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Assessing ﬁxed depth carbon stocks in soils with varying horizon depths and thicknesses, sampled by horizon Alina Premrov a,⁎, Thomas Cummins a, Kenneth A. Byrne b a b

UCD School of Agriculture and Food Science, University College Dublin, Belﬁeld, Dublin 4, Ireland Department of Biological Sciences, School of Natural Sciences, University of Limerick, Limerick, Ireland

a r t i c l e

i n f o

Article history: Received 1 July 2016 Received in revised form 23 November 2016 Accepted 29 November 2016 Available online xxxx Keywords: Soil organic carbon stocks Soil horizon Soil depth Forest mineral soil Trapezoidal computing approach

a b s t r a c t Soil surveys for improving carbon (C) stock estimates frequently involve soil sampling by pre-determined regular depth-intervals, in order to enable more convenient computation of soil organic carbon (SOC) stocks. As a result, soil horizons are often neglected in these surveys, although they represent distinct components of the soil proﬁle. When soil-horizon depths and thicknesses vary considerably within the same site, soil sampling by horizon with accompanying depth measurements may be more suitable. The main objective in this study was to investigate the potential differences in current SOC stocks in different afforested mineral soils, with varying horizon depths and thicknesses, and that were sampled by soil horizon, by using the trapezoidal SOC stock computing approach, and comparing it to the spline approach. An adaptation of the trapezoidal rule computation approach, enabling relatively simple crude estimations of the ﬁxed depth-interval SOC stocks from horizon data, was developed. Estimations of SOC stocks for 18 sites located on three different afforested mineral soils (Gleys, Podzols and Cambisols, aged ≥20 years) were done for 0–30 cm, 30–60 cm and 0–60 cm ﬁxed depth-intervals, excluding surface organic layers. The results indicate that the trapezoidal approach is likely to provide cruder estimates of SOC stocks than the spline approach, although no statistically signiﬁcant differences were observed between the ﬁxed depth-interval SOC stocks (for 0–30 cm and 30–60 cm) when computed by the two methods. Both methods showed a signiﬁcant effect of horizon and soil group on SOC stocks. The soil below the 30 cm depth was estimated to store over 22% of the total SOC stocks to 60 cm depth. Gleys showed signiﬁcantly greater mineral SOC stocks than Podzols, with differences mainly evident in the upper 30 cm, which was observed regardless of the computing methodology used (trapezoidal or spline). The adapted trapezoidal rule computing approach is hoped to facilitate the use of soil-horizon sampling in studies on SOC stocks. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Forest soil surveys which include C stock monitoring are becoming increasingly important due to greenhouse gas emissions reduction targets at national and international level, as well as assessing the role of forest soils in mitigating such emissions. The soil represents the largest terrestrial organic carbon (C) pool, globally estimated at 1115 · 109–2200 · 109 tC (Batjes, 1996). The total world soil organic carbon (SOC) stock of the upper 30 cm soil depth is estimated at 684 · 109– 724 · 109 tC, and for the upper 100 cm at 1462 · 109–1548 · 109 tC (Batjes, 2014). In particular, forest soil represents an important terrestrial organic C stock. The estimated soil C stock up to 100 cm depth for worlds forests is c. 383 ± 30 · 109 tC (Pan et al., 2011). According to Jobbágy and Jackson (2000), the global SOC storage of different temperate forests for 0–100 cm depth can be estimated in the range 73 · 109– 122 · 109 tC. Soil surveys, which aim to improve the estimates of soil C ⁎ Corresponding author. E-mail address: [email protected] (A. Premrov).

http://dx.doi.org/10.1016/j.catena.2016.11.030 0341-8162/© 2016 Elsevier B.V. All rights reserved.

stocks, frequently involve soil sampling to 30 cm depth or even less, and with soil sampling often performed by pre-determined regular soildepth intervals (Baritz et al., 2010; Cools and De Vos, 2010; UNECE, 2006). Shallow-depth sampling is often used in soil studies due to difﬁculties and costs associated with soil sampling at greater depths, as well as due to expectations that deeper soil horizons are more stable and less likely to change over the time although not all studies support this (Harrison et al., 2011). Soil sampling at shallow depths can result in an underestimation of C present in the soil proﬁle (Harrison et al., 2011). Although deeper subsoil horizons are known to have relatively low C content they should still be accounted for in the C-cycle (Rumpel and Kögel-Knabner, 2010). Also, soil sampling is often performed by pre-determined regular soil-depth intervals - e.g. at 10 cm depth-intervals, from a soil proﬁle, for forest soils (Stolbovoy et al., 2005; UNECE, 2010). The advantage of such pre-determined regular depth sampling is that it can enable relatively simple computation of a variable of interest, such as SOC stocks to a speciﬁc depth (Stolbovoy et al., 2005). This can be done by e.g. soil-depth normalisation (Freier

