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USGS2014

Applications of spatial statistical network models to stream data

Streams and rivers host a significant portion of Earth's biodiversity and provide important ecosystem services for human populations. Accurate information regarding the status and trends of stream resources is vital for their effective conservation and management. Most statistical techniques applied to data measured on stream networks were developed for terrestrial applications and are not optimized for streams. A new class of spatial statistical model, based on valid covariance structures for stream networks, can be used with many common types of stream data (e.g., water quality attributes, habitat conditions, biological surveys) through application of appropriate distributions (e.g., Gaussian, binomial, Poisson). The spatial statistical network models account for spatial autocorrelation (i.e., nonindependence) among measurements, which allows their application to databases with clustered measurement locations. Large amounts of stream data exist in many areas where spatial statistical analyses could be used to develop novel insights, improve predictions at unsampled sites, and aid in the design of efficient monitoring strategies at relatively low cost. We review the topic of spatial autocorrelation and its effects on statistical inference, demonstrate the use of spatial statistics with stream datasets relevant to common research and management questions, and discuss additional applications and development potential for spatial statistics on stream networks. Free software for implementing the spatial statistical network models has been developed that enables custom applications with many stream databases.

WIREs Water↗

USGS2002

Description and comparison of geologic maps with FRAGSTATS - A spatial statistics program

FRAGSTATS is a public-domain GIS implementation of a set of spatial statistics that address a fundamental problem in GIS applications, description and comparison of maps. The spatial statistics from the 1:2,500,000-scale United States geologic map of Nevada, the central United States, and the northeastern United States quantify the differences in complexity and variability between these three geologic terranes. Nevada is defined by a large number of patches of small size and low size variability, whereas the Central area has a small number of patches with smaller relative size variability. All three areas have similar map-unit shape complexity with Nevada having the lowest. Based on the density of edges, the areas can be ranked from highest to lowest, as Nevada, Central, and Northeast. The Shannon diversity index ranks the areas from highest to lowest, as Northeast, Nevada, and Central, but the Shannon evenness index ranks them from highest to lowest, as Northeast, Central, and Nevada. These rankings may reflect the influence of folding in the Northeast and Central areas as opposed to basin and range extension in Nevada. The core areas statistic ranks the areas for spatial accuracy from highest to lowest, as Central, Northeast, and Nevada, with Northeast and Nevada being similar. For a scale comparison, the FRAGSTATS statistics quantify the increased complexity and spatial accuracy that is inherent in going from small- to larger-scale maps. For example for 1:2,500,000-1:500,000-scale maps of Nevada, respectively, the area weighted fractal dimension increase from 1.1 to 1.18, and the total core areas index almost doubles from 39.09 to 63.38. In addition, the fractal dimensions discriminate gross lithology and tectonic terranes. ?? 2002 Elsevier Science Ltd. All rights reserved.

Computers & Geosciences↗

USGS2004

Use of spatial statistics and isotopic tracers to measure the influence of arsenical pesticide use on stream sediment chemistry in New England, USA

