Three-Dimensional Hydrodynamic and Sediment-Transport Modeling of a Shallow Urban Lake in the Brazilian Amazon

Abstract

A three-dimensional numerical model was developed using Delft3D-Flow to simulate temperature dynamics, flow circulation, and sediment transport in Água Preta Lake, a shallow urban lake in the Brazilian Amazon. The simulation incorporated meteorological and physical data—including water inflows, temperature, bathymetry, and bed roughness—collected through in situ campaigns and meteorological stations. It was calibrated using a temperature time series (RMSE = 0.27 °C; MAE = 0.87 °C; R² = 0.79; ρ = 0.89), and validated with two flow velocity measurements (RMSE = 0.009–0.012 m/s; ρ = 0.1–0.5) and with 19 temperature profiles over 4 months (RMSE = 0.08–0.93 °C; MAE = 0.12–2.04 °C; R² = 0.00–0.99; ρ = −0.29–0.99). Due to its shallowness, the lake does not develop thermal stratification, with a maximum vertical temperature difference of only 2 °C. The lake is fed by high-discharge inflows that significantly affect internal circulation and promote resuspension. This may increase turbidity and possibly alter ecological dynamics, favoring eutrophication processes. Additionally, the simulation showed sediment accumulation rate of 27,780 m³/year; if continuous, this indicates complete siltation in about 318 years. These results emphasize the importance of ongoing monitoring, effective management of anthropogenic pressures, and restoration efforts, to prevent further degradation of these systems.

1. Introduction

Lakes are ephemeral environments in the Earth’s landscape, characterized by their short duration on a geological scale. Their decline is intrinsically linked to their own internal processes, such as the accumulation of organic matter in sediment and the deposition of sediments carried by inflows [1].

Sediment dynamics and water quality of these systems are closely coupled to hydrodynamic and flow circulation patterns, particularly in shallow, tropical, wind-driven lakes [2]. Due to their limited depth, these lakes are unable to sustain thermal stratification. They are also frequently subjected to sediment resuspension events driven by wind-induced surface currents [3,4,5].

Shallow lakes generally exhibit lower resilience compared to larger and deeper lakes, making them more susceptible to impacts from pollution and eutrophication processes [6]. Their increased vulnerability stems from their sensitivity to metabolic disturbances, which can accelerate ecological degradation and lead to lake disappearance [7].

Sediment resuspension further disrupts lake metabolism by increasing nutrient concentrations and turbidity in the water column, reducing the depth of the photic zone. This favors the dominance of planktonic organisms [6,7] and promotes the proliferation of floating macrophytes on the lake surface [7,8,9,10].

Lakes can be characterized not only by their dimensions, but also by the spatial distribution of temperature. Their thermal structure is reflected in the interactions between lake morphology and external forcing mechanisms—particularly the wind, which plays a dominant role in shallow systems [7]. Lake temperature plays a key role in the analysis of circulation patterns. In shallow systems, the typically low flow velocities can fluctuate rapidly, often resulting in poor statistical agreement between observed and simulated data. This variability makes it challenging to calibrate models based solely on current measurements [11].

Many shallow lakes are located within large urban centers, where they play a significant role in regulating air temperature and humidity, two major factors contributing to human thermal and health. They can also mitigate climate change-related processes, such as extreme heat island effects, which are associated with increased morbidity and mortality [12,13].

Furthermore, urban lakes provide numerous ecosystem services that influence the quality of life, including water supply for domestic and industrial activities [14,15,16], maintenance of biodiversity in this ecosystem [6,14,17,18,19,20,21], adjustment of the urban microclimate [6,12,13,22,23,24], conservation of green areas [12,25], and recreational and educational activities [14,25,26].

Nestled in the Brazilian Amazon lies the capital of Pará, Belém, a large urban center with a population of 1.3 million, part of the Belém Metropolitan Region (BMR) [27]. The capital faces increasing pressure on nearby urban ecosystems, due to rapid and unplanned development [26]. One of the few remaining green areas in Belém is the Utinga State Park, which houses to two Amazonian lakes —Bolonha and Água Preta—that supply the BMR. These lakes are situated amidst residential areas and highways, ongoing urbanization and associated anthropogenic pressures [18,28,29]. Several studies have documented processes of silting, pollution, and eutrophication occurring in the Utinga lake system [30,31,32].

Three-dimensional numerical modeling is essential for enhancing understanding of lake dynamics, particularly regarding hydrodynamics and sediment transport, as it allows simulation across temporal and spatial scales. Despite this, lakes are defined as slow-moving or still environments, leading many studies to use one-dimensional vertical models that represents changes along the water column [33,34]. This approach, although useful in certain contexts, limits the spatial and temporal analysis of processes, thereby compromising a more comprehensive understanding of lake dynamics [34]. Similarly, this occurs in Lake Água Preta, where research focuses on two-dimensional hydrodynamic models [35,36].

Given the morphological complexity of shallow lakes, especially in terms of bathymetry and surrounding topography, these limitations underscore the need to apply three-dimensional models [37]. These models are valuable tools for obtaining more precise insights into lake behavior. In particular, they enable improved representation of hydrodynamic patterns, temperature profiles, and sediment transport dynamics.

