Solutions for Improving the Radar Refractivity Measurement by Taking Operational Constraints into Account (2024)

a. Refractivity measurement

This was initially developed for coherent radars, which operate at a constant frequency. However, most radar networks are composed of noncoherent radars, for which the frequency can drift with time. Parent du Châtelet et al. (2012, 2007) and Parent du Châtelet and Boudjabi (2008) have demonstrated that the correction to take into account the frequency variation mainly depends on the well-known local oscillator frequency and not on the transmitter frequency. After correction, refractivity is then obtained by a simple integration of δφ with time.

The sampling time of underlying refractivity field, generally 5 min, is determined by the operational mode of the radar. The main issue with this measurement is aliasing problems when the time becomes too long to correctly sample the signal, which in this case is undersampled. These aliasing problems have been studied by Besson et al. (2012), who showed that it depends on the range integration, the sampling time between two measurements, and the radar frequency (it is perceptible in the S band, serious in the C band, and even more serious in the X band). The radar frequency and the range integration are fixed, thus the only way to reduce the aliasing rate consists in decreasing the sampling time.

b. Radar data

The work presented here uses different radar datasets, all obtained with the S-band radar at Nîmes in the south of France and the C-band radar at Trappes (~30 km west of Paris). These two Doppler dual-polarization radars are part of the Météo France radar network ARAMIS.

Three different datasets have been used:

1. a 3-h experiment (1300–1600 UTC 1 August 2011) with the Trappes radar using a 0.4° elevation to test the effect of the rotation speed of the antenna (from 6° to 24° s⁻¹);

2. a 24-h experiment (1400 UTC 20 September–1400 UTC 21 September 2011) with the Nîmes radar using a 0.6° elevation to test the sampling time and the effect of the transmitted pulse length (1 and 2 μs; the antenna rotation speed was 11° s⁻¹);

3. a 24-h experiment (22 February 2012) with the Trappes radar to test the feasibility of refractivity measurements using two different interlaced elevations (i.e., 0.4° and 0.8°).

It is important to note that, in the present work, signal power is not corrected from the 1/r² range effect. The power is given in decibels and not in decibels of reflectivity, the noise level is about 4 dB, and the radar of Nîmes is subject to saturation for the closest ground targets.

a. Ground target identification

Hubbert et al. (2009a,b) have developed the clutter phase alignment (CPA) method to separate rain echoes from ground clutter in real time. Here, we use a similar approach also based on signal phase and amplitude by defining for each pixel a “short time signal stability” σ that is basically the inverse of the CPA:

where I and Q are respectively the real and imaginary parts of the signal. The terms in

represent averaging over one pixel (i.e., 240 m in range and 0.5° in azimuth or ~100-ms duration with the 6° s⁻¹ speed of the antenna).

A sample of a σ map is given in Fig. 1a for the Nîmes radar during a clear-air situation. The value of σ is close to 1 for ground targets, lower than 0.7 for meteorological echoes, and close to 0 for noise. A mixed echo (ground/rain) is in the range 0.7–0.9. In the following we apply a threshold of 0.9 on σ to select the ground clutter; the pixels for which σ is larger than this threshold are candidates for refractivity measurements.

b. Ground target quality index

The criterion defined in the previous subsection is used to evaluate the stability of the signal received during the integration time for a single measurement (about 100 ms), but we realized that it is not always enough. We therefore sought to define an additional quality index that allows quantifying of the risk of phase ambiguity over longer time intervals (typically 1 h). In this section, we proposed a simplistic quality index based on the phase change δφ [defined in Eq. (2)] between two successive PPIs scans (δt).

Using a large number n of phase measurements separated by δt, the quality index (QI) is defined as follows for each pixel:

where

is the number of time with

. The QI is normalized by the number of samples (1/n) of the studied period. Even if negative values are theoretically possible, QI is generally between 0 (totally noncoherent echoes with δφ uniformly distributed between −π and +π) and 1 (totally coherent echoes). In the QI map example, presented in Fig. 1b for the Nîmes radar, high- QI areas are observed (particularly in the northwest part of the figure) but also areas of low QI are observed (particularly in the southeast part of the figure), all located in ground target areas (Fig. 1a). To get a better understanding of the relative amount of pixels available for refractivity measurement, the distribution of QI is plotted in Fig. 2 for all the echoes selected as ground targets. It clearly appears that this distribution is bimodal, with a first group between −1 and 0.8 and a relatively sharp peak between 0.9 and 1. This last peak (about 30% of the ground clutter pixels) corresponds to the pixels useable for refractivity. A ground echo (σ > 0.9) can therefore be defined as a “good target for refractivity” if its QI is larger than 0.9; that is, the phase change after δt stays within the interval

95% of the time. The other ground clutter pixels (Fig. 2; QI < 0.9) frequently produce large phase changes, and they are not suitable for refractivity. Throughout the present paper, we will use the shape of the QI distribution as an indicator of the effectiveness of a number of data processing.

