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Keywords:

  • mesoscale;
  • stable boundary layer;
  • solitary waves;
  • FLOSS

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Cold microfronts
  6. 4. Other local events
  7. 5. Sensitivity to sampling criteria
  8. 6. Conclusions
  9. Acknowledgments
  10. References

Microfronts with abrupt changes of temperature and/or wind vector are found to be common for weak winds and thin stable boundary layers. In this study, microfronts and their parent structures on time-scales of minutes or tens of minutes are sampled from fast-response tower measurements of temperature and the three velocity components during FLOSSII. Cold microfronts are generally characterized by rising motion, followed by stronger stratification and weaker turbulence. Sinking warm air prior to the cold microfront, followed by rising cold air after the microfront passage, corresponds to conversion of kinetic energy to potential energy. This conversion requires a source of external energy for maintenance of the circulation. The shallow cold microfronts appear to be often related to deeper fast-moving disturbances in the horizontal velocity field. Warm microfronts generally lead to stronger wind and turbulence after the microfront passage. Gust microfronts induce rising motion in advance of the microfront. Solitary waves cause little net change of temperature and are systematically embedded within larger-scale deeper disturbances at this site. The sensitivity of the results to the sampling window width and sampling criteria is examined. Copyright © 2010 Royal Meteorological Society


1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Cold microfronts
  6. 4. Other local events
  7. 5. Sensitivity to sampling criteria
  8. 6. Conclusions
  9. Acknowledgments
  10. References

The stable boundary layer includes turbulence, waves, sharp changes and sudden wind shifts, and a wide variety of more complex signatures. Wave-like motions are common, particularly with ducting conditions near the surface (Nappo, 2002; Smith et al., 2007). Wave activity is further enhanced over complex terrain (Brown et al., 2003), although waves can be ubiquitous over even relatively simple terrain and vertically coherent over hundreds of metres (Anderson, 2003).

Often, wave-like motions include a single cycle sometimes referred to as a solitary wave (Rottman and Grimshaw, 2001; Rao et al., 2004; Koch et al., 2008). Rees et al. (1998, 2000) found that solitary waves are common within the surface inversion with weak winds, even over simple surfaces, and often propagate at speeds of 10–20 m s−1 or more. Detailed observations of oceanic solitary waves over a shelf are provided by Moum et al. (2003) and Klymak and Moum (2003). Solitary waves have been generated in numerical models by imposing initial disturbances as by Christie et al. (1978, and references therein). Such waves can become strongly nonlinear and lead to heat transport. Heat is transported downwards by the atmospheric solitary wave observed by Sun et al. (2004, their Figure 1) where upward transport of cooler air is followed by downward transport of warmer air. However, the heat flux appears to occur over a sufficiently deep layer (small flux divergence) for a sufficiently short period of time (as observed at a fixed point), that the net influence on the temperature is not detectable. Solitary waves may lead to little net change of temperature except through generation of secondary instabilities and turbulence (Christie et al., 1978; Rees et al., 1998).

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Figure 1. Fraction of within-sample variance explained by the Haar transform of temperature (Rθ) as a function of event number, where the magnitude of the Haar transform decreases monotonically with increasing sample number.

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Sharp changes of wind and temperature, sometimes referred to as microfronts, are common at the surface in the nocturnal boundary layer. Large-amplitude versions, such as occur with density currents, have been analyzed in some detail. However, the more common smaller-amplitude microfronts and attendant wind-direction shifts have received little attention. In contrast to solitary waves, microfronts are to some degree material surfaces driven by horizontal advection that lead to significant net change of temperature and/or wind direction. ‘Net change’ is defined on a horizontal- or time-scale that is large compared to the width of the microfrontal change. That is, in order to qualify as a ‘microfront’, the postfrontal conditions must extend much farther than the width of the front, as in the normal definition of a front.

Microfronts are generally part of a larger parent circulation and presumably generated by horizontal convergence. For example, the microfront at the leading edge of a cold density current in Sun et al. (2002), which leads to a net decrease of temperature, contrasts with the solitary wave in Sun et al. (2004), where the temperature decreases and then returns to its original value. However, more complex structures are common. For example, with the passage of the ‘solitary wave’ studied by Cheung and Little (1990, their Figures 4–5), the temperature decreases and then only partially recovers to its original value, leading to a modest net change.

Microfronts in the stable boundary layer can be generated by:

  • 1.
    Steepening or amplification of gravity waves. For example, surface drag may lead to wave amplification and steepening (Chimonas, 1994). Ducted waves can lead to sudden wind-direction reversals and sharp temperature changes, as in Figures 8–9 of Viana et al. (2009).
  • 2.
    Temporary sharp horizontal gradients resulting from random superposition of linear waves.
  • 3.
    Kelvin–Helmholtz and inflection-point instabilities.
  • 4.
    Leading edges of drainage flows (Blumen, 1984) or the pulses of drainage flows (Doran and Horst, 1981; Mahrt and Larsen, 1982; Aubinet, 2003).
  • 5.
    Density currents over relative flat terrain (Simpson, 1997; Sun et al., 2002; Blumen et al., 1999; Hohreiter, 2008).
  • 6.
    Mixing events which transport warmer faster air downwards (Mahrt, 2007).
  • 7.
    Surface heterogeneities that induce sharp horizontal differences during calm periods that are subsequently advected as microfronts.
  • 8.
    Disturbances induced by complex terrain (e.g. Grisogono and Enger, 2004, and references therein).
  • 9.
    Transient regions of horizontal divergence and convergence driven by pressure disturbances of unknown origin.

These mechanisms are difficult to rigorously examine without dense spatial coverage that would allow approximate tracking of individual disturbances. In the absence of such data, this study seeks new, albeit incomplete, information on microfronts and other solitary events from existing tower data. These ubiquitous events have received much less attention than waves, yet they frequently lead to significant changes of temperature and wind direction near the surface. We emphasize the relation of the microfront to its immediate parent circulation with less attention on the fine-scale structure of the microfrontal zone itself. This study departs from the existing literature and includes the ubiquitous weaker events, which allows description of much of the non-turbulent variance in the stable boundary layer.

2. Data

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Cold microfronts
  6. 4. Other local events
  7. 5. Sensitivity to sampling criteria
  8. 6. Conclusions
  9. Acknowledgments
  10. References

This study analyzes eddy correlation data from a 34 m tower in FLOSSII (Fluxes over Snow Surfaces; Mahrt and Vickers, 2006) instrumented from 20 November 2002 to 2 April 2003 by the National Center for Atmospheric Research (http://www.atd.ucar.edu/rtf/projects/FLOSS). The tower site is located over a locally flat grass surface south of Walden, Colorado, USA (40.8°N, 106.3°W) in the Arapaho National Wildlife Refuge. The grass is often covered by a thin snow layer during the field programme. This study is based on data collected at 1, 2, 5, 10, 15, 20 and 30 m with Campbell CSAT3 sonic anemometers. We also briefly analyze data collected at 2 m above brush approximately 3.3 km northnortheast of the tower site, and 2 m above a snow-covered dry lake bed, approximately 1.5 km northwest of the tower site.

The North Park Basin lies between two large mountain ranges oriented in the north–south direction with elevations of 1000–1500 m above the floor of the basin. The basin is approximately 50 km from south to north and 30 km from west to east. The FLOSSII tower is located at the south end of a shallow sub-basin about 4 km across. The sub-basin is defined by hills on all sides except for an outflow region towards the northeast to the larger main basin. The wind direction in FLOSSII shows a strong preference for south–southwest flow with a secondary maximum of northerly flow. The predominance of southerly flow is related to the prevailing synoptic pressure gradient and the north–south oriented mountain ranges on the east and west edges of the basin. The local slope at the tower site is weak depending on direction and distance from the tower. On average, the terrain slopes upwards toward the south with a magnitude of about 1%.

The turbulent fluctuations are computed as deviations from an average computed over a variable averaging width; the averaging width is chosen independently for each 1 h record based on the record cospectra for heat, as in Mahrt and Vickers (2006). This OGIVE approach (Friehe et al., 1991) defines the turbulence as the smaller-scale part of the cospectra where the heat flux is systematically gradient (positive diffusivity). Once the perturbation quantities are computed, covariances are averaged over 1 min records. We will emphasize the 2 m data where fluxes are thought to be normally a reasonable approximation to the surface flux. For the most stable cases, the 1 m flux appears to suffer some flux loss due to path-length averaging. More detailed structure of the microfront will be examined only briefly in terms of fast response data. Otherwise, this study analyzes 1 min averages within the nocturnal period 2000–0600 local standard time for the entire four-month winter season.

We define a local potential temperature, θ,

  • equation image(1)

where δz is the height above the surface, and the 0.01 constant has units K m−1. The sonic anemometer data is used for the temperature at each level. Based on strong-wind cases when well-mixed conditions are expected, the temperature at several of the levels was adjusted by ± 0.1 K.

The vertical motion shows a strong dependence on wind direction, particularly at higher levels on the tower. The attack angles for the 1 min flow are often small (mainly horizontal flow) so that small errors in the inability to correct for sonic misalignment and flow distortion could lead to serious errors in the vertical velocity. Acevedo and Mahrt (2010) found that the tilt coordinate rotation significantly influenced the computed mesoscale fluxes. In the current study, the tilt rotation did not significantly influence the composited within-sample structure of the vertical motion field, but did influence the mean vertical motion. We do not apply a tilt coordinate rotation to the 1 min winds used in this study, but do remove the sample mean vertical motion. In the analysis below, we use information on vertical velocity mainly at the top tower level, 30 m, where the horizontal structure of the vertical motion is best defined.

2.1. Detection of events

Solitary events will be detected in terms of changes of a detector variable, ϕ, such as temperature or one of the wind components across a sampling window of τF data points. To identify changes with time, we compute the similarity of the local structure with a detector function, H, such that in discrete form

  • equation image(2)

where ti is the relative time within the sampling window, equal to tto, and where to is the beginning of the sampling window. To select sharp changes with time, we assign the detector function to be the Haar function, which for a given sampling window can be written as

  • equation image(3)
  • equation image(4)

where the colon signifies sequentially incrementing through the data points. Application of the Haar function in Eq. (2) computes the difference between the means of ϕ for two halves of the sampling window, which we write equivalently as

  • equation image(5)

since

  • equation image(6)

and so forth. A time series of δt(ϕ) is computed by moving the sampling window of width τF through the data. To generate a time series of δt(ϕ), the sampling window is shifted 1 min between calculations throughout each of the 12 h nocturnal periods.

2.2. Sample selection

Samples are selected from the time series of δt(ϕ) by choosing the first sample to be centred about the largest magnitude of δt(ϕ) of the chosen sign within the entire dataset. The values of δt(ϕ) within this sampling window are then removed from further consideration. Subsequently, a second sample is selected centred about the largest magnitude of δt(ϕ) in the remaining time series, and so on. We will select the first 200 samples for analysis corresponding to the 200 largest magnitudes of δt(ϕ). The nominal value of the sampling window width will be 20 min. Sensitivity to the choice of sampling window width and number of selected samples will be examined in section 5.3.

2.3. Variance analysis

To examine the relative importance of the solitary structures, we now construct a variance analysis. We first remove the sample means for the variance analysis to simplify the ensuing algebra, such that

  • equation image(7)

where the square brackets indicate averaging over the sample window. The variance captured by the Haar transform of ϕ is then computed by first decomposing ϕ* at each point within the sampling window as

  • equation image(8)

where equation image is the deviation of the half-window means from the sample mean and projected onto all of the points within the sampling window. ϕ′ is the deviation of the point value of ϕ* from the half-window means and represents the more complex deviation of the parent motion from the Haar function and also includes smaller-scale minute-to-minute variations.

Since the Haar function corresponds to simple unweighted averaging for each half sampling window, the total within-sample variance is simply

  • equation image(9)

where the first term on the right-hand side is the residual variance due to structure not explained by the Haar function (half-window means). The second term is the variance due to the half-window means. The fraction of variance explained by the Haar transform for each sample is then

  • equation image(10)

which will be used to assess the relative importance of the structures similar to the simple Haar function.

We will also analyze the composited structure by averaging over all of the selected samples and assess the importance of the composited within-window structure compared to the between-sample variability. Towards this goal, we define the difference of ϕ*(ti) for a given sample from the average of ϕ*(ti) over all of the samples, such that for the jth sample

  • equation image(11)

where the operator < ·> averages over all of the J samples for a given point within the sampling window. Had we not removed the sample means, the computed between-sample variance might be dominated by differences between nights, for example between very cold nights and mild nights.

The variance between samples at point ti, equation image, is subsequently averaged over the sampling window, to obtain a total between-sample variance

  • equation image(12)

The within-window variance of the composited flow (<ϕ(ti)>) is defined as

  • equation image(13)

If the within-window variance of the composited structure, VARc, is small compared to the between-window variance, VARb, then the structure of the composited flow is of questionable significance. That is, the variance explained by the composited structure is less than the variability between the samples. Thus, a measure of the relative importance of the structure of the composited flow can be defined as

  • equation image(14)

This ratio can be converted to a version of the relative standard error with respect to the significance of the variation within the composited structure relative to the between-sample variation

  • equation image(15)

where J is the number of samples. Such tests indicate that the composited structure is highly significant for at least some of the variables, as discussed below. However, the significant skewness of equation image for some of the variables, and the unlikely existence of an ensemble average, both compromise the interpretation of Eq. (15) as a formal version of the standard error. That is, the structures contributing to the composite arise from different situations (analogous to different populations). Nonetheless, Eq. (15) remains a relative measure of the significance of the structure for different variables.

While the composited structure for the variables not used in the selection process could potentially be dissimilar to all of the individual structures, the collection of samples of solitary events in this study generally includes a substantial number of cases that qualitatively resemble the composited structure. At the same time, the samples also include numerous other signatures quite different from the composited structure.

