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  • View in gallery

    SNR low altitude mode at North Rose, NY, 11 Jan 1990. Darker shades represent lower SNR. Frontal passage occurred just prior to 2000 UTC

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    SNR low-altitude mode for North Rose, NY, 12 Jan 1990. Major single-banded activity occurred over the lake between 0800 and 1700 UTC

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    SNR low-altitude mode for North Rose, NY, 13 Jan 1990. Multiple-banded snowbands occurred to the southeast of the lake during this time. The intense gradient at 1900 UTC is an artifact of profiler malfunction

  • View in gallery

    SNR low-altitude mode for North Rose, NY, 14 Jan 1990. An unexpected single snowband developed to the east of the profiler, southeast of the lake prior to 0900 UTC. The top of the CBL is seen as a local maximum in SNR at 2-km AGL, decreasing through 1400 UTC

  • View in gallery

    SNR low-altitude mode for North Rose, NY, 25 Feb 1990. Multiple snowbands developed southeast of the lake after trough and shortwave passage near midrecord. Lower SNR is typical of the multiple-band events observed

  • View in gallery

    SNR low-altitude mode for North Rose, NY, 28 Feb 1990. Multiple snowbands developed southeast of the lake after frontal passage. Increase in SNR around 1800 UTC is related to development of snowbands near the profiler, and increased CBL depth

  • View in gallery

    Alpha (α2r) for North Rose, NY, 11–14 Jan 1990. Values near unity indicate the contribution to C2n are largely due to moisture variation in the mixed layer

  • View in gallery

    Rawinsonde derived specific humidity (q) for North Rose, NY, 12–13 Jan 1990. Systematic drying of the mixed layer is noted after 2100 UTC 12 Jan

  • View in gallery

    Humidity structure function parameter [log(C2q)] for North Rose, NY, 11 Jan 1990, prior to and after frontal passage

  • View in gallery

    Humidity structure function parameter [log(C2q)] for North Rose, NY, 12 Jan 1990. Large values between 1800 and 2100 UTC correspond to the development of shoreline band activity near the profiler

  • View in gallery

    Humidity structure function parameter [log(C2q)] for North Rose, NY, 13 Jan 1990. Intense gradients near 1900 UTC are due to a profiler malfunction

  • View in gallery

    Humidity structure function parameter [log(C2q)] for North Rose, NY, 14 Jan 1990. Local maxima between 1500- and 2000-m AGL, 0000 through 1400 UTC indicate the top of the CBL

  • View in gallery

    Rawinsonde derived specific humidity (q) for North Rose, NY, 1700 UTC 28 Feb 1990

  • View in gallery

    Humidity structure function parameter [log(C2q)] for North Rose, NY, 28 Feb 1990. Development of a CBL is indicated by the local maxima at 1500–2000-m AGL, between 0500 and 2000 UTC

  • View in gallery

    Humidity structure function parameter [log(C2q)] for North Rose, NY, 25 Feb 1990. Profiler performance was low during this event

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Moisture Analysis of a Type I Cloud-Topped Boundary Layer from Doppler Radar and Rawinsonde Observations

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  • 1 Department of Environmental and Atmospheric Sciences, Creighton University, Omaha, Nebraska
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Abstract

Moisture data from radar and rawinsonde observations during three lake-effect snow events are analyzed to determine entrainment rates. Type I convective boundary layers, which are those driven largely by surface heating, typically accompany these storms. Gathered during the winter of 1990, the data are a subset from the Lake Ontario Winter Storms (LOWS) Project, which deployed a mesoscale network of sensors.

Doppler wind profiler signal-to-noise ratio (SNR) data are used to derive humidity structure function parameter (C2q) time–height series analysis, which are then compared to rawinsonde specific humidity (q) plots. Visual comparison of log(C2q) and q analysis indicated a strongly positive correlation. Radar-derived humidity analysis is used to estimate the depth of the Type I (driven by surface heating), cloud-topped boundary layer (CTBL), which corresponded well with results from LOWS rawinsonde data. Calculations of the contribution of (C2q) to the refractive index structure parameter (C2n) showed the humidity correction factor (α2r) to range from 1.02 to 1.04 within the CTBL, consistent with previous findings for Type II CTBLs. A comparison of entrainment rates, computed via two different methods, were in agreement.

Corresponding author address: Dr. Richard Penc, Department of Environmental and Atmospheric Sciences, Creighton University, 2500 California Plaza, Omaha, NE 68178. Email: rspenc@creighton.edu

Abstract

Moisture data from radar and rawinsonde observations during three lake-effect snow events are analyzed to determine entrainment rates. Type I convective boundary layers, which are those driven largely by surface heating, typically accompany these storms. Gathered during the winter of 1990, the data are a subset from the Lake Ontario Winter Storms (LOWS) Project, which deployed a mesoscale network of sensors.

Doppler wind profiler signal-to-noise ratio (SNR) data are used to derive humidity structure function parameter (C2q) time–height series analysis, which are then compared to rawinsonde specific humidity (q) plots. Visual comparison of log(C2q) and q analysis indicated a strongly positive correlation. Radar-derived humidity analysis is used to estimate the depth of the Type I (driven by surface heating), cloud-topped boundary layer (CTBL), which corresponded well with results from LOWS rawinsonde data. Calculations of the contribution of (C2q) to the refractive index structure parameter (C2n) showed the humidity correction factor (α2r) to range from 1.02 to 1.04 within the CTBL, consistent with previous findings for Type II CTBLs. A comparison of entrainment rates, computed via two different methods, were in agreement.

