Research

Publications

Published

1. Lang, Y., Stanley, G. J., McDougall, T. J., & Barker, P. M. (2020). A pressure-invariant Neutral Density variable for the World's Oceans. Journal of Physical Oceanography, 50(12), 3585-3604.

In preparation

Minimizing the vertical velocity across approximately neutral surfaces

Current Research Areas

Neutral directions (First Ph.D. project)

The continuous movement of the ocean currents makes the seawater in the ocean never stop moving and mixing. Ocean mixing induced by irreversible mixing (millimeter scale) and small-scale eddies (centimeters to meters scale) is isentropic, which results in a background diffusivity in the ocean. While the mesoscale eddies, with a size of 20 - 200 km, mix tracers along with neutral directions only, and the lateral diffusivity (caused by mesoscale eddies) along the neutral directions is about a million times larger than the isentropic diffusivity. Thus, finding the neutral direction is essential for the ocean studying.

Pressure-invariant neutral density variable

There are several software that has already been developed to label the world ocean with neutral density and the iso-value surface of the neutral density is a neutral surface. The most famous one is the neutral density variable created by Jackett and McDougall (1997). The neutral density variable has dependencies on the salinity, potential temperature, pressure, latitude, and longitude. My first Ph.D. project is to create a density variable that is independent of the pressure and thus make it not influenced by the vertical heave of the ocean, called pressure-invariant neutral density.

Submesoscale Coherent Vortices:

How does our pressure-invariant neutral density create? The key is the submesoscale coherent vortices (SCV). The SCV is the motion of the water parcel when the salinity and potential temperature are conserved during its movement. When the water parcel moves in the neutral direction, it keeps mixing with the environment and makes it does not influence by the buoyant restoring force. When the water parcel moves along the SCV trajectory, it does not mix with the environment and keeps the salinity and potential temperature conserved but maintains its buoyancy balance by changing its pressure only. The difference between the SCV trajectory and neutral trajectory can be visualized by panel (a) of the above figure. Panel (b) of the above figure shows how to label an observational parcel with a neutral density value for both neutral density and pressure-invariant neutral density. The labeling procedure is based on a reference neutral density dataset created by Jackett and McDougall (1997) with very complicated methods and great neutrality. The neutral density of an observation point equals the weighted average of the neutral density value of the closest four reference casts. If we use neutral trajectory from the observation point to the reference casts, we get a neutral density label and if we use SCV trajectory from the observation point to the reference casts, we get a pressure-invariant neutral density label.

Material Derivative:

We have done the material derivative analysis on the pressure-invariant neutral density. We found that the contribution of lateral advection to the material derivative of the pressure-invariant neutral density is proportional to the water mass contrast of the observational data and the reference data. The contribution of irreversible mixing to the material derivative of the pressure-invariant neutral density follows the appropriate partial derivative of in-situ density evaluated using the salinity and potential temperature of the observational parcel.

We compared the total material derivative of the pressure-invariant neutral density with normal neutral density and their materiality is in the similar level.

Minimizing the vertical velocity across approximately neutral surfaces based on numerical optimization (Second Ph.D. project)

My second Ph.D. project is to create a surface with minimized vertical velocity on it. Due to the nonlinear nature of the equation of state, the neutral trajectory has helical nature in the ocean and thus makes the neutral surface ill-defined. So neutral surface does not exist in the ocean and we can only find the approximately neutral surface (ANS). The misalignment of the ANS and the neutral surface will cause fictitious diffusion and advection on the surface. Using an ANS with larger fictitious diapycnal diffusion and advection in the ocean model or inverse studies will result in computational errors. The nonlinear processes (including thermobaricity, cabeling and neutral helicity) in the ocean have been ignored by the ocean community for a long time, but the resulted advection has significant influences on ocean inverse studies, large-scale overturning circulations, water mass transformation studies, and the understanding of the ocean stratification.

We found that the fictitious advection along the ANS can cause larger spurious heat or salt tendency in the ocean thus creating a surface with minimized vertical velocity is meaningful. The thermobaricity and cabeling are the nature of the ocean and cannot be changed. So the surface aims to minimize the vertical velocity on the surface mainly deals with the vertical advection caused by neutral helicity. Panel (b) of the above figure shows that the vertical velocity of the surface which aims to minimize the vertical velocity is more than 40 times smaller than that on the surface aims to minimize the neutrality error (in panel (a)). Note that the surface in panel (a) is the surface with the best neutrality so far (Stanley, et al., 2021).

Numerical Optimization:

We use numerical optimization methods to create the surface with minimized vertical velocity. We firstly derive the cost function of the surface and then solve it. Due to the complexity of the Arakawa C-grid, the defining of the cost-function requires a deep understanding of the structure of C-grid. The solution provides us the information about how to optimize the surface. The mathematical meaning of our cost function is a transient two-dimensional transport equation (PDE). The classical Cholesky decomposition and Tikhonov regularization techniques are applied when we solve the following PDE.

