Estimates of the potential temperature profile from lidar measurements of boundary layer evolution

Transcription

1 WATER RESOURCES RESEARCH, VOL. 42,, doi: /2005wr004361, 2006 Estimates of the potential temperature profile from lidar measurements of boundary layer evolution H. E. Holder 1 and W. E. Eichinger 2 Received 21 June 2005; revised 16 May 2006; accepted 16 June 2006; published 20 October [1] The Soil Moisture-Atmosphere Coupling Experiment (SMACEX) was conducted in the Walnut Creek Watershed near Ames, Iowa, over the period from 15 June to 11 July A main focus of SMACEX is the investigation of the interactions between the atmospheric boundary layer, surface moisture, and canopy. A vertically staring elastic lidar was used to provide a high time resolution, continuous record of the mixed layer height at the edge between a soybean and a corn field. The height and thickness of the entrainment zone are used to estimate the vertical potential temperature profile in the boundary layer using surface energy measurements in the Batchvarova-Gryning mixed layer model. Calculated values of potential temperature compared well to radiosonde measurements taken simultaneously with the lidar measurements. The root-mean-square difference between the lidar-derived values and the balloon-based values is 1.20 C. Citation: Holder, H. E., and W. E. Eichinger (2006), Estimates of the potential temperature profile from lidar measurements of boundary layer evolution, Water Resour. Res., 42,, doi: /2005wr Introduction [2] The vertical temperature profile through the boundary layer (BL) is a critical boundary condition needed to model the convective BL [Albertson and Parlange, 1999;Albertson et al., 2001]. The temperature profile throughout the BL is problematic and expensive to measure directly, usually requiring measurements from a succession of balloon-borne instruments. Further, measurements made from a free balloon may lack sufficient vertical resolution or accuracy. The temperature and humidity sensors have a time constant that results in changes being reported with lower magnitudes and at higher altitudes than their true values. In addition, radiosonde measurements are quasi-instantaneous and may be made in the middle of an upwelling warm plume or in a downwelling air parcel, with appreciably different results. In extreme cases, the point measurements of the mixed layer height made by these instruments may vary more than 100% [Weckwerth et al., 1996]. To obtain meaningful temperature and humidity profiles, some degree of either time or space averaging is required. While this is difficult with radiosondes, it can be done with tethered balloons or kites, albeit with some limitations on the maximum altitude. Another option would be a method that could determine the temperature profiles with instruments already in use at the site. This work evaluates a method where, with a relatively simple vertically staring lidar, vertical potential temperature profiles can be inferred. A method to obtain temperature profiles throughout the day with a high temporal resolution to properly characterize boundary layer changes would be invaluable for modeling of the BL. [3] This work estimates the vertical profile of potential temperature by inverting a method of estimating the height of the mixed layer (ML). The method considers the surface virtual heat flux, as well as the general state of the atmosphere, including the stability and mixed layer height [Batchvarova and Gryning, 1991; Gryning and Batchvarova, 1994]. The data used for comparison was taken during the month of June 2002 as part of the Soil Moisture Atmospheric Coupling Experiment (SMACEX). SMACEX was conducted as part of the larger Soil Moisture Experiment 2002 (SMEX02) field campaign. The method presented here is also an inversion of the method presented by Eichinger et al. [2005] and more details of the lidar system and the data can be found there. 2. ABL Height Model [4] The Batchvarova-Gryning model [Batchvarova and Gryning, 1991, 1994] is based on a model originally developed by Betts [1973], Carson [1973], Tennekes [1973], and Zilitinkevich [1974]. The Carson and Tennekes model and its more simplified forms use a one-dimensional approach to model the growth of an inversion-capped ML and have been the basis for nearly all of the mixed layer height models that have been developed. The Batchvarova- Gryning model uses a parameterization of the turbulent kinetic energy budget within the mixed layer, and of the temperature jump at the top of the mixed layer. According to the model, the relationship between the virtual heat flux at the surface, w 0 q 0 v surface, the height of the mixed layer, h, and other atmospheric parameters can be expressed as: 1 Department of Civil and Environmental Engineering, Duke University, Durham, North Carolina, USA. 2 Department of Civil and Environmental Engineering, University of Iowa, Iowa City, Iowa, USA. Copyright 2006 by the American Geophysical Union /06/2005WR w 0 q 0 v surface g h 2 ¼ ð1 þ 2AÞh 2BkL þ Cu* 2 T dh gg½ð1 þ AÞh BkLŠ dt w s ð1þ 1of9

2 HOLDER AND EICHINGER: LIDAR-BASED POTENTIAL TEMPERATURE PROFILES where dh/dt is the growth rate of the mixed layer; t is time; L is the Monin-Obukhov length; k is the von Karman constant; g is the acceleration due to gravity; u* is the friction velocity; T is the temperature of the mixed layer; g is the potential temperature gradient above the mixed layer and w s is the subsidence velocity. B and C are normally taken to be parameterization constants with commonly accepted values: B = 2.5, and C = 8 [Melas and Kambezidis, 1992; Gryning and Batchvarova, 1996; Kailstrand and Smedman, 1997; Steyn et al., 1999]. [5] A is the ratio of the entrainment virtual heat flux (from the entrainment of warm air above the inversion into the mixed layer) to the surface virtual heat flux [Stull, 1988]. This quantity can be obtained directly from the lidar data. The entrainment heat flux is of major importance to boundary layer models, representing the amount of heat energy that is supplied to the mixed layer by entrainment. A is expressed as the ratio of the virtual heat fluxes: A ¼ w0 q 0 v entrainment w 0 q 0 v surface The virtual heat flux is zero near the bottom of the entrainment zone and the entrainment flux is a maximum at the average height of the top of the mixed layer, so by assuming that the heat flux changes linearly with height (as illustrated in Figure 1), A can be expressed in terms of the dimensions of the boundary layer [Davies et al., 1997]. This relationship is written as: A ¼ h h bottom 1 where h bottom is the height of the bottom of the entrainment zone. [6] Many studies have attempted to obtain values of the entrainment parameter, A. The value of A is dependent on the existing weather conditions. Laboratory experiments and some observational studies have shown the ratio to be approximately A 0.2 for thermally driven, dry, convective boundary layers [Stull, 1976, 1988; Nicholls and LeMone, 1980]. More complicated models including the mechanical generation of turbulence or forced convection [Mahrt and Lenschow, 1976; Zeman and Tennekes, 1977; Smeda, 1979; Driedonks, 1982] and more recent studies [Betts et al., 1990, 1992; Culf, 1992; Betts and Ball, 1994, 1995, 1998; Betts and Barr, 1996; Davies et al., 1997; Angevine, 1999; Margulis and Entekhabi, 2004] have found significantly larger values of this parameter (A 0.4) for windy conditions when large-scale forcing is strong. Because of the key role that the entrainment parameter plays in the model, it is useful that it can be expressed in terms of the physical size and shape of the top of the mixed layer (equation (3)) which can be measured directly by the lidar. [7] The first term on the right hand side of equation (1) represents the growth of the mixed layer due to warming of the air at the surface and to the entrainment of warm air from above the mixed layer. The second term, the correction proposed by Zilitinkevich, incorporates the contribution from the mechanical production of turbulent kinetic energy at the surface to the mixed layer temperature [Zilitinkevich, ð2þ ð3þ 1974]. Early in the morning when the atmosphere is near neutral and buoyancy is not important, the growth rate of the shallow mixed layer is proportional to the friction velocity. As the mixed layer grows, buoyancy becomes increasingly important. Mechanical turbulence at the surface is significantly less important than buoyancy when the mixed layer has grown to a height of approximately 1.4 L [Gryning and Batchvarova, 1990]. The lidar configuration that was used in SMACEX had a minimum altitude of 120 m, so the only conditions that could be observed were those in which the mixed layer height had already grown to altitudes that generally exceed this criterion. For the conditions found during SMACEX when the mixed layer height is greater than 120 m, the Zilitinkevich correction is small (less than a 2% contribution). Accordingly, the second term has been ignored. However, this approximation is not appropriate for use in the very early morning when mechanical turbulence is significant. The method is useful only during that period when the mixed layer is growing (until approximately the solar maximum), since dh/dt is the primary measure used to estimate the amount of energy added to the mixed layer. Once the mixed layer has grown to its maximum height, or has risen to the height of the cumulus cloud base, the method can no longer be applied. [8] Rearranging the thermodynamic model in equation (1), ignoring the contribution of mechanical turbulence and assuming a convective mixed layer (L is small), the following equation relating the lapse rate to the surface virtual heat flux and the characteristics of the mixed layer is obtained: g ¼ w 0 q 0 v