Twenty-five years of observations of soil organic carbon in Swiss croplands showing stability overall but with some divergent trends.

The temporal evolution of soil organic carbon (SOC) is of major importance given its status as a key parameter in many soil functions. Furthermore, soils constitute an important reservoir of carbon in our environment. In light of climate change, consistent SOC data over extended periods in combination with information on agricultural management are much required, but still scarce. We report SOC changes in the topsoil (0–20 cm) of Swiss cropland measured at well-defined monitoring sites resampled every 5 years from 1990 to 2014 by the Swiss Soil Monitoring Network NABO using consistent sampling protocols and quality assurance. Data on agricultural management practices were retrieved from farmers. Overall, SOC remained stable for the ensemble of monitoring sites, although increasing and decreasing trends were observed for individual sites, ranging from − 11 to + 16% relative change per decade. Changes in the agricultural management of cropland triggered substantial changes in SOC contents for some sites. Moreover, sites with a low ratio of SOC/clay (< 0.1) generally showed more positive trends than sites with higher ratios. We presume that SOC was either at or near steady state, given the consistency of management practices over the last few decades. Finally, our study provides insights into the uncertainties related to (real-world) SOC monitoring and underlines the relevance of short-term SOC variations that could hamper the detection of long-term trends. The minimum detectable change (MDC) by the applied monitoring scheme is estimated at 0.35% per year, in relative terms. Electronic supplementary material The online version of this article (10.1007/s10661-019-7435-y) contains supplementary material, which is available to authorized users.


SI1: Monitoring sites and soil sampling
For each (re)sampling, four replicate samples were collected from the top 20 cm (fixed sampling depth measured from the soil surface). The replicates per time point, as well as all repeated samplings, represent the same area of 10 m x 10 m, accurately relocated using well documented reference points and buried magnets. The relocation accuracy was estimated at < 0.2 m. Each replicate consisted of 25 subsamples obtained using a gouge auger 2.5 cm in diameter according to a stratified random scheme: the sampled area was divided into 100 subplots of 1 m 2 with one subsample taken randomly within each subplot. Subsamples were bulked accordingly ( Fig. S1; four replicates have an effective sampling support of 9 m x 9 m shifted by roughly 1 m for individual replicates). The soil samples were oven-dried at 40 °C and subsequently crushed and sieved to remove coarse soil components (> 2 mm diameter), before being archived in plastic containers. The whole process from sampling to lab analysis was standardised using standard operation protocols. Site characteristics and available management data are summarised in Table 2 and Fig. S2. Differences in management between two periods (1985-1999 vs. 2000-2014) are illustrated in Fig. S3   , mean of all sampling campaigns), differences P2-P1 in percentages of years featuring meadows (d.mead), cereals (d.cer), and so-called hoe crops (d.hc; includes maize, rape, beets, and potatoes) as main crop, and the differences P2-P1 in mean annual inputs of farmyard manure in total (TM; t dry matter ha -1 yr -1 ) and for solid (d.SM) and liquid (d.LM) manure separately. Lower panel: scatter plots with orange symbols representing permanent cropland sites (N=6) and green symbols representing sites with cropland-meadow rotations (N=15). Site 17 was omitted from this plot due to its extreme changes in manure inputs (c.f. Table 2 in the main text). The broken lines indicate the means, and the solid lines indicate the median of all sites. Upper panel: Spearman's rank correlation coefficients. The stars indicate significant correlations (* p < 0.05; ** p < 0.01; *** p < 0.001). Background colours indicate the degree of correlation.

SI3: Minimum detectable change (MDC) and variability
The aim of monitoring programs is to detect temporal trends. Dependent on their settings, changes in soil properties are captured with varying reliability. Hence, the minimum detectable change (MDC) is an important criterion of quality (Smith 2004). Generally, repeated sampling of the same set of well defined sites is considered more efficient than sampling different sites each time (Lark 2009). The regional mean change Y is estimated from the changes at the individual sites, e.g., using a hierarchical model. Estimates of Y may be considered realisations of a random variable with mean μ y (the 'true' change) and variance proportional to (i) the spatial variability of the SOC change (but not the spatial variability of the SOC itself), (ii) errors due to sampling, sample preparation, and chemical analyses, (iii) variance caused by relocation errors, and (iv) variance due to short-term variations in SOC (and soil properties in general). Over the short term, SOC fluctuates due to seasonal patterns and/or random processes (e.g., rainfall) regardless of the long-term evolution. In contrast to the other error sources mentioned, short-term variability has only been recognised by a few researchers. For instance, Leinweber et al. (1994) reported variations of up to 40 g SOC kg -1 (representing 15 % relative change) within one year for a single field, and Wuest (2014) reported relative variations of 14-16 % within 39 months. From a long-term perspective, short-term variability represents noise and hampers the detection of long-term trends.

