Lognormal and Moving Window Methods of Estimating Acid Deposition

Haas, Timothy C.

doi:10.2307/2289592

Cited by 33 publications

(17 citation statements)

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“…Thus, a single, global variogram is utilized for spatial interpolation. In some cases, data subsets in the vicinity of a cluster of estimation points are used to develop several local variograms rather than apply a single variogram derived from the global dataset, thereby improving interpolation results (see, e.g., Haas 1990, 1995and Abedini et al 2008. In this study, we capitalize on the very high data density of the SWL dataset to create a unique model variogram at each estimation point, using the nearest N1 and N2 points to develop the model semivariogram and perform kriging estimation, respectively (see the process loop in Figure 5).…”

Section: Separating Noise From Signalmentioning

confidence: 99%

Data‐Driven Approach for Analyzing Hydrogeology and Groundwater Quality Across Multiple Scales

Curtis

Li²,

Liao

et al. 2017

Groundwater

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Recent trends of assimilating water well records into statewide databases provide a new opportunity for evaluating spatial dynamics of groundwater quality and quantity. However, these datasets are scarcely rigorously analyzed to address larger scientific problems because they are of lower quality and massive. We develop an approach for utilizing well databases to analyze physical and geochemical aspects of groundwater systems, and apply it to a multiscale investigation of the sources and dynamics of chloride (Cl ) in the near-surface groundwater of the Lower Peninsula of Michigan. Nearly 500,000 static water levels (SWLs) were critically evaluated, extracted, and analyzed to delineate long-term, average groundwater flow patterns using a nonstationary kriging technique at the basin-scale (i.e., across the entire peninsula). Two regions identified as major basin-scale discharge zones-the Michigan and Saginaw Lowlands-were further analyzed with regional- and local-scale SWL models. Groundwater valleys ("discharge" zones) and mounds ("recharge" zones) were identified for all models, and the proportions of wells with elevated Cl concentrations in each zone were calculated, visualized, and compared. Concentrations in discharge zones, where groundwater is expected to flow primarily upwards, are consistently and significantly higher than those in recharge zones. A synoptic sampling campaign in the Michigan Lowlands revealed concentrations generally increase with depth, a trend noted in previous studies of the Saginaw Lowlands. These strong, consistent SWL and Cl distribution patterns across multiple scales suggest that a deep source (i.e., Michigan brines) is the primary cause for the elevated chloride concentrations observed in discharge areas across the peninsula.

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Section: Separating Noise From Signalmentioning

confidence: 99%

Data‐Driven Approach for Analyzing Hydrogeology and Groundwater Quality Across Multiple Scales

Curtis

Li²,

Liao

et al. 2017

Groundwater

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“…An approach to nonstationary spatial interpolation is a moving window method. The principal advocate of this methodology has been Haas [1990Haas [ , 1995T. C. Haas, unpublished data, 1996].…”

Section: Statistical Model For Air Pollutantsmentioning

confidence: 99%

Statistical assessment of geographic areas of compliance with air quality standards

Fuentes

2003

J. Geophys. Res.

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[1] A statistical method is developed to classify geographical regions according to the air quality standards for criteria pollutants. A geographic location is designated by the U.S. Environmental Protection Agency as an area of nonattainment when it does not meet the air quality standard for one of the criteria pollutants. A statistical model for air pollution is presented. This model is used to interpolate ground measurements of pollution levels at locations where there are no air quality monitors with the objective of determining the geographic areas of nonattainment. The approach presented here for interpolation takes into account that spatial patterns of air pollutants change with location. Estimates of probabilities of nonattainment are also provided, and they are used to classify the nonattainment areas by degree of severity. The approach is applied using available data from 513 sites throughout the eastern USA where ground-level ozone is measured hourly.

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“…The exact window should be a circle (or a ball). Haas [1990] of this paper is different from Haas's, a circular window (or a ball) for an isotropic problem is recommended. We use the anisotropic estimator ( Figure 3) when trying to estimate directional anisotropy in a plane.…”

Section: A New Semivariance Estimatormentioning

confidence: 91%

A moving window semivariance estimator

Li¹,

Lake²

1994

Water Resources Research

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nstract. Use of geostatistics in hydrology, reservoir engineering, soil physics, and environmental science has expanded vastly in the last few years. Since the semivariance is the. backbone of geostatistics, it is very important to estimate it accurately. Building on Matheron's classical formula, there are several improved semivariance estimators, but they are only reliable at small lag distances. For large lag distances all estimat0rs can produce erratic results that may lead to a misinterpretation of the spatial structure of a given data set. The lack of precision is primarily caused by a shrinking number of observation pairs as lag distance increases. This paper presents a new semivariance estimator that uses all given data at all lag distances. In addition, the new e•timator is not restricted to samples taken along lines, and it easily accounts for missing data. We compare the new estimator to existing ones on simulated data sets as well as three outcrop data sets. The results show that the new estimator is unbiased, robust, and resistant to contamination. IntroductionMost spatial data are so complicated that describing them forces us to rely on geostatistics, a hybrid discipline of engineering, geology, mathematics, and statistics. In recent years geostatistics has become an extremely powerful tool to study spatial data. In the sense of statistics the distribution of spatial dat•. is described with statistical moments. This kind of spatial behavior (autocorrelation or structure) is measured by a statistic, designated as the semivariogram, or simply the variogram. The variogram is a plot of the semivariance versus separation or lag distance.The original and most popular semivariance estimator (or "experimental" semivariance) in present use was given by Matheron [1962]. UmOortunately, the estimator is imprecise at moderate to large (compared to the extent of correlation in the data) lag distances. Early on, Matheron [1965] warned of the variability of his estimator for large lag distances. Yang and Lake [1989], analyzing the precision of Matheron's estimator using both analytical and numerical methods, also concluded that the precision of this estimator decreases as the lag distance and/or autocorrelation length increase (Figure 1). Therefore only the first few points of Matheron's estimator can be considered significant [Armstrong, 1984;Dowd, 1984]. Beyond these points the shape of the variogram is distorted, and the spatial structure obscured. The principal reason for the distortion is that the semivariance estimate is based on fewer and fewer data pairs as lag distance increases. Indeed, at the largest lag distance the semivariance is estimated on only one data pair for a one-dimensional problem. Matheron's estimator is unbiased, however. There are two other properties, robustness and resistance, that a good estimator should possess. An estimator is "robust" if its results are insensitive to a lack of conformance to underlying assumptions, usually in the form of the probability density function (PDF). An es...

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Lognormal and Moving Window Methods of Estimating Acid Deposition

Cited by 33 publications

References 0 publications

Data‐Driven Approach for Analyzing Hydrogeology and Groundwater Quality Across Multiple Scales

Data‐Driven Approach for Analyzing Hydrogeology and Groundwater Quality Across Multiple Scales

Statistical assessment of geographic areas of compliance with air quality standards

A moving window semivariance estimator

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