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1.
B.P. Marchant  R.M. Lark   《Geoderma》2007,140(4):337-345
The Matérn variogram model has been advocated because it is flexible and can represent varied behaviour at small lags. We show how the constraints on the spherical and exponential variogram at short lags ignore a possible source of uncertainty in the variogram and so in kriging surveys, that the Matérn model can describe. Matérn, spherical and exponential variogram models were fitted by maximum likelihood to a set of log10(K) observations made on a regular grid at Broom's Barn Farm, Suffolk, England. The likelihood profiles of the Matérn parameter estimates were asymmetric. Thus the uncertainty of these estimates could only be adequately assessed by a Bayesian approach. The uncertainty of estimated parameters of the Matérn variogram was larger than for the exponential variogram. This is an indication that the assumption of an exponential model limits the behaviour that may be described by the variogram. Thus uncertainty analyses where an exponential variogram is assumed may underestimate the uncertainty of kriged estimates. Bayesian analysis of the kriged estimates of log10(K) at Broom's Barn Farm using the Matérn variogram revealed an observable component of uncertainty due to variogram uncertainty. When an exponential variogram model was used, the estimate of this component of uncertainty was negligible. The Matérn variogram should therefore be used rather than the exponential model when assessing the adequacy of a variogram estimate. A method of designing sample schemes which is suitable for both estimating a Matérn variogram and interpolation is suggested.  相似文献   

2.
This paper develops a Bayesian approach for spatial inference on animal density from line transect survey data. We model the spatial distribution of animals within a geographical area of interest by an inhomogeneous Poisson process whose intensity function incorporates both covariate effects and spatial smoothing of residual variation. Independently thinning the animal locations according to their estimated detection probabilities results into another spatial Poisson process for the sightings (the observations). Prior distributions are elicited for all unknown model parameters. Due to the sparsity of data in the application we consider, eliciting sensible prior distributions is important in order to get meaningful estimation results. A reversible jump Markov Chain Monte Carlo (MCMC) algorithm for simulation of the posterior distribution is developed. We present results for simulated data and a real data set of minke whale pods from Antarctic waters. The main advantages of our method compared to design-based analyses are that it can use data arising from sources other than specifically designed surveys and its ability to link covariate effects to variation of animal density. The Bayesian paradigm provides a coherent framework for quantifying uncertainty in estimation results.  相似文献   

3.
A Bayesian approach to covariance estimation and spatial prediction based on flexible variogram models is introduced. In particular, we consider black-box kriging models. These variogram models do not require restrictive assumptions on the functional shape of the variogram; furthermore, they can handle quite naturally non isotropic random fields. The proposed Bayesian approach does not require the computation of an empirical variogram estimator, thus avoiding the arbitrariness implied in the construction of the empirical variogram itself. Moreover, it provides a complete assessment of the uncertainty in the variogram estimation. The advantages of this approach are illustrated via simulation studies and by application to a well known benchmark dataset.  相似文献   

4.
The uncertainty in estimation of spatial animal density from line transect surveys depends on the degree of spatial clustering in the animal population. To quantify the clustering we model line transect data as independent thinnings of spatial shot-noise Cox processes. Likelihood-based inference is implemented using Markov chain Monte Carlo (MCMC) methods to obtain efficient estimates of spatial clustering parameters. Uncertainty is addressed using parametric bootstrap or by consideration of posterior distributions in a Bayesian setting. Maximum likelihood estimation and Bayesian inference are compared in an example concerning minke whales in the northeast Atlantic.  相似文献   

5.
Sample adequately to estimate variograms of soil properties   总被引：17，自引：0，他引：17  
The variogram is central in the spatial analysis of soil, yet it is often estimated from few data, and its precision is unknown because confidence limits cannot be determined analytically from a single set of data. Approximate confidence intervals for the variogram of a soil property can be found numerically by simulating a large field of values using a plausible model and then taking many samples from it and computing the observed variogram of each sample. A sampling distribution of the variogram and its percentiles can then be obtained. When this is done for situations typical in soil and environmental surveys it seems that variograms computed on fewer than 50 data are of little value and that at least 100 data are needed. Our experiments suggest that for a normally distributed isotropic variable a variogram computed from a sample of 150 data might often be satisfactory, while one derived from 225 data will usually be reliable.  相似文献   

