171 RBCIAMB | v.58 | n.2 | Jun 2023 | 171-181 - ISSN 2176-9478 A B S T R A C T Due to limitations of hydrometeorological monitoring network related to spatial station distribution and extension of historical series, tools that aim to improve consistency and optimize available data analysis have become essential. In this context, regionalization techniques stand out, once the main focus is the delimitation of hydrologically homogeneous regions with the subsequent spatial transposition of hydrological variables of interest. Regional indicators, defined as the mean values of hydrological variables and characteristics of a homogeneous region, constitute an expeditious approach to hydrological regionalization. The main perspective of the study was to evaluate the use of regional indicators when quantifying reference flows associated with average flow, drought, or flood conditions. The study area selected was the Manhuaçu River basin, a major Doce River tributary, located in the state of Minas Gerais, Brazil. The results showed that the regional indicators allow estimates of diverse reference flows with mean errors lower than 30%, considered satisfactory for the study area. However, the conventional method of flow regionalization presented more consistent results, with mean errors usually lower than 20%, regardless of the reference flow analyzed. It was also observed that adopting historical flow series with varied extensions did not produce relevant differences when appropriating the diverse reference flows for the Manhuaçu River basin, with none exceeding 3%. Keywords: regionalization; indicators; droughts; floods; Manhuaçu River. R E S U M O Em função das limitações da rede de monitoramento hidrometeorológico, tanto do ponto de vista da distribuição espacial quanto da extensão das séries históricas, ferramentas que busquem dar consistência e otimizar a análises dos dados disponíveis vêm ganhando espaço. Neste contexto, destacam-se as técnicas de regionalização, cujo principal foco é a delimitação de regiões hidrologicamente homogêneas com a subsequente transposição espacial de variáveis hidrológicas de interesse. Os indicadores regionais, definidos como valores médios de uma variável hidrológica e característicos de uma região homogênea, constituem abordagem expedita de regionalização hidrológica. O presente estudo teve como principal perspectiva avaliar o emprego de indicadores regionais quando da quantificação de vazões de referência associadas às condições médias de escoamento, estiagens ou cheias. A área de estudo selecionada para a condução do estudo foi a bacia hidrográfica do rio Manhuaçu, importante afluente do rio Doce, Minas Gerais, Brasil. Os resultados demonstraram que os indicadores regionais permitem estimativas de diferentes vazões de referências com erros médios inferiores a 30%, considerados satisfatórios para a área de estudo. No entanto, o método convencional de regionalização de vazões apresentou resultados mais consistentes, com erros médios usualmente inferiores a 20%, independentemente da vazão de referência analisada. Observou-se, adicionalmente, que a adoção de séries históricas de vazões com diferentes extensões não produziu diferenças relevantes quando da apropriação das diferentes vazões de referência para a bacia hidrográfica do rio Manhuaçu, com diferenças que não superaram 3%. Palavras-chave: regionalização; indicadores; secas; cheias; rio Manhuaçu. Estimative of reference flows for water resources planning and control: hydrologic regional indicators application Estimativa de vazões de referência para planejamento e controle de recursos hídricos: aplicação de indicadores hidrológicos regionais Matheus Siqueira Piol1 , José Antonio Tosta dos Reis1 , Murilo Brazzali Rodrigues1 , Antônio Sergio Ferreira Mendonça1 , Fernando das Graças Braga da Silva2 , Alex Takeo Yasumura Lima Silva2 1Universidade Federal do Espírito Santo – Vitória (ES), Brazil. 2Universidade Federal de Itajubá – Itajubá (MG), Brazil. Correspondence author: José Antonio Tosta dos Reis – Avenida Fernando Ferrari, 514 – Goiabeiras – CEP: 29075-910 – Vitória (ES), Brazil. E-mail: jatreis@gmail.com Conflicts of interest: the authors declare no conflicts of interest. Funding: none. Received on: 04/13/2023. Accepted on: 06/28/2023. https://doi.org/10.5327/Z2176-94781598 Revista Brasileira de Ciências Ambientais Brazilian Journal of Environmental Sciences Revista Brasileira de Ciências Ambientais Brazilian Journal of Environmental Sciences ISSN 2176-9478 Volume 56, Number 1, March 2021 This is an open access article distributed under the terms of the Creative Commons license. https://orcid.org/0009-0007-8055-6445 https://orcid.org/0000-0001-9916-1469 https://orcid.org/0000-0003-1647-2785 https://orcid.org/0000-0003-4273-0266 https://orcid.org/0000-0002-3803-2257 https://orcid.org/0000-0003-1883-2414 mailto:jatreis@gmail.com https://doi.org/10.5327/Z2176-94781598 http://www.rbciamb.com.br http://abes-dn.org.br/ Piol, M.S. et al. 172 RBCIAMB | v.58 | n.2 | Jun 2023 | 171-181 - ISSN 2176-9478 Introduction The availability of water, which exhibits significant temporal and spatial variability (Lira and Cardoso, 2018), is a permanent social con- cern, particularly when considering the world’s population growth in a context of uncertainties associated with variations in precipitation due to climate changes (O’Gorman, 2015; Tabari, 2020), land use changes (Gomes et al., 2022; Silva et al., 2022). and increasing water pollution (Dutra et  al., 2022). Moreover, the large volumes of water discharged during flood periods can lead to significant social, economic, and en- vironmental problems in addition to the potential loss of human lives. Therefore, flow quantification becomes one of the most relevant stages for adequate decision-making associated with water resources plan- ning and control (Mendonça, 2003). The appropriation of reference flows that allows the characteriza- tion of different flow conditions (droughts, floods, or average long- term flows) usually requires historical flow