## 1. Introduction

Predicting the timing and location of convective cloud development is a fundamental challenge in the study of meteorology. Spatial variability in the atmospheric boundary layer (ABL) is closely related to the development of moist convection (e.g., Crook 1996; Rozoff et al. 2003; among many papers in the literature). The heterogeneity of the ABL is known to be caused by multiple factors including surface forcing and above-ABL conditions. The influence of land surface heterogeneity on the ABL structure and moist convection has been studied by numerous investigators using numerical models and observational data (for a comprehensive review, see Pielke 2001).

Mesoscale numerical model studies of the effects of land surface heterogeneity on the ABL structure and moist convection have focused on the generation of well-organized circulation with prescribed surface sensible and latent heat fluxes at the meso-*β* scale, which ranges from 20 to 200 km (e.g., Segal et al. 1989; Chen and Avissar 1994a, b to name a few). Much of the earlier research involved idealized conditions, while Zhong and Doran (1998) used a real-data case and found that heterogeneous conditions result in a very similar situation as that simulated with homogenous surface conditions. These results suggest that well-organized meso-*β*-scale circulations generated by land surface heterogeneity may be difficult to find outside of areas of extreme contrasts, such as on the boundary of irrigated/nonirrigated, urban/rural, or bare/vegetated ground.

To fully simulate the effect of surface heterogeneity on the ABL structure at the meso-*γ* scale (2–20 km), large-eddy simulations (LES) have been used (e.g., Shen and Leclerc 1995; Avissar and Schmidt 1998; Patton et al. 2005 to name a few). Many LES results have indicated that meso-*γ*-scale land surface heterogeneity can significantly influence the entire ABL structure. Most of the LES results, however, are limited by their use of idealized conditions for surface heat and moisture fluxes, mean winds, temperature and moisture soundings, lateral boundary conditions, and terrain.

There have been some observational studies that address the influence of land surface heterogeneity at the meso-*γ* scale on the ABL structure including existence of mesoscale circulations generated by land surface heterogeneity (e.g., Mahrt et al. 1994a; Shaw and Doran 2001; LeMone et al. 2002, 2007). However, compared to the numerical studies, there have been fewer observational studies. This is primarily due to the difficulty in obtaining appropriate observations that describe the ABL heterogeneity in a statistically robust manner. However, improvement in technology is expanding our ability to observe the heterogeneous ABL structure.

The International H2O Project (IHOP_2002; Weckwerth et al. 2004), in which multiple research components utilized various enhanced observational instruments, provides an opportunity to observe the heterogeneous ABL structure. Observational datasets collected in this field experiment can be used to assist the research toward a better understanding of the ABL structure over a heterogeneous land surface.

The goal of this study is to document the influence of meso-*γ*-scale land surface heterogeneity on the ABL structure under different background weather conditions using observational datasets collected from IHOP_2002. This research includes the investigation of the primary causes of surface heterogeneity over the study area. Datasets used for this research will be delineated in the next section, along with a description of the study area. Section 3 will discuss the causes of the surface heterogeneity over the study area mainly using the measurements at the surface flux sites. Section 4 will describe the influence of land surface heterogeneity on the low-level ABL structure under different background weather conditions by applying the statistical and spectral analysis methods to the data from the repeated low-level aircraft passes. In section 5, the influence of the land surface heterogeneity on the upper-level ABL structure is qualitatively assessed based on normalized variance profiles and observed spatial variations of the ABL depth. Section 6 summarizes the results and presents conclusions.

## 2. Data

The IHOP_2002 field experiment was conducted from 13 May to 25 June 2002 in the southern Great Plains (SGP) of the United States with the aim of improving our understanding of convective precipitation, including the development of heterogeneous boundary layer (BL) structure that might contribute to this understanding (Weckwerth et al. 2004). Numerous mobile observing systems, ground-based observation facilities, and six research aircraft were used in this project.

As a part of the IHOP_2002 field experiment, the University of Wyoming King Air (UWKA) flew over three tracks—the western track, the central track, and the eastern track—to obtain data for investigating the influence of heterogeneous land surface on the daytime ABL structure. [In this study, we will focus on the western track. For more information on the other two tracks, one can refer to LeMone et al. (2007) and/or Weckwerth et al. (2004)]. The UWKA was equipped with sensors that measure the state and motion of the ABL. Detailed information on the instrumentation of the UWKA is available online at http://flights.uwyo.edu/base. Thus, only the aircraft-borne instruments that provide the data used in this study are briefly introduced.

For the aircraft’s position and motion, the outputs from the Honeywell Laseref SM Inertial Reference System (IRS) were corrected based on the global positioning system (GPS). For the measurements of static pressure, temperature, and surface radiation temperature, a Rosemount 1201, a reverse-flow thermometer, and a downward-looking Heiman KT-19.85 radiometer were used, respectively. Potential temperature was derived from the measurement of static pressure by a Rosemount 1201 and from the measurement of temperature by a reverse-flow thermometer. For the water vapor mixing ratio, a Lyman-alpha hygrometer, whose long-term mean is adjusted to that of a chilled-mirror hygrometer, was used. Since the measurement instruments on the aircraft were not collocated, the lags between the sensors have been taken into account (LeMone et al. 2003, 2007). Thus, based on the peaks of the cross correlations between the measured variables, the observations of static pressure, temperature, potential temperature, and water vapor mixing ratio are adjusted to reconcile a 0.08-s lag as compared to the wind observations.

The western track, a 60-km north–south-oriented strip from approximately 36.4° to 37.0°N along 100.6°W (Fig. 1), shows the most heterogeneous surface temperature distribution along with the most sparse vegetation distribution as illustrated in Fig. 9 of Weckwerth et al. (2004). Over this track, the UWKA flew a total of 61 legs on the five boundary layer heterogeneity (BLH) mission days: 19, 20, 25A, 25B, 29 May, and 7 June 2002 (see Table 1 for detailed descriptions). Of the 61 legs, 30 are low-level legs, where the aircraft altitude was approximately 65 m above ground level (AGL). Those repeated low-level passes were done to obtain statistically reliable measurements (see Mann and Lenschow 1994). The observations were recorded at 25 Hz, which corresponds to a spatial resolution of about 3 m, between approximately 1700 and 2000 UTC (1100 and 1400 CST). General information regarding the UWKA flights and the ABL characteristics on the five days is summarized in Table 1. In addition, to characterize the ABL on each day, the vertical soundings of potential temperature and water vapor mixing ratio from the rawinsonde released over Homestead site (Fig. 1; 36.55°N, 100.6°W) at about flight start time are plotted in Fig. 2.

The surface elevation of the track from U.S. Geological Survey (USGS) global 30-s dataset varies within a range of 150 m (Fig. 1). The lowest elevation region, which is around 36.83°N, is occupied by the Beaver River Floodplain that is about 2 km wide. The vegetation cover over the track is estimated by the normalized difference vegetation index (NDVI; LeMone et al. 2007), which was measured from a downward-looking radiometer during the low-level passes of the UWKA flights (Fig. 1). The NDVI indicates sparse vegetation that became greener with time along the track except for the relatively green vegetated area that covers approximately 5 km of the track in the vicinity of the Beaver River. Thus, both terrain elevation and vegetation cover likely make up a relatively homogenous surface condition. However, as shown in Fig. 1, the State Soil Geographic (STATSGO) map exhibits varying soil types along the track.

Over the track on the five BLH days, it was fair weather. The direction of mean wind at 65 m AGL was usually southerly except on 25 May and the mean wind magnitude varied from 2.5 to 13.2 m s^{−1} (see Table 1). For each low-level leg, the relative importance of buoyant production compared to mechanical production of turbulence is compared through Obukhov length (Stull 1988). Here, Obukhov length is obtained from leg-averaged values of momentum flux, buoyancy flux, and virtual potential temperature. The range of the Obukhov length calculated for each low-level leg on a given day is shown in Table 1. Despite their larger surface heat fluxes, 19 and 20 May have relatively large Obukhov lengths due to the strong mean winds. Conversely, 25 and 29 May have relatively small Obukhov lengths due to the relatively weak mean winds although the surface sensible heat fluxes are smaller than those on the previous two days.

In addition to UWKA, other research instruments were concentrated around the track during IHOP_2002 (for the detailed experimental array, see Fig. 4 of Weckwerth et al. 2004). Among them were the three Integrated Surface Flux Facility (ISFF; Chen et al. 2003) sites, and the differential absorption lidar (DIAL; Poberaj et al. 2002) aboard the Deutsche Luft- und Raumfahrt (DLR) Falcon.

