Stochastic differential equations with memory and relations - Modelling of stratospheric dynamics
Sammendrag
The societal importance of weather drives a continuous effort to improve short- and long-term numerical weather prediction. A better knowledge of the conditions in the stratosphere, the atmospheric region from 10 to 50 kilometers altitude, could be key in enhancing long-term weather forecasts on the Earth’s surface. Due to sparseness of stratospheric wind observations, this thesis aims at contributing to the development of remote sensing techniques. Infrasound is inaudible low-frequency sound generated by, for example, ocean waves. These sound waves undergo little damping and can travel for long distances through atmospheric waveguides that include the stratosphere. Infrasound that has passed through the stratosphere to be recorded at ground level carries information about the wind and temperature of this region. This implies that if the signal characteristics are sufficiently interpreted and described, ground-based measurements of infrasound could function as a form of stratospheric remote sensing. In this thesis, mathematical modelling and machine learning techniques are developed to relate infrasound recordings to stratospheric weather dynamics. A derived model is verified by estimating stratospheric winds in the Arctic region solely from ground-based infrasound data. The results indicate a potential for using these low-frequency sound waves for near real-time probing of stratospheric winds.Artikkelliste
Paper I Benth, F.E, Eggen, M.D. and Eisenberg, P. “Ornstein-Uhlenbeck processes in Hilbert space and autoregressive moving-average time series”. Manuscript in preparation for submission. To be published. The paper is removed from the thesis in DUO awaiting publishing. |
Paper II Eggen, M.D., Dahl, K.R., Näsholm, S.P. and Mæland, S. “Stochastic modeling of stratospheric temperature”. In: Math Geosci. Vol. 54, no. 4 (2022), pp. 651—678. An author version is included in the thesis. The published version is available at: https://doi.org/10.1007/s11004-021-09990-6 |
Paper III Eggen, M.D. “The multivariate ARMA/CARMA transformation relation”. Review received from Scandinavian Journal of Statistics. Manuscript in preparation for resubmission. To be published. The paper is removed from the thesis in DUO awaiting publishing. |
Paper IV Eggen, M.D. and Midtfjord, A.D. “Delay-SDE-net: A deep learning approach for time series modelling with memory and uncertainty estimates”. Review received from Journal of Machine Learning Research. Manuscript in preparation for resubmission. To be published. The paper is removed from the thesis in DUO awaiting publishing. |
Paper V Eggen, M.D., Vorobeva, E., Midtfjord, A.D., Benth, F.E., Hupe, P., Brissaud, Q., Orsolini, Y. and Näsholm, S.P. “Near real-time stratospheric circulation diagnostics based on high-latitude infrasound data using a stochastics-founded machine learning model”. Manuscript in preparation for submission. To be published. The paper is removed from the thesis in DUO awaiting publishing. |