This post had a dual spark: the recent report in Science on how global tree restoration could contribute to climate change mitigation and a remark by Karst Klein of social enterprise Binthout (in Dutch only, sorry) during a field trip with the lectorate networks in a circular economy (NICE, also in Dutch only 😦 ). The remark was roughly this “in the interest of preventing climate change, we should cut trees sooner”

To state that the Netherlands is a densely populated country would be an understatement. It is in fact, one of the most densely populated countries in the world. According to the FAO, it is also one of the countries with the smallest percentage of forest area, if not in the world then certainly in Europe. According to the data it has slightly increased its forested area from 10% in 1990 to 11% in 2016.

These two facts are of course connected. In a densely populated country land is scarce, and land use is guided by opportunity costs. Forestry is hardly a profitable business, at least if one considers only the value of the timber, given the relatively low price of wood and the long time span between planting a tree and harvesting it. The latter is called the rotation time or age.

An extreme example of this is oak which is valuable wood, but it has a typical rotation time of 120 years. If a piece of land is taken up for 120 years by oaks, whereas you could have built an apartment block and rented out the apartments for a steady, although somewhat lower cash flow for 120 years, it is clear what a profit-maximizing homo oeconomicus would do. Other species have shorter rotation times, but the time until harvest is still relatively long; 50-60 years is is more rule than exception. It is no wonder that most of the Dutch forests we still have are planted on former drift sands and other marginal land.

This opportunity cost of land argument has made me wonder in how far the results in the report in Science holds up. The authors claim in the abstract that they have identified plenty of land where we can plant forests once they excluded agricultural and urban land. I wonder if they just looked at the biological feasibility or have also included the economic feasibility. Of course, if we could put a monetary value on captured CO2, that would raise the value of forestry and make planting forests more attractive. Disclaimer: I haven’t read the report as it is in a journal that for some reason my university doesn’t seem to have electronic access to. [Editor’s note: this is yet another crazy example of the distortion and monetization of scientific information at the expense of human well-being. I’ve sent Maarten a copy of the article, and tried to post it here but that does not seem possible. Spoiler alert for the rest of you without access: they don’t ‘have the ability to figure out what land is actually available’ and economics is not directly considered].

The scarcity of forest in the Netherlands has driven up the valuation of standing trees, and as a consequence trees have an almost holy status in the Dutch legal system, albeit less so for forests than for sole standing trees. For example one needs to request permission from the municipality to cut a tree that has a diameter of more than 30 cm, even if it is planted on your own land. Moreover, if you do cut a tree you have to replant it. For forests the Dutch law of nature conservation applies and it states that one has to report the intention to cut down the trees to the province, which then gets the opportunity to disallow the cut. Also, replanting the forest afterwards is obligatory.

The strong feelings attached to the cutting of trees can also be observed in the recent news in the Netherlands where both a large nature conservation NGO and the state forestry service have been accused of cutting way too many trees.

Karst’s argument was mainly a biological one. Most CO2 is captured in the beginning years when trees grow (at typical growth curve is shown in below). At a later age, growth decreases, and therefore if one would be interested in maximizing CO2 capture, that would equal maximizing the harvest, and hence cutting down trees before they start to detoriate. One can then replant them and replace the old trees with young trees to capture more CO2. However, one can also make an economic argument.

So when should we cut down a forest? Economists and foresters have thought long about this. Using a very simple model with a number of heroic assumptions, as Paul Samuelson called them: 1) We are only interested in the value of the timber/wood, 2) constant and known future price of wood and harvest costs result in a net price per cubic meter wood of p, 3) known function of the wood available for harvest at time T in the forest: S(T),  4) known and constant interest rate i,  and 5) we use a single-age forest with clear cutting and replanting. The forester Martin Faustmann showed in 1849 that the value of land with such a forest on it is:

$V(T)=\frac{pS(T)e^{iT}}{1-e^{iT}}\$

This formula can be used to determine the optimal rotation time, but also to explore the effect of the different parameters on this optimal rotation time. This model, simple as it is, does allow us to say something about the effect of wanting to capture CO2 in forests and when to cut down the forest

What is the effect of including CO2 in the formula above? To answer this question I will make two additional heroic assumptions: 1) the harvested wood is used in buildings,  furniture or similar; in any case it is not burned, so the CO2 stays locked in after harvest. 2) We can express the value of captured CO2 in monetary terms. Using those two assumptions we can simply argue that the wood becomes more valuable: not only does it have a value as raw material, it also has value as captured CO2. This simply means that p in the formula above becomes larger.

I won’t bore you with the math, but it turns out that the effect of an increase in p on the optimal rotation age is to shorten it. Intuitively this results from the fact that an increase in p makes future harvests more valuable so you want to bring these more to the present. So again, the effect of including an interest in capturing CO2 is to cut down forests sooner rather than later.

There are of course plenty of other reasons to lengthen the rotation time as well. Old forests are sources of biodiversity and, to many, usually look better than a collection of saplings. Also, dead and decaying wood is very necessary as food sources and many other things for insects, birds, mushrooms et cetera. And given that we have so few large trees and forests in the Netherlands I appreciate the strong feelings and tough law about it. But for the climate the title still holds: I’m a lumberjack and I’m ok…

Image credits:

Cover image: Mastbos in Breda, the Netherlands. Picture by doortjekl. https://pixabay.com/photos/mastbos-breda-netherlands-forest-4025728/

Lumberjack: Image by ZedH from Pixabay