Climate change is a reality of today. Paleoclimatic proxies and climate predictions based on coupled atmosphere-ocean general circulation models provide us with temperature data. Using Detrended Fluctuation Analysis, we are investigating the statistical connection between the climate types of the present and these local temperatures. We are relating this issue to some well-known historic climate shifts. Our main result is that the temperature fluctuations with or without a temperature scale attached to them, can be used to classify climates in the absence of other indicators such as pan evaporation and precipitation.
We introduce the special issue on the Statistical Mechanics of Climate published on the Journal of Statistical Physics by presenting an informal discussion of some theoretical aspects of climate dynamics that make it a topic of great interest for mathematicians and theoretical physicists. In particular, we briefly discuss its nonequilibrium and multiscale properties, the relationship between natural climate variability and climate change, the different regimes of climate response to perturbations, and critical transitions.
El Niño is a typical example of a coupled atmosphere--ocean phenomenon, but it is unclear whether it can be described quantitatively by a correlation between relevant climate events. To provide clarity on this issue, we developed a machine learning-based El Niño prediction model that uses the time series of climate indices. By transforming the multidimensional time series into the path signature, the model is able to properly evaluate the order and nonlinearity of climate events, which allowed us to achieve good forecasting skill (mean square error = 0.596 for 6-month prediction). In addition,…
There is a clear positive correlation between boreal summer tropical Atlantic sea-surface temperature and annual hurricane numbers. This motivates the idea of trying to predict the sea-surface temperature in order to be able to predict future hurricane activity. In previous work we have used simple statistical methods to make 5 year predictions of tropical Atlantic sea surface temperatures for this purpose. We now compare these statistical SST predictions with SST predictions made by an ensemble mean of IPCC climate models.
The last glacial period was punctuated by a series of abrupt climate shifts, the so-called Dansgaard-Oeschger (DO) events. The frequency of DO events varied in time, supposedly because of changes in background climate conditions. Here, the influence of external forcings on DO events is investigated with statistical modelling. We assume two types of simple stochastic dynamical systems models (double-well potential-type and oscillator-type), forced by the northern hemisphere summer insolation change and/or the global ice volume change. The model parameters are estimated by using the maximum like…
Palaeoclimate archives contain information on climate variability, trends and mechanisms. Models are developed to explain observations and predict the response of the climate system to perturbations, in particular perturbations associated with the anthropogenic influence. Here, we review three classical frameworks of climate modelling: conceptual, simulator-based (including general circulation models and Earth system models of intermediate complexity), and statistical. The conceptual framework aims at a parsimonious representation of a given climate phenomenon; the simulator-based framework co…
Emergent constraints use relationships between future and current climate states to constrain projections of climate response. Here, we introduce a statistical, hierarchical emergent constraint (HEC) framework in order to link future and current climate with observations. Under Gaussian assumptions, the mean and variance of the future state is shown analytically to be a function of the signal-to-noise (SNR) ratio between data-model error and current-climate uncertainty, and the correlation between future and current climate states. We apply the HEC to the climate-change, snow-albedo feedback, …
Most of the existing prediction methods gave a false alarm regarding the El Niño event in 2014. A crucial aspect is currently limiting the success of such predictions, i.e. the stability of the slowly varying Pacific climate. This property determines whether sea surface temperature perturbations will be amplified by coupled ocean-atmosphere feedbacks or not. The so-called Bjerknes stability index has been developed for this purpose, but its evaluation is severely constrained by data availability. Here we present a new promising background stability index based on complex network theory. This i…
The CMIP3 multi-model ensemble spread most likely underestimates the real model uncertainty in future climate predictions because of the similarity, and shared defects, of the models in the ensemble. To generate an appropriate level of uncertainty, the spread needs inflating. We derive the mathematical connection between an assumed level of correlation between the model output and the necessary inflation of the spread, and illustrate the connection by making temperature predictions for the UK for the 21st century using four different correlation scenarios.
