1998-01-13|Accuracy of Weather Forecast

To whom it may concern

I am looking for any systematic study on the accuracy of weather forecast.
I am helping my son's project to calculate weather forecast errors. The weather (sunny, cloudy, etc.) is too ambiguous, so he is focusing on the temperature errors for up to 4-day forecast. The calculation is done in a HyperCard stack, which could be made available if anybody is interested.

Here is the result so far for both "High" temperature and "Low" temperature, as published in the Ottawa Citizen. I would appreciate any comments on the methodology.

Weather Forecast Error Average (1997-12-15 to 1998-01-31, 45 days)

0-Day Forecast High = 2.6 degree Low = 6.1 degree

1-Day Forecast High = 3.5 degree Low = 6.0 degree

2-Day Forecast High = 3.7 degree Low = 6.3 degree

3-Day Forecast High = 4.7 degree Low = 5.6 degree

4-Day Forecast High = 4.2 degree Low = 5.6 degree

Here is an interesting screw-up. The "Yesterday's data" section in the Ottawa Citizen on 1998-01-06 has the following (High < Low).
- High = -1.6 C
- Low = 0 C
Thank you very much for your attention.

Weather Forecast Error Average (1997-12-15 to 1998-01-31, 45 days)
0-Day Forecast	High = 2.6 degree	Low = 6.1 degree
1-Day Forecast	High = 3.5 degree	Low = 6.0 degree
2-Day Forecast	High = 3.7 degree	Low = 6.3 degree
3-Day Forecast	High = 4.7 degree	Low = 5.6 degree
4-Day Forecast	High = 4.2 degree	Low = 5.6 degree

To whom it may concern

Thank you for your comments. Here is an example to show the algorithm to calculate the "Weather Forecast Error Average" in HyperCard.
- "Low" temperature for Sunday: 2-day forecast = -13 C, actual = -8.0 C
- "Low" temperature for Monday: 2-day forecast = -3 C, actual = 2.0 C
- Weather Forecast Error Average ("Low" temperature, 2-day forecast)
  = average (absolute ((forecast for that day) - (actual temperature)))
  = average ((absolute ((-13) - (-8.0)), (absolute ((-3) - (2.0)))
  = average (5.0, 5.0)
  = 5.0 degrees
So, according to this example, I believe that if you read in Wednesday's Ottawa Citizen that Friday's "Low" is forecasted to be -13 C, it means that, Friday's "Low" would be more likely to be -8 C or -18 C.

I believe it is meaningless to talk about percentage error unless the units are converted to (1/T) according to thermodynamics, where T is in Kelvin (Celsius + 273 degrees). I have not done the bias analysis, but here is the maximum error analysis.

Weather Forecast Error Maximum (1997-12-15 to 1998-01-31, 45 days)

0-Day Forecast High = 7.5 degree Low = 19.0 degree

1-Day Forecast High = 8.4 degree Low = 19.0 degree

2-Day Forecast High = 10.6 degree Low = 19.5 degree

3-Day Forecast High = 13.3 degree Low = 22.0 degree

4-Day Forecast High = 13.1 degree Low = 20.0 degree

If you are in doubt, the 3-day forecast in Ottawa Citizen 1998-01-24 (Saturday) for Tuesday's "Low" temperature was -1 C, where the actual "Low" temperature for 1998-01-27 (Tuesday) was -23.0 C, an error of 22.0 degrees!
Although my spouse is a mathematician/statistician, I am not good at statistics. So, I don't know how standard deviation in Gaussian distribution would apply to this case. In fact, I skipped Statistics in my university days because it was the only course on Wednesdays and I wanted to take a mid-week holiday...
Thank you very much for your attention.

Weather Forecast Error Maximum (1997-12-15 to 1998-01-31, 45 days)
0-Day Forecast	High = 7.5 degree	Low = 19.0 degree
1-Day Forecast	High = 8.4 degree	Low = 19.0 degree
2-Day Forecast	High = 10.6 degree	Low = 19.5 degree
3-Day Forecast	High = 13.3 degree	Low = 22.0 degree
4-Day Forecast	High = 13.1 degree	Low = 20.0 degree

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2025-10-15T16:49:27.000Z