A 3-Box Climate Model(atmosphere, land, water)
IntroductionSchematic Model of Climate System
RETURN TO CLIMATE MODELING INTRO
Introduction
This section advances from the more simple climate system model. If you have not studied that material that goes along with the development of the simple model, I urge you to do so. Click here to go to this material.
Our first model of the Earth's heating system -- our first climate model -- was intentionally simple. In this section, we explore a slightly more realistic model; one that separates the land reservoir into oceans and real land, the continental regions of the Earth. This new model will therefore store energy in three reservoirs instead of two, and this forces us to nearly double the number of flows.
In general, this model is very closely related to the first model and is based on the conceptual model shown in Figure 3.1 below.
In this model, we break up the flows between the atmosphere and Earth surface into fractions that are directly related to the fraction of the Earth's surface covered by the oceans and the land. Thus, the Land Heat to Atmos flow of the first model, which has an initial value of 119 units of energy, gets divided up into 119*0.3 for the Land Heat to Atmos and 119*0.7 for the Ocean Heat to Atmos. This same approach is applied to other flows as well. This schematic model shown above is tranlsated into a STELLA model, shown below.Return to Top
EQUATIONS FOR 3-BOX CLIMATE MODEL
This model will take a bit more time to construct and there are more possibilities for typing errors as you enter all of the information required for this model. If you have troubles with the construction and your model is not in a steady state to begin, download this model following the link below, but remember that your understanding of the system will generally be much stronger if you are involved in the construction of it.
DOWNLOADABLE 3-BOX CLIMATE MODEL
One very important aspect of this system is the very small initial value for the Land reservoir, relative to the sizes of the outflows (which again given in yearly flow rates). Because of this, the model needs to have a very short time step of 0.01. This makes the model run more slowly, which is a sacrifice we have to make in order to explore this more complex model.
Experiments
All of the experiments outlined for the simpler model above could be applied to this more complex one. But, since this model has some extra features, it creates the possibility for some new experiments. For instance, this model gives us the ability to investigate the different responses of the land and the ocean to various changes, and it gives us the possibility to explore the effects of changing the energy storage capacity of the two Earth surface reservoirs.
1. Comparison with Simpler Model
A simple way of comparing the performance of this model with our first model is to examine the response time and magnitude of warming caused by a 3% increase in the solar input, which was the very first experiment with the simpler model.
2. Seasonal Variations of the Oceans and Land
This is a variation on an experiment carried out on the simpler model, but the goal here is to see how the oceans and land respond to seasonal changes in solar input. In a way, this will give us some insight into what kinds of temperature variations might be expected in comparing a location near the ocean (or on an island) with one in the middle of a continent (a place like Minnesota). The way to do this is to define the Solar Input as being equal to 100 + SINWAVE(3,1). It should suffice to run the model for just a couple of years in this case. It will be helpful here to look at a graph with the four Delta T... converters (the change in temperature of the three reservoirs and the global composite) and the Solar Input. As mentioned above, this should give you some motivation to look up yearly temperature variations from different locations around the globe.
3. Changing the Relative Sizes of Ocean and Land
The relative sizes of the areas covered by ocean and land have not remained constant over the course of Earth's history. Very early on, about 3 billion years ago, the planet may have been about 85% ocean and 15% land. More recently, in the Late Cretaceous, about 90 Ma, sea level was about 300 m higher than today and vast areas of the continental interiors were covered by shallow seas, so that the Earth then may have also been about 85% ocean. Because of the distribution of different elevations of the continents, a big sea level drop does not affect the distribution of land and water so dramatically, so we might imagine that we could go to a world with 33% land and 67% water during a period of lower sea level. But, we could also use the model to investigate a hypothetical case where the distribution of land and water is 50-50.
How can we design an experiment to look into these effects? We need to have a control, and we also need to have some kind of perturbation to knock the system out of its steady state (if you just change the land and ocean fractions, making sure they still add up to 1.0, the system should be in a steady state). You could do this by putting a simple spike in the Solar Input, lasting just a year, occurring shortly after the beginning of the experiment, in about the first or second year. To do this, you'll need to make the Solar Input a graphical function of Time, as was explained in Experiment #1 with the simpler climate model. In the case of this model, it may not work too well to run parallel models unless you have a fast computer. As a general rule, if your goal to examine how some change affects the behavior of a system, the simplest approach is to compare the response times and magnitudes of change that are related to an equal perturbation such as a spike in the Solar Input.
4. Changing the Initial Energy Contents of the Ocean and Land
The initial amount of thermal energy in the ocean reservoir is dependent on the area covered by the oceans, the heat capacity of water, the initial temperature, and the depth of the mixed layer -- that part of the ocean that is mixed on a yearly basis and thus exchanges heat rapidly with the atmosphere. The depth of the mixed layer is largely a function of the winds that blow over the surface of the oceans. As you might expect, it does change over time and from place to place. The model initially has this depth set at 35 meters, but some people argue for a depth of 50 meters and we might imagine a windier climate than ours producing a mixed layer with a depth of up to 100 meters averaged around the globe.
The equivalent feature for the land reservoir is the thickness of the soil layer that is involved in annual temperature changes, and again, this is averaged around the whole world. There are no simple controls on the thickness of this layer, but we can still investigate the effects of changing this value.
With these experiments, you will once again need to establish a control and apply some kind of perturbation to knock the system out of is steady state in order to see how the changes you've made affect the overall behavior of the system. As before, the simplest way of comparing behaviors is to compare the response times and magnitudes of change that are related to an equal perturbation such as a spike in the Solar Input.