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- Material and methods
Uncertainties in soil organic carbon (SOC) stock assessments are rarely quantified even though they are critical in determining the significance of the results. Previous studies on this topic generally focused on a single variable involved in the SOC stock calculation (SOC concentration, sampling depth, bulk density and rock fragment content) or on a single scale, rather than using an integrated approach (i.e. taking into account interactions between variables). This study aims to apply such an approach to identify and quantify the uncertainties in SOC stock assessments for different scales and spatial landscape units (LSU) under agriculture. The error propagation method (δ method) was used to quantify the relative contribution of each variable and interaction involved to the final SOC stock variability. Monte Carlo simulations were used to cross-check the results. Both methods converged (r2=0.78). As expected, the coefficient of variation of the SOC stock increased across scales (from 5 to 35%), and was higher for grassland than for cropland. Although the main source of uncertainty in the SOC stock varied according to the scale and the LSU considered, the variability of SOC concentration (due to errors from the laboratory and to the high SOC spatial variability) and of the rock fragment content were predominant. When assessing SOC stock at the landscape scale, one should focus on the precision of SOC analyses from the laboratory, the reduction of SOC spatial variability (using bulk samples, accurate re-sampling, high sampling density or stratified sampling), and the use of equivalent masses for SOC stock comparison. The regional SOC stock monitoring of agricultural soils in southern Belgium allows the detection of an average SOC stock change of 20% within 11 years if very high rates of SOC stock changes occur (1 t C ha–1 year–1).
Amplitude et sources des incertitudes liées aux estimations des stocks de carbone organique dans le sol (COS) à différentes échelles
Les erreurs associées aux estimations du stock de carbone organique dans le sol (COS) sont rarement quantifiées bien qu’elles puissent empêcher l’obtention de résultats significatifs. Les quelques études qui le font focalisent en général sur une seule variable nécessaire au calcul du stock de COS (concentration en COS, profondeur échantillonnée, densité apparente et contenu en fragments rocheux) ou sur une échelle spatiale particulière, sans utiliser d’approche intégrée (prenant en compte les interactions entre les variables). Cette étude a pour objectif d’utiliser une telle approche pour identifier et quantifier les incertitudes liées aux estimations de stock de COS à différentes échelles spatiales et pour diverses unités spatiales de paysages (USP) agricoles. La loi de propagation des erreurs (méthode δ) permet de quantifier la contribution relative de chaque variable et interaction à la variabilité finale du stock de COS. Les simulations de Monte Carlo sont utilisées pour la vérification croisée des résultats. Les deux méthodes ont convergé (r2= 0.78). Comme prévu, le coefficient de variation du stock de COS a proportionnellement augmenté avec l’échelle spatiale considérée (de 5 à 35%), et était plus élevé pour les cultures que pour les prairies. Bien que la principale source d’erreur sur le stock de COS soit fonction de l’échelle spatiale et du type d’USP considérés, la variabilité du contenu en COS (du fait des erreurs de laboratoire et de sa grande variabilité spatiale) et du contenu en fragments rocheux étaient prédominants. Lors de l’estimation des stocks de COS à l’échelle du paysage, l’attention devrait prioritairement porter sur la précision des analyses en COS du laboratoire, la réduction de la variabilité spatiale du COS (en utilisant des échantillons composites, un ré-échantillonnage précis, une densité d’échantillonnage élevée ou un échantillonnage stratifié), et sur l’utilisation de masses équivalentes pour comparer les stocks de COS. Le réseau régional de suivi des stocks de COS des sols agricoles dans le sud de la Belgique permet la détection d’un changement de stock de COS moyen de 20% en 11 ans pour un taux très élevé de changement en stock de COS (1 t C ha–1 year–1).
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- Material and methods
Soil organic carbon (SOC) stock is an important issue in the context of climate change (soils being potential sinks or sources of CO2) and of soil degradation (EC, 2006). The Kyoto Protocol, the EU soil thematic strategy and the European Common Agricultural Policy rely on SOC stock assessment as part of the greenhouse gas emission budget, the verification of changes in soil organic matter, or for the implementation of agri-environmental measurements (SOC management). However, SOC stock assessments are associated with large uncertainties that may impair the detection of temporal SOC stock changes and the identification of the main driving forces involved (Falloon & Smith, 2003; Ogle et al., 2006).
Uncertainties are difficult to quantify and to identify because they stem from complex interactions between the variables involved in SOC stocks (i.e. SOC concentration, bulk density, sampling depth and rock fragment content). Uncertainties arise from manipulation, instrumental limitations and environmental variability in each variable. Different types of errors can be distinguished: systematic and random. Mathematical expressions of uncertainties may refer to the level of accuracy (usually represented by the mean error–ME) or precision (commonly represented by the standard deviation) (see Note 1, p 15). Although uncertainties need to be reduced, knowledge of uncertainty can also be used to optimise the design of a SOC stock monitoring scheme, as illustrated by the concept of the minimum detectable difference (MDD) in SOC stock: given the estimated variance in the SOC stock of a population and the MDD to achieve, the number of samples to collect can be adapted for a fixed level of confidence (Sokal & Rohlf, 1995; Zar, 1999). Besides, given a rate of SOC stock change, the time needed to detect the MDD can also be estimated (Smith, 2004). It is therefore essential to quantify and identify uncertainties in order not only to improve the design of SOC stock monitoring schemes, but also to use the results of SOC stock assessments properly for political and societal decisions (Saby et al., 2008).
