## 1. Introduction

Scintillometer measurements of turbulence are used in hydrological, micrometeorological, agricultural, and water resources studies. Their importance and effectiveness rise from the ability to provide path-averaged and area-averaged estimates of sensible (*H*) and latent (*LE*) heat flux that cover large spatial scales. Depending on the type of instrument, these estimates could cover several kilometers (Meijninger et al. 2002a,b; Chehbouni et al. 1999) as compared to Bowen ratio (BR) or eddy covariance (EC) systems, which essentially provide local-scale measurements on the order of hundreds of meters. They can be used as ground measurements for verification and calibration of hydrological, remote sensing algorithms, and regional atmospheric models that provide spatial estimates of surface energy fluxes.

Scintillometry is increasingly being applied as a method to estimate *H* after extensive studies and improvements to the theory of the scintillation method (Tatarskii 1961; Hill and Clifford 1978; Andreas 1990; De Bruin 2002). It is based on measuring light intensity fluctuations caused by the refractive scattering of turbulent eddies along a specific path of emitted electromagnetic radiation from a transmitter. These fluctuations represent a measure of the structure parameters of the refractive index (*H* and *LE* as described by Wyngaard et al. (1971) and Andreas (1988).

Since both the scintillation method and MOST were initially developed for, and hence have good performance in, conditions with homogeneous surfaces and flat terrain, their use over heterogonous surfaces and nonflat terrain is challenging and in some cases can provide less accurate estimates of surface energy fluxes. Also, because of the slanted path geometry of the scintillometer beam in certain situations, as well as varying topography and heterogeneously vegetated surfaces, their application for estimating surface energy balance fluxes under these conditions requires special considerations (Hartogensis et al. 2003).

Over the past two decades, most of the research effort on scintillometry has focused on its applicability in handling more practical situations including different climatic regions, areas characterized with variable terrain, heterogeneous surfaces, and relatively increased surface roughness. Examples of such applications include the work by Meijninger et al. (2002a,b) in which they provided estimates of area-averaged *H* and *LE* over the Flevoland agricultural fields that are completely flat but contained different kinds of crops representing the surface heterogeneity with no change in the roughness length, *z*_{0}, as estimated from traditional vegetation survey, and the study presented by Meijninger et al. (2006) over the LIFTASS-2003 area, which also contained different types of crops and trees but with slanted scintillometer path and variable terrain. In their analysis, they used topographic maps (1:25 000) to estimate the scintillometer beam height, *z*(*u*), with *u* as the dimensionless coordinate of the pathlength and roughness length *z*_{0}. De Bruin et al. (1995) used estimates of displacement height (*d*) and *z*_{0} from eddy covariance data in a study that took place over vineyard field in La Mancha, Spain. Their measurements were carried out during a fast growing stage of the vineyard so both *z*_{0} and *d* varied with time, which had introduced uncertainty in their estimates of *H*. They conducted a sensitivity analysis using different values for *d* and concluded that estimates of *H* were less sensitive to changes in *d*. Note that the vineyard was rather short with maximum vegetation height of about 1.0 m and leaf area index (LAI) of 0.4. As a result of the irregular terrain along the path, De Bruin et al. (1995) used weighted average effective beam height by utilizing topographic maps adding to the uncertainty in their estimates of *H*. Note that, unlike the studies by Meijninger et al. (2002a,b, 2006), in which the scintillometers were installed well above the surface and thus reliable estimates can be obtained with the free convection formula, in De Bruin et al. (1995) it was installed relatively close to surface at about 3.25 m. Hartogensis et al. (2003) developed formulas to properly estimate scintillometer effective height, *z*_{eff}, considering the effects of the slanted path of the scintillometer beam height, nonflat terrain, and the stability conditions that lead to improved estimates of *H*. Their analysis was carried over the La Poza region in Mexico—a region characterized by heterogeneous land surface and variable terrain—where *z*_{0} determined from vegetation survey and the *z*(*u*) estimated from topographic maps.

In most of these research examples the use of traditional methods [i.e., topographic maps and vegetation survey to estimate *z*(*u*) and the related surface roughness parameters] makes it less accurate and challenging to properly represent surface heterogeneity and roughness. These methods in some cases, such as for the conditions of the current study, could lead to misrepresentation of the actual variability of the terrain and hence *z*(*u*). To properly characterize surface heterogeneity in areas covered with mixed natural vegetation with variable height interspersed with bare soils, *z*_{0} and *d* need to be estimated reasonably well from *h _{c}* and this could be an important issue.

The recent and significant advances in the remote sensing technique known as light detection and ranging (lidar) has resulted in the unprecedented capability of providing highly accurate representation of the earth’s surface and its features. The lidar in this study is a system consisting of a sensor that emits a laser beam at high frequency (greater than 150 kHz) and receives the reflected light at a specific wavelength. It is an airborne mounted system, combined with global positioning system (GPS) and inertial measurements units (IMU). It collects point clouds of densely spaced, accurately geo-referenced elevation data with accuracy of a few centimeters. These data can later be used to generate maps of the three-dimensional earth’s surface and its features, including ground surface elevation and vegetation height maps (Schmid et al. 2008).

The question being asked is will the use of lidar-derived surface features (i.e., topography and canopy height) available at spatial resolutions of up to 1.0 m or less to represent surface roughness and heterogeneity, as opposed to using traditional methods, improve the scintillometer-based estimates of *H*? To answer this question we investigated the effect of incorporating lidar-derived surface features into large aperture scintillometer (LAS) measurements taken over a heterogeneous area to estimate *H* under unstable and stable atmospheric conditions. We considered the effects of representing the variability of surface features due to (i) topography and canopy height along the path of the LAS and (ii) canopy height within the footprint of the LAS that could cover several hundred meters in the upwind direction.

## 2. Methods

### a. Sensible heat flux

*n*) that mostly influence the propagation of electromagnetic radiation. This scintillation can be expressed in terms of the structure parameter of the refractive index (

*L*the path length, and

*D*the aperture diameter.

