• Bean, B. R., and E. J. Dutton, 1968: Radio Meteorology. National Bureau of Standards Monogr., No. 92, National Bureau of Standards, 435 pp.

  • Bevis, M., S. Businger, T. Herring, C. Rocken, R. Anthes, and R. Ware, 1992: GPS meteorology: Remote sensing of atmospheric water vapor using the Global Positioning System. J. Geophys. Res.,97, 15 787–15 801.

    • Crossref
    • Export Citation
  • Businger, S., and Coauthors, 1996: The promise of GPS in atmospheric monitoring. Bull. Amer. Meteor. Soc.,77, 5–18.

    • Crossref
    • Export Citation
  • Sachidananda, M., and D. Zrnic, 1987: Rain rate estimates from differential polarization measurements. J. Atmos. Oceanic Technol.,4, 588–598.

    • Crossref
    • Export Citation
  • Ware, R., and Coauthors, 1996: GPS sounding of the atmosphere from low earth orbit: Preliminary results. Bull. Amer. Meteor. Soc.,77, 19–40.

    • Crossref
    • Export Citation
  • View in gallery

    Illustration of the effect of index of refraction changes on the phase of ground targets. The phases of five arbitrary targets (T1, . . . , T5) at (a) an initial condition, and (b) its change as refractivity increases at all ranges, or (c) increases up to a given range and decreases beyond are presented. The dials illustrate either the current phase of the targets (top), or the difference between the current phase of the targets and the reference phase when n = no (bottom).

  • View in gallery

    Diagram illustrating the values that refractivity can take for given temperature and moisture for a pressure of 1000 mb. In inset, the formula used to compute N as well as some refractivity values calculated for a dry and saturated atmosphere at a few temperatures are shown.

  • View in gallery

    Illustration of the correlation between target phase and refractivity. Two targets on power lines at a similar range (20 km), but in opposite directions, were selected. Their position with respect to the radar and the Dorval airport (YUL) is shown at the top-left while the top-right window shows a 0.5° PPI of received power where the echoes selected are highlighted. In the bottom window, the time evolution of the phase of the two targets (solid and dotted line, right scale) is contrasted with refractivity computed from YUL observations (crosses, left scale). Some weather observations from YUL are also plotted at the top of the window using the station model; periods over which precipitation was observed are also indicated.

  • View in gallery

    (a) Low-level (0.5°) PPI of received power up to 45-km range illustrating the coverage of ground echoes around the McGill radar. (b) Sketch of the land usage and topography over the same area. (c) Mask of the ground echoes used for the measurement of refractivity. Coverage is good over areas covered by fixed targets (urban areas), while much poorer over areas covered by moving targets (forests).

  • View in gallery

    Procedure to extract refractivity measurements from ground targets. (a) The phase of ground targets is measured; (b) the phase of targets from the reference map are subtracted from them; (c) in regions where the phase difference data is well behaved, path-integrated measurements of refractivity are computed using (2) and a value of 325.6 N units for the refractivity at the reference time; (d) a field is generated using the path-integrated measurements of N. Range rings are every 10 km.

  • View in gallery

    Time series of refractivity over a 60-day period (16 June–14 August 1996) from radar (solid line) and surface stations (crosses) data. The radar refractivity data are field averages up to 45-km range measured every 5 min. The refractivity from surface stations was computed from hourly pressure, temperature, and moisture measurements at the eight stations plotted in Fig. 7.

  • View in gallery

    Example of a contrasted refractivity field. (a) Surface weather observations of temperature, dewpoint, cloud cover (when available), and winds at various stations around the radar site at 1400 UTC. The refractivity computed from these observations is indicated in brackets. (b) Refractivity field measured by radar 10 min later. A significant gradient in refractivity is observed because of the difference in the dewpoint temperature of the two air masses (Td = 10°C vs Td = 14°C). The two outer circles correspond to a distance of 45 km from the radar.

  • View in gallery

    Example of a refractivity field in light precipitation. (a) Reflectivity from weather echoes (moving from the west-southwest) over a 240 km × 240 km area around the radar. (b) Refractivity field measured for the same period. Higher refractivity can be seen toward the southwest due to an increase in surface moisture associated with the approaching rain. The two circles correspond to a distance of 45 km from the radar.

