Accuracy of Weather Predictions for Fallbrook, San Diego County, CA

The page reports the accuracy of the predicted high temperatures for Fallbrook, in north San Diego County, for summer 1997. The official reporting weather station is located approximately 14 miles from the coast. The predictions cover a period of 44 days from 17 July 1997 thru 29 August 1997, and come from:

Accuweather, as reported in the North County Times and the San Diego Union Tribune,
Weatherdata, as reported in the Los Angeles Times, and
Observed Fallbrook temperatures, lagged one day. (Prediction for tomorrow is today's high.)

I missed gathering the prediction from Weatherdata on 20 July 1997.

This period spanned the full range of expected temperatures in the summer, including one spell of extended heat above 100^o, as well as a period of cool temperatures when the marine layer spent some extended time over Fallbrook. See the plot on the left below for the actual and predicted temperatures during this period. For the lagged predictions, mentally shift the blue curve over 1 day.

The plot on the right shows the error in prediction from the 3 sources.

(Click on graph for bigger and better image.)
(Click on graph for bigger and better image.)

The plot on the right above reveals a high correlation between all predictions, which can also be seen on the plot on the left after lagging the observed temperatures 1 day. The only times of significant discrepancies are:

28-29 July, when the lagged temperature predictions outperformed the weather companies prediction (temperatures stayed the same instead of increasing by 5-6 degrees),
9-11 August, when Accuweather kept predicting that the heat wave would continue, even though temperatures had already cooled.

In addition, the red points for the lagged temperatures are often found at the bottoms of the zig-zags in the plot, implying that they have the most error whenever the temperatures increase rapidly. It is interesting that they do not dominate the excursions at the tops of the zig-zags, implying that the weather companies don't have much skill in predicting when there is cooler weather ahead, as is well-known by those of us waiting for relief from high temperatures!

The formal statistics on the prediction accuracies are in the following table:

Statistics of errors in predicted high temperatures

	Prediction Source
Measure	Accuweather	Weatherdata	Lagged temps	Ave. of accuweather and lagged temps	Ave. of weatherdata and lagged temps
Mean	2.0	1.2	0.0	1.0	0.7
Median	2.0	1.0	0.0	1.5	0.5
Scatter about mean (1 sigma)	4.6	4.4	4.8	4.3	3.8
Scatter about 0 (1 sigma)	5.0	4.6	4.8	4.4	3.8

The mean is the arithmetic average of all the prediction errors, and the median is the value of the predicted error that is in the middle of the error distribution, with half of the prediction errors below and half above. The median is less sensitive to the rarer errors larger than 10^o. The scatter is the Gaussian sigma; 68% of all prediction errors are within +- 1 sigma from the mean (third value above) or from 0 predicted error (fourth value above) if the distribution of errors is the usual bell-shaped curve. The scatter is very sensitive to the largest errors.

I included all points, without tossing any outliers, since the error plot above doesn't show any obvious typos in the temperatures.

I draw the following conclusions from the data above:

Both Accuweather and Weatherdata seem to have mislocated Fallbrook to be slightly farther from the coast than it actually is, since on average they predict Fallbrook high temperatures to be 1-2 degrees higher than they actually are. (See the change of temperature with distance from the coast for more info.)
There is little skill exhibited in the weather companies in forecasting Fallbrook's high temperature! The lagged temperatures have a comparable scatter about 0 prediction error, and have the desirable property of being unbiased.
Although the weather companies and the lagged temperatures have comparable accuracies, the combination of either weather company with the lagged temperature prediction results in about a 20% improvement in accuracy, with a scatter of ~4^o instead of ~5^o! This may be because the averaging gives you part of the best of both the weather companies predicting the onset of higher temperatures better and the lagged temperatures predicting the onset of cooler temperatures better. In addition, the combination ameliorates the worst errors of both methods. However, this conclusion must be tempered by the sensitivity of the sigma to the largest errors - the plot below shows that the combination of weatherdata and the lagged temperatures is superior for most of the predictions.

The following plot summarizes the distribution of prediction errors. It gives the fraction of predicted temperatures that were within a given temperature range. The legend gives the methods from best to worst.

Percentage of predicted temperatures within a given temperature range

The plot shows that half of all predictions are within less than 3^o for the best predictor - the average of the Weatherdata (the L.A. Times forecast) and the high temperature the day before. All the other prediction methods have half of their predictions within 3-4^o.

Hence my main conclusion: in the summer, the most accurate forecast temperature for Fallbrook is to take the L.A. Times predicted high and average that with yesterday's high.

The motivation for this analysis was two-fold. First, Scott Chester analyzed the accuracy of predicted temperatures for winter for a science fair project. Second, I gathered these temperatures to investigate how much hotter Fallbrook temperatures were compared to Vista temperatures, in response to a statement made by a real-estate agent touting the superiority of Vista's climate.

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Copyright © 1997 by Tom Chester.
Permission is freely granted to reproduce any or all of this page as long as credit is given to me at this source:
http://sd.znet.com/~schester/fallbrook/weather/analysis/accuracy_of_predicted_high_temperatures.html
Comments and feedback: Tom Chester
Last update: 30 August 1997 (url changed 31 December 1997).