Density and classification of the rainfall network and spatiotemporal analysis of rain in the upper Parana river region, Brazil

ABSTRACT Water management aims to ensure the water availability necessary to meet the current and future demand for water resources. For which it is essential to implement monitoring networks that support the investigation of events that interfere with the rainfall regime of watersheds, such the phases of the ocean-atmospheric phenomenon El Niño – Southern Oscillation (ENSO). The classification of the rainfall network was proposed according to the World Meteorological Organization (WMO) for 14 management watersheds in the Upper Parana River (UPR) region, Brazil. On the other hand, the spatial and temporal variability of annual rainfall was analyzed using geostatistical techniques and confronted with ENSO data. To this purpose, data from 408 stations were collected via the Hidroweb portal, for the period from 1990 to 2020. The low representativeness of data in the region was verified from the observational network. The areas with the lowest and highest rainfall reduction were the north and northwest regions of the UPR, and the areas surrounding the Paraná River, respectively. The years 2019 and 2020 were identified as the most critical period of the last 3 decades with below-average rainfall (-13.21%) in 49.55% of the studied area, indicating a persistence in the drought scenario.


INTRODUCTION
Efficient water management is crucial to maintain a balance between water availability and the ever-increasing demand for water resources.To achieve this, it is essential to establish efficient monitoring networks to support water resource planning and management.Investigating climate events like El Niño-Southern Oscillation (ENSO) is of utmost importance as it leads to prolonged droughts, floods, and extreme weather events.Addressing environmental issues related to water is vital as the world continues to experience the consequences of climate change.
The ENSO phenomenon stems from the variation in Sea Surface Temperature (SST) in the Pacific Ocean, which influences the intensity and seasonality of the rainfall regime on regional and global scales, directly affecting the water availability of river basins around the planet (Aryal et al., 2018;Mallakpour et al., 2018;Rocha & Santos, 2018;Kumar, et al., 2019;Dutta & Maity, 2021).
According to Hu et al. (2019), the spatial estimation of rainfall is the basis for understanding hydrological changes.Studies covering the various sectors of water resources depend on the availability of rainfall data, as they require the spatialization of rainfall on a micro and macro scale (Rafee et al., 2019).
According to Pruski et al ( 2012), regionalization methods have been applied to overcome the lack of data in different regions of the world.Geostatistical techniques, such as kriging, allow the interpolation of variables in unsampled locations, based on the theory of regionalized variables (Yamamoto & Landim, 2013).The use of kriging has been applied in the investigation of the spatial variability of precipitation in small basins, up to the simulation of rainfall meshes used in General Circulation Models (GCM), often proving to be more efficient compared to other conventional methods applied to rainfall mapping (Berndt & Haberlandt, 2018;Malfatti et al., 2018;Souza et al., 2020;Lima et al., 2021;Ricardi & Lima, 2021).
In Brazil, part of the Paraná River Basin that covers the Brazilian territory (Parana Hydrographic Region), entered a critical situation of quantitative water scarcity, due to the severe rainfall deficit in 2021, associated with the La Niña phase (Brasil, 2021).This region is responsible for ensuring part of the energy security in Brazil, Argentina and Paraguay, in addition to contributing to urban supply.However, the observational networks of several hydrographic units in the region, in addition to having very uneven densities of monitoring points, do not meet the minimum recommendations of the World Meteorological Organization (2008), which impairs the precision of the interpolation of rainfall data and consequently, decision-making involving rainfall phenomena.
Thus, this work contributes to the literature, allowing the recognition of the scope of rainfall data and better planning of water use in the management units covered by the Upper Paraná River region (UPR).Therefore, the present work aimed, in addition to classifying the density of the rainfall network in the UPR region, to evaluate the spatial and temporal variability of rainfall, analyzing the influence of ENSO on annual rainfall averages, during the period from 1990 to 2020, through the use of geostatistical techniques and Geographic Information Systems (GIS).
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and about 5,358,974 inhabitants (Agência Nacional de Águas e Saneamento Básico, 2019).The region is formed by the plateau of the Paraná Basin, presents flat relief, and a humid tropical climate typical of Brazil Central (Koppen classification type Aw), having as main acting systems the air masses of the Tropical Atlantic (mTa), air masses from the Polar Atlantic (mPa) and large masses of water vapor (flying rivers) from the Amazon (Fearnside, 2013).
Most of the reservoirs of the National Interconnected System (SIN) are concentrated in the UPR region, which includes the Urubupunga Complex, the sixth largest hydroelectric complex in the world with 3,444,000 KW of power (Mattosinho et al., 2022), part of the states of Goiás, Mato Grosso do Sul, Minas Gerais and São Paulo, influencing the navigation of the Tietê-Paraná Waterway, regional agriculture and the generation of hydroelectric energy.
The monthly rainfall series were obtained from the Hidroweb v.3.1.1 tool (Agência Nacional de Águas e Saneamento Básico, 2020), which grants access to the National Hydrometeorological Network (NHN).In total, 408 rainfall stations were used with data between 1990 and 2020.The data were submitted to regional consistency analysis according to the methodology of Hosking & Wallis (1997), aiming to verify the absence of gross errors in the historical series and subsidize the filling of faults in the stations.

