R. M. Lark

British Geological Survey , Nottigham, England, United Kingdom

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Publications (114)215.22 Total impact

  • [show abstract] [hide abstract]
    ABSTRACT: We analyzed data on nitrous oxide emissions and on soil properties that were collected on a 7.5-km transect across an agricultural landscape in eastern England using the discrete wavelet packet transform. We identified a wavelet packet "best basis" for the emission data. Wavelet packet basis functions are used to decompose the data into a set of coefficients that represent the variation in the data at different spatial frequencies and locations. The "best basis" for a set of data is adapted to the variability in the data by ensuring that the spatial resolution of local features is good at those spatial frequencies where variation is particularly intermittent. The best basis was shown to be adapted to represent such intermittent variation, most markedly at wavelengths of 100 m or less. Variation at these wavelengths was shown to be correlated particularly with chemical properties of the soil, such as nitrate content. Variation at larger wavelengths showed less evidence of intermittency and was found to be correlated with soil chemical and physical constraints on emission rates. In addition to frequency-dependent intermittent variation, it was found that the variance of emission rates at some wavelengths changed at particular locations along the transect. One factor causing this appeared to be contrasts in parent material. The complex variation in emission rates identified by these analyses has implications for how emission rates are estimated.
    Journal of Environmental Quality 07/2013; 42(4):1070-9. · 2.35 Impact Factor
  • R. Webster, R.M. Lark
    01/2013; Routledge., ISBN: 978-1849713672
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    ABSTRACT: Numerous scientific challenges arise when designing a soil monitoring network (SMN), especially when assessing large areas and several properties that are driven by numerous controlling factors of various origins and scales. Different broad approaches to the establishment of SMNs are distinguished. It is essential to establish an adequate sampling protocol that can be applied rigorously at each sampling location and time. We make recommendations regarding the within-site sampling of soil. Different statistical methods should be associated with the different types of sampling design. We review new statistical methods that account for different sources of uncertainty. Except for those parameters for which a consensus exists, the question of testing method harmonisation remains a very difficult issue. The establishment of benchmark sites devoted to harmonisation and inter-calibration is advocated as a technical solution. However, to our present knowledge, no study has addressed crucial scientific issues such as how many calibration sites are necessary and how to locate them.
    Pedosphere 08/2012; 22(4):456–469. · 1.23 Impact Factor
  • B. G. Rawlins, R. M. Lark, J. Wragg
    [show abstract] [hide abstract]
    ABSTRACT: Regulatory authorities need to establish rapid, cost-effective methods to measure soil physical indicators - such as aggregate stability - which can be applied to large numbers of soil samples to detect changes of soil quality through monitoring. Limitations of sieve-based methods to measure the stability of soil macro-aggregates include: i) the mass of stable aggregates is measured, only for a few, discrete sieve/size fractions, ii) no account is taken of the fundamental particle size distribution of the sub-sampled material, and iii) they are labour intensive. These limitations could be overcome by measurements with a Laser Granulometer (LG) instrument, but this technology has not been widely applied to the quantification of aggregate stability of soils. We present a novel method to quantify macro-aggregate (1-2 mm) stability. We measure the difference between the mean weight diameter (MWD; μm) of aggregates that are stable in circulating water of low ionic strength, and the MWD of the fundamental particles of the soil to which these aggregates are reduced by sonication. The suspension is circulated rapidly through a LG analytical cell from a connected vessel for ten seconds; during this period hydrodynamic forces associated with the circulating water lead to the destruction of unstable aggregates. The MWD of stable aggregates is then measured by LG. In the next step, the aggregates - which are kept in the vessel at a minimal water circulation speed - are subject to sonication (18W for ten minutes) so the vast majority of the sample is broken down into its fundamental particles. The suspension is then recirculated rapidly through the LG and the MWD measured again. We refer to the difference between these two measurements as disaggregation reduction (DR) - the reduction in MWD on disaggregation by sonication. Soil types with more stable aggregates have larger values of DR. The stable aggregates - which are resistant to both slaking and mechanical breakdown by the hydrodynamic forces during circulation - are disrupted only by sonication. We used this method to compare macro-aggregate (1-2 mm) stability of air-dried agricultural topsoils under conventional tillage developed from two contrasting parent material types and compared the results with an alternative sieve-based technique. The first soil from the Midlands of England (developed from sedimentary mudstone; mean soil organic carbon (SOC) 2.5%) contained a substantially larger amount of illite/smectite (I/S) minerals compared to the second from the Wensum catchment in eastern England (developed from sands and glacial deposits; mean SOC=1.7%). The latter soils are prone to large erosive losses of fine sediment. Both sets of samples had been stored air-dried for 6 months prior to aggregate analyses. The mean values of DR (n=10 repeated subsample analyses) for the Midlands soil was 178μm; mean DR (n=10 repeat subsample analyses) for the Wensum soil was 30μm. The large difference in DR is most likely due to differences in soil mineralogy. The coefficient of variation of mean DR for duplicate analyses of sub-samples from the two topsoil types is around 10%. The majority of this variation is likely to be related to the difference in composition of the sub-samples. A standard, aggregated material could be included in further analyses to determine the relative magnitude of sub-sampling and analytical variance for this measurement technique. We then used the technique to investigate whether - as previously observed - variations (range 1000 - 4000 mg kg-1) in the quantity of amorphous (oxalate extractable) iron oxyhydroxides in a variety of soil samples (n=30) from the Wensum area (range SOC 1 - 2%) could account for differences in aggregate stability of these samples.
