AIR-SEA SCALAR FLUX DUE TO WIND-GENERATED NEAR-SURFACE TURBULENT EDDIES: THE EDDY RENEWAL MODEL

Based on analyses of infrared images of the air-water interface, a new model of surface tracer flux is presented (eddy renewal model). In contrast to the currently used model (surface renewal model), which assumes that water motions are driven solely by breaking event-like conditions (or sudden bursts of turbulence), the new model posits that water motions are driven by Langmuir-like turbulent eddies (or more steady-state conditions). These wind-generated turbulent eddies arrange to create elongated warm patches of upwelled water between long streaks of colder downwelling water. In analyzing the images taken during GasEx2001 expedition in 2001 in the Equatorial Pacific waters and laboratory experiments in the AEOLOTRON wind wave tank at University of Heidelberg in October 2004, both breaking event-like motions and Langmuir-like eddies are present, and thus the new model complements the old (as opposed to replacing it). Analysis of the bulk temperature estimates from the new model show that they are quite similar to those from the old model, and, perhaps, hint at conditions where one model may be more appropriate than the other.

vi List of Tables   Table: Title  In any air-sea climatological model, the importance of the transfer of heat or gases (especially greenhouse gases such as CO2) between water and atmosphere cannot be understated. However, the physical processes that control such transfers are only recently being understood. Compounding the issue is that the transfers are affected by many variables, including, but not limited to, wave action, wind speed, temperatures of atmosphere and seas, concentrations of gases, coefficients of molecular diffusivity, and condition of surface waters (e.g. presence of surfactants). (Frew, et. al., 2004). Within the last few decades, strides have been made in understanding this complex system. Aside from understanding the individual variables, much research has been conducted to clarify how those variables interact with each other and how to best measure the transfer (Jähne and Haußecker, 1998).
Given the range of values that have been calculated through indirect and direct gas measurement techniques (McGillis, et. al., 2001), methods have been invented to use heat as a proxy tracer. One of the problems with direct gas transfer measurements is that it is extremely difficult to detect the concentration fluctuations or gradients, due to the physical limitations of in situ gas concentration measurements. Methods using tracers and patches heated with short-bursts of an infrared laser have been used to calculate transfer velocities (e.g. McGillis, et. al., 2001), however their efficacy has 2 been questioned (Jacobs, et. al., 2002). The use of infra-red imaging allows very accurate measurements of the water surface temperature to be collected with minimal impact on the system (Haußecker, Reinelt, and Jähne, 1995). If the heat transfer velocities are determined to high levels of accuracy using the infrared measurements, the gas transfer velocities can be estimated using the Schmidt number scaling and a small number of non-invasive gas concentration measurements (Frew, et. al., 2004).
In order to interpret observed surface temperature variation and to estimate the heat transfer velocity, a mechanical model of "surface renewal" has been used. In this model, it is assumed that there remains a boundary "thin-film" at the surface through which tracers must pass. This boundary is a result of the stronger effects of viscosity near the surface and can be visualized in experiments with reactant dyes and tracers, or by measuring the temperature profile and surface temperature field. The Surface Renewal Model assumes that this thin film is periodically renewed by bursts of turbulent eddies, which refresh the waters in the surface boundary layer. The transfer of the gas is determined by the frequency of these renewal events, which is related to the wind speed at ten meters. This model can be used to explain the observed surface temperature distribution in a statistical sense (Garbe, 2001). With finer scale measurements, however, it appears that this model may not be mechanistically correct.