Accurately modelling the Earth's climate has widespread applications ranging from forecasting local weather to understanding global climate change. Low-fidelity simulations of climate phenomena are readily available, but high-fidelity simulations are expensive to obtain. We therefore investigate the potential of Gaussian process-based multi-fidelity surrogate modelling as a way to produce high-fidelity climate predictions at low cost. Specifically, our model combines the predictions of a low-fidelity Global Climate Model (GCM) and those of a high-fidelity Regional Climate Model (RCM) to produc…
Meaningful climate predictions must be accompanied by their corresponding range of uncertainty. Quantifying the uncertainties is non-trivial, and different methods have been suggested and used in the past. Here, we propose a method that does not rely on any assumptions regarding the distribution of the ensemble member predictions. The method is tested using the CMIP5 1981-2010 decadal predictions and is shown to perform better than two other methods considered here. The improved estimate of the uncertainties is of great importance for both practical use and for better assessing the significanc…
While previous works have shown that machine learning (ML) can improve the prediction accuracy of coarse-grid climate models, these ML-augmented methods are more vulnerable to irregular inputs than the traditional physics-based models they rely on. Because ML-predicted corrections feed back into the climate model's base physics, the ML-corrected model regularly produces out of sample data, which can cause model instability and frequent crashes. This work shows that adding semi-supervised novelty detection to identify out-of-sample data and disable the ML-correction accordingly stabilizes simul…
Ensembles of climate models are commonly used to improve climate predictions and assess the uncertainties associated with them. Weighting the models according to their performances holds the promise of further improving their predictions. Here, we use an ensemble of decadal climate predictions to demonstrate the ability of sequential learning algorithms (SLAs) to reduce the forecast errors and reduce the uncertainties. Three different SLAs are considered, and their performances are compared with those of an equally weighted ensemble, a linear regression and the climatology. Predictions of four…
Objective probabilistic forecasts of future climate that include parameter uncertainty can be made by using the Bayesian prediction integral with the prior set to Jeffreys' Prior. The calculations involved in determining the prior can then be simplified by making parametric assumptions about the distribution of the output from the climate model. The most obvious assumption to make is that the climate model output is normally distributed, in which case evaluating the prior becomes a question of evaluating gradients in the parameters of the normal distribution. In previous work we have considere…
Eigen techniques such as empirical orthogonal function (EOF) or coupled pattern (CP) / maximum covariance analysis have been frequently used for detecting patterns in multivariate climatological data sets. Recently, statistical methods originating from the theory of complex networks have been employed for the very same purpose of spatio-temporal analysis. This climate network (CN) analysis is usually based on the same set of similarity matrices as is used in classical EOF or CP analysis, e.g., the correlation matrix of a single climatological field or the cross-correlation matrix between two d…
Multimodel ensembling has been widely used to improve climate model predictions, and the improvement strongly depends on the ensembling scheme. In this work, we propose a Bayesian neural network (BNN) ensembling method, which combines climate models within a Bayesian model averaging framework, to improve the predictive capability of model ensembles. Our proposed BNN approach calculates spatiotemporally varying model weights and biases by leveraging individual models' simulation skill, calibrates the ensemble prediction against observations by considering observation data uncertainty, and quant…
Generative assimilation and prediction for weather and climate
Chinese Academy of Sciences（中国科学院）；Nanjing University（南京大学）；Technical University of Munich（慕尼黑工业大学）；Potsdam Institute for Climate Impact Research（波茨坦气候影响研究所）；Chinese Academy of Meteorological Sciences（中国气象科学研究院）；National University of Defense Technology（国防科技大学）；Peking University（北京大学）；National Climate Center（国家气候中心）；Xiong’an Institute of Meteorological Artificial Intelligence（雄安气象人工智能研究院）
We describe a simple method that utilises the standard idea of bias-variance trade-off to improve the expected accuracy of numerical model forecasts of future climate. The method can be thought of as an optimal multi-model combination between the forecast from a numerical model multi-model ensemble, on one hand, and a simple statistical forecast, on the other. We apply the method to predictions for UK temperature and precipitation for the period 2010 to 2100. The temperature predictions hardly change, while the precipitation predictions show large changes.