Corresponding author address: Dr. Richard Penc, Department of Environmental and Atmospheric Sciences, Creighton University, 2500 California Plaza, Omaha, NE 68178. Email: rspenc@creighton.edu

1. Introduction

Much of the theory behind radar observations in clear air comes from turbulence studies. Researchers in the 1940s through the early 1960s laid the foundation for the stoichaotic description of the atmospheric turbulence. From the result, clear-air radar observation theory was refined in the late 1960s through the early 1990s. Operational applications rapidly followed theoretical developments. It was discovered early that the turbulent mixing of the atmosphere causes gradients of temperature, moisture, and pressure, and hence gradient of the refractive index. Radars of sufficient wavelength are capable of sensing these refractive index inhomogeneities, as they are almost always present within the turbulent atmosphere below the stratopause.

This paper presents a study of the moisture profiles within a Type I cloud-topped boundary layer (CTBL) using wind profiler and rawinsonde data. It closely mirrors the study of the moisture structure of a Type II CTBL conducted by White et al. (1991) off southern California. A Type II CTBL is defined as a convective boundary layer primarily driven by radiative cooling at cloud top (with nearly thermal equilibrium at the sea surface). The Type I CTBL is one driven largely by heating from below as cold air moves over relatively warm water (Agee and Hart 1990). The data utilized comes from the Lake Ontario Winter Storms (LOWS) Project, a detailed investigation of mesoscale motions within Lake Ontario lake-effect snowstorms (LESS) during the winter of 1990 (Reinking et al. 1993). In the LESS environment, surface fluxes of moisture and temperature drive convection that lead to localized snowfall events. The LOWS dataset includes in situ measurements of the planetary boundary layer using rawinsondes, instrument towers, and surface observations to increase knowledge of dynamic motions and meteorological variables within the mesoscale environment. Doppler radar wind profilers were also a key remote-sensing tool, having the advantage of increased spatial and temporal sensing. From the radar reflectivity and spectrum width data, important meteorological information can be derived. Reflectivity data caused by refractive index irregularities in clear air (Bragg scattering) will be used in this study to derive entrainment rates. These rates will be analyzed in regards to boundary layer growth at one wind profiler site. Comparisons will be made with the results of Type II CTBL studies and with previous conclusions from the 1990 LOWS study.

2. Data

Lake Ontario LESS events are unique. There is a well-defined snowbelt as a result of the lake's length and orientation to the prevailing winds, and due to the orographic enhancement effects of rising terrain on the leeward (in this case, eastern) portion of the lake. Single-band snowstorms frequent Lake Ontario and Lake Erie, but are infrequent on the other Great Lakes. However, Lake Ontario is much deeper than Lake Erie, helping to maintain large areas of ice-free lake surface and potential for heat and moisture fluxes into the boundary layer throughout most winters. On the other hand, Lake Erie's lake-effect snow season is considerably shorter, as ice often covers most of the lake surface by midwinter.

a. Lake-effect snowstorms

Primarily a mesoscale phenomena, lake-effect storms are, however, a complex interaction of synoptic scale, mesoscale, and microscale. Lake-effect snow events develop when the atmosphere is destabilized as postfrontal Arctic or polar air passes over a relatively warm lake surface. This causes a positive flux of heat and moisture into the atmosphere producing convection and thickening of the boundary layer through entrainment. Single or multiple parallel bands of precipitation form, which can produce localized heavy snowfalls. Wind speed and direction play an important role in determining band types and location. Advection lengthwise along the lake tends to produce intense single bands, while all other wind directions produce weaker multiple bands. Wind speed and direction can affect the structure of the convection as 2-d (strong) to 3-d (weaker flows). Additionally, orography serves to enhance vertical velocities and increase snowfall amounts. The primary and secondary factors which influence lake-effect snow development are listed in Table 1.

1) Lake-effect storm types

Single- or double-banded storms form parallel to the winds aloft and aligned along the long axis of the lake due to organized convergent flows that serve to force convection into the center of the lake. Typically, storm dimensions are 2–20 km wide and 50–200 km long, with cloud tops to 4 km (Peace and Sykes 1966). The single-banded storm is the most intense of lake-effect snow storms, capable of producing heavy localized snowfalls.

Multiple-banded storms occur when the winds are aligned along the short axis of the lake. Normally these storms are 5–80 km long with aspect ratios ranging from 5:1 to 12:1 (Peace and Sykes 1966). The boundary layer remains relative shallow with 1–2 km cloud tops. The bands drift with the wind at small angles from the mean wind, generating widespread, but light, precipitation.

