4. Discussion

[38] The convolution site models and methods used to determine when and where changes in stored heat energy were a considerable component of the surface energy budget revealed some results worthy of discussion. These results include (1) nighttime ‘‘inversions’’ of the wetland water column due to thermal convective mixing, (2) variability in regression-defined k_ex and coefficients, (3) data requirements and transfer value of the convolution models to locations other than the Everglades wetlands areas, and (4) the relative accuracy of the convolution models compared to simpler approaches for approximating wetland surface water temperature changes, and ultimately, fluxes of stored heat energy.

[39] In Everglades wetland areas, thermal stratification in the surface water column was common during the day, with near-surface water temperatures rising more than water temperatures at depth (Jenter et al., U.S. Geological Survey, written communication, 2003). During the evening, the water column was thermally mixed by a surface water inversion process (convective mixing). Mixing occurred when nighttime air temperatures caused cooling of a thin layer at the top of the surface water, creating a negatively buoyant boundary from which surface water ‘‘fingered’’ downward to the bottom of the water column. This process is noteworthy because field-measured water temperature changes used in S(b) were affected by this thermal stratification and convective mixing. Because regression was used to minimize S(b), regression-defined values of k_ex and likely account for some of the temperature variability caused by this inversion process.

[40] Spatial variability in the regression-defined k_ex coefficients provided some insight into the heat exchange processes acting on a wetland system. Regression-defined estimates of k_ex ranged from 0.11 m s^-1 at site 9 in 1998 to 5.94 m s^-1 at site 2 in 1997 (Table 2) and a statistically significant difference existed between open water and vegetated sites. Statistically significant difference was established using the nonparametric Kruskal-Wallis rank-sum test. This rank-sum test exceeded the critical value for chi-square at the significance level of 0.01 with one degree of freedom, suggesting the null hypothesis of equal distributions could be rejected and a statistically significant difference existed for k_ex between open water and vegetated sites. Several mechanisms may explain larger k_ex values over open water sites, including enhanced wind-driven and thermal convective mixing. Wind-driven mixing would be greater over open water sites because vegetational surfaces, such as plant leaves, stalks, and stems are not present to provide roughness obstacles. Likewise, thermal convective mixing would be greater over open water sites because vegetational surfaces are not present to increase frictional resistance to vertical surface water flow and reduce convective and radiative energy transport through the air-water interface. Increased mixing (either wind-driven or thermal convective) would homogenize the entire water column relatively quickly until the water temperature approximately equaled the air temperature. In contrast, decreased mixing in vegetated sites would homogenize the water column more slowly.

[41] Spatial variability in the regression-defined coefficients also was present, although not statistically significant, in the Everglades wetland areas. Alpha () coefficients ranged from 0.23 at site 4 to 0.94 at site 9 in 1998, with an average of about 0.5 and 0.6 for open water and vegetated sites, respectively (Table 2). Statistically significant difference between open water and vegetated sites also was examined using the nonparametric Kruskal-Wallis rank-sum test. This rank-sum test was less than the critical value for chi-square at the significance level of 0.01 with one degree of freedom, suggesting the null hypothesis of equal distributions could not be rejected and no statistically significant difference exists for between open water and vegetated sites.

[42] The ability of the convolution site models to compute water temperature changes and fluxes of stored heat energy at other locations depends on the area of interest. The convolution models and regression-defined k_ex and coefficients are more directly transferable in the winter to similar humid subtropical wetland areas, suggesting that the only data requirements in these areas are air temperature and wetland water column depth. The convolution models also may be applied in the winter over lakes or other land masses associated with a sluggish surface water drainage including coastal bays, mangrove or cypress swamps, and estuaries. The transfer value of this analysis, however, diminishes at locations with vegetation other than saw grass, cattails, rush, and open water wetlands because the regression-defined k_ex and coefficients (Table 2) may not apply. New regression experiments may be required to define values for k_ex and that are specific to the land cover of interest. This more complicated case requires time series data for water temperature in addition to time series data for air temperature and surface water depth.

[43] Considering the modest mathematical complexity of the convolution approach, an obvious question is: Do simpler methods exist with comparable or improved error statistics for computing 30 min and net daily changes in surface water temperature, and ultimately, fluxes of stored heat energy? Seven methods were evaluated at an open water site (site 3) and a dense saw grass site (site 4) for 30 min and daily time steps in 1996 (Table 4). These methods include, for the 30 min time step, (1) the convolution approach, (2) expressing water temperature changes as a simple regression- defined function of air temperature changes, and (3) setting water temperature changes equal to air temperature changes, and for the daily time step, (1) daily composites of the convolution results, (2) expressing net daily water temperature changes as a simple regression-defined function of net daily air temperature changes, (3) daily composites of the results of expressing 30 min water temperature changes as a simple regression-defined function of air temperature changes, and (4) setting net daily water temperature changes equal to net daily air temperature changes.

[44] For the 30 min time steps at the open water site (site 3), the convolution approach (method 1) clearly outperforms the simpler approaches (methods 2 and 3) for computing changes in the mean vertical water column temperature (Table 4). With method 1, the R² values were 0.65 and the mean absolute error was 0.09°C at site 3. A simpler approach, that is, setting the mean vertical water column temperature change equal to the air temperature change (method 3), produced the largest error statistics. With method 3, the R² values were 0.27 and the mean absolute error was 0.29°C at site 3. The results likely are similar for fluxes of stored heat energy because heat content is derived from water temperature changes.

[45] For the 30 min time steps at the dense saw grass site (site 4), the convolution approach (method 1) outperforms the simpler approaches (methods 2 and 3) for computing changes in the mean vertical water column temperature (Table 4). With method 1, the R² values were 0.64 and the mean absolute error was 0.10°C. Although the simpler method 2 produced a smaller mean absolute error (equal to 0.07°C) than method 1, the results for method 2 were almost completely uncorrelated (R² equal to 0.03) to measured mean vertical water temperature changes.

[46] For daily time step at the open water site 3, there may be simpler methods than daily compositing the site convolution model results for computing water temperature changes, and ultimately fluxes of stored heat energy, with comparable error statistics. For example, at site 3 in 1996, expressing daily mean water column temperature changes as a regression-defined function of net daily air temperature changes (method 5) produced a slightly lower R² (equal to 0.64 for method 5 versus 0.66 for method 4), and a slightly lower mean absolute error (equal to 15.69 W m^-2 for method 5 versus 16.14 W m^-2 for method 4). The regression relation for site 3 was (D), with ₁ and ₂ equal to 0.027 and 0.475, respectively.

[47] For daily time steps at the dense saw grass site 4, daily compositing the site convolution model approach (method 4) also clearly outperformed the simpler approaches (methods 5–7) for computing net daily fluxes of stored heat energy (Table 4). With method 4, the R² value was 0.82, and the mean absolute error was 2.35 W m^-2 at site 4. For the simpler approaches (methods 5-7), the R² values ranged from 0.45 (method 6) to 0.52 (methods 5 and 7), and the mean absolute errors ranged from 3.31 (method 5) to 6.41 W m^-2 (method 7).