series established through systematic monitoring of watercourses that involves daily water levels measurements, the establishment of key curves, and with the aid of this hydrological function, the conversion of levels into flows. It is import- ant to note that the monitoring work that allows the establishment of historical series of flows is not always simple due to adverse weather conditions, location of stations in difficult access places, occasional riv- er intermittencies, and in some cases, large widths of Brazilian water bodies (Tucci et al., 1995). The Brazilian hydrological monitoring network is limited, with heterogeneous station distribution. In different parts of the national territory, it presents low density with short historical series and/or ex- cess of failures. However, the knowledge of flows at different points of a hydrographic basin constitutes essential information for deci- sion-making associated with the adequate management of water re- sources (Piol et al., 2019). In this context, the creation of alternatives to optimize the available hydrological information becomes a necessity. Among the available methods, hydrological regionalization has been widely used by water resources management and control agencies and is recurrently the cen- tral tool for regulating water use grants and charges (Bazzo et al., 2017; Maciel et al., 2019; Piol et al., 2019). Hydrological regionalization is a set of statistical procedures that allow the maximum use of information existing in a site to estimate hy- drological variables or parameters in places without or with insufficient data, thus allowing knowledge about spatial distributions of hydrolog- ical variables or parameters and improvement of temporal estimation (Tucci, 2002). A relevant set of regionalization methods has been established, involving different hydrological variables and different method- ological approaches, as illustrated by Razavi and Coulibaly (2013), Boscarello et al. (2016), Swain and Patra (2017), Qamar et al. (2018), Silva et al. (2019), Althoff et al. (2021), Golian et al. (2021), and Singh and Devi (2022). Among the most recurrently applied methods in Brazil are the Char- acteristic Values Method (Baena et al., 2004; Pessoa et al., 2011; Moreira and Silva, 2014; Bazzo et al., 2017; Amorim et al., 2020), the Dimensional Curve Method (Tucci et al., 1995; Pinto, 2006; Piol, 2017), the Parameter Method (Wolff, 2014; Piol, 2017), and the Exponential Curve Method (Calmon et al. 2016; Piol et al., 2019; Rodrigues et al., 2022). Regional indicators, defined as the mean values of hydrological variables and characteristics of a homogeneous region, are consid- ered alternatives to the methods usually applied for hydrological vari- ables regionalization (Piol et al., 2019). It is an expeditious approach, substantially simpler than conventional hydrological regionalization methods. Reis et al. (2008) established regional indicators for the ap- propriation of mean, minimum, and maximum flows for the Itabapoa- na River basin, a region that covers municipalities in the states of Es- pírito Santo, Rio de Janeiro, and Minas Gerais. On the other hand, Piol et  al. (2019) established regional indicators associated with the flow duration curve for the Itapemirim River basin and for the Capixaba portion of the Itabapoana River basin, regions in the southern Espíri- to Santo. The mentioned authors observed that regional indicators al- lowed consistent appropriation of the evaluated flows. The Manhaçu River basin, a major Doce River tributary, has a drainage area of 9,189 km² and encompasses (partially or entirely) 32 municipalities in Minas Gerais state, Brazil. The watershed is located within the Atlantic Forest biome, with agriculture occupying 65% of its territory. The most significant water demands in the watershed are for irrigation and human supply, accounting for approximately 87% of the water extracted. Insufficient sewage treatment services in the munici- palities, combined with erosion and siltation processes, press the water resources of the region. In this context, appropriate assessment of the watercourse regime becomes relevant (ANA, 2021). This work aimed at evaluating the use of regional indicators for reference flow appropriation as an alternative to the approach usual- ly applied for watercourse flow regionalization. The objects of analysis were flows associated with average conditions, droughts, and floods. The study was conducted based on the analysis of the historical water- course flow series for the Manhuaçu River basin. Methodology Study area The Manhuaçu River basin is an important sub-basin of the Doce River watershed. According to information from the review and up- date of the Integrated Water Resources Plan for the Rio Doce Basin (ANA, 2021), the basin presents a 9,189 km² drainage area distributed in Minas Gerais, corresponding to approximately 10.48% of the Doce basin area. Manhuaçu basin covers, totally or partially, 32 municipal- ities (Aimorés, Alto Caparaó, Alto Jequitibá, Alvarenga, Caratinga, Chalet, Conceição de Ipanema, Conselheiro Pena, Durandé, Ibatiba, Imbé de Minas, Inhapim, Ipanema, Itueta, Iúna, Lajinha, Luisburgo, Estimative of reference flows for water resources planning and control: hydrologic regional indicators application 173 RBCIAMB | v.58 | n.2 | Jun 2023 | 171-181 - ISSN 2176-9478 Manhuaçu, Manhumirim, Martins Soares, Mutum, Piedade de Car- atinga, Pocrane, Reduto, Resplendor, Santa Bárbara do Leste, Santa Rita do Itueto, Santana do Manhuaçu, São João do Manhuaçu, São José do Mantimento, Simonésia, and Taparuba). According to the lat- est estimates from the Brazilian Institute of Geography and Statistics (IBGE, 2021), the resident population in the Manhuaçu River basin was 569,088 inhabitants. The main basin watercourse and springs of Manhuaçu River, are located in the Serra da Seritinga, on the border between the munici- palities of Divino and São João do Manhuaçu, traveling a distance of approximately 347 kilometers until it drains into the Doce River, near