dh dt w s surface h i ð4þ h 2 ð1þ2aþh 2BkL To use equation (4), an estimate of the subsidence velocity, w s, is needed. Vertical motion at the top of the boundary layer is caused by convergence or divergence in the mesoscale flow and is difficult to determine from meteorological measurements. However, the mixed layer grows into the residual layer from the day before, the height of which can be examined to obtain an estimate of the magnitude of the subsidence velocity. Figure 1 shows a typical lidar return during a convective morning period. The residual layer extends from the top of the mixed layer to an altitude of approximately 900 m. For this day, the altitude of the residual layer stayed approximately constant until about 12:30 pm, at which time the remaining portion of the residual layer was entrained into the mixed layer. We are aware of no work that has related the height of the residual layer to subsidence. However, it stands to reason that if the top of the residual layer is not falling, there cannot be subsidence. Since there is generally no active mixing of the residual layer with the free troposphere above, if the largerscale air mass is moving down, the top of this layer must decrease in altitude. [9] The height of the residual layer can be found from the same methods used to determine the height of the mixed layer. The residual layer is characterized by higher particulate concentrations than in the free troposphere above, but lower than in the mixed layer below. To determine the height of both the residual layer and the mixed layer, the routines discussed later detect the abrupt decrease in par- 2of9

3 HOLDER AND EICHINGER: LIDAR-BASED POTENTIAL TEMPERATURE PROFILES Figure 1. Traditional thermodynamic model of an unstable atmospheric boundary layer. A logarithmic layer near the surface blends into a constant potential temperature mixed layer that extends to the top of the mixed layer. A stable atmosphere with a temperature inversion acts as a lid to the vertical motions of the air below. The change in potential temperature is modeled as a discontinuous jump. A lidar signal showing the height of the mixed layer with time is shown on the right. Reds are highest particulate concentrations and blues are lowest. The thermodynamic diagram is shown to the left scaled to the lidar signal. 3of9

4 HOLDER AND EICHINGER: LIDAR-BASED POTENTIAL TEMPERATURE PROFILES Figure 2. Aerial photograph of the lidar site showing a bare soil condition. The vertically staring lidar was located at the boundary between a soybean field (below the lidar) and a corn field (above the lidar). The boundary between the fields can be seen as a line. High areas appear lighter in the photograph, while low areas are darker. ticulate concentration that characterizes the boundary between the regions. In the case of the residual layer top, the change in aerosol concentration occurs over a much smaller distance than the change between the mixed layer top and the residual layer. While the same methodology is used to find the center point of the transition, the uncertainty in the height of the residual layer top is much smaller than that of the mixed layer because of the sharpness of the transition. [10] The Obukhov length, L, is an atmospheric stability parameter that is obtained from the surface energy flux measurements as ru 3 L ¼ h i ð5þ kg H LE 0:61 Tc p L e where LE is the latent energy flux, r is the density of air and L e is the latent heat of evaporation for water. H is the sensible heat flux at the surface and c p is the specific heat capacity at constant pressure [Stull, 1988]. 3. Field Site and Data Collection [11] The Soil Moisture-Atmospheric Coupling Experiment (SMACEX) was an interdisciplinary field campaign conducted in conjunction with the Soil Moisture Experiment of 2002 (SMEX02). SMACEX was conducted from mid-june to mid-july of 2002 in the Walnut Creek watershed in central Iowa. The region represented typical Midwestern US cropland, specifically corn and soybean fields. A large variety of atmospheric and land variables were measured, including mixed layer height and water content, soil moisture, water, heat and carbon fluxes, cloud cover, vegetation biomass and other vegetation properties. [12] The wide variety of measurements collected simultaneously in the same location provides a unique opportunity to study the boundary layer. Measurements made on different scales can be compared and modeling efforts can be subsequently compared with measurements. One of the primary goals of SMACEX was to incorporate the measurements taken into Large Eddy Simulation (LES) models [Kustas et al., 2003] and another was to investigate the interactions between the BL, the surface moisture and the vegetation canopy [Kustas et al., 2005]. The large degree to which the BL was characterized during SMACEX means that boundary conditions are largely known, providing for a