2) Thermal instability indicators

Operationally, the Collier index1 is used to determine potential for and severity of lake-effect snow events, measuring the degree of thermal instability between the lake surface and the lower troposphere (Niziol 1987). Additionally, it has been noted that a deepening of the boundary layer is almost always associated with the events (Penc 1995). Boundary layer depths of 3–4 km are seen with the most severe storms (Niziol 1987). Numerical modeling studies have shown heating and moistening of the atmosphere are responsible for increasing boundary layer depth by hundreds of meters (Lavoie 1972). During LOWS, changes in the height, as well as the strength of the capping inversion were indicated to be the most important factors in lake-effect snowband intensity. LOWS researchers found the intensity of the convection was more closely related to the depth of the convective mixed layer than to the degree of lower atmospheric thermal instability. The greatest snowfalls occurred during single-band storms on 12 and 14 January 1990, where convective boundary layer (CBL) heights ranged between 2.5 and 4 km (Penc 1995).

b. Lake Ontario winter storms (LOWS)

The Lake Ontario Winter Storms project was conducted from 5 January to 1 March 1990 to demonstrate and evaluate mesoscale observation and forecasting techniques applicable to location-specific lake-effect storms and freezing rain. In order to resolve mesoscale features, an array of six specialized remote sensors (a dual-polarization short-wavelength radar, microwave radiometer, radio acoustic sounding system, and three wind profilers) were deployed, as well as a mesonet providing surface wind, temperature, and humidity measurements. Researchers from various universities, government agencies, and private consulting firms participated in the project as summarized in Reinking et al. (1993).

1) Meteorological conditions

Due to warmer than normal air temperatures during LOWS, occurrences of lake-effect snow events were below normal. To establish the scope of this study, lake-effect snow datasets were analyzed for the single-band storms of 11–13 January and 14 January, and the multiple-band storm events of 25–26 February and 27 February–1 March. These data encompassed the four “marginal” or greater episodes, as described by Penc (1995), and included subhourly radar and rawinsonde data collected during LOWS intensive observation periods (IOPs).

2) 11–14 January 1990

After the passage of an occluded front between 2100 and 2200 UTC on 11 January, the synoptic situation was favorable for development of lake-effect snow. During 12 January, an intense, 980-mb surface low, approximately 500 km north of Lake Ontario, tracked east producing west-to-southwest flow along the major axis of the lake from 0000 to 1800 UTC. Aloft at 500 mb, a broad trough also produced westerly flow. Surface air temperatures ranged from −1° to −3°C with the Collier index remaining in the conditional category. Deep cold-air advection along with moderated positive vorticity advection produced destabilization that supported development of a stationary single snowband over the lake. Four snowbands formed over the center portion of the lake beginning around 0130 UTC, with the final snowband dissipating around 1700 UTC. The snowbands formed over the warmest part of the lake (near 4°C) and moved inland over the eastern shores of the lake producing up to 80-cm snowfall amounts.

At 0000 UTC on 14 January, the surface low had moved to a position off the Canadian maritimes and was deepening, while a significant shortwave trough stretched from James Bay toward Minnesota. Surface air temperatures ranged from −13°C northwest of the lake to −6° to −9°C southeast of the lake. The Collier index remained in the conditional category, but approached moderate. The approaching shortwave trough and broadening longwave trough led to increased westerly flow and longer fetch over Lake Ontario. Snowfall with this event was confined to the southeast shore of the lake with accumulations up to 15 cm. Visibilities dropped to zero at Oswego, New York, at 0600 UTC, with occasional thunder and lightning.

Of note is the possibility that some of the snowfall during these two events may be attributed to synoptic forcings, as well as to lake-effect snow conditions. The resulting snowfall may be referred to as lake-enhanced snow. However, for the scope of this study, only the lake-effect factors will be considered.

3) 25–26 February 1990

Multiple lake-effect snowbands occurred after a west–east-oriented surface trough passed over the southern portion of the lake at approximately 1200 UTC on 25 February. Snow fell over the entire region just prior to the trough passage, which was then followed by light lake-effect snowfall for a 12-h period over the southeastern portion of the lake. A tight pressure gradient providing strong northwest winds after the passage of the trough advected in very cold surface temperatures (−20° to −26°C). Despite a short fetch, thermal instability was great enough to produce moderate to extreme Collier indices. By 1500 UTC, multiple north–south bands were seen over the southeastern portion of the lake and with a moderate burst of snowfall at the North Rose radar site. As the boundary layer winds continued backing, snowband orientation changed through northwest–southeast, and eventually northeast–southwest by 0300 UTC on 26 February. Strong surface to 850-mb ridging was evident by 0000 UTC on 26 February causing rapid slackening in the pressure gradient and decreasing cold air advection. By 1200 UTC, only a solitary weak dissipating snowband remained. In general, the lake-effect snowfall totals were very light in this short-lived event. Only 4 cm accumulated at North Rose, directly attributed to lake effects.

4) 27 February–1 March 1990

A cold front approached on 27 February and passed over the lake around 0000 UTC on 28 February, after which multiple snowbands developed. At 1200 UTC on 28 February there was high pressure centered over the upper Midwest producing northwesterly flow over the Great Lakes region. Surface temperatures ranged from −12°C north of the lake to −8°C southeast of the lake while 850-mb temperatures were −17° to −18°C, leading to a moderate Collier index. With a 500-mb trough providing westerly flow aloft, little directional shear was present in the troposphere. By 1400 UTC on 28 February, radar showed multiple snowbands extending inland on the southeastern shore of Lake Ontario. By 1700 UTC radar echoes ceased. More weak banded echoes resumed at 2200 UTC, then dissipated by 0400 UTC on 01 March. Snowfall along the southeastern portion of the lake was >5 cm with a maximum of 15 cm (Penc 1995).

c. Radar specifications and siting

Specifications for the Pennsylvannia State University 404-MHz wind profiler are listed in Table 2. The radar data analyzed were retrieved at North Rose, New York, on the southeast corner of Lake Ontario approximately 5 km inland from the lake shore. From this location, measurements could be taken within and near single and multiple-banded snow events. Multiple-band snow events frequent the North Rose site, whereas single-band events often occur farther north, allowing the North Rose site to provide measurements of parameters associated land-to-lake convergence areas. The data were recorded on magnetic media by the operators of the 404-MHz UHF Doppler wind profiler provided by the Pennsylvannia State University (PSU). This profiler used a three-beam system with two orthogonal off zenith and one vertical. Data archived included returned signal power, radial velocity, and wind spectral width, which are the zeroth, first, and second spectral moments, respectively. Measurements were made in high-altitude mode (east, north beams) followed by low-altitude mode (vertical, east, and north beam) every 3.5 min. For a radar pulse of 150 m, the data are oversampled to 100 m. During intensive observation periods, the subhourly information was recorded for all range gates (Penc 1991). For the scope of this study, the subhourly signal-to-noise ratio (SNR) data from the low-mode vertical beam was used.

