Conditional Sequential Gaussian Simulation Research Articles

Plurigaussian conditional simulation (PGS) of the Budenovskoe uranium roll-front deposit, central Kazakhstan: 3D model of the host sedimentary sequence

ABSTRACT The current paper presents case study of the Budenovskoe sandstone-hosted uranium deposit, the host sequence of which has been modelled geostatistically, using Plurigaussian conditional simulation (PGS) and Sequential Gaussian conditional simulation (SGS). The PGS method minimises subjectivism of the geological interpretations, by constraining the lithological models to geostatistical and lithostratigraphic characteristics of the host sequence, and accurately reproduces litho-stratigraphy of the sedimentary sequence, realistically conveying its complexity. This was integrated with the rock permeability generated using SGS. Integrating two models has significantly enhanced definition of the fluid infiltration passages in the host sequence. The model was built using stochastic algorithms of PGS and SGS, and therefore can be used for estimation the project risk. In practice, the errors, initially estimated to the blocks used for the conditional simulation, are grouped to the volumes of a practical interest, including the resource and reserve domains, production blocks and the leach cells.

Sampling Estimation and Optimization of Typical Forest Biomass Based on Sequential Gaussian Conditional Simulation

The traditional classical sampling statistics method ignores the spatial location relationship of survey samples, which leads to many problems. This study aimed to propose a spatial sampling method for sampling estimation and optimization of forest biomass, achieving a more efficient and effective monitoring system. In this paper, we used Sequential Gaussian Conditional Simulation (SGCS) to obtain the biomass of four typical forest types in Shangri-La, Yunnan Province, China. In addition, we adopted a geostatistical sampling method for sample point layout and optimization to achieve the purpose of improving sampling efficiency and accuracy, and compared with the traditional sampling method. The main results showed that (1) the Gaussian model, exponential model, and spherical model were used to analyze the variogram of the four typical forests biomass, among which the exponential model had the best fitting effect (R2 = 0.571, RSS = 0.019). The range of the exponential model was 8700 m, and the nugget coefficient (C0/(C0 + C)) was 11.67%, which showed that the exponential model could be used to analyze the variogram of forest biomass. (2) The coefficient of variation (CV) based on 323 biomass field plots was 0.706, and the CV based on SGCS was 0.366. In addition, the Overall Estimate Consistency (OEC) of the simulation result was 0.871, which can be used for comparative analysis of traditional and spatial sampling. (3) Based on the result of SGCS, with 95% reliability, the sample size of traditional equidistant sampling (ES) was 191, and the sampling accuracy was 95.16%. But, the spatial sampling method based on the variation scale needed 92 samples, and the sampling accuracy was 93.12%. On the premise of satisfying sampling accuracy, spatial sampling efficiency was better than traditional ES. (4) The accuracy of stratified sampling (SS) of four typical forest areas based on 191 samples was 97.46%. However, the sampling accuracy of the biomass variance stratified space based on the SGCS was 93.89%, and the sample size was 52. Under the premise of satisfying the sampling accuracy, the sampling efficiency was obviously better than the traditional SS. Therefore, we can obtain the conclusion that the spatial sampling method is superior to the traditional sampling method, as it can reduce sampling costs and solve the problem of sample redundancy in traditional sampling, improving the sampling efficiency and accuracy, which can be used for sampling estimation of forest biomass.

Quantificando a incerteza estratigráfica na modelagem de águas subterrâneas para projeto de infraestrutura

A methodology to quantify the stratigraphic uncertainty of the aquifer bottom is used in assessing the impact of sheet piles on the water table in the vicinity of a motorway. The method includes uncertainties on model parameters and depth of sheet piles. While parameter uncertainty dominates when simulating the existing groundwater conditions, the stratigraphic uncertainty dominates when predicting the impacts of the motorway sheet piles. The uncertainty of groundwater head predictions is a key element in risk assessments for infrastructure projects, where groundwater affects construction costs. While geological structural uncertainty often is a dominating source of uncertainty in large-scale water-resource studies, stratigraphic uncertainty (defined as the uncertainty of the location of geological boundaries between units/facies) becomes more important for small-scale infrastructure projects. The methodologies used so far for handling stratigraphic uncertainty typically use a somewhat simplistic approach basing the uncertainties of the geological surfaces on the kriging variance. The proposed methodology has two novel elements. Firstly, the uncertainties in the geological interpretation of the borehole data are explicitly included. Secondly, conditional sequential Gaussian simulation (sGs) is used to quantify the uncertainties. The advantage of sGs over standard kriging-based approaches is that sGs allows descriptions of small-scale variations that are crucial in some contexts. The methodology was tested on a case site in Denmark where a new motorway has been constructed below the water table and with sheet-pile walls designed to penetrate the aquifer down to 1 m above the aquifer bottom.