3. Cold microfronts

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Cold microfronts
  6. 4. Other local events
  7. 5. Sensitivity to sampling criteria
  8. 6. Conclusions
  9. Acknowledgments
  10. References

3.1. Variance explained

We now examine the stochastic behaviour of common cold microfronts δt(θ) < 0. We consider only microfronts for weak flow where the speed of the 2 m window-averaged wind vector is less than 3 m s−1. With stronger winds, the microfronts are generally characterized by weaker temperature decreases, examined briefly in section 4.3. The 200 strongest cold microfronts account for about 11% of the weak-wind data. When combined with sampled warm fronts, approximately 22% of the weak-wind data are selected. Segments of data between previously selected samples that are smaller than the sampling window width are not selectable. Some missing data (about 5%) also contribute to non-selected parts of the data. Increasing the number of samples accepts somewhat noisier samples, but does not qualitatively change the results below.

The 49 nights with selected cold microfronts often contain four or more cold microfronts, which sometimes occur in concert with warm microfronts passing before and/or after the cold microfront. Microfronts on nights with only one or two events are generally weak. Cold microfronts occasionally occur as a culmination of several weaker oscillations of temperature. The variation of microfront occurrence between weak-wind nights is not significantly related to the variation of the stratification of the tower layer, the time of night or the exact speed of the weak wind.

The fraction of the within-sample variance of temperature explained by the half-sampling window means, equation image, averages about 80% of the total within-sample variance (RT = 0.79, Eq. (10)), for the 200 samples. Thus, the Haar transform of the temperature for individual samples explains most of the within-sample variance for temperature. The fraction of the within-sample variance of the v-component explained by the half-sampling window means, δt(v), averages 53% for the v-component, a relatively large value considering that the sample selection was made independently of the v-component. The values of RT for the u and w components are much smaller. The fraction of the variance explained by the half-sampling window means (Eq. (10)) does not decrease monotonically with increasing sample number (decreasing magnitude of δt(θ)), as shown in Figure 1. Stronger events (larger magnitude of δt(θ)) can be associated with significant smaller-scale fluctuations, thus reducing Rθ.

The first three cold microfronts with the largest magnitudes of δt(θ) appear to be associated with larger-scale cold fronts. The fourth microfront is a strong version of the more common microfronts (Figure 2) except that the turbulent velocity and temperature fluctuations are relatively large after the microfront passage. In addition, this particular microfront includes a second pulse of a little stronger colder northerly flow about 6 min after the microfront passage. The main temperature jump for microfront in this example is very sharp and its passage spans only a few seconds, corresponding to a width of a few metres based on Taylor's hypothesis (of uncertain validity). The cold air in Figure 2 survives for little more than half an hour after the microfront passage. For this example, the amplitude of the wind change increases with height across the tower layer, consisting of sharply decreasing southerly flow at the top of the tower. In contrast, the amplitude of the temperature change decreases with height and vanishes above 20 m.

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Figure 2. An example of a relatively strong cold microfront centred at 0429 LST on 10 December 2002 (DOY 343): temperature (red), v-component wind (green) and vertical velocity (black).

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3.2. Distribution

We now examine the 200 selected samples, which include weaker versions of Figure 2. The frequency distribution of δt(θ) (Figure 3) is skewed towards negative values and includes a few especially large magnitudes. The stronger temperature events tend to extend to higher levels on the tower and may not vanish at the top of the tower.

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Figure 3. Distribution of changes of the (a) 2 m v-component (m s−1), (b) wind direction (°), (c) temperature (K) and (d) vertical velocity variance (m2s−2) for the strongest 200 cold microfronts. This figure is available in colour online at wileyonlinelibrary.com/journal/qj

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With passage of the cold microfronts, the wind direction often shifts by more than 90° (Figure 3). The cold microfronts frequently occur with a shift from southerly flow to northerly flow, which apparently advects colder air past the tower. That is, the coldest air is expected north of the tower in the lowest part of the sub-basin (cold pool). Large temperature decreases, greater than 3 K, occur only with the onset of northerly flow (Figure 4). This reveals the strong directional dependence at this site, in spite of the weak local terrain variation. The weakest temperature decreases (Figure 4, right-hand side) correspond to either the onset of northerly flow or decreased southerly flow. Even with weaker temperature decreases, the percentage of northerly flow cases is much greater than occurs with the distribution of the wind directions for the entire experiment, which is predominately southerly flow. For a few of the weaker events, the flow reverses to northerly only for a few minutes after the cold microfront passage, such that the 10 min averaged wind after the microfront passage remains southerly. Since the prevailing southerly flow increases with height and the frequency of northerly flow decreases with height, the overall wind direction variability decreases with height.

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Figure 4. The 10 min averaged v-component at 2 m following the cold microfront passage, as a function of temperature decrease, δt(θ), at 2 m.

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Some of the cold microfronts lead to a large decrease of turbulence corresponding to a negative change in the vertical velocity variance (Figure 3). The colder air is characterized by only weak mixing. The minimal mixing may have led to the formation of colder air. At the same time, the greater stability in the cold air constrains the turbulence. Decreasing turbulence, surface cooling and increasing stratification could evolve together.