1) Data processing and quality control

In order to accurately calculate atmospheric variables from radar reflectivity data, the radar must be properly calibrated. The PSU 404-MHz wind profiler was calibrated based comparison with Lyman-α moisture measurements at Otis Air Force Base in southeastern Massachusetts, 11 months before the LOWS project began. Calibration used data from an aircraft-mounted Lyman-α hygrometric sensor that was compared with radar-deduced humidity gradients. This radar is the same one used by White et al. (1991) in the study of humidity profiles in a Type II CTBL.

Signal processing is largely based on techniques developed at the National Oceanic and Atmospheric Administration Wave Propagation Laboratory (Strauch et al. 1984). Before archival, the raw data are filtered using a series of steps. First is a coherent integration or time domain averaging, which reduces the amplitude of components outside the maximum frequency measured. Next is a spectral or incoherent averaging, which improves the detection of the spectral peak by smoothing out the noise floor. For quality control, data below −18 dB are rejected. A 1-2-1 time–height smoothing was employed. In addition to the aforementioned filtering, data quality control was achieved by periodic monitoring of the SNR and comparison with collocated rawinsondes.

3. Remote sensing theory

Radar returns in clear air result from inhomogeneities in the refractive index caused by turbulence. The intensity of the return radar caused by the inhomogeneities can be used to derive temperature and humidity values. In the study of propagation of electromagnetic energy through a turbulent atmosphere, the refractive index structure parameter is the key to analyzing returned radar backscatter power (Pr) in terms of the refractive index (n), temperature (T), and moisture (specific humidity, q) analysis. It has been shown that the returned backscatter power received by the radar is proportional to the refractive-index structure parameter (VanZandt et al. 1978). The theory behind this remote sensing is presented.

a. Turbulence parameters

Following Fairall (1991), consider some atmospheric variable X(r) as a function of location r. The structure function Dx(d) of X is defined by
i1520-0426-18-12-1941-e1
where d denotes a separation distance and the overbar denotes an ensemble average. Assuming isotropic turbulent fluctuations within the inertial subrange, the structure function parameter can also be expressed in the 2/3-law form as (Tatarski 1961):
C2xDxdd2/3
For the refractive index (n),
Dndnrdnr2C2nd2/3
where n′ indicates perturbations in the spatial mean of the refractive index.

b. The radar equation

The radar equation can be expressed as a relation of backscattered power at the radar antenna Pr to the average reflectivity per unit volume η of the target (Battan 1973):
PrPtG2λ2θ2π2r2
where Pt is the radar transmitted power, G is antenna gain, λ is the radar wavelength, θ is the radar beamwidth (full-width at half-maximum) in radians, h is the transmitted pulse length, and r is the range to the target. From the radar equation a value of η can be obtained, since Pr can be measured and the remainder of the radar equation parameters known. Assuming the refractive index fluctuations are a result of isotropic turbulence in the inertial subrange and that the radar half-wavelength λ/2 lies within the inertial subrange, the reflectivity can be expressed as (Ottersten 1969)
ηC2nλ−1/3
From this expression, it can be observed that for radar wavelengths of 10 cm or more, the structure constant C2n is directly proportional to the radar reflectivity η. Radars of shorter wavelengths are sensitive to smaller scales, and therefore may be observing contributions of dissipation by molecular diffusion, depending on the energy dissipation rate (Ottersten 1969).

c. Humidity structure function parameter (C2q)

The radio refractive index is a function of temperature, humidity, and air pressure, where within the PBL, the effects of air pressure can be ignored. Refractive index fluctuations can be expressed as a linear combination of fluctuation in temperature and humidity. Equations (1) and (2) were used to obtain the scalar structure function parameters expressed as
C2n−4PT22C2qα2r
where C2q is the humidity structure function parameter (Wesely 1976) and
i1520-0426-18-12-1941-e7
In these expressions, the quantity (α2r − 1) gives the deviations from the pure moisture dominated C2n, C2T is the temperature structure function parameter, rTq is the temperature-moisture correlation coefficient, and
aqT
(Fairall 1991). Contributions of C2T and C2q to C2n were investigated by Wesely (1976). Within the lower troposphere, he found C2q dominated. VanZandt (1978) also extended this result above the boundary layer to a few kilometers of the troposphere based on a rawinsonde, radar, and model data correlation study. Above a few kilometers and into the ionosphere, C2T is the primary contributor to C2n. Exceptions within the PBL for C2q domination may exist in extremely dry and strongly convective atmospheres. Therefore, α2r = 1 for most marine and continental PBLs in the Tropics and midlatitudes.
Following White et al. (1991), after rearranging (2.6) in terms of C2q, substituting (5) into (6), and where T = 268 K, P = P0e(−z/H) is the pressure in millibars, z is the altitude in kilometers, P0 = 1000 mb, and H = 8 km yields
C2q3T2P2α−2rηλ−1/3
From this equation, the turbulent humidity structure of the atmosphere can be calculated. In order to relate η to a quantity measured by the Doppler radar we use the reflectivity equation given by VanZandt et al. (1978):
i1520-0426-18-12-1941-e11
where c = 2.998 × 108 m s−1 is the speed of light in a vacuum, k0 = 1.3803 × 10−23 J mol−1 K−1 is Boltzmann's constant, R is the range, and the remaining parameters are listed in Table 3.
Combining (10) with (11) and substituting values from Table 3 gives the form of the C2q equation used in this study:
C2q−15T2P2α−2rR2SNR/10
where SNR is now conveniently in decibels (dB), as it was recorded during the four LOWS IOPs used in this study.

