Thermal functioning of a tropical reservoir assessed through three-dimensional modelling and high-frequency monitoring

Denis Furstenau Plec: Lead the conceptualization, obtained the results and wrote the text. Talita Fernanda das Graças Silva: Lead the text writing-review and editing and lead the data collection. Brigitte Vinçon-Leite: Lead the conceptualization, formal analysis, methodology, supervision and validation. Contributed with technical notes and revised the text. Nilo Nascimento: Lead the project funding, administration and the supervision. Contributed with technical notes and revised the text.

Editor-in-Chief: Adilson Pinheiro.

Associated Editor: Cristóvão Vicente Scapulatempo Fernandes.

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Figure 1
Location of Lake Pampulha and its tributaries: (1) Olhos d’água; (2) AABB*; (3) Bráunas; (4) Água Funda; (5) Sarandi; (6) Ressaca; (7) Tijuco and (8) Mergulhão. *river not named, popularly known as AABB (Associação Atlética Banco do Brasil – Athletics Association from Brazil Bank). Red lines indicate the respective catchment of the tributaries. Monitoring station in triangle: (1) Fluviometric (SAR18F – Sarandi and RES17F – Ressaca; (2) Meteorological station (A521 -UFMG and 83587 - Belo Horizonte); (3) Lake monitoring (P1, red dot).

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Figure 2
Lake Pampulha bathymetry, inflow location, thin dam location (yellow line), monitoring point (P1 – cyan cross) and spillway and inflow locations (blue lines).

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Figure 3
Vertical resolution for σ and Z-grid in point P1. Blue X represents the measurement depths.

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Figure 4
Water temperature (ºC) measured at point P1 for surface (0.5 m), 2.5 m, 5.5 m and bottom (9.5 m) depth during the calibration period (May 16^th to June 3^rd 2016) and validation period (May 29^th to June 14^th 2016).

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Figure 5
Tributaries inflow water during the calibration period (May 16^th to June 3^rd 2016) and validation period (May 29^th to June 14^th 2016).

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Figure 6
Measured temperature at P1 at surface (0.5 m) depth from May 15^th 2015 to August 10^th 2015.

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Figure 7
Tributaries inflow water from May 15^th 2015 to August 10^th 2015.

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Figure 8
Radiation, air temperature, wind intensity and direction, cloud cover and humidity measured at a meteorology station during the calibration period (May 16^th to June 3^rd 2016) and validation period (May 29^th to June 14^th 2016).

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Figure 9
Radiation, air temperature, wind velocity and direction, cloud cover and humidity measured at the meteorology station during May 15^th 2015 to August 10^th 2015.

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Figure 10
Wind velocity and direction, Air temperature and humidity, Cloud Cover and Radiation measured in the meteorology station for Calibration (May 16^th to June 3^rd 2016), Validation 2016 (May 29^th to June 14^th 2016) and Validation 2015 (May 15^th to August 10^th 2015).

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Figure 11
Wind direction (degree) and velocity (m/s): Calibration period (May 16^th to June 3^rd 2016), Validation period in 2016 (May 29^th to June 14^th 2016) and Validation period in 2015 (May 15^th to August 10^th 2015).

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Figure 12
Measured and simulated temperatures for the calibration period from May 16^th to June 3^rd 2016 at P1 station.

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Figure 13
Difference of surface (0.5 m) and bottom (9.5 m) for measurement and simulated temperatures for the calibration period from May 16^th to June 3^rd 2016 at P1 station. Blue dashed line represents a mixing condition with difference between surface and bottom of 0.25 ºC and grey lines represent differences of 1.0 and 2.0 ºC.

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Figure 14
– Water temperature (ºC) simulated at point P1 for surface (0.5 m), 2.5 m, 5.5 m and bottom (9.5 m) depth during the calibration period (May 16^th to June 3^rd 2016).

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Figure 15
Measured and simulated temperature for the validation period (May 29^th to June 14^th 2016) at surface (0.5 m), 2.5 m, 5.5 m and 9.5 m depths.

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Figure 16
Difference of surface (0.5 m) and bottom (9.5 m) for measurement and simulated temperatures for the validation period from May 29^th to June 14^th 2016 at P1 station. Blue dashed line represents a mixing threshold with difference between surface and bottom of 0.25 ºC.

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Figure 17
Simulated temperature for the validation period (May 29^th to June 14^th 2016) at surface (0.5 m), 2.5 m, 5.5 m and 9.5 m depths.

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Figure 18
– Measured and simulated temperature at P₁ station at surface (0.5 m) depth from May 15^th to August 10^th 2015.