The main objective of this study is to develop a new model of the near surface turbulence, which is more consistent with the observed small scale 3 surface temperature patterns. Models of gas transfer being effected by eddies have been presented in the past (e.g. Fortescue and Pearson in 1967, Lamont and Scott in 1970, Csanady in 1990, and Atmane, Asher and Jessup in 2004, however none have developed a model based on steady-state assumptions (i.e. based on the apparent longevity of observed surface temperature patterns) or attempted to match a modeled temperature curve to infrared images of individual eddies, as is presented here. The model is applied to both field and laboratory data of infrared observations. The results are then compared with those based on the existing surface renewal model, in order to examine the validity of the new model. Although the temperature of the air can be warmer than that of the water, there usually exists a "cool-skin" of one millimeter or less at the interface (Soloviev and Schlüssel, 1994). This skin is a result of the latent heat transfer from water to air that persists, except in certain circumstances (e.g. fog). When environmental conditions are not changing rapidly, one can assume that there is a layer below the sea surface where the heat flux is constant with depth (that is, there is no significant heating or cooling within this layer). Also, it is apparent that turbulent flux is responsible for heat flux away from the boundary, and molecular diffusion is the primary mechanism only in a thin diffusive sublayer close to the boundary (Frew, et. al., 2004). In order to model the heat transfer process across the diffusive layer, one must, of course, start with the basic governing equations. The heat flux is proportional to the temperature gradient, as in where, jH is heat flux, T is temperature, and k is thermal conductivity or where κ is thermal diffusivity, ρ is density and CP is specific heat.
Solving [1.1.6] requires some understanding of the boundary conditions. One assumption of all of the heat transfer models is that the temperature at z   is uniform; this is called the "bulk temperature" (TB).
That is, at some distance below the surface, the turbulent mixing is sufficiently strong and the temperature approaches a constant. Given the definition of the "well-mixed layer," this is a good approximation for the temperature at a depth well below the surface, but still well above the thermocline. A constant bulk concentration is a good approximation for gasses, as well.
The surface boundary condition, however, differs between gasses and heat. In order to solve [1.1.6], at the surface, either the temperature (or gas concentration) or the flux must be specified. For heat, a constant flux is the more appropriate choice, because the net air-sea heat flux is mainly controlled by the air-side turbulence. For insoluble to slightly soluble gasses, however, a constant surface concentration is a better approximation, due to 6 the higher turbulence in the air near the water surface keeping the concentration of the gasses well mixed.
In principle, the temperature field can be obtained by solving [1.1.6] provided the water motion (u, v, w) is known. In reality, the velocity field due to near surface turbulent eddies is not explicitly known, and hence some assumptions must be made.
The Surface Renewal Model (as presented by Garbe in 2001) assumes that the diffusive sublayer is periodically renewed; that is, the waters in the surface boundary layer are periodically refreshed with bulk temperature waters, and thus the temperature is periodically equal to the bulk temperature. In between the renewal events, it is assumed that 1.) advection plays no role in heat diffusion and 2.) the gradients are zero in the horizontal.
[1.  (Garbe, 2001) where σ is the variance, μ is the mean, ΔT is TB -TS, and α is defined as An example of the theoretical distribution is shown in Figure 3a. Figure   3b shows how a typical observed temperature distribution compares with the theoretical curve. It is apparent from this example that this statistical treatment gives a reasonable fit. Although, the veracity of this method has been tested by simultaneously measuring the transfer velocities of various tracers, the assumption that heat can be used as a proxy tracer for gases like carbon dioxide is still being debated (e.g., Zappa, et. al. 2004).