3.3. Composited structure

The composited time structure of the 200 samples of strongest temperature decrease reveal more details of the time dependence (Figure 5). The ratio of the within-sample variance of the composited structure to the between-sample variance, Rc (Eq. (14)), is 1.3 for temperature, about 0.53 for the v-component and substantially less for the other variables. Both the variance explained by the composited structure as well as the between-sample variations seem important. The relative ‘standard error’ (Eq. (15)) is 0.06 for temperature and about 0.10 for the v-component. Since the sampling is based on temperature and not the v-component, the structure of the v-component seems particularly important, and again reflects the strong directional dependence at this site.

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Figure 5. Composited structure of the cold microfronts for the 2 m v-component (green, m s−1), u-component (blue, m s−1), temperature (red, K) and vertical velocity variance (cyan, 10−1m2s−2), and the 30 m vertical velocity (black, 10−2m s−1). The sampling window means of the temperature have been removed.

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Maximum rising motion is found above the microfront with weaker rising motion following the microfront passage. Recall that this structure is based on 1 min averages and does not include small overturning events at or immediately behind the microfront. The parent eddy is characterized by cold rising air and warm sinking air. The corresponding conversion of kinetic energy to potential energy requires an external source of kinetic energy.

The composited structure at the 2 m level indicates that the u-component averages near zero both before and after the passage of the cold microfront, such that the systematic change of wind is mainly the reversal from southerly to northerly flow or weaker southerly flow after the microfront passage. The cancellation of the v-component resulting from averaging over the samples with both southerly and northerly flow after the microfront contributes to the weakness of the composited northerly flow following the cold microfront. The width of the microfrontal zone in the composite is more than 1 min, much more than typical widths for individual samples. The sampling technique and compositing process leads to some smoothing of the structure.

The magnitude of δt(θ) decreases rapidly with height and is relatively small above 10 m, as can be inferred from Figure 6. In contrast, δt(v) decreases only slowly with height across the tower layer (Figure 6) and shows no obvious phase shift with height. The sharpest gradient of v within the sampling window decreases rapidly with height. However, δt(v) decrease more slowly with height, because the velocity change is spread over a longer time period at higher levels (Figure 6). The implied depth of significant δt(v) is greater than the tower layer, even though the samples are selected based on the 2 m temperature. Since the depth of the velocity perturbation is significantly deeper than the depth of the temperature perturbation (Figures 6–7), the propagation of the cold microfronts may be induced by a deeper pressure disturbance. On some occasions, the v-component appears to be associated with wave-like phenomena with periods of 15 min or more that lead to formation of one or more microfronts.

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Figure 6. Composited structure at different levels for (a) temperature (K) and (b) v-component (m s−1) for the cold microfronts.

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Figure 7. Composited structure of temperature (K) before the cold microfront (lower curve) and after the cold microfront passage (upper curve). This figure is available in colour online at wileyonlinelibrary.com/journal/qj

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The composited northerly flow reaches a maximum depth of about 11 m immediately after the microfront passage and begins to weaken a few minutes after the microfront passage (Figure 6). For the strongest cold microfronts, the northerly flow is generally stronger and extends beyond the 10 min averaging period. The velocity disturbance is deeper such that δt(v) increases with height across the tower layer. In contrast, many of the weaker cold microfronts occur without a deeper velocity perturbation. The turbulent vertical velocity variance increases with height (Figure 6), as often observed for weak-wind strongly stratified conditions.

While the time structure observed at a fixed point cannot be used to infer horizontal structure, the sharp time changes are most likely due to advection, as in the interpretation above. For example, the rapid decrease of temperature at the tower is much too large to be explained by local cooling due to turbulent and radiative flux divergence. Artificial fog releases at a number of sites identify horizontal advection behind common microfronts (http://www.submeso.org).

3.4. External modes and spatial coherence

The microfronts often occur almost simultaneously at the main tower site and the other two eddy-correlation stations. The three eddy-correlation sites form a distorted triangle with sides ranging from 1 to 3 km, that allows crude estimation of the disturbance propagation velocity. The phase velocity appears to be often on the order of tens of m s−1, as sometimes observed by Rees et al. (2000). Such propagation velocities are much faster than the northerly advective velocity, normally less than 1 m s−1. Therefore, the microfronts are not associated with advection of cold air on the scale of kilometres across the three-station observational domain. However, local advection is apparently induced on the microscale by the propagating disturbances. Thus, the actual horizontal advection might be restricted to a small local region on the time-scale of the passage of the external disturbance. For example, transport by northerly flow of 0.3 m s−1 for 10 min corresponds to a transport distance of 180 m. A dense observational network would be required to determine the actual horizontal scale of the advection.