Arsenical pesticides and herbicides, principally Pb arsenate, Ca arsenate, and Na arsenate with lesser use of other metal-As pesticides, were widely applied on apple, blueberry, and potato crops in New England during the first half of the twentieth century. Agricultural census data for this time period is used to define an agricultural index that identifies areas that are inferred to have used arsenical pesticides extensively. Factor analysis on metal concentrations in 1597 stream sediment samples collected throughout New England, grouped by agricultural-index categories, indicate a positive association of areas with stream sediment sample populations that contain higher As and Pb concentrations than samples from the region as a whole with sample site settings having high agricultural-index values. Population statistics for As and Pb concentrations and factor scores for an As-Pb factor all increase systematically and significantly with increasing agricultural-index intensity in the region, as tested by Kruskal-Wallis analysis. Lead isotope compositions for 16 stream sediments from a range of agricultural-index settings generally overlap the observed variation in rock sulfides and their weathering products; however, sediments collected from high agricultural-index settings have slightly more radiogenic Pb compositions, consistent with an industrial Pb contribution to these samples. Although weathering products from rocks are likely to be the dominant source of As and metals to most of the stream sediment samples collected in the region, the widespread use of arsenical pesticides and herbicides in New England during the early 1900-1960s appears to be a significant anthropogenic source of As and metals to many sediments in agricultural areas in the region and has raised background levels of As in some regions. Elevated concentrations of As in stream sediments are of concern for two reasons. Stream sediments with elevated As concentrations delineate areas with elevated background concentrations of As from both natural rock and anthropogenic sources that may contribute As to groundwater systems used for drinking water supplies. Conversion of agricultural land contaminated with arsenical pesticide residues to residential development may increase the likelihood that humans will be exposed to As. In addition, many stream sediment sites have As concentrations that exceed sediment quality guidelines established for freshwater ecosystems. Thirteen percent of the New England sediment sample sites exceed 9.79 mg/kg As, the threshold effects concentration (TEC), below which harmful effects are unlikely to be observed. Arsenic concentrations exceed 33 mg/kg, the probable effects concentration (PEC), above which harmful effects on sediment-dwelling organisms are expected to occur frequently, at 1.25% of the sediment sample sites. The sample sites that exceed the PEC value occur predominately in agricultural areas that used arsenical pesticides.

Conference Paper↗

USGS2002

Spatial and statistical differences between 1:250,000- and 1:24,000-scale digital soil databases

In this study, 1:250,000- and 1:24,000-scale digital soil databases for Kansas were compared statistically and spatially. The soil attributes used in this comparison were soil permeability, percent clay, and hydrologic group. Results indicate that, although the two databases were correlated, the potential exists for substantial site-specific variability between them. The largest differences between the two databases typically are in and along the stream networks. With distance away from the stream networks, the mean differences generally stabilize. The results also indicate the possibility of systematic bias between the two databases that varies with landscape position. For applications using mean soil attribute values, the two soil databases usually yield similar values for the three soil attributes analyzed, especially for areas of 25 km2 (9.7 mi2) or larger. However, for applications where more detailed information on soil variability and the spatial pattern of soil properties within the landscape is required, such as for studies focused on small areas or areas in and along stream networks, the two soil databases are sufficiently different such that using one or the other may result in substantially different results.

Journal of Soil and Water Conservation↗

USGS2019

Spatially-structured statistical network models for landscape genetics

A basic understanding of how the landscape impedes, or creates resistance to, the dispersal of organisms and hence gene flow is paramount for successful conservation science and management. Spatially structured ecological networks are often used to represent spatial landscape‐genetic relationships, where nodes represent individuals or populations and resistance to movement is represented using non‐binary edge weights. Weights are typically assigned or estimated by the user, rather than observed, and validating such weights is challenging. We provide a synthesis of current methods used to estimate edge weights and an overview of common model types, stressing the advantages and disadvantages of each approach and their ability to model landscape‐genetic data. We further explore a set of spatial‐statistical methods that provide ecologists with alternative approaches for modeling spatially explicit processes that may affect genetic structure. This includes an overview of spatial autoregressive models, with a particular focus on how correlation and partial correlation are used to represent neighborhood structure with the inverse of the covariance matrix (i.e., precision matrix). We then demonstrate how to model resistance by specifying an appropriate statistical model on the nodes, conditioned on the edge weights, through the precision matrix. This integration of network ecology and spatial statistics provides a practical analytical framework for landscape‐genetic studies. The results can be used to make statistical inferences about the relative importance of individual landscape characteristics, such as the vegetative cover, hillslope, or the presence of roads or rivers, on gene flow. In addition, the R code we include allows readers to explore landscape‐genetic structure in their own datasets, which will potentially provide new insights into the evolutionary processes that generated ecological networks, as well as valuable information about the optimal characteristics of conservation corridors.

