Measured and detected: radar hail sizes against spotter reports

Every record is filed under the kind of evidence that produced it

A hail size measured on the ground and a hail size computed from radar are different objects: one is a record of what fell at a place, the other is an estimate of what a storm could have produced over a grid cell, and no page or document on this site prints them in the same column. The distinction is not a matter of confidence. It is a matter of what kind of thing each figure is, and the record keeps it because a court will ask.

Every record in the archive carries the kind of evidence that produced it, in the vocabulary the document uses.

Ground observation

A person saw the hail and reported its size: a trained spotter, a cooperative observer, an emergency manager, a member of the public whose report an office accepted. Filed at a point and a time under the Weather Service's directive for preparing storm data.

Weather station

An instrument recorded a reading: a gust, a sustained speed, a temperature, a rainfall. Calibrated, maintained and logged on a schedule, whether or not a storm was passing.

Radar detection

A radar's return over a place at a time met the hail criterion, and the radar's own processing logged the signature with its location and its time. A record that the instrument saw something, filed as the instrument's record.

Official NWS warning

A forecast office issued a warning for a polygon and a period. A record that the office judged the storm severe at the time, not a record of what fell.

Federal declaration

A federal disaster declaration naming a county for an event and a period. A record of the administrative finding, at county resolution.

Satellite detection

An orbiting sensor detected a signature, such as a fire, at a point and a time.

Gridded analysis Analyzed

A value computed for every cell of a grid from instrument data, whether or not anyone was standing in the cell: the radar-derived hail size, the hourly wind field. Carries its qualifier wherever it is printed.

Reanalysis model Estimated

A value interpolated from a reanalysis: a model's reconstruction of the atmosphere, constrained by observations but measured nowhere. Carries its qualifier wherever it is printed.

The line falls between what was sampled and what was computed

The record draws one line through that list, and it is worth being exact about where. On the observed side sit the kinds that record a sample: a person's measurement, an instrument's reading, a radar's logged signature, an office's warning, an agency's declaration, a satellite's detection. Each is a record that something happened at a place and a time, filed by whoever or whatever witnessed it, traceable to its line in the federal archive.

On the other side sit the two computed kinds: the gridded analysis and the reanalysis model. Neither is a sample at the roof. An analysis takes the radar volume, or the station network, and computes a value for every cell of a grid; a model reconstructs the whole atmosphere and interpolates a value onto the same kind of grid. Both are useful, and the analysis in particular is the only kind of evidence that covers ground nobody reported from. But the value at the property is computed, not measured there, and so it stays on the estimated side of the line and carries its qualifier.

The point that is easy to miss is that a radar detection and a radar-derived size fall on opposite sides. A detection is a logged event: the radar's return over that place at that time met a criterion, and an office recorded that it did. A radar-derived size is a computation over the same return. The first is evidence that the radar saw hail-like returns there. The second is an estimate of size, and the record calls it one.

A radar-derived size is a ceiling on what the storm could have produced

A weather radar does not see hailstones. It measures how strongly the volume of air above a point returns its signal at a series of heights, and the hail algorithm takes the part of that return above the freezing level, where ice is more likely than rain, weights it by how far above freezing it sits, and fits the total to a hail size. The fit was published in the open literature and has been tested, reviewed and revised since, which is what a court asks of a method. What the literature says is what a reader needs to know before citing it.

• It was designed as an overforecast. The authors of the algorithm calibrated it so that most measured stones fall below the radar's estimate for the same storm, because a warning forecaster would rather be told a storm is capable of large hail than not. The figure is a ceiling by construction.
• It diagnoses hail more often than hail is reported. A climatology built at the Storm Prediction Center from the operational product found severe hail diagnosed by radar across far more hours and places than the report record holds, most of all overnight and over open country where nobody files a report. Some of that gap is hail that fell unreported; some of it is the overforecast.
• Its size depends on the fit. A long radar record rebuilt with the original relationship reads low against reported sizes, which themselves tend to understate the largest stones; relationships tuned to the largest reports read high in some regions and produce several times more hail days than the report record. A figure whose value moves with the choice of fit is an estimate, whichever fit is chosen.
• It misses in known ways. The training material for forecasters lists storms in which it underestimates: strongly tilted storms in deep shear, left-moving supercells, storms with a large weak-echo vault, storms producing low-density hail. Melting on the way down, the height of the beam at long range and contamination from the melting layer all sit between the echo and the ground.

None of this makes the figure worthless, and the report draws its hail swaths from it for the reason the literature gives: it is the only kind of evidence with coverage, and the only way to say that a storm's hail signature passed over a property nobody reported from. What it cannot say is that hail of that size fell there. A large radar-derived size over a roof is a reason to look at the roof and to look for a measurement nearby. It is not the measurement, and a document that prints it as one has made a claim the literature declines to make.

A filled mark and a hollow mark never look alike

Because the two kinds of figure are different objects, they are drawn as different objects everywhere a figure appears: on the free pages, in the report, on the map and in the exported document. The treatment is the same on every surface.

The shapes were chosen so that the difference survives every way a page can be degraded. A filled square and a hollow ring differ in shape as well as in colour, so the distinction holds in greyscale, on a photocopy and for a reader who cannot tell the two tones apart. The qualifier is text, so it survives being read aloud and pasted into a letter. Nobody has to remember which colour meant which; the hollow mark is the one with nothing inside it.

Reading the two side by side

Where the record holds both kinds of figure for a day, the useful reading is of the pair. Each answers a different question, and neither corrects the other.

A measurement without a detection

Hail was on the ground at a point; the radar did not compute a size there, or the analysis was not run for that hour. The measurement stands. Absence from the grid is not evidence against a person who held the stone.

A detection without a measurement

The storm was capable of hail over the cell, and nobody reported from it. The most common case in the open country and overnight. A reason to search the ground record more widely and to expect, at most, a size at or below the figure.

Both, and the detection is larger

The case the original fit was built for: the estimate was calibrated so that most measured stones fall below it. The measurement is the size of a stone that fell; the detection is the size the storm could have made.

Both, and the measurement is larger

It happens, and it is why the two are never averaged. The storm was one the algorithm is known to underestimate, or the largest stone fell where the observer stood and not where the grid cell's echo was strongest.

What a reader should not do is add them, average them, or let one stand in for the other. A day carried by a ground observation and a radar-derived size is attested by two independent kinds of evidence, not attested at the larger of the two sizes. A day on which the largest report reached 1.00″ counts as severe on these pages whichever kind of report it was, and the page says which.

What the report shows

A Titan Weather report for an address lists every measured record with its source, its time, its size in the source's own units, and its distance and bearing from the address, banded as primary within 3 miles and contributing within 10 miles. The radar-derived size for the property's own grid cell is printed beside them in its own column, with its qualifier, its time and the cell it was computed for, and the hail swath on the map is drawn from it and says so. Where a person measured hail on the same day, the two figures appear together with each one's source, and neither is adjusted toward the other.

The statement of compilation says that every value estimated rather than measured is labelled as such wherever it appears. The document states what fell, where it was measured, what the storm was capable of over the roof and how far each record is from it. What the storm did to the roof is the inspection's to say.

Questions this guide answers

What counts as severe hail

The National Weather Service sets a diameter at which hail counts as severe; warnings are issued against it and the record is logged against it. On these pages a day counts as severe when its largest report reached that criterion, and the page says whether the report was measured or detected.

What is the difference between measured and detected hail

A measured size is a stone a person or an instrument recorded on the ground at a point. A detected size is computed from radar for a grid cell, whether or not anything fell there. The first is a record of what fell; the second is an estimate of what the storm could have produced.

Is a radar-derived hail size accurate

It is a ceiling by construction: the algorithm was calibrated so that most measured stones fall below the estimate, and the size depends on the fit chosen. It is the only evidence with coverage over ground nobody reported from, and it is never printed as a measurement.

Should a measured size and a detected size be averaged

No. A day carried by a ground observation and a radar-derived size is attested by two independent kinds of evidence, not attested at the larger of the two figures. The report prints both, each with its source, and adjusts neither.