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Using model predictions of soil carbon in farmscale auditing  A software tool Gruijter, J.J. de; Wheeler, I. ; Malone, B.P.  \ 2019
Agricultural Systems 169 (2019).  ISSN 0308521X  p. 24  30. Julia  Map uncertainty  Prediction error  Soil carbon auditing  Stratified random sampling  Value of information
We introduce a software tool for optimal sampling design in the context of farmscale soil carbon auditing, where the amount of sequestered soil carbon will be estimated from a random sample. Existing tools do not use available ancillary information, or do not have the functionality needed for farmscale soil carbon auditing. Using a grid of predicted carbon content with associated uncertainty, the software optimises a stratified random sampling design, such that the profit is maximised on the basis of sequestered carbon price, sampling costs, and a trading parameter that balances farmer's and buyer's risks due to uncertainty of the estimated amount of sequestered carbon. As the algorithm is computationally intensive, the package is written in Julia for speed. From a case study we conclude that our software is an effective tool for farmscale soil carbon auditing, and that it outperforms the existing tools in terms of efficiency and functionality. 

Spatial Coverage Sampling and Random Sampling from Compact Geographical Strata. R package version 0.38 Walvoort, D.J.J. ; Brus, D.J. ; Gruijter, J.J. de  \ 2018
The Comprehensive R Archive Network (CRAN) Spatial coverage sampling and random sampling from compact geographical strata created by kmeans.


Towards a sampling design for monitoring global soil organic carbon stocks Heuvelink, G.B.M. ; Batjes, N.H. ; Brus, D.J. ; Gruijter, J.J. de; McBratney, A.B. ; Stockmann, Uta  \ 2017
In: Book of Abstracts Wageningen Soil Conference 2017.  Wageningen : Wageningen University & Research  p. 74  74. 

Effects of spatial pattern persistence on the performance of sampling designs for regional trend monitoring analyzed by simulation of spacetime fields Brus, D.J. ; Gruijter, J.J. de  \ 2013
Computers and Geosciences 61 (2013).  ISSN 00983004  p. 175  183. geostatistics
The effect of the persistence of spatial patterns on the performance of spacetime sampling designs is explored by a simulation study. The performance is evaluated on the basis of the covariance matrix of the two parameters (intercept and slope) of a linear model for the change over time of the spatial means or totals. The evaluated sampling approach is hybrid, i.e. designbased estimation of spatial means from spatial probability samples is combined with timeseries modelling of the spatial means. A simulation algorithm is presented for approximating the covariance matrix of the timeseries model parameters from a full spacetime model. Designs were evaluated on the basis of the determinant of this matrix and the variance of the estimated trend parameter. As a spacetime model a summetric spacetime variogram is used, the parameters of which are chosen such that the persistence of spatial patterns varies from nearly absent to very strong. Based on the extensive simulations, recommendations on the type of spacetime design can most easily be made for situations with either very strong or no persistence of spatial patterns. With strong persistence the supplemented panel (Sup) design is recommendable. With no persistence the independentsynchronous (IS) and serially alternating (SA) designs are the best choice. These designs performed well with regard to both quality criteria. With moderate persistence of spatial patterns the choice of design type is more complicated. The IS and staticsynchronous (SS) design performed best on one quality criterion, but worst on the other. Therefore, with moderate pattern persistence, the compromise designs, either SuP or SA, can be a good choice, unless one of the two quality criteria has priority. An R script is provided for ex ante evaluation of spacetime designs in realworld applications. (C) 2013 Elsevier Ltd. All rights reserved.


A hybrid design and modelbased sampling approach for regional trend monitoring Brus, D.J. ; Gruijter, J.J. de  \ 2012


A hybrid designbased and modelbased sampling approach to estimate the temporal trend of spatial means Brus, D.J. ; Gruijter, J.J. de  \ 2012
Geoderma 173174 (2012).  ISSN 00167061  p. 241  248. soil properties  optimization  variograms  patterns
This paper launches a hybrid sampling approach, entailing a designbased approach in space followed by a modelbased approach in time, for estimating temporal trends of spatial means or totals. The underlying space–time process that generated the soil data is only partly described, viz. by a linear mixed model for the temporal variation of the spatial means. The model contains error terms for model inadequacy (model or process error) and for the sampling error in the estimated spatial means. The linear trend is estimated by Generalized Least Squares. The covariance matrix is obtained by adding the matrix with designbased estimates of the sampling variances and covariances and the covariance matrix of the model errors. The model parameters needed for the latter matrix are estimated by REML. The error variance of the estimated regression coefficients can be decomposed into the model variance of the errorless regression coefficients and the model expectation of the conditional sampling variance. In a case study on forest soil eutrophication, inclusion of the model error led to a considerable increase of the error variance for most variables. In the topsoil the contribution of the process error to the standard error of the estimated trend was much larger than that of the sampling error. For pH there was no contribution of the model error. Important advantages of the presented approach over the fully modelbased approach are its simplicity and robustness to model assumptions.


Designbased Generalized Least Squares estimation of status and trend of soil properties from monitoring data Brus, D.J. ; Gruijter, J.J. de  \ 2011
Geoderma 164 (2011)34.  ISSN 00167061  p. 172  180. This paper introduces and demonstrates designbased Generalized Least Squares (GLS) estimation of spatial means at selected time points from data collected in repeated soil surveys with partial overlap, such as a rotating and a supplemented panel. The linear time trend of the spatial means can then be obtained as a linear combination of the estimated spatial means. The GLS estimator is the minimum variance linear unbiased estimator. Five space–time designs were compared under a first order autoregressive time series model for the spatial means, through the average and generalized sampling variances of the estimated spatial means, and through the sampling variance of the estimated linear trend. None of the designs scored best on all three quality measures. If the aim of soil monitoring is estimation of both status and trend, then these two conflicting aims must be prioritized in order to choose an efficient space–time design. The methodology is demonstrated by a case study on eutrophication and acidification of forest soils. The linear trends in the spatial means of pH and the ammonium and nitrate concentrations at three depths in the soil profile, as estimated from a rotational design with four sampling times at an interval of one year, were small and not significant. Exceptions were pH in the subsoil ( 0.06 pH units yr 1) and ammonium in the middle soil horizon ( 0.086 mg N kg 1 yr 1). The linear trend is here defined as a linear combination of the true and unknown, but fixed spatial means. In quantifying the uncertainty of the estimated trend, only the sampling error in the estimated spatial means is accounted for. If there is a need to include uncertainty due to fluctuations of the true spatial means around a linear trend, then a superpopulation or time series model for the spatial means must be postulated which comprises a model error term. The linear trend is then defined as a model parameter, that can be estimated by Generalized Least Squares as in generalized linear modeling. 


Application of fuzzy logic to Boolean models for digital soil assessment Gruijter, J.J. de; Walvoort, D.J.J. ; Bragato, G.  \ 2011
Geoderma 166 (2011)1.  ISSN 00167061  p. 15  33. land suitability  classification  interpolation  set
Boolean models based on expert knowledge are often used to classify soils into a limited number of classes of a difficulttomeasure soil attribute. Although the primary data used for these classifications contain information on whether the soil is a typical class member or a boundary case between two classes, this is not retained in the final result. Such information is relevant in land use planning and soil management as it enables more flexible decision taking, but in the predigital era it was unfeasible to prevent the loss of it. We can now retain this information by fuzzifying the Boolean model using fuzzy logic. Choices must then be made on the type of membership function, logical operators, and formulation of the assessment rules. From a review of the main types of membership functions we conclude that piecewise linear functions are most appropriate in practical applications. Combinations of different fuzzy union (or) and intersection (and) connectives were tested on a 2dimensional example. Nearly all combinations gave results that partly contradict the associated a priori knowledge, the exception being the Bounded sum connective for or, and the Product connective for and. We also found that in formulating the rules, overlap of predictor classes and negation should be avoided. Unrestricted choice of fuzzy connectives and rule formulation will generally lead to inconsistencies. The selected methods were tested in two case studies: one on suitability for seedpotatoes in an Italian region and one on suitability for grass farming in a Dutch region. The maps produced with the fuzzy and Boolean models are broadly similar. However, maps from the fuzzy models indicate that some areas represent a transition between two original Boolean classes, thereby providing relevant additional information. In the case study on seedpotatoes the quantitative prediction errors of the original Boolean suitability map were greatly reduced by the fuzzification.


Using additional criteria for measuring the quality of predictions and their uncertainties in a digital soil mapping framework Malone, B. ; Gruijter, J.J. de; McBratney, A.B. ; Minasny, B. ; Brus, D.J.  \ 2011
Soil Science Society of America Journal 75 (2011)3.  ISSN 03615995  p. 1032  1043. continuous depth functions  fuzzy kmeans  maps  extragrades  information
In this paper we introduce additional criteria to assess the quality of digital soil property maps. Soil map quality is estimated on the basis of validating both the accuracy of the predictions and their uncertainties (which are expressed as a prediction interval [PI]). The first criterion is an accuracy measure that is different in form to the usual mean square error (MSE) because it accounts also for the prediction uncertainties. This measure is the spatial average of the statistical expectation of the mean square error of a simulated random value (MSES). The second criterion addresses the quality of the uncertainties which is estimated as the total proportion of the study area where the (1a)–PI covers the true value. Ideally, this areal proportion equals the nominal value (1  a). In the Lower Hunter Valley, NSW, Australia, we used both criteria to validate a soil pH map using additional units collected from a probability sample at five depth intervals: 0 to 5, 5 to 15, 15 to 30, 30 to 60, and 60 to 100 cm. For the first depth interval (0–5 cm) in 96% of the area, the 95% PI of pH covered the true value. The root mean squared simulation error (RMSES) at this depth was 1.0 pH units. Generally, the discrepancy between the nominal value and the areal proportion in addition to the RMSES increased with soil depth, indicating largely a growing imprecision of the map and underestimation of the uncertainty with increasing soil depth. In exploring this result, conventional map quality indicators emphasized a combination of bias and imprecision particularly with increasing soil depth. There is great value in coupling conventional map quality indicators with those which we propose in this study as they target the decision making process for improving the precision of maps and their uncertainties. For our study area we discuss options for improving on our results in addition to determining the possibility of extending a similar sampling approach for which multiple soil property maps can be validated concurrently


An R package for spatial coverage sampling and random sampling from compact geographical strata by kmeans Walvoort, D.J.J. ; Brus, D.J. ; Gruijter, J.J. de  \ 2010
Computers and Geosciences 36 (2010)10.  ISSN 00983004  p. 1261  1267. constrained optimization  variance
Both for mapping and for estimating spatial means of an environmental variable, the accuracy of the result will usually be increased by dispersing the sample locations so that they cover the study area as uniformly as possible. We developed a new R package for designing spatial coverage samples for mapping, and for random sampling from compact geographical strata for estimating spatial means. The mean squared shortest distance (MSSD) was chosen as objective function, which can be minimized by kmeans clustering. Two kmeans algorithms are described, one for unequal area and one for equal area partitioning. The R package is illustrated with three examples: (1) subsampling of square and circular sampling plots commonly used in surveys of soil, vegetation, forest, etc.; (2) sampling of agricultural fields for soil testing; and (3) infill sampling of climate stations for mainland Australia and Tasmania. The algorithms give satisfactory results within reasonable computing time.


A sampling strategy for estimating plot average annual fluxes of chemical elements from forest soils Brus, D.J. ; Gruijter, J.J. de; Vries, W. de  \ 2010
Geoderma 159 (2010)33.  ISSN 00167061  p. 399  408. regional assessment  output fluxes  ecosystems  europe
A sampling strategy for estimating spatially averaged annual element leaching fluxes from forest soils is presented and tested in three Dutch forest monitoring plots. In this method sampling locations and times (days) are selected by probability sampling. Sampling locations were selected by stratified random sampling with five blocks of equal surface area as strata. At each selected day six composite soil solution samples were collected, consisting of five aliquots of equal volume, one per stratum. For most sampling days at some locations no soil solution was collected (nonresponse), and as a result the average of the six composite sample concentrations (the naïve estimator) is a biased estimator of the plot mean concentration. The plot mean concentration at these days was estimated by ordinary least squares. This estimation method eliminates the bias of the naïve estimator. This estimated concentration was multiplied by the modeled water flux to obtain an estimate of the daily element leaching flux. Sampling times (days) were selected by systematic ppssampling (sampling with probabilities proportional to size), with precipitation surplus, averaged over the past 30 years, as a measure of size. The spatially averaged annual leaching flux was estimated by the ratioestimator, accounting for the selection probabilities of the days, using the modeled daily water flux as an auxiliary variable.


Spatial coverage sampling and random sampling from compact geographical strata in R Walvoort, D.J.J. ; Brus, D.J. ; Gruijter, J.J. de  \ 2009


Spatial coverage sampling on various spatial scales Walvoort, D.J.J. ; Brus, D.J. ; Gruijter, J.J. de  \ 2009
Pedometron 26 (2009).  p. 20  22. 

Hoezo representatief? : over de betekenissen van representatief in de KRW literatuur Knotters, M. ; Brus, D.J. ; Gruijter, J.J. de  \ 2009
Stromingen : vakblad voor hydrologen 15 (2009)1.  ISSN 13826069  p. 3  14. hydrologie  gegevensanalyse  nomenclatuur  literatuur  monitoring  waterkwaliteit  ecologie  kaderrichtlijn water  hydrology  data analysis  nomenclature  literature  water quality  ecology  water framework directive
We gaan in op de selectie van representatieve locaties en representatieve tijdstippen bij monitoring voor de Europese Kaderrichtlijn Water. Het blijkt dat 'representatief' veel kan betekenen, wat niet altijd bijdraagt aan duidelijkheid over de steekproef opzet. Wij pleiten er daarom voor om het woord 'representatief' niet te gebruiken, maar de opzet en het doel van de steekproef gedetailleerd te beschrijven. 'Representatief' wordt wel eens in verband gebracht met kanssteekproeven, waarbij de eenheden aselect, at rondom, worden gekozen. Wij benadrukken dat, afhankelijk van het doel, in het ene geval een gerichte steekproef beter is en in het andere geval een kanssteekproef.


A soil sampling program for the Netherlands Visschers, R. ; Finke, P.A. ; Gruijter, J.J. de  \ 2007
Geoderma 139 (2007)12.  ISSN 00167061  p. 60  72. bodem  bemonsteren  bodemgeschiktheid  geostatistiek  soil  sampling  soil suitability  geostatistics  strategies  management  accuracy  table  map
Soil data users in The Netherlands were inventoried for current and future data needs. Prioritized data needs were used to design the Netherlands Soil Sampling Program (NSSP) as a framework containing 3 groups of related projects: map upgrading, map updating and upgrading of pedotransfer functions. In each one group, the sampling design, performance criteria and optimal sample size were defined. This paper focuses on the upgrading of the existing soil map of The Netherlands at scale 1:50,000, and extensively treats the user inventory and the sampling strategy. The sampling design, performance criteria of the sampling and associated optimal sample size were obtained by statistical analysis of soil data available before the sampling. The Phosphate Sorption Capacity (PSC) was chosen as target variable to optimize sampling, because it dominated total cost per sample. A prior analysis of a performance criterion related to the sampling error of PSC resulted in a cost saving of 13% relative to total cost determined earlier by expert judgment. A posterior analysis showed that the set quality criterion was reached or better in 6 out of 7 cases. The NSSP resulted in a data base with soil data from 2524 sample points selected by stratified random sampling, and a collection of 5764 aliquots taken at these points. The NSSP has been showing its usage potential for various kinds of environmental studies and could be a sound future basis for a national scale monitoring program.


Optimization of sample configurations for digital mapping of soil properties with universal kriging Heuvelink, G.B.M. ; Brus, D.J. ; Gruijter, J.J. de  \ 2007
In: Digital soil mapping : an introductory perspective / Lagacherie, P., McBratney, A.B., Voltz, M., Elsevier (Developments in soil science 31)  ISBN 9780444529589  p. 137  151. 