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et al., 2010), or by summing the calculated C stocks of the pre-determined regular depth-intervals (Lee et al., 2009). As a result of soil sampling by regular depth-intervals, soil horizons are often neglected in SOC stock surveys, even though they represent distinct components of the soil proﬁle. In order to increase the accuracy of SOC stock estimations, and clarify the effects of pedogenic processes on the storage of SOC, Wiesmeier et al. (2012) recommend that SOC inventories should have the soil analysis completed by horizon instead of by ﬁxed depth increments. Where the soil-horizon depths and thicknesses vary considerably within the same site, errors in C stock estimations may be generated if the differences in horizon thickness are not taken into account. These errors could be potentially omitted by e.g. excavating more soil pits at different locations within the same site, but this would require more labour-intensive procedures, and would consequently increase the cost of sampling and its duration. Field methods often need to be adapted in order to reduce the costs and to be feasible within limited project resources. Furthermore, soil pit excavation can also be especially challenging for forest soils due to potentially remote locations, rocky, difﬁcult and steep terrain, the presence of coarse roots, and use of manual methods because of other constraints. In cases when soil-horizon depths and thicknesses can vary within the same site, and when excavation of more soil pits is not an option, sampling by horizon with horizon-boundary depth measurements may be a more suitable approach (Premrov et al., 2014). However, such sampling may require more demanding computation procedures: e.g. due to differences in thicknesses among sampled horizons at different sampling points, separate computations of C stocks for the chosen ﬁxed depth-interval are required, taking into account the horizon thicknesses from sampled points, separately for each site. The approach taken in this study was to develop an adaptation of a trapezoidal rule computation by Lord and Shepherd (1993) that would allow relatively simple estimation of ﬁxed depth-interval SOC stocks for soils with varying horizons and depths, and to compare it with the more complex spline computation method based on the equal-area quadratic smoothing spline modelling explained by Bishop et al. (1999). Area-based SOC stocks were to be estimated by adapting the computation approaches in a way that would enable the use of the soil-horizon thicknesses and horizon volume-based C stocks (mass C per volume of soil), and would at the same time also account for varying number of samples obtained for each horizon. The main objective of this work was to investigate the differences in current SOC stocks in different mineral soils with varying horizon depths and thicknesses that were sampled by horizon, by using the adapted trapezoidal SOC stock computing approach, and comparing it with the more complex spline approach. Speciﬁc aims were to investigate the potential differences in SOC stock by soil group (in three Irish afforested mineral soils: Gleys, Podzols and Cambisols), by horizon, and by soil depth (0–30 cm, 30– 60 cm and 0–60 cm ﬁxed depth-intervals excluding surface organic layers). 2. Materials and methods 2.1. Field sites and sample speciﬁcations Eighteen afforested sites were sampled between March 2014 and March 2015 across the Republic of Ireland (Fig. 1a) as a part of the larger CForRep project (CForRep, 2013; http://www.ucd.ie/cforrep/), with sites being selected from Ireland's National Forest Inventory database (National Forest Inventory, 2012), after pre-screening the database for afforested sites located on selected mineral soils, and aged ≥ 20 years (Premrov et al., 2015). The CForRep project used the general Irish soil classiﬁcation, where the sites were classiﬁed into Podzols and peaty Podzols (Po and peaty Po), Brown Podzolics (BP), Acid Brown Earths (ABE), calcareous Brown Earths (BE) and Gleys (G) (Black et al., 2014; Gardiner and Radford, 1980). The sites were classiﬁed individually (on

site), and were further re-grouped into the three main soil groups: Gleys, Cambisols and Podzols. Po, peaty Po and BP were grouped as Podzols, ABE were assigned to Cambisols (Reidy et al., 2014), there were no sites with BE in this study, while classiﬁcation of Gleys remained unchanged. Gleys included sites with Stagnosol and Gleysol soils according to the World Reference Base for Soils (WRB) classiﬁcation (IUSS Working Group WRB, 2015), or Surface Water Gley and Typical Groundwater Gley, respectively, according to the Irish soil subgroup classiﬁcation (Reidy et al., 2014). Site locations are presented in Fig. 1a. Six sites were sampled in each soil group giving in total of 18 sampled sites (each site included sampling from a soil pit for bulk density measurements, as well as auger sampling from up to nine points on a 3 × 3 grid; further details are explained in Section 2.2). The woodland tree species were mainly determined on site but were later classiﬁed into three major woodland-type categories of coniferous, broadleaf and mixed. Mineral-soil horizon designation was also done on-site according to the FAO (2006) guidelines for master horizons, but the speciﬁc horizons were later grouped into ﬁve major categories [A, E, B, B2 and BC, where B2 refers to the second, often more water-saturated B horizon (e.g. Bg horizon), found in Gleys]. 2.2. Sampling methods Each site was positioned with a hand GPS (Geographic Positioning System) instrument, and the slope (in degrees) was measured with a clinometer at the central point. Soil sampling was performed at nine points (on a 3 × 3 grid over 20 × 20 m; Fig. 1b), up to 60 cm depth, by horizon. Organic forest-ﬂoor and peat horizons were also sampled under the CForRep project, but were not included in this study on mineral soil horizons. Soil samples for bulk-density measurements were collected from each horizon separately for each site, from a soil pit located in the centre of the sampling grid (Fig. 1b, c). Bulk-density sampling was performed either with 100 cm3 coring rings, or by the excavation method (i.e. excavation of soil material and replacement by sand, adapted from ISO (1998)) where the volume of excavated (replaced) material was determined on-site using ﬁne sand 300–600 μm in size. For bulk-density ring-sampling, a hammering-head for sample rings (Eijkelkamp, The Netherlands) was used to avoid compression. Where possible, the bulk-density sampling was done from the centre of each horizon, from up to three sides of the soil pit (Fig. 1c). Exceptionally, the two Gley sites in this study had missing bulk-density samples for a single soil horizon; measurements obtained from the most-similar horizon from the same site (of the same soil-horizon category) were used as replacements (i.e. a missing value for a Bg horizon that was under watertable was replaced with the Bg horizon sampled at that same site, but above the water-table; at another site a missing value for Bg(a) horizon was replaced with Bg horizon sampled at that site; details are provided in Fig. 4). Percentage coarse material was estimated on-site, from the soil pit, according to the FAO (2006) guidelines for soil description. Horizon samples for SOC analysis were taken with an Edelman auger (Eijkelkamp, The Netherlands), accompanied by the horizon depth measurements (depths to upper and lower boundary). Sampling was performed from up to nine sampling points (each arbitrarily located within one cell of the 3 × 3 sampling grid, Fig. 1b). The entire thickness of each soil horizon was sampled at each sampling point, and the samples from each horizon were bulked together into one composite soil sample by horizon, separately for each site. In order to minimize potential cross-contamination between horizons, the individual sampling by horizon from each sampling point was done by ﬁrst placing each separate augered soil material onto a clean tray. This was done with a special care not to disturb the sequence of the augered material. The material on the tray was then carefully separated into individual soil horizons. All collected soil samples were transported in cool-boxes and stored in a cold-room at 4 °C until further laboratory-processing and analysis. A total of 510 soil samples were collected from the eighteen afforested

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Fig. 1. Schematic presentation of site locations and soil sampling approach (a) site locations - not to scale; (b) composite soil sampling (per horizon) by arbitrary-choosing the sampling point within each sampling grid cell; (c) bulk-density soil sampling from a central soil pit. Note: (a) schematic illustration of the country-border was created with the help of R 3.2.3 (R Core Team, 2015) and R packages “maptools” (Bivand and Lewin-Koh, 2015) and “mapdata” (Becker and Wilks, 2016); (c) presented is one side of soil pit (at central grid-location V), sampling included up to three-sides of soil pit.

sites: 126 samples for bulk-density determination and 384 soil samples from the sampling grids (Fig. 1). Bulking of soil samples from individual sampling points (by horizon, separately for each site) resulted in total 50 composite soil-horizon samples. 2.3. Laboratory methods Bulk-density soil samples were oven-dried at 105 °C for N 16 h, in order to obtain their dry weights (adapted from ISO, 1998). Coarse material (N 2 mm) was separated from ﬁne-earth material (b 2 mm) by dry-sieving, followed by re-drying of coarse material at 105 °C for N16 h, in order to obtain its dry weight. Volume of coarse material was measured by water-displacement (by submerging the coarse material into a graduated cylinder ﬁlled with water). Processing of composite soil samples involved: bulking of individual horizon soil samples, separately for each site (to form a composite sample, in the minority of cases where this was not already done on-site); separation of live biomass; hand-crushing of soil-clods; mixing; and preliminary drying at 40 °C. Dry soil was packed and stored at ambient room conditions, to be used for further processing and laboratory analyses. Laboratory subsampling was done carefully by hand-mixing and -quartering in several steps (adapted from ISO, 2006). The air-moisture content was determined by drying 5 g of sample (ﬁne-earth b 2 mm obtained by sieving) at 105 °C for N16 h until dry (adapted from ISO, 1993). Composite soil samples were tested for pH on 2.5 mL ﬁne-earth: 12.5 mL distilled water soil-suspension (adapted from ISO, 1995; NSAI, 2011), which showed pH b 6.5. Therefore, it was assumed that the soil from the eighteen sites used in this study did not contain carbonates (ISO, 1995), and the samples were not treated for carbonate-removal. Elemental C analysis on composite soil sub-samples was performed on a CE440 Elemental CHN Analyser (Exeter Analytical Inc.), after ﬁrst homogenising the material by ﬁne milling using Mixer Mill MM200 (Retsch GmbH) and/ or Planetary Mono Mill Pulverisette 6 (Fritsch GmbH).

2.4. Computational methods The SOC stocks are expressed as volume-based SOC densities, in units of mass of C per volume of soil, and area-based SOC densities, in units of mass of C per area of soil for the speciﬁc ﬁxed soil depth-interval. Average horizon thicknesses, including average horizon starting-, ending- and horizon mid-depths were calculated separately for each site from the measurements obtained from the 3 × 3 sampling grid at the site (in continuation the average thickness was named as thickness, and the average mid-depth as mid-depth).The ﬁxed soil depth-intervals were named as follows: “shallow” (0–30 cm); “deep” (30–60 cm), and “total depth” (0–60 cm). 2.4.1. Estimating volume-based organic carbon densities for individual horizons The volume-based SOC density (SOCVD) of an individual soil horizon was calculated using the SOC content (dry mass-based C percentage) measured from the composite horizon sample, the corresponding horizon bulk-density of ﬁne-earth fraction taken from the soil pit [g soil/cm3], and the volume-based percent of stones (coarse fraction, also estimated from soil pit), as follows: SOCVD ¼ %C=100 ρ f CCF or SOCVD ¼ %C=100 ðmtot −mcoarse Þ=ðV tot −V coarse Þ CCF

ð1Þ

where SOCVD is the volume-based SOC density of the horizon [gC/cm3]; %C is the C content in the ﬁne earth (b 2 mm) from the composite horizon sample obtained as a dry mass-based percentage C content for oven-dry soil at 105 °C (UNECE, 2006; ISO, 1995); 1/100 is the conversion factor for converting percentage C to gC/g soil; ρf is a soil bulk-density of ﬁne-earth material b2 mm [g soil/cm3] [calculated as (mtot − mcoarse) / (Vtot − Vcoarse)]; mtot [g] is the total dry-mass (at 105 °C) of

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the whole bulk density sample; mcoarse [g] is the dry-mass (at 105 °C) of coarse fraction (N2 mm) obtained after sieving the material from the bulk density sample; Vtot [cm3] is the volume of the whole bulk density sample (e.g. 100 cm3 if sampled by core-ring); Vcoarse [cm3] is the volume of the coarse fraction (N 2 mm) obtained by displacement after sieving the material from bulk density samples; CCF is the coarse fraction correction factor, calculated as ((100 - %stones) / 100) (Baritz et al., 2010; Kessler et al., 2012), where %stones represent the volumebased percentage of coarse material estimated from the soil pit. 2.4.2. Estimating soil organic carbon stocks for ﬁxed depth-intervals using an adapted trapezoidal rule approach Area-based soil organic carbon stocks (SOCS, tC/ha) for ﬁxed depthintervals were ﬁrst estimated with a so-called trapezoidal rule computing approach, adapted from Lord and Shepherd (1993), who used it for calculating soil-solution nitrate leaching losses. The trapezoidal rule was adapted using SOCVD [Eq. (1)] expressed as the mass of C per volume of soil [gC/cm3], and the corresponding horizon thicknesses [cm], with the inclusion of the probability weights (IDRE UCLA, 2016) for each soil horizon, as follows: SOCSa−part I ¼ 0:5 ðSOCVDa0 þ SOCVDa Þ na =n La =2 100

ð2aÞ

SOCSa−part II ¼ 0:5 ðSOCVDa þ SOCVDb0 Þ na =n La =2 100

ð2bÞ

where ‘a’ and ‘b’ subscripts refer to two adjacent horizons; SOCSa-part I is carbon stock computed from horizon start to its mid-depth or La/2 (Fig. 2a); and SOCSa-part II is stock computed from horizon mid-depth to its end (or the start of the next horizon; Fig. 2a); La is thickness of ‘a’ horizon [cm]; SOCVDa0 value [gC/cm3] refers volume-based soil organic carbon density at the starting depth of ‘a’ horizon, and SOCVDb0 at the starting depth of next ‘b’ horizon; SOCVDa refers to carbon density at horizon mid-depth (obtained from composite ‘a’ horizon sample); na/n is the probability weight for horizon/layer ‘a’ where na represents the number of points where the soil horizon/sample ‘a’ was present out of total number of sampled/augered points n (i.e. n is 9 if all of the points from 3 × 3 grid were augered; similarly, the probability weight nb/n applies for next horizon ‘b’ when computing the carbon stocks for next b-horizon, etc.); 100 is the conversion factor for converting the SOCS units [from gC/cm2 to tC/ha]. This adaptation of trapezoidal rule formulae was applied because the horizons were often absent at some sampling locations and present at some other locations at the same site, resulting in varying number of samples obtained for each composite horizon sample that was accounted for in the computation of SOCS by applying the corresponding probability weights (IDRE UCLA, 2016).