Application of Sequential Gaussian Conditional Simulation to Underground Mine Design Under Grade Uncertainty

In mining projects, all uncertainties associated with a project must be considered to determine the feasibility study. Grade uncertainty is one of the major components of technical uncertainty that affects the variability of the project. Geostatistical simulation, as a reliable approach, is the most widely used method to quantify risk analysis to overcome the drawbacks of the estimation methods used for an entire ore body. In this work, all the algorithms developed by numerous researchers for optimization of the underground stope layout are reviewed. After that, a computer program called stope layout optimizer 3D is developed based on a previously proposed heuristic algorithm in order to incorporate the influence of grade variability in the final stope layout. Utilizing the sequential gaussian conditional simulation, 50 simulations and a kriging model are constructed for an underground copper vein deposit situated in the southwest of Iran, and the final stope layout is carried out separately. It can be observed that geostatistical simulation can effectively cope with the weakness of the kriging model. The final results obtained show that the frequency of economic value for all realizations varies between 6.7 M$ and 30.7 M$. This range of variation helps designers to make a better and lower risk decision under different conditions.

3-D static modelling of lateral heterogeneity using geostatistics and artificial neural network in reservoir characterisation of “P” field, Niger Delta

ABSTRACT The anisotropic and heterogeneous nature of the subsurface units at offset wells gets more complex at locations outside well control. However, qualitative and quantitative predictions of reservoir properties and geometries beyond well control are vital to understanding the intrinsic characteristics of subsurface formations. Supervised Multi-layer Perceptron neural network and conditional sequential Gaussian simulation were applied to a suite of well logs data set and three dimensional (3-D) seismic dataset acquired from P-field, Niger Delta to predict lateral continuity of hydrocarbon reservoir properties. Multilayer perceptron neural network was used to model effective porosity (Eϕ) at the root-mean-square error of 0.00531 with an estimated average effective porosity of 0.2952. Furthermore, MLPNN modelling of hydrocarbon saturation (Sh) at root mean square error of 0.02821 yielded an estimated average of 69.73%. The volume of shale (Vsh) was also modelled at the root mean square error of 0.0282, with an estimated Vsh average of 9% for the study area. It was discovered that a comparatively higher net-to-gross (N-T-G), relatively higher effective porosity, high hydrocarbon saturation, very low volume of shale, and high permeability were observed in the areas of interest in the study area. A geostatistical approach was also used to model petrophysical properties. The parametric semivariogram model shows the range of 94–5230 m, nugget effect of 0.062, and sills of 0.075, 0.093, and 0.0121. Realisations were generated and ranked using the SGS algorithm suggest that any one of the realisations can independently represent the real picture of the subsurface geology within the study area. The integration of these different prediction tools and analyses of the outcomes from the research has improved our understanding of delineated reservoirs and improved lateral variation prediction of its properties. These prediction tools served better as a complementary tool to each other rather than as a comparison tool.

Three-dimensional stochastic assimilation of gravity data in Lalor volcanogenic massive sulphide, Manitoba, Canada

We propose a new numerical workflow based on stochastic data integration where we merge a conceptual geological model, drillhole geophysical and geological logs, and surface geophysical data to compute a unified numerical model of a volcanogenic massive sulphide (VMS) deposit. The first step of the workflow consists in building a three-dimensional (3D) numerical conceptual model of the geology. This conceptual model, as well as geological logs, is then used to generate multiple equiprobable scenarios of the geology by means of multiple-point simulation (MPS). The MPS method studies high-order statistics in the space of a numerical conceptual model, making it possible to reproduce complex geological structures. We then use conventional conditional sequential Gaussian simulation, which is a method based on a node-by-node sequential process, to stochastically populate the geological grid with densities. For this purpose we use available density logs to simulate multiple equiprobable spatial distributions of the density at high spatial resolution within each geological unit separately. The stochastic high-resolution density models are iteratively combined by the gradual deformation method to minimize the difference between measured Bouguer anomaly data and the data computed on the combined realizations of density. Application of the proposed method to the Lalor deposit, a VMS deposit in Manitoba, Canada, produces a density model that honours the geology of the deposit and the Bouguer anomaly data. This unified model has the advantage to include all the available information (geological and density logs and surface geophysics) at scales appropriate for mining applications.

