Abstract

Turbulence inhomogeneities at 3-m scales can be either isotropic or anisotropic, and the degree of anisotropy can be measured with VHF wind profiler radars. Studies over a period of two years in Montreal, Quebec, Canada, have shown that for this site during nonwinter months, the occurrence of isotropic turbulence at 3-m scales serves as a useful diagnostic for the occurrence of rainfall. Turbulent eddies are expected to be most isotropic when wind shears are weak and the atmosphere is either unstable or close to instability. The measurements show that when the turbulence is most isotropic, rainfall is very common. Furthermore, the development of quasi-isotropic turbulence usually occurs before the onset of precipitation. Lead times are typically of the order of 1 to 6 h. Correlation coefficients between the occurrence of strong isotropy and the development of rain generally exceed 0.6, and can be as high as 0.7. Further studies will be required to determine whether this phenomenon is specific to the Montreal area, or can be applied to other locations as well.

1. Introduction

Turbulence refractive index inhomogeneities at 3-m scales are frequently anisotropic, with the structures typically having larger horizontal dimensions than vertical. VHF wind profiler radars can be used to determine the degree of anisotropy. There are several ways in which this can be done, but in general most methods rely on the fact that backscattered power changes as a function of radar viewing angle, with scatter from overhead generally being stronger than scatter observed when off-vertical beams are used. The phenomenon is especially dominant in the stratosphere (e.g., Roettger and Liu 1978; Gage and Green 1978; Tsuda et al. 1986; Hocking et al. 1990), but also exists in the troposphere. Discussions about this phenomenon often revolve around consideration of specular reflectors, but anisotropic turbulence can also contribute to the differences in relative powers. Hocking and Hamza (1997) have discussed the differences between specular reflections and anisotropic turbulence, and have described some methods that can help distinguish the phenomena. Other discussions about anisotropic turbulence can be found in Dalaudier and Gurvich (1997) and Gurvich (1997). In the troposphere, specular reflectors are less common than in the stratosphere, but they can occur. Regardless of the cause of zenithal variations in backscattered power, however, it is generally agreed that when the backscattered power varies only slowly as the zenith angle increases, or indeed shows no variation as a function of angle, then the cause of the backscattered power is generally isotropic or quasi-isotropic turbulence.

Radar measurements of turbulence anisotropy are usually based on the so-called theta-s (θs) parameter, although this is not the only parameter used. The theta-s parameter is defined under the assumption that the power detected by a pencil-beam radar varies as a function of pointing angle in the manner

 
formula

where θ is the viewing angle (with zero being overhead), and θs is a parameter that describes how quickly the power falls away as θ increases. The subscript s refers to scatterer.

According to theortetical studies (e.g., Hocking and Hamza 1997), turbulence should be most isotropic when wind shears are weakest and the atmosphere is convectively unstable, and therefore radar returns should be most isotropic, with large θs values. Unstable atmospheric conditions are often associated with clouds, convection, and possibly precipitation. Therefore, it is not unreasonable to expect a positive correlation between periods of near-isotropic turbulence and rainfall. This might be especially considered to be true for seasons when heating of the ground is at its strongest, such as summertime. The purpose of this paper is to examine the possibility that precipitation and near-isotropic turbulence are correlated in this way. Scatterers are considered for schematic purposes as ellipsoids [although a more realistic description is given by Hocking and Hamza (1997)], and will be considered to be “quasi-isotropic” if they have typical length-to-depth ratios less than about 1.5, and considered to be substantially anisotropic if the ratio exceeds about 3. For scatterers with e−1 full widths of about one-half of a wavelength, these transitions correspond to θs ∼ 20° for a ratio of 1.5, and θs equal to about 9°–10° for the latter case (Hocking 1987).

With this objective in mind, we present data from a VHF ST radar system that routinely measures the aspect sensitivity on a continuous basis, and compare our results to the occurrence of precipitation as determined by a nearby S-band radar. The VHF radar works at a frequency of 52 MHz, and receives its greatest scatter from Fourier scales of about 3 m. This corresponds to turbulent eddies with typical depths of the order of 2 to 3 m (see Hocking 1987, 1989; Lesicar et al. 1994; and references therein). The S-band radar operates at a frequency of 2.88 GHz.