In this study, we focus on understanding the hydrodynamic and morphodynamic processes of Água Preta Lake, in order to monitor the changes using three-dimensional numerical modeling (Delft3D Flow). By highlighting the sedimentation and erosion parameters and developing a diagnosis of the lake’s hydro-sedimentary dynamics, we aim to provide a new perspective on the current state and future trajectory of Lake Água Preta.

2. Materials and Methods

2.1. Study Area

Água Preta Lake is located within an Environmental Protection Area (APA), Utinga State Park. This APA was established primarily to preserve the potability of the waters of Bolonha and Água Preta lakes, while also providing a space for recreation and the development of ecological and scientific activities [38]. Together, these two lakes form a lake system that supplies 65% of the city of the BMR.

The lake system was engineered to function as a potable water reservoir for the BMR. The inflow and outflow are regulated by the Pará State Sanitation Company (COSANPA), which controls routing through the system to ensure continuous supply to the water treatment facility.

Thus, the system can be described as comprising three major water bodies: the Guamá River, Água Preta Lake and Lake Bolonha (Figure 1). To maintain a constant water level in Água Preta Lake, COSANPA diverts water from Guamá River into the Lake. This artificial inflow varies seasonally, reaching up to 7 m³/s during dry periods and 3 m³/s during rainy ones. Subsequently, water from Água Preta Lake flows into Bolonha Lake through an artificial, gravity-fed channel (i.e., without pumping), ultimately reaching the water treatment plant.

In addition, Água Preta Lake is classified as a shallow lake, with a maximum depth of 4 m, and small in size, approximately 7.2 km², resulting in a volume of approximately 9,905,000 m³ [38,39]. Given its limited depth and volume, there is significant concern regarding the inflow from the Guamá River, which carries a high suspended-sediment load [40]. This sediment input has potential to accelerate silting processes within the lake.

The meteorological parameters of the region differ from those of the surrounding urban environment, due to the extensive vegetation cover within the area. The vegetation contributes to the formation of a local microclimate, which lies between two climatic zones, Am and Af. Am is defined as a tropical climate with monsoons, and Af is the same as the city of Belém [38], which would be a tropical climate, without seasonal winter [41,42,43]. The region experiences two distinct seasonal periods: a rainy season from December to May, and a dry season from June to November.

2.2. Data Acquisition

Utinga State Park has its own linimetric station, which was implemented by the Observatory of the Amazon Coast (OCA) in November 2023. Consequently, part of the meteorological data used in the simulations was collected from this station, while additional data were obtained from the Belém Meteorological Station—monitored by the National Institute of Meteorology (INMET)—located approximately 3 km from Água Preta Lake (Figure 1). Both stations record meteorological data at 2 m above the surface.

The input data were primarily meteorological, including air temperature (C), relative humidity (%), and wind speed and direction (m/s), obtained by the OCA station, while solar radiation (J/m²·s), precipitation (mm/day), and cloud cover (%) data were obtained from the INMET station for the period from November 2023 to October 2024 (Figure 2), a period that covers both dry and rainy seasons.

To describe the morphology of the lake, a bathymetric survey was conducted in November 2023, using an echo sounder coupled with a Garmin GPS (Chartplotter Echomap UHD 62CV model, Garmin Ltd., Taipei, Taiwan).

The values for water–inflow discharge (m³/s) were obtained from COSANPA, and these values were adapted so that the hydrodynamic simulations more accurately reflected reality (

Table 1. Modified monthly inflow–discharge data provided by the Pará State Sanitation Company (COSANPA).

Monitoring Period	Discharge (m3/s)	Monitoring Period	Discharge (m3/s)
November 2023	20	May 2024	16
December 2023	19	June 2024	18
January 2024	16	July 2024	19
February 2024	14	August 2024	20
March 2024	14	September 2024	20
April 2024	14	October 2024	19

).

For the simulation calibration, a temperature time series was used. This dataset was collected from a Solinist LeveLogger 5 (Solinst Canada Ltd., Georgetown, ON, Canada) water-level sensor, installed on the A17 in February 2024.

Model validation was conducted using monthly temperature profiles collected at 19 locations across the lake with a CTD (Conductivity, Temperature, Depth) sensor—specifically, the SBE 19plus V2 SeaCAT Profiler (Sea-Bird Scientific, Washington, DC, USA)—with a sampling frequency of 4 Hz. Additionally, two current velocity time series were employed, obtained using an INFINITY-EM current meter (JFE Advantech Co., Ltd., Nishinomiya, Japan). These measurements were recorded at points A08 and A13 (Figure 3), positioned 0.5 m above the lakebed, over a one-day period.

Temperature was the main parameter used in the calibration and validation of the lake’s hydrodynamics, since the body of water has a controlled and constant level throughout the year, as well as slow circulation, with a maximum speed of approximately 0.31 m/s [36], subject to rapid fluctuations in direction. As such, temperature responds to variations in circulation and water-quality parameters, and is widely used in the calibration and validation of hydrodynamic and water-quality simulations in shallow lakes. Prior studies have demonstrated this approach in different lake systems, such as Otter Lake, Minnesota, USA [44], Lake Okeechobee, Florida, USA [45], and Créteil, Paris, France [46].

2.3. Model Description

The simulations were undertaken using the Delft3D-Flow (D3D) model, a numerical model capable of solving nonlinear differential equations in a discretized domain [47]. For the purpose of forcing movement in the simulated fluid, the model utilizes external forces to generate a flow circulation pattern. These equations are derived from the three-dimensional Navier–Stokes for incompressible surface flow, under shallow water and Boussinesq assumptions [47]. Additionally, the model adopts the continuity equations for solving vertical velocities [47] and heat transfer [21,47]. D3D was selected for its broad applicability, and demonstrated accuracy in the hydrodynamic modeling of deep lakes [48], shallow lakes [49], and urban lakes [46].

2.3.1. Heat Flux Model Description

D3D includes five different heat flux models, and their implementation often depends on the characteristics of the water body and the availability of input data for the simulation. In the case of Lake Água Preta, Heat Flux Model 1 (absolute flux using total solar radiation) was selected, as it provides a simplified representation of heat fluxes that is well-suited for small and shallow-water bodies [47].

The components of the heat balance are calculated by D3D, using a free surface area [47,50]. The heat balance is determined based on incident radiation, return radiation, evaporation, and convection, as in Equation (1). Vaporization and convection are processes influenced by air and water temperature, relative humidity, and wind speed. These variables are used as input data in the simulations of Água Preta Lake.

$$Q_{total}=Q_{sn}+Q_{an}-Q_{br}-Q_{ev}-Q_{co},$$

(1)

In this equation, the heat balance at the air–surface interface is solved by considering the main components of energy exchange. A total heat flux $Q_{total}$ (J/m²s) is determined by the sum of the contributions of different fluxes: $Q_{sn}$, net incident solar radiation (short waves); $Q_{an}$, net incident atmospheric radiation (long waves); $Q_{br}$, back radiation (long waves emitted by the surface); $Q_{ev}$, evaporative heat flux (latent heat); and $Q_{co}$, convective heat flux (sensible heat). In this way, the heat balance considers both energy gains and losses through different exchange mechanisms, with net solar radiation $Q_{sn}$ being one of the main sources of heat input into the system.

By using the total heat flow, we calculate the heat flow on the free surface of the body of water. Thus, it is possible to calculate the temperature variation of the lake surface and, in continuity, the temperature in the deeper layers, as in Equation (2).

$${\displaystyle \frac{\mathsf{\partial }{T}_s}{\mathsf{\partial }t}}={\displaystyle \frac{Q_{total}}{{\rho }_w{c}_p\mathrm{∆}{z}_s}},$$

(2)

Here, assuming that the heat flow model neglects heat exchange with the bottom, the model may lead to an overestimation of water temperature, especially in shallow areas, as in our case study. Given this, it follows that $c_p$ is the specific heat capacity of seawater (=3930 Jkg⁻¹ K), ${\rho }_w$ is the specific density of water (kg/m³), and $\mathrm{∆}{z}_s$ is the thickness of the upper layer (m).

2.3.2. Morphodynamics and Sediment-Transport Module Description

The D3D sediment-transport module uses two types of sediments, cohesive and non-cohesive. For this study, cohesive sediment types were used, defined as silt and/or clay, which are common in low-hydrodynamic environments, such as lakes. This module incorporates transport, erosion, and deposition, in the simulations.

For the transport of suspended sediments in three dimensions, it is calculated from the solution of the mass balance equation for suspended sediments [47,51], described by Equation (3):

$${\displaystyle \frac{\mathsf{\partial }c}{\mathsf{\partial }t}}+ {\displaystyle \frac{\mathsf{\partial }uc}{\mathsf{\partial }x}}+ {\displaystyle \frac{\mathsf{\partial }vc}{\mathsf{\partial }y}}+{\displaystyle \frac{\mathsf{\partial }(w-w_s)c}{\mathsf{\partial }z}}- {\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }x}}\left({\epsilon }_{s,x}{\displaystyle \frac{\mathsf{\partial }c}{\mathsf{\partial }x}}\right)-{\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }y}}\left({\epsilon }_{s,y}{\displaystyle \frac{\mathsf{\partial }c}{\mathsf{\partial }y}}\right)-{\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }z}}\left({\epsilon }_{s,z}{\displaystyle \frac{\mathsf{\partial }c}{\mathsf{\partial }z}}\right)=0$$

(3)

In this equation, $c$ is the mass concentration of sediment fraction i (kg/m³), terms ${\epsilon }_{s,x}$, ${\epsilon }_{s,y}$ and ${\epsilon }_{s,z}$ are turbulent diffusivities of the sediment fraction in the x, y, and z directions (m²/s), u, v, and w are components of the flow velocity in the x, y, and z directions (m/s), and $w_s$ is the sedimentation velocity of the sediment fraction (m/s).

