Calculating Organic Carbon Stock from Forest Soils

The organic carbon stock (SOC) (t/ha) was calculated in different approaches in order to enhance the differences among methods and their utility regarding specific studies. Using data obtained in Romania (2000-2012) from 4,500 profiles and 9,523 soil horizons, the organic carbon stock was calculated for the main forest soils (18 types) using three different methods: 1) on pedogenetical horizons, by soil bulk density and depth class/horizon thickness; 2) by soil type and standard depths; 3) using regression equations between the quantity of organic C and harvesting depths. Even though the same data were used, the differences between the values of C stock obtained from the three methods were relatively high. The first method led to an overvaluation of the C stock. The differences between methods 1 and 2 were high (and reached 33% for andosol), while the differences between methods 2 and 3 were smaller (a maximum of 23% for rendzic leptosol). The differences between methods 2 and 3 were significantly lower especially for andosol, arenosol and vertisol. A thorough analysis of all three methods concluded that the best method to evaluate the organic C stock was to distribute the obtained values on the following standard depths: 0 10 cm; 10 20 cm; 20 40 cm; > 40 cm. For each soil type, a correlation between the quantity of organic C and the sample harvesting depth was also established. These correlations were significant for all types of soil; however, lower correlation coefficients were registered for rendzic leptosol, haplic podzol and fluvisol.


Introduction
Soils represent the largest carbon reservoirs in the terrestrial ecosystem, with 11% of soil organic carbon held in forest soils worldwide (Eswaran et al., 1999; Dey, 2005; Negi et al., 2013;  Yuan et al., 2013).At a global level, forests store large amounts of carbon sequestered from the atmosphere and retained in living and lifeless biomass and soil (Pretince, 2001;Whithead, 2011).Over 40% of the soil carbon is found beneath forests.In Europe, forest soils store roughly 1.5-fold more carbon than tree biomass (De Vreis, 2003-EC/UN-ECE).The carbon stored in forest soils can be directly managed to absorb or release atmospheric carbon to a degree that might have global implications (Johnson and Curtis, 2001;Paul et al., 2002;Lal, 2005).
Forest soil carbon pools are not well studied compared to aboveground carbon pools (Lal, 2005; Peltoniemi et al., 2007).The large spatial variability in forest soil organic matter has also limited the ability to predict its spatial distribution (Johnson et al., 1991;Yanai et al., 2000;Fahey et al., 2005;Whitehead, 2011).Inventory analysis and the investigation of soil organic carbon are required for soil quality assessments (Sikora and Stott, 1996) and carbon cycling predictions (Ellert et al., 2002), which are valuable tools for state and regional planning (De Vries, 2001;Amichev and Galbraith, 2004).
Estimates of forest soil organic carbon have applications in biogeochemical science, soil quality studies, CO2 sequestration technologies, as well as for emission-reduction compliance or trading with the aim of determining long-term carbon fluxes, or to manage natural resources and to design carbon sequestration strategies (Campbell et al., 2008).Efforts to study the potential of soils to regulate global warming and greenhouse gas effects by the ability of soils to store large quantities of carbon are increasing worldwide (Aticho, 2013; Stockmann et al., 2013; Jandl et al.,  2014).The UNFCCC's national greenhouse gas inventory and the Kyoto Protocol on emission reductions require CO2 emissions or removal from carbon stock changes on land use and activities within the UNFCCC's Annex I countries to be reported as annual estimates over a specified period of time.In practice, it is first necessary to establish a baseline of the carbon stocks, to be able to estimate the changes in their levels.However, problems arising from soil sampling, soil variability and soil depth make this a difficult task (Swift, 2001).Furthermore, reliable national estimates are needed for international acceptance (Watson et al., 2000).
Most estimates of soil organic carbon stocks are based on extrapolations of the mean soil carbon content for broad categories of soil or vegetation types (Post et al., 1982; Sombroek  et al., 1993; Kern, 1994).Although significant uncertainties exist with respect to both the estimates of the mean soil organic