The ISFF sites 1, 2, and 3 were deployed along the track from south to north in ascending order (Fig. 1). Surface skin temperatures measured by the Everest 4000.4GL infrared surface temperature sensors at the three ISFF sites are used for the comparison with those observed by the UWKA. The tower-based eddy-covariance flux measurements are also compared with the airborne eddy-covariance measurements. In addition, the surface energy balance (SEB) components, surface skin temperature, and soil temperature were all measured at the three ISFF sites.

Some segments of the UWKA flights were flown concurrently with north–south transects of the DLR Falcon. From the aerosol backscatter data of the DIAL aboard the DLR Falcon, the ABL depths over the track were objectively determined by using the Haar wavelet technique of Davis et al. (2000) at a horizontal resolution of 700 to 1000 m.

## 3. Surface heterogeneity

### a. Surface skin temperature

The surface skin temperature at a given location, defined as the temperature at the air–soil interface, depends on the radiation balance, near-surface atmospheric exchange processes, presence of vegetation cover, and thermal properties of the subsurface medium (Arya 2001). Over surfaces with simple vegetation or bare soil, surface skin temperature can be used as an indicator for thermal heterogeneity of land surface (Mahrt 2000). The vegetation along the track was sparse, with the soil sometimes visible from the aircraft, consistent with the low NDVI values observed along the track (Fig. 1). Thus, for the five fair-weather days, this surface skin temperature distribution may represent the surface thermal heterogeneity over the aircraft track. Figure 3 shows the surface temperature distribution, which is the composite of overlapping 4-km means at every 1 km from the radiometric surface temperatures measured by repeated low-level passes of the UWKA on a given day. Surface skin temperatures are also measured at the three ISFF sites, and the daily averages covering the aircraft flight hours are shown in Fig. 3.

In Fig. 3, except on 25 May, the surface temperature distributions, which are consistent with those of surface heat flux and potential temperature at 65 m AGL (see section 4a), are generally characterized by warmer conditions in the north and cooler conditions in the south with the largest horizontal gradient of 12°C (50 km)^{−1} on 29 May and the smallest gradient of 5°C (50 km)^{−1} on 7 June. 25 May differs from the other days by having an area of higher temperatures around 36.64°N with a surface temperature gradient of −6°C (15 km)^{−1} to the north and −8°C (15 km)^{−1} to the south. The different pattern on 25 May is caused by more heating over the region around site 2 (36.62°N), which is likely associated with relatively small soil heat flux and weak mean winds (see sections 3d and 3e). The high temperature over the entire leg on 25B May is due to the late observation hours, from 1852 to 2021 UTC (Table 1). In Fig. 3, one can also notice that the surface temperatures at about 36.83°N where the Beaver River is located are 0.5°–1.5°C lower than those in surrounding areas all five BLH days.

### b. Rainfall, soil moisture, surface skin temperature, and soil temperature

Figure 4 shows the daily mean values of rainfall, volumetric soil moisture, surface skin temperature, and soil temperature at a depth of 5 cm measured at the ISFF sites 1, 2, and 3 from 13 May to 7 June 2002. There were four rainfall events: on 17 May less than 25 mm, on 24 May 3 mm, on 27 May 20–30 mm toward the north and over 80 mm to the south, and on 5 June 15–20 mm. Although the amount of rainfall differs widely, the four rainfall events always noticeably decrease both surface skin temperature and soil temperature. In spite of the variations in the surface environment, the surface and soil temperature at site 1 persistently gave the lowest values of any site, which is reflected also in the aircraft-measured surface radiation temperature (Fig. 3). We attempt to explain these persistent cooler conditions at site 1 in section 3d.

The significance of soil moisture in the interaction between land surface and atmosphere has been emphasized by numerous researchers (e.g., Chen and Avissar 1994a, b among many papers in the literature). The observed volumetric soil moistures at the three sites indicate that soil hydraulic properties, along with the different characteristics depending on surface cover (e.g., runoff and infiltration), need to be considered to explain the relationship between the spatial variability in rainfall and soil moisture. At site 2, the rainfall of 36 mm [maximum rainfall rate of 10 mm (5 min)^{−1}] on 27 May caused an increase of 29% in the 5-cm volumetric soil moisture. However, at site 1 the 5-cm volumetric soil moisture increased only 19% in spite of a total rainfall of 84 mm [maximum rainfall rate of 4.2 mm (5 min)^{−1}]. The difference in soil hydraulic properties between site 1 and site 2, a spatial difference of around 17 km, was seen again on 5 June (Fig. 4). On this day, the 12-mm rainfall at site 1 [maximum rainfall of 1.4 mm (5 min)^{−1}] caused almost no change, but the 14-mm rainfall at site 2 [maximum rainfall of 1.3 mm (5 min)^{−1}] increased the volumetric soil moisture by 6%.

### c. Sensible and latent heat fluxes

*ρ*is air density derived from the aircraft-measured variables using the ideal gas law,

*C*is specific heat of moist air, and

_{P}*L*is latent heat of vaporization computed as a function of temperature. The perturbations of vertical velocity (

_{υ}*w*″), potential temperature (

*θ*″), and water vapor mixing ratio (

*q*″) are defined from the leg average as

*ϕ*represents one of the variables. The daily mean values of sensible and latent heat flux are obtained by averaging the leg-averaged values over the repeated low-level aircraft passes on a given day. Second, the sensible and latent heat fluxes measured at each site during the aircraft flight are averaged to estimate the surface fluxes on a given day. The sensible and latent heat fluxes averaged over the three sites are used for the comparison with those of the UWKA. Figure 5 shows that aircraft measurements give smaller values than tower measurements by about 10%–20% for both sensible and latent heat fluxes, except for the cases of 29 May and 7 June. On 29 May, the aircraft latent heat flux is 30% higher than the tower measurements while the aircraft sensible heat flux is 10%–20% lower than the tower measurement. The sensible heat fluxes measured by an aircraft are expected to be smaller than those measured by a tower due to the aircraft flight height and the linear decrease of sensible heat flux with height to a negative value at the ABL top (Stull 1988). The latent heat fluxes measured by an aircraft are often higher than the surface fluxes measured by a tower. On 7 June, the aircraft-measured latent heat flux exceeds tower-measured latent heat flux by as much as 85% while the tower-measured sensible heat flux exceeds aircraft-measured sensible heat flux by 30%. This significant overestimation of aircraft-measured latent heat flux is likely caused by the considerable height dependence of this flux on this day (see Table 1 and section 6c).

### d. Surface energy balance

For the three surface flux sites, the diurnal curves of net radiation (Rnet), sensible heat flux (*H*), latent heat flux (LE), and heat flux into the soil (Gs) from 1200 to 0000 UTC (from 0600 to 1800 CST) averaged over the five days are shown in Fig. 6. In Fig. 6a, Rnet at site 2 is larger than those at sites 1 and 3. The smaller Rnet at site 3, compared with the Rnet at site 2, is likely caused by more frequent cloudiness based on the observed smaller incoming shortwave radiation during the daytime. However, the smaller Rnet at site 1 is likely associated with a relatively large albedo. The lower surface temperature (Figs. 3 and 4) indicates smaller upwelling longwave radiation (*Q*^{↑}_{LW}). Thus, based on Rnet ≈ *Q _{s}* (1 −

*A*) +

*Q*

^{↓}

_{LW}−

*Q*

^{↑}

_{LW}(Pielke 2001; Arya 2001; Stull 1988) with the assumption of no significant spatial variability in downwelling longwave radiation (

*Q*

^{−}

_{LW}) and insolation (

*Q*) between the sites, the smaller Rnet at site 1 implies a relatively large albedo (

_{s}*A*) at site 1.

The daytime available energy (Rnet − Gs) for the sensible and latent heat fluxes (H + LE) is estimated based on the closure of surface energy balance, Rnet − Gs ≈ H + LE, which is balanced to within 6% residual in this dataset. In addition to the most net radiation (Fig. 6a), the smallest soil heat flux (Fig. 6d) creates the most available energy at site 2. Here, we estimate soil thermal conductivity, which determines the soil heat flux, with thermal diffusivity and heat capacity (Arya 2001; Stull 1988). First, soil thermal diffusivity is estimated from the theoretical solution of thermal wave propagation in soil (Arya 2001; Stull 1988) by using the amplitudes of the changes in soil temperature measured at 5-cm depth and in surface temperature. Second, at each site, soil heat capacity is estimated by using *C _{s}* =

*ρ*/

_{s}*ρ*× 1.9 × 10

_{m}^{6}+

*Q*× 4.2 × 10

_{s}^{6}(where

*Q*is volumetric soil moisture) with the value of soil bulk density (

_{s}*ρ*) at each site and the density of mineral particles (

_{s}*ρ*), which are obtained from the ISFF/IHOP_2002 Web page (www.atd.ucar.edu/rtf/projects/ihop_2002/isff/). In Table 2, the soil thermal conductivity is usually the lowest at site 2, which is of course consistent with the smallest soil heat flux (Fig. 6d). Thus, although its soil moisture is always the highest, site 2 is warmer than site 1 (Figs. 3 and 4). Under relatively weak mean wind on 25 May, this local feature at site 2 is quite manifest in surface temperature distribution (Fig. 3). The small thermal conductivity indicates that thermal exchanges are concentrated near the uppermost surface. This surface, with a shallow active thermal-exchange layer, experiences extreme diurnal temperature fluctuations (Zhang and Huang 2004).

_{m}At site 3, where the soil moisture at 5 cm is the lowest (Fig. 4), the dry soil causes most of the available energy to be used for the surface sensible heat flux, which implies the lowest values of the surface latent heat flux (Fig. 6c). Thus, with the available energy similar to that at site 1, site 3 shows the highest values of the surface sensible heat flux (Fig. 6b) and the surface temperature among the three ISFF sites (Figs. 3 and 4). On the contrary, site 1, which distributes a significant amount of the available energy to the latent heat flux (Fig. 6c), shows the lowest surface heat flux (Fig. 6b) and the surface temperature (Figs. 3 and 4).

## 4. Stationary spatial variability

### a. Decomposition

*ϕ*, the

*i*th segment average over a fixed-length window in the

*j*th leg, [

*ϕ*]

_{i,j}, is computed. From the segment averages over the

*j*th leg, the leg average, 〈ϕ〉

_{j}, is obtained. The spatial deviation of the

*i*th segment in the

*j*th leg is defined from the leg average

*J*is the number of the repeated aircraft passes. From this stationary part of the spatial deviation, the transient part of the spatial deviation is defined as

Figure 7 shows the stationary spatial deviations, Eq. (5), of potential temperature and water vapor mixing ratio at 65 m AGL over the track. Consistent with the spatial variability of surface skin temperature (Fig. 3), the potential temperature at 65 m has the strongest gradient on 25A May, 1.2 K (22 km)^{−1} between 36.57° and 36.77°N, and the weakest gradient on 7 June, 0.2 K (42 km)^{−1} between 36.50° and 36.88°N. On 25A May, the water vapor mixing ratio has a gradient of 0.45 g kg^{−1} (24 km)^{−1} between 36.60°N around the warmer region, and 36.82°N around the cooler region, which creates warm–dry and cool–moist conditions. Similarly on 29 May, the potential temperature increases at a rate of 1.1 K (48 km)^{−1} from south to north whereas the water vapor mixing ratio decreases at a rate of 2.0 g kg^{−1} (48 km)^{−1}, which also creates warm–dry and cool–moist conditions.

Figure 8 exhibits the stationary spatial deviations of *υ* and *u* winds. Because the mean wind is within 20° of true south (see Table 1), *υ* is approximately the along-wind component and *u* is approximately the crosswind component for all days except 25 May. Excluding 25B May and 7 June, the magnitude of the horizontal wind is lower over more heated area (see Fig. 3). The stationary spatial deviations of vertical heat and moisture fluxes based on the leg averages at 65 m AGL are shown in Fig. 9. The vertical heat flux shows a correspondence with surface temperature, although less obvious than the potential temperature at 65 m.

### b. Variance decomposition

*ϕ*]〉}, was previously removed from the segment averages when a formula for variance was created. For example, the leg average in the first term on the right-hand side, 〈

*ϕ*〉, is obtained from the segment averages by removing the global average. Thus, the terms on the right hand side in Eq. (7) were named as temporal, spatial, and transient variances, respectively (Mahrt et al. 1994b). We used this variance decomposition with the five different segment lengths of 1, 4, 6, 8, and 12 km to evaluate the relative significance of spatial variance as a function of spatial scale. Thus it can be determined at which scales the spatially stationary patterns are the most significant on a given day. This variance decomposition is applied to potential temperature, water vapor mixing ratio, wind components, and vertical heat and moisture fluxes. Here, the deviations for vertical flux of a scalar

*ϕ*have been computed relative to the leg averages:

*ϕ*is potential temperature or water vapor mixing ratio. To avoid the complication in the interpretation that arises by introducing a different observation period and a different number of repeated flight passes, the five low-level legs between 1700 and 1900 UTC (1100 and 1300 CST) on 19 May, 25A May, and 7 June are used.

The variance decomposition results are shown in Fig. 10. For the potential temperature and the along-wind component, the spatial variance normalized by total variance reaches values greater than 0.5 on 19 and 25A May, implying significant horizontal variability on both days. Although temporal and transient variances are not insignificant for the vertical heat and moisture fluxes, stationary spatial variances exceed temporal and transient variances at 12 km on 19 May and at 8 km on 25A May. However, on 7 June, stationary spatial variance for all the variables is smaller than temporal and transient variances at all the segment lengths, which implies that the influence of land surface variability is relatively insignificant.

## 5. Low-level ABL properties

### a. MR spectra

Multiresolution (MR) spectrum is an alternative method to Fourier spectrum and a direct link to the definition of Reynolds averaging because it uses a wavelet basis set with a constant basis function. One can refer to Vickers and Mahrt (2003) for a detailed description of the MR spectrum. We use these MR spectra to estimate the relative significance of the contribution of variance (and covariance) at a segment length in comparison to the total values, and to identify the physical processes of the vertical heat and moisture fluxes at each segment length in the low-level ABL over the heterogeneous land surface.

Figures 11, 12 and 13 show the composites of the MR spectra (or cospectra) normalized by the total variance (or covariance) of each variable, namely, {*C _{wϕ}*(2

^{m})}, where {} implies averaging over all the low-level legs on a given day and 2

^{m}indicates a segment length of 2

^{m}points. In Figs. 11, 12 and 13, the segment lengths of 2

^{m}points are converted into

*meters*by using

*L*= 2

_{m}^{m}×

*u*

_{ac}/

*f*, where

*u*

_{ac}is true airspeed, which was about 80 m s

^{−1}and

*f*is the sampling frequency of 25 Hz.

The composites of the normalized MR spectra of potential temperature (*C _{θθ}*) and water vapor mixing ratio (

*C*

_{qq}) are shown in Fig. 11. For potential temperature and water vapor mixing ratio, turbulence and mesoscale variances can be separated based on the spectral gap defined approximately between 3 and 15 km. On 25 and 29 May, the peaks of mesoscale variances were more significant than those of turbulence variances both for potential temperature and water vapor mixing ratio. However, the composites of the normalized MR spectra of wind components (

*C*

_{uu},

*C*,

_{υυ}*C*

_{ww}) shows the spectral gap being about 10 km only in the along-track wind spectra (Fig. 12). That is to say, the spectra of cross-track wind and vertical wind have no spectral gap and mesoscale variance peak. Even for the along-track wind spectra, only on 25A May is the mesoscale variance peak relatively significant compared to the turbulent variance peak. Thus only on 25A May the higher peaks of mesoscale variances of potential temperature and mixing ratio can be linked to the more significant peak of mesoscale along-track wind variance.

The composites of the cospectra of *w*″ and *θ*″, *w*″ and *q*″, and *q*″ and *θ*″ normalized by the total covariance, {*C*_{wθ}}, {*C*_{wq}}, and {*C*_{qθ}}, respectively, are shown in Fig. 13. In Table 3, the combinations of total covariances with differing signs are summarized into four modes with accompanying physical interpretations. On 19, 20, and 25B May, heating and moistening from the surface, mode I, accounts for 97%, 95%, and 91% (95%, 98%, and 94%) of the total vertical heat (moisture) flux, respectively. However, the contributions of mode I to the total vertical heat (moisture) flux drop to 84%, 86%, and 82% (80%, 88%, and 83%) on 25A, 29 May, and 7 June. Interestingly on 25A May, the negative {*C*_{qθ}} has a peak at 25-km segment length with positive {*C*_{wθ}} and a negative {*C*_{wq}}. In Fig. 11a, the variance of potential temperature at 65 m AGL shows the mesoscale variance peaks at a 25-km segment length on 25A May. Similarly on 29 May the mesoscale variance peaks at a 50-km segment length in Fig. 11a can be linked to the peak of the negative {*C*_{qθ}} with positive {*C*_{wθ}} and negative {*C*_{wq}}. Considered the combination of warm and dry surface conditions with cool and moist surface conditions over the track as shown in previous figures (see Figs. 4, 5, 6, 7 and 9), this updraft of warm and dry air and downdraft of cool and moist air can be interpreted as a mesoscale circulation (mode III). The entrainment–drying processes (mode II) were also involved both on 25A and 29 May. On 25B May and 7 June, some portions of the vertical heat and moisture fluxes were described by the combinations of the negative {*C*_{qθ}} with positive {*C*_{wθ}} and positive {*C*_{wq}} (mode IV). For the case on 25B May, we hypothesized that mode IV is the consequence of the mixed signatures of heating and moistening from the surface and from mesoscale circulations. The {*C _{wθ}*} and {

*C*

_{wq}} are positive due to heating and moistening by thermals from the surface whereas {

*C*

_{qθ}} is negative because it is more influenced by warm and dry, and cool and moist, air associated with mesoscale circulations. For the case on 7 June, mode IV seems to be the consequence of the heating and moistening from a surface mixed with dry entrainment. The strong entrainment of dry air from the free atmosphere cause {

*C*

_{qθ}} to be highly negative even in the low-level ABL, while {

*C*

_{wθ}} and {

*C*

_{wq}} are still positive due to heating and moistening from the surface.

### b. Joint probability distributions

*q*″/

*q*

^{ML}

_{*}(

*q*

^{ML}

_{*}is the mixed-layer humidity scale; Stull 1988) and

*θ*″/

*θ*

^{ML}

_{*}(

*θ*

^{ML}

_{*}is the mixed-layer temperature scale; Stull 1988), within the grid of Δ

*q*/

*q*

^{ML}

_{*}and Δ

*θ*/

*θ*

^{ML}

_{*}, were counted. The counted occurrences at each grid were normalized by the total number of points. Thus,

*P*

_{qθ}is the probability of the occurrence within the grid of Δ

*q*/

*q*

^{ML}

_{*}and Δ

*θ*/

*θ*

^{ML}

_{*}. Similarly, the joint probability distribution was obtained for both

*w*″ and

*q*″, as well as

*w*″ and

*θ*″. For the scaling parameter, the value is first computed for each low-level leg. Next the average of the scales over all the low-level legs on a given day is obtained (see Table 4).

The JPDs categorize the six cases into two groups: 1) 19 May, 20 May, and 7 June, and 2) 25A May, 25B May, and 29 May. Figure 14 shows that on the days in the second group, the dry–warm and moist–cold quadrants become more significant than those in the first group. In addition, the vertical velocity–water vapor distribution looks more elliptical in the second group (Fig. 15). Finally, in Fig. 16, the JPD extends slightly more into the warm downdraft and cold updraft quadrants in the second group. These warm downdraft and cold updraft quadrants are associated with entrained free atmosphere and penetrative convection into the entrainment zone, respectively, while the warm updraft and cold downdraft quadrants are related to thermals (Mahrt and Paumier 1984; Deardorff and Willis 1985). These JPDs imply the existence of different processes associated with vertical heat and moisture fluxes in the low-levels of the ABL over the track, between those two groups.

## 6. Vertical extension

### a. Minimum length scale

*L*

_{TH}) that starts to influence the flow at a certain level, z:

*C*

_{TH}= 3.1 × 10

^{−3}is the nondimensional coefficient (Mahrt 2000), U is the mean horizontal wind velocity, Θ

_{υ}is the mean virtual potential temperature, and

*C*

_{CO}= 0.8 is the nondimensional coefficient (Mahrt 2000),

*w*

_{*}is the convective velocity scale, and

*z*is the ABL depth.

_{i}Using (10) the minimum surface heterogeneity scale that significantly influences the flow at 65 m AGL is computed for each low-level leg. Also for each low-level leg, the minimum surface heterogeneity scale for the flow at the ABL top is estimated by using (11). The composites of the length scales over all of the low-level legs on a given day are summarized in Table 5. On 25A May, the estimated values are one order smaller than those on the other days. This implies that surface heterogeneity on a much smaller scale can significantly influence the whole ABL structure on 25A May.

### b. Deviations from mixed-layer similarity

Quasi-steady and horizontally homogenous ABL conditions are assumed to obtain the vertical profiles of dimensionless variances of velocity, potential temperature, and moisture, which can be expressed by the mixed-layer similarity relationships (Figs. 4 and 5 of Lenschow et al. 1980; Stull 1988, 370–371). The dimensionless variance profiles are estimated from the aircraft measurements over the track for the five days. For vertical velocity, temperature, and moisture, the variances based on leg averages are normalized by their appropriate scaling parameters, 〈*ϕ*″^{2}〉/*ϕ*^{2}_{*}, where *ϕ*_{*} is convective velocity scale (*w*_{*}), mixed-layer temperature scale (*θ*^{ML}_{*}), or mixed-layer moisture scale (*q*^{ML}_{*}). For horizontal and vertical wind, the convective stress velocity scale (*u*^{ML}_{*} ≡ *u*^{2}_{*}/*w*_{*}; Stull 1988) is used to normalize the variances. The scaling parameters obtained from the data collected by the repeated low-level passes are summarized in Table 4. For each leg, the flight height is normalized by the ABL depth, which is estimated based on the UWKA soundings and the spatial averages of the ABL depths from the DLR Falcon over the track.

As shown in Fig. 17, except below the height of 0.1 *z _{i}* (

*z*is the ABL depth), the normalized variances of horizontal wind velocity are well fitted by 〈

_{i}*u*″

^{2}〉/

*u*

^{ML}

_{*}

^{2}= 〈

*υ*″

^{2}〉/

*u*

^{ML}

_{*}

^{2}= const. (Stull 1988). Normalized variances of horizontal wind on 25 and 29 May are aligned with the constant values that are 19 times and 4 times larger than that on the other three days, respectively. Also, the vertical velocity variances normalized by convective stress velocity, 〈

*w*″

^{2}〉/

*u*

^{ML}

_{*}

^{2}, can be fitted by constant values, which are 18 times larger on 25 May and 3 times larger on 29 May than that on the other days (Fig. 18a). However, the normalized variances of wind velocity at levels higher than 0.6

*z*on 7 June deviate from the similarity curves, which may be associated with the weak capping inversion of 2 K (200 m)

_{i}^{−1}measured at the Homestead profiling site at 1856 UTC (Fig. 2).

In Fig. 19a, the variances of potential temperature on 19 May, 20 May, and 7 June are well fitted by the similarity curve of 〈*θ*″^{2}〉/*θ*^{2}_{*} = 1.8 (*z*/*z _{i}*)

^{−2/3}(Lenschow et al. 1980; Stull 1988) except for the values near the ABL top where the effect of entrainment is significant (Wyngaard and LeMone 1980). The deviations of the potential temperature variances from the similarity curve on 25 and 29 May are likely associated with the significant mesoscale peaks in the spectra of potential temperature at 65 m AGL (Fig. 11a). Moisture variances are generally larger than the expected values from the similarity curve of 〈

*q*″

^{2}〉/

*q*

^{2}

_{*}= 1.8 (

*z*/

*z*)

_{i}^{−2/3}(Lenschow et al. 1980; Stull 1988). In general these large deviations can be linked to more sensitive response of moisture to entrainment or mesoscale motions than temperature and vertical wind (Mahrt et al. 1994a, b; Mahrt 1991). Also consistent with the large mesoscale peaks in the spectra of water vapor mixing ratio at 65 m AGL (Fig. 11b), the deviations of the variances on 25 and 29 May are much larger than those on the other days.

Assuming the departures from similarity are due to mesoscale motions, we recalculate the variances relative to segment averages. As shown in Fig. 20, the vertical profiles of the variances based on segment averages are well fitted to the similarity curve whereas some departures are still shown due to the negligence of the strong wind effect on 19 and 20 May and the deep entrainment on 7 June. This implies that filtering out the mesoscale motions makes the similarity more applicable.^{1} Here it is to be noted that—different than vertical velocity and moisture, which use a 1-km high-pass spatial filter—potential temperature uses a 4-km spatial filter to fit the observations onto the similarity curves.

### c. Observed spatial variations of the ABL depth

The spatial distributions of the ABL depths over the track for the five BLH days, which are estimated from the aerosol backscatter measurements of the DIAL aboard the DLR Falcon, are shown in Fig. 21. On 19, 20, and 29 May, the ABL was deeper to the north and shallower to the south, consistent with the surface skin temperature distribution (Fig. 3). On 25 May, a different ABL depth distribution, elevated around 36.60°N and depressed around 36.80°N, was also consistent with the surface temperature distribution on that day (Fig. 3). Smaller-scale surface heterogeneity was expected to significantly influence the whole ABL structure on 25 May based on the minimum length scale argument in section 6a. For the four days, these ABL depth distributions are consistent also with the potential temperature distributions measured at 65 m AGL. On 7 June, only the first leg, flown 1651 and 1704 UTC, showed the deeper-north pattern. On subsequent legs, the ABL grew rapidly across the entire track, associated with a weak capping inversion of 2 K (200 m)^{−1} measured at Homestead profiling site at 1856 UTC (Fig. 2); ABL heights were randomly distributed along the track. Thus one can conclude that the features of the surface heterogeneity over the track influenced the entire ABL structures except on 7 June. In other words, over the track for the four days among the five days, the blending height determined from the surface heterogeneity exceeded the ABL depths and the ABL established equilibrium with the local surface condition, a regime called macroscale heterogeneity (Mahrt 2000).

## 7. Summary and conclusions

This study analyzes data collected by aircraft on five fair-weather days during IHOP_2002 to investigate the ABL structures over a heterogeneous land surface along the track (36.4°–37.0°N, 100.6°W; Fig. 1) under different background weather conditions. The tower- and aircraft- measured surface skin temperature distributions both show the warm–north and cool–south pattern over the track. The surface skin temperature was increased by about 10°C or more from southern end to the northern end of the aircraft track for four of the five days, whereas on 7 June the surface temperature at the northern end of the track was slightly less than 5°C higher than at the southern end. On 25 May, the warm region around 36.64°N was superimposed on the warm–north and cool–south pattern.

The measurements at the surface flux sites suggest that the surface temperature distribution is mainly caused by the combination of soil thermal properties and soil moisture. With a similar amount of available surface energy (Rn-G) along the track, site 3, located around the northern end of the track (36.86°N), used most of the available energy to produce sensible heat flux due to dry soil, as shown in Fig. 6. At site 2 (36.62°N), the heat flux into ground (G) is less due to relatively small soil thermal conductivity (Table 2). Thus, even with similar amount of latent heat flux, site 2 could produce more sensible heat flux than site 1 due to more available surface energy. On 25 May, surface temperature around site 2 can more rapidly rise due to the shallower active thermal-exchange layer that is associated with the smaller soil thermal conductivity, especially under relatively calm winds. This additional heating around site 2 causes the small-scale heterogeneity superimposed on the large-scale pattern.

The stationary spatial variability described by the data collected from the repeated aircraft passes at 65 m AGL shows a slowdown of the along-wind component and warmer air temperatures over warmer surfaces. High vertical flux is also associated with warmer surfaces, but the association is less robust due to considerable temporal and transient variability.

Mesoscale circulations (warm, dry updrafts and cool, moist downdrafts) generated by the land surface heterogeneity can be seen through MR cospectra and JPDs on 25 and 29 May. On these two days, the ABL is likely dominated by buoyancy-generated turbulence, given the smallness of the Obukhov lengths, and the relatively small-scale surface heterogeneity needed to influence the whole ABL. On 25A May, MR spectra show a significant peak of mesoscale along-track wind variance (Fig. 12b), which is linked to the significant peaks of mesoscale variances of potential temperature and water vapor mixing ratio. Also on these two days, the vertical profiles of dimensionless variances of wind components, potential temperature, and moisture (Figs. 17, 18 and 19) exhibit significant deviations from the similarity curves, which are based on the assumption of homogeneous surface conditions. However, when we used high-pass spatial filters, these dimensionless variances fit the similarity curves better (Fig. 20), which also implies the existence of mesoscale circulation on 25 and 29 May.

On 25 and 29 May, however, the lack of a high-amplitude mesoscale peak in the wind spectra (Fig. 12), except for the along-track wind component on 25A May, makes the existence of well-organized mesoscale circulations doubtful. Considering the scales of the surface heterogeneity feature, which can be seen in the ABL depth distribution on these two days, the observed ABL seems to be in the mixed-scale ABL regime of turbulence and less-organized mesoscale circulations. With the similar horizontal scale of surface heterogeneity (20–40 km), LES studies (Patton et al. 2005; Avissar and Schmidt 1998) have shown that persistent turbulent thermals coexisting with less-organized mesoscale circulations over a sinusoidal-shaped heterogeneous land surface. However, they have mostly focused on the well-organized mesoscale circulations. In future research, we plan to simulate the ABL under the mixed-scale regime, which was likely observed on 25 and 29 May by using LES with the background weather conditions measured at the Homestead profiling site (Fig. 1) and the observed surface heat fluxes at the three ISFF sites. These simulations will allow us to investigate the ABL structure under the mixed-scale regime in detail and its potential link to convective cloud development.

## Acknowledgments

This research was supported by the National Science Foundation through Grant ATM-0130349. The third author’s participation is sponsored through NCAR. This work could not have been possible without the observational dataset collected by the great efforts of the staffs of UWKA, NCAR ISFF, and DLR Falcon. The authors thank Ken Craig for providing the ABL depth data estimated from the aerosol backscatter data of the DIAL aboard the DLR Falcon, Dean Vickers and L. Mahrt for providing MR spectra software and commenting on the spectra results, and Brian Reen and Robert B. Seigel for helping to prepare for this manuscript.

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Vertical profiles of (a) potential temperature and (b) water vapor mixing ratio from the rawinsonde released over the Homestead profiling site (Fig. 1; 36.55°N, 100.6°W) at 1740, 1731, 1733, 1741, and 1856 UTC 19 May, 20 May, 25 May, 29 May, and 7 Jun 2002, respectively.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Vertical profiles of (a) potential temperature and (b) water vapor mixing ratio from the rawinsonde released over the Homestead profiling site (Fig. 1; 36.55°N, 100.6°W) at 1740, 1731, 1733, 1741, and 1856 UTC 19 May, 20 May, 25 May, 29 May, and 7 Jun 2002, respectively.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Vertical profiles of (a) potential temperature and (b) water vapor mixing ratio from the rawinsonde released over the Homestead profiling site (Fig. 1; 36.55°N, 100.6°W) at 1740, 1731, 1733, 1741, and 1856 UTC 19 May, 20 May, 25 May, 29 May, and 7 Jun 2002, respectively.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Composite structure of surface radiation temperature with 4-km means at every 1 km from the repeated passes of the aircraft at 65 m AGL at a given day. The rectangles, circles, and triangles indicate the averages of the surface skin temperatures measured at ISFF sites 1, 2, and 3 over the aircraft flight hours at the written day beside the symbols. There were no surface radiation temperatures available on 7 June from the UWKA due to the malfunction of the measurement instrument (downward-looking Heiman KT-19.85 radiometer).

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Composite structure of surface radiation temperature with 4-km means at every 1 km from the repeated passes of the aircraft at 65 m AGL at a given day. The rectangles, circles, and triangles indicate the averages of the surface skin temperatures measured at ISFF sites 1, 2, and 3 over the aircraft flight hours at the written day beside the symbols. There were no surface radiation temperatures available on 7 June from the UWKA due to the malfunction of the measurement instrument (downward-looking Heiman KT-19.85 radiometer).

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Composite structure of surface radiation temperature with 4-km means at every 1 km from the repeated passes of the aircraft at 65 m AGL at a given day. The rectangles, circles, and triangles indicate the averages of the surface skin temperatures measured at ISFF sites 1, 2, and 3 over the aircraft flight hours at the written day beside the symbols. There were no surface radiation temperatures available on 7 June from the UWKA due to the malfunction of the measurement instrument (downward-looking Heiman KT-19.85 radiometer).

