Quantitative Detection of Dust Storms with the Millimeter Wave Radar in the Taklimakan Desert

In order to conduct real-time quantitative monitoring of dust storms, Ka-band millimeter wave radar (MMWR) was utilized for the consecutive detection of dust storms over the Taklimakan Desert from April to June 2018. The retrievals of the reflectivity factor, dust spectrum distribution and dust mass concentration were carried out with the power spectrum data detected by MMWR for three dust storm processes. The analysis shows that: The probability density distribution of dust conforms to the lognormal distribution. During the dust storm processes, the effective detection height of the reflectivity factor was within 2000 m and the range of the reflectivity factors was between −25 dBZ and 25 dBZ. During the floating dust period, the effective height of the dust spectrum distribution was lower than 300 m and the values of dust mass concentration were less than 31.62 μg·m−3, at a height of 200 m. Furthermore, during the blowing sand stage, the effective height of the dust spectrum distribution was normally lower than 600 m and the values of dust mass concentration were mainly less than 316.23 μg·m−3, at a height of 200 m. During the dust storm period, the effective height of the dust spectrum distribution exceeded 1000 m; when the height was 100 m, the values of dust mass concentration were between 1220 μg·m−3 and 42, 146 μg·m−3 and the average mass concentration was 9287 μg·m−3; whereas, the values of dust mass concentration were between 2 μg·m−3 and 820 μg·m−3 when the height was 1200 m and the average mass concentration was 24 μg·m−3. The relationship between the reflectivity factor Z and the dust mass concentration M is defined as Z = 651.6M0.796. Compared with the observational data from Grimm180 particle detector, the data of the retrieved dust mass concentration are basically accurate and this retrieved method proves to be feasible. Thus, the MMWR cans be used as a new device for quantitative monitoring of dust storms.


Introduction
Dust storms are a disastrous natural phenomenon, which can cause serious damage to human habitats, including breaking down industrial machinery, disrupting traffic, harming vegetation and deteriorating air quality [1][2][3][4][5]. High dust loading in the air due to the dust storms could also impact the solar radiation balance, cloud formation, secondary pollutant generation and marine primary productivity, which has a complex influence on the ecosystem [6][7][8]. The impact of a dust storm is not limited to the source areas but extends to larger regional or even global scales [9,10]. Therefore, the quantitative monitoring of dust storms is of great significance for disaster prevention, environmental protection and sustainable development.

Description of Dust Storm Processes
Three strong dust storms occurred over the Taklimakan Desert from April to June 2018. Based on the differences of the visibility and the ground wind speed during the stages of the dust events (Rashki [36,37]; the regulations of China Meteorological Administration): The weather is a dust storm when the ground wind speed is very large and the visibility is less than 1k m; however, when the ground wind speed is relatively large and the visibility is between 1k m and 10k m, the weather is considered as blowing sand, whereas, during floating dust, the ground wind speed is small and the visibility is between 1k m and 10k m. Table 2 shows the ground observation time for the three dust storm processes. This paper mainly uses the detection data of the three dust storms by the MMWR, the data retrieved by the LPSA and the observational data from Grimm180. Beijing time (BT) is applied in this study and the time of the Figures is displayed from left to right.

Description of Dust Storm Processes
Three strong dust storms occurred over the Taklimakan Desert from April to June 2018. Based on the differences of the visibility and the ground wind speed during the stages of the dust events (Rashki [36,37]; the regulations of China Meteorological Administration): The weather is a dust storm when the ground wind speed is very large and the visibility is less than 1 km; however, when the ground wind speed is relatively large and the visibility is between 1 km and 10 km, the weather is considered as blowing sand, whereas, during floating dust, the ground wind speed is small and the visibility is between 1 km and 10 km. Table 2 shows the ground observation time for the three dust storm processes. This paper mainly uses the detection data of the three dust storms by the MMWR, the data retrieved by the LPSA and the observational data from Grimm180. Beijing time (BT) is applied in this study and the time of the Figures is displayed from left to right.