Evaluatie van bemesting en bekalking in bossen en de ontwikkeling van onbehandelde bossen Olsthoorn, A.F.M. ; Berg, C.A. van den; Gruijter, J.J. de  \ 2006
Wageningen : Alterra (Alterra rapport 1337.1)  39 bossen  kunstmeststoffen  bosbedrijfsvoering  bekalking  calciummeststoffen  kalk  bemesting  geostatistiek  forests  fertilizers  forest management  liming  calcium fertilizers  lime  fertilizer application  geostatistics
Dit rapport doet verslag van een deelonderzoek uit de Evaluatie van effectgerichte maatregelen in multifunctionele bossen 20042005 en is gericht op de effecten van de maatregelen bemesting en bekalking in bossen als overbruggingsmaatregel in het kader van het Overlevingsplan Bos en Natuur (OBN). Na een vooronderzoek met de gegevens uit 1998, 1999 en 2000 om het aantal locaties te bepalen is er in 2004 een herbemonstering uitgevoerd om te zien hoe de bomen gereageerd hebben op een bemesting en een bekalking. Daarnaast zijn de veranderingen in onbehandelde opstanden bekeken. In het onderzoek zijn geen significante effecten aangetoond van bemesting met fosfor, kalium of magnesium op het nutriëntengehalte van de bladeren of naalden. Het effect van fosforbemesting was bijna significant. De meetvariatie was zeer hoog. In het onderzoek zijn geen significante effecten aangetoond van bekalking op de bodempH. De pH van de bodem daalde licht door bekalking, als tijdelijk effect. In de onbehandelde opstanden zijn in de periode tussen de eerste en de tweede meting geen veranderingen opgetreden. Door de grote meetvariatie heeft een opstand die eerst laag scoorde een grote kans om later hoger te scoren, en andersom voor de eerst hoogscorende opstanden. De diagnostische waarde van een eenmalige meting moet door de grote meetvariatie ter discussie worden gesteld. Ook kan bij een bijstelling van de diagnose naar meer aspecten van het ecosysteem worden gekeken (bodemecologie, vegetatie).


Sampling for natural resource monitoring Gruijter, J.J. de; Brus, D.J. ; Bierkens, M.F.P. ; Knotters, M.  \ 2006
Berlin (Germany) etc. : Springer  ISBN 9783540224860  322 natuurlijke hulpbronnen  monitoring  bemonsteren  gegevensanalyse  ruimtelijke verdeling  statistiek  methodologie  tijdreeksen  hydrologie  bodemkunde  geostatistiek  natural resources  sampling  data analysis  spatial distribution  statistics  methodology  time series  hydrology  soil science  geostatistics
The book presents the statistical knowledge and methodology of sampling and data analysis useful for spatial inventory and monitoring of natural resources. The authors omitted all theory not essential for applications or for basic understanding. This presentation is broader than standard statistical texts, as the authors pay much attention to how statistical methodology can be employed and embedded in reallife spatial inventory and monitoring projects. Thus they discuss in detail how efficient sampling schemes and monitoring systems can be designed in view of the aims and constraints of the project.


Sturen op nitraat: nitraatconcentraties in het grondwater en mogelijke indicatoren Hackten Broeke, M.J.D. ; Burgers, S.L.G.E. ; Smit, A.L. ; Berge, H.F.M. ten; Boels, D. ; Gruijter, J.J. de; Hoving, I.E. ; Radersma, S. ; Roelsma, J. ; Velthof, G.L.  \ 2005
In: Eindrapportage van de milieuresultaten behaald in de nitraatprojecten (19992003). Deel II. Resultaten per project / ten Berge, H.F.M., Hackten Broeke, M.J.D., Wageningen : Plant Research International (PRI rapport 75B)  p. 185  202. 

Optimization of sample locations for universal kriging of environmental variables Brus, D.J. ; Heuvelink, G.B.M. ; Gruijter, J.J. de  \ 2005
In: Pedometrics 2005 Frontiers in Pedometrics, Biannual meeting of commission 1.5 pedometrics, div. 1 of the international union of soil science (IUSS), Naples, 1214 September 2005.  Naples : University of Florida, IFAS  p. 12  13. 