1. Introduction
Numerous studies show that daytime fair-weather surface wind speeds predicted by numerical weather prediction (NWP) models tend to be slower than observed wind speeds. Applying five different planetary boundary layer (PBL) schemes in the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) to simulate the diurnal cycle of wind and temperature under weakly forced fair-weather conditions, Zhang and Zheng (2004) found that the daytime model winds were consistently 0.5–2.0 m s−1 weaker than those observed. Even after improving the boundary layer parameterization scheme, Liu et al. (2006) found that daytime winds produced by MM5 still averaged ∼0.5 m s−1 lower than measured surface winds around Oklahoma City, Oklahoma.
Aside from shortcomings in NWP model physics, two explanations are given for discrepancies between modeled and observed surface winds: the much greater area represented by a model grid area compared to a “point” measurement (which could lead to a discrepancy of either sign); and observations being taken in open areas with less effective roughness than the model grid average, which includes the effects of complex terrain, as well as trees and buildings (which should lead to model winds being slower than observed winds). Rife et al. (2004) summarize several previous studies of NWP model success in predicting surface variables in terrain of varying complexity, noting that reduction of grid size improved results down to about 10 km, but further reduction did not necessarily mean an improvement in forecast success. Their own 1.33-km-grid-size MM5 simulations of the flow in the Salt Lake City, Utah, area performed only slightly better than comparable models run on 30- and 40-km grids. They attributed some of the remaining discrepancy to still-unresolved effects at the smallest scales. De Rooy and Kok (2004) discussed the point measurement problem and dealt with it in a mesoscale model by developing a method to downscale surface winds using local roughness lengths.
We explore the daytime model–observation discrepancy associated with using point measurements by comparing surface winds observed at well-exposed locations to surface winds calculated by applying Monin–Obukhov (MO) similarity theory to aircraft data averaged along 50–60-km flight tracks, supplemented with thermodynamic data from nearby surface-flux towers (Fig. 1). The data were collected in the convective boundary layer over the Southern Great Plains of Kansas, Oklahoma, and Texas on fair-weather days during the May–June 2002 International H2O Experiment (IHOP_2002; Weckwerth et al. 2004; LeMone et al. 2007a). The surface-flux towers were sited in open areas along the three King Air flight tracks to provide representative samples of fluxes over the dominant surface-cover types (grassland, winter wheat, bare ground, sagebrush), while the aircraft data included the effects of trees, buildings, and terrain as well as the shallow vegetation. Given that the surface winds were measured over shallow vegetation, we expect them to be stronger than those calculated from MO similarity theory.
After outlining the data requirements using the theoretical background in section 2, we discuss data collection and processing in section 3. Section 4 outlines the data-analysis procedure, the random and bias errors, and removal of biases. Results are presented and discussed in section 5, with conclusions in section 6.
2. Theory
For MO similarity to apply, zac and z10 should lie within the surface layer. Physically, the surface layer is defined as that layer through which shear generates more turbulence than buoyancy (Glickman 2000). Since the Obukhov length is a ratio of shear to buoyancy effects, it follows that MO stability applies for −(z/L) < 1; in the Kansas-experiment surface-layer data of Businger et al. (1971), data fit the MO similarity curves out to −z/L ∼ 1.5, with a few points to 2.2. According to Wyngaard (1983) and Brutsaert (1998), the surface layer extends to ∼10% of the PBL depth. However, the definition can be more conservative than this: Mahrt (2000) uses 5% of the convective boundary layer depth as the upper limit for the surface-layer top, and the American Meteorological Society (AMS) Glossary of Meteorology (Glickman 2000) definition extends the surface layer up to a few tens of meters. Here, we require that zac < 0.1zi and look at data for both zac < −L and zac < −1.5L.
3. Data collection and processing
Measurements used for our analysis were collected during IHOP_2002 from the University of Wyoming King Air aircraft and NCAR surface-flux towers. The aircraft data are from the boundary layer heterogeneity (BLH) missions (Table 1), flown during fair weather, along the western, central, or eastern tracks, shown in Fig. 1. In Table 1, the mean winds U and V are in a right-handed coordinate system with U pointing east.
The most relevant aircraft measurements are summarized in Table 2. The winds were calculated by subtracting the velocity of the aircraft relative to the earth from the velocity of the air relative to the aircraft. The aircraft-relative wind was measured by the differential pressure gust-probe system, while the ground-relative motion and position were measured by the inertial navigation system and corrected using GPS data. Data were recorded at 25 Hz.
On a given day, the King Air flew 10 to 18 straight-and-level 50–60-km legs over one track at two or more levels within the boundary layer, from ∼65 m AGL to just over 1000 m AGL, interspersed with vertical soundings to determine PBL depth. These data were collected in fair weather during 4-h flights centered around local noon (∼1830 UTC), to sample the PBL after its most rapid growth but when it is still strongly coupled to the surface. For this analysis, only days with five or more legs at ∼65 m AGL were used. The seven days satisfying this requirement are 29, 30, and 31 May and 7, 17, 20, and 22 June (Table 1).
The surface data came from nine surface-flux towers operated by NCAR (numbered 1–9 in Fig. 1). Stations 1–3 were along the western track, 4–6 along the central track, and 7–9 along the eastern track. The fourth site (station 10) along the western track was not included since it did not collect all of the data necessary for this analysis and the winds were not measured at 10 m AGL. The stations were located to sample the major land-use types—grassland, winter wheat, bare ground, and sagebrush—along the three tracks. In addition to scattered buildings, there are trees along all three tracks, mainly located along rivers or bordering fields.
Relevant surface measurements are summarized in Table 3. We used half-hour data, available from www. rap.ucar.edu/research/land/observations/ihop.php. Sensible heat flux H and latent heat flux LE were computed relative to half-hour averages, using 5-min block averages that were quality-checked and postprocessed by the Integrated Surface Flux Facilities (ISFF) of NCAR using a standard suite of corrections that are summarized at http://www.eol.ucar.edu/rtf/projects/ihop_2002/isff/. The water vapor flux was estimated from the water vapor concentration and sonic anemometer vertical velocity. The temperature flux was calculated from the vertical sonic-temperature flux using the specific humidity flux in the standard way (Schotanus et al. 1983). Half-hour averaged temperature, mixing ratio, and pressure were used to convert the temperature and water vapor fluxes to H and LE. Because of problems with some of the water vapor sensors, we used the LE values found as a residual from the surface energy balance. The resulting surface fluxes were within 10%–15% of the aircraft fluxes extrapolated to the surface (LeMone et al. 2007a).
4. Data analysis
In (3), we use wind speed and momentum fluxes (from aircraft), virtual-temperature fluxes (from surface and aircraft), and virtual temperature (from surface and aircraft) to obtain S10. Ideally, we would use aircraft data only. However, we use surface thermodynamic fluxes to offset the typical biases between aircraft and surface data (e.g., Desjardins et al. 1992; Betts et al. 1992), and we use surface thermodynamic data to get a better average virtual temperature for use in calculating L. Only the aircraft legs at ∼65 m AGL are used for momentum-flux estimates. With typically more legs flown (a larger sample) and a smaller turbulence integral scale (and hence effectively more eddies sampled per leg) than at higher altitudes, the fluxes at ∼65 m have the least uncertainty. To mitigate the effects of time trends, all surface and aircraft fluxes and variables are computed so that their values apply to 1830 UTC.
a. Aircraft data
1) Flux calculation
The temperature flux (
A heading-related bias in both wind speed and momentum fluxes results from true airspeed and side-slip angle biases. For example, when the aircraft was flying south-to-north along the western track, the along-aircraft bias (due to true-airspeed bias) influenced V and
To calculate and remove the aircraft biases for the wind and momentum fluxes, plots were made for both fluxes as a function of time to compare values for opposing aircraft headings, and the data was fitted to straight lines using a least squares best-fit linear regression. Half the difference between the opposite-heading values at a common time (ideally the center time for both plots) was taken as the bias. Were the flight legs with opposite headings equal in number and evenly distributed through time, such a step would not be necessary. Typical momentum-flux biases were of the order of 0.1 m2 s−2 parallel to the aircraft and about 0.01 m2 s−2 normal to the aircraft; while typical wind speed biases were a few tenths of a meter per second.
For temperature and water vapor fluxes, the aircraft data were treated similarly. However, the surface values were based on the surface-station measurements.
2) Sources of error for aircraft wind and momentum flux
The mean wind estimate Sac, and hence S10 in (3), is affected by ground speed error εS10(Sac,gs) and a random error aircraft-relative wind from turbulent fluctuations εS10(Sac,r). We can estimate εS10(Sac,gs) from the King Air position uncertainty, which was ∼0.1 km during IHOP_2002 (A. Rodi 2005, personal communication). Thus the fractional error in distance traveled for a 50-km flight leg due to position error is 0.2 km/50 km or 0.004. For a ground speed of 80 m s−1, this translates to a 0.3 m s−1 uncertainty in ground speed for a single flight leg, or a standard error of 0.14 m s−1 for a five-leg average.
To find εS10(u*,r), the uncertainty εu*(r) was found by adding/subtracting σNlegs(
b. Surface data
1) Calculating surface values
For each day, the surface wind, virtual temperature, and virtual temperature fluxes were derived from half-hour averaged data for the three surface-flux sites along the track the King Air flew. The virtual temperature flux was derived from sensible heat flux H and latent heat flux LE, using corresponding values of pressure (P), temperature (T), and mixing ratio (Q). The 1830 UTC values for the track were found by averaging the values at 1815 and 1845 UTC at each site, and then averaging the result for all three sites.
2) Error in measured surface winds
The random error in the observed 10-m wind speed measurement εS10,obs(r) was found from averaging two estimates. The first estimate was based on (7), with the six individual flux-site half-hour values (three stations, two values) from empirical relationships (1.47) and (1.50) in Kaimal and Finnigan (1994). The aircraft integral scale for υ was used for days when the wind was out of the south; the average of the integral scales for υ and u was used for 30 May, when the wind was out of the SSE. Such estimates were necessary because only mean winds were recorded at 10 m. For the second estimate, we simply computed the standard error for the six 30-min averages used to estimate u10. The resulting estimates vary between 0.1 and 0.2 m s−1.
Instrument error for the surface wind is negligible. From Brock and Richardson (2001), the measurement error from propeller vanes varies as the cosine of the angle of the wind to the propeller; that is, the error comes from the vertical velocity (w). Using Eq. (13) of Lenschow et al. (1980) to estimate w, we found the contribution to be small. Since care is taken to ensure the flux towers are vertical, error due to departure from true vertical is also small.
c. Combined surface and aircraft data: Uncertainty in (3) from buoyancy-flux uncertainty
From the foregoing, aircraft and surface thermodynamic fluxes differed slightly, and LE was found as a residual from the surface energy budget. The uncertainty in buoyancy flux εS10(B) contributes to εS10 through modifying −L and thus to the stability corrections Ψac and Ψ10 in (3). We estimate εS10(B) by allowing the buoyancy fluxes to differ by ±7.5% relative to the mean (roughly the difference between aircraft and surface data) to obtain the associated range of S10. As for εS10(u*, r), the error is set to half the range of extreme values, namely, εS10(B) = 0.5[S10(1.075B) − S10(0.925B)]. The resulting values vary between 0.02 and 0.06 m s−1.
d. Total estimated random error in S10 (calculated) − S10 (observed)
Some sources of uncertainty are not accounted for, namely, the effects of aircraft flow distortion on the wind and momentum flux measurements (unknown but assumed to be small) and the effect of ground-speed error on momentum fluxes (assumed to be small). Further, the choice to use a best-fit linear trend to obtain flux and wind values at a common time eliminates the effect of an asymmetric time distribution of flight legs, but adds uncertainty related to the linear fit. An additional source of uncertainty is that we have to assume that the source regions for the aircraft wind and momentum-flux measurements are sufficiently uniform in a statistical sense that (3) applies. Similarly, the aircraft source regions for a given flight track are assumed similar to the broader environment of the corresponding set of surface sites. That is, differences in the regional “footprints” for wind and momentum flux do not matter. Finally, we assume that the smaller footprints of the surface sites are representative of open areas in the region.
5. Results and discussion
The 10-m wind speeds estimated from (3) are compared to those observed at nearby surface-flux stations for each day in Table 4. The estimates labeled “10 m” are based on L and u* calculated from averages at 10 m, while the estimates labeled “65 m” are calculated from the average of values at ∼65 and 10 m.
From the foregoing, (3) applies provided that both z10 and zac are within the surface layer. Whether zac is below the surface-layer top depends on the definition; however, z10 > lb and hence within the lower part of the surface layer for all seven days according to (4). From the table, zac < 0.1zi for all the days. If we define the surface layer as extending up to −1.5L, the last five days fit this criterion for (3) to apply. Only 7, 17, and 22 June fit the zac < −L criterion. Using the size of a section of land (1.6 km) in (4), the blending height is always less than 10 m, implying that (3) applies, provided that the most significant horizontal heterogeneity is at that scale or less. This is not an unreasonable assumption, since crop areas are typically less than a section in size. If we invert (4) and solve for λ, the horizontal scales corresponding to lb = 10 m vary from 2.8 km on 30 May to 6.6 km on 7 June. However, while (4) holds for −L > 76 m in Wood and Mason (1991), it could be argued that a blending-height estimate should involve w* for more convective conditions.
Applying the vertical shear criteria of section 4a (Table 4, last two columns) to the five cases fitting the more generous definition of surface layer reduces the number of satisfactory cases to four—17, 20, and 22 June, with 31 May included simply because the momentum-flux height correction is so small. The shear criteria and the stricter zac < −L criterion are all met on both 17 and 22 June, so these are designated good cases. The aircraft soundings reveal significant shear at zi for 31 May and 7 June [∼1.3 m s−1 (100 m)−1], and moderate shear on 29 and 30 May [∼0.4–0.6 m s−1 (100 m)−1], with values ∼0.3 m s−1 (100 m)−1 or less on 17, 20, and 22 June. To check this assessment, which is influenced by aircraft heading–dependent wind bias, we also estimated the entrainment ratio (5) assuming H and LE varied linearly with height, and found values <0.2 except for 31 May, when A was slightly larger than 0.2, and 7 June, when A was significantly larger than 0.2. However, we retained 31 May as marginally satisfactory since the magnitude of the momentum flux downward extrapolation is inversely proportional to zi, which was 1450 m.
In Table 4, the observed wind exceeds the predicted wind by 0.5–0.6 ± 0.2 m s−1, regardless of the qualifying days counted, or the averaging procedure to find L and u*. For the four “satisfactory” days, the mean measured wind is 6.09 m s−1, greater than the predicted speed for a 10- or 65-m constant flux layer (5.56 m s−1), with a difference of 0.53 ± 0.13 m s−1, with the uncertainty from (7). If we count only the two “good” days, the two values are 7.13 and 6.48 m s−1 (average of 6.46 and 6.51 m s−1), respectively, yielding an average difference of 0.65 ± 0.20 m s−1. Using flight-level momentum flux instead of extrapolating to the surface reveals similar differences: 0.5 and 0.6 m s−1 for the satisfactory and good cases, respectively. These differences are about the same as the smallest discrepancies in Liu et al. (2006) and Zhang and Zheng (2004).
Consistent with the reduced winds, the effective roughness length based on aircraft wind and momentum-flux data is larger than that for the surface sites. Applying either (3) or (10) to the data for 22 June, the effective roughness length for the eastern track was ∼0.14 m. For comparison Stull (2000) lists z0 = 0.25 m for high crops with occasional trees and hedgerows, and 0.1 m for low crops with occasional bushes. In contrast, z0 at the three corresponding surface-flux sites (all grassland) was between 0.012 and 0.023 m, which are fairly typical values for grassland.
These results are consistent with those of Kustas et al. (2005), who found that u* and z0 from aircraft were larger than values based on surface data over corn and soybeans. They attributed the difference to form drag from isolated obstacles such as buildings and trees and the borders between different crops. Such obstacles do not have to be very big or cover a very large area to have a significant effect. For example, Hasager et al. (2003) found that the influence of hedgerows covering only 1%–5% of an area increased the effective roughness length by more than 50% in some cases.
6. Conclusions
Based on fair-weather daytime (unstable) data collected during IHOP_2002, the observed 10-m wind at the surface-flux sites is ∼0.5–0.6 ± 0.2 m s−1 greater on average than modeled estimates found by applying MO similarity theory to data averaged along ∼50–60-km flight legs. The track averages are based primarily on aircraft data collected at 65 m AGL. The differences increase by about 0.1 m s−1 when the estimated ∼0.9-m displacement height is used. On individual days, particularly the uncertainty in momentum flux estimates leads to uncertainties as large as 0.4 m s−1. Combining the days that fit the shear and MO similarity criteria using (7), the uncertainty is reduced to ∼0.2 m s−1.
The stronger observed winds result from the surface-flux station sites being chosen in open areas with z0 of the order of a few centimeters; while the aircraft was taking measurements over and downstream not only of open fields, but also scattered buildings and trees, which bordered fields or were located along streams. These additional obstacles slowed the wind locally, and resulted in an effective roughness length for the Eastern Track of ∼0.14 m based on data from 22 June, the day with the largest −L and the least uncertainty. This z0 value is significantly larger than the ∼0.01–0.02-m values for the corresponding grassland flux sites 7–9.
The ∼0.5–0.7 m s−1 discrepancy between NWP model and observed 10-m winds is comparable to the best model–observation comparisons reported by Zhang and Zheng (2004) and Liu et al. (2006). Because NWP models have grids with areas of order 1–100 km2, the results imply that it is appropriate to compare surface winds derived from spatially averaged low-level aircraft data or take advantage of larger footprints represented by time-averaged data from taller towers (Hasager et al. 2003) or tethersondes for evaluation, rather than using averaged data from point 10-m measurements. In the absence of such data, the alternative for model evaluation is to allow for the fact that surface-site exposure can lead to measured winds stronger than representative of the area corresponding to a model grid using results from studies like this one.
Acknowledgments
Part of this work is extracted from D. Strassberg’s senior thesis at the University of Colorado, Boulder. The NCAR portion of this research was supported by USWRP Grant NSF 01, NCAR Water Cycle Initiative, and the Advanced Study Program. We gratefully acknowledge the critical review by Bob Kelly of the University of Wyoming, Jielun Sun of NCAR, and two anonymous reviewers, whose comments significantly improved the manuscript. We also acknowledge the commitment, enthusiasm, and expertise of the Wyoming King Air aircrew and the National Center for Atmospheric Research staff in maintaining the surface-flux instruments, without which this work would not have been possible.
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Location of the western, central, and eastern tracks with associated surface-flux sites (numbered 1–10), superimposed on a map of land-use types: open water (dark shading), winter wheat (dark gray shading), and grasslands (lighter shading).
Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2203.1
Characteristics of the days used in the analysis. Values interpolated to 1830 UTC (local solar noon). W = western track, E = eastern track, and C = central track.
Applicable measurements from University of Wyoming King Air.
Applicable measurements from surface stations.
Comparison of measured 10-m wind speeds to those predicted from (3) using averages from either 10 or 65 m (see text). Days in italics are not used; the remainder are considered satisfactory. Boldface days match shear and surface-layer criteria well and are designated good. W = western track, E = eastern track, and C = central track.