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    ABSTRACT: The spatial variability of soil nitrogen (N) mineralisation has not been extensively studied, which limits our capacity to make N fertiliser recommendations. Even less attention has been paid to the scaledependence of the variation. The objective of this research was to investigate the scale-dependence of variation of mineral N (MinN, N–NO3 − plus N–NH4 +) at within-field scales. The study was based on the spatial dependence of the labile fractions of SOM, the key fractions for N mineralisation. Soils were sampled in an unbalanced nested design in a 4-ha arable field to examine the distribution of the variation of SOM at 30, 10, 1, and 0.12 m. Organic matter in free and intra-aggregate light fractions (FLF and IALF) was extracted by physical fractionation. The variation occurred entirely within 0.12 m for FLF and at 10 m for IALF. A subsequent sampling on a 5-m grid was undertaken to link the status of the SOM fractions to MinN, which showed uncorrelated spatial dependence. A uniform application of N fertiliser would be suitable in this case. The failure of SOM fractions to identify any spatial dependence of MinN suggests that other soil variables, or crop indicators, should be tested to see if they can identify different N supply areas within the field for a more efficient and environmentally friendly N management. © 2011 Elsevier B.V. All rights reserved
    Agriculture Ecosystems & Environment 01/2012; 147:66-72. · 2.86 Impact Factor
  • Environmetrics 01/2012; 23(2):129-147. · 1.10 Impact Factor
  • Environmetrics 01/2012; 23(2):148-161. · 1.10 Impact Factor
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    ABSTRACT: Geostatistical techniques can be used to predict spatially correlated variables at unsampled locations. We can incorporate information from soil process models in the geostatistical methodology via regression kriging (RK), which we consider in a Bayesian statistical framework (BRK). The resulting predictions are better than those obtained from the process model alone or by ordinary kriging. We consider approaches to predict the nitrous oxide emissions from soil along a transect in Bedfordshire in the UK. In this case study, there exists uncertainty about the most appropriate model to represent the denitrification process. We account for this uncertainty by model averaging (MA); the MA predictions are a weighted average of the BRK predictions based on the individual models. We consider several approaches to calculate weights for MA. We use Bayesian model averaging (BMA) to investigate whether the local data from the neighbourhood of a prediction location can provide useful information for calculating the model weights. We use the opinions of an expert on the relevant soil processes to define probabilities for the candidate models, and investigate how this information benefits the MA and BMA predictions. If we would prefer not to base analysis on the opinions of a single expert, we could use a linear opinion pool to merge the opinions of multiple experts, which we demonstrate through a simple example. We show the conditions under which MA and BMA improve predictions in this case study, and suggest reasons for these improvements. We use the BMA model weights, which are calculated from local data, to provide information about the ability of the models to represent the spatial variability of the data along the transect.
    European Journal of Soil Science 04/2011; 62(3):359 - 370. · 2.65 Impact Factor
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    ABSTRACT: We analysed data on nitrous oxide emission rate and some other properties of soil cores collected on a 7.5-km transect across contrasting land uses and parent materials in eastern England. The variation on this landscape-scale transect was compared with that of a comparable set of measurements made in a previous study on within-farm spatial scales in the same region. We used the wavelet transform to analyse the scale dependence and spatial uniformity of the correlations between soil properties and emission rates from farm to landscape scale. The analysis revealed a complex pattern of scale dependence. Soil organic carbon was correlated with emission rates at within-field scales only. There was a pronounced correlation between emission rates and a process-specific function of the water-filled pore space, seen only at landscape scales. Emission rates were strongly correlated with soil nitrate content at intermediate and coarsest scales (and significantly, although weakly, at the finest within-field scales), and with pH at the intermediate scales. The wavelet analysis showed that these correlations were not spatially uniform. The correlation between nitrate concentration and emission rates at the finest landscape scale (between approximately 60 and 120 m) was not significant in the northern part of the transect corresponding primarily to soils over the Lower Greensand, but these variables were significantly correlated at this scale over other parent materials. These findings have implications for modelling and inventory of nitrous oxide emissions from soil. They indicate that, at the landscape scale, nitrate content and water-filled pore space are key soil properties for predicting nitrous oxide emissions and should therefore be incorporated into process models and emission factors for inventory calculations.
