Hi Darwin,

If available, maybe you could consider using a static model for the height-diameter relationship (there are plenty of them in the literature for many tree species and forest ecosystems, each one with its singularities). The correlation between dbh and tree height is usually quite high, although it also depends on the stand structure and so on. In this way you could predict the height of the tree at different time periods (i.e., at different dbhs according to the growth described by your tree rings).

Hope this helps.

Darwin,

Most allometric equations are species, and sometime site by species, specific. And typically they only rely upon DBH.  So if you can infer DBH from your growth rings data Iʻm not sure why you would need tree height as well in order to convert to total mass/carbon.  As Sergio said there are often standard species correlations for DBH to height that you can use.  Or alternatively there are sometimes height based allometric equations, so if you can find both a height based and DBH based allometric equation for your species and site you can back calculate to get the height from the DBH. 

Allometric equations exist that are based on DBH for most silviculturally valuable species.If you want to understand stand development over the history of the stand,  a stem analysis will provide that information To do so, you fell the trees in a stand and take cookies at 2 m intervals all the way up the tree. Then you can look at height relationships over the course of the stands' development. See attached paper. Alternatively, if you just want tree height, use a clinometer or a laser range finder that does tree heights from forestry suppliers.

An excellent comparison of methods on "correlation/inferring from measured radial stem growth between/on height growth" is given in: Kariuki, m. (2002): Height estimation in complete stem analysis using annual radial growth measurements. Forestry (UK) 75: 63-74. It includes references to Carmeans, Lenharts, Newberry and Fabbio et al. methods. Have fun reading!

Thank you all for your important answers. I have added more specifications in my question.

Sergio de Miguel, I have checked the height-diameter relationships and it is very useful for my calculations.

Noa Lincoln, thanks for the clarification I was not clear how works the allometric equations.

H. M. Poulos, thanks for the paper, I was looking also how to model the vertical/radial development of a forest but including annual carbon storage.

Hein Sebastian, thanks for this excellent paper that I was looking for calculate the annual volume.

There are some major risks when using height-free (i.e., diameter-only) allometric equations for the purpose you state.  The two most problematic situations arise when there are differences in site quality and when there are differences in stand density.  Diameter-only allometric equations "imply" a fixed height for any given diameter, so a 25-cm tree always returns the same biomass, regardless of its actual height.  You will always underestimate biomass on high-quality sites and overestimate on low-quality sites.  If you a consider two mature stands that are changing very little in terms of height growth (let's assume none), but have different densities, the incremental diameter growth is expected to be greater in the more open stand.  This will translate into an exaggerated biomass change, because the implied height of the open stand will be greater than the implied height of the denser stand.  This is easy to confirm with actual data, if you have some with height and do the calculations with and without height.  There are published examples where the failure to consider height leads to erroneous conclusions because of this difference,

I would also like to add that ht growth is not linear through the life span of a tree and scaling with allometry can create some errors. You certainly can do it if the forest is young and even aged (similar sizes and light environments). For example, In a very dry Ponderosa Pine site with multiple ages and canopy positions I had to measure internode difference to recreate 10 year of ht growth (very easy on pines). Using diameter change from tree rings and dendrometer bands and allometric equations resulted in tree heights that were up to 3-5m taller than actual tree height after only 10 years. Net ecosystem production is quite low in these forests and these errors had a very significant affect on the final number. Good luck!

If you will cut the tangential section of the stem from base to top you will get the conical structure and it will  help you in estimating the height of the tree annually in ring porous species. Please read the research article of Kariuki, m. (2002): Height estimation in complete stem analysis using annual radial growth measurements. Forestry (UK) 75: 63-74.

The stem form of trees change oover time, even on a specific site and in a given stand, due to e.g. changes in stand density. Internal wood density may also change, and will vary along the tree stems.

To estimate total carbon from increment cores taken at breast height on sample trees will always be a bit of a gamble. This technique can only give very rough estimates. If you want more reliable numbers you need to do like some of the others have proposed.  Cut the tree along the stem and do complete stem analysis on each tree, in order to get a more complete reconstruction of tree growth.

DBH can be used to estimate carbon storage using species-specific allometric equations such as the well-cited: Jenkins JC, Chojnacky DC, Heath LS, Birdsey RA. 2003. National-scale biomass estimators for United States tree species. Forest Science 49: 12-35.

To me, it seems better to use DBH allometric equations (such as those by Jenkins) than try to infer the tree height based on the tree DBH, then use a more advanced model to estimate carbon storage which uses both the variables: height and DBH. The only justification to infer the height so that you can use the more advanced model is if you have good local knowledge that is applicable to estimate the height of your trees. 

The precision of your carbon estimates using the DBH allometric equations will be coarse but this level of precision may be acceptable for your project depending on what you want to do with the data and what journal you plan to publish in. The precision will also vary depending on the stand density, age and condition of your forest (as pointed out in the comments of others). 

Hello, to estimate carbon fixed in tropical forest, you can try Chave et al. (2005) Tree allometry and improve estimation of Carbon stocks and balance in tropical forests. Oecologia 145. They developed two models: 1) includes tree diameter, total tree height, and wood density, and 2) includes diameter and density, useful when tree height is not available. And they explain their assumptions. They presented different equations for dry forests, moist mangrove forests and wet forests stands. You can find wood density data from several tropical and subtropical American trees in Chave et al 2006, Regional and phylogenetic variation of wood density across 2,456 neotropical tree species. Ecological Applications, 16: 2356-2367 also in INTI-CITEMA files. 

Thank everyone for your suggestions and comments, now I have a much better idea to continue this research.

As an aside, if you did want to start exploring the literature on annual height increment proxies, Risto Jalkanen's work is a good place to begin http://www.metla.fi/silvafennica/abs/sa39/sa394497.htm

Hi Darwin,

Here you can find allometric equations (Article Database of 478 allometric equations to estimate biomass for...

It would be possible to prepare a table that could be used as a quick indication guide from the published Forest Management Tables Forestry Commission UK Booklet No. 34 . The tables give top height and mean diameter for each yield class and , of course volume..