Spatio-Temporal Change and Pollution Risk of Agricultural Soil Cadmium in a Rapidly Industrializing Area in the Yangtze Delta Region of China.

The impacts of rapid industrialization on agricultural soil cadmium (Cd) accumulation and their potential risks have drawn major attention from the scientific community and decision-makers, due to the high toxicity of Cd to animals and humans. A total of 812 topsoil samples (0–20 cm) was collected from the southern parts of Jiangsu Province, China, in 2000 and 2015, respectively. Geostatistical ordinary kriging and conditional sequential Gaussian simulation were used to quantify the changes in spatial distributions and the potential risk of Cd pollution between the two sampling dates. Results showed that across the study area, the mean Cd concentrations increased from 0.110 mg/kg in 2000 to 0.196 mg/kg in 2015, representing an annual average increase of 5.73 μg/kg. Given a confidence level of 95%, areas with significantly-increased Cd covered approximately 12% of the study area. Areas with a potential risk of Cd pollution in 2000 only covered 0.009% of the study area, while this figure increased to 0.75% in 2015. In addition, the locally concentrating trend of soil Cd pollution risk was evident after 15 years. Although multiple factors contributed to this elevated Cd pollution risk, the primary reason can be attributed to the enhanced atmospheric deposition and industrial waste discharge resulting from rapid industrialization, and the quick increase of traffic and transportation associated with rapid urbanization.

Subsidence activity maps derived from DInSAR data: Orihuela case study

Abstract. A new methodology is proposed to produce subsidence activity maps based on the geostatistical analysis of persistent scatterer interferometry (PSI) data. PSI displacement measurements are interpolated based on conditional Sequential Gaussian Simulation (SGS) to calculate multiple equiprobable realizations of subsidence. The result from this process is a series of interpolated subsidence values, with an estimation of the spatial variability and a confidence level on the interpolation. These maps complement the PSI displacement map, improving the identification of wide subsiding areas at a regional scale. At a local scale, they can be used to identify buildings susceptible to suffer subsidence related damages. In order to do so, it is necessary to calculate the maximum differential settlement and the maximum angular distortion for each building of the study area. Based on PSI-derived parameters those buildings in which the serviceability limit state has been exceeded, and where in situ forensic analysis should be made, can be automatically identified. This methodology has been tested in the city of Orihuela (SE Spain) for the study of historical buildings damaged during the last two decades by subsidence due to aquifer overexploitation. The qualitative evaluation of the results from the methodology carried out in buildings where damages have been reported shows a success rate of 100%.

Monthly karstic spring flow forecasting using a sequential gaussian simulation technique

Analyzing groundwater hydrologic equations related to karstic aquifers and spring hydrograph simulation have become the focus of many researches. Having double or triple porosity structure, mixed flow nature, and varying conduit permeability have made these formations become complex heterogenic systems with great temporal and spatial hydrodynamic variability. In this paper, a conditional sequential gaussian simulation (SGS) is used to simulate monthly flow data of five karstic springs with different hydrogeological properties, located in Zagros Mountain Chain, in western Iran. To evaluate the performance of the SGS algorithm, the results are compared with those of an autoregressive integrated moving average (ARIMA) model. The results demonstrate the efficiency of the SGS model in simulation of monthly flows compared to the ARIMA model. They also show the suitability of this model for handling uncertainty associated with karstic spring flows through generation of several equally probable stochastic realizations.

Risk quantification in grade variability of gold deposits using sequential Gaussian simulation

Risk quantification in grade is critical for mine design and planning. Grade uncertainty is assessed using multiple grade realizations, from geostatistical conditional simulations, which are effective to evaluate local or global uncertainty by honouring spatial correlation structures. The sequential Gaussian conditional simulation was used to assess uncertainty of grade estimates and illustrate simulated models in Sivas gold deposit, Turkey. In situ variability and risk quantification of the gold grade were assessed by probabilistic approach based on the sequential Gaussian simulations to yield a series of conditional maps characterized by equally probable spatial distribution of the gold grade for the study area. The simulation results were validated by a number of tests such as descriptive statistics, histogram, variogram and contour map reproductions. The case study demonstrates the efficiency of the method in assessing risk associated with geological and engineering variable such as the gold grade variability and distribution. The simulated models can be incorporated into exploration, exploitation and scheduling of the gold deposit.

