Quantification of uncertainty in trace gas fluxes measured by the static chamber method

Fluxes of methane (CH₄) and nitrous oxide (N₂O) are commonly measured with closed static chambers. Here, we analyse several of the uncertainties inherent in these measurements, including the accuracy of calibration gases, repeatability of the concentration measurements, choice of model used to calculate the flux and lack of fit to the model, as well as inaccuracies in measurements of sampling time, temperature, pressure and chamber volume. In an analysis of almost 1000 flux measurements from six sites in the UK, the choice of model for calculating the flux and model lack‐of‐fit were the largest sources of uncertainty. The analysis provides confidence intervals based on the measurement errors, which are typically 20%. Our best estimate, using the best‐fitting model, but substituting the linear model in the case of concave fits, gave a mean flux that is 25% greater than that calculated with the linear model. The best‐fit non‐linear model provided a better (convex) fit to the data than linear regression in 36% of the measurements. We demonstrate a method to balance the number of gas samples per chamber (n_samples) and the number of chambers, so as to minimize the total uncertainty in the estimate of the mean flux for a site with a fixed number of gas samples. The standard error generally decreased over the available range in n_samples, suggesting that more samples per chamber (at the expense of proportionally fewer chambers) would improve estimates of the mean flux at these sites.     

Optimizing chamber methods for measuring nitrous oxide emissions from plot‐based agricultural experiments

Nitrous oxide emissions (N₂O) from agricultural land are spatially and temporally variable. Most emission measurements are made with small (? 1 m² area) static chambers. We used N₂O chamber data collected from multiple field experiments across different geo‐climatic zones in the UK and from a range of nitrogen treatments to quantify uncertainties associated with flux measurements. Data were analysed to assess the spatial variability of fluxes, the degree of linearity of headspace N₂O accumulation and the robustness of using ambient air N₂O concentrations as a surrogate for sampling immediately after closure (T₀). Data showed differences of up to more than 50‐fold between the maximum and minimum N₂O flux from five chambers within one plot on a single sampling occasion, and that reliability of flux measurements increased with greater numbers of chambers. In more than 90% of the 1970 cases where linearity of headspace N₂O accumulation was measured (with four or more sampling points), linear accumulation was observed; however, where non‐linear accumulation was seen this could result in a 26% under‐estimate of the flux. Statistical analysis demonstrated that the use of ambient air as a surrogate for T₀ headspace samples did not result in any consistent bias in calculated fluxes. Spatial variability has the potential to result in erroneous flux estimates if not taken into account, and generally introduces a far larger uncertainty into the calculated flux (commonly orders of magnitude more) than any uncertainties introduced through reduced headspace sampling or assumption of linearity of headspace accumulation. Hence, when deploying finite resources, maximizing chamber numbers should be given priority over maximizing the number of headspace samplings per enclosure period.     

An improved method for measuring soil N2O fluxes using a quantum cascade laser with a dynamic chamber

A dynamic chamber method was developed to measure fluxes of N₂O from soils with greater accuracy than previously possible, through the use of a quantum cascade laser (QCL). The dynamic method was compared with the conventional static chamber method, where samples are analysed subsequently on a gas chromatograph. Results suggest that the dynamic method is capable of measuring soil N₂O fluxes with an uncertainty of typically less than 1–2 µg N₂O‐N m^?2 hour^?1 (0.24–0.48 g N₂O‐N ha^?1 day^?1), much less than the conventional static chamber method, because of the greater precision and temporal resolution of the QCL. The continuous record of N₂O and CO₂ concentration at 1 Hz during chamber closure provides an insight into the effects that enclosure time and the use of different regression methods may introduce when employed with static chamber systems similar in design. Results suggest that long enclosure times can contribute significantly to uncertainty in chamber flux measurements. Non‐linear models are less influenced by effects of long enclosure time, but even these do not always adequately describe the observed concentrations when enclosure time exceeds 10 minutes, especially with large fluxes.     