Ecological Monographs↗

USGS2009

Statistical and Spatial Analysis of Bathymetric Data for the St. Clair River, 1971-2007

To address questions concerning ongoing geomorphic processes in the St. Clair River, selected bathymetric datasets spanning 36 years were analyzed. Comparisons of recent high-resolution datasets covering the upper river indicate a highly variable, active environment. Although statistical and spatial comparisons of the datasets show that some changes to the channel size and shape have taken place during the study period, uncertainty associated with various survey methods and interpolation processes limit the statistically certain results. The methods used to spatially compare the datasets are sensitive to small variations in position and depth that are within the range of uncertainty associated with the datasets. Characteristics of the data, such as the density of measured points and the range of values surveyed, can also influence the results of spatial comparison. With due consideration of these limitations, apparently active and ongoing areas of elevation change in the river are mapped and discussed.

Michigan;Ontario↗

USGS1989

Descriptive statistics and spatial distributions of geochemical variables associated with manganese oxide-rich phases in the northern Pacific

Tables, graphs, and maps are used to portray the frequency characteristics and spatial distribution of manganese oxide-rich phase geochemical data, to characterize the northern Pacific in terms of publicly available nodule geochemical data, and to develop data portrayal methods that will facilitate data analysis. Source data are a subset of the Scripps Institute of Oceanography's Sediment Data Bank. The study area is bounded by 0° N., 40° N., 120° E., and 100° W. and is arbitrarily subdivided into 14-20°x 20° geographic subregions. Frequency distributions of trace metals characterized in the original raw data are graphed as ogives, and salient parameters are tabulated. All variables are transformed to enrichment values relative to median concentration within their host subregions. Scatter plots of all pairs of original variables and their enrichment transforms are provided as an aid to the interpretation of correlations between variables. Gridded spatial distributions of all variables are portrayed as gray-scale maps. The use of tables and graphs to portray frequency statistics and gray-scale maps to portray spatial distributions is an effective way to prepare for and facilitate multivariate data analysis.

Bulletin↗

USGS1995

Spatial trends in Pearson Type III statistical parameters

Spatial trends in the statistical parameters (mean, standard deviation, and skewness coefficient) of a Pearson Type III distribution of the logarithms of annual flood peaks for small rural basins (less than 90 km2) are delineated using a climate factor CT, (T=2-, 25-, and 100-yr recurrence intervals), which quantifies the effects of long-term climatic data (rainfall and pan evaporation) on observed T-yr floods. Maps showing trends in average parameter values demonstrate the geographically varying influence of climate on the magnitude of Pearson Type III statistical parameters. The spatial trends in variability of the parameter values characterize the sensitivity of statistical parameters to the interaction of basin-runoff characteristics (hydrology) and climate. -from Authors

Journal of Hydraulic Engineering↗

USGS2009

Spatially referenced statistical assessment of dissolved-solids load sources and transport in streams of the Upper Colorado River Basin

The Upper Colorado River Basin (UCRB) discharges more than 6 million tons of dissolved solids annually, about 40 to 45 percent of which are attributed to agricultural activities. The U.S. Department of the Interior estimates economic damages related to salinity in excess of $330 million annually in the Colorado River Basin. Salinity in the UCRB, as measured by dissolved-solids load and concentration, has been studied extensively during the past century. Over this period, a solid conceptual understanding of the sources and transport mechanisms of dissolved solids in the basin has been developed. This conceptual understanding was incorporated into the U.S. Geological Survey Spatially Referenced Regressions on Watershed Attributes (SPARROW) surface-water quality model to examine statistically the dissolved-solids supply and transport within the UCRB. Geologic and agricultural sources of dissolved solids in the UCRB were defined and represented in the model. On the basis of climatic and hydrologic conditions along with data availability, water year 1991 was selected for examination with SPARROW. Dissolved-solids loads for 218 monitoring sites were used to calibrate a dissolved-solids SPARROW model for the UCRB. The calibrated model generally captures the transport mechanisms that deliver dissolved solids to streams of the UCRB as evidenced by R2 and yield R2 values of 0.98 and 0.71, respectively. Model prediction error is approximated at 51 percent. Model results indicate that of the seven geologic source groups, the high-yield sedimentary Mesozoic rocks have the largest yield of dissolved solids, about 41.9 tons per square mile (tons/mi2). Irrigated sedimentary-clastic Mesozoic lands have an estimated yield of 1,180 tons/mi2, and irrigated sedimentary-clastic Tertiary lands have an estimated yield of 662 tons/mi2. Coefficients estimated for the seven landscape transport characteristics seem to agree well with the conceptual understanding of the role they play in the delivery of dissolved solids to streams in the UCRB. Predictions of dissolved-solids loads were generated for more than 10,000 stream reaches of the stream network defined in the UCRB. From these estimates, the downstream accumulation of dissolved solids, including natural and agricultural components, were examined in selected rivers. Contributions from each of the 11 dissolved-solids sources were also examined at select locations in the Grand, Green, and San Juan Divisions of the UCRB. At the downstream boundary of the UCRB, the Colorado River at Lees Ferry, Arizona, monitoring site, the dissolved-solids contribution of irrigated agricultural lands and natural sources were about 45 and 57 percent, respectively. Finally, model predictions, including the contributions of natural and agricultural sources for selected locations in the UCRB, were compared with results from two previous studies.

Arizona, Colorado, Idaho, New Mexico, Utah, Wyomin↗

USGS2017

Enhanced and updated spatially referenced statistical assessment of dissolved-solids load sources and transport in streams of the Upper Colorado River Basin

Approximately 6.4 million tons of dissolved solids are discharged from the Upper Colorado River Basin (UCRB) to the Lower Colorado River Basin each year. This results in substantial economic damages, and tens of millions of dollars are spent annually on salinity control projects designed to reduce salinity loads in surface waters of the UCRB. Dissolved solids in surface water and groundwater have been studied extensively over the past century, and these studies have contributed to a conceptual understanding of sources and transport of dissolved solids. This conceptual understanding was incorporated into a Spatially Referenced Regressions on Watershed Attributes (SPARROW) model to examine sources and transport of dissolved solids in the UCRB. The results of this model were published in 2009. The present report documents the methods and data used to develop an updated dissolved-solids SPARROW model for the UCRB, and incorporates data defining current basin attributes not available in the previous model, including delineation of irrigated lands by irrigation type (sprinkler or flood irrigation), and calibration data from additional monitoring sites. Dissolved-solids loads estimated for 312 monitoring sites were used to calibrate the SPARROW model, which predicted loads for each of 10,789 stream reaches in the UCRB. The calibrated model provided a good fit to the calibration data as evidenced by R 2 and yield R 2 values of 0.96 and 0.73, respectively, and a root-mean-square error of 0.47. The model included seven geologic sources that have estimated dissolved-solids yields ranging from approximately 1 to 45 tons per square mile (tons/mi 2 ). Yields generated from irrigated agricultural lands are substantially greater than those from geologic sources, with sprinkler irrigated lands generating an average of approximately 150 tons/mi 2 and flood irrigated lands generating between 770 and 2,300 tons/mi 2 depending on underlying lithology. The coefficients estimated for six landscape transport characteristics that influence the delivery of dissolved solids from sources to streams, are consistent with the process understanding of dissolved-solids loading to streams in the UCRB. Dissolved-solids loads and the proportion of those loads among sources in the entire UCRB as well as in major tributaries in the basin are reported, as are loads generated from irrigated lands, rangelands, Bureau of Land Management (BLM) lands, and grazing allotments on BLM lands. Model-predicted loads also are compared with load estimates from 1957 and 1991 at selected locations in three divisions of the UCRB. At the basin scale, the model estimates that 32 percent of the dissolved-solids loads are from irrigated agricultural land sources that compose less than 2 percent of the land area in the UCRB. This estimate is less than previously reported estimates of 40 to 45 percent of basin-scale dissolved-solids loads from irrigated agricultural land sources. This discrepancy could be a result of the implementation of salinity control projects in the basin. Notably, results indicate that the conversion of flood irrigated agricultural lands to sprinkler irrigated agricultural lands is a likely process contributing to the temporal decrease in dissolved-solids loads from irrigated lands.

