1996 and 1997 summer observations

Observed Lake Michigan lake-breeze events along the eastern and western shores during the summers of 1996–97 were used to develop our lake breeze method and to evaluate its validity. Our focus was on lake breezes that had considerable inland penetration because of the ability to identify them using routinely collected observations and their greater impact on larger areas of the coastal region. The database used to identify 1996–97 lake-breeze events consisted of hourly observations at surface stations located in the Lake Michigan coastal region (see locations of open circles in Fig. 1), Geostationary Operational Environmental Satellite (GOES) visible satellite imagery, and National Weather Service (NWS) Weather Surveillance Radar-1988 Doppler (WSR-88D) data. Daily time series of temperature, wind speed, and wind direction were reviewed for each coastal station. The surface station data were examined for several distinct elements associated with the passage of a lake breeze. These included (a) a slight fall or general leveling off of temperature after the passage of the lake breeze, (b) an abrupt wind direction change from offshore to onshore at the time of passage, and (c) a short duration or steady increase in wind speed following the lake breeze passage. Each of these characteristics has been well documented for the passage of both lake (e.g., Keen and Lyons 1978; Lyons and Olsson 1973) and sea breezes (e.g., Simpson 1994; Laird et al. 1995). The 1996–97 GOES visible imagery was examined for clearing of cumulus clouds associated with the inland penetration of the lake breeze (e.g., Strong 1972; Purdom 1990; Rabin et al. 1990; Segal et al. 1997). In addition, WSR-88D reflectivity data were examined during numerous events for evidence of an identifiable boundary (i.e., thin line) associated with the lake-breeze front (e.g., Wilson et al. 1994).

A lake-breeze event was designated as having occurred along a particular shoreline when at least three surface stations on one side of Lake Michigan observed the passage of a lake breeze. It was necessary for at least one of the three stations to be located within 5 km of the shore. These criteria and the distance between surface stations limited our observed lake breezes during 1996–97 to events that generally penetrated more than 20 km inland and/or extended along more than 100 km of the shoreline. The GOES visible imagery was then used to confirm lake-breeze events and to determine when a lake breeze was unlikely to have occurred because of the presence of significant overcast conditions. Days having significant overcast conditions associated with a synoptic feature (i.e., low pressure center, frontal boundary) in the region were not included in the 1996–97 observed lake-breeze dataset.

In addition to the satellite, surface, and radar data, information from daily logs of the Chicago, Illinois, lake breeze completed by personnel at the Romeoville, Illinois, NWS Forecast Office were used to supplement the 1996–97 database. The daily lake-breeze logs were completed as part of an NWS and Iowa State University (ISU) Cooperative Program for Operational Meteorology, Education, and Training (COMET) study. These records focused on only the portion of Lake Michigan shoreline in the vicinity of Chicago, Illinois. Both lake breezes that penetrated far inland (e.g., >80 km) and moved onshore but remained near the lake shoreline (e.g., <2 km) were reported. Although lake breezes that remained near the coastline were recorded for Chicago during the summers of 1996–97, they were not included in our observed lake-breeze dataset because of the possible difficulty of identifying the occurrence of nearshore events on climatological timescales with hourly surface stations having low spatial resolution in the Great Lakes coastal regions. For example, because of their proximity to the lakeshore, stations at Milwaukee, Wisconsin (MKE), and Muskegon, Michigan (MKG), may identify lake breezes that penetrate inland at least 4 km. However, coastal stations positioned similar to Chicago O’Hare Airport, Illinois (ORD), can only detect lake breezes that penetrate at least 20–25 km inland.