The bathymetry of the water body is overwritten at each time step, based on changes in suspended- and bed-sediment loads, multiplied by the morphological scaling factor (MORFAC), which in this case study is set to the default value of MORFAC = 1. This factor can be adjusted to accelerate the morphological evolution within the simulation [47,52]. Therefore, the variation in bed-sediment load (Mb) is first calculated using Equation (4), then used to solve the bathymetric update in Equation (5).

$${\displaystyle \frac{\mathsf{\partial }{M}_b}{\mathsf{\partial }t}}=MORFAC\left(-{\displaystyle \frac{\mathsf{\partial }{S}_{b,c,x}}{\mathsf{\partial }x}}-{\displaystyle \frac{\mathsf{\partial }{S}_{b,c,y}}{\mathsf{\partial }y}}\right)$$

(4)

$${\displaystyle \frac{\mathsf{\partial }{z}_b}{\mathsf{\partial }t}}=-{\displaystyle \frac{MORFAC}{1-p}}{\displaystyle \frac{1}{\rho }}\left({\displaystyle \frac{\mathsf{\partial }{S}_{b,c,x}}{\mathsf{\partial }x}}+{\displaystyle \frac{\mathsf{\partial }{S}_{b,c,y}}{\mathsf{\partial }y}}\right)$$

(5)

where Mb is the integrated sediment mass in the bed (kg/m²), $S_{b,c,x}$ and $S_{b,c,y}$ are the bottom sediment loads (in x and y) transported by the currents, zb is the variation in bed level, p is the porosity, or water fraction of the total bed volume, and ρ is the specific density of the sediment (kg/m³).

2.3.3. Configuration and Parameterization of Simulation Input Variables

The simulation was run from November 2023 to September 2024, to encompass rainy and dry seasons, at a one-minute timestep resolution. The meteorological forcings and discharge scaling factors were parameterized through a one-at-a-time sensitivity analysis comparing simulated and observed temperature profiles, time series, and flow measurements at sites A08 and A13. Scaling factors were adjusted following the methodology proposed by [53]; therefore, statistical metrics were analyzed to assess the impact of each modification relative to the observed temperature time series and vertical profiles.

Since the D3D heat flux model 1 considers cloudiness as a constant parameter, this parameter was modeled for use in the simulations (75%). However, since we are dealing with an Amazonian region, i.e., one with high cloudiness, it was necessary to multiply the solar radiation by 1.8, so that the simulations would more accurately represent the actual data.

For wind data, it was verified that the input data for D3D must be 10 m from the surface (U₁₀). Therefore, the equation described by [54] was applied, which assumes a logarithmic behavior of the wind intensity profile, where its speed increases with height, also taking into account the roughness of the ground or degree of obstruction.

The wind measurements taken by the AP weather station occur on land, and not directly over the lake surface. For this reason, a correction factor of 1.5 was applied to the wind magnitude, as proposed by [55,56], in order to more accurately represent the conditions on the water surface in hydrodynamic models. This correction takes into account the difference in surface roughness between soil and water, which affects wind intensity near the surface, as described by [24]. In the simulations, the value entered for the wind drag coefficient was 0.003, according to [57], which adjusts the drag coefficient, assuming an empirical value of 0.003 for shallow and wide lakes.

The Água Preta Lake domain was discretized into a structured mesh, with 20 × 20 m elements and 10 vertical sigma-type layers (Figure 1), i.e., varying in size according to bathymetry and free surface [47]. At the free-surface boundary of the simulated domain, the movement is generated by the wind shear stress on the water surface, and the magnitude of the shear stress is defined in Equation (6) as

$$\left|{\tau }_s\right|={\rho }_a{C}_d{U}_{10}^2$$

(6)

where $\left|{\tau }_s\right|$ is the magnitude of wind shear stress, ${\rho }_a$ is air density, and $C_d$ is the wind drag coefficient, dependent on $U_{10}$.

At the inflow boundary, the time series provided by COSANPA was used, where a multiplication factor of 5 was applied so that the simulations would better reflect the actual data. The water temperature was the mean surface temperature of Guamá river, 29 °C [58], and sediment load entering the system was empirically defined as 0.2 kg/m³.

Since we assumed that the lake level is constant during the simulation period, the outflow limit was set as the water level, where the water level is constant throughout the simulation period, thus behaving as a response limit to the inflow.

The bottom roughness values were discretized in the simulation domain, determined from the calculation of the Manning coefficient and using the methodology described by [59], which takes into account the granulometric characteristics of the bottom sediment, the type of vegetation, and the degree of obstruction of the water body [60], to determine roughness. After discretizing the roughness by the particularity of the areas present in the domain, the roughness values were interpolated in the domain, as described in

Table 2. Calculated Manning’s roughness values, classified according to the specific characteristics of each region in the domain.

Region	Manning Roughness Value
Region dominated by macrophytes	0.030
Sandy sediment-predominance region	0.025
Sandy-silty sediment region	0.018
Silty sediment region	0.016

.

Four statistical metrics were applied in the model calibration stage: (i) root mean square error (RMSE), to analyze the difference between the modeled and actual data; (ii) Pearson’s correlation (r), to access the linear relationship between the data; (iii) the coefficient of determination (R²), to test the simulation skill in predicting real data; and (iv) the maximum absolute error (MAE), to quantify how much the simulation differs from the observed data. These metrics are commonly used for the validation and calibration stages of lake-environment simulations [33,46,48,61,62,63].

3. Results and Discussion

Given the complexity of shallow lakes and their ability to rapidly respond to external forcings, three-dimensional hydrodynamic models are commonly applied to characterize key processes such as temperature stratification and flow velocity profiles. This modeling approach enables the analysis of these parameters in both vertical and horizontal dimensions, providing a more comprehensive understanding of lake dynamics.

In Lake Biwa [15] and Taihu [2], for example, 3D simulations have been employed to accurately represent flow circulation and assess the influence of river inflows, highlighting the three-dimensional nature of the hydrodynamic processes [2]. Similarly, studies conducted in Lakes Okeechobee [16] and Créteil [46] have demonstrated the complexity of lake hydrodynamics and underscored the importance of three-dimensional modeling for evaluating water-quality evolution in response to circulation patterns.