RAINFALL NETWORK DENSITY CLASSIFICATION
The rainfall network can be designed using statistical methods (variance, least squares), geostatistics (interpolation), sampling methods, methods based on the physiography of watersheds, and methods that combine different design techniques (Mishra & Coulibaly, 2009).Among the methods based on the physiography of the basin, the criterion of number of stations per territorial extension of the WMO (World Meteorological Organization, 2008) is often used to evaluate rainfall networks in different river basins (Salgueiro, 2005;Chico & Dziedzic, 2015;Melati & Marcuzzo, 2015;Vianna et al., 2021).The WMO establishes institutional technical standards, with instructions to guide the institutions responsible for identifying and managing observational networks (World Meteorological Organization, 2008).
Thus, in order to classify the active rainfall network (with data), 5 density intervals were identified for the classes: insufficient, not very comprehensive, sufficient, comprehensive and very comprehensive (Companhia Ambiental do Estado de São Paulo, 2022), according to the minimum density recommended by the WMO (World Meteorological Organization, 2008), presented in Table 1.
For hydrometeorological networks inserted in undulating/ mountainous terrain, the minimum density is equivalent to 575 km 2 /station (Table 1).According to Rocha & Bade (2018) and Embrapa (Empresa Brasileira de Pesquisa Agropecuária, 2013), the relief of the Upper Paraná River region varies between smooth, wavy and mountainous classes.Therefore, the criterion used to determine the density intervals (station/km 2 ) presented in Table 2 was the number of stations every 575 km 2 , in order to identify the water units with the most critical observational networks in the Upper Rio Paraná region.
Therefore, only the stations located in the administrative areas of the management units were considered in this analysis, totaling 395 stations with at least 5 years of data recorded between 1990 and 2020.

