Comparison of methods for estimating reservoir sedimentation

Comparação de métodos de estimativa de assoreamento de reservatórios

ABSTRACT

In the face of climate change, water scarcity, and changes in land use, efficient management of energy generation is essential to ensure national energy security. In the context of Joint Resolution ANA/ANEEL n° 127/2022, this study aimed to compare four methods for estimating reservoir sedimentation: comparison of Depth-Area-Volume curves (DAV), sedimentometric analysis, use of computer programs with simplified methods, and comparison of cross-sections, with DAV method as the reference. The results showed that all methods indicated a reduction in reservoir volume due to sedimentation, however the cross-section method presented closest values to the reference method.

Keywords:
Depth-Area-Volume curve (DAV); Topobathymetric survey; Hydrosedimentometric data; Cross-sections; Simplified models

RESUMO

Diante das mudanças climáticas, escassez hídrica e alterações no uso do solo, uma gestão eficiente da geração de energia é essencial para garantir a segurança energética nacional. No contexto da Resolução Conjunta ANA/ANEEL nº 127/2022, esse estudo teve como objetivo comparar quatro métodos de estimativa de assoreamento em reservatórios: comparação de curvas cota-área-volume (CAV), análise sedimentométrica, uso de programas computacionais que reproduzem modelos simplificados, e comparação de seções transversais, sendo o método da CAV adotado como referência. Os resultados mostraram que todos os métodos indicaram redução no volume do reservatório devido ao assoreamento, entretanto, o método das seções transversais apresentou resultados mais próximos do método de referência.

Palavras-chave:
Curva Cota-Área-Volume (CAV); Levantamento topobatimétrico; Dados hidrossedimentométricos; Seções transversais; Modelos simplificados

INTRODUCTION

Currently, Brazil faces significant challenges arising from water shortage, aggravated by climate change, whether due to rainfall variability, prolonged droughts or rising global temperatures. This scenario is a growing concern, given that these factors have directly impacted both water supply and energy generation (Camargo, 2019), given that the Brazilian electricity matrix is largely dependent on hydraulic sources. Therefore, water resource management is crucial for national energy security, since 60% of the electricity consumed in Brazil is generated by hydroelectric power plants (HPP) (Empresa de Pesquisa Energética, 2023).

Another factor that can threaten the efficiency of hydroelectric power generation is reservoir sedimentation (also called siltation), a natural process due to the low current velocities caused by the impoundment (Carvalho, 1994). Furthermore, this is intensified by human activities (Teixeira & Soares-Filho, 2009), such as changes in land use (Lipski et al, 2023; Fagundes et al., 2023). Some of the main causes of erosion and sediment transport to water bodies are inadequate soil management, deforestation and intensive agriculture (Das et al., 2022; Carvalho et al., 2004), as they directly affect the sedimentary dynamics of the basin (Rabelo & Araújo, 2019). Although sediment retention in reservoirs has a beneficial effect by promoting water cleaning by reducing the concentration of sediment in the water, these sediments accumulate in the reservoirs, reducing their storage capacity (whether in the volume useful for storing water or regulating flows) and, consequently, energy generation, which demands monitoring and mitigation actions (Carvalho, 1994).

Estimating siltation provides valuable information for planning, corrective and preventive actions, ensuring the longevity of HPP and the security of the country's energy supply. It can generally be performed using different approaches, generally categorized as mathematical methods or empirical methods. The first of these uses computational models to predict the transport and sediment distribution in the reservoir, assisting in forecasting future conditions. However, these models require calibration and input information from monitoring with empirical methods, which correspond to the direct collection of data in the field. Measurements of suspended and bottom sediment concentration, granulometric analyses, and topobathymetric surveys (Cordeiro, 2023; Barbosa, 2019; Garrido Neto et al., 2018) are examples of this approach, as well as the use of sediment traps (Monteiro Zanona et al., 2024; Ono, 2020; Suplicy & Mannich, 2020) and remote sensing use (Yao et al., 2023; Alves and Santos et al., 2024; Condé et al., 2019). Among the empirical methods, the one that produces the most accurate result is the topobathymetric survey, which is also the most expensive method.

In this context, the ANA (Brazilian Water and Sanitation Agency)/ANEEL (Brazilian National Agency for Electric Energy) Joint Resolution nº 127/2022 (Brasil, 2022) (which replaced the former Joint Resolution ANA/ANEEL nº 03/2010) (Brasil, 2010) is an essential regulatory measure for the integrated management of water resources, as it establishes guidelines for both sedimentometric control at monitoring stations and for topobathymetric surveys to update the depth-area-volume (DAV) curves for reservoirs with generation greater than 1000 kW (ANA, ANEEL; 2022). However, although the resolution has been updated, some complementary documents were still being prepared at the time this study was prepared, such as the Guidelines for Preparing the Project and Report on Updating the DAV Tables (Agência Nacional de Águas e Saneamento Básico, 2024).

Considering only hydrosedimentometric data to estimate siltation simplifies geomorphological and hydrodynamic processes, despite using information with a monthly or quarterly measurement frequency. An alternative is to use a simplified mathematical model. Nevertheless, topobathymetric surveys provide more accurate results, but they are only performed every 10 years due to current regulations (Joint Resolution ANA/ANEEL n° 03/2010) and are expensive to implement. Thus, the implementation of control cross-sections can be an alternative to estimate siltation in reservoirs, in terms of costs and frequency. In view of this, this article aims to perform a comparative analysis of siltation in a HPP reservoir with four different methods: from the comparison of two DAV curves; from the simulation of computer programs with simplified methods; from sedimentometric data and from the cross-section’s comparison. This comparison aims to verify the performance of alternative methods to topobathymetric surveying due to the costs added to this monitoring technique, as well as the measurement frequency standardized by Joint Resolution ANA/ANEEL nº 03/2010.

MATERIALS AND METHODS

The study area is the main reservoir of the Belo Monte HPP complex, the Pimental HPP reservoir. This study is part of a research project (Research and Development Project - R&D ANEEL 07427-0423/2023), executed by Lactec and financed by the concessionaire that manages and operates the Belo Monte HPP, Norte Energia SA, related to the development of a “Decision-making system for updating the depth-area-volume curve in reservoirs”.