The disturbed wind field can lead to microfront formation through horizontal convergence and advection in the presence of a semi-stationary horizontal temperature gradient, as would occur with horizontal transport of air from a cold pool located to the north of the tower site in the lowest part of the sub-basin. The strong dependence of the cold microfronts on wind direction suggests that the semi-stationary temperature gradient is important much of the time. Southerly cold air drainage is uncommon at this site implying that any cold air drainage from higher terrain toward the south is warmer than the air in the basin and, therefore, flows above the surface inversion (cold pool). The role of external propagating modes as a catalyst for the cold microfronts would explain why the microfront occurrence and strength could not be related to local variables measured at the tower.

As an alternative explanation, transient horizontal temperature gradients could be generated by the wind disturbance itself. For example, rising motion in the cold stratified air (Figure 5) leads to cooling. Rough calculations of vertical advection using the 5 m composited vertical velocity and using the mean stratification in the lowest 10 m indicate that the observed rising motion in the stratified cold air would produce a cooling of about 2 K after 10 min. Vertical velocity estimates are subject to large errors and the Lagrangian time-scale over which a fluid element is affected by such vertical advection is not known. However, vertical advection cannot be ruled out as a non-stationary contributor to the heat budget of the cold air.

4. Other local events

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Cold microfronts
  6. 4. Other local events
  7. 5. Sensitivity to sampling criteria
  8. 6. Conclusions
  9. Acknowledgments
  10. References

We now select events corresponding to warm microfronts, wind-direction shifts, wind gusts and solitary waves. These events are not independent. For example, the wind-direction shifts are often cold microfronts.

4.1. Warm microfronts

The northerly cold microfronts examined above are generally advancing against the ambient southerly flow. These events contrast with the warm microfronts where the flow is generally southerly before and after the microfront, the prevailing wind direction for this site. The frequency distribution of changes across the 200 strongest warm microfronts (Figure 8) indicates a preference for increasing southerly flow and increasing turbulence after the microfront passage.

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Figure 8. As Figure 3, but for the strongest 200 warm microfronts. This figure is available in colour online at wileyonlinelibrary.com/journal/qj

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Sudden warming due to cloud elements is not a significant mechanism at this site. The increased turbulence after the passage is consistent with stronger downward mixing of warmer air with higher southerly momentum. This behaviour could be initiated by a mixing event rather than horizontal advection. The warm microfronts are associated with rising motion in the colder air ahead of the microfront and sinking motion in the warm air behind the microfront, requiring an external source of energy to maintain the circulation against conversion of kinetic energy to potential energy. The depth-scale of the temperature increase for the warm microfronts is similar to the depth-scale of the temperature decrease for the cold microfronts.

4.2. Wind-direction shifts

Common wind-direction shifts in the weak-wind stable boundary layer (Mahrt, 2008) strongly influence horizontal dispersion, but generally are not predicted by models. The wind-direction variability decreases with height, mainly due to the increase of the speed of the larger-scale wind with height. With extremely weak winds, large wind-direction shifts are almost continual and particularly sensitive to the choice of averaging time. We filter out these numerous shifts by arbitrarily imposing a minimum sampling window-averaged wind speed of 0.5 m s−1.

The 200 largest wind-direction shifts show a wide variety of signatures in terms of time and height structure, with a preference for cold microfronts and northerly flow behind the wind shift (not shown). Wind shifts are not correlated with vertical directional shear, suggesting that vertical mixing events are not the primary cause of the wind-direction shifts. The averaged vertical direction shear between 2 and 30 m is 3.5° (clockwise) in agreement with Ekman turning. However, this averaged vertical rotation of the wind direction is small compared to the between-event standard deviation of 44°. The structural difference between large clockwise and counterclockwise wind-direction shifts is not detectable. We conclude that large wind-direction shifts result from a variety of motion types, making the prediction problem difficult.

4.3. Gust microfronts

Microfronts in stratified flow can occur in very strong winds in the form of gust microfronts and wind-direction reversals, as generated for example by Kelvin–Helmholtz instability in Bora winds (Belušić et al., 2007). To identify gust microfronts, we selected 200 samples with the largest positive values of δt(speed), with no restriction on wind speed. This process selects primarily stronger wind cases with deeper structures compared to the above weak-wind microfronts. The gust microfronts are followed by stronger turbulence and slightly warmer air. The turbulence was greater behind the gust for all 200 events. The temperature response is limited by the generally weak stratification for windy conditions. The gust microfronts often correspond to a small clockwise shift from southerly flow to more southwesterly flow typically associated with downward turbulent transport of westerly momentum. In contrast to the other types of microfronts, the maximum rising motion occurs in advance of the gust, perhaps related to the pressure head induced by the gust (as depicted in Figure 11 below).

