796 WEATHER AND FORECASTING VOLUME 20 FORECASTERS’ FORUM Comments on “Discussion of Verification Concepts in Forecast Verification: A Practitioner’s Guide in Atmospheric Science” IAN T. JOLLIFFE AND DAVID B. STEPHENSON Department of Meteorology, University of Reading, Reading, United Kingdom (Manuscript received 22 December 2004, in final form 10 March 2005) 1. Introduction helps forecast users make better decisions despite the uncertainty inherent in the forecasts. These and other We congratulate Bob Glahn on his perceptive and factors have led to more than a century of fascinating thoughtful review (Glahn 2004; hereafter G04) of the ongoing developments in forecast verification. book we edited entitled Forecast Verification: A Prac- We agree with many of the points raised in G04 but titioner’s Guide in Atmospheric Science (Jolliffe and we wish to expand here on several that we consider to Stephenson 2003; hereafter JS03). His comments will be the most interesting and important issues. undoubtedly lead to an improved second edition. Fur- thermore, he has raised several very stimulating and 2. Verification from a forecast developer’s important verification and forecasting issues that could viewpoint benefit from a wider debate. We, therefore, wish to On p. 770, G04 states that “Much of the discussion take this opportunity to respond to some of the issues seems to have as an objective developing or improving raised in Glahn (2004) in the hope that a thought- a forecast system rather than judging the, possibly com- provoking verification debate appears in the literature. parative, goodness of a set of forecasts.” In other words, Rather than attempt to elicit and then present a con- our book is biased toward verification for the purposes sensus response that reflects the views of all our authors of the forecast developer rather than for the purposes (if such a thing were ever achievable!), we prefer to of the forecast user. For example, as G04 quite rightly respond more directly to G04 with our own subjective points out, throughout our book it is often assumed that editorial opinions. We hope that some of our authors poorly calibrated forecasts can easily be recalibrated, will comment separately. yet this is not always possible especially if one is a fore- Forecast verification is an essential part of atmo- cast user. Most forecast users would not even think of spheric sciences. It is the way in which the science of recalibrating the forecasts since they generally take the meteorology is ultimately judged—by the skill of its forecasts at face value; they quite naturally assume that predictions. Forecast verification is an intellectually the given forecasts are well calibrated. Unfortunately, stimulating and multidisciplinary area of research that many weather and climate forecasts are often not well requires careful summary and interpretation of pairs of calibrated (see below) and so great care needs to be past forecasts and observations. Despite its importance, exercised in judging and using such products. Further- forecast verification is not always fully acknowledged in more, suppose a (sceptical) forecast user did want to operational forecasting centers and is often completely recalibrate forecasts before verification, then he or she absent from atmospheric science courses. In addition to would often not be able to do so because of generally skill, forecasts should also provide information that having insufficient access to past observations and/or knowledge of changes in the forecasting system. Our emphasis on model-oriented rather than user-oriented Corresponding author address: Prof. Ian T. Jolliffe, Dept. of Meteorology, University of Reading, Earley Gate, P.O. Box 243, verification in part stems from our choice of authors for Reading RG6 6BB, United Kingdom. the chapters, many of whom are verification practition- E-mail: [email protected] ers employed at national weather forecasting services © 2005 American Meteorological Society OCTOBER 2005 FORECASTERS’ FORUM 797 around the world. However, it should be noted that information about marginal probabilities that can be forecast users are generally more interested in judging used to estimate forecast frequency bias. It is easy to how much added value forecasts can bring to their spe- show that the frequency bias of binary forecasts is given cific decision-making processes, and so are often more by B ϭ H ϩ [(1 Ϫ p)/p]F, where p is the probability of concerned with the assessment of user-specific forecast the observed event to occur (the base rate) and so re- value (utility) rather than overall forecast quality.To quires knowledge of the base rate p as well as ROC take an extreme view, if, paradoxically, there is no guar- quantities H and F. This helps to resolve G04’s remark antee that skillful forecasts will provide value to a given in the sixth paragraph of p. 772: “It is not clear to me user, then why should any users be interested in the how reliability (calibration), which is generally ignored assessment of forecast quality? by ROC, cannot be crucial in determining the actual As pointed out in chapter 1 of our book, our focus economic value of forecasts.” As explained in chapter 8 was primarily on methods for the assessment of forecast of JS03, the economic value is not simply a function of quality (forecast verification) rather than the assess- H and F but also strongly depends on the base rate p. ment of utility, which has been addressed elsewhere Diagnostics based on ROC quantities such as the area (e.g., Katz and Murphy 1997). Nonetheless, we agree under the ROC curve H(F) are useful because they with Glahn that it would be good to see more user- focus attention on resolution rather than reliability of oriented approaches to forecast verification in the lit- the forecasts but they require careful interpretation erature and we hope that such approaches will be de- (see Göber et al. 2004). The major deficiency in ROC veloped in the future. A more user-oriented approach not considering calibration is also a major strength—in to verification will help minimize some of the potential much the same way that the product moment correla- conflicts of interest caused by forecast providers assess- tion coefficient does not measure bias but is neverthe- ing the quality of their own forecast products. less a useful measure of linear association for continu- ous forecasts. It should also be noted that, unlike ROC, economic value measures of performance have a major 3. Resolution, reliability, and ROC for poorly deficiency in that they generally have a strong depen- calibrated systems dence on the base rate and so are extremely sensitive to Calibration is a topic of fundamental importance in how forecasts are calibrated. This leads to the undesir- verification. There are basically two reasons why fore- able, yet rarely mentioned, property that economic casts do not match observations: value measures can usually be improved by hedging the forecasts. • they are unable to discriminate between different ob- served situations, and 4. Who should do the calibration and how should • they are poorly labeled, for example, the forecasts it be done? are on average 5°C too warm. As pointed out by G04, there is a big difference be- The ability of forecasts to discriminate between ob- tween recalibration in principle and what is possible in served situations is known as resolution, and its exis- practice. To be able to recalibrate, one needs to have tence is a necessary yet not sufficient condition for fore- access to a suitably large sample of past pairs of fore- casts to have skill. Forecast accuracy also depends on casts and observations (not often issued to the forecast the reliability (i.e., good labeling—calibration)ofthe user!) and one must make certain assumptions about forecasts. However, unlike resolution, reliability can be past and future stationarity of forecast–observation re- improved, in principle, by recalibration of the forecasts lationships in order to be able to develop a regression using past information about pairs of forecasts and ob- model suitable for performing the recalibration (such as servations. In other words, resolution is a necessary that used in operational postprocessing schemes such as condition for skill whereas reliability is not. If forecasts model output statistics). Perhaps more importantly, one have poor resolution, there is not much one can do to also needs the motivation to embark upon calibration. improve them whereas if they have poor reliability It is often not clear who should be doing the recalibra- there is still hope. tion. For example, should it be the forecast providers or On p. 770, G04 points out that presenting only the should it be the forecast users themselves? It might relative operating characteristic (ROC) quantities of hit seem obvious that it should be the forecast provider rate (H) and false alarm rate (F) has “a major defi- who ensures that the forecasts are well calibrated. How- ciency—it does not consider calibration.” This is true ever, it can also be argued that each user has more since hit rate and false alarm rate are both conditional detailed knowledge of their particular needs and so can probabilities and so do not by themselves contain any calibrate more optimally for their own area of applica- 798 WEATHER AND FORECASTING VOLUME 20 tion. For example, one user may be more interested in verification methods specific for ensemble forecasts, for extreme temperatures in the tail of the distribution example, the rank histogram (Anderson 1996), multi- whereas another user may be more interested in more dimensional scaling (Stephenson and Doblas-Reyes central temperatures; the calibration could then be tai- 2000), bounding boxes (Weisheimer et al. 2005), the lored to these specific applications. Statistical postpro- minimum spanning tree (Wilks 2004; Smith and Hansen cessing of weather and climate model predictions is an 2004), etc.