Section 4. Limitations of the Surface Renewal Model
Even though the Surface Renewal Model is able to describe the surface conditions statistically, it is still limited by the lack of an explanation for the renewal event itself. Images of the surface field show that the patches tend to remain coherent for longer than the average renewal time-scale.
Although the Surface Renewal Model assumes that renewal events happen instantaneously, this cannot be physically correct. Even breaking waves take some measurable amount of time to stir up the warmer waters through induced turbulent action. This time will allow cooling or mixing to occur, reducing the observed surface temperature.
Another limit of the Surface Renewal Model is that it assumes the bulk temperature to be identical to the highest measured temperature on the surface. If waters advected up do not arrive instantaneously (i.e. renewal is not instantaneous), some cooling will have taken place by the time bulk waters reach the surface. The determination of this cooling, however, is precluded by the assumption that the renewal is instantaneous.
There is also a question as to whether the relation of transfer velocities In viewing the images collected (see Figure 4 for a typical sea-surface temperature image), it appears that distinct turbulence patterns exist at the surface, namely, Langumir turbulence. This is shown in elongated patches Figure 4: A representative infrared sea-surface image. In this image, the water and wind is moving from right to left. The temperature scale (shown on the right of the figure) is in degrees Celsius; the size scaling is given in pixels (with one pixel approximately four millimeters). The whole image is 0.5m by 0.5m.
of warm water alternating with cold water filaments, with axes aligned with the predominant wind direction. From this, it can be assumed (for the sake of easing calculations) that, if the long axis is selected as y,  y is negligible and can be set to zero. Scaling arguments can be used to show that x  is also negligible in the diffusion term. Lastly, since the surface patches tend to exist for a relatively long time,  t is also considered zero. These or, in the case of a gas concentration, In  where jg is the gas flux. The solution for the concentration is [2.
Combining these with equation [2.1.6], we obtain [2.2.8] In order to compare this solution to that for the upwelling region, it will need to be reverted back to the (x, z  In further examining the model presented in previous sections, it is apparent that there are three parameters that define the characteristics of a particular eddy, namely, the size of the eddy, the intensity of the motions found within the eddy, and the bulk temperature. However, mathematically, only the intensity and eddy size determine the shape of the temperature distribution, while the bulk temperature sets the specific value of the temperature curve. The intensity and eddy size can be treated as one parameter measuring the surface divergence, as shown below.
Starting from the equation of temperature diffusion, and using the same assumptions as before, These equations can be normalized by introducing the following normalized variables: giving one equation for the temperature distribution that is independent of the size of the eddy. Model. This will be further discussed in following sections.
By using the above equations and coding in mathematical analysis software (such as MatLab), generalized solutions for the temperature field and gas concentration field were obtained. These solutions can be compared to the known solutions for the Surface Renewal Model. The basic structures of these fields deserve some discussion (and are presented in Figure 6).
The temperature solution obtained through computation (Figure 6a) shows an eddy, in which warm waters are advected up to the surface (on the left), along the surface (from left to right) and then down (on the right). Rather than the motion of the water being described by an instantaneous event, the motion is described as a continuous flow from upwelling to downwelling.
Once the waters have traveled sufficiently far from the surface, it is assumed that the turbulent motions of the mixed layer will blend the downwelled waters with the existing mixed layer. Since the difference in scale between the 28 mixed layer and the surface-cooled layer is enormous, it is appropriate to assume that the mixed layer is infinite, for the purposes of these calculations.
There is an inherent anomaly in the temperature model presented It should also be noted that there is an underlying assumption that these eddies are paired with a mirrored eddy. That is, for every eddy rotating with a positive spin, there is one next to it rotating with a negative. This gives a symmetrically decreasing temperature profile (moving away from the center). This form is qualitatively consistent with the temperature signal of temperatures on the right of both models. The temperature distributions of the two eddies show the difference in the cooling between the models (in Figures 7a and b).
In the temporal model, as the breaking event moves through the area, it stirs up bulk temperature water, which then cools off (as a function of the time Another way to interpret the difference between the models is to compare histograms of the surface temperatures ( Figure 8). This will be most useful because the previous research based on the Surface Renewal Model Once again, the difference between the two models is striking. In the Surface Renewal Model, it is clear that the waters reach colder temperatures more quickly than they do in the Eddy Renewal Model. However, the maximum value of the bulk temperature is never observed at the surface in the Eddy Renewal Model.
In order to compare the vertical temperature distributions, one would need to match not only the size of the region, the bulk temperature, and the mean surface temperature, but also the surface heat flux. For instance, if the size is taken to be 5cm x 5cm x 1mm, the surface flux is set as 100 W/m 2 , and the mean surface temperature is arbitrarily defined as 0.1°C below the bulk temperature, one would obtain (through proper scaling) the results in  In the Eddy Renewal Model, the equations were normalized based on two parameters: k and u0, the size and strength, respectively, of the eddy.