Fig. 2. Schematic presentation of the adapted trapezoidal rule calculation approach for estimating soil organic carbon stocks (SOCS) in units of mass C per area for required soil horizons and ﬁxed depth-intervals [ﬁctive example]: (a) simpliﬁed C stock estimation approach for mineral soil horizons (labelled with a, b, c, etc.), including crude linear regression estimation of the “starting” SOCVD at zero depth (used in this study); (b) scenario that accounts for organic layers/horizons (not included in this study).

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SOCS of whole ‘a’ horizon was computed by summing SOCSa-part I and SOCSa-part II: SOCSa ¼ SOCSa−part I þ SOCSa−part II

ð3Þ

where SOCSa is soil organic carbon stock [tC/ha] of whole thickness of ‘a’ horizon (La; Fig. 2). The estimated SOCS for the total ﬁxed depth-intervals (“shallow”, “deep” and “total”) were next calculated by summing the SOCS of individual horizons, as follows:

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computed for each horizon/horizon-section after applying the horizon sampling probability weights (as explained in Section 2.4.2), and summed up to ﬁxed depth-intervals (30 cm and 60 cm depth) according to Eq. (4). SOCSs were computed with approximate integration using 1 cm intervals. The spline-modelled SOCVD value at 1 cm depth was assigned as the “starting SOCVD” value at zero depth (Fig. 3), and in case if the sampling ceased before reaching the required ﬁxed depth, the “zero” SOCVD value was assigned to the “ending” SOCVD (as in Section 2.4.2). 2.5. Statistical analysis methods

SOCS ¼ ∑SOCSi

ð4Þ

where SOCSi refers to carbon stocks of individual horizons (i.e. SOCSa, SOCSb, etc. Eq. (3)) computed from their thicknesses (Eqs. (2a) and (2b)) between: 0–30 cm depth for “shallow”; 30–60 cm depth for “deep”, and 0–60 cm depth for “total” ﬁxed depth-interval (Fig. 2a). In case if the horizon was cut at the 30 cm depth, SOCSi of the corresponding horizon-section was included in Eq. (4) in order to compute the SOCS of “shallow” and “deep” ﬁxed depth-intervals (Fig. 2a). Fig. 2b represents a computing scenario that accounts for organic layers/horizons (not included in this study): organic layers are often thinner than mineral soil horizons and are assumed to have relatively constant SOCS throughout their thickness (e.g. area-based stock values obtained from frame sampling). In order to calculate the SOCS of ﬁxed depth-intervals, the SOCVD values at 30 cm and the individual horizon starting- and endingSOCVD values had to be estimated ﬁrst, for each site, using linear interpolation (Fig. 2a.) The “starting SOCVD” value of the ﬁrst mineral horizon at zero depth was estimated by applying linear regression to c. ﬁrst three horizon SOCVD points (if available) as presented in Fig. 2a, calculated using INTERCEPT Microsoft Excel function. The linear regression was chosen in order to simplify the estimation approach. Although this may result in potential error in the estimation of C-stocks, it was considered that non-linear model application (such as power or logarithmic regression) could also result in estimation errors of the “starting” SOCVD values. This issue may be potentially avoided in case if the “starting” SOCVD values would be known (measured): e.g. by sampling the ﬁrst few centimetres of the top mineral horizon. A “zero” SOCVD value (Fig. 2a), was assumed for the “ending” SOCVD at the ﬁnal sampling depth, as the sampling often ceased before reaching the required ﬁxed depth. This assumption was based on an expectation that sampling stopped due to high stone/rock content. It should be noted that this assumption can result in the potential underestimation of C stocks for the last horizon and the “deep” soil depth-interval, which needs to be considered when interpreting results, especially if the sampling stopped due to other reasons than the high stone/rock content. 2.4.3. Estimating soil organic carbon stocks for ﬁxed depth-intervals using a spline approach The second approach for estimating area-based soil organic carbon stocks (SOCS, tC/ha) for ﬁxed depth-intervals in this study was an already known spline approach, which is based on the equal-area quadratic smoothing spline modelling, explained by Bishop et al. (1999). Splines were ﬁtted to the data with the help of the “mpspline” function from package “GSIF” (Hengl, 2016) in R (R Core Team, 2015), using average horizon starting and ending depth values for each site, and the corresponding SOCVD values from the individual horizon composite samples (Eq. (1)). The parameter lambda (λ) for the “mpsline” function was set to 0.1 as in De Vos et al. (2015). The output obtained was the modelled spline in the form of SOCVD values at 1 cm depth-intervals. In order to be able to compare the spline computing approach (dashed curve in Fig. 3) with the trapezodial approach (“trapezodial” line in Fig. 3), each spline was next split into separate horizons (or horizonsections up to 30 and 60 cm ﬁxed depth-intervals). The SOCSs were