*T*is the temperature (K),

*P*is the air pressure (Pa), and

*β*. Generally, for

*β*> 1 the effect of humidity correction is negligible and for

*β*> ~0.6 it is less than 10% (Hartogensis et al. 2003) and can safely be neglected (De Wekker 1996). Most of the time in this study, the values of

*β*> 1 with only a few instances having values around 0.60. Moreover, Wesely (1976) based Eq. (2) on the assumption that the correlation coefficient between the temperature and humidity |

*R*| = 1. However, as discussed later, this might not always be fulfilled as pointed out by De Bruin et al. (1999).

_{Tq}*H*aswhere

*z*

_{eff}is the scintillometer effective height (m),

*d*the displacement height (m),

*k*the von Kármán constant taken as 0.40 and

*g*the gravitational acceleration,

*ρ*the air density (kg m

^{−3}) and

*c*the specific heat of air (J kg

_{p}^{−1}K

^{−1}), and

Note that a value of 9.0 was reported by De Bruin et al. (1993) for the constant 6.1 (Wyngaard et al. 1971; Andreas 1989). The effect of using a constant 9.0 is briefly discussed in section 4 as it is beyond the objective of the paper.

Under free convection (i.e., very unstable conditions) with −(*z − d*)/*L*_{MO} > 1, *H* becomes independent of *L*_{MO} and can be estimated as described by Andreas (1991) as *b* = 0.47 following Wyngaard et al. (1971). Note that *b* = 0.57 when following De Bruin et al. (1993).

### b. Utilizing lidar data

The lidar data were incorporated in the analysis first by using the detailed surface topography to estimate the LAS beam height along the path, *z*(*u*), which is a term that is necessary for estimating *z*_{eff}. Secondly, we used the detailed vegetation height, *h _{c}*, map to estimate the surface roughness parameters (i.e.,

*d*and

*z*

_{0}). Note that the spatial resolution of lidar-derived topographic and vegetation height maps was 1.0 m.

*z*

_{eff}needs be estimated iteratively using the approach described by Hartogensis et al. (2003) where they showed the importance of considering the effect of the stability conditions represented by

*L*

_{MO}:where

*z*(

*u*) is the variable scintillometer beam height along the path,

*z*

_{eff}estimated at every time increment of the available data as

*L*

_{MO}changes with time, and

*W*(

*u*) the LAS weighting function along the path representing the contribution of

*u*) to the total LAS signal at each location

*u.*The weighting function

*W*(

*u*) has a bell shape with the maximum value occurring at the center of the path and zero at both ends (appendix).

*d*, which represents and quantifies surface obstacles and roughness due to the presence of vegetation, can be estimated as ⅔

*h*(Brutsaert 1982). Because of the varying canopy height along the LAS path, an integrated displacement height

_{c}*d*is estimated by evaluating the elemental

*d*(

*u*)

*=*⅔

*h*(

_{c}*u*) at each increment

*u*along the path and then weighted by incorporating the LAS weighting function

*W*(

*u*)—an aggregation approach described by Shuttleworth et al. (1997) and Chehbouni et al. (1999):

*z*

_{0}(

*u*) and

*d*(

*u*) (Shuttleworth et al. 1997) aswhere

*z*

_{0}is the area-averaged or path-averaged roughness length, and

*L*(the horizontal length scale of heterogeneity),

_{h}*U*(the spatially averaged wind speed) as

*z*, is the height above ground level at which the values of the measured micrometeorological variables integrate the local variation in surface properties. An iterative approach was followed by first assuming an initial value for

_{b}*z*

_{0}, based on

*h*as described in Brutsaert (1982) and then solving for

_{c}*z*.

_{b}Moreover, in cases where the surface exhibits some variability in topography, canopy height, or both in all directions of the LAS path especially in the upwind direction, these variables (i.e., *d* and *z*_{0}) need to be evaluated by considering the effects of the LAS footprint as recommended by Hartogensis et al. (2003). Herein we also considered representing these variables using a 3D footprint model as discussed in section 2c.

### c. Footprint model

Turbulence fluxes measured, for example, with Bowen ratio and eddy covariance flux towers represent the weighted contribution of the fluxes from the upwind area to the tower that is called the source area or the footprint. In the case of LAS measurements, a 3D footprint can be utilized to determine the weighted contribution of surface features or topography in the upwind direction. Specifically, in areas that exhibit surface heterogeneity and topographic variability, the use of 3D LAS footprint is the recommended approach to better represent these features (Hartogensis et al. 2003; Hoedjes et al. 2002; Meijninger et al. 2002a). To obtain the weighted contribution of the footprint, different models have been suggested in the literature. We opted to use the model described by Horst and Weil (1992, 1994) that is based on the analytical solution of the advective-diffusion equation.

*f*relates the vertical turbulence flux measurements

*F*(

*x*,

*y*,

*z*) at height

_{m}*z*to the spatial distribution of the surface fluxes

_{m}*x*and

*y*representing the upwind and the crosswind distances, respectively, from the point of measurement. Horst and Weil (1994) showed the crosswind-integrated footprint function

*z*is the measurement height,

_{m}*A*,

*b*, and

*c*are functions of the gamma function, Γ, and

*r*is the Gaussian plume model shape parameter. For further details on how to estimate these coefficients refer to Horst and Weil (1992, 1994). The footprint function

To estimate the 3D footprint for the LAS, the footprint function *W*(*u*) as suggested in Hoedjes et al. (2002, 2007) and Meijninger et al. (2002a, 2006). Note that in this analysis, the 3D footprint for the LAS was estimated at a 1-m spatial resolution and the contribution considered was ~95% of the source area.

### d. Correction for saturation effects

LAS measurements in some cases can be affected by the saturation of the *H* (Kohsiek et al. 2006). For a particular LAS setting, the limits of *H*. Inspection of the *H* estimated by the LAS versus the Bowen ratio method over the study area indicated that the saturation limit falls between *H* values of 200–300 W m^{−2}, which typically matched the maximum limits of the LAS measurements while the Bowen ratio sometimes measured higher values, indicating possible saturation effects.

We corrected for saturation effects following the procedure recommended by Kohsiek et al. (2006), specifically using the algorithm proposed in Hill and Clifford (1981). Kohsiek et al. (2006) described how to obtain the saturation correction parameter for the specified LAS setting based on the pathlength (*L*), aperture diameter (*D*), and operating wavelength (*λ*); the inner-scale length (*l*_{0}); and *l*_{0}. However, Kohsiek et al. (2006) showed that the saturation correction has some dependency on *l*_{0} as supported by better agreement with measurements. Note that we experienced saturation effects on two different LAS configurations out of the three used at the study area, specifically over paths 2 and 3 as described in the results and discussion section.

### e. The BR method

Sensible and latent heat fluxes, *H* and *LE*, were measured based on the standard Bowen ratio method of Bowen (1926) modified later by Monteith and Unsworth (2008). The BR method assumes that the sources and sinks for heat and water vapor are the same. In other words the exchange coefficients for heat and water vapor are equal (i.e., *K _{h}* =

*K*; see, e.g., De Bruin et al. 1993, 1999), which is not necessarily always valid and applicable over tall heterogeneous vegetation. The validity of this assumption and its effect on the BR measurements will be discussed in more detail in this section and in section 4.

_{e}Note that the Bowen ratio method analysis does not need estimates of zero plane displacement height, *d*; however, the main assumption of similar sources and sinks of heat, vapor, and momentum implies similar values of *d*. Hence, the violation of this assumption leads to differences in the *d* for heat, vapor, and momentum fluxes as the surface becomes more heterogeneous. The vegetation at the study area was relatively dense with average LAI ranging between 2.5 at Swamp tower to 4.0 at Slytherin tower. So assuming that the value of *d* is similar for heat and momentum flux transfers might not have resulted in significant errors. In addition, BR systems are known to have a problem in accurately estimating fluxes under relatively small gradients of *T* and *q* that can occur over forests either because of mixing or because of low evaporation rates (Baldocchi et al. 1988). However, tamarisk trees are phreatophytes and have significant transpiration rates that are enough to enhance humidity gradients. Therefore, we used the BR measurements for comparison purposes. Another factor to point out is that most scintillometer-based studies referenced earlier, used eddy covariance measurements for verification purposes. These systems measure *H* and *LE* independently and typically result in an energy balance closure of about 85% (Massman and Lee 2002) with currently no standard procedure for establishing energy closure. The BR method forces energy balance closure using the Bowen ratio. Therefore when comparing LAS-based estimates of H with either BR or EC data, one should consider closure issues as it could add to the uncertainties.

## 3. Study area and data collection

### a. The study area

The study was conducted in a riparian forest at the Cibola National Wildlife Refuge (CNWR), Southern California. The data were collected during the summer of 2008 over an area of approximately 5 × 4 km^{2} centered at 33°16′N, 114°41′W. The region is considered arid to semiarid with an annual rainfall of less than 100 mm. The study area is surrounded on the north, east, and south sides by an agricultural drain, running from north to south, which drains the excess water from the Palo Verde Irrigation District (PVID). The Colorado River is located east of the study area. The west side consists of highlands and hills with sparse desert vegetation (Fig. 1). The research area is covered (90%) mainly with dense tamarisk (*Tamarix ramosissima*). The remaining vegetation is a mixture of native trees and shrubs including arrowweed, mesquite, and cottonwood interspersed with bare soil (Fig. 2). The data were acquired as part of a larger study funded by the U.S. Bureau of Reclamation with the purpose of improving water resource management at the PVID and in the Colorado River.

### b. The LAS data

Two LAS instruments were installed within the research site under three different layout configurations designed to capture the effect of variable vegetation density. The LAS layout consisted of three paths (Fig. 2): path 1 with a length of 1832 m extended over high-density and relatively tall tamarisk stands between the Mulligan tower with the transmitter at a height of 5.84 m above ground and Sara Hill where the receiver was on a hill at a higher elevation positioned on a tripod at 1.53 m above ground, path 2 with a length of 1052 m between the Mulligan tower (transmitter) and the Diablo tower with the receiver at a height of 6.16 extending over medium-density and medium-height tamarisk canopy, and path 3 with a length of 1621 m between the Swamp tower with the transmitter at a height of 5.19 m and the Diablo tower (receiver) extending over a low-density shorter canopy with mixed tamarisk and arrowweed. Examining the profiles of these three paths (Fig. 3), it can be seen that the slanted beam for path 1 has an elevation difference of about 10 m between the transmitter and the receiver, with less than a 2-m elevation difference for paths 2 and 3. Note that the slanted path of path 1 is a result of topographic variability. The variability of surface roughness can also be observed, resulting from vegetation density and height ranging from low, medium, to high over paths 3, 2, and 1, respectively.

The LAS system used was a Boundary Layer Scintillometer BLS900 from Scintec AG Rottenburg, Germany, with an aperture diameter *D* = 0.15 m operating at a wavelength of 880 nm. There were a separate set of air temperature and atmospheric pressure sensors connected to the LAS system that provided measurements of *T _{a}* and

*P*. The LAS measurements were sampled at 1 Hz and averaged over 1-min time periods to provide

*H*. The measurements for path 1 were taken during 12–18 May, providing a total of 7 days of data; for path 2 a total of 6 days during September; and for path 3 between 14 April and 31 May, as well as 7 days in June, providing a total of 51 days.

