More than twice as much carbon is held in soils as in vegetation or the atmosphere, and changes in soil carbon content can have a large effect on the global carbon budget. The possibility that climate change is being reinforced by increased carbon dioxide emissions from soils owing to rising temperature is the subject of a continuing debate. But evidence for the suggested feedback mechanism has to date come solely from small-scale laboratory and field experiments and modelling studies. Here we use data from the National Soil Inventory of England and Wales obtained between 1978 and 2003 to show that carbon was lost from soils across England and Wales over the survey period at a mean rate of 0.6% yr(-1) (relative to the existing soil carbon content). We find that the relative rate of carbon loss increased with soil carbon content and was more than 2% yr(-1) in soils with carbon contents greater than 100 g kg(-1). The relationship between rate of carbon loss and carbon content is irrespective of land use, suggesting a link to climate change. Our findings indicate that losses of soil carbon in England and Wales--and by inference in other temperate regions-are likely to have been offsetting absorption of carbon by terrestrial sinks.

Summary The standard estimator of the variogram is sensitive to outlying data, a few of which can cause overestimation of the variogram. This will result in incorrect variances when estimating the value of a soil property by kriging or when designing a sampling grid to map the property to a required precision. Several robust estimators of the variogram, based on location and scale estimation, have been proposed as improvements. They seem to be suitable for analysis of soil data in circumstances where the standard estimator is likely to be affected by outliers. Robust estimators are based on assumptions about the distribution of the data which will not always hold and which need not be made in kriging or in estimating the variogram by the standard estimator. The estimators are reviewed. Simulation studies show that the robust estimators vary in their susceptibility to moderate skew in the underlying distribution, but that the effects of outliers are generally greater. The estimators are applied to some soil data, and the resulting variograms used for ordinary kriging at sites in a separate validation data set. In most cases the variograms derived from the standard estimator gave kriging variances which appeared to overestimate the mean squared error of prediction (MSEP). Kriging with variograms based on robust estimators sometimes gave kriging variances which underestimated the MSEP or did not differ significantly from it. Estimates of kriging variance and the MSEP derived from the validation data were generally close to estimates from cross‐validation on the prediction set used to derive the variograms. This indicates that variogram models derived from different estimators could be compared by cross‐validation.

across the full extent of the IGB. The aquifer system is usually represented as a single category on 66 hydrogeological maps [6]. However, in practice the system is complex and heterogeneous with large 67 spatial differences in permeability, storage, recharge and water chemistry as well as having an 68 important depth dimension. This complexity strongly influences how each part of the aquifer 69 responds to stresses [7]. The IGB is home to the largest surface water irrigation system in the world, 70 constructed during the 19 th and early 20th century to redistribute water from the Indus and Ganges 71 through a canal network >100,000 km long. Leakage from this irrigation infrastructure has had a 72 profound impact on the current quantity and quality of groundwater resources and is a significant 73 factor governing its response to contemporary and future pressures. Increasing groundwater use for 74 irrigation poses legitimate questions about the future sustainability of abstraction from the basin 75 and future groundwater security of this region is a major social-political concern [8]. 76Recent discussion of water security has been dominated by interpretations of remotely-sensed 77 gravity data from the GRACE mission gathered at a coarse scale of 400x400 km are poorly constrained by ground-based observations; local field studies nonetheless provide partial 82 insight into system dynamics. These include evidence of: declining groundwater levels [11,12,13], 83 groundwater security has been introduced by forecasts of climate change and the potential for 88 significant change to precipitation, river flows and groundwater recharge [20,21,22]. 89Here we present for the first time an analysis of the status of groundwater across the IGB alluvial 90 aquifer based entirely on in situ measurements. We use a statistical analysis of multiyear 91 groundwater-level records from 3652 water-wells and a compilation and interpretation of existing 92 high resolution spatial datasets and studies within Pakistan, India, Nepal and Bangladesh to assess: 93 (1) groundwater-level variations; (2) groundwater salinity; and (3) We find that the water-table within the IGB alluvial aquifer is typically shallow (< 5 m below ground 98 surface) and the long-term trend is relatively stable throughout much of the basin, with some 99 important exceptions. In areas of high groundwater abstraction in northwest India and the Punjab in 100 Pakistan ( Figure 2) the water-table can be >20 m bgl and in some locations is falling at rates of > 1 101 m/a (Figure 3). In areas of equivalent high irrigation abstraction within Bangladesh, the average 102 water-table remains shallow (<5 m bgl) due to greater direct recharge and high capacity for induced 103 recharge. Groundwater levels are deep and falling beneath many urban areas, and particularly in 104 large groundwater dependant cities such as Lahore, Dhaka and Delhi [23]. Shallow and rising water-105 tables are found in the Lower Indus, parts of the lower Bengal basin and in places throughout the 106 IGB aqui...

Geostatistical estimates of a soil property by kriging are equivalent to the best linear unbiased predictions (BLUPs). Universal kriging is BLUP with a fixed-effect model that is some linear function of spatial coordinates, or more generally a linear function of some other secondary predictor variable when it is called kriging with external drift. A problem in universal kriging is to find a spatial variance model for the random variation, since empirical variograms estimated from the data by method-of-moments will be affected by both the random variation and that variation represented by the fixed effects.The geostatistical model of spatial variation is a special case of the linear mixed model where our data are modelled as the additive combination of fixed effects (e.g. the unknown mean, coefficients of a trend model), random effects (the spatially dependent random variation in the geostatistical context) and independent random error (nugget variation in geostatistics). Statisticians use residual maximum likelihood (REML) to estimate variance parameters, i.e. to obtain the variogram in a geostatistical context. REML estimates are consistent (they converge in probability to the parameters that are estimated) with less bias than both maximum likelihood estimates and method-of-moment estimates obtained from residuals of a fitted trend. If the estimate of the random effects variance model is inserted into the BLUP we have the empirical BLUP or E-BLUP. Despite representing the state of the art for prediction from a linear mixed model in statistics, the REML-E-BLUP has not been widely used in soil science, and in most studies reported in the soils literature the variogram is estimated with methods that are seriously biased if the fixed-effect structure is more complex than just an unknown constant mean (ordinary kriging). In this paper we describe the REML-E-BLUP and illustrate the method with some data on soil water content that exhibit a pronounced spatial trend.