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QI distribution of 40 000 ground targets selected around the Nîmes radar on 20 Sep 2011 for 12 h. The horizontal hatching, diagonal hatching, solid black, and vertical hatching correspond to a 1-, 2-, 5-, and 10-min sampling time, respectively.

Citation: Journal of Atmospheric and Oceanic Technology 30, 8; 10.1175/JTECH-D-12-00167.1

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c. Quality index stability with time

Such a criterion to select “good pixels” can be used in the operational only if it is stable with time. To check this point, QI distributions are compared for two different days obtained with the Trappes C-band radar (QI_2011-10-15 for 15 October 2011 and QI_2012-01-01 for 1 January 2012). The result is shown in Fig. 3, where we have also indicated the percentage of pixels that appear at both dates in the class considered (vertical hatching). The percentage of “good targets” is similar for QI_2011-10-15 (57%) and for QI_2012-01-01 (50%; respectively, horizontal and diagonal hatching in Fig. 3). The common radar pixels (vertical hatching distribution in Fig. 3) in the highest class [0.9, 1] is close to 93%: whatever the day of QI calculation, the greatest ground targets inside the highest class remain there even several months later.

Although most pixels available for refractivity remain available whatever the season, we know that some changes may occur, like vegetation growing, buildings, and so on. It is also likely that some pixels, declared acceptable for calm propagation conditions, can become difficult to exploit during more complex propagation conditions, as in the presence of strong boundary layer turbulences. Therefore, it seems necessary to reevaluate from time to time the target selection. Even if we do not currently have enough experience to decide the frequency of this type of reassessment, it seems prudent and logical to do this every season in the temperate region.

a. Sensitivity to the sampling time

For the particular case of the Météo France radar network, the operational time sampling is 5 min. This is good enough for S-band radar and most of the time enough for the C band, but clearly too long for the X band. Using the Nîmes 24-h experiment, a statistical study is realized to evaluate the impact of changing time between two successive PPIs from 60 to 600 s. To achieve it, as the interval between two PPIs is 60 s, increasing this interval is obtained by taking 1 of 2 PPI for a sampling time of 120 s and so on, and 1 of 10 for a sampling time of 600 s. The pool of ground targets has been selected, as described in section 3a, with a QI threshold equal to 0.9, leading to a selection of approximately 40 000 pixels out of 96 480. The QI of each pixel is computed as explained in section 3b.

By focusing on the impact of the time sampling (Fig. 2), the reduction of the time between successive measurements (from 600 to 60 s) leads to an increased percentage of pixels in the higher class (i.e., [0.9, 1]) and to a decreased percentage in other classes. This improvement, significant for this calm situation, will certainly be much more important during convective or turbulent atmospheric conditions.

b. Sensitivity to the antenna speed rotation

A first option to decrease the sampling time consists in increasing the rotation speed of the antenna, but this will be at the expense of measurement accuracy, especially considering that an individual pixel is 240 m deep in distance (one gate) by 0.5° in azimuth and the number of radar pulses used in the average is inversely proportional to the antenna rotation speed: approximately 35 pulses for a rotation speed of 6° s⁻¹ and only about 9 pulses at 24° s⁻¹. The test experiment, with the Trappes C-band radar, consists of realizing four successive PPIs with four different speeds (i.e., 6°, 12°, 18°, and 24° s⁻¹) for 3 h at a fixed elevation angle of 0.4°. From these data, four phase changes and refractivities are calculated for each of the selected antenna speeds.

As illustrated in Figs. 4a and 4b, for a single ground target the four time series are close to each other, confirming the low impact of the antenna rotation speed on phase change and refractivity measurements accuracy. Indeed, if a 6° s⁻¹ is considered as the benchmark, the determination criterion (R²) calculated against this reference are never lower than 0.93 for refractivity.

