Research

Research Fields

Data Analysis and Mining

Time series analysis; Data visualization; Remote sensing data mining; Signal extraction

Data Assimilation

Bayes inference; Kalman filter; 4D-Var algorithm

Numerical Model

Computational Fluid Dynamics; Algorithm development; Numerical equilibrium; High performance computation;

Numerical Simulations of Oceanic Internal Waves

Numerical simulation is one of the most effective ways to illustrate the generation, propagation and dissipation process of internal waves and has been widely used in different regions around the world. This section consists two parts of my previous numerical works in the study of internal waves.

Simulated internal tides gradually reach an equilibrium status. (Jin et al., 2017)

On the Equilibration of Numerical Simulations for Internal Tides

It is well known that barotropic tides, stratified fluids and varying topographies are the three factors for internal tide generation. In order to clarify the influence of these factors, many numerical simulations have been carried out on idealized or real topography. However, it is found that the Equilibration of Numerical Simulation (ENS) for the internal tide is scarcely mentioned. Although different types of numerical models are used by researchers, almost all the models start from a stationary state. Actually, ENS should be attained after a certain run time (the total calculation time for the model) before the feature and mechanism of the internal tide is investigated using the numerical model.

Simulated NLIWs vs. satellite image. (Lai et al., 2019)

On the Generation Mechanism of Nonlinear Internal Waves in SCS

Over the past decades, the SCS has been a hotspot for strong nonlinear internal waves (NLIWs). Observations show that these waves are different in characteristics from observations in many other regions of the ocean since they may arrive the continental shelf two times a day with alternate large/small amplitudes and constant/delayed arrival time, a well-known phenomenon of the named type-A and type-B internal waves in the SCS. Due to the temporal and spatial scale of nonlinear internal waves, it is always difficult and expensive to carry out numerical analysis of them, especially for three-dimensional real cases.

Processes of NLIW generation in the Luzon Strait. (Lai et al., 2019)

Spatial and temporal dynamic and energetic evolutions of a NLIW from Luzon Strait to the continental shelf of NSCS.

Spatial and Temporal Characteristics of Nonlinear Internal Wave Energy in the Northern South China Sea

The energy features of nonlinear internal waves (NLIWs) are relatively less known and should be an important term in the energy budget of the northern South China Sea (NSCS). Using the realistic three-dimensional nonhydrostatic model, we investigated the spatial and temporal characteristics of NLIW energy across the NSCS basin.

The total area integrated KE (a) and APE (b) contained in NLIWs at different propagation stages.

NLIW energy importation rate into different regions of NSCS.

Observational Analysis of Internal Waves in the Ocean

For over a decade, many studies have been put forward in the South China Sea (SCS), where the oceans’ most powerful known internal waves are generated from the Luzon Strait and propagate towards the west. Internal waves can travel thousands of kilometers from sources before breaking, making it challenging to observe them. My recent research focuses on the observational analysis of internal tides and nonlinear internal waves in the SCS.

Time series of the filtered baroclinic current data in the upper 200m and the baroclinic velocity variances. (Gao et al., 2017)

Temporal Variations of Internal Tide Multimodal Structure on the Continental Shelf of SCS

Internal tides are internal waves with tidal or quasi-tidal periods, resulting from the interaction of barotropic tidal flow with bottom topography in a stratified ocean. The modal structures of internal tides are closely related to the dynamic process while higher mode indicating tendency of dissipating and lower mode in favor of propagation. Based on 2-month moored acoustic Doppler current profiler observations, we investigated the temporal variations in multimodal structures of diurnal (D1) and semidiurnal (D2) internal tides on the continental slope of the Dongsha Plateau with different kinds of methods. The multimodal structures for internal tides in different frequency bands reveal obvious temporal variations, indicating complex dynamic conditions in this region.

The original harmonic statistical model and the enhanced harmonic analysis model. (Jin et al., 2018)

Results of time-varying zonal current amplitudes (black lines) and the corresponding 95% confidence intervals (gray band) obtained by EHA. (Jin et al., 2018)

Determination of Harmonic Parameters with Temporal Variations

Over centuries great progress has been made to explain and predict oceanic tides. Our understanding of tides deepened with several breakthroughs made by some scientific pioneers (e.g., Newton’s theory of gravitation and equilibrium tide, and Laplace’s expression about the tidal potential). There is an increasing need to understand the dynamic behavior of oceanic internal tides and internal tidal currents. The harmonic method for tidal analysis is an effective tool to distinguish different tidal components and is widely used in the study of oceanic tides or tidal current and internal tides or internal tidal currents. However, there are many situations in which the observed tides or tidal currents are modulated by some nontidal processes, some of which occur in the tidal frequency band, resulting in irregular temporal variations for the internal tides, which can not be resolved by the classical harmonic analysis.

