The effect of timber harvesting on water yield from mountain ash forest has been studied for decades. It is topical because mountain ash forests supply a large amount of water to Melbourne, a city of more than 4 million people.
Mountain ash forests are also the main source of wood for the timber and pulp industry in the state of Victoria. There seems to be an enduring debate about the extent to which timber harvesting influences water yields.
Let’s start with an aspect of the topic that is reasonably well resolved. Because of different rates of evapotranspiration, the amount of water that arrives in streams depends on the age of the trees. When the trees are old, their rate of growth is low, the trees are widely spaced, and water use by the forest is low; streamflow is at it highest. Immediately after a fire that kills the trees or after a timber harvesting event, water use is also low; again streamflow if high.
However, as the trees grow in dense stands, their water use increases and streamflow declines. However, some trees die as the forest ages, and the rate of water use of the survivors does not increase to compensate, and eventually water use of the forest declines again; streamflow begins to increase.
The change in streamflow with forest age can be represented by a curve – it is commonly referred to as the “Kuczera curve”, named after one of the researchers who first documented the relationship between forest age and water yield. Such a curve can be represented by the mathematical equation:
Here the water yield , y(x), is expressed as a proportion of the maximum possible yield (the yield achieved in an old growth forest or immediately after timber harvesting or a fire). The age of the forest stand is x, and the parameters b and c control the shape of the curve. I’ll use b = 0.022 and c = 0.07 for the remainder of this post*. This results in the yield curve shown above.
In this case, the water yield reaches its smallest level when the forest is about 20 years of age, at which point the yield is almost 50% less than the maximum achievable.
So, this shows that if we were able to keep the forest as old growth (or at zero years of age), then we could maximize the water yield. However, as noted in my previous post, it is overly optimistic to assume that mountain ash forest won’t burn.
The chance that a forest will survive for x years given fires occur randomly in time with a mean interval of m years is:
or equivalently the cumulative distribution function of the time of fire is:
From this we can get the expected age structure from the derivative of F(x), which is defined by the probability density function:
Now, we can get the expected water yield E(Y) by integrating the product of the expected age structure f(x) and the water yield curve y(x). The range of the integration is zero to infinity, which are all possible ages for the forest (OK, an infinite age is impossible – I am about to impose an upper limit on forest age via timber harvesting).
This might look a bit complicated, but it is simply the average water yield, but it is a weighted average based on the amount of forest that is expected to be of different ages.
For the water yield curve I have used (y(x)), solving this integral leads to:
Plotting this expected yield versus the mean fire interval, we have:
So, we see that as mean fire intervals increase above about 20 years, the expected water yield increases. If we assume the average fire interval in mountain ash forests is 100 years (assuming tree-killing fires), then the expected water yield is about 20% less than that obtained for an old growth forest.
Now, the main question was about how timber harvesting might influence the water yield. The influence will occur via the effect on the forest age structure. If we assume that forests are harvested when they reach the rotation age R, then the age structure of the forest becomes truncated at R. The probability density of f(x) above the value of R needs to “redistributed” to values below R. Hence, the truncated probability density function is given by:
Using the same logic as above, the expected water yield given a mean fire interval of m and a rotation age of R is:
One can solve this integral. I’m not going to bore you with the solution – it is not particularly simple. And rather than focusing on this, I calculate the ratio:
This is the expected water yield from a forest under a rotation age of R years relative to the expected water yield of an unharvested forest. In both cases I am accounting for unplanned fires that occur with a mean interval of m years.
When p is less than 1, timber harvesting reduces the expected water yield from the forest. When p is greater than 1, timber harvesting increases water yields. Plotting the relative yield p versus the rotation age R gives:
This shows that as the rotation age increases above approximately 40 years, the water yield increases. Increasing the rotation age from 50 to 100 years increases expected water yield by approximately 10% in those areas exposed to timber harvesting. A further ~10% increase would be obtained by increasing the rotation age from 100 years to 200 years. At a rotation age of 200 years, the water yield is only about 5% below what would be expected in the absence of timber harvesting (but in the presence of fires).
Of course, these increases in water yield need to be weighed against the other possible benefits (e.g., more large trees for wildlife, possibly more sawlogs) and costs (e.g., fewer stands reaching rotation age due to fire) of increased rotations. Also, note that this analysis is limited to those parts of the forest exposed to timber harvesting. Effects will be moderated proportionally depending on how much of the forest is harvested.
Interestingly, water yields can be increased by reducing rotation ages below 40 years. In fact, when the rotation age is 8 years or less, timber harvesting actually increases water yield above that obtained in the absence of timber harvesting. This is because it keeps the water yield curve near it maximum at x=0. Such short rotation ages might not be feasible because sawlogs would not grow within this time. Water quality problems due to frequent harvesting might also be problematic, as might regeneration due to paucity of seed.
Given that nominal rotation ages in mountain ash forests are greater than 50 years, the right hand section of the graph is probably more relevant to the question about effects of timber harvesting on water yields. This simple model shows that it is reasonable to claim that clearfall timber harvesting reduces water yield in mountain ash forest.
*If you would like to investigate different parameters for yourself, I have created an Excel spreadsheet that does the various calculations displayed here.
In case you are interested in trying different values for the parameters b and c, note that the minimum yield occurs at x = ln[(b+c)/b]/c. At this point, the reduction in streamflow below the maximum is: