Forwards or backwards. Or, the mysterious case of the missing carbon.

Siddharth Krish.The original uploader was Siddharthkrish at English Wikipedia., CC BY-SA 3.0

Toby Maclean, posted 22nd February 2021

It sometimes seems that it is possible to make the topic of sequestration of carbon in timber products as complex as one likes. It can also be made quite simple – click here – but one thing is for sure, the carbon we are talking about is in the timber that timber products are made from. If you want you can measure it. But if you don’t have a carbon-in-timber-measuring kit to hand you can instead adopt this mathematical proof.

As some background there appears to be two schools of thought about when sequestration occurs. Some people say that when you build a building from timber you first find some trees that happen to be growing somewhere and chop them down and turn them into a building. You then replant the trees and they will start to absorb CO2 from the atmosphere and eventually they will have absorbed as much CO2 as there was in the timber that you built your building from. This is sometimes referred to as the forward-looking approach and it implies that it takes decades for the carbon in the timber in your building to be reabsorbed from the atmosphere.

Almost everyone else subscribes to a second view – the backward-looking view – whereby they recognise that a sustainable commercial forestry industry exists and a lot of timber is going to be felled each year and some of that timber could be used in buildings. There is no waiting decades for a handful of trees to reabsorb the CO2 that was in the timber that was used in the building because sustainable commercial forestry, as a minimum, balances its carbon on an annual basis (new growth of timber being larger than timber removals).

This distinction becomes important when one considers the climate impact of buildings with lots of timber in them, particularly when the assessment tries to account for the timing of the CO2 emissions as you might in a dynamic life cycle assessment. As CO2 emissions early in life lead to a greater impact on the climate that CO2 emissions later in life, by adopting a forward-looking approach the benefit of sequestration is not realised for years later (and is therefore significantly reduced) as compared to the backward-looking approach.

You can read more about these two approaches and the difference it can make in this paper Exploring the climate impact effects of increased use of bio-based materials in buildings” (2016 Peñaloza, Erlandsson and Falk).

If you are not too keen on maths, even though we have skipped all the formulae, then you can make a note that the backward-looking approach is shown to be correct and then you can stop reading.

This is how the proof is going to work. First we’re going to keep tabs on how much carbon is in the timber in the forests that is waiting to be felled and then we are going to work out how much carbon is in all the timber buildings that were ever made from the felled timber, allowing for 100% emission of the carbon to atmosphere at the end or the timber buildings’ lifetimes. The sum of these two numbers is all the carbon that we need worry about to answer the question.

Then we will do this exercise using a forward-looking approach and, hey presto, we will magically make thousands of millions tonnes of carbon disappear (which is a bad thing as we are considering carbon stores here, not carbon emissions).

By the way the CO2 emissions caused by harvesting the timber and producing products (chainsaws, forest roads, transport, energy etc) are not included in this analysis because they are a constant for both approaches.

So, in time honoured mathematical tradition, let us consider the whole population of felled timber that produces for the sake of argument a constant supply of timber each year (in the EU-28 countries around 430M m3 in 2020 [source]) and the timber products that are made from that pool of timber.

Let’s assume the carbon profile in the forestry that produces one year's supply of timber (say, 430M m3 in this case) once every 50 years (or whatever the rotation period is) looks like Figure 1 below. Note that this is only the carbon in the timber that is actually felled that year, not the timber in all the forests that you need so you can fell that much timber each year.

Figure 1

Figure 1


The sawtooth profile is made up of flat bits where the newly planted trees are establishing themselves and not absorbing much CO2, and a steep bit where they are growing and turning carbon from the atmosphere into wood, and a vertical drop to zero every 50 years when they are felled.

Then in Figure 2 below the orange line is the average CO2 in a year’s worth of felled timber. And this is also the annual increment of CO2 in timber that will be felled across all forestry large enough to produce the 430M m3 yield every year.

Figure 2

Figure 2


And so then the total CO2 in all the timber to be felled in forestry large enough to produce the 430M m3 yield every year is the grey line in Figure 3 below (in this case 50 times the orange line, because you need 50 times the size of forest that you fell each year). It shows that we have 5,300 Mt CO2 in timber that will be felled across all the forestry needed to yield 430 M m3 of timber each and every year. This figure does not change (except sub-annually) unless we change how much timber we fell. This is only the CO2 in timber waiting to be felled. Other CO2 stores in forests can continue to grow.

