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Register a new userIdentifying efficient ensemble perturbations for initializing subseasonal-to-seasonal prediction
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The prediction of the weather at subseasonal-to-seasonal (S2S) timescales is dependent on both initial and boundary conditions. An open question is how to best initialize a relatively small-sized ensemble of numerical model integrations to produce reliable forecasts at these timescales. Reliability in this case means that the statistical properties of the ensemble forecast are consistent with the actual uncertainties about the future state of the geophysical system under investigation. In the present work, a method is introduced to construct initial conditions that produce reliable ensemble forecasts by projecting onto the eigenfunctions of the Koopman or the Perron-Frobenius operators, which describe the time-evolution of observables and probability distributions of the system dynamics, respectively. These eigenfunctions can be approximated from data by using the Dynamic Mode Decomposition (DMD) algorithm. The effectiveness of this approach is illustrated in the framework of a low-order ocean-atmosphere model exhibiting multiple characteristic timescales, and is compared to other ensemble initialization methods based on the Empirical Orthogonal Functions (EOFs) of the model trajectory and on the backward and covariant Lyapunov vectors of the model dynamics. Projecting initial conditions onto a subset of the Koopman or Perron-Frobenius eigenfunctions that are characterized by time scales with fast-decaying oscillations is found to produce highly reliable forecasts at all lead times investigated, ranging from one week to two months. Reliable forecasts are also obtained with the adjoint covariant Lyapunov vectors, which are the eigenfunctions of the Koopman operator in the tangent space. The advantages of these different methods are discussed.
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The atmosphere is chaotic. This fundamental property of the climate system makes forecasting weather incredibly challenging: its impossible to expect weather models to ever provide perfect predictions of the Earth system beyond timescales of approximately 2 weeks. Instead, atmospheric scientists look for specific states of the climate system that lead to more predictable behaviour than others. Here, we demonstrate how neural networks can be used, not only to leverage these states to make skillful predictions, but moreover to identify the climatic conditions that lead to enhanced predictability. Furthermore, we employ a neural network interpretability method called ``layer-wise relevance propagation to create heatmaps of the regions in the input most relevant for a networks output. For Earth scientists, these relevant regions for the neural networks prediction are by far the most important product of our study: they provide scientific insight into the physical mechanisms that lead to enhanced weather predictability. While we demonstrate our approach for the atmospheric science domain, this methodology is applicable to a large range of geoscientific problems.
We study the impact of three stochastic parametrizations in the ocean component of a coupled model, on forecast reliability over seasonal timescales. The relative impacts of these schemes upon the ocean mean state and ensemble spread are analyzed. The oceanic variability induced by the atmospheric forcing of the coupled system is, in most regions, the major source of ensemble spread. The largest impact on spread and bias came from the Stochastically Perturbed Parametrization Tendency (SPPT) scheme - which has proven particularly effective in the atmosphere. The key regions affected are eddy-active regions, namely the western boundary currents and the Southern Ocean. However, unlike its impact in the atmosphere, SPPT in the ocean did not result in a significant decrease in forecast error. Whilst there are good grounds for implementing stochastic schemes in ocean models, our results suggest that they will have to be more sophisticated. Some suggestions for next-generation stochastic schemes are made.
This paper has been written to mark 25 years of operational medium-range ensemble forecasting. The origins of the ECMWF Ensemble Prediction System are outlined, including the development of the precursor real-time Met Office monthly ensemble forecast system. In particular, the reasons for the development of singular vectors and stochastic physics - particular features of the ECMWF Ensemble Prediction System - are discussed. The author speculates about the development and use of ensemble prediction in the next 25 years.
The earth system is exceedingly complex and often chaotic in nature, making prediction incredibly challenging: we cannot expect to make perfect predictions all of the time. Instead, we look for specific states of the system that lead to more predictable behavior than others, often termed forecasts of opportunity. When these opportunities are not present, scientists need prediction systems that are capable of saying I dont know. We introduce a novel loss function, termed the NotWrong loss, that allows neural networks to identify forecasts of opportunity for classification problems. The NotWrong loss introduces an abstention class that allows the network to identify the more confident samples and abstain (say I dont know) on the less confident samples. The abstention loss is designed to abstain on a user-defined fraction of the samples via a PID controller. Unlike many machine learning methods used to reject samples post-training, the NotWrong loss is applied during training to preferentially learn from the more confident samples. We show that the NotWrong loss outperforms other existing loss functions for multiple climate use cases. The implementation of the proposed loss function is straightforward in most network architectures designed for classification as it only requires the addition of an abstention class to the output layer and modification of the loss function.
In this work we use the random matrix theory (RMT) to correctly describethe behavior of spectral statistical properties of the sea surface temperatureof oceans. This oceanographic variable plays an important role in theglobalclimate system. The data were obtained from National Oceanic and Atmo-spheric Administration (NOAA) and delimited for the period 1982 to 2016.The results show that oceanographic systems presented specific $beta$ values thatcan be used to classify each ocean according to its correlation behavior. Thenearest-neighbors spacing of correlation matrix for north, central and south ofthe three oceans get close to a RMT distribution. However, the regions delim-ited in the Antarctic pole exhibited the distribution of the nearest-neighborsspacing well described by the Poisson model, which shows astatistical changeof RMT to Poisson fluctuations.
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