Study area and data

Located on the Xingu River, in the Volta Grande do Xingu region, in southwestern Pará, Brazil, the Belo Monte HPP complex comprises two run-of-river generation facilities, the main one being the Belo Monte HPP (11,000 MW) and another complementary one, the Pimental HPP (233 MW), corresponding to two reservoirs, one of which is the intermediate reservoir (119 km²) and the main reservoir (359 km²), respectively – the latter is the focus of this work – which are interconnected by a diversion channel (20 km) as illustrated in Figure 1. These hydroelectric projects began operating in January 2016 (Norte Energia, 2024).

Figure 1
Location of the study area with the main fluviometric stations used in the study (upstream: 18821000 (UHE Belo Monte Montante), downstream Pimental HPP: 18865003 (UHE Belo Monte Mangueiras), downstream Belo Monte HPP: 18935000 (UHE Belo Monte Jusante) and tributary: 18867900 (UHE Belo Monte Foz Do Bacajá)).

The hydrosedimentometric database used in the analyses was provided by Norte Energia SA, which provided data on water level elevation, discharge, rating curve, cross-sectional profiles, concentration of suspended sediment, among others, for stations located on the Xingu River and tributaries in the region. Four stations were selected for analysis due to their strategic locations, three of which were on the Xingu River: station 18821000 (UHE Belo Monte Montante), located upstream of the complex; station 18865003 (UHE Belo Monte Mangueiras), located downstream of the Pimental HPP; station 18935000 (UHE Belo Monte Jusante), located downstream of the Belo Monte HPP; and station 18867900 (UHE Belo Monte Foz do Bacajá), located on a tributary of the Xingu River (Rio Bacajá), downstream of the Pimental HPP, as illustrated in Figure 1.

In addition, two DAV curves were also provided by Norte Energia, the first of which was resulting from a survey before reservoir filling, in the consolidated basic project of the HPP (2011) and the second of which was resulting from a survey after the start of operation (2018) (Ruraltech, 2019).

Method 1: Depth-area-volume curve comparison

The reservoir sedimentation through two DAV curves was made by comparing the volume measurements associated with the Maximum Normal level (97.0 m) and the lowest level (65.0 m) coinciding between the two DAV curves. It is important to highlight that the period used to siltation estimative is from 2016 to 2018 (owing to the fact that Xingu River was dam in 2015) and not between the DAV measurement dates (2011 to 2018).

The first curve was prepared through a survey in 2011, in which technical cartography, bathymetry and geodesy activities were carried out to meet the requirements of ANA Resolution nº 48/2011, which granted Norte Energia SA authorization to use water resources for the construction of the Belo Monte HPP complex. Thus, the survey corresponds to the phase prior to the filling of the reservoir (2016) and consists of 13 sections with a regular spacing of 1.5 km between each one. Additionally, between the 13th section and the planned location for the dam, sections were carried out with a distance of 30 meters between them.

For the second DAV curve, dated 2018, bathymetric surveys were conducted after the reservoir impoundment and the reservoir filled (Ruraltech, 2019). However, the distance between the sections was, on average, 350 meters across the entire length of the reservoir, so that the 2018 DAV curve was generated from much more cross-sections, compared to the 2011 DAV curve.

In both surveys, DGPS (Differential Global Positioning System) systems were used for positioning and single-beam echo sounders for depth measurements, as well as an aerial survey to characterize the dry area of ​​the topobathymetric sections. In total, numerous processes were carried out during the surveys, such as remeasurement and implementation of landmarks, survey of cross-sections, bathymetric survey, determination of the waterline and its changes and mapping of dry areas with laser profiling were included.

Although no information was found about the specific equipment used during the 2011 survey, it is important to note that considering the 7-year interval between the 2011 and 2018 surveys, there were significant updates to the versions and accuracies of the devices used in 2011. For the bathymetric survey, echo sounders were used single-beam, in conjunction with GNSS RTK, allowing the processing of coordinates in real time, with an accuracy of less than 10 cm. These receivers were integrated with the DGPS system, which allowed greater precision of the coordinates at the support points. This technology was essential for collecting accurate data on the bed of the water body. RTK ensured an accurate determination of the position during the survey, being vital for applications in aquatic environments.

In both periods, the Geodetic Vertex Network landmarks were remeasured using precision geodetic GNSS, in the static method, which served as control for all subsequent surveys. In 2018, laser mapping covered the entire reservoir area with an approximate accuracy of 15 cm and was carried out to support topobathymetry and restitution activities, highlighting the generation of surface and terrain models, which were integrated with the bathymetry to prepare the DAV curve. The waterline, which comprises the region between the dam and the end of the reservoir, was determined with dual-frequency GNSS receivers, which ensured the accuracy of the coordinates obtained. These receivers were integrated with DGPS systems, allowing precise coordinates at the support points. However, factors such as errors in the ionosphere, troposphere and satellite orbits impacted positioning accuracy, limiting the distance between the base station and the mobile receiver to a few kilometers.

After the surveys, the DAV curve was obtained from the volume calculation using a Digital Terrain Model (DTM) generated in the ArcGIS software, specifically through the Surface Volume tool, using a reference elevation (operating elevation) and the respective slicing from this elevation.

Therefore, the results obtained through this method were used as reference to evaluate other methods, since it is a widely used method (Morris & Fan, 1998; Schleiss et al., 2016).

Method 2: Sedimentometric analysis

The analysis began by verifying the temporal availability of hydrosedimentometric data, which, in general, occurred between 2011 and 2023, for the four monitoring stations: 18821000 (UHE Belo Monte Montante), 18865003 (UHE Belo Monte Mangueiras), 18935000 (UHE Belo Monte Jusante) and 18867900 (UHE Belo Monte Foz do Bacajá) (Figure 1). In terms of discharge data, it is worth noting that, for station 18935000 (UHE Belo Monte Jusante), it was necessary to use the rating curve combined with the historical level series to estimate the historical discharge series, as well as filling gaps in the discharge series through linear interpolation. Although the analyses were concentrated in the period 2016 to 2018, it was decided to use the largest amount of data available for compose the analysis of the solid discharge curve.

