3. Results

[24] The Florida Everglades, or ‘‘river of grass’’ [Douglas, 1947], is characterized by its low topographic relief; a broad array of aquatic, semiaquatic and upland habitats; and extensive wetland areas that include saw grass, cat tails, cypress strands, and tree islands (Figure 1). Evolution of the Everglades landscape, including natural processes, consequences of urbanization and water management activities, has been discussed extensively in many publications [Douglas, 1947; Parker et al., 1955; Renken et al., 2005] and therefore is not repeated here. It is reasonable to expect that Everglades wetland areas may store or release considerable amounts of heat energy, mostly because of the relatively large heat capacity of surface water and the extensive wetland areas covered by a column of surface water.

3.1. Surface Energy Budget

[25] A closer examination of terms in the surface energy budget for the study area (Figure 1) is discussed in this section. German [2000] reported that the mean annual magnitude of net radiation (R_n) ranged from 121 to 134 W m^-2 at nine sites in the Everglades wetland areas. Subdaily mean values of R_n were less than zero during the evening and night when long-wave radiation emitted from the vegetation, land, and surface water generally exceeded incoming atmosphere radiation. The magnitude of 30 min mean R_n was relatively large during the day, sometimes exceeding 500 W/m² when the intensity of incoming solar radiation was greatest.

[26] Energy is stored in the ecosystem biomass, specifically, in vegetation (G_veg), and in subsurface geologic media. When present, surface water generally is the primary medium for energy storage [Bidlake et al., 1996], largely because of its relatively high heat capacity, which is about double the heat capacity of vegetation, soil minerals, and soil organic matter [Brutsaert, 1982]. Vegetation is rarely dense enough to create a large reservoir for energy. For example, vegetation density was measured at several locations along five transects in the Everglades wetland areas [Childers et al., 2003]. The maximum vegetation density was about 4100 g/m² (dry weight). Assuming plant matter is 90% water, the equivalent surface-water depth of the maximum plant density was about 4 cm. This depth is minimal when considering water depths in the Everglades wetland areas can exceed 1 m.

[27] A component of the available energy for evapotranspiration not included in the surface energy budget (equation (1)), is the energy that is added to, or removed from, the wetlands through rainfall. An analysis of data [German, 2000] in the Everglades suggested energy fluxes attributed to rainfall can be considerable in hourly surface energy budgets; however, rainfall energy fluxes are relatively small compared to mean daily fluxes of net radiation. From 1996 to 2000, rainfall data were collected at sites 4 to 9 (Figure 1), and the energy flux from rainfall events was computed as described by Bogan et al. [2003, equation (12)] assuming the rainfall temperature was equal to the dew point temperature. The maximum and minimum energy fluxes from rainfall at the sites were 10 and -40 W m^-2, respectively, over the 4 year period. A positive flux implies the rainfall is warmer than the wetland surface water, and increases the amount of heat energy to the system. Conversely, a negative flux implies the rainfall is colder than the wetland surface water, and decreases the amount of heat energy within the system. Fluxes of 10 and -40 W m^-2 could be considerable within hourly surface energy budgets during rainfall events when incoming solar radiation is dampened by cloud cover. More than 93% of the time, however, the magnitude of heat energy flux from rainfall was less than one twentieth the magnitude of the mean daily net radiation.

3.2. Magnitude of Stored Heat Energy

Figure 7. Net daily fluxes of stored heat energy (W), mean daily net radiation (Rn), and mean daily wetland water depth (DEPTH) at site 3 in 1997. [larger image]

[28] A time series plot shows mean daily net radiation (R_n), mean surface water depth, and daily fluxes of stored heat energy in the wetland surface water (W) at site 3 in 1997 (Figure 7). Fluxes of stored heat energy (W) were computed as the product of T_w, D and heat capacity divided by the number of seconds in one day. During the winter, net radiation was relatively low, and air temperature varied considerably (Figure 4), resulting in fluxes of heat energy stored in wetland surface water that approached and even exceeded 50 W m^-2 (Figure 7). Stored heat energy sometimes exceeded the magnitude of net radiation and thus, in some instances, was the dominant component of the daily wetland surface energy budget, particularly during the winter when solar radiation was relatively low.

[29] To assess the importance of W in wetland surface energy budgets, an importance ratio (R_imp), defined as the ratio of the absolute value of W to net radiation, was computed (Figure 8). The (1) heat capacity of water, (2) net change in mean vertical water column temperature from the beginning to the end of the time period of interest, and (3) mean surface water depth within the time period of interest were used to compute W for R_imp. For example, if daily R_imp were desired, W was computed as the product of the heat capacity of water, net change in mean vertical water column temperature from the beginning of the day to the end of the day, and the mean daily depth of surface water divided by the number of seconds in a day. In this daily case, R_imp was computed as the absolute ratio of mean daily net radiation and W. If a weekly R_imp was desired W was computed as the product of the heat capacity of water, net change in mean vertical water column temperature from the beginning of the week to the end of the week, and the weekly mean depth of the surface water divided by the number of seconds in a week. In this weekly case, R_imp values were computed as the absolute ratio of mean weekly net radiation to W.