1982–96 climatological surface observations

The 1982–96 Lake Michigan lake-breeze “climatology,” here used to mean a description of frequency of occurrence, was completed using hourly surface observations from three meteorological stations near the lakeshore, three inland stations at a distance greater than 110 km from the shore, and lake surface water temperature measurements from a moored buoy station positioned in south-central Lake Michigan (see Fig. 1). The three shoreline stations include: MKG, located about 4 km from the eastern shore, MKE, about 4 km from the western shore, and ORD, located nearly 22 km from the southwestern shore. These sites were chosen based on their complete long records of observations and their proximity to the Lake Michigan shoreline. The three inland stations included: Rockford, Illinois (RFD;∼105 km inland), Madison, Wisconsin (MSN; ∼130 km inland), and Flint, Michigan (FNT; ∼190 km from Lake Michigan). These inland stations were chosen for their long records of observations and the lack of lake-breeze influence in their observations. Lake water temperatures used for this investigation were collected at 0.6 m below the surface by the National Oceanographic and Atmospheric Administration (NOAA) No. 45007 moored buoy. The historical buoy data are not available prior to 1981, thereby limiting the duration of our analyses.

Lake-breeze methodology

Our method to determine the occurrence of a lake breeze was designed to use a minimum set of parameters that would adequately describe properties observed at the surface during the evolution of lake breezes and conditions favorable for their development. Based on methods used during previous investigations (e.g., Ryznar and Touma 1981; Borne et al. 1998), knowledge of lake and sea breezes (e.g., Simpson 1994), and the examination of the 1996–97 Lake Michigan lake-breeze data, the following criteria were used to identify lake-breeze occurrences from 1982 to 1996 at the coastal climatological sites (MKE, ORD, and MKG).

1. A change in average wind direction from offshore or calm conditions in the morning (0500–0700 LST) to onshore during the afternoon (1600–1800 LST). Onshore and offshore flows were defined using a north–south (0°–180°) coastline orientation for MKE and MKG. For ORD, the perpendicular shoreline flow was defined using a coastline orientation of 330°–150°.

2. A positive difference in temperature between the daily maximum at an inland station and the lake surface measured at the same hour, that is, (ΔT)_max > 0°C.

3. An average air temperature in the morning (0500–0700 LST) lower than during the afternoon (1600–1800 LST).

4. An average wind speed in the morning (0500–0700 LST) less than 5.5 m s⁻¹.

Criteria (1) and (2) were designed to identify the passage of a lake breeze, and criteria (3) and (4) were found to effectively exclude other atmospheric events, such as synoptic fronts, that may have several characteristics similar to lake breezes in hourly collected surface datasets (e.g., surface wind direction change).

Our criteria were applied to hourly surface observations from May through September during 1982–96 to distinguish days when lake breezes occurred along the eastern shore (ES), western shore (WS), and both shores (BS) of Lake Michigan. A lake breeze on both shores was identified when the criteria were simultaneously met for both MKG and MKE. Our approach is somewhat limited in representing all lake breezes that occur along the Lake Michigan shoreline because of the small number of climatological stations available and their distances from the shoreline. For example, some lake breezes remain near the shoreline (i.e., < 4 km inland) and may not be detected at surface observation sites. In addition, the development of a nighttime ES land breeze may cause our criteria to identify a lake breeze for the following day. This would occur when an offshore land breeze develops in a light gradient westerly flow. As the boundary layer reestablishes after sunrise, turbulent mixing would transport westerly momentum downward resulting a wind shift from offshore to onshore. Although this situation does not inhibit the development of a lake breeze, it would tend to enhance slightly our estimates of ES frequencies. Events of these kinds are difficult to identify when examining a single climatological station. Therefore, our method identifies only lake breezes that penetrate inland at least 4 km at MKG and MKE or approximately 22–25 km at ORD during opposing offshore or calm conditions.

Synoptic analyses

An examination of the synoptic environments associated with lake-breeze occurrences on the ES, WS, and BS of Lake Michigan used daily mean large-scale circulation fields, including sea level pressure and wind, obtained from the NCEP–NCAR reanalysis (Kalnay et al. 1996) for the study period of 1982–96. The surface (10-m height) wind data are provided on T62 (∼1.9° in midlatitudes) resolution, and other fields (e.g., sea level pressure) are on 2.5° latitude by 2.5° longitude grids. For consistency, all fields were mapped into the 2.5° grid mesh.

