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Forecast verification: Past, present, and future
Published January 24, 2008
Forecasts are issued by meteorologists, climatologists, and hydrologists to predict future weather, climate, and streamflows for a wide variety of purposes including saving lives, reducing damage to property and crops, or even so people can decide what to wear in the morning. Forecast verification is how the quality, skill, and value of a forecast is assessed. The process of forecast verification compares the forecast against a corresponding observation of what actually occurred or an estimate of what occurred. This article discusses some of the many different forecast verification methods, the concept of forecast value to users, and offers some suggestions for forecast users when considering any forecast.
Overview of Forecasts
The three types of forecasts discussed here are weather, climate, and streamflow forecasts. Weather forecasts predict the weather that will occur during a short time frame from six hours to two weeks into the future. Climate forecasts, also called outlooks, predict the average weather conditions for a season or period from several months to years in advance. Climate forecasts do not predict the weather for a certain day, but predict the average weather over several days or months. Examples of climate forecasts from the NOAA Climate Prediction Center (CPC) are on pages 14–15. Streamflow forecasts predict water supply conditions, including streamflow at a point or volume for a period, based upon variables like precipitation and snowmelt. Streamflow forecasts can be daily or seasonal time scales. An example of a streamflow forecast map is on page 17.
History of Forecast Verification
n order to create better forecasts, scientists monitor the forecasts for accuracy and compare different forecasting Forecast Verification: Past, Present, and Future continued on page 4 techniques to see which is better and why (IVMW, 2007). Weather forecasting based upon interpreting weather maps began in the 1850s in the United States, but serious efforts in forecast verification began in the 1880s. In 1884, Sergeant John Finley of the U.S. Army Signal Corps began forecasting tornado occurrences for 18 regions east of the Rocky Mountains. His forecasts were made twice a day and would be either “Tornado” or “No Tornado”. This is an example of a dichotomous forecast, where there are only two possible choices. He reported a 95.6–98.6 percent accuracy for the first three months. Ironically, other scientists pointed out that he could have had 98.2 percent accuracy if he forecasted “No Tornado” for all the regions and all the time periods. A 10-year debate started after Finley’s publication, referred to as “The Finley Affair.” This debate made forecasters realize the need for valid verification methods in order to improve forecasts, and led to the development of verification methods and practices (Murphy, 1996).
Types of Verification
In order for a forecast to be verified, it must be compared with observed conditions. Observational data such as rain gauges, thermometers, stream gauges, satellite data, radar data, eyewitnesses, etc. are used as “truth.” In many cases, however, it can be difficult to know the exact “truth” due to instrument error, sampling error, or observation errors. Accurate observations and observation systems, then, are critical to forecast verification.
Forecasters and forecast users have many different ways to verify forecasts and assess quality. Two of the traditional ways are looking at the accuracy and the skill of the forecast. Accuracy is the degree to which the forecast corresponds to what actually happened and depends on both the forecast itself and the accuracy of the measurement or observation. As mentioned above, observation data can be a limitation in all verification measures, not just accuracy. In addition, the person verifying the forecast uses expert judgment to decide what makes a forecast accurate. For example, a forecast for a high temperature of 75 degrees Farenheit might be considered inaccurate either when the observed high temperature was 76 degrees F or when the high temperature was 85 degrees F.
The second common forecast verification measure is skill. Skill is the accuracy of a forecast over a reference forecast. The reference forecast might be random chance, persistence forecasts, climatology, or even another forecast. A random chance forecast would be like flipping a coin to decide whether or not to forecast precipitation. Persistence forecast is forecasting the same conditions that are happening at the time of the forecast. For example, if it is currently snowing, a persistence forecast is for snow to continue. A forecast of climatology is forecasting the average conditions for the forecast period. A “skillful” forecast must show improvement over a reference forecast.
Other measures of forecast quality besides accuracy and skill include bias,resolution, and sharpness. Bias measures if forecasts on average are too high or too low relative to the truth. Resolution measures the ability of a series of forecasts to discriminate between distinct types of events, even if the forecast itself is wrong. Sharpness indicates if the forecasts can predict extreme values. Sharpness is important because forecasters can sometimes achieve high skill scores by predicting average conditions but in some cases the occurrence of extreme events may be more important to users. In general, focusing on just one measure of forecast quality may be misleading. For example, in the case of Findley’s forecasts, their apparent high accuracy obscured the fact their skill was less than a constant forecast of no tornado.
Methods of Forecast Verification
Forecast verification methods are chosen depending on the type of verification (accuracy or skill) and the type of forecast (dichotomous, continuous, probabilistic, etc.). Examples of verification methods range from simply “eyeballing” the forecast compared to observations, to statistically advanced methods.