Aimorés (ANA, 2021). The basin is located in the Atlantic Forest biome, one of the biomes with the greatest biodiversity in Brazil. Currently, it is estimated that ap- proximately 65% of the soil of the basin is destined for agriculture. Irri- gation accounts for 59% of water consumption in the basin, followed by human supply, responsible for about 28%. Water use for animal watering and industrial purposes is less relevant in the basin (ANA, 2021). Fluviometric data The historical series of flows and the fluviometric station drainage ar- eas of the Manhuaçu river basin were obtained from the National Agency for Water and Basic Sanitation (ANA) Hidroweb site. Figure 1 shows the location of the fluviometric stations selected for the regional flow analysis. Table 1 presents the selected fluviometric stations with each corre- sponding drainage area, Hidroweb site identification codes, and histor- ic series extensions. The reference flows and flow indicators were initially appropriated assuming 30 years of long historical series, from 1984 to 2014, with data available for all stations. In a subsequent work stage, seeking to evaluate the influence of historical series extensions, reference flows, and flow indicators were estimated considering the complete fluvio- metric station flow series as indicated in Table 1. This was reproduced based on the approach employed by Piol (2017) when conducting studies on the regionalization of long-term average flows, characteris- tic flows of the flow permanence curve, and minimum flows associated with different return periods. Figure 1 – Fluviometric stations located in the Manhuaçu River basin. Piol, M.S. et al. 174 RBCIAMB | v.58 | n.2 | Jun 2023 | 171-181 - ISSN 2176-9478 Reference flows and regional indicators evaluation According to ordinance no. 48 of the Minas Gerais State Water Man- agement Institute (Igam), issued on October 4, 2019 (Igam, 2019), the reference flow for the calculation of maximum grants of water withdraw- al from rivers in the state is the minimum streamflow of seven consec- utive days and ten years of return period (Q7.10). Due to this condition, Q7.10 was the first minimum reference flow rate considered in the present study. The minimum flows with permanence of 90% (Q90) and 95% (Q95) were also considered for the appropriation of the regional indicators r7.10, Rcp90, and Rcp95 because they constitute the flows that regulate water use grants in most Brazilian states. The granting of water use, an instrument established by the National Water Resources Policy (Law No. 9.433, Jan- uary 8, 1997), has as its main objectives the control of water uses and the effective exercise of rights to access water. In Brazil, water supply for hu- man or industrial purposes, irrigation, aquaculture, hydroelectric power generation, final disposal of effluents, and other uses that may alter the regime, quantity, or quality of water resources, require granting. For the appropriation of regional flow indicators associated with the average flow conditions (q and Rcp50), the average long-period flow (Qm) and the flow rate with permanence of 50% (Q50) were selected. The as- sessment of average flow conditions is a central aspect for water resources planning and management, as it establishes the limit for watercourses reg- ulation in a basin. The description of maximum streamflow behavior is relevant for the development of risk management policies and urban planning. In- formation on maximum flows associated with different return periods allows for the identification of high-risk areas, land use and land oc- cupation planning, and implementation of flood mitigation measures such as the creation of buffer zones and the development of alert sys- tems. For the appropriation of regional flow indicators associated with the maximum flows r2 and r100, the maximum daily flows with return periods of two and one hundred years, respectively, were selected. Ac- cording to Tucci et al. (2003) and Reis et al. (2008), the flow associated with a two-year return period indicates the average flooding flow, a val- ue which corresponds approximately to the limit of the lower bed of al- luvial rivers; the flow associated with the return period of one hundred years usually represents the upper limit of the riverside flood range. Table 2 presents the regional indicators evaluated in this work. For the appropriation of the Q50, Q90, and Q95 flows, the permanence curves of the fluviometric stations’ flow were constructed considering the division of the historical series into 50 class intervals. The definition of class intervals was based on a logarithmic scale because of the large variations of flow magnitudes. To evaluate the Q7.10 flow and the maximum daily flows with return periods of two and one hundred years, Gumbel, Weibull, Log-Normal type II, Log-Normal type III, Pearson type III, and Log-Pearson type III distributions were chosen. All probability distributions used for evaluations of maximum and minimum reference flows were present- ed in detail by Kite (1988). All the flow values used for the appropria- tion of regional flow indicators were estimated through SisCAH soft- ware, a publicly available program, produced and released by the Water Resources Research Group at the Universidade Federal de Viçosa. The selection of the probability distribution used for the evalua- tion of the maximum and minimum flows occurred as a function of the analysis of the standard error of estimation, assuming the distri- bution that was not rejected in any of the fluviometric stations and that presented the lowest standard error of estimation in most of the stations analyzed. Table 1 – Fluviometric stations installed and in operation in the Manhuaçu River basin. Station River Code Drainage Area (km²) Series Extension (Years) Fazenda Vargem Alegre Manhuaçu 56960005 1,070 30 São Sebastião da Encruzilhada Manhuaçu 56990000 8,720 75 Assarai Montante Pocrane 56989400 3,190 37 Mutum São Manoel 56989001 1,180 40 Ipanema José Pedro 56988500 1,410 75 Dores de Manhumirim José