**3.1 Itapeva Lake**

34 Hydrodynamics – Natural Water Bodies

smaller Chezy's resistance factor than was used in other lake areas (Wu et al., 1999). Calibration and validation of the hydrodynamic parameters were done using two different time-series of water level and wind produced for two locations in Lake Mangueira (North

**Parameter Description Unit Values /Ref.** 

1 Ah Horizontal eddy viscosity coefficient m1/2 s-1 5 – 15 1 2 CD Wind friction coefficient - 2e-6 – 4e-6 2 3 CZ Chezy coefficient - 50 – 70 3

1 Gmax Maximum growth rate algae day-1 1.5 – 3.0 4

3 k'e Light attenuation coefficient in the water m-1 0.25 – 0.65 5 4 θT Temperature effect coefficient - 1.02 – 1.14 6 5 θR Respiration and excretion effect coefficient - 1.02 – 1.14 5

6 kP Half-saturation for uptake phosphorus mg P m-3 1 – 5 7 7 kN Half-saturation for uptake nitrogen mg N m-3 5 – 20 7 8 kre Respiration and excretion rate day-1 0.05 – 0.25 8 9 kgz Zooplankton grazing rate day-1 0.10 – 0.20 8 Sources: 1 White (1974); 2 Wu (1982); 3 Chow (1959); 4 Jørgensen (1994); 5 Schladow & Hamilton (1997); 6

Table 1. Hydrodynamic and biological parameters description and its values range.

For the parameters of the phytoplankton module, we used the mean values for the literature range given in Table 1. To evaluate its performance, we simulated another period of 86 days, starting 12/22/2002 at 00:00 hs (summer). Solar radiation and water temperature data were taken from the TAMAN meteorological station, situated in the northern part of Lake Mangueira. Photosynthetically active radiation (PAR) at the Taim wetland was assigned as 20% of the total radiation, in order to represent the indirect effect of the emergent macrophytes on the phytoplankton growth rate according to experimental studies of emergent vegetation stands in situ. For the lake areas, we assumed that the percentage of

The resulting phytoplankton patterns were compared with satellite images from MODIS, which provides improved chlorophyll-a measurement capabilities over previous satellite sensors. For instance, MODIS can better measure the concentration of chlorophyll-a associated with a given phytoplankton bloom. Unfortunately, there were no detailed chlorophyll-a and nutrient data available for the same period. Therefore, we compared only

the median simulated values with field data from another period (2001 and 2002).

cal cm-2dia-1 100 – 400 5

2 IS Optimum light intensity for the algae

th

Eppley (1972); 7 Lucas (1997); 8 Chapra (1997)

PAR was 50% of the total solar radiation (Janse, 2005).

and South).

Hydrodynamic:

Biological:

In Itapeva Lake, wind action generated oscillations of the water level between the North and South parts of the lake. The meteorological and hydrological variables were characterized for daily and seasonal periods.

Simulations using a mathematical bidimensional horizontal hydrodynamic model succeeded in reproducing this phenomenon, and helped to calculate the synthesis of velocity and direction of the water. It was possible to confirm the complexity of the circulation in the lake and to distinguish different behaviors among the South, Center and North. Besides the similarities in morphometry between the Center and South parts, the flow from the Três Forquilhas River enters the center part of the lake and the prevailing N-NE winds move water toward the South part of the lake (Figs 4 and 5).

Fig. 4. Numerical simulation of the vertically averaged velocity field in Itapeva Lake during the combination of high-flow condition in the Três Forquilhas River and low wind speed. Red arrows indicate the direction of the prevailing currents.

The hydrological variables analyzed and modeled showed a quite characteristic seasonal behavior at each sampling point in Itapeva Lake, closely related to the velocity and direction of the wind. The water level responded to wind action in a very direct manner, since NE winds displaced water from north to south, along the main lake axis. Winds from the SW quadrant produced the opposite effect.

The environmental sources selected for the analysis were suspended solids and turbidity, due to their influence on many physical, chemical and biological factors. The results for hydrodynamics, such as water column and water velocity generated by the model for the sampling points, were used as the basis for the study of the environmental variations. The waves generated by wind action were the third source used to explain the variations of suspended solids and turbidity in the lake (Figs 6 and Table 2).