Materials and Methods
The soil samples were taken from different regions of the Romanian territory and then analysed for pH, carbonates, humus, organic carbon, total nitrogen, the sum of exchangeable hydrogen, the sum of exchange basis, total cationic exchange capacity, the degree of saturation, as well as K + , Na + , Mg ++ and Ca ++ contents.The hereby study is based on soil samples harvested between years 2000 and 2012 from 4,500 profiles and 9,523 horizons.
Analyses were performed by INCDS Bucharest, which implemented its own quality assurance system (e.g.10% of samples were processed blind) and quality control, including regular participation in the European inter-calibration exercises of the FutMon Project (Cools and De Vos, 2009).The preparation of soil samples was based on the ISO 11464 method (ISO, 1994).Soil samples were air-dried to constant weight and were then grounded and sieved through a 2-mm sieve to obtain the fine-earth fraction (Cools and De Vos, 2010) for laboratory analysis, which was stored until chemically analysed.The organic carbon was established using a dry combustion method and an automatic LECO Tru Spec CN Analyser.
Currently, the SOC stock for a given soil stratum is estimated by extrapolating the SOC content per soil mass to the SOC pool per soil volume, obtained by multiplying the SOC by soil bulk density and soil layer depth.However, this approach does not take into account the variation in soil bulk density between soils (Balesdent, 1996), which might be a source of errors when soils with very different bulk densities are compared.To eliminate this problem, different soil density values have been used, based on the soil type and standard depth.Thus, to calculate the quantities of organic carbon accumulated in different types of soils, according to the method described by Batjes (1996), the values for each soil type were multiplied by the bulk density and the standard depths.Therefore, the following formula was used: ) where C-stockmin is the C stock in the mineral soil (kg/m 2 × 10 = t/ha), d is the depth class/horizon thickness (m), C-conc is the concentration of organic carbon (g/kg), BD is the bulk density (kg/dm 3 ) and CFst is the correction factor for stoniness.
Bulk density can be estimated using pedo-transfer functions.A typical example of a pedo-transfer function is the Adams (1973) equation: where %OC is the percentage of total organic carbon and MBD is the mineral bulk density (usually estimated at 1.33 kg/m 3 or determined based on the 'Mineral Bulk Density Chart' developed by Rawls and Brakensiek, 1985).