6.
A sampling strategy is presented for soil survey in which an individual soil property is of interest and can be measured. It depends on first determining accurately the semi-variogram for the property, and this must be done in a prior reconnaissance stage of a survey. Then from the semi-variogram estimation variances can be found for any combination of block size and sampling density by the methods of kriging. Alternatively for a given block size the sampling density needed to achieve a predetermined precision (maximum estimation variance) can be determined. The strategy is optimal in the sense that the sampling effort is the least possible to achieve the precision desired. An equilateral triangular configuration of sampling points is best where variation is isotropic, but a square grid at the same density is very nearly as good, and will usually be preferred for convenience. Where there is simple anisotropic variation optimal sampling is achieved by choosing a rectangular grid with sides in the same proportion to one another as the slopes of the semi-variogram in the directions of maximum and minimum variation.  相似文献   

7.
The incorporation of measures of soil variability at the reconnaissance stage of soil survey is considered as a possible alternative to, or additional feature of, present procedures. A straightforward hierarchical sampling design based upon the major parent materials of the upland section of the study area and associated analysis of variance model are described. This allowed the estimation of scale components for five levels of the sampling design at separation distances from over two kilometers down to five meters. Principal components analysis is used to economise on the number of variables for further analysis. Analysis of the pattern of principal component scores shows the first six components to have distinctive variability patterns both within and between strata. It is concluded that present soil survey procedures take too little account of soil variability patterns, and that inclusions of such information at the reconnaissance stage would greatly improve the detailed survey.  相似文献   

8.
A series of five papers compares the cost-effectiveness of different procedures for soil survey at medium scale. The first three are presented here. The whole trial area of 120 km2 in Berkshire, in south-central England, was mapped in soil series by free survey at 1:25 000 for publication at 1:63 360. Three contrasting sample areas of 1.26 km2 were resurveyed to the same legend by free survey at 1:10 560, and by grid survey at a range of scales between 1:20 000 and 1:70 000, to both general purpose (soil series) and fifteen–twenty different single-property legends. The direct costs of producing each map were recorded. The study confirmed how much the free survey procedure depended on the external features of soil boundaries to locate them. The density of soil observations required to map soil series by free survey at the same map scale in different terrains was approximately proportional to the length of mapped boundary/km2, or to the number of separately mapped soil occurrences/km2. The density was least where the soil boundaries had the clearest external expression. Survey effort/km2 increased in proportion to the density of observations but was also affected by local differences in the ease of cross-country access, or in the effort necessary (by spade or auger) to identify the soil at a point. For soil series grid surveys there are approximately linear relations between log(cost) and log(map scale) with gradients between 1.3 and 1.7. A map of soil series by grid survey is more expensive than a map of the same units, based upon the same density of observations by the same surveyor, by free survey. But a series map by grid survey by a scientific assistant is cheaper than a series map based on the same density of soil observations by free survey by a scientific officer (diplomate or graduate). The cost of an isoline map of a single soil property depends very much upon the cost of determining the property mapped, and to some extent upon the number of different isoline maps produced from a single set of samples or observations. Even at the unusually low costs of chemical analyses assumed here, an isoline map of one chemical property costs nearly twice as much as a series map by grid survey.  相似文献   

9.
This paper develops the concept of the quality of a soil map in terms of the proportion of soil boundaries that have remained undetected as a result of point sampling. This proportion is equated to the risk of omitting such boundaries during survey. A risk function is defined, and the optimal strategy is such that the risk is maintained at some predetermined acceptable level. In general the risk depends on the distribution of boundary spacings, the distance travelled from the last boundary and the projected sampling interval. Where the distribution is exponential, the position of the last encountered boundary is immaterial, and for a constant risk the sampling interval is also constant. The optimal strategy is a regular grid. The same principles enable the total sampling effort for a survey of constant risk to be forecast once the distributions of boundary spacings have been estimated from reconnaissance. The sampling effort for a risk of 0.1 is shown to be within the range of traditional practice.  相似文献   

