a. Satellite imagery

Visible satellite images (Fig. 1) can be used to identify the SCE presence and delineate some of its features. Under typical summer conditions, stratus clouds (i.e., fog) cover most of the eastern Pacific and provide a marker for the rotation associated with the SCE. It typically begins as a tongue of fog that starts to rotate counterclockwise from the southeastern part of Monterey Bay (Figs. 1a,c). Although the main flow off the California coast is northwesterly, the eddy causes surface winds to blow from the east in the northern part of Monterey Bay and advects fog into the otherwise clear Santa Cruz area (see Fig. 2 for the location of Santa Cruz).

The horizontal size of the SCE can vary. It can cover most of Monterey Bay (Figs. 1b,d) or can be limited to the northern or northeastern part of Monterey Bay (Figs. 1a,c). Like the Denver Cyclone and the Catalina eddy, the SCE often has a warm core; that is, it has a warm and dry “eye” in its center (Figs. 1b,d). The SCE can start as early as 1600 Pacific daylight time (PDT)² (Fig. 1a), but a fully closed circulation usually does not form until later. For this reason, the SCE can be considered a nighttime phenomenon. Satellite images taken in the early morning after an SCE event sometimes still show the presence of the vortex (e.g., Figs. 1b,d). The eddy never survives past ∼1000 PDT, since the strong westerly flow associated with the sea breeze destroys the weaker circulation of the SCE.

b. Surface winds

Data were acquired from 10 surface stations during the summers of 2000 and 2001 from the National Weather Service (through the Unidata datafeed) and the Naval Postgraduate School (NPS) of Monterey [through the real-time environmental information network and analysis system (REINAS) database]. Of the 10 surface stations, 3 were buoys (Fig. 2). Data from one profiler (Fort Ord) were also provided by the NPS. To determine the relationship between the winds at these stations and the SCE development, special emphasis was placed on the 25 August 2000 event, when the eddy formation and partial evolution could be observed in the satellite imagery. More details can be found in Archer (2004).

The winds observed during the SCE event of 25 August 2000 are shown in Fig. 3. The sea breeze was established in the afternoon, at about 1300 PDT, with westerly winds at Santa Cruz [Long Marine Laboratory (LML)] and Fort Ord (ORD), northwesterly at Monterey (MRY) and buoy M1B, and north-northwesterly at buoys M2B and M4B. Note that the sea breeze was characterized by southwesterly winds at the Watsonville station (WVI). As shown in the satellite image in Fig. 1c, an SCE event started out that afternoon as a small eddy initially limited to the northern part of the bay. The image shows fog being advected toward the Santa Cruz area from the east at about 1600 PDT, but the circulation does not yet appear to be closed at that hour. An hour later, a sudden wind shift from westerly to easterly occurred at LML (not shown). This shift coincided with the beginning of the SCE, since winds at all 10 locations were for the first time consistent with a closed circulation. At WVI, the transition from sea breeze to SCE was more gradual, as winds slowly turned from southwesterly at 1300 PDT to southerly at 1700 PDT (not shown).

Later, this SCE developed into a larger eddy, as shown in Fig. 3b. In fact, by 2000 PDT most of the stations indicated the presence of a larger SCE over the bay. Winds had shifted to southwesterly at MRY and ORD, southeasterly at WVI, and northwesterly at M1B. The two buoys outside of the Monterey Bay—that is, M2B and M4B—showed the undisturbed north-northwesterly main flow, and the Salinas (SNS) site had a strong flow into the Salinas Valley. The eddy dissipated by 2200 PDT and was replaced by light and variable winds, as shown in Fig. 3c.