Other surfaces:

Using similar numerical optimization techniques, we have also created surfaces that aim to minimize slope error (the slope difference between the ANS and the neutral direction), the fictitious diapycnal diffusion, the salt advection, and the heat advection on the surface. Users can freely choose which one to use for specific purposes.

Interested Research Areas

My Ph.D. projects are mainly about creating ocean analyzing frameworks, which are fundamental ocean projects. In my future research, I would like to apply my neutral surface framework to do the ocean investigations, such as water mass transformation investigations, inverse studies, and ocean mixing analyses. I am also happy to extend my future research to the ocean's influence on the climate system. The ENSO and thermohaline circulation are essential to the climate system. Since climate change is highly related to human beings, studying the ocean and climate system interaction is a great direction to apply my oceanographic knowledge. What's more, I am also interested in ocean modeling research. Solving the conservation equation on our neutral surface framework will have a great increase. I am willing to join the ocean modeling work to increase the accuracy of ocean models.

Water mass transformation

The ocean influences on the climate system are mainly based on the combined effects of subduction of water masses, the overturning circulation, and ventilation of thermodynamic properties (Groeskamp, et al., 2019). Quantifying and simulating these phomena accurately are important to learn the past climate and thus predict future climate change. The water mass transformation analyses based on a neutral surface framework would make people have a better understanding of the ocean's influence on the climate system.

Estimating the ocean diffusivity based on Inverse model

The ocean mixing induced by eddy stirring must be parameterized since the size of the eddies is too small to be resolved by the circulation models. Estimating the lateral and diapycnal diffusivity using the inverse model is always a classical work for oceanographers. Since the isopycnal framework always generates large fictitious diapycnal diffusivities sometimes even comparable with the background diffusivity, doing the inverse model with small fictitious diapycnal diffusivity and advection can significantly increase the accuracy of the estimation.

It has been shown that the changing of the lateral diffusivity can influence the model's overturning circulation by changing surface and interior water mass transformation (Holmes, et al. 2022).

Ocean mixing

Ocean mixing can shape the ocean circulation by altering surface wind and buoyancy forcing, altering density gradients, and producing and consuming water masses (de Lavergne, et al., 2022). Ocean mixing is a complicated process and it can shape the mean state of the ocean, which has influences on climate change. Studying ocean mixing is a big topic. I am happy to apply the neutral surface framework to study the ocean mixing in the lateral direction and diapycnal direction.

ENSO

The ENSO is probably the most important inter-annual climate phenomenon on Earth. It has a significant impact on people's life. In 1998, the La Nina brings very big floods to China, it takes thousands of people's lives and makes more than 200 million people away from home (Cai, et al. 2021). At the same time, the El Nino in Australia causes one of the biggest bush fires in history. So investigating ENSO and predicting the potential change of ENSO is meaningful and urgent. Due to anthropogenic warming, the ENSO activity has been observed to be stronger than before. However, the ENSO system is nonlinear and chaotic, which makes the prediction to be fairly difficult. Besides the research on the observation of ENSO and its climate impact, more fundamental investigations on the ENSO system should be done in the future.

Thermohaline circulation

The time scale of the thermohaline circulation is hundreds of years and its space scale is the world ocean. Global warming can influence thermohaline circulation and its variation can backward influence the climate system as well, however, these are fairly long-term impacts. Studying such large-scale oceanic circulation, such as Atlantic Meridional Overturning Circulation (AMOC) and Global Overturning Circulation relates to the destiny of human beings.

Ocean modeling

The investigation of the ocean is mostly based on the ocean models. The creation of the ocean model requires observation data and oceanographic theories. Creating a more accurate ocean model definitely benefits the ocean community. Also, as the machine learning technique rapidly spread in recent years, combing the ocean model with the observation data together with statistical techniques might make the unpredictable systems to be kind of predictable such as ENSO.

References

Cai, W., Santoso, A., Collins, M., Dewitte, B., Karamperidou, C., Kug, J. S., ... & Zhong, W. (2021). Changing El Niño–Southern Oscillation in a warming climate. Nature Reviews Earth & Environment, 2(9), 628-644

de Lavergne, C., Groeskamp, S., Zika, J., & Johnson, H. L. (2022). The role of mixing in the large-scale ocean circulation. Ocean Mixing, 35-63.

Groeskamp, S., Griffies, S. M., Iudicone, D., Marsh, R., Nurser, A. G., & Zika, J. D. (2019). The water mass transformation framework for ocean physics and biogeochemistry. Annual review of marine science, 11, 271-305.

Holmes, R. M., Groeskamp, S., Stewart, K. D., & McDougall, T. J. (2022). Sensitivity of a Coarse‐Resolution Global Ocean Model to a Spatially Variable Neutral Diffusivity. Journal of Advances in Modeling Earth Systems, e2021MS002914.

Jackett, D. R., & McDougall, T. J. (1997). A neutral density variable for the world’s oceans. Journal of Physical Oceanography, 27(2), 237-263.

Stanley, G. J., McDougall, T. J., & Barker, P. M. (2021). Algorithmic improvements to finding approximately neutral surfaces. Journal of Advances in Modeling Earth Systems, 13(5), e2020MS002436.