# Inverting COSMIC-2 Phase Data to Bending Angle and Refractivity Profiles Using the Full Spectrum Inversion Method

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## Abstract

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## 1. Introduction

## 2. Data

#### 2.1. COSMIC-2

#### 2.2. ERA5

#### 2.3. Vaisala RS92 Radiosonde

## 3. NOAA STAR RO Data Inversion System Using FSI

#### 3.1. Data Inputs

#### 3.2. Convert L1 Data from Cartesian Earth-Centered Inertial (ECI) Coordinate to Earth-Center Earth-Fixed (ECEF) Coordinate

#### 3.3. Transform the Reference Frame to the Local Center of Earth’s Curvature

#### 3.4. Determine the Signal Truncation Point

#### 3.5. Noise Filtering of the Signal

#### 3.6. Using the FSI Method to Determine L1 and L2 Bending Angles

#### 3.7. Ionosphere Correction and Optimization of Bending Angle

#### 3.8. Quality Control on the Inverted Bending Angles

#### 3.9. Calculation of Refractivity Using Abel Integration

## 4. Assessment of COSMIC-2 Positioning and Excess Phase

#### 4.1. Stability of Satellite Positions

#### 4.2. Quality Assessment of Signal to Noise Ratio (SNR) and Excess Phase

## 5. Assessment of the Quality of the STAR FSI COSMIC-2 Data Products

#### 5.1. Comparison to Radiosonde Observations

#### 5.2. Comparisons to ERA-5

#### 5.3. Comparisons to UCAR Data Products

#### 5.4. Assessment of Penetration Depth

## 6. Discussions and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Daily count of COSMIC-2 RO observations from 16 July–31 October 2019. The count includes data obtained during the provisional data acquisition period.

**Figure 3.**Distribution of COSMIC-2 observations (

**a**) in the region ±45° latitude at 5 × 5° longitude and latitude bins and (

**b**) at local solar times for the region ±30° latitude using observations from 1–31 October 2019.

**Figure 4.**Flow chart depicting the different steps used in the NOAA STAR inversion of geometry and phase data to bending angle and refractivity profiles.

**Figure 5.**An example of the signal truncation scheme used in NOAA STAR processing, (

**a**) SNR of the original/truncated signal in black/red and (

**b**) excess Doppler of the original/truncated signal in black/red.

**Figure 8.**Incremental velocity vectors as a function of time for (

**a**–

**c**) COSMIC-2 and (

**d**–

**f**) GPS for the RO measurements at 00:21 Z on 9 October 2019.

**Figure 10.**COSMIC-2 SNR characteristics: (

**a**) the daily average SNR and (

**b**) frequency distribution of SNR for October 2019.

**Figure 12.**Fractional difference of STAR-RAOB (Vaisala RS92) refractivity for RO and radiosonde data collocated between 1–31 October 2019; (

**a**) mean, (

**b**) standard deviation at different latitude bands, (

**c**) mean, and (

**d**) standard deviation at different SNR ranges. The count of collocated RO-ROAB pairs is shown by thin lines in (

**b**,

**d**).

**Figure 13.**Fractional differences of STAR–ERA5 (

**a**) bending angles and (

**b**) refractivity for data from 1–31 October 2019. The thick red line represents the mean, and the thin lines represent one standard deviation from the mean. Green curves show the number of profiles used for the comparison.

**Figure 14.**Latitudinal distribution of the STAR-ERA5 (

**a**) fractional bending angle, (

**b**) fractional refractivity, STAR–ERA5 (

**c**) fractional bending angle, and (

**d**) fractional refractivity at different SNR values. The thick lines represent the mean values, and the corresponding thin lines represent standard deviation.

**Figure 17.**(

**a**) The probability density function of the penetration depth at 0.1 km height bins, and (

**b**) variations of the penetration depth as a function of SNR at 100 v/v intervals at different latitude ranges. Vertical bars represent the standard error of the mean.

Processing Step | Implementation Approaches |
---|---|

Input data | Input UCAR orbit in Cartesian ECI coordinates, L1 and L2 excess phase, and SNR data |

Coordinate Transform | Transforming ECI coordinates to ECEF Coordinate |

Signal Truncation | Based on L1 SNR, truncating signals using a threshold on calculated base SNR |

Excess Phase Reconstruction | Computation of excess phase after Fourier filtering of Doppler using 0.5-s window |

Bending Angle Computation | Full-Spectrum Inversion |

Ionospheric Correction | Linear combination and statistical optimization of L1 and L2 bending angles |

Quality Control | Mean L1–L2 difference at 25–50 km < 100 μrad, mean fractional bending angle difference (COSMIC2-CIRAQ) at 25–40 km < 0.5 |

Initialization | Exponential fit above 55 km |

Refractivity Calculation | Abel inversion of the ionospheric corrected bending angle with the exponential fit |

**Table 2.**The mean (Standard Deviation) of the RO-ROAB fractional difference and the number of collocated profiles at different latitude bands and SNR ranges.

