Q. J. R. Meteorol. Soc. (2003), 129, pp. 1373–1393 doi: 10.1256/qj.02.108 Modelling sources and sinks of CO 2 ,H 2 O and heat within a Siberian pine forest using three inverse methods By M. SIQUEIRA 1 ¤ , R. LEUNING 2 , O. KOLLE 3 , F. M. KELLIHER 4 and G. G. KATUL 1 1 Duke University, USA 2 CSIRO Land and Water, Australia 3 Max Planck Institut f¨ ur Biogeochemie, Germany 4 Manaaki Whenua–Landcare Research, New Zealand (Received 26 April 2002; revised 14 October 2002) SUMMARY Source/sink distributions of heat, CO 2 and water vapour in a Siberian Scots pine forest were estimated from measured concentration and temperature proles using three inverse analysis methods. These methods include: a Eulerian second-order closure model (EUL); a localized near-eld Lagrangian dispersion model (LNF); and a hybrid model (HEL) which uses the Eulerian second-order turbulence model to calculate the ow statistics combined with the regression analysis used with the Lagrangian model. Model predictions were compared to heat ux proles measured at ve levels in the canopy, and to CO 2 and water-vapour uxes measured close to the ground and above the forest. Predictions of sensible-heat ux proles by the LNF and HEL schemes were systematically better than results from the EUL analysis. This improvement was attributed to the redundancy in the measured prole (scalar concentration and temperature) data for LNF and HEL and to the imposed smoothness condition used in the regression analyses, whereas the EUL approach calculates a source for each level without any redundancy. The LNF and HEL schemes were also better than EUL in predicting source distributions for CO 2 and water vapour, although errors were larger than for sensible heat. The main novelty in our study is the use of EUL to decompose the vertical variability in scalar (or heat) sources into variability produced by the inhomogeneity in ow statistics and variability inferred from the measured mean scalar concentration (or temperature) prole. Hence, it is possible with this analysis to assess how much ‘new information’ about the source variability is attributed to vertical variation in the measured mean scalar concentration (or temperature) proles. The analysis shows that measured water vapour concentration proles provide little information on the inferred source distribution, whereas the CO 2 proles contain more information. Monte Carlo simulations show that computed sources from all three inverse methods have similar sensitivities to errors in measured temperatures. Errors are reduced when the reference temperature above the canopy is held xed, implying that errors in this temperature propagate throughout the entire domain. When information content and error estimations are combined, a valuable tool to assess the quality of source prediction by inverse methods can be generated. KEYWORDS: Canopy scalar source/sink Canopy scalar transport Inverse problem Siberian Scots pine forest 1. I NTRODUCTION The possibility of inferring scalar source/sink distributions (S c ) and vertical uxes (F c ) within plant canopies from measured mean concentration proles . c/, commonly called the ‘inverse problem’ (Raupach 1988), has received much attention recently. This approach offers the possibility of estimating S c at scales larger than individual leaves (e.g. porometry or chambers) to validate multi-layer canopy models (Leuning 2000; Styles et al. 2002). Two practical approaches to utilizing inverse methods have emerged over the last two decades: the Lagrangian localized near-eld theory (LNF) and higher-order Eulerian closure models. The LNF approach, originally proposed by Raupach (1989a,b), was used successfully to infer S c and F c from measured c in several eld experiments (Raupach et al. 1992; Denmead and Raupach 1993; Denmead 1995; Katul et al. 1997, 2001; Massman and Weil 1999; Denmead et al. 2000; Leuning 2000; Leuning et al. ¤ Corresponding author: Nicholas School of the Environment and Earth Sciences, Box 90328, Duke University, Durham NC 27708-0328, USA. e-mail: mbs4@duke.edu c ° Royal Meteorological Society, 2003. 1373