Determining Monthly Discharge on the Tapajos River Using a Rainfall-Runoff Model

To develop a historical flow profile for hydro projects in Brazil’s Tapajos River Basin, a mathematical model was used. Data from this model filled gaps in measurements available from rainflow gauging stations, and data generated correlated well with available rainflow measurements.

By Eurico de Carvalho-Filho, Iara P.G. Machado, Humberto Jacobsen Teixeira, Gabriel S.C. Rocha and Maria Tereza F.R. Campos

This article has been evaluated and edited in accordance with reviews conducted by two or more professionals who have relevant expertise. These peer reviewers judge manuscripts for technical accuracy, usefulness, and overall importance within the hydroelectric industry.

Brazil has more than 110 GW of installed electric capacity, 77% of which comes from hydroelectric sources, according to the 2010 National Energy Balance. The country has unexploited hydro potential of 160 GW, meaning Brazil has implemented only 35% of the available total. This makes the Brazilian hydroelectric market very attractive.

To perform inventory studies of Brazilian rivers, it is imperative to follow the Electrobras/MME Inventory Manual, published in 2007. This manual provides guidelines for these studies to determine the best alternative for exploring the hydropower potential of a river basin, maximizing the energy generated with minimum cost and environmental impact.

One of the main outputs of this inventory study is a monthly discharge serial for each dam site inventories from 1931 until two years before the study began. This period was defined based on regulations from the Brazilian Electrical Agency (ANEEL). These series cannot necessarily be determined using level or discharge measurements from gauging stations because early data may not be available, there may be failures in data capture during certain periods of time because of the absence of observers or damage to the equipment, or some of the data may be inaccurate. The alternative to deal with this situation is to use a rainfall-runoff model to provide the missing data.

This method was applied for the Tapajos River Basin’s Inventory Study, which was delivered in 2010, because there were no gauging stations installed for this river basin from 1931 to 1972.

The model involves reproducing the physical process of the hydrological cycle using mathematical expressions and algorithms, in situations where the physical characteristics are represented as unknown factors. Simply speaking, this model considers the river basin as three hypothetical and independent reservoirs: evapotranspiration of the superficial flow soil, infiltration phenomena of the superficial flow soil, and groundwater flow. For each time step, measurements are performed as a mass balance process, in which total precipitation is partially intercepted by the vegetation and then evaporates,1 while the remaining precipitation is shared between superficial soil reservoirs depending on the soil moisture rate. The infiltrated part of the precipitation goes into the mass balance on the soil reservoir, while evapotranspiration and groundwater recharge are derived from another balance considering the groundwater-soil moisture saturation process.

A Newtonian exponential decay is used to draw down the superficial and subterranean flow that could be combined to generate the discharge from every gauging station. This allows a comparison between the calculated and observed discharge. The parameters could then be calibrated to provide more adherence to the mathematical model, as well as preserve statistical factors such as long-term average and standard deviation.

River basin characterization

The Tapajos River basin is in the north central region of Brazil, east of the Madeira River basin and west of the Xingu River basin. Its surface covers an area of 492,481 km² in the states of Mato Grosso, Para, Amazonas and Rondonia. According to the regulation adopted by Agencia Nacional de Energia Eletrica (ANEEL), the Tapajos River basin belongs to Basin 1 (called the Amazonas River Basin). The Amazonas River Basin is divided into 10 sub-basins numbered 10 to 19, with Tapajos identified as sub-basin 17.

The Tapajos River is formed by the confluence of Juruena and Teles Pires rivers, which together are responsible for almost 70% of its discharge. From the point where these two rivers meet, the river stretches 825 km before draining into the right bank of the Amazonas River. Water levels and flooding in the final stretch of the Tapajos River are affected by the backwater of the Amazonas River and the tidal influence. The main tributaries of the Tapajos River are the Crepori and Jamanxim rivers. Figure 1 shows the Tapajos River basin and its tributaries.

Figure 1 Tapajos River Basin

The Juruena River has a drainage area of 190.931 km² and originates in the slopes of Serra dos Parecis at Elevation about 700 meters. It receives many tributaries along the 850 km-long stretch to its confluence with the Arinos River. The Arinos River originates in Serra Azul at Elevation about 400 meters. It travels 760 km to join the Juruena River. Its slope is stressed in the first 50 km, softening in the remainder. Arinos and Juruena Rivers are not considered navigable because of many obstacles in the riverbeds.

The Teles Pires River originates in Serra Azul at Elevation about 800 meters, growing as it flows northwest to its confluence with the Juruena River, where it forms the Tapajos River at Elevation about 95 meters. The Teles Pires River runs a total length of 1.638 km and has a total area of 141.718 km².

The Tapajos River presents an asymmetrical shape, with larger tributaries along the right bank, such as the Jamanxim River, which has a basin area of 58.633 km². The Arapiuns River is the largest tributary feeding into the left bank of the Tapajos River, near its drainage into the Amazonas River.

The last 100 km of the river before it flows into the Amazonas River is an estuary, with the distance between the two banks being more than 20 km. Flow into the Amazonas River drains through a channel 1.12 meters wide. This phenomenon is related to the backwater effect from the Amazonas River. The influence at the mouth of the Tapajos River results in a river level oscillation of about 0.4 meters.

All the drainage area of the Tapajos River presents geomorphologic characteristics of soils of crystalline basement covered by exuberant vegetation. In this wet climate with large amounts of precipitation, this leads to an extremely dense drainage. These climate factors lead to a very positive water balance, with high specific yield, emphasizing its aptitude for multiple uses.

Periods to be generated using hydrological simulation

To fill in the missing data for the Tapajos River basin, mathematical modeling of rain-flow was performed for the time period ranging from January 1931 to the beginning of the 1970s. To perform this modeling, some precedent stages are necessary. These include preparing the database for the model, consolidating drainage areas near the project and the gauging stations installed in the river basin before 1971, and consolidating the average monthly precipitation series for the period of study.

Simulation model adopted

There are many hydrological simulation models available. Some of them present the phases of the hydrological cycle in a very detailed manner, while others consider only portions of the phenomenon, presenting limited applications.

CNEC WorleyParsons developed a simulation rainfall-runoff model to be used to translate the monthly precipitation data into the monthly flow data, using for that expressions and functions that represent physical processes in the hydrological cycle.

The transformation process of the total monthly rainfall into runoff is represented in the model by 11 physical parameters. Eight of these represent the physical characteristics of the basin, and three represent the conditions in the first moment of the simulation. The physical parameters are: evapotranspiration, the recession value of runoff and underground flow, water content of soil, field factor, soil’s nominal capacity, runoff regulation and groundwater recharge.

The model is represented by three hypothetical reservoirs:

– Superficial (Rsup), which represents the portions of runoff and superficial discharge;

– Sub-superficial (Rsoil), which represents the water content in the soil influenced by the roots; and

– Subterranean (Rsub), which represents the underground aquifer.

During each precipitation event, a mass balance is done. Initially, a portion of the rain is intercepted by the vegetal coverage and lost by evaporation. Remnant precipitated volumes are divided between runoff and infiltration, whose division of flow is regulated by the water content in the soil. This implicates that the greater the water content of the soil, the greater the portion directed to runoff.

The infiltrated portion in the ground is added to the reservoir to represent the water content in the soil. In this reservoir, water content is updated over time through the contributions of infiltration and loss of water due to evapotranspiration and groundwater recharge. Groundwater recharge is limited by the soil’s field capacity, which is the water content in the soil below which water does not flow toward the subterranean reservoir. Both subterranean and superficial reservoirs suffer a drawdown in an exponential rate, resulting, respectively, in basic and superficial flows.

The storage capacity of these reservoirs adheres to the hierarchic order described above, where the water content rate in the soil is the common denominator that governs the portions of remnant rain to be add in each reservoir.