In addition to the fluviometric data, sedimentometric data were also evaluated, which consisted of data on the suspended sediment concentration, as well as measurements of water level elevation, discharge, wetted area, width and average velocity in the aforementioned cross-sections. This set of data allowed the calculation of the total solid discharge using the simplified method of Colby (1957). Briefly, this method uses abacuses to relate the aforementioned variables to two parcels of total solid discharge: measured solid discharge (suspended) and unmeasured solid discharge, the latter parcel corresponding to bedload transport, is determined from the average velocity, average depth, measured concentration and width of the section.

Using data on total solid discharge and simultaneous flow measurements, a solid discharge rating curve was established for each station through a potential curve adjustment (Equation 1), where: Q_ST = Total solid discharge (t/d); Q_Líq = Liquid discharge (m³/s); a and b = coefficients of the equation.

$Q_{ST}=a.Q_{Líq}{}^b$ (1)

For each station, based on the equation of the established total solid discharge curves, the historical flow series monitored in the period from 2012 to 2022 were used to determine a historical series of solid discharge, since this is the common period of data from all stations. The solid discharge values were evaluated in total terms per year and accumulated daily.

Through cumulative analysis, the calculation of the deposited volume was performed through a mass balance calculation where the amount deposited in the reservoir is M_reservoir = M_donwstream – M_upstream, where M_reservoir is the deposited mass, M_upstream the cumulative mass that entered through the reservoir (dam), represented by sum of station 18821000 discharge with the incremental area mass between the dam and station 18821000 (calculated by drainage area proportion) and; M_donwstream the cumulative mass that exited through the downstream section, represented by station 18865003. Colby method was also applied for the downstream section since structures of Pimental dam are close to the bottom of the reservoir, allowing bedload transport to occur downstream of it.

Finally, the difference in mass between the stations was converted to volume based on the soil's apparent specific gravity. Since there is no fluviometric or sedimentometric station at the inlet of the diversion channel, this balance will not consider this outlet. The data period evaluated here begins in 2016, since this is the year in which the operation of the water treatment plants begins and ends in 2018. However, as in the simplified model method, since data are available until 2022, the analyses were extended until that year in order to estimate a future extrapolation for this method, even if there is no DAV curve in 2022 for comparison.

Diversion channel

As presented in the study area, Pimental reservoir has another outflow represented by the diversion channel, which takes the flow to the Belo Monte HPP. This outflow is not monitored in relation to sediment, so it is not possible to close the mass balance. However, given the importance of that outflow, diversion channel suspended sediment concentration data were extract by remote sensing techniques with Sentinel-2 imagery (level 2A) (unpublished results) and used to close the mass balance. This was made considering the outlet mass as a sum between the mass diversion channel and the station 18865003. In this way, both the method results are going to be present.

Method 3: Computer programs with simplified methods (Sediment and Dposit)

The reservoir sedimentation estimate using computer programs with simplified methods was performed using the Borland & Miller (1958) method, which allows the calculation of sediment distribution along the reservoir bed, resulting in new area and new volume values (Carvalho, 1994). This method was applied using two computer programs with simplified methods:

1. Sediment (Braga, 2005a): calculates the silted volumes throughout the dam's operational life. This method uses the methodologies of: Lara & Pemberton (1963) to determine the apparent specific weight of the sediment deposited in the reservoir; of Borland & Miller (1958) to evaluate silting and uses the curves of Brune (1953) or Churchill (1948) to determine the efficiency of sediment retention in the reservoir.

2. Dposit (Braga, 2005b): simulates the distribution of deposited sediment volumes calculated by Sediment along the reservoir using the methodology of Borland & Miller (1958).

The Sediment model (Figure 2) requires as input data information about the reservoir characteristics: type of reservoir operation (Type I – Sediment always or almost always submerged); reservoir water volume at the maximum Normal WL (2272 hm³ at the 97.0m elevation); and the deposited volume at the beginning of the analysis (year zero, i.e., 2015), considered as zero in this analysis. In addition, it was also necessary to inform liquid and solid discharge data, granulometric data, solid transport increase rate and selection of the calculation mode.

Figure 2
Sediment model interface.

The liquid discharge and solid discharge inputs were estimated using data from station 18821000 add to the incremental contribution, according to the sedimentometric method (item 2.3). The average annual liquid discharge values into the reservoir were calculated using the average daily flow rates, in m³/s, from 01/01/2011 to 12/31/2022, which corresponds to 7380 m³/s. The average annual solid discharge values inserted come from the calculation of the sum of values within each year, from 2011 to 2022, and subsequent average of the accumulated values for each year (5,308,328 t/year). Although the analyses were carried out within the period from 2016 to 2018, it was decided to use the largest amount of data available to compose the calculations of the input variables, to obtain a better representation.

For the granulometry data, it is necessary to insert data that includes both the suspended load and bedload transport fractions. The characteristic percentages of suspended and bedload sediment estimated in the Basic Consolidated Project of the Belo Monte HPP complex (Intertechne, 2011) were used, which indicate that 40% of the total sediment is transported as bedload and 60% is suspended, which resulted in the final granulometric composition of 24% clay, 32% silt and 44% sand. This data was used due to a partial absence of necessary data at station 18821000.

Regarding the rate of increase in solid transport in the basin, the value of 2% per year was used, based on studies by Carvalho et al. (2004) and the calculation option selected was the use of the average Brune curve to calculate the reservoir's sediment retention efficiency (Er).

Using this data, the Sediment model calculates the silted volumes for each simulated year, as well as values of apparent specific weight, retention efficiency, among others. Since data availability is up to 2022, the analyses were extended to that year in order to estimate a future extrapolation for this method, even if there is no DAV curve in 2022 for comparison. Therefore, 7 years were simulated (year 0 = 2015, year 1 = 2016, ..., year 3 = 2018, ..., year 7 = 2022). These Sediment output data are entered as input in Dposit, together with a DAV curve (DAV calculated in 2011). As a result of this model, new DAV curves were obtained for each of the simulated years.

Method 4: Cross-section comparison

The estimate of reservoir sedimentation through cross-sections was made by comparing the topobathymetric profiles of 13 sections surveyed during the preparation of the 2011 and 2018 DAV, with the purpose of investigating the accumulation of material contained in the riverbed over this period. The database for analysis was constructed using values of coordinates and elevations of two surveys, as well as the analysis of the influence of the reservoir backwater water level in each section (Intertechne, 2012). Once again, like in the DAV curve comparison method, it is important to highlight that the period used to siltation estimative is from 2016 to 2018.