Section 4. Comparison of Identical Parameter Distributions
Using the previous results for the spatial temperature curve (Eddy Renewal Model) and the temporal temperature curve (Surface Renewal Model), it is possible to compare a distribution of eddies to a distribution of renewal times. This allows the comparison of the two models over a region encompassing more than just one sample eddy and renewal event.
When identical distributions of the parameters are applied to the meannormalized surface temperature curves, the resulting surface temperature distributions are very different. As discussed in section two of chapter one, the temperature distribution obtained for the SRM with a log-normal distribution of  is shaped like the plot in Figure 10a and described by equation [1.2.2]. However, when the same distribution is applied to a meannormalized ERM surface temperature curve, the resulting temperature distribution is much different (Figure 10b). For quick reference, the difference between these plots can be seen in Figure 10c.
This difference in temperature distributions comes about from the differences in the surface temperature curves. The SRM curve starts from the bulk temperature and decreases with time up to the renewal time of  (as seen in the histogram in Figure 8a). This gives a lowest temperature as defined by each  . The ERM curve highly favors the mean value, has a defined maximum temperature value lower than the bulk temperature, and has no clearly defined lowest temperature value (as seen in the histogram in Figure 8b).  tion may still be justified since the observed temperature patterns tend to show more variation in the cross wind direction than in the along wind direction (Figure 11a). Therefore the ERM is applied to the surface in a direction that is nearly perpendicular to the predominant wind direction, as shown in Figure 11b. The application of the model along one column of data allows the fit of the theoretical temperature curve to be individualized for each eddy, as explained below.
Several methods were tested to optimize this matching. The bulk temperature, as the most basic parameter in the model, must first be defined.
Initially, the bulk temperature was defined simply as the highest recorded surface temperature, much as in the modeled SRM field. Using a single value for the bulk temperature for the entire image led to poor model / data fits. It was found that the fit of the model to the data could be much improved by allowing the bulk temperature to vary throughout the image. These variations were created by matching the mean temperature of the model to the mean temperature of each eddy, then allowing the bulk temperature to be found by a least-squares best fit analysis. Two different methods of bulk temperature variation were tested: dividing each image in to subsections and defining the bulk temperature within each subsection (i.e. assuming constant bulk temperature within each subsection) and allowing the bulk temperature to be defined for each eddy analyzed (in each line of analysis).
From a physical perspective, the former would make more sense; that is, any variation of the temperature in the well mixed layer should occur over a region much larger than an individual eddy scale. However, when the bulk temperatures were allowed to vary eddy by eddy and line by line, it was found that the mean of such bulk temperature estimates over a subsection of the image was very close to the single bulk temperature estimate for the same region assuming that the bulk temperature was uniform. (See one notices that the model has a stagnation point at the downwelling region. That is, the velocity at the surface goes to zero, and the waters are allowed to cool infinitely. As discussed earlier, the model is not Figure 12: Comparison of results for two different bulk temperature estimation methods a.) Bulk temperature constant within one area b.) Bulk temperature allowed to vary line-by-line and eddy-by-eddy, averaged into the same areas as in 12a.
applicable to this region; the real surface temperature is not infinitely cooler.
In order to reduce error caused by this singular point, the model curve is not applied to the pixel corresponding to the temperature minima. This gives the result of a better fit to the data (i.e. mean squared error square per pixel) and a method of eliminating a physical discrepancy. On the other hand, this also necessitates the removal of two-pixel eddies from the model application.
The analysis of the remaining (three-pixel and larger) eddies shows that the bulk temperature values for the smaller eddies show a larger variation than those of the larger eddies. It also appears that these smaller eddies tend to yield a lower bulk temperature estimate (on average) than the larger eddies. To reduce the effect of this possible bias, eddies smaller than five pixels have simply been removed in the final bulk temperature estimate (as defined by the spatial average of the remaining bulk temperatures). More details about the specifics of the application method are given in Appendix B, along with the MatLab code used in the application of the model to the observed data.
Lastly, some of the older data analyzed had obvious instrumentation errors. In one of the data sets analyzed, there were 'dead' pixels (i.e. pixels in the infrared camera's charge coupled device that failed to register any temperature), and in the two older sets, the image was grainy due to pixilation. Given that the algorithm developed applies the model to every line of data between a maximum and a minimum, higher levels of pixilation To summarize the procedures, the following steps were taken to apply the Eddy Renewal Model to the observed data.