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On the Extraction of Near-Surface Index of Refraction Using Radar Phase Measurements from Ground Targets

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  • 1 National Center for Atmospheric Research, Boulder, Colorado
  • | 2 J. S. Marshall Radar Observatory, McGill University, Montreal, Quebec, Canada
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Abstract

The speed at which electromagnetic waves travel between a radar and a target is dependent on the index of refraction of the atmosphere between the radar and the target. Modern radars can have sufficiently accurate time bases and digitizing equipment to observe small changes in the time it takes a radar signal to travel to a fixed target and back. These changes are related to small perturbations in the refractive index caused by changes in humidity, temperature, and pressure. Using the phase information from ground targets and its time evolution as a proxy for the changes in travel time of radar waves, a procedure for measuring the near-surface index of the refraction field around the radar is demonstrated and implemented on the McGill Doppler S-band radar. This paper describes the theory behind the measurement, and a technique used to extract refractive index data from ground targets. Early measurements of the index of refraction field are also presented, and some of the possibilities offered by this new radar-measured variable are identified.

Corresponding author address: Dr. Frédéric Fabry, Radar Observatory, McGill University, P.O. Box 198, Macdonald Campus, Ste-Anne de Bellevue, PQ H9X 3V9, Canada.

Email: frederic@radar.mcgill.ca

Abstract

The speed at which electromagnetic waves travel between a radar and a target is dependent on the index of refraction of the atmosphere between the radar and the target. Modern radars can have sufficiently accurate time bases and digitizing equipment to observe small changes in the time it takes a radar signal to travel to a fixed target and back. These changes are related to small perturbations in the refractive index caused by changes in humidity, temperature, and pressure. Using the phase information from ground targets and its time evolution as a proxy for the changes in travel time of radar waves, a procedure for measuring the near-surface index of the refraction field around the radar is demonstrated and implemented on the McGill Doppler S-band radar. This paper describes the theory behind the measurement, and a technique used to extract refractive index data from ground targets. Early measurements of the index of refraction field are also presented, and some of the possibilities offered by this new radar-measured variable are identified.

Corresponding author address: Dr. Frédéric Fabry, Radar Observatory, McGill University, P.O. Box 198, Macdonald Campus, Ste-Anne de Bellevue, PQ H9X 3V9, Canada.

Email: frederic@radar.mcgill.ca

1. Concept

The index of refraction has traditionally been seen in radar meteorology as the quantity whose unusual vertical structure may cause anomalous propagation of radar waves. In parallel, it has long been recognized that the index of refraction is strongly related to atmospheric parameters such as pressure, temperature, and moisture (Bean and Dutton 1968, and references therein). The link between index of refraction and meteorological parameters makes it an interesting quantity to measure. In recent years, considerable work has been done to measure it using the Global Positional System (GPS) on earth–space paths and space–limb–space paths (Bevis et al. 1992; Businger et al. 1996; Ware et al. 1996). The link between index of refraction and the propagation of radar waves suggests the possibility that some aspects of this quantity may be measured by radar.

Let us consider the simplest radar equation involving the index of refraction n: The time t taken by electromagnetic waves to reach a target at range r and return to the radar is
i1520-0426-14-4-978-e1
with c being the speed of light in vacuum. This equation is ordinarily used to determine the range of radar targets even though this single equation has in reality two unknowns, r and n. However, n typically varies by at most 0.03% and can therefore be assumed constant for most weather radar applications. On the other hand, for fixed targets, r is constant and only n varies; hence, if t could be measured precisely for such targets, the average value of the refractive index over the path between the radar and these targets could be determined.

2. Feasibility and sensitivity calculations

The first problem to be addressed in order to transform this theoretical concept into a practical technique is the precision required for the time of echo return t and for the distance r to the echo-producing target. It is clear that neither of the two can be measured in an ordinary radar to the needed accuracy of a few parts per million. However, if the range to the target is fixed, but only known to a fair accuracy, say better than 1%, it would be enough to allow us to relate changes in t to changes in n; the absolute calibration would then have to be done by other means. By using this stratagem, we are only required to determine changes in t, something that can be done by measuring the phase of the target.

Figure 1 is helpful to understand how this works. At an initial time (Fig. 1a), measurements of phases are made at five targets when n = no. The phase of each of these targets could be anything: It is a function of the range to the target, the average refractive index between the radar and the target, and the shape and nature of the target itself. If the refractive index increases everywhere (Fig. 1b), the radar wave gets compressed by a small amount, and this results in a change of the measured phase of the targets. The magnitude of the change is a linear function of the change in the two-way travel time Δt of electromagnetic waves between the radar and the targets;
i1520-0426-14-4-978-e2
where f is the radar frequency. As a result, the phase difference caused by changes in refractive index of air in the path increases linearly with range and can be easily measured to derive Δn. Note that if the index of refraction then diminishes over a small region to a value smaller than no (Fig. 1c), the slope of the phase difference of ground echoes between the current time and the reference time reverses itself locally. This implies that if enough ground clutter is available along many radials, fields of refractive index could be retrieved by radar up to a range of 20 to 40 km. Beyond this range, few ground targets are visible on flat terrain.
What kind of phase changes can be expected for a given change in n, and what does it mean in terms of real meteorological variables? It is customary to express the index of refraction in terms of the refractivity N, defined as the amount that the index of refraction (in parts per million) exceeds the value in vacuum (e.g., Bean and Dutton 1968);
Nn6
At microwave frequencies, the relationship between N and the meteorological variables pressure, temperature, and moisture is
i1520-0426-14-4-978-e4
where P is pressure expressed in millibars, T is temperature in kelvins, and e is the water vapor pressure in millibars. Equation (4) has two terms: a density term, and an additional wet term, that makes the index of refraction fairly sensitive to moisture. Figure 2 illustrates how refractivity varies with temperature and moisture: at cold temperatures, the air cannot hold much moisture, and the index of refraction is mostly a function of temperature. As air temperature increases, the potential magnitude of the additional wet term increases so that the index of refraction becomes more sensitive to changes in moisture than to changes in temperature. As a simple rule, a change in N of one unit corresponds roughly to a change of 1°C in temperature or 0.2 mb (0.2 g kg−1 at sea level) in water vapor. Using (2), it can be seen that for a change of one unit in Nn = 10−6), a path of 1 km, and an S-band radar system (f = 3 GHz), Δϕ is 0.125 radians or 7.2°. This implies that a change in temperature of 1°C will result in a specific phase change (between the time when N = N0 and the time when N = N0 + 1) of 7.2° km−1. This is a significant phase change. For comparison, researchers working on rainfall measurements techniques relying on differential propagation (e.g., Sachidananda and Zrnic 1987) will observe such a specific differential phase signal (two way) between vertical and horizontal polarization for downpours of over 100 mm h−1. Such a large signal when dealing with measurements of the phase of ground targets forewarn potential aliasing problems as N can span up to 200 N units between dry and damp days (Fig. 2), and the range between two neighboring ground targets may reach several kilometers. For a radar wavelength of 10 cm (f = 3 GHz), the Nyquist interval is ±25 N units for a 1-km path or ±1 N unit for a 25-km path. Note, however, that the use of the various pathlengths between the many ground targets around the radar offers considerable possibilities to make dealiasing feasible.

No mention of hardware issues has been made so far because the technique can essentially be implemented on existing radars and data processing systems using only additions to the processing software. The only hardware requirement that may or may not be met in existing systems is to ensure a stable transmit frequency over long periods. To make proper refractive index measurements, good frequency stability is required. Although this is also the case for the phase measurements used in the computation of Doppler velocity, the length of time over which such stability must be achieved is significantly different. While stability over a few hundred milliseconds is enough for Doppler processing, stability over a period of several months to a few years is required to make accurate measurements of N. For example, a change in one part per million in frequency (3 kHz for S-band radars) over any given period will result in a bias of 1 N unit in refractivity measurements. Since this kind of long-term stability is not required for other weather radar applications, the stable local oscillator (STALO) in current operational radars may be inappropriate. Because the technique relies on the difference in the phase of targets between the current time and a reference time that may be months old, a drift in transmit frequency of less than 0.5 ppm between these two times is required to have better than 0.5-N-unit accuracy on the refractivity measurement. Except for the stability issue, if the radar can measure the phase of targets and sufficient ground echoes are present, this technique can be implemented readily.