10.
The inclusion of covariates in models for analyzing variety × environmental data sets allows the estimation of variety yields for specific locations within a region as well as for the region as a whole. Here we explore a Bayesian approach to the estimation of such effects and to the choice of variety using a possibly incomplete variety × location × year data set that includes location × year covariates. This approach allows expert knowledge of the crop and uncertainty about local circumstances to be incorporated in the analysis. It is implemented using Markov chain Monte Carlo simulation. An example is used to illustrate the approach and investigate its robustness.  相似文献   

11.
Forecasting the end-of-year crop yield is critical for agricultural decision-making and inherently difficult. Historically, a panel of commodity specialists known as the Agricultural Statistics Board convene regularly to set estimates based on expert review of a combination of survey data and administrative/auxiliary information. To make this process less subjective and more repeatable, we develop a Bayesian hierarchical model that produces superior yield forecasts/estimates, while quantifying different sources of uncertainty. The proposed hierarchical model naturally combines information from multiple monthly surveys measured on different temporal supports, including a field measurement survey and two farmer interview surveys. The dependence between the monthly updated surveys and the serial dependence of the annual yield are incorporated at different levels of the hierarchy. The effectiveness of our approach is demonstrated through an application from the US Department of Agriculture. Empirical results indicate that the hierarchical model produces superior forecasts to both the panel of experts and the composite estimator developed by Keller and Olkin (Technical Report, National Agricultural Statistics Service, 2002), while providing an accurate measure of uncertainty.  相似文献   

12.
A problem of interest for ecology and conservation is that of determining the best allocation of survey effort in studies aimed at estimating the proportion of sites occupied by a species. Many species are difficult to detect and often remain undetected during surveys at sites where they are present. Hence, for the estimator of species occupancy to be unbiased, detectability needs to be taken into account. In such studies there is a trade-off between sampling more sites and expending more survey effort within each site. This design problem has not been addressed to date with an explicit consideration of the uncertainty in assumed parameter values. In this article we apply sequential and Bayesian design techniques and show how a simple two-stage design can significantly improve the efficiency of the study. We further investigate the optimal allocation of survey effort between the two study stages, given a prior distribution for the parameter values. We address this problem using asymptotic approximations and then explore how the results change when the sample size is small, considering second-order approximations and highlighting the value of simulations as a tool for study design. Given the efficiency gain, we recommend following the sequential design approach for species occupancy estimation. This article has supplementary material online.  相似文献   

13.
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.  相似文献   

14.
When data streams are observed without error and at regular time intervals, discrete-time hidden Markov models (HMMs) have become immensely popular for the analysis of animal location and auxiliary biotelemetry data. However, measurement error and temporally irregular data are often pervasive in telemetry studies, particularly in marine systems. While relatively small amounts of missing data that are missing-completely-at-random are not typically problematic in HMMs, temporal irregularity can result in few (if any) observations aligning with the regular time steps required by HMMs. Fitting HMMs that explicitly account for uncertainty attributable to location measurement error, temporally irregular observations, or other forms of missing data typically requires computationally demanding techniques, such as Markov chain Monte Carlo (MCMC). Using simulation and a real-world bearded seal (Erignathus barbatus) example, I investigate a practical alternative to incorporating measurement error and temporally irregular observations into HMMs based on multiple imputation of the position process drawn from a single-state continuous-time movement model. This two-stage approach is relatively simple, performed with existing software using efficient maximum likelihood methods, and completely parallelizable. I generally found the approach to perform well across a broad range of simulated measurement error and irregular sampling rates, with latent states and locations reliably recovered in nearly all simulated scenarios. However, high measurement error coupled with low sampling rates often induced bias in both the estimated probability distributions of data streams derived from the imputed position process and the estimated effects of spatial covariates on state transition probabilities. Results from the two-stage analysis of the bearded seal data were similar to a more computationally intensive single-stage MCMC analysis, but the two-stage analysis required much less computation time and no custom model-fitting algorithms. I thus found the two-stage multiple-imputation approach to be promising in terms of its ease of implementation, computation time, and performance. Code for implementing the approach using the R package “momentuHMM” is provided.Supplementary materials accompanying this paper appear online.  相似文献   

15.
In the scheme of agrochemical surveys, sampling is one of the most costly stages. The use of a priori information about the distributions of properties (Bayesian approach) allows one to reduce the number of samples to be taken by 5–10% without deteriorating the accuracy of the estimation. The maintenance of regional soil-mapping databases is a necessary condition for applying the Bayesian approach.  相似文献   