Statistical analysis was performed in R 3.2.3 (R Core Team, 2015) and selected R-packages. Detailed description is provided in sections below. 2.5.1. Statistical analysis of volume-based soil organic carbon densities The differences in horizon SOCVD results [gC/cm3] were assessed by applying linear mixed effects (LME) models followed by analysis of variance (ANOVA) (Fox and Weisberg, 2011). ANOVA Type III [Wald χ2 test], was chosen due to unbalanced horizon data-design (King, 2016). The LME models were ﬁtted via maximum likelihood (ML) (Pinheiro et al., 2016) to the natural logarithm (ln) transformed SOCVD values (ln transformation was used in order to achieve normality and homoscedasticity of the data). Non-weighted and weighed LME models were used, where the ﬁxed weighing was done using the measured number of soil bulk-density samples in order to specify that the residual variance for each horizon SOCVD value was inversely proportional to the number of sampled bulk-density samples per horizon at each site (Bolker, 2015). The “relative” SOCVD standard deviations (computed by standard deviation error-propagation (Caldwell et al., 2016), used in Fig. 4), were not used for LME weighing because they lacked the uncertainty of the SOC component, due to absence of SOC standard deviations from composite soil samples. A random effect was assigned to the site, and ﬁxed effects to the mid-depth, slope [measured in degrees and converted to radians], soil group [Podzols (P), Cambisols (C) and Gleys (G)], and woodland-type [Coniferous, Broadleaf and Mixed]. Variables slope, woodland-type and mid-depth (main effects and interactions) were later excluded from the analysis due to non-signiﬁcance, and the testing for the potential spatial non-independence of sampled sites was done on the ﬁnal LME model. Different spatial correlation structures were included and evaluated using the Akaike's Information Criterion (AIC). For this, a small random noise (of 0.5 m) was assigned to the measured GPS coordinates (due to coordinates repetition for data measured at the same site), which were ﬁrst transformed to Universal Transverse Mercator (UTM) coordinates (Bivand et al., 2015). The differences in SOCVD between different soil groups and horizons were further assessed using least-squares (LS) means (“lsmeans”) pairwise comparison t-tests derived from LME with results averaged over the horizon/soil group using weights proportional to their frequencies in the data-set (Lenth, 2016)). 2.5.2. Statistical analysis of soil organic carbon stocks The correlations between the area-based SOCSs [tC/ha], slope (in radians) and maximum depth of the soil depth-interval (30 cm for “shallow” and 60 cm for “deep”) were ﬁrst evaluated with the Pearson's correlation coefﬁcient matrix (Harrell et al., 2015). The SOCS results were next assessed by applying the LME models, followed by ANOVA Type II [Wald χ2 test] (Fox and Weisberg, 2011). LME was ﬁtted via ML (Pinheiro et al., 2016) to the square-root SOCS transformed results. The square-root transformation (SOCS)0.5 was used in order to achieve normality and homoscedasticity of the data. Analysis was ﬁrst performed on combined “shallow” and “deep” depth-interval data. A random effect was assigned to the site, and the ﬁxed effects to the soil group, depth-interval, slope, and woodland-type. The differences between “shallow” and “deep” depth-interval SOCSs were assessed after excluding variable woodland-type (due to non-signiﬁcance). Testing

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Fig. 3. Schematic presentation of the modelled spline (dashed curve, obtained from the spline approach) ﬁtted to the horizon volume based soil organic carbon density (SOCVD) data with accompanying average horizon starting- and ending-depths, and the “trapezoidal” line (obtained from adapted trapezoidal approach) for estimating soil organic carbon stocks (SOCS) for ﬁxed depth-intervals [ﬁctive example].

Fig. 4. Horizon volume-based soil organic carbon density (SOCVD) and corresponding horizon average mid-depth for Irish afforested Podzols, Cambisols and Gleys.

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for spatial auto-correlation of SOCS results was done using Moran's I statistics (Paradis et al., 2004), and by inclusion of different spatial correlation structures (as explained in Section 2.5.1). The differences in the SOCS results between three different soil groups were further assessed separately for “shallow”, “deep” and “total depth” data, by applying the models separately to each data-set. Differences between depthinterval and soil group SOCSs were assessed by applying LS means (“lsmeans”) pairwise comparison t-tests derived from LME models (Lenth, 2016).

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3. Results and discussion

(41.9–54.8 cm). In general, weighted LME models appeared to explain the data better than the non-weighted model (lower AIC). Spatial auto-correlation was not detected, which may be a consequence of a relatively small number of sites (eighteen sites) used in this study. Significant effect on SOCVD results was observed for both horizon and soil group, but not for mid-depth. The interaction mid-depth – horizon was also found to be not signiﬁcant (p N 0.1, ANOVA Type III Wald χ2 test). However, in case of absence of the horizon variable, the middepth did show a signiﬁcant effect on SOCVD results. Horizon appeared to explain the data better than mid-depth, which may be due to variations in horizon depths and thicknesses between different locations, and limited number of sites. The results showed statistically signiﬁcant difference in horizon SOVCD between Gleys and Podzols (Table 1), but not between the Cambisols and Gleys, or between Cambisols and Podzols. In Ireland Gleys are classiﬁed as poorly-drained mineral soils (Radford and Short, 2013), typically located in low-lying wet areas (Fay et al., 2007). If excluding peaty soils, Podzols, on the other hand, are well-drained soils typically located on hill-land areas (Radford and Short, 2013). There was a strong effect of horizon (p b 0.0001, Table 1) on SOCVD, where A-horizons (that had highest SOCVD) signiﬁcantly differed from almost all other horizons. Nevertheless, some other horizons, that were generally considered not to be in direct neighbouring sequence to eachother (within the soil proﬁle), also showed differences in SOCVD (Table 1). Considering that Gleys showed the greatest SOCVD in this study, and that they can be rich in clay, future investigations of the clayassociated organic substances and their potential relation to other factors, such as soil type, soil-physical properties, texture, and management (Leinweber et al., 1993) are recommended, in order to obtain further insights into the effect of horizons on SOC storage from this study.