3. Measuring fields of refractivity

The proposed technique relies on (2) to accurately evaluate changes in index of refraction from changes in targets phases. The first test to be made is therefore to look at the correlation between the two quantities. For such a test, two targets (power poles) located 20 km away from the radar but in nearly opposite directions were monitored for 48 h. Surface meteorological observations from the nearby Dorval airport (YUL) were used to compute the index of refraction near the ground using (4). The result of this test, showed in Fig. 3, shows a remarkable correlation between the two target phases as well as between the target phases and the computed index of refraction. The target to the south-southwest, generally more upstream given the southerly winds and the movement of weather patterns from the west, often changes in phase ahead of the northeast target. This bodes well for attempts to extract the two-dimensional structure of the refractivity field.

Two additional points must be made clear before trying to extract fields of N. First, whatever the elevation pointing angle used, the refractivity measured from a ground target at a specific azimuth and range would always be expected to be the same. This is because this technique uses fixed ground echoes for reference points. Even if the antenna is raised to a higher elevation, the target is still near the ground. One would expect only the strength of the ground echo to change, and the path to the target remains essentially the same. Since the antenna is generally from a few meters to a few tens of meters from the ground, and because most visible ground targets are generally elevated (buildings, towers, higher than usual terrain, etc.), the measurement of refractivity will generally be representative of conditions a few tens of meters above the ground, with this sampling level slightly increasing with range beyond the radar horizon. The second key point is that the measurement of fields of N is only practical in relatively flat terrain. This is because each target phase provides information about the average index of refraction over the radar–target (R–T) path. In order to compute fields of N, the contribution of the path R–T1 must be removed from the measurement along path R–T2 in order to obtain a valid measurement for the path T1–T2. This is only possible if the radar and the two targets are reasonably aligned. This situation generally occurs only in flat terrain, although it is conceivable that a constantly sloping terrain would also provide appropriate conditions. In hilly terrain, such alignment is unlikely for many targets. On the other hand, if horizontal stratification is assumed, the echoes from various levels could be used to retrieve an average vertical structure of N from the level of the lowest targets to the level of the highest targets using an inversion technique similar to the one used in radiometric observations of the earth by satellite. Since the radar used by the authors in this study sits in the middle of a sedimentary plain, focus was put on the flat terrain variation of the technique.

The type of ground targets also turns out to be an important factor. Not all ground targets give suitable returns. The ideal ground target must not move; this may seem trivial, but this rules out all extended ground targets that are covered by vegetation that can move with the wind, or very tall towers that also move significantly with the wind. All areas covered by water are also ruled out, including the radar-reflecting buoys used for navigation. The best ground echoes are those where the returns are dominated by a single “pointlike” target. Communication towers and power poles are good examples of such targets. In these cases, the phase of the target is also relatively insensitive to subbeamwidth inaccuracy in antenna pointing (as opposed to the case of extended targets where complex interference may complicate matters). The easiest method to determine the reliability of a ground echo for the purpose of this technique is to measure the phase of all targets for a period greater than an hour in steady meteorological conditions, selecting the echoes whose phase show the least high-frequency variability in time to eliminate capricious targets. Figure 4 shows (a) the ground targets around the McGill radar, (b) the land usage that characterizes the targets, and (c) the targets selected by such a process. It is seen that appropriate targets can be plentiful, especially over the city. Over several large areas, however (e.g., tree-covered hills, shadow areas due to obstacles), the coverage drops down significantly. One lingering problem with the automatic selection of targets is that echoes from sidelobes are often selected. The sidelobe echoes are unwanted, mainly because they contaminate measurements made at a given radial with information from another radial. Ideally, one would want to somehow prevent any computation from being performed in the contaminated cells, but this has not yet been done in our implementation.

To extract the refractivity information from the ground clutter data, one can proceed as follows. In regions with limited ground echoes, individual “good” ground echoes are identified, and careful phase measurements are made at every scan. Each of these good echoes is then paired with a neighboring one along the same radial from the radar to form a path. This allows us to measure refractivity along the path between these two targets by using (2) at the two extremities. The difference between the phase of these two targets is computed to obtain a pathlength in number of radar wavelengths modulo the closest integer number of radar wavelengths (since only phases can be easily measured). This pathlength measurement is then further subtracted to a similar pathlength measurement made between the same two targets during a calibration step (described below) at a previous time. Because the pathlength change between the calibration time and the current time may be larger than a wavelength, a dealiasing step must follow. Yet, there will be paths short enough so that aliasing will not occur since any possible change in refractive index will not be sufficient to change the pathlength by a wavelength. Hence, ΔN is first computed for short paths. These ΔN measurements are then used as first guesses for the next longer paths, constraining the dealiasing problem. In theory, the best dealiasing method is then a pyramid-like system, where short paths are computed first, providing guidance for the next longer paths and so on until the largest path is dealiased. In practice, given the variability in the measurements of refractivity, a point will be reached in pathlengths beyond which the variability in ΔN will result in variability in pathlength differences that becomes comparable to or exceed a Nyquist interval. For the longest paths, accurate dealiasing may be impossible.

In clutter-rich situations, if the phases of all the targets at the reference time are subtracted from the phases of the same targets at the current time, one can observe fringes in the phase difference Δϕ field (Fig. 5b). This image corresponds to the phase difference plotted at the bottom of Fig. 1b. The multiple rings occur because of the multiple folding of the phase difference as range increases. In this case, in regions where good clutter is present (mostly in the northeast and south for the McGill radar) Δϕ decreases regularly with range as the ambient N (≈310.5 N units) is smaller than the reference N (≈325.6 N units). Using (2), one can expect folding of Δϕ every 3.5 km, and this is actually observed. If the difference between the current and reference refractivity is uniform, fringes should make concentric circles around the radar. If they do not, gradients in refractivity must be present in the radar coverage area. In regions where good ground echo coverage is large and where such fringes appear, it is possible to measure directly dϕ)/dr using, for example, a covariance algorithm (such as is used in pulse-pair processing of Doppler radar data), but in range as opposed to in time. From this information, measurements of refractivity averaged over the path between the targets used by the technique (or in the regions over which the pulse-pair computation is done) can be made (Fig. 5c).

A final optional step is to transform the path measurements of refractivity into a field (Fig. 5d). This does not add any information but generally eases the interpretation of the data. Various approaches can be used. In our case, we start with an initial guess field that may be constant or the field deduced from the previous volume scan. An iterative two-step process follows. First, the points in the field that lie along the measured paths are forced up or down so that the field data respect the constraints set by the path integral values. Then the information is diffused by smoothing each point in the field with its immediate neighbors. After several iterations, in data-rich regions, an equilibrium is reached as efforts to smooth the field are exactly canceled out by the forcing process. The final result is the smoothest field that meets the constraints set by the path measurements. Because of the noise in the path measurements of refractivity, the resulting field shows a noticeable amount of small-scale artifacts, especially in the form of strong–weak couplets aligned along radials. Despite the noise, a clear larger-scale signal can generally be observed. In this example, a weak north–south gradient can be noticed with larger refractivity values observed to the north because of somewhat cooler and more humid conditions there than to the south.

The main weakness of the whole technique is the need for accurate reference or calibration information for all the targets. Ideally, during calibration, phase measurements of targets should be made only if the refractivity along the radar-to-target path is known using other means. Except in the case of a very limited number of targets, this solution is impractical. The easiest method, and the one that has been used here, is to collect phase data during a short period for which limited gradients of refractivity in space and time are anticipated and claim that these phase measurements are representative of what should be expected for N = Nref everywhere, with Nref computed from surface observations of temperature, dewpoint, and pressure. An ideal moment for such a measurement turns out to be immediately after a long-duration (several hours) stratiform precipitation event, preferably in windy conditions and cool temperatures: The combined effect of the precipitation and wind homogenizes the atmosphere, while the cool temperatures tend to narrow the possible range of values that refractivity can take if the homogeneous conditions are not perfectly reached.

4. Early results

Surface refractivity fields have been generated in real time at McGill University since early June 1996 using a calibration made in the end of April. Longer-term comparisons made with refractivity computed from surface stations (Fig. 6) suggest that the radar measurements have definite skill.

In general, in the Montreal area, horizontal gradients over the 30–40-km range covered by the radar are limited to about 5 N units, and except for exceptional events, changes in time are also fairly slow (Fig. 6). As a result, this makes refractivity one of the least contrasted of the fields that can be generated by a radar. However, preliminary data collected with the National Center for Atmospheric Research’s S-Pol radar suggest that in other regions, like in the Colorado high plains for example, considerably more small-scale variability can be observed both in time and in space.

Even in Montreal, more rapid changes can be observed when mesoscale or synoptic fronts are within range (Fig. 7), or when surface moisture is being modified by the passage of precipitation (Fig. 8). At this stage, the measured boundaries between regions of contrasting refractivity are somewhat fuzzy (Fig. 7) mostly because of limitations in the current algorithm: Reluctance in the algorithm to accept phase difference measurements when strong refractivity contrasts are present, computation of refractivity over paths of at least 1 km, smoothing of the information during the transformation from path information to field data, etc. Better techniques to use the phase data exist and will have to be tried.

