Supplement of Hydrogen dynamics in soil organic matter as determined by

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1 Supplement of Biogeosciences, 13, , doi: /bg supplement Author(s) CC Attribution 3.0 License. Supplement of Hydrogen dynamics in soil organic matter as determined by 13 C and 2 H labeling experiments Alexia Paul et al. Correspondence to: Alexia Paul (alexia.paul@inra.fr) and Jérôme Balesdent (jerome.balesdent@inra.fr) The copyright of individual parts of the supplement might differ from the CC-BY 3.0 licence.

2 Supplementary material S1. Incubation characteristics The isotopic characteristics of the labeling experiment are summarized in the table S1. Table S1 : Incubation characteristics and the initial isotopic compositions of the labeling experiments. 13 A m, A m and A w are respectively the 13 C and 2 H abundance of the added labeled source (molecule or water) and 13 A tot_i, A tot_i are respectively the 13 C and 2 H abundance of the total soil at the initial conditions (time 0). 13 A m % 13 A tot_i % ± 0.02 A m or A w % A tot_i % ± Experience Added molecule mg 2 H 2 O Cambisol Podzol Leptosol Cambisol Podzol Leptosol Cambisol Podzol Leptosol Cambisol Podzol Leptosol Experiment C 2 H + 1 H 2 O yes yes Experiment yes C 1 H + 2 H 2 O 25 yes yes yes Experiment yes Control

3 S2. Mass balance calculations All the variables are summarized in the table S2. Carbon: C tot = C dfm + C dfs (SI1) 13 A tot *C tot = 13 A m *C dfm + 13 A tot_0 *C dfs (SI2.a) 13 A tot *C tot = 13 A m *C dfm + 13 A tot_0 *(C tot - C dfm ) (SI2.b) from SI1 and SI2 we derive: C dfm = ( 13 A tot - 13 A tot_0 )/ ( 13 A m - 13 A tot_0 )* C tot (1) Hydrogen: After freeze-drying, hydrogen is considered in three compartments: (i) NEH derived from labeled molecule atoms, (ii) NEH from unlabeled sources, and (iii) exchangeable hydrogen, which is by definition equilibrated with the atmosphere with a given fractionation ε 1 H tot = H dfm + H dfs + H e A tot *H tot = A m *H dfm + A dfs *H dfs + (A atm + ε 1 )*H e (SI3) (SI4) from SI3 and SI4 we derive: A tot *H tot = A m *H dfm + [A dfs *H dfs + (A atm + ε 1 )*H e ]/(H dfs +H e )*(H tot - H dfm ) (SI5) The term [A dfs *H dfs + (A atm + ε 1 )*H e ]/ (H dfs +H e ) is the average composition of unlabeled hydrogen. It is derived from the analysis of the unlabeled sample: H tot_0 = H dfs + H e A tot_0 = [A dfs *H dfs + (A atm + ε 1 )*H e ]/(H dfs +H e ) (SI6) (SI7) from SI5 and SI7 we derive: A tot *H tot = A m *H dfm + A tot_0 *(H tot - H dfm ) (SI8) H dfm = [(A tot - A tot_0 )/(A m - A tot_0 )]*H tot (2) By similarity, for Experiment 2 (labeled water), we write: 2

4 H dfw = (A tot - A tot_0 )/(A w - A tot_0 ]*H tot (3) These equations are based on approximations: the isotope fractionation term between atmosphere and exchangeable H is supposed to be equal in labeled and : this is supported by the fact that the amount of exchangeable hydrogen is considered unaffected by the (small) amount of introduced labeled material. The amount of unlabeled HNE (H dfs ) and its abundance (A dfs ) are considered equal in the labeled and. Inequality would affect the denominator in equations (2) and (3). Equality is a numerical approximation without consequence, owing to the very high enrichment of labeled material (A m, A w, see table S1). Table S2: Definition of the variables used for mass balance calculation Quantity (mg g -1 dry soil) Abundance Variables C tot H tot C m H m H w H e C dfs C dfm H dfs H dfw H dfm 13 A tot A tot 13 A tot_0 A tot_0 Definition Total amount of carbon in the soil Total amount of hydrogen in the dry soil Initial amount of carbon in the added molecule Initial amount of non-exchangeable hydrogen in the added molecule Total amount of water hydrogen in the soil Amount of exchangeable hydrogen in the dry soil Amount of unlabeled carbon already present in the soil Amount of carbon derived from molecule Amount of unlabeled non-exchangeable hydrogen present in the soil Amount of non-exchangeable hydrogen derived from water Amount of non-exchangeable hydrogen derived from molecule 13 C abundance of the total bulk soil 2 H abundance of the total bulk soil 13 C abundance of the unlabeled experiment (control) 2 H abundance of the unlabeled experiment (control) 13 A m Initial 13 C abundance of the labeled molecule A m A w A atm Initial 2 H abundance of the labeled molecule Initial 2 H abundance of the labeled water 2 H abundance of the atmosphere 3

5 To calculate the incorporation of the water hydrogen coming from the mineralisation of the added molecule (recycling), we assume that the labelled molecule is completely mineralised in water. The resulting isotopic composition of water in experiment 1(A w2 ) can be calculated from the isotopic composition of the labelled molecule as follow: A w2 = (A m *H m )/H w (SI9) Then, the amount of non-exchangeable hydrogen that can be derived from this water (H dfw2 ) can be calculated using the value H dfw calculated in equation (3) : H dfw2 = (A w2 A tot_0 )/ (A m - A tot_0 )*H dfw (4) The proportion of deuterium derived from the molecule but incorporated in the soil by the water is given by (H dfw2 /H dfm )*100 where H dfm is calculated in equation (2). S3. Propagation error calculation Uncertainties on the element and isotope ratio measurements affect the estimate of the amount of labeled-source derived carbon or hydrogen atoms. To assess the uncertainty σ Cdfm (err7), σ Hdfm (err8), σ 2 Hdfw (err9) or on the calculated values C dfm (Eq. 6), H dfm (Eq. 7), and H dfw (Eq.8) we calculated the statistical error propagation of the uncertainties on measured isotopic compositions and element content of replicated samples presenting in supporting information. σ 2 Cdfm = (σ 2 13Atot + σ 2 13Atot_0)*[C tot /( 13 A m - 13 A tot_0 )] 2 + (σ 2 13Am - σ 2 13Atot_0)*( 13 A tot 13 A tot_0 ) ²*C tot ²/( 13 A m - 13 A tot_0 )² + σ 2 Ctot*[( 13 A tot 13 A tot_0 )/( 13 A m - 13 A tot_0 )]² (err6) σ 2 Hdfm = (σ 2 Atot +σ 2 Atot_0)*[H tot /(A m A tot_0 )] 2 + (σ 2 Am - σ 2 Atot_0)*(A tot A tot_0 )² * H tot ²/(A m A tot_0 )² + σ 2 Htot*[(A tot A tot_0 )/(A m A tot_0 )]² (err7) σ 2 Hdfw = (σ 2 Atot +σ 2 Atot_0)*[H tot /(A w A w_0 )] 2 + (σ 2 Aw - σ 2 Aw_0)*(A tot A tot_0 )² * H tot ²/(A w A w_0 )² + σ 2 Htot*[(A tot A tot_0 )/(A w A w_0 )]² (err8) where the indices of the terms σ X stand for the standard deviation of the respective variable. In this calculation, the uncertainties σ 2 Am, σ 2 Aw and σ 2 13Am were considered as negligible. 4

6 S4. δ 13 C and δ 2 H results of the incubation samples δ 2 H δ 2 H 2920 a acide palmitique b 370 labeled sample δ13c c unlabeled sample Figure S4.1: Cambisol 13 C and 2 H isotopic variation a. δ 2 H variation through time of the bulk soil that received labeled,, and and. b. δ 2 H variation through time of bulk soil that received labeled water and. c. δ 13 C variation through time of the bulk soil that received labeled,, and and. Standard deviations are less than 3 for. 5

7 δ 2 H a δ 13 C c 280 b labeled samples δ 2 H Figure S4.2: Podzol 13 C and 2 H isotopic variation a. δ 2 H variation through time of the bulk soil that received labeled,, and and. b. δ 2 H variation through time of bulk soil that received labeled water and. c. δ 13 C variation through time of the bulk soil that received labeled,, and and. Standard deviations are less than 3 for. 6

8 δ 2 H a isolueucine δ 2 H b labeled samples δ 13 C c Figure S4.3: Leptosol 13 C and 2 H isotopic variation a. δ 2 H variation through time of the bulk soil that received labeled,, and and. b. δ 2 H variation through time of bulk soil that received labeled water and. c. δ 13 C variation through time of the bulk soil that received labeled,, and and. Standard deviations are less than 3 for. 7

Supplementary Figure 1. Example used to demonstrate the additive. sources, soil and PyOM, are conclusively partitioned. In Experiment 2, the

Supplementary Figure 1. Example used to demonstrate the additive approach. Arrows represent CO2 flux, in µmol m -2 s -1. In Experiment 1, the two sources, soil and PyOM, are conclusively partitioned. In