In order to understand the relative importance of various geophysical fields to the evolution of a lake breeze using the MC2 model, a series of sensitivity tests was conducted. The parameters tested were: albedo (AL), surface roughness (Z0), soil moisture availability (HS), deep soil temperature (TP) and lake surface temperature (TM). Due to the time involved in running and analyzing these simulations, only a few model runs were performed for each parameter. In each run, changes were made to the geophysical field so that values were significantly more or less than the baseline value. For instance, simulations testing the sensitivity of the model to changes in albedo used the albedo at 50% of the baseline value and at 150% of the baseline value. The following sections describe in more detail the geophysical fields that were tested and results of the comparisons of the sensitivity test runs to the baseline run.

4.1 Geophysical Fields

In this section, the geophysical fields used as input to the model are briefly discussed and baseline values are compared to 'textbook' values (Oke, 1987) to ascertain that they are reasonable in each case. The changes made to each parameter for the purposes of sensitivity testing are also discussed.

a. Surface Albedo (AL)
The 5 km albedo field, shown in Figure 4.1, is interpolated from a 25 km grid monthly climate file. Thus, the resolution is coarse and locally high and low values of albedo are smoothed. Albedo values range from a low of 0.08 over water surfaces to a maximum of 0.19 over land. The median value is near 0.16. These values are within the range of accepted values for water and the land surfaces typical of the area.

b. Surface Roughness (Z0)
Surface roughness values from the 5 km field, shown in Figure 4.2, are from a high resolution data set at CMC so the resolution of this field is much finer than for the albedo. However, it appears that the resolution in most areas on the United States side of the border is much lower than on the Canadian side. Values range from 1.5 x 10-5 m over water to a maximum of about 1.8 m over land. The region of greatest average roughness lies to the north of Lake Ontario in a mixed coniferous / deciduous forest region. Values near 1.0 m are given over Metro Toronto. The median value is near 0.23 m in countryside. All of these values fall well within the range of accepted values for surface roughness.

c. Soil Moisture Availability (HS)
The representation of soil moisture used as input by the model is 'soil moisture availability', given in the form of a fraction (kg/kg). This field, shown in Figure 4.3, is interpolated onto the 5 km grid from a 25 km grid monthly climate file. Thus, not only is the resolution coarse but the values are unlikely to accurately represent soil moisture for any particular day. Values here range from 1.00 over water to a minimum of 0.25 over land. The mean value over land is near 0.30.

d. Deep Soil Temperature (TP)
The deep soil temperature is interpolated from a 100 km grid global field that is measured by satellite twice daily. This field, shown in Figure 4.4, has very coarse resolution but in reality local variations should be relatively small (note that MC2, with the aid of the land-sea mask, MG, combines deep soil temperature, TP, and sea surface temperature, TM, to form a new field, TX). Deep soil temperatures input to the model range from about 292 K northeast of Lake Ontario to about 290 K northwest of Lake Ontario.

e. Lake Surface Water Temperature (TM)
Water temperatures used as input to the standard simulation were interpolated from a 25 km grid monthly climate file and have coarse resolution and values that are higher than measured. Lake surface temperatures, shown in Figure 4.4, range from 21.2°C over western Lake Ontario, 20.9°C over the central part and 20.7°C over eastern sections. This is in contrast to values of 17°C, 18.5°C and 19°C, respectively, that were measure by infrared satellite. Past experience has shown that these infrared satellite measurements are often 1-2°C higher than lake surface temperatures observed by buoys, so the difference between the model field values and actual values may be even greater. However, using measured values of lake surface temperature as input to the model is an involved process and use of values from the climate file was found to be sufficient for the purpose of sensitivity testing.

4.2 Sensitivity Test Analysis

In the following section, simulations of conditions on August 8, 1993 are tested for their senstivity to significant changes in five fundamental surface geophysical fields described in the previous section that are used as input to the model. In particular, we are looking for changes in the geophysical fields that produce identifiable differences in the character of the lake breeze circulation on Lake Ontario including the circulations strength and the inland penetration distance. With the exception of the lake surface temperature (TM), all changes to geophysical fields were made to land points only with the rationale being that values of these fields over water are relatively well known while over land there is greater uncertainty.

The following prognostic fields will be used to gauge the impact of changes to a geophysical field: UV (10 m vector winds), DD (500 m divergence), TT (1.5 m air temperature), TG (surface temperature), H (boundary-layer height), FC (sensible heat flux), FV (latent heat flux), FQ (scalar momentum flux) and NT (total cloud cover). As discussed previously, we detected problems with the way in which the model handled the moisture fields over water at the first model level (for example, relative humidity in some locations over Lake Ontario greatly exceeds 100%). Thus, we have refrained from analyzing moisture fields.

To reduce the amount of data to be compared, comparisons were made at only two times, 2000Z and 2200Z. The 2000Z time corresponds approximately with maximum daytime heating observed at the Hastings site. The 2200Z time corresponds roughly with the time of arrival of the Lake Ontario lake breeze front at the Hastings site.

a. Surface albedo (AL)
Simulations testing the sensitivity of the model to changes in albedo used the albedo at 50% of baseline values (ALd) and at 150% of baseline values (ALi). Changes in the surface albedo affect the land absorption of short wave (solar) radiation. Thus, changes to AL should result in changes in the land surface energy budget and ultimately to the air temperature.

For both the ALd and ALi cases, no significant change was noted in the character of the lake breeze. Wind patterns were nearly identical though, in the ALi case, wind speeds were about 10% less than the ALd and baseline cases. There were no significant differences in the surface divergence field.

Figure 4.5 shows surface temperatures for the ALi, baseline and ALd cases. At peak heating (2000Z), increasing / decreasing AL by 50% resulted in about a maximum negative / positive 1°C change in TG. Thus, surface air temperatures at 1.5 m increased slightly with decreasing albedo having a maximum difference of about 0.75 °C . This small change in air temperature could not cause much change to the character of the lake breeze. Correspondingly, only small changes were noted in the sensible heat flux and the boundary-layer height. Lastly, no significant differences were found in total cloud cover for either of the tests.

b. Surface roughness (Z0)
For sensitivity testing, surface roughness values were decreased (ZPd) and increased (ZPi) by an order of magnitude relative to the baseline values. The field submitted to the model as input is the natural logarithm of surface roughness, ZP.

There were slight changes in the character of the lake breeze circulation after altering the values of ZP over land. The greatest change was an increase in the wind speed within the lake breeze circulation over land with decreasing ZP. However, there were significant differences in 10 m wind speeds away from Lake Ontario. In the large area to the north of the lake, ZPd winds were roughly 5 knots higher than for ZPi. This is due to differences in the effect of friction between the two cases since areas to the north of Lake Ontario are more heavily forested. Figure 4.6 shows surface winds for the ZPi, baseline and ZPd cases. Also, the momentum flux for the ZPi case was significantly higher than for the ZPd case. The comparisons for this field are shown in Figure 4.7. For the divergence field, ZPd convergence zones at the lake breeze fronts were noticeably stronger but the inland pentration distance remained the same.

Even though wind speeds were significantly different between the ZPi and ZPd cases, this difference was not reflected in the 1.5 m temperatures. ZPd temperatures were slightly higher than that of the ZPi case only near the lake breeze fronts and to the north of Lake Ontario. This corresponds with sensible heat flux which shows greater values for the ZPi case near the shores of Lake Ontario. The boundary-layer heights near the lakes were significantly higher (by about 300 m) for the ZPi case than the ZPd case. The boundary-layer heights for the ZPi, baseline and ZPd cases are shown in Figure 4.8. So, due to increased friction at the surface causing enhanced boundary-layer turbulence, there is a greater sensible heat flux from the surface which results in slightly lower temperatures near the surface. The enhanced turbulence also results in the higher boundary-layer heights. Lastly, no significant changes in total cloud cover were noted with changes in surface roughness.

c. Soil Moisture Availability (HS)
For sensitivity testing, values were decreased (HSd) and increased (HSi) by 50% relative to the baseline values. Values over 1.0 were clipped to 1.0. The soil moisture availability is a major factor in the calculation of land evaporation in the model. Therefore, tuning the soil mositure availability is equivalent to tuning the contribution of the latent heat flux in the surface energy budget and should eventually affect the land surface temperature.

We observed little in the way of significant changes to the character of the lake breeze by varying HS. The surface winds showed only small differences between the cases, mainly near the lakes. The inland penetration distance was not affected.

The surface temperature showed significant differences between the HSd and HSi cases. Increasing / decreasing the soil moisture resulted in a lower / higher surface temperatures with maximum differences of about 1°C. This corresponds with the significantly greater latent heat flux with the HSi case. Figure 4.9 shows the latent heat flux for each case while Figure 4.10 shows surface temperatures (note that, in the latent heat flux plots, maximum values located around the perimeter of the lakes are due to interpolation errors associated with the coarse resolution of the HS field). Air temperatures at 1.5 m were at most 1°C higher in the HSd case. Thus, the increase in latent heat flux due to the increased surface moisture corresponds to lower 1.5 m air temperatures. The boundary-layer height was greatest in the HSd case with the largest differences observed away from the lakes. Lastly, changes in soil moisture availability had very little effect on the total cloud cover.

d. Deep Soil Temperature (TP)
For sensitivity testing, values of deep soil temperature were decreased (TPd) and increased (TPi) by 10 K.

No significant change in the character of the lake breeze circulation was observed upon changing the values of deep soil temperature. The wind pattern remained the same in each case. However, 10 m wind speeds did increase slightly with increasing TP. There was little change in the magnitude of the divergence field between simulations though fronts appeared better defined in the horizontal with the TPi case.

One might expect that, with higher deep soil temperatures, the surface temperature would also increase and, indeed, this was found. The surface temperature was approximately 5°C higher / lower than baseline values with the TPi / TPd case. These changes at the surface resulted in significant changes to the air temperature at the 1.5m level. The air temperature was found to have a maximum difference of about 1.5°C. Figure 4.11 shows plots of the difference between ground temperatures and 1.5m air temperatures (TG - TT). The difference increases with increasing TP to a maximum of 12°C in the TPi case. Although sensible heat fluxes increase greatly with increasing deep soil temperatures, the flux convergence appears to be too low to prevent the unrealistically high TG - TT values. Plots from the heat flux tests for TPi, baseline and TPd cases are shown in Figure 4.12. The boundary-layer heights were also signficantly different from the baseline values with TPi heights being the greatest and TPd heights the least. Finally, the total cloud cover experienced significant changes when the deep soil temperature was altered with the most cloud cover occurring with the highest TP values. Values of NT for each of the cases is shown in Figure 4.13.

e. Lake Surface Water Temperature (TM)
For sensitivity testing, lake temperature values were decreased (TMd) and increased (TMi) by 10°C. In the latter case, this results in lake surface temperatures greater than the land surface temperatures. These changes cause significant differences in the lake breeze character for each case (TMi and TMd). For this reason, analyses for each case will be discussed separately below.

Decreasing the lake surface temperature values resulted in significant changes to the character of the lake breeze circulation. This is due to the increased difference in temperature between the air over the land and over the lake. The inland penetration distance increased slightly but by an amount less than 5km along the north shore of Lake Ontario. The wind speeds within the lake breeze circulation also increased slightly. However, the lake breeze still failed to pass the Hastings site even by the end of the integration at 0000Z on August 9. This case also exhibited stronger convergence-divergence couplets at the fronts than the baseline case. TMd winds and divergence values are compared to those of the baseline case in Figures 4.14 and 4.15 respectively.

In the TMd case, the stronger lake breeze circulation resulted in somewhat clearer skies over the lake. However, skies behind the lake breeze fronts remained much cloudier than the clear skies that were observed. The boundary-layer height was also much more uniform over the lake with a height of about 100 m consistently produced over the water. Total cloud cover and boundary-layer heights for the TMd, baseline and TMi cases are shown in Figures 4.16 and 4.17 respectively.

For the MC2 model, lake surface temperatures remain constant through the integration so a difference of 10°C was maintained between the baseline and test cases. In the TMi case, the lake surface temperature was always warmer than the land surface temperature. However, 1.5 m air temperatures over the lake were very slow to respond to the increased lake surface temperature. Figure 4.18 compares the difference between surface temperatures and 1.5 m air temperatures (TG - TT) for each of the test cases at 2000Z. In the TMi case, the maximum difference between the surface temperature and the 1.5 m air temperature over Lake Ontario was 9°C. This difference was -2°C for the TMd case. The temperature difference is slowly overcome during the twelve hour integration demonstrating the low rate of adjustment to the lake surface temperature for air above the lake. However, the sensible heat flux over the lake (plots shown in Figure 4.19) in the TMi case was of the same order as that over land. It has also been shown with the ZP tests that changes in the roughness have a small effect on the air temperature. Thus, there is not a good explanation of the slow adjustment rate. Different surface schemes are used by the model over land and over water. There is a possibility that the sensible heat flux algorithm over water needs to be adjusted.

Since the air temperature over the lake was so slow to change, a partial lake breeze did develop even though in the TMi case the skin temperature of the water was several degrees greater than that over land. This partial circulation resulted in less penetration distance along the north shore and no penetration along the south and east shores. The TMi case also had weaker convergence / divergence couplets at the lake breeze fronts than the baseline case. The comparisons of winds and divergence for each case are shown in Figures 4.14 and 4.15.

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