Believe it or not, the question regarding the accuracy of weather forecasts is actually not a pertinent question to ask. The reason is because it's not the accuracy that matters!!
Let me explain further with an example. Suppose two weather forecasters are trying to predict the occurrence of tornadoes in the city of Norman, OK. Forecaster #1 always predicts there will be no tornadoes. Forecaster #2 predicts no tornadoes on 86 of the 90 days in summer but does predict tornadoes on 4 of the days. Suppose tornadoes happen on 1 of the days that Forecaster #2 predicts but there are no more tornadoes the rest of summer.
In this scenario, Forecaster #1 had an error rate of 1.11% (1 wrong forecast out of 90) and Forecaster #2 had an error rate of 3.33% (3 wrong out of 90). So the error rate for Forecaster #2 was three times higher than that of #1. But was Forecaster #1 really better despite a lower error rate?
Let's examine more closely. Forecaster #2 was correct on all 86 of his no-tornado predictions. On 3 of his 4 tornado forecasts he was wrong, causing people to take cover when none was necessary. However 1 of his tornado forecasts was correct, saving countless lives.
In contrast, Forecaster #1 was correct on 89 of 90 no-tornado forecasts, but missed the one day when tornadoes did occur, causing the deaths of hundreds of people.
So wouldn't you rather have Forecaster #2 as your meteorologist over #1? I think the answer is obvious since you might be dead with #1 but still alive with 2 despite the higher error rate. That is the reason why percent correct scores are misleading. They assume the value of a correct positive forecast is the same as the value of a correct negative forecast. That is the reason why the question "how accurate are weather forecasters" is not pertinent.
The real question is do weather forecasters add economic value and save lives? I believe the answer is an unequivocal yes. Rather than show endless charts and graphs to support that, I'll just leave you with the following forecast from the National Weather Service issued prior to the arrival of Hurricane Katrina. I wonder how many lives were saved.
URGENT — WEATHER MESSAGE NATIONAL WEATHER SERVICE NEW ORLEANS LA ...DEVASTATING DAMAGE EXPECTED... HURRICANE KATRINA...A MOST POWERFUL HURRICANE WITH UNPRECEDENTED STRENGTH... RIVALING THE INTENSITY OF HURRICANE CAMILLE OF 1969. MOST OF THE AREA WILL BE UNINHABITABLE FOR WEEKS...PERHAPS LONGER. AT LEAST ONE HALF OF WELL CONSTRUCTED HOMES WILL HAVE ROOF AND WALL FAILURE. ALL GABLED ROOFS WILL FAIL...LEAVING THOSE HOMES SEVERELY DAMAGED OR DESTROYED. THE MAJORITY OF INDUSTRIAL BUILDINGS WILL BECOME NON FUNCTIONAL. PARTIAL TO COMPLETE WALL AND ROOF FAILURE IS EXPECTED. ALL WOOD FRAMED LOW RISING APARTMENT BUILDINGS WILL BE DESTROYED. CONCRETE BLOCK LOW RISE APARTMENTS WILL SUSTAIN MAJOR DAMAGE...INCLUDING SOME WALL AND ROOF FAILURE. HIGH RISE OFFICE AND APARTMENT BUILDINGS WILL SWAY DANGEROUSLY...A FEW TO THE POINT OF TOTAL COLLAPSE. ALL WINDOWS WILL BLOW OUT. AIRBORNE DEBRIS WILL BE WIDESPREAD...AND MAY INCLUDE HEAVY ITEMS SUCH AS HOUSEHOLD APPLIANCES AND EVEN LIGHT VEHICLES. SPORT UTILITY VEHICLES AND LIGHT TRUCKS WILL BE MOVED. THE BLOWN DEBRIS WILL CREATE ADDITIONAL DESTRUCTION. PERSONS...PETS...AND LIVESTOCK EXPOSED TO THE WINDS WILL FACE CERTAIN DEATH IF STRUCK. POWER OUTAGES WILL LAST FOR WEEKS...AS MOST POWER POLES WILL BE DOWN AND TRANSFORMERS DESTROYED. WATER SHORTAGES WILL MAKE HUMAN SUFFERING INCREDIBLE BY MODERN STANDARDS. THE VAST MAJORITY OF NATIVE TREES WILL BE SNAPPED OR UPROOTED. ONLY THE HEARTIEST WILL REMAIN STANDING...BUT BE TOTALLY DEFOLIATED. FEW CROPS WILL REMAIN. LIVESTOCK LEFT EXPOSED TO THE WINDS WILL BE KILLED.