1.)
Any necessary preprocessing is preformed to eliminate dead pixels and/or pixilation errors from older cameras. Figure 14: The results of preprocessing on an image with dead pixels and high levels of pixilation a.) (top) Original infrared image from the Aeolotron wind-wave tank at the University of Heidelberg, Germany. b.) (bot) Image after averaging out dead pixels, convolution with a simple 6x6 filter, rotation (90° counterclockwise to match water motion between image and model), further averaging, and resizing.

2.)
The direction for line-analysis is selected perpendicular to the direction of mean current, which is assumed to be the wind direction.

3.)
Each line of data is analyzed to determine the temperature maxima and minima. Each interval between temperature maximum and minimum (inclusive) is defined as one eddy.

4.)
The model is applied to each eddy, excepting the temperature minimum pixel; any two-pixel eddies are not modeled.

5.)
The model curve is divided into (n -½) segments (where 'n' is the number of pixels in the observed eddy, including the maximum and minimum) and averaged for each segment; the ½ segment is applied to the maximum point.

6.)
The model is matched to the data by matching the temperature of the pixels to the mean temperature of the model curve segments.

7.)
The bulk temperature is allowed to vary for each eddy and is determined by a least-squares best fit analysis between the model curve and the observed data.

8.)
Any pixels not assigned a model value in this analysis (minima of all eddies and maxima of two-pixel eddies that are not shared with a larger eddy) are assigned the value of the original data point (for continuity's sake), but this value is not included in the error analysis.
The above algorithm is then applied over an entire image to obtain the modeled temperature and bulk temperature fields. The results of this analysis are given in the following section.

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Section 2. Results of Image Analysis By applying the methods discussed in the previous section over an entire image (i.e. all lines of data), an entire modeled temperature field is generated, along with the associated bulk temperature field. This modeled temperature field can then be compared to the original image to determine the mean-squared error. (This error analysis was used to determine the best way to apply the model curve to the observed data, and to determine how the bulk temperature would be allowed to vary.) In total, more than 13,000 images were analyzed using this method. These images come Model are obtained: the estimate from all eddies (3 pixels and larger), and the estimate from eddies 5 pixels and larger. Next, the mean bulk temperature estimate for each image is obtained using the size of the eddies to weight the mean. The size of each eddy is defined as (n-1) pixels, where n is the number of pixels from maximum to minimum, inclusive.
If the analysis is completed over a series of images, the resulting bulk temperature estimate (spatial average) can be viewed as a time series of these spatial averages. This can be directly compared with the bulk temperature estimate based on the Surface Renewal Model , which is also spatially averaged.