Some studies have focused on particular aspects of uncertainties in SOC stocks, such as the impact of using different analytical methods for SOC concentration determination. It has been shown that the precision (CV) of such analytical methods could range from 1.2 to 15.8% for the loss-on-ignition method (LOI), from 1.6 to 4.2% for the Walkley & Black method (WB), and from 1.3 to 7.1% for dry combustion (Lowther et al., 1990; Soon & Abboud, 1991; Sutherland, 1998; Bowman et al., 2002), and that the relationships between the results from these different methods depended on the type of soil considered. Furthermore, the general underestimation of the total organic carbon concentration (TOC) by the WB method requires a correction factor that may vary from 1 to 1.6 according to land use, soil type (especially soil texture), SOM quality, sampling depth, or climate (Wang et al., 1996; Jolivet et al., 1998; Díaz-Zorita, 1999; Brye & Slaton, 2003; Lettens et al., 2007). Therefore, the choice of a method to determine the SOC concentration already has an impact on the quality of the results and the use of empirical relationships or correction factors should preferably be related to the situation studied. Other studies on uncertainties in SOC stocks assessment have highlighted the importance of directly measuring the soil bulk density (BD), as indirect BD estimates based on pedotransfer functions can lead to errors from 9% up to 36% of the SOC stock (Boucneau et al., 1998; De Vos et al., 2005). The use of random errors in the SOC concentration either in geostatistics for spatial issues or in the MDD approach for monitoring design purposes has also been widely illustrated. While geostatistical models provided SOC maps at various scales based on the spatial variability of SOC, they still gave large variability at short distances (i.e. nuggets) resulting in inherent errors of prediction (Robertson et al., 1993; Delcourt et al., 1996; Geypens et al., 2000; Zhang & McGrath, 2004). The application of the MDD for SOC stock, usually at the microsite scale (Conant et al., 2003), the field scale (Johnson et al., 1990; Garten & Wullschleger, 1999; Kucharik et al., 2003; Poussart et al., 2004) or more recently the regional scale (Saby et al., 2008), showed the high sampling density needed to detect differences in SOC stocks between two locations or surveys. While these studies provided insights into various sources of variability, they (i) do not consider uncertainties in the SOC stock in an integrated approach, i.e. resulting from the propagation of individual errors and their interaction and (ii) only focus on a single variable or a single scale. It is therefore difficult to compare the results from these different studies in order to identify the relative weights of the main errors involved in the total uncertainty in SOC stock assessment, and for different scales of interest.
However, the concept of error propagation can be directly applied to the mathematical expression of SOC stock, since the random error (i.e. the variance, σ2) in the SOC stock comes from the propagation of the random errors in each variable used in the SOC stock equation. Given that these individual random errors and interaction are first estimated, their propagation can be assessed by different methods: i) the Monte Carlo simulation method (MC), which generates numerous SOC stocks using random values for each individual variable (stochastic approach) (Hammersley & Handscomb, 1964; Rubinstein, 1981), or ii) the classical method of the law of covariances associated with the Taylor method (also called “the statistical differentials method” or the “δ method”) (Goodman, 1960; Ku, 1966; Wells & Krakiwsky, 1971; Mardia et al., 1979), which gives a general equation for the error propagation in non-linear functions (deterministic approach). The advantage of the “δ method” is to give an explicit equation for the final SOC stock variability (i.e. the solution comes in an analytical form), which allows one to quantify the relative contribution of the individual sources of uncertainties as well as their interaction (Heuvelink, 1998). However, when more complex functions than the SOC stock are considered, the MC method is easier to implement even if a large number of runs might be needed. Note that the MC simulations can also be used to cross-check the result (i.e. the SOC stock variability) given by the “δ method”.
Goidts & van Wesemael (2007) presented a methodology to assess SOC stocks and their evolution at a regional scale (southern Belgium) by re-sampling a reasonable number of locations belonging to spatial landscape units (LSU). Many questions still remain about the accuracy of a method based on stratified re-sampling, the sources of uncertainties and their importance across different scales. Given these questions, the main objective of this study was to identify and quantify the uncertainties in this particular SOC stock assessment using an integrated approach. The specific objectives were (1) to quantify the uncertainties in SOC stock occurring at different scales and for different types of LSU under agriculture, (2) to identify the main sources of these uncertainties, together with their relative importance, and (3) to provide guidelines to increase the potential of a regional SOC monitoring scheme to detect SOC changes.
Therefore, both the “δ method” and the MC analysis were used at various scales (sample, microsite, field and landscape) and for different types of LSU encountered in the study area. The results obtained were then used to assess the accuracy and precision of the SOC stock monitoring implemented in southern Belgium and to give guidance for setting up such a monitoring scheme.