Summer 1996–97 lake breezes

A detailed examination of observational data for the summers of 1996–97 provided a catalog of days when a Lake Michigan lake breeze occurred. The development of this lake-breeze catalog was critical to determine the accuracy of our method. Figure 2 shows the average frequency of observed lake-breeze events along the ES, WS, and BS for May–September from 1996 and 1997. On average, ES and WS lake breezes occurred during 35% and 21% of the days, respectively, and BS events occurred on 17% of the days. Of interest, the 1996–97 data show ES lake breezes occurred about 14% more frequently than WS lake breezes. This difference may be accounted for by WS lake breezes that develop and remain stationary within several kilometers of the lakeshore or slightly offshore during time periods with westerly ambient flow (e.g., Strong 1967; Arritt 1993). This would result in very few inland surface sites observing the passage of the lake breeze. To examine this hypothesis, we temporarily included all lake breezes observed during the 1996–97 NWS–ISU COMET project irrespective of the inland penetration distance (open squares on Fig. 2). When these days were included, we found the average observed WS lake-breeze frequency increased from 21% to 41%. The frequency of BS events increased to 23% because of an increase of limited inland penetrating WS events that occurred during observed ES events. These results suggest that WS lake breezes may not penetrate as far inland as ES lake breezes for Lake Michigan and that climatological surface data, particularly for Chicago, may underestimate the occurrence of WS and BS lake breezes.

For comparison, also shown on Fig. 2 are the average monthly lake-breeze frequencies from Lyons (1972) (open triangles) for ES, BS, and Chicago, Illinois, and from Ryznar and Touma (1981) (open circles) for the ES. Both Lyons (1972) and Ryznar and Touma (1981) examined data collected by high-spatial-resolution surface station networks located within 15 km of the Lake Michigan shore. The average frequency of ES lake breezes reported by Ryznar and Touma (1981) (16%) is lower than that determined for 1996–97 and that reported by Lyons (1972). Lyons (1972) showed lake breezes occurred an average of 13% more frequently along the Chicago, Illinois, shore (37%) than along the ES (24%) of Lake Michigan. This is consistent with our findings when the ES and adjusted WS (i.e., including all NWS–ISU COMET observations) lake-breeze frequencies were considered. Because of the limited number of years examined, it is difficult to determine whether the difference between our 1996–97 observed lake-breeze frequencies and those of Lyons (1972) and Ryznar and Touma (1981) are statistically significant or are a result of interannual variability in the number of Lake Michigan lake-breeze events.

Validity of lake-breeze method

Table 1 summarizes the results when a lake-breeze or non-lake-breeze event was identified using our method and compared with the observed occurrence of an event on the ES, WS, and BS. For this comparison, hourly surface data from the MKG, MKE, and ORD climatological stations were used. The 1996–97 NWS–ISU data were not included. Some useful measures for evaluating the accuracy of the lake-breeze method can be illustrated concisely if the hindcasts and observations are placed into a matrix as shown in Figure 3, where the variables “B” and “N” refer to an observation that contains a lake breeze (LB) or no LB, respectively, and the subscripts “o” and “h” refer to observations and hindcasts, respectively. Correct hindcasts thus lie in cells B_oB_h (i.e., an LB was identified and it occurred) and N_oN_h (i.e., an LB was not identified and none occurred). Definitions of the measures used to evaluate the accuracy of the method for events when a lake breeze was observed are shown below. These measures were also used to evaluate the accuracy of the method in identifying non-lake-breeze events (see Table 1). Probability of detection (POD) of lake-breeze events:

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False alarm rate (FAR) of lake-breeze events:

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Bias of lake-breeze events:

