**1.1 Study areas**

Itapeva Lake is the first (N→S) in a system of interconnected fresh-water coastal lakes on the northern coast of the state of Rio Grande do Sul, Brazil (Fig. 1). The lake has an elongated shape (30.8 km × 7.6 km) and a surface area of ≈125 km2, and is shallow, with a maximum depth of 2.5 m. The lake is oriented according to the prevailing wind direction (NE – SW quadrants), where the northern part is more constricted and consequently the water is more confined. Two rivers enter the lake: Cardoso River, in the northern part, and Três Forquilhas River in the southern part. The former is small and the flow was not important for the input; however, the contribution of the latter river was modeled and influenced the spatial pattern. Lake Mangueira (33°1'48"S 52°49'25"W) is a large freshwater ecosystem in southern Brazil (Fig. 2), covering a total area of 820 km2, with a mean depth of 2.6 m and maximum depth of

of this effort has been expended on the description of phytoplankton in temperate lakes; thus, multi-nutrient, photo-acclimation models are now not uncommon (e.g., Olsen & Willen, 1980; Edmondson & Lehman, 1981; Sas, 1989; Fasham et al., 2006; Mitra & Flynn, 2007; Mitra et al., 2007). In subtropical lakes, eutrophication has been intensively studied, but only with a focus on measuring changes in nutrient concentrations (e.g., Matveev & Matveeva, 2005; Kamenir et al., 2007). A wide variety of phytoplankton models have been developed. The simplest models are based on a steady state or on the assumption of complete mixing (Schindler, 1975; Smith, 1980; Thoman & Segna, 1980). Phytoplankton models based on more complex vertical 1-D hydrodynamic processes give a more realistic representation of the stratification and mixing processes in deep lakes (Imberger & Patterson, 1990; Hamilton et al., 1995a; Hamilton et al., 1995b). However, the vertical 1-D assumption might be too restrictive, especially in large shallow lakes that are poorly stratified and often characterized by significant differences between the pelagic and littoral zones. In these cases, a horizontal 2-D model with a complete description of the hydrodynamic and ecological processes can offer more insight into the factors determining

Currently, computational power no longer limits the development of 2-D and 3-D models, and these models are being used more frequently. Of the wide diversity of 2-D and 3-D hydrodynamic models, most were designed to study deep-ocean circulation or coastal, estuarine and lagoon zones (Blumberg & Mellor, 1987; Casulli, 1990). However, only a few models are coupled with biological components (Rajar & Cetina, 1997; Bonnet & Wessen,

In this chapter, we present the results of comparative modeling of two subtropical shallow lakes where the wind, and derived hydrodynamics, and river flow act as the main factors controlling plankton dynamics on temporal and spatial scales. The basic hypothesis is that wind and wind derived-hydrodynamics are the main factor determining the spatial and temporal distribution of plankton communities (Cardoso et al. 2003; Cardoso & Motta Marques, 2003, 2004a, 2004b, 2004c, 2009), in association with point incoming river flows. The spatial heterogeneity of phytoplankton in Lake Mangueira is influenced by hydrodynamic patterns, and identifying zones with a higher potential for eutrophication and phytoplankton patchiness (Fragoso Jr. et al., 2008). The spatial patterns of chlorophyll-a concentrations generated by the model were validated both with a field data set and with a cloud-free satellite image provided by a Terra Moderate Resolution Imaging

Itapeva Lake is the first (N→S) in a system of interconnected fresh-water coastal lakes on the northern coast of the state of Rio Grande do Sul, Brazil (Fig. 1). The lake has an elongated shape (30.8 km × 7.6 km) and a surface area of ≈125 km2, and is shallow, with a maximum depth of 2.5 m. The lake is oriented according to the prevailing wind direction (NE – SW quadrants), where the northern part is more constricted and consequently the water is more confined. Two rivers enter the lake: Cardoso River, in the northern part, and Três Forquilhas River in the southern part. The former is small and the flow was not important for the input; however, the contribution of the latter river was modeled and influenced the spatial pattern. Lake Mangueira (33°1'48"S 52°49'25"W) is a large freshwater ecosystem in southern Brazil (Fig. 2), covering a total area of 820 km2, with a mean depth of 2.6 m and maximum depth of

Spectroradiometer (MODIS) with a spatial resolution of 1.0 km.

local water quality.

