Will it rain? Predictability, risk assessment and the need for ensemble forecasts
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1 Will it rain? Predictability, risk assessment and the need for ensemble forecasts David Richardson European Centre for Medium-Range Weather Forecasts Shinfield Park, Reading, RG2 9AX, UK Tel , Fax , A traditional numerical weather forecast is a single best-estimate prediction of the future weather. This deterministic forecast provides a simple yes or no answer to the question Will it rain?. However, uncertainties in the initial conditions and in the formulation of the weather prediction model mean that the forecast will not always give the correct answer. The deterministic forecast gives no indication of the sensitivity to these uncertainties - how likely is a given forecast to be correct? A user must decide whether to act or not without knowing how much trust to put in the forecast information. The aim of ensemble forecasting is to provide a more detailed picture of the range of possible future weather states consistent with our knowledge of the current state. Giving a fuller picture of what may happen and how likely the various alternatives are, allows the user to better access the risk and to make more informed decisions. Uncertainty in initial conditions is one important source of forecast error. On some occasions small changes to the initial conditions can produce large differences in the forecast. However, at other times there is less sensitivity, and errors in the initial conditions do not greatly affect the forecast. This case-to-case variation in predictability is illustrated for a simple system in Figure 1, which shows the evolution of sets, or ensembles, of initial points on the famous Lorenz "butterfly" attractor. The two wings of the Lorenz attractor can be imagined as two different weather types, say dry on the left and wet on the right. The initial points represent estimates of the current state of the atmosphere; the arrows show how subsequent forecasts are affected by the small initial errors. The three panels show how the effect of these errors can vary depending on the initial "true state". When we are in a predictable state (left panel), small errors in the starting conditions will not affect the forecast: we can be confident that the weather will become wet - it will rain. If, however, we are in a less predictable situation (middle panel), the points stay together only for a limited time before diverging. While we can be confident of the forecast for a few days ahead, we cannot be sure if it will ultimately stay dry or become wetter dry at first, but it may rain later. Sometimes the situation is so unpredictable that we can have little confidence in the outcome even a short period ahead (right panel) - we have no idea what will happen next. Figure 1. Ensemble forecasts on the Lorenz attractor: an example of how forecast uncertainty can vary depending on the location of the initial state. See text for details.
2 The 10-day Ensemble Prediction System (EPS) of the European Centre for Medium-Range Weather Forecasts (ECMWF) is designed to account for uncertainties in the operational ECMWF analysis (Molteni et al., 1996). One forecast, known as the control, is run from the operational ECMWF analysis (the best estimate of the current atmospheric state). 50 additional integrations, the perturbed ensemble members, are made from slightly different initial conditions that are designed to represent the uncertainties in the operational analysis. The number of ensemble members is limited by the available computer power, while the number of ways to perturb the analysis is many orders of magnitude larger. Because of this limitation on ensemble size, the perturbations are selected to sample fast-growing structures rather than simply by random sampling. The ECMWF perturbations are created by adding to the operational ECMWF analysis perturbations that produce the fastest energy growth during the first two days of the forecast period (using what is known as the singular vector technique). In the extra-tropics, the perturbations are allowed to grow anywhere in the hemisphere. Perturbations in the tropics are designed to sample the uncertainty in tropical storms and are therefore targeted to maximize total-energy growth inside a limited area centred on tropical storms (Puri et al. 1999). The tropical singular vector calculation takes account of the physical processes that may contribute significantly to perturbation growth in tropical areas (Barkmeijer et al., 2001). An example of an ECMWF ensemble prediction for the track of typhoon Rusa is shown in Figure 2. The operational deterministic forecast predicts the track to be too far to the west. However, a significant proportion of the ensemble members correctly predict the track to curve north-eastwards. The strike probability (calculated as the fraction of the 51 ensemble members passing within 65 nm of a given location in a 120 hour period) clearly indicates a higher probability for this alternative solution. Figure 2. ECMWF ensemble prediction of typhoon Rusa. The thick black line shows the track from the operational deterministic forecast, the thin blue lines show the tracks from the ensemble members, and the large black circles show the observed positions. The shading shows the strike probability calculated from the ensemble.
