# Weather Forecast prediction accuracy metric

I'm looking to better understand the following statement on the reliability of weather forecasts from NOAA's SciJink:

A seven-day forecast can accurately predict the weather about 80 percent of the time and a five-day forecast can accurately predict the weather approximately 90 percent of the time. However, a 10-day—or longer—forecast is only right about half the time.

In this context what metric / threshold is used to evaluate, "can accurately predict the weather".

• Interesting question. I wonder what the sentiment would be on the statistics Stack, Cross Validated.
– Dave
Commented Dec 7, 2022 at 5:10

The climatological forecast for 1 July 2023 for some region is computed as follows, based on the meteorological record for that region and that date:

• The predicted high is the average high for that date from all of the meteorological stations in that area, possibly weighted by some weighting scheme.
• The predicted low is the average low for that date from all of the meteorological stations in that area, again possibly weighted by some weighting scheme.
• The chance of precipitation is the product of the percentage of past first of July records where any weather station in the area measured a significant amount of precipitation multiple by the percentage of weather stations that did observe precipitation on those days.

The question then becomes how skillful is a forecast based on current and recent meteorological data compared to the climatological forecast? If it's a coin toss which of the two will be closer to observation, one might as well use the climatological forecast. This coin toss boundary currently is about where a ten days. The coin toss boundary used to be at seven days. Before then, it was four or five days, before that, just two or three days, then just one day. Before that, it was weather adages such as "red sky at night, sailors' delight," which itself is a bit of a coin toss.

A more qualitative approach is a skill score. For example, suppose the meteorological forecast for the high temperature for some day in the future is $$H_f$$ (f for forecast) while the climatological forecast is $$H_r$$ (r for reference). Wait until that day passes and note the actual high temperature $$H_p$$. The skill score for the meteorological forecast is $$SS_H = \frac{H_f - H_r}{H_p - H_r}$$

There are multiple schemes by which skill scores for multiple scores, multiple metrics, and multiple regions are combined. Weather forecasts are a bit more skillful at predicting high and low temperatures than they are at predicting chance of precipitation. I'm not sure what combination scheme is used in determining that the ten day forecast remains a coin toss compared to the climatological forecast.

References:

Murphy, Allan H., and Edward S. Epstein. "Skill scores and correlation coefficients in model verification." Monthly weather review 117.3 (1989): 572-582.

Wheatcroft, Edward. "Interpreting the skill score form of forecast performance metrics." International Journal of Forecasting 35.2 (2019): 573-579.

• A reasonable forecast for my area for 1 July 2023 is high of 92° F, a low of 74° F, and a 10% to 20% chance of rain. Summer in my area would be easy to predict were it not for the low chance of a tropical storm (which is low in early July). Commented Dec 7, 2022 at 12:26

It comes down to data, time and computer modelling. Putting a confidence level on weather forecasts was not possible 30 to 40 years because of the lack of data and computer modelling capabilities.

Meteorologists weren't able to predict hurricanes/cyclones/typhoons until the advent of weather satellites in the 1960s. These days meteorologists have a significant amount of current data available to them because of data gathering methods such as satellites, ocean buoys, etc. They also have benefited from fast and reliable data dissemination methods provided by the internet and from global weather observation databases continuously updated available for use.

Access to inexpensive high powered computers running various computer models forecasting the weather, using all the latest data is key. Weather systems are dynamic, they can change quickly. This is where time is a factor. Predicting weather for the next few days is more reliable than doing do for several days ahead.

No matter how good computer models are they can only consider so much, so they each have their own level of biases and inaccuracies. This is why a number of computer model are run to forecast weather; depending on the weather service, usually at least four.

Each model takes the latest data and runs scenarios of what pressure systems might look like and where frontal systems might be as time passes. The more models that agree with each other the higher the confidence that meteorologists have concerning weather forecasts.

• This answer essentially says that forecasting has improved. It doesn't answer the question about a metric for that improvement, which is what the question asks for. Commented Dec 7, 2022 at 11:46
• Meteorologists weren't able to well predict TCs until satellites. We had weather maps (including ship/aircraft reports to know of storms before landfall). There were rules of thumb in local conditions to indicate a hurricane may be nearby/approaching, even back centuries. Commented Dec 11, 2022 at 5:37