In Água Preta Lake, previous studies have implemented only two-dimensional models, focusing primarily on calibrating adjacent water bodies [35] or meteorological forcings [36]. However, these efforts did not include calibration or validation using in situ flow or temperature data, potentially compromising the reliability of the models. To address this limitation, we conducted dedicated calibration and validation procedures using observed temperature profiles and current flow data within the lake, aiming to improve the accuracy and robustness of the model simulations.

3.1. Calibration

During the calibration stage at point A17, the statistical metrics related to the temperature curves (RMSE = 0.27 °C and MAE = 0.87 °C) show that the simulation accurately represents the ambient temperature (Figure 4).

The MAE should be less than 20% of the maximum annual variation in lake temperature [61], a criterion met by the simulations. For Lake Água Preta, with seasonal minimum temperatures of 25 °C and maximum temperatures of 34 °C during the rainy (February–April) and dry (July–October) periods, this threshold corresponds to 1.8 °C. The obtained MAE and RMSE values were below this limit.

Furthermore, the Pearson correlation coefficient (ρ = 0.89) and coefficient of determination (R² = 0.79) indicate good agreement with observed data. Regression analysis confirmed a strong positive correlation between simulated and measured temperatures (Figure 4).

3.2. Model Validation

For flow velocities at monitoring points A08 and A13, only RMSE and Pearson correlation were used to compare observed and simulated data. The RMSE values were 0.009 m/s and 0.012 m/s, while the Pearson correlation coefficients (ρ) were 0.1 and 0.5, respectively. As previously stated, these statistical metrics are relatively weak, which is expected in shallow-lake simulations, due to the predominantly lentic flow conditions. Shallow lakes often experience rapid velocity fluctuations caused by wind gusts and rainfall [49,63]. Additionally, tall trees along the banks of Lake Água Preta obstruct wind flow, leading to a slight overestimation of modeled velocities (Figure 5).

When comparing the simulated and observed temperature profiles from points A01 to A19, it was possible to verify that the largest errors in the simulation are found at points A01, A09, A11, and A19 (

Table 3. Statistical metrics calculated between the simulation and CTD profile data collected at points A01 to A19, highlighting points with higher uncertainties associated with their specific local characteristics: A01, A09, A11, and A17.

	ρ				RMSE (°C)				R2				MAE (°C)
Sites	Dec	Feb	Jun	Aug	Dec	Feb	Jun	Aug	Dec	Feb	Jun	Aug	Dec	Feb	Jun	Aug
A01 *	−0.05 *	0.85	0.82	0.96	0.78	0.78	0.87	0.34	0.00	0.72	0.68	0.91	0.98	1.31	1.16	0.39
A02	0.95	0.85	0.94	0.83	0.80	0.26	0.42	0.26	0.91	0.74	0.89	0.69	0.91	0.43	0.64	0.28
A03	−0.29	0.86	0.99	0.96	0.24	0.41	0.57	0.37	0.08	0.73	0.99	0.91	0.27	0.70	0.75	0.50
A04	0.91	0.79	0.41	0.36	0.25	0.39	0.69	0.41	0.83	0.63	0.17	0.13	0.33	0.51	1.19	0.45
A05	0.98	0.86	0.97	0.47	0.24	0.46	0.43	0.25	0.96	0.74	0.94	0.22	0.29	0.49	0.69	0.35
A06	0.92	0.86	0.86	0.69	0.40	0.41	0.62	0.51	0.84	0.74	0.74	0.48	0.56	0.46	0.97	0.63
A07	0.90	0.91	0.84	0.89	0.38	0.60	0.50	0.55	0.82	0.82	0.70	0.80	0.47	0.72	0.97	0.91
A08	0.95	0.96	0.86	0.91	0.55	0.66	0.39	0.47	0.90	0.91	0.74	0.83	0.65	0.71	0.69	0.62
A09 *	0.73	0.69	0.97	−0.30 *	0.52	0.75	0.19	0.32	0.53	0.48	0.93	0.09	0.56	0.91	0.30	0.41
A10	0.97	0.99	1.00	0.93	0.37	0.63	0.59	0.46	0.93	0.97	0.99	0.86	0.48	0.68	0.82	0.75
A11 *	0.95	0.31	−0.65 *	0.94	0.50	0.52	0.08	0.56	0.90	0.10	0.42	0.89	0.62	0.68	0.12	0.72
A12	0.94	0.99	0.94	0.86	0.25	0.81	0.26	0.18	0.87	0.98	0.88	0.73	0.38	0.87	0.43	0.24
A13	0.94	0.95	0.91	0.98	0.35	0.67	0.40	0.14	0.88	0.90	0.82	0.95	0.72	0.75	0.60	0.24
A14	0.84	0.88	0.80	0.98	0.21	0.50	0.30	0.48	0.70	0.77	0.63	0.97	0.34	0.71	0.56	0.72
A15	0.98	0.87	0.92	0.67	0.35	0.51	0.44	0.29	0.96	0.76	0.84	0.45	0.64	0.61	0.65	0.50
A16	0.87	0.88	0.88	0.90	0.43	0.57	0.49	0.31	0.75	0.78	0.77	0.82	0.68	0.94	0.73	0.53
A17 *	0.99	0.92	−0.19 *	0.95	0.18	0.10	0.87	0.56	0.97	0.85	0.04	0.90	0.33	0.18	2.04	0.83
A18	0.96	0.55	0.89	0.89	0.56	0.77	0.44	0.20	0.93	0.30	0.80	0.80	0.96	1.40	0.63	0.41
A19	0.56	0.65	0.99	0.98	0.74	0.62	0.53	0.93	0.32	0.42	0.97	0.96	1.07	1.16	0.60	1.34

Note: * Values with low statistical metrics due to specific local conditions affecting these observation points.