Because the sections of the different DAV curves were surveyed close together but did not coincide, the 2018 elevation values were obtained by intersecting coordinates of the 2011 bathymetry points with the surface generated by the 2018 bathymetry. It should be noted that in 2011, the topographic measurement (dry areas) of section 13 was not carried out, but in 2018, with the reservoir already full, the measurement carried out was complete (topographic and bathymetric). Due to this difference between them, the coincident section between these two were limited to only the 2011 wet area (bathymetric). Although the current official system is SIRGAS 2000, all coordinates were referenced to the SAD-69 planimetric datum, with the central meridian at 51°W (time zone 22), and to the vertical datum of Imbituba-SC. The original system was maintained to avoid inaccuracies resulting from data reprojection (Brasil, 2015).

After this step, the following procedure was performed in each of the 13 sections evaluated. In order to determine the wet area, the cross-section was restricted on the Z axis from the lowest value to the backwater level, with points outside this range (dry region of the cross section) being disregarded, since there can be no deposition there. The analyses were performed considering backwater levels associated with three flow scenarios: MLT (long-term discharge), TR = 5 years and TR = 10 years. The differences between the levels of the 2011 and 2018 surveys were calculated at each common point in the section. All the median differences in the section were calculated, which allowed them to be classified as silted or eroded.

In order to quantify the volume of silting or erosion in the whole reservoir, it was necessary to group all the data from all sections into a single database. Thus, the median differences and the median elevation of the 2011 were calculated, with the latter value being associated with an area from 2011 DAV curve. Thereby, the volume was obtained by multiplying the median of the differences by area associated with the median of the 2011 elevation.

RESULTS AND DISCUSSION

Method 1: Depth-area-volume curves comparison

Regarding the graphical comparison between the DAV curves for the years 2011 and 2018, in general, a similarity between curves is noted. However, above the 90.0 m, it is noted that for the same mark, the corresponding volume is smaller in the 2018 curve compared to that of 2011 (Figure 3).

Figure 3
Comparison between the 2011 and 2018 DAV curves.

This pattern was corroborated when examining the reservoir's operational levels in Table 1, where it is shown that the difference between the two surveys resulted in approximately 250 hm³, which corresponds to 11% of the previous total volume.

Table 1
Difference between total reservoir volumes with the 2011 and 2018 DAV curves.

Common Water Level (m)		Reservoir Volume (hm3)						Difference Between Total Volumes
Max.	Min.	Curve 2011			Curve 2018
		Max.	Min.	Total	Max.	Min.	Total	(hm3)	(%)
										97.0	65.0	2271.5	0.0	2271.5	2022.1	0.3	2021.8	-249.7	-11.0

Barbosa (2019) also evaluated the comparison between two DAV curves (2010 and 2018) for the Lobo reservoir in São Paulo, and obtained a volume loss of 0.4% considering the volume comparison. In this study, the 2010 topobathymetric survey was carried out with a very high level of detail, with sections spaced every 10 m, and the 2018 survey with sections spaced according to the guidelines of the ANA/ANNEL Joint Resolution nº3 of 2010, which resulted in sections every 100 m (given the characteristics of the reservoir). The author emphasizes that more spatially detailed bathymetries can quantify siltation more accurately. However, for the reservoir under study, this spacing should be around 160 m, approximately 10 times smaller than that used in the survey, considering the area (359 km²) and the length of the reservoir (80 km).

Method 2: Sedimentometric analysis

Once the discharge series for station 18935000 was determined using the rating curve and the water level elevation series, as well as filling in gaps by interpolation, the four stations analyzed showed annual seasonal variations (Figure 4), with emphasis on the year 2016, which presented the lowest flow values recorded – a year that coincides with the start of operation of the hydroelectric projects. Conversely, the year 2014 recorded the highest peaks. It is also noteworthy that the discharge magnitude in the Xingu River is 20 times on average greater than the discharge observed in the Bacajá River.

Figure 4
Upstream and downstream fluviograms of HPP Pimental, downstream of HPP Belo Monte and in a tributary downstream of HPP Pimental (Stations 1821000, 18865003, 18935000 and 18867900).

From the available series of suspended sediment concentration, as well as the corresponding measurements of water level elevation, liquid discharge, wet area, width and average velocity, the total solid discharge was calculated using the Colby method (1957). Using these new series and the respective flow measurements, a sediment rating curve was adjusted through a potential curve adjustment for each station (Table 2). From the determined equations and the historical discharge series, the historical series of total solid discharge were calculated for the four stations (Figure 5). The incremental mass between the dam and station 18821000 calculated by drainage area proportion represented only about 2.6% of the station 18821000.

Table 2
Sediment rating curve coefficients equation for stations 18821000, 18865003, 18935000 and 18867900.

Station	Coefficient a	Coefficient b	R2	Data amount
18821000	0.180946	1.2535	0.8212	130
18865003	0.019441	1.4997	0.9126	136
18935000	0.002656	1.6861	0.8904	136
18867900	0.766267	1.2272	0.9275	128

Figure 5
Historical series of solid discharge upstream and downstream of the Pimental HPP, downstream of the Belo Monte HPP and in a tributary downstream of the Pimental HPP (Stations 1821000, 18865003, 18935000 and 18867900).

The annual accumulations were calculated for each station from the solid discharge historical series, as illustrated in Figure 6. From 2012 onwards, when all four stations had daily data throughout the entire year, it is possible to see the proportion between the solid discharge values between the stations of the Xingu River, as drainage area between the stations increases, so that this pattern persists until 2015.

Figure 6
Historical series of annual accumulated solid discharge upstream and downstream of the Pimental HPP, downstream of the Belo Monte HPP and in a tributary downstream of the Pimental HPP (Stations 1821000, 18865003, 18935000 and 18867900).

