The Regional Atmospheric Modeling System was used in two previous studies to simulate mesoscale circulations forced by surface heterogeneity in the Central U. S. and Amazonia. In this work, spectral analysis is used to compare the horizontal length scales of these simulated circulations with the scale of the surface heterogeneity. For both cases, the organized mesoscale circulations are confined within a preferred length scale range (10–20 km) that is significantly different from the dominant length scale of the surface heterogeneity. Multiscale landscape patchiness in these two regions tend to produce eddies at a wide range of scales, but the land-atmosphere interaction processes act as a medium-pass filter to select intermediate-scale circulations. This scale of response remains relatively unchanged despite significant day-to-day variations in the synoptic situation and the mean surface heat flux.
 Differential heating of the planetary boundary layer (PBL) due to heterogeneity in the underlying earth surface gives rise to atmospheric circulations over a wide range of spatial and temporal scales. At the mesoscale, sea and lake breezes produced by the thermal gradient between adjacent land and water bodies are examples of this type of circulation. Significant natural and human-induced heterogeneity existing within the land surface, in the form of patches whose radiative and thermal properties differ from those of their surroundings, can also produce horizontal temperature and pressure gradients strong enough to generate and sustain organized mesoscale circulations of a similar nature [Segal and Arritt, 1992].
 The exchange of energy, moisture and momentum between the land surface and the atmosphere is an important component of the climate system. It has been suggested that by affecting these fluxes, mesoscale circulations can potentially affect atmospheric circulations at much larger scales, with possibly even global implications [Copeland et al., 1996; Pielke et al., 1991, 1998]. Most of the surface patches and the consequent circulations are subgrid scale for typical General Circulation Models (GCM) with a horizontal grid-spacing between 1° and 3° (hundreds of kilometers). Hence, these circulations cannot be explicitly resolved by GCMs and have to be accounted for via appropriate subgrid parameterizations. Work on developing and implementing such a parameterization for GCMs and other large-scale models is currently ongoing.
 A fundamental requirement for such a parameterization is to understand the temporal and spatial structures of these coherent circulations. Baidya Roy and Avissar  used a large-eddy simulation (LES) model to investigate the scale of response to periodic surface forcings. Spectral analysis of their model outputs showed that surface heterogeneity produces organized circulations with the same horizontal length scale as that of the heterogeneity. However, if the surface patches are longer than 5–10 km, randomly distributed turbulent thermals also coexist with the organized circulations and affect their structure.
 The aforementioned LES study provided a glimpse at the mesoscale processes at play, albeit under simplifying assumptions. First, the simulations were performed without any moisture and background wind. Second, the surface heterogeneity had only one scale of variability: the wavelength of the forcing function. In nature, the landsurface patchiness is complex with a wide range of superposed spatial scales. The background meteorological conditions are also very diverse. Hence, there is a need for exploring the scales of atmospheric flow forced by complex surface heterogeneity under realistic meteorological conditions.
 Owing to lack of suitable observational data sets at high spatial and temporal resolution, the dynamics of organized circulations in the convective boundary layer (CBL) forced by surface patchiness can only be studied using very high resolution numerical model simulations constrained by and validated against appropriate observational data. Weaver and Avissar  (hereafter referred to as WA01) simulated the organized mesoscale circulations produced by large-scale agriculture in the central U. S. Baidya Roy and Avissar  (hereafter referred to as BA02) modelled similar circulations caused by deforestation in Amazonia. Both these studies were performed under realistic boundary conditions, obtained from field experiments, and the simulation results were validated against satellite and surface-based observations.
 In this paper we investigate the horizontal length scales of the atmospheric flow fields in the CBL simulated by the two aforementioned numerical experiments using angle-integrated two-dimensional Fourier transforms. The goal is to explore the relationship of the scale of the atmospheric response to that of the surface forcings for complex surfaces and realistic meteorological conditions. In the next section the numerical studies are briefly described. Section 3 contains the results of the spectral analysis and finally, the implications of this study are discussed in section 4.