Vents and seals in non-steady-state chambers used for measuring gas exchange between soil and the atmosphere

Despite decades of research to define optimal chamber design and deployment protocol for measuring gas exchange between the Earth's surface and the atmosphere, controversy still surrounds the procedures for applying this method. Using a numerical simulation model we demonstrated that (i) all non‐steady‐state chambers should include a properly sized and properly located vent tube; (ii) even seemingly trivial leakiness of the seals between elements of a multiple‐component chamber results in significant risk of measurement error; (iii) a leaking seal is a poor substitute for a properly designed vent tube, because the shorter path length through the seal supports much greater diffusive gas loss per unit of conductance to mass flow; (iv) the depth to which chamber walls must be inserted to minimize gas loss by lateral diffusion is smaller than is customary in fine‐textured, wet or compact soil, but much larger than is customary in highly porous soils, and (v) repetitive sampling at the same location is not a major source of error when using non‐steady‐state chambers. Finally, we discuss problems associated with computing the flux of a gas from the non‐linear increase in its concentration in the headspace of a non‐steady‐state chamber.     

A comparison of linear and exponential regression for estimating diffusive CH4 fluxes by closed-chambers in peatlands

The closed-chamber method is the most common approach to determine CH₄ fluxes in peatlands. The concentration change in the chamber is monitored over time, and the flux is usually calculated by the slope of a linear regression function. Theoretically, the gas exchange cannot be constant over time but has to decrease, when the concentration gradient between chamber headspace and soil air decreases. In this study, we test whether we can detect this non-linearity in the concentration change during the chamber closure with six air samples. We expect generally a low concentration gradient on dry sites (hummocks) and thus the occurrence of exponential concentration changes in the chamber due to a quick equilibrium of gas concentrations between peat and chamber headspace. On wet (flarks) and sedge-covered sites (lawns), we expect a high gradient and near-linear concentration changes in the chamber. To evaluate these model assumptions, we calculate both linear and exponential regressions for a test data set (n = 597) from a Finnish mire. We use the Akaike Information Criterion with small sample second order bias correction to select the best-fitted model. 13.6%, 19.2% and 9.8% of measurements on hummocks, lawns and flarks, respectively, were best fitted with an exponential regression model. A flux estimation derived from the slope of the exponential function at the beginning of the chamber closure can be significantly higher than using the slope of the linear regression function. Non-linear concentration-over-time curves occurred mostly during periods of changing water table. This could be due to either natural processes or chamber artefacts, e.g. initial pressure fluctuations during chamber deployment. To be able to exclude either natural processes or artefacts as cause of non-linearity, further information, e.g. CH₄ concentration profile measurements in the peat, would be needed. If this is not available, the range of uncertainty can be substantial. We suggest to use the range between the slopes of the exponential regression at the beginning and at the end of the closure time as an estimate of the overall uncertainty.     

Non‐invasive characterization of pore‐related and elastic properties of soils in linear Biot–Stoll theory using acoustic‐to‐seismic coupling

Soil structure, moisture content and strength have profound effects on plant growth. Traditional methods for monitoring soil condition are invasive and therefore may affect the samples of interest. We have demonstrated the potential of a non‐invasive measurement technique for the in situ monitoring of soil physical properties in the field. When soils are regarded as porous and elastic media, sub‐surface wave propagation can be indicative of the soil status. Such propagation can be initiated by airborne sound through acoustic‐to‐seismic (A–S) coupling. Measurements of near‐surface sound pressure and acoustically induced soil particle motion can be exploited to estimate the pore‐related and elastic properties of soils. We have conducted laboratory measurements on dry and wet sand and field measurements on an arable soil growing wheat using a compression driver, microphones and a laser Doppler vibrometer. The excitation levels were chosen so as to reduce the influence of soil non‐linearity while still yielding sufficient signal‐to‐noise ratios. Measured data were compared with model predictions based on wave propagation in layered homogeneous isotropic poro‐elastic media described by linear Biot‐Stoll theory. Soil properties were estimated through an optimization process minimizing the differences between the measurements and predictions. Latin hypercube sampling was adopted to ensure uniform seeding for optimization throughout the multi‐dimensional search space. The fitted soil characteristics are air permeability, porosity, P‐/S‐wave speeds (related to bulk and rigidity moduli) and a loss factor. Layer depth was also estimated for multi‐layered samples. The current work has demonstrated that soil can be characterized non‐invasively by using A–S coupling. It is also shown that field soils can be represented adequately by multiple homogeneous layers.     

