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  • View in gallery
    Fig. 1.

    NOAA aircraft flight track on 26 Aug 2011 with flight-level wind vectors extending in the downwind direction at 2-min intervals. Hurricane Irene was moving north-northeast and the three circles on the flight track indicate the progression of the eye. The two circles near the coast indicate the locations of the KLTX and KMHX NEXRAD radar sites.

  • View in gallery
    Fig. 2.

    Variation of power returned to the WSRA as the aircraft entered a region of heavy rain.

  • View in gallery
    Fig. 3.

    Convective rainfall attenuation at 16.15 GHz for 15°C (blue) and 25°C (red) ambient temperatures.

  • View in gallery
    Fig. 4.

    (top) Convective and (bottom) stratiform rainfall attenuation at 16.15 GHz for 15°C (blue) and 25°C (red) ambient temperatures.

  • View in gallery
    Fig. 5.

    WSRA rain rate represented by cross-track lines whose width is proportional to rain rate and whose color coding is green < 5 mm h−1 < blue < 15 mm h−1 < red < 25 mm h−1 < black.

  • View in gallery
    Fig. 6.

    (top) Variation of NOAA aircraft distance from KMHX (solid curve) and KLTX (dashed curve), and width of the two-way half-power beam at that distance. (bottom) Aircraft height (thick curve) and vertical extent at the aircraft location of the two-way half-power beam for KMHX (solid) and KLTX (dashed) for the 0.5° antenna elevation angle.

  • View in gallery
    Fig. 7.

    NEXRAD mosaic rain rates for (right) 2222 and (left) 2247 UTC. The color coding (mm h−1) is blue (7.5, 15), green (22.5, 30), red (37.5, 45), and black (52.5, 60). The large red circles near the shoreline indicate the locations of two NEXRAD stations. The NOAA aircraft track during the 5 min before (blue) and after (red) the time of the NEXRAD data.

  • View in gallery
    Fig. 8.

    SFMR surface wind speed (black dots) and the aircraft pitch (blue) and roll (red) as a function of time. Time period represented is 2151–2303 UTC 26 Aug 2011.

  • View in gallery
    Fig. 9.

    Calculated exp(−τa) value decreases with increasing frequency for the rain layer beneath the aircraft at 2.44-km height for the SFMR frequencies (a) 4.74, (b) 5.31, (c) 5.57, (d) 6.02, (e) 6.69, and (f) 7.09 GHz.

  • View in gallery
    Fig. 10.

    Dots indicate WSRA rain rate. Black curve is SFMR rain rate. Colored curves show NEXRAD weighted average rain rates extracted assuming a −3-min time bias (red) and a −2-min time bias (blue) relative to the mosaic time tags. Time period represented is 2151–2303 UTC 26 Aug 2011.

  • View in gallery
    Fig. 11.

    Scatterplots comparing rain-rate values from the WSRA, NEXRAD, and SFMR. Red dots are NEXRAD weighted average rain rates extracted assuming a −3-min time bias relative to the mosaic time tag, and blue dots assume a −2-min time bias. Solid lines are least squares fitted.

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Airborne Rain-Rate Measurement with a Wide-Swath Radar Altimeter

Edward J. WalshProSensing, Inc., Amherst, Massachusetts

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Ivan PopStefanijaProSensing, Inc., Amherst, Massachusetts

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Sergey Y. MatrosovCooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, and Physical Sciences Division, NOAA/Earth System Research Laboratory, Boulder, Colorado

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Jian ZhangNOAA/National Severe Storms Laboratory, Norman, Oklahoma

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Eric UhlhornHurricane Research Division, NOAA/AOML, Miami, Florida

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Brad KlotzHurricane Research Division, NOAA/AOML, Miami, Florida

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Abstract

The NOAA Wide-Swath Radar Altimeter (WSRA) uses 80 narrow beams spread over ±30° in the cross-track direction to generate raster lines of sea surface topography at a 10-Hz rate from which sea surface directional wave spectra are produced. A ±14° subset of the backscattered power data associated with the topography measurements is used to produce independent measurements of rain rate and sea surface mean square slope at 10-s intervals. Theoretical calculations of rain attenuation at the WSRA 16.15-GHz operating frequency using measured drop size distributions for both mostly convective and mostly stratiform rainfall demonstrate that the WSRA absorption technique for rain determination is relatively insensitive to both ambient temperature and the characteristics of the drop size distribution, in contrast to reflectivity techniques. The variation of the sea surface radar reflectivity in the vicinity of a hurricane is reviewed. Fluctuations in the sea surface scattering characteristics caused by changes in wind speed or the rain impinging on the surface cannot contaminate the rain measurement because they are calibrated out using the WSRA measurement of mean square slope. WSRA rain measurements from a NOAA WP-3D hurricane research aircraft off the North Carolina coast in Hurricane Irene on 26 August 2011 are compared with those from the stepped frequency microwave radiometer (SFMR) on the aircraft and the Next Generation Weather Radar (NEXRAD) National Mosaic and Multi-Sensor Quantitative Precipitation Estimation (QPE) system.

Additional affiliation: Physical Sciences Division, NOAA/Earth System Research Laboratory, Boulder, Colorado.

Additional affiliation: Cooperative Institute for Marine and Atmospheric Studies, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida.

Corresponding author address: Ivan PopStefanija, ProSensing, Inc, 107 Sunderland Road, Amherst, MA 01002-1098. E-mail: popstefanija@prosensing.com

Abstract

The NOAA Wide-Swath Radar Altimeter (WSRA) uses 80 narrow beams spread over ±30° in the cross-track direction to generate raster lines of sea surface topography at a 10-Hz rate from which sea surface directional wave spectra are produced. A ±14° subset of the backscattered power data associated with the topography measurements is used to produce independent measurements of rain rate and sea surface mean square slope at 10-s intervals. Theoretical calculations of rain attenuation at the WSRA 16.15-GHz operating frequency using measured drop size distributions for both mostly convective and mostly stratiform rainfall demonstrate that the WSRA absorption technique for rain determination is relatively insensitive to both ambient temperature and the characteristics of the drop size distribution, in contrast to reflectivity techniques. The variation of the sea surface radar reflectivity in the vicinity of a hurricane is reviewed. Fluctuations in the sea surface scattering characteristics caused by changes in wind speed or the rain impinging on the surface cannot contaminate the rain measurement because they are calibrated out using the WSRA measurement of mean square slope. WSRA rain measurements from a NOAA WP-3D hurricane research aircraft off the North Carolina coast in Hurricane Irene on 26 August 2011 are compared with those from the stepped frequency microwave radiometer (SFMR) on the aircraft and the Next Generation Weather Radar (NEXRAD) National Mosaic and Multi-Sensor Quantitative Precipitation Estimation (QPE) system.

Additional affiliation: Physical Sciences Division, NOAA/Earth System Research Laboratory, Boulder, Colorado.

Additional affiliation: Cooperative Institute for Marine and Atmospheric Studies, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida.

Corresponding author address: Ivan PopStefanija, ProSensing, Inc, 107 Sunderland Road, Amherst, MA 01002-1098. E-mail: popstefanija@prosensing.com

1. Introduction

Both National Oceanic and Atmospheric Administration (NOAA) WP-3D hurricane research aircraft have long carried operational instruments that can produce hurricane rainfall estimates [stepped frequency microwave radiometer (SFMR), tail Doppler radar, and lower fuselage radar]. Hurricane rainfall estimates can also be provided by the ground-based Next Generation Weather Radar (NEXRAD) system and the Tropical Rainfall Measuring Mission (TRMM) satellite precipitation radar when the opportunity arises. This paper describes the rain measurement capability of the NOAA Wide-Swath Radar Altimeter (WSRA), recently made operational on one of the NOAA WP-3D aircraft. The WSRA technique is contrasted with some of the other systems and a detailed comparison of WSRA rain estimates is made in Hurricane Irene with estimates from NEXRAD and the SFMR.

Since signals at the WSRA Ku-band 16.15-GHz operating frequency are noticeably attenuated by rain, they can be used for rain-rate R retrievals. Attenuation-based techniques have been previously used with the Ku-band TRMM precipitation radar (Meneghini et al. 2004). Attenuation-based techniques have also been used for retrievals of rainfall, including rainfall associated with hurricanes, using millimeter-wavelength ground-based and spaceborne radars (Matrosov 2005, 2011).

Attenuation-based approaches estimate path-integrated attenuation coefficients α and then relate them to R. These approaches have an advantage over traditional radar methods of rain estimation based on measurements of equivalent reflectivity factor Ze because α–R relations show less variability due to drop size distribution (DSD) details than Ze–R relations.

When the radar wavelength is large compared to the raindrop diameters, such as in the case of the NEXRAD network, then the Rayleigh scattering approximation results in Ze being approximately equal to the theoretical reflectivity factor, Z, calculated as
e1
where D is the diameter of spherical raindrops summed over the drop size distribution within the volume Vc. The rain rate would be
e2
where Δrj is the contribution to rain rate from each raindrop and wj is the fall velocity of each raindrop. Since wj is approximately proportional to the 0.68 power of D, rain rate is proportional to the 3.68 power:
e3

The attenuation coefficient α is, for frequencies between 2.5 and 40 GHz, approximately proportional to a DSD moment typically between 3.5 and 4.5 (Matrosov et al. 2006), which is similar to the moment (3) indicates for R. Since Ze is proportional to a much higher moment [e.g., the sixth DSD moment (1) in the Rayleigh scattering regime], α and R show more consistency than Z and R as DSD varies.

The WSRA technique is similar to that used by the TRMM precipitation radar (PR). Meneghini et al. (2004) describe various techniques to develop a surface reference radar cross section for the PR to use in computing the path-integrated attenuation to determine rain rate. The surface radar cross section for the PR rain-filled beam can be computed by fitting a quadratic curve through rain-free beams to the left and right of that beam at the time of the observation, or using values from the same beam before or after it encountered the rain, or some combination of the cross-track and along-track observations. Since the PR beams are spaced at 4.3 km along the surface, the wind conditions might have been different when beams displaced significantly from the beam in question are used in the process, particularly when the entire 220-km swath is used to generate a hybrid reference curve (Meneghini et al. 2004, their Figs. 4, 5, 7, 8).

Since rain-free beams are used, the PR technique also does not account for possible changes in the radar cross section of the surface within the rain-filled beam caused by the rain impinging on the surface. The WSRA has the distinct advantage that within its 1.2-km swath, it obtains the returns from all incidence angles simultaneously. The sea surface mean square slope (mss) can be calculated from these returns whether it is raining or not. In the presence of rain, the calculated mss includes any rain drop effect. This paper describes the WSRA rain retrieval technique and compares the WSRA rain rates in Hurricane Irene with the National Mosaic and Multi-Sensor Quantitative Precipitation Estimation (QPE) system (Zhang et al. 2011; Lakshmanan et al. 2006) archive product from the NEXRAD network measurements, and with rain-rate estimates from the NOAA SFMR operating at six frequencies (4.74, 5.31, 5.57, 6.02, 6.69, 7.09 GHz) and flown on the same aircraft as the WSRA.

2. WSRA rain measurement technique

The primary function of the WSRA is to document sea surface directional wave spectra. Figure 1 shows the aircraft flight track and flight-level wind vectors in the vicinity of Hurricane Irene as it moved north-northeast on 26 August 2011.

Fig. 1.
Fig. 1.

NOAA aircraft flight track on 26 Aug 2011 with flight-level wind vectors extending in the downwind direction at 2-min intervals. Hurricane Irene was moving north-northeast and the three circles on the flight track indicate the progression of the eye. The two circles near the coast indicate the locations of the KLTX and KMHX NEXRAD radar sites.

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00111.1

The WSRA sequentially transmits a linear-FM chirp waveform spanning 16.075–16.225 GHz on each of the 62 linear strip elements that are parallel to the aircraft centerline. The 62 along-track strips are spaced at half-wavelength (0.93 cm) intervals across the width of the antenna (from left to right across the aircraft frame). Each strip produces a fan beam in the cross-track direction and a narrow 1.36° beam in the along-track direction with amplitude weighting reducing the sidelobes to −25 dB. The 62 return pulses are compressed to provide range information. In the next step, FFT is calculated using the 62 radar range returns padded with 18 zero points, to produce 80 narrow beams over ±30° in the cross-track direction. The synthetized beams have a two-way beamwidth of 1.06° with −18 dB or better sidelobes. Near-nadir adjacent beams are separated by 0.72°.

At a 10-Hz rate, the WSRA determines the range to the sea surface for each of the 80 cross-track positions. The ranges from the 64 beams nearest nadir (generally within about ±23°) are used to generate a map of sea surface topography from which directional wave spectra are produced.

In addition to determining the range to the sea surface, the backscattered power data within ±14° of nadir (generally about 40 beams) are used to produce independent measurements of rain rate and sea surface mss (the small-scale roughness) at 10-s intervals. The normalized radar cross section per unit area σ0 (also called the scattering coefficient) characterizes the ability of a surface to scatter the intercepted energy back toward the radar. Walsh et al. (1998) showed that when the power received by a narrow-beam airborne radar is multiplied by the square of the range to the surface and the cosine of the off-nadir angle, the result is proportional to σ0. The WSRA is not absolutely calibrated in power but such calibration is unnecessary to determine the mss and the rain rate.

To demonstrate the simplicity and robustness of the WSRA rain measurement technique, the variation of the sea surface radar reflectivity in the vicinity of a hurricane will be reviewed. Hurricane large-scale wave fields are complex, frequently containing bimodal and trimodal wave systems, and dominant waves propagating at significant angles to the local wind (Wright et al. 2001; Walsh et al. 2002). The characteristics of the large-scale wave field may affect the amount of small-scale roughness, but not the near-nadir scattering characteristics of the roughness.

In general, the falloff of the sea surface radar cross section with increasing incidence angle is not Gaussian and contains higher-order terms (Walsh et al. 1998, 2008). However, in the quasi-specular scattering regime within 14° of nadir used to calculate mss, it does not matter how the small-scale roughness was generated—by the wind, by breaking waves, by impinging rain, or by straining of the surface by larger waves; the scattering is well represented by the slope-dependent specular point model of radar sea surface scattering and approximated by a geometric optics form (Barrick 1968, 1974; Valenzuela 1978). For an isotropic Gaussian surface,
e4
where here R(0°) is the Fresnel reflection coefficient for normal incidence and θ is the off-nadir incidence angle. The computation is done precisely but, since sec4θ changes by less than 13% between θ = 0° and θ = 14°, the slope of the power falloff is approximately inversely proportional to mss when the logarithm of the backscattered power is plotted versus tan2θ. It is also apparent from (4) that the power backscattered from nadir will be inversely proportional to mss.

Figure 2 shows the variation in power returned to the WSRA over a 50-s interval as the aircraft at 2450-m altitude entered a region of heavy rain in Hurricane Irene on 26 August 2011. Each of the four plots of the relative power variation with incidence angle (from 0° to about 14° off nadir) was derived from nonoverlapping averages of 100 WSRA raster lines of sea surface topography and backscattered power acquired during 10-s intervals. The highest power data (Fig. 2a) can be thought of as derived from raster lines 101–200, when the rain rate was 3 mm h−1; the second highest power data (Fig. 2b) was from lines 301 to 400 as the aircraft was entering the region of heavy rain; the third highest power data (Fig. 2c) was from lines 401 to 500; and the lowest power data (Fig. 2d) was from lines 501 to 600. The peak rain rate was about 30 mm h−1, and the increase to that level occurred in the 5-km distance the aircraft traveled in the 30 s it took to acquire lines 301–600. The 30 mm h−1 rain rate caused the signal returned from nadir to decrease by about 11 dB.

Fig. 2.
Fig. 2.

Variation of power returned to the WSRA as the aircraft entered a region of heavy rain.

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00111.1

The volumes interrogated by the WSRA during each 10-s interval are nonoverlapping and have a square or parallelogram base, depending on the aircraft drift angle, which is about 1.2 km in the cross-track direction and 1.2–1.7 km in the along-track direction, depending on the aircraft ground speed.

The most common deviation from the near-nadir isotropic scattering represented by (4) is having an upwind/downwind asymmetry in the scattering. The asymmetry generally begins to develop when the wind speed exceeds 7 m s−1. As the wind speed increases, the peak of the backscattered power can shift away from nadir, 2° or 3° in the downwind direction (Walsh et al. 2008). The variation of the backscattered power is still generally symmetrical with respect to its peak, so the backscattered power at 14° off nadir in the downwind direction (11° or 12° from the peak) would be significantly higher than 14° off nadir in the upwind direction (17° or 16° from the peak), suggesting too high of an mss in the downwind direction and too low of an mss in the upwind direction.

This effect is largely mitigated by binning the backscattered power for averaging using the absolute off-nadir angle, folding the left side of the swath onto the right side. This also eliminates any effect of a real cross-track gradient in mss caused by wind speed variations as well as mitigating the effect of a cross-track gradient in rain rate.

The least squares fitted straight lines through the 100-line averages of power variation with incidence angle such as those shown in Fig. 2 are used to determine the mss (from the slope) and the nadir power value (from the 0° intercept). The chirped signal the WSRA transmits has a constant amplitude and bandwidth, but the duration of the chirp adjusts with the aircraft altitude to maximize the average transmit power. This power variation is accounted for when the mss and aircraft altitude are used to calculate a nadir power value Pn normalized to a constant altitude (3 km) and mss value (0.04):
e5
where ha is the aircraft altitude and hai (m) is the initial aircraft altitude at the time the chirp duration was established.
The highest value of the normalized power is assumed to represent a rain-free region with any lower value being the result of rain attenuation. The mean attenuation coefficient α (dB km−1) would be
e6
where 0.002 ha is the round-trip distance to the sea surface (km). The path-averaged rain rate is then estimated from the αR relation.

The very large atmospheric volume illuminated by the low-power, long-duration transmitted chirp pulse is not of concern because the essence of the pulse compression technique is that the processed return signal is what would have resulted had the transmission actually been 1 m in range extent corresponding to the 150 MHz of the transmitted bandwidth.

Attenuation estimates from (6) do not account for volume multiple-scattering effects. Such effects can lead to observed reflectivity enhancement when flying over rain, but they are generally negligible at Ku-band frequencies even for larger radar footprints (~4–5 km) unless a significant amount of ice is also present along the radar signal propagation path (Battaglia et al. 2006), which is never the case at the WSRA flight altitude.

Fluctuations in the sea surface scattering characteristics caused by changes in wind speed or rain impinging on the surface cannot contaminate the rain measurement because their effect is contained within the mss measured by the WSRA. The values derived from the four datasets shown in Fig. 2 were (top to bottom) mss = 0.050, 0.047, 0.060, 0.073 and rain rate = 3.0, 10.3, 19.1, 29.5 mm h−1.

The data points shown in Fig. 3 are theoretical calculations of rain attenuation at the WSRA 16.15-GHz operating frequency for 15°C (blue) and 25°C (red) ambient temperatures using measured drop size distributions for mostly convective rainfall observed during the Cirrus Regional Study of Tropical Anvils and Cirrus Layers–Florida-Area Cirrus Experiment (CRYSTAL-FACE) in Florida (Matrosov 2005). The numbers in Table 1 and the curve in Fig. 3 indicate a piecewise linear fit to the data that the WSRA processing uses as the attenuation coefficient for a 20°C average air column temperature beneath the aircraft.

Fig. 3.
Fig. 3.

Convective rainfall attenuation at 16.15 GHz for 15°C (blue) and 25°C (red) ambient temperatures.

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00111.1

Table 1.

Piecewise linear fit used by the WSRA processing for the average attenuation coefficient beneath the aircraft.

Table 1.

The top panel of Fig. 4 is a blowup of Fig. 3 but with the plotting order reversed, blue (15°C) points plotted second instead of the red (25°C) points. Below 10 mm h−1 there is so little difference in attenuation that whichever temperature data are plotted second obscure the first. The bottom panel of Fig. 4 shows the theoretical calculations of rain attenuation using measured drop size distributions for mostly stratiform rainfall observed at Wallops Island, Virginia, during winter/spring 2001 (Matrosov 2005). The piecewise linear curve is the same one fit to the convective data points of Fig. 3 and the top panel of Fig. 4, demonstrating that the attenuation at the WSRA operating frequency is relatively insensitive to both temperature and type of precipitation.

Fig. 4.
Fig. 4.

(top) Convective and (bottom) stratiform rainfall attenuation at 16.15 GHz for 15°C (blue) and 25°C (red) ambient temperatures.

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00111.1

Figure 5 shows in a storm-relative coordinate system, the WSRA rain-rate measurements that were close enough to the North Carolina shoreline to compare with NEXRAD rain-rate measurements. The rapid increase in rain rate shown in Fig. 2 occurred as the aircraft flew toward the southwest about 95 km west and 170 km north of the eye.

Fig. 5.
Fig. 5.

WSRA rain rate represented by cross-track lines whose width is proportional to rain rate and whose color coding is green < 5 mm h−1 < blue < 15 mm h−1 < red < 25 mm h−1 < black.

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00111.1

3. NEXRAD rain measurement technique

The NEXRAD rain-rate data from the QPE system (Zhang et al. 2011; Lakshmanan et al. 2006) uses the latest radar volume scans within a 15-min time window, but mostly within the 5 min prior to the time tag when the radars are operating in the precipitation scan modes. After the individual NEXRAD radar volume scan reflectivity data are quality controlled to remove nonprecipitation echoes, the lowest elevation angle data without significant blockages are mosaicked to produce a two-dimensional Cartesian base reflectivity field. Then a Z–R relationship for the precipitation type determined from environmental and radar data is applied at each Cartesian grid pixel (0.01° in both latitude and longitude) to produce a precipitation rate.

During the 26 August 2011 time period of interest, the stratiform Z–R relation (Z = 200R1.6) had originally been used to generate the NEXRAD rain rates in the mosaic archive, which updated at integer 5-min intervals. When the initial comparisons were made, those NEXRAD rain rates were about a factor of 2 lower than the WSRA rain rates. Using the stratiform Z–R relation would reduce the rain rate by about a factor of 2 relative to using the tropical NEXRAD Z–R relation (Z = 250R1.2) if the precipitation had actually been tropical in nature in the 10–40 mm h−1 range.

It is understandable that there could be some uncertainty as to which Z–R relation to use in the case of NEXRAD stations near the coast, where half of their field of view is over land. Since the tropical Z–R relation would be better justified physically than the stratiform for the overwater region of Hurricane Irene under consideration, the NEXRAD stratiform rain rates from the archive, Rs, were converted to tropical rain rates, Rt, by equating the reflectivity from the stratiform and tropical Z–R relations, that is,
e7
Because the contour plots of the NEXRAD rain rate were difficult to use due to large point-to-point fluctuations, the values were smoothed with uniform weighting over 3 × 3 points of the 0.01° spatial resolution in both latitude and longitude.

The two NEXRAD radars closest to the NOAA aircraft flight path were the North Carolina cities Wilmington (KLTX; 33.98°N, 78.43°W) and Morehead City (KMHX; 34.78°N, 76.88°W). The transmit frequencies in use at KLTX and KMHX were 2.755 and 2.77 GHz, respectively, which result in a half-power beamwidth of 0.94° at each facility and a two-way half-power beamwidth of about 0.66°.

There are nine NEXRAD volume coverage patterns (VCP) available, each being a predefined set of instructions controlling antenna rotation speed, transmit/receive mode, and elevation angles. The scan pattern in use during the comparison time interval was VCP212, which is typically used for widespread severe convective events. The antenna elevation angle is sequenced through 14 values (0.5°, 0.9°, 1.3°, 1.8°, 2.4°, 3.1°, …, 19.5°) in about 4.5 min. However, only the 0.5° elevation data, acquired within the first 17–38 s, depending on range, are used for rain-rate retrievals.

The NOAA aircraft autopilot is generally set to maintain a constant barometric altitude while executing its flight pattern in the vicinity of a hurricane. During the flight into Hurricane Irene on 26 August 2011, the actual aircraft altitude varied between about 2500 m at 300 km from the eye to a little over 2000 m in the eye as a result of the variation of barometric pressure in the hurricane. The average air temperature at the aircraft altitude in the vicinity of the storm was about 16°C. The temperature at the surface was about 30°C and decreased to 9°C at the 3.5-km transit altitude of the aircraft, indicating a lapse rate of 6°C km−1 and 5-km height for 0°C.

In the top panel of Fig. 6, the left scale shows the variation over the comparison time interval of the NOAA aircraft distance from KMHX (solid curve) and KLTX (dashed curve) and the right scale shows the width of the two-way half-power beam at that distance. In the bottom panel, the thick curve shows the aircraft height and the thin curves indicate, including the effects of earth curvature and refraction, the vertical extent of the two-way half-power beam for KMHX (solid) and KLTX (dashed) for the antenna elevation angle of 0.5°. The data shown in this figure were calculated using approaches from Doviak and Zrnić (1993).

Fig. 6.
Fig. 6.

(top) Variation of NOAA aircraft distance from KMHX (solid curve) and KLTX (dashed curve), and width of the two-way half-power beam at that distance. (bottom) Aircraft height (thick curve) and vertical extent at the aircraft location of the two-way half-power beam for KMHX (solid) and KLTX (dashed) for the 0.5° antenna elevation angle.

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00111.1

Although the update times of the archive mosaic were exactly integer 5-min intervals, the update intervals of KLTX and KMHX were approximately 4 min 36 s and 4 min 40 s, respectively—not in sync with each other or with the mosaic update times. An entire scan pattern does not have to be completed before the lower elevation angle observations are processed. The data transfer and processing time is difficult to quantify, since it depends on the size of the data files, which depend on how much rain is in the data. It usually takes at least 1 min to get observations into the system.

The aircraft data were registered to the NEXRAD rain-rate mosaics, assuming the mosaics were “instantaneous” snapshots of the geographical distribution of the rain. Completing the 0.5° elevation scan within 17–38 s, depending on the range, would approximate that compared to a 5-min mosaic update interval. The snapshot was assumed to be offset a fixed time interval prior to the time tag of the NEXRAD mosaic.

The WSRA rain rates were compared with NEXRAD assuming offsets of the NEXRAD data relative to the time tag of the mosaics of −1 through −5 min in half-minute increments. The highest overall correlation occurred for an offset time of −3 min and that is the offset assumed in Fig. 7.

Fig. 7.
Fig. 7.

NEXRAD mosaic rain rates for (right) 2222 and (left) 2247 UTC. The color coding (mm h−1) is blue (7.5, 15), green (22.5, 30), red (37.5, 45), and black (52.5, 60). The large red circles near the shoreline indicate the locations of two NEXRAD stations. The NOAA aircraft track during the 5 min before (blue) and after (red) the time of the NEXRAD data.

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00111.1

Figure 7 is a time composite with the region to the right of the dashed line showing the NEXRAD rain-rate map for the 2222 UTC snapshot, and the region to the left showing the rain-rate for the 2247 UTC snapshot. The two red circles indicate the locations of the KLTX and KMHX NEXRAD radars.

There are some additional uncertainties other than the time offset in trying to extract the rain rate along the aircraft flight track from the NEXRAD mosaic data. The blue lines indicate the aircraft tracks during the 5 min prior to the snapshot time of that NEXRAD mosaic. The red lines indicate the aircraft track during the 5 min after the snapshot time of that mosaic.

These particular aircraft tracks provide good examples of the aircraft diverting its flight path to avoid the heaviest rain rates, which are generally associated with the greatest turbulence. Because the aircraft sometimes passes close to heavy rain rates, the cross-track rain-rate gradient can be large and result in significant changes in the NEXRAD rain rate extracted due to small time or position errors.

The blue and red lines indicate the effective position of the aircraft within the NEXRAD rain-rate map rather than its actual geographical path. If each mosaic is an instantaneous snapshot, then only the aircraft location at the time of that snapshot corresponds to the same latitude and longitude within the mosaic. Other aircraft positions need to be shifted either downwind or upwind within the mosaic depending on whether their time was before or after the snapshot time. The magnitude of the shift depends on the time difference and the wind speed at the aircraft altitude.

For each time along the aircraft flight track, there will be pairs of NEXRAD rain-rate values from sequential mosaics, such as 2 min after the snapshot time of one mosaic and 3 min prior to the snapshot time of the next mosaic. Those two sets of rain-rate values were combined in a weighted average:
e8
where RN is the NEXRAD weighted average for a particular time of interest; RNb and RNa are the NEXRAD rain rates at the extrapolated aircraft locations within the mosaics before and after that time, respectively; and s is the seconds past the snapshot time of the mosaic preceding the time of interest.

The comparison in Hurricane Irene will be deferred until after the SFMR rain measurement technique is discussed.

4. SFMR rain measurement technique

The Jiang et al. (2006) validation of the SFMR rain-rate estimation in hurricanes used data from an SFMR built in 1994 under the NOAA/Office of the Federal Coordinator for Meteorology’s Improved Weather Reconnaissance System program. It used frequency channels 4.55, 5.06, 5.64, 6.34, 6.96, and 7.22 GHz with an 18-in. antenna that was mounted below the fuselage on the center line of the aircraft. The Hurricane Irene data in the present analysis were acquired with a newer design, first put in service in 2002, using a 9-in. antenna installed in a wing pod. The frequencies of the new SFMR (4.74, 5.31, 5.57, 6.02, 6.69, 7.09 GHz) were shifted somewhat from those of the earlier design to minimize the standing wave ratio with the new antenna.

For rain rates less than 40 mm h−1, there is little difference between the attenuation and absorption coefficients at the SFMR frequencies and the terms will be used interchangeably. Appendix A of Uhlhorn and Black (2003) described the complex SFMR algorithm in detail. At its six frequencies, the SFMR measures the brightness temperature of the scene below the aircraft, which has frequency-dependent contributions from both the emissive and reflective properties of the ocean, and the emissive and absorptive properties of rain and the atmosphere.

Uhlhorn and Black (2003) indicated that the sensitivity of brightness temperature to changes in rain rate becomes so weak that a determination is not possible for values below 5 mm h−1. Similarly, the sensitivity of brightness temperature to changes in wind speed becomes so weak that a solution is not possible for wind speeds less than 10 m s−1.

Operationally, a least squares inversion method is applied to the six brightness temperatures to determine surface wind speed and rain rate. However, a simplified expression (9) can provide an intuitive sense of the various contributions to the nadir-viewing SFMR brightness temperature when rain is present. It disregards the small cosmic radiation contribution, volume scatter, and the absorption/emission due to cloud and atmospheric gases, which can be neglected in the presence of significant rain at the SFMR frequencies,
e9
where all temperatures are in kelvins and TB(ha) is the brightness temperature measured by the down-looking SFMR at the aircraft height ha.

The first term on the right side of (9) is composed of ε, which is the sea surface emissivity; Ts is the sea surface temperature; and exp(−τa) is the transmissive property of the rain. The term τa is the optical thickness of the rain layer computed by integrating the rain attenuation coefficient over the distance between the surface and the aircraft, and τa = αa ha, where αa is the average attenuation coefficient for the rain layer below the aircraft.

In the second term in (9), T1 is the effective emitting temperature for the layer between the surface and the aircraft, and [1 – exp(−τa)] is the emissivity of the rain over that path. In the third term, (1 − ε) is the sea surface reflection coefficient; T2 is the effective emitting temperature of the entire precipitation layer; and [1 – exp(−τ)] is the emissivity of that layer whose optical thickness is τ = αh, where α is the effective absorption coefficient for the entire rain layer, whose thickness is h. A reasonable assumption for T1 and T2 would be the mean temperatures in those respective layers.

The aircraft height during the intercomparison time period ranged from 2.3 to 2.53 km with an average value of 2.44 km. During this time frame, the SFMR surface wind speed generally averaged about 0.8 times the wind speed at the aircraft altitude. The black dots in Fig. 8 show the SFMR wind speed during the intercomparison interval. There are anomalies in the SFMR wind speed due to land contamination in the vicinity of 22.36 and 22.48 as the aircraft passed by Cape Lookout, North Carolina, flying northeast and then flew over it after turning toward the west. It is apparent that the large roll attitudes in the vicinity of 22.43, 22.575, and 23.03 also caused erroneous wind speed values. However, in general the surface wind speed was about 26 ± 4 m s−1. Uhlhorn and Black (2003) indicated that the excess surface emissivity for that wind speed, with some minor frequency dependence, would be about 0.05 above the typical specular emissivity of about 0.35.

Fig. 8.
Fig. 8.

SFMR surface wind speed (black dots) and the aircraft pitch (blue) and roll (red) as a function of time. Time period represented is 2151–2303 UTC 26 Aug 2011.

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00111.1

If f is the frequency, R is the rain rate, and expo = 2.6 × R0.0736, then the long-standing relationship in use for SFMR retrievals during the Hurricane Irene flight was
e10
Uhlhorn et al. (2007) pointed out that when (10) was discussed in Uhlhorn and Black (2003, Appendix A, p. 113), the exponent of R was mistakenly presented as 1.35.
Figure 9 shows the calculated exp(−τa) for the rain layer beneath the aircraft at 2.44-km height for the SFMR frequencies and various rain rates. The equations below, (11a) and (11b), substitute specific numbers from (10) and from Uhlhorn and Black (2003, Fig. A2) into (9) to put the various contributions in perspective for a wind speed of about 26 m s−1 and 30 mm h−1 rain rate for the lowest and highest SFMR frequencies, respectively, used in Hurricane Irene on 26 August 2011:
e11a
e11b
Fig. 9.
Fig. 9.

Calculated exp(−τa) value decreases with increasing frequency for the rain layer beneath the aircraft at 2.44-km height for the SFMR frequencies (a) 4.74, (b) 5.31, (c) 5.57, (d) 6.02, (e) 6.69, and (f) 7.09 GHz.

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00111.1

The emission from the sea surface attenuated by the rain (first term) produces a 9.7-K decrease in the brightness temperature (114.0 – 104.3 K) with the increase in frequency. But the emission from the rain itself produces a 53.9-K increase in the brightness temperature with the increase in frequency, resulting in a net increase of 44.2 K. This increase in brightness temperature spread caused by the emission properties of the rain is the main characteristic of its presence (Uhlhorn and Black 2003, Fig. 12).

5. Rain-rate comparison and discussion

Figure 10 shows the WSRA, SFMR, and NEXRAD estimates of rain rate. The dots indicate the WSRA rain-rate values. The WSRA produces estimates of rain rate from nonoverlapping datasets every 10 s. The SFMR produces rain-rate estimates (thin black line) once a second, but they are computed from data acquired over the previous 10 s, so the temporal resolutions are comparable. The NEXRAD weighted average rain rates were extracted assuming a −3-min time bias (red) relative to the NEXRAD mosaic time tags, which produced the best overall agreement with the WSRA, and a −2 min time bias (blue) to indicate the sensitivity of the result to the time bias.

Fig. 10.
Fig. 10.

Dots indicate WSRA rain rate. Black curve is SFMR rain rate. Colored curves show NEXRAD weighted average rain rates extracted assuming a −3-min time bias (red) and a −2-min time bias (blue) relative to the mosaic time tags. Time period represented is 2151–2303 UTC 26 Aug 2011.

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00111.1

WSRA data gaps occur when the aircraft roll is large (22.43, 22.575, and 23.03) or the range window has to be adjusted due to altitude changes. The WSRA data during the Cape Lookout land contamination time intervals (22.36 and 22.48) were deleted.

Figure 11 shows scatterplots comparing the rain-rate values from the WSRA, NEXRAD, and SFMR. The dashed lines indicate perfect agreement. The red dots are the NEXRAD rain rates assuming a −3-min time bias relative to the NEXRAD mosaic time tags, and the blue dots are for a −2-min time bias. The red and blue lines were least squares fitted using those respective datasets.

Fig. 11.
Fig. 11.

Scatterplots comparing rain-rate values from the WSRA, NEXRAD, and SFMR. Red dots are NEXRAD weighted average rain rates extracted assuming a −3-min time bias relative to the mosaic time tag, and blue dots assume a −2-min time bias. Solid lines are least squares fitted.

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00111.1

In the top panel, the red line (for the time bias that resulted in the best overall agreement) had a y intercept of 0.104 and a slope of 0.964. The blue line had a higher intercept (1.046) and a lower slope (0.852).

In the middle panel, the fitted line intercepts are significantly larger (5.204, 6.055) and the slopes significantly lower (0.686, 0.593). In the bottom panel, the line fitted to the WSRA data has a y intercept of 5.495 and a slope of 0.659, both of which lie between the values for the lines fitted to the NEXRAD data in the middle panel.

The middle and bottom panels indicate that, compared to both NEXRAD and the WSRA, the SFMR is biased low for rain rates above 20 mm h−1 and biased high for rain rates below 15 mm h−1. The SFMR high bias at low rain rates might be attributable to the reduced sensitivity of the SFMR.

If the WSRA and SFMR rain-rate trends had been similar but disagreed with the NEXRAD, then the discrepancy might have been attributed to the significant differences in the volumes interrogated by NEXRAD and the aircraft sensors. But the WSRA and SFMR simultaneously interrogate almost the same atmospheric volume. Over the 10-s averaging times of both systems, the aircraft typically advances about 1.2–1.7 km, depending on the wind vector. The WSRA rain-rate determination used data within ±14° of nadir for a swath width of about 1.2 km. The nadir-looking SFMR antenna has a half-power beamwidth that varies from 13° to 20° over the six frequencies, so its swath is narrower than that of the WSRA. The smaller volume interrogated by the SFMR might be expected to produce greater variability at higher rain rates because they tend to be more localized, but not the low bias observed.

It has been recognized that the absorption coefficient values produced by the present SFMR algorithm (10) are too large. There is a NOAA Joint Hurricane Testbed project (Uhlhorn and Klotz 2012) in progress to improve the SFMR absorption coefficient algorithm as well as the significant high bias in surface wind retrievals during strong precipitation with winds below hurricane force.

Attenuation coefficients were computed for the lowest and highest SFMR frequencies using drop size distributions measured in Florida, which were for mostly convective rain (Matrosov 2005). At 30 mm h−1, the attenuation coefficients computed from the drop size distributions were about half of the SFMR values produced by (10). Using the smaller attenuation coefficients in (9), (12a) and (12b) show the results a 26 m s−1 wind speed and a 30 mm h−1 rain rate, respectively:
e12a
e12b

Therefore (12a) and (12b) indicate that the actual spread in SFMR brightness temperature caused by a 30 mm h−1 rain rate would be about 31.2 K. Since the too-large attenuation coefficients (10) of the present SFMR algorithm predicted a spread of 44.2 K [(11a) and (11b)], the SFMR algorithm would interpret the smaller observed brightness temperature spread as a rain rate less than 30 mm h−1, resulting in the SFMR low bias observed in Fig. 11.

In addition to the difference in attenuation coefficients, 5 km was used for the rain height in (12a) and (12b) instead of the 4 km used in (11a) and (11b). The present SFMR retrieval algorithm uses a fixed value of 4 km for the rain height. The difference between the actual rain height and the fixed value presently used is another source of error in the SFMR-retrieved rain-rate estimates observed at subhurricane wind speeds. A study is underway to mitigate the effect of variation in the actual rain height, using an up-looking SFMR installed on one of the NOAA hurricane research aircraft to directly measure the total emissivity of the rain above the aircraft (Goodberlet and PopStefanija 2013).

The WSRA rain measurement technique is the most simple of the three considered. The WSRA direct measurement of the transmitted signal attenuation by rain is much less complex than the SFMR technique. At the WSRA operating frequency, theoretical calculations of rain attenuation using measured drop size distributions indicate that there is little difference in the attenuation caused by convective and stratiform rain—that is in sharp contrast to the NEXRAD radar backscatter technique, where the ZR relationship selected can change the result by a factor of 2.

The only thing affecting the WSRA signal in addition to the round-trip attenuation by rain is the reflectivity of the sea surface. Since variation in the sea surface reflectivity is determined by the sea surface mean square slope, which is measured by the WSRA, it cannot degrade the accuracy of the rain measurement.

The attenuation coefficient at the WSRA frequency (16.15 GHz) is more than an order of magnitude greater than at the SFMR frequencies, making it sensitive to even light rain rates. The downside is that a rain rate of 40 mm h−1 attenuates the WSRA signal too much and seriously degrades the performance at the typical 2450-m aircraft altitude. Alternatively, if the aircraft flew at 1500 m, then it would require a rain rate of about 69 mm h−1 to cause the same degradation as 40 mm h−1 at the 2450-m altitude.

Both the WSRA and the SFMR have two disadvantages compared to NEXRAD. First, these airborne nadir-looking systems only measure the rain at the aircraft location. Since the area interrogated is approximately indicated by the flight line width in Fig. 7, they cannot produce area maps of rainfall. Second, their measurements are not generally statistically representative of the overall hurricane rainfall, since the aircraft generally avoids the regions of greatest rain rate.

Acknowledgments

The authors thank the NOAA Aircraft Operations Center personnel and flight crew and the NOAA/AOML/Hurricane Research Division scientists, with special thanks to Shirley Murillo, the 2011 HFP Field Program Director, who added the near-shore leg to the flight pattern that made the NEXRAD comparison possible. S. Y. Matrosov acknowledges support from NASA Grant NNX13AQ31G.

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