As radar beams travel away from radars, they increase in elevation and widen. Have any studies attempted to quantify the rate at which warning skill (such as in FAR and POD) deteriorates as a function of radar distance? It would seem quite useful in objectively diagnosing where new radar sites may be most vital (and where to put them in countries that do not yet have radars), and could be useful in guiding warning decisions as well. I'm particularly interested in tornado warnings in the US, though any related data/studies would be very interesting.
This may/may not actually answer your question "Do warnings verify better" because of the qualitative word "better" and other factors that play a role, such as terrain and forecasting office. Another factor to consider is the nature of the warning and size of the phenomenon. A radar, for example, may not be the best tool to show verification of a hurricane, but it may be better for verification of a tornado. I hope to answer your question by taking arguments to the extreme.
If warnings verify more and more accurately as the warnings get closer to the radar, they may end up in the "cone of silence," where the angle of the radar would not be able to capture the phenomenon.
The opposite of that statement would be that warnings are more accurate the farther away the phenomenon is from the radar. This is also absurd, not only is resolution of the radar cut, but the curvature of the earth also makes this idea absurd.
Conclusion: there is some middle ground. If you get to close, you may not only be endangering your radar (depending on the phenomenon) but you may miss data. It also matters what angle your scan is at. I would hypothesize that anything within the highest elevation angle of the radar would have the highest accuracy, but it would really matter what the phenomenon warned is and what size the phenomenon is.
Warning zones are issued by people, and people have flaws. I would hypothesize that your results may not be conclusive, since the habits of each WFO may vary. For example, a winter storm warning in Georgia is an inch of snow and ice, while Boston would need 6 inches of snow to issue a winter weather watch. Some areas see tornadoes more often than others, leading to some inherent biases, etc.
Aha, it's all about what search terms you use. I stumbled across a series of papers that gives a great range of calculations from J. Brotzge and Erickson. The key one for this topic appears to be Brotzge, Erickson, and Brooks: A 5-yr Climatology of Tornado False Alarms. The key figure is:
The take-homes are:
- As distance increases, tornadoes are missed more by advanced warning. This is shown by the black circles [probability of detection] trending down slowly on the left graph. The drop-off is certainly very gradual, going from near 80% of tornadoes with advanced warning in sites just outside the cone of silence, to nearer 60% out beyond 100 miles (160 km) from the radar. But this does mean that near the radar about 1 in 5 tornadoes is missed, while beyond 100 miles, it's nearer 2 in 5 tornadoes missed.
- Oddly, it appears that warnings actually verify BETTER out beyond 100 miles (160 km). This is shown by the open circles [success ratio] increasing in the left graph, and is further confirmed by the same increase when breaking it down into group bins in the right graph.
The authors give a few theories to attempt to explain the increase in success beyond 100 miles (160 km). They hint that it may be due in part to the fact that forecasters wait to issue warnings until receiving confirmation because the radar data is less helpful in properly identifying developing rotation. However, this seems it should likely be matched by a giant dropoff in POD if it were a large contributing factor.
They also suggest the increased success in long ranges verification may be simply due to the fact less tornadoes are reported at large distances. Reasons given include: people won't know where to look for weak tornado damage due to the poor radar quality; the disposition for these areas to typically have fewer residents... fewer residents mean less people to potentially see the tornadoes, and also less houses and such to be damaged [they did try to eliminate this factor as an option, but did not seem to do so adequately to me]; and perhaps the cause of less reports could in part be due to less NWS surveys because of the large distances to travel.
Regardless, the key is the slow dropoff in tornadoes getting properly warned. If the strange decrease in unnecessary warnings is legitimate, that might almost counteract any benefit to adding radars. But it's very unlikely the lack of data somehow makes forecasters much better. If that proved true, it'd be remarkable, and lead to heavy investigation into what we could do to duplicate the effects everywhere!
Of course none of this considers places at even longer-range distances (particularly those beyond the 143 mile short-range limit), which is where attention is often first placed when fomenting support for additional radars. And the study could probably also do with some additional years of data to further eliminate any potential biases due to inter-annual weather patterns. But it's definitely a very fair start towards addressing the cost-benefit of radar installation.