A modified McIntyre and Phillip approach to measure top‐soil gas diffusivity in‐situ

The McIntyre and Phillip method yields the product of a gas‐diffusion coefficient (D_S) and the gas‐filled proportion of soil volume ε. Until now, ε had to be measured independently from soil cores in order to obtain D_S. To avoid soil sampling, we broke up chamber measurement results by means of an empirical relationship D_S= f(ε). In contrast to an exclusive use of such an empirical relationship, this approach is advantageous in that the site‐specific information concerning pore continuity is integrated into the result. Another modification involves the use of a non‐linear regression technique, which fits the unknown parameters of the mechanistic dilution function of the tracer gas to the measured values. In this way, the independent measurement of chamber clearance with a ruler could be replaced with an estimation based on the dilution function. We could then show, by means of a Monte Carlo simulation, that the exponential parameter of the dilution function contributes to the highest error of the diffusion coefficient estimation from the 6 input parameters. We then compared the results of the following methods at 6 sites. The methods included: (a) the approach described above, (b) the laboratory measurement on soil cores, and (c) the original McIntyre and Philip method. This method is a combination of in‐situ chamber measurement and laboratory measurement of the air‐filled soil fraction. We did not detect any significant differences in the means of our method (a) in any of the aforementioned cases, as well as in the laboratory measurement (b). Deviations between individual measurements could be attributed to differences in spatial integration. These deviations are a result of scale‐dependent spatial heterogeneity and thereby provide site‐specific information on soil structure.     

A comparison of regression methods for estimating soil-atmosphere diffusion gas fluxes by a closed-chamber technique

Continuous changes in methane (CH₄) and carbon dioxide (CO₂) concentrations inside a closed chamber were measured on the forest floor at three sites: a deciduous forest and a coniferous forest in Hokkaido, Japan, and a birch forest in West Siberia, Russian Federation. Flux estimations by three types of regression methods, exponential, nonlinear, and linear, were examined using field-collected concentration data. The pattern of change with time of the gas concentration in the headspace differed, mainly according to site but also, to a lesser extent, according to the gas. This was a function of both the chamber height and surface soil property relating to soil gas diffusion and the gas concentration profile. Flux estimations did not differ statistically between the exponential and nonlinear methods for either gas at any site, because both of those regression methods were based on diffusion theory. However, the flux values estimated by linear regression were significantly different from those estimated by the other two methods for both CH₄ and CO₂ at the deciduous forest site and for CO₂ at the coniferous forest site. Shortening the chamber deployment period improved the linearity of the curve, but did not completely eliminate the error. Our results suggest that linear regression is not a good model of the change in headspace concentration with time.     

The equivalence of the Calcium‐Acetate‐Lactate and Double‐Lactate extraction methods to assess soil phosphorus fertility

A large variety of extraction methods are used worldwide for the estimation of “plant‐available P” in soils. In Germany, the standard extractants are Calcium‐Acetate‐Lactate (CAL) and Double‐Lactate (DL). Until now there is no validated transformation procedure available and studies on the comparability of both methods have reported conflicting evidence. The uncertainty about the equivalence of CAL‐P and DL‐P hinders a direct comparison of the P fertility status and P fertilizer recommendations across Germany. Based on 136 datasets for soil samples from an interlaboratory comparison program and three P fertilization field trial sites, for which plant‐available P had been determined by both the CAL and DL method, we assessed the comparability of both extraction methods and derived simple and multiple regression equations to transform DL‐P into CAL‐P values. On average, DL extracted 30% more P than CAL. However, this strongly depended on soil pH and carbonate content. A simple linear regression model explained 70% of the variance. However, if simple linear regression models were fitted to pH‐specific samples (pH range 4.5 to 7.0) the R² increased to 0.96. Based on an independent validation dataset (n = 48) we demonstrated that such pH‐specific models were more accurate than models that did not consider pH when transforming DL‐P to CAL‐P values. Multiple regression results showed that out of soil pH, C_org, N_t, and C : N ratio, only soil pH improved the model. The transformation equations in this study provide a step towards an improved comparability of P fertility status assessments of soils across Germany.     