Section 3. Discussion of Image Analysis Results
In general, the Eddy Renewal Model is able to reproduce the surface temperature field quite well. In the images presented in the previous section, the average total squared error is on the order of 0.5(°C) 2 for the entire image, with a mean error square on the order of 5x10 -5 (°C) 2 for images free of reflected infrared. This suggests that the general shape of the surface temperature curve, as derived in section two of chapter three, is a good description of the real temperature distribution in the eddies observed at the sea-surface. The one notable exception is the colder end of the model, for reasons that have already been discussed.
It is also evident that the agreement between the modeled and observed temperature profile is generally poor when the image suffers from incidents of infrared reflectance. In the error field in Figure 18d, higher error values show up in the regions with IR reflectance. These same locations also correspond to much higher bulk temperature estimates. In the time series in Figure 18e, IR reflectance shows up as periods of unusually high bulk temperature estimates. In contrast, Figures 15, 16, 17, 19, and 20 all show very limited (or no) levels of IR reflectance. These observations, suggest that it might be possible to use a certain threshold of the mean squared error to detect, and possibly eliminate, incidents of infrared reflectance.
The SRM uses a statistical method of analysis based on intermittent surface renewal events, such as breaking events, whereas the ERM is based 56 on the physics of small-scale stationary turbulent eddies. Therefore it is natural to question the new model's ability to adequately describe the temperature field at and behind a breaking event. Figures 16 and 17 are images taken during the same breaking event. In the first image, the edge of the breaking event is clearly visible (as the large crescent of warmer waters).
In Figure 17 (which was taken one tenth of a second later than Figure 16), the breaking event has disintegrated into intense small-scale turbulent eddies. In examining the error field, it seems that the new model is able to describe the temperature during and after breaking events quite well. This would make sense if the breaking event has generated small scale turbulent eddies that quickly become quasi-stationary, and if the surface renewal is mainly controlled by such eddies rather than the instantaneous passing of the breaking front itself.
To quantify the accuracy of the fit of the model curve to the observed data, error analyses are included with each analyzed image. Furthermore, in order to see the average shape of the eddy temperature curve, it is useful to take a large number of observed eddy temperature curves, nondimensionalize them, and average them so that the mean "basic shape" curve is compared against the Eddy Renewal Model temperature curve. In order to non-dimensionalize the eddies, one needs to remove the characteristics of length, temperature spread, and highest temperature value. This can be done by first subtracting the calculated bulk temperature from the observed temperature and then dividing the results by the eddy intensity. This analysis 57 is done separately for each eddy size, so that the ERM model applicability is examined as a function of the eddy size. (See Figure 21.) Figure 21: Non-dimensionalized eddy temperature curves compared to ERM curve by eddy size. Averaged by using the intensity and bulk temperature as found during image analysis to remove individual characteristics (such as highest temperature and range of temperature values) but leaving the basic shape of the temperature curve along an eddy. Numbers in the boxes are the average error squared per pixel for each curve (excepting minima).
For eddy sizes 5 through 11 or 12 pixels long, it would seem that the ERM curve is a good basic fit (except at the minima, as noted earlier). The smaller eddies, although still a good fit, as defined by the error squared values in each plot, were found to have too much variation in their bulk temperature estimates. It has always been assumed that the largest eddies would show a better fit to the model curve, as they would have less area that could be effected by the horizontal temperature gradients near the downwelling, however, analysis of the basic curve fit suggests that this may not be so. The three largest eddy cases (in Figure 21) show that the observed temperature curve has positive curvature near the maximum, resembling the model curve of the Surface Renewal Model. It is possible that the quasistationary assumption may not be applicable for very large eddies.
Even though the data curves in Figure 21 show a good basic fit to the model, it is possible that eddies with a poor fit are distorting the shape of the mean curves. This could be easily shown if a large percentage of eddies have an error squared per pixel (ESPP) smaller than the mean value. Figure 22 shows that this is the case for the smaller eddies.
Using only eddies with an ESPP smaller than Figure 22: Percent of Eddies with an Error Squared Per Pixel value smaller than the mean value (numbers in boxes in Figure 21). These eddies are the ones used to generate the curves in Figure 23.
59 the mean, the mean temperature curves are again found (Figure 23). This plot confirms that the basic shape of the eddy renewal model curve is a good match for the majority of the observed eddies. Figure 23: Average, non-dimensionalized eddy curves, using only the eddies with an error squared per pixel smaller than the mean values (numbers in boxes of Figure 21). The numbers in the boxes of these plots represent the resulting mean error squared per pixel.

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In summary, the Eddy Renewal Model is able to accurately model the sea surface temperature variations due to near surface turbulence. The application of the model to data taken in a wind-wave tank generally yields very similar results. In Figure 20 the surface temperature pattern is very similar to the GasEx2001 data. In Figure 19, the surface temperature patterns show larger and more elongated eddy patterns. In both cases, the ERM reproduces the temperature patterns equally well.

