Global Uncertainty Accounting for Forest Carbon

Abstract:

Uncertainty in Global Forest Carbon

 

There are 11.3 E9 global hectares of biologically productive surface, of which approximately 4E9 are forested. The terrestrial biosphere reservoir contains carbon in organic compounds in vegetation living biomass (450 to 650 PgC, IPCC AR5 ). Houghton et al (2009) give 385 - 650 GtC, of which 70 ~90% is forest. Using 80%, that gives a range of 360 ~ 520 (IPCC) or 308 ~ 520 (Houghton) GtC in Earth's forests. The IPCC values give a forest carbon global density range of 90 ~ 130 tC/ha. Assuming that 360 and 520 GtC are two independent samples from our uncertainty on the global forest carbon pool, we may ballpark this uncertainty as

STD(global forest carbon pool) ~ [½(160)² [GtC]²]^½= 113 E9 [tC].

If X_i,…X_N have average variance s² and average covariance c then VAR(SX_i) = s²N + N(N-1)c, and:

1) 28.3 = s(2.5E-10 + r)^½.

where s is the root of the average variance of forest carbon in [t/ha], and r = c/s² is the "global correlation".  r is equal to the average correlation over all pairs of hectares if the variances per hectare are constant, but r £ 1 holds in any case.

Uncertainty accounting.

If r = 0, then (1) entails that s = 1.8 E6 tC, which is not defensible. Suppose an uncertainty requirement for carbon monitoring systems stipulates that the standard deviation per hectare should not exceed 10% of the mean. With a mean of 110 tC/ha, s = 11, and substitution in (1) would give r^½ = 2.6, which is impossible. If r = 1, then s = 28.3 which is 26% of the mean. In this case it can be shown that the error in the estimate in any hectare is perfectly correlated with errors in every other hectare: removing the uncertainty in ONE hectare on the Earth would remove uncertainty in ALL hectares. Neither r = 0, r = 1 are reasonable. Uncertainty accounting requires consistent estimates of global forest carbon uncertainty, uncertainty in hectare-wise estimates and global correlation. Consistent estimates do not exist at present. This research charts a course.

Reference

Houghton, R.A., Hall, Forrest and Goetz, S.J. (2009) Importance of biomass in the global carbon cycle, J of Geophysical Research, Vol 114, GooE03, doi:10.1029/2009JG000935.