Hydrodynamic Control of Plankton Spatial and

Observed Values

Itapeva Lake.

**3.2 Lake Mangueira** 

southwestern areas (Fig. 7).

simulation period.

Calculated vs. Observed Values Dependent variable: Turbidity

Temporal Heterogeneity in Subtropical Shallow Lakes 37

Observed Values

Calculated vs. Observed Values Dependent variable: Suspended Solids

> 95% Confidence Interval

95% Confidence Interval

Calculated Values Calculated Values

Fig. 6. Comparison between observed and calculated values for turbidity and suspended solids through multiple regression model using the three monitoring station along the

The simulated and observed values of water levels at two stations of Lake Mangueira during the calibration and validation period are shown in Fig. 7. An independent validation data set showed a good fit to the hydrodynamic module (R2 ≥ 0.92). The model was able to reproduce the water level well in both extremities of Lake Mangueira. Wind-induced currents can be considered the dominant factor controlling transport of substances and phytoplankton in Lake Mangueira, producing advective movement of superficial water masses in a downwind direction. For instance, a southwest wind, with magnitude approximately greater than 4ms−1, can causes a significant transport of water mass and substances from south to north of Lake Mangueira, leading to a almost instantaneous increase of the water level in the northeastern parts and, hence the decrease of water level in

Our model results showed two characteristic water motions in the lake: oscillatory (seiche) and circulatory. Lake Mangueira is particularly prone to wind-caused seiches because of its shallowness, length (ca. 90 km), and width (ca. 12 km). These peculiar morphological features lead to significant seiches of up to 1 m between the south and north ends, caused by moderate-intensity winds blowing constantly along the longitudinal axis of the lake (NE-SW). Depending on factors such as fetch length and the intensity and duration of the wind, areas dominated by downwelling and upwelling can be identified (Fig. 8). For instance, if northeast winds last longer than about 6 h, the surface water moves toward the south shore, where the water piles up and sinks. Subsequently a longitudinal pressure gradient is formed and produces a strong flow in the deepest layers (below 3 m) toward the north shore, where surface waters are replaced by water that wells up from below. Such horizontal and vertical circulatory water motions may develop if wind conditions remain stable for a day or longer. The model was also used to determine the spatial distribution of chlorophyll-a and to identify locations with higher growth and phytoplankton biomass in Lake Mangueira. Fig. 9 shows the spatial distribution of the phytoplankton biomass for different times during the

Specifically, in Lake Mangueira there is a strong gradient of phytoplankton productivity from the littoral to pelagic zones (Fig. 9). Moreover, the model outcome suggests that there

Fig. 5. Numerical simulation of the vertically averaged velocity field in Itapeva Lake during the combination of low-flow condition in the Três Forquilhas River and high wind speed from the Northeast quadrant (20/05/1999 - 21/05/1999). Red arrows indicate the direction of the prevailing currents.

The hydrodynamic variable explained 70% to 95% of the environmental variations for each seasonal campaign, using mean values for four-hour periods. Considering the entire lake and all seasonal campaigns, this explained 68% of the variation for turbidity and 49% for suspended solids. The hydrodynamic and environmental study were capable of evaluating that the changes in the water level as a function of runoff occur slowly, compared with the changes in the water level and seiches created by the effect of the wind on the lake. These variations in water levels and wind speeds have significant effects on the variability of the environmental variable tested.


Legend: Hydrological Variable – 1. water level (N), 2. water velocity (V); 3. wave height (H); 12- N-V; 13. N-H; 23. V-H; 123. N-V-H; R – correlation factor; C1, C2, C3 – N, V and H coefficients, respectively.

Table 2. Results of multiple regression between water quality variable (dependent variable) and hydrological variables (independent variable) in Itapeva Lake considering the three monitoring stations: South, Center and North.

Fig. 6. Comparison between observed and calculated values for turbidity and suspended solids through multiple regression model using the three monitoring station along the Itapeva Lake.