Five hours after the eddy dissipated, at approximately 0300 PDT, a second circulation formed, similar in size to the previous one, but characterized by generally lower wind speeds (Fig. 3d). It lasted until about 0800 PDT. The formation of a second circulation was not unique to the 25 August 2000 case. In fact, two consecutive eddies were a commonly observed feature in the database, with some cases even showing three vortices in one night. In no case was one single eddy able to last the entire night. Hereafter, the eddy forming in the evening is indicated as either the “first” or the “evening” eddy, while the eddy forming at night is called either the “second” or the “nocturnal” eddy.

c. Sea level pressure and temperature

Surface wind analysis was necessary to identify the main characteristics and timings of the SCE, but it could not provide much insight into the eddy formation mechanism. As noted earlier, past studies have consistently found surface pressure patterns to be important factors in the eddy formation. Sea level pressures were thus analyzed for two key locations (MRY and LML) for 24 h beginning at 1200 PDT on 25 August (Fig. 4a). Sea level pressure decreased toward the north of the Monterey Bay, as the most northern location (LML) had an average sea level pressure 0.2–0.4 hPa lower than the southernmost location (MRY). This south-to-north pressure gradient³ suggests the presence of a local low on the southern side of the Santa Cruz Mountains, near Santa Cruz.

The pressure difference (proportional to the pressure gradient strength) between MRY and LML increases before the eddy forms (Fig. 4a); the maximum difference occurred at 1700 PDT on 25 August, just as the eddy reached LML and caused the wind shift from westerly to easterly. The pressure gradient fell after the eddy started, creating a pattern of rising and then falling pressure, which is referred to here as a “pressure bump.”⁴ Figure 4a shows that the pressure gradient rose again at about 2300 PDT, approximately the same time as surface winds in Fig. 3c showed the eddy to be dissipated. After a few hours, the pressure gradient decreased again (second pressure bump), at about the same time (∼0400 PDT) that surface winds at LML were again consistent with the presence of an SCE in Fig. 3d.

So far, the wind and pressure analysis on 25 August 2000 suggests a strong similarity between the SCE and the Catalina eddy, in that a reversed pressure gradient appears to be the cause of both eddies. However, an extensive analysis of over 100 other days proved this hypothesis to be wrong. In fact, the north-to-south pressure gradient is observed over Monterey Bay during all analyzed days, with and without SCE, and therefore it does not appear to be a sufficient condition for eddy formation. Although, in general, the strength of the south-to-north pressure gradient showed a correlation with the eddy, as seen in Fig. 4 for 25 August 2000, about one-third of the eddy cases exhibited no pressure bumps, perhaps due to comparable amounts of surface convergence and vertical divergence. There were also days without eddies that had a pressure bump. For this reason, the mechanism of the SCE formation cannot be explained solely on the basis of the pressure pattern, which was the fundamental mechanism for most other mesoscale eddies.

If not the SCE, what causes this north-to-south pressure gradient? The Santa Cruz Mountains to the north of Monterey Bay protect the Santa Cruz area from the cold marine air. This allows increased surface heating, which results in an average summer temperature that is about 1.5°C higher than in nearby Monterey (Table 1). Increased surface heating may then form the localized area of low pressure in the northeastern part of Monterey Bay, which would contribute to the south-to-north pressure gradient. Furthermore, the mountains of the Santa Lucia Range to the south of the bay block the main northwesterly flow and may increase the cool marine layer depth in the southern part of the bay (because of both horizontal convergence and suppression of vertical motion by the marine inversion), causing a local area of higher pressure in the Monterey area, a feature consistent with the observations. Thus, the south-to-north gradient seems to be the product of two topographical effects on the steady northwesterly summer winds.

For consistency, higher temperatures are expected in the Santa Cruz area, where sea level pressure was lower (Fig. 4b). However, the diurnal temperature cycle at LML was more typical of a marine location than one would expect for the sheltered Santa Cruz area. Climatology data show that the average monthly temperature in Santa Cruz⁵ is 0.4°–1.8°C higher than in Watsonville or Monterey in the summer (Table 1). This apparent inconsistency can be explained by the fact that the LML station is located about 5 km to the west of the city of Santa Cruz, on the edge of a cliff, exposed to the strong and cool marine flow entering Monterey Bay.