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The POD ranges from 0 to 1, where 1 indicates that hindcasts identified every lake breeze. Note that neither correct hindcasts of LB nonoccurrence (i.e., events in cell N_oN_h of Fig. 3) nor incorrect hindcasts of LB occurrence (i.e., N_oB_h) affect the POD. The FAR ranges from 0 to 1, where 0 indicates that incorrect hindcasts of lake breezes were not made, and is unaffected by observations in which no LB is forecast (i.e., B_oN_h and N_oN_h). The bias ranges from 0 to infinity with an ideal value of 1. It is important to note that these measures should not be used separately but must be applied jointly. For example, POD = 1 could be obtained by always hindcasting that a lake breeze will occur, while FAR = 0 could be obtained by never hindcasting a lake breeze. Likewise, although it is usually desired for the bias to equal unity, the bias alone does not necessarily indicate whether the hindcasts are correct. For example, a bias of 1 could be obtained if all of the identified lake breezes are incorrect (i.e., B_oB_h = 0), with N_oB_h = B_oN_h.

The POD values for non-lake-breeze events indicate the lake-breeze method was ≥86% accurate for all locations. In addition, FAR and bias values for non-lake-breeze events were ⩽0.16 and near unity, respectively. These measures suggest that our method will characterize very few non-lake-breeze events as lake-breeze events, an important issue when developing a climatological database to examine the key parameters of lake breezes. The POD values show that the method distinguished 69%, 73%, 52%, and 45% of observed 1996–97 lake breezes for MKG, MKE, ORD, and BS, respectively. The results for ORD are not surprising, given the inland distance of the station from the Lake Michigan shoreline (∼22 km inland) and our earlier finding that WS lake breezes in the vicinity of Chicago can often be restricted to several kilometers inland of the shoreline. This result is consistent with the statement by Lyons (1972) and Lyons and Olsson (1973) that the Chicago lake breeze penetrates inland >15 km on only about 30%–40% of lake-breeze days. The inland penetration of the Chicago lake-breeze is likely influenced by several factors, such as predominant offshore winds (e.g., Arritt 1993), increased surface roughness due to the urban area, and thermal modification of the boundary layer in response to the urban heat island (e.g., Arya 1988).

Although the lake breeze frequencies at MKG and MKE seem to be underestimated on average by ∼30%, this value was reasonably consistent within the 5-month periods during 1996 and 1997. This suggests that the month-to-month variations present in our estimated frequencies may be representative of the actual seasonal variability of lake-breeze occurrences from May through September. We may expect that atmospheric conditions leading to the occurrence of a lake breeze along the entire Lake Michigan shoreline, BS, could be easily captured by an objective method because of the likely strength of the circulations. However, only 45% of all BS events during 1996–97 were detected using our method, even though 93% of all BS non-lake-breeze events were correctly identified. One explanation may be the failure of identifying an ES or WS lake breeze during BS events because of the constraint of our criteria (a), a change from morning calm or offshore winds to afternoon onshore winds. This situation may occur when the center of high pressure is shifted slightly east or west relative to Lake Michigan resulting in morning onshore flow along one of the shorelines (see section 6).

Comparison with the Lake Michigan 1996–97 observed records has shown that our objective method can reasonably identify lake-breeze events. An examination of the method’s validity for identifying lake-breeze events at several climatological stations showed a higher rate of success at MKG and MKE than at ORD or for BS events. The comparison also demonstrates the notable ability of our method to distinguish non-lake-breeze events, a problem experienced by previously developed methods (i.e., Biggs and Graves 1962; Lyons 1972).

Monthly frequency

The May–September 15-yr average lake-breeze frequency and 95% confidence interval are shown for MKG, MKE, ORD, and BS of Lake Michigan in Fig. 4. Lake-breeze events tended to occur most frequently at MKG, with fewer lake breezes occurring at MKE and ORD. Figure 4 shows that June and July are the only months when the difference in average frequency is statistically significant between MKE and MKG. When MKE and ORD are compared, the difference is only statistically significant in August. Table 2 shows that, on average, 3.5 more lake-breeze events occur at MKG than MKE during June and July, and the difference is ⩽2.5 events for May, August, and September. Although MKG and MKE experience more than nine and six lake-breeze events each month, respectively, only 20%–50% actually occur on the same day and result in a Lake Michigan BS lake-breeze event. This result suggests that environmental conditions favorable for lake breeze development on both shores occur less frequently than conditions necessary for lake breezes on the ES or WS.

