My MSc project: a simple ray-tracing radiative transfer model (with code!)
My PhD was done through a Doctoral Training Centre, and as part of this I had a taught year at the beginning of my PhD. During the summer of this year I had to do a ‘Summer Project’, which was basically a MSc thesis. My thesis was called “Can a single cloud spoil the view?”: modelling the effect of an isolated cumulus cloud on calculated surface solar irradiance” (I think the best thing about my thesis was the title!). It gained a ‘Distinction’ mark, and I was very pleased that it won the RSPSoc MSc thesis prize (again, I think they gave me the prize based on the title alone!). This is the story of this project…
During the year before my MSc, I had been doing a lot of investigation into Radiative Transfer Modelling. These models (known as RTMs) are used to estimate how light travels through the atmosphere: you basically tell them what the atmosphere is like (how hazy, how much water vapour etc), and they simulate the effect on light passing through the atmosphere.
I’d investigated a range of models – including simple models like SPCTRL2, good standard models like 6S, and advanced models like SCIATRAN. One thing that I noticed was that none of these models seemed to be able to incorporate clouds very well. SCIATRAN did support modelling clouds, but you had to have either an entirely clear or entirely overcast sky – you could have vertical variation in optical properties (ie. multiple layers of clouds) but not horizontal variation. I decided that I’d write some code to use one of these RTMs to model light passing through an atmosphere which is partially cloudy and partially clear – like most of the skies that we have in the UK.
So, I started reading more about these RTMs, and tried to work out how I might be able to extend them so that I could have a spatially-variable amount of cloud (eg. cloud on the left-hand side of my ‘simulated atmosphere’ and clear sky on the right-hand side – or even a single small cloud moving across the sky). I struggled with this for a while and didn’t really have much success at working out what I’d need to do. I naively thought that I would be able to write a tiny bit of code to replace the ‘homogenous atmosphere’ that SCIATRAN used with a ‘spatially-variable atmosphere’ and that would be it. Unfortunately, that wasn’t the case…
It turns out that the horizontally-homogeneous nature of the atmosphere is a fundamental assumption of the mathematics that these models are based upon. And I’d come up with a MSc project that required me to break this assumption. Ooops.
So – after panicking a bit and deciding that I can’t do a PhD or even a MSc – I decided that if the standard models wouldn’t let me do what I wanted then I’d have to implement a new Radiative Transfer Model myself, from scratch! A bit of a tall order…but I decided to have a go, figuring that even if it didn’t work I’d learn a lot in the process.
With a bit more reading I realised that the only way to take into account horizontally-varying atmospheric properties would be to implement a ray-tracing model. In this sort of model, individual rays of light are followed from their source (the sun), and each individual interaction with the atmosphere is simulated (scattering, absorption etc). They are far more time-consuming to run than ‘standard’ models – but allow far more interesting parameterisations, as the atmosphere is basically represented by a grid, which can be ‘filled’ with different atmospheric properties in each cell. Normally the grid would be a 3D grid, but I decided to use a 2D grid to make life easier – just taking into account vertical height into the atmosphere (sun at the top, sensor at the bottom) and horizontal distance along the ground.
I decided to base my model on SPECTRL2, which meant I could use a lot of the constants that were defined in the SPECTRL2 code – for things like Earth-sun distances, absorption at different wavelengths, etc. I then built a simple Monte Carlo Ray Tracing procedure that followed the flowchart below (click to enlarge):
I say “simple” – it took quite a while to get it working properly! Of course, after actually getting the model working, I had to work out how to actually parameterise the atmosphere, how to create a realistic cloud to put in this atmosphere, and then what computational experiments to run to actually answer my original question.
Answering the actual question I set out to answer was actually very easy to do once I’d got the model running – and it gave some interesting answers. For example, if there is a cloud near a sensor on the ground, but not directly between the sensor and sun, then the sensor will actually record a higher irradiance than it would if there were no cloud. This makes perfect sense when you think about it (the cloud will scatter some extra light towards the sensor), but I hadn’t thought of it before I did the experiment!
I don’t think there’s really much more to say here, apart from to direct you to my thesis for more information (including my detailed conclusions) and to say that the code is now available on Github. I have tested the code in the latest version of IDL (v8.5) and it is still working – although I should warn you that the code runs rather slowly!
Also, if you’re interested in using a proper 3D ray tracing RTM then look into the Discrete Anisotropic Radiative Transfer Model (DART). I’ve always been meaning to replicate my experiments with DART, but have never quite had the time…that’s another thing for my ‘list of papers to publish when I have time’.