    European Journal of Soil Science 04/2011; 62(3):467 - 478. · 2.65 Impact Factor
  • R. Webster, R. M. Lark
    Mathematical geosciences 01/2011; 43(2):261-263. · 1.44 Impact Factor
  • European Journal of Soil Science 01/2011; 62(6):891-901. · 2.65 Impact Factor
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    ABSTRACT: The uncertainty of a prediction of a spatial property may only be fully described if the property is assumed to be a realization of a multivariate random variable. Model-based geostatistical methods are generally based on the assumption that the random variable is multivariate Gaussian. However this model is implausible for many soil properties. For example, observations of cadmium concentrations from the French National Soil Monitoring Network include outliers which arise because of isolated pollution and other local anomalies. We introduce a more general multivariate function for the spatial analysis of soil properties based on copulas. The dependence structure and marginal distributions of this function are specified separately. A copula-based model with a Gaussian dependence structure and generalized extreme value marginal distributions is fitted to the observations of cadmium across France. The expected concentration of cadmium is permitted to vary with parent material. This model is used to predict the distribution of cadmium concentrations at unsampled sites conditional on the observed data. Upon cross-validation the copula-based model performs better than existing model-based approaches. However further generalizations, such as the use of non-Gaussian copulas, are required to ensure a complete description of the complexity of the variation of cadmium in French soils. (C) 2011 Elsevier B.V. All rights reserved.
    Geoderma 01/2011; 162(3-4):327-334. · 2.35 Impact Factor
  • R. M. Lark
    [show abstract] [hide abstract]
    ABSTRACT: Efficient designs for nested sampling are needed in many areas of science. In the geosciences they are used to discover the important spatial scales on which properties vary. However, while the practical advantages and disadvantages of various nested designs have been discussed, no attempt has been made to optimize nested sampling schemes. This paper shows how an optimal nested sampling design can be found by a method of numerical combinatorial optimization: simulated annealing. The sample design is optimized over a space of possible designs for a fixed sample size and predetermined levels (spatial scales). The objective function for optimization is based on the expected covariance matrix for errors in the estimates of variance components, and so depends on what those components are. By simulation it was shown that optimized sampling schemes can detect scale-dependent variance components with common requirements for statistical power on smaller total sample sizes than are required with commonly used spatially nested sample designs such as the balanced design. Although the optimized design depends on the underlying covariance structure, sampling designs can be identified that perform better than the commonly used ones over a wide range of conditions.
    Computers & Geosciences 01/2011; 37:1633-1641. · 1.83 Impact Factor
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    ABSTRACT: National-scale soil monitoring networks are required to identify where the soil quality is threatened and evaluate the effectiveness of any remediation efforts. In particular, trace elements (TEs) should be monitored to assess human exposure to potentially toxic elements and to ensure that crops take up sufficient quantities of elements that have essential functions in the human body. However the spatial variation of TEs is often highly complex since hot-spots at point sources are superimposed upon more regular patterns produced by diffuse pollution and natural processes. Geostatistical methods used to analyse national-scale soil monitoring networks must be general enough to accommodate such behaviour but simple enough to be computed in a reasonable time for large datasets. We show how a simplified version of a recently developed robust geostatistical algorithm to map the underlying variation of six TEs (Cr, Cu, Pb, Ni, Th and Zn) across France using observations from the French National Soil Monitoring Network (Reseau de Mesures de la Quake des Sols). Cross-validation results suggest that these TEs cannot be modelled by non-robust methods but that the simplified robust approach is sufficient Differences between the maps of different elements and the abundance of TEs from different parent materials are evident. Large concentrations of Cr, Ni and Zn occur in soils on Jurassic rocks whereas Pb and Th concentrations are large in soils on crystalline rocks. Volcanic parent material leads to large concentrations of Cr, Cu, Ni and Zn but small concentrations of Pb and Th. Diffuse pollution of certain elements (mainly Pb, and to a lesser extent Zn) is evident in industrial regions in the north and the north-east of France and close to Paris. The pattern of outlying values is indicative of local anthropogenic processes such as industrial pollution in the north of France and close to Paris, and application of Cu on vineyards and of geological anomalies such as large concentrations of some TEs in the south of the Massif Central Mountains. Future phases of the RMQS will describe the spatial and temporal trends of the concentrations of these TEs. (C) 2011 Elsevier B.V. All rights reserved.