Pedro 56983000 384 75 Santo Antônio do Manhuaçu Manhuaçu 56978000 2,350 48 Table 2 – Regional flow indicators evaluated. Indicator type Indicator Unit Average flow (1) L/s.km² (2) Dimensionless Minimum flow (3) Dimensionless (4) Dimensionless (5) Dimensionless (6) Dimensionless Maximum flow (7) Dimensionless (8) Dimensionless http://s.km Estimative of reference flows for water resources planning and control: hydrologic regional indicators application 175 RBCIAMB | v.58 | n.2 | Jun 2023 | 171-181 - ISSN 2176-9478 To evaluate the regional flow indicators responses, we considered the percentage errors between flows appropriated from the fluviomet- ric records and flows estimated through regional flow indicators and coefficients of variation, according to Equations 1 and 2, respectively. (1) (2) In Equations 1 and 2: Qestimated: the value of the reference flow rate obtained from the regional flow indicators; Qreal: flow rate estimated from the fluviometric stations flow records; CV: coefficient of variation expressed in percentage; S: standard deviation of the indicators; ri: average value of each indicator obtained for the Manhuaçu Riv- er basin. Conventional regionalization of reference flows Regional functions were established by regression analysis to ap- propriate the different reference flows. The functions produced were potential and the area was the independent variable used for the con- formation of all regional functions. Although other physiographic and climatological variables can be regarded as independent variables for the definition of regional functions, only the area was considered be- cause it is the only physiographic variable used to define regional flow indicators, as stated by Silva Junior (2003) and Novaes et  al. (2007). Additionally, it is important to note that the drainage area is one of the physical variables with significant relevance for conducting hydro- logical regionalization studies, as suggested by Lall and Olds (1987), Mwakalila (2003), Baena et al. (2004), and Bárdossy (2007). All regression analyses necessary to define the regional functions were conducted using a Microsoft Excel spreadsheet. The correlation coefficients associated with regression analyses, the percentage errors between flows appropriated from the fluviometric records, and flows estimated through regional functions constituted parameters to evalu- ate the responses of the regional functions produced. Results and Discussion Table 3 summarizes the average long-term flows associated with different permanencies (50, 90, and 95%), maximum flows for return periods of two and one hundred years, and Q7.10 flows, estimated with SisCAH software for the Manhuaçu River basin fluviometric station series, considering the period from 1984 to 2014. As for the appropriation of the minimum flows Q7.10, the Log-Pearson type III probability distribution was applied, while for the maximum flows associated with return periods of two and one hun- dred years, the Log-Normal type II distribution was considered. The values of the indicators estimated for the diverse fluviometric stations, as well as their estimated means and coefficients of variation for the study area are shown in Table 4. It is worth noting that the mean values of the indicators define the regional indicator for the study area. The coefficients of variation appropriated for the Manhuaçu River basin ranged between 4% (Rpc50) and 22% (r7.10 and r100). This variation range is considerably smaller than that reported by Reis et al. (2008), who presented coefficients of variation between 6 and 52% when appropriating the same set of indicators. As for the aforementioned authors, the lowest co- efficients of variation were associated with the rcp50 and rm indicators. Addi- tionally, it is relevant to cite that the appropriated coefficient of variation for the specific flow (20%) was similar to that obtained by these authors (22%). Through a Microsoft Excel spreadsheet, potential equations were generated that correlate the values of drainage areas with the different reference flow rates evaluated. Figure 2 presents the scatter plots gen- erated between drainage areas of the streamflow stations and the ref- erence flows under analysis, as well as the produced regional functions and their corresponding correlation coefficients. Table 3 – Reference flows for Manhuaçu River basin fluviometric stations. Station Reference flows (m³.s-1) Qm Q50 Q90 Q95 Q7,10 Q2years Q100years Fazenda Vargem Alegre 17.26 11.08 4.25 2.93 1.70 118.29 327.91 São Sebastião da Encruzilhada 99.52 67.00 33.81 28.94 19.98 585.92 1,390.04 Assaraí Montante 36.68 23.87 12.01 10.35 7.55 297.25 986.05 Mutum 13.37 8.06 4.09 3.44 2.40 127.47 453.37 Ipanema 20.57 13.84 6.88 5.97 4.41 173.19 461.43 Dores de Manhumirim 6.80 4.44 2.16 1.86 1.30 45.62 80.42 Santo Antônio do Manhuaçu 40.96 27.76 14.16 12.21 8.64 248.16 628.10 Qm: average long-period flow; Q50: flow rate with permanence of 50%; Q90: flow rate with permanence of 90%; Q95: flow rate with permanence of 95%; Q7,10: minimum streamflow of seven consecutive days and ten-year return period; Q2years: maximum daily flows with return periods of two years; Q100year: maximum daily flows with return period of one hundred years. Piol, M.S. et al. 176 RBCIAMB | v.58 | n.2 | Jun 2023 | 171-181 - ISSN 2176-9478 Table 4 – Regional flow indicators for the Manhuaçu River basin. Stations Indicators q (L/s.Km2) Rcp95 Rcp90 Rcp50 r7,10 rm r2 r100 Fazenda Vargem Alegre 16.13 0.17 0.25 0.64 0.10 1.72 6.85 2.77 São Sebastião da Encruzilhada 11.41 0.29 0.34 0.67 0.20 1.45 5.89 2.37 Assaraí Montante 11.50 0.28 0.33 0.65 0.21 1.37 8.10 3.32 Mutum 11.33 0.26 0.31 0.60 0.18 1.39 9.53 3.56 Ipanema 14.59 0.29 0.33 0.66 0.12 1.35 8.42 2.66 Dores do Manhumirim 17.71 0.27 0.32 0.65 0.19 1.43 6.71 1.76 Santo Antônio do Manhuaçu 17.43 0.30 0.35 0.68 0.21 1.41 6.06 2.53 Average 14.30 0.27 0.32 0.65 0.19 1.45 7.37 2.71 Variation coefficient (%) 20 17 11 4 22 9 18 22 q and rpc50: average flow indicators; rcp90, rcp95, r7,10, and rm: minimum flow