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The Savannah River Technology Center (SRTC) measured water skin temperatures at four of the Multi-spectral Thermal Imager (MTI) core sites. The depression of the skin temperature relative to the bulk water temperature (D T) a few centimeters below the surface is a complex function of the weather conditions, turbulent mixing in the water and the bulk water temperature. Observed skin temperature depressions range from near zero to more than 1.0°C. Skin temperature depressions tend to be larger when the bulk water temperature is high, but large depressions were also observed in cool bodies of water in calm conditions at night. We compared D T predictions from three models (SRTC, Schlussel and Wick) against measured D T’s from 15 data sets taken at the MTI core sites. The SRTC and Wick models performed somewhat better than the Schlussel model, with RMSE and average absolute errors of about 0.2°C, relative to 0.4°C for the Schlussel model. The average observed D T for all 15 databases was -0.7°C.

Keywords: remote sensing, water skin temperature, thermal imagery

All bodies of water have a thin surface layer on the order of a millimeter thick in which viscous effects dominate and heat transfer is via molecular, not turbulent mixing processes. The temperature of this surface or "skin" layer is typically a few tenths of a degree Celsius lower than the bulk water temperature below. The difference between the skin temperature and the bulk water temperature is called the skin temperature depression (D T). The skin temperature is usually lower than the bulk water temperature because most natural bodies of water experience net losses of energy (evaporative, sensible and longwave radiation) to the atmosphere. These energy losses are balanced by a sensible heat flux from below that is driven by forced and/or free convection. Heat transfer through the viscous skin layer is inefficient relative to the turbulence-dominated processes above and below. So much of the temperature drop between the water and air is concentrated in that thin layer.

Remote sensing is widely used to measure water temperatures in remote areas such as the open ocean for climate research and other applications. Remote sensing is also becoming more frequently used to monitor temperatures of heated bodies of water such as cooling lakes, cooling canals and thermal plumes discharged to rivers and the ocean. Since the bulk water temperature is usually the quantity that is desired both for research and regulatory purposes, it is important to be able to estimate the difference between the skin temperature that is measured by the remote sensing device, and the bulk water temperature. Much of the research on D T has been done on the open ocean. Wick et al.¹ summarizes much of the recent work on this problem, including the different modeling approaches. The models described in this paper are semi-empirical combinations of expressions based on basic heat transfer theory. The more recent models show some skill at prediction of D T, although there is still significant scatter in the best of the observed versus predicted plots.

The work described in this paper focused on skin temperature measurement and prediction in heated and unheated lakes and reservoirs. This research is part of the ground truth program for the Department of Energy’s (DOE) Multi-spectral Thermal Imager (MTI) demonstration satellite project. One of MTI’s objectives is very accurate water temperature retrieval using only the sensor’s 15 wavebands. For this reason, we chose lakes and reservoirs as the primary ground truth sites, because they are more controlled environments than the open ocean, where high seas, foam and spray make data acquisition more difficult. However, since lakes and reservoirs are small, there are horizontal gradients of temperature and other variables in the water and air, which complicate the data collections and analyses.

In the following section, we summarize the modeling approach, describe the MTI ground truth collections at four sites and present the modeling results.

SRTC developed a model for prediction of D T that is based as much as possible on the physics of the problem. However, some empirical coefficients are inevitable for this type of model, which attempts to reduce a fully 3D, time-dependent fluid-gas interface problem to a steady state, single node approximation. A 3D model would not be more accurate, because the effort required to collect the data would be more expensive and difficult than directly measuring D T over the entire water body of interest.

The starting point for the model is the time-dependent energy conservation equation for the water skin layer:

This equation states that the rate at which energy leaves or enters the skin layer is determined by the net flux of sensible heat being brought to the surface from below and the evaporative, sensible and radiation fluxes of energy entering the atmosphere above. The variables in the equation are: r = density of water, c_pw = specific heat of water, d = thickness of skin layer, T_sk = skin temperature, T_b = bulk water temperature, r_sk = resistance function for heat transfer through skin layer, H_L = latent (evaporative) heat flux, H_S = sensible heat flux, LW_d = downwelling longwave radiation, e = emissivity of water, s = Stefan-Boltzmann constant.

This equation can be solved with the time-dependent term on the left. However, essentially identical solutions are found for T_sk when this term is dropped and T_sk is solved for iteratively:

Solving this version of Equation 1 eliminates the time step constraint imposed by the time dependent term. All of the terms in Equation 2 are either observed quantities or can be computed using standard models, except for the skin layer resistance function (r_sk). We note in passing that the models used to compute evaporative and sensible heat fluxes to the atmosphere assume horizontal homogeneity in the atmospheric boundary layer, which is a questionable assumption for small to medium-sized bodies of water. The expression for r_sk is derived from standard engineering theory on mass and energy transfer at a gas-liquid interface:

Where k_w is the thermal conductivity of water. The expression for d is a modified version of a relationship hypothesized by Saunders²:

where n is the molecular viscosity of water, u_* is the friction velocity of the water, w_* is a free convection velocity scale for the surface layer of the water and f an empirical term that is a function of the surface energy fluxes. These terms are evaluated using standard boundary layer theory. The addition of w_* to the expression for d was motivated by the observation that u_* is zero in calm conditions, which occur fairly frequently over inland bodies of water, but rarely over the open ocean. In calm conditions there is still usually a significant net loss of energy to the atmosphere via long-wave radiation and free convection. These losses are balanced by an upward-directed heat flux in the water driven by free convection.

