Related papers: Application of Continuous Data Assimilation in Hig…
Continuous data assimilation (CDA) is a method that continuously integrates observational data into a dynamical system to improve model accuracy in real-time. The AOT algorithm is one of the most widely used methods in CDA due to its…
We study the use of the Azouani-Olson-Titi (AOT) continuous data assimilation algorithm to recover solutions of the Navier--Stokes equations modified to have higher-order fractional diffusion. The fractional diffusion case is of particular…
Continuous data assimilation methods, such as the nudging algorithm introduced by Azouani, Olson, and Titi (AOT) [2], are known to be highly effective in deterministic settings for asymptotically synchronizing approximate solutions with…
In this work, we study the applicability of the Azouani-Olson-Titi (AOT) nudging algorithm for continuous data assimilation to evolutionary dynamical systems that are not dissipative. Specifically, we apply the AOT algorithm to a partially…
We introduce three new nonlinear continuous data assimilation algorithms. These models are compared with the linear continuous data assimilation algorithm introduced by Azouani, Olson, and Titi (AOT). As a proof-of-concept for these models,…
Accurate and efficient global ocean state estimation remains a grand challenge for Earth system science, hindered by the dual bottlenecks of computational scalability and degraded data fidelity in traditional data assimilation (DA) and deep…
We adapt a continuous data assimilation scheme, known as the Azouani-Olson-Titi (AOT) algorithm, to the case of moving observers for the 2D incompressible Navier-Stokes equations. We propose and test computationally several movement…
Accurate mapping of ocean bathymetry is a multi-faceted process, needed for safe and efficient navigation on shipping routes and for predicting tsunami waves. Currently available bathymetry data does not always provide the resolution to…
In this paper, we provide conditions, \emph{based solely on the observed velocity data}, for the global well-posedness, regularity and convergence of the Azouni-Olson-Titi data assimilation algorithm (AOT algorithm) for a Leray-Hopf weak…
This work investigates the effectiveness of the Back-and-Forth Nudging (BFN) data assimilation algorithm, specifically its performance when employing the Azouani-Olson-Titi (AOT) continuous data assimilation downscaling nudging algorithm,…
This paper applies variational data assimilation to inundation problems governed by the shallow water equations with wetting and drying. The objective of the assimilation is to recover an unknown time-varying wave profile at an open ocean…
Today's ocean numerical prediction skills depend on the availability of in-situ and remote ocean observations at the time of the predictions only. Because observations are scarce and discontinuous in time and space, numerical models are…
Deep learning-based tropical cyclone (TC) forecasting methods have demonstrated significant potential and application advantages, as they feature much lower computational cost and faster operation speed than numerical weather prediction…
We study a nonlinear-nudging modification of the Azouani-Olson-Titi continuous data assimilation (downscaling) algorithm for the 2D incompressible Navier-Stokes equations. We give a rigorous proof that the nonlinear-nudging system is…
We study different approaches to implementing sparse-in-time observations into the the Azouani-Olson-Titi data assimilation algorithm. We propose a new method which introduces a "data assimilation window" separate from the observational…
Shallow water equations are extensively considered in the domains of oceans, atmospheric modelling, and engineering research (Franca et al., 2022), which play significant roles in floods and tsunami governance. Nonetheless, the accurate…
Accurate, high-resolution ocean forecasting is crucial for maritime operations and environmental monitoring. While traditional numerical models are capable of producing sub-daily, eddy-resolving forecasts, they are computationally intensive…
In this article, we show that the continuous data assimilation algorithm is valid for the 3D primitive equations of the ocean. Namely, the $L^2$ norm of the assimilated solution converge to that of the reference solution at an exponential…
This paper presents and investigates a novel methodology for validating high-resolution ocean models using satellite imagery. High-resolution ocean models provide detailed information in coastal areas where other available data products are…
In-situ ocean wave observations are critical to improve model skill and validate remote sensing wave measurements. Historically, such observations are extremely sparse due to the large costs and complexity of traditional wave buoys and…