The Physical Earth System and the Role of Turbulence

It is important to understand the Earth system, both for understanding past climates and also for making future predictions. Numerical simulations of the Earth system are undertaken using high performance computing facilities over different time periods for differing means. 

• Numerical Weather Prediction simulates 1-7 days of a virtual Earth, and can be used to determine what the weather be over the following next week. This is important for planning of public events, renewable energy power plant management and operation, and early warnings of extreme events (eg: bushfire, flood, strong winds).
• Seasonal Prediction simulates 1-2 years of a virtual Earth. This type of simulation estimates for example if the following summer will be hotter and/or wetter than this year?
• Climate Projections are simulated over 100's of years, and estimate the properties of future climates under various scenarios of human activity?
• Paleo-climate Simulation are undertaken over 100,000's of years, and are used to understand previous significant changes to the Earth, and also to test if current climate simulations can replicate past observed trends.

The Earth system comprises of various components including the:

• Atmosphere - moves heat, dust, sea spray, air pollution and other aerosols throughout the Earth.
• Ocean - moves heat, salt, water pollution and aquatic life throughout the Earth.
• Ice sheet - solid ice fixed to the Earth's sea floor (eg: at Antarctica). It melts and freezes as a result of natural variability and human activities. 
• Sea ice - frozen ice that floats on the ocean surface (eg: encircling Antarctica), which also grows and recedes due to natural variability and human activities.
• Vegetation - on land (eg: forests), and in the ocean (eg: coral reefs).
• Biology - large scale biological growth can effect the Earth system, for example rapid growth in the phytoplankton population can change the chemical composition of the ocean.
• Carbon cycle - the exchange of carbon throughout the Earth. For example burning vegetation releases carbon into the atmosphere, some of which is then dissolved into the ocean.

In computer simulations of the Earth system, the atmosphere and ocean are subdivided into a series of three-dimensional grid boxes, with the atmospheric wind, oceanic currents, rain and other quantities solves in each grid box location. The interaction of the atmosphere and ocean with the remaining components in the Earth system are approximated by some form of model. These interactions effect the atmospheric and oceanic circulation, which in turn effect all of the Earth system components.

In order to correctly represent the ice sheet, sea ice, vegetation, biology and carbon cycle, as a first step the atmospheric and oceanic circulation must be correctly simulated. Turbulence plays an essential role in correctly simulating the atmosphere and ocean. In the atmosphere for example, the vortices (or eddies) range from the largest ones ~1000km in horizontal diameter down to the smallest approximately 1mm in diameter, and everything in between. These different sizes of vortices is what we refer to as "scales of turbulence". To make things even more complicated each of the these vortices of different sizes interact with each other.

The difficulty in simulating the atmosphere and ocean, is that even if we were to pool together all of the most powerful super-computers, it would still be impossible to simulate all of the scales of turbulence. In reality the grid we use to simulate the atmosphere is broken down into grid boxes ~100km in the horizontal direction, and model the influence of the vortices smaller than ~100km on the larger vortices that are explicitly represented by the grid. This type of model is called a "subgrid turbulence model", the development of which has been the focus of my own research.

If the influence of the small unresolved vortices on the large resolves ones is not modelled correctly, then this an produce resolution dependent results, which has been a significant and long standing problem since the earliest climate simulations [1]. I recently solved this problem by developing subgrid turbulence models for both the atmosphere and ocean using stochastic data mining techniques [2,3,4]. I generated high resolution (very small grid box sizes) atmospheric and oceanic data sets, and determined the model structure from this data. Simulations adopting these scaling laws are shown to produce resolution independent statistics, with orders of magnitude improvement in computational efficiency. I have also more recently successfully applied this technique to numerical simulations of boundary layer flows [5].

Here is an animation of the winds generated from the simulations of the atmosphere. Red is fast wind and blue is slow wind. You can get more details in my Journal of the Atmospheric Sciences paper in reference [2] listed below.

Below is an animation of the currents generated from the simulations of the ocean. Here we are looking at the southern hemisphere. You can get more details in my Ocean Modelling journal paper reference [3].

As a side note, when you are in a plane and the pilot announces that they are approaching some turbulence, they are referring to the regions in the atmosphere that more turbulent / complex / disordered. My following post will discuss how fluids flow over aircraft wings.

References:

[1] Smagorinsky, J., 1963, General circulation experiments with the primitive equations. I. The basic experiment. Mon. Wea. Rev., 91, 99–164.

[2] Kitsios, V., Frederiksen, J.S. & Zidikheri, M.J., 2012, Subgrid model with scaling laws for atmospheric simulations, Journal of the Atmospheric Sciences, 69, pp 1427-1445. [link]

[3] Kitsios,V., Frederiksen, J.S. & Zidikheri, M.J., 2013, Scaling laws for parameterisations of subgrid eddy-eddy interactions in simulations of oceanic circulations, Ocean Modelling, 68, pp 88-105. [link]

[4] Kitsios,V., Frederiksen, J.S. & Zidikheri, M.J., 2013, Theoretical comparison of subgrid turbulence in atmospheric and oceanic quasigeostrophic models, Nonlinear Processes in Geophysics, 23, pp 95-105. [link]

[5] Kitsios,V., Sillero, J.A., Frederiksen, J.S. & Soria, J., 2015, Proposed stochastic parameterisations of subgrid turbulence in large eddy simulations of turbulent channel flow, Journal of Turbulence, 16, pp 729-741. [link]