Since temperature generally decreased at LML during the SCE and rose after it dissipated, advection of cool, moist air from the southern bay into the Santa Cruz area may appear to be associated with the presence of an SCE. However, temperature (and relative humidity; not shown) over Monterey Bay is rather uniform at night (Fig. 4b), and therefore no significant cool (and moist) air advection could be associated with the second eddy. From the several cases analyzed, the timing of temperature change is not always synchronized with the SCE. Thus, temperature changes are not a cause of the SCE. This finding will be supported in Part II, where simulations obtained without any heat exchange still show the formation of an SCE.

d. Vertical structure

In addition to the 10 surface observations, a vertical profiler was operating at Fort Ord during both summers under study, retrieving virtual temperature and wind speed and direction every 30 min. These data were useful for evaluating some aspects of the eddy and the marine boundary layer (MBL) evolution. However, given the shallow nature of the SCE, in most cases no additional information could be extracted from the profiler data. Furthermore, observations retrieved at the lowest points (112 and 168 m above ground), which would have been most useful for discerning SCE details, were often incorrect or missing.

For example, the flow at the lowest levels on 25 August 2000 was westerly during the afternoon (Fig. 5). At approximately 1800 PDT, a more southerly component, with higher wind speed around 2000 PDT, was observed for approximately 4 h at the lowest points, followed by lowering and warming of the MBL. The top of the MBL is marked approximately by the 16°–18°C contour lines. This happened at the same time that the SCE was detected at the surface. Light southwesterly winds continued through the night within the layer (and up to the inversion top), together with a rise of the MBL, until the westerly flow associated with the onset of the sea breeze started at about 1100 PDT.

Low-level winds with a southerly component, lowering and then rising of the marine layer (“MBL dip”), and warming near the surface were observed (not always simultaneously) during ∼65% of the satellite-confirmed eddy cases. However, in the remaining 35% of these cases, an eddy was present even though none of these indicators was detected from the profiler data. The profiler data showed no evidence of converging (or downslope) flow from either the Gabilan Range or the Sierra de Salinas. This is not surprising, since the tops of the mountains surrounding Monterey Bay are located within or above the inversion. Figure 5 shows temperatures greater than 25°C at elevations of about 1000 m, and hence no cold drainage would be expected.

Profiler data generally showed that the SCE was more likely to occur when the MBL was <500 m deep. When the marine layer is >500 m deep, strong synoptic northwesterlies can pass directly over the Santa Cruz Mountains and suppress the easterly flow associated with the SCE.

In sum, observations show that SCE events are somewhat correlated with sea level pressure patterns (pressure bumps) and MBL behavior (MBL dips). Since none of these conditions is consistently present prior to eddy formation, another factor must be responsible for the eddy formation. Differential heating, invoked for example for the Midchannel and the Gaviota eddies, is not likely the reason, since the nocturnal SCE forms in the middle of the night, when no strong difference between air temperature above water and land can be detected. Convergence of drainage flow or downslope flow, associated for example with the Gulf of Antalya eddy, does not occur either, because the surrounding mountains are typically warmer than the coastal locations. Bay configuration and topography thus appear to be the only factors that may generate enough curvature and shear in the flow to produce the vorticity necessary for the SCE. However, their effect on the SCE cannot be verified directly from observations. A numerical approach, described in Part II of this study, will explore all the factors contributing to the SCE formation. Below, the observational approach is utilized one more time to determine the climatological importance of the SCE for the Monterey Bay area.

a. Empirical orthogonal functions

Almost 50 yr ago, Lorenz (1956) introduced EOFs as a method of reducing the number of variables required to describe distribution of atmospheric pressure and temperature with minimal loss of information. Since then, the EOF approach has been widely used, and it often goes by various names, such as principal component analysis, factor analysis, and eigenvector analysis. EOF analysis has many desirable properties, such as the fact that the resulting features are based on the characteristics of the data themselves; they are linearly independent of one another; and a measure of their relative importance is provided. This technique also has the advantage of often revealing physically important connections in the data.

Most EOF applications in meteorology have focused on scalar features. For example, Lumley (1981) used EOF analysis to extract coherent structures from turbulent flows. Hardy (1977) suggested a similar approach for classifying wind datasets, an application closely related to this study. Ludwig and Byrd (1980) also applied the concept to vector fields, identifying patterns of variability in the inputs used for a linear diagnostic wind model in order to simplify the resulting calculations. Sirovich (1988) described the analysis of turbulent flows by a similar procedure, and Mahrt (1991) and coworkers (Manning and Frank 1988) applied closely related methods to the analysis of wind variability along an aircraft line of flight. Similarly, Kaihatu et al. (1998) applied EOFs to oceanic surface currents. Ludwig and Street (1995) described a method by which preferred small-scale patterns within a larger scale flow could be determined using EOFs. Dorman and Winant (2000) found the signatures of synoptic and diurnal variations in the EOF analysis of winds in the Santa Barbara Channel.

b. Theory of EOFs

The following description of EOFs is based on Lorenz (1956). Details can be found in Archer (2004). Given a meteorological variable (such as pressure, or the u and v components of the horizontal wind) observed at a station m (m = 1 . . . M) at time n (n = 1 . . . N), let 𝗣 be the N × M matrix containing the deviations of such variable around its mean (p_n,m).

The starting point is to find two matrices 𝗬 and 𝗤 such that

View Expanded

where 𝗤 and 𝗬 are N × M and M × M matrices, respectively. The coefficients q_n,k and the vectors y_k are chosen to minimize the sum of the mean square errors between the observed values p_n,m and their approximations given by the linear combination of q_n,m and y_m,m. Note that the vectors y_k are not a function of time.

A solution to this problem can be obtained by requiring that the matrices 𝗤 and 𝗬 are orthonormal and orthogonal, as follows:

View Expanded

View Expanded

where I is the M × M unit matrix and Λ is an M × M diagonal matrix whose diagonal elements are arranged in decreasing order. The superscript T denotes the transpose. By substituting 𝗤 = 𝗣𝗬^T [derived from Eq. (3.1)] in (3.2b), one obtains

View Expanded

which means that the elements of the diagonal matrix Λ are the eigenvalues of 𝗔 = 𝗣^T 𝗣 = 𝗣 𝗣^T. By design, matrix 𝗔 contains the variances of the meteorological variable of interest. Note that 𝗔 is symmetric by definition. The rows of Y (y_k) are the eigenvectors of 𝗔 and are referred to as EOFs. The columns of Q are referred to as EOF coefficients.

In Eq. (3.2b), the eigenvalues λ_k,k represent the variances associated with each eigenvector y_k. Since the columns of ¹ are arranged in decreasing order, the maximum amount of variance is associated with the first eigenvector, and progressively lower variances are associated with the next eigenvectors. It is thus possible to retain only a subset K of the M eigenvectors; the amount of variance explained by the first K largest eigenvectors is in fact proportional to their sum. This variance can be decided a priori.

The vectors y_k can be thought of as patterns of variability about the mean. If matrix P contains wind vector components, the resulting y_ks can be plotted at the observing sites on a map to display the important patterns of flow variability. Each q_n,k coefficient can be thought of as the intensity of the flow pattern defined by its corresponding EOF y_k at time t_n.

Figure 6 illustrates how accurately EOFs can represent original data. The u′ and υ′ wind components at the four stations with the highest variances are compared with those estimated from the first six EOFs (corresponding to 95% of the variance) for the 25 August 2000 case.