2. Instrumentation

Two main instruments are used in this study. The first is a VHF wind profiler radar that has been modified by its supplier to record additional information apart from standard winds. It also produces measurements of backscattered power, tropopause heights, turbulence strengths, as well as measurements of the anisotropy of the scatterers. As a result, it is called a WindTtracker radar (wind and turbulence tracker) by its suppliers because it is also designed for turbulence studies. (These parameters are updated hourly and shown online at http://mardoc-inc.com/.) Our main interest in this paper will be in regards to the anisotropy of the scatterers. The WindTtracker is located at 45°24′33″N and 73°56′12″W, at the MacDonald Campus of McGill University located in Montreal, Quebec, Canada. The second instrument is an S-band radar, located within 2 km of the VHF radar. Both instruments are less than 100 m above sea level, with the WindTtracker at 30 m and the S band at 80 m.

The McGill University WindTtracker radar uses a peak transmitter power of 40 kW, with a maximum allowed duty cycle of 15%. Typically duty cycles of the order of 5%–8% are most commonly used. The radar frequency is 52.00 MHz, with a corresponding wavelength of 5.77 m, and the system comprises 128 × 3-element Yagi antennas arranged in the form of a cross, in a similar manner to that for the Clovar radar (Hocking 1997), with one small change. The end sets of four antennas (quartets) on each arm shown in Hocking (1997) have been moved closer to the center for the McGill University radar, partly filling in the gaps in the diagonal regions between the arms, which improves the sidelobes with quite modest effects on the main beam. The array has a width of approximately 90 m, and the width of each arm is approximately 10 m. However, due to the fact that the array is not fully filled, the effective area of the whole array (as determined by numerical integration of the polar diagram) is approximately 1350 ± 150 m2. The main beam at the McGill University radar has a half-power one-way half-width of 2.3° (compared to 2.1° for the Clovar radar). The two-way beam half-power half-width is 1.6°. Cables are used to tilt the beam in five possible directions, these being 10.9° from vertical to approximately the northeast, southeast, southwest, and northwest, as well as vertical. In fact the true alignment of the arms is 48° west of north. Other pointing directions may be selected by changing the phasing cables. Cables have been used for beam tilting because of their robustness in preserving phase shifts.

The McGill University radar is controlled by a UNIX (FreeBSD) computer, and computer selection of operating parameters is easy and flexible. The user can modify pulse codes, pulse lengths, PRFs, start times, receiver gain, and almost all radar parameters in software. The system also regularly reports on system temperature, standing wave ratios, available disk space, system mismatches, forward transmitter voltages, and many other parameters, all of which are e-mailed to the user on a daily basis.

The radar can be operated in a variety of modes, but under standard operation it cycles between 57 different configurations, which include variations in beam direction, pulse length, pulse codes, filter widths, pulse repetition frequencies, and other operational parameters. Different modes are used to record different heights, with monopulses being used at the lowest heights and Barker and Complementary codes at the greater altitudes. Both Doppler and spaced antenna modes are enacted, and useful winds are typically recorded between 400-m altitude and 14-km altitude. The digitizers are set to record signal between typically 200-m and 21-km altitude. The spaced antenna mode is used primarily to obtain winds below 1.5-km altitude. PRFs vary from typically a few thousand hertz for upper-level data to tens of thousands of hertz for the lower-altitude spaced antenna mode. Each PRF is tuned to optimize data from the specified height range but at the same time avoid the effects of range aliasing. For example, a PRF of over 10 000 Hz is only ever used in spaced antenna mode with low transmitter power and short pulses, while data recorded at the upper heights usually uses a PRF more like 3000 Hz but employs pulse coding to optimize signal. Generally in Doppler mode, experiments are performed in subgroups that involve rotation through five different beam directions, specifically to the northwest, northeast, southeast, southwest, and vertical. Rotation through full set of five beams takes typically 4–5 min. A typical complete sequence takes just over half an hour. Because of the multiple selection of operating parameters, the vertical resolution of the system varies as a function of height, being typically 250 m below 1.5 km, increasing to 500 m at 3 km, 750 m at 7-km altitude, and slowly increasing to about 1.0 km at 14-km altitude. In this paper, we will use only Doppler data. The same sequences are used on each beam, so comparisons of powers on different beams (as will be performed in this paper) may be reliably performed and are not biased by the choice of operational parameters.

With regard to the S-band radar, its carrier frequency is 2.88 GHz, with a corresponding wavelength of 10.416 cm. Typical pulse lengths are 150 m (1 μs), and PRFs of 1200, 600, and 480 Hz (staggered) are the most common. No pulse coding is used, but some coherent integration is applied. Peak power is 750 kW. The RF filter has a width to 3 dB of 5 MHz, and the IF filter width is 1 MHz. The signal is transmitted from a radar dish that points approximately horizontally, and scans all azimuths six times per minute. It can also be altered in elevation through 13 different angles. The dish is a parabolic reflector, with a diameter of approximately 9.14 m, and is positioned approximately 31 m above the ground (to the center feed). The polar diagram has a beamwidth (3-dB point) of 0.82° in elevation and 0.75° in azimuth. The radar is especially sensitive to precipitation and can detect storms, rainfall, snow, and hail out to a distance of 240 km. When precipitation exists, profiles of winds can be deduced using the velocity–azimuth display (VAD) method (Doviak and Zrnic 1993, section 9.3.3), although our interest in this paper will be solely in its ability to detect, locate, and quantify precipitation.

3. Method

The aspect sensitivity of radar scatter is most simply measured by comparing the VHF signal strengths determined on an off-vertical beam and a vertical beam. For a very narrow beam, the relative powers are of the form given by Eq. (1). For a beam of finite width, the parameter θs is found according to the expression

 
formula

where θt is the tilt of the off-vertical beam; θ0 is the 1/e half-width of the (two-way) beam; and P(0) and P(θt) are the powers received on the vertical and off-vertical beams, respectively (e.g., Hocking 2001; Hooper and Thomas 1995). For all of our data we have used hourly averages for the powers, and noise has been subtracted from the powers before further processing. This avoids short-term variability at scales of minutes and seconds, which can be dominated by other advective effects (e.g., see Worthington 2004). Use of hourly data gives good statistical reliability, since this means we use typically over 100 separate datasets per hour. Each separate dataset comprises typically 30–40 s of recorded information, and all beams (four off-vertical and one vertical) share the available time equally, so that no biases appear due to unequal times spent on any one beam. As described in the last section, the sequence of beam rotations is usually from vertical to successive azimuths of northwest, northeast, southeast, southwest, and back to vertical, and such a cycle takes place in less than 5 min (i.e., a much shorter timeframe than the aspect-sensitivity averaging time).

The parameter θs is small when the scatterers are highly stretched horizontally relative to their vertical extent, and θs is large when the scatterers are close to isotropic. Hocking (1987, 1989), Lesicar et al. (1994), and Hocking and Hamza (1997) have described how θs relates to the length-to-depth ratio of the scatterers in greater detail. The parameter θs is a standard output from the McGill University VHF WindTtracker radar. It should be noted that other approaches have been used to describe the degree of anisotropy (e.g., Doviak and Zrnic 1984). For our purposes, however, θs is the most suitable parameter for our investigations.

A typical height–time diagram of θs is shown in Fig. 1. Notice in particular that there are frequent occurrences where θs exceeds 20°. The transition can be quite sharp, changing rapidly between values of the order of 9° or less and values of over 20° within less than 1 or 2 h. The values for θs of 9° and 20° correspond to power ratios on the vertical and off-vertical beams for our radar of 6.0 and 1.3, respectively. A further example, demonstrating the onset and cessation of enhanced isotropy, is shown in Fig. 2.

Fig. 1.

The θs parameter plotted vs height and time from 1200 UTC 15 Sep to 1200 UTC 17 Sep 2003. The onset of enhanced isotropy is not seen, but the enhanced isotropy disappears around 1400 UTC 16 September, with a brief return at 2100 UTC and then disappears again at 0200 UTC 17 September.

Fig. 1.

The θs parameter plotted vs height and time from 1200 UTC 15 Sep to 1200 UTC 17 Sep 2003. The onset of enhanced isotropy is not seen, but the enhanced isotropy disappears around 1400 UTC 16 September, with a brief return at 2100 UTC and then disappears again at 0200 UTC 17 September.