In general for each site and BS, there is an increase of about 1.3 days per month in the number of lake-breeze events from May through August, then a 24% to 37% decrease into September. This is consistent with an August maximum in the number of ES lake breezes found by Ryznar and Touma (1981). Interestingly, Lyons (1972) found maxima in May and July for ES and WS lake breezes, respectively. These differences could be indicative of interannual variability in the number of lake-breeze events for a particular month and potential shifts in the timing of the maximum each year for a station.

Some of the monthly variations in lake-breeze occurrence can be understood by examining average monthly wind speeds and the difference between maximum inland-air and lake temperatures—important factors for the development of lake breezes. Figure 5 shows the 1982–96 average monthly lake temperature for buoy 45007 and wind speed, wind direction, and maximum air temperature at MSN, RFD, and FNT for May–September. Based on the average (ΔT)_max alone, May and June would be expected to have the greatest occurrences of lake breezes, with average temperature differences of nearly 16°C. However, stronger offshore flow for the WS of Lake Michigan in May, June, and September may result in lake-breeze circulations being located offshore or suppressed (e.g., Strong 1967; Lyons 1972; Arritt 1993), and stronger onshore flow for the ES during these months may inhibit the development of lake breezes or produce weak circulations superimposed on the ambient flow (e.g., Estoque 1962; Arritt 1993; Atkins and Wakimoto 1997). Although July and August have (ΔT)_max values of about 10° and 5.5°C, respectively, the lower average wind speeds are less likely to inhibit the development of lake breezes and their inland penetration. Temperature differences are an important factor for lake-breeze development, but their relation to seasonal lake-breeze frequency is not readily apparent and should be examined further. However, our analysis suggests that seasonal variations in wind speed have a first-order inverse relation to the May–September average lake-breeze frequencies.

Interannual frequency

A listing of the average monthly lake-breeze frequency for May–September during 1982–96 at MKG, MKE, and ORD and for BS is shown in Table 2. The interannual variability of lake breezes for each station and BS is large during the 15-yr period. For example, MKE and MKG exhibit decreases in August lake-breeze frequency from 0.52 to 0.36 between 1993 and 1994. Figure 6 shows the interannual variability of September lake-breeze frequency. Although the fluctuations at all sites are large, there are extended time periods (e.g., 3–5 yr) when the lake-breeze frequency is noticeably above or below the average values shown in Fig. 6 and Table 2. For example, during 1983–88 (1989–92), MKE experienced an extended time period when the frequency of lake-breeze occurrences was below (above) average. Although not shown, similar extended time periods were observed in other months and are present for MKG, ORD, and BS frequencies. This finding suggests that interannual fluctuations in the frequency of the Lake Michigan lake breeze, a mesoscale circulation, may be responsive to regional-scale atmospheric changes (e.g., winds and air temperature) and their influence on environmental conditions (e.g., lake water temperatures).

Atmospheric conditions important for lake-breeze development

The parameters examined during each lake-breeze event include: (a) maximum daily air–lake temperature differences determined using data from inland surface stations and NOAA buoy 45007, (b) average daytime (1000–1600 LST) wind speed, (c) average daytime shore-perpendicular wind speed, and (d) total opaque cloud cover. The total opaque cloud cover indicates the amount of celestial dome covered by clouds or obscuring phenomena through which the sky or higher cloud layers could not be seen.

