# Temperature and Circulation Dynamics in a Small and Shallow Lake: Effects of Weak Stratification and Littoral Submerged Macrophytes

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Site

^{2}and a shoreline length of 5.9 km with mean and maximum water depths of 2.7 m and 4.3 m (excluding two small dredge holes), respectively. The largest fetch is approximately 2 km along the N–NE wind directions. Along the prevailing S and SW direction, the fetch ranges between 400 and 1000 m. The riparian shoreline is mostly undeveloped, being largely surrounded by trees with heights typically 10 m above the water surface. The wind-sheltering due to these trees reduces the wind exposure of the lake [20]. Lake Wingra is a eutrophic drainage lake in a highly urbanized watershed [45,46]. During the summer, approximately 30% of the lake surface area is littoral habitat containing macrophytes of various species. Although the abundance of individual species might vary significantly from year to year [47,48], long-term observations indicated that the most common macrophytes are submerged milfoils and the second most abundant plants are Ceratophyllum demersum, commonly knowns as coontails. Both species mostly spread offshore up to 2.0 m depth [49]. The spatial distribution of littoral macrophytes has generally remained constant over decades [47,48,50,51]. Figure 1 shows the spatial distribution of littoral-zone vegetation in Lake Wingra: https://olw-lwrd.countyofdane.com/Management/Aquatic-Plants/Aquatic-Plant-Management).

#### 2.2. Field Observations

^{2}plots throughout the littoral zone. The spatial distribution of littoral macrophytes was obtained by tracking the littoral boundary using a boat-mounted GPSmap 188 sounder, Garmin (International Inc., Olathe, KS, USA) with a horizontal spatial resolution of 25 m.

#### 2.3. Hydrodynamic Model

_{w}is the water density, λ is the total projected area of vegetation in a unit volume of mixture of water and vegetation (λ = D

_{v}N

_{v}, with D

_{v}being the diameter of the single vegetation stand and N

_{v}is the total number of vegetation stands per m

^{2}); C

_{D}is the bulk drag coefficient, where u and v are horizontal velocity components in x and y coordinate directions, respectively; F

_{z}is zero by assuming the vegetation field as an anisotropic dissipative media [37,65].

_{v}is the vertical eddy diffusivity; C

_{hb}is a dimensionless convective heat exchange coefficient; ρ

_{b}, C

_{pb}and T

_{b}are the density, specific heat and temperate of the bottom sediments, respectively; u

_{b}and v

_{b}are the velocity components at the lake bed; and T

_{w}is the water temperature at the lake bed.

#### 2.4. Model Setup

^{−1}(1000 macrophyte stands per 1 m

^{2}with diameter of 0.01 m), while λ = 1 m

^{−1}(100 macrophyte stands per 1 m

^{2}with diameter of 0.01 m) is used to classify the sparse area. Figure 1 shows the spatial pattern of macrophyte distribution from the 2004 survey and the distribution generally agrees with patterns obtained in 1991 and 1992 surveys (i.e., Figure 4 in Reference [48]). At last, the bulk drag coefficient of macrophytes is chosen to be 1.13 based on Garcia, et al. [65].

^{−1}is appropriate for the period of simulations [74]. The bottom friction coefficient is selected as 0.002 [20,72]. A time step of 60 s is chosen, yielding a ratio of simulation time to real time of about 1:15. The model is initialized on Day 253 at midnight with a zero velocity over the lake and a temperature measured at the central location (see Figure 1) at that time. The simulation lasts for 8 days until Day 261, and the first 24 h are used to spin up the model. Prior to the simulation, the model was carefully calibrated with field measurements and the water velocities and temperature fields predicted by the model are in good agreement with field observations within 10% errors.

## 3. Results and Discussion

#### 3.1. Temperature Structures

_{pb}= 0.001 [77] and ρ

_{b}ranging from 1010 kg/m

^{3}for mud to 1800 kg/m

^{3}for sand, enables the model to reliably capture weak stratification. Overall, both field measurements and modeling results indicate that the heat exchange at the water-lakebed interface can play an important role in maintaining weak stratification. Second, the model, however, does not fully resolve the high-frequency oscillations of small-scale internal waves [78,79], since the model was run under a spatial resolution of 50 m, which is unlikely to simulate complex sub-grid scale oscillations [80].

#### 3.2. Velocity Prfoiles

#### 3.3. Effects of Macrophytes

#### 3.4. Effects of Weak Stratification

## 4. Summary and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Lake Wingra bathymetry and the distribution of littoral-zone vegetation. Symbols (●, □ and ×) represent the locations of wind (W1-W8), water temperature (WT, CT, ET), and velocity profile measurements (A, B, C, D, and E), respectively.

**Figure 3.**Measured and modelled water temperature time series at different depths at the central (CT) location. The lines with double arrows indicate the period of velocity measurements using ADCP.

**Figure 4.**Comparison of eastward (u) and northward (v) velocity component profiles on the upper and lower panels, respectively, between modelled results (solid lines) and field observations (circles) with error bars at the five velocity measurement locations (see

**A**,

**B**,

**C**,

**D**, and

**E**in Figure 1). Model results are averaged over the 5-h measurement interval, while observations represent half hour averages.

**Figure 5.**Modelled circulation patterns with and without the littoral macrophytes at the surface and at 2 m below the surface. The solid contour lines delineate the area where velocity magnitude changed at least with 50% by the inclusion of macrophytes. The circulation field represents the same 5-h averages as Figure 4.

**Figure 6.**Comparison of velocity profiles between field observations (circles) with error bars and modelled results with (solid red lines) and without (black dashed lines) littoral macrophytes at location

**B**in the pelagic area and location

**E**in the littoral zone. The upper panel shows velocity magnitudes and the lower panel shows directions.

**Figure 8.**Modelled temperature fields and velocity circulation patterns of a cross section following (

**upper panel**), and perpendicular to (

**lower panel**), the wind direction without and with littoral macrophytes. The upper panel is the cross section along x = 1250 m and the lower panel is the cross section along y = 500 m, which are marked by the dashed lines in Figure 7.

**Figure 9.**Model results of total horizontal velocity |v| and eddy viscosity ν

_{ν}profiles with (red solid line) and without (black dashed line) weak stratification effects. Measured total horizontal velocity profiles are denoted as circles with error bars.

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**MDPI and ACS Style**

Torma, P.; Wu, C.H.
Temperature and Circulation Dynamics in a Small and Shallow Lake: Effects of Weak Stratification and Littoral Submerged Macrophytes. *Water* **2019**, *11*, 128.
https://doi.org/10.3390/w11010128

**AMA Style**

Torma P, Wu CH.
Temperature and Circulation Dynamics in a Small and Shallow Lake: Effects of Weak Stratification and Littoral Submerged Macrophytes. *Water*. 2019; 11(1):128.
https://doi.org/10.3390/w11010128

**Chicago/Turabian Style**

Torma, Péter, and Chin H. Wu.
2019. "Temperature and Circulation Dynamics in a Small and Shallow Lake: Effects of Weak Stratification and Littoral Submerged Macrophytes" *Water* 11, no. 1: 128.
https://doi.org/10.3390/w11010128