). There were special cases, where the validation metrics were low, at points A01, A03 in December, and A17 in June. Floating macrophytes tended to settle in these regions of the lake. As a result, the lake surface in these locations was covered by this vegetation, resulting in changes in the temperature profile behavior in these locations. These uncertainties are associated with local anthropogenic changes and variables not included in the simulations.

Sampling points confined to or close to the margins are subject to local influences that can alter temperature dynamics through the discharge of domestic effluents, tree canopies, and small local springs. This is the case at points A01 and A19, located at the northern ends of the lake, where the greatest temperature differences occur. These points are located in sheltered and morphologically funneled regions, keeping the site shaded by tree canopies during the day. In addition, they are subject to the discharge of domestic effluents.

Points A09 and A11 are located closest to the lake’s inflow, which may explain the lower correlation indices observed at these sites. The artificial water supply has the potential to disrupt the lake’s natural hydrodynamics, altering previously established circulation patterns. These changes can affect temperature distribution and influence other water quality parameters.

3.3. Zonation

To organize the presentation and discussion of the simulation results, the domain was divided into three areas, according to the particularities of each zone, namely, west, the portion influenced by inflow and outflow; central, the location that directly receives the inflow, with the most intense water flow in the system and the deepest regions of the lake; and east, the most controlled portion of the lake, without a water inflow or outflow system (Figure 6).

Observation points A07, A10, and A16 were selected to represent the western, central, and eastern portions, respectively. This enables an understanding of the stratification patterns over time in the system.

3.4. Circulation Patterns of Água Preta Lake

Given the lentic nature of lakes, the flow present in this environment is of low magnitude, primarily resulting from the action of wind on surface waters, presenting a logarithmic vertical profile [64].

Figure 7 shows the surface- and bottom-circulation pattern of Água Preta Lake in February (rainy) and June (dry) 2024. These months were chosen because they represent seasonality, and, according to [36], they show that February and June are the months with the lowest and highest wind speeds, respectively.

The average surface velocity ranged from 0 m/s to 0.19 m/s and from 0 to 0.15 m/s at the bottom. From this, it was observed that the domain has low velocities throughout, with maximum velocities associated with inflow and outflow.

The inflow waters enter the lake through a funnel-shaped channel and then reach the central region. This flow is slowed down when it encounters the domain waters, which are characterized by being slower than the channel flow, and which results in directing the inflow waters to deeper layers [15]. This circulation forms currents in the central region that behave similarly to a vortex, highlighting the locations that tend to have greater sedimentation. In the outflow, the artificial channel between the Água Preta and Bolonha lakes increases the magnitude of the currents, explained by the difference in elevation between these areas, which can reach 6 m, culminating in gravity flow [35].

The recorded values show that the rainy season has lower average speeds when compared to the dry season, due to the local wind pattern and the morphological characteristics of the lake (Figure 7). Winds in the region are stronger during periods of low precipitation, due to the influence of the Intertropical Convergence Zone in the region [41]. In addition, Água Preta Lake has a large fetch region, resulting in higher current speeds during the dry season, since wind is one of the controlling agents of the current field in lake systems.

In the eastern region, without the influence of inflow and outflow, the average surface and bottom currents have speeds of 0.008 m/s and 0.001 m/s, respectively. In the central and western regions, the average speeds are higher, at 0.02 and 0.009 m/s at the surface and 0.016 and 0.013 m/s at depth. The western region shows a peculiar flow in relation to the other sections, forming a constant flow at depth, which connects the inflow and outflow points (Figure 7).

This constant flow, occurring at the bottom of the lake, can promote the resuspension of sediments and organic matter along the analyzed stretch. Such resuspension may lead to the release of substances previously bound within the sediments—such as nutrients [9]. Once released, these nutrients become available in the water column, and can be assimilated by aquatic organisms, including macrophytes, potentially stimulating their growth [1]. Additionally, resuspension processes might release gases generated during the decomposition of organic matter and influence physical–chemical parameters such as pH, dissolved oxygen, and redox potential [19].

In general, no significant variations in horizontal circulation patterns were observed between the periods analyzed. In June, speeds greater than 0.005 m/s were recorded in a larger portion of the domain, possibly associated with increased wind intensity and the predominance of winds from the north (10–15°). On the other hand, the lower velocity values observed on the western side of the lake in February are attributed to the incidence of NNE winds (20–25°) during this period. This influence is also a reflection of the morphology of the lake, which has north–south oriented corridors, expanding the area of action of winds from the north. In this context, the horizontal speeds of Lake Água Preta exhibited relatively uniform behavior throughout the simulated periods, with occasional variations in intensity throughout the seasons.