In addition to presenting the lowest values at all stations, in 2016 there was also an inversion between stations 18821000 and 18865003, where the station upstream (18821000) presented higher accumulations compared to the station downstream of the Pimental HPP dam (18865003). This behavior continued until 2022 and may indicate sediment retention in the main reservoir. Furthermore, during the period from 2017 to 2022, it is graphically observed that accumulations at stations 18935000 and 18867900 returned close to the levels observed in previous years (2012 to 2015). This fact shows that the station located on the Bacajá River (18867900) is not influenced by the reservoir. However, for station 18935000, located on the Xingu River approximately 30 km from the Belo Monte HPP outflow, this behavior may be linked to a region where sedimentometric equilibrium has returned. However, this statement is only speculative, since the lack of sedimentometric monitoring in the diversion channel and in the Belo Monte HPP reservoir makes it impossible to confirm this fact.

Solid discharge series of each station was daily accumulated considering only the period in which the reservoir was already implemented, that is, from 2016 onwards, reservoir sedimentation estimates were calculated by the difference in accumulated volume between stations 18865003 and 18821000 (Figure 7). For this, from accumulated solid discharge series of stations 18821000 and 18865003, the difference between them was calculated. Next, the values corresponding to December 31 of each year were selected a mass loss of 3.49 Mt was obtained at the end of 2018. When extrapolating to the entire reservoir (359 km) and considering the 3 years evaluated (1095 days), this value translates into a sedimentation rate of 8.8 g/m²/d, higher than that obtained with sediment traps by Monteiro Zanona and collaborators (2024) for the Passaúna water supply reservoir under the influence of a floating photovoltaic system (6 g/m²/d). Using the average value of apparent specific weight of the soil obtained in Sediment model (1181 kg/m³), the accumulated solid discharge was converted to accumulated volume (Table 3), resulting in 3.01 hm³ of sediment deposited at the end of 2018. Analogous to the previous analysis, this deposited sediment volume represents 0.1% of the total reservoir volume. When extrapolating this analysis until 2022, in total, 14.7 hm³ of sediment was deposited in the reservoir, equivalent to 0.6% of the total volume.

Figure 7
Comparison of the historical series of accumulated solid discharge (2016-2022) upstream and downstream of HPP Pimental, downstream of HPP Belo Monte and in a tributary downstream of HPP Pimental (Stations 1821000, 18865003, 18935000 and 18867900).

Table 3
Estimated volume of accumulated sediment from 2016 to 2022 at Pimental HPP.

Date	Cumulative daily solid discharge (106 t/d)			Accumulated volume in the year (hm3)
	Input 1	Output 2	Output - Input
12/31/2016	2.29	1.70	-0.59	-0.50
12/31/2017	7.46	5.96	-1.50	-1.27
12/31/2018	12.50	8.94	-3.56	-3.01
12/31/2019	17.27	10.87	-6.40	-5.42
12/31/2020	22.79	13.31	-9.48	-8.02
12/31/2021	27.75	14.71	-13.03	-11.03
12/31/2022	34.82	17.42	-17.40	-14.73

• ¹
  Station 18821000 plus incremental contribution.
• ²
  Station 18865003.

Carvalho and collaborators (2004) carried out an analysis of the lifetime of the reservoir prior to its filling and already pointed out the need to increase the measurements of total solid discharge and sediment control, as well as the implementation of forest preservation programs in the catchment. Other studies pointed to the use of remote sensing as an alternative to conventional monitoring, as it allows estimating regional variations and even interdecadal variations (Yao et al., 2023).

Regarding the result obtained by the sedimentometric method, the lack of monitoring in both the Belo Monte HPP reservoir and the diversion channel is understood as an uncertainty inherent to the method, making it impossible to estimate the amount of sediment that leaves the Main reservoir through the diversion channel, how much sediments is in the Intermediate reservoir, and how much is returned to the Xingu River by the outflow from the Belo Monte HPP.

Likewise, when considering the estimate of sediment transported by the diversion channel as part of the sediment output from the reservoir (Table 4), the volume of sediment silted into the reservoir is smaller, as in 2018 it was obtained about half of what was previously observed (without considering this portion in the mass balance).

Table 4
Estimated volume of accumulated sediment from 2016 to 2022 at Pimental HPP.

Date	Cumulative daily solid discharge (106 t/d)			Accumulated volume in the year (hm3)
	Input 1	Output 2	Output - Input
12/31/2016	2.29	1.90	-0.38	-0.32
12/31/2017	7.46	6.80	-0.66	-0.56
12/31/2018	12.50	10.89	-1.61	-1.36
12/31/2019	17.27	14.39	-2.88	-2.43
12/31/2020	22.79	18.61	-4.18	-3.54
12/31/2021	27.75	21.98	-5.76	-4.88
12/31/2022	34.82	27.08	-7.74	-6.55

• ¹
  Station 18821000 plus incremental contribution.
• ²
  Station 18865003 plus diversion channel with remote sensing estimate.

Method 3: Computer programs with simplified methods (Sediment and Dposit)

From the simulation of the Sediment model, for each year, values were obtained for deposited solid volume, effluent solid volume, retention efficiency, specific weight and influent and effluent solid discharges (Table 5).

Table 5
Sediment model simulation results.

Year	Solid volume deposited (hm3)	Effluent solid volume (hm3)	Retention Efficiency (%)	Apparent range (kg/m3)	Solid Q Influent (t/year) x 103	Q solid Effluent (t/year) x 103	Deposited solid volume/Total reservoir volume
2016	2.14	5.20	45.13	1.142	5414	2971	0.001
2017	4.24	7.76	45.11	1.164	5523	3032	0.002
2018	6.35	10.36	45.08	1.177	5633	3094	0.003
2019	8.48	12.99	45.06	1.186	5746	3157	0.004
2020	10.64	15.66	45.04	1.194	5861	3221	0.005
2021	12.83	18.37	45.02	1.200	5978	3287	0.006
2022	15.04	21.12	45.00	1.206	6098	3354	0.007

The retention efficiency was always around 45%, which means that a little less than half of the sediment was retained in the reservoir, corroborated by the values obtained for influent and effluent solid discharge. Regarding the apparent specific weight of the soil, this parameter was calculated based on Lara & Pemberton (1963) and an average value of 1181 kg/m³ was obtained, 45% lower than the theoretical value of specific soil mass of 2650 kg/m³ (Fageria, Stone, 2006). It is important to highlight that a specific weight value is expected to be lower than the theoretical value of the particle (2650 kg/m³), since during the silting process some compaction factors such as variation in granulometry, presence of organic matter, presence of water and air between the particles may affect the value of the apparent specific weight. Therefore, in the apparent specific weight of the sediment, water density was subtracted.