3.1. Horizon volume-based soil organic carbon densities

3.2. Soil organic stocks of ﬁxed depth-intervals

Gleys had the greatest average horizon SOCVD: the average SOCVD was 0.029 gC/cm3 for Gleys, 0.027 gC/cm3 for Cambisols, and 0.017 gC/cm3 for Podzols (Table 1). A decrease in SOC density was observed from the top A horizons (0.047 gC/cm3), followed by E and B (0.019 gC/cm3 for E and 0.018 gC/cm3 for B), to B2 and BC horizons (0.011 gC/cm3 for B2 and 0.014 gC/cm3 for BC; Fig. 4, Table 1). The mid-depth for A horizons ranged from 3.8–13.8 cm, followed by E (6.6–26.5 cm), B (12.8–45.2 cm), B2 (29.5–51.4 cm), and BC horizons

The relationships between the area-based SOCSs results, slope and the maximum depth of soil depth-interval (i.e. 30 cm and 60 cm depth) that were assessed using Pearson's correlation coefﬁcient matrix, showed a signiﬁcant negative correlation between SOCS values and depth (with decrease in SOCS at greater depth), as expected, but no signiﬁcant correlation between SOCS and the slope. This result was observed for both SOCSs obtained via trapezoidal and spline approach. A signiﬁcant effect of slope that was only occasionally derived from

2.5.3. Statistical comparison of trapezoidal- and spline- computed soil organic carbon stocks The SOCS results obtained from trapezoidal and spline computing methods were compared using Welch two sample t-test (performed on transformed (SOCS)0.5, separately for “shallow” and “deep” depthintervals). In addition, the results were further assessed for separate depth-intervals, as well as for separate soil groups of “shallow” and “deep” depth-intervals, by obtaining 95% bootstrap conﬁdence intervals of (SOCS)0.5 means, based on the approach explained in De Vos et al. (2015), which assumes statistically signiﬁcant differences if conﬁdence intervals do not overlap. However, due to limited number of sites the bootstrap conﬁdence intervals were not used as an independent statistical testing in this study, but they were used merely for checking the ﬁndings in conjunction with the earlier statistical t-test. Calculations were performed with the help of function “boot” (with 5000 bootstrap replications) from R package “boot”, using the “boot.ci” function set to type “bca” for the adjusted bootstrap percentile interval (Canty and Ripley, 2016; Davison and Hinkley, 1997).

Table 1 Mean SOCVD and horizon mid-depth along with soil group (a) and horizon (b) comparisons using pairwise t-test derived from LME applied to ln-transformed SOCVD [signiﬁcant variables and contrasts are highlighted in bold]. (a) ANOVA type III, Wald χ2 testc e

p-Value

Soil groupdf2 Horizon df4

b0.05 b0.0001

Soil groupa

Mean |ln(SOCVD)| ± SD

P C G

|4.360| ± 0.840 |3.824| ± 0.686 |3.915| ± 0.930

Back-transformed mean SOCVD [gC/cm3]

Arithmetic mean SOCVD ± SDb [gC/cm3]

n

0.013 0.022 0.020

0.017 ± 0.014 0.027 ± 0.016 0.029 ± 0.025

17 16 17

LS means pairwise comparisond Comparing soil groups

t-Ratiodf17e

p-Value

C vs. G. C vs. P G vs. P

−0.90 1.91 2.70

N0.65 N0.17 b0.04

(b) Horizon

Mean mid-depth ± SD [cm]

Mean |ln(SOCVD)| ± SD

Back-transformed mean SOCVD [gC/cm3]

Arithmetic mean SOCVD ± SDb [gC/cm3]

n

Comparing horizons

p-Value [t-statisticsdf26e]

A E B B2 BC

9 ± 2.2 14 ± 8.5 31 ± 7.8 44 ± 7.9 49 ± 5.4

|3.125| |4.291| |4.166| |4.727| |4.638|

0.044 0.014 0.016 0.009 0.009

0.047 0.019 0.018 0.011 0.014

13 5 20 6 6

A vs. B, A vs. B2, A vs. BC

b0.0001

B vs. B2 A vs. E; B vs. E, BC; B2 vs. E; BC vs. E, B2

b0.05 N0.05

a

± ± ± ± ±

0.363 0.941 0.538 0.736 0.978

± ± ± ± ±

0.019 0.019 0.008 0.007 0.016

P - Podzols, C - Cambisols, G – Gleys. SD standard deviation without inclusion of error propagation. Derived from non-weighted/weighted LME applied to ln(SOCVD), with inclusion of ﬁxed effects (soil group, horizon) and random effect (site); the applied LME was also used for testing the potential presence of SAC. d Results (derived from LME) are averaged over the horizon/soil group using weights proportional to their frequencies in the data-set, and with the Tukey method p-value adjustment. e df - degrees of freedom. b c

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A. Premrov et al. / Catena 150 (2017) 291–301

LME models ﬁtted to separate soil depth-interval data (Table 2b and c) turned to be non signiﬁcant after excluding a single value for “deep” SOCS with the highest measured slope of c. 0.37 rad (the remaining sites all had slope b 0.21 rad). This indicates that the present study may not have sufﬁcient data for SOCS at higher slopes in order to investigate the effect of slope on soil C storage. The geo-statistical analysis on LME also showed no spatial auto-correlation, most likely due to limited number of sites; this was further conﬁrmed by Moran's I statistics. SOC content is generally known to decrease with soil depth. In agreement with this, the “shallow” mean SOCSs observed in this study were signiﬁcantly greater (p b 0.0001) than the “deep” ones (Table 2a). This was observed for both SOCSs obtained using trapezoidal and

spline computing approaches. The soil below 30 cm depth could store over 22% of the “total depth” SOCSs (Fig. 5a, b). These ﬁndings appear to be in general agreement with the total SOC content estimations based on the global soil database by Batjes (1996), who estimated the total of SOC content of the upper 100 cm mineral soil depth-interval at 39–70%, and the SOC content of the upper 30 cm at 58–81%. Nevertheless, the results from this study should not be generalised, considering the limited number of sites (eighteen) that has been used, and the maximum total sampling depth of only up to 60 cm. The mean “shallow” and “total depth” SOCSs were greatest in Gleys followed by Cambisols and Podzols (Fig. 5), whereas the mean “deep” SOCS values of the three soil groups were relatively close to each

Table 2 Mean SOCSs for ﬁxed depth-intervals and different soil groups along with comparisons between different main effects, derived from LME models applied to square-root transformed SOCSs (calculated by adapted trapezoidal- and spline- approach): (a) analysis on combined “shallow” and “deep” depth-interval data; (b) analysis on separate ﬁxed depth-interval data computed by adapted trapezoidal approach; (c) analysis on separate ﬁxed depth-interval data computed by spline approach [signiﬁcant variables and contrasts are highlighted in bold]. (a) Combined “shallow” and “deep” data ANOVA type II, Wald χ2 testa (Tr & Sp)c Main effectf p-Value b0.0001 Depth-interval df1 Soil groupdf2

b0.005

Depth-intervalc

Mean (SOCS)0.5 ± SD

Back-transformed mean SOCS [tC/ha]