Calculating organic C stock on pedogenetic horizons (Method 1)
The values obtained for organic C and bulk density were arranged according to soil types and pedogenetic horizons and the mean values were then calculated for minimal depth, maximum depth, organic C and bulk density.Based on these values and by applying the first formula (1), the organic C stock to a maximum depth of 1 m was obtained.carbon content and the estimates of area for each category (Davidson and Lefebvre, 1993), regional studies are necessary to refine global estimates obtained by the aggregation of regional estimates, mainly at a country scale (Bernoux et al., 2002).Don et al. (2011) reported the worldwide mean SOC stocks to be 106 Mg C ha -1 (up to 1 m depth), while Gorte (2009) reported it to be 68.75Mg C ha -1 (1 m depth) in tropical forests.Hoffmann et al. (2014) reported a mean of 64 Mg C ha -1 to a depth of 30 cm in the Rocky Mountains of Alberta, Brahim et al. (2010) reported a mean of 71.4 Mg C ha -1 and 101 Mg C ha -1 SOC stocks to the depth of 100 cm in Spain and Tunisia, respectively, while Woollen et al. (2012) found a mean SOC stock to the depth of 40 cm of 40.1 Mg C ha -1 for the Miombo woodlands in Mozambique.
According to Rojas et al. (2012) for soils of Southern Spain and Batjes (2002) for soils of Central and Eastern Europe, cambisols have higher SOC stocks than fluvisols and leptosols.
In Serbia, Kadovič et al. (2012) studied the regression dependence between carbon content and soil depth and found a modest correlation for dystric brown soils (25 profiles) and a strong correlation for eutric brown soils (31 profiles) and for eutric rankers (12 profiles).
In Romania, Dinca et al. (2012) have established the stocks of organic C in forest soils, based on data from forest management activity.This information was collected from pedogenetic horizons, but was translated to standard depths.
Studies in different parts of the world by Hoffmann et al.  (2007) and Yoo et al. (2006) established that the SOC stock increase with an increase in elevation.This has been explained by variations in dominant vegetation types and species richness with elevation (Yao et al., 2010;Giliba et al., 2011;Grand and Lavkulich, 2011;Sreekanth et al., 2013).Studies by Cambule et al., (2014) in Mozambique, Wiesmeier et al., (2012) in Germany and Aticho (2013) in Ethiopia have reported soil thickness to be among the important factors that affect SOC stocks.However, Xiaojun et al. (2013) and Wang et al., (2012) in China, Karchegani et al., (2012) in Iran, Fantappiè et al. (2011) in Italy, Djukic et al., (2010) in the Alpine region and Koulouri and Giourga (2007) in the Mediterranean region, reported the slope gradient also to be an important factor in determining spatial and temporal variation in SOC stocks.
As shown in Equation 3.2.16from IPCC Good Practice Guidance for LULUCF, the total SOC content is obtained by summing the SOC contents of the constituent soil horizons or layers; the SOC content of each horizon or layer is calculated by multiplying the concentration of soil organic carbon in a sample (g C kg soil -1 ), by the corresponding depth and bulk density (mg m -3 ) and adjusting for the soil volume occupied by coarse fragments.
The calculations initially appear to be simple, but when they are performed problems appear because the soil samples have often been extracted from different depths.Therefore, the authors propose the identification of an optimal calculation method of organic C stocks for the mineral part of forest soils by comparing and analysing the results obtained from 6,334 values of organic C from Romania's forest soils using three different calculation methods.
Calculating organic C stock on standard depths (Method 2) The database was further structured according to soil type (following Romanian nomenclature, adopted from the FAO) and standard depths (e.g.0 -10 cm; 10 -20 cm; 20 -40 cm; > 40 cm), following European monitoring activity procedure (Cools and De Vos, 2010).
The values of organic C and bulk density corresponding to the harvesting depths of the soil samples were distributed within one of the standard depths mentioned above.The calculations were thus similar to those of Method 1.
When the total organic C stock was calculated, the total depth of soil profiles was taken into consideration.For example: 70 cm for a rendzic leptosol, 80 cm for an entic podzol, etc.

Calculating organic C stock using regression equations (Method 3)
The regression equation between the quantity of organic C and the harvesting depth was calculated for each soil type (since only one value is required, but an interval was registered during harvesting, the middle of this interval was taken; for example, for a sample harvested between 5 and 15 cm, the mean value was 10 cm).A logarithmic equation was used for the regression equation, because it is closer to the real variation of the registered values (Fig. 1).
For each equation, the organic C quantity was established at depths from 10 to 100 cm, until the depth of 1 m (e.g. 5 cm, 15 cm, 25 cm, 35 cm, 45 cm, 55 cm, 65 cm, 75 cm, 85 cm and 95 cm).For superficial soils, the calculation depth was that established within Method 2.
Based on these values and the corresponding values for bulk density, the organic C stock was calculated for all forest soils within Romania.The formula used was the following: C stoc = Cconc5 cm x BD5 cm x 1 (depth in dm) + Cconc15 cm x BD15 cm + Cconc25 cm x BD25cm+... (3)

Calculating organic C stock on pedogenetical horizons
The values obtained for organic C and bulk density were arranged according to soil types and pedogenetic horizons and the mean values were then calculated for minimal depth, maximum depth, organic C and bulk density.Based on these values and by applying formula (1), the organic C stock to a maximum depth of 1 m was obtained (Table 1).
Calculating organic C stock on standard depths When the total organic C stock was calculated, the total depth of soil profiles was taken into consideration.The obtained results are presented in Table 2.  Calculating the organic C stock with the help of regression equations By calculating the variation and standard deviation for Method 1 (calculating organic C on horizons) and for Method 2 (calculating organic C on depth), values were very similar in the superior horizons, respectively Ao and the 0-10 cm layer.However, progressing to inferior horizons, the differences became larger (e.g. for andosol, the standard deviation in the Au horizon was 39.1 (Method 1), whereas it was 38.8 in the 0-10 cm layer (Method 2).As the depth further increased, the differences became even larger, thus for the Bv horizon, the standard deviation was 17.9 (Method 1) and for a depth of 10 -20 cm it was 11.2 (Method 2); in the 571 A/R horizon it was 21.1 (Method 1), whereas at a depth of 20 -40 cm, it was 9.7 (Method 2).
Using Method 2, the variations and standard depths were smaller as the soil depth increased in comparison with those from Method 1 from the inferior horizons.Thus, the data were more homogenous for Method 2.
To calculate the total organic C stock, the total depth of soil profiles established by Methods 1 and 2 were considered.The results based on the regression equations are shown in Table 3.

