Group-II season.

Figure 7
Monthly average of precipitation presented by Group-III.

Figure 8
Monthly average of precipitation presented by Group-IV.

Figure 9
Total monthly precipitation values for the weather stations in the city of Rio de Janeiro.