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    The official best track for TC Ingrid. Note that it was a long-lived storm with several cycles of intensification depending on land influences. The date and pressure tags are at 0000 UTC, and additional pressure estimates at 1200 UTC are shown. This paper focuses on the period from 0200 UTC 13 Mar to 2000 UTC 13 Mar 2005.

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    A scattergram of the operational rain gauge measurements within the radar-sampling volume against the polarimetric rainfall accumulation estimate. The diagonal line is perfect agreement.

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    A geostationary satellite IR image of TC Ingrid at 0700 UTC 13 Mar 2005.

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    Radar reflectivity at an elevation angle of 0.5° at 0730 UTC 13 Mar 2005. The cross section of velocity and reflectivity through the eye (solid line) and the cross section of reflectivity and microphysical classification (dashed line) are shown. The storm center is at approximately (25 km, 100 km). Note the asymmetries of the eyewall and the presence of several rainbands.

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    The 24-h rainfall accumulations begin at 0000 UTC 13 Mar 2005, along with the storm best track and time of each fix. Note the impact of the storm asymmetry on the rainfall pattern.

  • View in gallery

    (top) A time–height cross section of max reflectivity in the eyewall as a function of height. Contours are drawn every 10 dBZ from 15 dBZ with a heavy contour drawn at 35 dBZ. The temperature heights were taken from the 1100 UTC Darwin sounding, and thus may be biased somewhat low when compared with the eye. (middle) The area greater than 45 dBZ around the eye (solid line) and the time sequence of the maximum reflectivity in the eyewall at 3-km altitude (dashed line). (bottom) The maximum Doppler velocity in the eyewall on the left-hand (west, solid line) and right-hand (east, dashed line) sides.

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    The quasi-north–south cross section of the radar reflectivity and polarimetric microphysical classification at 0730 UTC along the dashed line in Fig. 4; E marks the center of the eye and R marks rainbands.

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    The cross section of (top) reflectivity and (bottom) Doppler velocity at 0730 UTC along the solid line marked on Fig. 4. The location of rainbands (R) and the eyewall (EW) are shown on the reflectivity. The Doppler velocity has an overlay of the expected profile for a vortex with an R−1 (light solid line) and R−1/2 (light dotted line) radial dependence and linear variation inside the radius of maximum wind. Distance is in kilometers from the zero isotach.

  • View in gallery

    The modeled flow in the boundary layer of TC Ingrid: (a) radial and (b) azimuthal earth-relative flow at 10 m, and (c) vertical velocity and (d) azimuthal flow at 1.05 km. The land occupies the southern half of the domain, the sea is to the north, and the Southern Hemisphere storm is moving to the left at 3.4 m s−1. Contour intervals are 5 (20) m s−1 for light (heavy) contours for the radial and azimuthal flow and 1 (3) m s−1 for the vertical flow. Darker shading corresponds to outflow, stronger swirling flow, and a stronger updraft, respectively.

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    Vertical profiles of (a) earth-relative radial wind and (b) earth-relative azimuthal wind components, at the radius of maximum gradient wind in the front of the storm. The heavy profiles are over the land at two grid points (6 km) south of the coast, while the light profiles are downwind of this over the sea at two grid points north of the coast. The change in surface roughness causes the reduced near-surface shear in the oversea profiles, but the near-surface inflow is stronger than that over land because of the mixing down of radial momentum from aloft, which in turn increases the radial advection of angular momentum and helps accelerate the near-surface azimuthal wind.

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Polarimetric Radar Observations of the Persistently Asymmetric Structure of Tropical Cyclone Ingrid

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Abstract

Tropical Cyclone Ingrid had a distinctly asymmetric reflectivity structure with an offshore maximum as it passed parallel to and over an extended coastline near a polarimetric weather radar located near Darwin, northern Australia. For the first time in a tropical cyclone, polarimetric weather radar microphysical analyses are used to identify extensive graupel and rain–hail mixtures in the eyewall. The overall microphysical structure was similar to that seen in some other asymmetric storms that have been sampled by research aircraft. Both environmental shear and the land–sea interface contributed significantly to the asymmetry, but their relative contributions were not determined. The storm also underwent very rapid changes in tangential wind speed as it moved over a narrow region of open ocean between a peninsula and the Tiwi Islands. The time scale for changes of 10 m s−1 was of the order of 1 h. There were also two distinct types of rainbands observed—large-scale principal bands with embedded deep convection and small-scale bands located within 50 km of the eyewall with shallow convective cells.

Corresponding author address: Dr. Peter May, BMRC, GPO Box 1289, Melbourne, 3001 Victoria, Australia. Email: p.may@bom.gov.au

Abstract

Tropical Cyclone Ingrid had a distinctly asymmetric reflectivity structure with an offshore maximum as it passed parallel to and over an extended coastline near a polarimetric weather radar located near Darwin, northern Australia. For the first time in a tropical cyclone, polarimetric weather radar microphysical analyses are used to identify extensive graupel and rain–hail mixtures in the eyewall. The overall microphysical structure was similar to that seen in some other asymmetric storms that have been sampled by research aircraft. Both environmental shear and the land–sea interface contributed significantly to the asymmetry, but their relative contributions were not determined. The storm also underwent very rapid changes in tangential wind speed as it moved over a narrow region of open ocean between a peninsula and the Tiwi Islands. The time scale for changes of 10 m s−1 was of the order of 1 h. There were also two distinct types of rainbands observed—large-scale principal bands with embedded deep convection and small-scale bands located within 50 km of the eyewall with shallow convective cells.

Corresponding author address: Dr. Peter May, BMRC, GPO Box 1289, Melbourne, 3001 Victoria, Australia. Email: p.may@bom.gov.au

1. Introduction

The structure and intensity of tropical cyclones (TCs) around landfall are a major topic of research because of the potential impact on human populations and property. The dynamics of the storms are complicated because of the proximity of the coastline and the corresponding variations in surface fluxes and friction. This often leads to distinct asymmetries in the storm rainfall structure (e.g., Chan et al. 2004). In addition to the high winds, intense rainfall can be a major factor in storm damage. Polarimetric weather radars offer the possibility of much more accurate measurements of rainfall compared with conventional radar and of obtaining the precipitation microphysical structure of storms nearing landfall, which are key issues relating to the impact of tropical storms. Polarimetric capabilities are a key component of the planned upgrade of the U.S. weather radar network. There are several research radars with this capability, but there have not been TC observations using the published polarimetric radar.

In March 2005, an intense tropical cyclone, TC Ingrid, moved within 100 km of the Darwin research polarimetric radar (Keenan et al. 1998). Ingrid was a long-lived storm that reached Australian category 5 intensity twice—initially before it crossed the North Queensland coast, and then again as it reintensified over the Gulf of Carpentaria, where the eye structure was quite symmetric. On the Australian scale, category 3 is defined by gusts >170 km h−1, category 4 by gusts >225 km h−1, and category 5 by gusts >280 km h−1. This is different from the Saffir–Simpson scale used in the United States (details are available online at http://www.nt.bom.gov.au/ntregion/sevwx/cyclones/tccat.html). Ingrid then moved along the north coast of Australia along the monsoon trough axis where it lost some intensity, but remained a severe tropical cyclone (Fig. 1). This included the period of the most interest herein, while it moved near the polarimetric radar facility (0200–2000 UTC 13 March 2005). Following the passage past the Darwin area it moved into the Timor Sea, where it again reintensified before recurving and making its final landfall.

While this storm did not cross the coast near Darwin, it did propagate along an extended section of east–west-oriented coastline, with the circulation center very close to the coastline. As will be shown, this resulted in some remarkable asymmetries in the storm structure. The best-track estimates of the central pressure when it was in radar range had the storm filling from 950 to 970 hPa, with 965 hPa being measured at Cape Don (11.31°S, 131.77°E), and an analyzed intensity dropping from that of a category 4 to a category 3 storm. The Doppler wind speeds estimated near the eyewall at low elevations (but still about 1.8 km above the ground) at the time of the closest approach to the radar were as high as ∼55 m s−1, consistent with the category 3 rating, but there were significant high-frequency variations in the storm intensity that can be related to the surface properties beneath the eye. This paper will describe the rainfall and microphysical structure of the storm as it moved past the radar at a speed of about 3.5 m s−1. Thus, the observations here present a case study of asymmetric tropical cyclone structure associated with a relatively simple land–sea interface as well as a demonstration of the utility of polarimetric radars for tropical cyclone research.

2. Polarimetric radar

A polarimetric weather radar differs from conventional Doppler radar by its ability to transmit and receive on different polarizations. In the case of the 5.5-cm-wavelength Darwin C-band dual-polarization Doppler (C-Pol) radar, alternate pulses of horizontally and vertically polarized radiation are transmitted and received (Keenan et al. 1998). The radar is located at Gunn Point (12.25°S, 131.04°E), approximately 25 km northeast of Darwin and about 100 km south of the closest approach of Ingrid’s center. The radar has a beamwidth of 1°, giving it an angular resolution of about 2 km at a range of 100 km. The range resolution of the data used here is 300 m and the data are interpolated onto a Cartesian grid with a spacing of 2.5 km in the horizontal and 1 km in the vertical for the classification data and 1 km in the horizontal for the rainfall estimates. The minimum detectable signal at 150 km (maximum range used in this study) is approximately 0 dBZ. The velocity data used in these analyses were from the raw radar data after extensive manual velocity dealiasing.

Detailed descriptions of the enhanced capabilities associated with such systems can be found in Zrnić and Ryzhkov (1999), but the germane issue here is their capability for much greater accuracy of rainfall estimates compared with conventional radar and the ability to estimate the microphysical characteristics of the precipitation. Polarimetric radars offer several advantages over standard reflectivity-based rainfall radar estimates. The polarimetric radar measures several variables in addition to the reflectivity at horizontal polarization (ZH). In particular, the difference in reflectivity at the two polarizations (ZDR = ZH/ZV) provides information on the mean raindrop size that is at the core of rainfall measurement uncertainties, while the differential phase on propagation (ΦDP) provides a measure of the attenuation of the signals. The radial gradient of ΦDP, the specific differential phase KDP, provides an attenuation-free estimate of the rainfall rate that is particularly useful in high-rain-rate situations or when mixed-phase precipitation is present. The final parameter measured by the C-Pol radar is the cross correlation of the signal at the two polarizations [ρHV(0)] that enables the detection of mixtures of precipitation type. These capabilities have been discussed at length in many papers (e.g., Bringi et al. 2002; Zrnić and Ryzkhov 1999; May et al. 1999).

The rain field has been estimated using a combination of polarimetric estimators that are dominated by reflectivity at low rain rates, and that use the differential reflectivity and reflectivity at moderate rates and the KDP at high rain rates. The particular algorithms are described in Bringi et al. (2001, 2004. Much of the area of interest is at a fairly long range, so that the beamwidth is ∼2 km. This may lead to some beam-filling issues, but the features of interest here are of a large enough scale and the freezing level is high enough (∼5 km) that this does not appear to be a significant issue. Cell movement combined with the radar 10-min sampling can also produce unrealistic gaps in the spatial pattern of the rainfall, which is essentially a strobe effect, but the storm movement is slow enough and the rainfall features are large enough that the accumulations here do not show this problem. Comparisons between the rain gauges in the region with the 24-h radar estimates of storm accumulations show excellent agreement (Fig. 2), with a correlation of 0.86. On average the gauges are slightly higher, with a mean gauge-to-radar ratio of 1.3. The two high accumulations (>90 mm) were both from gauges that were near the eyewall passage and experienced strong winds, while most of the other gauges were more than 100 km from the circulation center and sampled bands. Many of these gauges were in areas with very high rainfall gradients. The strong winds tend to bias gauge measurements down, indicating that the radar may be underestimating the rain, but overall these comparisons give confidence in the radar estimates of rain totals. This is particularly the case given the substantial spatial gradients in the accumulated rainfall.

The substantial tangential winds in the eyewall did produce some quality control problems, because the spectral width of the signals was greater than about 2.5 m s−1; that is, about a quarter of the Nyquist velocity. This significantly impacts the accuracy of the phase measurements that are part of the velocity and differential phase measurements, leading to some uncertainties in the KDP and attenuation corrections. Note that this would be less of an issue with 10-cm-wavelength radars because they have twice the Nyquist velocity, although the fractional error for the KDP estimates is larger for 10-cm radars because KDP scales as the inverse of the wavelength. Where the quality control deleted polarimetric-based estimates, the rainfall estimate was replaced by an attenuation-corrected reflectivity-based estimate.

Attenuation of the radar signals can also be significant for 5-cm-wavelength radars. Attenuation up to about 5 dBZ was seen behind the intense northern side of the eyewall for the period of around 0630–0800 UTC. As discussed by May et al. (1999) and Carey et al. (2000), the ΦDP is approximately proportional to the water path, and therefore attenuation. Thus, a simple methodology for attenuation estimates is the loss in dBZ = 0.02 ΦDP. The uncertainties therein are associated with the dependence of the coefficient (0.02) on drop size distributions and the linear approximation, as well as the statistical uncertainties in the ΦDP measurement itself. More precise estimates of the attenuation are difficult because of the quality control impacts of the wide spectral widths discussed earlier. It is important to make these corrections to minimize bias in rainfall estimates, particularly for a 5-cm-wavelength radar, because there was significant attenuation observed through the eyewall, in particular. The ability to use the ΦDP is a significant advantage of polarimetric radars over simple Doppler radars.

Another useful application of the polarimetric data is to estimate the hydrometeor type. Different species of hydrometeors occupy various ranges of the multiparameter phase space, so combinations of measurements can be used to separate different types of precipitation, as well as nonmeteorological echoes (Schuur et al. 2003) and the presence of hail, in particular (e.g., May et al. 2001). However, there is considerable overlap in these parameter ranges, so a fuzzy-logic approach is used to perform the microphysical classification (Keenan 2003) similar to the approach of Straka et al. (2000). These retrievals have found good validation in thunderstorm data (May and Keenan 2005). It should be noted that the large velocities caused considerable aliasing and also appeared to impact some of the data quality in the eyewall region, probably because of the large spectral widths as noted above. However, the results presented here show spatial and temporal consistency. In particular, it is possible to discriminate between rain, rain–hail mixtures, wet and dry graupel, and snow. These retrievals appear to be robust down to the minimum detectable signal levels, for example, showing snow in anvil cloud (e.g., May and Keenan 2005).

3. Core structure

As shown in Fig. 1, TC Ingrid passed along the north coast of Australia and was decreasing in intensity as it passed the Tiwi Islands. This extended path along the coast can be compared with a storm making landfall for a period of over 12 h, and as such it can offer useful insight into cyclone structures undergoing landfall. An IR satellite image at 0700 UTC 13 March (Fig. 3) shows continuous cloud coverage with no clear eye. This is consistent with decreasing intensity and, as we will show, the reflectivity structure of the eye itself. The cold IR temperatures are concentrated on the north and east sides of the eye circulation, along with some cold cloud tops associated with parts of the rainbands. We will see that this is consistent with the radar structure as well as a Tropical Rainfall Measuring Mission (TRMM) overpass (not shown, but available online at http://trmm.gsfc.nasa.gov/publications_dir/ingrid_11-15mar05.html).

A radar scan at 0730 UTC (Fig. 4) shows the very asymmetric reflectivity structure about the storm center with the maximum reflectivity on the north (offshore) side consistent with the satellite imagery. This asymmetry persisted for the entire storm passage (>12 h) past the islands and is reflected in the total rainfall estimated from the polarimetric data (Fig. 5). The time for a cell to be advected around the entire eye is ∼1 h, so the relatively steady state of the convective asymmetry is noteworthy. This resulted in a very asymmetric rainfall distribution, with totals of more than 500 mm offshore and much less, but there are still significant totals on the islands and mainland associated with rainbands and the southern part of the eyewall. Comparisons with gauge data on the coastal region and Cape Don show good agreement (Fig. 2), although it should be remembered that gauge estimates tend to underestimate rainfall in high wind speeds. Similar asymmetries have been observed in several storms close to land (e.g., Blackwell 2000; Geerts et al. 2000).

The period around 0730 UTC corresponds to a maximum in the convective intensity as defined by both the maximum reflectivities in the eyewall and the maximum height that reflectivities greater than 35 dBZ reach (Fig. 6). A part of the weakness before 0400 UTC and after about 1700 UTC is associated with the eye leaving the radar-sampling domain. However, there is a clear maximum in convective intensity around 0730 UTC that had implications for the microphysics of the eyewall, as will be discussed later. After about 0900 UTC the convective intensity decreased and this corresponded to a weakening in the wind speeds. Around 1400 UTC there was a subsequent intensification and the highest echo tops, as the circulation was again moving offshore and the storm was beginning to reintensify.

The radar cross sections at 0730 UTC through the eyewall (Fig. 7) show that the intense side is always characterized by echo tops in the vicinity of 18–20 km, that is, the convection on the north side of the eye is reaching to the tropopause and overshooting while the reflectivity structure on the south side is not only much shallower, but seems to be feeding into the outflow mask between altitudes of 10 and 15 km. This altitude range is consistent with the outflow layer in Darwin sounding data (not shown). The reflectivity cross section includes a cloud layer over the central eye, which is consistent with the lack of a clear eye in the satellite imagery. Within the eyewall there remained echoes of about 25 dBZ and evidence of a bright band extending across the eye, indicating some drizzle. There may be some smearing of reflectivity at the upper heights for ranges beyond 100 km, but the radar echoes near the tropopause and overshooting were consistent with IR satellite brightness temperatures below −90°C. The coldest cloud-top temperatures were to the north, consistent with the radar data. The IR image also displays some cyclonic curvature of the cold cloud-top temperatures around to the eastern side of the storm. This is not necessarily inconsistent with the radar data, which show substantially less rotation, because it may be explained by the radar reflectivity being dominated by large ice crystals that fall out relatively quickly while the small crystals remain at high altitudes (e.g., Houze et al. 1992). The picture that emerges from these observations is consistent with the schematics of Heymsfield et al. (2001, their Fig. 12).

The polarimetric radar also allows us to estimate the precipitation microphysical structure. Figure 7b shows the microphysical structure in a north–south cross section through the storm. In the intense convection of the northern eyewall segment there appears to be an almost continuous volume of rain–hail mixtures in the region between 3 and 5 km in altitude, with a substantial volume of wet graupel overlying this. This is indicative of the strong updrafts in the high-reflectivity area. May and Keenan (2005) saw significant hail signatures only in storms that had updraft strengths near the freezing level of about 10 m s−1 or more. Soundings taken from Darwin show a typical tropical cyclone profile with relatively low convective available potential energy (CAPE), but also almost no convective inhibition (CIN; not shown). Nevertheless, this environment was clearly supporting substantial updraft strengths in the eyewall region and, as will be shown, in convective cores in the rainbands. This is also seen by wet graupel, implying the presence of supercooled water extending to heights corresponding to nearly −20°C. The high implied vertical motions and consequent mixed-phase regions are consistent with aircraft observations of hurricanes with high vertical velocities in very asymmetric eyewalls as described by Black et al. (1994, 1996, Black and Hallett (1986, 1999, and Marks and Houze (1987). The remainder of the eyewall convection and the shallow cells visible south of the eyewall, which are associated with the small rainbands visible in Fig. 4, do not show any substantial mixed-phase regions. Interestingly, there are rain–hail mixture regions that are produced in cells of intense convection in the rainbands. These cells are often initiated near the point where the rainband circulation crossed onto the land and presumably frictional convergence led to initiation of new convection (e.g., Parrish et al. 1982). However, there was also substantial convective activity and higher lightning rates in the later bands over the water as the storm was reintensifying after it moved offshore.

Figure 8 shows a cross section of the maximum Doppler velocity across the storm (i.e., a cross section of the storm azimuthal wind speed). The velocity cross section shows a maximum velocity of about 50 m s−1 and a radius of maximum wind (RMW) of 20 km slightly inside the highest reflectivity. There is also some asymmetry in the radial dependence. On the northwest side the Doppler velocity initially falls off as the radius R−1/2 with a transition to a 1/R dependence, which is inertially neutral, between the eyewall and the first rainband. On the southeast side, downwind from the major convection, the falloff was midway between these dependencies. This profile is consistent with low values of vorticity outside of the eyewall region despite the large circulation.

The Doppler data also allow us to examine the time evolution of the storm intensity as estimated by the maximum in Doppler velocity on both the inbound (east) and outbound (west) side of the circulations (Fig. 6, lower panel). Remember that these observations are at a range of approximately 100 km, so the vertical resolution of the radar beam is about 2 km and the beam center is about 1.5 km above the ground. The time series shows the general tendency for the storm to decrease in intensity as it traverses the northern part of the Tiwi Islands. However, there are interesting short-period variations in both the intensity and the asymmetry between the strength of the circulation on the two sides. There were significant asymmetries when part of the circulation was over the water, with the winds over the water between Cape Don and Melville Island showing differences of more than 5 m s−1. The impact of the warm ocean is also reflected in the rapid increase in intensity as the eye moved over this relatively narrow gap between these two landmasses, and the corresponding decay as the circulation is partly over the land. Interestingly, the asymmetry in the wind had no significant effect on the reflectivity structure around the eyewall, with the northern side being far more intense regardless of whether the air motion at the radar beam height indicated convergence or divergence. This must mean that low-level convergence is dominating the supply of high-θE air. As the storm center moved slightly farther inland around 1500 UTC, the eyewall became more circular as rainbands appeared to be wrapped around it. By this time the maximum reflectivities had decreased somewhat (but were still greater than 50 dBZ, indicating heavy rain), but there were no hail signatures present in the estimates of the precipitation microphysics near the eye. By 1800 UTC the storm was moving away off the islands, and again the eyewall assumed a very asymmetric structure with the maximum reflectivity to the northwest (directly offshore and perpendicular to the coast) and with significant hail signatures again being present.

The picture of the reflectivity and microphysical structure of the eye at its maximum sampled convective intensity is remarkably similar to the electrically active eyes discussed by Black and Hallett (1999). Over several aircraft penetrations they sampled unusually strong updrafts, extending above the −40°C level, and significant graupel, and implied supercooled water to the −20°C level and associated charging in highly asymmetric storms, including Hurricane Emily (Black et al. 1994). The hail signatures that were detected in the polarimetric radar data are consistent with vertical motions comparable to those of Emily (cf. May and Keenan 2005). Lightning data for the area at this time are somewhat limited, but data from a global network of very low frequency (VLF) emission lightning detection (Dowden et al. 2002) show flashes in the high-reflectivity zone on the northern eyewall, with a local maximum in occurrence around 0700 UTC of a few flashes per minute. Higher rates were seen in the rainbands of the system during a convective burst outside the spatial domain considered in detail here as the storm reintensified. Long-range radar scans show that these were periods of significant convective areas aligned along the bands (not shown). It is difficult to be quantitative about this, because detection efficiencies are quite low and dependent on the absolute geometry of the detectors, but are likely less than 1% and primarily, but not completely, cloud-to-ground strikes (Jacobson et al. 2006). Very high reflectivities and asymmetric rain distributions with an offshore maximum also characterized Hurricane Danny (Blackwell 2000) and it may be reasonable to infer a similar microphysical structure for that storm as well.

4. Origin of the asymmetry: Large-scale shear and surface friction?

Asymmetries in the eyewall structure of a tropical cyclone have previously been ascribed to both the effect of wind shear across the storm and the impact of land surface being near the storm center. Both of these mechanisms are probably having some impact for this case and need to be considered in some detail.

a. Shear

Vertical wind shear values were calculated from the National Centers for Environmental Prediction (NCEP) reanalysis, over a storm-centered 200–800-km annulus, as used for the wind shear prediction in the Statistical Hurricane Intensity Prediction Scheme (SHIPS) model (DeMaria et al. 2005). Examination of individual analyses showed that the storm was well located, so removal of the storm circulation was not necessary. From 12 to 13 March the 850–200-hPa shear decreases gradually from 9 to 7 m s−1 from the east-southeast. Beginning around 1200 UTC 14 March, the shear began to weaken more rapidly and was only a few meters per second by 0000 UTC 15 March. Both theory (e.g., Jones 1995) and observations (e.g., Black et al. 2002; Corbosiero and Molinari 2002; Rogers et al. 2003) have shown that the vortex tilts with, and to the right of, the shear vector (in the Southern Hemisphere), with low-level convergence and eyewall ascent enhanced down tilt and suppressed up tilt. The consequences for cloud and rainfall are complex, because both are rapidly advected around the storm from the near-surface forcing region. While there is strong agreement that the rainfall maximum is cyclonically rotated from the maximum forced updraft, the observed degree of rotation is somewhat variable and will clearly depend on the angular velocity of the wind in the vicinity of the feature. Recently, Halverson et al. (2006) have shown that the maximum convective tops can be rotated as much as halfway around the storm from the low-level convergence maximum.

The observed reflectivity, eyewall height, and cloud-top temperature asymmetries (Figs. 3 and 4) are thus at least qualitatively consistent with environmental shear, in that the brightness temperature minimum is located cyclonically from the rainfall maximum, which is in turn located cyclonically from the downshear side of the storm.

b. Influence of asymmetric surface friction

Asymmetric friction resulting from storm motion will force an asymmetric updraft at the top of the boundary layer (Shapiro 1983; Kepert 2001; Kepert and Wang 2001), with the maximum updraft being to the left front of a Southern Hemisphere storm. More recently, it has been recognized (Kepert 2002a, b) that proximity to land is also a source of asymmetric surface friction and will have similar dynamic consequences for the BL structure. The inner-core surface flow asymmetry in a tropical cyclone is usually oriented with the maximum storm-relative inflow in the right-forward quadrant, and the maximum storm-relative azimuthal flow in the left-forward quadrant, 90° downstream of the inflow maximum. The motion-induced surface flow asymmetry has been known since the pioneering work of Redfield (1830), Reid (1838), and Piddington (1848) in the first part of the nineteenth century, and is described in numerous observational (e.g., Arakawa and Suda 1953; Frank 1976; Powell 1982, 1987; Frank 1984; Black et al. 1988; Powell and Houston 1998) and theoretical (Shapiro 1983; Kepert 2001; Kepert and Wang 2001) papers, although we caution that it may, at times, be overwhelmed by other sources of asymmetric forcing. The storm-relative motion-induced wind asymmetry rotates anticyclonically with height through the boundary layer. Kepert (2001) and Kepert and Wang (2001) have studied the three-dimensional dynamics of the tropical cyclone boundary layer and have shown that this structure can be understood as a frictionally modified wavenumber 1 inertia wave, forced by the asymmetric surface friction, whose vertical structure is such that vertical diffusion and vertical advection act to reduce the wave’s phase speed to zero. Detailed analyses (Kepert 2006a, b) of GPS dropsonde data in Hurricanes Georges and Mitch found structures very similar to this, except that in Mitch the orientation of the asymmetry was displaced almost 180° in azimuth, with the maximum near-surface inflow on the left flank in the offshore flow, and the maximum azimuthal wind to the rear. At the time, Mitch was very slowly moving and about 80 km off the Honduras coast. Kepert (2006b) argued that the motion-induced asymmetric friction was dominated by that resulting from the proximity to land in this case, and presented a model simulation in support of this mechanism. The eyewall updraft asymmetry in this simulation was consistent with the observed radar reflectivity asymmetry in Mitch, although it was not possible to rule out environmental shear as a cocontributor to the asymmetric forcing.

Ingrid represents an interesting example of a storm being influenced by asymmetric surface friction, because with the land to the left of the track, both sources of asymmetric friction are nearly in phase, and so a very strong frictional asymmetry would be expected.

The three-dimensional tropical cyclone boundary layer (TCBL) model of Kepert and Wang (2001) is used to examine the flow asymmetry more closely. This model is a very high vertical resolution boundary layer model, with a translating parametric pressure field intended to represent the remainder of the cyclone, and is not intended to depict the full physics of a tropical cyclone. Rather, the focus is on the dynamical structure of the boundary layer, excluding the impact of deep convection, to isolate the dynamical impact of the surface friction and its inhomogeneities, which may have a significant impact on the real storm structure. For details of the model physics and initiation, the reader is referred to Kepert and Wang (2001). The free-atmosphere flow was derived by fitting a Holland (1980) profile to mean sea level pressure (MSLP) observations from Cape Don and McCluer Island (11.05°S, 132.98°E) renavigated into storm-relative coordinates, which gave a maximum gradient wind of 50 m s−1 at a radius of 17 km (consistent with the Doppler radar data) and a B parameter of 1.4. The central pressure of 950 hPa and the mean storm motion of 3.4 m s−1 from the postanalysis best track by the Australian Bureau of Meteorology Tropical Cyclone Warning Centre in Darwin were used. The coast was simplified to a straight line along the track, with land with a roughness length of 0.3 m to the south, and sea to the north. Land and sea temperatures were taken to be equal at 300 K.

The modeled 10-m horizontal wind components and 1-km vertical motion are shown in Fig. 9. The increased inflow over land, resulting from the greater surface roughness, is readily apparent. As the flow passes from land to sea the surface friction reduces, but vertical mixing remains strong because of the horizontal advection of turbulent kinetic energy, which drives an adjustment of the air columns to a less sheared state. The inflow thus strengthens near the surface but weakens aloft, with the height of the maximum inflow falling from 200 to 300 m over the land to about 100 m immediately offshore (Fig. 10). Similarly, the near-surface azimuthal flow accelerates, not just because of the reduction in surface friction, but also because the inward advection of the angular momentum by the radial flow is now stronger than that which would apply in an equilibrium all-sea situation, as the boundary layer adjusts to the changed surface condition. Examination of the model output shows that the azimuth of the strongest winds rotates anticyclonically with height, consistent with Kepert’s (2001) stalled inertia wave argument, and that the strongest winds below about 1.5 km are over the sea, even though the strongest gradient winds are over the land to the south (where the storm motion adds to the swirling flow). The eyewall updraft is strongly asymmetric, with a 6.6 m s−1 updraft at the front left of the storm extending around to the right, and a downdraft to the rear. This asymmetry is qualitatively consistent with the observed rainfall and cloud height asymmetries, if some allowance for cyclonic advection is made. A further interesting feature is a weaker band of upward motion that spirals out from the front of the eye toward the southeast, and is similar in structure to bands seen in the radar imagery (e.g., Fig. 3). This band may be related to the instability modeled by Nolan (2005) in an axisymmetric model, although here it is clearly dependent on the storm asymmetry also. Finally, comparison of the horizontal flow at 10 m with that at 1 km shows a marked outward slope of the RMW with height. Because the model contains no warm core, this is not baroclinic in origin, but rather must be a result of the frictional forcing.

Sensitivity calculations with a variety of surface forcings were done to estimate their relative importance in producing the frictionally forced updraft, and are summarized in Table 1. Comparing the stationary storms entirely over both sea and land (i.e., the symmetric cases), the latter has a much greater updraft because of the greater surface roughness. For a storm wholly over sea, the effect of motion is to moderately increase the mean updraft, but greatly increase the peak, due to the development of a marked asymmetry with ascent to the front, and descent to the rear, of the maximum wind belt. Adding a land–sea contrast to the situation produces an increase in the mean updraft to values between the sea- and land-only cases, because half of the storm now experiences increased surface roughness. The peak updraft experiences a relatively greater increase than the mean, because of the increased asymmetric forcing. The three cases with asymmetric surface friction have similar patterns of vertical motion in the inner core, because the phase of the motion- and land-induced asymmetries is similar. The magnitudes, however, are markedly different.

The rainfall asymmetry is thus qualitatively consistent with both the environmental shear and with asymmetric friction resulting from proximity to land. Determining the relative contributions would be difficult in this case, because both the boundary layer flow (Kepert 2006a, b) and the response to shear (Reasor et al. 2004) are known to be sensitive to small details of the storm structure, and there is insufficient data to determine this. Frank and Ritchie (1999, 2001 have considered the relative effects of the motion-induced boundary layer asymmetry and shear-induced tilt of the vortex axis in determining the updraft, cloud, and rain asymmetries in tropical cyclones. For the cases they considered, the effects of the forcings tend to reinforce if they are in phase, but shear dominates if they are out of phase, with the frictional asymmetric updraft extending only a modest distance above the boundary layer. However, their cases were relatively slowly moving, so the frictional asymmetric forcing was much weaker than in this case. Here the shear is toward the lower end of the range considered by Frank and Ritchie (1999, 2001, while the frictional updraft asymmetry is strong; thus, one might plausibly speculate that the latter mechanism dominates. The evolution toward symmetry as the bulk of the eye moved over the islands and the subsequent asymmetry to the northwest as the storm was recrossing the coast lend additional support to this inference. The fact that Ingrid then regained much of its symmetry as it moved well away from the islands is likely due to both the declining land influence and the decrease in environmental shear. If the proximity to land is indeed having a substantial influence on the boundary layer wind structure, and this is affecting the eyewall depth and cloud-top temperature asymmetries, then there may be implications for Dvorak analysis of cyclone intensity near landfall.

5. Rainband structures

There were two distinct types of rainbands observed in the radar data. There were some large-scale, long-lived bands that extended from near the north side of the eyewall around to the south of Darwin and a similar, but less well developed, line that connected to the southwest side of the eyewall (Fig. 4). These lines were almost stationary. The band was largely stratiform in nature, except for some embedded convective elements. These were mostly, but not always, initiated near coastal boundaries where there is an increase of surface friction, and therefore the potential for an updraft to be triggered (e.g., Parrish et al. 1982). The convection in these elements was often deep, reaching to the tropopause and with rain–hail mixtures detected between heights of 3 and 5 km. This is in marked contrast to most convection in monsoon conditions at Darwin where there is almost no hail reported (May and Keenan 2005).

As well as the large-scale bands there were a number of small lines with a length of about 50 km within a radius of about 60 km. Several of these can be seen in Fig. 4, including one that is intensifying significantly. As can be seen in the cross section, these were often made up of shallow cells. Animations show that these rotated about the storm much faster than the outer bands before stalling and merging near the intersection of the large band. This relatively rapid motion is undoubtedly partly due to the radial variation of angular velocity within the storm. It is not clear if these lines were propagating azimuthally with respect to the storm circulation, but their regularity certainly gives them a wavelike appearance, and an isochrone analysis suggests outward radial propagation at speeds of 6–8 m s−1. These speeds are quite low compared with those expected from the likely phase speeds of gravity waves generated at the RMW, as was hypothesized to explain similar propagating lines in TC Laurence (May 1996), but a gravity wave initiation source cannot be ruled out given the low inertial stability outside the RMW. Gall et al. (1998) analyzed radar imagery of hurricanes and found, along with the major inner-core bands, strong evidence for the existence of numerous smaller bands on the scale of 2–20 km, mostly near the eyewall. Similar bands have been seen in high-resolution numerical simulations by Yau et al. (2004) and Romine and Wilhelmson (2006). The bands appear to propagate too slowly to be gravity waves, while the vortex Rossby wave theory of Montgomery and Kallenbach (1997) predicts a radial propagation speed of 2.5–3.5 m s−1 for wavenumber 2 disturbances, or less for higher wavenumbers or lower vorticity gradients. However, the bands do appear to be confined to the region with significant vorticity gradient (Fig. 8). Nolan (2005) and Foster (2005) have shown that the Ekman-like boundary layer in a TC is unstable and can produce streamwise rolls on a range of scales; Nolan adds that they may spiral inward, outward, or neither.

The reflectivity in these bands reached reasonably high values (40–45 dBZ), as can be seen in Figs. 4, 5 and 6, but tended to be shallow because the echoes were confined mainly below the freezing level, and essentially there is no component above 10 km.

6. Discussion and conclusions

The most dramatic feature of the cross sections and rainfall in the region of the eye is the persistent asymmetry in the eyewall height and intensity. Interestingly, the maximum eyewall height and rainfall rate were on the ocean side of the vortex center, rather than over land. It may be thought that the increase in surface roughness on the onshore flow would have enhanced the local convergence, and hence rain, on the land side of the islands, but the reverse pattern is evident. A triggering effect of increased surface friction at the coastline for convection can occasionally be seen in some of the rainband structure as the main band rotated across the coastline (cf. Parrish et al. 1982). Another clear feature on the south side is the spinning off of small wavelike rainbands.

This paper represents the first documentation of tropical cyclone microphysical structure with a polarimetric radar. A particular feature is the volume where hail is forming, but not reaching the surface around the eyewall, and in some of the more intense cells of the rainbands. Hail was an indication of strong vertical motions with updrafts greater than about 10 m s−1 near the freezing level in the observations of May and Keenan (2005), so that there are substantial supercooled water droplets. The distribution of maximum updraft speeds in aircraft penetrations of eyewall convection shows the 90th percentile of the distribution of core updraft maxima is less than 10 m s−1 (Lucas et al. 1994), but updrafts with magnitudes greater than 20 m s−1 have been observed on occasion at altitudes near the freezing level (Black et al. 1994; Black et al. 1996). It is interesting to note that the Black et al. (1994) observations were also of a storm with a very asymmetric eye reflectivity structure. There is also an extensive region of wet graupel overlaying the hail. These are consistent with the strong updrafts present in the deep convection and the conceptual model described in Fig. 16 of Black and Hallett (1999), although graupel has been observed coincident with moderate strength updrafts (e.g., Houze et al. 1992).

The outflow from the storm had substantial radar echoes between 10 and 14 km in elevation and was composed mostly of snow with a tendency for either larger or denser crystals with higher reflectivities near the lower parts of the cloud (Fig. 5). This outflow extended well past the eye, at least for a radius of 70 km, and covered part of the eye itself, although the height of the reflectivity contours was a minimum in the eye. The satellite image showed a dense overcast over the whole storm at this time, consistent with the radar images. The eye only cleared after the storm had moved past the islands and was in the open ocean. Some filling of the eyewall, including weak radar echoes as well as in satellite imagery, was observed in both Ingrid and landfalling Hurricane Georges (e.g., Geerts et al. 2000).

Both environmental shear and the presence of a coastline contributed to the asymmetries. The surface frictional forcing was strongly asymmetric, because both the motion and the land–sea contrast gave the strongest forcing on the left (south) of the track. Calculations using a boundary layer model showed that this caused a peak frictionally forced updraft in excess of 6 m s−1 in the western part of the eyewall. This is much stronger than the asymmetry forced by motion alone, and likely made a substantial contribution to the observed cloud and rainfall asymmetries. Further circumstantial evidence for this factor is provided by the storm becoming more symmetric when most of its inner circulation was over the island and a northwest–southeast asymmetry perpendicular to the coast developing as the storm moved off the islands. The maximum rainfall was located offshore as in observations by Chan et al. (2004) and Blackwell (2000).

Soundings from Darwin showed a typical near-cyclone sounding that was almost moist adiabatic with high humidity through its depth and with little CAPE or convective inhibition. The high-speed updrafts implied in the eyewall and in the convective cores of the stationary rainbands appear at odds with the soundings. The available moisture and low CIN also make the weakness of the eye over the islands puzzling, but it appears that enhanced moisture availability over the ocean was a key (e.g., Chan et al. 2004). Another possibility is a delay while the cells developed as they rotated over the land, but there was no clear signature of this around the eyewall.

The right-front convection and rainfall maximum observed here is an extreme case of what has often been observed as storms are making landfall. For example, papers by Blackwell (2000) and Chan et al. (2004), as well as references cited by those papers, document convective maxima to the left or left front of Northern Hemisphere storms as they are making landfall, although models tend not to produce this result. The long lifetime of the asymmetry and the propagation along a coast rather than perpendicular to the coast may make TC Ingrid a good test for models.

Acknowledgments

This work has been partially supported by the U.S. DOE Atmospheric Radiation Measurement (ARM) program. The Worldwide Lightning Location Network lightning data have been supplied by Prof. Holzworth of the University of Washington. The rainfall estimation code was developed during a sabbatical visit of Prof. V. N. Bingi to BMRC, supported by Colorado State University and BMRC.

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Fig. 1.
Fig. 1.

The official best track for TC Ingrid. Note that it was a long-lived storm with several cycles of intensification depending on land influences. The date and pressure tags are at 0000 UTC, and additional pressure estimates at 1200 UTC are shown. This paper focuses on the period from 0200 UTC 13 Mar to 2000 UTC 13 Mar 2005.

Citation: Monthly Weather Review 136, 2; 10.1175/2007MWR2077.1

Fig. 2.
Fig. 2.

A scattergram of the operational rain gauge measurements within the radar-sampling volume against the polarimetric rainfall accumulation estimate. The diagonal line is perfect agreement.

Citation: Monthly Weather Review 136, 2; 10.1175/2007MWR2077.1

Fig. 3.
Fig. 3.

A geostationary satellite IR image of TC Ingrid at 0700 UTC 13 Mar 2005.

Citation: Monthly Weather Review 136, 2; 10.1175/2007MWR2077.1

Fig. 4.
Fig. 4.

Radar reflectivity at an elevation angle of 0.5° at 0730 UTC 13 Mar 2005. The cross section of velocity and reflectivity through the eye (solid line) and the cross section of reflectivity and microphysical classification (dashed line) are shown. The storm center is at approximately (25 km, 100 km). Note the asymmetries of the eyewall and the presence of several rainbands.

Citation: Monthly Weather Review 136, 2; 10.1175/2007MWR2077.1

Fig. 5.
Fig. 5.

The 24-h rainfall accumulations begin at 0000 UTC 13 Mar 2005, along with the storm best track and time of each fix. Note the impact of the storm asymmetry on the rainfall pattern.

Citation: Monthly Weather Review 136, 2; 10.1175/2007MWR2077.1

Fig. 6.
Fig. 6.

(top) A time–height cross section of max reflectivity in the eyewall as a function of height. Contours are drawn every 10 dBZ from 15 dBZ with a heavy contour drawn at 35 dBZ. The temperature heights were taken from the 1100 UTC Darwin sounding, and thus may be biased somewhat low when compared with the eye. (middle) The area greater than 45 dBZ around the eye (solid line) and the time sequence of the maximum reflectivity in the eyewall at 3-km altitude (dashed line). (bottom) The maximum Doppler velocity in the eyewall on the left-hand (west, solid line) and right-hand (east, dashed line) sides.

Citation: Monthly Weather Review 136, 2; 10.1175/2007MWR2077.1

Fig. 7.
Fig. 7.

The quasi-north–south cross section of the radar reflectivity and polarimetric microphysical classification at 0730 UTC along the dashed line in Fig. 4; E marks the center of the eye and R marks rainbands.

Citation: Monthly Weather Review 136, 2; 10.1175/2007MWR2077.1

Fig. 8.
Fig. 8.

The cross section of (top) reflectivity and (bottom) Doppler velocity at 0730 UTC along the solid line marked on Fig. 4. The location of rainbands (R) and the eyewall (EW) are shown on the reflectivity. The Doppler velocity has an overlay of the expected profile for a vortex with an R−1 (light solid line) and R−1/2 (light dotted line) radial dependence and linear variation inside the radius of maximum wind. Distance is in kilometers from the zero isotach.

Citation: Monthly Weather Review 136, 2; 10.1175/2007MWR2077.1

Fig. 9.
Fig. 9.

The modeled flow in the boundary layer of TC Ingrid: (a) radial and (b) azimuthal earth-relative flow at 10 m, and (c) vertical velocity and (d) azimuthal flow at 1.05 km. The land occupies the southern half of the domain, the sea is to the north, and the Southern Hemisphere storm is moving to the left at 3.4 m s−1. Contour intervals are 5 (20) m s−1 for light (heavy) contours for the radial and azimuthal flow and 1 (3) m s−1 for the vertical flow. Darker shading corresponds to outflow, stronger swirling flow, and a stronger updraft, respectively.

Citation: Monthly Weather Review 136, 2; 10.1175/2007MWR2077.1

Fig. 10.
Fig. 10.

Vertical profiles of (a) earth-relative radial wind and (b) earth-relative azimuthal wind components, at the radius of maximum gradient wind in the front of the storm. The heavy profiles are over the land at two grid points (6 km) south of the coast, while the light profiles are downwind of this over the sea at two grid points north of the coast. The change in surface roughness causes the reduced near-surface shear in the oversea profiles, but the near-surface inflow is stronger than that over land because of the mixing down of radial momentum from aloft, which in turn increases the radial advection of angular momentum and helps accelerate the near-surface azimuthal wind.

Citation: Monthly Weather Review 136, 2; 10.1175/2007MWR2077.1

Table 1.

Influence of various factors on the mean and peak updraft strength at 1-km height within 1.5 times the RMW of the modeled storm center.

Table 1.
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