# Sediment Transport Modeling for Run-of-River Hydropower in the Madeira River: Calibration with Conventional and Remote Sensing Data

Leonardo Zandonadi Moura, Jean-Michel Martinez, William Santini, Sergio Koide, Henrique Roig, Diego R.A. E Santos, Alexandre Kepler Soares

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Leonardo Zandonadi Moura, Jean-Michel Martinez, William Santini, Sergio Koide, Henrique Roig, et al. Sediment Transport Modeling for Run-of-River Hydropower in the Madeira River: Calibration with Conventional and Remote Sensing Data. International Journal of Sediment Research, 2025, 10.1016/j.ijsrc.2025.07.002. hal-05193588

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Sediment Transport Modeling for Run-of-River Hydropower in the Madeira River: Calibration with Conventional and Remote Sensing Data

Leonardo Zandonadi Moura, Jean-Michel Martinez, William Santini, Sergio Koide, Henrique Roig, Diego R.A. e Santos, Alexandre Kepler Soares

PII: S1001-6279(25)00068-X

DOI: https://doi.org/10.1016/j.ijsrc.2025.07.002

Reference: IJSRC 656

To appear in: *International Journal of Sediment Research*

Received Date: 8 November 2024

Revised Date: 26 June 2025

Accepted Date: 7 July 2025

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Please cite this article as: Zandonadi Moura L., Martinez J.-M., Santini W., Koide S., Roig H., e Santos D.R.A. & Kepler Soares A., Sediment Transport Modeling for Run-of-River Hydropower in the Madeira River: Calibration with Conventional and Remote Sensing Data, *International Journal of Sediment Research*, https://doi.org/10.1016/j.ijsrc.2025.07.002.

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© 2025 International Research and Training Centre on Erosion and Sedimentation. Publishing services by Elsevier B.V. on behalf of KeAi Communications Co. Ltd.
# Sediment transport modeling for run-of-river hydropower in the Madeira River: Calibration with conventional and remote sensing data

Leonardo Zandonadi Moura<sup>a,*</sup>, Jean-Michel Martinez<sup>b,c,d</sup>, William Santini<sup>d</sup>, Sergio Koide<sup>a</sup>, Henrique Roig<sup>a,b</sup>, Diego R. A. e Santos<sup>b</sup>, Alexandre Kepler Soares<sup>a</sup>

<footnote><sup>a</sup> PTARH/UnB – Graduate Program in Environmental Technology and Water Resources, University of Brasília. Address: Programa de Pós-Graduação em Tecnologia Ambiental e Recursos Hídricos, Anexo SG-12, Térreo, Campus Universitário Darcy Ribeiro Universidade de Brasília, CEP: 70.910-900 Brasília-DF, Brazil</footnote>

<footnote><sup>b</sup> University of Brasília, Institute of Geosciences, Graduate Program in Applied Geosciences and Geodynamics, Geoprocessing Laboratory (GeoLab), Address: Universidade de Brasília, Campus Darcy Ribeiro, Instituto Central de Ciências - ICC Centro, CEP: 70.910-900 Brasília, DF, Brazil</footnote>

<footnote><sup>c</sup> Géosciences Environnement Toulouse (GET), UMR5563, Institut de Recherche pour le Développement (IRD)/Centre National de la Recherche Scientifique (CNRS)/Université Toulouse 3, 14 Avenue Edouard Belin, 31400 Toulouse, France</footnote>

<footnote><sup>d</sup> Institut de Recherche pour le Développement, Laboratoire GET (IRD, Centre National de la Recherche Scientifique, Université de Toulouse, Centre National d'Études Spatiales), Toulouse, France</footnote>

<footnote>* Corresponding author:</footnote>

<footnote>E-mail address: lzmoura@unb.br, lzmoura.unb@gmail.com (L. Moura)</footnote>
1 Sediment Transport Modeling for Run-

of-River Hydropower in the Madeira

3 River: Calibration with Conventional

and Remote Sensing Data

5 Abstract

6 This study aims to evaluate sediment transport processes in the Madeira River, a high-load
7 Amazon tributary altered by the Jirau run-of-river hydropower dam. A methodology for
8 sensitivity analysis and calibration of the HEC-RAS one-dimensional morphodynamic model is
9 developed. It integrates multiple model to measured comparisons, including conventional
10 monitoring and water color remote sensing data. The study underscores the value of employing
11 products derived from satellite imagery, refining model differentiation and improving the spatial
12 and temporal resolution of sediment transport predictions. A simple, regionally significant
13 method of estimating depth-integrated concentrations form surface index concentrations is
14 discussed, showing that for high concentrations a 1.10-2 multiplicative factor suffices. Sensitivity
15 analysis highlights the dominant influence of sand content in the upstream sediment load and the
16 necessity of using the Krone-Partheniades transport formula to simulate fine sediment retention.
17 The calibrated model estimates a sediment retention efficiency of 21.3% in the backwater-affected
18 reach over a five-year period, with over 90% of the sand fraction being deposited. Results suggest
19 that the wash load threshold for this system is medium to coarse silts and clay-silt flocs larger
20 than 0.016 mm. These are the key size classes to understand deposition of fines. Flocculation
processes may play a role, requiring adjustments in the input sediment load grain size distribution.

A multivariate sediment rating curve, incorporating tributary discharge dynamics, enhances model performance, particularly in reproducing seasonal concentration variations in the backwater reach. These findings provide insights into the best practices for sediment modeling in high-load rivers impacted by hydropower and highlight the importance of multi-objective calibration approaches.

Keywords

Amazon sediment; Madeira River; run-of-river hydropower; morphodynamic modeling; multi-objective calibration; remote sensing;

1. Introduction

The Andean tributaries of the Amazon River carry significant sediment loads, that are key to the morphology and ecological function of riverine and floodplain environments downstream (Constantine et al., 2014; Latrubesse et al., 2017; Vauchel et al., 2017). Construction of dams in Amazon River tributaries brings many concerns about the consequent social and environmental impacts of sediment retention (Best, 2019; Flecker et al., 2022; Nittrouer et al., 2021). The Madeira River sub-basin is the most endangered (Latrubesse et al., 2017), being the main tributary in terms of sediment load, accounting for about 50%. Two large run-of-the river dams were completed in its course around 2013. Sediment retention and possible restriction of supply to downstream environments will change ecosystems and the important – 600 million to 1.1 billion tons of sediment per year (Ayes Rivera et al., 2019; Latrubesse et al., 2017) – Amazon delivery to its delta and the ocean. However, the exploitation of hydropower potential is important for the development of the nations that compose the Amazon basin

When forecasting or monitoring the impacts of the installation of infrastructure in a river or estuary, morphodynamic models are important tools (Brand et al., 2021; Creech et al., 2018, 2021; Miodrag Spasojevic & Forrest M. Holly, Jr, 2008; William A. Thomas & Howard Chang, 2008). They provide a means to interpolate in time and space the information from environmental
47 monitoring, and constitute a synthesis tool, to provide explanatory insights into operating mechanisms behind observed trends and patterns (Launay et al., 2019; Ma et al., 2020; B. Zhang et al., 2021).
48
49

50 Important sources of uncertainty affect the modeling of sediment transport processes, such as the
51 effects of flocculation (Lamb et al., 2020; Santini et al., 2019), the transport regime and resistance
52 characteristics of fine sediment deposits (Brand et al., 2021; Chen et al., 2021; Ma et al., 2020)
53 and grain size distribution shifts with flow (S. A. Gibson & Cai, 2017). Wide ranges of resistance
54 parameters for cohesive sediments have been reported in the scientific and gray literature (Brand
55 et al., 2021; Langland & Koerkle, 2014; Travis A. Dahl et al., 2018). Grain size distribution has
56 been reported as an uncertain and sensitive input factor (Beckers et al., 2018; S. Gibson et al.,
57 2017; Launay et al., 2019). Methods are varied among modeling studies of reservoir
58 sedimentation (S. Gibson & Crain, 2019; Habib-ur-Rehman et al., 2018; Hussain & Shahab, 2020;
59 Omer et al., 2015; B. Zhang et al., 2021). Literature on numerical sediment transport simulation
60 for run-of-the river hydropower backwater affected reaches is scarce (Anderson et al., 2015).

61 Additionally, satellite remote sensing (RS) has become an established tool for monitoring of
62 inland waters, and the retrieval of suspended particulate matter (SPM) concentration has been
63 demonstrated by experimental (Villar et al., 2013) and theoretical (Pinet et al., 2017) approaches.
64 It is possible to obtain robust models to estimate SPM by employing as input band ratio
65 formulations (Martinez et al., 2015), usually with red and infrared wavelengths. This has been
66 successfully used to map sediment retention processes in reservoirs (Alves e Santos et al., 2024;
67 Condé et al., 2019; Moragoda et al., 2023). Innovatively, water color RS is employed here as a
68 source of model calibration information alongside in-situ monitoring data.

69 There is an open debate about protocols or procedures to calibrate a morphodynamic model
70 (Beckers et al., 2020), especially by employing multiple calibration metrics. For instance, they
71 rarely match, at the same time, observations of morphology of mobile bed environments and the
72 rate of sediment transport (Baar et al., 2019). When it comes to the use of remote sensing
73 information in modelling, studies are also few (Fagundes et al., 2019; P. Zhang et al., 2014).
74 Regulating agencies have established impact assessment and monitoring requirements (RHA
75 Engenharia e Consultoria & Jirau Energia, 2022; Santo Antônio Energia & PCE Projetos e
76 Consultorias de Engenharia Ltda, 2015) for the construction of the Madeira River hydroelectric
77 complex, and the protocols for usage of data that is available for modelling studies are a vast
78 research field. Negreiros et al. (2022) present the challenge of developing model calibration
79 metrics using bathymetric data. Pixel-by-pixel comparisons may fail to differentiate the
80 performance of a random, unrepresentative model from morphodynamic models, which are
81 physically-based.

82 This study aims to develop and test a method for evaluating a morphodynamic model against
83 multiple calibration targets, including metrics derived from RS estimates of suspended particulate
84 matter (SPM). The Jirau run-of-river hydropower affected reach of the Madeira River serves as a
85 case study for assessment of sediment transport impacts. Focus is given to uncertainties in grain
86 size distribution of inflowing sediment, transport capacity formulas and parameters governing
87 shear resistance. Key research questions include: Which of these input factors most influence
88 model? What defines the wash load threshold for this system? How can diverse monitoring data
89 sources be integrated into a unified model evaluation metric?

90 Next, a Regional Setting description will be presented, then Materials and Methods section with
91 four subsections. The first three describe the data processing, and the last details 1D HEC-RAS
92 model settings and calibration objective function. A synthesis of monitoring data is presented in
93 Results and Discussion, as well as the model reproduction. Finally, the Conclusion summarizes
94 findings and suggests further work.

## 2. Regional Setting

95 The Madeira River basin represents 1,380,000 km² (about 23% of the whole Amazon basin, or
96 29% of the basin up to Óbidos - Li et al., 2020), contributing, on an annual basis, an average
97 discharge of 26,500 m³ s⁻¹ and sediment load of 430*10⁶ t (Creech et al., 2021; Vauchel et al.,
98 2017), which makes it the largest Amazon tributary in sediment and the second or third in water.
99 Almost 95% of its sediment load is supplied by the Andean basin (Aalto et al., 2006; Baby et al.,
100
2009), with larger erosion rates observed in the Eastern Cordillera and its immediately adjacent subandean belt (Kober et al., 2015).

It can be classified as an anabranching megariver (Latrubesse, 2008), where the bed, margins and floodplain are over layers of Holocene alluvium. Resistant units of granite, mud clasts and conglomerates, dated from the Pleistocene, confine the lateral extent of morphological activity. Where the channel reaches the edges of confining units, distinct geological controls in its planform and profile pattern manifest (S. Gibson et al., 2019), forming deep pools (13 to 30 m) every 50-60 km (40 channel widths).

The two headwaters that form the Madeira River are the Beni (280k km², 21% of the Madeira Basin) and Mamoré (612k km², 45% of the Madeira Basin) Rivers. They drain two foreland basins with contrasting geomorphological and climatological characteristics. The Beni basin (41% of its area in the Andes, 43% Amazon plains) is the first conveyor of suspended sediment to the Madeira River, with $346 *10^6$ t yr$^{-1}$, while the Mamoré only delivers $62 *10^6$ t yr$^{-1}$ (Vauchel et al., 2017).

The Mamoré Andean basin receives less precipitation - down to 1,000 mm/year in the southernmost part - than the Beni, which occupies a northern position, where average annual precipitation is 2200 mm (Espinoza et al., 2019; Molina-Carpio et al., 2017), with hotspots in the eastward side of the Andes of up to 6,000 mm. The Beni River also has steeper slopes over its course, giving it more transport capacity down to the Madeira forming confluence (Santini, 2020; Vauchel et al., 2017).

Two large run-of-river hydroelectric plants, the Madeira Hydroelectric Complex (MHC), were constructed in the middle stretch of the river circa 2013. In total the installed electric capacity is of nearly 7,000 Mw (~11% of Brazil's capacity when built). Jirau is the upstream one and Santo Antônio follows. Concerns about their impact on sediment transport motivated technical and scientific studies that present mixed conclusions. In terms of infrastructure, besides the MHC, the river downstream is an important waterway for the transport of agricultural commodities (Creech et al., 2021).
A 30% reduction of fine sediment concentration at the river surface was found downstream of the MHC, at Porto Velho (Ayes Rivera et al., 2019). That study detected 36% reduction in fine sediment concentration at the river surface for the Beni River (at Cachuela Esperanza gauge, unaffected by the MHC), possibly linked (Ayes Rivera et al., 2019, 2021) to a reduction in October to December precipitation in the Madre de Dios sub-basin (1981-2017 period). However, another study (Espinoza et al., 2019) has detected significant increases in precipitation from December to February, in the northern part of the Madeira basin and no trend for September to November (1982-2017 period).

## 3. Materials and Methods

This section is organized into four subsections. Section 3.1 presents the available data, including a database of concurrent measurements of liquid and solid discharge. Section 3.2 describes the procedures used to derive weekly time series and construct a sediment budget from this database. Section 3.3 outlines the techniques employed to process satellite remote sensing data for estimating sediment concentrations. Finally, Section 3.4 details how these various data sources are integrated into a model calibration metric, along with the heuristic used for calibration.

### 3.1. Conventional hydrological and sedimentological data

Table 1 presents the 11 cross-sections where some or all of river discharge, water level, sediment discharge and grain size distribution hydro-sedimentological data are collected. They are displayed in Figure 1. A division between upstream and downstream cross-section groups is used throughout this work for sediment data. The upstream cross-section group is more than 100 km upstream of the Jirau dam, comprising Abunã, Jusante Rio Beni, Tamborete and Pederneiras. The downstream group is composed of Porto R4, Bananal and Palmeiral and is less than 50 km away from the dam.

Table 1 – Cross-sections where hydro-sedimentological measurements are carried out. The Code column is filled for those that have discharge and water level data (6 sites, 5 within the study area or close to it). Others have an asterisk signaling that daily water level is available, but
153 not discharge (9 cross-sections, 8 within or close). Next to the code, the parenthesis informs if

154 site sediment data was used. The Time Span column is for hydrological information.

<table><thead><tr><th>Cross-Section Name</th><th>River</th><th>Coordinates – River Station</th><th>Time Span</th><th>Code (Sediment Yes/No)</th><th>Agency/ Observatory</th></tr></thead><tbody><tr><td>UHE Jirau - Porto R4</td><td>Madeira</td><td>09°14'40" S / 64°37'24" W - -3.2 km</td><td>2014-2020</td><td>15340600 (Y)</td><td>ANA</td></tr><tr><td>UHE Jirau Barramento</td><td>Madeira</td><td>09°16'60" S / 64°39'14" W - 0 km</td><td>2014-2020</td><td>15340500 (N)</td><td>ANA</td></tr><tr><td>Bananal</td><td>Madeira</td><td>9,283°S / 64,653°W - 4,4 km</td><td>2015-2020</td><td>- (Y)</td><td>IBAMA</td></tr><tr><td>Palmeiral – RJ 3</td><td>Madeira</td><td>09°31'51" S / 64°49'17" W - 47.1 km</td><td>2015-2020</td><td>*</td><td>IBAMA</td></tr><tr><td>Mutum – RJ 4</td><td>Madeira</td><td>09°35'25" S / 64°56'51" W - 63.9 km</td><td>2014-2020</td><td>*</td><td>IBAMA</td></tr><tr><td>Tamborete – RJ 5</td><td>Madeira</td><td>09°31'37" S / 65°19'26" W - 112.9 km</td><td>2015-2020</td><td>*</td><td>IBAMA</td></tr><tr><td>Pederneiras</td><td>Madeira</td><td>9,645°S / 65,447°W - 131,7 km</td><td>2016-2020</td><td>- (Y)</td><td>IBAMA</td></tr><tr><td>Abunã</td><td>Madeira</td><td>09°42'18" S / 65°21'56" W - 144.4 km</td><td>1976-2021</td><td>15320002 (Y)</td><td>ANA</td></tr><tr><td>UHE Jirau Jusante Rio Beni</td><td>Madeira</td><td>10°21'25" S / 65°21'41" W - 212 km</td><td>2014-2020</td><td>15318000 (Y)</td><td>ANA</td></tr><tr><td>Cachuela Esperanza</td><td>Beni</td><td>10°32'14" S / 65°35'5" W - NA</td><td>1983-2021</td><td>CachEsperanz (Y)</td><td>HYBAM</td></tr><tr><td>UHE Jirau Guajará-Mirim</td><td>Mamoré</td><td>10°47'35,16" S / 65°20'52,08" W - NA</td><td>2014-2020</td><td>15250001 (N)</td><td>IBAMA</td></tr></tbody></table>

155

156
<figure><img src="image_4.png" /></figure>

157

158 Figure 1 – Madeira River basin with (a) main tributary rivers, sub-basins and reach of interest.

159 (b) location map in Amazon basin and South America. (c) sediment and bathymetry monitoring
160 and model cross-sections.

161 Daily river discharge is estimated by means of rating curves and daily water level readings. A
162 dataset containing 321 *in situ* measurements of sediment discharge and concentration was used.

163 It covers the time span between 2009 and 2020, where the period from June/2015 to
164 November/2020 is the most data-rich and post dam construction, therefore chosen for this study.

165 Before that, only Abunã (Mar/2009 to Oct/2013) and Jusante Rio Beni (Jan/2013 onwards) are
166 available. Three sites were monitored with a monthly frequency (Jusante Rio Beni, Abunã and
167 Porto R4), while others (Bananal, Palmeiral, Mutum, Tamborete and Pederneiras) only have
168 measurements in February, May, August and November.

169 Most measurements are accompanied by suspended load grain size distributions, which are
170 relevant for the input boundary conditions, since morphodynamic models estimate transport,
erosion and deposition by grain size class. Bed grain size distribution is an important initial condition, and possible validation information. The sediment grain size distributions for the suspended load and bed gradations are displayed on Supplementary Information S1 and S2. They come from field campaigns and are organized for before and after the Jirau dam was constructed.

## 3.2. Rating curve and sediment budget analysis

The relation between liquid and solid discharge was described in this work by means of empirical power law functions (rating curves). They were fitted for locations in the Jirau hydroelectric dam backwater reach and the Madeira River to the total load data, as well as specifically for the sand grain size range.

A univariate rating curve relates the liquid discharge to sediment discharge at the monitoring site. Multivariate (composite) curves were also employed in the present work, inspired on previous works (K. Ahn et al., 2017; K. Ahn & Steinschneider, 2019; K.-H. Ahn & Steinschneider, 2018).

The sediment discharge becomes a function of discharges of two tributaries ($Q_{líq1}$ = Beni river discharge at Cachuela Esperanza, $Q_{líq2}$ = Mamoré discharge at Guajará Mirim). Another combination is the main river along with one tributary ($Q_{líq1}$ = Beni river discharge, $Q_{líq2}$ = Madeira river discharge minus Beni discharge). The Madeira River discharge is measured either at Jusante Rio Beni or Abunã stations, downstream of its forming confluence. Multiple combinations were used in the model adjustment tests.

Rating curve functions with a power law form such as Eqs. (1) and (2) were employed. Eq. (1) is the standard form of a univariate rating curve, which would represent the physical process of sediment transport. Meanwhile, Eq. (2) does not necessarily have a direct physical explanation, even though the tributaries do interact through backwater processes. However, Eq. (2) brings the convenience of being linear with respect to the different log discharges when log-transformed. This form was employed in previous works (with covariates such as month or rate of discharge variation - Ahn and Steinschneider, 2018). Standard linear regression tools were then employed with these log linearized forms: the HEC-RAS rating curve analysis and the R programming
language, function lm – Fitting Linear Models, (Ihaka et al., 2023). The second option also provides confidence intervals and goodness of fit measures.

$$QS_{sed} = \alpha Q_{líq}^{\beta} \qquad \log QS_{sed} = \log \alpha + \beta \log Q_{líq} \quad (1)$$

$$QS_{sed} = \alpha Q_{líq1}^{\beta1} Q_{líq2}^{\beta2} \qquad \log QS_{sed} = \log \alpha + \beta_1 \log Q_{líq1} + \beta_2 \log Q_{líq2} \quad (2)$$

Where: QS<sub>sed</sub> = sediment discharge [t/day]; Q<sub>líq</sub> = Madeira river, Q<sub>líq1</sub> = Beni river, Q<sub>líq2</sub> = Mamoré or Madeira minus Beni liquid discharge m³/s; α = intercept; β, β<sub>1</sub>, β<sub>2</sub> = exponents or slope coefficients. Curve-fitting with the function’s logarithmic form may generate a lowering bias (Ferguson, 1986, 1987; USACE HEC, 2023). A multiplicative correction factor, larger than 1, called Duan smearing factor, was applied to the predictions to compensate this.

With the fitted rating curves and the daily liquid discharge from hydrological data, inflow sediment loads and the difference between upstream and downstream sediment discharge were estimated. This difference corresponds to a daily series of retained sediment in the backwater reach of the Jirau dam, and a cumulative sum was calculated for the analysis period. Budgets were estimated for the total sediment load as well as for the sand fraction and were used as calibration targets for the modeling step.

## 3.3. Remote sensing

Monthly longitudinal profiles of surface sediment concentration derived from remote sensing reflectance (Alves e Santos et al., 2024; Martinez et al., 2015) were also used as model calibration targets. Sentinel-2 MSI imagery for the 2016-2021 period (329 images) were processed for atmospheric and glint correction. A regression equation based on the b8a/b4 (865 [nm] visible and near infrared / 665 [nm] red) band ratio was employed as a suspended particle matter retrieval method.

## 3.4. Model calibration and objective function

The HEC-RAS 6.2 (USACE HEC, 2022) sediment transport model was employed in this work, with its quasi-unsteady version. Figure 2 displays the hydrological boundary conditions that were used for the model – upstream discharge and downstream water level. Data on river stage on
intermediate sites (Mutum ~64 km upstream, Tamborete ~113 km and Abunã ~144 km) were used for calibration of Manning's n coefficient $m^{1/3}$/s. Simulated and observed water level were compared and the calibration metrics were the Nash-Sutcliffe coefficient (NS) and Bias. Changes were applied until a NS above 0.9 and an error of less than 0.5 m were reached.

<figure><img src="image_5.png" /><figcaption>Figure 2 – Time series of discharge (a) ANA, and water level (b) IBAMA used as model boundary conditions.</figcaption></figure>

A 188.3km long reach was modeled, with 89 cross-sections, spaced 2.1 km apart, on average. The 2015-2020 period was simulated, with 30-minute time steps. The shortest interval for input data variation is one day, namely hydraulic information: river discharge and water level. To better discretize in time sediment pulses and transport between cross sections, a shorter time step was adopted, which did not penalize excessively model run times.