The maximum speeds of the lake occur at the surface, due to the action of the winds, which generate surface currents through turbulent stress, transmitting energy vertically through the interaction between adjacent layers of the water column. This energy dissipates progressively, so that the deeper layers are influenced by the substrate, resulting in a loss of speed, due to friction generated by the flow in contact with the bottom [7,65,66]. This phenomenon gives rise to a vertical speed profile that resembles a logarithmic curve.

However, because it is a shallow lake with a maximum depth of approximately 4 m, the attenuation of velocity in the deeper layers is less significant. Thus, when horizontal currents interact with the bed, a differential flow is formed at depth. This flow can have a magnitude similar to, or even greater than, that of surface currents; however, it tends to move in the opposite direction to the prevailing surface flow [7].

This phenomenon generates zones of minimal horizontal velocity, intensifying vertical velocity and promoting the resuspension of the surface layer of unconsolidated sediments. This resuspension can enrich the water column with nutrients, potentially altering water-quality parameters such as turbidity, and impacting the lake’s ecology. Increased turbidity tends to reduce light penetration into deeper layers, limiting the establishment of submerged macrophytes [7]. On the other hand, emergent species, adapted to the surface, can proliferate, due to the increased bioavailability of nutrients in the water column. This process can favor excessive colonization of the lake by certain species, resulting in a possible imbalance in the food chain [67].

3.5. Temperature Patterns and Stratification

Figure 8 shows the expected pattern for a shallow lake located in an equatorial region. There is slight thermal stratification during the day, with an average difference of 0.1 °C and a maximum of up to 2 °C between the surface and the bottom. This stratification occurs between 12 p.m. and 2 p.m., when the highest daily temperatures and radiation indices are recorded. The greatest temperature differences are between day and night, with minimum temperatures of 29 °C and maximum temperatures of 31 °C. Throughout the simulated period between dry and rainy seasons, we have a maximum difference of up to 10 °C, with a minimum of 26 °C and a maximum of 36 °C.

The lowest temperatures in the simulation occurred in February, due to the variation in air temperature and solar radiation incident on the lake surface (Figure 8). The month of June had the highest temperatures among the periods analyzed, resulting from the increase in temperature and solar radiation, promoting greater heating of the surface layers and, consequently, heat diffusion to greater depths (Figure 8).

The points located in the western (A08) and central (A10) areas have similar behaviors, showing more accelerated cooling at night, since this area is wider and strongly influenced by the inflow, causing greater intensity in the circulation of this location. The eastern section (A16) showed lower temperatures than the other zones, as the influence of inflow is minimal in relation to the western and central zones, which, combined with the wind pattern of the system coming from the NNE, moves the water to the other zones.

In the three sections of the lake, the absence of a well-pronounced thermocline was observed during the four months of analysis, and so remaining unstratified for most of the time, with minimal stratification during periods of greater solar intensity. In shallow lakes, winds have the capacity to mix the surface and bottom layers, resulting in total circulation between the layers. Between the dry and rainy seasons of 2024, there was no significant difference in wind intensity, only 10° in its direction from NE to NNE, so the stratification pattern is the same in both seasonal periods.

Thus, Lake Água Preta, according to its temperature pattern, is classified as a polymictic lake, with multiple daily circulations, a classification characteristic of shallow and large lakes [1].

February showed a practically homogeneous distribution pattern, both horizontally and vertically, with average horizontal variations of 0.7 °C and vertical variations of 0.8 °C. In contrast, June showed some heterogeneity in the horizontal temperature gradients, with the highest average temperatures concentrated in the eastern arm of the lake, both at the surface and at depth.

In the central region, the inflow from the Guamá River generates a temperature gradient, where, closer to the inflow, the temperature tends to decrease by about 0.5 °C. This occurs due to the simulation settings, where the water inflow was defined at a temperature of 29 °C.

In the western zone of the system, a temperature gradient is formed from the inflow to the outflow, due to the lower velocities in the zone, which tend to transfer less heat between the layers. To the north of this section, the temperature decreases, due to the increase in velocity that promotes heat exchange with the outflow currents, evidenced by colder waters leaving the simulation domain (Figure 9).

The occurrence of total daily circulation in the lake has several implications for its metabolism. This phenomenon allows the movement of substances and organisms that inhabit the environment [68] and demonstrates that phosphorus concentrations in the surface and bottom layers of Lake Água Preta have similar values, whereas lakes normally accumulate this element mainly in sediments [64]. This suggests the circulation of this nutrient in the water column, which is made possible by the thermal destratification of the lake, leading to greater availability of this substance.

This process can, therefore, contribute to eutrophication through the constant circulation of nutrients. It also influences the permanence of potentially toxic metals in the water column, which are found in sediments located on the banks near the lake’s occupied areas [69,70].

Based on this temperature dynamic, it is possible to state that Água Preta Lake fits the pattern of polymictic lake environments; i.e., they stratify several times during the year. In addition, through the hydrodynamic behavior of the lake, the system presented circulation predominantly dominated by the action of winds, with opposite flows between the surface and the bottom (reverse flow), a phenomenon characteristic of shallow and wide lakes, dominated by the intensity and direction of the winds [7].

The simulations showed a sectorization of the lake due to the hydrodynamic particularities of each sector. The central and western sections are strongly influenced by the artificial pumping of water into the lake, modifying the circulation and temperature of the system. The eastern sector has more homogeneous flow and temperature gradients, reflecting variations in wind intensity and direction.