INTERPOLATION OF ANNUAL RAIN AND ENSO INFLUENCE
According to Salgueiro (2005), in hydrology the first application of geostatistical methods was carried out by Delhomme in 1976.Since then, geostatistics has been used in several studies of evaluation of water resources, based on the estimation of parameters in the spatialization of rainfall (Muthusamy et al., 2017;Berndt & Haberlandt, 2018;Malfatti et al., 2018;Hu et al., 2019).
According to Journel & Huijbregts (1978), the local values of a regionalized variable obey a probability function of occurrence and are distributed in space in a structured way, allowing global analysis through a spatial function.According to Sturaro (2015), linear geostatistics makes use of the moments of the casual function (mathematical expectation and variance), based on the hypothesis of spatial stationarity (when the statistical moments of the random variable are equal for any distance), assuming that all the analyzed samples are part of the same population.
In cases of phenomena that have high dispersion capacity and infinite variance, geostatistics assumes the intrinsic hypothesis, where the first 2 moments depend only on the distance between the values of the analyzed variables.Thus, the spatial dependence was performed using the GeoStatistics for the Environmental Sciences -Gamma Design (GS+) version 7.0 software.(Robertson, 2004).For each year, the experimental semivariogram was calculated, according to Equation 1 (Yamamoto & Landim, 2013):  Density and classification of the rainfall network and spatiotemporal analysis of rain in the upper Parana river region, Brazil where, ( ) + , apart from each other on a regular basis h.After the construction of the semivariogram, a theoretical model was adjusted to the semivariance graph, in order to verify the spatial dependence of the sampled data.
For the semivariographic adjustments, the following were initially observed: a) the smallest sum of squared deviations (SQD); b) the highest coefficient of spatial determination (R 2 ) and, c) the greatest evaluator of spatial dependence (ADE), according to Equation 2.
The final definition of the adjustment model was performed with the highest correlation coefficient (r) between the observed versus estimated values of the cross-validation (CV) as a parameter.The cross-validation process was used to verify the reliability of each adjusted mathematical model, and consists of removing the observed value, belonging to the data set, by its estimated value (of the analyzed variable, in this case rainfall data), using the ordinary kriging interpolation method, in order to obtain a graph correlating these values (Landim, 2006).
Therefore, the final model chosen will be the one that best estimated the observed values, that is, the one that produced a linear regression equation between the observed values, as a function of the estimated values closest to the bisector (intercept [a] = zero and angular coefficient [B] = 1) (Isaaks & Srivastava, 1989;Ricardi & Lima, 2021).
Thus, the interpolation by ordinary kriging was performed, described in Equation 3 (Yamamoto & Landim, 2013): where "z*" is the value to be estimated at the unsampled point x0; "N" the number of measured values z(xi) involved in the estimate and "λi" the weights associated with each measured value z(xi).The final maps for the years 1990 to 2020 were edited in the software Geographic Information System -QGIS v. 3.4 (QGIS, 2021).
The rainfall averages obtained from the annual maps were compared with the ENSO phases (La Niña and El Niño), represented by the annual averages of the Oceanic Niño Index (ONI), estimated by the continuous averages of 3 months of SST anomaly in the Niño 3.4 region (National Oceanic and Atmospheric Administration, 2023).
According to the National Oceanic and Atmospheric Administration (NOAA), the ENOS pattern can occur in three states or phases: El Niño (warm phase), neutral conditions, or La Niña (cold phase) (National Oceanic and Atmospheric Administration, 2023).Each phase tends to last about 1 to 2 years, alternating irregularly every 2 to 7 years (Wu et al, 2019).
According to Berlato & Fontana (2003), the impacts of ENSO affect the precipitation regimes in different areas of the planet and different regions of Brazil.During the El Niño phase, during spring-summer (December to February), the north and northeast regions of Brazil experience a predominantly dry period, while during autumn-winter (June to August), the climate warms up in the southeast and northeast regions of the country, favoring the occurrence of heavy rains.In the La Niña phase, the conditions of drought and above-average rainfall are reversed for the same analyzed periods (Grimm et al., 2020).

RESULTS AND DISCUSSION
The density classification of the rainfall network for each management basin is presented in Table 3 and Figure 2.
It was found that 9 of the 14 units had insufficient density (1, 2, 4 and 7) or little embracing (3, 5, 6, 8 and 9), characterizing a worse availability of data in the north/west area of the UPR and a need implementation of 226 stations.Together, the units in the state of São Paulo presented a rainfall network density of 218 km 2 /station, close to the average indicated by Sarmento (2021) for the Southeast region (200 km 2 /station), with SWRPMU 14 ("Turvo-Grande") the better data distribution (191 km 2 /station), equivalent to 3 stations per 575 km 2 .

