hello and welcome in this lesson we're going to explore some of the choices climate modelers make climate models vary widely from those that include few processes and average over large space and time scales to those that explicitly attempt to model many interrelated processes and deal with smaller increments in space and time it is impossible to truly capture a representation of the actual Earth so modelers make choices their choices depend on the question of interest and also are ultimately limited by time and computing power computing power does keep increasing which increasingly makes it possible to add
complexity to climate models or allows modelers to increase spatial and temporal resolution or to model longer time periods or to run the model more times through here we're going to talk about some of the choices you might face if you become a climate modeler the simplest kind of energy balance models like we did before basically average over the whole earth and make some big assumptions but those models are still useful to do things like estimate how long it might take for Earth to regain energy balance after a perturbation or to estimate what might happen to
Earth's average temperature if say overall reflectivity changed for example but we can get more complicated and model smaller scale processes if we conceptually divide Earth up into smaller pieces the size of the pieces depends on what processes we're interested in studying for example if you're learning to identify continents you don't need a particularly detailed world map but if you're trying to find an address in an unfamiliar City you need some small scale detail here one might choose to divide up the earth into latitude bands just getting more detail by latitude can be informative because there
are different things going on at the equator compared to the poles particularly regarding energy coming in and leaving the next step might be to also divide the Earth up by longitude and create smaller boxes instead of bands you can imagine this grid over the surface of the Earth and the model is keeping track of what happens in each grid cell the cells are connected to one another and they exchange matter and energy with one another the boxes or grid cells can extend into three spatial Dimensions what's shown here is how one could divide up the
atmosphere vertically too so the cells stack on top of one another not shown here but done in climate models that include ocean Dynamics our cells extending downward into the oceans as well one detail to note on this image is that in the model The Chosen layers of the atmosphere are thinner near Earth's surface where there are more molecules and and then the layers get thicker so have less detailed resolution as you go up away from the surface the same pattern is typically chosen in the ocean where a lot of the action is closer to the
surface layer so it's useful to have higher spatial resolution there then they average bigger pieces deeper down in the ocean the cells don't all need to be the same size also not shown here is surface topography like mountain ranges which stick up into the atmosphere and sometimes need to be taken into account depending on what questions you're trying to answer when should you stop dividing the earth into smaller pieces in your model if you model only the average Earth you can address questions about the average Earth if you want to answer questions about say temperature
and precipitation patterns that happen on spatial scales of continents you have to divide the earth into enough cells that you can resolve the variations at the scale of interest if you wanted to include hurricanes in your climate model you need to have small enough cells to resolve hurricanes and typically that would mean having at least four cells in the space covered by one hurricane if you're not answering questions where you need to know what the hurricanes are doing though you don't need to have cell sizes that small typical grid cell sizes for a general circulation
model or GCM would be about 100 to 200 kilometers on a side like the coarsest resolution image shown here in the upper left and would have maybe 20 vertical layers in the atmosphere and 20 more in the oceans but cell sizes continue to get smaller as computers get faster in designing a climate model you'll need to decide how often your model takes a snapshot of the system it turns out that spatial scales and temporal scales are closely linked together imagine for example you're trying to model a soccer game you've set up your equations so that
your virtual players have rules to follow you divide the field into squares and you're going to keep track of the number of players in each Square over time and the location of the ball how often should you collect data in order to be able to follow the action you want the snapshots to make sense in time so if for example you only looked at the field every 5 minutes each successive snapshot would be disconnected from the last you'd probably need to choose a time scale that was fast enough that your model could follow the ball
traveling from one square to the next to the next if you choose tiny squares you'd have to choose a very short time step too because the ball can travel across a small square f fter than it can travel across a bigger Square so the smaller the square the smaller the time step required for a typical General circulation model that's trying to capture the action in the atmosphere at spatial scales of 1 to 200 kilometers a typical time step is 20 minutes to an hour if you're trying to model the growth and decay of massive ice
sheets on time scales of thousands of years you don't need to have your model look every virtual 20 minutes in a socer game there aren't that many things to keep track of in a climate model for variables in the atmosphere it would be pretty normal to keep track of temperature and humidity how much water was in what phase that is solid ice liquid droplets or water vapor and the mass of the atmosphere the model would also be tracking energy flows from the surface into the atmospheric cells right next to the surface and from those to
the cells around them it would also be tracking motions from one cell to another both horizontally and vertically like the soccer players running around models can get more complex and can add more variables people might add aerosols or dust or carbon to their models and track how those move around and influence other parts of the system they might link their atmospheric model to a model of the oceans which would track other variables in each ocean cell like temperature and salinity or sea ice at the surface each variable would be determined for each cell in the