Accuracy Assessment of Geostatistical Modelling Methods of Mineral Deposits for the Purpose of their Future Exploitation - Based on One Lignite Deposit

Safe mine operations and optimal economical decision making in the context of lignite resources require an adequate level of knowledge about the spatial distribution of critical attributes in terms of geometry and quality in the deposit. Therefore, ore body models are generated using different approaches in geostatistics, depending on the problem to be solved.In this article the analysis of geostatistical methods used for deposits modeling has been presented. Based on exploration data concerning caloric value Q, models of one exemplary lignite deposit has been made. Two models of deposit were prepared using two different methods: ordinary kriging (OK) and sequential Gaussian conditional simulation (SGSIM). Different models of the same deposit were analyzed and compared with source data using criterion of fidelity to statistical attributes like: mean value, variance, statistical distribution. Models, which have been created based on exploration data, were compared with in-situ data gained from survey activities in the exploitation process. As a result of comparison correlation factor and measures of deviations were computed: average relative error, absolute relative error. Models were compared with in situ data, considering statistical features and local variability as well.In conclusion, the study gives valuable information into the benefits of using certain geostatistical approaches for variable tasks and problems in the lignite deposits design process. For the assessment of average values of deposit parameters ordinary kriging provides appropriate effects. Geostatisical simulation (e.g. sequential Gaussian simulation - SGSIM) provides much more relevant information for tasks connected to probability (or risk) of defined threshold exceedences than ordinary kriging. Models made with simulation method are characterized by high fidelity of spatial distribution in comparison to source data.

Modelling Uncertainty of Stream Networks Derived from Elevation Data Using Two Free Softwares: R and SAGA

Stream networks are considered important units in many environmental decision making processes. The extraction of streams using digital elevation models (DEMs) presents many advantages. However it is very sensitive to the uncertainty of the elevation datasets used. The main aim of this paper is to implement geostatistical simulations and assess the propagated uncertainty and map the error of location streams. First, point sampled elevations are used to fit a variogram model. Next two hundred DEM realizations are generated using conditional sequential Gaussian simulation; the stream network map is extracted for each of these realizations, and the collection of stream networks is analyzed to quantify the error propagation. At each grid cell, the probability of the occurrence of a stream and the propagated error are estimated. The more probable stream network are delineated and compared with the digital stream network derived from topographic map. The method is illustrated using a small dataset (8742 sampled elevations) for Anaguid Saharan platform. All computations are run in two free softwares: R and SAGA. R is used to fit variogram and to run sequential Gaussian simulation. SAGA is used to extract streams via RSAGA library.

A comparative study between sequential Gaussian simulation and kriging method grade modeling in open-pit mining

Grade estimation is very important in designing open pits. In the process of grade estimation, underestimation can result in loss of economic ore, whereas overestimation would unnecessarily increase stripping ratio. Normally, kriging method, which suffers from underestimation and/or overestimation due to smoothing effect, is used for grade estimation. To overcome drawbacks of the kriging method, more efficient techniques such as conditional simulation can be applied. In this paper, utilizing sequential Gaussian conditional simulation, grade models were constructed for Sungun copper deposit situated in the North West of Iran. According to the obtained results, it was observed that conditional simulation can effectively cope with the weakness of kriging method. Also, it was observed that as compared to the kriging method, grade distribution, resulted from the conditional simulation, is almost identical to that of the real exploration data. Accordingly, using conditional simulation, the amount of mineable ore was significantly increased, and also, average net present value as the mines’ most important economic indicator was improved by 40%.

Analysis and Comparison in Arithmetic for Kriging Interpolation and Sequential Gaussian Conditional Simulation

Analysis and Comparison in Arithmetic for Kriging Interpolation and Sequential Gaussian Conditional Simulation

Optimisation of the grade control procedures at the Yandi iron-ore mine, Western Australia: geostatistical approach

Effectiveness of ore grade control at operating mines depends on both the quality and quantity of the samples used. Therefore, optimisation of grade control procedures requires analysis of sample quality and their spatial distribution. This approach, implying quantitative estimation of both these factors and quantification of their contribution to the grade control errors, was used for comparing two different grade control procedures at the Yandicoogina (Yandi) iron-ore open pit mine, located in the eastern part of the Pilbara region of Western Australia. At Yandi, pisolitic iron oxide mineralisation is distributed within a meandering palaeoriver channel, characterised by abundant clay pods that contain the deleterious components; in particular Al2O3 and SiO2. The irregular shapes and highly erratic distribution of the clay pods are a serious challenge for grade control at this mine. Current grade control procedures at the Yandi open pit are based on sampling 10 m deep blast holes on a 6 × 6 m grid. An alternative approach was considered of using reverse circulation (RC) holes. However, study of the sample duplicates and direct comparison of the blast holes and RC holes drilled at distances approximately 1 m apart (i.e. twin holes) have revealed that use of RC drilling does not guarantee an improvement in the quality of the samples. Reverse circulation samples exhibit precision errors similar to that of the blast holes and both sets of data are characterised by large nugget effects on the variograms of Al2O3 values. It was also noted that RC samples were biased, underestimating Al2O3 and SiO2 grades, and overestimating Fe grades. The Sequential Gaussian conditional simulation model was used for estimation of grade control errors associated with both grade control techniques. This model has shown that using a grid of 25 × 25 m for grade control leads to 12·3% of the selective mining unit sized blocks being misclassified, which is more than a two-fold increase in comparison with current procedures based on sampling blast holes, when approximately 5·8% of SMU blocks are misclassified. In general, comparative analysis of the two grade control approaches at the Yandi mine shows that using the RC holes drilled as the 25 × 25 m grid will not reduce the grade control errors. In fact, it can produce the opposite effect, significantly increasing the number of misclassified ore and waste blocks.

On the uncertainty of stream networks derived from elevation data: the error propagation approach

Abstract. DEM error propagation methodology is extended to the derivation of vector-based objects (stream networks) using geostatistical simulations. First, point sampled elevations are used to fit a variogram model. Next 100 DEM realizations are generated using conditional sequential Gaussian simulation; the stream network map is extracted for each of these realizations, and the collection of stream networks is analyzed to quantify the error propagation. At each grid cell, the probability of the occurrence of a stream and the propagated error are estimated. The method is illustrated using two small data sets: Baranja hill (30 m grid cell size; 16 512 pixels; 6367 sampled elevations), and Zlatibor (30 m grid cell size; 15 000 pixels; 2051 sampled elevations). All computations are run in the open source software for statistical computing R: package geoR is used to fit variogram; package gstat is used to run sequential Gaussian simulation; streams are extracted using the open source GIS SAGA via the RSAGA library. The resulting stream error map (Information entropy of a Bernoulli trial) clearly depicts areas where the extracted stream network is least precise – usually areas of low local relief and slightly convex (0–10 difference from the mean value). In both cases, significant parts of the study area (17.3% for Baranja Hill; 6.2% for Zlatibor) show high error (H>0.5) of locating streams. By correlating the propagated uncertainty of the derived stream network with various land surface parameters sampling of height measurements can be optimized so that delineated streams satisfy the required accuracy level. Such error propagation tool should become a standard functionality in any modern GIS. Remaining issue to be tackled is the computational burden of geostatistical simulations: this framework is at the moment limited to small data sets with several hundreds of points. Scripts and data sets used in this article are available on-line via the www.geomorphometry.org website and can be easily adopted/adjusted to any similar case study.

A geostatistical approach for mapping and uncertainty assessment of geogenic radon gas in soil in an area of southern Italy

Spatial distribution of concentrations of radon gas in the soil is important for defining high risk areas because geogenic radon is the major potential source of indoor radon concentrations regardless of the construction features of buildings. An area of southern Italy (Catanzaro-Lamezia plain) was surveyed to study the relationship between radon gas concentrations in the soil, geology and structural patterns. Moreover, the uncertainty associated with the mapping of geogenic radon in soil gas was assessed. Multi-Gaussian kriging was used to map the geogenic soil gas radon concentration, while conditional sequential Gaussian simulation was used to yield a series of stochastic images representing equally probable spatial distributions of soil radon across the study area. The stochastic images generated by the sequential Gaussian simulation were used to assess the uncertainty associated with the mapping of geogenic radon in the soil and they were combined to calculate the probability of exceeding a specified critical threshold that might cause concern for human health. The study showed that emanation of radon gas radon was also dependent on geological structure and lithology. The results have provided insight into the influence of basement geochemistry on the spatial distribution of radon levels at the soil/atmosphere interface and suggested that knowledge of the geology of the area may be helpful in understanding the distribution pattern of radon near the earth’s surface.