4. Data analysis procedures

A number of steps were taken to organize the raw radar and rawinsonde data into a format suitable for computational and visual analysis. In order to compute entrainment, C2q values had to be derived from the raw radar data. To compute moisture/temperature contributions to C2q, α2r must be derived from rawinsonde data. For convenience sake, personal computer–based display and spreadsheet software were used.

a. Radar data

Information from each beam (north, south, and vertical) and mode (low, high) that was recorded every 3 min (subhourly data). The subhourly data incorporated raw spectra and moments tables, consisting of the following parameters in tabular form by range gate: horizontal velocity, returned power, noise, SNR, and spectral width. In this study, only the SNR fields from the moments tables for the vertical beam were required for computations and analysis. Additionally, the higher-resolution low range mode data was desired as the boundary layers in the study remained below the low mode top range gate (2600 m). Finally, a neural network algorithm (Clothiaux et al. 1994) was used to separate ground clutter and precipitation peaks in the spectra from the clear-air returns.

Equation (12) was applied to the original SNR data to obtain C2q and log(C2q). Next a 1-2-1 smoothing was applied to the log(C2q) grids and then plotted.

b. Rawinsonde data

Raw rawinsonde data were used to determine temperature and moisture contributions to C2n and combined with log(C2q) values to obtain entrainment velocities (we). Sparse linear data interpolation was necessary to maintain consistent height data, however, because the resolution of the sounding data (∼50 m) is significantly better than the radar data in low mode (∼150 m), there should be little error injected into the entrainment computations. Thermodynamic properties were derived from the original rawinsonde data.

c. α2r calculations

To accurately assess the individual temperature and humidity structure parameter contributions, α2r must be estimated using (12), as the quantity (α2r − 1) gives the deviation from pure moisture dominated C2n. It is generally agreed upon that α2r is near unity in the nonconvective PBL. However in the LOWS cases studied, the PBL is highly convective, therefore a detailed analysis was required using sounding data. A method from Burk (1981) was adapted for determining relative contribution to C2n using the following equation, which is another version of (7):
i1520-0426-18-12-1941-e13
where A is a coefficient in microwave refractivity (77.6 × 10−6 K mb−1), C is a coefficient in microwave refractivity (0.375 K2 mb−1), p is pressure (mb), T is absolute temperature, e is vapor pressure (mb), ɛ is the molecular weight of water/dry air (0.622), ρ is the density of air, and r = Δqθυ across the interfacial layer. To obtain the changes of specific humidity and virtual potential temperature at a specific height, gradients were calculated from rawinsonde data using respective values immediately below and above the layer in question. All computations were accomplished on spreadsheets from which time–height series graphs were constructed and analyzed.

d. Entrainment velocity (we) calculations

Entrainment is the mixing down of less turbulent air into the PBL, thereby enhancing boundary layer growth (Stull 1988). The entrainment velocity is therefore one of the key parameters to evaluate interactions occurring in the inversion near the cloud tops. After applying the moisture deviation from (14) to C2q values obtained from (12), entrainment values can be calculated following Wyngaard and LeMone (1980):
weθυ1/3C2qq2−1
evaluated at the middle of the interfacial layer where θυ is the virtual temperature, Γ is the lapse rate of θυ above the inversion, Δ denotes changes across inversion, and ɛ is the rate of dissipation of turbulent kinematic energy for cloudy conditions (1.0 × 10−3 m2 s−3). The base and the top of the inversion were taken to be the span of the lowest temperature inversion identified in virtual temperature profiles and/or visual analysis of moisture profiles, and Γ was calculated for the first 1000 m above the inversion.

5. Interpretation of data

In order to obtain reliable estimations of the height of the convective boundary layer and entrainment velocity from the radar data, accurate moisture profiles were needed. The radar refractivity observed by the profiler is proportional to gradients of moisture and temperature. It has previously been determined that in Type II CTBLs, the radar reflectivity of clear air is primarily dependent upon moisture contributions (Fairall 1991). The humidity structure function parameter serves as a relative measure of these gradients of turbulent mixed moisture and can be calculated from radar reflectivity data. Since it is known that moisture generally decreases with height and the moisture gradients are largest at the top of the CTBL, time–height graphs of log(C2q) values can be used to monitor CTBL depths. In order to ensure this relationship is valid, either a parameterization concerning the contributions of moisture to the index of refraction must be made or a calculation from rawinsonde data. The radar humidity data have the temporal advantage of observations every 3.5 minutes, whereas rawinsondes were launched at various frequencies (1–5 day−1). However, in the vertical, the rawinsonde's humidity data resolution was 50 m, compared with 150 m for the radar.