Simulation model calibration

The model is calibrated through a process of successive tries, until the differences between the flow hydrographs generated by the model and the hydrographs observed at the chosen flow gauging stations are at an acceptable level of error.

Calibration for the period being studied (1975 to 2008) was established based on research of the common data serial available for precipitation and flow, resulting in definition of the period from January 1931 to December 2008. For model calibration, the following inputs were considered:

– Average monthly precipitation in the basin. Because of the lack of large periods of observation, precipitation series considered in the modeler were composed by three points around the river basin: Diamantino, Vilhena and Alto Tapajos.

– Average monthly evaporation (Class A) data. The values of climatological normals were obtained from the climatologic station of Itaituba, which represents the climatic conditions of the Tapajos River. Table 1 presents patterns of evaporation considered in the model; and

Table 1: Monthly Evaporation Data of Itaituba Climatologic Station

– Input parameters of the model. These values were presented according to the flow gauging station used in the modeler of the Tapajos River.

The portion of the rain intercepted by the vegetation (leaves, bushes, etc.) is also an important input parameter for the calibration. In the simulation model, this is calculated through an equation generated from a parametric study for values of interception ranging from 3 to 5 mm. Calculations were run to provide a monthly accounting of the precipitation with values similar or inferior to daily precipitation values, which represent the amount of precipitation that remains in foliage and is lost by evapotranspiration.

For each initial value of interception, a monthly data series was obtained and correlated with the correspondent value of monthly precipitation. This correlation originated the adjustment equation between interception and monthly precipitation for each studied station. From the five equations, the average of coefficients a and b were calculated, generating one equation for determining the daily interception for each initial interception value.

Figure 2 Average Monthly Flow Hydrographs

The calibration was realized by comparing values of observed and simulated flows from 1930 to 2008 to the average monthly flow hydrographs and flow duration of the average monthly flow. Average, standard deviation and coefficient of determination of the observed series were considered as well.

Jatoba flow gauging station

The calibration was completed at the Jatoba station in the Tapajos River, which covers a drainage area of 387,634 km².

Figure 3 Monthly Flow Hydrographs

Parameters and graphs related to the period of calibration, January 1975 to December 2008, also are presented. This permits evaluation of the performance of the rainfall-runoff modeler against this station. Figure 2 provides a comparison between monthly flow hydrographs observed and simulated. Figure 3 provides a comparison between monthly hydrographs observed and simulated. Finally, Figure 4 shows a comparison between flow duration curves observed and simulated.

Figure 4 Flow Duration Curves of Average Monthly Flows

As it is possible to see, the completed series has the same behavior, temporal and statistical, as the previous one. This shows that the model preserves not only the seasonality of the data series (an intrinsic characteristic of the regional climate) but also some statistical parameters, thus making them part of the same statistical universe.


The use of mathematical modeling enabled generation of a monthly flow serial covering January 1931 to December 2008. Data for the more recent period (1975 to 2008) was replaced by data generated through correlation between the three stations previously mentioned, resulting in a final series of monthly flows.

The full series can be transferred to an axis of hydroelectric developments placed next to this gauging station through the relation between the drainage area (catchment area) of both places. In this case, the series was used to generate the average monthly flow at the Sao Luiz do Tapajos and Jabota hydroelectric plants, two projects on the Tapajos River that together will have installed capacity of 8,500 MW and generate about 40,800 MWh.


1. ANA – Agencia Nacional de Aguas, Sistema de Informacoes Hidrologicas HidroWeb,

Eurico de Carvalho-Filho and Iara P.G. Machado, junior engineers with CNEC WorleyParsons, develop inventory and technical feasibility studies. Humberto Jacobsen Teixeira, a civil engineer at the Polytechnic School of the Sao Paulo University, specializes in developing studies and projects in hydrology, hydraulics and the environment. Gabriel S.C. Rocha is a project manager and Maria Tereza F.R. Campos, MBA, is superintendent with CNEC WorleyParsons Rocha focuses on hydro plant studies and Campos focuses on power projects.

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