model at each time step so each cell would just have one value for each of those variables for each time step we wouldn't see any of the variation that might be happening at smaller scales it would be highly unusual for a single model to include all the items shown in this cartoon of the climate system and in fact greater complexity is not necessarily helpful there's way more going on in the climate system than any model can explicitly track and there are important things happening at smaller spatial scales than the typical grid cell size of models
processes that turn out to matter on the larger spatial scale of the model for example photosynthesis is happening on really small scales like the scale of a leaf or if you want even smaller than a leaf each Leaf might not really matter for the climate system but the aggregate effects of photosynthesis on the scale of a forest might be relevant so there are choices to be made regarding at what level you explicitly model some of the processes in the climate system do you model each leaf or do you make some reasonable assumptions and approximations and
come out with an estimate of how the whole Forest is interacting with the rest of the climate system when modelers choose to approximate some process using reasonable assumptions and related variables what they're doing is called parameterization they're approximating aggregate effects and using those aggregate approximations in the model probably the most common example of parameterization in climate models is how people represent clouds clouds are tricky because they're typically smaller than a grid cell size and cloud formation depends on lots of processes like evaporation and condensation that are happening at really tiny scales we simply can't realistically
model the formation of each raindrop everywhere on Earth so modelers use other variables like temperature and relative humidity which are related to cloud formation to approximate how much cloud cover there would likely be in a particular grid cell and to estimate the range of droplet sizes which matters for things like reflectivity of the clouds so parameterizations are reasonable and useful approximations some models are specifically designed to simulate short time periods on the order of decades these are usually the most complex models with the highest resolution and the most things to keep track of other models
are typically run out a century or so which is common for questions of interest to humans alive today since it's a time frame we can get our heads around we can imagine one fairly Long human lifetime some models however are designed to simulate thousands of years these models are often tested against geological observations and are run thousands of years into the future to address questions like what's the long-term fate of our atmospheric CO2 emissions or maybe how long might it take to melt most of the on Greenland given some future emissions trajectory so you'll need
to choose how much virtual time to cover all of these choices have trade-offs one of the trade-offs involves Computing time the time it's going to take to run your model is how long it takes the computer to do one math operation like add two numbers together times the number of math operations per equation times the number of equations that have to be solved for every grid cell times the number of grid cells in your model times the total number of time steps and this is just for one run of your model if you want to
say change one of the starting values to something slightly different to see whether that changes the model's output you'd repeat all these computational costs so we also have to multiply by the number of model runs these can really add up for high resolution complex models so we have constraints on climate models imposed by computer power and the speed at which we can solve the millions of equations this constraint becomes less important over time with increasing computer power and as computers get faster we can explicitly incorporate more processes into models and we can increase the resolution
and sophistication some Global models now are aiming for grid cells just a few kilometers on a side with Associated quite short time steps this will allow the models to capture processes at small scale that previously couldn't be modeled but also limits the time span that can model to just a couple of decades but there is also a fundamental issue with model complexity it's tempting to try to model everything to include all possible processes at all possible scales in a climate model it seems like including more processes more explicitly would naturally get us closer to truly
representing the climate system and certainly modeling specific parts of the system can help us better understand those parts but things can get a little off every number in a climate model has the potential to be a little different from the True Value in the real world and if enough little things get a little bit off in a complex model it can translate into a larger range of possibility for the big predictions that come out of the model nomia rcus has called this the complexity Paradox in her words a complex model may be more realistic yet
ironically as we add more factors to a model the certainty of its predictions May decrease even as our intuitive faith in the model increases this is a good reminder that models are not exact replicas of the climate system instead they are useful tools for learning tools which require continual checks against what we know about physics chemistry and biology checks against Real World observations and checks against one another so modelers make choices you can design a fairly simple model with large spatial scales and time scales or a detailed model with small grid cells short time steps
and many variables you could choose to explicitly model more processes or you could choose to approximate using parameterizations you'll be able to run your simple model faster and it will be able to model longer time spans and run your model more times than you can do with your complex model But ultimately your choices will depend on what questions you want to address through modeling