For Monterey Bay winds, at least one EOF should resemble the SCE, since the eddy represents a deviation from the typical summer flow. This suggests two possible ways of using EOF analysis: 1) on a day-by-day basis, or 2) from the complete body of data. In the first approach, the EOFs can be calculated each day to see if any of them are eddy-like. In the second case, one average eddy-shaped EOF is sought and the magnitude of the coefficients of that particular EOF at each hour is used as a measure of how well the winds correspond to an SCE circulation. Both approaches are described below.

c. Day-by-day EOFs

With this approach, different EOFs were obtained for each day. Twenty-four hourly observations of the u and v components of the horizontal wind retrieved from eight stations were inserted into matrix 𝗣 (24 × 16) for each of the 62 days considered in the database. The value of K was chosen so that more than 95% of the variance would be retained. In general, K was smaller than 8, meaning that at most the first 8 eigenvectors (out of 16) were used. It was found that the three stations with the highest variances were always LML, WVI, and ORD, which (combined) represented approximately 96% of the total variance of the wind field.

Since the SCE represents a variation superimposed on the mean flow, it was reasoned that the SCE-like pattern would be pronounced enough on eddy days that one of the first three EOFs would be likely to resemble the eddy itself. If such an EOF is found, the day can be classified as an eddy day, otherwise the day can be classified as a non-eddy day.

To illustrate this methodology, the eddy event of 25 August 2000 is presented again. The daily mean flow, in Fig. 7a, was typical of summer days: strong onshore flow in the southern bay and near-zero diurnal average along the more sheltered north bay. The highest variance (λ_1,1 = 42.4%) was associated with the flow pattern (EOF1 or y₁) shown in Fig. 7b. The pattern obviously represents the sea/land-breeze component of the diurnal wind cycle, and this thermally driven flow is consistently a major factor in daily wind changes. When EOF1 has a positive coefficient q_n,1, the average onshore flow will be augmented by the sea breeze. When the coefficient is negative, the flow is weakened or reversed by the land breeze. The second EOF (Fig. 7c) had the cyclonic pattern associated with the SCE: easterly flow at LML and WVI, southwesterly in the south bay, and west-northwesterly at buoy M1B. This pattern explained 26.4% of the variance. The explained variance dropped to 11% for the third EOF, whose disorganized, convergent pattern had no obvious physical meaning.

In cases when the satellite showed no eddy, the average still showed winds to be generally from the northwest (not shown). The first EOF (explaining ∼45% of the variance) still reflected the sea-breeze cycle, but neither the second nor third EOF resembled an SCE.

Since each EOF pattern occurs just as frequently as its exact reverse, depending upon the values of the corresponding coefficients q_n,k, it is also important to look at the temporal evolution of the time-varying q_n,k (k = 1, . . . , 3), shown in Fig. 8. Roughly speaking, positive coefficients for EOF1 are found during sea breezes, and negative coefficients during land breezes. Thus, as expected, the EOF1 coefficients became positive just before noon and stayed positive until the late afternoon. The land-breeze effect is indicated by the more negative values around 0300 PDT. Note that since EOFs represent patterns associated with the deviations of u and υ from their means, finding a land-breeze signature in the EOF1 coefficients does not necessarily mean that the actual winds became offshore at night. The effect of the land breeze, although present in the flow, might be masked by the strong synoptic flow.

Similarly, the SCE is associated with EOF2 in Fig. 8. The EOF2 coefficients were negative (indicating a superimposed circulation with negative vorticity) during late afternoon. After that, the coefficients became positive. The highest values indicate that the eddy was strongest around 1900 PDT on 25 August 2000. The reappearance of the eddy is mirrored in the second peak for EOF2 in Fig. 8. The third EOF explained little variance and did not have well-organized patterns. It is not surprising that it had small coefficients and little evidence of diurnal behavior.