Arithmetic mean SOCS ± SDe [tC/ha]

n

Sh (Tr) Dp (Tr) Sh (Sp) Dp (Sp)

9.150 5.342 9.342 5.205

83.7 28.5 87.3 27.1

91.0 31.7 95.1 30.4

18 18 18 18

± ± ± ±

2.781 1.824 2.871 1.867

± ± ± ±

50.46 20.29 53.64 20.29

LS means pairwise comparisong Dp vs. Sh Tr

t-Ratiodf17f -7.33

p-Value b0.0001

Sp

-7.18

b0.0001

(b) Separate ﬁxed depth-interval data computed with adapted trapezoidal approach Soil groupd ANOVA type II, Wald χ2 testb p-Value Main effectf “Shallow” [0–30 cm] depth-interval b0.005 P Soil groupdf2 Slopedf1 N0.05 C G

Mean (SOCS)0.5 ± SD

Back-transformed mean SOCS [tC/ha]

Arithmetic mean SOCS ± SDe [tC/ha]

n

LS means pairwise comparisong Comparing t-Ratio df14f p-Value

7.130 ± 2.397 10.004 ± 1.456 10.317 ± 3.320

50.8 100.1 106.4

55.6 ± 29.92 101.8 ± 30.08 115.6 ± 66.99

6 6 6

C vs. G C vs. P G vs. P

−0.87 2.08 2.74

0.668 0.130 0.040

“Deep” [30–60 cm] depth-interval 0.044h P Soil groupdf2 b0.05i C Slopedf1 G N0.05h,i

4.394 ± 1.505 5.864 ± 1.966 5.766 ± 1.886

19.3 34.4 33.28

21.2 ± 13.93 37.6 ± 25.64 36.2 ± 18.68

6 6 6

C vs. G C vs. P G vs. P

−0.72 1.54 2.10

0.758 0.310 0.125

“Total depth” [0–60 cm] depth-interval b0.05 P Soil groupdf2 b0.05i C Slopedf1 G N0.05i

8.503 ± 2.329 11.661 ± 2.040 11.848 ± 3.710

72.3 136.0 140.4

76.8 ± 35.93 139.4 ± 48.24 151.8 ± 82.19

6 6 6

C vs. G C vs. P G vs. P

−0.93 2.13 2.84

0.633 0.119 0.033

(c) Separate ﬁxed depth-interval data computed with spline approach Soil groupd ANOVA type II, Wald χ2 testb p-Value Main effectf “Shallow” [0–30 cm] depth-interval b0.005 P Soil groupdf2 N0.05 C Slopedf1 G

Mean (SOCS)0.5 ± SD

Back-transformed mean SOCS [tC/ha]

Arithmetic mean SOCS ± SDe [tC/ha]

n

LS means pairwise comparisong Comparing t-Ratiodf14f p-Value

7.248 ± 2.426 10.025 ± 1.403 10.755 ± 3.457

52.5 100.5 115.7

57.4 ± 31.30 102.1 ± 28.98 125.6 ± 71.31

6 6 6

C vs. G C vs. P G vs. P

−1.13 1.97 2.89

0.514 0.157 0.030

“Deep” [30–60 cm] depth-interval N0.05 P Soil groupdf2 N0.5 C Slopedf1 G

4.514 ± 1.740 5.395 ± 1.963 5.704 ± 2.015

20.4 29.1 32.5

22.9 ± 17.24 32.3 ± 24.04 35.9 ± 20.41

6 6 6

C vs. G C vs. P G vs. P

−1.01 0.86 1.79

0.580 0.672 0.210

“Total depth” [0–60 cm] depth-interval b0.05 P Soil groupdf2 b0.05i C Slopedf1 i N0.05 G

8.674 ± 2.474 11.462 ± 1.921 12.224 ± 3.813

75.2 131.4 142.4

80.3 ± 41.08 134.5 ± 44.92 161.5 ± 86.17

6 6 6

C vs. G C vs. P G vs. P

−1.25 1.84 2.90

0.445 0.193 0.029

a

Derived from LME applied to (SOCS)0.5 [slope was signiﬁcant on combined data, if all data were included]. Derived from LME applied to (SOCS)0.5. c Sh - “shallow”, Dp - “deep”, Tr - adapted trapezoidal computing approach; Sp - spline computing approach. d P - Podzols, C - Cambisols, G - Gleys. e SD standard deviation without inclusion of error propagation. f df - degrees of freedom. g Results derived from model are averaged over the levels of soil/depth, with the Tukey method p-value adjustment (for soil). h Close to ‘border signiﬁcant’. i Signiﬁcant if including all deep SOCS data, but non-signiﬁcant if excluding one value for deep SOCS at the highest measured slope (the exclusion of the value appeared not to change the outcome of post-hoc soil group contrast-signiﬁcance/non-signiﬁcance). b

A. Premrov et al. / Catena 150 (2017) 291–301

299

Fig. 5. Mean soil organic carbon stocks (SOCSs) of ﬁxed depth-intervals for Irish afforested Podzols, Cambisols and Gleys (six sites per soil group): (a) computed by trapezoidal approach, (b) computed by spline approach.

