101: Weather Radar (Polarimetry)

Much of the science behind dual-polarimetric radar concepts is rather complicated, so only basics will be covered here. For a more in-depth explanation see the National Weather Service's manual here and an extended one from their training course here.



Dual-Polarimetric Radar


Polarimetry

Scientifically speaking, light is nothing more than a type of electromagnetic energy. When conceptualized as a wave, electromagnetic energy is comprised of two oscillations: an electric wave and a magnetic wave (figure 1). These two components are oriented at right angles to each other and are self-propagating. This means that the electric wave induces the magnetic wave, which then induces the electric wave, and so on. These two waves have a specific orientation when emitted. In the case of television broadcasts, the waves are oriented with the electric field component horizontal to the ground, therefore they are considered to be horizontally polarized. Traditionally, weather radar has also been horizontally polarized, which is useful since most rain drops flatten out as they descend. However, rain is not the only target radars pick up on, thus having multiple polarities yields more information about what the radar is seeing.

Figure 1: The basic representation of an electromagnetic wave. The E axis is the electric wave, the B axis is the magnetic wave, and z is the direction of propagation. The distance indicated by the brackets is one wavelength. In this case, the beam would be considered vertically polarized.

Although the concept of radar with multiple polarization dates back to WWII, the first radars to actually implement it did not come about until the 1970s. However, this was limited to a few research radars, since the computing power required to process various polarity signals simultaneously and in real time did not exist on a large scale. As computing power matured, the concept of a dual-polarity ("dual-pol") radar network was considered. The remaining limiting factor was the cost of the hardware itself. To create a dual-pol network, radars would have to include equipment that switched the polarity of the beam from horizontal to vertical rapidly. Such a configuration would be far too expensive to implement. Furthermore, requiring the beam to constantly switch polarity would greatly increase the time the radar would need to complete a volume scan. The solution was to take existing radar hardware and adjust it to emit a beam at a 45 degree angle to the vertical. When this beam was backscattered back to unit, the radar's computer would separate the horizontal and vertical components of the signal and compare them as if two separate signals had been emitted. With the software and hardware now available, the National Weather Service approved a conversion of all existing WSR-88D units into dual-pol radars in 2003 and by the end of 2013 the entire NEXRAD network had been updated (figure 2).

Figure 2: The Lubbock, TX, radar (KLBB) being upgraded for dual-pol capability.

Dual-pol radar allows for the comparison of the strength of the horizontal and vertical components of the beam (figure 3). This does not mean the radar is able to directly detect the actual horizontal and vertical dimensions of the targets its sampling, only the general shape of the targets. This can be compared to observing a large cluster of buildings from far away. It is impossible to know how tall or wide the buildings are, but it is possible to compare their height to their width. With this knowledge, one can make some inferences about the nature of those buildings, even if their actual size is unknown. For example, observing a large cluster of buildings that were many times taller than they were wide might indicate to the observer that the buildings were part of the downtown area of a major city. On the other hand, a large number of building that were much wider than they were tall could mean they were part of an industrial district full of warehouses. Finally, a cluster of buildings whose width was generally similar to their height would likely indicate a suburban neighborhood with lots of one or two story houses. Dual-pol radar works in much the same way, however it expresses its information in the form of three different base products: differential reflectivity, correlation coefficient, and specific differential phase. The products are packaged along with the original three base products (reflectivity, velocity, and spectrum width) in the level II data stream of all dual-pol radar data.

Figure 3: Conceptual diagram of the two different polarities measured by dual-pol radar. The E indicates that the electric portion of the wave is being shown.

Differential Reflectivity

Commonly abbreviated as ZDR, differential reflectivity is the ratio of the power returned in the horizontal from that returned in the vertical (figure 4). Like traditional reflectivity, ZDR is expressed in dBZ (some sources label express it in units of dB), a logarithmic unit (i.e. ZDR=10*log(horizontal reflectivity/vertical reflectivity)).  Therefore, positive values indicate stronger returns in the horizontal, while negative values indicate predominately vertically polarized reflectivity. Thus, this product provides information on the shape of the targets and values typically fall between -2 and +6 dB.

Figure 4: Comparison of differently shaped targets and how they affect the ZDR value. The values of Z with subscripts H and V refer to the horizontal and vertical polarity of reflectivity, respectively.

Since large rain drops, typically associated with heavy convective showers, tend to flatten out as they fall due to drag, areas of heavy rain will typically have ZDR values of at least 3 (figure 5). On the other hand, large hail that has accreted from multiple smaller stones tend to take on more of an irregular shape. When these fall, they tend to orient themselves vertically due to wind, generally resulting in ZDR values between -1 and 0. Very light rain, snow, ice crystals, and small hail tends to yield a ZDR near zero due to their relatively spherical nature (figures 6 and 7). Tornado debris also tends to appear as near zero values, not because the particles of debris are spherical, but because they are of all different shapes (and often rotating rapidly) the net result is nearly equal returns in the horizontal and the negative (figure 6). Biological targets such as birds and insects generally produce very large positive ZDR values because their wings are typically oriented horizontally.

Figure 5: Drop size affects its shape and therefore its ZDR value as these images of drops captured on high speed camera during a laboratory experiment demonstrate.

Figure 6: ZDR and reflectivity data of the supercell that produced the EF-5 Moore, OK, tornado on  May 20th, 2013. This scan is from 2003 UTC and two unique ZDR signatures, highlighted by the white boxes. In the southwest portion of the image is the debris ball produced by the tornado. The debris itself produced a very noisy signal, but overall the values tended to be around 0 dB. To the north, hail was occurring, which also resulted in ZDR values near 0 dB. Neither of these features are immediately obvious from the reflectivity image alone. The 0.9 degree tilt was used here instead of the 0.5 degree tilt due to the storm's close proximity to the radar (the tornado was about 15 nautical miles (nm) away from the radar (KTLX) at the time).

Figure 7: These two supercells formed during the same 2013 outbreak. The ZDR image uses a high tilt which, judging by the generally low values, intersected the storm above the melting layer. However, a few isolated areas of high values do occur. The cluster of high values near Purdy (about 40 nm south-southwest of the radar) represents the updraft core of the storm, which is lofting water drops above the freezing level before they have a chance to freeze. These are called ZDR columns and they are useful in identifying the core of severe storms.

Figure 8: This cross-section directed towards the northeast away from the radar intersected several storms. While noisy, most gates drop down to near 0 dB around 11,000 feet, the level of the white line, which indicates this is the top of the melting layer. A few spikes of higher values above the line are ZDR columns from various storms.

Correlation Coefficient

Often referred to simply as CC or the Greek letter rho, correlation coefficient compares the consistency between the returned power in the horizontal from that in the vertical. Therefore, little change in the orientation of targets from pulse to pulse results in high values, while inconsistent returns produce a low value. CC is expressed in unit-less values between 0 and 1, or as a percent between 0% and 100%. In general CC values between 0.97 and 1 are considered high, between 0.95 and 0.96 medium, 0.6-0.94 low, and 0-0.6 very low. Low and very low values are generally due to non-meteorological targets, medium values are often associated with a high diversity in hydrometeor (the general term for all types of precipitation) types and shapes, and high values are associated with uniform precipitation that does not consist of particles that change orientation significantly (figures 9 and 10).

Figure 9: The same frame used in figure 6 is used here to show the incredibly low CC values the tornado debris produced. The area of hail to the north, which was likely mixed with some rain, also produced relatively low values. Regardless of their reflectivity intensity, precipitation outside these areas tended to have high values due to their uniformity.

Figure 10: Looking at the reflectivity image, it appears that a small shower was occurring over Seattle, WA, just after midnight on New Year's day, 2016. However a look at the very noisy CC signal indicates otherwise. The night was perfectly clear and the "shower" was actually smoke from a large fireworks display happening at the Space Needle.

One key strength of CC is its ability to highlight the melting layer. As frozen precipitation falls below the freezing level it begins to melt. While melting, these hydrometeors consist of ice coated with a layer of liquid water, resulting in high reflectivity values. On a radar display of reflectivity, this zone will appear as a "bright band" of high values, since the beam gets higher with distance. From the freezing level to the level in which all the ice has melted (leaving only rain drops) there is a wide variety of shapes present that all have different aerodynamic properties and therefore fall in slightly different ways. As a result, this melting layer will have often have CC values less than 0.95, while above and below the layer values will be very close to 1 (figures 11 and 12).

Figure 11: This area of precipitation near the TX/LA border on January 6, 2016, shows the bright band in both CC (left) and reflectivity (right). The rings indicate the top and bottom of the melting layer. A high tilt was used to capture higher parts of the precipitation and to lessen the noise that often occurs closer to the ground.

Figure 12: A CC cross section along the leading edge of the main area of precipitation shows the lower values associated with the bright band, the center of which is indicated by the white line.

Specific Differential Phase

This product, also known as KDP, essentially applies the concept used in radial velocity measurements to the two component polarization returns and compares them. The basis of this product is a value known as differential propagation phase (sometimes simply called differential phase). To conceptualize this measurement, consider the wave shape concept introduced in the velocity post. Recall that differences between two pulses' waves, the phase shifts, were expressed in units of degrees. To obtain differential phase the phase shift to the vertical component is subtracted from the phase shift to the horizontal component. Differential phase is additive along each radial; that is, the value will change every time the beam passes through precipitation as it propagates outward without returning to any base value. For example, imagine there are two rain shafts the radar beam encounters along a radial: the first causes a differential phase of 11 degrees, and the second causes 14 degrees. The value along the radial would be 0 until the first shower, after which each gate would keep the value of 11 degrees until reaching the second shower. After the second shower the remaining gates in the radial would not have a value of 14 degrees, but 25 degrees (the total shift), since the value never reverted back to 0. This property gives radar images of differential phase a streaked appearance that makes interpretation difficult (figure 13).

Figure 13: The differential phase image of supercells, some of which were featured in figure 7, says very little about the storms except that the beam must have passed through some heavy, non-spherical targets, as indicated by the red and purple streaks.

To address the issue differential reflectivity produces, specific differential reflectivity (KDP) presents difference per kilometer. Thus KDP is displayed in values of degrees per kilometer. In the example used above, KDP would be 0 between the two showers since the value of differential phase was not changing along that portion of the radial. Essentially, KDP is the gradient of differential phase with distance; the more differential phase changes with distance, the greater the KDP value. This product has been found very useful for detecting heavy rain, as that produces high KDP values, while filtering out most spherical hydrometeors, since they behave similarly in both the horizontal and vertical (figure 14). Thus, in winter weather situations, KDP can help single out areas of liquid rain. Unfortunately, the archived level II data only offers differential phase; KDP is only available in NWS offices and as level III data.

Figure 14: The KDP image of the same storms as in figure 13 is much more meaningful and  highlights areas of heavy rain.

Level III Products (and their product codes)


Level III Differential Reflectivity (N0X, N1X, N2X, N3X, and others)
These are simply flat, individual files of the lowest few tilts of base ZDR with some quality control.


Level III Correlation Coefficient (N0C, N1C, N2C, N3C, and others)
These are simply flat, individual files of the lowest few tilts of base CC with some quality control.


Level III Specific Differential Phase (N0K, N1K, N2K, N3K, and others)
These are simply flat, individual files of the lowest few tilts of base KDP with some quality control. Note that this is specific differential phase, not differential phase (which is not offered as a level III product).

Melting Layer (N0M, N1M, N2M, N3M, and others)
The Melting Layer Detection Algorithm (MLDA) uses ZDR and CC to try to identify the bright band by assuming it is comprised of wet snow. In cases where there is not enough echoes to reliably establish the melting layer, the MLDA uses elevations provided by either the radar operator or the most recent computer weather model output. In radar programs that support the display of the melting layer, the data will appear as four overlaid rings; typically two bold rings in the middle and two dull or dashed rings on either side of the bold ones. Since the radar beam's altitude increases with range, the rings' radius acts as sort of a proxy for their height above ground. The inner bold ring represents the altitude that the center of the beam enters the melting layer while the second bold ring represents where the center of the beam exits the melting layer. Furthermore, the innermost ring (dull or dashed in appearance) corresponds to the height at which the top of the beam enters the melting layer, while the outermost ring (dull/dashed) represents where the bottom of the beam leaves the melting layer. Therefore, all mixed phase precipitation should fall somewhere between the inner and outermost rings.

The MLDA is not without its own issues, however. In cases of intense convective updrafts the melting layer will increase locally, which may or may not be captured by the MLDA. Furthermore, the radar assumes that once the precipitation has melted, it will not refreeze. In winter weather situations, such as the area just to the cold side of a warm front, a layer of cold air will exist near the surface. If this layer is deep and/or cold enough, precipitation will refreeze and sleet or ice crystals will occur at the surface. Since this will not be picked up by the MLDA, those using radar data should check to see if there is a sharp increase in ZDR or decrease in CC below the identified melting layer if a refreezing layer is suspected (figure 15). Finally, small zig-zag patterns often appear on the melting layer rings (figure 16). Since the MLDA is highly sensitive to the radar's tilt, the slight wobble that occurs as the radar settles after it changes its tilt during scanning will produce these small errors. The longer the radar takes to complete a scan, the more errors will occur. Therefore, in clear air modes, such as VCP 32, far more errors will be noticeable than in fast scans such as VCP 12.

Figure 15: An ice storm near Grand Rapids, MI, on December 22, 2013 illustrates a shortcoming of the MLDA. The CC image on the left indicates that the melting layer, marked by the white rings, was relatively accurate. However, a layer of cold air near the surface caused much of the precipitation to refreeze, as indicated by the low CC values. The MLDA does not account for the refreezing layer, so a simple display of reflectivity and the melting layer rings would give an observer a false understanding of the surface weather. The ZDR image on the right also shows the melting layer, but does not pick up the refreezing layer quite as well.

Figure 16: Using different tilts, the melting layer's altitude at different locations can be determined. On this night in western WA, the freezing level was fairly uniform across the region. At the time, the radar (KATX) was in a clear air mode. The slow rotation rate of the antenna in this VCP produced the many "jumps" in the melting layer rings as it changed its tilt.

Hydrometeor Classification  (HCC, N0H, N1H, N2H, N3H, and others)
The Hydrometeor Classification Algorithm (HCA) might be seen as the ultimate product of the dual-pol upgrade. The HCA uses every base product, except spectrum width, along with the output from the MLDA to try to determine what the primary type of target the radar is sampling (figure 17). It is imperative to remember that the HCA only estimates the type of target it is sampling at the height of the beam. This means that while the HCA might indicate snow, it may be raining at the surface, since the snow has melted between the level of the radar beam and the ground. Due largely to its association with the MLDA, it also assumes a refreezing layer does not exist, thus it may indicate rain even if that rain has refroze into sleet. Above all, the HCA is a new technology that is regularly being revised, so expect some errors to occur and cross-reference its output with other base products (figures 18 and 19).

A special product of the HCA is the Hybrid Hydrometeor Classification (HCC). This product decides what best estimate of target type is being sampled for each gate in the best/lowest available scan. This information is then sent to the dual-pol precipitation products: OHA and PTA (see the radar post on reflectivity). Since the relationship between reflectivity and precipitation amount varies with the type of precipitation, the HCC information allows the proper reflectivity-precipitation algorithm to be applied to each gate, greatly improving the accuracy of the precipitation products. Like the other HCA products, this product is still very much a work in progress, but early studies have already found it to be much more accurate than the old precipitation estimation methods.

Figure 17: From the same scan as figures 6 and 9, the HCA seems to have been quite successful in estimating the target type. The only exception is the area of hail noted where the tornado was located. This was almost certainly tornado debris being misidentified as hail. The fact that somehow a single gate of "ground clutter (GC)" was identified near the middle of the debris ball corroborates with this theory.

 

 

Figure 18: Later in the same ice storm featured in figure 15, the HCA  (top left) erroneously estimated that dry snow (DS) was occurring all the way to the ground, even though surface maps from that time (bottom) indicated that stations throughout the area were experiencing freezing rain or drizzle.

Figure 19: Whenever in doubt of of the HCA, use this table to try to diagnose target type by using reflectivity along with the full range of dual-pol products. None of these values are strict rules, but this table can act a a great "second opinion".

Note: Much of the information used in these radar posts was based on content covered in the Weather Radar Handbook (2013) and Severe Storm Forecasting (2009) both by Tim Vasquez and published by Weather Graphics Technologies.