# Small talk – the model way

A (left) shows the simple case where under one atmospheric cell one has four ocean cells. B (right) on the other hand shows a bit more complicated situations with nine ocean cells influencing one atmospheric cell

This snack is hopefully the first in a series  discussing the uncertainties and errors in climate simulations. I feel this important topic is often misunderstood by public and even by scientists, but it is of great importance when trying to understand the results.

There are plenty of sources of model uncertainties and errors, such as initial conditions1, sub grid scale parameterizations2, underlying physics, uncertainties in forcing and many others. I will discuss one of the smallest ones which is often neglected, but which is interesting at least in terms of model development: coupling between different components of earth system models.

Earth system models are the latest tool in climate predictions. An earth system model is actually a collection of different sub-models which are linked together with a program simply called a coupler. The different sub-models are usually ocean, sea-ice, atmosphere and land models and sometimes additional components such as a carbon cycle and land-ice models. Originally most of the sub-models have been developed separately and that is one of the reasons3 why their structure might differ significantly. However, when they are coupled together to form an earth system model the sub-models have to be able to communicate and the coupler is there to facilitate this conversation. A familiar example of communication is the ocean which influences the atmosphere and vice verse.

The first issue arising from this is that the models don’t always ‘speak’ the same language, the units may differ between models. In the same way as with people speaking different languages have to be translated in order to be understood the units have to be converted between the models. Like an interpreter usually knows exactly what the words mean we also know how to transform precipitation from mm/day to m2/s without mistakes. However, if you need to make up your mind when four or more people are simultaneously giving suggestion, some whispering and some yelling, it wouldn’t be surprising that your answer might not be perfect. This is exactly the main challenge in coupling different models together.

These issues arise from the use of different grids4 in the different models. Figure 1 illustrates this problem. One might, for example, have in the ocean 25 • 25 km wide grid cell while just above in the atmosphere the grid cell could be 50 • 50 km wide. Now when the atmosphere needs, for example, the surface temperature information from the ocean component, this causes a problem. In a simple case there might be four ocean grid cells below one atmospheric grid cell and what happens then is that the coupler interpolates the values from the ocean cells to the atmospheric grid. With a linear interpolation in our simple case, this would be an average of the four ocean values. Additional complexity follows from the fact that the ocean grid is not necessarily rectangular and almost certainly it is not centred with the atmospheric grid. This means that below one atmospheric grid cell there might be for example different fractions of 8 or even more different ocean grid cells.

In open ocean these facts might not be much of a problem since the ocean temperature change is relatively small in horizontal direction (this is often referred as horizontal homogeneity). However, in areas where warm and cold waters meet in the open ocean and in the areas close to the coast or close to the sea-ice boundary the temperature change is faster causing immediately some error. The sharp temperature difference is smoothed by the interpolation (although it should be noted that the interpolation methods used in real life are more sophisticated than just linear interpolation (Craig, 2010, Redler et al. 2010)). Furthermore, this is not just a problem for the temperature, but for all the exchange happening across the surface also from the atmosphere towards the ocean (precipitation, evaporation etc.). The problematic areas with sharp gradients are often also the places where the strongest ocean-atmosphere interactions take place, so it would be desirable that these regions would be modelled accurately.

In addition to the issues caused by the different grids also different time stepping between the models has to be taken into account. For example glaciers and ice-sheets are such slow moving systems that it doesn’t make sense to calculate changes every minute, whereas this is necessary in the atmosphere and ocean. In this case one has to interpolate in time, which again can cause errors.

Although it might sound like coupling is one of the largest sources of uncertainty in the climate predictions this is generally not the case. The errors caused by interpolating between the different grids are usually close to zero, but in some areas they can be larger (Redler et al, 2010). Since the grids between the models are likely to differ also in future we are not likely to get fully rid of the interpolation errors.

The final model output is a sum of all of it is components and their errors. Therefore, in some areas the model produces results close to the truth, not because the model actually reproduced the physical processes, but because the small errors in the various processes cancelled each other out. This is also one of the challenges of the model development. If one of the sub-processes is developed and it produces better results it doesn’t necessarily mean that the results of a complex earth system model are any better. In fact it might be quite likely that in some prospect they will be worse than before. The same applies for increasing the grid resolution and thus it is crucial that every change is well tested before taken into use.

In my next snack I will discuss a considerably larger source of error and uncertainty, the sub-grid scale parametrizations. This source is also quite different since there are multiple ways to decrease or avoid it.

1Initial conditions, the conditions where the simulations starts, are important especially for short simulations
2Sub grid scale phenomena are the phenomena so small that the model cannot solve them
3There are also fundamental reasons why, for example, the ocean and atmosphere grids differ. One of them is the baroclinic Rossby radius which is in atmosphere in order of 1000 km and in ocean in order of 10 km (changes with latitude and stratification). In order to solve most of the features of the circulation, eddies in the ocean and cyclones in the atmosphere, one should have a grid-size of similar order. It is evident that much finer grid is required in the ocean than in the atmosphere in order to solve similar processes. This is one of the physical reasons behind the different grids.
4Grid means that the surface is divided into small pieces and the equation are solved for each piece. On the purpose of this snack we can imagine them being rectangular as illustrated in Figure 1.

T. Craig. (2010, April 22, 2013). CPL7 User’s Guide. Available: http://www.cesm.ucar.edu/models/cesm1.0/cpl7/cpl7_doc/ug.pdf
Dunlap, Rocky, Rugaber, Spencer and Mark, Leo (2011), A Feature Model of Coupling Technologies for Earth System Models. Availabe: http://www.cc.gatech.edu/~rocky/papers/coupler_features_v1.pdf
Redler, R, Valcke, S and Ritzdorf, H (2010) OASIS4–a coupling software for next generation earth system modelling, Geoscientific Model Development. Available: http://www.geosci-model-dev.net/3/87/2010/gmd-3-87-2010.pdf

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#### Aleksi Nummelin

I am PhD student in climate dynamics at the Geophysical Institute, University of Bergen. My main research interest is how the climate change affects ocean dynamics and vice versa in different time scales. My research is based on model studies with idealised column models as well as full 3D climate models.

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