Stochastic analysis of air–sea heat fluxes variability in the North Atlantic in 1979–2022 based on reanalysis data

Gorshenin, Andrey K.; Osipova, Anastasiia A.; Belyaev, Konstantin P.

doi:10.1016/j.cageo.2023.105461

Cited by 3 publications

(1 citation statement)

References 25 publications

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“…This makes it possible to smooth out individual outliers that arise both directly in the data themselves and due to computational errors during the calculation of point estimates. The results of applying the nonparametric method to the same data and their analysis from the geophysical point of view for this period can be found in the paper [24].…”

Section: Reanalysis Data Experimentsmentioning

confidence: 99%

Comparison of Statistical Approaches for Reconstructing Random Coefficients in the Problem of Stochastic Modeling of Air–Sea Heat Flux Increments

Belyaev,

Gorshenin,

Korolev

et al. 2024

Mathematics

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This paper compares two statistical methods for parameter reconstruction (random drift and diffusion coefficients of the Itô stochastic differential equation, SDE) in the problem of stochastic modeling of air–sea heat flux increment evolution. The first method relates to a nonparametric estimation of the transition probabilities (wherein consistency is proven). The second approach is a semiparametric reconstruction based on the approximation of the SDE solution (in terms of distributions) by finite normal mixtures using the maximum likelihood estimates of the unknown parameters. This approach does not require any additional assumptions for the coefficients, with the exception of those guaranteeing the existence of the solution to the SDE itself. It is demonstrated that the corresponding conditions hold for the analyzed data. The comparison is carried out on the simulated samples, modeling the case where the SDE random coefficients are represented in trigonometric form, which is related to common climatic models, as well as on the ERA5 reanalysis data of the sensible and latent heat fluxes in the North Atlantic for 1979–2022. It is shown that the results of these two methods are close to each other in a quantitative sense, but differ somewhat in temporal variability and spatial localization. The differences during the observed period are analyzed, and their geophysical interpretations are presented. The semiparametric approach seems promising for physics-informed machine learning models.

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Section: Reanalysis Data Experimentsmentioning

confidence: 99%

Comparison of Statistical Approaches for Reconstructing Random Coefficients in the Problem of Stochastic Modeling of Air–Sea Heat Flux Increments

Belyaev,

Gorshenin,

Korolev

et al. 2024

Mathematics

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Methods for approximating the coefficients of a stochastic differential equation and their application to the analysis of intra-annual variability of heat fluxes in the North Atlantic

Tuchkova,

Belyaev,

Mikhaylov

et al. 2024

Scientific Conference “Scientific Services &Amp; Internet”

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To analyze heat fluxes, observational data for 1979-2018 were used in the North Atlantic. The spatiotemporal variability of the total heat flux was modeled by a stochastic diffusion process. The coefficients of the stochastic differential equation representing the stochastic process were statistically estimated using nonparametric statistics methods. Previously, the existence and uniqueness of a solution in the strong sense of the stochastic differential equation generated by the constructed diffusion process was proven using the Kolmogorov's criterion. In this work, the coefficients of the equation were approximated in time by trigonometric polynomials, the amplitudes and phases of which depended on the flow values. Using a given series of 40 years in length from 1979 to 2018, spatial maps and time curves were constructed, the results are shown for 1999 as examples, and also studied average monthly heat flow data from 1979 to 2022. Numerical calculations realized on the Lomonosov-2 supercomputer of the Lomonosov Moscow State University.

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Machine Learning Models Informed by Connected Mixture Components for Short- and Medium-Term Time Series Forecasting

Gorshenin,

Vilyaev

2024

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This paper presents a new approach in the field of probability-informed machine learning (ML). It implies improving the results of ML algorithms and neural networks (NNs) by using probability models as a source of additional features in situations where it is impossible to increase the training datasets for various reasons. We introduce connected mixture components as a source of additional information that can be extracted from a mathematical model. These components are formed using probability mixture models and a special algorithm for merging parameters in the sliding window mode. This approach has been proven effective when applied to real-world time series data for short- and medium-term forecasting. In all cases, the models informed by the connected mixture components showed better results than those that did not use them, although different informed models may be effective for various datasets. The fundamental novelty of the research lies both in a new mathematical approach to informing ML models and in the demonstrated increase in forecasting accuracy in various applications. For geophysical spatiotemporal data, the decrease in Root Mean Square Error (RMSE) was up to 27.7%, and the reduction in Mean Absolute Percentage Error (MAPE) was up to 45.7% compared with ML models without probability informing. The best metrics values were obtained by an informed ensemble architecture that fuses the results of a Long Short-Term Memory (LSTM) network and a transformer. The Mean Squared Error (MSE) for the electricity transformer oil temperature from the ETDataset had improved by up to 10.0% compared with vanilla methods. The best MSE value was obtained by informed random forest. The introduced probability-informed approach allows us to outperform the results of both transformer NN architectures and classical statistical and machine learning methods.

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Stochastic analysis of air–sea heat fluxes variability in the North Atlantic in 1979–2022 based on reanalysis data

Cited by 3 publications

References 25 publications

Comparison of Statistical Approaches for Reconstructing Random Coefficients in the Problem of Stochastic Modeling of Air–Sea Heat Flux Increments

Comparison of Statistical Approaches for Reconstructing Random Coefficients in the Problem of Stochastic Modeling of Air–Sea Heat Flux Increments

Methods for approximating the coefficients of a stochastic differential equation and their application to the analysis of intra-annual variability of heat fluxes in the North Atlantic

Machine Learning Models Informed by Connected Mixture Components for Short- and Medium-Term Time Series Forecasting

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