3 A similar philosophy of selectively choosing particular growing structures is followed by the National Centers for Environmental Prediction (NCEP) in Washington, although the perturbation methodology is different (Toth and Kalnay 1993; Tracton and Kalnay 1993). The breeding vector method used at NCEP calculates perturbations that grow fastest during the analysis cycle, while the singular vector method used by ECMWF calculates perturbations that will grow fastest during the forecast. Not all ensemble systems use such selective strategies. For example the Canadian Meteorological Centre uses a Monte-Carlo technique, perturbing the observations and running an ensemble of data assimilations to produce a set of equally likely initial conditions for the ensemble forecast (Houtekamer et al., 1996, 1997). The main focus of medium-range ensemble forecasting has been on the simulation of uncertainties in the initial conditions. However, forecasts are also sensitive to uncertainties in model formulation. At ECMWF, each ensemble member is run using slightly different model equations (Buizza et al., 1999). The current implementation is a first attempt to simulate random model errors due to parametrized physical processes. It is assumed that these random errors are coherent between the various parametrization modules and over certain space and time scales. The scheme assumes that larger tendencies from the parametrization will have a larger random error component. This has the benefit that it is easy to implement and maintain, but it is not designed to compensate for model biases or to fully sample the uncertainties in the model formulation. The Canadian ensemble system takes a more direct approach to model uncertainty by including forecasts made using two different models and also by using different two physical parametrization schemes in each model. This more directly addresses the uncertainty in the model formulation although it does have the disadvantage of needing to maintain more than one model. The use of more than one model in an ensemble, the multi-model approach, is particularly important at longer time ranges where the effects of model error are more significant. For seasonal and longer timescales, multi-model ensembles can bring substantial benefits for ensemble forecasts. An ensemble made by combining forecasts from different models with different systematic and flow-dependent errors should give a much better representation of the full range of future states than just using a single model. Figure 3 shows an example of sea-surface temperature (SST) predictions from the Demeter multimodel seasonal forecasting project (see Seasonal predictions have been run using a number of different coupled atmosphere-ocean general circulation models; a 9-member ensemble is produced for each model by perturbing the initial conditions. Figure 3 shows predictions for the SST for the Nino 3 region of the tropical east Pacific from some of these multimodel sets. As for the simple example of Figure 1, the uncertainty in the predictions is not constant, but shows considerable variation between predictions starting in different years. Examples of high predictability can be seen for some of the strong ENSO years, with little impact from perturbing initial conditions or from using different models. However, at other times, there are substantial differences between forecasts started from only slightly different initial conditions. There are also cases where the different model formulations have a significant impact on the range of predicted values.
4 Figure 3. Sea-surface temperature (SST) predictions for the Nino 3 area of the tropical Pacific from the Demeter seasonal forecast project. The solid line shows the observed seasonal (3-month) mean SST anomaly. The crosses show the predicted anomaly from the members of the Demeter multi-model ensemble, averaged over months 2-4 of the forecasts for each season (the predictions are initialised with analyses from the beginning of the month before the start of the season). Ensemble forecasting is becoming increasingly important on all timescales from the short range (1 or 2 days ahead) to the seasonal range and beyond (ensembles are equally valuable in assessing the uncertainty in climate change predictions). The ensemble approach aims to provide a probability distribution for the range of possible future states, consistent with known sensitivities in the system, such as uncertainty in the initial conditions and in the formulation of the forecast model. An ensemble provides information on the probability of future weather events. This allows each user to properly assess the risks associated with their own applications and to take action accordingly. While some users will be prepared to act when there is only a small chance of adverse weather, others will wait until the outcome is more certain before taking a decision. References and further reading Barkmeijer, J, Buizza, R., & Palmer, T. N., 1999: 3D-Var Hessian singular vectors and their potential use in the ECMWF Ensemble Prediction System. Q. J. R. Meteor. Soc., 125, Barkmeijer, J., Buizza, R., Palmer, T. N., Puri, K., & Mahfouf, J.-F., 2001: Tropical singular vectors computed with linearized diabatic physics. Q. J. R. Meteorol. Soc., 127, Buizza, R., & Palmer, T. N., 1995: The singular vector structure of the atmospheric general circulation. J. Atmos. Sci., 52,
5 Buizza, R., Miller, M., & Palmer, T. N., 1999: Stochastic simulation of model uncertainties. Q. J. R. Meteorol. Soc., 125, Houtekamer, P L, Lafaivre, L, Derome, J, Ritchie, H & Mitchell, H L, 1996: A system simulation approach to Ensemble Prediction. Mon. Wea. Rev, 124, Houtekamer, P L & Lefaivre, L, 1997: Using ensemble forecasts for model validation. Mon. Wea. Rev, 125, Molteni, F., Buizza, R., Palmer, T. N., & Petroliagis, T., 1996: The new ECMWF ensemble prediction system: methodology and validation. Q. J. R. Meteorol. Soc., 122, Puri, K., Barkmeijer, J. & Palmer, T. N., 1999: Ensemble prediction of tropical cyclones using targeted diabatic singular vectors. Q. J. R. Meteor. Soc., 127, Richardson, D. S., 2000: Skill and economic value of the ECMWF Ensemble Prediction System. Q. J. R. Meteorol. Soc., 126, Richardson, D. S., Ensembles using multiple models and analyses. Q. J. R. Meteorol. Soc., 127, Toth, Z, & Kalnay, E., 1993: Ensemble Forecasting at NMC: the generation of perturbations. Bull. Amer. Meteorol. Soc., 74, Tracton, M S, & Kalnay, E, 1993: Operational ensemble prediction at the National Meteorological Center. Weather & Forecasting, 8, Zhu, Yuejian, Zoltan Toth, Richard Wobus, David Richardson, and Kenneth Mylne, The Economic Value Of Ensemble-Based Weather Forecasts. Bull. Am. Meteorol. Soc., 83,
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