Representing uncertainty in initial conditions: experimentation from lagged average forecasting to singular vectors

Franco Molteni

ECMWF and Abdus Salam International Centre for Theoretical Physics, Trieste, Italy

This contribution summarises my presentation at the Symposium held to celebrate 30 Years of Ensemble Forecasting and Tim Palmer’s 70th birthday, with a few personal additions.

Research on ensemble forecasting at ECMWF started in 1984, as a project in the Numerical Experimentation Section led by Stefano Tibaldi. Around that time, I was working for the Italian Electricity Board on a project aimed at using numerical rainfall forecasts for the management of reservoirs in hydro-electric power plants; luckily, I managed to get funding from their environmental laboratory in Milan to spend one year at ECMWF and assess the potential of numerical long-range predictions. So, I joined the Numerical Experimentation Section in early January 1984, and this was the start of my career at ECMWF.

In Stefano’s section, Ulrich Cubasch had already started some numerical experiments on the monthly time scale in ‘deterministic’ mode. Stefano proposed to use the technique of lagged-average forecasting recently proposed by Hoffman and Kalnay (1983) for ensemble experiments on the monthly time-scale. It should be mentioned that a first attempt at so-called Monte-Carlo forecasting had previously been done by Tony Hollingsworth (1979), but because of the random spatial nature of the imposed perturbations, most of the signal was already filtered out by the normal-mode initialization used at the time, and no significant perturbation growth occurred in that ensemble.

Four 9-member time-lagged ensembles were run with the T21 spectral model in 1984, using analyses separated by 6-hour intervals as initial conditions, with initial dates from winter 1983/84. Noting that the predicted anomalies were strongly affected by the model systematic error, we estimated the model bias from runs started in the previous two winters, and we subtracted the mean error from the forecast anomalies in the 1983/84 cases (no re-analysis was available at the time: we had to work with just a few years of ECMWF operational analyses). In all cases, the skill of 10-day and 30-day means from the lagged-average forecast exceeded that of the single forecast started from the latest initial conditions. With typical beginner’s luck, our first ever experiment was particularly successful, and we managed to get further encouragement and support from the ECMWF Director (Lennart Bengtsson) and Head of Research (David Burridge). As a result, the project was continued in 1985, when the same experiments were re-run at T42 resolution.

Unfortunately, the ECMWF Council did not share the same enthusiasm when such results were presented by Lennart: the ‘jump’ into long-range predictions was seen as too ambitious in view of the Centre’s focus on medium-range forecasting. For a while, there was uncertainty about the continuation of research on ensembles and monthly forecasting. However, the ECMWF management was successful in pointing out the usefulness of such research for the assessment of systematic errors, and experimentation was allowed to continue. It was in such a ‘front-line’ situation that Tim Palmer joined the new Diagnostic and Predictability Research Section, still led by Tibaldi. His previous experience at the Met Office was fully in line with the goal of expanding predictability research in both the medium and the ‘extended’ range (‘extended’ being chosen as a less controversial name for the monthly-scale forecasts). Coincidentally, just after Tim joined the new section in 1986, the first paper on ensemble prediction at ECMWF (Molteni, Cubasch & Tibaldi, 1988) was presented by Tibaldi at a workshop on “Persistent Meteo-Oceanographic Anomalies and Teleconnection” held in September 1986 at the Pontifical Academy of Sciences in Rome, also attended by Tim and other ECMWF scientists: so, ensemble prediction got a high-level endorsement!

When Stefano left ECMWF in autumn 1987, Tim became Head of Section. In the meanwhile, I had re-joined the section in May 1987, taking the staff position left vacant by Ulrich Cubasch. I have to admit that, at the very beginning, I felt a bit intimidated by Tim. It was his previous academic background in Cosmology and Relativity that put him, in my eyes, on a level above. I had been fascinated by cosmology and astrophysics during my high-school and university years, although in the end I chose to make my thesis in meteorology. Having a boss who had interacted with scientists I had dreamed about meeting, after reading their books, gave me a humbling feeling. Of course, after a short while I managed to restore my self-confidence and my working relationship with Tim grew better and better.

During my first two years in Tim’s section, ensemble predictions were not my main area of activity, although I contributed to the analysis of the time-lagged ensembles run at that time by Cedo Brankovic (see Brankovic et al. 1990). We were looking for an explanation of the strange ‘return of skill’ we found in the scores of lagged-average forecasts: namely, the fact that scores for the 21-to-30-day ensemble-mean anomaly were often better than those for the previous ten days. This was shown to be the result of the ensemble spread growing at a slower rate than the actual error, so that the benefit of filtering out unpredictable signals only became apparent at the end of the monthly forecast range.

Because of the relatively slow growth of perturbations, time-lagged ensembles showed little benefit over deterministic forecasts in the medium-range. Tim was determined to bring the ensemble approach into the medium range, and he proposed to explore the finite-time instability analysis advocated by Farrell (1989) and Lacarra and Talagrand (1988). The IFS was still under development at that time, and although the ultimate goal was to compute perturbations for a primitive equation model, Tim was fully supportive of the idea of first developing a proper understanding of this approach using simplified models. So, my main task became the computation of fastest-growing finite-time perturbations (defined as singular vectors of a linearised model) in a barotropic and a 3-level quasi-geostrophic (QG) model, which I coded for such a purpose. We learned a lot about the nature and propagation of these finite-time perturbations from this work (see Molteni and Palmer 1993). The patterns of the QG perturbations, mainly concentrated at the beginning of the Atlantic and Pacific storm tracks, were sufficiently realistic to lead us to a further step: interpolate the QG perturbations onto the operational model grid and test ensembles perturbed by singular vectors. This was accomplished in a set of experiments led by Robert Mureau (Mureau et al. 1993), and singular vectors proved to be more effective than alternative methods in producing ensemble spread with growth rates comparable to actual errors.

Following early work on the (still developing) IFS by Joe Tribbia, the computation of primitive-equation singular vectors using IFS code was achieved by Roberto Buizza (Buizza et al. 1993), and this led to the operational implementation of the ECMWF medium-range ensemble (Molteni et al. 1996) in late 1992. Although such an operational achievement gave us great satisfaction, I still look at the years of research preceding that event as probably the most challenging and productive in my career. I have to give full credit to Tim for his guidance during that period: he led me and the whole section in directions which were at the forefront of both theoretical and operational meteorology.

Although I left ECMWF at the end of 1994, my collaboration with Tim did not end there. We continued to interact while I was working in Italy (see the work on regimes in Corti et al. 1999), he brought me back to ECMWF in 2006 as Head of the Seasonal Forecast Section, and recently he invited me to join his research group in Oxford as visiting professor. Through all these years, he has continued to provide new stimuli for ground-breaking research. Many thanks and congratulations Tim! You are turning 70, but I am sure you will continue to make best use of your “little grey cells”!