The correlation between the quantity of organic C and the sample harvesting depth
The lowest correlations between the quantity of organic C and the sample harvesting depths (although no values were significant) were recorded for rendzic leptosol (due to the variability of organic C at the depth of 20-40 cm), haplic podzol (due to the variation in soil profile, with a decrease in the Es and an increase in Bhs horizons, which means a different curve to a logarithmic one) and for fluvisol (due to the great variability in the amount of slime material that also contained variable quantities of organic C).The strongest correlation was recorded for acid soils (umbric-entic podzol, alosol, entic podzol etc.) (Fig. 2).

Main aspects regarding the approach of different organic C stock calculation methods
Problems encountered for Method 1 (calculating the organic C stock on pedogenetical horizons) refer to several aspects:  -The framing limits of a horizon can lead to significant errors.For example, if for eutric cambosols, based on diagnostic criteria, it was considered that the Ao horizon has a mean depth of 10 cm, whereas the total reserve of organic C was 155 t/ha, while for Ao the medium depth was 20 cm and organic C reserve was 186 t/ha; -The mean limits for framing successive soil horizons do not follow exactly sequentially from one another.For example: El = 10 -45 cm, Bt = 32 -85 cm.This problem does not exist for soils where the horizons do not have variants of soil subtypes.For example: haplic luvisol, Ao = 0 -8, El = 8 -39, Bt = 38 -89; -The dimensional framing of A/B transition horizons.In many cases, the transition between horizons was trenchant (A, B), but when transition areas were present (A/B), the dimension of these horizons can partially or totally overlap with A or B horizons; -Some horizons from the soil subtypes cannot be properly framed as profile depths (because they overlap on other horizons).For example: the G horizon from gleic fluvisol overlaps with the C horizon; -The absence of samples for great depths (e.g.depths > 8 cm for stagnosol).
Aspects encountered applying Method 2 (calculating the organic C stock on standard depths) may be as follows: -The correct framing on depths for 0 -and 10 -20 cm; e.g.Corg = 20.4 for 0 -20 cm at dystric cambosol, can also be framed at 0 -10, as well as at 10 -20 cm; -The main advantage of this method was that by analysing each value, a better repartition could be realised concerning the harvesting depths, thus modifying the errors that occurred from estimating the depths; e.g.C = 8.9 recorded in the field for a dystric cambosol at a depth of 0 -6 cm was, in reality, somewhere between 10 -20 cm; -The large volume of work needed for framing each organic C value on certain standard depth may be a problem when applying this method.
Problems encountered for Method 3 (calculating the organic C stock using regression equations): -The wrong estimate of the harvesting depth can lead to significant errors.For example, the value of 48.3 for the depth of 0 -25 might be recorded as 12.5 cm, whereas in reality, it can be harvested at a depth of 5 cm; -The main advantage is that this method renders the carbon stock precisely at the harvesting depth of the samples (for example: 35 cm and not the B horizon in Method 1, or 20-40 cm in Method 2), assuming that the harvesting depth was measured very accurately; -At some depths (80 -100 cm), negative values of organic C quantity can sometimes appear (in alosols or haplic luvisols), due to the regression equation.These values should not be taken into consideration, because the loss of organic C from these calculations is minimal.