Modeling of the spatial variability of biogeochemical soil properties in a freshwater ecosystem

Ecosystem services are dependent on the geospatial composition, structure, and function of an ecosystem. Our goal was to gain a better understanding of the variability of biogeochemical soil properties along gradients of impacted and unimpacted zones within a subtropical wetland in Florida. Our objectives were to (i) characterize the spatial variability and distribution of soil total phosphorus (TP), (ii) identify the magnitude and scale at which multiple biogeochemical soil properties account for variability within the ecosystem, and (iii) map the distribution of this variability. We collected soil samples (0–10 cm) at 266 sites within the Blue Cypress Marsh Conservation Area (4900 ha) in Florida that were analyzed for 18 different biogeochemical properties. Conditional sequential Gaussian simulation and principal component analysis was used to identify three major groups of behavior: (i) labile, fast response properties with fine-scale spatial autocorrelation; (ii) stable, slow response properties with regional spatial autocorrelation; (iii) properties showing intermediate response. The uncertainty of the spatial variability measures was described using small and large realizations as well as standard deviation maps. The first principal component (PC) [group (i)] contributed with 33.91%, the second PC [group (ii)] with 15.93%, and the third PC [group (iii)] with 11.32% to the total variance. Properties that explain much of the underlying variability in a wetland are expected to be more sensitive to change than others that show more homogeneous patterns. More research is needed to reveal geospatial interrelationships of biogeochemical properties and their underlying spatial structure in aquatic ecosystems.

Comparison of regression and geostatistical methods for mapping Leaf Area Index (LAI) with Landsat ETM+ data over a boreal forest

This study compared aspatial and spatial methods of using remote sensing and field data to predict maximum growing season leaf area index (LAI) maps in a boreal forest in Manitoba, Canada. The methods tested were orthogonal regression analysis (reduced major axis, RMA) and two geostatistical techniques: kriging with an external drift (KED) and sequential Gaussian conditional simulation (SGCS). Deterministic methods such as RMA and KED provide a single predicted map with either aspatial (e.g., standard error, in regression techniques) or limited spatial (e.g., KED variance) assessments of errors, respectively. In contrast, SGCS takes a probabilistic approach, where simulated values are conditional on the sample values and preserve the sample statistics. In this application, canonical indices were used to maximize the ability of Landsat ETM+ spectral data to account for LAI variability measured in the field through a spatially nested sampling design. As expected based on theory, SGCS did the best job preserving the distribution of measured LAI values. In terms of spatial pattern, SGCS preserved the anisotropy observed in semivariograms of measured LAI, while KED reduced anisotropy and lowered global variance (i.e., lower sill), also consistent with theory. The conditional variance of multiple SGCS realizations provided a useful visual and quantitative measure of spatial uncertainty. For applications requiring spatial prediction methods, we concluded KED is more useful if local accuracy is important, but SGCS is better for indicating global pattern. Predicting LAI from satellite data using geostatistical methods requires a distribution and density of primary, reference LAI measurements that are impractical to obtain. For regional NPP modeling with coarse resolution inputs, the aspatial RMA regression method is the most practical option.

Spatial variability, distribution and uncertainty assessment of soil phosphorus in a south Florida wetland

AbstractPhosphorus enrichment has been of major concern in the Greater Everglades (GE) ecosystem since the early 1980s. Our objectives were to estimate spatio–temporal patterns of soil total phosphorus (TP) in Water Conservation Area 2A (WCA‐2A) in the GE ecosystem and to compare two different geostatistical methods: ordinary kriging (OK) and conditional sequential Gaussian simulation (CSGS), addressing spatial variability, continuity and uncertainty of TP estimations.Overall, TP estimated with OK and CSGS were higher in 1998 than in 1990. Both methods generated spatial patterns of TP in 1998 which showed a spatial expansion of the phosphorus enrichment identified in the 1990 dataset. Cross‐validation using OK produced a mean prediction error of −10.71 (1990) and −6.07 (1998). CSGS modeled the spatial uncertainty of TP estimations explicitly with 50 generated realizations. Uncertainty was modeled using the E‐type mean of TP, which ranged from 216 to 2100 mg kg−1 in 1990 and 325.2 to 3660 mg kg−1 in 1998. Standard deviations ranged from 0 to 550 mg kg−1 maximum.To evaluate TP exceeding a threshold of 450 TP mg kg−1, which represents natural historic wetland conditions, we produced probability maps. Results suggested a distinctly higher retention of TP using CSGS when compared to the OK generated probability maps. Spatial probability patterns are valuable to guide the restoration process of this wetland.Jackknifing was used to estimate the bias of the descriptive statistics and semivariance. The total number of samples was robust enough to produce stable variograms; however, jackknifing suggested that more samples at closer distances from each other should be collected to reduce the uncertainty of the semivariance and to address short‐range spatial variability. Copyright © 2004 John Wiley & Sons, Ltd.