Colorado River Basin↗

USGS2016

Latent spatial models and sampling design for landscape genetics

We propose a spatially-explicit approach for modeling genetic variation across space and illustrate how this approach can be used to optimize spatial prediction and sampling design for landscape genetic data. We propose a multinomial data model for categorical microsatellite allele data commonly used in landscape genetic studies, and introduce a latent spatial random effect to allow for spatial correlation between genetic observations. We illustrate how modern dimension reduction approaches to spatial statistics can allow for efficient computation in landscape genetic statistical models covering large spatial domains. We apply our approach to propose a retrospective spatial sampling design for greater sage-grouse ( Centrocercus urophasianus ) population genetics in the western United States.

Annals of Applied Statistics↗

USGS2016

Evaluating land cover influences on model uncertainties—A case study of cropland carbon dynamics in the Mid-Continent Intensive Campaign region

Quantifying spatial and temporal patterns of carbon sources and sinks and their uncertainties across agriculture-dominated areas remains challenging for understanding regional carbon cycles. Characteristics of local land cover inputs could impact the regional carbon estimates but the effect has not been fully evaluated in the past. Within the North American Carbon Program Mid-Continent Intensive (MCI) Campaign, three models were developed to estimate carbon fluxes on croplands: an inventory-based model, the Environmental Policy Integrated Climate (EPIC) model, and the General Ensemble biogeochemical Modeling System (GEMS) model. They all provided estimates of three major carbon fluxes on cropland: net primary production (NPP), net ecosystem production (NEP), and soil organic carbon (SOC) change. Using data mining and spatial statistics, we studied the spatial distribution of the carbon fluxes uncertainties and the relationships between the uncertainties and the land cover characteristics. Results indicated that uncertainties for all three carbon fluxes were not randomly distributed, but instead formed multiple clusters within the MCI region. We investigated the impacts of three land cover characteristics on the fluxes uncertainties: cropland percentage, cropland richness and cropland diversity. The results indicated that cropland percentage significantly influenced the uncertainties of NPP and NEP, but not on the uncertainties of SOC change. Greater uncertainties of NPP and NEP were found in counties with small cropland percentage than the counties with large cropland percentage. Cropland species richness and diversity also showed negative correlations with the model uncertainties. Our study demonstrated that the land cover characteristics contributed to the uncertainties of regional carbon fluxes estimates. The approaches we used in this study can be applied to other ecosystem models to identify the areas with high uncertainties and where models can be improved to reduce overall uncertainties for regional carbon flux estimates.

Mid-Continent Intensive Campaign region↗

USGS2013

Modelling dendritic ecological networks in space: anintegrated network perspective

Dendritic ecological networks (DENs) are a unique form of ecological networks that exhibit a dendritic network topology (e.g. stream and cave networks or plant architecture). DENs have a dual spatial representation; as points within the network and as points in geographical space. Consequently, some analytical methods used to quantify relationships in other types of ecological networks, or in 2-D space, may be inadequate for studying the influence of structure and connectivity on ecological processes within DENs. We propose a conceptual taxonomy of network analysis methods that account for DEN characteristics to varying degrees and provide a synthesis of the different approaches within the context of stream ecology. Within this context, we summarise the key innovations of a new family of spatial statistical models that describe spatial relationships in DENs. Finally, we discuss how different network analyses may be combined to address more complex and novel research questions. While our main focus is streams, the taxonomy of network analyses is also relevant anywhere spatial patterns in both network and 2-D space can be used to explore the influence of multi-scale processes on biota and their habitat (e.g. plant morphology and pest infestation, or preferential migration along stream or road corridors).