It can be observed that there was an average increase of 2 hm³ each year in the solid volume deposited, resulting in 6.35 hm³ of sediment deposited in the reservoir until 2018. This represents a loss of 0.28% of the total volume (2272 hm³). When extrapolating this analysis until 2022, a total of 15 hm³ of sediment was deposited in the reservoir, equivalent to 0.7% of the total volume.

By inserting information from the 2011 DAV curve into the Dposit model, the model automatically classified the reservoir as Type I - Flatland Reservoir, which is consistent with the geomorphological characteristics of the reservoir, given the other available options: Type II - Reservoir in flood zones or hills; Type III - Reservoir in mountainous regions; or Type IV - Reservoir in deep gorges. Combining this information with the data on the total volume deposited by Sediment (Table 5), the Dposit model generated a new DAV curve for each simulated year.

Similar to the comparison analysis between DAV curves presented previously, based on the new DAV curve simulated by Dposit for the year 2018, in terms of total volume the reservoir lost approximately 6.35 hm³ (value obtained in Sediment). Analogous to the previous method, this value corresponds to 0.3% of the total volume. Extrapolating the analysis to the year 2022, 15 hm³ was obtained, practically the same value as the sedimentometric model for that year (14.73 hm³).

Previous studies carried out at the Belo Monte HPP generation complex also used this model to estimate the lifetime of the reservoir (Intertechne; Engevix; PCE; 2011), in which the sedimented volume was 1.8 hm³ and 8.8 hm³ for the first and fifth years of simulation, respectively. By interpolating these values for the third year of simulation (2018), resulting in 5.32 hm³, approximately 15% lower than that obtained in the present study. This proportion was also obtained by extrapolating the analysis to 2022 (12.33 hm³ by previous study) compared to the 145 hm³ obtained in the present study.

These differences could be linked to the average annual solid and liquid discharge values entered as input data, which is a function of the data period used. Since the data used in the previous study refers to the period 1987 to 1989, and those used in this study are from 2012 to 2022, an increase in the amount of sediment present in the Xingu River can be estimated, which may be due to changes in land use in the catchment, as assessed with data from MapBiomas (Figure 8) and results obtained in other studies (Lipski et al., 2023; Fagundes et al., 2023). Lipski and collaborators (2023) found trends of increased anthropic use in the Xingu River basin, with use for agriculture being the main cause of changes in the basin.

Figure 8
Variation in land use in the Xingu River basin between 1985 and 2020 by MapBiomas.

For validation purposes, the DAV curve simulated by Dposit model for the year 2018 was compared with the DAV curve from the topobathymetric surveys carried out in the field. It was observed that both volumes (useful and total) of the 2018 DAV generated by Dposit simulation are greater than the DAV generated by the topobathymetric surveys (Table 6), that is, the curve generated by Dposit model is overestimated by 243 hm³ for the total volume.

Table 6
Difference between total reservoir volumes with the 2018 DAV curves and the curve resulting from the Dposit model simulation for the year 2018.

Common Water Level (m)		Reservoir Volume (hm3)						Difference Between Total Volumes
Max.	Min.	Curve 2018 - Survey			Curve 2018 - Deposit
		Max.	Min.	Total	Max.	Min.	Total	(hm3)	(%)
										97.0	65.0	2022.1	0.3	2021.8	2265.0	0.0	2265.0	243.2	12.0

Although these values are similar to the comparisons made between both DAV curves collected in loco (2011 and 2018), it is an indication of the uncertainty that Dposit model is subject to, considering the quality of the DAV curve inserted as input data (2011 DAV curve).

Method 4: Cross-section comparison

By defining the wet areas of the sections from the backwater level, the differences between elevations of the 2011 and 2018 surveys were calculated for each common point in a section. Figure 9 shows the statistical variation of the results for all sections, considering MLT discharge. It was possible to see that in all sections there was a degree of erosion and sedimentation, since the differences varied mainly between -5 and 5 m. It is worth noting the smaller variation of the values in section 7, compared to the other sections, which can be explained by the region being shallower and presenting rocky bed material of the Xingu River.

Figure 9
Topobathymetric differences between 2018 and 2011 at each point in each section considering the MLT flow.

In section 9, the high number of outliers stands out, which was also corroborated by the difficulty of navigation due to the presence of exposed tree trunks in the region which were not removed during the filling of the reservoir), which caused differences in the surveys. However, in general, there was a higher degree of sedimentation in all sections, with the exception of section 13, which presented a majority of null values, and a high number of positive outliers. This fact may be associated with the absence of the dry region (topographic survey) in 2011. Table 7 shows the medians of the differences between the water elevation, for all the flows evaluated (MLT, TR = 5 years and TR = 10 years), as well as the classification of sedimentation or erosion

Table 7
Median of the difference between the elevations of the cross-sections in common between the DAV curves and the classification of sediment dynamics by cross section.

Flow / Section	MLT		TR = 5 years		TR = 10 years
	Difference (m)	Classif.	Difference (m)	Classif.	Difference (m)	Classif.
01	0.09	S	0.08	S	0.08	S
02	0.95	S	0.23	S	0.23	S
03	0.85	S	0.72	S	0.71	S
04	0.62	S	0.27	S	0.26	S
05	0.51	S	0.40	S	0.39	S
06	0.15	S	0.18	S	0.18	S
07	0.00	S	0.00	S	0.00	S
08	0.31	S	0.31	S	0.31	S
09	0.37	S	0.37	S	0.37	S
10	0.38	S	0.38	S	0.38	S
11	0.31	S	0.30	S	0.30	S
12	0.32	S	0.32	S	0.32	S
13	0.00	E	0.00	E	0.00	E
Median	0.25	-	0.18	-	0.18	-

• Note: S – Sedimentation; E – Erosion.

Similarly, Figure 10 shows the spatial variation of the differences between the elevations for the 2011 and 2018 surveys. In general, the regions that suffered erosion correspond to areas that are higher in relation to the main channel, whether they are composed of rocky material (sections 2, 7 and 8) or relative to the margins of the section (sections 3 and 6). In contrast, sedimentation occurred in lower regions.

