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Kindly pardon my poor knowledge, my area of expertise is not biology.

I am currently working on project where I have access to tree's stump and breast diameter and its species. We are trying to estimate tree's impact on microclimate on its surrounding.

To simulate it, we need approximation on tree height. So is there a database or textbook I can refer which provide information on estimating tree height from these features?

I understand that there would be no absolute value here but rather a distribution.

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    $\begingroup$ Yes and no. Allometric equations exist and are sometimes used. However, they are incredibly finicky - dependent on both species and specific growing area. With soil and water ability varying sometimes at sub-meter levels and known competitive impacts from neighboring trees likewise depending on species, the ability to model such allometric equations accurately and precisely is very difficult. This is further complicated by random events (e.g.wind damage, etc.). What are you trying to use this approach for? Most major journals might sneer at the approach given better methods (e.g. Lidar). .. $\endgroup$ – theforestecologist Feb 20 at 12:03
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    $\begingroup$ For southern ( USA) pines; no. In the forest they reach about 100 ft high at less than 2 ft diameter , then the diameter grows to over 4 ft. In an open area they are much shorter. $\endgroup$ – blacksmith37 Feb 20 at 22:24
  • $\begingroup$ @blacksmith37 exactly -- under different competition scenarios, trees grow quite drastically different. Remember, trees are fighting for sun and nutrients -- as you alter the availability of one or more of these resources through environmental shifts or community interactions (e.g., competition) you inherently should expect a shift in size, growth habit, etc. $\endgroup$ – theforestecologist Feb 20 at 22:49
  • $\begingroup$ @theforestecologist: For an example, I was cross-country skiing through a pine forest of mixed age this afternoon (eastern SIerra Nevada), after having read this question in the morning. Trees with a trunk diameter about 1 ft/25 cm were around 70-80% of the height of ones with a 3 ft/1 m diameter. And from other observations, younger trees in a dense stand will have tall trunks with few branches until the top, while those growing in an open area will be shorter and bushy, with branches down to the ground. $\endgroup$ – jamesqf Feb 21 at 6:21
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This is an interesting question for me because my first research internship centered pretty much entirely around this. It got pretty deep into the weeds as this was a CS, rather than biology, internship and we were mostly analyzing the math behind the allometry (e.g. Log-transformed linear vs. nonlinear regression for fitting the curve, OLS vs. RMA regression, traditional vs. monte carlo methods for comparing curves with different numbers of parameters, etc.) but much of the work we did is applicable here.

So, what you have here is DBH, or Diameter at Breast Height, which, lucky for you, happens to be the most common method for estimating the biomasses of trees. Here is the way that it works. Basically, a research team will go out and measure the diameter of a bunch of trees. Then they will cut down those trees and weigh them. What they will end up with is a graph with a bunch of points that give you the weight of trees of particular diameters. Then you fit a curve to this graph and, next time you want to estimate the biomass of a tree, you plug that tree's diameter into the equation for your curve. There are a bunch of databases containing allometric equations for different tree species. You just need to find one that contains the trees that you are interested in. Given that you are working in New York, this might have what you need:

https://www.fs.fed.us/psw/publications/documents/psw_gtr253/psw_gtr_253.pdf

Though you are better off figuring out the species of the trees you are looking at and seeking out allometric equations for those specifically. There might even be allometric information included with the data you are being provided. One thing that may be an issue is that correlations between DBH and biomass are much more common than correlations between DBH and height. Though both exist, you may have more trouble tracking down the latter for specific cases. Additionally, these numbers are very rough estimates that vary a great deal depending on the techniques used to collect the data, fit the curve, and extract the equation. In my own research, I found that log-transformed linear regression tended to be more successful over all (oddly enough) but that nonlinear regression was more effective on young forests dominated by stands of small trees. We also had a rather odd finding that log-transformed linear regression of two lines with a breakpoint tended to be less accurate in both situations but more accurate overall (i.e. it did better on big trees than nonlinear regression and better on small trees than linear regression) but we weren't able to come up with a mechanism to explain why this would be the case so we scrapped the findings. At any rate, all of this should illustrate that these numbers are very rough estimates that can be heavily influenced by environmental biases and that different research teams may even disagree on the proper allometric equations to use on a given species. This is why databases are helpful, as they tend to average out a large number of allometric studies rather than relying on a single one, but even these should be taken with something of a grain of salt.

If you are expected to actually come up with these equations yourself, then you need to actually measure the diameter and heights of a bunch of trees, plot them, and fit a curve to them. But from the sounds of it, you are only expected to estimate tree height based on diameter. If that is the problem you are being asked to solve, chances are that there are allometric equations available to help solve it, perhaps even ones that were provided to you.

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    $\begingroup$ not only do you need to find a set of equations for your species, but these numbers very certainly vary between growth regions (and likely even at smaller scales). The equation(s) by Jenkins et al is an example of an attempt to get around this to a degree. The question, though, is: do you want to do your study, or do you want to do it well. @Jeremiah you're right that this is a common approach, but it has slowly fallen out of favor as we have developed more accurate (though more expensive) methods. $\endgroup$ – theforestecologist Feb 20 at 22:43
  • $\begingroup$ If a best-fit-model approach is being utilized, I would suggest that the models you've mentioned are all too constrained and will very likely not capture all of the (realistic) variation. Sometimes that's ok -- again, this is why I asked the OP for his/her end goal. If this model approach is used, however, I'd suggest building stronger models using mixed effects modelling or various nonparametric approaches. If the solution is a simple one (as in using a log curve), in this case, it almost certainly can be improved upon.... $\endgroup$ – theforestecologist Feb 20 at 22:46
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    $\begingroup$ @theforestecologist I am aware of this. My own work in this area, specifically, involved the use of differential evolution, genetic, and particle swarm algorithms to improve on these sorts of models. But this is clearly not the sort of thing that one would be responsible pointing the questioner to. He doesn't know what allometry is and started the question by apologizing for his lack of knowledge of the subject. In this situation, one needs to start with the basics. In this case, that means learning what an allometric equation is and how best-fit models work. He didn't ask for a better $\endgroup$ – Jeremiah Feb 20 at 23:15
  • $\begingroup$ way to estimate tree height. He said that he had DBH and wanted to know if there were databases or anything he could use to estimate height with that. There are hundreds of them and if he had any business coming up with better models he would have already known that. The questioner didn’t leave his level of knowledge of this subject ambiguous. He was quite clear about it. If someone in a bio 101 class asked you how metabolic rate scales with size, would you start going on about computer-aided modelling solutions that can more accurately $\endgroup$ – Jeremiah Feb 20 at 23:16
  • $\begingroup$ account for non-size related variability, or simply explain the mathematical relationship between surface area and volume to them? You have to start somewhere and the questioner made it quite clear they are at the start line. A useful answer should meet him there. $\endgroup$ – Jeremiah Feb 20 at 23:16

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