Latitude Bands | STAR-ROAB | |

Mean (Std. Dev) | Count | |

All | 0.75 (5.33) | 620 |

45°N–30°N | −2.32 (5.00) | 91 |

10°N–30°N | 0.38 (5.59) | 69 |

10°S–10°N | 1.65 (5.15) | 290 |

10°S–30°S | 1.64 (5.35) | 155 |

30°S–45°S | −1.81 (3.76) | 15 |

SNR (v/v) | STAR-ROAB | |

Mean (Std. Dev) | Count | |

<500 | −1.23 (3.20) | 23 |

500–1000 | 0.00 (4.57) | 112 |

1000–1500 | 1.19 (5.58) | 179 |

1500–2000 | 0.59 (5.56) | 237 |

>2000 | 1.35 (4.92) | 69 |

**Table 3.**Bending angle and refractivity fractional difference mean and standard deviation between STAR retrievals with ERA-5 and UCAR retrievals. The standard deviations are given in parenthesis.

0–40 km | 8–40 km | 0–2 km | 2–8 km | |||||
---|---|---|---|---|---|---|---|---|

ERA5 | UCAR | ERA5 | UCAR | ERA5 | UCAR | ERA5 | UCAR | |

Bending Angle | 0.10 (4.67) | 0.33 (3.56) | −0.06 (2.29) | −0.08 (1.41) | −2.39 (18.88) | 3.73 (15.75) | 1.70 (12.63) | 1.25 (10.74) |

Refractivity | −0.06 (2.29) | 0.11 (1.19) | 0.05 (1.14) | 0.01 (0.88) | −0.36 (4.20) | 1.14 (3.45) | 0.37 (2.54) | 0.25 (1.97) |

**Table 4.**The mean and standard deviation (in parenthesis) of the fractional bending angle and refractivity difference between STAR and ERA-5 at different latitude and SNR bands for the 0–2-km height range.

Latitude Bands | STAR-ERA5 | SNR (v/v) | STAR-ERA5 | ||
---|---|---|---|---|---|

Bending Angle | Refractivity | Bending Angle | Refractivity | ||

45°N–45°S | −2.57 (19.02) | −0.33 (4.19) | <500 | −6.14 (16.20) | −1.10 (3.85) |

45°N–30°N | −2.94 (18.66) | −0.49 (4.06) | 500–1000 | −3.56 (17.35) | −0.33 (4.08) |

10°N–30°N | −2.67 (18.72) | −0.36 (4.29) | 1000–1500 | −2.54 (19.07) | −0.21 (4.22) |

10°S–10°N | −2.57 (18.97) | −0.04 (4.38) | 1500–200 | −2.41 (19.17) | −0.41 (4.16) |

10°S–30°S | −2.92 (20.76) | −0.74 (4.28) | 2000–2500 | −1.82 (20.11) | −0.34 (4.29) |

30°S–45°S | −1.56 (15.41) | −0.32 (2.97) | >2500 | −1.85 (20.72) | −0.53 (4.33) |

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**MDPI and ACS Style**

Adhikari, L.; Ho, S.-P.; Zhou, X. Inverting COSMIC-2 Phase Data to Bending Angle and Refractivity Profiles Using the Full Spectrum Inversion Method. *Remote Sens.* **2021**, *13*, 1793.
https://doi.org/10.3390/rs13091793

**AMA Style**

Adhikari L, Ho S-P, Zhou X. Inverting COSMIC-2 Phase Data to Bending Angle and Refractivity Profiles Using the Full Spectrum Inversion Method. *Remote Sensing*. 2021; 13(9):1793.
https://doi.org/10.3390/rs13091793

**Chicago/Turabian Style**

Adhikari, Loknath, Shu-Peng Ho, and Xinjia Zhou. 2021. "Inverting COSMIC-2 Phase Data to Bending Angle and Refractivity Profiles Using the Full Spectrum Inversion Method" *Remote Sensing* 13, no. 9: 1793.
https://doi.org/10.3390/rs13091793