Markov based transition probability geostatistics in groundwater applications: assumptions and limitations

Langousis, Andreas; Kaleris, Vassilios; Kokosi, Angeliki; Mamounakis, George

doi:10.1007/s00477-017-1504-y

Cited by 13 publications

(12 citation statements)

References 111 publications

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Section: Methods Comparisonmentioning

confidence: 99%

“…An example of a trickle-down effect is how dell'Arcipreti et al ( 2012) becomes a main reference in He et al (2017) for promoting application of mps, then (He et al, 2017) becomes a main reference in Langousis et al (2018) for criticizing the 3-D Markov chain modeling approach of Carle and Fogg (1997). To "reveal" limitations of Markov chain models, Langousis et al (2018) execute a "simple test-case" of a 2-D dipping layer with a coordinate system anchored in the vertical and horizontal directions of their statistical analysis. Neither dell' Arciprete et al (2012) nor Langousis et al (2018) appeared to grasp the concept that bivariate geostatistical analysis and simulation should be applied in a geologically-based coordinate system, as demonstrated for at least 30 years (e.g., Gomez-Hernandez and Srivastava, 1990).…”

Section: Methods Comparisonmentioning

confidence: 99%

“…To "reveal" limitations of Markov chain models, Langousis et al (2018) execute a "simple test-case" of a 2-D dipping layer with a coordinate system anchored in the vertical and horizontal directions of their statistical analysis. Neither dell' Arciprete et al (2012) nor Langousis et al (2018) appeared to grasp the concept that bivariate geostatistical analysis and simulation should be applied in a geologically-based coordinate system, as demonstrated for at least 30 years (e.g., Gomez-Hernandez and Srivastava, 1990). The geological realism of the mps application by He et al (2017) stands wide open to geological criticism too, with a mps-generated "real world buried valley system" showing unrealistic topography and isolated occurrences of the valley fill buried beneath pre-valley-fill strata.…”

Section: Methods Comparisonmentioning

confidence: 99%

“…The model of spatial variability is another limitation to any geostatistical approach. A methods limitations analysis by Langousis et al (2018) criticizes the interpretive framework of transition probability-based Markov chain model development as "based on unverified/untested simplifying assumptions" and "adhoc manipulations." Langousis et al (2018) further contend that.…”

Section: Methods Limitationsmentioning

confidence: 99%

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Integration of Soft Data Into Geostatistical Simulation of Categorical Variables

Carle

Fogg

2020

Front. Earth Sci.

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Uncertain or indirect "soft" data, such as geologic interpretation, driller's logs, geophysical logs or imaging, offer potential constraints or "soft conditioning" to stochastic models of discrete categorical subsurface variables in hydrogeology such as hydrofacies. Previous bivariate geostatistical simulation algorithms have not fully addressed the impact of data uncertainty in formulation of the (co) kriging equations and the objective function in simulated annealing (or quenching). This paper introduces the geostatistical simulation code tsim-s, which accounts for categorical data uncertainty through a data "hardness" parameter. In generating geostatistical realizations with tsim-s, the uncertainty inherent to soft conditioning is factored into both 1) the data declustering and spatial correlation functions in cokriging and 2) the acceptance probability for change of category in simulated quenching. The degree or sensitivity to which soft data conditions a realization as a function of hardness can be quantified by mapping category probabilities derived from multiple realizations. In addition to point or borehole data, arrays of data (e.g., as derived from a depth-dependency function, probability map, or "prior realization") can be used as soft conditioning. The tsim-s algorithm provides a theoretically sound and general framework for integrating datasets of variable location, resolution, and uncertainty into geostatistical simulation of categorical variables. A practical example shows how tsim-s is capable of generating a large-scale three-dimensional simulation including curvilinear features.

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Section: Methods Comparisonmentioning

confidence: 99%

Section: Methods Comparisonmentioning

confidence: 99%

Section: Methods Comparisonmentioning

confidence: 99%

Section: Methods Limitationsmentioning

confidence: 99%

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Integration of Soft Data Into Geostatistical Simulation of Categorical Variables

Carle

Fogg

2020

Front. Earth Sci.