### c. The BR data

Bowen ratio (BR) systems developed by Radiation and Energy Balance Inc., Seattle (REBS), were used to provide the energy balance fluxes, including the net radiation (*R _{n}*), the latent heat (

*LE*), soil heat (

*G*), and sensible heat (

*H*) fluxes. The BR has an automatic exchange mechanism (AEM), which reduces the measurement biases in the temperature and humidity gradients by switching the positions of the upper and the lower sensors every 15 min. Soil heat flux plates combined with soil moisture and temperature sensors provided measurements of

*G*. An REBS Q7.1 net radiometer and a pyranometer were used to measure net radiation and incoming solar radiation. There were also wind speed and direction sensors; a set of two temperature and humidity sensors installed on the two arms of the AEM, 1 m apart; a barometric pressure sensor; and a Campbell Scientific Inc. CR10X datalogger. Measurements were taken at 30-s intervals and the fluxes were estimated at 30-min moving averages. Three BRs were deployed in the CNWR—the first BR deployed on the Slytherin tower at a height of 7.32 m above the ground surface near the center of path 1 in an area characterized by dense tall tamarisk trees with average height of about 5.5 m, the second BR deployed at the Diablo tower at a height of 6.8 m in an area characterized by medium-density trees with average height of 4.0 m, and the third BR deployed at the swamp tower at a height of 5.5 m in an area characterized by a mixture of tamarisk and arrowweed shrubs with average height of 2–3 m interspersed with bare soil. The final BR measurements of

*H*were cleaned of spikes that occur during transition from stable to unstable conditions or at sunrise and sunset when the Bowen ratio approaches negative 1 (for detailed description of the data see Chatterjee 2010).

### d. The lidar data

Lidar data were collected with the Utah State University (USU) Lidar-Assisted Stereo Imager (LASSI) system from an altitude of approximately 600 m above ground level at an average point density of over 2 points per square meter. The LASSI system mounted in the USU Cessna TP206 remote sensing aircraft consists of a full-waveform Riegl Q560 lidar transceiver, a NovAtel SPAN LN-200 GPS/IMU navigation system. The absolute point accuracy is approximately 7 cm and relative accuracy is approximately 2 cm. The point cloud data were processed and classified to separate ground returns from canopy returns and obtain 1-m digital elevation models and vegetation height layers. The resulting topography and vegetation maps are shown in Fig. 4.

To evaluate the performance of the LAS without the use of lidar data, we also used traditional topographic maps for the region to estimate *z*(*u*). A digital scan topographic map was obtained from the U.S. Geological Survey (USGS) at scale 1:24 000 (USGS 2010) to compare with our lidar-derived topographic map.

## 4. Results and discussion

Three different estimates of *H* were made—*H*_{Map_Ln}, *H*_{LiD_Ln}, and *H*_{LiD_Ftp}—based on the surface roughness representation. The estimates *H*_{Map_Ln} were based on using topographic maps for determining *z*(*u*) and on using an average *h _{c}* estimated based on vegetation survey in areas around the center of the LAS path because of the considerable weighted contribution to LAS measurements as described in section 2. Estimates

*H*

_{LiD_Ln}were those based on using lidar-derived measurements of

*z*(

*u*) and

*h*along the LAS path. Estimates

_{c}*H*

_{LiD_Ftp}refer to estimates of

*H*based on

*z*(

*u*) and

*h*from the lidar-derived measurements weighted with the LAS 3D footprints oriented with the upwind direction. These estimates of

_{c}*H*

_{Map_Ln},

*H*

_{LiD_Ln}, and

*H*

_{LiD_Ftp}were compared to measured

*H*

_{BR}and comparison statistics presented in terms of the root-mean-square error (RMSE), mean absolute error (MAE), and the mean bias error (BIAS).

Note that De Bruin et al. (1993) reported a value of 9.0 for the constant 6.1 in Eq. (4), which was used in this analysis (Wyngaard et al. 1971). Their value was based on data from the plains of La Crau, France, while Wyngaard et al. (1971) was based on data from Kansas. Note that both values were based on studies conducted over areas that we believe have a different type of heterogeneity than CNWR as discussed later. We compared the effect of using both coefficients on the estimates of *H* with data from paths 1 and 2.

As Eq. (2) by Wesely (1976) resulted from the assumption that |*R _{Tq}*| = 1, additionally, De Bruin et al. (1999) showed that the BR method is based on the same assumption. However, the findings from other studies by Hoedjes et al. (2007) and De Bruin et al. (1999) suggested that |

*R*| may deviate from 1. De Bruin et al. (1999) showed that

_{Tq}*T*and

*q*behave similarly when |

*R*| =1 based on theoretical review and data collected by eddy covariance and BR systems over different types of surfaces and climatic regions. However, De Bruin et al. (1999) also showed that in some cases |

_{Tq}*R*| < 1, but without confirming that if |

_{Tq}*R*| < 1,

_{Tq}*T*and

*q*do not behave similarly. The findings of De Bruin et al. (1999), which were solely based on experimental evidence from reviewing several studies, showed that when |

*R*| < 1,

_{Tq}*T*and

*q*are similar. The implications of this are represented in the violation of the Bowen ratio method assumptions and additional uncertainty in Eq. (2).

### a. Path 1

Over path 1, both *H*_{Map_Ln} and *H*_{LiD_Ln} systematically overestimated *H*_{BR} (Fig. 5) with a BIAS of 28 and 11 W m^{−2}, respectively (Table 1), though *H*_{LiD_Ln} performed better. Using *H*_{LiD_Ln} resulted in lower RMSE and MAE of 34 and 27 W m^{−2} compared to 44 and 35 W m^{−2}, respectively, for *H*_{Map_Ln} (Table 1). Also *H*_{LiD_Ln} resulted in reduced scattering around the 1:1 line compared to *H*_{Map_Ln} as shown in Fig. 5. This indicates the improvements in estimates of *H*_{LiD_Ln} as compared to *H*_{Map_Ln}. We looked into the values used to represent the surface roughness and the LAS beam height [i.e., *h _{c}*,

*d*,

*z*

_{0}, and

*z*(

*u*)] as well as the weighted average of the LAS beam height along the path (

*z*

_{wt_ave}) in both estimates of

*H*

_{Map_Ln}and

*H*

_{LiD_Ln}. It appears that there were no differences between both values of

*h*(3.2 m) and

_{c}*z*

_{0}(0.26 m) used to estimate

*H*

_{LiD_Ln}and those for

*H*

_{Map_Ln}. In other words, there were basically less or no differences in surface roughness due to vegetation when using data either from lidar or the traditional vegetation survey. On the other hand, the value of

*z*

_{wt_ave}used to estimate

*H*

_{LiD_Ln}showed a difference of about 2.0 m less than the value used to estimate

*H*

_{Map_Ln}. This supports the evidence that using the lidar-derived topography has improved the LAS estimates of

*H*.

Summary of statistical comparison between estimates and measurements of *H* for path 1 with *L _{P}* = 1.8 km.

We looked into the effect of using the value of 9.0 (De Bruin et al. 1993) instead of the constant 6.1 (Wyngaard et al. 1971; Andreas 1989) in Eq. (4). Estimates of *H*_{Map_Ln} resulted in higher values of RMSE of 61 W m^{−2}, MAE of 51 W m^{−2}, and BIAS of 48 W m^{−2} compared to those obtained using a constant of 6.1 shown in Table 1. Improvements from the use of lidar-derived canopy heights were also observed for *H*_{LiD_Ln} with RMSE of 44 W m^{−2}, MAE of 34 W m^{−2}, and BIAS of 26 W m^{−2} but were still worse than using a value of 6.1. It appears that the values suggested by Wyngaard et al. (1971) worked better for this dataset. Note that the data collected in Kansas used in Wyngaard et al. (1971) were taken over an area of 2.4 km with flat, homogenous terrain. The measurements were taken over winter wheat stubble approximately 18 cm in height during dry surface conditions with the mean to max wind speed of about >6 m s^{−1}. While the La Crau data used in De Bruin et al. (1993) were taken over an area of 5-km flat homogenous terrain covered with grasses and herbs, pebbles and stones 15 cm diameter, and the wind speed >10 m s^{−1}. In terms of the surface type, terrain, moisture condition, and wind speed, there was no specific reason for preferring either the Wyngaard et al. (1971) or De Bruin et al. (1993) equation to estimate *H* under unstable conditions. However, De Bruin et al. (1993) showed that their modified function provided slightly better fitting to Kansas data but provided no explanation for possible reasons for these differences. In another study, De Bruin et al. (1995) supported the findings of De Bruin et al. (1993) as their function worked well over dry vineyard fields in Spain. However, and because of the importance of the study in describing the effects of the surface heterogeneity in the LAS-based measurements of *H*, we included such a comparison. We don’t have specific reasons to explain why Wyngaard et al. (1971) worked better than De Bruin et al. (1993) for this dataset. However, both methods indicated the importance of including detailed surface feature data from lidar for improved LAS-based measurements of *H* and the main reason we present these results. Note that there was no attempt to consider similar analysis for stable atmospheric conditions as there were not enough data for such analysis.

### b. Path 2

Both estimates of *H*_{Map_Ln} and *H*_{LiD_Ln} underestimated *H*_{BR} (Fig. 6) with a BIAS of −18 and −6 W m^{−2} (Table 2). Note that the saturation correction for path 2 was on the average about a 30% increase. The study by Kohsiek et al. (2006) showed that, in some cases, even when correcting for saturation, the LAS estimates would still result in an underestimation of sensible heat flux values and this partially explains the related underestimation we obtained. Estimates of *H*_{LiD_Ln} resulted in a slightly better performance with about 3 W m^{−2} lower RMSE compared to *H*_{Map_Ln}. Similarly, as shown for path 1, we looked into the values of *z*_{wt_ave}, *h _{c}*, and

*z*used for both estimates of

_{0}*H*

_{Map_Ln}and

*H*

_{LiD_Ln}(Table 2). The values of

*z*

_{wt_ave}used in both estimates of

*H*

_{Map_Ln}and

*H*

_{LiD_Ln}did not show much difference while

*h*had slightly lower values for those used with

_{c}*H*

_{Map_Ln}compared to

*H*

_{LiD_Ln}. Relating the value of

*h*to the performance of the LAS estimates of

_{c}*H*, it can be concluded that lowering

*h*and, hence,

_{c}*z*

_{0}has led to improved estimates of

*H*

_{LiD_Ln}.

Summary of statistical comparison between estimates and measurements of *H* for path 2 with *L _{P}* =1.0 km.

The effect of using a value of 9.0 instead of 6.1 for the constant in Eq. (4) on data from path 2 was similar to path 1, resulting in higher RMSE, MAE, and BIAS.

### c. Path 3

Over path 3, *H*_{LiD_Ln} overestimated *H*_{BR} with a BIAS of 12 W m^{−2} while *H*_{LAS} underestimated with a value of −20 W m^{−2} (Table 3). In Fig. 7 it can be seen that the resulting *H*_{Map_Ln} underestimated most *H* values of ≈250 W m^{−2} and higher—an expected behavior even when considering saturation correction, and similar to the findings of Kohsiek et al. (2006). The saturation correction over path 3 on average resulted in a 45% increase, which was higher than the correction estimated for path 2. Estimates of *H*_{LiD_Ln} showed a better performance with a lower RMSE of 41 W m^{−2} compared to 52 W m^{−2} for *H*_{Map_Ln}. The value of *z*_{wt_ave} used to estimate *H*_{LiD_Ln} was about 1.3 m higher than the value used to estimate *H*_{Map_Ln}, while the value of *h _{c}* was about 1.0 m higher.

Summary of statistical comparison between estimates and measurements of *H* for path 3 with *L _{P}* =1.6 km.

Note that over path 3 we used the average of *H*_{BR} from the two towers at Diablo and swamp as well as the average wind speed in the analysis. When we compared our estimates with *H*_{BR} from only the Diablo tower using the corresponding wind speed, the results of the comparison, not shown here, provided generally similar results but with higher RMSE values.

The results shown for all three paths indicate that path-averaged estimates of *H* made by incorporating lidar-derived data [e.g., *z*(*u*), *h _{c}*, and

*z*

_{0}] improved estimates of

*H*. Differences in representative values of either

*z*(

*u*),

*h*, or both, depending on the path, affected the performance of the LAS in estimating

_{c}*H*. We noticed (i) the effects of lidar data were most prevalent when the variation in surface roughness (see the values of

*h*and

_{c}*z*

_{0}in Table 3) were large, while they were less for topography (see

*z*

_{wt_ave}in Table 3) with no slanted path such as path 3; (ii) that less variability in both topography, with no slanted path, and surface roughness resulted in the least effect; and (iii) with less or no variability in surface roughness but with topographic variability (with slanted path), the effects were noticeable but less than when compared to (i).

### d. Footprint analysis

We further studied the effect of applying the 3D footprint of the LAS on its estimates of *H*. For this part of the analysis we considered path 3 as there were enough data to use (about 45 days). Generally, even though saturation effects have been corrected for section 3a, we noticed that most of the error in path 3 (Fig. 7) appears to occur at values of *H* higher than about 200 W m^{−2}. This basically represents all estimates made during the day between 0800–0900 and 1600–1700 under unstable atmospheric condition. Note that for this part of our analysis (i.e., LAS footprint effects) we considered only unstable conditions over path 3. The LAS footprints were studied as follows: we first obtained estimates of the hourly values during the considered daytime hours for the footprint models’ parameters (e.g., *L*_{MO}, *U*, and other parameters); secondly, these parameters with the corresponding wind direction were analyzed. As the LAS footprint changes with time we found that a representative footprint can be used for each day during the daytime hours when considering the predominant wind direction. Note that for this dataset there were minor variations in the LAS footprint. However, it would be appropriate to carry out the analysis by obtaining estimates of hourly LAS footprints for each day. The wind direction over path 3 was analyzed for the 51 days of the data. Five preferential wind directions were found (Table 4) and the corresponding analysis dates grouped accordingly. The data needed for estimating the 3D footprint of the LAS were analyzed (e.g., *L*_{MO} and

Summary of performance statistics showing the different estimates of *H* compared with measurements for path 3 with *L _{P}* =1.6 km under unstable atmospheric conditions. Statistics shown for

*H*are for all wind directions.

_{LiD_Ftp}It is clear that, based on the LAS 3D footprint and wind direction, the roughness parameters (e.g., *h _{c}*,

*d*, and

*z*

_{0}) have different values (Table 4). Note that the footprint analysis was conducted to represent the variability due to vegetation height but not the topography; hence,

*z*

_{wt_ave}is constant in Table 4. Using these values, we estimated the sensible heat flux

*H*

_{LiD_Ftp}for the selected days and provided the corresponding

*H*

_{Map_Ln}and

*H*

_{LiD_Ln}. An example of the LAS 3D footprint effects on the sensible heat flux estimates is shown for the two days in Figs. 8c,d that correspond to the footprint and wind direction in Figs. 8a,b. The improvement in

*H*

_{LiD_Ftp}estimates compared to both

*H*

_{Map_Ln}and

*H*

_{LiD_Ln}can clearly be seen. During both dates, 17 and 20 April,

*H*

_{Map_Ln}considerably underestimated

*H*

_{BR}while both

*H*

_{LiD_Ln}and

*H*

_{LiD_Ftp}showed good agreement with

*H*. For all 51 days, estimates of

_{BR}*H*

_{Map_Ln},

*H*

_{LiD_Ln}, and

*H*

_{LiD_Ftp}compared to

*H*

_{BR}are shown in Fig. 9. It indicates an overall better performance by the LAS estimates of

*H*

_{LiD_Ftp}when considering its footprints as supported by the statistics in Table 4. Estimates

*H*

_{LiD_Ftp}showed the lowest RMSE of 37 W m

^{−2}compared to 54 and 42 W m

^{−2}for

*H*

_{Map_Ln}and

*H*

_{LiD_Ln}, respectively. It also resulted in the lowest MAE of 29 W m

^{−2}compared to 42 and 35 W m

^{−2}for

*H*

_{Map_Ln}and

*H*

_{LiD_Ln}, respectively. Also,

*H*

_{LiD_Ftp}resulted in less scattering around the 1:1 line compared to

*H*

_{LiD_Ln}(Fig. 9).

The point we would like to raise from this exercise is that, generally, the scintillometer measures the intensity fluctuations due to turbulent eddies along its path without knowledge of its source or direction. The turbulence that passes through and is measured in the LAS path basically has the combined signature, depending on the blending height, from the individual patches in the upwind footprint direction. It is therefore necessary to properly define the corresponding surface roughness parameters (i.e., *h _{c}*,

*d*, and

*z*

_{0}) in the upwind footprint. Also using the LAS weighting function to estimate the corresponding effective height

*z*

_{eff}is legitimized by the notion that it describes the weight of contribution of the scintillation measured by the propagating wave along its path (Hartogensis et al. 2003). Using

*W*(

*u*) to obtain a weighted average estimate for the corresponding roughness parameters could be a reasonable approximation in conditions with similar type of heterogeneity along and around the LAS path as in the case of path 1 and to some extent path 2. This also suggests that a preanalysis of wind direction, selection of the path, and investigation of the surface heterogeneity are important tasks to perform before setting up the scintillometer as it will define the need of using the LAS footprint approach in estimating a representative sensible heat flux.

Another issue to consider is that the upwind footprint of the BR tower did not necessarily match the LAS footprint because of its size and location. However, despite being heterogeneous, the surface in this study is extensive and the scale of heterogeneity is small relative to the size of the footprint. This kind of surface can be considered as type A (Shuttleworth 1988); hence, these conditions provide spatially homogenous fluxes. This was supported by inspecting thermal and multispectral reflectance images of the area (not shown). The preferred location of a BR or EC tower is near the center of the LAS path, where the LAS signal is significantly weighted, also allowing the overlap of the BR and LAS footprints for most wind directions. Note that this was the case for path 1, while for paths 2 and 3 the BR towers were located at the ends of the LAS path (i.e., next to the transmitter and/or receiver) and sometimes there were partial or no overlap of the footprints. In the analysis for path 3, we used the average BR data from the two flux towers that were located on each end of this path. Considering the associated uncertainty in both BR and LAS measurements, the results obtained are comparable and do not invalidate the findings of this research. The main purpose of this paper was not to ascertain whether or not the LAS provided accurate estimates of *H* under those conditions, but to address the need for using detailed surface roughness data—for example, obtained from airborne lidar—to improve the LAS estimates in heterogeneous situations.

## 5. Conclusions

In this study we investigated the effects of incorporating lidar-derived topography and surface roughness on the scintillometer-based estimates of sensible heat flux (*H*). The study was conducted at the Cibola National Wildlife Refuge in Southern California. The region is characterized by arid to semiarid climatic conditions and considerable surface heterogeneity imposed by riparian vegetation that consists mostly of tamarisk trees and shrubs interspersed with bare soil. This setting provided interesting conditions to test the application of the scintillometer and its performance. Two large aperture scintillometers (LAS) were set up in the area to capture the variability of the surface roughness with paths 1, 2, and 3 having low, medium, and high surface heterogeneity, respectively.

LAS measurements, specifically *H*. The effect of using different representations of surface roughness and heterogeneity was investigated. First, *H*_{Map_Ln} was estimated using topographic maps and vegetation surveys to estimate the LAS beam height *z*(*u*) as well as an average canopy height (*h _{c}*) around the center of the LAS path; secondly,

*H*

_{LiD_Ln}was estimated based on lidar-derived topographic and canopy height maps to obtain

*z*(

*u*),

*h*,

_{c}*d*, and

*z*

_{0 }along the LAS path. Estimates of

*H*

_{Map_Ln}and

*H*

_{LiD_Ln}were made over the three different LAS paths 1, 2, and 3. The results indicate that incorporating lidar-based canopy data into LAS-based estimates of

*H*improved its performance. This improvement can be explained by the fact that either increased variability in topography and/or surface roughness that could be present along and around the LAS path, as in the case of paths 1 and 3, were well represented by the lidar data. On the other hand, if less variability exists in both topography and surface roughness, as in the case of path 2, the improvements were less dramatic.

We also investigated the effects of representing surface roughness using the LAS 3D upwind footprint on the estimates of *H*. Estimates of *H*_{LiD_Ftp} were obtained using roughness parameter values (i.e., *h _{c}*,

*d*, and

*z*

_{0}) determined from combining the LAS 3D footprint and lidar-derived canopy height maps as we considered only the case of path 3. The results showed a considerable improvement in the sensible heat flux estimates as we compared

*H*

_{Map_Ln},

*H*

_{LiD_Ln}, and

*H*

_{LiD_Ftp}with

*H*

_{BR}. These findings showed the importance of considering the 3D footprint in scintillometer analysis as well as the benefits of using detailed surface roughness (e.g., lidar-derived surface features) over heterogeneous areas.

Finally, this analysis was carried out using scintillometer data collected within the boundary layer, relatively close to the surface, and it showed the importance of including detailed surface features in the estimations of *H*. However, we cannot generalize that this would be the case nor have the same effect if the LAS measurements would have been conducted higher above the surface within the mixed layer. This is an important issue that will have to be addressed in future studies.

## Acknowledgments

This research was supported in part by the Remote Sensing Services Laboratory and the LASSI Service Center, both in the Department of Civil and Environmental Engineering at Utah State University, the Utah Agricultural Experiment Station, and the Utah State Water Research Laboratory. The scintillometer data were acquired under funding from the U.S. Bureau of Reclamation through a contract with the Alliance of Universities and Central State University, Wilberforce, Ohio, under Grant 04FC811041. We thank Professor Subramania Sritharan of Central State University for his assistance and support in this project.

## APPENDIX

### Scintillometer Weighting Function

*W*(

*u*) can be estimated aswhere

*L*,

*k*the turbulent spatial wavenumber,

*D*is the aperture diameter. An example of

*W*(

*u*) for the LAS used in this analysis is shown in Fig. A1.

## REFERENCES

Andreas, E. L, 1988: Atmospheric stability from scintillation measurements.

,*Appl. Opt.***27**, 2241–2246.Andreas, E. L, 1989: Two-wavelength method of measuring path averaged turbulent surface heat fluxes.

,*J. Atmos. Oceanic Technol.***6**, 280–292.Andreas, E. L, Ed., 1990:

*Selected Papers on Turbulence in a Refractive Medium.*SPIE Milestone Series, Vol. 25, SPIE, 693 pp.Andreas, E. L, 1991: Using scintillation at two wavelengths to measure path averaged heat fluxes in free convection.

,*Bound.-Layer Meteor.***54**, 167–182.Baldocchi, D. D., , Hicks B. B. , , and Meyers T. P. , 1988: Measuring biosphere-atmosphere exchange of biologically related gases with micrometeorological methods.

,*Ecology***69**, 1331–1340.Bowen, I. S., 1926: The ratio of heat losses by conduction and by evaporation from any water surface.

,*Phys. Rev.***27**, 779–787.Brutsaert, W., 1982:

*Evaporation into the Atmosphere: Theory, History, and Applications.*Springer, 299 pp.Chatterjee, S., 2010: Estimating evapotranspiration using remote sensing: A hybrid approach between Modis derived enhancement vegetation index, Bowen ratio systems, and ground based micro-meteorological data. Ph.D. dissertation, Wright State University, 175 pp.

Chehbouni, A., and Coauthors, 1999: Estimation of area-average sensible heat flux using a large-aperture scintillometer during the Semi-Arid Land-Surface-Atmosphere (SALSA) experiment.

,*Water Resour. Res.***35**, 2505–2511.De Bruin, H. A. R., 2002: Introduction: Renaissance of scintillometry.

,*Bound.-Layer Meteor.***105**, 1–4.De Bruin, H. A. R., , Kohsiek W. , , and van den Hurk B. J. J. M. , 1993: A verification of some methods to determine the fluxes of momentum, sensible heat and water vapour using standard deviation and structure parameter of scalar meteorological quantities.

,*Bound.-Layer Meteor.***63**, 231–257.De Bruin, H. A. R., , van den Hurk B. J. J. M. , , and Kohsiek W. , 1995: The scintillation method tested over a dry vineyard area.

,*Bound.-Layer Meteor.***76**, 25–40.De Bruin, H. A. R., , van den Hurk B. J. J. M. , , and Kroon L. J. M. , 1999: On the temperature-humidity correlation and similarity.

,*Bound.-Layer Meteor.***93**, 453–468.De Wekker, S. F. J., 1996: The estimation of areally-averaged sensible heat flux over complex terrain with a large-aperture scintillometer. M.S. thesis, Dept. of Meteorology, Wageningen Agricultural University, 42 pp.

Hartogensis, O. K., , and De Bruin H. A. R. , 2005: Monin–Obukhov similarity functions of the structure parameter of temperature and turbulent kinetic energy dissipation rate in the stable boundary layer.

,*Bound.-Layer Meteor.***116**, 253–276.Hartogensis, O. K., , Watts C. J. , , Rodriguez J.-C. , , and De Bruin H. A. R. , 2003: Derivation of an effective height for scintillometers: La Poza experiment in northwest Mexico.

,*J. Hydrometeor.***4**, 915–928.Hill, R. J., , and Clifford S. F. , 1978: Modified spectrum of atmospheric temperature fluctuations and its applications to optical propagation.

,*J. Opt. Soc. Amer.***68**, 892–899.Hill, R. J., , and Clifford S. F. , 1981: Theory of saturation of optical scintillation by strong turbulence for arbitrary refractive-index spectra.

,*J. Opt. Soc. Amer.***71**, 675–686.Hill, R. J., , Clifford S. F. , , and Lawrence R. S. , 1980: Refractive-index and absorption fluctuations in the infrared caused by temperature, humidity and pressure fluctuations.

,*J. Opt. Soc. Amer.***70**, 1192–1205.Hoedjes, J. C. B., , Zuurbier R. M. , , and Watts C. J. , 2002: Large aperture scintillometer used over a homogeneous irrigated area, partly affected by regional advection.

,*Bound.-Layer Meteor.***105**, 99–117.Hoedjes, J. C. B., , Chehbouni A. , , Ezzahar J. , , Escadafal R. , , and De Bruin H. A. R. , 2007: Comparison of large aperture scintillometer and eddy covariance measurements: Can thermal infrared data be used to capture footprint-induced differences?

,*J. Hydrometeor.***8**, 144–159.Horst, T. W., , and Weil J. C. , 1992: Footprint estimation for scalar flux measurements in the atmospheric surface layer.

,*Bound.-Layer Meteor.***59**, 279–296.Horst, T. W., , and Weil J. C. , 1994: How far is far enough?: The fetch requirements for micrometeorological measurement of surface fluxes.

,*J. Atmos. Oceanic Technol.***11**, 1018–1025.Kohsiek, W., , Meijninger W. M. , , De Bruin H. A. R. , , and Beyrich F. , 2006: Saturation of the large aperture scintillometer.

,*Bound.-Layer Meteor.***121**, 111–126.Massman, W. J., , and Lee X. , 2002: Eddy covariance flux corrections and uncertainties in long term studies of carbon and energy exchanges.

,*Agric. For. Meteor.***113**, 121–144.Meijninger, W. M. L., , Hartogensis O. K. , , Kohsiek W. , , Hoedjes J. C. B. , , Zuurbier R. M. , , and De Bruin H. A. R. , 2002a: Determination of area-averaged sensible heat fluxes with a large aperture scintillometer over a heterogeneous surface—Flevoland field experiment.

,*Bound.-Layer Meteor.***105**, 37–62.Meijninger, W. M. L., , Hartogensis O. K. , , Kohsiek W. , , Hoedjes J. C. B. , , Zuurbier R. M. , , and De Bruin H. A. R. , 2002b: Determination of area-averaged water vapor fluxes with a large aperture and radio wave scintillometer over a heterogeneous surface—Flevoland field experiment.

,*Bound.-Layer Meteor.***105**, 63–82.Meijninger, W. M. L., , Beyrich F. , , Lüdi A. , , Kohsiek W. , , and De Bruin H. A. R. , 2006: Scintillometer-based turbulent fluxes of sensible and latent heat over a heterogeneous land surface—A contribution to LIFTASS-2003.

,*Bound.-Layer Meteor.***121**, 89–110.Monteith, J. L., , and Unsworth M. H. , 2008:

*Principles of Environmental Physics.*Academic Press, 418 pp.Panofsky, H. A., , and Dutton J. A. , 1984:

*Atmospheric Turbulence: Models and Methods for Engineering Applications.*John Wiley and Sons, 397 pp.Schmid, K., , Waters K. , , Dingerson L. , , Hadley B. , , Mataosky R. , , Carter J. , , and Dare J. , 2008: Lidar 101: An introduction to lidar technology, data, and applications. NOAA Coastal Services Center, 68 pp.

Shuttleworth, W. J., 1988: Macrohydrology—The new challenge for process hydrology.

,*J. Hydrol.***100**, 31–56.Shuttleworth, W. J., , Yang Z.-L. , , and Arain M. A. , 1997: Aggregation rules for surface parameters in global models.

,*Hydrol. Earth Syst. Sci.***1**, 217–226.Tatarskii, V. I., 1961:

*Wave Propagation in a Turbulent Medium.*McGraw-Hill, 285 pp.USGS, cited 2010: Seamless data warehouse. [Available online at http:\\seamless.usgs.gov.]

Wang, T. I., , Ochs G. R. , , and Clifford S. F. , 1978: A saturation resistant optical scintillometer to measure

*C*2*n*.,*J. Opt. Soc. Amer.***69**, 334–338.Wesely, M. L., 1976: The combined effect of temperature and humidity fluctuations on refractive index.

,*J. Appl. Meteor.***15**, 43–49.Wood, N., , and Mason J. P. , 1991: The influence of static stability on the effective roughness length for momentum and heat transfer.

,*Quart. J. Roy. Meteor. Soc.***117**, 1025–1056.Wyngaard, J. C., , Izumi Y. , , and Collins S. A. Jr., 1971: Behavior of the refractive index structure parameter near the ground.

,*J. Opt. Soc. Amer.***15**, 1177–1188.