Method for the Retrieval of Dust Spectrum Distribution
Dust spectrum distribution is the distribution of sand-dust density, varying in terms of different sand-dust particle diameters per unit volume (1 m 3 ). The original data used in this paper is the frequency power spectrum data observed by the MMWR. The retrieval method is illustrated with the example of the power spectrum data (S(f i )) observed by the MMWR at a height of 100 m at 15:40 on 24 May (Figure 2a).

Method for the Retrieval of Dust Spectrum Distribution
Dust spectrum distribution is the distribution of sand-dust density, varying in terms of different sand-dust particle diameters per unit volume (1 m ). The original data used in this paper is the frequency power spectrum data observed by the MMWR. The retrieval method is illustrated with the example of the power spectrum data ( (f )) observed by the MMWR at a height of 100 m at 15:40 on 24 May (Figure 2a).

The Calculation of the Reflectivity Factor
With the radar meteorological equation (Zhang et al. [38]), the reflectivity factors (Z) can be calculated by the following formula.
Where λ is the wave length (8.26 mm), R is the target distance, L is the feeder loss (1.2 dB), is the radar transmitting power (10 w), c is the transmitting speed of the electromagnetic wave (3 × 10 m • s ), τ is the pulse width (2560 μs), G is the antenna gain (40 dB), φ is the horizontal beam width (0.02 rad), θ is the vertical beam width (0.02rad) and is the square of the complex refraction index (0.3). In Equation (1), the represents the echo power received by the radar, which can be calculated with the power spectrum S(f ). The equation is given as:

The Calculation of the Reflectivity Factor
With the radar meteorological equation (Zhang et al. [38]), the reflectivity factors (Z) can be calculated by the following formula.
where λ is the wave length (8.26 mm), R is the target distance, L is the feeder loss (1. In Equation (1), the P r represents the echo power received by the radar, which can be calculated with the power spectrum S(f i ). The equation is given as: where N is the number of FFT (Fast Fourier Transform) points (256), K is Boltzmann constant (1.38 × 10 −23 J/K), B is the receiver bandwidth (4 MHz), T 0 is the radar antenna temperature expressed by absolute temperature (290 K) and N f is the noise factor. By Equations (1) and (2), the reflectivity factor Z can be obtained by utilizing the power spectrum S(f i ). The Z calculated by S(f i ) is 18.97 dBZ in Figure 2.

The Probability Density Distribution of Dust Particles
Firstly, with the LPSA, the particle proportion distributions of the three dust storms are retrieved by analyzing the dust particles collected by the dust collection instruments. Secondly, the particle proportion distributions at the 47 m, 63 m and 80 m heights of the three events are shown in Figure 3. Form the Figure 3, the maximum diameter of dust particles is less than 300 µm and the minimum diameter of dust particles is larger than 0.5 µm in the three events. Hence, the range of particle diameters analyzed in this paper was between 0.5 µm and 300 µm.
where N is the number of FFT (Fast Fourier Transform) points (256), K is Boltzmann constant (1.38 × 10 J/K), B is the receiver bandwidth (4 MHz), T is the radar antenna temperature expressed by absolute temperature (290 K) and N is the noise factor. By Equations (1) and (2), the reflectivity factor Z can be obtained by utilizing the power spectrum S(f ). The Z calculated by S(f ) is 18.97 dBZ in Figure2.

The Probability Density Distribution of Dust Particles
Firstly, with the LPSA, the particle proportion distributions of the three dust storms are retrieved by analyzing the dust particles collected by the dust collection instruments. Secondly, the particle proportion distributions at the 47 m, 63 m and 80 m heights of the three events are shown in Figure 3. Form the Figure 3, the maximum diameter of dust particles is less than 300 μm and the minimum diameter of dust particles is larger than 0.5 μm in the three events. Hence, the range of particle diameters analyzed in this paper was between 0.5 μm and 300 μm. As shown in Figure 3, the particle proportion distributions of the three dust storms basically conform to the lognormal distributions, which are consistent with the results of Dong et al. [39] and Wang et al. [20]. Hence, the probability density function can be shown as: As shown in Figure 3, the particle proportion distributions of the three dust storms basically conform to the lognormal distributions, which are consistent with the results of Dong et al. [39] and Wang et al. [20]. Hence, the probability density function can be shown as: where p(D) is the probability density distribution, D is the particle diameter, σ is the standard deviation and µ is the mean. By the discrete Equation (3), when the particle diameter is D i , the probability p(D i ) can be expressed as: where N stands for the total number of discretization, and ∆D is the resolution of particle diameter. Utilizing the no-linear least square method; the lognormal distributions of the particle proportions retrieved by the LPSA are fitted and shown in Figure 4, where all of R-square coefficients are larger than 0.95.
The statistical data of the mean µ and the standard deviation σ of the fitted lognormal distributions in Figure 4 are shown in Table 3. In Table 3, the µ decreases as the height increases; however, the σ increases with the height increases. At the same height, the values of the µ and those of σ are basically the same, which indicate that the variations of the probability density distributions are very small at the same height in the three dust storms.
Atmosphere 2019, 10, 511 6 of 18 where ( ) is the probability density distribution, D is the particle diameter, is the standard deviation and μ is the mean. By the discrete Equation (3), when the particle diameter is D , the probability p(D )can be expressed as: Where N stands for the total number of discretization, and ∆ is the resolution of particle diameter. Utilizing the no-linear least square method; the lognormal distributions of the particle proportions retrieved by the LPSA are fitted and shown in Figure4, where all of R-square coefficients are larger than 0.95.
The statistical data of the mean μ and the standard deviation σ of the fitted lognormal distributions in Figure 4 are shown in Table 3. In Table 3, theμ decreases as the height increases; however, the σ increases with the height increases. At the same height, the values of the μ and those of σ are basically the same, which indicate that the variations of the probability density distributions are very small at the same height in the three dust storms.  In their study on the distributions of dust particles, Dong et al. [40] pointed out that the variations of the standard deviation σ and the mean μ, with height conform to the exponential distribution. Utilizing the average values of the μ and the σ at the 47 m, 63 m and 80 m heights in Table 3, and the fitted exponential distributions those of theμ and the σ,with height R (mas the unit) are obtained and expressed as: Hence, utilizing Equations (5) and (6), the values of μ and σ of the different heights are obtained. Furthermore, the particle probability distributions of different heights can be obtained by Equations (4)-(6). In Figure 2b, ( )is the particle probability distribution at 100m height.

The Calculation of theDust Spectrum Distribution
During the dust storm period, the echo power received by the radar is mainly triggered by the back-scattering of dust particles. The reflectivity factor Z can be defined by the dust spectrum distribution ( ) as follows (Zhang et al. [38]): Where N is for the total number of discretizations, is the particle diameter and ∆ is the resolution of the particle diameter. The dust spectrum distribution ( )can be described with the particle probability ( ) and the total number of particles as follows:  In their study on the distributions of dust particles, Dong et al. [40] pointed out that the variations of the standard deviation σ and the mean µ, with height conform to the exponential distribution. Utilizing the average values of the µ and the σ at the 47 m, 63 m and 80 m heights in Table 3, and the fitted exponential distributions those of the µ and the σ, with height R (mas the unit) are obtained and expressed as: Hence, utilizing Equations (5) and (6), the values of µ and σ of the different heights are obtained. Furthermore, the particle probability distributions of different heights can be obtained by Equations (4)-(6). In Figure 2b, p(D i ) is the particle probability distribution at 100 m height.

The Calculation of theDust Spectrum Distribution
During the dust storm period, the echo power received by the radar is mainly triggered by the back-scattering of dust particles. The reflectivity factor Z can be defined by the dust spectrum distribution N(D i ) as follows (Zhang et al. [38]): where N is for the total number of discretizations, D i is the particle diameter and ∆D is the resolution of the particle diameter. The dust spectrum distribution N(D i ) can be described with the particle probability p(D i ) and the total number of particles N 0 as follows: Through inserting Equation (8) into Equation (7), the relationship among the reflectivity factor Z, the particle probability p(D i ), the total number-density of particles N 0 and the diameter of the particle D i can be expressed as: Utilizing Equations (8) and (9), the dust spectrum distribution N(D i ) can be calculated by the Z and the p(D i ), as shown in Figure 2c.

