P ERSPECTIVES recombination events between nonallelic among alleles, they found that the “hot” alle- example, are the density and intensity of copies. The finding of a recombinagenic les were their top-scoring seven and nine hotspots constrained within circumscribed motif within the repeats may therefore help oligomer motifs and that in both cases, the regions of the genome? With more sperm- to explain the observation that the break- “colder” alleles were a mutation away from typing experiments and extensive linkage points of nonallelic recombination events that motif. This result strongly suggests that disequilibrium data collection in close evo- are often clustered (12). The overall influ- these sequences modulate hotspot activity lutionary relatives of humans, answers to ence of mobile DNA elements on recombi- (see the figure). Further evidence will come these questions should no longer be elusive. nation remains unclear, however, with from sperm-typing studies of other hotspots some over- and some underrepresented polymorphic at the same motifs, as well as at References 1. T. Hassold, P. Hunt, Nat. Rev. Genet. 2, 280 (2001). within hotspots. other candidate sequences. 2. A. Lynn, T. Ashley, T. Hassold, Annu. Rev. Genomics The seven-nucleotide motif is not among In light of recent reports that hotspot Hum. Genet. 5, 317 (2004). those previously associated with recombina- locations are largely discordant in humans 3. S. Myers, L. Bottolo, C. Freeman, G. McVean, P. Donnelly, tion in other species. However, its role in influ- and chimpanzees (9, 13), the discovery of Science 310, 321 (2005). 4. N. Arnheim, P. Calabrese, M. Nordborg, Am. J. Hum. encing recombination is supported by sperm- human motifs that appear to influence Genet. 73, 5 ( 2003). typing experiments, as is the role of another hotspot activity raises a number of addi- 5. L. Kauppi, A. J. Jeffreys, S. Keeney, Nat. Rev. Genet. 5, nine-nucleotide motif motif (CCCCACCCC) tional questions: Can changes to sequence 413 (2004). identified by the authors. Indeed, at a subset of motifs explain most of the interspecies dif- 6. T. D. Petes, Nat. Rev. Genet. 2, 360 (2001). 7. D.C.Crawfordet al., Nat. Genet. 36, 700 (2004). hotspots in humans, mouse, and yeast, varia- ferences, or do other genomic features, such 8. G.A. McVean et al., Science 304, 581 (2004). tion in hotspot intensity among individuals as chromatin accessibility or transposable 9. S. E. Ptak et al., Nat. Genet. 37, 429 (2005). has been shown to depend on particular alle- element activity, explain their rapid evolu- 10. D.A. Hinds et al., Science 307, 1072 (2005). les, with recombination events occurring tion? Given that most recombination events 11. P. Fearnhead, N. G. C. Smith, Am. J. Hum. Genet., www.journals.uchicago.edu/AJHG/home.html. more often initiating on the background of the take place within hotspots, and hotspot 12. J. R. Lupski, Genome Biol. 5, 242 (2004). “hot” variant. When Myers et al. examined the locations appear to be rapidly evolving, is 13. W.Winckler et al., Science 308, 107 (2005). sequence context of two human hotspots there any constraint on recombination rates whose intensity has been shown to vary below that of a chromosomal arm? For 10.1126/science.1120154

ATMOSPHERIC SCIENCE turbation method (3) and the singular-vec- tor technique (4), respectively. The Weather Forecasting Meteorological Service of Canada (MSC) uses the Monte Carlo–like perturbed-obser- vation approach (5), in which the model with Ensemble Methods physics parameterizations vary as well. Ensemble forecasting and atmospheric data Tilmann Gneiting and Adrian E. Raftery assimilation (the melding of weather obser- vations into a numerical model) can mutu- radical change has occurred in the ing of the model output, in that model ally benefit from each other, and there are practice of numerical weather pre- biases, insufficient representations of fore- promising options for a linked system (6). Adiction over the past decade. Until cast uncertainty, and the differing spatial A recent comparative study suggests that the early 1990s, atmospheric scientists scales of model gridboxes and observations the ECMWF data assimilation, numerical viewed weather forecasting as an intrinsi- need to be addressed. In concert with statis- modeling, and ensemble generation system cally deterministic endeavor: For a given tical postprocessing, ensembles provide has the best overall performance, with the set of “best” input data, one “best” weather flow-dependent probabilistic forecasts in NCEP system being competitive during the prediction is generated. Armed with sophis- the form of predictive probability distribu- first few days, and the MSC system during ticated computing resources (including tions over future weather quantities or the last few days, of the 10-day forecast supercomputers), weather centers ran care- events. Probabilistic forecasts allow one to period (7). The successful operation of fully designed numerical weather predic- quantify weather-related risk, and they have forecast ensembles on the global scale has tion models to produce deterministic fore- greater economic value than deterministic motivated the development of limited-area casts of future atmospheric states. Although forecasts in a wide range of applications, short-range ensembles driven by initial and this is still the case today, weather predic- including electricity generation, aircraft boundary conditions supplied by different tion has been transformed through the and ship routing, weather-risk finance, and weather centers, such as the University of implementation of ensemble forecasts. An disease modeling (1). Washington ensemble system (8–10) over ensemble forecast comprises multiple (typ- A maturing area is that of medium-range the North American Pacific Northwest (see ically between 5 and 100) runs of numerical probabilistic forecasting at prediction hori- the figure). weather prediction models, which differ in zons up to 10 days, which involves ensem- Probabilistic forecasting has become an the initial conditions and/or the numerical bles of global numerical weather prediction integral part of seasonal prediction as well representation of the atmosphere, thereby models (1, 2). Three operational methods (1, 11). Forecasts on seasonal to interannual addressing the two major sources of fore- for the generation of medium-range initial time scales rely on comprehensive global cast uncertainty. condition ensembles have been developed. coupled ocean-atmosphere models and Realizing the full potential of an ensem- The U.S. National Centers for Environ- have become feasible with an improved ble forecast requires statistical postprocess- mental Prediction (NCEP) and the Euro- understanding of the coupling between sea pean Centre for Medium-Range Weather surface temperature anomalies and atmo- Forecasts (ECMWF) seek directions of spheric circulation patterns. A recent spe- The authors are in the Department of Statistics, University of Washington, Box 354322, Seattle, WA rapid error growth in selective sampling cial issue of Tellus (12) is dedicated to 98195, USA. E-mail: [email protected] procedures, known as the bred-vector per- results from the European Union–spon-

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Ensemble of three forecasts dependent probabilistic forecast distribu- tions, particularly of weather fields, as A B C opposed to forecasts at individual sites. In keeping with the remarkable pace of progress since the early 1990s, we antici- pate notable improvements in deterministic and probabilistic forecast skill through the continued development of multimodel, multi–initial condition ensemble systems and advanced, grid-based statistical post- processing techniques. Additional effort is required in the com- –20 –16 –12 –8 –4 0 4 8 12 16 20 24 28 32 munication, visualization, and evaluation of °C probabilistic forecasts, and differing inter- Combined forecast via BMA Forecast uncertainty via BMA Possibility of freezing pretations of probability need to be recon- D E F ciled, to avoid the risk of perfecting ensem- ble methodologies without a clear aim (15, 16). To this end, the paradigm of maximiz- ing the sharpness of the probabilistic fore- casts under the constraint of calibration may offer guidance. Calibration refers to the sta- tistical consistency between the probabilis- tic forecasts and the observations; sharp- ness refers to the spread of the predictive 0 2 4 6 8 10 12 14 16 3.9 4.1 4.3 0 10 30 50 70 90 distributions and is a property of the fore- °C °C % casts only. The goal is to increase sharpness An improved forecast. Ensemble forecast of surface temperature over the North American Pacific in the forecasts, without compromising the Northwest, with postprocessed probabilistic forecast products derived by Bayesian model averaging validity of the probability statements. (BMA) (14). (A to C) The ensemble consists of nine 48-hour forecasts (of which three are shown) valid at 4 p.m. local standard time on 2 April 2005, using the MM5 mesoscale model with initial conditions References and Notes 1. T. N. Palmer, Q. J. R. Meteorol. Soc. 128, 747 (2002). provided by different weather centers (8–10). (D) The BMA combined forecast is a weighted average 2. For real-time ensemble forecasts, see NCEP of the bias-corrected ensemble members (10, 14). (E) The uncertainty plot is a map of the half-width Operational Ensemble Forecasts (www.cdc.noaa.gov/ of the BMA forecast intervals. Higher values correspond to more uncertainty. (F) The BMA probability map/images/ens/ens.html) and MSC Ensemble of freezing refers to the 24-hour period ending at the valid time. Forecasts (http://weatheroffice.ec.gc.ca/ensemble/ index_e.html). 