indicators; r2 and r100: maximum flow indicators. In the equations presented in Figure 2, for drainage area A, the unit is km² and the reference flows are calculated in m³.s-1. The region- al functions, fitted by regression analyses presented correlation coef- ficients (R2) ranging from 0.91 to 0.98. These can be considered very good values when conducting regional flow analysis, as suggested by Eletrobras (1985) when regionalizing flows for the Upper Paraguay River basin (distributed among the states of Amazonas, Mato Grosso, and Mato Grosso do Sul), and also by Piol et al. (2019) when conduct- ing the regionalization of flow duration curves and defining regional flow indicators for the Itapemirim River basins (watercourse within Espírito Santo state). In order to verify the relevance of the appropriation of regional flow indicators from historical series presenting the same extension (homogeneous series), indicators appropriation was repeated assum- ing the complete available historical series (heterogeneous series), a perspective that allows maximum use of the available data for each sta- tion even though presenting beginning and ending in different years. Considering heterogeneous series, regional indicators q, Rcp50, r2, and r100 presented coefficients of variation equal to or lower than those estimated from homogeneous historical series; inverse condition was observed for indicators Rcp95, Rcp90, r7.10, and rm. It is important to note that the coefficient of variation differences, in both situations, were small, not exceeding 3%. Table 6 summarizes the varied reference flows appropriated for the Manhuaçu River basin by different approaches in the present study. Table 7, in turn, presents the percentage errors for the estimat- ed flows for the different approaches (regional functions, indicators obtained from homogeneous, and heterogeneous series) in relation to the flows appropriated from the fluviometric station flow records (gathered in Table 2). From a simple inspection of regional indicators, flows (actual and estimated), and estimated percentage errors gathered in Tables 3 to 7, the following observations were considered relevant: • For the Manhuaçu River basin, the average errors between flows estimated from historical series and appropriated by regional anal- ysis, regardless of the approach, did not exceed 30% — a condition considered satisfactory by Piol (2017) when conducting studies on flow regionalization; • The regional functions established for flow appropriation, assum- ing exclusively the drainage area as an explanatory variable, pro- duced, for all the reference flows analyzed, mean errors lower than those associated with the use of regional flow indicators; • The lower errors in flow estimates were associated with Q m and Q50 flows, which usually present a strong correlation with drain- age areas, as noted by Eletrobras (1985) and Piol (2017), and for the maximum flows for a two-year return period. Regardless of the regionalization approach employed, the average errors associated with these flows did not exceed 20% for the Manhuaçu River ba- sin data. It is relevant to note that Reis et al. (2008) and Piol et al. (2019) reported that the indicators associated with the mean flow conditions (q and rcp50) are generally consistent, usually producing satisfactory responses. For the Itabapoana River basin, Qm and Q50 were estimated by Reis et al. (2008) with mean errors of 19 and 5%, respectively. Piol et al. (2019), in turn, appropriated the Q50 flow for the Itapemirim River with an error of 17%; • The consideration of estimated regional flow indicators and the adoption of historical series with the same or different extensions did not produce relevant differences when appropriating the diverse reference flows. This fact may be due to the maintenance of the aver- age and extreme flows (maximum and minimum) behaviors in the Estimative of reference flows for water resources planning and control: hydrologic regional indicators application 177 RBCIAMB | v.58 | n.2 | Jun 2023 | 171-181 - ISSN 2176-9478 Figure 2 – Scatter plots associated with different reference flows and produced regional functions. complementary parts of the historical series, for the common peri- od between 1984 and 2014. Piol (2017), using a series of different lengths to evaluate reference flows, obtained variations below 10% for long-term mean flows and maximum variations of 30% for flows with different durations (Q50, Q90, and Q95), and minimum flows as- sociated with return periods of ten and one hundred years; • Although the mean errors associated with the different reference flows were considered satisfactory for the Manhuaçu River basin, the responses for the diverse fluviometric station series showed pronounced variations. For the Mutum station series, significant errors in the appropriation of minimum and average flows were noted. For the Santo Antônio do Manhuaçu station series, relevant errors in the appropriation of only the minimum reference flows were observed. On the other hand, for the São Sebastião da En- cruzilhada and Dores do Manhumirim series, larger errors derived from maximum flow estimation. Piol, M.S. et al. 178 RBCIAMB | v.58 | n.2 | Jun 2023 | 171-181 - ISSN 2176-9478 Table 5 – Regional flow indicators for the Manhuaçu River basin considering historical series and presenting different extensions (heterogeneous series). Stations Indicators q (L/s.Km2) Rcp95 Rcp90 Rcp50 r7,10 rm r2 r100 Fazenda Vargem Alegre 16.13 0.17 0.25 0.64 0.10 1.72 6.85 2.77 São Sebastião da Encruzilhada 11.51 0.28 0.35 0.71 0.19 1.51 5.32 2.47 Assaraí Montante 12.11 0.28 0.33 0.65 0.20 1.40 7.64 3.19 Mutum 11.56 0.26 0.31 0.63 0.18 1.38 8.89 3.49 Ipanema 14.75 0.31 0.35 0.69 0.23 1.34 6.95 2.88 Dores do Manhumirim 17.73 0.26 0.31 0.67 0.19 1.39 6.19 1.86 Santo Antônio do Manhuaçu 17.16 0.31 0.35 0.69 0.23 1.34 5.64 2.53 Média 14.42 0.27 0.32 0.67 0.19 1.44 6.78 2.74 Variation coefficient (%) 19 18 12 4 23 10 18 19 q and rpc50: average flow indicators; rcp90, rcp95, r7,10, and rm: minimum