Correlation coefficient on radar

Correlation coefficient (CC, written ρ_hv in the literature) is a dual-polarization radar product that measures how similarly the horizontally and vertically polarized returns behave from pulse to pulse, which makes it a gauge of how alike the targets in one sample volume are. High values mean one kind of target; low values mean a mixture, or something that is not weather at all.

The how to read weather radar guide introduces CC in a few lines. This page is the working reference: what the number responds to, the ranges for each target type, and the artifacts that lower it for no meteorological reason.

What CC responds to, and what it ignores

The NWS dual-pol reference guide published by the Corpus Christi forecast office defines CC as a measure of how similar the horizontal and vertical pulses are behaving from pulse to pulse. Matthew Kumjian’s three-part review in the Journal of Operational Meteorology (2013) gives the physical version: CC measures the diversity of how each scatterer in the volume contributes to the two signals. A variety of particle types, shapes or orientations lowers it.

Two consequences are easy to miss. First, Kumjian notes that a range of sizes alone does not lower CC unless shape changes with size, so CC is not a hail-size meter. Second, CC is also lowered by non-Rayleigh (resonance) scatterers, objects large relative to the 10 cm wavelength, which is part of why giant hail and melting snowflakes drag it down. Part III of the review also states that CC is not affected by attenuation, a point that matters in the pitfalls below.

On the WSR-88D the product runs from about 0.2 to 1.05, per NWS Jackson, Mississippi. A true correlation cannot exceed 1, so values above it are estimation noise rather than an especially uniform target.

Typical values

These are S-band ranges from operational training and review literature. They overlap, which is the point: CC narrows the possibilities and the other fields decide.

The NWS Warning Decision Training Division’s dual-pol decision aid sums up the precipitation side: CC values of 0.9–1.0 are most likely for precipitation, and its rain values assume pure rain, with lower values expected when precipitation types mix.

Meteorological or not

Discrimination is CC’s most common job. Kumjian lists the non-meteorological targets that generally produce CC below 0.80: military chaff, smoke and ash from fires or volcanoes, insects, birds and bats, sea clutter, dust, and tornadic debris. Warm-season biological “blooms” around a radar are the everyday example; on reflectivity they look like light rain, on CC they fall apart into low, noisy values.

Wildfire smoke is the clearest case. Kumjian’s Part I shows a grassfire north of the Melbourne, Florida radar (KMLB) at 2114 UTC on 31 January 2012, its plume marked by CC below 0.50 on the 0.5° scan.

One caution from the same paper: man-made clutter such as buildings, water towers and wind turbines can produce low CC, but the observed values overlap with the high values typical of precipitation. Low CC argues against pure rain; high CC is not proof of weather. The tornado application, where low CC sits on a velocity couplet, has its own page: the tornado debris signature.

The NWS dual-pol quality-control step used for precipitation estimates leans on the same idea. WDTD describes it as starting from a CC filter that removes pixels below 0.95, which it calls very aggressive, then adding back precipitation that is legitimately low in CC, such as hail or areas of non-uniform beam filling.

The melting layer and the rain–snow line

In stratiform precipitation the melting layer is, in Kumjian’s words, “unmistakable” in CC. Snowflakes acquire meltwater, a mixture of partly melted flakes and small drops forms, and the largest wet flakes scatter outside the Rayleigh regime. CC dips most near the bottom of the layer. On a higher tilt this shows as a ring of lowered CC around the radar where the beam crosses the layer.

The WSR-88D’s melting layer detection algorithm uses reflectivity, ZDR and CC at elevation angles of 4° to 10°, and Kumjian notes it generally agrees well with sounding and model estimates of the layer top. It is built for widespread stratiform precipitation; in convection, well-defined melting layers are often absent.

Near the ground the same signal marks transitions in winter storms. Kumjian’s Part II walks through the Upton, New York radar (KOKX) at 1604 UTC on 21 January 2012: dry snow to the north with high CC, a band of wet snow with reduced CC, and rain or freezing rain with high CC inside it. That band moved north over time and marked the changeover across Long Island. CC alone does not name the surface precipitation type; the paper pairs it with soundings and surface observations.

Hail

Hail lowers CC through mixing and shape, not size. Kumjian notes that pure dry hail aloft can give CC as high as rain; wet hail gives values below 0.95, and very large hail can drop below 0.85, likely because of lobes and spikes grown in wet growth. He is explicit that reduced low-level CC and hail size do not have a direct relation. For hail size, CC is a flag, not a measurement.

Artifacts that fake low CC

• Non-uniform beam filling. A radial stripe of low CC behind a strong core is, in Kumjian’s Part III, “often confused with attenuation” but caused by non-uniform beam filling. The beam broadens with range; if one part of it sits in heavy rain or melting particles and another in ice, the spread of differential phase inside the volume lowers CC. It is common with distant storms.
• Three-body scatter spike. Energy scattered from hail to the ground and back produces a spike of weak echo extending away from the radar behind the core. Kumjian reports CC below 0.5 near the storm. William Martin of NWS Glasgow, in a 2014 AMS conference paper, calls CC near 0.5 a universal feature of these artifacts and found spikes far easier to see in CC than in reflectivity. The spike is a hail indicator in its own right, but its CC says nothing about the targets along that radial.
• Weak signal. CC estimates get noisy where returned power is low: storm edges, light echo, long range. Kumjian notes that reduced CC raises statistical fluctuations in every polarimetric variable, and the NWS Corpus Christi reference guide notes that KDP is not displayed in AWIPS where CC is below 0.90. Judge low CC against reflectivity before reading anything into it.

A working read

Read CC beside reflectivity, never alone. Ask whether the low values sit in solid echo or at its fringes, whether they form a radial stripe pointing away from the radar, and whether they form a ring at a fixed height. Then check ZDR to decide between hail, melting snow and non-weather targets. When low CC sits on rotation instead, the reading moves to the tornado debris signature.

WeatherStory Radar decodes correlation coefficient from raw Level II alongside reflectivity, velocity, ZDR and KDP, and shows the exact value at any gate you click.