The Weather Overview
Since the weather backgrounds of the three dust storms are basically the same, the event on 20 May, 2018 is taken as the example to illustrate the situations. From the 500 hPa geopotential height field at 08:00 on 18 May (Figure 5a), there was a trough in Siberia, behind which there was strong cold air. As time progressed, the trough moved from west to east, further developed and strengthened. By 08:00 on 20 May (Figure 5b), the trough entered the Tazhong area. Affected by the eastward movement of the trough, the ground wind speed gradually increased, which resulted in the occurrence of dust storm in Taklimakan desert. Through inserting Equation (8) into Equation (7), the relationship among the reflectivity factor Z, the particle probability ( ), the total number-density of particles and the diameter of the particle can be expressed as: Utilizing Equations (8) and (9), the dust spectrum distribution ( ) can be calculated by the Z and the ( ), as shown in Figure 2c.

The Weather Overview
Since the weather backgrounds of the three dust storms are basically the same, the event on 20 May, 2018 is taken as the example to illustrate the situations. From the 500 hPa geopotential height field at 08:00 on 18May (Figure 5a), there was a trough in Siberia, behind which there was strong cold air. As time progressed, the trough moved from west to east, further developed and strengthened. By 08:00 on 20 May (Figure 5b), the trough entered the Tazhong area. Affected by the eastward movement of the trough, the ground wind speed gradually increased, which resulted in the occurrence of dust storm in Taklimakan desert.

The Ground Wind Speed
Since the wind is the dynamic condition of dust storms, it is necessary to analyze the ground wind speed. The ground wind speed during the three dust storm processes observed by the Tazhong meteorological station is shown in Figure6. From 08:00 to 09:00, the wind speed was less than 5m/s; as time progressed, the wind speed continuously increased, and a large amount of floating dust appeared in the air when the wind speed was larger than 5m/s. When the wind speed reached 6m/s, the weather was converted into blowing sand, and the wind speed generally was between 6m/s to 8m/s in that period. When the wind speed was greater than 8m/s, the weather turned into a dust

The Ground Wind Speed
Since the wind is the dynamic condition of dust storms, it is necessary to analyze the ground wind speed. The ground wind speed during the three dust storm processes observed by the Tazhong meteorological station is shown in Figure 6. From 08:00 to 09:00, the wind speed was less than 5 m/s; Atmosphere 2019, 10, 511 9 of 18 as time progressed, the wind speed continuously increased, and a large amount of floating dust appeared in the air when the wind speed was larger than 5 m/s. When the wind speed reached 6 m/s, the weather was converted into blowing sand, and the wind speed generally was between 6 m/s to 8 m/s in that period. When the wind speed was greater than 8 m/s, the weather turned into a dust storm; in that period, the wind speed generally was between 9 m/s to 10 m/s, with the maximum wind speed having been larger than 11 m/s (Figure 6b). After the dust storm, the wind speed dropped below 8 m/s. the maximum wind speed having been larger than 11m /s (Figure 6b). After the dust storm, the wind speed dropped below 8m /s.

Reflectivity Factor
Utilizing Equations (1) and (2), the temporal and altitudinal distributions of the reflectivity factors are obtained with the power spectrum data for the three dust storm processes detected by the MMWR, as shown in Figure 7. According to the observation time in Table 2, it is revealed that during the floating dust period, the effective height of the reflectivity factors is normally lower than 300 m, and the reflectivity factors are around 5 dBZ when the height is 100 m. During the blowing dust period, the effective height of the reflectivity factors is normally lower than 600 m, and the reflectivity factors are around 10 dBZ when the height is 100 m. Conversely, during the dust storm period, the effective height of the reflectivity factor is between 1000 m and 2000 m, and the reflectivity factors are larger than 15 dBZ when the height is 100 m.