The central and western sectors, influenced by artificial pumping from the Guamá River, have a rich suspended-sediment load that increases their turbidity. This phenomenon can cause possible impacts on the system’s metabolism, such as the unavailability of light, the excessive increase of suspended nutrients (which can generate eutrophication, mainly on the lake’s shores), and the disappearance of submerged vegetation when critical turbidity is reached, resulting in a murky lake dominated by phytoplankton [8,71].

When a lake reaches a critical point of turbidity, it becomes resistant to restoration alternatives, hindering water-clarification processes, such as the establishment of submerged macrophytes that reduce turbidity and prevent sediment resuspension [8,71,72]. The change in turbidity can result in toxic algal blooms, odor, and significant loss of ecosystem services, such as water potability [71,73].

3.6. Transport and Sedimentation of Lake Água Preta

In Figure 10, it can be observed and confirmed that, in both the dry and rainy seasons, sediment transport occurs mainly through the Guamá River’s inflow into Lake Água Preta.

This sediment load from the system’s inflow tends to flow from the central sector to the western sector, due to the current formed between the inflow and outflow points, resulting in the western side of the lake having more turbid waters than the eastern side. Between seasonal periods, there is no significant difference in transport. However, there is a slight contrast in the way the sediments dispersed. In June, due to the increased intensity of the lake currents, the sediment load tends to concentrate more in the central region, as the velocity vectors of the lake coming from the north push the sediment load towards the central region. However, in February, this speed decreases, which allows for greater spreading of these suspended sediments. This can be observed at the tip of the transport cloud in the easternmost region, where in February, transport tends to be directed slightly more to the east.

Based on the sediment transport occurring in the domain, it was possible to verify the difference between the bathymetries, highlighting the locations where the greatest sediment deposition occurs in the lake. The areas with the most significant accumulation are predominantly concentrated in the central region of the lake. These vary, with local sediment accretion that may reach up to approximately 0.30 m, especially in the area near the Guamá inlet. In addition, the lake, considering its entire domain, reached an average elevation of 0.05 m.

This deposition is associated with the behavior of the inflow, which has a high sediment load and high velocities, compared to the rest of the system. Upon entering the lake, this flow slows down considerably, reducing its sediment-transport capacity. As a result, preferential depositions occur in the central region, especially near the inflow entry point, where the energy of the flow is dissipated more quickly.

Previous hydrodynamic- and elevation-based studies of Lake Água Preta have estimated sediment-accumulation rates based on comparisons of lake elevation over time, but with validation of only elevation [35] or meteorological forcings [36]. One such study compared bathymetric data from 1975 and 2009, estimating sedimentation rates between 23,000 and 29,000 m³/year [35]. In our study, three-dimensional numerical simulations confirmed that the sedimentation rate remains within this range, yielding an estimate of approximately 27,780 m³/year for the year 2024.

Based on this sedimentation rate, it is possible to estimate the lake’s lifespan. Assuming a constant rate of sediment input, and using the volume of Água Preta Lake of 8,847,061 in 2006 as calculated by [35,68], the lake is projected to become entirely silted in approximately 318 years from 2024. This estimate aligns with the findings of [35], which reported a silting timeframe between 295 and 381 years.

4. Conclusions

Three-dimensional numerical modeling was developed using Delft3D for Água Preta Lake, simulating the lake’s circulation and sedimentation patterns. The simulations showed good results in calibrating and validating the temperature both over time and for spatial differences in the system. However, time-series analysis revealed that the model tended to underestimate both maximum and minimum temperature values. This discrepancy is likely related to the shallow nature of the lake, which complicates the model’s ability to capture extreme thermal fluctuations. The greatest disparities in statistical metrics were associated with site-specific conditions at individual monitoring points, such as shading from trees or the influence of anthropogenic effluents that locally alter water temperature.

Água Preta Lake did not show large seasonal variations in temperature and velocity. However, the dry season showed higher temperatures and velocities in the lake as a whole. Due to the region being equatorial, that is, subject to slight temperature fluctuations, these variations are small. As the lake studied has shallow depths and is subject to intense solar radiation throughout the day, the temperature showed a maximum difference of 2 °C between the surface and the bottom. The phenomenon of reverse flow was also observed in the lake, understood as a deep flow that has the opposite direction to the surface flow.

Under natural conditions, the lake is mainly dominated by the action of the winds. However, based on the sectorization of the lake, the central region showed that the intense artificial inflow of the Guamá River into the system has the capacity to alter the circulation and sedimentation parameters of the lake. This process increases turbidity and the sedimentation rate in the vicinity of the inflow, which may lead to future degradation of the lake’s water quality, re-releasing nutrients into the water column and decreasing the rate of light entering the lake.

This can result in a system equilibrium of a turbid lake dominated by phytoplankton, reducing the amount of submerged macrophytes in the environment, which serve to regulate water color and transparency. This indicates that Água Preta Lake needs more monitoring projects, given its importance to the Belém metropolitan area, promoting ecosystem services, regulating the local climate, and providing drinking water.

Therefore, based on the diagnosis of Água Preta Lake, which highlights the need for further studies on the lake’s dynamics, numerical modeling performed as a strong tool, and it could also be used to predict new solutions for monitoring this lake that supplies the city of Belém.