Model calibration and sensitivity analysis were performed in stages. Hydraulic calibration was the first, following the principle that erroneous water levels would lead to incorrect energy slopes and water depths. This would lead to wrongly modeled shear stress and stream power, undermining the quality of sediment transport simulations. Having a hydraulically satisfactory model enabled stage 2, which was to evaluate whether the behavior of this river reach could be reproduced using only grain size distribution of inflowing sediment load as an uncertain input.
On this second step, a generalist sediment transport formula was used. Then, on stage 3 a different transport formula for fines was calibrated to the monitoring data.

Manning's n flow resistance coefficient was calibrated based on water level measurements on multiple sites. A constant base value of n= 0.034 was adopted for both the in-channel part of the cross sections and the floodplain. The available information does not allow for a detailed calibration of in vs. out of channel flows. It was found that river stations from the dam to 81 km upstream were more controlled by the water level imposed by the dam operation, with little sensitivity to the parameter.

The 81.5 – 180 km upstream reach, however, had practically the entire range of flows as in-channel, and water levels were affected by the n value. The initial procedure was trial and error, manual adjustment of the constant value to reduce errors, focusing mainly on the floods. However, it was observed that the modeled levels had flow-dependent bias, with overprediction on floods and underprediction during droughts. This demanded a manual calibration of Manning's n. with variations for different discharges (flow-dependent n) being beneficial to the model adjustment.

Calibration was verified by plotting modelled vs. observed levels on monitoring sites, calculating Nash-Sutcliff (NS) coefficients and bias after each round of manual adjustment. It was observed at which discharge ranges the bias would shift from under to overprediction, and if necessary, another discretization of flow vs. resistance was inserted. The final choice was to vary the flow resistance factor in seven steps, to make transitions smoother. A NS value above 0.9 accompanied by a bias of less than 0.5 meters were the goals.

On the stage 2 of model calibration, the Laursen-Copeland (LC) formula was employed for all grain size classes. There, concentration (C) is a function of three dimensionless parameters. They are: ratio of the representative particle size (d) to the water depth (D); rouse number (ratio of the shear velocity u* to the fall velocity ω); and dimensionless form of excess shear stress. The LC formula was developed and calibrated to a wide range of particle sizes, including coarse silts. It has been applied on large sand bed rivers, such as the Missouri, Mississippi, Cowlitz, Sacramento
and Madeira by the USACE (Copeland & Thomas, 1992; Creech et al., 2018). The original Laursen equation has gone through many modifications throughout the years, but may over predict silt transport and under predict fine sand transport (Kodoatie et al., 2000). Grain size distribution of the inflowing sediment load was varied.

Initial modeling results allowed a partition of fine sediment load into muds and wash load, which either does not deposit in the riverbed or gets quickly re-suspended in the hydraulic conditions of this reach. The fact that a 1D model was employed, and the monitoring data not specifying the exact collection locations, rather an average bed composition, does not allow a differentiation between channel and overbank/bar deposit granulometries. The grain size classes that were classified as wash load (W) correspond to fine mud/silt dimensions and smaller, $d \le 0.016$ mm. Medium to coarse muds/silts (M) ($0.016 < d \le 0.0625$ mm) do deposit, so the percentage of inflowing load in these classes was also evaluated. A code convention was adopted for models, where the annual mean proportion of the inflowing load in each class (Wash load W, Mud M, Sands S) was part of the model code. For example, a model whose name contains W06-M80-S14 receives inflowing load with proportions 6% wash load, 80% muds and 14% sands, on an average year. A detailed graphical description of grain size distributions among models is given on Supplemental Information S3. Here, a summary of mean annual percentage of macro grain classes is presented for the groups in Table 2.

Table 2 – Mean annual affluent sediment grain size distribution for model groups. Mud is sediment with $0.016 < diameter \le 0.0625$ mm, Wash is smaller.

<table><thead><tr><th rowspan="2">Model Groups →<br>Grain Class % ↗</th><th colspan="10">1</th><th colspan="5">2</th><th colspan="5">3</th><th colspan="5">4</th></tr><tr><th>21</th><th>18</th><th>16</th><th>16</th><th>14</th><th>14</th><th>14</th><th>14</th><th>14</th><th>12</th><th>14</th><th>14</th><th>14</th><th>14</th><th>14</th><th>14</th><th>14</th><th>14</th><th>14</th><th>14</th><th>14</th></tr></thead><tbody><tr><th>Sand %</th><td>21</td><td>18</td><td>16</td><td>16</td><td>14</td><td>14</td><td>14</td><td>14</td><td>14</td><td>12</td><td>14</td><td>14</td><td>14</td><td>14</td><td>14</td><td>14</td><td>14</td><td>14</td><td>14</td><td>14</td><td>14</td></tr><tr><th>Mud %</th><td>29</td><td>29</td><td>30</td><td>30</td><td>80</td><td>64</td><td>43</td><td>38</td><td>28</td><td>27</td><td>80</td><td>64</td><td>61</td><td>60</td><td>57</td><td>43</td><td>57</td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>Wash %</th><td>50</td><td>52</td><td>54</td><td>54</td><td>6</td><td>22</td><td>43</td><td>48</td><td>58</td><td>62</td><td>6</td><td>22</td><td>26</td><td>27</td><td>29</td><td>43</td><td>29</td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

From the third stage onwards, it was found that more calibration parameters were necessary, so subsequent model groups employed the Krone-Partheniades (KP) formula for fines (silts and clay - cohesive), with: thresholds for particle ($\tau_{cp}$) and mass wasting erosion ($\tau_{MW}$); slope of the
289 shear-erosion rates in the particle (M) and mass wasting ranges, (M<sub>MW</sub>). These were varied, with
290 a fixed load gradation.

291 The mud content of a sand-mud mixture, and the degree of consolidation (dry bulk density) of the
292 mud component control the critical shear stress (τ<sub>c</sub>) for erosion (Chen et al., 2021). The
293 composition of clay mineral, particle shape, surface roughness, pH and ions of pore water also
294 influence, with variations of one to two orders of magnitude of τ<sub>c</sub> reported by Chen et al. (2021).
295 This makes it highly site-specific, demanding calibration. The rate of erosion is even less
296 predictable. Critical thresholds for particle and mass wasting erosion spanned three orders of
297 magnitude (0.1 to 12 Pa). Corresponding rate slopes varied five orders of magnitude (0.5 to 11,400
298 Kg/m<sup>2</sup>/s). Table 3 below summarizes the settings.

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<table><caption>301 Table 3 – Shear stress parameter variation employed on model group 2.</caption><thead><tr><th>Shear Stress parameters</th><th>K1</th><th>K2</th><th>K3</th><th>K4</th><th>K5</th><th>K6</th><th>K7</th><th>K8</th><th>K9</th><th>K10</th><th>K11</th></tr></thead><tbody><tr><td>τ<sub>c</sub></td><td>0.1</td><td>0.1</td><td>1.5</td><td>1.5</td><td>2.5</td><td>4</td><td>6</td><td>6</td><td>6</td><td>6</td><td>6</td></tr><tr><td>τ<sub>MW</sub></td><td>0.8</td><td>0.8</td><td>2.5</td><td>2.5</td><td>4</td><td>6</td><td>8</td><td>8</td><td>9</td><td>9</td><td>12</td></tr><tr><td>M</td><td>3,700</td><td>1,000</td><td>1,000</td><td>2</td><td>2</td><td>2</td><td>2</td><td>2</td><td>0.5</td><td>0.5</td><td>0.5</td></tr><tr><td>M<sub>MW</sub></td><td>11,400</td><td>2,000</td><td>2,000</td><td>105</td><td>105</td><td>105</td><td>105</td><td>105</td><td>10</td><td>10</td><td>2</td></tr></tbody></table>

302

303 Differences in the model geometry, flow resistance and specific transport settings such as the use
304 of the pool-riffle discrimination within HEC-RAS are coded as G#, in the end of the model name.
305 Finally, the last model (single member of Group 4) utilizes a sediment load time series (suffix
306 _TS), based on the multivariate rating curve, instead of a fixed upstream sediment rating curve.
307 The most relevant information about the 32 models is summarized on the Supplemental materials,
308 Table S1.