2. Numerical Simulations
 The state-of-the-art Regional Atmospheric Modeling System (RAMS) [Pielke et al., 1992; Liston and Pielke, 2000] was used in both WA01 and BA02. RAMS solves the full three-dimensional, compressible, nonhydrostatic dynamic equations, a thermodynamic equation and a set of microphysics equations in a terrain-following coordinate system. It also includes parameterizations for subgrid-scale processes, radiative transfer and cumulus convection. The numerical experiments and the results of these studies are only briefly described here. Details can be obtained from the relevant publications referred to above.
2.1. Simulations Over the Central United States
 These simulations (WA01) were conducted over the Department of Energy Atmospheric Radiation Measurement (ARM) Cloud and Radiation Testbed (CART) in Oklahoma and Kansas in the Central U. S. [Stokes and Schwartz, 1994]. The landscape in this region was a composite of native vegetation and large patches of partially harvested agricultural fields. The model domain was a 250 km × 250 km grid resolved by a 2 km spacing, nested within two coarser grids. The model was initialized with the six-hourly National Center for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis data [Kalnay et al., 1996]. The same data was used to weakly nudge the atmospheric lateral boundaries of the coarsest grid. Weaver et al.  have shown that simulated mesoscale circulations are not sensitively dependent on lateral nudging of this type. The bottom boundary of the finest grid was driven by sensible and latent heat fluxes corresponding to the July 13 case described by Doran et al. . This flux data was obtained by using the Simple Biosphere Model forced with observed soil, vegetation and meteorology and validated against surface observations. The RAMS soil-vegetation model was used for the coarsest grid while in the middle grid they used a composite of the land model and the flux data. The model was run for 12 hours (6 am–6 pm) during six selected days, July 6, 7, 10, 12, 13 and 21, 1995.
 Intense mesoscale circulations were produced on each of the simulated days. The synoptic conditions and the magnitude of the surface fluxes varied from day to day, but the intensity and viability of the eddies were generally independent of these factors. However, the orientation of the coherent circulations were solely determined by the background meteorological conditions. For instance, southerly winds on July 13 resulted in elongated, meridionally aligned eddies while a south-easterly wind on July 12 produced eddies oriented in that direction. By contrast, on July 10, when the background wind was very weak, the mesoscale circulations were fairly stationary in space with the convergence zones anchored to the boundaries of the warm patches. Comparison with data from the GOES-8 satellite as well as composited raingauge/radar rainfall measurements from the Arkansas-Red Basin River Forecast Center (ABRFC) showed that the simulations were realistic. No coherent circulations were produced when the model was forced with spatially homogeneous surface fluxes.
2.2. Simulations Over Amazonia
 The BA02 study area was a partially deforested region of the Amazonian rain forest in Rondônia, Brazil. The structure of deforestation was unique to this region: small patches of farmlands and pastures along a network of highways and local roads leading to the well-known “fishbone” pattern. The model domain was a 101 km × 101 km area covered with a 1 km mesh, nested within two coarser grids. The dominant feature of the domain was the highway BR-364 that passed through the south-western part of the grid. The model was initialized and weakly nudged at the lateral boundaries of the outermost grid with the NCEP/NCAR reanalysis data. The bottom boundary was forced with observed fluxes of sensible and latent heat collected during the Rondônia Boundary Layer Experiment phase 3 (RBLE-3) conducted during the Anglo-Brazilian Amazonian Climate Observation Study (ABRACOS) [Gash et al., 1996]. The surface flux data was available only for two days - August 17 and 22, 1994. The model was run for 12 hours (7 am–7 pm) on both these days.
 Early in the morning on both case study days, stronger sensible heating over deforested areas, compared to that over the forest, led to the formation of numerous small eddies with convergence zones right above the bare patches. While most of the eddies remained small and weak, those over the highway and the adjacent deforested areas continued growing, ultimately coalescing into fairly intense (vertical wind speed up to 0.4 ms−1 on August 17) coherent circulations by early afternoon.
 On August 17, a strong south-westerly synoptic-scale wind that entered the region late in the afternoon advected these circulations northward. By contrast, on August 22, the circulations, considerably weakened by a strong, persistent westerly low-level jet, were carried eastward. The existence of these circulations were validated by comparing the model outputs with data from the GOES-7 satellite. As in the previous study, no such circulations developed in numerical control experiments where the surface was assumed to be homogeneous.
2.3. Conclusions From the Simulations
 The major conclusion from the WA01 and BA02 studies is that the patchiness of realistic landscapes (in diverse geographical areas) can produce strong organized mesoscale circulations under a much wider range of background conditions than previously acknowledged. Furthermore, these circulations significantly affect the vertical transports of heat and moisture, and may also produce local clouds and precipitation. Synoptic flow usually advects and reorients the circulations; ambient meteorology can completely eliminate these eddies only under extreme circumstances.
3.1. Surface and Atmospheric Scales
3.1.1. Spectral Analysis
 We use a discrete two-dimensional Fourier transform to objectively estimate the horizontal spatial scale of the mesoscale eddies. One-dimensional Fourier transforms have been extensively used for quasi-random processes like isotropic turbulence [Deardorff, 1974] where the horizontal cross-section of the eddies are approximately circular and directionality is not important. As will be discussed later, the horizontal cross-sections of the surface-forced mesoscale circulations are often strongly anisotropic, due to the anisotropy of the surface heterogeneity and the background wind. Hence, a two-dimensional Fourier transform, where the power is expressed as a function of the length scales along the two cardinal directions, is a more appropriate tool for our purpose.
 The discrete two-dimensional Fourier transform of a two-dimensional field f(x, y) defined within a domain of size Lx × Ly, discretized by Nx and Ny points with grid-spacing of Δx and Δy respectively, is given by
 In order to collapse the two-dimensional spectrum into a one-dimensional one, the angle-integrated two-dimensional transform can be defined by averaging F(kx, ky) as follows
Thus for features such as the mesoscale eddies we are studying, F(k) is only a function of their scale and independent of their orientation. The normalization accounts for the area of the annulus. In the physical sense, the power spectral density F(k)2 gives the variance (energy, if f represents a wind speed component) contained by eddies whose updrafts are separated by a distance (Lx)/k [Press et al., 1992]. Here Lx = Ly = 101 km for Amazonia and 250 km for the central U. S. For all practical purposes, the separation between the updraft maxima can be interpreted as the size or horizontal scale of the eddies, and for the remainder of the paper, this is what we will mean when we refer to eddy “scale”. Thus this definition of eddy scale, by no means absolute, includes one downdraft surrounded by two updrafts.
3.1.2. Flow Over the Central United States
Figure 1a shows the surface sensible heat flux over the domain at 1 pm (approximately the time when the flux peaks) for July 13. To the eye, areas of similar flux are clumped into fairly large-scale sub-regions, with a few main patches seeming to dominate the variability. This is consistent with the spectrum (Figure 1b), which shows strong variability at low wave numbers (<10, corresponding to length scales larger than approximately 25 km).
 As discussed in WA01, the heterogeneity in the surface sensible heat flux distribution produces mesoscale circulations which are best observed in the map of the vertical velocity (w) in the middle of the CBL as depicted in Figure 2 for the July 13 case. It can be seen that the weak and broad zones of rising motion earlier in the day get organized into a larger number of intense narrow updrafts by mid-to-late afternoon. This is also corroborated by the corresponding angle-integrated 2-dimensional Fourier spectra of w for July 13 shown in Figure 3. We see a strong increase in the total energy at the peak scales from earlier to later, reflecting the increased intensity of the circulations, and a shift of the wave number of the peak scale from about 5 (50 km) to about 15–20 (12–17 km). Regardless of the different synoptic-scale dynamics on each of the six July case study days producing different updraft patterns, the evolution of the scales is roughly the same for each case, and in particular, the final scale of the mature mesoscale circulations is quite similar for each case.
3.1.3. Flow Over Amazonia
 The noontime surface sensible heat flux and the corresponding spectrum for August 17 has been shown in Figure 4. While a significant amount of variance is at the highest wave numbers due to numerous small grid-cell size bare patches, the main peak is found at wave numbers 20–30 (3–5 km) associated with the highway running through the domain and the adjacent heavily deforested areas. The surface heterogeneity forces mesoscale circulations, the evolution of which can be seen in the map of mid-CBL w presented in Figure 5. Weak updrafts develop over most of the deforested patches in the morning, however only the ones in the vicinity of the road intensify and finally coalesce into a series of mesoscale rolls by mid-afternoon. These rolls are significantly larger and much less numerous than the individual small deforested patches, a fact that is evident in the w spectra (Figure 6) showing the growth of energy at 11–16 km scale (wave numbers 7–9) over the course of the day. Though the peak scale of the spectra do not change much with time, the energy contained in the low wave numbers, in absolute terms as well as relative to the energy in the high wave numbers, grows by a significant amount.
3.2. Explanation of Scales Results
 As demonstrated in WA01 and BA02, the heterogeneity in the surface sensible heat flux is the forcing behind the mesoscale circulations in both cases. Over Amazonia the scale of response of the atmosphere (scale of the mesoscale eddies) is larger than the scale of the forcing (dominant scale of the surface hot regions), while the opposite holds true for the central U. S. In other words, though the magnitudes, distributions and characteristic length scales of surface forcing are very different between the two regions, the dominant w scale corresponding to the landscape-forced mesoscale circulations for both cases is in an intermediate range. Thus based on these two regions, it appears that there exists a preferred scale (or finite scale range) of atmospheric response to complex, multiscale surface heterogeneity. The question is, what are the dynamical processes underlying this result, and what factors is the atmospheric response scale sensitive to?
 The key factor seems to be that, even though the variability in surface flux might be dominated by a certain scale (as reflected in the spectra), for real surfaces, significant variability usually exists at a variety of other scales. As will be shown later, the atmosphere responds by producing circulations at almost all of the forcing scales. However, only the eddies within a narrow range of scales intensify and organize into coherent mesoscale circulations that dominate the atmospheric dynamics of the region. Thus land-atmosphere interaction processes seem to act as a medium-pass filter, selecting against both the smaller and larger scales, so that the peak atmospheric response is at an intermediate scale.
 At this stage it should be noted that, similar to the spectra of the mesoscale w field, as discussed in Section 3.1.1, the spectra of surface sensible heat flux refers to the scale of separation of the various hot regions, or “patches”, in the domain. Thus the peaks of the sensible heat flux spectra describe this peak separation scale, which is not equivalent to the characteristic “size” of the patches. In earlier work with numerical simulations forced by more idealized, single-scale surface flux heterogeneity patterns (e.g., checkerboards or longitudinal stripes), this distinction between “patch size” and “patch separation” was unnecessary and the two terms could be used interchangeably. For the real surfaces with multiple, overlapping scales of variability considered here, however, it is much more difficult to generalize an exact correspondence between the characteristic size of patches and their characteristic distribution throughout the domain. Nevertheless, for the Amazonia and central U. S. cases being investigated, we can state that the smaller surface patches tend to be more numerous and spaced closer together than the larger patches. Therefore in the spectra of surface sensible heat flux, we can qualitatively take the smaller wavelengths as contributed by the smaller patches, and vice versa. Accordingly, throughout the rest of the paper, we will use “small (large) scale of surface variability” and “small (large) patches” interchangeably. Furthermore, we note that the range of surface variability is continuous, and “small” and “large” as descriptors of patches is relative and not wholly precise; we use such terminology for conceptual clarity.
 In the next section, we attempt to construct a framework that can provide a consistent phenomenological explanation of the mesoscale atmospheric response to the surface heterogeneity in these two regions.
3.2.1. Basic Hypothesis
 Here we briefly discuss the physical mechanism behind the formation of these mesoscale circulations. The details can be found in WA01 and BA02 and the references therein. Various “hot spots” (local maxima in surface sensible heat flux), large and small, exist in the patchy domain. The relatively high upward buoyancy forcing over these warm patches leads to a localized low pressure zone, and consequently a horizontal pressure-gradient-driven convergence resulting in patch-scale circulations. As the surface sensible heat flux increases toward early afternoon, the circulations intensify and gradually become more dynamically distinct from the background, e.g., they develop strong downdrafts adjacent to the updraft that inhibit the formation of other updrafts and break up the mean (background) flow. As the boundary layer deepens and these circulations penetrate higher, they are more susceptible to being advected and distorted by the mean winds (typically greater at higher altitudes). They tend to become elongated into rolls in the direction of the prevailing wind at the top of the CBL, with horizontal convergence continuing in the cross-wind direction. At this stage (by mid-afternoon), the circulations behave as individual, coherent dynamical entities and are sustained by general domain buoyancy and their own inertia as the surface sensible heat flux passes its peak and starts decreasing. During early-to-mid afternoon, the mesoscale updrafts are still buoyant (depending on the surface heating), but many of them are no longer anchored to the surface heterogeneity. The circulations, now decoupled from the surface trigger, move with the horizontal flow within which they are embedded without losing their integrity. By this time the circulations have reached their peak intensity (lagging the surface sensible heat flux peak by the typical mesoscale timescale of a few hours) and have come to dominate the overall dynamics in the domain; hence their signature dominates the spectral analysis. By evening the circulations gradually spin down.
 Now, the key question to answer is, what determines the horizontal length scale of the mature mesoscale eddies? As evident from Figure 1a, smaller-scale “patchlets” exist within larger-scale “patches” in the central U. S. case. Early in the day there is general (weak) rising motion over all the large “hot” patches, and the individual, patchlet-scale circulations are not intense enough to impose any kind of signature on the w spectra. Hence, the variability is dominated by the larger-scale areas of broadly similar, elevated surface sensible heat flux, with a corresponding lower wave number of peak response (Figure 3a).
 Later in the day, as the patchlet-scale circulations become more intense, their signature on the w spectra begins to emerge from that of the larger-scale areas of similar fluxes and broad, weak updrafts. Distinguishing the areas of enhanced rising motion over the smaller-scale patchlets becomes easier as the circulations start to influence their surrounding environment through the production of compensating downdrafts. This explains the scale shift (from larger to smaller) in the central U. S. w spectra.
 By contrast, for the Amazonian cases, there is a great deal of high-frequency variability in surface sensible heat flux, but it is only over the larger clumps that we observe the evolution of mesoscale circulations that eventually intensify and reach maturity in the mid-afternoon. This explains the oppositely directed scale shift in the Amazonia w spectra.
 In both cases, the preferred surface scale is “expressed” by the interaction of the atmospheric dynamics with the unique pattern of surface heating. Strong mesoscale circulations at both very large and very small scales seem to be precluded. In other words, there appear to be factors that favor the impact of the smaller-scale surface variability (small patches) and factors that favor the impact of the larger-scale surface variability (large patches), and the atmospheric response emerges from a competition between these factors.
 From previous work and the results shown here, we can make an attempt at formulating a basic hypothesis for how this competition plays out. This hypothesis relies on the following assumption: the mesoscale circulations that reach a certain “critical” level of intensity and become self-sustaining the fastest, because they exert such a strong dynamical influence on the overall mesoscale dynamics (e.g., strong downdrafts in between the individual updraft zones), tend to preclude the formation of strong circulations at other scales (either smaller or larger) that might take longer to reach a comparable level of intensity. For example, assuming smaller-scale patches produce intense mesoscale circulations the fastest, the larger-scale patches (e.g., within which the smaller-scale patches might be embedded) will not be able to produce their own mesoscale rolls because their coherent effect over a larger area will be broken up by the smaller-scale updrafts and downdrafts. Therefore the circulations over the smaller patches would tend to persist and come to dominate the spectral characteristics of the domain-wide dynamics.
 Therefore the first question we can ask is, what are the factors that tend to produce the most rapidly intensifying circulations? They are:
 1. A stronger surface sensible heat flux contrast between a given patch and its surroundings. This will tend to result in a stronger pressure gradient in the overlying air, and a stronger pressure gradient will lead to a greater acceleration of the horizontal inflows into the patch center and hence stronger and faster convergence.
 2. A stronger mean surface sensible heat flux. This has two effects. First, for a given atmospheric thermodynamic profile, stronger surface sensible heat flux will lead to stronger buoyancy acceleration everywhere. This creates more rapidly increasing rising motion wherever it is predisposed to occur (i.e., over the generally “warm” areas). Second, even given the same surface sensible heat flux gradient, the pressure gradient that it forces between the patch and the patch surroundings will be larger with a larger mean surface sensible heat flux; in other words, the dependence of pressure gradient on mean heat flux is nonlinear [see Baidya Roy and Avissar, 2000, Figure 2a].
 3. A smaller patch size. This simply reflects the fact that an equivalent pressure drop over a smaller distance (e.g., from the exterior of the patch to the patch center) will result in a stronger pressure gradient [Baidya Roy and Avissar, 2000]. It also shortens the time for the converging inflows to meet at the center of the patch center, the trigger for rapid intensification.
 In addition, all of the above factors will result in more rapid growth of the CBL and deeper penetration of the mesoscale circulations to higher altitude, where they can be influenced by larger wind speeds. As noted earlier, this influence will tend to elongate and stretch the circulations in the direction of the prevailing wind. This elongation/stretching, by changing (on average) the aspect ratio of the circulation to be more “roll-shaped” reinforces the tendency for horizontal convergence in the perpendicular (cross-wind) direction.
 All other factors being equal, then, factor 3 above suggests that smaller patches will have an advantage over larger patches. This is certainly at least somewhat consistent with the central U. S. results, which show a shift in the spectra from larger to smaller spacing in the w field as it evolves to reflect the spatial distribution of the mesoscale circulations, but it is at odds with the Amazonia results, which show the opposite behavior. In addition, there are certainly smaller scales present in the central U. S. surface sensible heat flux field than are expressed in the w spectra. What is selecting against the smaller scales?
 Therefore we come to the second part of the hypothesis, which relies on the observation that there is a natural tendency for advection, turbulent mixing and diffusion to blur the thermal/dynamical signature of any given surface patch on the overlying air with that of its surroundings. This works against the ability of any patch to influence the atmosphere enough to produce its own distinct circulation. We argue that this effect is most pronounced for the smallest patches. For example, the heating of the air by the patch's elevated sensible heat flux is the driving force for the subsequent buoyancy and pressure gradient accelerations that in turn drive the mesoscale circulations. Isolated small patches will be unable to sustain the necessary level of heating of the low-level air in the face of mixing/advection of cooler air from their surroundings. In addition, small patches that are close neighbors will tend to have their thermal and dynamical influences merged, therefore forcing the atmospheric dynamics as single larger “effective” patches.
 We propose that the spectra for both the central U. S. and Amazonia cases can be explained in the context of this basic framework: competition between the above-described processes governing the land-atmosphere interaction over patchy surfaces tends to select for atmospheric circulations at scales intermediate to the largest and smallest surface forcing scales in the given domain; in effect these intermediate scales are preferred. We now briefly examine the results from a few additional simulations, based on the simulations discussed above, and designed as sensitivity tests to evaluate the validity of proposed influence of the mean surface heat flux.
3.2.2. Test With Sensitivity Study
 We perform five additional simulations by uniformly enhancing or reducing the surface sensible heat flux throughout the domain for both cases. Over the central U. S. we increase and decrease the flux for the July 13 case by 200 Wm−2, while in Amazonia we increase the flux by 100, 200 and 400 Wm−2 for the August 17 case. This changes the mean surface sensible heat flux but leaves the horizontal gradients unchanged. The surface fluxes in the Amazonia case were so low that simulating a realistic reduced flux case was not possible.
 The results of the modified central U. S. cases show that with enhanced surface flux more “small” patches are capable of producing organized circulations (Figure 7). The key to the survival of these small scale circulations is that, with the enhanced surface sensible heat flux, even quite small, closely-spaced patches reach maturity early enough so that they are not destroyed by the mixing process or blended with their neighbors (thus losing their distinct spectral signature). By contrast, in the reduced flux case (Figure 8), only a handful of coherent circulations are produced; it is only the larger-scale, denser clumpings of hot patches that are able to sustain a strong enough atmospheric heating to eventually produce mature mesoscale circulations in the face of overall weaker domain-wide surface sensible heat flux. The generally longer timescale of formation of the mesoscale circulations in the reduced flux case facilitates this blurring, by horizontal mixing, of the signatures of the individual patches in these clumps into a unified forcing for a single circulation. Thus while in the former case, the domain is packed with numerous narrow, intense eddies, only a handful of broad, weak circulations cover the domain in the latter. This is reflected in the spectra (Figure 9) with the peak energy at wave numbers 20 (12 km lengthscale) and 5 (50 km) for the enhanced and reduced flux cases respectively. Note that the spectra were scaled to fit the y-axis range and hence the magnitude of the power spectral density does not reflect the actual energy content.
 Similar results are obtained in the modified Amazonian cases. For example, the 200 Wm−2 enhanced flux case shown in Figure 10 is characterized by numerous densely packed organized mesoscale eddies. The level of maturity reached by the mesoscale circulations by the early afternoon in the control case (Figure 5a) is already attained in this case by 9 am, consistent with the idea that the timescale of formation of coherent circulations decreases with increasing surface heat flux. By mid-to-late afternoon, the dynamics of the two cases cease to have any resemblance at all. The corresponding spectra (Figure 11) validate this shift of energy from lower to higher wave numbers with increased surface heat flux. These spectra were also scaled.
 Thus it appears that as the surface sensible heat flux increases, the size of the surface patches capable of producing coherent self-sustaining mesoscale circulations decreases. This process continues till the atmosphere gets saturated with rolls such that no new circulations can be added. More work is needed to identify this limiting lengthscale. Additionally, at very high mean surface sensible heat fluxes, since the domain is dynamically unstable, the surface-forced rolls can trigger further secondary circulations that can also influence the response lengthscale.
4. Conclusion and Discussions
 The spectral properties of mesoscale flow forced by complex, multiscale landscape heterogeneity over the Central U. S. and Amazonia were explored in this paper. While both regions exhibit significant surface heat flux heterogeneity over a wide range of scales, for the central United States cases, the strongest variability is at relatively large scales (longer than 25 km), while over Amazonia, variability at much smaller scales (3–5 km) dominates the surface forcing. Initially, the atmosphere responds by producing circulations at almost all possible forcing scales. However, only those eddies confined within a narrow range of scales (10–20 km) intensify, and organize into coherent mesoscale circulations that, by the early afternoon, dominate the dynamics of the entire domain.
 This implies that a preferred length scale range probably exists for the mesoscale atmospheric system and that is expressed via the interaction of the atmospheric dynamics with the unique pattern of surface heating. There appear to be factors that favor the impact of the smaller-scale surface variability (small patches) and factors that favor the impact of the larger-scale surface variability (large patches), and the atmospheric response emerges from a competition between these factors.
 It seems that this peak atmospheric response scale at any given time of the day remains fairly constant despite day-to-day variations in the ambient meteorology and the mean surface heat flux. For instance, the horizontal length scale of the mesoscale eddies over Amazonia at 5 pm was about 11 km on both case study days. Similarly, the length scale of response was approximately 15 km at 5 pm for all days in the central U. S. simulations. Significant shifts in this scale were only produced by the extreme increases or decreases in domain-average surface sensible heat flux imposed for the sensitivity tests of Section 3.2.2.
 These findings can be interpreted within the framework of nonlinear dynamics. Some studies [Wang et al., 1996, 1998] have suggested that the mesoscale system has a inherent length scale and, like the resonance phenomenon in many dynamical systems, mesoscale circulations are produced when the scale of the surface forcing is close to this characteristic length scale. However, we find that significant mesoscale flow can also be forced by surface heteorgeneity with scales that are significantly different (even by an order of magnitude) from this preferred scale of response. In other words, the scale of forcing and the scale of response do not necessarily coincide and can be quite different. These findings are not unusual because nonlinear dynamical systems can have multiple scales of variability and it is possible for the system to respond at scales that are quite different from the scale of forcing [Palmer, 1993, 1999]. The dynamical mechanism proposed here is probably the pathway through which variabilities in the land surface can elicit atmospheric response at scales other than that of the forcing.
 This finding has various implications. For example, linear theory [Dalu et al., 1991], supported by non-linear numerical simulations [e.g., Chen and Avissar, 1994a, 1994b], have shown that the intensity of mesoscale circulations forced by a landscape of patches of uniform size (i.e., with a single surface forcing scale), should increase with increasing patch size up to patches of roughly the local Rossby radius of deformation (i.e., on the order of 100 km). This is because, for a given pressure gradient, the inflows toward the patch center will converge at a greater velocity for a larger compared to a smaller patch, owing to their longer acceleration time. The results shown here suggest that this optimum condition may not be likely to be realized in nature; i.e., very large areas of broadly similar surface fluxes might, under most circumstances, be expected to contain enough significant smaller-scale variability that would end up outcompeting the larger scales for the production of mesoscale circulations. Coherent flow structures over the larger areas, because they take longer to develop, would be broken up by the already-mature mesoscale rolls forced by the embedded smaller patches, thereby precluding the development of mesoscale circulations at the scale of the large patches. This scenario is in fact analogous to the outcome of the central United States cases.
 There are also implications for regional and global numerical modeling. It has been suggested that these organized circulations forced by surface heterogeneity have the potential to affect weather patterns on regional scales, and the aggregate impact of these processes over large regions might have global climate implications [e.g., Pielke et al., 1991, 1998]. The horizontal length scale of the landscape patches and the consequent mesoscale circulations considered for this study are subgrid-scale for typical GCMs with a 2.5° (hundreds of kilometers) grid spacing. Hence, these circulations cannot be explicitly resolved by GCMs and their impacts on resolved-scale processes have to be accounted for via appropriate subgrid parameterizations. Several parameterizations of these organized eddies have been proposed but none have been implemented in a GCM yet [Arola, 1999; Lynn et al., 1995b, 2001; Zeng and Pielke, 1995; Lynn and Tao, 2001]. One parameter common to all such schemes is the horizontal length scale (characteristic size) of the surface patches, which is assumed to be a proxy for the scale of the organized circulations. However, it is readily apparent from this study that the length scale of the surface heterogeneity and that of the CBL response will not in general be equal. In fact, the findings here suggest that a better first-order assumption might be that the characteristic length scale of the surface forcing is only a weak constraint on the characteristic scale of the resulting atmospheric dynamics. That is, large-scale modelers might instead assume that multiple surface scales will exist in any given region, and the land-atmosphere dynamics will select from them and produce a response over a much narrower scale range, thereby obviating the need to generate a detailed description of the fine scale surface spatial structure in each model grid cell in order to produce the approximately correct grid-cell-average mesoscale contribution to the resolved variables (e.g., the mean and variance of the surface sensible heat flux might suffice). Within this schema, the surface length scale can be used, in conjunction with the surface mean heat flux, as a switch to turn the parameterization on or off, depending on whether the conditions required for the triggering of the mesoscale circulations have been met or not.
 Clearly, more work needs to be done to determine whether the existence of a preferred scale for landscape-forced mesoscale circulations is a strong property of land-atmosphere interaction, occurring generally for a wide range of surface types and meteorological/climatological conditions, or a weaker one, with limited application confined to a few specific regions and case studies. Analysis of satellite data for evidence of systematic organization of convection at preferred scales over land, for example in the 10–20 km scale range suggested by this work, is expected to be critical for this effort. In addition, in the absence of field data with the appropriate spatial and temporal coverage and resolution, numerical simulations constrained by and validated against available observations will continue to be the primary tool for investigating the detailed dynamics of these circulations. Improving our understanding in this area will contribute to an improved understanding of the coupled land-atmosphere system in general, and will assist in better representing the impact of land-atmosphere coupling in GCMs.
 This research was supported by the National Aeronautics and Space Administration (NASA) under grants NAG5-8213 and NAG5-9359 and the National Oceanic and Atmospheric Administration (NOAA) under the grant NA16GP1618. The views expressed herein are those of the authors and do not necessarily reflect the views of NASA or NOAA.