These examples indicate that the day-by-day technique can be successful at identifying SCE eddy cases. The results of applying it to each day in the database for which satellite information is available are shown in Table 2, and the final statistics are presented in Table 3. The day-by-day EOF method has a 100% success rate at identifying eddy days (i.e., classifying as “eddy day” a day during which an eddy did occur; outcome indicated as E/E in Table 2). Furthermore, it has a high success rate at identifying noneddy days (63%); that is, classifying as “noneddy day” a day during which no eddy occurred (outcome N/N). The overall success rate (given by the sum of days classified as E/E and N/N in Table 2 over the total number of days) for the day-by-day EOF technique was 87% (20/23). The frequency of SCE events obtained by this method is 79% (Table 3).

d. Multiday EOFs

The results discussed to this point suggest that the SCE occurs on a majority of the days in the summer, albeit for only a few hours each day. It seemed worth determining if this was sufficiently frequent that the eddy pattern would explain a major part of the variance in the complete dataset (i.e., the same 62 days used for the day-by-day EOF approach). Therefore, EOFs were determined using all hours available simultaneously from seven⁶ of the stations used for the daily EOFs. The resulting EOF patterns are shown in Fig. 9.

The mean and first two EOFs are quite similar to those shown earlier for the 25 August 2000 case. The explained variances are also about the same (42% and 28%, respectively). These results indicate that the coefficients for the second EOF q_n,2 are a single function that can be used for identifying the eddy days. Figure 10 shows the values of the coefficients for the first two EOFs plotted versus hour of the day for all days combined. Although the scatter from day to day is considerable, the diurnal sea-breeze pattern is clearly visible in Fig. 10a. Figure 10b for EOF2 coefficients shows a clear, but less pronounced diurnal cycle. The hours when eddies generally form (between about 1700 and 2000 PDT) are marked by a bimodal distribution of values; that is, only a few values are found around zero. This gap separates the values into two groups having either positive (eddy pattern) or negative (noneddy pattern) coefficients. This suggests that only two patterns are likely to verify at those hours: either an eddy or no eddy at all. Furthermore, since the mean curve is positive in that time interval, the eddy pattern is more likely to occur.

The days with satellite imagery were used to develop an appropriate threshold, that is, a value such that days with one or more coefficients q_n,2 above it can be classified as eddy days and vice versa. Several thresholds were tested, varying between 3 (most restrictive) and −1 (most inclusive). No threshold had a 100% success rate at identifying eddy days, a desirable feature that the previous method showed. With the multiday approach, by definition, one single eddylike pattern (EOF2) is used to identify all eddies, no matter what their size, duration, or center might be. It is therefore likely that some eddy days might not match the imposed SCE pattern very well. Similarly, it is possible that some days characterized by strong shear in the Santa Cruz area might be wrongly classified as eddy days. With this limitation in mind, the best threshold appeared to be 3, since it had the highest success rate (93%) at identifying eddy days, as opposed to 86%–89% for thresholds between 2 and −1 (not shown). Although its overall performance is only 78% (Table 4), it was preferred over the 0 and −1 thresholds, which both had 87% overall performances, but lower success rates on eddy days. Based on threshold 3, the frequency of eddy days as determined from the multiday approach was 79% (Table 3).

In summary, the application of the EOF technique to the SCE case was overall successful at identifying eddy and noneddy days, especially with the day-by-day approach. Since the SCE is such a common occurrence over Monterey Bay, it was not surprising that its signature was present in the variance of the wind field. However, results from the EOF analysis should only be interpreted qualitatively and not quantitatively. Trends of q_n,k from Fig. 8 simply suggest that conditions compatible with the eddy presence were detected twice that night. The exact hours and duration of these conditions cannot be reliably inferred from this plot. Such limitation would be less significant if the SCE were a stationary feature that formed and stayed in the same place at all times. Since it moves around instead, matching one single eddylike pattern to either all days of the summer (multiday approach) or even just all the hours of a day (day-by-day approach) can be difficult. This study suggests that future applications of the EOF technique will be more succesful at identifying features that are stationary and do not vary considerably in size.