309 The model contains a pool option, to represent geological controls where secondary circulation
310 and turbulence keep deep reaches in the river from filling up with sediment. These features are
persistent in large sand bed rivers (S. Gibson et al., 2019), but not well represented by a 1-D model, requiring careful modeler intervention. This option keeps transport capacity constant since their upstream end. Judicious use of this option and conveyance reduction with ineffective flow areas is summarized on Table 4.

<table><caption>Table 4 – Details on geometry and sediment transport special settings.</caption><tr><td>Pools 1</td><td colspan="7">Pools 144.4 - 131.7 km; 34.8 - 33.1 km; 12 - 10.8 km</td></tr><tr><td>Pools 2</td><td colspan="7">Pools: 154.7 - 131.7 km; 38.8 - 26.3 km; 12 - 10.8 km</td></tr><tr><td>Var_Mn</td><td colspan="7">Flow adjustment factor for Manning's n</td></tr><tr><td>Flow m³/s</td><td>2,500</td><td>5,000</td><td>10,000</td><td>15,000</td><td>25,000</td><td>30,000</td><td>35,000</td></tr><tr><td>Manning's n</td><td>0.0425</td><td>0.0391</td><td>0.0374</td><td>0.034</td><td>0.0306</td><td>0.0272</td><td>0.02448</td></tr><tr><td>IneF</td><td colspan="7">Ineffective Flow Areas: 61.9 - 33.1 km</td></tr></table>

The monitoring data available provided a quantification of different aspects of the siltation process in this backwater reach. A way to evaluate models that would leverage most of the available information through the analysis period (mid-2015-2020) was developed. Four metrics were used: i) the estimated total sediment budget; ii) the sands budget; iii) the monthly longitudinal concentration variation from RS and; iv) the surveyed cross sections.

Model outputs on longitudinal cumulative mass for total sediment and sand grain classes only were compared to budgets from rating curves. The root mean squared error (RMSE) between the modelled-monitored data was calculated throughout the time series, as in Eq. (7).

$$RMSE_{sediment\ budget} = \sqrt{\frac{\sum_{t=1}^{T_{outputs}} \left( M_{accum\ sediment\ rating\ curve} - M_{accum\ sediment\ HEC-RAS\ mod.} \right)^2}{T}} \quad (7)$$

Monthly clay and silts concentration variation (ΔC) from the upstream (km 183-144) part of the backwater reach to downstream (km 50-0,5) were also an evaluation metric. An RMSE error between variations from RS longitudinal profiles and model results was calculated, by Eq. (8).
$$RMSE_{\Delta C} = \sqrt{\frac{\sum_{m=1}^{12} (\Delta C_{RemSens} - \Delta C_{HECRAS})^2}{12}} \quad (8)$$

An average cross-section bottom variation was evaluated from repeated surveys, and compared to the model output on mean effective invert change, producing an RMSE across all sections and surveys – Eq. (9).

$$RMSE_{bottom \ elev} = \sqrt{\frac{\sum_{1}^{K_{sect}} \sum_{1}^{N_{surv}} \left( \frac{\overline{\Delta_{bottom \ level \ monit.}} - \overline{\Delta_{bottom \ level \ HEC-RAS}}}{K * N} \right)^2} \quad (9)$$

Since these four metrics were on very different scales, the way to produce an objective function that would encompass all information was to normalize the RMSE’s by dividing them by the median RMSE among models. Each of these normalized RMSEN became a parcel in an additive objective function, to be minimized, Eq. (10).

$$f_{\substack{\text{obj} \\ \text{model i}}} = \frac{RMSE_{\substack{\text{total sed.} \\ \text{budget i}}}}{RMSE_{\substack{\text{total sed.} \\ \text{budget median}}}} + \frac{RMSE_{\substack{\text{sand.} \\ \text{budget i}}}}{RMSE_{\substack{\text{sand} \\ \text{budget median}}}} + \frac{RMSE_{\Delta C i}}{RMSE_{\Delta C median}} + \frac{RMSE_{\substack{\text{bottom} \\ \text{elev i}}}}{RMSE_{\substack{\text{bottom} \\ \text{elev.median}}}} \quad (10)$$

An evaluation of the relative model distinction capacity between these RMSEN parcels was conducted. This provides methodological insights on how to better leverage these diverse sources of information. The objective function variance among models would be the numerical proxy of distinction capacity. Since it is an additive objective function, the total variance $[\sigma^2(f_{obj})]$ is a sum of variances of the parcels $[\sigma^2(RMSEN_i)]$ and their correlation $(\rho_{ij})$ effects, Eq. (11). Therefore, by ranking parcels by their variance and evaluating the correlation of each subsequent parcel to the previous sum, it is possible to infer which parcels “add more information” to the function.

$$\sigma^2(f_{obj}) = \sum_{i=1}^{4} \sigma^2(RMSEN_i) + \sum_{\{(i,j):i \neq j\}} \sigma(RMSEN_i) * \sigma(RMSEN_j) * \rho_{ij} \quad (11)$$
343

# 4. Results and Discussion

344

## 4.1. Sediment transport processes

345

### 4.1.1. Rating curves

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In logarithm space, simple and multivariate rating curves for total load have a good fit to the data, with R² ranging from 0.92 to 0.96. All discharges are statistically significant predictors and there is a small gain in log space model fit when employing multivariate versions (for more details see Moura et al., 2023). Further work will detail the influence of different rating curve formulations on budgets, but preliminary results indicate that the difference in accumulation for a 5-year period can be of 40% (Moura, 2025). Rating curves for the total sediment discharge and the sand fraction are displayed on Figure 3.

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A relevant gain in information, however, is the quantification of the sediment contributions from each tributary that comes from the fitted log angular coefficients or exponents of variables before log transformation. The Beni River discharge has an exponent that is more than three times higher than that of the Mamoré River. This further evidences its leading role in sediment contributions to the reach, documented in Vauchel *et al.* (2017) as a 5.6 times Beni/Mamoré load ratio. A steeper rating curve indicates a river that transports most of its sediment load on higher discharges, with higher availability of sediment and transport capacity. Exponents of 0.5 (Mamoré) to 1.8 (Beni) are common in the literature (Asselman, 2000), with the higher value occurring for instance in the mountainous part of the River Rhine and lower values further downstream near its delta.
<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>Figure 3 – Sediment discharge measurements at multiple sites and fitted rating curves for A) total and B) sand fractions. C) Difference between univariate and multivariate rating curves with different proportions of Beni River discharge.</figcaption></figure>
### 4.1.2. Total sediment and sand budget

On the early stages of the model construction process, the sand budget was the most relevant calibration target. The first model group represents mainly the adjustment of input load gradation to fit the estimated accumulated sand mass (Figure 4, panel B). The sand proportion in the best-fitting model was from then onwards fixed.

<figure><img src="image_10.png" /></figure>

Figure 4 – Estimated (black lines) total sediment (panel A, solid line) and sand (panel B, dashed line) mass accumulation, based on rating curves, along with model results. Different colors depict intergroup differences. Model intragroup variability range is displayed as colored bands – range = 10^th^ and 90^th^ percentiles of sediment accumulation among group models. The best-fitting model in each group is represented as a colored line.

All models deposit most of the sand supply. The use of the pools setting was important in the mitigation of excessive deposition, especially in the upstream part of the model. A more detailed hydraulic and transport function calibration should first address the model's sand transport behavior, alongside water levels.

A change to the Krone-Partheniades (KP) sediment transport formula for the fines was attempted for group 2, to adjust model behavior to the estimated total sediment accumulation. The coarsest gradation for silts and clays from the previous step of model construction was employed. The maximum modeled shear stresses were on the order of 15 Pa, so the mass wasting erosion regime
threshold was kept under this magnitude. Total sediment accumulation is very sensitive to KP parameters, as viewed for group 2 (blue) on panel A of Figure 4, with a wide range of model behaviors.

### 4.1.3. Remote sensed concentration variation

For the third and fourth steps of model construction and refinement, the remote sensing data were crucial. An excessive deposition was verified in the dry months for group 2 models (see Figure 6, months Aug and Nov). Sediment deposit resistance parameters were kept constant in the values of the best fitting model in group 2, while grain size distribution was again changed to address this issue.