    Geoderma 01/2011; 162(3-4):303-311. · 2.35 Impact Factor
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    ABSTRACT: Analysis of data from the National Soil Inventory of England and Wales obtained between 1978 and 2003 shows widespread increases in soil pH – i.e., soils became less acid – across both countries during the survey period. In general, soil pH increased under all land uses. At least part of the increase and its regional variation could be explained by decreased sulphur deposition from the atmosphere. Changes in liming practices on arable land probably also contributed. The effect of decreased sulphur deposition was moderated by land use, soil properties – particularly soil pH and organic carbon content – and the level of past sulphur deposition.
    Global Change Biology 10/2010; 16(11):3111 - 3119. · 6.91 Impact Factor
  • B. P. Marchant, R. M. Lark
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    ABSTRACT: If farmers are to manage the soil–crop system efficiently through variable application of fertilizers within fields they require information of the within-field variation of soil properties. To ensure that precision agriculture is cost-effective, soil sampling must be as efficient as possible. This chapter demonstrates the potential to optimize the design of soil sampling schemes if the variation of the target property is represented by a linear mixed model. If the parameters of the model are known prior to sampling we see that it is possible to optimize the sampling design with a numerical algorithm known as spatial simulated annealing. In general the parameters are unknown when the sample scheme is designed and the model is fitted to the observations. However it can be sufficient to assume a model which was fitted to a previous survey of the target variable over a similar landscape. When we do not have existing information about the variation of the target variable multi-phase adaptive sampling schemes may be used. We describe such a scheme for a survey of top-soil water content. The data are analysed as they are collected, and the sample design is modified to ensure that it is suitable for the particular target variable. The technologies described in this chapter represent the state of the art for sampling design in the geostatistical context. We discuss the developments required for them to be implemented as standard tools for precision agriculture. KeywordsSampling-Linear mixed models (LMM)-Spatial simulated annealing-Adaptive sampling-Residual maximum likelihood (REML)
    07/2010: pages 65-87;
  • R. M. Lark
    [show abstract] [hide abstract]
    ABSTRACT: Geostatistical analysis of soil properties is undertaken to allow prediction of values of these properties over regions or at unsampled locations. A key step in geostatistical analysis is the estimation of a variogram function that describes the spatial covariance structure of the variable in question. If it can be assumed plausibly that the data are a realization of a second-order stationary multivariate normal random function then this function is entirely characterized by its mean (expectation) and spatially dependent covariance. Because of this, the variogram is sometimes computed as a general ‘descriptor’ of spatial variation, and used, for example, to compare the spatial structure at within-aggregate scales of soils under different management, or to compare soils from different land uses with respect to the spatial structure of their microbial populations. The objective of this paper is to draw attention to the limited value of the variogram for characterizing spatial variation (as opposed to deriving best linear unbiased predictions). Specifically, it is shown how two contrasting processes, one of which gives rise to a multivariate normal random function (a convolution filter applied to independent identically distributed random values) and one which does not (a partition of space into random sets), may have the same variogram function. A diagnostic is proposed that indicates which of these two processes is most plausible as a model for a data set. This will allow the spatial analysis of soil data to give greater insight into the factors underlying the variation of a soil property, and may permit more realistic simulation of soil properties.
    European Journal of Soil Science 06/2010; 61(4):479 - 492. · 2.65 Impact Factor
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    ABSTRACT: Mathematical models of processes in soil science are often used to test our understanding of these processes, highlight where this is wanting and identify new hypotheses. Process models are also practically useful, for example, a soil process model can predict how the soil system will respond to changes in management or environment. They can therefore be used to help managers make decisions, or to help government predict the effects of new policy, trends in land use or climate change. Models are therefore needed to make predictions at different scales, scales which are often different from the scale at which the model was developed, or the scale at which information on model inputs is available. Soil process models are typically developed at a particular spatial scale, depending on the processes described, experimental setup or measurements used to construct the model, and this scale is typically at that of a soil core or small field plot. This scale does often not correspond to the scale at which the model application scale or for which input information is available. When this happens, the model and its inputs require aggregation or disaggregation to the application scale, and this is a complex problem. The problem of disaggregation depends on the variability of the inputs, and on the mathematical structure of the model. Whether model output can be simply aggregated to the required scale depends on whether the model describes the key processes that determine the process outcome at that target scale. We present a diagnostic framework which evaluates whether a model is appropriate for use at one or more target spatial scales. This evaluation is based on the performance of the predictions of variations at those target scales and also in the requirements for disaggregation of the inputs. We show that spatially nested analysis of the covariance of predictions with measured process outcomes is an efficient way to determine this performance. From the spatially nested analysis of covariance, we identified the component correlations as the diagnostic with which to evaluate model behaviour. The concordance correlation is a measure of agreement between two variables which reflects both their linear correlation and the extent to which they agree with respect to their mean and variance. These correlations show how well the model emulates components of spatial variation of the target process at the scales of the sampling scheme. In the case only the model is used to predict, and the most useful diagnostic is the concordance aggregate correlation. Aggregate correlations were identified as the most pertinent to evaluate models for prediction at particular scales since they measure how well aggregated predictions at some scale correlate with aggregated values of the measured outcome. The aggregate correlations are computed from the aggregated covariance matrices. In this case model predictions are assimilated with observations which should correct bias in the prediction, and errors in the variance; the aggregate correlations would be the most suitable diagnostic. This diagnostic framework is demonstrated using a set of models of the soil processes associated to ammonia volatilization from urea.