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Figure 19
Computed inflow water temperature used as an input during the validation period (May 29^th to June 14^th 2016). Red dash line represents the sensitivity analysis with an inflow water temperature with a constant temperature during June 03^rd (scenario D1) and the black dash line during June 02^nd to 03^rd (scenario D2).

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Figure 20
Simulated temperature for the validation period (May 29^th to June 14^th 2016) at surface (0.5 m), 2.5 m, 5.5 m and 9.5 m depths at the upstream region of the lake (UP point, see ).

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Figure 21
Longitudinal transect of the lake model in red and observation points in black cross.

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Figure 22
Water level variation during the validation period (May 29^th to June 14^th 2016)

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Figure 23
Simulated lake water temperature during high inflow on June 03^rd 2016 at 13h along the reservoir longitudinal transect

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Figure 24
Measured and simulated temperatures at point P1 at the surface (0.5 m), 2.5 m, 5.5 m, 9.5 m depths for the validation period simulated (May 29^th to June 14^th 2016) for different inflow water temperatures (variating and constant).

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Figure 25
Simulated temperature for the validation period (May 29^th to June 14^th 2016) at surface (0.5 m), 2.5 m, 5.5 m and 9.5 m depths at the downstream region of the lake (DOWN point in ).

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Figure 26
Simulated velocity module at UP point (see ) for the validation period (May 29^th to June 14^th 2016) at surface (0.5 m) and bottom (2.0 m).

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Figure 27
Simulated velocity module at DOWN point (see ) for the validation period (May 29^th to June 14^th 2016) at surface (0.5 m) and bottom (13.85 m)

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Figure 28
Schmidt stability variation during the validation period (May 29^th to June 14^th 2016) at point P1

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Figure 29
Lake number variation during the validation period (May 29^th to June 14^th 2016) at point P1

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Table 1
Lake Pampulha climate characteristics measured between 1961 and 2001 at Belo Horizonte’s INMET meteorological station.

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Table 2
Lake Pampulha discharge frequenccy.

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Table 3
Characteristics of measuring devices at Lake Pampulha P1 station.

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Table 4
Range of parameter values tested in calibration.

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Table 5
Mathematical indicators for the hourly water temperature estimation methods.

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Table 6
Mathematical indicators for temperature with different values of wind intensity correction factor (dimensionless).

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Table 7
Mathematical indicators for lake temperature using Z-grid and σ-grid option.

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Table 8
Set of parameter values for hydrodynamic simulation in Lake Pampulha.

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Table 9
Number of days with difference between surface (0.5 m) and bottom (9.5 m) for measurement and simulated temperatures for the calibration period from May 16^th to June 3^rd 2016 at P1 station.

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Table 10
Model performance indicators for the calibration and validation period.

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Table 11
Water velocity module (cm/s) at station P1 durring the passage of 3^rd June peak flow.

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Climate	Tropical altitude
Air temperature	Monthly maximum of 28.8 ºC (February)
Air temperature	Monthly minimum of 13.1 ºC (July)
Dry season	April to September (monthly minimum 14 mm)
Rainfall season	October to March (monthly maximum 320 mm)

Return Period	Discharge (m³/s)
Annual mean flow	1.30
2 years	106.7
10 years	172.0
50 years	234.0
100 year	261.0

Variable	Sensor manufacturer	Monitoring Depth	Monitoring period	Frequency	Measuring Range	Sensor Resolution	Measuring Precision
Water Temperature	NKE	0.5 m	05/2015 to 06/2016	1 hour	−5 °C to +35 °C	0.05 °C	0.020 °C at 20 °C
Water Temperature	NKE	2.5, 5.5, 9.5 m	02/2016 to 06/2016	1 hour	−5 °C to +35 °C	0.05 °C	0.020 °C at 20 °C

Parameter	Range tested in calibration
Secchi (m)	-
Wind Factor (-)	0.40 to 1.40
Background Horizontal Eddy Viscosity (m²/s)	0.0025 to 0.025
Background Horizontal Eddy Diffusivity (m²/s)	0.0025 to 0.025
Dalton (-)	0.0013 to 0.0007
Stanton (-)	0.0007 to 0.0013

Method	Indicators	Values
Linear Regression	RMSE (ºC)	1.02
	R²	0.82
	NSE	0.82
MSSWF	RMSE (ºC)	1.50
	R²	0.75
	NSE	0.56