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The years with the highest rainfall rates observed in the historical series, namely 1997, 2009 and 2017, occurred in El Niño years (Very Strong), transition from La Niña to El Niño (Moderate) and La Niña (Weak), respectively, in agreement with Minuzzi et al. (2006), who found the extension of the rainy season in the Southeast during the El Niño period 1997-1998, and Terassi et al., (2018)), who related the increase in annual precipitation in Southern Brazil in the years 2007 and 2009.
In the critical years with average totals below 1,300 mm (1999, 2002, 2019 and 2020) the occurrence of La Niña (Strong and Moderate) was observed in the 2 most critical periods (1999 and 2020) and El Niño (Moderate and Weak) in the other two (2002 and 2019).According to Grimm (2004) and Nery et al. (2005), the reduction of rainfall during the occurrence of La Niña events occurs due to the rapid passage of frontal systems, which influence the generation of rainfall.
The La Niña event has been related to droughts in the country and the extension of the dry period in the southeast region, causing a reduction in rainfall in the Paraná River basin as a whole (Minuzzi et al., 2006;Fearnside, 2013), as in the present study, the monthly data, which would better characterize the dry periods, were not analyzed, this interaction cannot be observed.
RBRH, Porto Alegre, v. 28, e17, 2023 8/12 Density and classification of the rainfall network and spatiotemporal analysis of rain in the upper Parana river region, Brazil Figure 6 shows the long-term averages of the annual total for each SWRPMU with their respective graphs of average rainfall variation (mm) for the decades 1990-1999, 2000-2009 and 2010-2020 (11 years).
Considering the normal average rainfall of the last 31 years (1990 to 2020), SWRPMUs 1 ("Baixo Paranaíba") and 2 ("Aporé") had higher rainfall than the other sub-basins, both totaling 1,510 mm of total annual rainfall.Such values are consistent with the average annual precipitation estimated by Cardoso et al. (2014) for the state of Goiás, referring to 1,500 mm.Mato Grosso do Sul was the state in which the SWRPMUs presented the greatest variation in annual rainfall (1,340 mm to 1,510 mm).
The estimated values for the SWRPMUs in São Paulo state are in the rainfall threshold determined by Nery et al. (2004) and Marcuzzo (2016) for the same area (1,360 mm).On the other hand, SWRPMUs 8 ("Baixo Rio Grande") and 9 ("Baixo Rio Paranaíba") showed average annual rainfall values equivalent to 1,400 mm and 1,440 mm, coinciding with the values quantified by Santos & Ferreira (2016), who estimated annual totals below 1,450 mm for the "Triângulo Mineiro" region and transition values for the central area varying between 1,400 mm and 1,600 mm.

CONCLUSION
The proposed classification for the rainfall network density can be adapted for use in hydrographic basins located on different types of terrain, enabling the identification of areas that require greater investments in the rainfall network according to the number of stations and their territorial extension.
The general data pointed to a decrease in the availability of stations/rainfall data in the ARP region.This fact negatively affects the planning and management of water, especially in situations of water crisis, since the observation of climate variation is based on the time scale of the measurement of hydroclimatic processes.
The final maps of the geostatistical analysis allowed us to observe that the northern and northwestern portions were the regions with the lowest rainfall rate reduction in the 31-year period, compared to the other regions, mainly on the areas that surround the course of the Paraná River.In addition, the analyzes allowed the identification of 2019 to 2020 as the most critical period of the historical series, with below-average rainfall (-13.21%) in 49.55% of the area, for 2 consecutive years, mainly affecting the "Aguapeí" and "Turvo-Grande".
The rain maps presented are important tools for water resource agencies and managers, since it is possible to verify the management basins that were most impacted by excess or lack of rain, in addition to the most critical periods in relation to rainfall scarcity, allowing better decision-making in face of the reflexes of water availability on the environment and society.
For a better investigation of the effects of ENSO on the rainfall of the water units that contemplate the Upper Paraná River, it is suggested that the monthly averages be analyzed so that it is possible to verify the influence of the El Niño and La Niña phases in the dry and rainy periods of the region, allowing climatological trends to be identified.
Furthermore, based on the identification of the most critical management units regarding the density of the rainfall network, it is recommended to compare this classification with other physical, climatological and socioeconomic variables, such as the occurrence of droughts, land use, population density, urban supply and electricity generation, in order to measure the vulnerability of rainfall monitoring according to the reality of the basin.

Figure 1 .
Figure 1.Location of the Upper Parana River region, rainfall stations and management units.

Figure 2 .
Figure 2. Classification of the active rainfall network density in the Upper Parana River region.

Figure 4 .
Figure 4. Total annual rainfall in the Upper Parana River region from 2001 to 2011.

Figure 5 .
Figure 5.Total annual rainfall in the Upper Parana River region from 2012 to 2020.
accentuated decrease in rainfall in the SWRPMUs located near the headwaters of the Paraná River, mainly in the northeast region of the study area, reaching mainly the northwest of São Paulo state and the tip of the "Triângulo Mineiro" region.

Table 2 .
Rainfall network density classes and ranges for inland plains and rolling/mountain terrain.

Table 3 .
Density of the rainfall network in the Upper Parana River region in 2020 *= World Meteorological Organization Recommendation; SWRPMU = State Water Resources Planning and Management Unit, where: