# Validation of the High-Altitude Wind and Rain Airborne Profiler during the Tampa Bay Rain Experiment

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## Abstract

**:**

## 1. Introduction

## 2. HIWRAP Measurements, Calibration and Geophysical Retrieval Algorithms

#### 2.1. HIWRAP Instrument

#### 2.2. Data Processing

#### 2.2.1. Radar Calibration

#### 2.2.2. Rain Rate Retrieval

_{t}is the transmit power (Watts), G

_{0}is the antenna peak gain (power ratio), $c\tau $ is the pulse volume length (m), $\lambda $ is the wavelength (m), ${\beta}_{\theta}$ and ${\beta}_{\varphi}$ are the antenna pattern half power beamwidths (radians) in the elevation and azimuthal planes, 1024ln(2) is a constant used in approximating the volume, 10

^{18}is the conversion factor between ${\mathrm{m}}^{6}{\text{}\mathrm{m}}^{-3}$ to ${\mathrm{mm}}^{6}{\text{}\mathrm{m}}^{-3}$, and |K|

^{2}= 0.93 is the complex index of refraction for liquid water.

^{b}, where R is the rain rate in $\mathrm{mm}{\mathrm{h}}^{-1}$, and the values of the “a” and “b” coefficients are estimated based on the type of precipitation. Using the calculated reflectivity, the rain rate is then calculated for HIWRAP using Z = 340.56R

^{1.52}from [11], and for NEXRAD using Z = 300R

^{1.4}, which is the default from the NEXRAD meteorological handbook [5].

^{th}range gate (k

_{n}) is calculated according to Ulaby and Long [12] as:

_{n}is the unknown rain rate in ${\mathrm{mm}\text{}\mathrm{h}}^{-1}$, the coefficient k

_{l}is 0.0246 for the inner beam frequency (0.0227 for outer beam) and the exponent b is 1.1485 for the inner beam frequency (1.1515 for outer beam). Thus, by calculating the attenuation for each RG, the PIA, is found as the sum of the two-way path attenuations in dB, as

#### 2.2.3. HIWRAP OVW Retrievals

## 3. HIWRAP Geophysical Retrieval Validation

#### 3.1. Collocated Measurements

#### 3.2. HIWRAP Ocean Wind Vector Validation

#### 3.3. HIWRAP Rain Rate Validation

_{H}/R

_{N}), where R

_{H}is the HIWRAP rain rate and R

_{N}is the corresponding NEXRAD.

#### 3.3.1. HIWRAP and NEXRAD Rain Rate Comparisons at Low Resolution

^{−1}in Figure 9), are presented in Table 1. There are four different sub-categories for HIWRAP rain retrievals (combinations of inner and outer beams and fore and aft-looks), and within each, there are three statistical metrics, namely, average of HIWRAP rain rates, average of NEXRAD rain rates, and averages of rain rate ratios (R

_{H}/R

_{N}).

_{H}/R

_{N}= 0.84 for inner beam and equal 0.63 for outer beam. This minor difference could be related to the geometry differences and possibly in the radar calibration, which will be investigated in future work.

#### 3.3.2. HIWRAP and NEXRAD Rain Rate Comparisons at High Resolution

## 4. Discussion

_{H}/R

_{N}) for four different HIWRAP retrievals (2 beams and fore and aft-looks) ranging between 0.84 (inner beam) and 0.63 (outer beam). On the other hand, when comparing HIWRAP and NEXRAD rain rate vertical profiles at high resolution (500 m), we conclude that HIWRAP rain rate profile measurements are superior to NEXRAD because of the top-down viewing geometry and the excellent RG resolution in altitude.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. HIWRAP Calibration and Rain Retrieval Algorithms

#### Appendix A.1. Airborne Calibration Using the Ocean Normalized Radar Cross-Section ${\sigma}^{o}$

#### Appendix A.1.1. Measured Normalized Radar Cross-Section (${\sigma}^{\mathrm{o}}$)

_{r}in the surface RG as;

_{t}is the transmit power, $\lambda $ is the wavelength, ${\sigma}^{o}$ is the ocean normalized radar cross-section, T is the round-trip time, r is the range, $\tau $ is the integration period (transmit pulse length), $\theta $ and $\varphi $ are spherical coordinates with the Z axis aligned with the line of sight for inner and outer beams, and the differential solid angle is $d\mathsf{\Omega}={\mathrm{r}}^{2}\mathrm{sin}\left(\theta \right)d\theta d\varphi $.

#### Appendix A.1.2. Calibration

_{m}is the average received power (at the antenna output), which is amplified by the receiver gain and digitized at the receiver output. Since the system gain is unknown, we define the calibration factor C to be the dB offset between the input and output of the receiver,

^{o}(at the receiver output) and modeled ${\sigma}_{m}^{o}$ (at the receiver input).

#### Appendix A.2. Single-Frequency Rain Rate Retrieval (SFR3)

_{1}(using the default Z–R relationship with the a = 340.56 and b = 1.52 from [11]) and then using the iterative equation below to solve for the PIA.

#### Divergence Mitigation through Z–R Correction

_{r}measurements were perturbed by Gaussian measurement noise of 1 dB std. Using the simulated backscattered power in RGs, the SFR3 algorithm was run by setting the max threshold values (maxR = 150 ${\mathrm{mm}\text{}\mathrm{h}}^{-1}$ and maxPIA = 30 dB) and a-coefficient increments ($\Delta a$ = 2 and $\alpha $ = 50). The root-mean-square rain rate error for the 3 simulation cases were, respectively, 3.24, 3.41, and −8.67 ${\mathrm{mm}\text{}\mathrm{h}}^{-1}$, which corresponded to a percent error of 17.2%, −13.0%, and −36.6% from the modeled rains. An example of a single trial of the retrieval for the 125 ${\mathrm{mm}\text{}\mathrm{h}}^{-1}$ case can be seen in Figure A1, where the triangle function rain profile is simulated in blue, and the SFR3-retrieved rains are in red.

**Figure A1.**Simulated triangular rain profile with a maximum rain at 125 ${\mathrm{mm}\text{}\mathrm{h}}^{-1}$. The blue is the simulated rain profile, while the red is the retrieved rain rates using the SFR3 algorithm (single random noise trial).

## Appendix B. NEXRAD Spatial Interpolator

#### Appendix B.1. Temporal Alignment

#### Appendix B.2. Ellipsoid Earth Geometry

#### Appendix B.3. Refraction Model

#### Appendix B.4. Trilinear Interpolation of Rain

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**Figure 1.**KTLH-NEXRAD radar reflectivity image, color contoured in 5 dBZ steps, on 16 September 2013 at 0137 UTC, where white lines are the range–azimuth grids in 25 km and 45$\xb0$ steps. The HIWRAP measurement swath is denoted by the “red box”, the locations of two ocean buoys, East and West (black circles), and the corresponding ASCAT measurements coverage in the orange dashed line boundary. The NEXRAD image was produced using the NOAA Weather Climate Toolkit.

**Figure 2.**HIWRAP dual-beam, conical scan patterns on the surface of the earth, and the insert shows the antenna surface footprint (IFOV) dimensions.

**Figure 3.**HIWRAP viewing a selected wind vector cell at 4 different azimuth looks: outer beam fore-look (OB-FL), inner beam fore-look (IB-FL), inner beam aft-look (IB-AL), and outer beam aft-look (OB-AL) as the GH moves from bottom to top.

**Figure 5.**Composite ocean surface wind and rain independent estimates for the TBRE, where the dashed rectangle is the HIWRAP swath, the color-coded grid cells are ASCAT WS (white denotes no data), the red vectors are ASCAT OVW gridded at 25 km, the black-filled circles are NOAA buoys (labeled East and West), and NEXRAD rain reflectivity data are shown in dBZ color contours ranging from 10 to 55 dBZ.

**Figure 6.**Ocean buoy anemometer timeseries during the TBRE. Panel (

**a**) shows the NEXRAD reflectivity image as the atmospheric front passes over the East buoy (top) and West buoy (bottom), and Panel (

**b**) shows the anemometer timeseries of WS and WD from the East (orange) and West (blue) buoys, where the x axis is the relative time since the start of TBRE. The vertical red and blue lines indicate the times when the atmospheric front passes over the East (−1.75 h) and West buoy (+1.25 h), respectively, and the middle (black) line indicates the time (0:00 h) of the GH overflight.

**Figure 8.**ASCAT and HIWRAP wind vectors superimposed on the NEXRAD reflectivity image. The red box indicates the HIWRAP swath, where the wind magnitude and direction change as the aircraft passes over the squall line. Buoys are indicated by large black dots.

**Figure 9.**Rain rate CAPPIs at 4 km altitude gridded in 2 km cubes and in units of dBR for (

**a**) HIWRAP and (

**b**) NEXRAD.

**Figure 10.**NEXRAD and HIWRAP collocated rain rate CAPPI images. Columns L-1, L-2 and L-3 correspond to the altitudes (3.5, 4.5, and 6 km) of the first three layers of the NEXRAD volume scan. Each column contains NEXRAD (top panels (

**a**–

**c**)) and HIWRAP (lower panels (

**d**–

**f**)). The color bar represents rain rate in dBR. The red circles indicate the region of NEXRAD rain rate vertical profile aliasing.

**Figure 11.**HIWRAP and NEXRAD aft looking outer beam vertical rain rate profiles along the aircraft ground track, where rain intensity color bar is in dBR and the red boundary is the minimum detectible height due to surface echo contamination. Panel (

**a**) is HIWRAP, panel (

**b**) is HIWRAP convolved with NEXRAD IFOV, and panel (

**c**) is NEXRAD.

**Figure 12.**Single Beam Profile Comparison, where (

**a**) is the HIWRAP vertical rain rate profiles from the outer beam aft looking, with the selected beam denoted by the magenta line. Panel (

**b**) presents the key measured radar parameters versus RG position, where 270 is the surface RG.

Rain Rate (mm h^{−1}) | Mean | std | Points |
---|---|---|---|

Inner Beam Forward Looking | |||

HIWRAP | 9.39 | 9.93 | 75 |

NEXRAD | 9.60 | 9.35 | 87 |

HIWRAP/NEXRAD | 0.85 | 0.37 | 61 |

Inner Aft Looking | |||

HIWRAP | 9.92 | 11.53 | 75 |

NEXRAD | 9.03 | 9.34 | 87 |

HIWRAP/NEXRAD | 0.82 | 0.26 | 45 |

Outer Beam Forward Looking | |||

HIWRAP | 7.88 | 9.06 | 87 |

NEXRAD | 10.15 | 9.71 | 115 |

HIWRAP/NEXRAD | 0.62 | 0.23 | 78 |

Outer Beam Aft Looking | |||

HIWRAP | 7.57 | 10.10 | 92 |

NEXRAD | 9029 | 9.62 | 116 |

HIWRAP/NEXRAD | 0.63 | 0.22 | 81 |

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**MDPI and ACS Style**

Coto, J.; Jones, W.L.; Heymsfield, G.M.
Validation of the High-Altitude Wind and Rain Airborne Profiler during the Tampa Bay Rain Experiment. *Climate* **2021**, *9*, 89.
https://doi.org/10.3390/cli9060089

**AMA Style**

Coto J, Jones WL, Heymsfield GM.
Validation of the High-Altitude Wind and Rain Airborne Profiler during the Tampa Bay Rain Experiment. *Climate*. 2021; 9(6):89.
https://doi.org/10.3390/cli9060089

**Chicago/Turabian Style**

Coto, Jonathan, W. Linwood Jones, and Gerald M. Heymsfield.
2021. "Validation of the High-Altitude Wind and Rain Airborne Profiler during the Tampa Bay Rain Experiment" *Climate* 9, no. 6: 89.
https://doi.org/10.3390/cli9060089