A bayesian analysis was conducted, using a dataset of field spectrometer reflectance ratio vs field samples of fine SPM concentration, from Alves e Santos *et al*. (2024). There is a significant scatter in the data, which can be conveyed by the 95% confidence prediction interval for the bayesian regression equation of reflectance vs concentration. The interval at 200 mg/L is 73 to 505 mg/L. For other concentrations, mean (lower; higher limits): 500 (220;1,172), 1,000 (465;2,282), 1,500 (710;3,392) mg/L.

A verification was conducted with monthly average concentrations at conventional monitoring sites, and the corresponding monthly concentration from RS longitudinal profiles. With RS, for a given concentration value, there is an upper and lower limit of the interval for the regression. Some sites have data every month, others have every three months, so 50 points data points result. Of these 50, only 7 monthly averages from conventional measurements fall outside the prediction interval.

Then, a factor for conversion to a depth-integrated concentration was evaluated, considering clay and silt sediment fractions. The measurements of depth-integrated concentration (*in-situ*) were averaged monthly, across the study reach. The ratio between these reach-averaged concentrations and RS index concentration – at the water surface, also reach-averaged – was employed as a multiplicative factor. Figure 5 displays this data for months when longitudinal profiles are available. There is a seasonal behavior where in the intermediate to high flows (8 months), depth
434 integrated concentrations are higher (1.10≤ratio≤2) than RS estimates. Conversely, in the dry
435 months (August to November), they are lower (0.25≤ratio≤ 1).

436 The methods for the determination of sediment concentration and grain size distribution through
437 conventional methods varied according to concentration. For concentrations ~220 mg/L and
438 below, the bottom-withdrawal tube tends to be used, whereas for higher concentrations, the
439 pipette method is employed. The bottom-withdrawal tube technique has higher uncertainty for
440 concentrations around 200 ppm (Subcommittee on Sedimentation, 1953). This Subcommittee
441 study revealed that at 200 ppm, 22% of samples had errors of more than ±80%, and 39% had
442 more than ±60% errors.

443 Besides this possible systematic difference in method for estimation of concentrations, the grain
444 size distribution also has a seasonal pattern, which may influence the water's optical properties.
445 The details are given in Supplemental Information, Figures S5 and S6. The D50 for the suspended
446 material is in the fine silts range (0.0157 mm upstream, 0.0144 mm downstream) in the flood and
447 ebb phases (months of February to June) of the annual cycle. Conversely, during the drought
448 (August to November) it is 0.0082 (0.0094) mm upstream (downstream), in the very fine silts
449 range. The flood D90 is 0.0764 (0.0656) mm upstream (downstream), therefore in the sands range,
450 and the drought D90 is 0.0347 (0.0376) – coarse silts. The band ratio technique neutralizes in part
451 this effect, but a residual uncertainty remains. When looking at the raw reflectance data, the
452 campaign that was conducted in September (end of drought) is the one that deviates the most from
453 the data cloud. This is similar to the findings of Villar *et al.* (2013), where bias in the rising water
454 period was found.
<figure><img src="image_11.png" /><figcaption>Figure 5 – Monthly longitudinal profiles of sediment concentration, where points represent conventional monitoring cross-sections and lines represent RS estimates. (a) Cross-section median concentrations (points) with their standard deviation (bars) and RS profiles before correction. (b) Overlay of corrected RS profiles on the conventional data.</figcaption></figure>

The main advantage of using this simple method is the historical data availability for depth integrated measurements, since 2009 for some sites, even longer for sites such as Porto Velho. There are conversion methods (Santini et al., 2019) that consider the nonuniform sediment distribution in the water column, but require unavailable data. The work of Santini *et al.* (2019) required a database of 249 point concentration profiles, accompanied by ADCP measurements. In the material gathered by this research, only 18 sets of measurements of point concentrations in various depths were found. They were done at 3 sites, 6 measurements on each site, with 3 verticals, but without velocity profiles.

Monthly reach-averaged concentration variations from upstream (km 183-144) – downstream (km 50-0,5), were calculated from RS profiles. Taken along with mean discharges, they allow estimates of mean deposition of fines (silts+clay), shown on Table 5. Ranges of yearly average deposition from model results and monthly errors (when compared with these estimates) are displayed on Table 6. Model Group 4 has the smallest RMSE, and closest simulation of yearly deposition. Again, the strong sensitivity of results to the KP parameters is evident in the wide range verified in group 2. There were even two models showing an average tendency to erode.
<table><caption>Table 5– Remote sensing estimates of monthly deposition of fines $10^6$ t yr$^{-1}$ in the Jirau backwater.</caption><thead><tr><th>Month</th><th>Jan</th><th>Feb</th><th>Mar</th><th>Apr</th><th>May</th><th>June</th><th>Total</th></tr></thead><tbody><tr><td>Mton</td><td>9,000</td><td>19,132</td><td>-1,912</td><td>3,836</td><td>6,760</td><td>6,626</td><td>(Mton/year)</td></tr><tr><td>Month</td><td>July</td><td>Aug</td><td>Sept</td><td>Oct</td><td>Nov</td><td>Dec</td><td></td></tr><tr><td>Mton</td><td>2,102</td><td>983</td><td>247</td><td>593</td><td>2,117</td><td>1,963</td><td>51,449</td></tr></tbody></table>

<table><caption>Table 6 – Simulated ranges of yearly deposition of fines for model groups and monthly differences w.r.t. RS estimates.</caption><thead><tr><th rowspan="2">Model<br>Group</th><th colspan="2">Deposition (Mton/year)</th><th>RMSE (Mton/month)</th></tr><tr><th>Average</th><th>Range</th><th>Range</th></tr></thead><tbody><tr><td>1</td><td>31,296</td><td>23,443 – 50,160</td><td>228 – 378</td></tr><tr><td>2</td><td>40,146</td><td>-901 – 87,216</td><td>197 – 451</td></tr><tr><td>3</td><td>62,459</td><td>47,072 – 70,951</td><td>157 – 255</td></tr><tr><td>4</td><td>52,685</td><td>-</td><td>141</td></tr></tbody></table>

<figure><img src="image_12.png" /><figcaption>Figure 6 – Concentration of fines longitudinal profiles for selected months: converted remote sensing estimates (black lines), model group simulated ranges (quantiles 10 and 90) and median values.</figcaption></figure>

The reach variation of fine sediment concentration was agnostic to model bias, focusing only on reproduction of the trend – see Figures 5 and 7. As shown in section 4.3, this parcel of the objective function is not dominant, so the uncertainties in the RS calibration data are secondary in the calibration process. The use of a sediment load time series, produced from a multivariate
rating curve in group 4, brought the capacity to better reproduce concentration dynamics (Figure 7).

In remote sensing estimates, there is a switch from depositional to equilibrium/slightly erosional conditions after the peak of the flood season, in March. This is one month delayed in the model group 4 simulation results. Model group 3 is the next best performing but still appears over depositional during the dry season (Jun-Aug) and rising limb of the annual hydrological cycle (Nov-Dec).

<figure><img src="image_13.png" /><figcaption>Figure 7 – Monthly reach averaged upstream – downstream concentration variation from RS and simulated range for model groups g1, 2, 3, 4.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Figure 8 – Seasonal variation of (a) total sediment concentration; (b) concentration relative to upstream cross section - longitudinal profiles for Group 4.</figcaption></figure>
The longitudinal trend of sediment deposition is displayed in Figure 8, for the multivariate rating curve model (G4). A comparison of simulated downstream concentrations with measurements is displayed in Figure 9 for all model groups. Quantitative evaluations are detailed on the supplementary information, including comparison with rating curve predictions (Tables S2, S3, Figure S4). Group 4 has the best match to measurements (see Table S3) in R2=0.7 and MAE=170 mg/L metrics, and second best in Bias=52.49 mg/L and Relative Bias=10%. This aligns with the overall performance evaluation by a multi-objective function carried out on the following section 4.2. A multivariate rating curve in group 4 enabled better reproduction of seasonal patterns of fine sediment transport.