3. Z. Toth, E. Kalnay, Bull. Am. Meteorol. Soc. 74, 2317 sored DEMETER (Development of a through stochastic representations of para- (1993). European Multimodel Ensemble system for meterized physical processes, as imple- 4. F. Molteni, R. Buizza, T. N. Palmer, T. Petroliagis, Q. J. R. Meteorol. Soc. 122, 73 (1996). seasonal to inTERannual prediction) proj- mented in the ECMWF medium-range 5. P. L. Houtekamer, L. Lefaivre, J. Derome, H. Ritchie, H. L. ect. A single supercomputer hosted seven ensemble, thereby introducing random- Mitchell, Mon. Weather Rev. 124, 1225 (1996). independent state-of-the-art models, which ness into the model runs (13). Both options 6. G. Evensen, J. Geophys. Res. 99, 10143 (1994). produced a series of 6-month ensemble link flow-dependent forecast uncertainty 7. R. Buizza et al., Mon. Weather Rev. 133, 1076 (2005). 8. E. P. Grimit, C. F. Mass, Weather Forecast. 17, 192 reforecasts with common archiving systems and model-related errors, and it remains to (2002). and diagnostics. Each model was run nine be seen whether they are superior in any 9. F. A. Eckel, C. F. Mass, Weather Forecast. 20, 328 times with different initial conditions, way to approaches based purely on statisti- (2005). 10. Real-time forecast products are available at the resulting in global multimodel, multi–ini- cal postprocessing (7, 14). Nor has the University of Washington Mesoscale Ensemble tial condition ensemble reforecasts over the debate on selective versus Monte Carlo (www.atmos.washington.edu/~ens/uwme.cgi) past 50 years. The DEMETER ensemble sampling of initial condition uncertainty and Bayesian Model Averaging (http://isis.apl. washington.edu/bma/index.jsp) sites. improved both deterministic and proba- been resolved, although it may evolve in 11. T. N. Palmer et al., Bull. Am. Meteorol. Soc. 85, 853 bilistic forecast skill when compared to the novel directions as operational experience (2004). single-model ensembles, in ways that can- with various methods of sequential data 12. T. N. Palmer, Ed., Special issue on the DEMETER project, not be attributed to the increase in ensemble assimilation accrues. Tellus A 57 (May 2005), pp. 217–512. 13. R. Buizza, M. Miller, T. N. Palmer, Q. J. R. Meteorol. Soc. size only. Applications to malaria incidence From daily to seasonal time scales, prob- 125, 2887 (1999). and crop yield prediction have shown the abilistic forecasts based on ensembles have 14. A. E. Raftery, T. Gneiting, F. Balabdaoui, M. Polakowski, benefits of linking seasonal forecast ensem- become a prominent part of numerical Mon. Weather Rev. 133, 1155 (2005). 15. I. T. Jolliffe, D. B. Stephenson, Forecast Verification: A bles to end-user models that are also run in weather prediction. The ability of ensemble Practitioner’s Guide in Atmospheric Science (Wiley, ensemble mode. Building on the success of systems, in concert with statistical postpro- New York, 2004). the DEMETER project, an operational real- cessing, to improve deterministic fore- 16. R. de Elía, R. Laprise, Mon. Weather Rev. 133, 1129 (2005). time seasonal ensemble prediction system casts—in that the ensemble mean forecast 17. While preparing this Perspective,T.G. was on sabbati- has been established at ECMWF. outperforms the individual ensemble mem- cal leave at the Soil Physics Group, Universität Current challenges include the repre- bers—and to produce probabilistic and Bayreuth, Germany.We thank C. Mass for comments; sentation of forecast uncertainty due to the uncertainty information to the benefit of J. Baars, E. Grimit, and P. Tewson for assistance in preparing the figure; and the U.S. Department of use of imperfect numerical models. Model weather-sensitive public, commercial, and Defense Multidisciplinary Research University uncertainty can be addressed through the humanitarian sectors has been convincingly Initiative (MURI) for financial support. use of multimodel ensembles (in which established. More work needs to be done to each single model run is deterministic), or routinely provide fully reliable, flow- 10.1126/science.1115255

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