D T predictions from the model described above will be compared to observed values in the next section. In addition, predictions from two other models will be compared to the measured D T’s. The first model is purely statistical and was developed by Schlussel³. The second model (Wick et al.¹) is semi-empirical and employs many of the same concepts used to develop the SRTC model.

SRTC developed an apparatus that can make simultaneous measurements of the variables needed to validate the model described in the previous section. These variables are: bulk water temperature at several levels, air temperature and dew-point temperature, up and down welling long-wave radiation, skin temperature (measured with a broad-band Heimann radiometer), solar radiation and wind speed. Skin temperature measurements and associated data from three locations will be described in this section: the H. B. Robinson power plant’s cooling lake in South Carolina, the Savannah River Sites’ (SRS) L-Lake and the HPIW reservoir at the NASA Stennis Space Center (SSC).

SRTC and SSC personnel measured skin temperatures on August 10, 2000 for about a five-hour period centered on the time that MTI imaged SSC. The two groups made simultaneous independent data collections in the HPIW reservoir with two floating "skin temperature rigs" that were separated by about 30 m (Figure 1). SSC developed its own skin temperature rig to duplicate the measurements taken by the SRTC rig. Figure 2 compares bulk and skin temperature measurements from the two rigs. Both rigs measured bulk temperature measurements with radiometers by turning on a small, submerged pump. The pumps mixed the water under the radiometers sufficiently to briefly eliminate the D T. Figure 2 shows that D T was a few tenths of a degree Celsius. The two sets of measurements were in close agreement, with average D T’s agreeing to within about 0.1°C. One-minute averages of two-second data are plotted in Figure 2. The close agreement between the two independently developed rigs is strong evidence that the D T’s are correct. Figure 3 compares bulk and skin temperatures measured by SSC with skin temperatures computed by the SRTC model described in the previous section. In this case, predicted D T’s averaged 0.1 to 0.2°C less than the measured values.

Figure 4 compares predicted D T’s by the SRTC, Schlussel and Wick models. The comparison is not completely fair, because the Schlussel and Wick models were developed for open oceanic D T prediction, whereas the SRTC model was developed for D T prediction in heated and unheated lakes, where the range of D T’s is greater. The Schlussel and Wick models contain empirical coefficients specific to the oceanic conditions, whereas the SRTC model contains coefficients specific to lake data sets. The effects of these differences are apparent in Figure 4, which shows that the Schlussel and Wick models under-predicted the SSC D T’s to a greater degree than the SRTC model.

The cooling lake for the H. B. Robinson power plant receives waste heat from the power plant and attains temperatures greater than 40°C near the cooling water discharge during the summer. The hot summer temperatures are also partly the result of natural features, which include the shallowness of the lake and the tannins, which darken the water and increase its absorption of solar radiation. SRTC collected skin temperature data there to test the accuracy of MTI’s temperature retrieval algorithms at high temperatures.

Figure 5 compares D T’s from the three models to observations taken on April 7, 1999. The bulk water temperature was about 33°C. The D T’s were fairly large because the temperature difference between the water and air was elevated due to the heat being added to the lake by the power plant. The measurements were taken near the cooling water discharge, which is the warmest area in the lake. In this case, the Schlussel and Wick models again significantly under-predicted the D T’s. The SRTC predictions were slightly low on the average, and more correctly predicted the scatter and trend in the observed D T’s. The variability in the observed D T’s appears to be partly due to variable wind speeds.

Figure 6 compares D T’s from the three models to observations taken on July 27, 1999. Although the measurements were taken some distance from the cooling water discharge, the bulk water temperature was still a hot 42°C. In this case, the three models were all in better agreement, with the Wick model performing a little worse than the SRTC and Schlussel models.

Note the large excursion in the observed D T’s in Figure 6 at about 14.45 hours. This excursion in D T was accompanied by close to a 1°C spike in the bulk water temperature, but no change in atmospheric conditions. None of the three models responded to the spike in bulk water temperature, because a small drop in the wind speed at the same time cancelled out the increase in energy loss that it otherwise would have caused. The spike in the D T’s predicted by the SRTC model at about 15.0 hours was caused by an increase in the wind speed. We cannot explain the spike in the observed D T’s at about 14.45 hours, other than to attribute it to an unknown 3-D effect. There was no floating debris or oil on the water that could have been responsible.