4.4. Solitary waves

The examination of solitary waves with little net change requires that the detection procedure (Eq. (12)) be applied to only a part of the sampling window, here a 4 min sub-window centred within the sampling window. This procedure will help impose the restriction of small net change. We use vertical motion as the detector variable and seek an updraught–downdraught pair. We apply the Haar transform to the sub-window. Application of a sine function defined between − π/2 and π/2, to emphasize solitary waves, captures most of the same events as sampled with the Haar function. We require that the magnitude of the net change of temperature change, δt(θ), is less than 0.5 K. This restriction imposes our working criterion that the solitary waves do not lead to significant net change after passage. This condition excludes 34% of the 200 cases with the largest magnitudes of δt(w). We have made no attempt to filter out solitary waves that are captured as the highest amplitude wave in a wave train of several cycles. Inspection of individual selected samples reveals that some of the captured solitary waves are the second and stronger oscillation of a two-cycle event.

For the case δt(w)> 0, the composited vertical velocity shows the expected downdraught–updraught couplet with an additional weaker updraught prior to the solitary event (not shown). The solitary event vertical velocity field is relatively independent of height, implying a disturbance that is much deeper than the tower layer. While the net temperature change is small, as required by the sampling criterion, the air is warmest at the centre of the event. The composited v-component (Figure 9(b)) is organized by a well-defined wave with a period of about 15 min and a relatively height-independent amplitude of 0.4 m s−1, even though the vertical motion does not show coherence on this scale. The solitary waves are systematically embedded at a preferred phase within the larger-scale structure of the horizontal wind field. The solitary waves also differ from the microfronts in that the u-component (cross-valley flow) is significantly perturbed.

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Figure 9. Vertical cross-section of (a) potential temperature (K) and (b) v-component wind (m s−1) for the composited solitary waves based on an increase of vertical velocity across the 4 min sub-sample window, as indicated by vertical arrows in (a).

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Selection of the solitary waves in terms of a decrease of vertical motion (δt(w)< 0), rather than an increase of vertical motion, yields similar structures. The solitary waves with δt(w)< 0 are also systematically embedded within larger-scale motions.

4.5. Contrasting the modes

Given the information on vertical motion at the top of the tower (Figure 10) and plots analogous to Figures 5 and 6 for each event type, the different modes are casually sketched in Figure 11. The cold microfronts (blue in Figure 10) are characterized by rising motion above the microfrontal passage with somewhat weaker rising motion on the cold-air side while sinking motion occurs in the warm air ahead of the front. Conversely, warm microfronts (red in Figure 10) show rising motion in the cold air ahead of the microfront and sinking motion in the warm air following the microfront passage. The gust microfronts lead to rising motion just ahead of the microfront, perhaps induced by positive pressure perturbation in advance of the gust. Consequently, the different types of solitary event are characterized by distinctly different vertical motion fields.

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Figure 10. Composited structure of vertical velocity (m s−1) at 30 m for the cold microfronts (blue), warm microfronts (red) and gust fronts (black).

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Figure 11. A sketch of the wind field for the different types of solitary events tenuously inferred from the tower time series. The temperature variation associated with the gust fronts is much weaker than that for the cold and warm microfronts. This figure is available in colour online at wileyonlinelibrary.com/journal/qj

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5. Sensitivity to sampling criteria

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Cold microfronts
  6. 4. Other local events
  7. 5. Sensitivity to sampling criteria
  8. 6. Conclusions
  9. Acknowledgments
  10. References

We now return to the class of cold microfronts to investigate the dependence on the sampling criteria.

5.1. Event threshold

To capture a greater fraction of the data, the number of events can be increased beyond 200 until there are no remaining pieces of the data as wide as the sampling window width. With a greater number of samples, the average magnitude of δt(ϕ) decreases as result of acceptance of weaker events. As an example, the fraction of the temperature variance explained by the cold microfront structure, RT, and the variance explained by the composited structure relative to the between-sample variance, Rc(T), both monotonically decrease with increasing number of accepted samples. The microfront structure for the weaker events is qualitatively similar to stronger microfronts, but no longer large compared to other superimposed structures.

5.2. Wind speed dependence

For this dataset, the Richardson number is strong inversely correlated with the wind speed, partly because skies are generally clear. The stratification is determined primarily by the wind speed. For higher wind speeds > 3 m s−1, the cold microfronts are characterized by a deeper structure compared to the weak-wind case < 3 m s−1, with smaller change of wind direction and smaller more diffuse temperature decrease. Imposing stricter restrictions on the maximum wind speed to form a very weak-wind sub-class, such as < 1.5 m s−1, does not lead to significant qualitative changes from the above weak-wind subclass < 3.0 m s−1.

5.3. Dependence of vertical scale on sampling window width

The dependence of the flow structure on the time-scale (sampling window width) is now examined in terms of the composited δt(θ) as a function of height for the 200 strongest cold microfronts. The depth-scale for δt(θ) is determined from fitted profiles as the level where δt(θ) decreases to 1/e of its 2 m magnitude based on the 200-sample composite (Figure 12, circles). This depth-scale is computed independently for each sampling window width. The above calculations may underestimate the depth-scale because of phase change with height, although the composited data show no significant change of the phase of the microfront or its parent eddy with height.