Figure 7a shows that nearly 70% of all lake-breeze events occurred with a (ΔT)_max ⩽12°C and that values of (ΔT)_max >20°C were infrequently (∼15%) recorded. All of the lake-breeze events with a (ΔT)_max >20°C occurred during May and early June when the average monthly values are still greater than 16°C (see Fig. 5). The finding that large values of (ΔT)_max are not required for lake breezes is consistent with the modeling results from Segal and Pielke (1985) and Arritt (1987). Arritt (1987) found that, once the water is cold relative to the air above, stable stratification acts to suppress turbulent heat fluxes, insulating the air from the cold water (i.e., the “coldness” is not efficiently conducted up into the air). Thus, beyond a certain (ΔT)_max the lake breeze is nearly insensitive to the water temperature because further cooling of the water does not significantly cool the air temperatures above the lake.

Figures 7b,c show the frequency of the average daytime wind speed and shore-perpendicular wind speed, respectively. During nearly 95% of all lake-breeze events, the average daytime wind speed observed at an inland station was ⩽5 m s⁻¹. The largest number of events occurred with inland wind speeds of 2–4 m s⁻¹, and nearly 75% of all lake-breeze events occurred during conditions when shore-perpendicular wind speeds were ⩽|2 m s⁻¹|. Using numerical model simulations, Arritt (1993) showed that wind speeds in this regime lead to the most intense sea breezes when the flow was offshore and still allowed sea breezes to develop during events with onshore flow of this magnitude.

The influence of cloud cover was taken into account by Lyons (1972) when refining a lake-breeze prediction method for Chicago, Illinois. He found that the accuracy of his method was increased when it was assumed that no lake breeze would form on days having greater than 40% sunshine reduction from extensive nonconvective middle and high clouds. Figure 8 shows the frequency of total opaque cloud cover observed at MSN and FNT for WS and ES lake breezes, respectively, BS days, and on days when a lake breeze did not occur. The cloud cover was examined during the hour when the maximum daily inland temperature was reported. For lake-breeze days, MSN and FNT generally reported clear sky or partly cloudy conditions. Nearly 70%–80% of the days had cloud cover ⩽5/10. As may be expected, there was a lower frequency of clear skies (∼50% ⩽ 5/10) and a higher frequency of overcast conditions (∼30% ≥ 8/10) on days with no lake breeze.

Lake-breeze index

The prediction of a lake breeze for a specific location (e.g., Chicago, Illinois) has garnered much attention, and several simple empirical criteria and forecasting procedures have been developed to address this issue (e.g., Biggs and Graves 1962; Hall 1954). Empirical criteria have often been developed using data from a limited number of years (⩽3 yr) and their validity has typically been examined using only a small independent data sample (∼1 yr). Biggs and Graves (1962) and Lyons (1972) used the following empirical relationship to forecast lake-breeze occurrences on the western shores of Lakes Erie and Michigan:

View Expanded

where V is the average surface wind speed (m s⁻¹) irrespective of direction at an inland station, (ΔT)_max is the maximum inland-air and lake surface water temperature difference (K), C_p is the specific heat of dry air at constant pressure (1.003 J K⁻¹ gm⁻¹), and ε is an empirically derived constant called the lake-breeze index. We retain the mixture of cgs and SI units in C_p so the index can be compared with prior studies. Biggs and Graves (1962) and Lyons (1972) found that when the index was below the critical values of 3.0 and 10.0, respectively, greater than 90% hindcast accuracy in predicting lake-breeze events was achieved. However, Biggs and Graves (1962) and Lyons (1972) found 65% and 58% of the error, respectively, was associated with the failure of an expected lake breeze to occur, indicating the methods tended to overestimate the number of lake breezes. Even when Lyons (1972) refined the index by including cloud cover information, 36% of the error still remained from overprediction of lake breezes. Lyons (1972) suggested that opaque cloud cover is not necessary to limit the formation of a lake breeze. For this investigation, the data were not available to examine nonopaque cloud information, and our analysis of opaque cloud cover (see Fig. 8) did not suggest a well-defined threshold to identify non-lake-breeze events. Therefore, the definition of the lake-breeze index presented by Biggs and Graves (1962) was used for our analyses.