Reflectivity Factor
Utilizing Equations (1) and (2), the temporal and altitudinal distributions of the reflectivity factors are obtained with the power spectrum data for the three dust storm processes detected by the MMWR, as shown in Figure 7. According to the observation time in Table 2, it is revealed that during the floating dust period, the effective height of the reflectivity factors is normally lower than 300 m, and the reflectivity factors are around 5 dBZ when the height is 100 m. During the blowing dust period, the effective height of the reflectivity factors is normally lower than 600 m, and the reflectivity factors are around 10 dBZ when the height is 100 m. Conversely, during the dust storm period, the effective height of the reflectivity factor is between 1000 m and 2000 m, and the reflectivity factors are larger than 15 dBZ when the height is 100 m. Table 4 shows the distribution ranges and the average values of the reflectivity factors observed at different heights during the dust storm period. As shown in Table 4

The Dust Spectrum Distributions
Firstly, three representative time points (the floating period at 10:00 on 24 May, the blowing sand period at 12:32 on 24 May and the dust storm period at 16:00 on 24 May) were selected for analyzing the characteristics of the dust spectrum distributions. Furthermore, utilizing Equations (8) and (9), the dust spectrum distributions of the three time points were retrieved by the Z and the ( ), as shown in Figure 8. During the floating dust period (Figure 8a), the height of the effective dust spectrum was less than 300 m, and the distribution range of the particle diameters was quite small. During the blowing sand period (Figure 8b), the height of the effective particle spectrum was

The Dust Spectrum Distributions
Firstly, three representative time points (the floating period at 10:00 on 24 May, the blowing sand period at 12:32 on 24 May and the dust storm period at 16:00 on 24 May) were selected for analyzing the characteristics of the dust spectrum distributions. Furthermore, utilizing Equations (8) and (9), the dust spectrum distributions of the three time points were retrieved by the Z and the p(D i ), as shown in Figure 8. During the floating dust period (Figure 8a), the height of the effective dust spectrum was less than 300 m, and the distribution range of the particle diameters was quite small. During the blowing sand period (Figure 8b), the height of the effective particle spectrum was lower than 600 m; when the height was less than 200 m, the range of the particle diameters was 0-300 µm, with the maximum number density of 10 3.5 ; when the height was 300 m, the range of the diameter was 0-150 µm, with the maximum number density of 10 2 ; when the height was 400 m, the range of the diameter was 0-100 µm, with the maximum number density of 10; when the height was higher than 400 m, the diameter was less than 100 µm. During the dust storm period (Figure 8c), the height of the effective particle spectrum was higher than 1000 m; when the height was less than 500 m , the range of the particle diameters was 0-300 µm. , while the maximum number density was larger than 10 3.5 ; when the height was 600 m, the range of the particle diameters was 0-200 µm, with a maximum number density of 10 2 ; when the height was 1000 m, the range of the particle diameters was 0-100 µm, with a maximum number density of 10 1 . Due to the differences of the ground wind speed during three stages of the dust events (V dust storm > V blowing sand > v floating dust ), the number of dust particles (N) blowing in the air varied in the three stages (N dust storm > N blowing sand > N floating dust ), which led to the differences in dust spectrums among floating dust, blowing sand and dust storms. range of the diameter was 0-100 μm, with the maximum number density of 10; when the height was higher than 400 m, the diameter was less than 100 μm. During the dust storm period (Figure8c), the height of the effective particle spectrum was higher than 1000 m; when the height was less than500m , the range of the particle diameters was0-300 μm, while the maximum number density was larger than 10 . ; when the height was 600 m, the range of the particle diameters was 0-200 μm, with a maximum number density of 10 ; when the height was 1000 m, the range of the particle diameters was 0-100 μm, with a maximum number density of 10 . Due to the differences of the ground wind speed during three stages of the dust events ( V V v ), the number of dust particles (N) blowing in the air varied in the three stages (N N N ), which led to the differences in dust spectrums among floating dust, blowing sand and dust storms.