flow indicators; r2 and r100: maximum flow indicators. Table 6 – Reference flows (m3.s-1) appropriated for the Manhuaçu River basin by different methodological approaches. Reference flows Fluviometric stations Fazenda Vargem Alegre São Sebastião da Encruzilhada Assaraí Montante Mutum Ipanema Dores do Manhumirim Santo Antônio do Manhuaçu Qm Regional function 15.97 99.72 41.45 17.40 20.32 6.53 31.74 Indicator–Homogeneous series 15.30 124.70 45.62 16.87 20.16 5.49 33.60 Indicator–Heterogeneous series 15.43 125.75 46.00 17.02 20.33 5.54 33.89 Q50 Regional function 10.31 66.67 27.25 11.25 13.18 4.14 20.76 Indicator–Homogeneous series 9.96 81.14 29.68 10.98 13.12 3.57 21.87 Indicator–Heterogeneous series 10.34 84.25 30.82 11.40 13.62 3.71 22.71 Q 90 Regional function 4.94 34.16 13.52 5.41 6.37 1.92 10.21 Indicator–Homogeneous series 4.85 39.49 14.45 5.34 6.39 1.74 10.64 Indicator–Heterogeneous series 4.95 40.37 14.77 5.46 6.53 1.78 10.88 Q95 Regional function 4.07 29.18 11.35 4.46 5.27 1.55 8.52 Indicator–Homogeneous series 4.07 33.17 12.13 4.49 5.36 1.46 8.94 Indicator–Heterogeneous series 4.10 33.44 12.23 4.53 5.41 1.47 9.01 Q7.10 Regional function 2.77 20.46 7.85 3.04 3.60 1.04 5.86 Indicator–Homogeneous series 2.86 23.27 8.51 3.15 3.76 1.02 6.27 Indicator–Heterogeneous series 2.90 23.64 8.65 3.20 3.82 1.04 6.37 Q2years Regional function 119.00 662.40 290.90 128.92 149.14 51.45 226.54 Indicator–Homogeneous series 112.71 918.57 336.04 124.30 148.53 40.45 247.55 Indicator–Heterogeneous series 104.69 853.18 312.11 115.45 137.96 37.57 229.93 Q100years Regional function 304.87 1,979.16 807.42 332.67 389.91 122.27 614.84 Indicator–Homogeneous series 305.56 2,490.19 910.98 336.98 402.66 109.66 671.10 Indicator–Heterogeneous series 294.60 2,400.86 878.30 324.89 388.21 105.73 647.02 Qm: average long-period flow; Q50: flow rate with permanence of 50%; Q90: flow rate with permanence of 90%; Q95: flow rate with permanence of 95%; Q7,10: minimum streamflow of seven consecutive days and ten-year return period; Q2years: maximum daily flows with return period of two years; Q100years: maximum daily flows with return period of one hundred years. Estimative of reference flows for water resources planning and control: hydrologic regional indicators application 179 RBCIAMB | v.58 | n.2 | Jun 2023 | 171-181 - ISSN 2176-9478 Table 7 – Estimated errors (%) obtained from the reference flows appropriated for the Manhuaçu River basin. Reference flows Fluviometric stations Average Error (%)Fazenda Vargem Alegre São Sebastião da Encruzilhada Assaraí Montante Mutum Ipanema Dores do Manhumirim Santo Antônio do Manhuaçu Qm Regional function 7.46 0.65 7.30 27.59 2.30 4.08 21.29 10.10 Indicator–Homogeneous series 11.35 24.24 18.09 23.75 3.06 19.32 16.68 16.64 Indicator–Heterogeneous series 10.60 25.28 19.09 24.80 2.24 18.64 15.97 16.66 Q50 Regional function 6.94 6.38 6.14 31.74 8.62 8.64 25.16 13.37 Indicator–Homogeneous series 10.14 13.94 15.62 28.60 9.04 21.21 21.18 17.10 Indicator–Heterogeneous series 6.69 18.31 20.05 33.52 5.55 18.19 18.16 17.21 Q 90 Regional function 16.41 1.82 6.65 29.48 13.41 9.40 28.52 15.10 Indicator–Homogeneous series 14.11 13.51 13.93 27.90 13.26 18.07 25.46 18.03 Indicator–Heterogeneous series 16.64 16.03 16.46 30.74 11.33 16.25 23.81 18.75 Q95 Regional function 38.75 2.70 5.47 27.88 17.21 13.16 30.96 19.45 Indicator–Homogeneous series 38.87 16.73 12.79 28.76 15.75 18.32 27.53 22.68 Indicator–Heterogeneous series 40.02 17.69 13.72 29.82 15.05 17.65 26.93 22.98 Q7.10 Regional function 63.02 8.95 1.97 20.66 24.24 19.09 36.16 24.87 Indicator–Homogeneous series 67.95 23.93 10.61 24.88 20.93 20.58 31.74 28.66 Indicator–Heterogeneous series 70.62 25.89 12.36 26.86 19.68 19.32 30.66 29.34 Q2years Regional function 0.60 23.97 1.47 6.35 3.12 22.02 0.32 8.26 Indicator–Homogeneous series 4.71 71.91 13.82 2.54 2.69 4.06 8.93 15.52 Indicator–Heterogeneous series 11.50 59.67 5.72 4.76 4.62 10.89 1.17 14.05 Q100years Regional function 7.03 44.64 16.51 22.21 7.46 45.63 1.80 20.76 Indicator–Homogeneous series 6.82 81.99 5.81 21.20 4.44 30.62 11.12 23.14 Indicator–Heterogeneous series 12.46 70.97 11.51 25.97 10.22 22.71 4.39 22.60 Qm: average long-period flow; Q50: flow rate with permanence of 50%; Q90: flow rate with permanence of 90%; Q95: flow rate with permanence of 95%; Q7,10: minimum streamflow of seven consecutive days and ten-year return period; Q2years: maximum daily flows with return period of two years; Q100years: maximum daily flows with return period of one hundred years. Conclusions The regional flow indicators established for the evaluation of dif- ferent reference flows were consistent, producing average estimation errors for the Manhuaçu River basin that varied between 14 and 30%, not exceeding the limit considered adequate for estimating flows based on hydrological regionalization studies. The regional functions established for flow appropriation, assum- ing exclusively the drainage area as an explanatory variable, were more consistent than the flow indicators, producing average errors ranging between 8 and 20%, invariably lower than those associated with the use of regional flow indicators. For the Manhuaçu River basin, the regional flow indicators es- timated from historical series with similar or different extensions did not produce relevant differences in the appropriation of the diverse reference flows, with the highest variations not exceed- ing 3%. Contribution of authors: PIOL, M. S.: Data curation; Investigation; Methodology; Software; Validation; Visualization; Writing — original draft; Writing — review & editing. REIS, J. A. T.: Conceptualization; Data curation; Investigation; Methodology; Supervision; Validation; Visualization; Writing — original draft; Writing — review & editing. RODRIGUES, M. B.: Data curation; Validation; Visualization; Writing — original draft; Writing — review & editing. MENDONÇA, A. S. F.: Validation; Visualization; Writing — original draft; Writing — review & editing. SILVA, F. G. B.: Validation; Visualization; Writing — original