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Figure 12. Dependence of the vertical depth-scale of the temperature change (°) and vertical depth-scale of the change of the v-component scaled by the mean wind speed (+), as a function of the sampling window width. The depth-scale for the v-component without scaling by the wind speed is too deep to estimate from the tower data. This figure is available in colour online at wileyonlinelibrary.com/journal/qj

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The depth-scale of the temperature change increases systematically with increasing sampling window width (Figure 12), consistent with the expectation that circulations with longer time-scales occupy deeper layers. Estimation of the depth for sampling window widths greater than 60 min involves tenuous extrapolation above the 30 m tower layer. The time change of the v-component, δt(v), decreases too slowly with height to estimate the 1/e decay depth. Even though the amplitude of the velocity perturbation deceases with height, the time-scale of the velocity change increases with height; that is, the velocity change occupies more of the sampling window with increasing height. We therefore normalize δt(v) with the averaged value of the v-component over the sampling window. The normalized time change of the v-component decreases with height faster than the decrease of un-normalized δt(v). However, the depth-scale is still greater than the tower depth for sampling window widths greater than 20 min and is almost twice the depth of the temperature change. Since the stratification decreases with height, the temperature response decreases with height more rapidly than the momentum response. The temperature field is more tied to surface cooling while the momentum response is presumably generated by pressure disturbances over a deeper layer. Blumen (1984) also observed that the velocity perturbation extended much deeper than the depth of an advancing drainage wind.

6. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Cold microfronts
  6. 4. Other local events
  7. 5. Sensitivity to sampling criteria
  8. 6. Conclusions
  9. Acknowledgments
  10. References

The above study examined the time–height structure of common nocturnal microfronts and other solitary events on scales of tens of minutes that include cold and warm microfronts, large wind-direction shifts, gust fronts and solitary waves. To emphasize weak winds, most of the analyses were confined to nocturnal cases with 2 m wind speeds less than 3 m s−1. Each class of events is associated with large within-class variation of structure. The wide variety of flow structures on scales of minutes or tens of minutes in the nocturnal boundary layer is an important conclusion of this work. In fact, wave trains and microfronts are, to some degree, prototype modes; sub-meso motions typically show structure in between these two types of motion.

The cold microfronts are generally propagating against the ambient flow at this site leading to rising motion above the microfront. In contrast, the warm microfronts generally correspond to flow acceleration in the ambient wind direction with increased turbulence in the warmer air behind the microfront. Both cold and warm microfronts are associated with sinking warm air and rising cold air, suggesting that external energy is required to generate or maintain these thermally indirect circulations, as opposed to self-generated density currents. The vertical extent of many of the cold microfronts is about 10 m or less and usually less than the 30 m tower depth. The cold microfronts are often, but not always, associated with much deeper perturbations of the velocity field of unknown origin. The perturbation pressure field of such disturbances might be an external source of energy for advancing the cold air against the ambient flow and maintenance of kinetic energy, and might also explain the inability to predict microfronts in terms of local variables. Deeper disturbances could not be detected with all of the cold microfronts and the wide variety of structures of the parent motions prevent crisp classification.

Inclusion of data from two other towers to form a distorted triangle indicates that most of the microfronts are associated with disturbances that propagate much faster than the weak surface flow. Evidently, the cold microfronts viewed at a given station result from local horizontal temperature gradients and surface wind-direction reversals that are often induced by the rapidly propagating disturbances.

Gust microfronts were selected without restrictions on wind speed and induce rising motion immediately ahead of the microfront, followed by warmer more turbulent air after microfront passage. The solitary waves were selected in terms of small net change and may not conform to rigorous definitions of solitary waves. The solitary waves in this study are found to be systematically embedded within larger-scale wave motions.

Analysis of several other datasets, not included in this study, indicate that the microfronts are common at all of the sites, but show systematic differences between sites, particularly with respect to the dependence of the events on wind direction. The current study failed to identify the dynamics of the microfronts partly due to lack of sufficient spatial information. More detailed spatial information based on a dense sonic anemometer array and improved three-dimensional remote sensing of the wind field would allow evaluation of the frontogenesis equation and more meaningful estimation of the phase velocities of the propagating modes. Observations over a deeper layer would allow additional investigation of the deeper disturbances in the wind field that accompany many of the shallow microfronts at the surface.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Cold microfronts
  6. 4. Other local events
  7. 5. Sensitivity to sampling criteria
  8. 6. Conclusions
  9. Acknowledgments
  10. References

T he important comments of Jielun Sun, Danijel Belušić and the reviewers are gratefully acknowledged. This material is based upon work supported by NSF grant ATM-0607842 and ARO contract W911FN05C0067.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Cold microfronts
  6. 4. Other local events
  7. 5. Sensitivity to sampling criteria
  8. 6. Conclusions
  9. Acknowledgments
  10. References