Over the last few decades, climate scientists have devoted much effort to the development of large numerical models of the atmosphere and the ocean. While there is no question that such models provide important and useful information on complicated aspects of atmosphere and ocean dynamics, skillful prediction also requires a phenomenological approach, particularly for very slow processes, such as glacial-interglacial cycles. Phenomenological models are often represented as low-order dynamical systems. These are tractable, and a rich source of insights about climate dynamics, but they also igno…
Current techniques for predicting climate change are mainly based on "massive" deterministic numerical modeling. However, the ocean-atmosphere system is a so-called "complex system", made up of a large number of interacting elements. We show that, in such systems, owing to the particularly large sensitivity to initial conditions, the approach of a possible tipping over a critical point cannot be evidenced "by construction" using numerical modeling, due to the divergence of computation time in the vicinity of the tipping point. On the other hand, the increasing amplitudes of observed climatic i…
Using observational data and an elementary rigorous statistical fact it is easily shown that the distribution of Earth's climate is non-stationary. Examination of records of hundreds of local Industrial Era temperature histories in the Northern Hemisphere were used to show this fact. Statistically, the mean of the ensemble has been rising during the Industrial Era. All of this confirms what climate scientists already know. The issue of predictions under uncertainties was tackled as well: a simple balance model was tuned to track an ensemble of climate records. Stochastic parametrizations were …
Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as subgrid-scale parameterizations as well as for model error representation, uncertainty quantification, data assimilation and ensemble prediction. The need to use stochastic approaches in weather and climate models arises because we still cannot resolve all necessary processes and scales in comprehensive numerical weather and climate prediction models. In many practica…
Extreme events, such as wave-storms, need to be characterized for coastal infrastructure design purposes. Such description should contain information on both the univariate behaviour and the joint-dependence of storm-variables. These two aspects have been here addressed through generalized Pareto distributions and hierarchical Archimedean copulas. A non-stationary model has been used to highlight the relationship between these extreme events and non-stationary climate. It has been applied to a Representative Concentration Pathway 8.5 Climate-Change scenario, for a fetch-limited environment (Ca…
Some issues which are relevant for the recent state in climate modeling have been considered. A detailed overview of literature related to this subject is given. The concept in modeling of climate, as a complex system, seen through Godel's Theorem and Rosen's definition of complexity and predictability is discussed. It is pointed out to occurrence of chaos in computing the environmental interface temperature from the energy balance equation given in a difference form. A coupled system of equations, often used in climate models is analyzed. It is shown that the Lyapunov exponent mostly has posi…
In this paper, we assess and develop a climate service focused on the production of seasonal predictions for summer wildfires in a Mediterranean region through a participatory approach with end-users. We start by building a data-driven model that links a drought indicator (Standardised Precipitation Evapotranspiration Index; SPEI) with a series of burned areas in Catalonia (northeastern Spain). Afterwards, we feed this model with SPEI forecasts obtained through a combination of the antecedent observed conditions and climatology. Finally, we assess the forecasting skill of the system by using c…
Reliable prediction of large chaotic sytems in the short to middle time range is of interest in a number of fields, including climate, ecology, seismology, and economics. In this paper, results from chaos theory, and statistical theory are combined to suggest rulse for building linear predictive models of chaotic systems. The rules are tested on a problems identified as hard in the climate literature, interseasonal to interannual prediction of regional seasonal precipitation. In a test of prediction the method yields third season ahead predictions in 4 regions over 5 seasons which beat the NOA…
Numerical weather prediction has traditionally been based on physical models of the atmosphere. Recently, however, the rise of deep learning has created increased interest in purely data-driven medium-range weather forecasting with first studies exploring the feasibility of such an approach. To accelerate progress in this area, the WeatherBench benchmark challenge was defined. Here, we train a deep residual convolutional neural network (Resnet) to predict geopotential, temperature and precipitation at 5.625 degree resolution up to 5 days ahead. To avoid overfitting and improve forecast skill, …