high-quality reference. In addition, model results can easily be compared with actual conditions. In order for a model to accurately simulate the conditions, the vertical temperature profile must be known with a great deal of reliability. [13] Figure 2 is an aerial photograph of the site taken during a period with little or no vegetation. The patchiness of the photograph is indicative of the small variations in surface topography (1 4 m) in the field. The lidar was located at the boundary between a corn and a soybean field. During the field campaign, the lidar operated daily during daylight hours. [14] The lidar used in this study is a portable, vertically staring lidar system, operated at a single wavelength (1064 nm). The basic parameters of the transmitter and receiver of the LANL/UI vertically staring lidar system are given in Table 1. The laser beam is emitted parallel to the axis of the receiving telescope at a distance of 24 cm from the center of the telescope. There is a minimum distance for which the lidar produces useful data. This is the distance at which the telescope images the entire laser beam, approximately 120 m for this lidar. Only that portion of the lidar signal that comes from the area of complete overlap between the field of view of the telescope and the laser beam can be reliably used for analysis. [15] The virtual heat fluxes that were used for reference were obtained from four CSAT3 sensors (Campbell Scientific 3-D sonic anemometer) each collocated with a LI7500 (Li-Cor CO 2 /H 2 O analyzer) using the eddy covariance (EC) method. These systems provide high frequency (20 Hz) data of wind (u, v, and w components), sonic temperature (T S ), water vapor and CO 2 concentrations. Two of the eddy covariance systems were placed in the cornfield and two in soybeans within 600 m of the lidar location. The eddy Table 1. Operating Characteristics of the Vertically Staring Lidar System Property Wavelength Pulse length Pulse repetition rate Pulse energy Beam divergence Type Diameter Focal length Filter bandwidth Field of view Range resolution Transmitter Receiver Value 1064 nm 10 ns 50 Hz 125 mj maximum 3 mrad Schmidt-Cassegrain m 2.5 m 3.0 nm 1.0 to 4.0 mrad adj. 1.5, 2.5, 5.0, 7.5 m 4of9

5 HOLDER AND EICHINGER: LIDAR-BASED POTENTIAL TEMPERATURE PROFILES Figure 3. Plot of the lidar data for 29 June from 10:00 am through 12:30 pm. The data are shown as altitude versus time with color showing the relative aerosol content (reds are highest concentrations with blues being the lowest). The blue color above the mixed layer is the residual layer from the previous day. White areas are regions of low aerosol content, generally indicating air from the free troposphere. covariance data were processed in the usual manner to apply a coordinate transformation that forces v = w =0[Kaimal and Finnigan, 1994] and to correct for oxygen and density effects on the evaporative and CO 2 fluxes (Webb-Pearman-Leuning (WPL) correction [Webb et al., 1980]). The EC flux data was also adjusted to close the energy balance as a function of the measured Bowen ratio [Twine et al., 2000]. [16] The temperature gradient of the lower atmosphere was measured with standard meteorological balloons that were launched at approximately 0700, 1000, 1400, and 1600 hours each day (all times referenced are local time). The balloons were launched and monitored from the lidar location and monitored from there. The data from 29 June, shown in Figure 3, is typical of the kind of boundary layer found during SMACEX. 4. Lidar Data Analysis Methodology [17] The height of the mixed layer is commonly estimated using potential temperature and specific humidity profiles. At the top of the mixed layer, the potential temperature undergoes an abrupt change. Similarly, a decrease in the specific humidity and all other scalar quantities with surface sources occurs at the same height. In a fair weather, convective mixed layer, warm, particulate-rich parcels of air rise from the surface while cooler, cleaner parcels of air move down toward the surface. From elastic lidar data, the top of the mixed layer exhibits a sharp contrast between the backscatter signals from particulate-rich structures below and cleaner air above (Figures 1 and 3). Because the lidar data are sampled approximately every second, a considerably higher temporal resolution than a radiosonde, the determination of the height of the mixed layer and thickness of the entrainment zone is more complex. [18] Given that the height of the mixed layer can be determined for each of the individual lidar scans at one second intervals, for a half-hour period there will be a set of approximately 1800 individual height measurements. There is thus a distribution of heights rather than a single height as might be measured by a balloon. The height of the mixed layer is taken to be the arithmetic mean of the individual heights in this set. The entrainment zone thickness (EZT) was defined by Deardorff et al. [1980, p. 41] as the depth being confined between the outermost height reached by only the most vigorous penetrating parcels and by the lesser height where the mixed layer fluid occupies usually some 90 to 95 percent of the total area. Many of the lidar-based methods to determine the EZT use the standard deviation, s, of the set of mixed layer heights for a given period of time as a measure of the EZT. Then the bottom of the entrainment zone, where the mixed layer fluid occupies 95 percent of the total area, is that height for which 5 percent of the measured mixed layer heights in the set are below. For example, Steyn et al. [1999] estimate the EZT = 2.77s (i.e., h top = h *s and h bottom =h 1.38*s,), corresponding to 8 to 92 percent of the total variation in heights (assuming a Gaussian distribution). Melfi et al. [1985] used a nonsymmetric cutoff in which the bottom of the entrainment zone, h bottom, corresponded to a cumulative probability of 4 percent while h top corresponded to a cumulative probability of 98 percent. This study used h top = h *s and h bottom =h 1.64*s, corresponding to 5 and 95 percent of the variation, similar to those suggested by Deardorff et al. [1980]. The estimates of A can be considerably different depending upon the values used for the cutoff. The difference between assuming the mixed layer fluid occupies 92 versus 95 percent of the total area leads to a difference of approximately 20% in A. A detailed description of various methods for the determination of mixed layer height and entrainment zone thickness from lidar data is given by Kovalev and Eichinger [2004]. [19] The height of the mixed layer for an individual lidar scan is found using an edge detection method originally developed for digital photography [Davies, 1992]. The method determines, at each point, the absolute value of the second derivative of the lidar signal with respect to altitude divided by the first derivative of the lidar signal with respect to altitude. The function has a sharp negative minimum at an inflection point in which the signal is decreasing with distance. The use of this function is 5of9

6 HOLDER AND EICHINGER: LIDAR-BASED POTENTIAL TEMPERATURE PROFILES Figure 4. Example of a lidar scan showing the top of the mixed layer and the values for the edge detection function (blue line). The black line is the lidar signal showing the decrease in aerosol concentration at the top of the mixed layer. The value of the edge detection function shows a sharp decrease at inflection points. The boundary layer is taken to be the location of the large negative peak at 1635 m. Note that the scale is logarithmic. intended to find the point at which the slope of the decrease in the lidar signal is largest. This point is generally midway between the high particulate levels indicative of the mixed layer and the lower levels indicative of the free troposphere and is commonly taken to be the height of the mixed layer [Kovalev and Eichinger, 2004]. The minimum of this function is a more sensitive and reliable indicator of this point than the use of the first derivative alone in situations where noise is present. Extended derivatives are used to calculate the derivatives to minimize the effects of noise in the lidar signal. The derivatives are extended over a distance of twenty points on either side of the point in question. Figure 4 is an example of a lidar scan showing the top of the mixed layer and the values for the edge detection function. While there are inflection points at several places in the lidar signal (darker line) indicated by peaks in the function, the inflection point that is midway between the boundary layer aerosol concentration and the clear atmosphere concentration can be seen at 1635 m and indicated by a peak that is more than an order of magnitude larger than the others. [20] The lidar is a spatially stationary point, measuring a system that varies with both space and time. Therefore Taylor s hypothesis must be valid as different air parcels move across the line of sight of the lidar [Stull, 1988]. This requires that the eddies do not evolve significantly in the time it takes for that turbulent eddy to advect past the lidar. The need to limit data collection time so that the average does not change appreciably competes with the need to collect sufficient measurements so that all of the spectral modes are captured. Averaging over enough plumes to obtain statistically meaningful mixed layer heights may take too long during times when the height of the mixed layer is changing rapidly (during midmorning or late afternoon for example). For this study, 30 min averages were used because this was the averaging period used for flux calculations in SMACEX. This time is occasionally too long during periods when the mixed layer grows rapidly or when g is not constant with height. [21] It should be noted that the averaging period, the growth rate of the boundary layer and the vertical resolution obtainable for the temperature profile are intrinsically related. The limitation on the vertical resolution is strongly related to the averaging period, which must be long enough to provide statistical convergence in order to obtain reliable estimates for the mixed layer height, the entrainment zone thickness and the surface heat fluxes. Since typical growth rates range from 100 to 400 m per hour, vertical resolutions of less than 50 m are probably not possible for a vertically pointing system. However, it may be possible to use a scanning lidar to examine a large enough volume so that averaging timescales less than 10 min are possible. This would enable vertical resolutions on the order of 15 m to 50 m. [22] The mixed layer heights and EZTs for the 30 min periods were determined for three days. The days used (25, 27, and 29 June) were chosen by the availability of both balloon and lidar data. The coefficient A is estimated from these values using equation (3). The subsidence velocity is obtained from measurements of the residual layer height and all other parameters are obtained from surface micrometeorological instruments. Then using these values, for each 30 min period a value for the potential temperature gradient is obtained using equation (4). Associated with each 30 min period and gradient value is the height of the top of the mixed layer at that time. [23] In order to convert these values to a temperature profile, the temperature of the atmosphere at the top of the mixing layer must be known at the start time. In the ideal case, the analysis would start early in the morning when the top of the boundary layer is very near the surface. A local measurement of temperature near the surface could be extended to higher altitudes using Monin-Obukhov similarity theory. In this study, the temperature determined by the sonic anemometer over the cornfield eddy covariance tower was used to estimate the temperature at the lowest altitudes (generally m). This application was not anticipated during the experiment so that the lidar was not set up to enable data collection close to the surface. However, the system is capable of collecting data as low as 35 m above the surface. So while we are not comfortable with extending a surface measurement to 200 m (which may be one cause of the differences in temperature between the balloons and these estimates), extending a near surface measurement to 35 m is not unreasonable. Having the temperature of the top of the mixed layer at the beginning of the first 30 min analysis period, the temperature at the height of the mixed layer at the end of the analysis period is found by multiplying the temperature gradient by amount of growth in the mixed layer during the period. This process is repeated until the data set is exhausted. 5. Results [24] The results of the method for 25, 27, and 29 June 2002 are presented in Figures 5 7. The temperature profile from the balloons launched at 0700 on the respective dates is shown in Figures 5 7. In every case, the calculations begin at 0830 local daylight savings time and continue at 6of9

7 HOLDER AND EICHINGER: LIDAR-BASED POTENTIAL TEMPERATURE PROFILES Figure 5. Lidar-derived temperature profiles for 25 June The temperature profiles from the radiosonde are also shown. half hour intervals until the mixed layer ceases to grow. The first value on the plot is an estimation of the actual potential temperature of the atmosphere at that time, and subsequent points are the offset from this point using the calculated value of g. The calculated temperature profiles match the measured ones well, with a root-mean-square difference of 1.20 C. This is a rough estimate of the uncertainty in the method, although the values were obtained from two very different types of measurements, each with its own errors, at different times of the day. [25] The method performs less favorably at the region where the atmosphere changes from strongly stable to weakly neutral. In this region, the implicit assumption that dg/dz is constant is not valid. In this case, the half hour averaging period is too long to capture the rapid changes in dg/dz. In other words, the rate at which the mixed layer height changes (@ 2 h/@t 2 ) is faster than the 30 min temporal resolution used here to capture the change in g, resulting in a smoothing of the computed temperature profile. In addition, the distribution of entrainment zone heights is not symmetric when dg/dz is not constant; it is skewed toward the part of the atmosphere that is more neutral (in this case, to higher altitudes). For this reason, a better method would consider the bottom of the distribution only, rather than the entire distribution. During most of the days in the SMEX02 experiment, the capping inversion was relatively strong to an altitude of about 500 m and then weakly neutral to about 1600 m. The result was a slow growth in the boundary layer Figure 7. Lidar-derived temperature profiles for 29 June The temperature profiles from the radiosonde are also shown. Data collection on 29 June started later in the morning, so the profile starts higher in the atmosphere. until just before noon with a rapid expansion for the next 2 hours. [26] It should be noted that there are several limitations to this approach. In order to use the method in the early morning the lidar would need to obtain data very close to the surface. The method is applicable only during those times when the mixed layer is growing into the residual layer from the previous day. Once the mixed layer has reached its maximum height or the cloud base, the method should not be used. Therefore the method can be used from approximately 8 am to 1 pm. In addition, a starting value of potential temperature is needed. It may be difficult to obtain a temperature measurement at an altitude of 150 m above the surface. The lidar could be reconfigured to sample at a lower altitude, or a tethered balloon could be used. Alternately, a boundary layer model could be used to estimate the starting temperature, although this may enter another source of error into the calculations. [27] In estimating the values of the entrainment parameter, A, it was noted that the range of values was quite large, from 0.1 to 1.6. There appears to be a relationship between A and the gradient of potential temperature, g. Figure 8 is a plot of the values of A for these three days against g. While there is considerable scatter in the values, Figure 6. Lidar-derived temperature profiles for 27 June The temperature profiles from the radiosonde are also shown. 7of9 Figure 8. Plot of the values of A for the three study days against g. While there is considerable scatter in the values, there is a clear trend in which large values of the entrainment parameter occur when the potential temperature gradient is small.

8 HOLDER AND EICHINGER: LIDAR-BASED POTENTIAL TEMPERATURE PROFILES there is a clear trend in which large values of the entrainment parameter occur when the potential temperature gradient is small. This is likely due to the fact that a smaller gradient presents a smaller barrier to vertical buoyant motion. This allows upward moving parcels to travel to higher altitudes, which in turn results in more downward motion, allowing for greater mixing. To our knowledge, this relationship between A and g has not been noted previously. We note that there are not many methods capable of measuring the width of the entrainment zone or the entrainment parameter, A (aircraft methods being the most common). 6. Conclusions [28] A method has been presented to estimate the vertical profile of potential temperature from vertically staring, elastic lidar measurements using the Batchvarova-Gryning model for energy balance in the mixed layer. Values of potential temperature calculated using the method for three days compare with values obtained from a balloon-borne radiosonde with a root-mean-square difference of 1.20 C. To use the method, auxiliary measurements of the surface heat and momentum fluxes are required. Three variables are obtained from the lidar data; the average mixed layer height, h, the time rate of change in this height, dh/dt, and the ratio of the downward virtual heat flux at the top of the mixed layer to the surface virtual heat flux, A. All three variables are derived from measurements of instantaneous mixed layer heights (here approximately one second apart) over some averaging period. [29] At this point, it is not possible to obtain time averaged temperatures aloft during the day. While we have great confidence in the ability of temperature sensors, balloon measurements are limited because they represent a semi-instantaneous transect through an evolving system. Thus it is not possible to assert with any confidence that the difference between the lidar-derived temperatures and balloon measured values is significant. That the method reproduces balloon profiles to the accuracy that it does is in indicator that most of the physics is accounted for. However, there is room for improvement. The use of a scanning lidar will increase the quality of the data while decreasing the time required for the measurement. This will increase the accuracy while decreasing the vertical resolution of the measurements. Starting data collection closer to the lidar, i.e., at a lower altitude, will also increase the reliability of the initial temperature estimate. [30] Vertically staring lidars are quite common, so a method capable of estimating regional virtual heat fluxes from that type of data has the potential for widespread application, especially when it is not possible to have a radiosonde colocated with the lidar. 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