The work of the scientists, who will benefit from the Antarctic Quest 21 expedition is intricate, complex, interdisciplinary and connected to many environmental issues that matter to all of us. Here I’ll try to bring closer to you the work of Andrew Smedley.
His project, for which the expedition will collect data on the intensity of ultraviolet light at the Earth’s surface while crossing the Antarctic Peninsula, I have introduced on the Science Page of the Antarctic Quest 21 website. Here, in the first of the AQ21 Scientist series of publication digests, I am covering a different aspect of his work, which highlights his expertise in using solar irradiation data to understand the internal temperature profile of ice and in turn, processes that affect ice sheet near-surface melting or ice shelf crack formation.
The paper ‘Solar radiative transfer in Antarctic blue ice: spectral considerations, subsurface enhancement, inclusions and meteorites’ was published by Andrew RD Smedley, Geoffrey W Evatt, Amy Mallinson and Eleanor Harvey in the scientific journal The Cryosphere (Volume 14, pages 789-9809) in March 2020. It is open access and you can read it here: LINK.
The article’s title may not roll of your tongue easily, but the story is intriguing: it’s a deep dive into detail and offers a glimpse into the world of modelling. This story is about the behaviour of ice in sunlight and, at its core, is a puzzle stone of knowledge relevant to one the most important environmental challenges of the day: climate change.
At first glance, it’s all common sense: sunlight (solar radiation) arrives at the Earth’s surface and, depending on the properties of that surface, it is either reflected or absorbed. Different surfaces reflect and absorb different amounts of radiation. You know that from daily life: Wear a black t-shirt in the sunshine and you’ll feel the warmth of the absorbed sunlight more intensely than while wearing a white, but otherwise identical, t-shirt. The glare reflecting off a large snow surface has a different effect on your eyes than sunlight filtered through the canopy of a woodland in full leaf. You’ll see light scattering in action when you watch the appearance of a freshly pulled pint of real ale change, as tiny bubbles swirl and finally clear out of the liquid…
When it comes to understanding the processes that determine the temperature profile of ice, and therefore the way ice melts and cracks, we need to go beyond common sense and consider a lot more detail.
Andrew and his colleagues combined the laws of physics with Monte Carlo simulation to extend insights from previously developed models with a broader inclusion of processes that affect ice behaviour. Monte Carlo simulations are a widely used approach to simulating physical, biological and economic processes that uses randomness in the generation of numerical results. I will not go further into the mathematical detail here.
The model simulates photons (of which sunlight, or solar irradiance, consists) that have entered the ice (i.e. they were not reflected at its surface) travelling along random pathways into and through the ice. They may be scattered by trapped air bubbles, absorbed by the ice or particles enclosed within it, or escape the ice through its surface into the air. Figure 1 illustrates these ideas schematically. The purpose of the model is to calculate how light travels up and down in ice and how much of the incoming light is present at a given depth below the surface.
Figure 1 Schematic illustration of interaction between solar irradiance (sunlight) and the ice surface (reflection, admittance), trapped air bubbles (scattering, absorption) and embedded particles (absorption), as well as with the ice itself (movement through, absorption).
By definition, a model is a simplified version of the system we are seeking to understand. The architect’s drawing of a house is not the house itself, but it conveys information for the purpose of illustrating design. Equally, in the design of a mathematical model, the number of processes and parameters considered, the resolution in time or space, the sophistication of the algorithms used, depend on what we want to know and on what we know already.
To me, discovering the level of detail incorporated into the model of how sunlight interacts with ice, reinforced my respect for the art of modelling:
Think back to school and you’ll remember that light consists of a whole spectrum of electromagnetic radiation, waves of different wavelengths. These may be in the visible range (think of a rainbow) or outside the visible range, for example the ultraviolet light we tend to protect ourselves from using sun cream and sunglasses. The solar irradiance that arrives at the Earth’s surface depends on the angle of the sun (solar zenith angle) and its interaction with the atmosphere. Light of different wavelengths interact differently with the atmosphere, including clouds, particles and vapour. The model uses parameters for solar irradiance spectra measured near a mountain range in Antarctica for both, diffuse and direct sunlight.