Figure 10
Differences between the cross-sectional elevations for each point in common between the 2011 and 2018 DAV curves.

Similarly, Garrido Neto and collaborators (2018) verified the sedimentary dynamics through cross-sections, in which it was observed that, in general, the region most upstream of the dam remained practically unchanged, the region immediately before the dam was where there was the greatest amount of sedimentation, while the region downstream of the dam suffered from erosion. In this study, it was observed that, in general, all sections upstream the dam suffered from sedimentation. This behavior was also observed in studies in the Passaúna reservoir (Ono, 2020), in which, when using sediment traps, it was found that the spatial variation of the sedimentation rate occurs at higher rates (5.8 cm/year) and gradually decreases to downstream reservoir (0.01 cm/year).

To quantify the volume of sedimentation in the entire reservoir, the differences in the water elevation of all sections were grouped and the median was calculated. In the same way, the median of all water elevation in 2011 was also calculated, and this value was associated with an area from the 2011 DAV curve. Thus, the volume was obtained by multiplying the median of the differences by the area associated with the median of the 2011 water elevation (Table 8). When performing this procedure for the three flow scenarios (MLT, TR = 5 years and TR = 10 years), it was noted that as the flow increased, the water level elevation of the backwater increased, which in turn increased the evaluated cross-section. Therefore, as the area of the evaluated section increased, the region of margins, which are areas susceptible to erosion, also increased. Thus, in the occurrence of higher discharges, there is more erosion due to the water reaching the margin regions. At the same time, higher speeds are reached, favoring the transport of sediments, that is, reducing the sedimented volume.

Table 8
Median of the difference between the cross-section elevations, median of the DAV 2011 elevation, area and volume of silted sediment throughout the reservoir.

Flow rate	Difference (m)	Elevation (m)	DAV Area (km2)	Silted sediment
				Volume (hm3)	Mass (106 t)
TLM	0.25	91.54	197.90	49.28	58.21
TR: 5 years	0.18	92.53	222.02	40.85	48.26
TR: 10 years	0.18	92.17	213.51	39.07	46.16

Considering the analysis with the MLT flow rate as a basis, a sedimentation volume of 49.28 hm³ was estimated, which indicates a loss of 2.2% in relation to the total volume.

Methods comparison

A common point in all analyses was the indication of a decrease in the reservoir volume (Table 9). For comparison purposes, the results were presented in terms of volume, mass and deposited sediment thickness. Thus, volumes were converted into mass using the apparent specific weight from the computer programs with simplified methods (1181 kg/m³) and vice versa, in the same way that the thicknesses of sediment deposited were calculated considering the volume of the same area used in the section comparison method (197.40 km²). A siltation rate per year it also was calculated in terms of volume, mass and sediment thickness, as illustrated in Table 10. In this same table, the proportion of the siltation obtained in each method in relation to the reference method (DAV curves comparison method) also can be observed. This value is the same, regardless of whether the value is expressed in volume, mass or sediment thickness due to the conversion is calculated from constant values.

Table 9
Comparison between values of sedimented volume in the reservoir in the period 2016 and 2018 between different methods and relation to the reservoir volume.

Method	Siltation		Method volume / total reservoir volume ratio (%)
	Volume (hm3)	Mass (106 t)
DAV	-249.73	-295.01	-10.99
Sedimentometric	-3.01	-3.56	-0.13
Sedimentometric + RS1	-1.36	-1.61	-0.06
Sediment / Dposit	-6.35	-7.50	-0.28
Cross Sections	-49.28	-58.21	-2.17

• ¹
  Remote Sensing techniques.

Table 10
Comparison between values of silted volume in the reservoir in the period 2016 and 2018 between different methods in relation to the methods applied.

Method	Mass per year (106 t/year)	Volume per year (hm3/ year)	Thickness per year (cm/ year)	Relation to the DAV method (%)
DAV	-98.34	-83.24	-42.06	NA
Sedimentometric	-1.19	-1.00	-0.51	1.21
Sedimentometric + RS1	-0.54	-0.45	-0.23	0.55
Sediment / Dposit	-2.50	-2.12	-1.07	2.54
Cross Sections	-19.40	-16.43	-8.30	19.73

• Note: NA – Not applicable.
• ¹
  Remote Sensing techniques.

The DAV curves comparing method was the one that presented the greatest siltation, approximately 295 Mt over the entire period, and around 83 Mt, 98 hm³, 42 cm per year each. In addition to sediment retention, this difference may be related to the lower resolution of the 2011 DAV curve, that may have smoothed or omitted important topographic variations, which may result in inaccurate estimates when comparing areas and volumes. These accumulated errors can lead to under - or overestimations of volume, affecting the accuracy of analyses that use this curve as input data.

The sedimented mass of 3.56 Mt obtained for the year 2018 by the sedimentometric method was the lowest among the methods evaluated, being 1.19 Mt, 1.00 hm³, 0.51 cm per year, each. This result may be biased by the limitation of the representation of the study area due to the absence of sedimentometric monitoring in the diversion channel for the intermediate reservoir, since the analysis was based on the principle of mass balance and conservation. Even though, the diversion of sediment into the intermediate reservoir would decrease the sedimented volume even more. With the estimate of solid discharge from the diversion channel extracted by satellite image, 1.61 Mt was obtained at the end of 2018, being 0.54 Mt, 0.45 hm³ and 0.23 cm per year, each, that is, about half of what was observed without considering this portion. Even so, this method represented only 1.21% and 0.55% of what was observed with the DAV curves comparing method.

With the simplified Sediment model, the sedimentation obtained resulted in a total value of 7.50 Mt for the third year of analysis (2018), being 2.50 Mt, 2.12 hm³, 1 cm per year, each. This result is equivalent to 2.5% of the value obtained when comparing the DAV curves (Table 10). This method uses part of the same sedimentometric data used in the sedimentometric method but includes granulometry analyses. A major advantage of using Sediment was obtaining information such as the apparent specific weight of the deposited sediment and the reservoir retention efficiency, in addition to the sediment volume itself. As with the CAV comparison method, the use of Dposit corroborated higher volume, impacting the analysis precision of that use this curve as input data.