Coverage stays relatively constant in time except under two circumstances. The first one occurs when vertical gradients of N are significantly different than when the calibration step was made and manifest itself by an increase in the small-scale variance of Δϕ. This increase in variance is due to the fact that all the targets are not exactly at the same height. Consider two neighboring targets of different heights but similar range. Because of the difference in target height, the actual paths from the radar to the higher target will be slightly over the one to the lower target. The small height difference combined with strong vertical N gradients will result in measurable differences in the travel time of radar waves, resulting in a phase difference. This additional variance in Δϕ makes the computation of Δϕ slopes in range more difficult, and fewer refractivity measurements are made. The second cause of reduction in coverage occurs when the reflectivity from precipitation clutter becomes strong enough to mask the ground echo signal. Another effect of precipitation is to add an additional delay in the travel time of electromagnetic waves between the radar and the target. This effect is, however, relatively minor: A sustained rainfall rate of the order of 15 mm h−1 along a path is required to cause a bias of 1 N unit in the measured refractivity for that path.

Although the refractivity field does not often contain structures with high contrast, the frequency with which weaker mesoscale gradients in refractivity can be observed has been larger than we expected. Since such gradients are not constant in time, they are unlikely to be artifacts solely due to a bad calibration done in nonideal conditions. As a result, it seems reasonable to conclude that radar measurement of surface refractivity may provide some additional information on surface temperature and moisture fields that is not available from point measurements made at conventional surface stations. Establishing the value of such information is the subject of ongoing work.

5. Conclusions and potential

We have shown in this paper that ground echoes could be successfully used to obtain information about the atmosphere between them and the radar. The use of the radar phase information from ground targets to extract a measurement of refractivity near the surface has been demonstrated to be theoretically feasible and practically workable, to the point where it is now computed in real time around the clock. While all the work presented here involved “natural” ground echoes with their limitation, nothing prevents the addition of intentional targets (corner reflectors, etc.) to enhance the coverage, usability, and reliability of the measurement.

Although the interpretation of the refractivity field can be ambiguous, it offers the possibility of getting some glimpse on the two-dimensional structure of the temperature and moisture fields in a similar way that radar reflectivity allowed us to get a better appreciation of precipitation variability. Detailed observations of front passages, microbursts and cold pools associated with thunderstorm outflow, and other possible dry or wet spots may be made using refractivity information derived by radar.

Possible uses of refractivity will likely depend on the sensitivity of the measurement and the coverage that can be obtained. Examples include extraction of low-level moisture information for the purposes of data assimilation in models and thunderstorm initiation prediction; boundary layer studies where refractivity allows us to see a proxy field for temperature and moisture evolve in space and in time; and of course electromagnetic wave propagation work.

REFERENCES

  • Bean, B. R., and E. J. Dutton, 1968: Radio Meteorology. National Bureau of Standards Monogr., No. 92, National Bureau of Standards, 435 pp.

  • Bevis, M., S. Businger, T. Herring, C. Rocken, R. Anthes, and R. Ware, 1992: GPS meteorology: Remote sensing of atmospheric water vapor using the Global Positioning System. J. Geophys. Res.,97, 15 787–15 801.

    • Crossref
    • Export Citation
  • Businger, S., and Coauthors, 1996: The promise of GPS in atmospheric monitoring. Bull. Amer. Meteor. Soc.,77, 5–18.

    • Crossref
    • Export Citation
  • Sachidananda, M., and D. Zrnic, 1987: Rain rate estimates from differential polarization measurements. J. Atmos. Oceanic Technol.,4, 588–598.

    • Crossref
    • Export Citation
  • Ware, R., and Coauthors, 1996: GPS sounding of the atmosphere from low earth orbit: Preliminary results. Bull. Amer. Meteor. Soc.,77, 19–40.

    • Crossref
    • Export Citation

Fig. 1.
Fig. 1.

Illustration of the effect of index of refraction changes on the phase of ground targets. The phases of five arbitrary targets (T1, . . . , T5) at (a) an initial condition, and (b) its change as refractivity increases at all ranges, or (c) increases up to a given range and decreases beyond are presented. The dials illustrate either the current phase of the targets (top), or the difference between the current phase of the targets and the reference phase when n = no (bottom).

Citation: Journal of Atmospheric and Oceanic Technology 14, 4; 10.1175/1520-0426(1997)014<0978:OTEONS>2.0.CO;2

Fig. 2.
Fig. 2.

Diagram illustrating the values that refractivity can take for given temperature and moisture for a pressure of 1000 mb. In inset, the formula used to compute N as well as some refractivity values calculated for a dry and saturated atmosphere at a few temperatures are shown.

Citation: Journal of Atmospheric and Oceanic Technology 14, 4; 10.1175/1520-0426(1997)014<0978:OTEONS>2.0.CO;2

Fig. 3.
Fig. 3.

Illustration of the correlation between target phase and refractivity. Two targets on power lines at a similar range (20 km), but in opposite directions, were selected. Their position with respect to the radar and the Dorval airport (YUL) is shown at the top-left while the top-right window shows a 0.5° PPI of received power where the echoes selected are highlighted. In the bottom window, the time evolution of the phase of the two targets (solid and dotted line, right scale) is contrasted with refractivity computed from YUL observations (crosses, left scale). Some weather observations from YUL are also plotted at the top of the window using the station model; periods over which precipitation was observed are also indicated.

Citation: Journal of Atmospheric and Oceanic Technology 14, 4; 10.1175/1520-0426(1997)014<0978:OTEONS>2.0.CO;2

Fig. 4.
Fig. 4.

(a) Low-level (0.5°) PPI of received power up to 45-km range illustrating the coverage of ground echoes around the McGill radar. (b) Sketch of the land usage and topography over the same area. (c) Mask of the ground echoes used for the measurement of refractivity. Coverage is good over areas covered by fixed targets (urban areas), while much poorer over areas covered by moving targets (forests).

Citation: Journal of Atmospheric and Oceanic Technology 14, 4; 10.1175/1520-0426(1997)014<0978:OTEONS>2.0.CO;2

Fig. 5.
Fig. 5.

Procedure to extract refractivity measurements from ground targets. (a) The phase of ground targets is measured; (b) the phase of targets from the reference map are subtracted from them; (c) in regions where the phase difference data is well behaved, path-integrated measurements of refractivity are computed using (2) and a value of 325.6 N units for the refractivity at the reference time; (d) a field is generated using the path-integrated measurements of N. Range rings are every 10 km.

Citation: Journal of Atmospheric and Oceanic Technology 14, 4; 10.1175/1520-0426(1997)014<0978:OTEONS>2.0.CO;2

Fig. 6.
Fig. 6.

Time series of refractivity over a 60-day period (16 June–14 August 1996) from radar (solid line) and surface stations (crosses) data. The radar refractivity data are field averages up to 45-km range measured every 5 min. The refractivity from surface stations was computed from hourly pressure, temperature, and moisture measurements at the eight stations plotted in Fig. 7.

Citation: Journal of Atmospheric and Oceanic Technology 14, 4; 10.1175/1520-0426(1997)014<0978:OTEONS>2.0.CO;2

Fig. 7.
Fig. 7.

Example of a contrasted refractivity field. (a) Surface weather observations of temperature, dewpoint, cloud cover (when available), and winds at various stations around the radar site at 1400 UTC. The refractivity computed from these observations is indicated in brackets. (b) Refractivity field measured by radar 10 min later. A significant gradient in refractivity is observed because of the difference in the dewpoint temperature of the two air masses (Td = 10°C vs Td = 14°C). The two outer circles correspond to a distance of 45 km from the radar.

Citation: Journal of Atmospheric and Oceanic Technology 14, 4; 10.1175/1520-0426(1997)014<0978:OTEONS>2.0.CO;2

Fig. 8.
Fig. 8.

Example of a refractivity field in light precipitation. (a) Reflectivity from weather echoes (moving from the west-southwest) over a 240 km × 240 km area around the radar. (b) Refractivity field measured for the same period. Higher refractivity can be seen toward the southwest due to an increase in surface moisture associated with the approaching rain. The two circles correspond to a distance of 45 km from the radar.

Citation: Journal of Atmospheric and Oceanic Technology 14, 4; 10.1175/1520-0426(1997)014<0978:OTEONS>2.0.CO;2

* The National Center for Atmospheric Research is funded by the National Science Foundation.

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