L-Lake served as a cooling lake for the Savannah River Site (SRS) production reactors during the Cold War. It now receives no manmade heat load. SRTC has collected skin temperature data at L-Lake for fairly lengthy periods that included nearly calm periods during the night. SRTC collected one of these data sets on May 28, 1999.

Figure 7 shows observed and predicted D T’s from the three models. In this case, the SRTC model does best during the night, but over-predicts the D T’s during the day. None of the models predicts the reversal of the sign of the D T’s from negative to positive during the end of the observation period. The failure of the models to do this can be explained by Figure 8, where we see that following a night of locally unstable conditions (water temperature higher than air temperature and dewpoint temperature one meter above surface), the air becomes warmer than the water. But the dewpoint temperature is still well below the water temperature, so the evaporative energy losses are larger than the sensible energy losses, and the net radiation is still negative. Since the observed D T’s became positive, we must conclude that there was a net energy transport from the air to the water. This means that the usual flux-profile relationships used to compute energy transfer between water and air must not have been valid at that time. Flux-profile relationships assume horizontally homogeneous, steady state conditions. These conditions probably were not met over L-Lake at this time. Positive D T’s have been observed at L-Lake on other occasions when weather conditions were similar, i.e., when winds and temperatures rose rapidly in the morning after a calm, cool night.

The Comanche Peak power plant near Fort Worth, Texas uses a 13 km² lake to dissipate waste heat from its two 1125 MWe reactors. About 4500 MW of waste heat is discharged to the lake during normal operations. Discharge temperatures can rise above 40°C during the summer. The semiarid, windy climate of this region promotes rapid losses of energy from the lake, which often results in large D T’s. Figure 9 shows observed and computed D T’s from data collected about 0100 on August 9, 2000. Waypoints correspond to locations where measurements were taken from a boat, starting near the cooling water intake and progressing to close to the discharge, where bulk water temperatures were about 41°C. The D T’s are close to 1.0°C near the cooling water intake, where the bulk water temperatures were about 36°C. They rise to around 1.5°C at waypoints 4, 5 and 6, and then to about 2.5°C at the waypoint closest to the discharge. These observations are averages of data taken with hand-held radiometers and thermometers. Conditions were much more variable at waypoint 7, so that D T is the least reliable. The models were able to predict these large D T’s fairly successfully. This is particularly impressive for the Schlussel and Wick models, which were developed with data taken over the ocean, where D T’s are rarely larger than 0.5°C.

SRTC collected a total of 15 skin temperature data sets at L-Lake, Lake Robinson, Stennis Space Center’s (SSC) HPIW reservoir and the H. B. Robinson power plant’s cooling lake. We looked at average model performance by comparing average observed and predicted D T’s from these four sites. Although the number of data points in some data sets is much larger than in others, this seemed to be the fairest way to make the comparison, because each data set was taken in different locations and conditions. Table 1 below summarizes the results.

The statistical results are somewhat of a mixed bag, with SRTC having the lowest R² value, but also the lowest root-mean-square-error (RMSE), average absolute error, average and average absolute percent errors (relative to observed D T). SRTC’s average D T over all data sets was also closer to the observed average.

We have compared observed D T’s from 15 data sets taken at four of the MTI core sites to predicted values from three different models. The SRTC and Wick models performed at about the same level of skill, whereas the purely empirical Schlussel mode was somewhat less accurate. Over all 15 data sets, the RMSE and average absolute errors for the SRTC and Wick models were about 0.2°C. The average D T for all 15 data sets was –0.7°C.

There were unexplained excursions in the D T’s measured during this research project, notably the large one observed at Lake Robinson on July 27, 1999 and the positive D T’s observed at L-Lake. Future research should attempt to explain these excursions and determine if model failures to predict them were caused by horizontal non-homogeneities in the atmosphere and water.

Finally, D T’s measured at the MTI core sites were often much larger than those observed over the ocean. This is partly due to the elevated bulk water temperatures caused by waste heat from power plants and partly because drier air from the adjacent land blows over these small bodies of water, maintaining steep vertical gradients in water vapor pressure and strong evaporation. These larger D T’s emphasize the need to account for skin temperature depressions when using thermal imagers to measure the temperatures of inland bodies of water.

1. Saunders, P. M., 1967: the temperature at the ocean-air interface. J. Atmos. Sci., 24, 269-273.
2. Schlussel, P., W. J. Emery, H. Grassl, and T. Mammen, 1990: On the bulk-skin temperature difference and its impact on satellite remote sensing of sea surface temperature. J. Geophys. Res., 95, 13341-13356.
3. Wick, G. A., W. J. Emery, and L. H. Kantha, 1996: The behavior of the bulk-skin sea surface temperature difference under varying wind speed and heat flux. J. Phys. Oceanogr., 26, 1969-1988.