The total sediment input to the reservoir is monitored in station 18821000 plus the incremental area, and the greatest possible siltation would occur if all the input is deposited entirely (about 10.6 hm³ or 12.5 Mt, considering 2016-2018). In this scenario, the average sediment inflow is 3,53 hm³/year in volume and 4,17 Mt/year in mass. Based on these values, the sediment retention efficiency was calculated for each method, using the annual volumes (Table 10). As in Table 11, the methods based on the DAV and cross-sections comparison indicated values greater than 100% retention, which suggests a greater sedimentation than the total amount of sediment available. This can be attributed to possible underestimations by station 18821000 monitoring (this may be an indication of the gap in carrying out punctual monitoring, with the absence of rain events that end up not representing the largest sediment transport), overestimations or errors in the measurements of the methods (DAV and cross-sections) or to the unmonitored contribution such as bank erosion. The methods that indicated values lower than 100% may reflect the predominance of finer sediments, which escape the system due to low granulometry, combined with high flow rates that hinder the sedimentation process.

Table 11
Retention efficiency obtained from the methods used.

Method	Volume per year (hm3/ year)	Retention efficiency (%)
Total Sediment Input	3.53	NA
DAV	-83.24	-2361
Sedimentometric	-1.00	-28
Sedimentométrico + SR	-0.45	-13
Sediment / Dposit	-2.12	-60
Cross Sections	-16.43	-466

• Note: NA – Not applicable.

Finally, the method of comparison between cross-sections showed a total sedimentation of 58,21 Mt, which is 19.40 Mt, 16.4 hm³, 8 cm per year, each. This value is approximately 20% of that obtained with the comparison between DAV curves, which are generated from these cross-sections.

To compare different methods, siltation estimates ended up being obtained in different ways, each one presenting some advantage. Therefore, it is recommended to evaluate data in three forms: i) volume scales – as they allow a comparison with the reservoir volume. providing specific information with respect to the study site; ii) mass scales – as it is the unit commonly used in physical or empirical methods of erosion and sedimentation, for example, serving as input data for models; and iii) length scales (i.e. sediment thickness) – as it allows a comparison with low complexity methods that can be carried out in the field, such as core measurements, making it possible to map the entire reservoir. In this context it is also recommended to carry out field measurements with sediment traps – an inexpensive and easy-to-use equipment (Suplicy & Mannich, 2020) which provides an estimate of sedimentation rates in mass scales (Monteiro Zanona et al., 2024) and sediment thickness (Ono, 2020) – with the same frequency as cross-section monitoring, in order to evaluate the interaction between both monitoring methods.

Another advantage of obtaining siltation results for sediment thickness is that they can be used as a parameter to be considered in determining the frequency of need for new topobathymetric surveys. If the sedimentation rate obtained is lower than the precision of the equipment used in the topobathymetric measurements, there would be no need to update the DAV curve in that period and the opposite is also true.

With the analyses applied in this study it was possible to observe that the use of monitored information in accordance with what is provided for in the Joint Resolution ANA/ANEEL nº 03/2010 can be satisfactorily complemented with other measurements such as control cross sections and measurements with sediment traps, to obtain intermediate data about siltation in reservoirs while DAV curve is not updated.

CONCLUSIONS

This paper was prepared considering the discussion about changing Joint Resolution ANA/ANEEL n° 127/2022, in which a proposal is to monitor control cross-sections to define if DAV curve must be updated. Therefore, in this paper, it was compared the sedimentation results with the DAV curve and the cross-sections (considering they are control sections) and also compare with sediment data analysis.

The comparative analysis showed, although all the methods indicated sedimentation, each one with its own particularities and limitations, that the cross-section method presented closest results to the reference method (comparison between two DAV curves). Thus, the methods that used hydrosedimentometric data and the computer programs with simplified methods, despite presenting similar results, had a lower performance than the comparison between cross-sections. Therefore, we suggest that the cross-section method to be used to monitor siltation in reservoirs, allowing higher resolution monitoring (for example every 1 or 2 years), as an intermediate method in comparison to the topobathymetric surveys that we suggest to be carried out every 10 years, as long as the cross-section method indicates significant siltation.

The comparison between two DAV curves was the one that resulted in the largest sedimentation. However, it is worth noting that 2011 DAV curve was prepared based on 13 cross sections only, equivalent to 10% of that recommended by Joint Resolution ANA/ANEEL nº 03/2010, which may have contributed to smoothing or omitting important topographic variations, resulting in inaccurate estimates of areas and volumes. Therefore, we suggest that in this case a new topobathymetric survey should be carried out in the future with resolution and equipment similar to those used in the 2018 DAV curve, to eliminate these uncertainties.

Regarding the hydrosedimentometric method, its main limitation was the impossibility of closing the mass balance with measured data. With this in mind, it we suggest to implement new hydrosedimentometric stations in the region of the diversion channel and in the intermediate reservoir, as well as to carry out future analyses using hydrodynamic and sediment transport modeling to complement the data of the hydrosedimentometric monitoring in the diversion channel. To minimize the impact of not using sediment data from the diversion channel, unpublished results from suspended sediment obtained by satellite images were used to close the mass balance. A comparison showed 45% difference in results, including data from the diversion channel. Therefore, it is suggested to evaluate the use of other techniques in addition to conventional monitoring carried out by stations, such as the use of satellite images to obtain the concentration of suspended sediments where measured data is not available.

Another limitation of the sedimentometric method is the lack of measurements in flow peaks, which are important for sediment transport and reservoir sedimentation. A recommendation of this study is to evaluate if these events are contemplated in the measurements used.

ACKNOWLEDGEMENTS

Project funded by Norte Energia SA. within the scope of the Research. Development and Innovation Program - PROPDI of ANEEL. “Decision-making system for updating the depth-area-volume curve in reservoirs” (PD-07427-0423/2023). Tobias Bleninger acknowledges the support of the productivity grant from the National Research Council. CNPq. process: 313491/2023-2. notice: nº 09/2023.

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Edited by

• Editor-in-Chief:
  Adilson Pinheiro

• Associated Editor:
  Iran Eduardo Lima Neto

Publication Dates

• Publication in this collection
  16 June 2025
• Date of issue
  2025

History

• Received
  20 Dec 2024
• Reviewed
  31 Mar 2025
• Accepted
  29 Apr 2025