An evaluation of Colwell‐P as a measure of plant‐available phosphorus in soils of volcanic and non‐volcanic origins in the highlands of Papua New Guinea

Various soil test methods including Olsen, Colwell, Bray and Truog have been used to assess the levels of plant‐available P (PAP) in soils situated in the highlands of Papua New Guinea (PNG). Up until now, though, there has been no guarantee that these tests provide valid assessments of PAP in these somewhat atypical organic matter‐rich tropical soils. Furthermore, the critical soil‐P concentrations associated with the tests have been based on studies conducted elsewhere in sub‐tropical and temperate latitudes and as such may or may not be valid for soils or cropping situations in PNG. Soil (Colwell)‐P and leaf‐P data collected during a recent survey of sweet potato gardens in the highlands of PNG were therefore used to determine if useful relationships existed between these variables for different groups of soils, and if they do, to use these relationships to evaluate critical soil Colwell‐P concentrations corresponding to a known critical concentration of P in sweet potato index leaf tissue. Separate, highly significant linear relationships were obtained between leaf‐P and Colwell‐P for soils of volcanic and non‐volcanic origins. Based on these relationships, the critical Colwell‐P concentration for volcanic soils was found to be four times greater than that for non‐volcanic soils, presumably because much of the P extracted from the former soils with alkaline sodium bicarbonate had been chemically ‘fixed’ via sorption and precipitation reactions with sesquioxides and rendered unavailable to plants at ambient soil pH. These critical Colwell‐P concentrations if adopted as benchmark values for the soil groups in question should ensure that the results of future soil fertility surveys involving Colwell‐P assessments are correctly interpreted.     

Expanded measurement uncertainty of soil parameters derived from proficiency‐testing data

Basic parameters for the calculation of the expanded measurement uncertainty (U) of 33 soil parameters were derived from the data base of proficiency tests of the Association of German Agricultural Analytical and Research Institutes (VDLUFA) over the years 1993–2005. The underlying statistical model was the regression of the standard deviations of the means for all participating laboratories on the mean of all laboratories. In general, the linear model fits U very well. Only in three cases, a curvilinear equation showed a better significance. The calculated regressions were nonsignificant only in the cases of copper (using the Westerhoff method), pH, and the percentage of sand in the soil samples. All regressions were tested for plausibility using the Horwitz equation (HORRAT). Given a medium range of concentrations, practically all analytes fell well within a ratio of 2, only the results for manganese (Schachtschabel method) did not comply. Plausibility could be proven also for higher‐concentration ranges with the single exception of boron (hot‐water extraction). At very low–concentration ranges, for some of the analytes a HORRAT value of 2 was exceeded, presumably due to the proximity of the limit of detection in conjunction with some methodological problems. For all of these cases, a concentration limit for the reliability range of the regression for the analytes was calculated, at which the HORRAT values just met the critical ratio of 2. Laboratories are recommended to integrate the regression functions for U into their specific laboratory information and management system (LIMS) or other documentation systems in order to specify U for the measured values. Results are also considered as a solid basis for the evaluation of legally defined limits in agricultural fertilization of soils.     

Applicability of the soil gradient method for estimating soil–atmosphere CO2, CH4, and N2O fluxes for steppe soils in Inner Mongolia

For evaluating the applicability of the soil gradient method as a substitute for CO₂‐, CH₄‐, and N₂O‐flux measurements in steppe, we carried out chamber measurements and determined soil gas concentration at an ungrazed (UG99) and a grazed (WG) site in Inner Mongolia, China. The agreement of the concentration‐based flux estimates with measured chamber‐based fluxes varied largely depending on the respective GHG in the sequence CO₂ > CH₄ >> N₂O. A calibration of the gas‐transport parameter used to calculate fluxes based on soil gas concentrations improved the results considerably for CO₂ and CH₄. After calibration, the average deviation from the chamber‐based annual cumulative flux for both sites was 11.5%, 10.5%, and 59% for CO₂, CH₄, and N₂O. The gradient method did not constitute an adequate stand‐alone substitute for greenhouse‐gas flux estimation since a calibration using chamber‐based measurements was necessary and vigorous production processes were confined to the uppermost, almost water‐saturated soil layer.     