Fig. 2.

Another example of VHF anisotropy variability, demonstrating the onset of isotropy at around 0000 UTC 30 Oct 2004. The period of enhanced isotropy finishes around 0700 UTC 31 Oct 2004. The parameter is only plotted to an altitude of 12 km in this case.

Fig. 2.

Another example of VHF anisotropy variability, demonstrating the onset of isotropy at around 0000 UTC 30 Oct 2004. The period of enhanced isotropy finishes around 0700 UTC 31 Oct 2004. The parameter is only plotted to an altitude of 12 km in this case.

We have carried out a detailed comparison between the θs parameter measured with the VHF radar and the occurrence of precipitation determined with the S-band radar. An example of a typical precipitation map seen with the S-band radar is shown in Fig. 3. This map, which refers to the time of 0600 UTC 16 September 2003, coincides with the occurrence of strong isotropy seen in Fig. 1. S-band radar reflectivities may be converted to approximate rain rates through relation

 
formula

where ϒ is the reflectivity in dBZ, and R is the rain rate in mm h−1. This relation has been taken from Lee and Zawadzki (2005), and is an improvement on the earlier Marshall–Palmer ZR relation (Rogers and Yau 1989). The relation is somewhat instrument and analysis dependent (Campos and Zawadzki 2000). For the purposes of this paper, the precise relationship is not essential, since we will be mostly interested in the existence or otherwise of precipitation, rather than absolute rates, but the relation is included for completeness. As examples, a reflectivity of 25 dBZ corresponds to a rain rate of 1.3 mm h−1 (typical spring/fall rain rates, which are generally fairly light), and 45 dBZ corresponds to about 30 mm h−1 (heavy rain).

Fig. 3.

S-band radar map of precipitation, 0600 UTC 16 Sep 2003. The S-band radar is located in the center of the field of view, at the point labeled ×. Circles with radii that are multiples of 30 km are shown.

Fig. 3.

S-band radar map of precipitation, 0600 UTC 16 Sep 2003. The S-band radar is located in the center of the field of view, at the point labeled ×. Circles with radii that are multiples of 30 km are shown.

To compare the two radar sets, we decided to develop simple parameters to represent each data type. For the VHF radar, we examined the aspect sensitivity parameter within any given hour, and found the percentage of the height range between 1 and 11 km (approximately the tropopause) in which θs exceed 20°. Initially, this percentage was estimated by an observer who visually examined graphs like those shown in Figs. 1 and 2, and in this case a value of 1 was assigned if this number was less than 25%, 2 if it lay between 25% and 50%, 3 if it lay between 50% and 75%, and 4 if it exceeded 75%. This term will be called the “isotropy index.” Later, the process was automated, using computer techniques, and the isotropy index became a real number, although we retained the scaling from 0.0 to 4.0 (see shortly). We then performed a five-point running mean of this parameter, in order to introduce a small level of smoothing. At the same time, we examined the hourly precipitation maps (like those in Fig. 3) and searched for signs of precipitation. The maps had a width of 240 km, and the largest radius from the S-band radar seen on the map is 170 km (at the corners). Any events that occurred within a radius of 120 km from the S-band radar could be seen, irrespective of direction. If precipitation existed in at least 1% of the viewing area (equivalent to a rain cell of diameter typically 15 km—note that the range rings on the map are 30 km apart), and the backscattered signal exceeded 18 dBZ, a number 1 was assigned to that hour. If no precipitation was present, or precipitation was present in only small quantities, the period was assigned a value of 0. This parameter is called the “precipitation index.”

The results of our initial studies confirmed a strong correlation between enhanced isotropy and the existence of precipitation, so we then extended the study to cover a longer time period, and also automated the parameterization of the isotropy index. The results of all of these studies will be presented in the next section. In the initial visual investigations, the isotropy index was always taken as an integer, but in the later automated computer-based procedures, higher precision was possible and the isotropy index was taken as a real number, and changed slightly in definition; it was taken as simply the percentage of the height range between 1 and 11 km with θs exceeding 20°, divided by 25.0. The division by 25.0 was undertaken in order to retain consistency with the visual technique, which used values of 0, 1, 2, 3, and 4, but of course the newer (and ultimately most commonly used) index was a real number. A comparison of the “visual” and the automated isotropy index during October 2002, when both techniques were used, showed a correlation coefficient of about 75%. Bearing in mind that the first dataset comprised integer values only (1 to 4), whereas the second were real numbers (which would in itself degrade the comparison), this indicates that the two techniques were generally equivalent. Likewise, the precipitation parameter was also made more flexible at this time—a number 1 was assigned if precipitation existed in a region of effective diameter 20 km or less, and a number 2 was assigned for precipitation that covered a larger area. A record was also kept of whether each rain cell passed over the radars, or skirted around it, and indeed two separate data files were stored for the precipitation index—one including all events, and one including only those cases where the precipitation event actually passed overhead of the radar. The latter events will be called “local” events, and both the local and nonlocal events will be considered (both separately and together) in the sections to come.

4. Results

The data for the studies discussed here covered the periods 17 August 2002 to 31 October 2002, and 20 August to 29 November 2003. VHF data prior to 17 August 2002 were not available for analysis, and during the period from 31 October 2002 to 17 August 2003, the S-band radar was inoperative due to repair work. Nevertheless, visual studies of the isotropy index were still carried out during the winter of 2002/03, and compared with ground reports of precipitation, but the focus of our studies is the period from later summer through fall (August to October–November) of each of the years 2002 and 2003.

To begin our studies, a comparison of the isotropy index and the precipitation index for a subset of the 2002 data, specifically for the period from 18 October to 18 November 2002, was performed. This period was chosen because it was the first dataset for which the correlation between precipitation and anisotropy was recognized. The results are shown in Fig. 4a, where all available indices were hourly averaged data recorded at 3-hourly steps. These data were obtained by visual procedures. In other words, the percentage of altitude ranges below 11 km with θs in excess of 20° was estimated visually from figures like those shown in Figs. 1 and 3, rather than by automated procedures, as described in the last section. It is apparent from this graph that for most of the time frame, incidences of enhanced isotropy correspond to occurrences of precipitation. Approximately 200 coincident measurements were possible. Vertical broken lines show times where precipitation starts shortly after the onset of an increase in θs to values in excess of 20°.

Fig. 4.

(a) Plots of the isotropy index (upper graph) and precipitation index (lower graph) as a function of time in October and November 2002. (b) Cross correlation between the isotropy index and the precipitation index.

Fig. 4.

(a) Plots of the isotropy index (upper graph) and precipitation index (lower graph) as a function of time in October and November 2002. (b) Cross correlation between the isotropy index and the precipitation index.

Figure 4a shows that if the isotropy index equals 3 or 4, precipitation is generally found. If the isotropy index is 2, there may be some precipitation (e.g., case C) or there may be none (cases A and B). If the isotropy index is 1, there is usually no precipitation. Generally the isotropy parameter increases before the precipitation index rises to 1, so that enhanced isotropy is a precursor to the precipitation. The delay varies between 1 and 12 h. The incidences of enhanced θs often also persist for a short time after the precipitation has disappeared.

To make the process more quantitative and complete, we have also calculated the cross-correlation coefficient between the two parameters, and the results are shown in Fig. 4b. Cases where data were missing for either the VHF or S-band radar were not included in the calculation of the cross-correlation coefficient. The cross-correlation coefficient at zero lag is 0.656, and it is in fact slightly larger at a lag of 3–4 h, being 0.722 at the peak. There were about 200 occasions for which the observer was able to determine both the anisotropy index and the precipitation index available for one month. The 95% confidence limits on these estimates are 0.57 and 0.72 at zero lag, and 0.65 and 0.78 at a lag of 3 h, indicating a strong correlation. The fact that the cross-correlation function peaks at a temporal lag of 3–4 h arises because the isotropy parameter usually reaches values of 20° before the precipitation arrives, as discussed in regard to Fig. 4.

As noted in the previous section, our next step was to move to a more automated analysis procedure, in order to be able to analyze larger datasets, and to ensure better data continuity. Nevertheless, we have retained the results obtained visually because we wish to emphasize that the correlation is strong enough that it is quite clear even without any special computer analysis. Indeed it turns out that there are additional subtle effects that can be detected by a trained observer that are less amenable to programming into a computer program, and we want this to be recognized. Therefore, both the “trained observer” approach and the automated approach have advantages and disadvantages, with the former allowing a more adaptable approach, and the automated approach being more objective and less prone to possible bias on the part of an observer. For these reasons we have retained both approaches.

We now turn to consideration of the automated approach. To begin, the scopes of both the isotropy index and the precipitation index were also increased—in the case of the isotropy index, it became a real number (but still took values between 0 and 4, in order to maintain some level of consistency with the earlier visual analysis), and in the case of the precipitation index, an extra option (number 2) was added, so that we could distinguish between cases of small areas of scattered precipitation and more intense, larger cells. An indicator of whether the rain region passed over the radar was also kept, being designated “local” if it passed over the radar. All indices were determined hourly.

Figure 5a shows the results of applications of this analysis for the period from August 2003 to November 2003. The S-band radar was inoperative in 2003 before August, due to a system upgrade, so the data covers only the months of August, September, October, and November. A similar analysis was also applied for the 2002 August, September, and October data (not shown). The two sets of precipitation indices shown in the figure refer to the cases where all rain cells are included (“all”) and those cases for which the cells were required to pass over the radar (“local”).

Fig. 5.

(a) (i) The VHF isotropy index, and the precipitation index, for cases where (ii) the rain cell passed over the radars, and (iii) all incidences of precipitation are included, irrespective of whether they passed over the radar. (b) Cross-correlation functions between the isotropy index and the precipitation indices.

Fig. 5.

(a) (i) The VHF isotropy index, and the precipitation index, for cases where (ii) the rain cell passed over the radars, and (iii) all incidences of precipitation are included, irrespective of whether they passed over the radar. (b) Cross-correlation functions between the isotropy index and the precipitation indices.

A variety of cross-correlation coefficients were calculated. Initially no specific averaging was applied, and the raw isotropy index was correlated against the raw precipitation index, with no further processing. Correlation coefficients of the order of 0.5 were found for this case, and the correlation functions for 2002 and 2003 are shown as the broken lines in Fig. 6. This represents a baseline against which other correlations can be referenced. We then tried other variations on the isotropy index. It was found that optimum values for the correlation coefficients were obtained when the isotropy index was set to zero if its value was less than about 2.5 (approximately 62.5% filling). Cases where the isotropy index exceeds 2.5 were occasions when the height range was significantly filled with isotropic turbulence. In addition, a five-point box-car running mean was applied to the data series for both indices, in order to smooth out some of the intermittency, before the correlation coefficients were determined. Figure 5b shows the correlation function between the isotropy index and the precipitation indices for the cases where all the rain cells are considered (labeled “all”) and those cases where only cells that passed over the radar were included (labeled “local”). The correlation coefficients are clearly larger in the latter case. Notice also that the correlation coefficients are smoother in form than those from Fig. 4, largely because the isotropy index is now a real number. All correlation coefficients exceed 0.5, and we believe this is a lower limit. This point is discussed further in the next section.

Fig. 6.

Cross-correlation functions for 2002 and 2003, for various methods of determination of the isotropy index, and for different descriptions of the precipitation. As in previous cases, “all” means all rain cells observed by the radar were considered, while “local” uses only those cases where the rain cells passed over the radar(s). “Raw” means no preprocessing of the isotropy data.

Fig. 6.

Cross-correlation functions for 2002 and 2003, for various methods of determination of the isotropy index, and for different descriptions of the precipitation. As in previous cases, “all” means all rain cells observed by the radar were considered, while “local” uses only those cases where the rain cells passed over the radar(s). “Raw” means no preprocessing of the isotropy data.

Figure 6 shows cross-correlation functions for a variety of cases, as indicated, including the case of correlation of the raw isotropy index versus the raw precipitation index. Maximum values always exceed 0.5, and can be higher than 0.7. It can also be seen that the peaks lie generally at zero lag or slightly to the right, which indicates that the mean times of the regions of enhanced isotropy occur slightly prior to the precipitation central locations.

The offset in mean positions of the isotropy index and the precipitation index is interesting, but an additional point needs to be addressed. Early indications were that the isotropy enhancement begins prior to the onset of rain. To properly confirm this, it is necessary to look at a new parameter—the time of onset of each index. This is especially important if we wish to examine the capabilities of the isotropy index as a forecast diagnostic.

To do this, an edge detector algorithm was developed. The program searches the time series and determines the difference between the current and previous value. If this difference is positive and exceeds a user-specified limit, and the preceding four differences did not exceed this limit, and the next two values in the time series (actual values, not differences) exceed another user-defined cutoff, then the point is determined to be an upward-rising edge. A value of 1 is assigned to any such leading edges, and all other points are assigned zeros. The procedure is designed to detect only rising edges, although we will simply refer to it as an edge detector. Some experimentation by the user is required to determine the optimum cutoffs for both the difference and the minimum absolute allowed values, but some quick experimentation soon allows the start times of the increases in either the isotropy index or the precipitation index to be evaluated. An example is shown in Fig. 7a.

Fig. 7.

(a) (i) Isotropy index, (ii) time of leading edge for isotropy increase, (iii) precipitation index, and (iv) time of start of precipitation for the period from August to November 2003. (b) Cross-correlation function between the second and fourth functions in (a).

Fig. 7.

(a) (i) Isotropy index, (ii) time of leading edge for isotropy increase, (iii) precipitation index, and (iv) time of start of precipitation for the period from August to November 2003. (b) Cross-correlation function between the second and fourth functions in (a).

In Fig. 7a, the isotropy start times have missed a few occasions where there was an increase in isotropy, but some of these were very short-lived phenomena and so can reasonably be expected to not be found, or even be relevant. Some others are cases in which the isotropy grew relatively slowly with time, so did not show a rapid enough change to be detected. But in general the edge detector performs moderately well. The same can be said for the precipitation edge detector.

The two “edge detector” time series were then cross correlated. It should be borne in mind that it is very difficult to cross correlate two time series that are essentially each a quasi-irregularly spaced series of delta functions, so high correlations cannot be expected—if one delta function is displaced by 1 h, it can result in a significant change in correlation coefficient since that point may now correlate with a zero in the other time series whereas previously it may have been associated with a unit value. With this in mind, the correlation function is shown in Fig. 7b. The correlation coefficient reaches 0.3 at a lag of typically 2 to 3 h. We would consider correlation coefficients below 0.1 to be statistically insignificant, but importantly, all the significant positive correlations occur to the right of zero. This certainly indicates that the isotropy index almost always increases prior to the precipitation index. The correlation could perhaps be improved with a more sophisticated edge detector, but that is not the main point here—the main point is that there is definitely a time lag, and the isotropy index leads the precipitation index. Hence the isotropy index could even act as a forecast diagnostic for precipitation.

5. Discussion

Several issues arise as a result of the above studies. First, return to Fig. 5, which showed the correlation coefficients between the isotropy index and the precipitation index using the computer algorithm to determine the isotropy index. Although the correlation coefficients are generally in excess of 0.55, it is interesting that the values shown in Fig. 4 (determined by visual study) are higher. This is because the human eye and brain can actually do a slightly better job of identifying regions of strong isotropy that are likely to lead to rain. For example, if the tropopause was low in height, the eye could readily tell that the percentage should be calculated only to the top of the isotropic region, whereas the computer algorithm calculated the value using all data to 11-km altitude. Of course there is an element of possible bias in the “visual” approach, although determinations of the isotropy index and the precipitation index were made independently and without recourse to each other. Other subtle effects, too difficult at this time to properly quantify, could also be recognized by a human observer, which made it possible to determine the isotropy index with slightly enhanced reliability compared to the computer program. One example is the structure of the regions of isotropy enhancement—if the enhancement consisted of small to moderately sized, but partly isolated regions of enhanced isotropy, joined at various points but not continuous (i.e., slightly broken in continuity—we will refer to such structure as “fragmented”), they were less likely to lead to rain than the case where a similar percentage occurred, but the region of isotropy was more concentrated and more continuously connected. The tendency was for the observer to give less weight to fragmented regions, relative to fully filled regions, than the automated program did, based on experience gained from examination of many graphs. Over time, it may be possible to incorporate these effects into a robust computer algorithm, but for now we simply recognize that, regardless of whether a human or a computer was used to determine the indices, there is a fairly strong correlation between the two indices, with stronger correlation when the cases of precipitation over the radar are considered exclusively. We believe that this correlation can be further increased by development of an isotropy index that better considers the height of the tropopause and the distribution of the regions of enhanced isotropy, as well as other effects that have not yet been fully quantified.

It has already been noted that the correlations were less obvious in winter. Unfortunately, the S-band radar was not operative during the winter of 2002/03, so we had to rely on ground-level reports of precipitation. Nevertheless, these reports, and examination in other winters, suggested that the correlations in winter were less strong. We expect that the reason for this is because much of the nonwinter rain arises due to convection, and we expect enhanced convection to correspond to greater isotropy for the turbulent eddies (Hocking and Hamza 1997). Nevertheless, a more intensive investigation during winter time would still be a worthy study, although outside the scope of the current investigation.

With regard to the summer and fall data used in our comparisons, we envisage that the convection may encompass a much larger area than the precipitation, with the region(s) of precipitation embedded inside it. This explains why the enhanced isotropy precedes the precipitation—it covers a larger area, and so as the region drifts across the radars, the outskirts, where there is no precipitation, cross the radars first. It therefore appears that the aspect-sensitivity parameter is often a precursor to precipitation, as proposed in the introduction. This argument is consistent with the argument presented by Harrold and Browning (1971), who also found indicators of precipitation development using high-power radar (although their measurements did not involve measurements of anisotropy), and also proposed that cells of precipitation were embedded inside a larger convective region.

In view of the fact that convection is associated with instability, it could perhaps be expected that occasions of more isotropic scatterers might correspond to periods of stronger turbulence. The VHF radar calculates turbulence strengths as part of its standard output, and we have investigated this possibility. In general other events dominate the turbulence variability, and the correlation between precipitation and turbulence strengths is not nearly as strong as the correlation between precipitation and isotropy. This is not terribly surprising, since convection does not have to be associated with strong turbulence. Indeed if wind shears are weak, then the turbulence strengths can be quite low and yet turbulence can still be isotropic (Hocking and Hamza 1997). It is also possible that some of the determinations of turbulence could be affected by rapidly varying nonturbulent motions (e.g., Hooper et al. 2005).

At this time we cannot say that the observed correlation between precipitation and isotropy occurs at all sites, and it is possible that it is a regional effect. Many more studies at other sites are certainly needed. However, an interesting side note of this study is that it appears that the isotropy index may be a very good indicator of convection. This might be true even at sites that do not have the same correlation between isotropy and rainfall as that reported herein. The type of rainfall may also be an interesting parameter to study in connection with the isotropy index. This is beyond the scope of the current paper, although it is noteworthy that other studies have found relationships between rain type and other radar characteristics (e.g., Lucas et al. 2004; McDonald et al. 2004; Chu and Song 1998).

6. Conclusions

  1. Reduction in anisotropy of turbulence at 2–3-m scales, as determined by a VHF wind profiler radar, is well correlated with the occurrence of liquid precipitation at Montreal, Quebec, Canada, with turbulence being most isotropic during rainfall events.

  2. The correlation coefficient exceeds 0.5, and can exceed 0.7.

  3. The onset of near-isotropic turbulence precedes the occurrence of rain by typically 1–6 h, depending on circumstances, and with better understanding may in the future be useful as a forecast diagnostic for rain.

  4. Detailed wintertime studies were not possible, but available evidence suggested that the correlation may be weak or nonexistent in winter, when the main forms of precipitation are snow and other types of solid water, and convection is less important in forming clouds.

  5. The theta-s parameter deduced with VHF radars may be a good way to parameterize the level of convection in the atmosphere, and more studies along these lines are warranted.

  6. Although the correlation at Montreal is strong, further studies at other sites are required to ascertain whether this is a global or local phenomenon.

Acknowledgments

We especially acknowledge the support of Prof. Isztar Zawadzki, Director, J. S. Marshall Radar Observatory, Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada.

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Footnotes

Corresponding author address: Wayne Hocking, Dept. of Physics and Astronomy, University of Western Ontario, London ON N6A 5B9, Canada. Email: mardoc-inc@rogers.com