The sensitivity of climate models to increasing CO2 concentration and the climate response at decadal time scales are still major factors of uncertainty for the assessment of the long and short term effects of anthropogenic climate change. While the relative slow progress on these issues is partly due to the inherent inaccuracies of numerical climate models, this also hints at the need for stronger theoretical foundations to the problem of studying climate sensitivity and performing climate change predictions with numerical models. Here we demonstrate that it is possible to use Ruelle's respon…
Tongji University（同济大学）；College of Civil Engineering, Tongji University（同济大学土木工程学院）
An extreme wind speed estimation method that considers wind hazard climate types is critical for design wind load calculation for building structures affected by mixed climates. However, it is very difficult to obtain wind hazard climate types from meteorological data records, because they restrict the application of extreme wind speed estimation in mixed climates. This paper first proposes a wind hazard type identification algorithm based on a numerical pattern recognition method that utilizes feature extraction and generalization. Next, it compares six commonly used machine learning models u…
Data-driven Seasonal Climate Predictions via Variational Inference and Transformers
Barcelona Supercomputing Center, Earth Sciences Department, Spain（巴塞罗那超级计算中心，地球科学部门，西班牙）；Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona（巴塞罗那大学物理学院，Martí i Franquès 1，08028 巴塞罗那）；Lobelia Earth, Barcelona, 08005, Spain（Lobelia Earth，巴塞罗那，08005，西班牙）；Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain（加泰罗尼亚高级研究与教育研究所（ICREA），巴塞罗那，西班牙）
Monthly streamflow records from a set of gauging stations, selected to form a reference hydrologic network, are analyzed together with precipitation and temperature data to establish whether the streamflows in the Guadalquivir River Basin have experienced changes during the last half of the XXth century that can be attributed to hydrological forcing. The observed streamflows in the reference network have undergone generalized and significant decreases both at seasonal and annual scales during the study period. Annual rainfall, though, did not experienced statistically significant changes. The …
Brookhaven National Laboratory（布鲁克海文国家实验室）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
Since model bias and associated initialization shock are serious shortcomings that reduce prediction skills in state-of-the-art decadal climate prediction efforts, we pursue a complementary machine-learning-based approach to climate prediction. The example problem setting we consider consists of predicting natural variability of the North Atlantic sea surface temperature on the interannual timescale in the pre-industrial control simulation of the Community Earth System Model (CESM2). While previous works have considered the use of recurrent networks such as convolutional LSTMs and reservoir co…
Using optimal detection techniques with climate model simulations, most of the observed increase of near surface temperatures over the second half of the twentieth century is attributed to anthropogenic influences. However, the partitioning of the anthropogenic influence to individual factors, such as greenhouse gases and aerosols, is much less robust. Differences in how forcing factors are applied, in their radiative influence and in models' climate sensitivities, substantially influence the response patterns. We find standard optimal detection methodologies cannot fully reconcile this respon…
The provision of accurate methods for predicting the climate response to anthropogenic and natural forcings is a key contemporary scientific challenge. Using a simplified and efficient open-source general circulation model of the atmosphere featuring O($10^5$) degrees of freedom, we show how it is possible to approach such a problem using nonequilibrium statistical mechanics. Response theory allows one to practically compute the time-dependent measure supported on the pullback attractor of the climate system, whose dynamics is non-autonomous as a result of time-dependent forcings. We propose a…
Modeling the risk of extreme weather events in a changing climate is essential for developing effective adaptation and mitigation strategies. Although the available low-resolution climate models capture different scenarios, accurate risk assessment for mitigation and adaption often demands detail that they typically cannot resolve. Here, we develop a dynamic data-driven downscaling (super-resolution) method that incorporates physics and statistics in a generative framework to learn the fine-scale spatial details of rainfall. Our method transforms coarse-resolution ($0.25^{\circ} \times 0.25^{\…
