Training of supermodels - in the context of weather and climate forecasting

Given a set of imperfect weather or climate models, predictions can be improved by combining the models dynamically into a so called `supermodel'. The models are optimally combined to compensate their individual errors. This is different from the standard multi-model ensemble approach (MME), where the model output is statistically combined after the simulations. Instead, the supermodel can create a trajectory closer to observations than any of the imperfect models. By intervening during the forecast, errors can be reduced at an early stage and the ensemble can exhibit different dynamical behavior than any of the individual models. In this way, common errors between the models can be removed and new, physically correct behavior can appear. In our simplified context of models sharing the same evolution function and phase space, we can define either a connected or a weighted supermodel. A connected supermodel uses nudging to bring the models closer together, while in a weighted supermodel all model states are replaced at regular time intervals (i.e., restarted) by the weighted average of the individual model states. To obtain optimal connection coefficients or weights, we need to train the supermodel on the basis of historical observations. A standard training approach such as minimization of a cost function requires many model simulations, which is computationally very expensive. This thesis has focused on developing two new methods to efficiently train supermodels. The first method is based on an idea called cross pollination in time, where models exchange states during the training. The second method is a synchronization-based learning rule, originally developed for parameter estimation. The techniques are developed on low-order systems, such as Lorenz63, and later applied to different versions of the intermediate-complexity global coupled atmosphere-ocean-land model SPEEDO. Here the observations are from the same models, but with different parameters. The applicability of the method to real observations is tested using sensitivity to noisy and incomplete data. The characteristics the individual models should have in order to be combined together into a supermodel are identified, as well as which physical variables should be connected in a supermodel, and which ones should not. Both training methods result in supermodels that outperform both the individual models and the MME, for short term predictions as well as long term simulations. Furthermore, we show that the novel use of negative weights can improve predictions in cases where model errors do not cancel (for instance, all models are too warm with respect to the truth). A crucial advantage of the proposed training schemes is that in the present context relatively short training periods suffice to find good solutions. Although the validity of our conclusions in the context of real observations and model scenarios has yet to be proved, our results are very encouraging. In principle, the methods are suitable to train supermodels constructed using state-of-the art weather and climate models.Doktorgradsavhandlin

Improving weather and climate predictions by training of supermodels

Recent studies demonstrate that weather and climate predictions potentially improve by dynamically combining different models into a so-called “supermodel”. Here, we focus on the weighted supermodel – the supermodel's time derivative is a weighted superposition of the time derivatives of the imperfect models, referred to as weighted supermodeling. A crucial step is to train the weights of the supermodel on the basis of historical observations. Here, we apply two different training methods to a supermodel of up to four different versions of the global atmosphere–ocean–land model SPEEDO. The standard version is regarded as truth. The first training method is based on an idea called cross pollination in time (CPT), where models exchange states during the training. The second method is a synchronization-based learning rule, originally developed for parameter estimation. We demonstrate that both training methods yield climate simulations and weather predictions of superior quality as compared to the individual model versions. Supermodel predictions also outperform predictions based on the commonly used multi-model ensemble (MME) mean. Furthermore, we find evidence that negative weights can improve predictions in cases where model errors do not cancel (for instance, all models are warm with respect to the truth). In principle, the proposed training schemes are applicable to state-of-the-art models and historical observations. A prime advantage of the proposed training schemes is that in the present context relatively short training periods suffice to find good solutions. Additional work needs to be done to assess the limitations due to incomplete and noisy data, to combine models that are structurally different (different resolution and state representation, for instance) and to evaluate cases for which the truth falls outside of the model class

Improving weather and climate predictions by training of supermodels

Recent studies demonstrate that weather and climate predictions potentially improve by dynamically combining different models into a so-called "supermodel". Here, we focus on the weighted supermodel - the supermodel's time derivative is a weighted superposition of the time derivatives of the imperfect models, referred to as weighted supermodeling. A crucial step is to train the weights of the supermodel on the basis of historical observations. Here, we apply two different training methods to a supermodel of up to four different versions of the global atmosphere-ocean-land model SPEEDO. The standard version is regarded as truth. The first training method is based on an idea called cross pollination in time (CPT), where models exchange states during the training. The second method is a synchronization-based learning rule, originally developed for parameter estimation. We demonstrate that both training methods yield climate simulations and weather predictions of superior quality as compared to the individual model versions. Supermodel predictions also outperform predictions based on the commonly used multi-model ensemble (MME) mean. Furthermore, we find evidence that negative weights can improve predictions in cases where model errors do not cancel (for instance, all models are warm with respect to the truth). In principle, the proposed training schemes are applicable to state-of-the-art models and historical observations. A prime advantage of the proposed training schemes is that in the present context relatively short training periods suffice to find good solutions. Additional work needs to be done to assess the limitations due to incomplete and noisy data, to combine models that are structurally different (different resolution and state representation, for instance) and to evaluate cases for which the truth falls outside of the model class

Framework for an Ocean-Connected Supermodel of the Earth System

A supermodel connects different models interactively so that their systematic errors compensate and achieve a model with superior performance. It differs from the standard non-interactive multi-model ensembles (NI), which combines model outputs a-posteriori. Supermodels with Earth system models (ESMs) has not been developed because it is technically challenging to combine models with different state space. Here, we formulate the first supermodel framework for ESMs and use data assimilation to synchronise models. The ocean of three ESMs is synchronised every month by assimilating pseudo sea surface temperature (SST) observations generated by them on a common grid to handle discrepancies in grid and resolution. We compare the performance of two supermodel approaches to that of the NI. In the first (EW), the models are connected to the equal-weight multi-model mean, while in the second (SINGLE), they are connected to a single model. Both versions achieve synchronisation in the ocean and in the atmosphere, where the ocean drives the variability. The time variability of the supermodel multi-model mean SST is reduced compared to observations, most where synchronisation is not achieved and is lower-bounded by NI. The damping is larger in EW, for which variability in the individual models is also damped. Hence, under partial synchronisation, the unsynchronized variability gets damped in the multi-model average pseudo-observations, causing a deflation during the assimilation. The SST bias in individual models of EW is reduced compared to that of NI, and so is its multi-model mean in the synchronised regions. A trained supermodel remains to be tested.publishedVersio