draft; Writing — review & editing. SILVA, A. T. Y. L.: Validation; Visualization; Writing — original draft; Writing — review & editing. Piol, M.S. et al. 180 RBCIAMB | v.58 | n.2 | Jun 2023 | 171-181 - ISSN 2176-9478 References Agência Nacional de Águas e Saneamento Básico (ANA), 2021. Consolidação do estado da arte sobre a situação e a gestão de recursos hídricos na bacia – PP03. Brasília: ANA. Althoff, D.; Ribeiro, R.B.; Rodrigues, L.N., 2021. Gauging the ungauged: Regionalization of flow indices at grid level. Journal of Hydrologic Engineering, v. 26, (4), 04021008. https://doi.org/10.1061/(ASCE)HE.1943- 5584.0002067. Amorim, J.S.; Junqueira, R.; Mantovani, V.A.; Viola, M.R.; Mello, C.R.; Bento, N.L., 2020. Streamflow regionalization for the Mortes River Basin upstream from the Funil Hydropower Plant, MG. Revista Ambiente & Água, v. 15, (3), e2495. https://doi.org/10.4136/ambi-agua.2495. Baena, L.G.N.; Silva, D.D.; Pruski, F.F.; Calijuri, M.L., 2004. Regionalização de vazões com base em modelo digital de elevação para a bacia do rio Paraíba do Sul. Engenharia Agrícola, v. 24, (3), 612-624. https://doi.org/10.1590/S0100- 69162004000300013. Bárdossy, A., 2007. Calibration of hydrological model parameters for ungauged catchments. Hydrology and Earth System Sciences Discussions, v. 11, (2), 703- 710. https://doi.org/10.5194/hess-11-703-2007. Bazzo, K.R.; Guedes, H.A.S.; Castro, A.S., Siqueira, T.M.; Teixeira-Gandra, C.F.A., 2017. Regionalização da vazão Q95: comparação de métodos para a bacia hidrográfica do Rio Taquari-Antas, RS. Revista Ambiente & Água, v. 12, (5), 855-870. https://doi.org/10.4136/ambi-agua.2032. Boscarello, L.; Ravazzani, G.; Cislaghi, A.; Mancini, M., 2016. Regionalization of flow-duration curves through catchment classification with streamflow signatures and physiographic-climate indices. Journal of Hydrologic Engineering, v. 21, (3), 05015027. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001307. Brasil. Presidência da República, 1997. Lei nº 9.433, de 8 de janeiro de 1997. Diário Oficial União. Brazilian Institute of Geography and Statistics (IBGE), 2021. Population (Accessed October 13, 2021) at:. https://www.ibge.gov.br/estatisticas/sociais/ populacao.html. Calmon, A.P.S.; Souza, J.C.; Reis, J.A.T.D.; Mendonça, A.S.F., 2016. Combined use of river water quality flow-duration curves and modeling as a tool to support class definition according to conama 357/2005 regulation. Revista Brasileira de Recursos Hídricos, v. 21, (1), 118-133. https://doi.org/10.21168/ rbrh.v21n1.p118-133. Centrais Elétricas Brasileira (Eletrobras), 1985. Metodologia para regionalização de vazões. Rio de Janeiro: Eletrobras. Dutra, W.C.P.; Fia, R.; Ribeiro, C.B.M., 2022. Water quality modeling in the Paraibuna River in Juiz de Fora/MG: diagnosis and prognosis. Brazilian Journal of Environmental Sciences, v. 57, (2), 256-267. https://doi.org/10.5327/ Z2176-94781288. Golian, S.; Murphy, C.; Meresa, H., 2021. Regionalization of hydrological models for flow estimation in ungauged catchments in Ireland. Journal of Hydrology: Regional Studies, v. 36, 100859. https://doi.org/10.1016/j. ejrh.2021.100859. Gomes, D.J.C.; Nascimento, M.M.M.; Pereira, F.M.; Dias, G.F.M.; Meireles, R.R., Souza, L.G.N.; Picanço, A.R.S.; Ribeiro, H.M.C., 2022. Flow variability in the Araguaia River Hydrographic Basin influenced by precipitation in extreme years and deforestation. Brazilian Journal of Environmental Sciences, v. 57, (3), 451-466. https://doi.org/10.5327/Z2176-94781358. Instituto Estadual de Gestão das Águas de Minas Gerais (Igam), 2019. Portaria nº 48, de 4 de outubro de 2019, CONAMA nº 357, de 17 de março de 2005. Diário Executivo, Minas Gerais. Kite, G.W., 1988. Frequency and risk analyses in hydrology. 5. ed. Highlands Ranch, Colorado: Water Resources Publications, 257 p. Lall, U.; Olds, J., 1987. A parameter estimation model for ungagged streamflows. Journal of Hydrology, v. 92, (3-4), 245-262. https://doi. org/10.1016/0022-1694(87)90016-3. Lira, F.A.; Cardoso, A.O., 2018. Estudo de tendência de vazões de rios das principais bacias hidrográficas brasileiras. Brazilian Journal of Environmental Sciences, (48), 21-37. https://doi.org/10.5327/Z2176-947820180273. Maciel, A.L.; Vieira, E.M.; Monte Mor, R.C.; Vasques, A.C., 2019. Regionalização e espacialização de vazões de permanência: estudo aplicado na bacia rio Piracicaba-MG. Revista Brasileira de Climatologia, v. 24, (1), 114- 133. https://doi.org/10.5380/abclima.v24i0.58420. Mendonça, A.S.F., 2003. Introdução – Razões para quantificação. In: Paiva, J.B.D.; Paiva, E.M.C.D. (eds.), Hidrologia aplicada à gestão de pequenas bacias hidrográficas. Porto Alegre: ABRH, p. 32. Moreira, M.C.; Silva, D.D., 2014. Análise de Métodos para Estimativa das Vazões da Bacia do Rio Paraopeba. Revista Brasileira de Recursos Hídricos, v. 19, (2), 313-324. https://doi.org/10.21168/rbrh.v19n2.p313-324 Mwakalila, S., 2003. Estimation of stream flows of ungauged catchments for river basin management. Physics and Chemistry of the Earth, v. 28, (20-27), 935-942. https://doi.org/10.1016/j.pce.2003.08.039. National Agency for Water and Basic Sanitation, 2023. Hidroweb Portal (Accessed September 19, 2022) at:. https://www.snirh.gov.br/hidroweb/. Novaes, L.F.; Pruski, F.F.; Queiroz, D.O.; Del Giudice Rodriguez, R.; Silva, D.D.; Ramos, M.M., 2007. Avaliação do desempenho de cinco metodologias de regionalização de vazões. Revista Brasileira de Recursos Hídricos, v. 12, (2), 51-61. https://doi.org/10.21168/rbrh.v12n2.p51-61. O’Gorman, P.A., 2015. Precipitation extremes under climate change. Current Climate Change Reports, v. 1, 49-59, 2015. https://doi.org/10.1007/s40641- 015-0009-3. Pessoa, F.C.L.; Blanco, C.J.C.; Martins, J.R., 2011. Regionalização de Curvas de Permanência de Vazões da Região da Calha Norte no Estado do Pará. Revista Brasileira de Recursos Hídricos, v. 16, (2), 65-74. https://doi.org/10.21168/ rbrh.v16n2.p65-74. Pinto, J.A.O., 2006. Avaliação de métodos para a regionalização de curvas de permanência de vazões para a bacia do rio das Velhas. Dissertação (Mestrado) – Curso de Saneamento, Meio Ambiente e Recursos Hídricos, Universidade Federal de Minas Gerais, Belo Horizonte, 242p. Piol, M.V.A., 2017. Análise regional de curvas de permanência e de curvas de probabilidade de vazões mínimas – Avaliação do desempenho de diferentes métodos de regionalização. Dissertação (Mestrado) – Curso de Engenharia Ambiental, Universidade Federal do Espírito Santo, Vitória, 228p. Piol, M.V.A.; Reis, J.A.T.; Mendonça, A.S.F.; Caiado, M.A.C., 2019. Performance evaluation of Flow Duration Curves regionalization methods. Revista Brasileira de Recursos Hídricos, v. 24, e9. https://doi.org/10.1590/2318- 0331.241920170202. Qamar, M. .; Ganora, D.; Claps, P.; Azmat, M.; Shahid, M.A.; Khushnood, R.A., 2018. Flow duration curve regionalization with enhanced selection of donor basins. Journal of Applied Water Engineering and Research, v. 6, (1), 70-84. https://doi.org/10.1080/23249676.2016.1196621. Razavi, T.; Coulibaly, P., 2013. Streamflow prediction in ungauged basins: review of regionalization methods. Journal of Hydrologic Engineering, v. 18, (8), 958-975. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000690. https://doi.org/10.1061/(ASCE)HE.1943-5584.0002067 https://doi.org/10.1061/(ASCE)HE.1943-5584.0002067 https://doi.org/10.4136/ambi-agua.2495 https://doi.org/10.1590/S0100-69162004000300013 https://doi.org/10.1590/S0100-69162004000300013 https://doi.org/10.5194/hess-11-703-2007 https://doi.org/10.4136/ambi-agua.2032 https://doi.org/10.1061/(ASCE)HE.1943-5584.0001307 https://www.ibge.gov.br/estatisticas/sociais/populacao.html https://www.ibge.gov.br/estatisticas/sociais/populacao.html https://doi.org/10.21168/rbrh.v21n1.p118-133 https://doi.org/10.21168/rbrh.v21n1.p118-133 https://doi.org/10.5327/Z2176-94781288 https://doi.org/10.5327/Z2176-94781288 https://doi.org/10.1016/j.ejrh.2021.100859 https://doi.org/10.1016/j.ejrh.2021.100859 https://doi.org/10.5327/Z2176-94781358 https://doi.org/10.1016/0022-1694(87)90016-3 https://doi.org/10.1016/0022-1694(87)90016-3 https://doi.org/10.5327/Z2176-947820180273 https://doi.org/10.5380/abclima.v24i0.58420 https://doi.org/10.21168/rbrh.v19n2.p313-324 https://doi.org/10.1016/j.pce.2003.08.039 https://www.snirh.gov.br/hidroweb/ https://doi.org/10.21168/rbrh.v12n2.p51-61 https://doi.org/10.1007/s40641-015-0009-3 https://doi.org/10.1007/s40641-015-0009-3 https://doi.org/10.21168/rbrh.v16n2.p65-74 https://doi.org/10.21168/rbrh.v16n2.p65-74 https://doi.org/10.1590/2318-0331.241920170202 https://doi.org/10.1590/2318-0331.241920170202 https://doi.org/10.1080/23249676.2016.1196621 https://doi.org/10.1061/(ASCE)HE.1943-5584.0000690 Estimative of reference flows for water resources planning and control: hydrologic regional indicators application 181 RBCIAMB | v.58 | n.2 | Jun 2023 | 171-181 - ISSN 2176-9478 Reis, J.A.T.; Guimarães, M.A.; Barreto Neto, A.A.; Bringhenti, J., 2008. Indicadores Regionais Aplicáveis à Avaliação do regime de vazão dos cursos d’água da bacia hidrográfica do rio Itabapoana. Geociências, v. 27, (4), 509-516. Rodrigues, M.B.; Reis, J.A.T.D.; Sá, G.D.L.N.; Almeida, K.N.; Mendonça, A.S.F., 2022. Perspectivas para revisão do enquadramento da bacia hidrográfica do Rio Benevente pelo emprego de curva de permanência e modelagem da qualidade da água. Engenharia Sanitária e Ambiental, v. 27, (4), 831-843. https://doi.org/10.1590/S1413-415220210295. Silva, L.S.; Ferraz, L.L.; Sousa, L.F.; Silva Santos, C.A.; Rocha, F.A., 2022. Trend in hydrological series and land use changes in a tropical basin at Northeast Brazil. Brazilian Journal of Environmental Sciences, v. 57, (1), 137-147. https:// doi.org/10.5327/Z2176-94781097. Silva, R.S.; Blanco, C.J.C.; Pessoa, F.C.L., 2019. Alternative for the regionalization of flow duration curves. Journal of Applied Water Engineering and Research, v. 7, (3), 198-206. https://doi.org/10.1080/23249676.2019.1611493. Silva Junior, O.B.D.; Bueno, E.D.O.; Tucci, C.E.M.; Castro, N.M.D.R., 2003. Extrapolação espacial na regionalização da vazão Revista Brasileira de Recursos Hídricos, v. 8, (1), 21-37. Singh, N.M.; Devi, T.T., 2022. Regionalization methods in ungauged catchments for flow prediction: review and its recent developments. Arabian Journal of Geosciences, v. 15, (11), 1019. https://doi.org/10.1007/s12517-022- 10287-z. Swain, J.B.; Patra, K.C., 2017. Streamflow estimation in ungauged catchments using regionalization techniques. Journal of Hydrology, v. 554, 420-433. https://doi.org/10.1016/j.jhydrol.2017.08.054. Tabari, H., 2020. Climate change impact on flood and extreme precipitation increases with water availability. Scientific Reports, v. 10, (1), 13768. https:// doi.org/10.1038/s41598-020-70816-2. Tucci, C.; Silveira, A.; Sanchez, J.; Albuquerque, F., 1995. Flow regionalization in the upper Paraguay basin, Brazil. Hydrological Sciences Journal, v. 40, (4), 485-497. https://doi.org/10.1080/02626669509491434. Tucci, C.E.M., 2002. Regionalização de Vazões. Porto Alegre: ABRH/UFRGS, 256 p. Tucci, C.E.M.; Clark, R.T.; Collischonn, W.; Dias, P.L.S.; Oliveira, G.S., 2003. Long-term flow forecasts based on climate and hydrologic modeling: Uruguay River basin. Water Resources Research, v. 39, (7), SWC3-1. https://doi. org/10.1029/2003WR002074. Wolff, W.; Duarte, S. N.; Mingoti, R., 2014. Nova metodologia de regionalização de vazões, estudo de caso para o Estado de São Paulo. Revista Brasileira de Recursos Hídricos, v. 19, (4), 21-33. https://doi.org/10.21168/ rbrh.v19n4.p21-33. https://doi.org/10.1590/S1413-415220210295 https://doi.org/10.5327/Z2176-94781097 https://doi.org/10.5327/Z2176-94781097 https://doi.org/10.1080/23249676.2019.1611493 https://doi.org/10.1007/s12517-022-10287-z https://doi.org/10.1007/s12517-022-10287-z https://doi.org/10.1016/j.jhydrol.2017.08.054 https://doi.org/10.1038/s41598-020-70816-2 https://doi.org/10.1038/s41598-020-70816-2 https://doi.org/10.1080/02626669509491434 https://doi.org/10.1029/2003WR002074 https://doi.org/10.1029/2003WR002074 https://doi.org/10.21168/rbrh.v19n4.p21-33 https://doi.org/10.21168/rbrh.v19n4.p21-33