Moisture fields and models for lidar

216 D.I. Cooper et al. Agricultural and Forest Meteorology 114 2003 213–234 increments from +35 ◦ in azimuth to −145 ◦ in azimuth required about 15 min. The absolute accuracy of the li- dar was shown to be ±0.34 gkg at the 95 confidence level Cooper et al., 1996; Eichinger et al., 1994 .

3. Moisture fields and models for lidar

This section describes scalar observations over the Bosque and the present technique for flux esti- mation when locally available wind–field data are available. The Monin–Obukhov M–O length scale L is a critical micrometeorological variable used to characterize local stability and estimate latent energy fluxes. The quantity L was derived for the Bosque site from wind–field measurements by a three-axis sonic anemometer eddy covariance sensor using the equation: L = − θ v u 3 ∗ kqw ′ θ ′ v 1 where θ v is the potential temperature, u ∗ is the friction velocity, k is Von Karmen’s constant, g is the accel- eration due to gravity, and w ′ θ ′ v is the sensible heat flux. Monin–Obukhov similarity was used to estimate latent energy flux from the Bosque site by integrating wind–field and M–O data with lidar-derived water va- por profiles extracted from two-dimensional vertical scans Eichinger et al., 2000 . 3.1. Vertical scans and stability Lidar vertical scans were typically between 500 and 600 m long and up to 40 m in height above the canopy top. The water vapor field over the Bosque was mea- sured by repeatedly scanning over the canopy directly Table 1 Lidar scan acquisition and meteorological variables at 2.7 m above the canopy associated with selected figures Figure DOY Time Az. ◦ θ v ¯ u σ u u ∗ Dir. ◦ L z−d L H LE Rn Figs. 2A and 9A 256 14:30 35 31.3 1.2 0.67 0.29 6 − 15.4 − 0.20 62 279 521 Figs. 2B and 9B 256 15:30 35 30.5 0.9 0.77 0.17 193 + 28.9 + 0.16 − 22 329 166 Fig. 2C 256 15:22 100 30.5 1.2 0.76 0.17 193 − 15.4 − 0.30 − 7 210 282 Fig. 2D 256 15:36 30.5 0.9 0.77 0.17 193 + 28.9 + 0.16 − 22 329 166 Figs. 5A and B 255 13:41 35 30.6 1.4 1.03 0.24 8 − 9.59 − 0.41 179 431 584 Units for Time is in LST, θ v is in degrees C, u, σ u and u ∗ are in ms, L is in m, H, LE, and Rn are in Wm 2 . adjacent to the north tower and stepping in 5 ◦ az- imuthal increments from north to south, creating a well sampled three-dimensional water vapor field. Within any given 30 min period, between three and six ver- tical scans were recorded over the northern tower at a 35 ◦ angle from the lidar resulting in profiles that were averaged in both space and time. The vertical scans shown in Fig. 2A and B illustrate the spatial structure of the ABL surface layer lidar scan orientation relative to north and micrometeo- rological variables are listed in Table 1 . Depending upon the prevailing stability conditions as defined by L , various structures are shown in the images: the image generated from the vertical scan acquired dur- ing an unstable period shows the effects of convection and mixing, as the interaction of dry air from above and moist air from the surface produces intermittent microscale structures. In contrast, a vertical scan taken during a locally stable period shows a wetter region just above the canopy, as well as a region 10–15 m above the canopy surface that shows multiple moist microscale structures red features at about the same height Fig. 2B . Earlier studies on forest–atmosphere interactions under convective conditions show multi- ple microscale structures at various heights Cooper et al., 1994; Cooper et al., 2000 . The 10 m tall structures between 10 and 15 m above the canopy in Fig. 2B suggest that the lower portion of the surface layer is constrained, presumably by stable thermal stratification L 0, which limits the exchange of water vapor between the surface and the atmosphere. The effect of stability on structure size suggests that under locally stable conditions, larger microscale fea- tures persist over relatively long periods of time and space, whereas under unstable conditions, microscale features will be transported away from the surface and dissipate over shorter time–space scales. D.I. Cooper et al. Agricultural and Forest Meteorology 114 2003 213–234 217 Fig. 2. Vertical lidar scans acquired over the salt cedar showing high-water vapor mixing ration as red and low values as blue. Panel A shows the typical unstable condition enhancing mass exchange from microscale convective structures, While panel B illustrates the affects of local stable conditions on microscale structures. Panel C shows the relatively dry atmosphere over the levee and panel D shows a scan perpendicular to the mean wind, where advected dry air mixes with the moist air over the canopy. 218 D.I. Cooper et al. Agricultural and Forest Meteorology 114 2003 213–234 Each 500–600 m long range-height scan adja- cent to the north tower was sectioned into segments that can be defined as narrow as 5 m or as wide as 150 m in 1.5 m increments. The three-dimensional segments were then aggregated and plotted into two-dimensional profiles of water vapor versus height above the canopy. Depending on where the segment was extracted, the profiles extended up to 40 m above the canopy; the radial location along the scan deter- mines the total height due to the polar-coordinate tri- angular shaped range-height scanning pattern. These profiles were then corrected for terrain and canopy height using lidar-derived topographical information Eichinger et al., 2000 . Vertical profiles of water vapor were extracted from two vertical scans shown in Fig. 2 . These profiles were extracted from the region in the scans covering 350–375 m ±1.5 m of the north tower the mix- ing ratio as a function of height is shown in Fig. 3 . The profile from the unstable period z − dL = − 0.20 shows a well-mixed lower surface layer with near-constant water vapor distribution above 5 m; be- low 5 m the distribution follows a curvilinear trend described by the classical Dyer–Hicks profiles for passive scalars Monteith, 1973 . Profiles displaying this shape are ideal for applying M–O similarity to estimate fluxes. In contrast, the profile extracted from the local stable period z − dL = +0.16 is not only a wetter profile than the earlier example, but it also shows a moisture inversion between 7 and 13 m, indi- cated by the increase in moisture with height instead of the expected constant moisture profile. While the lower portion of the profiles from 0 to 7 m follows a curvilinear shape, the inversion above it sharply deviates from a log-normal water vapor distribution, limiting the application of M–O theory for these profiles to a few meters above the canopy Fig. 3 . 3.2. Lidar derived LE and q ∗ The lidar elastic backscatter data are used to iden- tify both canopy geometry and topography since the backscatter from the canopy is several orders of mag- nitude larger than the Raman backscatter. The height of the canopy–surface water vapor observations were determined from the last high-value elastic-backscatter canopy-pixel from the lidar data. This height infor- mation is used to correct for topography and canopy roughness variations Eichinger et al., 2000 . Water vapor versus height profiles are created from water vapor measurements that are taken over a range of a few centimeters above the canopy to tens of meters into the atmosphere Cooper et al., 2000 . The topo- graphically corrected water vapor profiles along with friction–velocity measurements are input into the clas- sical one-dimensional equation to estimate LE by the profile method Brutsaert, 1982 . The water vapor pro- file equation for latent energy is given by LE = q z − q λ ku ∗ ρ ln z − d z − ψ sv ζ − 1 ∼ = λkρw ′ q ′ 2 where q z is the water vapor mixing ratio at some height; q the surface water vapor mixing ratio; λ the latent heat of vaporization; k the Von Karman’s constant; u ∗ the friction velocity; ρ the air density; z the measurement height; d the displacement height; z the roughness length; ψ sv ζ the stability correc- tion and, w ′ q ′ is the covariance of the vertical wind with water vapor. In theory, the profile equation for LE flux should be equivalent to the eddy covariance derived flux, assuming that the source areas for the two techniques are similar Wilson et al., 2001 . A question outside the scope of this paper, but which will be addressed in the future is—in what region of space can a u ∗ measurement observed at a point also be assumed to be valid for this technique? Recent re- search on the spatial variability of turbulent flux sug- gests that u ∗ is less variable than LE Katul et al., 1999 . By utilizing lidar-measured high-resolution, spa- tially resolved profiles of mixing ratio and friction velocity measurements from a local three-dimensional sonic anemometer, spatially resolved fluxes were esti- mated with footprint diameters between 5 and 150 m centered over the north tower. A comparison of the eddy covariance fluxes versus lidar fluxes over several days is presented in Fig. 4A . The plot shows that la- tent energy fluxes estimated by the two methods are in good agreement to within ±15, which is within the instrument uncertainty for eddy covariance-derived fluxes. The wind values measured by the three-dimensional sonic anemometer located in the center of the scans were used in both the eddy covariance fluxes w ′ and D.I. Cooper et al. Agricultur al and F or est Meteor olo gy 114 2003 213–234 219 Fig. 3. Vertical profiles of water vapor for both stable and unstable periods. Zero height is at the top of the canopy. Individual data points are shown as dots. 220 D.I. Cooper et al. Agricultural and Forest Meteorology 114 2003 213–234 Fig. 4. Comparison of eddy covariance derived and lidar estimated LE plot A and q ∗ plot B for days of year 252, 254, and 255 with two different footprints. Data acquired over north tower Fig. 1 at 35 ◦ azimuth from lidar. D.I. Cooper et al. Agricultural and Forest Meteorology 114 2003 213–234 221 the Monin–Obukhov derived fluxes u ∗ . A more ro- bust analysis was used by partially eliminating u ∗ from the estimate by calculating q ∗ from Eq. 2 as q ∗ = q z − q ln z − d z − ψ sv ζ − 1 ∼ = w ′ q ′ u ∗ 3 It should be noted that Eq. 3 does not completely remove the effect of u ∗ from the analysis since the stability correction employs the Monin–Obukhov length L and this requires a friction velocity mea- surement. An eddy covariance-derived q ∗ versus lidar derived q ∗ is shown in Fig. 4B . Again, the plot shows that lidar derived estimates for q ∗ are within ±15 of the point sensors. In addition, the analysis was performed for two footprint regions: 25 m×25 m and 50 m × 50 m. Regression values suggest satisfactory slopes and small intercepts for both cases. Of interest is that the standard deviation of the regression and the coefficient of determination are better for the larger footprint, supporting the hypothesis that spatial sam- ple size plays an important role in the estimation of derived moisture quantities. 3.3. Advection, stability, and the effect of source area Periodically in the mid-afternoon, the wind direc- tion would change from the north to the southwest. Westerly winds import dry warm air from the sparsely vegetated desert to the relatively moist, cool salt cedar canopy, creating locally stable atmospheres. Stability is determined here from eddy covariance measure- ments of L Eq. 1 where L is positive for stable conditions and negative for unstable conditions. The effect of “hot to cold” advection on the stability of turbulent heat and moisture fluxes in semi-arid en- vironments is sometimes referred to as the “oasis effect.” The oasis effect is when hot dry air blows over a vegetated field in a desert, increasing transpira- tion and thus generating relatively cool moist air, such as at the Bosque. The dry air moving over the moist canopy increases the local vapor pressure deficit, in turn has a profound effect on the temperature gradi- ent and the sensible heat flux in that the direction of the gradient and thus the flux will change from go- ing away from the surface to going into the surface. The local advection equation relating the potential temperature gradient to the sensible heat flux is u ∂ ¯ θ ∂x = − 1 ρC p ∂w ′ θ ′ v ∂ z 4 A change in the direction of the flux was observed by the eddy covariance flux sensors over the salt cedar between 1430 and 1530 h on September 12,1998. In this 1-h period, the wind direction changed from northerly parallel to the river to southwesterly from the desert into the Bosque and, as expected when L became positive, the sensible heat went into the canopy, from +62 Wm − 2 at 1430 h to −22 Wm − 2 at 1530 h see Table 1 . The process of advection can account for some of the structures shown in Fig. 2B , as well as the afternoon stable conditions observed by the microm- eteorological instruments, and the moisture inversion shown in Fig. 3 . Additional lidar and micrometeoro- logical data are used to support the hypothesis that the observed local stability is due to dry air transported over the Tamarisk canopy. For instance, in the lidar scan shown in Fig. 2B , the high-moisture-containing structures red features located between 10 and 15 m above the canopy were observed during a locally sta- ble period z − dL 0. The false-color IR image of the site Fig. 1 shows the location where scans 2B–D where taken as well as the direction of the mean wind during this period, and Table 1 lists the lidar scan orientations and associated micrometeorological vari- ables. These scans illustrate how the source of the rel- atively dry air that was advected over the canopy was ultimately the cause of the local stability and associ- ated moisture-containing structures found in the lidar data. A lidar scan taken nearly perpendicular to the mean wind Fig. 2C shows the effect of dry air being ad- vected into the salt cedar, as the dynamic range of this data is approximately 50 higher than that shown in Fig. 2B . The air near the canopy surface in Fig. 2C is found to have the expected moisture of 13–14 gkg, while the upper portions of the scan are relatively dry, between 8.5 and 11 gkg. In addition, a scan Fig. 2D was taken over the non-vegetated levee adjacent to the western portion of the study site. Scans at this azimuthal angle are almost parallel to the mean wind. 222 D.I. Cooper et al. Agricultural and Forest Meteorology 114 2003 213–234 This scan measured atmospheric moisture between 1 and 1.5 gkg drier than those shown in Fig. 2B , re- flecting the relatively dry source area for this portion of the site. From the footprint analysis that will be presented later in more detail Section 4.2 , for a stability of z − dL = +0.16 the expected length of the source-area footprint will be about 450 m to achieve 90 of the cumulative water vapor flux. Using this footprint result, advected air from 193 ◦ moving to- ward the region where Fig. 2B was acquired will be an admixture of high-moisture air from the Tamarisk and the dry air from the desert. This mixing is illustrated in Fig. 2C which is intermediate between the “dry” scan of Fig. 2D and the “wet” scan of Fig. 2B . The moist structures occurring between 10 and 15 m high Fig. 2B have moisture concentrations up to 14 gkg, while at similar heights in the dry scan Fig. 2D , the structures have lower concentrations between 12 and 13 gkg; the background moisture below these structures is drier still, with water concentrations be- tween 9.5 and 11 gkg. Since the profiles extracted from Fig. 2B were only 25 m wide, and the cumu- lative flux at this width is about 45, it is logical to assume that 55 of the air in these profiles are non-local. The mixture of dry desert air 8 m above the Tamarisk with the moist air rising from the canopy Fig. 2C has a moisture concentration between 10.5 and 11.5 gkg; this relatively dry air was advected over the canopy creating the inversion conditions observed by the lidar-derived water vapor profiles Fig. 3 . From this analysis, we have shown that advection is one of the critical processes that is involved in the development of the local stable inversions observed in the data. A theoretical structure for surface layer “hot to cold” advection was developed using potential temperature profiles as a function of distance between two sur- face roughness conditions, such as from bare soil to irrigated fields as outlined by Kaimal and Finnigan 1994 . They predicted as Dyer and Crawford 1965 observed earlier, that an advective inversion develops above the canopy and the intensity of that inversion is a function of distance from the dry region into an irrigated field as measured with temperature profiles. The effect of stability and mass advection is also es- timated for water vapor where moisture variables are substituted for thermal variables in Eq. 4 as ¯ u ∂ ¯ q ∂x = −   ∂ w ′ q ′ ∂ z   ∼ = − ∂q ∗ ∂ z 5 Brutsaert, 1982 . The development of advectively driven inversions under daytime convective conditions should be ob- servable in water vapor scalar profiles from lidar, from heat or moisture flux profiles, or from profiles of q ∗ using Eq. 5 Kaimal and Finnigan, 1994 . Profiles of q ∗ were created from the lidar and mi- crometeorological data collected within a selected 75 m wide section of the vertical scans shown in Fig. 3 and coincident measured u ∗ and L observations from the north tower, using the similarity equation for non-dimensional moisture outlined in Eq. 2 . Us- ing these derived q ∗ values, the right side of Eq. 5 is solved directly as a function of height above the canopy. The first of these profiles was for a region that began near the inner edge of the riparian zone and progressed above the Tamarisk stand toward the eastern edge of the study site directly adjacent to the Rio Orande. The q ∗ profiles in Fig. 5A were acquired at 1430 h under convective conditions when L 0. The unstable conditions are evident in the increasing values of q ∗ , as relatively small inversions are seen at 3–4 m above the canopy presumably where eddy mixing occurs between moist rising plumes and drier down-welling air. In contrast, when L 0 as in Fig. 5B , dry air advection creates deep inversions 2–3 m above the canopy near the western edge of the Tamarisk . The intensity of these inversions decays as a function of distance into the riparian forest as the dry air is mixed with the moister canopy air. Wind tunnel studies by Charnay et al. 1979 generated sensible heat flux profiles for “hot-to-cold” advection that are similar to those in shown in Fig. 5B . The biggest discrepancy between the lidar observations over the Tamarisk and the wind tunnel studies is the change in profile structure between 288 and 313 m. It appears from thermal IR aircraft data that there is a 100 m wide drainage system on the western edge of the Tamarisk that brings ground water close to the surface, maintaining higher plant transpiration that in turn reduces the canopy surface temperature and the vapor pressure deficit in the Tamarisk and consequently reduces the inversion intensity. D.I. Cooper et al. Agricultural and Forest Meteorology 114 2003 213–234 223 Fig. 5. Profiles of q ∗ for day 256 during an unstable period at 14:30 LST A, and for a stable period at 15:30 LST B. Range values adjacent to each profile are radial distances from the lidar, specific lidar azimuths and meteorological parameters for these profiles are listed in Table 1 . 224 D.I. Cooper et al. Agricultural and Forest Meteorology 114 2003 213–234

4. Spatial analysis of sampling size