Decadal climate predictions, which are initialized with observed conditions, are characterized by two main sources of uncertainties--internal and model variabilities. Using an ensemble of climate model simulations from the CMIP5 decadal experiments, we quantified the total uncertainty associated with these predictions and the relative importance of each source. Annual and monthly averages of the surface temperature and wind components were considered. We show that different definitions of the anomaly results in different conclusions regarding the variance of the ensemble members. However, some…
Setting the Standard: Recommended Practices for Data Preprocessing in Data-Driven Climate Prediction
University of Oklahoma（俄克拉荷马大学）；University of Maryland（马里兰大学）；Colorado State University（科罗拉多州立大学）；University of Lausanne（洛桑大学）；Ocean Associates, Inc.（海洋关联公司）；National Ocean Service, NOAA（国家海洋服务处，国家海洋管理局）；NOAA/NWS/NCEP/Climate Prediction Center（国家海洋和大气管理局/国家天气服务局/国家气候预测中心）；Northern Illinois University（北伊利诺伊大学）；University of California（加州大学）；NOAA/GFDL（国家海洋和大气管理局/地球科学实验室）；Cooperative Programs for the Advancement of Earth System Science, UCAR（地球系统科学促进合作计划，国家大气研究中心）；Macquarie（麦考瑞）
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；University of California, Davis（加州大学戴维斯分校）
Almonds are one of the most lucrative products of California, but are also among the most sensitive to climate change. In order to better understand the relationship between climatic factors and almond yield, an automated machine learning framework is used to build a collection of machine learning models. The prediction skill is assessed using historical records. Future projections are derived using 17 downscaled climate outputs. The ensemble mean projection displays almond yield changes under two different climate scenarios, along with two technology development scenarios, where the role of t…
The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject to various external forcings, natural as well as anthropogenic. This paper reviews the observational evidence on climate phenomena and the governing equations of planetary-scale flow, as well as presenting the key concept of a hierarchy of models as used in the climate sciences. Recent advances in the application of dynamical systems theory, on the one hand…
Advancing Seasonal Prediction of Tropical Cyclone Activity with a Hybrid AI-Physics Climate Model
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Google Research（谷歌研究院）；Geophysical Fluid Dynamics Laboratory, National Oceanic and Atmospheric Administration（美国国家海洋和大气管理局地球流体动力学实验室）
Hard-Constrained Deep Learning for Climate Downscaling
Fraunhofer ITWM（弗劳恩霍夫信息技术与数学研究所）；Mila Quebec AI Institute（米拉魁北克人工智能研究所）；University of Montreal（蒙特利尔大学）；New York University（纽约大学）；IBM Research（IBM研究院）；McGill University（麦吉尔大学）
Virginia Tech（弗吉尼亚理工大学）；IBM Research Africa（IBM非洲研究院）；IBM Research Europe（IBM欧洲研究院）
As acute climate change impacts weather and climate variability, there is increased demand for robust climate impact model predictions from which forecasts of the impacts can be derived. The quality of those predictions are limited by the climate drivers for the impact models which are nonlinear and highly variable in nature. One way to estimate the uncertainty of the model drivers is to assess the distribution of ensembles of climate forecasts. To capture the uncertainty in the impact model outputs associated with the distribution of the input climate forecasts, each individual forecast ensem…
Understanding current global climate requires an understanding of trends both in Earth's atmospheric temperature and the El Nino-Southern Oscillation (ENSO), a characteristic large-scale distribution of warm water in the tropical Pacific Ocean and the dominant mode of year-to-year climate variability (Holbrook et al. 2009. However, despite much effort, the average projection of current climate models has become statistically significantly different from the observed 21st century global surface temperature trend (Fyfe 2013)and has failed to reflect the statistically significant evidence that an…
Extreme events provide relevant insights into the dynamics of climate and their understanding is key for mitigating the impact of climate variability and climate change. By applying large deviation theory to a state-of-the-art Earth system model, we define the climatology of persistent heatwaves and cold spells in key target geographical regions by estimating the rate functions for the surface temperature, and we assess the impact of increasing CO$_2$ concentration on such persistent anomalies. Hence, we can better quantify the increasing hazard {\color{black}due} to heatwaves in a warmer clim…
This paper describes some of the astronomical effects that could be important for understanding the ice ages, historic climate changes and the recent temperature increase. These include changes in the sun's luminosity, periodic changes in the earth's orbital parameters, the sun's orbit around our galaxy, the variability of solar activity and the anticorrelation of cosmic ray flux with that activity. Finally recent trends in solar activity and global temperatures are compared with the predictions of climate models.