Figure 3

Figure 3


Then we can look at the timber building side of things, starting with the timber building built in one year from the timber felled in one year (we've optimistically assumed all timber goes to buildings and of course it does not, you can either factor the volume of wood going into buildings if you want or, more accurately, just adjust the average lifespan of the timber once felled). Anyway, the blue line in Figure 4 below is the CO2 stored in the buildings built from one year's supply of timber, assuming a 60-year life. Note there is a carbon balance between the carbon in the timber that was felled and removed from the forest store in a year and the carbon that was introduced to the timber products store in the same year.

Figure 4

Figure 4


And then we can consider that this many buildings are built every year and add the orange line in Figure 5 below. The orange line is therefore all the CO2 stored in all timber buildings ever built since year 0.

Figure 5

Figure 5


Assuming we are currently at year zero (which we are not), the orange line slopes up until it we get to the maximum lifespan of the products the timber was made into and then tops out. The value it tops out at is the average lifetime of the timber products that are made each year multiplied by the mass of CO2 in the timber that is made into those products each year. If you double the average lifespan of timber products you can double the total CO2 store in timber products. If you double the amount of sustainable timber that goes into timber products each year then you can double the total CO2 store in timber products.

In this case, using the assumptions mentioned above, we can create a CO2 store in timber products of 20,600 Mt CO2.

So, we have a permanent CO2 store in the timber waiting to be felled in the forests of somewhere over 5,300 Mt CO2. And we can build a CO2 store in timber products of somewhere over 20,600 Mt CO2. Or if we said the average life of timber products were 30 years rather than 60, then somewhere over 10,300 Mt CO2. Or put another way, for every 10 years we can extend of the average lifespan of timber products by we can add over 3,400 Mt CO2 to the total carbon store we can build in timber products. By comparison the EU28 annual CO2 (not CO2e) emissions are c. 3,500 Mt CO2.

However whatever we choose as the average life of timber products, the total amount of CO2 stored is the sum of the CO2 in timber in forests waiting to be felled and the CO2 store in timber products. For a 60 year average timber product life then this is 20,600 Mt CO2 in the timber products and 5,300 Mt CO2 for the timber waiting to be felled = 25,900 Mt CO2.

But now, as promised, let's look at the forward-looking approach, starting in Figure 6 below with the forward-looking profile for the CO2 stored in all the buildings built from a single year's felled timber.

Figure 6

Figure 6


And we see that 50 years after the buildings were built, the trees that were planted to replace the same number of trees used in the buildings have accumulated the same amount of CO2 as the CO2 in the timber that was used to build them (344 Mt CO2). This is the same total as in Figure 4 as you would expect. The difference is that it’s not until year 50 of the 60-year building life that the carbon that is physically in the buildings that were built is assumed to have materialised. At this point if you had your carbon-in-timber-measuring kit to hand you could probably check the carbon was actually in your building from year zero but if you still can’t find that kit then read on.

If we now, using the forward-looking profile in Figure 6, accumulate all the CO2 in all the buildings that are built every year from timber that is felled every year we get the orange line in Figure 7 below (again based on an average 60-year building/product life).

Figure 7

Figure 7


And we see the forward-looking approach yields a total carbon store in timber products of around 8,800 Mt CO2 based on a 60-year average lifespan compared to 20,600 Mt CO2 in Figure 5.

Therefore according to this forward-looking approach we have a total store of 5,300 Mt CO2 for the timber waiting to be felled + 8,800 Mt CO2 in timber products = 14,100 Mt CO2 compared to the 25,900 Mt CO2 we know we actually have.

So, somewhere 11,800 Mt CO2 has gone missing...

The forests simply contain the carbon that they contain and when you fell timber that carbon is removed from the forest and placed in products. But the forward-looking approach misses this.

And we’ll finish with a challenge: can anyone think of another way to account for the missing 11,800 Mt CO2?

Answers, comments and corrections are welcome via social media, by email, or through the Contact page on this website.