Dust Mass Concentration
Dust mass concentration is the total mass of the dust particles per unit volume (1 m ). Dust mass concentration M can be described by dust spectrum distribution ( ) as follows: where ρ is the dust density (2.65 × 10 kg/m ). From the dust spectrum distributions retrieved by the Z and the ( ), the temporal and altitudinal distributions of the dust mass concentration for the three dust storms were calculated via Equation (10), and shown as Figure 9. Compared to Figure 7, the temporal and altitudinal variations of the dust mass concentration exhibit a good consistency with the variations of the reflectivity

Dust Mass Concentration
Dust mass concentration is the total mass of the dust particles per unit volume (1 m 3 ). Dust mass concentration M can be described by dust spectrum distribution N(D i ) as follows: where ρ is the dust density (2.65 × 10 3 kg/m 3 ). From the dust spectrum distributions retrieved by the Z and the p(D i ), the temporal and altitudinal distributions of the dust mass concentration for the three dust storms were calculated via Equation (10), and shown as Figure 9. Compared to Figure 7, the temporal and altitudinal variations of the dust mass concentration exhibit a good consistency with the variations of the reflectivity factor. During the floating dust period, the effective height of the dust mass concentration was lower than 300 m; moreover, the values of mass concentration were less than 10 1.5 µg·m −3 when the height was 200 m. During the blowing sand period, the effective height of the dust mass concentration was lower than 600 m; furthermore, the values of dust mass concentration were around 10 2.5 µg·m −3 at a height of 200 m, and around 10 1.5 µg·m −3 at a height of 300 m; whereas, if the height exceeded 400 m, the values of mass concentration were less than 10 1 µg·m −3 . During the dust storm period, the effective height of the detected mass concentrations was higher than 1000 m. height was 200 m. During the blowing sand period, the effective height of the dust mass concentration was lower than 600 m; furthermore, the values of dust mass concentration were around 10 . μg · m at a height of 200 m, and around 10 . μg · m at a height of 300 m; whereas, if the height exceeded 400 m, the values of mass concentration were less than 10 μg. m . During the dust storm period, the effective height of the detected mass concentrations was higher than 1000 m. The distribution ranges and the average values of the dust mass concentration at different heights during the dust storm period are shown in Table 5. It is shown that the average value of dust mass concentration decreases as the height increases. Moreover, when the height rises from 100 to 200m , the average value of dust mass concentration drops from 9287 μg · m to 515 μg · m , with a decrease of 8772 μg · m . Furthermore, when the height goes up from 200 to 500 m, the average value of dust mass concentration declines from 515 μg · m to 70 μg · m , with a decrease of 445 μg. m . Whereas, when the height increases from 800m to 1200 m, the average dust mass concentration falls from 36 μg • m to 24 μg • m , with a decrease of 12 μg • m . Hence, the decrease in dust mass concentration weakens as the height increases.  The distribution ranges and the average values of the dust mass concentration at different heights during the dust storm period are shown in Table 5. It is shown that the average value of dust mass concentration decreases as the height increases. Moreover, when the height rises from 100 to 200 m, the average value of dust mass concentration drops from 9287 µg·m −3 to 515 µg·m −3 , with a decrease of 8772 µg·m −3 . Furthermore, when the height goes up from 200 to 500 m, the average value of dust mass concentration declines from 515 µg·m −3 to 70 µg·m −3 , with a decrease of 445 µg·m −3 . Whereas, when the height increases from 800 m to 1200 m, the average dust mass concentration falls from 36 µg·m −3 to 24 µg·m −3 , with a decrease of 12 µg·m −3 . Hence, the decrease in dust mass concentration weakens as the height increases.