These observations have been generalized for all ground targets (4438), and the scores are reported in the Table 1. It can be noted that the correlation between the refractivity from the reference speed versus faster speed are good (R² > 0.90 and no bias). The decrease of R² depending on the rotation speed is not because of an increase of speed but to the nonsynchronization of the measurements. Indeed, between the PPI at 6° s⁻¹ and the one at 24° s⁻¹ a time delay of 110 s exists, leading to a significant decorrelation between measurements. To the contrary, the results are much worse for the phase differences (Table 1) with a determination coefficient close to 0.2 and a bias between 3 and 5. This is certainly due to a high-frequency noise of the phase difference time series, which is completely filtered by the integration leading to the refractivity measurement. Previous studies have shown that the phase measurement error because of the radar performance is very small, close to 6° for an individual measurement (only one radar pulse). Rapid fluctuations of the atmosphere between the radar and the target during the experiment (such as turbulent cells and cloud effects) may produce such a noise simply because the measurements are not made at the same time (see the last line of Table 1). For example, a local cooling on the order of 1°C because of a cloud above the propagation line is sufficient to explain a phase fluctuation of more than 10° (for a C-band radar with a 2-km range integration). Such changes may be coherent (between time 1.30 and 3 in Fig. 4b) or not (between time 0 and 1). The fact that the impact of rotation speed on refractivity measurement is negligible confirms previous work undertaken by Cheong et al. (2008) based on the use of phased-array radar to access a fast recovery refractivity with a low number of radar pulses.

It can be concluded that the azimuthal speed has a negligible impact on refractivity measurements. Moreover, the increase in speed is an indirect way to improve the measurement accuracy. The speed increase frees some time. With this time, more PPIs can be done at low elevations, leading to a decrease in the time between successive measurements.

c. Interleaving of two elevation angles

A second approach to decrease the sampling time is to use interlaced elevation angles. As the geographic positions of the radar and the target are both fixed, the optical path is strictly the same regardless of the elevation angle; the altitude reached by the beam is the same and the refractivity profiles encountered by the wave during its path remain the same. Even if the refractivity can be affected, in a general sense, by the variations of the vertical gradient of refractivity through the atmospheric propagation conditions (Park and Fabry 2010, 2011) and uncertainty (Bodine et al. 2011), this effect will not particularly be enhanced by interleaving time series from different elevation angles. However, the part of the beam that illuminates the target is not the same, and the signal amplitude should be significantly different for the two elevation angles.

To test this hypothesis, the refractivity measurement has been implemented on the C-band radar for the two interlaced elevations of 0.4° and 0.8°. The two elevations are each repeated every 5 min so that there is only 2.5 min between each elevation. Three radar refractivity time series have been retrieved with the 0.4° elevation alone (R04), with the 0.8° elevation alone (R08), and with the two elevations interleaved (R0408).

A particular ground echo, located at 2° in azimuth and at range gate 15 (~3.6 km), has been selected to evaluate the three radar refractivity time series (Fig. 5). For this target, the three different refractivities are identical, as confirmed by R² that is never lower than 0.95 (Table 2). However, it is noted (not shown) that the phase change measurement for R0408 is slightly noisier than other restitutions (R04 and R08). This is probably a result of variations in amplitude between the two elevations, which results in a change of approximately 15 dB for successive samples in the R0408 series. This strong amplitude modulation of the signal results in a frequency broadening, and thus an increase of phase noise.

The use of two successive elevation angles presents a clear advantage in view of the reduction of the sampling time, leading to a possible increase of the useful ground targets' number. A new quality index QI′, taking into account different elevation angles, can be calculated in order to evaluate the improvement brought about by this technique. This QI′ is obtained by a combination of the QI calculated with only the 0.4° elevation angle , with only the 0.8° elevation angle , and with the two elevation angles . Then, the QI′ is based on the best score obtained for a given ground target for the three different quality indices.

Figure 6 illustrates the improvement using two elevation angles in terms of the quality index. As expected, presents a slightly better discrimination between good and “bad” targets than or . This improvement is because of the decrease in the sampling time between successive measurements. This observation is in accordance with previous results on the time sampling illustrated by Fig. 2a. Here, the QI improvement is not very important, but, as explained by Besson et al. (2012), during extreme events or rapid fluctuations, reducing the sampling time will be very useful in order to reduce phase aliasing.

a. Transmitted pulse duration impact on the refractivity signal

For two close targets, the received signal might be a blend of two echoes, leading to some interference. This could possibly be problematic for the refractivity restitution, especially for large pulse durations.

In this section, the dataset used is described in section 2b. The measurement is done alternatively with a 2-μs and a 1-μs pulse width. The sampling time between two PPIs with the same pulse width is about 2 min. This time sampling is chosen in order to limit the probability of phase aliasing because of too large an integration time. At first we focus on a simple signal that consists of a single isolated ground target; then we examine a more complex signal that consists of several targets blended together.

b. Dual polarization

The ARAMIS network is now mainly composed of dual-polarization radars and the advantages brought out by this technique for rain-rate estimation are described by Bringi and Chandrasekar (2001). The refractivity measurement can be done regardless of the polarization, but the objective here is to evaluate the potential benefit of polarimetric signals to improve refractivity measurements.

As illustrated by Fig. 9, the quality index, defined by Eq. (4) (see section 3b) for a single echo, is not necessarily identical for the two polarizations. Indeed, a ground target can have a good QI on the horizontal (or vertical) polarization but a low QI for the vertical (or horizontal) polarization. Through the quality index, the pool of ground target could be classified in two groups:

1. a similar quality index (area I in Fig. 9), and

2. a better quality index on one of the two polarizations (horizontal or vertical; area II in Fig. 9).

Two geographically close pixels, each representing one of the two groups described above, are selected to illustrate the particular behavior of these different populations (Fig. 10). Figure 10a illustrates the first group of ground targets. For this particular pixel, both QI_υ and QI_h are equal or higher than 0.978. As it can be observed, the two refractivity restitutions are similar as it is confirmed by good determination criterion and bias (0.994 and −0.105, respectively).

For the second group of ground targets, QIs are significantly different for the two polarizations; this will have consequences on the refractivity measurement. To illustrate that point, we choose one specific pixel having a very good QI (i.e., 0.993) for the horizontal (H) polarization and a relatively low QI for the vertical (V) polarization (i.e., 0.881). As shown by Fig. 10b, this difference leads to a divergence between the two refractivity restitutions. The horizontal refractivity seems correct, while the vertical suffers from several obvious aliasing problems (at time 0, 2, 5, 9, and 15 and also 6 successive aliasings between time 21 and 23; Fig. 10b). This leads to lower determination criterion and bias (0.847 and 6.158, respectively) between the two polarizations.

This difference in behavior can be explained by considering that, inside the scene, each polarization preferably selects the corresponding lines, horizontal or vertical. The horizontal and vertical targets can therefore be significantly different; for example, one can be an isolated target while the other is more complex. This could be used in some way to unalias the worst restitution.

To improve the refractivity measurement, a first possibility is to consider for each pixel only the polarization having the best QI. Distributions of these QIs are shown by Fig. 11. Without having a clear explanation, it is observed that the horizontal polarization gives slightly better results than the vertical polarization, 29% and 26%, respectively. The use of the best QI for each pixel [max(QI_h, QI_υ)] leads to an improvement of ground targets availability from 29% to 26%, respectively, with QI_h and QI_υ up to 33% for max(QI_h, QI_υ) (Fig. 11).

To take full advantage of polarimetry, another idea would be to detect the phase changes that are larger than a threshold (for example π/2) and to replace it with the phase change from the other polarization at this time. To validate this hypothesis, four different QIs have been calculated using the same dataset as for Fig. 2: QI_h obtained with the horizontal phase change [Eq. (4)], QI_υ obtained with the vertical phase change [Eq. (4)], max(QI_h, QI_υ) (which is the best QI for each pixel), and QI_hυ obtained with the horizontal and the vertical phase change, defined by the following equation:

where

is the number of time with

or

.

The most spectacular result is that QI_hυ is much larger than QI_h and QI_υ separately: while only 26%–30% of the ground echoes stay in the higher-QI class for single polarization, this number increases up to 45% by taking the best of the two polarizations by changing the polarization each time the phase change is larger than π/2. This result clearly indicates how polarimetry could lead to an improvement in the estimation of refractivity by radar.

The distribution of the different QIs confirms that the dual polarization clearly improves the quality of ground targets and of the refractivity retrieval. This QI_hυ calculation still has to be improved and tested with different radar frequencies and datasets, particularly as there is a risk that this method of calculation of QI_hυ [Eq. (5)] could lead to a systematic bias through an underestimation of the phase change.