16.
Small scale digital soil mapping in Southeastern Kenya   总被引：1，自引：0，他引：1  
Digital soil mapping techniques appear to be an interesting alternative for traditional soil survey techniques. However, most applications deal with (semi-)detailed soil surveys where soil variability is determined by a limited number of soil forming factors. The question that remains is whether digital soil mapping techniques are equally suitable for exploratory or reconnaissance soil surveys in more extensive areas with limited data availability. We applied digital soil mapping in a 13,500 km2 study area in Kenya with the main aim to create a reconnaissance soil map to assess clay and soil organic carbon contents in terraced maize fields. Soil spatial variability prediction was based on environmental correlation using the concepts of the soil forming factors equation. During field work, 95 composite soil samples were collected. Auxiliary spatially exhaustive data provided insight on the spatial variation of climate, land cover, topography and parent material. The final digital soil maps were elaborated using regression kriging. The variance explained by the regression kriging models was estimated as 13% and 37% for soil organic carbon and clay respectively. These results were confirmed by cross-validation and provide a significant improvement compared to the existing soil survey.  相似文献   

17.
Abstract. In general, agricultural management has focused on differences between fields or on the gross differences within them. Recent developments in agricultural technology, yield mapping, Global Positioning Systems and variable rate applications, have made it possible to consider managing the considerable variation in soil and other properties within fields. This system is known as precision agriculture. More precise management of fields depends on a better understanding of the factors that affect crop input decisions. This paper examines the spatial variation in crop yield, soil nutrient status and soil pH within two agricultural fields using geostatistics. The observed properties vary considerably within each field. The relation between yield and the measured soil properties appears to be weak in general. However, the range of spatial correlation for yield, shown by the variogram, is similar to that of the soil chemical properties. In addition the latter changed little over two years. This suggests that information on the scale of variation of soil chemical properties can be derived from yield maps, which can also be used as a guide to a suitable sampling interval for soil properties.  相似文献   

18.
Abstract

The formation of soils in any region is influenced by many factors such as the parent materials and the secondary materials derived from them, the vegetation and the history of land use. These factors vary from place to place, and they contribute to the spatial variation in properties of the soil. Quantification of the magnitude, location, and causes of spatial variability is an essential, but insufficient ingredient of soil surveys. Soil samples from the 0‐ to 20‐cm depth were taken covering soils in the Asuansi‐Akroso‐Nta‐Ofin compound association (Lixisol, Cambisol, and Fluvisol association) at the study site by following the nested balanced hierarchical sampling technique. This covered distances between 100 and 0.80 m. Standard laboratory analyses were performed to quantify the selected properties, namely, pH, organic carbon, total nitrogen, total phosphorus, exchangeable potassium, and content of sand, silt, and clay. Classical statistics and geostatistical procedures were performed on the data and models fitted to the variability patterns. Physical and the more stable properties, such as sand, silt, and clay, were fitted with spherical variogram models. These models indicate a high level of spatial dependence, therefore, such properties may be said to be fairly stable in the field. On the contrary, chemical properties, such as exchangeable potassium, were fitted with exponential variogram models, indicating that these properties were less stable and showed dependence over longer distances. The scale of variation of the properties ranged between 35 and 62 m. The degree of uncertainty associated with time and space can be reduced by improved documentation of field variability using the tools of geostatistics.  相似文献   

19.
Snapper (Pagrusauratus) stocks found inside Shark Bay, Western Australia, are the basis of important recreational fisheries. An evaluation of the daily egg production method for annual snapper stock assessment commenced in 1997. Initial spawning biomass estimates were inconclusive due to wide confidence intervals around egg production in particular. In 1998, more comprehensive surveys were conducted in an effort to improve the accuracy and precision of the estimated parameters. Egg survey design used information on the location of the main spawning areas and spawning times identified in 1997 and employed a systematic stratified adaptive sampling approach. Further refinements to the daily egg production method included use of nonlinear regression and nonparametric bootstrapping techniques. Results are discussed in relation to the precision of parameter estimates, with reference to egg production in particular, and the appropriateness of analytical methods used.  相似文献   

20.
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