Figure 8. Percent of Rimp greater than 0.2 within a specified time period (white bars) and available Rimp expressed as a percent of the total possible Rimp (gray bars). [larger image]

[30] The percentage of time R_imp values were equal to or greater than a filter threshold of 0.2 (Figure 8) highlights time periods when W was a considerable part of the wetland surface energy budget. Also computed were the data availability of R_imp, expressed as the percentage of time sufficient data were available to compute R_imp. Data availability trends for R_imp were independent of the filter threshold trends for R_imp, which demonstrates the filter threshold trends are not an artifact of missing data.

[31] During week 1 (1-7 January) of years 1996–2000, about 40% of the daily R_imp values were equal to or greater than 0.2 at sites 2 to 5 and 7 to 9. A total of 105 daily R_imp values were calculated during week 1, of which 42 were equal to or greater than the filter threshold value. During week 29 (early July), however, less than 5% of the daily R_imp values were equal to or greater 0.2. Although 165 daily R_imp values were calculated during this period, only 3 ratios were equal to or greater than the filter threshold value. This analysis suggests that W is more often a considerable component of the mean daily surface energy budget during the winter than the summer.

[32] As expected, temporal upscaling reduces the importance of changes in heat energy stored in wetland surface water in the surface energy budget. This assertion is supported by comparing the percentages of the R_imp values that exceed 0.2 over different time scales (Figure 8). For example, during week 1 (1-7 January) of years 1996–2000, about 40% of the daily R_imp were equal to or greater than the 0.2 filter threshold; however, during the entire month of January, less than 20% of the monthly total number of weekly R_imp were equal to or greater than the same filter threshold. This result is not surprising considering fluxes of stored heat energy in wetland surface water are inversely proportional to time, such that longer time periods result in smaller fluxes of stored heat energy.

3.3. Convolution Site Models

[33] Parameter estimation was applied to the discrete form of the convolution integral (equation (9)) and transfer function at 30 min time steps at sites 2 to 5 and 7 to 9 (Figure 1) for the 1996–2000 period. Each site/year combination defines a convolution site model. A total of 20 convolution site models were constructed (Table 2). The naming convention used for the site models is SN_XX, where N represents the site number (Figure 1) and XX represents the year. Graphical comparisons (Figures 9, 10, 11, and 12) of convolution computed water temperature changes and fluxes of stored heat energy versus residuals from measured values are presented for models with roughly average error statistics.

Table 2. Summary of Regression-Estimated Coefficients and Error Statistics for Comparison of 30 min Measured and Convolution Site Model Water Temperature Changes and Fluxes of Stored Heat Energya         Measured and Convolution Site Model-Computed Water Temperature Changes T Measured and Convolution Site Model-Computed Fluxes of Stored Heat Energy W Convolution Site Model Regression- Defined Thermal Exchange Coefficient kex, m s-1 Regression- Defined Number of Comparisons R2 of the Comparison Mean Absolute Error of the Comparison, °C R2 of the Comparison Mean Absolute Error of the Comparison, W m-2 S2_96 5.46 0.36 4,849 0.56 0.08 0.56 134.71 S2_97 5.94 0.46 6,050 0.60 0.09 0.56 154.25 S3_96 4.31 0.55 8,137 0.65 0.09 0.65 108.32 S3_97 3.88 0.57 8,089 0.65 0.08 0.63 95.90 S4_96 0.48 0.51 7,080 0.64 0.10 0.57 46.45 S4_97 1.53 0.33 4,585 0.57 0.09 0.47 50.56 S4_98 3.17 0.23 6,396 0.45 0.06 0.40 68.14 S4_99 0.45 0.73 2,578 0.70 0.12 0.69 35.40 S5_96 0.83 0.43 8,136 0.68 0.08 0.66 50.34 S5_97 0.85 0.44 5,042 0.75 0.08 0.69 31.60 S7_96 1.53 0.74 8,137 0.71 0.07 0.72 73.35 S7_97 1.46 0.71 7,469 0.68 0.09 0.65 61.58 S7_98 1.71 0.74 8,089 0.64 0.07 0.65 71.51 S7_99 1.85 0.65 7,915 0.70 0.08 0.70 77.46 S7_00 2.09 0.60 5,208 0.61 0.09 0.60 109.18 S8_97 1.50 0.54 1,079 0.54 0.14 0.67 27.90 S8_98 0.88 0.91 5,671 0.68 0.16 0.69 28.01 S8_99 1.33 0.83 2,706 0.73 0.11 0.72 39.38 S8_00 1.06 0.87 2,212 0.73 0.16 0.73 37.39 S9_98 0.11 0.94 1,287 0.70 0.06 0.65 8.99 aSite locations are shown in Figure 1.