Section 4. Statistics Obtained From Image Analysis Results
In order to apply the modeled temperature curve to the observed data, only two variables were used: the bulk temperature and the "intensity" of the eddy. The "intensity" comes from equation [2.3.7] and is defined as δj0/κ which is proportional to the difference between the bulk temperature and the mean temperature of the curve. Thus, once the normalized temperature solution was obtained, this curve could be applied to the observed data by finding the bulk temperature and intensity with the least mean squared error.
Given that the δ is proportional to the square root of if the heat flux is assumed to be constant over the image. It is, therefore, of interest to examine whether a high correlation exists between the eddy size and eddy intensity. As seen in Figure 24a, there does not appear to be such a correlation between eddy size and intensity. Neither does there appear to be a correlation between the size of the eddy and the bulk temperature estimate for that eddy (Figure 24b). Instead, the variance of the estimates increases as the eddy size decreases. This suggests that the individual estimate of the bulk temperature or the eddy intensity is less accurate for smaller eddies (as expected), but the mean estimates are robust and are not influenced by the eddy size. This also suggests that the overall variation of the bulk temperature and intensity estimates is overestimated based on our method; part of the variation is likely due to the inaccurate model application 62 to smaller eddies. In fact, Figure 26c and 26d show that the variability of the bulk temperature is larger than that of the surface temperature. However, it is likely that the true variation of the bulk temperature is less than that of the surface temperature. The variation of the intensity in Figure 26b is also most likely overestimated. That is, a bulk temperature value that is artificially too high will produce an intensity value that is also artificially too high. However, for a given bulk temperature, the distribution of the eddy intensity likely represents the true   Figure 11) Black dots are from eddies sized 3 or 4 pixels; blue stars are from eddies 5, 6, or 7 pixels; red crosses are from eddies 8 pixels and larger. shows that the basic shape of the model is a good first-order approximation of the temperature distributions found in these small-scale turbulent eddies.
One clear advantage of the ERM is that it explicitly incorporates the water motions of individual eddies. Although the ERM is not a fully threedimensional model; as a first order approximation, the ability of the model to estimate the temperature variation below the surface is novel. One way to verify (or disprove) this model's applicability would be to make use of a device similar to the one currently being used to measure small-scale vertical temperature gradients near the sea surface (Ward, 2005).
There are benefits and disadvantages to each model. One of the major disadvantages of the ERM is the long data processing time required to analyze each image. Although more study is needed to fully understand all of the implications from these results, it would appear that both methods complement each other and are ultimately useful in bulk temperature estimations.
In the future, the ERM could be improved in different directions. First, by incorporating a more fully-three dimensional eddy field, the water motions  These times series plots are the results of analysis from the wind-wave tank data. It is interesting to note the differences between these plots and the time series plots for the in situ data. The difference between the surface temperature and the estimated bulk temperature is much smaller than that for the in situ data. (For reference, the temperature scale for these plots is the same as the GasEx2001 plots -0.3°C). The validity of this observation (and the analysis) is born out by other analyses of wind-wave tank temperature profiles, which state that this condition (smaller difference between surface and bulk temperatures) is common. There are no Surface Renewal Model bulk temperature estimates for these data.   to 010 were discarded due to possible errors in calibration or data acquisition.) The black line is the mean surface temperature; the blue is the ERM estimate (using all eddies); the magenta is the ERM estimate, from eddies 5 pixels and larger.
Figure A-09: Time series plots from Aeolotron files 012, 013, and 014. The black line is the mean surface temperature; the blue is the ERM estimate (using all eddies); the magenta is the ERM estimate, from eddies 5 pixels and larger.
78 Figure A-10: Time series plots from Aeolotron files 015, 016, and 017. The black line is the mean surface temperature; the blue is the ERM estimate (using all eddies); the magenta is the ERM estimate, from eddies 5 pixels and larger.