Comparison between the methods
Greater values were always obtained in the current study from Method 1 (calculating the organic C stock on pedogenetical horizons) than from Method 2 (calculating the organic C stock on standard depths) (Table 4).These differences were more significant for soils rich in organic C (andosols, umbric-entic podzols, humic umbrisols or haplic podzols).This situation might be caused by the predominant harvesting of soil samples from the superior part of horizons that are thicker and due to uneven distribution in the case of two samples from the same horizon (Fig. 3).
Thus, calculating the C stock on pedogenetical horizons leads to an overestimation of the stock (Fig. 4).
For soils with a strong decreasing curve (based on correlation between organic C -soil depth) the differences were very small, whereas for soils with a flattened curve, the differences were greater.The flatter the curve was at higher values for greater harvesting depths, the larger were the differences (rendzic leptosol).
For many analysed samples, the correlation between the sample harvesting depth and the stock of organic C was significant for all types of soil.However, lower correlation coefficients were observed for rendzic leptosol (due to the large variability in organic C quantity at depths of 20-40 cm), haplic podzol (due to variation in the soil profile, with a decrease in the Es horizon and an increase in Bhs), and fluvisol (due to the great variability of slime material that also contains variable amounts of organic C).
Advantages for each method used within the current study are as follows: -Method 3 allows a mean curve to be realised for all the points; it is recommended to realise arithmetical means for some depths; -The chosen depths within Method 2 (0 -10, 10 -20, 20 -40 and 40 -100 cm) corresponded to different variations in the quantity of organic C: a strong decrease for the first two intervals and a low decrease for the subsequent intervals; -For Method 2, the number of intervals for which the organic C stock was calculated increased.For example, for dystric cambosol, Method 1 used three intervals (Ao, Ao/Bv, Bv), whereas the second method generated four intervals (0 -10, 10 -20, 20 -40, 40 -100 cm), thus offering more reliable data; -Within Method 3 it was assumed that the soil sample was homogenous throughout the entire harvesting depth (for example, for 20-40 cm, a similar soil quantity should be taken throughout the mentioned interval, when in reality, the quantity is taken only from the upper part).This leads to an overvaluation of the carbon stock; -By applying Method 2, possible errors in writing harvesting depths can be identified.An example of adjustment: the C org = 24.4 between 5-85 cm, with a mean of 45 cm, but in reality sample was harvested at a depth between 10-20 cm (the entire thickness of the horizon was recorded, but the sample was harvested only from the upper part);  -For some soils, regardless of the number of soil samples harvested, the correlation coefficient for the curves established through Method 3 was low due to some properties of these soils.However, Method 3 is easier to apply, because Method 2 requires the establishment of each value to a standard depth, which implies a long time and a lot of effort.

Conclusions
Calculating the stock of organic carbon based on pedogenetic horizons, as well as the method using regression equations led to considerable overestimation of this stock.Taking into consideration that the harvesting of soil samples was not uniform for some depth intervals, and that by distributing organic C quantities on standard depths, more categories were obtained than by registering these values on pedogenetic horizons, it can be concluded that the best method for evaluating the organic C stock is one that distributes the obtained values onto the following standard depths: 0 -10 cm; 10 -20 cm; 20 -40 cm; > 40 cm.Method 2 (using standard depths) was more accurate for evaluating the organic C quantity, because the variation and standard deviations were lower compared to those obtained from Method 1 (based on pedogenetic horizons) for most all the studied soil types.Even so, depending on the samples and the procedure during harvesting, all methods present different criteria which correspond to various results and have therefore objective representations of the data collected.

Fig. 1 .
Fig. 1.The regression equation between the quantity of organic C and the harvesting depth of soil samples, for a haplic luvisol

Fig. 2 .
Fig. 2. The variation in organic C within soil harvesting depth (samples of different forest soils)

Fig. 3 .
Fig. 3. Harvesting soil samples in the case of thicker horizons (left-the present work method, right-the standard method).The colour black is used to show the location of sample harvesting

Table 1 .
Organic C stock calculated on pedogenetical horizons

Table 2 .
Organic C stock calculated on standard depths

Table 3 .
Organic C stock calculated using regression equations

Table 4 .
Results and differences between the tested methods