SNR time–height series data appears in Figs. 1–4 for the 11–14 January single-band events, and in Figs. 5 and 6 for the 25–26 February and 28 February–1 March multiple-band events. Not surprisingly, the SNR generally decrease with height, with a few exceptions. One major exception is in Fig. 3 for 13 January, where the radar malfunctioned for a short period around 1900 UTC. Weaker returns generally were noted during the multiple-band events largely due to the limited moisture within the CBL. Without the known temperature and moisture contributions to the refractive index, other direct interpretations as related to convective boundary layer features are premature. Therefore, the indepth discussion of radar data will be later in this section.

a. α2r calculations

As previously stated, the quantity (α2r − 1) gives the deviation from pure moisture dominated C2n. Studies of nonconvective PBLs have shown α2r near unity. Model studies have produced values for α2r near unity for cloud-free convective boundary layers. According to Fairall (1991) there are three ways clouds change the radar refractivity potential of the boundary layer: an additional thermodynamic coupling between temperature and moisture results due to condensation processes, the entrainment rate is greatly enhanced by cloud-top radiative cooling, and cloud liquid water droplets provide an additional scattering mechanism for radar. Fairall states, based on simple physical reasoning, the results for α2r are approximately valid for the entrainment-induced effects associated with clouds. Similar conclusions were reached in a modeling study of two maritime boundary layer cases even in the presence of clouds by Burk (1981).

The results of α2r for the LOWS data are best shown by Fig. 7. Throughout the time frame, values for α2r ranged from 1.02 to 1.04 within the boundary layer. Therefore, based on (3.6), contributions of C2q to C2n are 96% to 98%. Additionally, for modeling studies and calculations involving the refractive index structure parameter, an assumption of α2r near unity will introduce very little error (<4%). Figure 9 shows the humidity structure function parameter, log(C2q), prior to and following frontal passage on 11 January 1990. Of note in the figure, the boundary layer depth decreased under the effects of subsidence, α2r showed increasing variability above the boundary layer. By visual inspection, this result appears to be directly correlated with the specific humidity vertical profile in Fig. 10. However, these moisture gradients still have little effect on the overall contributions of C2q to C2n within the convective boundary layer.

b. Humidity data

A visual comparison of specific humidity (Fig. 8) with log(C2q) for 11–14 January (Figs. 9–12) shows excellent correlation. Specifically, Fig. 8 at 2300 UTC on 11 January shows increased specific humidity at 600, 1600, and 2500 m; whereas, Fig. 9 shows increased log(C2q) values at 600, 1600, and 2200 m. This corresponded with the passage of a surface front, after which lake-effect snowbands formed in the postfrontal environment. Cold front–trough passages were typified by moderately narrow uniform vertical log(C2q) fields. In Fig. 9, 1900–2100 UTC on 11 January, uniform vertical values of log(C2q) exceed −3.6 then rapidly transitioned to −4.5. Light snowfall in the prefrontal environment was seen as high values (>−4.2) of log(C2q) with loose vertical gradients and a boundary layer depth of around 2200 m. Three distinct snowbands are seen in Fig. 10 on 12 January, 0400–0800 UTC, indicated by very narrow uniform vertical log(C2q) fields.

Continuing the visual comparison, Fig. 8 at 1600 UTC on 13 January indicates specific humidity increases at 1000–1200, 1600–2000, and 2250–2450 m; whereas, Fig. 11 shows increased log(C2q) values 1000–1300, 1600–1800, and 2200–2400 m. In Fig. 12 on 14 January, the last snowband is seen around 0900 UTC, then frontal passage at 1400 UTC, with considerable drying of the atmosphere thereafter. Figure 13 depicts specific humidity for the 1700 UTC 28 February sounding. While the change in specific humidity is nearly linear, closer inspection reveals decreases in the rate of change at 500–800, 1250–1600, 2250–2450 m. Figure 14 shows a similar pattern; however, visual correlation is not as prominent as in the previous examples.

c. Boundary layer heights

The depth of the boundary layer limits convective eddies and therefore the intensity of lake-effect snow events. From vertically pointed radars we can obtain moisture profile [time–height series log(C2q)] data that may be used to estimate boundary layer heights. Normally, atmospheric moisture content, and hence C2q, decreases with height. However, sharp moisture gradients near the inversion cause local C2q maxima, from which depth of the boundary layer can be distinguished. For the most part, these features are easily recognized. As one might expect, the banded snow events that frequent the North Rose site can be seen as sharp changes in boundary layer depth.

The 25–26 February multiple snowband event exemplifies the approach to determining boundary layer heights. Although others have used the range corrected SNR to estimate CBL depths (i.e., Angevine et al. 1994; White et al. 1999; Marsik et al. 1995) the presence of convective elements in the CBL make such a technique difficult to use since an increase in turbulence and Rayleigh scattering from hydrometeors gives such peaks within the CBL (Angevine et al. 1994). Visual inspection of log(C2q) profiles show the rapid decrease within the free atmosphere. In Fig. 15 at around 0200 UTC, a rapidly moving “Alberta Clipper” was transitioning through the area producing widespread light snow. The boundary layer remained around 2300 m until approximately 0800 UTC when cold, dry air moved rapidly in behind the system. By 1200 UTC, the boundary layer depth was reduced to 1200 m. Despite the short fetch due to northerly surface winds, convection was seen around 1630 UTC as the boundary layer quickly rose to 2300 m when a lake-effect snowband moved over the radar site. At 2100 UTC the boundary layer dropped back to 1200 m. Then the last snow band passed overhead 0230–0400 UTC, after which the boundary layer rapidly deflated as strong high pressure and subsidence moved in. This event left 4 cm of snow at the radar site.

d. Entrainment velocity (we)

The entrainment velocities in Table 4 are within a factor of 2 to 3 of calculations made by Penc (1995) for the LOWS data. In the Penc entrainment velocity calculations, a lake-scale average for each major snow event was obtained using a kinematic equation for growth of a convective boundary layer initially presented by Deardorff and Peterson (1980). This technique uses boundary layer height differences averaged across the lake to compute growth rates, from which entrainment is derived. Our calculations apply only to the North Rose radar site, but are within expected ranges. Between 0200 and 0300 UTC the kinematic derived we was 0.3 cm s−1, and 1.3–1.7 cm s−1 from 1800 UTC 12 January through 2000 UTC 13 January, by comparison (Penc 1995).

Table 5 shows calculated entrainment velocities for two multiple snowband events. Due to limited rawinsonde data for the 25–26 February and 28 February–1 March 1990 multiple snowband events, entrainment velocities could only be calculated for two time periods. The 25 February at 0300 UTC we calculation result appears rather large compared with the results from Table 4. However, a rough order of magnitude calculation derived from Fig. 15 between 0200 and 0300 UTC reveals the boundary layer grew approximately 400 m, or the entrainment velocity averaged 11.2 cm s−1. In comparison, the kinematic derived values were between 1.0 and 3.0 cm s−1 for these events, and dZi/dt at 1800 UTC 25 February was 16.1 cm s−1. Because of the consistency between we determined from two approaches, the instantaneous entrainment velocity result for 0300 UTC appears to be reasonable.

6. Conclusions

Consistent with previous findings by White et al. (1991) for Type II CTBLs and cloudless convective boundary layers, gradients of moisture are the primary contributor to the radar index of refraction within a Type I CTBL, and therefore can be reliably sensed using vertical beam radars.

The increased temporal resolution of the radar moisture analysis makes this an excellent tool for monitoring cloud-topped boundary layer depths. Moisture profiles obtained from satellites are sufficient for sensing the upper and midlevels of the atmosphere. However, because of the poor resolution of satellite-based moisture sensors for boundary layer application, wind profiler networks will remain necessary. Boundary layer height and cold front/trough passage can be gauged using the humidity data from these wind profiler radars. Because of the presence of convection in the CBL, using range corrected SNR peaks to diagnose CBL depth in these cases was difficult, however combination with measurements of profiler derived wind shear the technique should be applicable here as well.

Additionally, using the assumption (α2r = 1) for a Type I CTBL is valid and will introduce very little error (<4%) in radar applications and modeling studies. Entrainment velocity rates and boundary layer growth can be reliably estimated using humidity-derived SNR radar data, as entrainment velocity calculations for the North Rose site were consistent with a lake-averaged kinematic equation for growth of the convective boundary layer. Also, rough order of magnitude entrainment velocity rates obtained from time-averaged radar data appeared to validate the instantaneous we calculations.

Acknowledgments

Primary support for the field phase of the Lake Ontario Winter Storms (LOWS) project came from Niagara–Mohawk Power Corporation's Research and Development Department. Analysis of remote sensing data and signal processing work was supported by the United States Department of Energy Atmospheric Radiation Measurement (ARM) Program under Grant DE-FG02-90ER-61071. Rawinsonde data was graciously provided by Dr. Gregory Byrd of the State University of New York College at Brockport, Dr. Alfred Stamm of State University of New York at Oswego, and Mr. Frank Froude of the Canadian Atmospheric Environment Service (AES). The SUNY rawinsondes were supported by National Science Foundation Grant ATM 89-14546. Profiler installation and development were supported by Mr. Bob Peters and Mr. Scott Williams, then at the Pennsylvannia State University.

I also wish to also acknowledge the support of Major John P. Dreher who was supported during the course of this research by the U.S. Air Force, Air Force Institute of Technology. His support of this project allowed this research to be completed.

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Fig. 1.
Fig. 1.

SNR low altitude mode at North Rose, NY, 11 Jan 1990. Darker shades represent lower SNR. Frontal passage occurred just prior to 2000 UTC

Citation: Journal of Atmospheric and Oceanic Technology 18, 12; 10.1175/1520-0426(2001)018<1941:MAOATI>2.0.CO;2

Fig. 2.
Fig. 2.

SNR low-altitude mode for North Rose, NY, 12 Jan 1990. Major single-banded activity occurred over the lake between 0800 and 1700 UTC

Citation: Journal of Atmospheric and Oceanic Technology 18, 12; 10.1175/1520-0426(2001)018<1941:MAOATI>2.0.CO;2

Fig. 3.
Fig. 3.

SNR low-altitude mode for North Rose, NY, 13 Jan 1990. Multiple-banded snowbands occurred to the southeast of the lake during this time. The intense gradient at 1900 UTC is an artifact of profiler malfunction

Citation: Journal of Atmospheric and Oceanic Technology 18, 12; 10.1175/1520-0426(2001)018<1941:MAOATI>2.0.CO;2

Fig. 4.
Fig. 4.

SNR low-altitude mode for North Rose, NY, 14 Jan 1990. An unexpected single snowband developed to the east of the profiler, southeast of the lake prior to 0900 UTC. The top of the CBL is seen as a local maximum in SNR at 2-km AGL, decreasing through 1400 UTC

Citation: Journal of Atmospheric and Oceanic Technology 18, 12; 10.1175/1520-0426(2001)018<1941:MAOATI>2.0.CO;2

Fig. 5.
Fig. 5.

SNR low-altitude mode for North Rose, NY, 25 Feb 1990. Multiple snowbands developed southeast of the lake after trough and shortwave passage near midrecord. Lower SNR is typical of the multiple-band events observed

Citation: Journal of Atmospheric and Oceanic Technology 18, 12; 10.1175/1520-0426(2001)018<1941:MAOATI>2.0.CO;2

Fig. 6.
Fig. 6.

SNR low-altitude mode for North Rose, NY, 28 Feb 1990. Multiple snowbands developed southeast of the lake after frontal passage. Increase in SNR around 1800 UTC is related to development of snowbands near the profiler, and increased CBL depth

Citation: Journal of Atmospheric and Oceanic Technology 18, 12; 10.1175/1520-0426(2001)018<1941:MAOATI>2.0.CO;2

Fig. 7.
Fig. 7.

Alpha (α2r) for North Rose, NY, 11–14 Jan 1990. Values near unity indicate the contribution to C2n are largely due to moisture variation in the mixed layer

Citation: Journal of Atmospheric and Oceanic Technology 18, 12; 10.1175/1520-0426(2001)018<1941:MAOATI>2.0.CO;2

Fig. 8.
Fig. 8.

Rawinsonde derived specific humidity (q) for North Rose, NY, 12–13 Jan 1990. Systematic drying of the mixed layer is noted after 2100 UTC 12 Jan

Citation: Journal of Atmospheric and Oceanic Technology 18, 12; 10.1175/1520-0426(2001)018<1941:MAOATI>2.0.CO;2

Fig. 9.
Fig. 9.

Humidity structure function parameter [log(C2q)] for North Rose, NY, 11 Jan 1990, prior to and after frontal passage

Citation: Journal of Atmospheric and Oceanic Technology 18, 12; 10.1175/1520-0426(2001)018<1941:MAOATI>2.0.CO;2

Fig. 10.
Fig. 10.

Humidity structure function parameter [log(C2q)] for North Rose, NY, 12 Jan 1990. Large values between 1800 and 2100 UTC correspond to the development of shoreline band activity near the profiler

Citation: Journal of Atmospheric and Oceanic Technology 18, 12; 10.1175/1520-0426(2001)018<1941:MAOATI>2.0.CO;2

Fig. 11.
Fig. 11.

Humidity structure function parameter [log(C2q)] for North Rose, NY, 13 Jan 1990. Intense gradients near 1900 UTC are due to a profiler malfunction

Citation: Journal of Atmospheric and Oceanic Technology 18, 12; 10.1175/1520-0426(2001)018<1941:MAOATI>2.0.CO;2

Fig. 12.
Fig. 12.

Humidity structure function parameter [log(C2q)] for North Rose, NY, 14 Jan 1990. Local maxima between 1500- and 2000-m AGL, 0000 through 1400 UTC indicate the top of the CBL

Citation: Journal of Atmospheric and Oceanic Technology 18, 12; 10.1175/1520-0426(2001)018<1941:MAOATI>2.0.CO;2

Fig. 13.
Fig. 13.

Rawinsonde derived specific humidity (q) for North Rose, NY, 1700 UTC 28 Feb 1990

Citation: Journal of Atmospheric and Oceanic Technology 18, 12; 10.1175/1520-0426(2001)018<1941:MAOATI>2.0.CO;2

Fig. 14.
Fig. 14.

Humidity structure function parameter [log(C2q)] for North Rose, NY, 28 Feb 1990. Development of a CBL is indicated by the local maxima at 1500–2000-m AGL, between 0500 and 2000 UTC

Citation: Journal of Atmospheric and Oceanic Technology 18, 12; 10.1175/1520-0426(2001)018<1941:MAOATI>2.0.CO;2

Fig. 15.
Fig. 15.

Humidity structure function parameter [log(C2q)] for North Rose, NY, 25 Feb 1990. Profiler performance was low during this event

Citation: Journal of Atmospheric and Oceanic Technology 18, 12; 10.1175/1520-0426(2001)018<1941:MAOATI>2.0.CO;2

Table 1.

Primary LESS and secondary related factors. Adapted from Penc (1995)

Table 1.
Table 2.

Radar characteristics and operating parameters for the Pennsylvania State 404-MHz wind profiler deployed at North Rose, NY (Penc 1991)

Table 2.
Table 3.

Radar characteristics and signal processing parameters used in deriving the relationship between reflectivity and SNR for the Pennsylvania State 404-MHz wind profiler (Penc 1995)

Table 3.
Table 4.

Values of variables derived from radar and rawinsonde data from 12–13 Jan 1990 used in calculating entrainment velocities along with their units

Table 4.
Table 5.

Values of variables derived from radar and rawinsonde data from 25 and 28 Feb 1990 used in calculating entrainment velocities along with their units

Table 5.

1

The Collier index plots lake–850-mb temperature versus lake–700-mb temperature and categorizes the degree of instability as conditional, moderate, or extreme. It is used as a predictor for the likelihood of a lake-effect event.

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