Data Comparison
Grimm180 particle detector was used as the tool to supplement the dust storms' observation, so as to verify the accuracy of the dust mass concentrations retrieved by the MMWR.
The Grimm 180 detector was installed at an 80 m height on the flux tower, and consecutive observation was carried out between 14:40 and 16:20 on 20 May, and between 15:29 and 17:20 on 24 May. Figure 10 shows both the temporal variation of the dust mass concentrations with the particle diameters of less than 10 µm (shown as PM10) observed by Grimm 180 and the temporal variation of the dust mass concentration at a height of 80m (shown as TSP) retrieved from the MMWR. During the blowing sand period (16:08-16:20 on 20 May and 17:10-17:20 on 24 May), the real-time values of PM10 were between 1500 µg·m −3 and 4000 µg·m −3 and the real-time values of TSP were mainly between 5500 µg·m −3 and 10, 000 µg·m −3 ; moreover, the values of PM10 TSP (the proportion of the PM10 observed by Grimm180 to the TSP retrieved by MMWR) were generally larger than 30% in the blowing sand, which is consistent with the result of Liu et al. [41]. During the dust storm period (14:40-16:08 on 20 May and 15:30-17:10 on 24 May), the real-time values of PM10 were between 2000 µg·m −3 and 5500 µg·m −3 , and the values of TSP were mainly between 25, 000 µg·m −3 and 40, 000 µg·m −3 . Furthermore, the values of PM10 TSP were mainly between 5% and 13% in dust storms, which are consistent with the proportion distributions observed by the LPSA (Figure 3), also consistent with the PM10 TSP values of, generally, between 5% and 10% for ten dust storms in the Taklimakan Desert (Huo et al. [42]). Hence, it is proven that the values of the dust mass concentration retrieved from MMWR are basically accurate at low altitude.
When the height exceeds 500 m , due to the lack of other dust mass concentration detection data, the values of the dust mass concentration retrieved by MMWR are not verified directly. Using aircraft measurements, Niu et al. [43] and You et al. [44] studied the dust storms in the Tengger Desert and found that the dust mass concentration ranged between 10 µg·m −3 and 400 µg·m −3 when the height was from 1000 m to 2000 m . The dust mass concentration range retrieved by MMWR in this paper is basically consistent with their results. Hence, the values of dust mass concentration retrieved by MMWR are basically credible.

Z-MRelationship
Since both the reflectivity factor Z and the dust mass concentration M can be calculated by the dust spectrum distribution, the temporal and altitudinal variation trend of the reflectivity factor ( Figure 7) is consistent with that of the dust mass concentration (Figure 9). The relationship between the reflectivity factor Z and the dust mass concentration M can be defined as:

Z-MRelationship
Since both the reflectivity factor Z and the dust mass concentration M can be calculated by the dust spectrum distribution, the temporal and altitudinal variation trend of the reflectivity factor (Figure 7) is consistent with that of the dust mass concentration (Figure 9). The relationship between the reflectivity factor Z and the dust mass concentration M can be defined as: where both A and b are constants. Logarithms taken on both sides of Equation (11) results in: With the reflectivity factors Z of the three dust storm processes detected by MMWR and the values of dust mass concentration M (g·m −3 as the unit) retrieved from the dust spectrum distribution, the parameters lgA and b of Equation (12) can be obtained by the least square method. Then, A is acquired by taking lgA's exponent. Then, Equation (11) is as follows: Z = 651.6M 0.796 (13) By utilizing the 200 m height data of the three dust storms, the temporal variations of the dust mass concentration are calculated with the dust spectrum distribution (by Equation (10)) and the reflectivity factor (by Equation (13)), and it is shown in Figure 11. The variation trends of the dust mass concentration calculated by two different methods are consistent with each other, with little difference in the values. Therefore, Equation (13) which stands for the Z-M relationship, is of certain creditability.

Discussions
(1) Since the diameter of dust particles is obviously smaller than that of precipitation, and the complex refractive index of dust particles is smaller than that of precipitation, MMWR with millimeter wavelength is used to detect dust particles more effectively.
(2) Compared with satellite remote sensing and Micro Pulse Lidar, the MMWR is of higher vertical resolution (10m ), as well as temporal resolution (a set of data is generatedper1 min), which enables observations of the reflectivity factors of dust storms in real-time. Based on the retrieved