Besides IC uncertainty being considered, the uncertainty in model physics and dynamics is also taken into account in a 2-D EPS. There are currently many approaches used on this regard such as multi-model, multi-physics, multi-dynamics, multi-ensemble system and stochastic physics. Based on favorable research results such as Mullen et. al. (1999) and Tracton et. al. (1998), NCEP pioneeringly implemented a “multi-ensemble system” approach-based SREF in operation consisting of two sub-ensemble systems where each of them was based on a different regional model from the very beginning of its development (Du and Tracton, 2001). Currently, NCEP SREF consists of four sub-ensemble systems with four regional models (Du et. al., 2006). Obviously, multi-ensemble system approach is a grand mixture of multi-model, multi-dynamics, multi-physics, multi-IC and multi-LBC etc. methods. Multi-model ensemble system is considered to be an ad hoc approach but has been proven to be very effective and work very well (in both reducing the error of ensemble mean forecast and increasing ensemble spread) in practice (Du et. al., 2003; Mylne et. al., 2002). The simplest version of multi-model ensemble is the so-called Poor-Man ensemble where multiple single forecasts from various available models are just pulled together to form an ensemble if one cannot afford to run his own “normal-cost” ensemble (Wobus and Kalnay, 1995; Ebert, 2001). Multi-model approach has been widely accepted and used nowadays. A recent development of multi-model approach is a mixture of multi-ensemble systems from multi-centers such as TIGGE (THORPEX Interactive Grand Global Ensemble) and NAEFS (North American Ensemble Forecasting System) etc. international efforts, which should be now called Rich-Man ensemble (in addition to his own “normal-cost” ensemble). Obviously, a disadvantage of multi-model approach is the cost to develop and maintain many models if it is run by one institute. In addition, multi-model approach can also be utilized in deterministic scope rather than ensemble scope such as the Florida State University’s “superensemble” approach (Krishnamurti, 1999) which is a multi-model based MOS-type approach using linear regression technique. It significantly improves forecast accuracy over the original forecasts by correcting model biases. However, this method provides only a most likely deterministic solution with no forecast variance or uncertainty information attached.

    Within one model, an ensemble can be formed by alternating physics schemes from one member to another. This multi-physics approach is found to be effective in predicting convective systems with weak large-scale forcing (Stensrud et. al., 2000; Jankov et. al., 2005). Using multiple convective schemes, Du et. al. (2004) compared the relative roles of multi-physics vs. multi-IC in contributing to ensemble spread in short range (1-3 days). Their result showed that IC uncertainty is a dominant contributor to ensemble spread of large-scale basic fields such as wind, pressure, height and temperature, while physics difference provides extra valuable spread mainly being confined to isolated, smaller-scale storm areas. However, for precipitation and convective instabilities such as CAPE, both IC and physics diversities are found equally important. Similar result is also seen for fine-resolution (4km) storm-scale ensemble (Kong et. al., 2007). Therefore, it’s recommended that both IC and physics diversity should be taken into account at the same time in a mesoscale ensemble to maximize forecast diversity. With the NCEP SREF, it is found that the interaction between IC perturbation and physics diversity indeed greatly enhances ensemble spread during warm seasons when combing IC and physics perturbations together although the impact from physics diversity seems minimal in cold seasons. It is expected that multi-physics might be an effective way to build an ensemble system for convection-dominate tropics. A problem noticed of multi-physics approach by simply alternating different physics schemes is that the extra growth rate in ensemble spread gained initially will soon die out with time and cannot sustain over the entire forecasting length.

    A more theoretically sounding and sophisticated version of multi-physics approach is Stochastic Physics. Since part of forecast uncertainty stems from parameterization of sub-grid physical processes (Stensrud, 2007) and truncation etc. imperfections of a model, certain parameter values or relevant terms such as tendency, diffusion and energy can be altered (e.g. via multiplying) by, in a stochastic fashion, a factor to account for those possibly missing effects. Therefore, by applying such stochastic process during model integration, forecast value will be altered accordingly. By repeating this stochastic process many times, an ensemble of forecasts can thus be formed. This stochastic process could either be confined within each member without interaction with other members during the entire model integration (“individualism”) or be carried out across different members by interactively exchanging information among them during the model integration (“collectivism”). Although this is a promising method both scientifically and economically, a couple of key issues need to be demonstrated before it’s fully convinced to replace the current multi-model approach such as (a) can this method steadily outperform the multi-model based ensemble (in terms of mean error, spread-skill relation and probability reliability etc.), and (b) can the extra spread growth rate injected by stochastic physics be sustained during the entire model integration. Some research was done on this in the past (Hotekamer et. al., 1996; Buizza et. al., 1999b; Bright and Mullen, 2002b; Gray and Shutts, 2002; Shutts, 2004) and more is needed to make it a mature method. ECMWF has implemented a version of this method in their global ensemble system (Buizza et. al., 1999b; Shutts, 2004), while NCEP has a plan to do the same for both its global and regional ensemble systems in near future (Hou and Toth, 2007, personal communication).

    It is still not clear and an issue to be investigated that how important multi-dynamics is relative to multi-physics in contributing to ensemble spread. Some expect that physics might be more important than dynamics to forecast diversity. This is a very practical issue at NWP centers such as should one model core or multiple model cores be maintained in an ensemble system. It’s always easier and cheaper to maintain only one model dynamic core but with varying physics for ensembling.