Figure 9. Comparison of 1996 residuals from measured values and convolution-computed mean vertical water temperature changes from site 3. Site location is shown in Figure 1. [larger image]

Figure 10. Comparison of 1996 residuals from measured fluxes of stored heat energy and convolution computed fluxes of stored heat energy from site 3. Site location is shown in Figure 1. [larger image]

Figure 11. Measured and convolution-computed net daily water temperature changes from site 3. Site location is shown in Figure 1. Missing data indicate that analysis was not performed for the period. [larger image]

Figure 12. Measured and convolution-computed net daily fluxes of stored heat energy (W) from site 3. Site location is shown in Figure 1. Missing data indicate that analysis was not performed for the period. [larger image]

[34] Site 1 (not shown in the figures and tables) was not considered for analysis because of concerns that water temperature mostly was a function of water management activities, rather than natural changes in air temperature. Site 1 is located south of agricultural areas surrounding U.S. Highway 98 (Figure 1). During the rainy season when water levels were high in the agricultural areas, surface water pumps conveyed water southward toward the Water Conservations Areas and impacted water temperatures measured at site 1. Site 6 (also not shown in the figures and tables) was similarly removed from consideration because air temperatures were recorded only to 1°C precision, resulting in relatively large error statistics for the convolution site models. Because stored heat energy changes in wetland surface water are more often a considerable component of the surface energy budget during winter (Figures 7 and 8), all convolution site models included only the November to April winter season. During the summer, net radiation dominates the surface energy budget because of the magnitude of solar radiation, and therefore the need for accurate estimates of stored heat energy changes in wetland surface water is less critical.

[35] In general, the convolution site models performed adequately in computing 30 min mean vertical water column temperature changes during winter (Table 2). The R² values for computed and measured water temperature changes ranged from 0.45 to 0.75, with an average of 0.65. The mean absolute error for the comparison ranged from 0.06 to 0.16°C, with an average of 0.10°C. A graphical comparison of 1996 convolution computed water temperature changes versus the residuals from field-measured water temperature changes at site 3 (Figure 9) indicates that declines in water temperature are more precisely computed than increases in water temperature. This bias was present within each convolution site model (Table 2) based on visual inspection of computed versus residual plots. Although a mechanism for this bias is unclear, its consequence is that in general during the winter releases of heat energy from surface water storage (-W) will be more accurately computed by the convolution sites models than fluxes of heat energy into surface water storage (+W).

[36] The water temperature changes computed from the convolution site models also seem to work well for approximating 30 min fluxes of stored heat energy in wetland surface water in the Everglades (Table 2). Fluxes of stored heat energy in wetland surface water were approximated as the product of T_w (computed by the convolution site models), D, and heat capacity divided by the number of seconds in 30 min and compared to the fluxes of stored heat energy computed with field-measured changes in mean vertical water column temperature. The R² values determined for the comparison ranged from 0.40 to 0.73, with an average of 0.63. The mean absolute error for the comparison ranged from about 8.99 to 154.25 W m^-2, with an average of 65.52 W m^-2. A graphical comparison of 1996 convolution-computed fluxes of stored heat energy versus residuals from field-measured fluxes of stored heat energy at site 3 (Figure 10) indicates bias similar to that in Figure 9 because heat content is derived from water temperature changes. As a consequence, each convolution site model computes fluxes of heat energy leaving surface water storage more precisely than fluxes of energy into surface

[37] The site convolution models yielded reasonable estimates of net daily changes in both wetland surface water temperature and fluxes of stored heat energy during winter months (Table 3). Net daily water temperature changes were estimated as the daily sum of water temperature changes that occurred during 30 min increments. The R² values between measured and computed net daily water temperature changes ranged from 0.46 to 0.85, with an average of 0.69. The mean absolute error for the comparison ranged from 0.42 to 1.04, with an average of 0.64°C. A graphical comparison of measured and convolution-computed net daily water temperature changes at site 3 in 1996 is shown (Figure 11). For computing net daily fluxes of stored heat energy, R² statistics for the convolution site models ranged from 0.45 to 0.85, with an average of 0.67. The mean absolute error for the comparison ranged from 1.28 to 22.24 W m^-2,with an average of 9.36 W m^-2. A graphical comparison of measured and convolution-computed net daily fluxes of stored heat energy at site 8 in 1998 is shown in Figure 12.