Eyeballing a forecast is as simple as it sounds and can be use for a variety of forecasts. A forecaster simply looks at the forecast and the observations side by side to see how well they match up (Figure 1). “Eyeballing” verification is very subjective and can lead to different outcomes depending on the judgment of the individual forecasters looking at the data.
A contingency table is typically used to verify dichotomous forecasts, like the tornado example above, over a period of time. The table shows the “yes” and “no” forecasts and observations (Table 1). To find the accuracy of the forecasts, one must sum “hits” and “correct negatives” and divide by the “Total.” This will give a number between 0 and 1; the closer to 1, the more accurate the forecast. This type of score can be very misleading in rare events when forecasting “No” will lead to a high “correct negatives” category such as the occurrence of tornados as in the Findley Affair. Numbers in the contingency table can be combined in many other ways than just accuracy. For example, the False Alarm Ratio is the number of events that were forecasted to occur but did not.
|Yes||hits||false alarms||forecast yes|
|No||misses||correct negatives||forecast no|
|Total||observed yes||observed no||Total|
One can numerically verify or calculate the error between the forecast and the observed values with the help of graphical representations. Graphical displays, such as scatter or box-and-whisker plots, are used to verify forecasts of continuous variables such as maximum temperature over a period of days. Scatter plots show the observed amount plotted against the forecast amount. An accurate forecast in this case would lie along the diagonal of the scatter plot.
Box-and-whisker plots can show the distribution of the observed values relative to the forecasted values, which can provide a measure of the resolution of the forecast. continued on page 5 In a well-resolved forecast, the box plot of the forecast would appear to have the same spread as the observed values. Skill scores can be calculated for almost all types of forecasts, but they are most often used for categorical and probabilistic forecasts, like the seasonal climate outlooks issued by NOAA’s Climate Prediction Center (CPC) (see pages 14 and 15). All skill scores measure the fraction of correct forecasts to total forecasts after correcting for the number of correct forecasts a reference forecast – generally persistence, climatology or random chance – would obtain. Three types of skill scores are the Heidke skill score, the Brier skill score, and the Ranked Probability skill score. A score between negative infinity to 1 is calculated, with 1 being a perfect score. If forecasts are consistently better than the reference forecast, the score will be closer to 1, a score of 0 indicates no improvement over the reference forecast, and a negative score indicates the forecast performs worse than the referenceforecast. Note that a perversely high negative score may actually provide considerable value if the forecast can be ‘inverted’. For this reason, substantial negative skill scores are rarely seen. When comparing skill scores for different forecasts, it is important to use the same method for all forecasts. For example, if you want to compare the CPC seasonal forecast to WWA climatologist Klaus Wolter’s experimental seasonal guidance (http://www.cdc.noaa.gov/people/klaus.wolter/SWcasts/index.html), make sure you are looking at either the Heidke or Brier skill score for both.
Forecast Value and Forecast Users
Another important attribute of forecasts is value. A forecast might be highly accurate, skillful, unbiased, sharp and well resolved, and still not be very useful. A valuable forecast best helps a decision maker. For example, a forecast of clear skies over a desert is probably not very helpful. On the other hand, if a forecast helps a decision maker to gain some benefit, the forecast is considered valuable. Accurately forecasting a drought will help water managers to better prepare for low water supply. Forecasting the April 1 snowpack as early as possible would help improve the annual water management operations. In essence, useful forecasts need a wide variety of attributes including accuracy, skill, and value.
NOAA is creating ways to educate decision makers and create better consumers of forecasts. Making forecast verification measures available and explaining the techniques to users will increase the value of forecasts. For example, the Forecast Evaluation Tool and the new verification tools on the NOAA National Weather Service Western Water Supply Application Suite both make verification tools readily available to users (see pink box at right). Users will be able to decide which forecasts they want to use for what purpose, and will know the weaknesses, strengths, or biases of particular forecasts. For example, a certain forecast might tend to predict wetter conditions in the spring.
Verifying a forecast should ultimately lead to improvement in the forecasting techniques and an increase in value to the users.
Overall, forecasters are starting to understand that they need to think about who is using their forecasts and the value of the forecast to the users, not just the skill score or the accuracy of a forecast. While accuracy is very important, it is not the only element of a good forecast. Whether a forecast is for weather, climate, or streamflows, a user should know what information the forecast provides, how the forecast is verified, and limitations of the forecasts and verification methods. If users are educated about forecasts and forecast verification, they will ultimately be better consumers of those forecasts.
Murphy, A.H. 1996. The Finley Affair: A Signal Even in the History of Forecast Verification. Weather and Forecasting. 11(1): 3-20.
Third International Verification Methods Workshop (IVMW). 2007. Reading, UK. http://www.cawcr.gov.au/projects/verification/
This article originally appeared in the the Intermountain West Climate Summary (http://wwa.colorado.edu/IWCS/index.html). It is reprinted here with their permission.