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Daily mean values of precipitation (solid line and filled symbol), volumetric soil moisture (dotted line and filled symbol), surface skin temperature (solid line and unfilled symbol), and soil temperature at a depth of 5 cm (dotted line and unfilled symbol) measured at the ISFF sites 1 (square), 2 (circle), and 3 (triangle) from 13 May to 7 Jun 2002.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Daily mean values of precipitation (solid line and filled symbol), volumetric soil moisture (dotted line and filled symbol), surface skin temperature (solid line and unfilled symbol), and soil temperature at a depth of 5 cm (dotted line and unfilled symbol) measured at the ISFF sites 1 (square), 2 (circle), and 3 (triangle) from 13 May to 7 Jun 2002.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Daily mean values of precipitation (solid line and filled symbol), volumetric soil moisture (dotted line and filled symbol), surface skin temperature (solid line and unfilled symbol), and soil temperature at a depth of 5 cm (dotted line and unfilled symbol) measured at the ISFF sites 1 (square), 2 (circle), and 3 (triangle) from 13 May to 7 Jun 2002.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

(a) Relationship between averages of sensible heat fluxes derived from the data collected by the repeated low-level aircraft passes vs average of the sensible heat fluxes measured at the three ISFF sites during the aircraft flights. (b) Same as in (a) but for latent heat fluxes. Unfilled star denotes the relationship between the aircraft values and the spatial averages of the values at the three sites. The error bar over the star indicates standard error defined as the standard deviation between the low-level legs divided by the square root of the number of the low-level legs (Mahrt 1998). Here standard error is computed by dividing std dev by the square root of the number of the repeated low-level passes. Square, circle, and triangle represent the relationship between the aircraft values and the values measured at sites 1, 2, and 3, respectively.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

(a) Relationship between averages of sensible heat fluxes derived from the data collected by the repeated low-level aircraft passes vs average of the sensible heat fluxes measured at the three ISFF sites during the aircraft flights. (b) Same as in (a) but for latent heat fluxes. Unfilled star denotes the relationship between the aircraft values and the spatial averages of the values at the three sites. The error bar over the star indicates standard error defined as the standard deviation between the low-level legs divided by the square root of the number of the low-level legs (Mahrt 1998). Here standard error is computed by dividing std dev by the square root of the number of the repeated low-level passes. Square, circle, and triangle represent the relationship between the aircraft values and the values measured at sites 1, 2, and 3, respectively.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

(a) Relationship between averages of sensible heat fluxes derived from the data collected by the repeated low-level aircraft passes vs average of the sensible heat fluxes measured at the three ISFF sites during the aircraft flights. (b) Same as in (a) but for latent heat fluxes. Unfilled star denotes the relationship between the aircraft values and the spatial averages of the values at the three sites. The error bar over the star indicates standard error defined as the standard deviation between the low-level legs divided by the square root of the number of the low-level legs (Mahrt 1998). Here standard error is computed by dividing std dev by the square root of the number of the repeated low-level passes. Square, circle, and triangle represent the relationship between the aircraft values and the values measured at sites 1, 2, and 3, respectively.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The surface energy balance components measured at the ISFF sites 1 (solid), 2 (dotted), and 3 (dashed) averaged for the five days. Rnet, H, LE, and Gs represent net radiation, sensible heat flux, latent heat flux, and soil heat flux at a depth of 5 cm. Here, the soil heat flux was measured with a heat flux plate at a depth of 5 cm. For Rnet and Gs, a positive sign is used for downward flux. However, for H and LE, a negative sign is used for upward flux.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The surface energy balance components measured at the ISFF sites 1 (solid), 2 (dotted), and 3 (dashed) averaged for the five days. Rnet, H, LE, and Gs represent net radiation, sensible heat flux, latent heat flux, and soil heat flux at a depth of 5 cm. Here, the soil heat flux was measured with a heat flux plate at a depth of 5 cm. For Rnet and Gs, a positive sign is used for downward flux. However, for H and LE, a negative sign is used for upward flux.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The surface energy balance components measured at the ISFF sites 1 (solid), 2 (dotted), and 3 (dashed) averaged for the five days. Rnet, H, LE, and Gs represent net radiation, sensible heat flux, latent heat flux, and soil heat flux at a depth of 5 cm. Here, the soil heat flux was measured with a heat flux plate at a depth of 5 cm. For Rnet and Gs, a positive sign is used for downward flux. However, for H and LE, a negative sign is used for upward flux.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Composite structures of potential temperature, {*θ ^{S}*}, and water vapor mixing ratio, {

*q*}, using 4-km means at every 1 km from the repeated passes of the aircraft at 65 m AGL over the western track on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 Jun 2002. The error bar indicates standard error defined as the standard deviation between the low-level legs divided by the square root of the number of the low-level legs (Mahrt 1998).

^{S}Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Composite structures of potential temperature, {*θ ^{S}*}, and water vapor mixing ratio, {

*q*}, using 4-km means at every 1 km from the repeated passes of the aircraft at 65 m AGL over the western track on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 Jun 2002. The error bar indicates standard error defined as the standard deviation between the low-level legs divided by the square root of the number of the low-level legs (Mahrt 1998).

^{S}Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Composite structures of potential temperature, {*θ ^{S}*}, and water vapor mixing ratio, {

*q*}, using 4-km means at every 1 km from the repeated passes of the aircraft at 65 m AGL over the western track on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 Jun 2002. The error bar indicates standard error defined as the standard deviation between the low-level legs divided by the square root of the number of the low-level legs (Mahrt 1998).

^{S}Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Composite structures of along-track wind, {*υ ^{S}*}, and cross-track wind, {

*u*}, using 4-km means at every 1 km from the repeated passes of the aircraft at 65 m AGL over the western track on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 Jun 2002. The error bar indicates standard error defined as the standard deviation between the low-level legs divided by the square root of the number of the low-level legs (Mahrt 1998).

^{S}Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Composite structures of along-track wind, {*υ ^{S}*}, and cross-track wind, {

*u*}, using 4-km means at every 1 km from the repeated passes of the aircraft at 65 m AGL over the western track on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 Jun 2002. The error bar indicates standard error defined as the standard deviation between the low-level legs divided by the square root of the number of the low-level legs (Mahrt 1998).

^{S}Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Composite structures of along-track wind, {*υ ^{S}*}, and cross-track wind, {

*u*}, using 4-km means at every 1 km from the repeated passes of the aircraft at 65 m AGL over the western track on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 Jun 2002. The error bar indicates standard error defined as the standard deviation between the low-level legs divided by the square root of the number of the low-level legs (Mahrt 1998).

^{S}Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Composite structures of vertical heat fluxes, {(*w*″*θ*″)* ^{S}*}, and moisture fluxes, {(

*w*″

*q*″)

*}, using 4-km means at every 1 km from the repeated passes of the aircraft at 65 m AGL over the western track on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 Jun 2002. The error bar indicates standard error defined as the standard deviation between the low-level legs divided by the square root of the number of the low-level legs (Mahrt 1998).*

^{S}Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Composite structures of vertical heat fluxes, {(*w*″*θ*″)* ^{S}*}, and moisture fluxes, {(

*w*″

*q*″)

*}, using 4-km means at every 1 km from the repeated passes of the aircraft at 65 m AGL over the western track on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 Jun 2002. The error bar indicates standard error defined as the standard deviation between the low-level legs divided by the square root of the number of the low-level legs (Mahrt 1998).*

^{S}Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Composite structures of vertical heat fluxes, {(*w*″*θ*″)* ^{S}*}, and moisture fluxes, {(

*w*″

*q*″)

*}, using 4-km means at every 1 km from the repeated passes of the aircraft at 65 m AGL over the western track on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 Jun 2002. The error bar indicates standard error defined as the standard deviation between the low-level legs divided by the square root of the number of the low-level legs (Mahrt 1998).*

^{S}Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The ratio of spatial variance to total variance in the variance decompositions of (a) potential temperature and water vapor mixing ratio, of (b) along-track and cross-track winds, and of (c) vertical heat and moisture fluxes; th, q, *υ*, u, wth, and wq represent potential temperature, mixing ratio, along-track wind, cross-track wind, vertical heat flux, and vertical moisture flux, respectively. Here, 1-, 4-, 6-, 8-, and 12-km nonoverlapping segments are used for the data from the five low-level legs between 1700 and 1900 UTC 19 May (square), 25A May (diamond), and 7 June (triangle).

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The ratio of spatial variance to total variance in the variance decompositions of (a) potential temperature and water vapor mixing ratio, of (b) along-track and cross-track winds, and of (c) vertical heat and moisture fluxes; th, q, *υ*, u, wth, and wq represent potential temperature, mixing ratio, along-track wind, cross-track wind, vertical heat flux, and vertical moisture flux, respectively. Here, 1-, 4-, 6-, 8-, and 12-km nonoverlapping segments are used for the data from the five low-level legs between 1700 and 1900 UTC 19 May (square), 25A May (diamond), and 7 June (triangle).

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The ratio of spatial variance to total variance in the variance decompositions of (a) potential temperature and water vapor mixing ratio, of (b) along-track and cross-track winds, and of (c) vertical heat and moisture fluxes; th, q, *υ*, u, wth, and wq represent potential temperature, mixing ratio, along-track wind, cross-track wind, vertical heat flux, and vertical moisture flux, respectively. Here, 1-, 4-, 6-, 8-, and 12-km nonoverlapping segments are used for the data from the five low-level legs between 1700 and 1900 UTC 19 May (square), 25A May (diamond), and 7 June (triangle).

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The composite of the normalized MR spectra of (a) potential temperature (*θ*) and (b) water vapor mixing ratio (*q*) over all the low-level legs on 19, 20, 25A, 25B, 29 May, and 7 June. The error bar indicates standard error defined as the standard deviation between the low-level legs divided by the square root of the number of the low-level legs.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The composite of the normalized MR spectra of (a) potential temperature (*θ*) and (b) water vapor mixing ratio (*q*) over all the low-level legs on 19, 20, 25A, 25B, 29 May, and 7 June. The error bar indicates standard error defined as the standard deviation between the low-level legs divided by the square root of the number of the low-level legs.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The composite of the normalized MR spectra of (a) potential temperature (*θ*) and (b) water vapor mixing ratio (*q*) over all the low-level legs on 19, 20, 25A, 25B, 29 May, and 7 June. The error bar indicates standard error defined as the standard deviation between the low-level legs divided by the square root of the number of the low-level legs.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The composite of the MR spectra of horizontal (*u, υ*) and vertical velocity (*w*) components over all the low-level legs on 19, 20, 25A, 25B, 29 May, and 7 June. The error bar indicates standard error.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The composite of the MR spectra of horizontal (*u, υ*) and vertical velocity (*w*) components over all the low-level legs on 19, 20, 25A, 25B, 29 May, and 7 June. The error bar indicates standard error.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The composite of the MR spectra of horizontal (*u, υ*) and vertical velocity (*w*) components over all the low-level legs on 19, 20, 25A, 25B, 29 May, and 7 June. The error bar indicates standard error.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The composites of the normalized MR cospectra of *w*″*θ*″ (solid), *w*″*q*″ (dotted), and *q*″*θ*″ (dashed) over all the low-level legs on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 June. The error bar represents standard error. The vertical solid line indicates boundary between mode I and other modes. Modes I, II, III, and IV are explained in Table 3.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The composites of the normalized MR cospectra of *w*″*θ*″ (solid), *w*″*q*″ (dotted), and *q*″*θ*″ (dashed) over all the low-level legs on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 June. The error bar represents standard error. The vertical solid line indicates boundary between mode I and other modes. Modes I, II, III, and IV are explained in Table 3.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The composites of the normalized MR cospectra of *w*″*θ*″ (solid), *w*″*q*″ (dotted), and *q*″*θ*″ (dashed) over all the low-level legs on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 June. The error bar represents standard error. The vertical solid line indicates boundary between mode I and other modes. Modes I, II, III, and IV are explained in Table 3.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Joint probability distributions of the perturbations of water vapor mixing ratio and potential temperature on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 June. The color bar indicates the range of the probability in percent within a grid of Δ*q*″/*q*^{ML}_{*} and Δ*θ*″/*θ*^{ML}_{*}. Here Δ*q*″ is 12 g kg^{−1}, and Δ*θ*″ is 6 K. For each day, the values of *q*^{ML}_{*} and *θ*^{ML}_{*} are given in Table 4.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Joint probability distributions of the perturbations of water vapor mixing ratio and potential temperature on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 June. The color bar indicates the range of the probability in percent within a grid of Δ*q*″/*q*^{ML}_{*} and Δ*θ*″/*θ*^{ML}_{*}. Here Δ*q*″ is 12 g kg^{−1}, and Δ*θ*″ is 6 K. For each day, the values of *q*^{ML}_{*} and *θ*^{ML}_{*} are given in Table 4.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Joint probability distributions of the perturbations of water vapor mixing ratio and potential temperature on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 June. The color bar indicates the range of the probability in percent within a grid of Δ*q*″/*q*^{ML}_{*} and Δ*θ*″/*θ*^{ML}_{*}. Here Δ*q*″ is 12 g kg^{−1}, and Δ*θ*″ is 6 K. For each day, the values of *q*^{ML}_{*} and *θ*^{ML}_{*} are given in Table 4.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Joint probability distributions of the perturbations of vertical velocity and water vapor mixing ratio on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 June. The color bar indicates the range of the probability in percent within a grid of Δ*w*″/*w*^{ML}_{*} and Δ*q*″/*q*^{ML}_{*}. Here Δ*w*″ is 0.8 m s^{−1}, and Δ*q*″ is 12 g kg^{−1}. For each day, the values of *w*^{ML}_{*} and *q*^{ML}_{*} are given in Table 4.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Joint probability distributions of the perturbations of vertical velocity and water vapor mixing ratio on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 June. The color bar indicates the range of the probability in percent within a grid of Δ*w*″/*w*^{ML}_{*} and Δ*q*″/*q*^{ML}_{*}. Here Δ*w*″ is 0.8 m s^{−1}, and Δ*q*″ is 12 g kg^{−1}. For each day, the values of *w*^{ML}_{*} and *q*^{ML}_{*} are given in Table 4.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Joint probability distributions of the perturbations of vertical velocity and water vapor mixing ratio on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 June. The color bar indicates the range of the probability in percent within a grid of Δ*w*″/*w*^{ML}_{*} and Δ*q*″/*q*^{ML}_{*}. Here Δ*w*″ is 0.8 m s^{−1}, and Δ*q*″ is 12 g kg^{−1}. For each day, the values of *w*^{ML}_{*} and *q*^{ML}_{*} are given in Table 4.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Joint probability distributions of the perturbations of vertical velocity and potential temperature on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 June. The color bar indicates the range of the probability in percent within a grid of Δ*w*″/*w*^{ML}_{*} and Δ*θ*″/*θ*^{ML}_{*}. Here Δ*w*″ is 0.8 m s^{−1}, and Δ*θ*″ is 6 K. For each day, the values of *w*^{ML}_{*} and *θ*^{ML}_{*}are given in Table 4.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Joint probability distributions of the perturbations of vertical velocity and potential temperature on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 June. The color bar indicates the range of the probability in percent within a grid of Δ*w*″/*w*^{ML}_{*} and Δ*θ*″/*θ*^{ML}_{*}. Here Δ*w*″ is 0.8 m s^{−1}, and Δ*θ*″ is 6 K. For each day, the values of *w*^{ML}_{*} and *θ*^{ML}_{*}are given in Table 4.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Joint probability distributions of the perturbations of vertical velocity and potential temperature on (a) 19 May, (b) 20 May, (c) 25A May, (d) 25B May, (e) 29 May, and (f) 7 June. The color bar indicates the range of the probability in percent within a grid of Δ*w*″/*w*^{ML}_{*} and Δ*θ*″/*θ*^{ML}_{*}. Here Δ*w*″ is 0.8 m s^{−1}, and Δ*θ*″ is 6 K. For each day, the values of *w*^{ML}_{*} and *θ*^{ML}_{*}are given in Table 4.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The vertical profiles of the normalized horizontal velocity variances. The dotted lines are the curves of (a) 〈*u*″^{2}〉/ *u*^{ML}_{*}^{2} = const. and (b) 〈*υ*″^{2}〉/*u*^{ML}_{*}^{2} = const. Here the convective stress velocity scale, *u*^{ML}_{*}, is defined as *u*^{2}_{*}/*w*_{*}, where *u*_{*} is friction velocity and is convective velocity scale (Stull 1988). The constants are 30, 110, and 580 for the (a) along-track wind variance and (b) the cross-track wind variances.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The vertical profiles of the normalized horizontal velocity variances. The dotted lines are the curves of (a) 〈*u*″^{2}〉/ *u*^{ML}_{*}^{2} = const. and (b) 〈*υ*″^{2}〉/*u*^{ML}_{*}^{2} = const. Here the convective stress velocity scale, *u*^{ML}_{*}, is defined as *u*^{2}_{*}/*w*_{*}, where *u*_{*} is friction velocity and is convective velocity scale (Stull 1988). The constants are 30, 110, and 580 for the (a) along-track wind variance and (b) the cross-track wind variances.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The vertical profiles of the normalized horizontal velocity variances. The dotted lines are the curves of (a) 〈*u*″^{2}〉/ *u*^{ML}_{*}^{2} = const. and (b) 〈*υ*″^{2}〉/*u*^{ML}_{*}^{2} = const. Here the convective stress velocity scale, *u*^{ML}_{*}, is defined as *u*^{2}_{*}/*w*_{*}, where *u*_{*} is friction velocity and is convective velocity scale (Stull 1988). The constants are 30, 110, and 580 for the (a) along-track wind variance and (b) the cross-track wind variances.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The vertical profiles of the normalized vertical velocity variances normalized by (a) convective stress velocity scale, *u*^{ML}_{*}, and (b) convective velocity scale, *w*_{*}. The dotted lines are the curve of (a) 〈*w*″^{2}〉/*u*^{ML}_{*}^{2} = const. and (b) 〈*w*″^{2}〉/*w*^{2}_{*} = 1.8 (*z*/*z _{i}*)

^{−2/3}(1 − 0.8

*z*/

*z*)

_{i}^{2}(from Lenschow et al. 1980). The constants are 30, 90, and 550 for the vertical velocity variances normalized by convective stress velocity.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The vertical profiles of the normalized vertical velocity variances normalized by (a) convective stress velocity scale, *u*^{ML}_{*}, and (b) convective velocity scale, *w*_{*}. The dotted lines are the curve of (a) 〈*w*″^{2}〉/*u*^{ML}_{*}^{2} = const. and (b) 〈*w*″^{2}〉/*w*^{2}_{*} = 1.8 (*z*/*z _{i}*)

^{−2/3}(1 − 0.8

*z*/

*z*)

_{i}^{2}(from Lenschow et al. 1980). The constants are 30, 90, and 550 for the vertical velocity variances normalized by convective stress velocity.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The vertical profiles of the normalized vertical velocity variances normalized by (a) convective stress velocity scale, *u*^{ML}_{*}, and (b) convective velocity scale, *w*_{*}. The dotted lines are the curve of (a) 〈*w*″^{2}〉/*u*^{ML}_{*}^{2} = const. and (b) 〈*w*″^{2}〉/*w*^{2}_{*} = 1.8 (*z*/*z _{i}*)

^{−2/3}(1 − 0.8

*z*/

*z*)

_{i}^{2}(from Lenschow et al. 1980). The constants are 30, 90, and 550 for the vertical velocity variances normalized by convective stress velocity.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The vertical profiles of the normalized potential temperature and water vapor mixing ratio variances. The dotted lines are the curve of (a) *z*/*z _{i}*)

^{−2/3}and (b)

*z*/

*z*)

_{i}^{−2/3}(from Lenschow et al. 1980).

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The vertical profiles of the normalized potential temperature and water vapor mixing ratio variances. The dotted lines are the curve of (a) *z*/*z _{i}*)

^{−2/3}and (b)

*z*/

*z*)

_{i}^{−2/3}(from Lenschow et al. 1980).

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The vertical profiles of the normalized potential temperature and water vapor mixing ratio variances. The dotted lines are the curve of (a) *z*/*z _{i}*)

^{−2/3}and (b)

*z*/

*z*)

_{i}^{−2/3}(from Lenschow et al. 1980).

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The vertical variance profiles of (a) vertical velocity, (b) potential temperature, and (c) water vapor mixing ratio normalized by convective velocity scale, mixed-layer temperature scale, and mixed-layer moisture scale, respectively. For vertical velocity and water vapor mixing ratio, 1-km spatial filters are used. For potential temperature, 4-km spatial filters are used. The dotted lines are the curve of (a) 〈*w*″^{2}〉/*w*^{2}_{*} = 1.8 (*z*/*z _{i}*)

^{−2/3}(1 − 0.8

*z*/

*z*)

_{i}^{2}, (b)

*z*/

*z*)

_{i}^{−2/3}, and (c)

*z*/

*z*)

_{i}^{−2/3}(from Lenschow et al. 1980).

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The vertical variance profiles of (a) vertical velocity, (b) potential temperature, and (c) water vapor mixing ratio normalized by convective velocity scale, mixed-layer temperature scale, and mixed-layer moisture scale, respectively. For vertical velocity and water vapor mixing ratio, 1-km spatial filters are used. For potential temperature, 4-km spatial filters are used. The dotted lines are the curve of (a) 〈*w*″^{2}〉/*w*^{2}_{*} = 1.8 (*z*/*z _{i}*)

^{−2/3}(1 − 0.8

*z*/

*z*)

_{i}^{2}, (b)

*z*/

*z*)

_{i}^{−2/3}, and (c)

*z*/

*z*)

_{i}^{−2/3}(from Lenschow et al. 1980).

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The vertical variance profiles of (a) vertical velocity, (b) potential temperature, and (c) water vapor mixing ratio normalized by convective velocity scale, mixed-layer temperature scale, and mixed-layer moisture scale, respectively. For vertical velocity and water vapor mixing ratio, 1-km spatial filters are used. For potential temperature, 4-km spatial filters are used. The dotted lines are the curve of (a) 〈*w*″^{2}〉/*w*^{2}_{*} = 1.8 (*z*/*z _{i}*)

^{−2/3}(1 − 0.8

*z*/

*z*)

_{i}^{2}, (b)

*z*/

*z*)

_{i}^{−2/3}, and (c)

*z*/

*z*)

_{i}^{−2/3}(from Lenschow et al. 1980).

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The estimated ABL depths based on the aerosol backscatter measurements of the DIAL aboard the DLR Falcon flown over the western track on (a) 19 May, (b) 20 May, (c) 25 May, (d) 29 May, and (e) 7 Jun 2002. The circles, filled circles, squares, and filled squares indicate first, second, third, and fourth legs. The first leg on 19 May is flown at 1650–1704 UTC. The first and second legs on 20 May are flown at 1920–1932 and 1941–1953 UTC, respectively. The first, second, and third legs on 25 May are flown at 1745–1758, 1807–1818, and 1844–1857 UTC. The first, second, third, and fourth legs on 29 May are flown at 1806–1820, 1829–1839, 1904–1918, and 1927–1938 UTC. The first, second, third, and fourth legs on 7 Jun are flown at 1651–1704, 1754–1803, 1829–1835, and 1932–1944 UTC.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The estimated ABL depths based on the aerosol backscatter measurements of the DIAL aboard the DLR Falcon flown over the western track on (a) 19 May, (b) 20 May, (c) 25 May, (d) 29 May, and (e) 7 Jun 2002. The circles, filled circles, squares, and filled squares indicate first, second, third, and fourth legs. The first leg on 19 May is flown at 1650–1704 UTC. The first and second legs on 20 May are flown at 1920–1932 and 1941–1953 UTC, respectively. The first, second, and third legs on 25 May are flown at 1745–1758, 1807–1818, and 1844–1857 UTC. The first, second, third, and fourth legs on 29 May are flown at 1806–1820, 1829–1839, 1904–1918, and 1927–1938 UTC. The first, second, third, and fourth legs on 7 Jun are flown at 1651–1704, 1754–1803, 1829–1835, and 1932–1944 UTC.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

The estimated ABL depths based on the aerosol backscatter measurements of the DIAL aboard the DLR Falcon flown over the western track on (a) 19 May, (b) 20 May, (c) 25 May, (d) 29 May, and (e) 7 Jun 2002. The circles, filled circles, squares, and filled squares indicate first, second, third, and fourth legs. The first leg on 19 May is flown at 1650–1704 UTC. The first and second legs on 20 May are flown at 1920–1932 and 1941–1953 UTC, respectively. The first, second, and third legs on 25 May are flown at 1745–1758, 1807–1818, and 1844–1857 UTC. The first, second, third, and fourth legs on 29 May are flown at 1806–1820, 1829–1839, 1904–1918, and 1927–1938 UTC. The first, second, third, and fourth legs on 7 Jun are flown at 1651–1704, 1754–1803, 1829–1835, and 1932–1944 UTC.

Citation: Journal of Hydrometeorology 8, 2; 10.1175/JHM567.1

Information regarding the UWKA flights and the ABL characteristics over the western track at the five days. Here L shows the range of the Obukhov length calculated for each low-level leg.

Estimated soil thermal conductivity (W m^{−1} K^{−1}).

Combinations of the composited MR cospectra of *w*″and *θ*″, {*C*_{wθ}}, *w*″and *q*″, {*C*_{wq}}, and *q*″ and *θ*″, {*C*_{qθ}} ({} is omitted in the table).

The mixed-layer scaling parameters on the five case days. For the definitions of these scaling parameters, refer to Stull (1988).

^{1}

In the absence of a significant spectral gap (between f/3 to 5f/3, where f is the cutoff frequency for a perfect filter separating the mesoscale from turbulence; LeMone 1976), one would still expect nonlinear transfer of variance from the mesoscale motions to higher frequencies, so similarity theory would probably underestimate variances slightly.