Methods
The MDC of the NABO monitoring program was assessed by conducting a power analysis for simulated datasets with varying temporal SOC trends. The (log-transformed) SOC data of five sampling campaigns from 1990 to 2014 served as a basis for the simulations. First, the slopes per site (linear trend) were extracted and centred giving a mean of 0 to represent the population ̂= {̂1,̂2, … ,̂ } of potential slopes. ̂ reflects the variability of linear trends between sites (term σ 2 Y in Equation 1). Second, we derived the deviations � of the individual samplings from the linear trends obtained. � reflects the variance introduced both by short-term variations and the various error sources (remaining terms in Equation 1). We simulated datasets containing 30 sites with 7 samplings separated by five years as follows: a) we drew a bootstrap sample of size 30 from ̂, yielding an individual slope per hypothetical site i; b) for each site i, we drew a bootstrap sample of size 7 from � representing the residuals of 7 samplings; c) we combined the data of steps a and b to receive a dataset X 0 without a global trend Y; d) we derived the datasets X 1 , X 2 , … with varying global trends Y by adding a relative increase of 1, 2, 2.5, 3, …, 6, 7, 8 % per 10 years to X 0; e) we subsequently derived datasets with varying observation periods by retaining data from two, three… seven sampling campaigns; f) we tested for a linear trend (α = 0.05) by fitting a linear-mixed model or, for datasets including only two sampling campaigns, by performing a paired t-test. Steps a to f were iterated 500 times. Then, the proportion of iterations where the model correctly identified a linear trend corresponded to the power (i.e., the probability of detecting an inherent trend). The smallest simulated SOC trend where the power ≥ 0.8 was considered the MDC. Similarly, we assessed the MDC of datasets with less/more monitoring sites by repeating the same procedure for simulated datasets containing 20, 60, and 100 sites.
We assessed the variability of the replicate samples per site and sampling by calculating the sample standard deviation s of the log-transformed data (natural logarithm). Equally, the variability of the repeated samplings per site was assessed by calculating s for the deviations of the individual samplings from the linear trends (this may be considered an estimate of the minimum variability between samplings). For easier comparison with other reports, (page 7/13) we additionally estimated the coefficient of variation (CV) defined as s (of the original, untransformed data) divided by their mean. For the sake of simplicity, we estimated CV by CV(x 1..N ) ≈ s(log [x 1..N ]) being appropriate for CV up to about 0.25.

Results & Discussion
After five sampling campaigns (time points), a monitoring scheme according to NABO is able to detect a relative global SOC change provided that it is at least 0.35 % per year (Table S1, Fig. S8, Fig. S9). This roughly corresponds to a 7 % relative change after 20 years. The inclusion of additional time points makes no further substantial improvement to the MDC, but using fewer time points increases it. Using two or three time points makes the longterm trends barely detectable because they are confounded with artefacts and short-term variations in SOC; this causes an elevated risk of false positives (type I error: "the test indicates a significant change although there is none"). The MDC of course reflects the probability of false negatives (type II error: "there is a real trend but it cannot be seen"), which reflects the sensitivity of our system. Various factors influence MDC, as discussed above.
Although relocation errors seem negligible with our monitoring system due to the high accuracy of relocation, further sources of variance are briefly discussed below.  Comparing SOC across individual replicates per sampling for each site (variability within sampling: V w ) and across repeated samplings per site (variability between samplings: V b ) highlighted differences between sites (SI.5 for detailed results). The standard deviation s (of the log 10 -transformed SOC) of the four replicates per site and sampling captures the overall variance of sampling, sample preparation, and chemical analyses. For our study, s pooled per site (s p ) ranged from 0.006 to 0.027 with mean 0.014 and median 0.013 ( Fig. S10; or expressed as CV: 1.3 to 6.1 %, mean 3.2 %, median 3.0 %). There was no correlation between s p and SOC content, meaning that the relative variability was constant for the whole concentration range of 10 to 40 g kg -1 . In addition, the variance within samplings fluctuated slightly between sampling campaigns, but there was no consistent trend over time (Fig. S11); hence, the variability of the replicates did not change over time. The variability between samplings at the same site was expressed as s for the residuals relative to the linear regression line. For our sites, s ranged from 0.005 to 0.039 with mean 0.018 and median 0.014 ( Fig. S12; or expressed as CV: 1.1 to 8.9 %, mean 4.1 %, median 3.3 %). The variability between samplings observed for individual sites was correlated neither with SOC content nor with s p (the variability within individual samplings; Fig. S13). Hence, we assume that short-term variability of SOC was the dominant factor for V b , while further sources of error were largely balanced out by averaging over four replicates.
(page 8/13) In consequence, short-term variability of SOC, and thus V b , cannot be estimated from data from a single survey.
Similarly, spatial variability of SOC trends can only be estimated from repeated samplings. Because these two factors strongly influence MDC, the same applies for estimating MDC. However, to our best knowledge, only one previous study used data from resampled sites: for England and Wales, the MDC for croplands was estimated at 2 g kg -1 using two time points separated by 12 years (Saby et al. 2008). This corresponded roughly to a 7 % relative change in total or 0.6 % per year, in line with the MDCs reported in Table S1 (England & Wales: one site per 73 km 2 ).