Bayesian Maximum Entropy prediction of soil categories using a traditional soil map as soft information

Bayesian Maximum Entropy was used to estimate the probabilities of occurrence of soil categories in the Netherlands, and to simulate realizations from the associated multi‐point pdf. Besides the hard observations (H) of the categories at 8369 locations, the soil map of the Netherlands 1:50 000 was used as soft information (S). The category with the maximum estimated probability was used as the predicted category. The quality of the resulting BME(HS)‐map was compared with that of the BME(H)‐map obtained by using only the hard data in BME‐estimation, and with the existing soil map. Validation with a probability sample showed that the use of the soft information in BME‐estimation leads to a considerable and significant increase of map purity by 15%. This increase of map purity was due to the high purity of the existing soil map (71.3%). The purity of the BME(HS) was only slightly larger than that of the existing soil map. This was due to the small correlation length of the soil categories. The theoretical purity of the BME‐maps overestimated the actual map purity, which can be partly explained by the biased estimates of the one‐point bivariate probabilities of hard and soft categories of the same label. Part of the hard data is collected to describe characteristic soil profiles of the map units which explains the bias. Therefore, care must be taken when using the purposively selected data in soil information systems for calibrating the probability model. It is concluded that BME is a valuable method for spatial prediction and simulation of soil categories when the number of categories is rather small (say < 10). For larger numbers of categories, the computational burden becomes prohibitive, and large samples are needed for calibration of the probability model.     

Robust estimation of the pseudo cross‐variogram for cokriging soil properties

The pseudo cross‐variogram can be used for cokriging two or more soil properties when few or none of the sampling locations have values recorded for all of them. The usual estimator of the pseudo cross‐variogram is susceptible to the effects of extreme data (outliers). This will lead to overestimation of the error variance of predictions obtained by cokriging. A solution to this problem is to use robust estimators of the pseudo cross‐variogram, and three such estimators are proposed in this paper. The robust estimators were demonstrated on simulated data in the presence of different numbers of outlying data drawn from different contaminating distributions. The robust estimators were less sensitive to the outliers than the non‐robust one, but they had larger variances. Outliers tend to obscure the spatial structure of the cross‐correlation of the simulated variables as described by the non‐robust estimator. The several estimators of the pseudo cross‐variogram were applied to a multitemporal data set on soil water content. Since these were obtained non‐destructively, direct measurements of temporal change can be made. A prediction subset of the data was subsampled as if obtained by destructive analysis and the remainder used for validation. Estimators of the auto‐variogram and pseudo cross‐variogram were applied to the prediction data, then used to predict the change in water content at the validation sites by cokriging. The estimation variances of these predictions were best calculated with a robustly estimated model of coregionalization, although the validation set was too small to conclude that the non‐robust estimators were unsuitable in this instance.     

An explanation of linear increases in gas concentration under closed chambers used to measure gas exchange between soil and the atmosphere

Earlier models describing the accumulation of gases under closed chambers are based on the assumption of a constant concentration source that does not change during the time of chamber deployment. A new model is proposed which is based on the assumption of a constant production source, and takes into account possible changes in gas concentrations at the source during chamber deployment. Using N₂O as an example, simulations have been carried out for different source strength and depth, diffusivities and air porosities. The main finding was a chamber‐induced increase in gas concentrations in the upper part of the soil profile, including the depth where the N₂O source is located. The increase started immediately after chamber closure. Nevertheless, fluxes calculated from increasing concentrations within the chamber's headspace were always less than those expected under undisturbed conditions, i.e. in the absence of a chamber. This was due to a proportion of the gas produced being stored within the soil profile while the chamber was in place. The discrepancy caused by this effect increased with increasing air‐filled porosity and decreasing height of the chamber, and a procedure for correcting chamber flux measurements accordingly is proposed. The increase in soil gas concentrations after chamber closure was confirmed in a laboratory experiment.     