Data Assimilations of Internal Tides

Satellite remote sensing technology and other related technologies provide us with large amount of oceanic data. Thus, it is one of the most important missions in physical oceanography to make use of the data efficiently and precisely as well as to combine the observation data with present numerical models. Four-dimensional variational data assimilation such as the adjoint method is one effective access to the combination of dynamic controlled numerical models with observation data. The key issue for the adjoint method is to construct the adjoint dynamic equations and derive the gradient of the cost function with respect to control parameters of the original model. This work is based on a three-dimensional internal tidal model involving adjoint methodand consists of the following two subsections.

Prescribed VEVC (up) and model inversion results obtained by two optimization method (down). (Jin et al., 2015)

Inversion Study of Parameters in Internal Tidal Model

Based on the internal tidal model with the adjoint method, inversion of two kinds of model coefficients which are the one-dimensional open boundary conditions (OBC) and the spatially varying vertical eddy viscosity coefficient (VEVC) are investigated by a series of idealized numerical experiments. Along with the numerical model, the independent point scheme (IPS) which reduce the ill-posedness of the inversion problem is introduced. Moreover, we examine the performances of different optimization methods with different numerical experiments.

Topography of the domain. White dots indicate the observation sites of the T/P altimeter in the domain.

Numerical Simulations of Internal Tides with the Adjoint Internal Tidal Model

With the experiences of parameter inversion, we are confident to carry out experiments based on real environment and topography. The horizontal resolution for the model is 1/12° x 1/12°. We only apply the M2 constituent on the open boundaries for simplicity. The TOPEX/Poseidon (T/P) satellite altimeter data are used as observation data in the experiment. One thing should be reminded is that the initial values of OBC, VEVC, bottom friction coefficient and horizontal eddy viscosity coefficient are set to zero. Their values will be inverted in the adjoint model.

M2 co-tidal chart from OSU model.

Simulated M2 co-tidal chart.

Simulated M2 internal tidal displacements in the SCS.

Simulated M2 internal tidal velocity in the SCS.

Data-driven Image Transformation

The classical method for auto-animation uses detailed kinematic equations for each object in the starting images. It is usually precise but time consuming. We aim to propose an efficient and universal algorithm for inbetweening auto-animation based on the Fokker-Planck dynamics on manifold and thresholding.

Inbetweening Auto-animation via Fokker-Planck Dynamics and Thresholding

An equilibrium-driven deformation algorithm (EDDA) to simulate the in-betweening transformations starting from an initial image to an equilibrium image is proposed. The application covers images varying from a greyscale type to a colorful type on planes or manifolds. The algorithm is based on the Fokker-Planck dynamics on manifold, which automatically incorporates the manifold structure suggested by dataset and satisfies positivity, unconditional stability, mass conservation law and exponentially convergence. The thresholding scheme is adapted for the sharp interface dynamics and is used to achieve the finite time convergence. Using EDDA, three challenging examples, (I) facial aging process, (II) coronavirus disease 2019 (COVID-19) pneumonia invading/fading process, and (III) continental evolution process are computed efficiently.

Example I: RGB colored facial aging transformation

Simulated facial aging transformation from initial to equilibrium. The updated results after time step 40, 100, 200, 400, 1000, 2000, 4000, 10000 are shown and compared to the initial and equilibrium images. (Gao et al., 2021)

Example II: COVID-19 pneumonia invading and fading away on CT scan images.

Simulated pneumonia invading and fading away process to a patient's lungs on the CT images caused by COVID-19. The simulation is carried out based on an equilibrium-driven deformation algorithm. The white part inside the lungs shown on images indicates the evidence of pneumonia. Red circles indicate the significant COVID-19 pneumonia invading areas and blue circles indicate the significant pneumonia fading away areas. (Gao et al., 2021)

Example III: Continental evolution process with thresholding for shape dynamics.

Simulate evolutions of continental movements on the unit sphere based on the equilibrium-driven deformation algorithm with a thresholding scheme. The orange and blue patch indicate the land and ocean, respectively. ‘TH’ is short for ‘thresholding step’. The formation of the Antarctic is revealed at the bottom (southern part) of the globe (black arrow in TH 5). Note that the globes are shown in the same view angle so the Antarctic continental is out of view in the last two subplots. (Gao et al., 2021)

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