Depth (m)	Indicator	1.40	1.20	1.00	0.80	0.60
0.5	MAE (ºC)	0.53	0.44	0.39	0.36	0.37
	RMSE (ºC)	0.60	0.51	0.45	0.43	0.45
	RE (%)	2.29	1.9	1.67	1.56	1.57
	R²	0.76	0.76	0.77	0.76	0.73
2.5	MAE (ºC)	0.43	0.38	0.33	0.28	0.22
	RMSE (ºC)	0.50	0.44	0.38	0.33	0.27
	RE (%)	1.90	1.66	1.45	1.24	0.99
	R²	0.81	0.82	0.84	0.83	0.85
5.5	MAE (ºC)	0.40	0.34	0.29	0.23	0.17
	RMSE (ºC)	0.50	0.41	0.36	0.29	0.22
	RE (%)	1.77	1.50	1.27	1.00	0.77
	R²	0.89	0.88	0.93	0.94	0.95
9.5	MAE (ºC)	0.46	0.40	0.35	0.29	0.24
	RMSE (ºC)	0.57	0.51	0.45	0.38	0.32
	RE (%)	2.05	1.81	1.55	1.30	1.07
	R²	0.89	0.89	0.89	0.89	0.89

Depth (m)	Indicators	Grid type
Depth (m)	Indicators	σ-grid	Z-grid
0.5	MAE (ºC)	0.30	0.40
	RMSE (ºC)	0.42	0.51
	RE (%)	1.30	1.68
	R²	0.73	0.72
2.5	MAE (ºC)	0.15	0.18
	RMSE (ºC)	0.20	0.21
	RE (%)	0.64	0.77
	R²	0.84	0.86
5.5	MAE (ºC)	0.13	0.08
	RMSE (ºC)	0.15	0.09
	RE (%)	0.56	0.34
	R²	0.93	0.95
9.5	MAE (ºC)	0.16	0.16
	RMSE (ºC)	0.18	0.19
	RE (%)	0.70	0.72
	R²	0.90	0.90

Parameter	Value	Range tested in calibration
Secchi (m)	0.3 (measured)	-
Wind Factor (-)	1.0 (calibrated)	0.40 to 1.40
Background Horizontal Eddy Viscosity (m²/s)	0.025 (calibrated)	0.0025 to 0.025
Background Horizontal Eddy Diffusivity (m²/s)	0.025 (calibrated)	0.0025 to 0.025
Dalton (-)	0.0007 (calibrated)	0.0013 to 0.0007
Stanton (-)	0.0013 (default)	0.0007 to 0.0013

Value	Measured	Simulated
ΔT ≤0.25°C	4	5
ΔT ≤ 0.50°C	9	13
ΔT ≥1.0°C	15	17
ΔT ≥2.0°C	4	8

Depth (m)	Performance indicators	Calibration Period	Validation Period 2016
Surface (0.5)	MAE (ºC)	0.30	0.34
	RMSE (ºC)	0.42	0.45
	RE (%)	1.30	1.51
	R²	0.73	0.63
2.5	MAE (ºC)	0.15	0.23
	RMSE (ºC)	0.20	0.31
	RE (%)	0.64	1.04
	R²	0.84	0.41
5.5	MAE (ºC)	0.13	0.12
	RMSE (ºC)	0.15	0.16
	RE (%)	0.56	0.56
	R²	0.93	0.80
Bottom (9.5)	MAE (ºC)	0.16	0.20
	RMSE (ºC)	0.18	0.24
	RE (%)	0.70	0.95
	R²	0.90	0.81

Depth (m)	Scenario
Depth (m)	Validation period (cm/s)	D1 (cm/s)	D2 (cm/s)
0.50	1.5	1.0^/1.1^/1.3^**	0.50
2.50	1.4	0.9/1.1/1.2**	0.50
5.50	1.4	1.4/1.3/1.3**	0.50
9.50	7.0	5.8/6.1/6.2**	4.5

Q_{e v, f r e e} = {[0.14 \{\frac{g ϑ_{a i r}^{2}}{{0.7}^{2} \bar{ρ_{a}}}\} (ρ_{a 10} - ρ_{a 0})]}^{1 / 3} \bar{ρ_{a}} L_{v} (q_{s} (T_{s}) - q_{a} (T_{a})

Q_{c o, f r e e} = {[0.14 \{\frac{g ϑ_{a i r}^{2}}{{0.7}^{2} \bar{ρ_{a}}}\} (ρ_{a 10} - ρ_{a 0})]}^{1 / 3} \bar{ρ_{a}} c_{p} (T_{s} - T_{a})

[1] E-mails: denisfp@ufmg.br (DFP), talita.silva@ehr.ufmg.br (TFGS), b.vincon-leite@enpc.fr (BVL), niloon@ehr.ufmg.br (NN)

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Thermal functioning of a tropical reservoir assessed through three-dimensional modelling and high-frequency monitoring

Comportamento térmico em um lago tropical urbano avaliado por modelagem tridimensional e monitoramento em alta frequência

ABSTRACT