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    ABSTRACT: Precision agriculture (PA) offers opportunities for the development of new approaches to on-farm experimentation to assist farmers with site-specific management decisions. Traditional agricultural experiments are usually implemented in fields with the least possible soil heterogeneity under the assumption that responses to inputs and inherent variation of the soil are additive components of yield variation. However, because the soil in typical fields is not homogeneous, PA has much to offer. Farmers faced with variable conditions need to optimize their management to the variation over space and time on their farm, a problem that is not solved by conventional approaches to experimentation. New designs for on-farm experiments were developed in the 1990s for cereal production in which the whole field was used for the experiment rather than small plots. We explore the extension of this type of experiment to a vineyard in the Clare Valley of South Australia aiming to evaluate options to increase grape yield and vine vigour. Manually sampled indices of vine performance measured on georeferenced ‘target’ grapevines were analysed geostatistically. The major advantage of such an approach is that the spatial variation in response to experimental treatments can be examined. Linear models of coregionalization, pseudo cross-variograms and standardized ordinary cokriging are used to map treatment responses over the experimental area and also the differences between them. The results indicate that both treatment responses and the significance of differences between them are spatially variable. Thus, we conclude that whole-of-block on-farm trials are useful in vineyards. KeywordsOn-farm trials-Viticulture-Geostatistical analysis-Linear models of co-regionalisation (LMCR)-Pseudo cross-variogram
    Precision Agriculture 01/2010; 11(2):198-213. · 1.73 Impact Factor
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    ABSTRACT: In this paper we present a linear mixed model for the potassium content of soil across a large region of eastern England in which the mean is modelled as a linear function of the passive gamma-ray emissions of the earth surface in the energy interval commonly associated with potassium decay. Non-stationary models are proposed for the random effect, which is the variation not captured by this regression. Specifically, we assume that the local spectrum of the standardized random effect can be obtained by tempering a common (stationary) spectrum, that is to say raising its values to a power, the tempering parameter, which is itself modelled as a linear function of the radiometric data. This allows the `smoothness' of the random effect to vary locally. In addition the local spatially correlated variance and `nugget' variance (apparently uncorrelated given the resolution of the sampling) can also be modelled as a function of the radiometric data. Using the radiometric signal as a covariate gave some improvement in the precision of predictions of soil potassium at validation sites. In addition, there was evidence that non-stationary models for the random effect fitted the data better than stationary models, and this difference was statistically significant. Non-stationary models also appeared to describe the error variance of predictions at the validation sites better. Further work is needed on selection among alternative non-stationary models, since simple procedures used here, based on comparing log-likelihood ratios of nested models and the Akaike information criterion for non-nested models, did not identify the model which gave the best account of the prediction error variances at validation sites.
    Biogeosciences. 01/2010; 7(7):2081-2089.

Publication Stats

1k Citations
215.22 Total Impact Points


  • 2012
    • British Geological Survey
      Nottigham, England, United Kingdom
  • 1970–2011
    • Rothamsted Research
      Harpenden, England, United Kingdom
  • 2009
    • Agri-Food and Biosciences Institute
      Béal Feirste, N Ireland, United Kingdom
  • 2008–2009
    • University of Florida
      • Department of Soil and Water Science
      Gainesville, FL, United States
  • 2007
    • University of Reading
      Reading, England, United Kingdom
  • 2006
    • Cranfield University
      Cranfield, England, United Kingdom
  • 1995–1998
    • University of Oxford
      • Department of Plant Sciences
      Oxford, ENG, United Kingdom