Role of atmosphere-ocean interactions in supermodeling the tropical Pacific climate

The supermodel strategy interactively combines several models to outperform the individual models comprising it. A key advantage of the approach is that nonlinear improvements can be achieved, in contrast to the linear weighted combination of individual unconnected models. This property is found in a climate supermodel constructed by coupling two versions of an atmospheric model differing only in their convection scheme to a single ocean model. The ocean model receives a weighted combination of the momentum and heat fluxes. Optimal weights can produce a supermodel with a basic state similar to observations: a single Intertropical Convergence zone (ITCZ), with a western Pacific warm pool and an equatorial cold tongue. This is in stark contrast to the erroneous double ITCZ pattern simulated by both of the two stand-alone coupled models. By varying weights, we develop a conceptual scheme to explain how combining the momentum fluxes of the two different atmospheric models affects equatorial upwelling and surface wind feedback so as to give a realistic basic state in the tropical Pacific. In particular, we propose a mechanism based on the competing influences of equatorial zonal wind and off-equatorial wind stress curl in driving equatorial upwelling in the coupled models. Our results show how nonlinear ocean-atmosphere interaction is essential in combining these two effects to build different sea surface temperature structures, some of which are realistic. They also provide some insight into observed and modelled tropical Pacific climate.publishedVersio

An efficient training scheme for supermodels

Weather and climate models have improved steadily over time as witnessed by objective skill scores, although significant model errors remain. Given these imperfect models, predictions might be improved by combining them dynamically into a so-called supermodel. In this paper a new training scheme to construct such a supermodel is explored using a technique called cross pollination in time (CPT). In the CPT approach the models exchange states during the prediction. The number of possible predictions grows quickly with time, and a strategy to retain only a small number of predictions, called pruning, needs to be developed. The method is explored using low-order dynamical systems and applied to a global atmospheric model. The results indicate that the CPT training is efficient and leads to a supermodel with improved forecast quality as compared to the individual models. Due to its computational efficiency, the technique is suited for application to state-of-the art high-dimensional weather and climate models.publishedVersio

Synchronicity From Synchronized Chaos

The synchronization of loosely coupled chaotic oscillators, a phenomenon investigated intensively for the last two decades, may realize the philosophical notion of synchronicity. Effectively unpredictable chaotic systems, coupled through only a few variables, commonly exhibit a predictable relationship that can be highly intermittent. We argue that the phenomenon closely resembles the notion of meaningful synchronicity put forward by Jung and Pauli if one identifies "meaningfulness" with internal synchronization, since the latter seems necessary for synchronizability with an external system. Jungian synchronization of mind and matter is realized if mind is analogized to a computer model, synchronizing with a sporadically observed system as in meteorological data assimilation. Internal synchronization provides a recipe for combining different models of the same objective process, a configuration that may also describe the functioning of conscious brains. In contrast to Pauli's view, recent developments suggest a materialist picture of semi-autonomous mind, existing alongside the observed world, with both exhibiting a synchronistic order. Basic physical synchronicity is manifest in the non-local quantum connections implied by Bell's theorem. The quantum world resides on a generalized synchronization "manifold", a view that provides a bridge between nonlocal realist interpretations and local realist interpretations that constrain observer choice .Comment: 1) clarification regarding the connection with philosophical synchronicity in Section 2 and in the concluding section 2) reference to Maldacena-Susskind "ER=EPR" relation in discussion of role of wormholes in entanglement and nonlocality 3) length reduction and stylistic changes throughou

Training a supermodel with noisy and sparse observations: a case study with CPT and the synch rule on SPEEDO – v.1

As an alternative to using the standard multi-model ensemble (MME) approach to combine the output of different models to improve prediction skill, models can also be combined dynamically to form a so-called supermodel. The supermodel approach enables a quicker correction of the model errors. In this study we connect different versions of SPEEDO, a global atmosphere-ocean-land model of intermediate complexity, into a supermodel. We focus on a weighted supermodel, in which the supermodel state is a weighted superposition of different imperfect model states. The estimation, “the training”, of the optimal weights of this combination is a critical aspect in the construction of a supermodel. In our previous works two algorithms were developed: (i) cross pollination in time (CPT)-based technique and (ii) a synchronization-based learning rule (synch rule). Those algorithms have so far been applied under the assumption of complete and noise-free observations. Here we go beyond and consider the more realistic case of noisy data that do not cover the full system's state and are not taken at each model's computational time step. We revise the training methods to cope with this observational scenario, while still being able to estimate accurate weights. In the synch rule an additional term is introduced to maintain physical balances, while in CPT nudging terms are added to let the models stay closer to the observations during training. Furthermore, we propose a novel formulation of the CPT method allowing the weights to be negative. This makes it possible for CPT to deal with cases in which the individual model biases have the same sign, a situation that hampers constructing a skillfully weighted supermodel based on positive weights. With these developments, both CPT and the synch rule have been made suitable to train a supermodel consisting of state of the art weather and climate models