Introduction
Mountain wakes have been the subject of extensive research because of their dynamic importance to the atmospheric circulation and because of their impact upon local meteorological conditions. Wakes can be characterized by low-wind-speed air parcels (having a reduced Bernoulli constant) in a flow laterally bounded by confluent shear layers. The vertical thermodynamic structure within a wake may differ from that outside and, as we shall demonstrate, these structural differences can have implications for electromagnetic (EM) propagation.
In aerodynamic flows, wakes typically are formed by separation of a frictional boundary layer. However, Smolarkiewicz and Rotunno (1989a) demonstrated that a leeside vertical vorticity dipole may be produced in adiabatic, inviscid flow of a density-stratified fluid past a three-dimensional mountain, even when the upstream flow is irrotational. In the absence of dissipation, however, the vorticity dipole remains in the immediate lee of the mountain rather than extending downwind in a long wake. Recent studies of wake formation have focused on potential vorticity (PV) generation by dissipative processes, such as gravity wave breaking and surface friction. Once PV anomalies are generated, PV conservation downstream of the generation region can be a significant factor in maintaining vortices shed by the mountain (Schär and Smith 1993a,b; Smith 1989; Smolarkiewicz and Rotunno 1989b; Grubišić et al. 1995; Schär and Durran 1997; Rotunno et al. 1999).
When the mountain-generated PV is weak and the Coriolis force is not strong (low latitudes), wakes can be remarkably long and straight. Smith et al. (1997, hereinafter S97) show instances in which the ∼1-km-high and ∼20-km-wide island of Saint Vincent and other Windward Islands produce straight wakes exceeding 300 km in length. At higher latitudes and/or with stronger PV generation, island wakes tend to take several forms such as a large, elongated pair of counterrotating eddies attached to the island lee (Smith and Grubišić 1993) or unsteady, meandering wakes in which eddies are shed and advected downwind of the island. Spectacular trains of periodically shed eddies known as a von Kármán vortex street occasionally are seen in satellite imagery (e.g., DeFelice et al. 2000; Chopra 1973).
We are particularly concerned with horizontal surface-layer inhomogeneities created by an island wake and with the alterations in the shape of surface-layer wind, temperature, and moisture profiles in the wake as compared with the ambient flow. Strong horizontal gradients in near-surface wind speed (shear lines) provide evidence of a wake's boundaries. Because of the wake's velocity deficit and altered reference height temperature and moisture values, the stability-dependent shapes of surface-layer temperature and moisture profiles within the wake differ from those outside. Surface-layer temperature and moisture profiles determine the surface-layer refractivity profile, which controls EM propagation adjacent to the surface.
Microwave and millimeter-wave propagation near the ocean surface are affected greatly by the vertical atmospheric refractivity profile and the oceanic surface state. In the portion of the EM spectrum affecting shipboard radars—that is, from 900 MHz to 20 GHz—refractivity is a strong function of water vapor density, is less so a function of temperature, and is only a weak function of pressure. The marine atmospheric surface layer generally contains a substantial vertical moisture gradient in which vapor pressure is near the saturated value at the surface and logarithmically approaches its ambient value a few meters, or tens of meters, above the surface. This moisture lapse often creates a rapid decrease in refractivity such that microwaves launched near horizontally in this layer may be trapped in the so-called evaporation duct. At greater heights, sharp temperature and moisture gradients [such as those associated with an inversion capping the marine boundary layer (MBL)] can trap EM energy either in an elevated layer or in a layer that extends to the surface (a “surface-based duct”).
Mesoscale models are capable of forecasting vertical boundary layer structure with sufficient resolution to depict occurrences of elevated trapping and surface-based ducts (Burk and Thompson 1997; Atkinson et al. 2001; Haack and Burk 2001a). However, mesoscale model grids do not resolve the pronounced gradients in the surface layer responsible for the evaporation duct. Therefore, bulk aerodynamic formulas, coupled with similarity theory relationships, typically are employed to determine stability-dependent profiles. Surface-based ducts generally are substantial deeper than the evaporation duct; they more profoundly affect propagation by trapping a broader range of EM frequencies. However, the evaporation duct is present a high percentage of the time over much of the ocean surface; surface-based ducting is much less common (Anderson 1987; Paulus 1985).
The detection of slow-moving targets at low elevations often is limited by the signal-to-clutter ratio; for radars having moving-target indication or pulse-Doppler processing, the detection of fast-moving targets generally is limited by the signal-to-noise ratio. Both the signal and clutter powers are strongly influenced by the evaporation duct, and the latter is also a function of the sea clutter's radar backscattering cross section (σ°).1 Thus, prior knowledge of the evaporation duct and σ° can provide the ranges at which it may be possible to detect targets of a given cross section.
For naval operations, the most common way of nowcasting the evaporation duct is to perform shipboard measurements of air temperature, sea surface temperature (SST), wind speed, and relative humidity and to put these “bulk measurements” into similarity theory expressions such as those of Liu et al. (1979, hereinafter LKB). Although model values cannot be expected to be as accurate as direct measurements at a particular place and time, the model provides broad coverage at locations for which there are no observations, describes horizontal variability, and, perhaps most important, adds forecast capability.
Rogers et al. (2000) demonstrated that it is possible to infer the ducting structure from the observed sea clutter by comparing observed clutter power as a function of range with modeled clutter power as a function of EDH. EDH values are estimated in 10° sectors, and then an average is calculated over the 36 sectors. The averaging serves to mitigate some scales of variability that might otherwise corrupt the estimate of EDH were it based on data from a single azimuth. The technique is referred to as “refractivity from clutter (RFC) for evaporation ducts (ED).” Because the output is a single estimate, the same question of horizontal representativeness arises as with the output of the bulk method.
A demonstration of Lockheed Martin's Tactical Environmental Processor (TEP) took place aboard the USS O'Kane during the autumn of 1999 as the ship sailed from Bath, Maine, to Pearl Harbor, Hawaii, and during ship operations in the vicinity of Kauai, Hawaii. TEP extracts detailed environmental measurements from the “AN/SPY-1” phased-array radar aboard the U.S. Navy's Aegis cruisers and destroyers. Using normally scheduled radar dwells, TEP generates spectral moment measurements (reflectivity, radial velocity, and spectrum width).
When the RFC-ED procedure was implemented on data from these tests, it produced a reasonable match to the EDH values determined from bulk measurements performed on the O'Kane. For open-ocean cases, the standard deviation of the EDH estimates was typically on the order of 2 m. However, in the lee of Kauai, the standard deviation was considerably larger, on the order of 8 m, suggesting the presence of an island wake. An effort was undertaken to determine the degree to which the output of a numerical weather prediction model could explain the clutter observed using the TEP system. This also permits comparison of NWP model EDH forecasts with methods that directly use in situ measurements to compute EDH (e.g., bulk methods, RFC ED) in a region of substantial horizontal variability. Furthermore, mapping the model output into the space of the radar observations may contribute to adapting, for example, a variational method to the problem of fusing the output of the NWP model with radar observations of clutter from TEP.
In this paper, we examine the dynamics creating the Kauai wake and the impact of the wake upon the refractivity field, particularly the EDH distribution, and then explore the effect of the refractivity and wind fields on the radar clutter. We initially conduct mesoscale-model simulations in which select aspects of the thermodynamic structure and flow have been idealized so as better to isolate features of interest. High-resolution real data forecasts are subsequently conducted that encompass the time period (3 December 1999) of the TEP demonstration experiment leeward of Kauai. The U.S. Navy's Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS)2 is used in this study (Hodur 1997).
Section 2 provides a description of COAMPS and discussion of the numerical experiments conducted. To examine the dynamics of the Kauai wake and its impact upon the field of EDH, we first address several idealized COAMPS simulations in section 3. These simulations are idealized in that the environment is taken to be horizontally homogeneous initially. Section 4 describes the island wake forecast by COAMPS in the real data case and analyzes the resultant EDH field. Computations of modeled radar clutter maps, using both an EM propagation model and a clutter model, are compared with the azimuthal and range-dependent clutter distribution observed during the TEP demonstration aboard the USS O'Kane. Section 5 contains a discussion and concluding remarks.
The mesoscale model
Model description
COAMPS consists of a nonhydrostatic, fully compressible atmospheric model coupled to a hydrostatic ocean model. In this investigation, we use only the atmospheric component of COAMPS because the oceanic model is undergoing further development and testing. The atmospheric model's prognostic variables are specified on a horizontally staggered “C” grid, and a terrain-following sigma-z coordinate system with irregularly spaced levels is used in the vertical. COAMPS contains a multinested grid hierarchy in which each interior mesh has a factor-of-3 finer resolution than its parent grid.
High-frequency modes are integrated with a time-splitting technique, and vertical derivatives are treated semi-implicitly, thereby handling sound and gravity waves in a computationally efficient manner (Klemp and Wilhelmson 1978). Several subgrid-scale turbulence parameterization options exist within COAMPS. Here we use the Mellor and Yamada (1974, 1982) level-2.5 closure in which a prognostic equation is used for turbulent kinetic energy while all other turbulence variables are computed diagnostically. Cloud microphysics is formulated in the manner described by Rutledge and Hobbs (1983) that includes budget equations for water vapor, cloud water, raindrops, ice, and snow. Detailed long- and shortwave radiative flux computations follow Harshvardhan et al. (1987). The Kain and Fritsch (1990) cumulus parameterization is used for meshes having grid spacing greater than 10 km (hence, the outermost grid in our real data case). Surface fluxes over water use Chamock's roughness-length (z0) expression, which expresses z0 as a function of surface friction velocity. We currently do not consider the effects of sea state (e.g., wave height, wave age) that may alter surface drag. The Louis (1979) parameterization of surface fluxes is used, and diurnal variations in ground temperature and moisture are described by a force–restore technique (Deardorff 1978). The terrain field is taken from the National Imagery and Mapping Agency's Digital Terrain Elevation Data (DTED) level-0 database that has 1-km resolution.
The atmospheric portion of COAMPS recently has been evaluated in numerous studies of coastal MBL phenomena using observational datasets. These include a “southerly surge” event (Thompson et al. 1997); a low-level jet and rainband simulation (Doyle 1997); a field experiment using COAMPS forecast fields (Rogers et al. 1998); a study of critical flow behavior around topographic bends (Burk et al. 1999); comparison of observed versus modeled MBL structure for June–July 1996 (Dorman et al. 2000); a study of boundary layer adjustment near Point Sur, California (Dorman et al. 1999); an investigation of wave clouds upwind of coastal orography (Burk and Haack 2000); a study of supercritical flow interaction between Capes Blanco and Mendocino (Haack and Burk 2001b); and an examination of summertime California MBL refractivity conditions (Haack and Burk 2001a). Further COAMPS description appears in Hodur (1997).
Setup of idealized model simulations
Prior to confronting the complexities associated with real data forecasting of island wake structure leeward of Kauai, we address a simpler problem in which the initial fields are homogeneous and time-invariant conditions are specified at the upstream boundary. For these idealized simulations, we use a single grid mesh of 151 × 91 points with Δx = 3 km and 40 vertical levels distributed as shown in Table 1. In the first idealized simulation (S1), the terrain field comes from DTED and is smoothed by use of three passes through a 25-point filter. Figure 2 shows the computational domain used in S1, the terrain of Kauai and the smaller island (Niihau, Hawaii), and lines north–south and east–west along which vertical cross sections will be displayed in several subsequent figures. The domain extends from 20.95° to 23.20°N and from 158.46° to 161.51°W. The peak island elevation in the model's terrain field is hm ≅ 1300 m. The spanwise and streamwise dimensions of Kauai are similar, yielding a horizontal aspect ratio near unity.
Based on the real data forecast that we discuss in section 4, a sounding upstream of Kauai (Fig. 3) was selected and used (with a slight alteration described below) to homogeneously initialize the COAMPS domain. Removing horizontal inhomogeneities in the initial state permits clear delineation of flow perturbations caused by the island. Fixed inflow–outflow conditions are used at the east–west boundaries, and extrapolated boundary conditions are used north–south in which the values on the boundaries are assigned to be equal to their neighboring interior grid point. The SST is set to a constant 298.5 K everywhere, which is the SST at the upwind location of the selected sounding from the real data case.
The sounding in Fig. 3 has a typical trade wind boundary layer structure and resembles aircraft soundings displayed by Smith and Grubišić (1993) upwind of the “Big Island” of Hawaii from July of 1990. We have made the marine layer from the surface to about 800 m slightly stable (dΘ/dz ∼ 0.001 K m−1, where θ is potential temperature) to minimize convective activity. A layer of relatively strong stability (0.015 K m−1) exists between 800 and 1000 m, and above this stable layer lies a region of modest stability (0.0031 K m−1), where trade wind cumulus normally are found, extending to 1800 m. Above 1800 m, greater stability (0.005 K m−1) occurs to the top of the model domain at about 27 km.
Figure 3 also shows the initial wind profile for S1. A purely easterly wind direction is specified initially at all levels, and the geostrophic wind, which agrees with the actual wind except in the weakly stable layer adjacent to the surface, is held fixed. Beneath about 800 m, the geostrophic wind speed is held fixed at its 800-m value and the actual wind is allowed to spin down from frictional drag.
The trade wind boundary layer structure upwind of Kauai varies little throughout the time period of the real data case. Therefore, we do not investigate the sensitivity of wake structure to a range of different initial vertical profiles. We are, however, interested in the dynamic response and impact upon the evaporation duct field for differing island heights such as might occur in an island chain. In experiments S2, S3, and S4, all of the Kauai terrain height values are made, respectively, ½, ¾, and 2 times the original terrain heights. Note that altering the height of the terrain while leaving the horizontal dimensions of Kauai unchanged changes the obstacle slope in addition to the nondimensional mountain height. Given the small slopes involved, we expect the impact of the slope changes alone to be weak, although this topic bears further investigation. Upwind flow conditions are altered in experiment S5 by changing the wind direction to either 65° or 115°; otherwise the initial conditions and island topography are the same as in S1.
Results from the idealized simulations
Benchmark case S1
Wake dynamics
This case uses the Kauai terrain field shown in Fig. 2 and holds the upwind thermodynamic and wind profiles fixed, as shown in Fig. 3. Figures 4a–d show the evolution of the 10-m wind field (wind speed and streamlines) from COAMPS at 6, 12, 18, and 24 h into the forecast. After 6 h, the flow at 10 m is deflected and decelerated for a distance of about 40 km upwind of Kauai (Fig. 4a), with a small region of flow stagnation present on the windward side of the island. The flow accelerates by several meters per second in lobed regions on the northern and southern flanks of the island. The flow sweeps around the island's flanks and dovetails together well downstream. The island perturbation extends about 150 km downwind of the island, which corresponds to an average speed of 7 m s−1 that agrees well with the advective speed.
At 12 h, the island perturbation at 10 m (Fig. 4b) extends approximately 250 km downstream and has developed a sinuous structure. The lobes of flow acceleration on the island's flanks have expanded considerably in areal extent, although the maximum wind speed is similar to that at 6 h. This region of flow acceleration has begun to split into two centers on each flank. There appear to be two regions of downslope flow acceleration over Kauai itself (northwest and southwest quadrants, labeled M1), and separate maxima (M2) farther from the island associated with the flow cornering around, rather than over, the island. The perturbed flow on the windward side is very similar to the 6-h structure, evidently having attained near stationarity. At 18 h (Fig. 4c), the wake extends to the western boundary of the computational grid and the region of flow acceleration continues to be split into two centers on each flank. The 24-h forecast results (Fig. 4d) do not differ greatly from those at 18 h. A dynamical structural similarity, rather than true stationarity, is attained in which large-scale features of the wake remain relatively unaltered despite its sinuous, oscillatory character.
Figure 5 displays the vertical component of the 10-m relative vorticity ζ at 6, 12, 18, and 24 h. A banner of positive vorticity extends downstream from the northern flank of the island while a negative vorticity banner trails from the southern flank. These two principal banners, created by the wind shear lines on either side of the island, remain attached to the island throughout the integration, but downstream they become unstable and separate into individual vorticity centers, which is particularly noticeable at 12 and 18 h (Figs. 5b,c). Successively shed vortex centers (labeled 1, 2, and 3 in Figs. 5a–c) appear in approximately the same position as they move downstream almost with conveyor belt–like regularity. (The actual shedding period appears to be closer to 5 than to 6 h.) The dimensionless frequency, or Strouhal number S = fD/U, often is used in engineering studies of eddy shedding. Here, f is the observed (or modeled) shedding frequency, D is the (island) diameter, and U is the wind speed. For our benchmark Kauai simulation, D ∼ 40 km, f ∼ (5 h)−1 = 5.6 × 10−5 s−1, and U ∼ 7 m s−1, which yields S ∼ 0.32. This value of the Strouhal number is somewhat large when compared with neutral, high-Reynolds-number flow past a circular cylinder for which S ∼ 0.21 (e.g., Schlichting 1968) but agrees well with laboratory and model results of stratified flow over cones (Castro et al. 2001).
Isentropic surfaces near or below the island peak contain two long depressions, or “valleys,” extending downwind from the island flanks with a central “ridge” separating them. The 297-K isentropic surface at 24 h in Fig. 6 shows evidence of upwind blocking and pronounced descent to the sea surface (blue) in the immediate lee of Kauai. Because this isentropic surface is shaded by vorticity, the connection between baroclinity (sloping isentropic surface) and the vorticity banners is made clearly evident. Farther downstream, vorticity may wrap the isentropic valleys into isolated vortices that have an associated near-circular depression in the isentropic surface. Thus, the vortices have warm cores, irrespective of the sign of the vorticity. The island wake forms along the seam, or zero line, between the two vorticity banners where the flow in each banner tends to curl back toward the island, counter to the prevailing flow.
S97 developed a regime diagram (their Fig. 1) designed to indicate roughly the parameter space in which flow past an isolated mountain or island may create no wake, a long straight wake, a pair of steady counterrotating vortices, or an eddy-shedding regime. Important to this diagram is the value of nondimensional mountain height ĥ = Nh/U at which gravity-wave breaking will occur. Here, N is the buoyancy frequency, U is the wind speed, and h is the mountain height. For uniform stratification and wind, using a 2D witch of Agnesi–shaped ridge, S97 find ĥ ≅ 0.85 for wave breaking, and they conclude that the critical mountain height needed to create a wake is hc ≅ 0.85U/N. However, for uniform stratified flow past a 3D Gaussian-shaped mountain, Smith and Grønås (1993) find the critical value for stagnation and wave breaking is ĥc = 1.1 ± 0.1. Our studies involve a nonuniformly stratified atmosphere with a variable wind profile and a real terrain field. We compute ĥ by using layer-averaged values (〈N〉 and 〈U〉) obtained by integrating from the surface to 2.6 km, which is 2 times the mountain height so as to include a representative depth of flow perturbed by the mountain. This method yields 〈N〉 = 0.0072 s−1 and 〈U〉 = 6.5 m s−1, giving ĥ = 1.4 and (taking ĥc = 1.1) hc ≅ 990 m. We thus find h/hc ≅ 1.3, which, based on the S97 regime diagram, would imply a long, straight wake, whereas a sinuous wake is actually simulated. Thus, caution is warranted in attempting to extend the simple regime diagram to more complex atmospheric states. The trade wind layered stability, with an inversion near 1 km, can effectively promote a decoupling of the boundary layer flow from that aloft. However, our sensitivity studies (S2, S3, and S4) with the terrain height altered do indicate that the general trend anticipated by S97 holds here as well. These sensitivity studies will be discussed further in section 3b.
The vertical structure of ζ is shown in Fig. 7a along the north–south line of Fig. 2 at hour 24. This figure, which extends from the surface to 4 km, may be regarded as the view of the vorticity banners looking downwind (west) from Kauai. The north–south cross section is about 70 km west of Kauai's western shore. The positive and negative vorticity banners extend upward to ∼2 km, although the individual maxima within the banners are attained only several hundred meters above the surface. Schär and Durran (1997) present similar results (although looking upwind in their case) from nonrotating simulations having uniform wind, uniform stratification, and free-slip boundary conditions. In the lowest kilometer, the two vorticity centers (Fig. 7a) tilt away from one another with height; between 1 and 2 km, both vorticity banners tilt to the north. Thus, the banners not only have a sinuous structure horizontally, but they are wavy in the vertical direction as well. Figure 7b shows the PV distribution in the same plane as in Fig. 7a. The relative vorticity attains its positive and negative maxima near the surface, but PV does not because the near-surface stratification is weak.
A vertical cross section from the surface to 4 km of potential temperature and wind speed along the east–west line in Fig. 2 is displayed in Fig. 8 at hour 24. This cross section cuts through the wake and shows that the reduction in wind speed in the island's lee extends from the surface to substantially higher than the peak island elevation. In Fig. 8, the shear lines flanking the wake (Fig. 4d) meander across the E–W cross section (Fig. 2). Above 900 m (Fig. 8), the wind speed upwind of the island decreases with height, giving a positive horizontal component of vorticity (η = ∂u/∂z − ∂w/∂x) along the y axis (north–south). With maximum negative vertical velocity w directly in the lee of the island, tilting of the ambient vorticity tends to yield a positive vortex on the northern flank and a negative vortex on the southern flank. Thus, in this simulation the tilting of ambient vorticity adds to the tilting of baroclinically produced vorticity.
Evaporation-duct height
To obtain EDH, similarity theory is used to compute temperature and specific humidity profiles on a special grid within the surface layer. A uniform vertical grid, separate from the COAMPS computational grids and having 1-m grid spacing from the surface to 40 m, is used to compute the similarity profile expressions from Liu et al. (1979). The modified refractivity M profile, such as illustrated in Fig. 1, is computed from Eq. (1), and the height of the minimum in M is located, yielding the EDH. These EDH calculations are performed only diagnostically at selected output times. The COAMPS surface and 10-m values of temperature, wind, and specific humidity provide the input for calculation of the similarity profiles on the special grid as discussed by Cook and Burk (1992).
Wind speed is a strong factor determining EDH. For a given SST and wind speed, Paulus (1984, 1985) computes EDH over a range of air–sea temperature differences (ASTD) and plots the results parametrically for a family of relative humidity values. (Because the SST is fixed for a given family of curves, the ASTD range amounts to a range in air temperature.) For convenience, in Fig. 9 we reproduce two plots from Paulus (1984) that differ only in mean 10-m wind speed. Because our primary interest is with unstable conditions, we plot only negative ASTD values (the ASTD values in the Kauai case typically are about −1°C). For negative ASTD, the entire family of curves in these plots shifts toward larger EDH values with increasing wind speed. For example, for an ASTD of −1.0°C, wind speed of 2.5 m s−1, SST = 25°C, and relative humidity of 85%, the EDH is approximately 8 m (see bold dot in Fig. 9a); with a wind speed of 10 m s−1, the EDH is approximately 16 m (Fig. 9b). These values of wind speed, relative humidity, and ASTD are typical of those found within and outside of the island wake in the current study.
The EDH at hours 6, 12, 18, and 24 of the COAMPS forecast for case S1 is shown in Fig. 10. Upwind of Kauai, the horizontally homogeneous temperature and moisture profiles yield an EDH of 11 m. After 6 h of integration, Fig. 10a shows that the EDH has increased to a maximum of about 14 m in the high-wind regions on the island's flanks while the EDH attains a minimum of about 6 m in the low-wind-speed wake developing in the island's lee. In the blocked flow region on the windward side of the island, EDH values are slightly reduced.
The EDH field provides a particularly clean delineation of the island wake. Lengthening and meandering of the wake by hour 12 is very evident in Fig. 10b, although the splitting of the maxima on the island flanks that was present in the wind field (Fig. 10b) is not evident in EDH. By hours 18 and 24 (Figs. 10c,d), the tail end of the wake has broken into several isolated centers, consistent with the development and subsequent weakening of separate vorticity centers in the perturbed flow downwind of the island (Fig. 6). As we will demonstrate in the real data results of section 4, the pronounced gradient of EDH across the island's wake and the reduced EDH values along the wake axis can be significant factors that affect EM propagation.
Altered terrain cases S2, S3, and S4
As indicated previously, we conducted simulations with the Kauai terrain multiplied by ½ (S2), ¾ (S3), and 2 (S4). However, the nondimensional mountain heights ĥ are not simply altered by these same factors because the depth over which N and U are averaged (2 times the mountain height) is different for each simulation. Table 2 presents the values of 〈N〉, 〈U〉, and ĥ for each simulation and characterizes the wake type.
In S2, ĥ ≅ 0.5 and, in accordance with S97, vortices do not shed from the island and there is not a long wake. Rather, a small pair of counterrotating vortices form and remain attached to the lee side of the island. As a consequence only a relatively short EDH wake forms (Fig. 11), although the lateral EDH gradients are substantial where the wake is present. There is no upstream blocking to cause a reduction of EDH in this simulation.
In S3, the island's peak elevation is approximately 1 km and ĥ ≅ 0.87. In this simulation, a long, narrow, nearly straight wake develops. The maximum PV generated in this case is less than that in the benchmark case, and the PV does not wrap itself into eddies. Figures 12a,b show the 10-m winds and the EDH field at hour 12 of the simulation. The cross-wake shear appears slightly stronger in the benchmark case (Fig. 4d), as does the cross-wake gradient in EDH (Fig. 10d).
With the terrain height doubled to 2.6 km in S4, a smaller average wind speed and larger average stability are obtained in the computation of ĥ than in the previous cases. This set of conditions yields ĥ ≅ 3.5 (Table 2), indicating that the flow is strongly blocked and can be expected to split around the island with very little mountain-wave activity. The solution shows the development of pronounced von Kármán vortices. The 10-m wind and vertical component of relative vorticity at hour 24 are shown in Figs. 13a,b. Comparison of Figs. 4d and 13a shows that, with the higher terrain in S4, the amplitude of the horizontal flow perturbation in the 10-m wind field is significantly greater and there is less indication of two maxima along each flank. The wake appears somewhat broader in the immediate lee of Kauai, and the surface wind maxima over the island are positioned farther windward (east) in S4 than in S1. In comparing the 10-m relative vorticity fields of Figs. 5d and 13b, it is seen that the positive and negative vorticity centers associated with the wake's sinusoidal wind field extend considerably farther downstream in S4.
The PV generation in S4 occurs primarily along the island flanks where the potential temperature field and trajectories both indicate the presence of jumplike features. In a manner described by the shallow-model results of Schär and Smith (1993b), the jump features oscillate back and forth with an accompanying variation in shock strength such that, when the shock on the right flank is strongest, that on the left flank is weakest, and vice versa. Isosurfaces of PV reveal that PV banners form in these jump regions and then extend downstream. In conjunction with the dissipation occurring from the hydraulic jump features (such as discussed in S97) are local turbulent kinetic energy (TKE) maxima on the island flanks and other localized TKE maxima that advect with the wake vortices. In addition to dissipation within the jump features, the frictional boundary layer may be particularly important to PV generation in the shallow, high-speed flow present along the island flanks, thereby making it difficult to isolate the primary PV generation mechanism(s). Of course, unlike the conservative quantity PV, in the vicinity of the jumps the vertical component of relative vorticity, ζ (a nonconservative quantity), can be strongly altered by processes other than dissipation, such as tilting and stretching. As demonstrated in Fig. 7, the mixed-layer value of ζ is substantial within the wake, thereby providing a useful diagnostic of wake presence, whereas mixed-layer PV is small because of the weak stratification. Both PV and ζ aid in diagnosing fluid motion; whether one provides more fundamental insight into wake generation is an interesting topic in its own right but is not pursued further in this paper.
Figure 13c displays the EDH field from S4 at hour 24, which may be compared with the benchmark results in Fig. 10d. The amplified perturbations in the wake affect the EDH field over a longer fetch in S4. Also, in the immediate lee of the island there is a narrow region in which the EDH is greater than that in the benchmark case (Fig. 10d). This region is caused by enhanced return flow toward the island in the immediate wake region. Also, substantial reduction in EDH values is evident in this simulation because of blocked flow upwind of the island.
Altered wind direction cases S5
We now briefly discuss the two cases (collectively called S5) in which the upstream wind direction is rotated ±25° from easterly. If the island were symmetric, we would expect the entire flow pattern around the island to rotate with the upstream wind, particularly given that the initial conditions are homogeneous. However, in simulations using the benchmark conditions, but with the upstream wind rotated ±25° from easterly, we find substantial differences in the wake pattern and EDH distribution (Figs. 14a,b). Figure 14a shows that the EDH field with the wind from the east-southeast appears similar to a rotated version of the benchmark case (Fig. 10d) but differs significantly when the wind is from the east-northeast (Fig. 14b). Of likely importance is the fact that the island silhouette (not shown) appears cone shaped when viewed from the east and the east-southeast but is less symmetric (very steep north face, gentler slope to the south) and somewhat broader when viewed from the east-northeast. From Fig. 14b it is evident that the northern coastline of Kauai aligns very well with an east-northeast wind; thus, the flow is more streamlined, and less cornering acceleration occurs on the northern flank. Downstream of Kauai, there are further differences in appearance of Kauai's wake in the two S5 simulations because of the influence of Niihau. With east-northeast wind, Niihau lies virtually in the center of Kauai's wake (Fig. 14b), and its own wake likely contributes to further reduction of EDH values downwind.
Results from real data forecasts during the TEP demonstration
Real data case initialization
The real data case uses intermittent data assimilation (DA). To begin the DA sequence, global fields are obtained from the U.S. Navy Operational Global Atmospheric Prediction System (NOGAPS; Hogan and Rosmond 1991) and a COAMPS multivariate optimum interpolation analysis (MVOI) is performed, producing initialization fields for a so-called COAMPS cold start. At 12-h forecast intervals on each grid, COAMPS performs an MVOI that incorporates routinely available data into the model fields while carrying forward in time the model-developed mesoscale structure. The quality-controlled operational dataset incorporated into the MVOI includes surface reports, upper-air soundings, satellite-derived parameters of both the surface and atmosphere, and aircraft observations. Thus, prior to the period of interest we begin with a cold start having the resolution of the global model and permit mesoscale detail to develop and be carried forward in the DA procedure. On the outermost COAMPS mesh, time-dependent boundary conditions are supplied from 6-hourly spaced NOGAPS fields. Surface characteristics are specified from the Fleet Numerical Meteorology and Oceanography Center operational database. Ocean temperatures are analyzed at model grid resolution and are held fixed for the length of a given forecast.
For the real data COAMPS investigation of the Kauai wake during the period of the TEP experiment, the DA cycle begins with a cold start from NOGAPS fields at 0000 UTC 2 December 1999. Following two 12-h forecasts, the COAMPS forecast initialized at 0000 UTC 3 December 1999 is of primary interest because it includes the period of TEP observations. COAMPS is run triply nested in these real data forecasts, using an outer mesh of 61 × 61 (x, y) points and 27-km grid spacing (Δx = Δy). The second mesh has 91 × 76 grid points with Δx = 9 km, and the third has 151 × 91 with Δx = 3 km. Each mesh has the same 40 vertical levels as enumerated in Table 1. The triply nested grid structure used for this real data simulation is shown in Fig. 15.
COAMPS forecasts
The COAMPS short-range forecast on the inner grid (Fig. 15) for 3 December 1999 during the TEP experiment is presented in this section. Although the upstream conditions are considerably more inhomogeneous, the island wake forecast by COAMPS is similar to that in the idealized, benchmark simulation. The 10-m wind speed at 0600 UTC 3 December 1999 (Fig. 16a) shows a meandering low-speed wake that is bounded by accelerating flow cornering around the island flanks. This wind field may be compared with those from the idealized case in Fig. 4. A vertical cross section (also at 0600 UTC) of wind speed and potential temperature appears in Fig. 16b along the west–east line of Fig. 2. This cross section also bears a strong resemblance to Fig. 7 of the benchmark case, indicating that the general nature of the island wake dynamics is not highly sensitive to introduction of upstream inhomogeneities provided that the mean vertical stratification and wind profile remain similar. Slight terrain differences between the idealized and real data cross section are caused by smoothing.
As in the benchmark idealized case, a substantial wake is evident in the EDH field. Figure 16c shows that the wake in EDH extends in a continuous manner downwind of the island for a distance of about 150 km and then becomes a broken field having multiple local maxima that are associated with eddies that have shed from the island or are created by regions of convection. As a consequence, the EDH field contains much more inhomogeneity in the lee of the island, beyond just that across the wake itself, than is found upwind of the island. Although we are unable to verify this aspect of the forecast with the data available on this day, we are able to make model comparisons with the radar clutter data gathered aboard the USS O'Kane.
Observed and modeled clutter maps
The effect of the evaporation duct on ΔP(r, θ, rc) for a situation in which σ° is constant is shown in Fig. 17a (modeled for the O'Kane radar system). It is clear that, for EDH values of 25 m or less, the slope of the clutter power becomes increasingly less negative as the EDH increases. The value of the sea clutter radar cross section as a function of wind speed, parametric in grazing angle ψ, is shown in Fig. 17b. The model used is the Georgia Institute of Technology (GIT) clutter model as used by Paulus (1990). The GIT model is formulated in a manner to accept average wave height hav, the grazing angle ψ, look direction θ, and local wind speed u as arguments. In the GIT model, hav is based on the assumption of a fully developed sea. However, in the lee of an island, an average wave height predicted from a local wind speed might be considered as suspect because the long-wavelength components of the sea spectrum (i.e., the swell) will be relatively insensitive to local wind speed variations. Figure 17c shows the output of the model if we assume hav is a constant value of 0.45 m (the significance of that value will be discussed later).
Details of calculating the modeled clutter power are as follows:
We obtain the wind speed V and EDH as a function of range and azimuth from the COAMPS fields by circling the USS O'Kane's position in steps of 1.5°.
These range-dependent wind and refractivity profiles, along with parameters specific to the radar, are input to the EM propagation model. Values of propagation loss L and grazing angle ψ are generated at a height of 1 m over a range interval of 1–200 km.
The GIT sea clutter model is used to compute the normalized radar cross section σ° as a function of radar wavelength λ, ψ, θ, and V; and an estimated average wave height hav.3 (Note: values from a wave model will be used in place of hav in the future.) A polar plot of σ° as a function of range and bearing is shown in Fig. 18a. Figure 18b shows what happens when the local wind speed from COAMPS is used to calculate hav; it will later be seen (based on Figs. 19b,d) that Fig. 18a is far more realistic than Fig. 18b.
The clutter power predicted in this manner is PLM(r, θ), where the subscript LM indicates it corresponds to the linked models.
The clutter power determined by following this outlined procedure is shown in Fig. 19b; Fig. 19a shows an observed clutter map taken from aboard the USS O'Kane. The linked models have produced output in the format typically used for the observations, rather than requiring the observations to be restructured to fit the format of an existing model product. (The observed clutter map shows the islands of Kauai and Niihau; the modeled map does not.) By design, the modeled azimuthally averaged clutter power at 10 km agrees with the observed average at this range; however, the computed azimuthal and range dependence is freely determined by the linked models. The red lines in Fig. 19b represent the maximum range of clutter power (in 10° sectors) taken from the observations (Fig. 19a) and placed on Fig. 19b for comparison with the modeled clutter power ranges.
In a qualitative sense, the modeled map displays many of the features of the observed clutter map. They both have clutter power extending farther out in range in the northerly and southerly directions from the center (i.e., from the radar). This pattern coincides with the higher wind speed and larger EDH in those directions as shown in Figs. 16a,c. Looking toward the island of Kauai (90° radial), the clutter falls off much more rapidly; this is indicative of lower EDH's and speeds, also in accordance with Figs. 16a,c. The island of Niihau, however, does appear to perturb the clutter field more than is represented by the modeled clutter map.
To provide a relative metric to gauge the advantage of using the linked models as implemented here, Fig. 19c shows clutter maps based upon assuming a standard atmosphere and range-and-azimuth-independent σ°. It is clear that assuming standard propagation (i.e., EDH = 0) results in much faster falloff in the clutter power. Figure 19d shows the result of using local hav values, illustrating the very poor performance thereof.
Quantitative assessments of the linked models are given in Tables 3 and 4 for four different clutter maps. The first three rows correspond to clutter observations 70 and 49 min prior, and 44 min after the COAMPS 0600 UTC nowcast. A fourth row contains data from an open-ocean event to provide reference values by which to judge those in the first three columns.
A first metric for examining COAMPS-generated fields is a comparison of the EDH values at the location of the USS O'Kane with those calculated via the bulk method and the value obtained using the RFC technique. The bulk and RFC methods use data directly from the ship; COAMPS does not. These are shown in Table 3. It is clear that the EDH values from COAMPS are lower than those estimated via bulk models or the RFC method. A qualifying note is that the in situ measurements showed a positive ASTD, and the LKB model is highly sensitive to the ASTD when that value is positive.
A second quantitative metric is the skill of PLM(r, θ) in predicting the observed clutter Pobs(r, θ) using a criterion such as an area-normalized rms error. Benchmarks for that skill arise from implementing Eqs. (2) and (3) in a manner consistent with assuming a standard atmosphere, having EDH estimates generated via a bulk model, or having EDH generated via the RFC technique. These benchmarks are denoted PSTD(r, θ), PLKB(r, θ), and PRFC(r, θ), respectively. The information from COAMPS is not used in these estimates. When generated in this manner, PSTD(r, θ) and PLKB(r, θ) are based on the same information from the clutter (the average clutter power at range rc over 360° of azimuth) as PLM(r, θ). The EDH value used in the generation of PRFC(r, θ) is an rms error–minimizing duct height that is based on the assumption of the EDH being range and azimuth independent and σ° being azimuth dependent but not range dependent. Although the RFC objective function is not exactly the same as our objective criteria here, PRFC(r, θ) is significantly more dependent upon information derived from clutter than are PSTD(r, θ), PLM(r, θ), or PLKB(r, θ).
The rms error of clutter maps generated via the linked model and the described benchmarks are given in Table 4. The rms error for the linked models is nominally the same as with the bulk models and with RFC and is far less than that of the assumption of a standard atmosphere. On the other hand, we might consider the rms error of an open-ocean case—in which the EDH and σ° will vary far less with range—as something approaching the limit of that value. By that standard, there is certainly room for improvement in the performance of the linked models. However, it should also be pointed out that if the bias in Table 3 were removed from the COAMPS EDH predictions, there would be a significant drop in the errors of the linked models.
Concluding remarks
We have studied the dynamics of the Kauai wake, using both idealized and real data mesoscale-model (COAMPS) simulations, and investigated the wake's impact upon the wind, temperature, and moisture profiles, as well as the refractivity field. In the idealized experiments, as the average nondimensional mountain height is progressively increased by altering the island's terrain height, the wake configuration varies from two small counterrotating vortices to a straight wake to a meandering wake to a von Kármán vortex street. The evaporation-duct height field, computed diagnostically in these runs, is strongly affected by the wake, and this field, in turn, is found to be capable of strongly altering near-surface EM propagation.
A COAMPS real data forecast, in the form of a triply nested data assimilation cycle, was conducted to examine the Kauai wake structure during the period of radar tests aboard the USS O'Kane. Despite considerable inhomogeneity in the background field, a meandering wake forms that is very similar to the wake in the idealized benchmark run. Although very preliminary, we find it encouraging that forecast output from COAMPS, supplemented by wave-height information and ingested within an EM propagation model and a clutter model, yields radar clutter distribution maps that qualitatively agree with radar observations. COAMPS assimilated only routinely available meteorological data in this study. Also, the wave state was specified as an input parameter to the clutter model, but work with colleagues is under way to incorporate into the clutter model results from a wave model driven by COAMPS winds. A COAMPS–wave model–propagation model–clutter model nowcast/forecast system could, with sufficient computational time and power, be produced operationally. Our work in the immediate future will focus on full utilization of the modeled wave state, extension to a broader range of cases, and exploration of fusing model and radar data.
A final point to be made involves the use of clutter data. When a system such as TEP is present, some radars on naval vessels may be able to provide clutter data as a by-product of their normal operation. Insomuch as the vagaries of the clutter models are taken into account (for example, in this paper we use the clutter model to explain spatial variations but not to explain the absolute signal levels), these observations may be used to assess the NWP model's performance in estimating the EDH and factors affecting σ°. Fusing the NWP model predictions of the EDH with the clutter observations may become possible when the background error in predicting the EDH and the errors of the mapping from the EDH to the clutter are quantified. A particular problem that one might solve is the estimation of EDH values under stable conditions. The surface-layer models that are used to map both the bulk measurements and the output fields from COAMPS into the EDH are highly sensitive to the air–sea temperature difference when that value is positive; that is, small input errors lead to large output errors. The mapping from the EDH to the clutter, however, is independent of the ASTD.
Acknowledgments
The support of the sponsor, the Office of Naval Research, through program elements 0601153N and 0602435N is gratefully acknowledged. The comments of the three anonymous reviewers constructively aided in improving the manuscript. The NRL team development of COAMPS was vital to this study.
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Schematic depiction of modified refractivity M profile determined by similarity theory. Height of minimum in M determines the EDH
Citation: Journal of Applied Meteorology 42, 3; 10.1175/1520-0450(2003)042<0349:IWDAWI>2.0.CO;2
Model domain for idealized simulations (Δx = Δy = 3 km). Lines N–S (north–south) and E–W (east–west) show locations at which vertical cross sections are presented in subsequent figures
Citation: Journal of Applied Meteorology 42, 3; 10.1175/1520-0450(2003)042<0349:IWDAWI>2.0.CO;2
Initial temperature T (°C), dewpoint temperature Td (°C), and wind speed U (m s−1) profiles used for all idealized simulations.
Citation: Journal of Applied Meteorology 42, 3; 10.1175/1520-0450(2003)042<0349:IWDAWI>2.0.CO;2
Wind speed (m s−1, shaded) and streamlines of the benchmark idealized simulation at (a) 6, (b) 12, (c) 18, and (d) 24 h. Wind speed maxima associated with downslope flow (M1) and cornering winds (M2) are indicated
Citation: Journal of Applied Meteorology 42, 3; 10.1175/1520-0450(2003)042<0349:IWDAWI>2.0.CO;2
Relative vorticity (× 10−5 s−1) of the benchmark idealized simulation at (a) 6, (b) 12, (c) 18, and (d) 24 h. Contour interval is 20 × 10−5 s−1. Successive positive vortex centers are marked 1, 2, and 3
Citation: Journal of Applied Meteorology 42, 3; 10.1175/1520-0450(2003)042<0349:IWDAWI>2.0.CO;2
View from above looking east at the 297-K isentropic surface at hour 24 of the benchmark simulation. Light blue appears on leeside of Kauai where this Θ surface intersects the sea surface. The isentropic surface is shaded by relative vorticity (blue is negative, red is positive, green is zero), with regions of enhanced vorticity filling sloping depressions in the Θ surface
Citation: Journal of Applied Meteorology 42, 3; 10.1175/1520-0450(2003)042<0349:IWDAWI>2.0.CO;2
Vertical cross sections at 24 h from the benchmark simulation along the north–south line of Fig. 2: (a) relative vorticity (× 10−5 s−1) and (b) potential vorticity. The contour interval is 20 × 10−5 s−1 in (a), and is 1.0 m2 s−1 K kg−1 (1 PVU) in (b)
Citation: Journal of Applied Meteorology 42, 3; 10.1175/1520-0450(2003)042<0349:IWDAWI>2.0.CO;2
Vertical cross section of wind speed (m s−1, shaded) and potential temperature (K, contours) at 24 h of the benchmark simulation along the east–west line of Fig. 2
Citation: Journal of Applied Meteorology 42, 3; 10.1175/1520-0450(2003)042<0349:IWDAWI>2.0.CO;2
EDH (m) vs ASTD (°C) parametric in reference-height (10 m) relative humidity (5% contour increments) for a wind speed of (a) 2.5 and (b) 10 m s−1 (based on Paulus 1984). Heavy dots for ASTD = −1°C, RH = 85%
Citation: Journal of Applied Meteorology 42, 3; 10.1175/1520-0450(2003)042<0349:IWDAWI>2.0.CO;2
EDH (m) from benchmark simulation at (a) 6, (b) 12, (c) 18, and (d) 24 h
Citation: Journal of Applied Meteorology 42, 3; 10.1175/1520-0450(2003)042<0349:IWDAWI>2.0.CO;2
EDH (m) at 24 h in simulation S2 in which the terrain height is halved
Citation: Journal of Applied Meteorology 42, 3; 10.1175/1520-0450(2003)042<0349:IWDAWI>2.0.CO;2
Simulation-S3 results at 24 h in which terrain heights have been multiplied by ¾ for (a) wind speed (m s−1, shaded) and streamlines, and (b) EDH (m)
Citation: Journal of Applied Meteorology 42, 3; 10.1175/1520-0450(2003)042<0349:IWDAWI>2.0.CO;2
Simulation S4 results at 24 h in which terrain heights have been multiplied by 2 for (a) wind speed (m s−1, shaded) and streamlines, (b) relative vorticity (contour interval is 20 × 10−5 s−1), and (c) EDH (m)
Citation: Journal of Applied Meteorology 42, 3; 10.1175/1520-0450(2003)042<0349:IWDAWI>2.0.CO;2
Altered upstream wind direction simulations, S5: results at 24 h for wind from (a) east-southeast (115°) and (b) east-northeast (65°)
Citation: Journal of Applied Meteorology 42, 3; 10.1175/1520-0450(2003)042<0349:IWDAWI>2.0.CO;2
Triply nested model grid used for the real data forecast. The outer mesh has Δx = 27 km, the second mesh has Δx = 9 km, and the inner mesh has Δx = 3 km. All meshes have 40 vertical levels
Citation: Journal of Applied Meteorology 42, 3; 10.1175/1520-0450(2003)042<0349:IWDAWI>2.0.CO;2
Results from real data forecast valid 0600 UTC 3 Dec 1999 for (a) wind speed (m s−1, shaded) and streamlines, (b) vertical cross section of wind speed (m s−1, shaded) and potential temperature (K, contours) along the east–west line of Fig. 2, and (c) EDH (m)
Citation: Journal of Applied Meteorology 42, 3; 10.1175/1520-0450(2003)042<0349:IWDAWI>2.0.CO;2
(a) Clutter power as a function of range referenced to the clutter power at 10 km, parametric in duct height; (b) σ° predicted by GIT clutter model as a function of wind speed, parametric in grazing angle (°). Average wave height hav is based on local wind speed and the assumption of a fully developed sea. (c) Same as (b) except that hav is set to a constant value of 0.45 m
Citation: Journal of Applied Meteorology 42, 3; 10.1175/1520-0450(2003)042<0349:IWDAWI>2.0.CO;2
Predictions of σ° using wind fields from COAMPS (a) using average hav value and (b) using hav based on local wind fields
Citation: Journal of Applied Meteorology 42, 3; 10.1175/1520-0450(2003)042<0349:IWDAWI>2.0.CO;2
(a) Observed clutter map (dB) from the USS O'Kane radar on 3 Dec 1999. (b) Modeled clutter map from linkage of COAMPS with an EM propagation code and a radar clutter model. (c) Clutter map based on assumption of standard atmosphere. (d) Same as (b) but using hav based on local wind speeds
Citation: Journal of Applied Meteorology 42, 3; 10.1175/1520-0450(2003)042<0349:IWDAWI>2.0.CO;2
Vertical distribution of gridpoint heights
Layer-averaged values and nondimensional mountain heights
Evaporation duct heights (m) from four different methods at ship location
Rms errors of computed, area-normalized clutter power values (PLM, PSTD, PLKB, PRFC)
Battan (1973) defines backscattering cross section as the area intercepting that amount of power, which, if scattered isotropically, would return to the receiver an amount of power equal to that actually received.
COAMPS is a trademark of the Naval Research Laboratory.
The average wind speed is found on each 1.5° azimuth around the ship and is used to compute an equilibrium wave height for each azimuth. The mean of the azimuthal wave heights (0.45 m) is put into the clutter model for computation of radar cross section.