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“…The latter makes use of available lithological/ sedimentological data to evaluate transition probabilities between facies, which are then interpreted through Markov-chain modeling techniques. This approach, as well as other Markov-chain based methods (e.g., Elfeki and Dekking 2001;Li 2007;Langousis et al 2018), also (1) enables one to include information on spatial juxtapositional tendencies and soft conditioning data and (2) is deemed as more accurate than its covariance-based counterparts to represent volumetric proportions, mean lengths, and connectivity patterns driven by facies distributions (Weissmann et al 1999;He et al 2014He et al , 2015Koch et al 2014).…”

Section: Introductionmentioning

confidence: 99%

Impact of geostatistical reconstruction approaches on model calibration for flow in highly heterogeneous aquifers

Siena

Riva

2020

Stoch Environ Res Risk Assess

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Our study is aimed at assessing the extent at which relying on differing geostatistical approaches may affect characterization of the connectivity of geomaterials (or facies) and, in turn, model calibration outputs in highly heterogeneous aquifers. We set our study within a probabilistic framework, by relying on a numerical Monte Carlo (MC) approach. The reconstruction of the spatial distribution of geomaterials and flow simulations are patterned after a field scenario corresponding to the aquifer system serving the city of Bologna (Northern Italy). Two collections of MC realizations of facies distributions, conditional on available lithological data, are generated through two alternative geostatistically-based techniques, i.e., Sequential Indicator and Transition-Probability simulation. Hydraulic conductivity values of the least- and most-conductive facies are estimated within each MC simulation in the context of a Maximum Likelihood (ML) approach by considering available piezometric data. We provide evidence that the choice of the facies reconstruction technique (1) impacts the degree of connectivity of facies whose proportions are close to the percolation threshold while (2) is not sensibly affecting the connectivity associated with facies whose proportions are much larger than the percolation threshold. By relying on the unique (lithological and hydrological) data-set at our disposal, we also explore the performance of ML-based model identification criteria to (1) discriminate amongst competitive facies reconstruction geostatistical models and (2) quantify the (posterior probabilistic) weight associated with each model. We then show that ML-based model averaging provides estimates of hydraulic heads which are slightly more in agreement with available data when compared to the best-performing realization in the T-PROGS set than considering its counterpart associated with the SISIM-based collection.

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Identification of hydraulic conductivity field of a karst aquifer by using transition probability geostatistics and discrete cosine transform with an ensemble method

Duan

Deng

Chu

et al. 2022

Hydrological Processes

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Knowledge of the spatial distribution characteristics of hydraulic parameters is essential for the management and protection of karst groundwater resources. In this study, we propose a workflow integrating the transition probability geostatistics (T‐PROGS) and the discrete cosine transform (DCT) with the ensemble smoother with multiple data assimilation (ES‐MDA) method to map the hydraulic conductivity of karst aquifers that usually follow a multimodal distribution. The priori parameter ensemble is constructed from the T‐PROGS and transformed into an approximately Gaussian distributed coefficient field containing critical spatial structural features about the aquifer using DCT. The ES‐MDA method is employed to update the DCT coefficients by assimilating the measurements. In addition, a postprocessing process based on cumulative distribution function (CDF) mapping is used to address the problem of parameters gradually tending to a Gaussian distribution after updating using the ES‐MDA and the inappropriate selection of initial parameter values. In practice, the limited amount of available data makes it difficult to fully capture the spatial distribution of the parameters in the initial ensemble of a single realization. Therefore, we suggest a new strategy for structuring the initial ensemble by mixing samples from multiple realizations. We then apply the proposed approach to four single realization models and a combined multiple realizations model in a field hydraulic tomography investigation of a real karst aquifer. The computed results show that this method can effectively identify the characteristics of the spatial distribution of hydraulic conductivity in karst aquifers. Compared with an individual realization model, the uncertainty of the hydraulic conductivity estimated by the combined multiple realizations model is significantly reduced. Therefore, including more uncertainty of the aquifer in the initial ensemble is beneficial to improve the accuracy of the parameter estimation.

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Markov based transition probability geostatistics in groundwater applications: assumptions and limitations

Cited by 13 publications

References 111 publications

Integration of Soft Data Into Geostatistical Simulation of Categorical Variables

Integration of Soft Data Into Geostatistical Simulation of Categorical Variables

Impact of geostatistical reconstruction approaches on model calibration for flow in highly heterogeneous aquifers

Identification of hydraulic conductivity field of a karst aquifer by using transition probability geostatistics and discrete cosine transform with an ensemble method

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