- Optical properties of ice that contains bubbles.
Perhaps suffice to say that a set of mathematical expressions is used to describe the optical properties of the ice in relation to the wavelength of the photons being tracked through the ice, the number and size of the trapped bubbles and the way they scatter and absorb photons.
Only one set of data seems to exist that describes the density and properties of ice bubbles in Antarctic blue ice. These were used and adjusted with other data from literature to provide a more general estimate of bubble number concentration and their geometry in ice with and without cracks, for use in the model. As an example, one of the results presented in the paper was based on 415 bubbles of 0.4 mm diameter in each cubic centimetre of ice.
Particles trapped within the surface ice literally fall from the sky, as part of ‘atmospheric deposition’ (entrained and carried by wind or snow) or meteorites, which is surprisingly common. Particles of different geometries were considered, including spherical, planar and ellipsoidal (‘balls’, ‘plates’ and ‘eggs’) of less than 1 mm in size. The model was also applied specifically to iron-rich meteorites of several cm across.
In the model, the positions of individual photons of specific wavelengths are tracked. Where they arrive at the surface of the ice at a particular angle, their reflection or entry into the ice is calculated, as well as refraction. Once within the ice, photons either return to the atmosphere, are absorbed or pass below a depth where they are deemed not to make a significant contribution (below 16 m ice) to ice behaviour. The model uses an innovative set of calculations that determines whether, where and how a photon interacts with a bubble or particle and at what point it will cease to be tracked because it left the ice or travelled below 16 m depth. The record of photon position over time provides the data necessary to calculate the fluxes of and number of photons at each depth.
Every scientific experiment requires quality control and has limitations. Mathematical models are no different, and quality assurance is undertaken in a process called validation, which compares model output data against independently generated data set or empirical data, running the model repeatedly to check reproducibility and tweaking individual parameters within the model to assess the model’s sensitivity and stability. In this paper that was an elaborate process and let’s just summarise: the model lived up to the standard required for its purpose.
The model calculation results confirmed some phenomena already known to science: photons with lower wavelength, such as infrared, were attenuated rapidly in the surface layer of the ice, while shorter wavelength in the ultraviolet and short visible range penetrated to greater depths. There were also some new findings. For example, the scattering of photons by air bubbles means that eventually, some photons return to the surface, where they may be undergoing internal reflection back into the ice. This means that, at any given time, there may be up to 73.5% more low wavelength photons bouncing around within the ice than are supplied to the ice from the sun.
Why is this relevant? Photons are energy and if they are absorbed by small contaminants, inclusions or heating the ice itself, they contribute to the energy budget of the ice at depth and hence, the behaviour of the ice with respect to cracking and melting. In addition, the model showed that particle inclusions within the ice may absorb enough energy from photons to cause the surrounding ice to melt and the particle to sink within the resulting cavity. This in turn, at very small scales, means that the melting of ice surrounding particles causes the released air bubbles to gather in the molten cavity, and photons will be refracted in different ways at the water-air, air-ice and water-ice interfaces within this cavity, with yet more consequences for the energy budget (sub-surface radiative field) within the ice.
Although the paper concludes with an application of this work to explaining the differences between rocky and iron meteorites when it comes to sinking within the ice and where they may be found, it clearly has wider implications. The insights provided here show that the energy budget within surface ice needs to be re-considered in modelling of ice behaviour and for direct measurements of irradiance within the ice column.
If you were interested enough to read to the end, I thank you and share a final thought with you: when you next hear about model predictions of global warming, sea level rise or glacial melt, think back to what you have read here and reflect upon the intricate work that lies behind this specific, seemingly small contribution to the field of climate change. Perhaps it will be easier to understand the large uncertainty associated with some predictions that go far into the future and appreciate that each new model is constructed with the best current expertise, breaking new ground, while the scientists behind it know that their effort is just one along a timeline of improvements that reaches from the beginning of modelling into the future.