In the years of 2018 and 2019 none of the model groups reproduce well the ebbing phase of the annual cycle. Again, group 2 has the widest range of simulated concentrations, due to the sensitivity of KP parameters.

<figure><img src="image_15.png" /><figcaption>Figure 9 – Measured and simulated time series of downstream sediment concentrations.</figcaption></figure>

Similarly to the work of Launay *et al.* (2019), this model allows the verification of the importance of understanding the dynamics of tributaries that contribute sediment inflows to the system. Different from their work, fine material (medium and coarse silts) does deposit in the backwater. High sediment load rivers require careful evaluation of their wash load threshold. A sensitivity analysis for uncertain inputs and parameters is a key step for a transparent and responsible estimate of impacts.
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## 4.2. Model calibration – hydraulics and sediment transport

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The hydraulic calibration was iterated until modelled water levels were slightly lower (0.11 to 0.32 m) than measured, but within an acceptable range. Metrics (Nash-Sutcliffe coefficient, Bias and Mean Absolute Error) for the monitoring sites are displayed on Table 7, showing good agreement. To evaluate roughly the significance of a 0.31 m bias, one can take shear stress as the product of water specific weight, hydraulic radius (proxied by water depth for very wide sections) and energy slope. Also, considering that in Abunã, where the most bias occurs, the average water depth during the flood is 34.43 m. An error of 1% in the shear stress results from a bias of this magnitude in the period where most sediment input occurs. For sediment transport purposes, this is an acceptable model, but perhaps not for decision of flood defense heights, for instance.

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<table><caption>Table 7 –Metrics for the quality of model fit to observed water levels.</caption><thead><tr><td>Monitoring Site</td><td>Nash-Sutcliffe</td><td>Bias (m)</td><td>MAE (m)</td></tr></thead><tbody><tr><td>RJ07 - Abunã -15320002</td><td>0.991</td><td>-0.317</td><td>0.357</td></tr><tr><td>RJ05 - Tamborete</td><td>0.994</td><td>-0.239</td><td>0.263</td></tr><tr><td>RJ04 - Mutum</td><td>0.997</td><td>-0.111</td><td>0.179</td></tr><tr><td>RJ03 - Palmeiral</td><td>0.997</td><td>-0.112</td><td>0.170</td></tr></tbody></table>

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Magnitude ranges of different model evaluation metrics regarding sediment transport are shown in Table 8. It is possible to perceive from there the progression in importance of different objective function parcels. From group 1, where simulated deposition was overpredicted for sand and underpredicted for fines, the calibration has evolved to an adjusted sand budget. Then, finding an adequate range for KP parameters has compressed the RMSE range for the total sediment budget, evolving from group 2 to group 3. The dry bulk density of the mud component in a sand-mud mixture is the main driver of variation of its critical shear stress (Chen et al., 2021), which can seasonally affect this parameter or impose a trend on it, as the silting progresses in this reach.
Finally, adjusting seasonal dynamics with RS concentration variation was the improvement group 543 2 to groups 3 and 4. Flocculation may be relevant (Lamb et al., 2020; Santini et al., 2019), for the 544 model only reproduced the monitoring results with a slightly coarser grain size distribution for 545 the input load. The hydraulic conditions in the affected reach enable the retention of silts and clay- 546 silt flocs smaller than 16 µm. Recent research (Ma et al., 2020) shows that there is a threshold of 547 bed composition when if the bed is fine-grained enough (median bed grain size between 81 to 548 154 µm), transport is greatly enhanced, and the Generalized Engelund Hansen (GEH) formulation 549 reproduces measurements better. This bed fining took place in the reach immediately upstream 550 of the dam, up to 50-70 km, which may require separate calibration. Most models do not have the 551 GEH implemented, and HEC-RAS should allow for time-series input separated by grain size 552 classes. 553

Normalization of such different scales is part of the objective function calculation and was 554 performed by dividing RMSE by the median value among models. Figure 10 displays the 555 variability of model normalized scores between and within groups. The large range of sediment 556 deposit resistance parameters in Group 2 was the strongest factor for variability. 557

The importance of RS estimates is highlighted by the monthly concentration variation parcel 558 being the second largest contributor, in terms of model differentiation capacity (Table S4 – Supp. 559 Information). This metric was the only one capable of capturing the effect of changing the 560 upstream boundary condition from a static rating curve to a sediment time series. Therefore, it 561 evidenced a payoff for the use of multivariate rating curves, where different sediment inputs from 562 different tributaries could be considered. Figure 10 and Table S4 show this evaluation for groups 563 2 to 4 only, for in group 1 the sand budget parcel overshadows all others. 564

For groups 2 to 4, the total sediment budget and concentration variation parcels represent 565 approximately 72% and 29% of the objective function variability. It would have a higher variance 566 if it was composed only of them. These first and second parcels are moderately correlated. The 567 sands budget and cross-section variation are strongly correlated to the previous sums. Those last 568 two add very little variance, but for sand budget one can argue that they still provide information, 569
because the correlation is negative. Cross-section mean bottom elevation change has proven not to be a useful model differentiation metric, with similar RMSE ranges between all groups (Table 8).

<table><caption>Table 8 – Model groups RMSE and Bias ranges.</caption><thead><tr><th rowspan="3">Metric</th><th rowspan="3">Range</th><th colspan="6">Model Group</th></tr><tr><th colspan="2">1</th><th colspan="2">2</th><th colspan="2">3</th><th colspan="2">4</th></tr><tr><th>RMSE</th><th>Bias</th><th>RMSE</th><th>Bias</th><th>RMSE</th><th>Bias</th><th>RMSE</th><th>Bias</th></tr></thead><tbody><tr><td rowspan="2">Sands Budget<br>(10<sup>6</sup> ton yr<sup>-1</sup>)</td><td>max</td><td>101</td><td>77.9</td><td>7.4</td><td>-1.5</td><td>8.1</td><td>-1.6</td><td rowspan="2">8.1</td><td rowspan="2">0.7</td></tr><tr><td>min</td><td>6.8</td><td>-27.5</td><td>7.2</td><td>-1.7</td><td>7.3</td><td>-5.6</td></tr><tr><td rowspan="2">Total Sed. Budget<br>(10<sup>6</sup> ton yr<sup>-1</sup>)</td><td>max</td><td>189</td><td>-41.2</td><td>235</td><td>99.3</td><td>81.1</td><td>44.5</td><td rowspan="2">50.1</td><td rowspan="2">-10.2</td></tr><tr><td>min</td><td>55.9</td><td>-150</td><td>85.8</td><td>-198</td><td>46.3</td><td>-31.8</td></tr><tr><td rowspan="2">Concentration<br>Variation (mg/L)</td><td>max</td><td>180</td><td></td><td>238.3</td><td></td><td>161.5</td><td></td><td rowspan="2">81.4</td><td></td></tr><tr><td>min</td><td>99</td><td></td><td>109.9</td><td></td><td>94.3</td><td></td></tr><tr><td rowspan="2">Cross-section<br>bottom variation (m)</td><td>max</td><td>1.8</td><td></td><td>1.87</td><td></td><td>1.66</td><td></td><td rowspan="2">1.55</td><td></td></tr><tr><td>min</td><td>1.58</td><td></td><td>1.57</td><td></td><td>1.55</td><td></td></tr></tbody></table>

<figure><img src="image_16.png" /><figcaption>Figure 10 – Objective function and normalized RMSE parcels for model groups 2, 3 and 4, in</figcaption></figure>

order of variance.
578

## 4.3. Discussion on sediment monitoring practices

579

Brazil's regulatory demands of monitoring for the hydroelectric sector are inspired in the USGS practices. Government agencies do not make available raw ADCP data to end users, if they receive them at all from operators. Point concentration measurements at multiple depths are not required by default, being demanded on a case-by-case basis within the impact assessment step.

580

581

582

583

In South America, Brazil's water resource monitoring system is one of the most sophisticated, with this arguably being the best monitored reach in the country. Methods for conversion of surface to depth averaged concentration that are much more sophisticated than the one employed here would be challenging to use in this regional context.

584

585

586

587

Emerging technologies like LISST could improve sediment concentration profiling and enable high-resolution, continuous monitoring (Miles et al., 2021). However, calibration remains essential due to variations in particle properties (Lawler et al., 2017). The LISST-SL2, for instance, struggled with fine sediment detection, requiring adjustments using physical samples, which significantly improved accuracy (Ahammad et al., 2023). Targeted field campaigns for calibration could improve sediment transport assessments over time (Moodie et al., 2022), justifying the high investment.

588

589

590

591

592

593

594

When modeling and monitoring sediment transport for a river reach affected by a run-of-river dam, it may be necessary to first estimate what changes in sediment transport regime and dominating processes are expected. Then, to choose observation sites and model boundaries accordingly. The downstream ~70 km of the Jirau reservoir/backwater display a behavior that is clearly different from the rest of the affected reach (Moura et al., 2024, 2024b). The shear stresses for this final reach create conditions where even medium to coarse silts deposit.

595

596

597

598

599

600

The Tamborete and Pederneiras sites, chosen probably because of drowned waterfalls/geological features, are too close together, and one of them could be replaced by more intensive monitoring at a more significant site. The upstream (Jirau) and downstream (Santo Antônio) dams are owned by different companies (Fearnside, 2014), who may want their own independent information. However, the Porto R4 and Jusante Caldeirão do Inferno stations seem redundant. There is too

601

602

603

604
much uncertainty in sand discharge measurements, especially at low concentrations. Alternative techniques could be applied to measure bed load (Ashley et al., 2020; Claude et al., 2012; Gaeuman & Jacobson, 2006; Le Guern et al., 2021; USGS, 2010).

## 5. Conclusion

A detailed case study is presented for the Jirau run-of-river hydropower facility, in the Madeira River, Amazon tributary. This work's best calibrated model indicates that the Madeira River reach affected by the Jirau dam has an average 21.3% sediment load retention for the 2015-2020 period. For the sands fraction, with the Laursen-Copeland transport function, more than 90% of the supply is retained in the backwater. A recommended modeling good practice is to start calibrating the model with a sand budget. Simple transport formulas such as Engelund-Hansen may bring better results, since the sediment fall velocities and critical values of shear stress or stream power bring uncertainties that are difficult to unpack. Future work will discuss the use of other transport capacity formulations, and modeling with more spatial dimensions (bidimensional).

A simple calibration objective function was proposed, that allows for the consideration of multiple calibration targets, with different measurement scales, resulting in a single numerical metric for model differentiation. This was an important tool to prioritize work fronts in model calibration, showing that sediment budgets were the most relevant monitoring product for this case, while bathymetry cross-sections were the least.

Monitoring data reveals that the deposition of fines (medium to coarse silts and clay flocs) cannot be overlooked for this backwater reach. Part of the fine sediments are retained – the key size classes to understand deposition of fines are medium to coarse silts and clay-silt flocs larger than 0.016 mm. This is what could be called the wash load threshold for this system, and the model only reproduced the monitoring results with a slightly coarser grain size distribution for the input load, which can indicate flocculation processes. Changes brought by bed fining in the 50-70 km closest to Jirau dam may mean a different transport regime, with a need to calibrate there
separately. A monitoring station at the entrance of this reach with monthly data would be very
useful.

The Krone-Partheniades formula for fines became necessary to calibrate the model. The current best estimate for KP erosion shear stress thresholds and erosion rates are τc=6 Pa, M=0.5 N/m²/h for particle erosion; τMW=12 Pa M=MW=2 N/m²/h for mass wasting. A literature search for values for these parameters highlighted their uncertainty. With the seasonal variation of modeled shear stress, thresholds were set so that the different processes would activate during the hydrological year.

The seasonal behavior is best described when sediment input to the model is estimated with techniques that consider the dynamics of contributions from the two forming tributaries, Mamoré and Beni. A multivariate rating curve using the discharge of the tributaries as explanatory variables shifts the highest bias in concentration temporally from the ebbing phase of the seasonal cycle to the flood phase. Only by using remote sensing data was it possible to distinguish these benefits.

Overall, the modelling exercise has strengthened some hypotheses that come up with the monitoring data, such as the sediment retention rate and accumulation of some fine grain size fractions. It was more useful to evaluate the model reproduction of the sediment budget and the seasonal behavior of fine sediment deposition. A partition of the reservoir and backwater in reaches with distinct dominant processes – sand retention in the backwater, medium to coarse silts / clay flocs in the reservoir became clearer. Many useful insights into future monitoring-modelling efforts were provided.

Acknowledgements

The first author has been supported by a scholarship from CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Brazil, during part of the research period. He would also like to thank his postgraduate program, PTARH and University, UnB, as well as public institutions that have granted access to data: ANA – Agência Nacional de Águas e Saneamento Básico and IBAMA - Instituto Brasileiro do Meio Ambiente e dos Recursos Naturais Renováveis.

657
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853 Moura, L. Z., Mesquita, G. de S., Liborio, M. M., Koide, S., Martinez, J.-M., & Roig, H. L. (2024b). *Modeling Sand Transport in a Madeira River Run-of-River Dam – Evaluation of Transport Capacity Formulas in HEC-RAS 1D*. Paper presented at the Encontro Nacional de Engenharia de Sedimentos - XVI ENES 2024, Curitiba, Brazil. Paper retrieved from https://anais.abrhidro.org.br/jobs.php?Event=239

854 Negreiros, B., Schwindt, S., Haun, S., & Wieprecht, S. (2022). Fuzzy map comparisons enable objective hydro-morphodynamic model validation. *Earth Surface Processes and Landforms*, 47(3), 793–806. https://doi.org/10.1002/esp.5285

855 Nittrouer, C. A., DeMaster, D. J., Kuehl, S. A., Figueiredo, A. G., Sternberg, R. W., Faria, L. E. C., Silveira, O. M., Allison, M. A., Kineke, G. C., Ogston, A. S., Souza Filho, P. W. M.,
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883 Pinet, S., Martinez, J.-M., Ouillon, S., Lartiges, B., & Villar, R. E. (2017). Variability of apparent and inherent optical properties of sediment-laden waters in large river basins—Lessons from in situ measurements and bio-optical modeling. *Optics Express*, 25(8), A283–A310. https://doi.org/10.1364/OE.25.00A283

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939
<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>
<figure><img src="image_20.png" /><figcaption>Concentration (mg/L)</figcaption></figure>

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /></figure>
<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /></figure>

<figure><img src="image_26.png" /></figure>

Legend (a)

Reach of Interest
Madeira and main tributaries

Madeira Basin

Tributaries Basins

Amazonas Basin

Adean domain

Legend (b)

Reach of Interest

Madeira Basin

Amazonas Basin

Andean domain

Legend (c)

★ Waterfall

● Stations Jirau

● Stations Santo Antônio

● Stations bathymetry

● Cross sections

● Madeira river
<figure><img src="image_27.png" /></figure>

<figure><img src="image_28.png" /></figure>
<figure><img src="image_29.png" /></figure>

<figure><img src="image_30.png" /></figure>

<figure><img src="image_31.png" /></figure>

<figure><img src="image_32.png" /></figure>
<figure><img src="image_33.png" /></figure>

<figure><img src="image_34.png" /></figure>
<figure><img src="image_35.png" /></figure>

<figure><img src="image_36.png" /></figure>
<figure><img src="image_37.png" /></figure>

<figure><img src="image_38.png" /></figure>

<figure><img src="image_39.png" /></figure>
<figure><img src="image_40.png" /></figure>

<figure><img src="image_41.png" /></figure>
<figure><img src="image_42.png" /></figure>

<figure><img src="image_43.png" /></figure>

Conc.
delta

<figure><img src="image_44.png" /></figure>

<figure><img src="image_45.png" /></figure>

Cross
sect.

<figure><img src="image_46.png" /></figure>

Group 2

Group 3

Group 4

<figure><img src="image_47.png" /></figure>
**Declaration of Interest Statement**

[x] The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

[ ] The author is an Editorial Board Member/Editor-in-Chief/Associate Editor/Guest Editor for this journal and was not involved in the editorial review or the decision to publish this article.

[ ] The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: