# Algorithms for Doppler Spectral Density Data Quality Control and Merging for the Ka-Band Solid-State Transmitter Cloud Radar

^{1}

^{2}

^{*}

## Abstract

**:**

^{−1}, causing a large negative bias in the reflectivity and radial velocity when large drops were present. In contrast, two rounds of coherent integration affected the reflectivity spectra to a lesser extent. The reflectivity spectra were underestimated for low signal-to-noise ratios in the low-sensitivity mode. Secondly, pulse compression improved the radar sensitivity and air vertical speed observation, whereas the precipitation mode and coherent integration led to an underestimation of the number concentration of big raindrops and an overestimation of the number concentration of small drops. Thirdly, a comparison of the individual spectra with the merged reflectivity spectra showed that the Doppler moments filled in the gaps in the individual spectra during weak cloud periods, reduced the effects of coherent integration and pulse compression in liquid precipitation, mitigated the aliasing of Doppler velocity, and removed the artefacts, yielding a comprehensive and accurate depiction of most of the clouds and precipitation in the vertical column above the radar. The recalculated moments of the Doppler spectra had better quality than those merged from raw data.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data and Instrument Description

_{DR}) in cloud and light precipitation. Meanwhile, it records Doppler spectral density data (SP). Table 1 lists the major technical parameters of the radar. The main purpose of using the solid-state transmitter is to realize continuous measurements, as statistical cloud characteristics are especially important in cloud and precipitation physics.

_{gate}), the range sample volume spacing (R

_{space}), the maximum range (R

_{max}), the minimum range (R

_{min}), the pulse width (τ), the pulse repetition frequency (PRF), the number of coherent integrations (N

_{coh}), the number of incoherent integrations (N

_{ncoh}), the number of fast Fourier transform points (N

_{FFT}), and the radial velocity resolution (ΔV). When applying coherent integration, the maximum range is conversely proportional to PRF. The Nyquist velocity can be expressed as

_{max}and R

_{min}are calculated by

#### 2.2. Methods

#### 2.2.1. QC for Doppler Spectra

- (i)
- Deleting the data below the corresponding minimum range

^{−1}are flagged as non-precipitation echoes.

- (ii)
- Dealiasing singly wrapped aliased Doppler spectral density algorithm based on the three types of spectra

^{−1}and 9.27 m·s

^{−1}, respectively. In the presence of large droplets or strong airflows in convective systems, the Doppler spectra measured by M1 and M2 may be folded. However, the Nyquist velocity for M3 is 18.67 m·s

^{−1}. The fall velocity of rain drops with a diameter of 6 mm at the ground is about 9.4 m·s

^{−1}. Precipitation in a downdraft of 9.27 m·s

^{−1}can cause folded SZ3, which is apparently rare in real clouds and weak precipitation. The key to dealiasing Doppler spectra is to choose a reference radial velocity. The reference commonly used is from the dealiased values at a nearby gate under the assumption that the velocity within the cloud and precipitation is continuous. Errors are caused by either rapid sinking of hydrometeors or a strong updraft in the interior of a convective system. Therefore, a dealiasing algorithm based on Doppler spectra observed by M3 or M2 is proposed. Firstly, SZ3 is iteratively determined based on the folding type, and it is dealiased from the cloud top to base; then, the dealiased SZ3 is used as the reference Doppler velocity to determine the folding type in SZ2 dealiasing when these valid SZ3 observations are obtained in the sample bin. Finally, SZ1 is dealiased using the dealiased SZ3 and SZ2 as references.

- (iii)
- Detecting and removing artefacts produced by pulse compression in SZ2

#### 2.2.2. Merging Algorithms for the Reflectivity Spectra Obtained Using the Three Operational Modes

- 1.
- Principles of merging of the reflectivity spectra

- 2.
- Merging the reflectivity spectra

- (1)
- The data below the defined SNR threshold and all of data below the corresponding minimum range are deleted.
- (2)
- The noise level is determined and all continuous spectral bins above the noise level with an SNR threshold and a bin-number threshold are picked up, as cloud signals typically have higher power and larger spectral width than noise. An objective method presented by Hildebrand and Sekhon is commonly used for millimeter-wave cloud radar studies [18]. However, a recent study argues that this approach can overestimate the radar noise power and, thus, it is not appropriate for solid-state cloud radars. In contrast, a segmental approach reported by Petitdidier et al. can achieve better accuracy and stability [19]. Hence, in this study, simple eight-segment technology was utilized to calculate radar noise level.
- (3)
- For merging the reflectivity spectra from SZ1, SZ2, and SZ3, we individually compare and evaluate the 256 reflectivity spectral bins of SZ1, SZ2, and SZ3, and choose the best bins to compose the newly merged reflectivity spectrum SZm. Aliasing and artefact flags for each spectral bin are used as the criteria to determine the spectra to be used. The amplitudes of the spectral bins are considered a key factor to avoid the influence of coherent integration and low SNR on the merged spectra.

- (4)
- The reflectivity, radial velocity, and spectral width are recalculated from the merged reflectivity spectrum SZm.$$Zm(R)={\displaystyle \sum _{i=1}^{n}SZm(i,R)\Delta V}$$$$Vrm(R)=\frac{{\displaystyle \sum _{i=1}^{n}{V}_{i}\xb7SZm(i,R)\Delta V}}{{\displaystyle \sum _{i=1}^{n}SZm(i,R)\Delta V}}$$$$Swm(R)={\left[\frac{{\displaystyle \sum _{i=1}^{n}{({V}_{i}-Vrm(R))}^{2}\xb7SZm(i,R)\Delta V}}{{\displaystyle \sum _{i=1}^{n}SZm(i,R)\Delta V}}\right]}^{1/2}$$

_{m}, V

_{rm}, and S

_{wm}are the reflectivity, radial velocity, and spectral width, respectively.

## 3. Results

#### 3.1. Doppler Spectral Evaluation and Effects of Observation Parameters in Different Operational Modes

#### 3.1.1. Consistency Analysis of Reflectivity and Velocity for the Three Modes

^{−1}. Below the bright band at 4 km, velocity increased downward. Here, the velocity from the M3 mode was negative because of the falling of precipitation particles. A large proportion of these negative velocities exceeded the M1 Nyquist velocity of 4.67 m·s

^{−1}. Note that the radial velocity obtained from the M1 mode and parts of velocity from M2 were simultaneously positive, indicating that the radial velocity was aliased. Four rounds of coherent integration in M1 resulted in a negative bias of reflectivity below the bright band when the radial velocity exceeded 4 m·s

^{−1}. Two rounds of coherent integration in M2 had no obvious effects on reflectivity measurement. That is, the full of gain of coherent integration was not applicable for Doppler velocity, and a large Doppler velocity led to radar returns that decorrelated rapidly in time.

^{−1}, resulting in alteration of the Doppler spectral shapes. The facts indicate that four rounds of coherent integration not only attenuated reflectivity, but also changed the shape of Doppler spectra in the liquid precipitation region. However, two rounds of coherent integration deployed in M2 yielded full gain and had less of an effect on reflectivity and velocity. Note that CR was operated at PRF = 8333 Hz.

#### 3.1.2. Consistency Analysis of Doppler Spectral Density for the Three Modes

^{5}·m

^{−3}·s) is calculated from the Doppler spectral density SP as follows:

^{−1}were lower than those of SZ2 and SZ3. The parts of the Doppler spectra in liquid hydrometeors below 4.0 km exceeded the maximum velocities of M1 and M2, and were aliased to the left side (Figure 3a,b).

^{−1}. When V > 10 m·s

^{−1}, SZ2 was weaker than SZ3 by 2 dB. For solid hydrometeors, when the Doppler velocity was less than 3 m·s

^{−1}, all three reflectivity spectra were similar. The obvious left shifts of the spectra were probably due to the microscale updraft.

^{−1}for SZ1, SZ2, and SZ3, respectively. If the effects of turbulence on the spectra were negligible, the vertical speeds of air retrieved by SZ1, SZ2, and SZ3 were −1.8, −0.95, and −2.12 m·s

^{−1}, respectively. Positive air vertical velocities are upward. Also, the SZ on the left side was underestimated by M3 for low signal-to-noise ratio (SNR).

^{−1}were attributed to solid hydrometeors, whereas others were attributed to small liquid hydrometeors, because solid hydrometeors and small liquid hydrometeors have small fall velocities and their return power is low. Since the variational patterns of the averaged bias and SZ3 with Doppler velocity are opposite, we deduced that the overestimation of the reflectivity spectra for V < 2.0 m·s

^{−1}by M1 and M2 mainly resulted from the differences in SNR between M1 and M3. Underestimations of the reflectivity spectra for V > 2.0 m·s

^{−1}by M1 and for V > 8.0 m·s

^{−1}by M2 resulted from coherent integration. The underestimations of reflectivity by M1 for liquid precipitation were attributed to the underestimations of spectra with larger Doppler velocities, which also produced biases in the radial velocity and spectral width measurements.

#### 3.1.3. Pulse Compression Effects on SZ2

^{−1}; therefore, the SZ2 for V > 5 m·s

^{−1}was from the range sidelobe for big liquid hydrometeors below 4.0 km. Figure 6b shows the vertical profiles of SZ2 points at 5, 240, and 250 FFT points, and the Doppler velocities for the three FFT points were 9.79, 8.156, and 8.88 m·s

^{−1}, respectively. The SZ2 points had different values between 3.9 and 5.7 km. Figure 3 shows that the Doppler velocity did not exceed 6 m·s

^{−1}above 3.9 km in any spectrum. The three SZ2 points above 3.9 km were range sidelobe artefacts from the hydrometeors below this level. The variations in the SZ points with altitude depended on the number of radar bins of range sidelobes that contributed to the artefacts. For example, only one sidelobe contributed to SZ2 at 5.7 km, whereas 60 sidelobes contributed in the case of SZ2 at 4.2 km. The difference between SZ2 points of the range sidelobe at 5.7 km and the main lobe at 3.9 km was 56 dB; this difference was consistent with fact that the range sidelobe of pulse compression was −60 dB. This difference was 39 dB for SZ2 points between 4.2 km and 3.9 km. The difference between the range sidelobe of SZ2 at 5.7 km and 4.2 km was 17 dB, which was consistent with the gain of 17.7 dB attributed to pulse compression in M2.

#### 3.2. SZ Quality Control and Merging Result

^{−1}≤ V ≤ 8 m·s

^{−1}) and from SZ3 for high (V > 8 m·s

^{−1}) Doppler velocities for liquid precipitation, while SZ1 did not contribute to SZm. In this case, the spectra with large velocity were underestimated. For weak cloud and precipitation below 2.1 km and solid cloud, SZ1 was used to produce SZm.

## 4. Discussion

^{−1}), liquid water content LWC (g·m

^{−3}), total number density Na (m

^{−3}), and average diameter Dm (mm) from the retrieved DSD are calculated as follows:

^{−1}), liquid water content LWC (g·m

^{−3}), total number density Na (m

^{−3}), and average diameter Dm (mm) from the retrieved DSD.

^{−1}in T1, whereas they remained unchanged in T3. Furthermore, in T3, Na, LWC, and R were underestimated, and Dm is overestimated. If the updraft of air motion was neglected, Na, LWC, and R were overestimated, and Dm was underestimated.

^{−1}, respectively, resulting in a leftward shift of SZ1 and SZ3 in T1. Na, LWC, and R from SZ1 and SZ3 were overestimated, and Dm was underestimated in T2. That is, the low-sensitivity modes such as M1 and M3 underestimated V0, resulting in the overestimation of Na, LWC, and R.

_{10}(4)). Similarly, two rounds of coherent integration were performed for the M2 mode, and the pulse compression ratio was 60. Theoretically, the minimum detectable reflectivity could be reduced by 20.8 dB (10.0*log

_{10}(2*60). M1 and M2 underestimated V0 by 0.32 and 1.17 m·s

^{−1}, respectively, due to the extension of the reflectivity spectra and the leftward shift of V0. The leftward shift of V0 increased the corresponding velocity of SZ1 and overestimated the average diameters. M1 also underestimated the reflectivity and SZ1 for larger Doppler velocities, which underestimated the number of larger raindrops. The observation obtained from M1 underestimated Na, LWC, R, and Dm. In the case of S2, Na, LWC, and R were underestimated, and Dm was overestimated (Figure 7c,d).

## 5. Conclusions

- (i)
- In mode M1, four rounds of coherent integration with a PRF of 8333 Hz underestimated the reflectivity spectra for Doppler velocities exceeding 2 m·s
^{−1}. This resulted in a large negative bias in the reflectivity and radial velocity when large drops were present. The reflectivity spectra were underestimated by mode M3 at low SNR. Additionally, two rounds of coherent integration in M2 had less of an effect on the reflectivity spectra. - (ii)
- Pulse compression in M2 improved the radar sensitivity and air vertical speed observation, whereas M3 overestimated V0. This resulted in an underestimation of the number of big drops and an overestimation of the number of small drops. The number of larger drops was underestimated by M1.
- (iii)
- A comparison of the three individual spectra from modes M1, M2, and M3 showed that the merged reflectivity spectra filled in the gaps during weak cloud periods, reduced the effects of coherent integration and pulse compression in liquid precipitation, mitigated the aliasing of Doppler velocity, and removed the artefacts. The range sidelobe produced by pulse compression could be easily removed from the Doppler spectral density data than from the reflectivity data.
- (iv)
- The reflectivity, radial velocity, and spectral width recalculated from the merged reflectivity spectra were immune to the effects of coherent integration and pulse compression, and were consistent for clouds and weak and intermediate precipitation.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Time–height cross-sections of raw reflectivity and radial velocity measurements from (

**a**,

**b**) M1, (

**c**,

**d**) M2, and (

**e**,

**f**) M3 for 500 radar profiles for the period between 4:07 p.m. and 5:21 p.m. Beijing time (BT) on 4 June 2016. The height is given above ground level. The reflectivity below 4.5 km is underestimated by M1 in (

**a**), while the velocities in (

**b**) and (

**d**) are aliased.

**Figure 2.**(

**a**) Reflectivity and (

**b**) dealiased velocity profiles obtained from the three modes for the 30th profile.

**Figure 3.**Reflectivity spectra across different heights for the 30th profile observed by (

**a**) M1, (

**b**) M2, and (

**c**) M3. Positive velocities are downward. The left sides of the spectra are aliased in SZ1 and SZ2. Note that there are different maximum velocities for the three work models.

**Figure 4.**SZ1, SZ2, and SZ3 for (

**a**) liquid hydrometeors at 2.7 km, and (

**b**) solid hydrometeors at 6.6 km. The merged reflectivity and velocity (marked with “Mer”) is also shown.

**Figure 5.**Variations in the averaged bias of the reflectivity spectra with Doppler velocity between SZ1 and SZ3 and between SZ2 and SZ3. The averaged SZ3 is also shown.

**Figure 6.**(

**a**) SZ1, SZ2, and SZ3 for solid hydrometeors at 4.5 km, and (

**b**) vertical profiles of SZ2 points at 5, 240, and 250 fast Fourier transform (FFT) points, produced by the liquid hydrometeor. The Doppler velocities for the three FFT points were 9.79, 8.156, and 8.88 m·s

^{−1}, respectively, which exceeded the fall velocity of the solid hydrometeor.

**Figure 7.**The same data as shown in Figure 3 but for dealiased SZ1, SZ2, and SZ3.

**Figure 9.**Recalculated (

**a**) reflectivity, (

**c**) radial velocity, and (

**e**) spectrum width only after dealiasing. The corresponding results (

**b**), (

**d**), and (

**f**) after dealiasing and artefact removal from SZ2. The biases of velocity and spectral width introduced by range sidelobe artefacts are shown with the red arrows in (

**c**) and (

**e**).

**Figure 10.**Merged (

**a**) reflectivity, (

**b**) velocity, and (

**c**) spectral width from the three moments of Doppler spectra observed using the three models with the previous algorithm.

**Figure 11.**Recalculated (

**a**) reflectivity, (

**b**) radial velocity, and (

**c**) spectral width profiles for modes M1, M2, and M3 and the merged result from SZm for the 30th profile. Note that the spectral width for M2 was calculated before range sidelobe artefacts were removed. The range sidelobe artefacts in M2 are marked by the red arrow. The merged results from SZm are marked as “Mer”.

**Figure 12.**Processed reflectivity spectra (mm

^{−5}·m

^{−3}·s) and retrieved raindrop size distribution (DSD) (m

^{−3}·mm

^{−1}) in (

**a**,

**b**) T1, (

**c**,

**d**) T2, and (

**e**,

**f**) T3.

**Table 1.**Major technical parameters for the Ka-band solid-state transmitter cloud radar. Z—reflectivity, Vr—radial velocity; Sw—spectrum width; L

_{DR}—linear depolarization ratio; SP—Doppler spectral density.

Order | Items | Technical Specifications |
---|---|---|

General technical parameters of the cloud radar system | ||

1 | Radar system | Coherent, pulsed Doppler, solid-state transmitter, pulse compression |

2 | Radar frequency | 33.44 GHz (Ka-band) |

3 | Beam width | 0.35° |

4 | Pulse repeat frequency | 8333 Hz |

5 | Detecting parameters | Z, Vr, Sw, L_{DR}, SP |

6 | Detection capability | ≤−30 dBZ at 5 km |

7 | Range of detection | Height: 0.120–15 km reflectivity: −50 dBZ to +30 dBZ radial velocity: −18.67 m·s ^{−1} to 18.67 m·s^{−1} (maximum)velocity spectrum width: 0 m·s ^{−1} to 4 m·s^{−1} (maximum) |

8 | Spatial and temporal resolutions | Temporal resolution: 3–9 s (adjustable) Height resolution: 30 m |

Order | Items | Boundary Mode (M1) | Cirrus Mode (M2) | Precipitation Mode (M3) |
---|---|---|---|---|

1 | τ | 0.2 μs | 12 μs | 0.2 μs |

2 | PRF | 8333 Hz | 8333 Hz | 8333 Hz |

3 | N_{coh} | 4 | 2 | 1 |

4 | N_{ncoh} | 16 | 32 | 64 |

5 | N_{FFT} | 256 | 256 | 256 |

6 | Dwell time | 2 s | 2 s | 2 s |

7 | Num_{gate} | 256,128 | 512,256 | 512,256 |

8 | R_{space} | 30 m | 30 m | 30 m |

9 | R_{min} | 30 m (theoretical) 120 m (practical) | 1800 m (theoretical) 2010 m (practical) | 30 m (theoretical) 120 m (practical) |

10 | R_{max} | 18 km | 18 km | 18 km |

11 | V_{max} | 4.67 m·s^{−1} | 9.34 m·s^{−1} | 18.67 m·s^{−1} |

12 | ΔV | 0.036 m·s^{−1} | 0.072 m·s^{−1} | 0.145 m·s^{−1} |

_{coh}, number of incoherent integrations N

_{ncoh}, number of fast Fourier transform (FFT) points N

_{FFT}, number of range gates Num

_{gate}, range sample volume spacing R

_{space}, minimum range R

_{min}, maximum range R

_{max}, and radial velocity resolution ΔV.

**Table 3.**Microphysical parameters retrieved in the three experiments. R—rain rate; LWC—liquid water content; Na—total number density; Dm—average diameter.

Work Mode | Experiment | Z (dBZ) | V0 (m·s ^{−1}) | R (mm·h ^{−1}) | LWC (g·m ^{−3}) | Na (m ^{−3}) | Dm (mm) |
---|---|---|---|---|---|---|---|

M1 | T1 | 17.8 | 0.95 | 0.39 | 0.029 | 449 | 1.01 |

T2 | 17.8 | 1.8 | 0.67 | 0.065 | 3144 | 0.67 | |

T3 | 17.8 | 0 | 0.21 | 0.012 | 42 | 1.63 | |

M2 | T1 | 25.6 | 0.95 | 1.33 | 0.07 | 787 | 1.13 |

T2 | 25.6 | 0.95 | 1.33 | 0.07 | 787 | 1.13 | |

T3 | 25.6 | 0 | 0.85 | 0.038 | 96 | 1.8 | |

M3 | T1 | 25.0 | 0.95 | 1.01 | 0.05 | 196 | 1.59 |

T2 | 25.0 | 2.12 | 2.04 | 0.145 | 2629 | 0.94 | |

T3 | 25.0 | 0 | 0.87 | 0.03 | 26 | 2.6 |

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## Share and Cite

**MDPI and ACS Style**

Liu, L.; Zheng, J.
Algorithms for Doppler Spectral Density Data Quality Control and Merging for the Ka-Band Solid-State Transmitter Cloud Radar. *Remote Sens.* **2019**, *11*, 209.
https://doi.org/10.3390/rs11020209

**AMA Style**

Liu L, Zheng J.
Algorithms for Doppler Spectral Density Data Quality Control and Merging for the Ka-Band Solid-State Transmitter Cloud Radar. *Remote Sensing*. 2019; 11(2):209.
https://doi.org/10.3390/rs11020209

**Chicago/Turabian Style**

Liu, Liping, and Jiafeng Zheng.
2019. "Algorithms for Doppler Spectral Density Data Quality Control and Merging for the Ka-Band Solid-State Transmitter Cloud Radar" *Remote Sensing* 11, no. 2: 209.
https://doi.org/10.3390/rs11020209