**1.1 Study areas** 

2001).

Fig. 1. Itapeva Lake in southern Brazil, with the three sampling points (North, Center and South).

Fig. 2. Lake Mangueira in southern Brazil. The meteorological and sampling stations in the North, Center and South parts of Lake Mangueira are termed TAMAN, TAMAC and TAMAS, respectively.

6.5 m. Its trophic state ranges from oligotrophic to mesotrophic (annual mean PO4 concentration 35 mg m-3, varying from 5 to 51 mg m-3). This lake is surrounded by a variety of habitats including dunes, pinus forests, grasslands, and two wetlands. This heterogeneous landscape harbors an exceptional biological diversity, which motivated the Brazilian federal authorities to protect part of the entire hydrological system as the Taim Ecological Station in 1991 (Garcia et al., 2006). The watershed (ca. 415 km2) is primarily used

Hydrodynamic Control of Plankton Spatial and

or less complex.

January to December 1999.

given in Fig. 3.

**2.2 Modeling in Lake Mangueira** 

Temporal Heterogeneity in Subtropical Shallow Lakes 31

Subsequently, we used a 2-D hydrodynamic model to evaluate the roles of the Três Forquilhas inflow and wind effects on the hydrodynamics and mixture processes of the lake. For the watershed analysis we used the IPH2 model, a rainfall, runoff-lumped model developed at the Instituto de Pesquisas Hidráulicas (IPH). Its mathematical basis is the continuity equation composed of the following algorithms: (a) losses by evapotranspiration and interception by leaves or stems of plants; (b) evaluation of infiltration and percolation by Horton; and (c) evaluation of surface and groundwater flows (Tucci, 1998). The model works by regarding a drainage basin as series of storage tanks, with rainfall entering at the top, and being split between what is returned to the atmosphere as evaporation, and what emerges from the basin as runoff (stream flow). Depending on the number of tanks and the number of parameters controlling the passage of water between them, it can be made more

For the output analysis we used the MOLABI model (Ecoplan, 1997), a water-budget model based on the Puls method, which represents the continuity equation applied to the whole lake. The input data is rainfall over the lake, inflows from the watershed, and groundwater flux estimated by the Darcy equation. Evaporation was estimated using the Penman method. The hydrodynamic patterns in Itapeva Lake were modeled using the model IPH-A (2D; Borche, 1996). The main inputs of the model were: water inflow, wind, rainfall and evaporation, spatial maps (including waterbody, bathymetry, bottom and surface stress coefficient). This model was applied because Itapeva Lake is a polymictic environment with no significant difference among depths (surface, middle and bottom), neither for the physical and chemical data nor for the plankton communities. The model was run from

For Lake Mangueira, we applied a dynamic ecological model describing phytoplankton growth, called IPH-TRIM3D-PCLake (Fragoso Jr. et al., 2009). Although this model can represent the three-dimensional flows and the entire trophic structure dynamically, in this study case we used a simplified version of the model consisting of three modules: (a) a detailed horizontal 2-D hydrodynamic module for shallow water, which deals with winddriven quantitative flows and water levels; (b) a nutrient module, which deals with nutrient transport mechanisms and some conversion processes; and (c) a biological module, which describes phytoplankton growth in a simple way. An overview of the modeling processes is

The hydrodynamic model is based on the shallow-water equations derived from Navier-

*tx y*

 

*uuu u v g u A u fv txy x* 

*vvv u v g v A v fu txy y* 

 <sup>0</sup> *hu hv*

 

(1)

2

2

*x h*

*y h*

(3)

(2)

Stokes, which describe dynamically a horizontal two-dimensional flow:

for rice production, and many of the local waterbodies are used for irrigation, with a total water withdrawal of approximately 2 L s-1 ha-1 on 100 individual days within a 5-month period, and a high input of nutrients from the watershed during the rice-production period.