An examination of the utility of ε for the ES, WS, and southwestern shoreline (i.e., ORD, or Chicago, Illinois) of Lake Michigan using data from the three inland stations (i.e., MSN, RFD, and FNT) was performed. Figures 9a–d show some of our results when comparing critical lake-breeze indices with data collected at MSN during 1982–96 WS lake-breeze and non-lake-breeze events. Critical values of ε = 2, 3, 4, 5, and 6 were used for comparison with the data. Figures 9a–c show values of ε determined using (ΔT)_max and the shore-perpendicular wind component U for offshore gradient flow, |U| for both onshore and offshore gradient flow, and wind speed, respectively. If the lake-breeze indices were accurate in their prediction of lake-breeze events, all calculated values of ε would have been located to the left of the critical ε curves shown in Figs. 9a–c. Table 3 shows the percentage of events that are constrained by different critical values of ε. When using either U or |U| to calculate ε, 95% of WS lake-breeze events were resolved based on a critical ε value of 2. However, when wind speed, irrespective of wind direction, was used to calculate ε, the success of the indices noticeably decreased. For example, a decrease of 26% was experienced for a critical value of ε = 2, and a reduction of about 18% resulted for a threshold of ε = 3.

Figure 9d shows ε calculated from (ΔT)_max and wind speed for non-lake-breeze events. This figure clearly demonstrates the finding by previous studies that the lake-breeze index has a considerable tendency to overestimate the number of lake-breeze events. Table 3 shows that 60% of non-lake-breeze events were characterized as lake-breeze days for ε = 3, the critical value determined by Biggs and Graves (1962). Although our lake-breeze method described in section 2 partially contributed to this error by underestimating the number of lake-breeze events from 1982–96 and placing them in the non-lake-breeze category, Biggs and Graves (1962) showed that both frontal passages and days with onshore gradient flow may be distinguished as lake-breeze events for ε = 3. Based on our analyses of ε values calculated using wind speed, a critical threshold of ε = 3 would tend to underestimate the actual number of lake-breeze events by about 20% and to identify nearly 60% of non-lake-breeze days as lake breezes. Similar results (not shown) were found when data from RFD and FNT, the two other inland sites, were examined and compared with critical values of lake-breeze indices.

Biggs and Graves (1962) and Lyons (1972) stated that the critical value of their lake-breeze index would likely need to be modified for different locations, thus making the index problematic when conducting regional lake-breeze investigations. However, Walsh (1974) showed that a theoretically derived criterion to distinguish lake-breeze from non-lake-breeze events agreed with the criterion (ε = 3.0) of Biggs and Graves (1962) to within 1°C when (ΔT)_max was estimated for |U| ⩽ 10 m s⁻¹. This finding provided theoretical support for the observed linear empirical relationship between V² and the critical (ΔT)_max. The approaches used by Biggs and Graves (1962) and Walsh (1974) suggest that there is no physical basis for variations in the critical value of ε at different locations except due to changes in topography or coastline shape. The data from three inland sites were compared to investigate the likely significance that changes in location (i.e., topography and coastline shape) may have on the critical value of the lake-breeze index. Figure 10 shows ε determined using observed (ΔT)_max and |U| for MSN, RFD, and FNT. The relationships developed using critical values of ε from 2 to 6 correctly identify nearly the same percentage of lake-breeze events irrespective of location (see Table 3). This confirms the theoretical finding of Walsh (1974) and demonstrates that ε may not be significantly affected by changes in location as suggested by both Biggs and Graves (1962) and Lyons (1972). Although this result is encouraging, further examination of ε for other locations in the Great Lakes (e.g., Cleveland, Ohio; Gary, Indiana) and smaller lakes (e.g., Lake St. Clair, Lake Champlain) is necessary to corroborate this finding.