other, with the greatest SOCS observed in Cambisols and Gleys, followed by Podzols (Fig. 5). The statistical analysis performed on separate soil depth-interval data (separately for “shallow”, “deep” and “total depth”) showed signiﬁcant effect of soil group on the “shallow” and on the “total depth” SOCSs (p b 0.05, Table 2b, c). However, soil group had a less signiﬁcant or non-signiﬁcant effect on the “deep” SOCSs (Table 2b, c). Gleys had signiﬁcantly greater SOCSs than Podzols for both “shallow” (G vs. P: p b 0.05; Table 2b, c) and “total depth” depthintervals (G vs. P: p b 0.05; Table 2b, c); whereas the “deep” SOCS results showed no signiﬁcant differences among the three soil groups (Table 2b, c; results derived from LME with inclusion of slope). No signiﬁcant differences were observed in SOCSs (of any depth-intervals) between the Cambisols and Gleys, and Cambisols and Podzols. These ﬁndings appear to be in agreement with the results from statistical analysis performed on SOCVD (Section 3.2), and were observed regardless of which computing approach was used (trapezoidal or spline). The above results indicate that differences in SOCSs between soil groups

are diminishing at greater (“deep”) soil depth-interval, which is in agreement with a study by Wiesmeier et al. (2015), who also found no signiﬁcant differences between different soil classes for deeper soil horizons (C horizons). Furthermore, Wiesmeier et al. (2015) also observed (among others) signiﬁcantly higher SOC stocks for Gleysols compared to Podzols. Despite the fact that this study used relatively approximate estimation of “starting” and “ending” SOCVD values (Fig. 2a) that are required for the computation of ﬁxed depth-interval SOCSs, the results were found to be generally in agreement with the relatively broad range of soil C stocks reported in some examples of studies on mineral forest soils. Some examples are: - a study on Irish forested sites to 30 cm depth by Wellock et al. (2011) [66.7–148.8 tC/ha for Podzols, 38.4– 136.6 tC/ha for Cambisols, and 86.6–164.3 tC/ha for Gleys]; - European forest soil study to 20 cm depth by Baritz et al. (2010) [with values for temperate-oceanic to suboceanic climate zones estimated from published ﬁgures of c. 53 tC/ha for Podzols, c. 55 tC/ha for Cambisols and

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c. 65 tC/ha for Gleysols]; - a study by Batjes (2014) with estimated C stocks for up to 50 cm depth based on the global soil database [173 tC/ha for Podzols, 69 tC/ha for Cambisols and 97 tC/ha for Gleysols]. The total depth-interval (0 up to 60 cm) SOC stocks from all eighteen sites in this study were estimated at 122.7 tC/ha (arithmetic mean) if using trapezoidal approach, and c. 125.4 tC/ha if using spline approach. These estimates appear to be lower than SOC stocks for e.g. Belgium forests to 1 m depth [c. 153 tC/ha (Lettens et al., 2005)], but greater than the average stocks for forest soils in Bavaria, Germany to about 93 cm depth or parent material [c. 98 tC/ha (Wiesmeier et al., 2012)]. Nevertheless, the sampling depth of only 60 cm (or less) used in this study can still be considered as relatively shallow, and therefore, it can be expected that certain soils in this study could potentially have some additional carbon stored at greater depths. For example, an ICP Forestsbased study (including most of the European forests) by De Vos et al. (2015) estimated SOC stocks up to 1 m depth at 182 tC/ha for Gleysol, and 121 tC/ha for Podzols (bootstrapped mean), with both being greater than SOC stocks to 60 cm depth estimated for Gleys and Podzols from this study (Table 2b, c). 3.3. Comparison of trapezoidal and spline computing approaches for estimating soil organic carbon stocks of ﬁxed depth-intervals The results showed that the trapezoidal approach is likely to provide more crude estimates of SOC stocks than the spline approach: it estimated the overall “shallow” SOCSs for c. 4.1 tC/ha less than the spline approach, and the overall “deep” SOCSs for c. 1.3 tC/ha more than the spline approach (Table 2b, c). This is not surprising, considering that the trapezoidal approach is assuming a simple linear relationship between horizon SOCVD values in the soil proﬁle (Fig. 2a) Nevertheless, the trapezoidal approach has an advantage of being relatively simple (i.e. it can be implemented in Excel) and computationally less demanding. No statistically signiﬁcant differences were observed between the ﬁxed depth-interval SOCSs computed by the two methods: trapezoidal vs. spline p N 0.5, Welch two sample t-test on “shallow” and “deep” data. This was further conﬁrmed by overlapping of the 95% bootstrap conﬁdence intervals of (SOCS)0.5 means from both computing methods. The overlapping of conﬁdence intervals occurred in case of the “shallow” and deep” depth-interval SOCSs, as well as in case of SOCSs of separate soil groups of “shallow”, and “deep” depth-intervals. This comparison needs to be interpreted with caution due to limited number of sites used for bootstrapping in this study. Nevertheless, SOCS results obtained from the two computing methods, trapezoidal and spline, showed the similar signiﬁcant differences between depth-intervals and soil groups (Table 2b, c), which indicate that the trapezoidal SOC stock computing approach (despite being cruder) may be suitable when investigating the differences between different SOCSs. 4. Conclusions This study on organic carbon (C) in soils, with varying horizon depths and thicknesses, demonstrates that sampling by horizon with accompanying depth measurements can enable computational estimations of soil organic carbon (SOC) stocks for ﬁxed soil depth-intervals. The development and application of a simple trapezoidal rule computing approach (adapted from Lord and Shepherd (1993)) is hoped to facilitate the use of soil-horizon sampling in studies on SOC stocks. The comparison of the presented trapezoidal SOC stock computing approach with the more complex spline approach (Bishop et al. 1999) showed that both computational methods can enable estimates of ﬁxed depth-interval SOC stocks to be computed from measurements of mineral soil horizons sampled by auger boring, for the three Irish mineral afforested soils (Gleys, Podzols and Cambisols), aged ≥20 years. The study showed that horizon and soil group had a signiﬁcant effect on SOC stocks. The soil below the 30 cm depth was estimated to store over c. 22% of the total upper 60 cm SOC stocks. This result

should not be generalised considering that it is based on limited number of sites (eighteen sites) used in this study; nevertheless, it conﬁrms the importance of including the deeper soil horizons in the soil C-cycle. Although the trapezoidal approach is thought to be much more crude than the spline computing approach (and likely to be more suitable for more crude SOC stock estimations), no statistically signiﬁcant differences were observed between the ﬁxed depth-interval SOCSs for “shallow” and deep” data computed by the two methods. Gleys were shown to have signiﬁcantly greater mineral SOC stocks than Podzols, with differences mainly evident in the upper 30 cm soil depth, which was observed regardless of computing methodology used (trapezoidal or spline).

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