# Space can substitute for time in predicting climate-change effects

Here I will describe a method used to predict the consequences of climate change for ecosystems in professional scientific research. This method is interesting for laymen too because they can apply it too to get a rough estimate of the consequences of climate change.

The method is named space-for-time substitution. How it works? We have some prediction about how the key variables like temperature and precipitation (or whatever matters most) will change in time. We have a particular place, and want to predict what will happen at that place in future because of climate change.

To find out what will happen we simply try to find another place, a place which actually now has the temperature and precipitation (or whatever matters most) which are predicted for the future of our starting point. So, we substitute the actual situation of another place in space for the situation expected to happen in the future of our initial point, we substitute space for time.

## How laymen can use this method

The advantage of this method is that this is something which can be done by laymen too. Climate change predicted a temperature increase of 2 degrees. What will happen at your home town? Find out the average temperature of your home town. Then add these two degrees, and try to find a place which actually has this average temperature of two degrees more. Then you can look yourself how this looks like.

In the mountains this can be done on quite small distances, given that the average temperature depends on the altitude - we know very well that in the mountains the weather is colder. Moreover, this temperature dependence is the same everywhere, and the formula for this, which holds for altitudes up to 11 km is quite simple: The temperature does down by 1 degree C per 150 m of higher altitude.

So let's see how this would apply to the particular place in the picture. We see here three different ecosystems: The highest one, which survives the lowest temperatures, is simply grass. Below this, there are bushes. And down in the valley we can see wood.

Of course, there is also another factor beyond temperature which is important in the mountains - exposure to wind. If a place is better protected from wind, plants can survive even if the temperature is lower. But if one compares the places where one would not expect that the average wind will be different, as on the other side of the lake, the border between grass and bushes is almost exactly a straight line defined by the same altitude.

The border between the wood and the bushes is similarly a quite straight line, and it has even a well-established name: timber line or tree line.

To apply the space-for-time substitution, let's see how one can predict what happens at this place if the temperature increase is two degrees of Celsius in 100 years. Given the relation of 1 degree C per 150 m, this translates into 300 m of altitude, in the direction down the hill because in this direction it becomes warmer. So, go down until you reach an altitude 300 m below this point and you will see how the place on the picture will look like in a century.

We can also predict, with the same method, when what happens. Say, the prediction is a 2 degrees increase in 100 years. Then, if the increase is linear, that means 1 degree in 50 years or 0.2 degrees in ten years. This translates into 150 m corresponding to 50 years and 30 m corresponding to 10 years, and 3 m to 1 year. You want to know when the bushes will be replaced by wood? Find out the altitude of the actual position, then go down to the timber line - the altitude where the bushes end and the wood begins. Find out the altitude of that place. Compute the difference in meter, divide the result by 3 and you have the number of years you have to wait until it is warm enough for wood to grow at your starting point.

## Unpredictable thresholds?

As you can see from the example, the prediction which we would make based on the space-for-time substitution method appear to be quite nontrivial. Namely, the result will be some quite well-defined year when the bushes will be replaced by wood. Up to this year, all the warming does not change much, at least nothing which would be easily visible - bushes look like bushes all the way down to the timber line. Then, quite sudden, the situation at that place changes completely - the bushes will be replaced by wood. After this, again, not much will change - wood remains wood, at least for the naive layman looking at it.

This pattern of change, which we have derived based on the space-for-time substitution method together with the picture above, has been observed by ecologists too. And also by alarmists. They use it to present those sudden changes as unpredictable sudden changes of the whole ecosystem.

If one looks at what happens from a purely local point of view, the alarmist's description looks accurate. Indeed, there is a long period where nothing visible happens, but then there is a sudden, sharp change, and the ecosystem will be replaced by another, different one. As you can see from above, this is a quite accurate prediction of what will happen according to our application of the space-for-time substitution.

So, one can sell this in a really horrible way: Even if you actually don't see anything seriously changing, this does not mean that the climate change will not be harmful. What is predicted is that over a long time nothing changes, but there will be thresholds which lead to sharp, sudden changes, serious changes which you cannot predict.

The lie is that the same space-for-time substition method used to find this result also defines a simple way to predict these sudden changes long before they actually happen. As we have explained how to compute the number of years before the place in the picture will suddenly change from bushes to woods.

## Is the space-for-time substitution method reliable?

As described in Blois at al. 2013, "space-for-time" substitution is widely used in biodiversity model- ing to infer past or future trajectories of ecological systems from contemporary spatial patterns. Moreover, this paper adds support for the reliability of the method.

But there is no scientific method which does not have some limitations. As appropriate for scientific papers, this has been mentioned in Berdugo et al. 2020:

While space-for-time substitutions have been proven successful in some situations (121), they have also been criticized as spatial gradients may include drivers different than those driving temporal changes in ecosystem variables and do not include adaptation of ecosystems to the new environment (122,123). The interpretation of these results, thus, must consider this limitation. For instance, prospects in areas that are not drylands today, which delimit the spatial extent of the data used in our analyses, are extrapolations.

Are these limitations important for laymen who want to apply the method to get an independent, panic-free estimate of the expected climate change? Only partially. One has to be aware that it is not the temperature alone which defines the climate. Precipitation plays a very important, usually even more important role. And locally other circumstances (like the wind in the mountains) may play an important role too. But you cannot handle more than two such variables at the same time. You can easily find places with the same average temperature. It is harder to find places with the same average temperature and the same average precipitation. If you include even more parameters into your search, this becomes hopeless.

But this is anyway not what a layman would try to do.