Characterization of diffusivity‐based oxygen transport in Arctic organic soil

Arctic terrestrial ecosystems are characterized by large deposits of near‐surface soil organic carbon in poorly drained areas. Recent changes in Arctic regions such as warming and changes in water balance have adverse effects on the dynamics of near‐surface oxygen, leading to a potential increase in oxidation of near‐surface carbon and emission of CO₂. This study investigated oxygen diffusivity characteristics, in both gaseous and liquid phases, in the upper 10 cm of an organic soil profile from a peatland in Disko, West Greenland (69°N). Two commonly used methods for calculating diffusivity of gaseous‐phase oxygen were applied and discussed to select the most appropriate method for highly porous media, for example peat soil. We measured diffusivity of gaseous‐phase oxygen with a one‐chamber diffusion set‐up in soil at different air contents (mimicking draining), and described it numerically with a previously developed parametric diffusivity model. We obtained precise measurements of liquid‐phase oxygen diffusivity along a depth profile (0–2 cm) in water‐saturated peat soil with a diffusivity microsensor coupled to a micromanipulator. The results show that the choice of an appropriate diffusivity model is critical for predicting oxygen diffusivity in organic soil and that diffusivity in mineral soil is not representative for organic soil. Furthermore, the importance of the non‐linear functionality between water saturation and diffusivity is demonstrated. This highlights the importance of measuring and modelling oxygen diffusivity rather than relying on measurements of observed water content in future studies of CO₂ and CH₄ dynamics in Arctic soil systems subject to climate changes.     

Determination of the different components of cadmium short‐term uptake by roots

As the various components of the cadmium (Cd) root sink have not been clearly described, there is a need to precisely measure the respective contributions of apoplast and symplast to short‐term root Cd uptake and to explain the linear component of the absorption isotherms. A new method of fractionating Cd in roots was applied to two plant species with contrasting abilities to accumulate Cd: maize (Zea mays) and a Cd‐hyperaccumulating ecotype of alpine pennycress (Noccaea caerulescens). Their roots were exposed for 1 h to increasing concentrations of labeled Cd. Series of desorption baths were used to obtain the root apoplastic Cd in combination with a brief freezing step in liquid nitrogen to separate the intracellular metal from the apoplastic one. The apoplastic uptake accounted for 15% to 82% and for 48% to 96% of the total Cd uptake of maize and of alpine pennycress roots, respectively. In the case of maize, the concentration‐dependent symplastic net flux fitted a biphasic Michaelis‐Menten function, while in the case of alpine pennycress, a Michaelis‐Menten‐plus‐linear function proved a better fit. The second component of the symplastic net flux may reflect absorption through a low‐affinity transport system. Short‐term Cd uptake by roots is dominated by the high‐affinity transport system for exposure concentrations below 1 μM for maize and 0.2 μM for alpine pennycress, while cell‐wall binding prevailed for higher exposure concentrations.     

Model‐based analysis using REML for inference from systematically sampled data on soil

The general linear model encompasses statistical methods such as regression and analysis of variance (anova ) which are commonly used by soil scientists. The standard ordinary least squares (OLS) method for estimating the parameters of the general linear model is a design‐based method that requires that the data have been collected according to an appropriate randomized sample design. Soil data are often obtained by systematic sampling on transects or grids, so OLS methods are not appropriate. Parameters of the general linear model can be estimated from systematically sampled data by model‐based methods. Parameters of a model of the covariance structure of the error are estimated, then used to estimate the remaining parameters of the model with known variance. Residual maximum likelihood (REML) is the best way to estimate the variance parameters since it is unbiased. We present the REML solution to this problem. We then demonstrate how REML can be used to estimate parameters for regression and anova ‐type models using data from two systematic surveys of soil. We compare an efficient, gradient‐based implementation of REML (ASReml) with an implementation that uses simulated annealing. In general the results were very similar; where they differed the error covariance model had a spherical variogram function which can have local optima in its likelihood function. The simulated annealing results were better than the gradient method in this case because simulated annealing is good at escaping local optima.