Ecology Letters↗

USGS2022

Are existing modeling tools useful to evaluate outcomes in mangrove restoration and rehabilitation projects? A minireview

Ecosystem modeling is a critical process for understanding complex systems at spatiotemporal scales needed to conserve, manage, and restore ecosystem services (ESs). Although mangrove wetlands are sources of ESs worth billions of dollars, there is a lack of modeling tools. This is reflected in our lack of understanding of mangroves’ functional and structural attributes. Here, we discuss the “state of the art” of mangrove models used in the planning and monitoring of R/R projects during the last 30 years. The main objectives were to characterize the most frequent modeling approach, their spatiotemporal resolution, and their current utility/application in management decisions. We identified 281 studies in six broad model categories: conceptual, agent-based (ABM), process-based (PBM), spatial, statistical, and socioeconomic/management (ScoEco). The most widely used models are spatial and statistical, followed by PBM, ScoEco, and conceptual categories, while the ABMs were the least frequently used. Yet, the application of mangrove models in R/R projects since the early 1990s has been extremely limited, especially in the mechanistic model category. We discuss several approaches to help advance model development and applications, including the targeted allocation of potential revenue from global carbon markets to R/R projects using a multi-model and integrated approach.

Forests↗

USGS2017

A dynamic spatio-temporal model for spatial data

Analyzing spatial data often requires modeling dependencies created by a dynamic spatio-temporal data generating process. In many applications, a generalized linear mixed model (GLMM) is used with a random effect to account for spatial dependence and to provide optimal spatial predictions. Location-specific covariates are often included as fixed effects in a GLMM and may be collinear with the spatial random effect, which can negatively affect inference. We propose a dynamic approach to account for spatial dependence that incorporates scientific knowledge of the spatio-temporal data generating process. Our approach relies on a dynamic spatio-temporal model that explicitly incorporates location-specific covariates. We illustrate our approach with a spatially varying ecological diffusion model implemented using a computationally efficient homogenization technique. We apply our model to understand individual-level and location-specific risk factors associated with chronic wasting disease in white-tailed deer from Wisconsin, USA and estimate the location the disease was first introduced. We compare our approach to several existing methods that are commonly used in spatial statistics. Our spatio-temporal approach resulted in a higher predictive accuracy when compared to methods based on optimal spatial prediction, obviated confounding among the spatially indexed covariates and the spatial random effect, and provided additional information that will be important for containing disease outbreaks.

Wisconsin↗

USGS1994

Spatial and temporal statistical analysis of a ground-water level network, Broward County, Florida

The U.S. Geological Survey has developed a method to evaluate the spatial and temporal statistics of a continuous ground-water level recorder network in Broward County, Florida. Because the Broward County network is sparse for most spatial statistics, a technique has been developed to define polygons for each well that represent the area monitored by the well within specified criteria. The boundaries of these "confidence polygons" are defined by the endpoints of radial lines oriented toward the other wells. The lengths of these lines are determined as the statistically estimated distances to the points at which ground-water levels can be predicted within specirfied criteria. The confidence polygons indicate: (1) the areal coverage of the network, (2) locations where data are unavailable, and (3) areas of redundant data collection. Comparison with data from a noncontinuous recorder well indicates that the confidence polygons are a good represen- tation of areal coverages. The temporal analysis utilizes statistical techniques similar to those used in the spatial method, defining variations in time rather than in space. Consequently, instead of defining radial distances to points, time intervals are defined over which water-level values can be predicted within a specified confidence. These "temporal confidence intervals" correspond to maximum allowable periods between field measure- ments. To combine all results from the analyses, a single coefficient reflecting the spatial and temporal results has been developed. The coefficient is referred to as the Spatial and Temporal Adequacy and Redundancy Evaluation (STARE) and is determined by three factors: the size of the confidence polygon, the number of times the well is part of a redundant pair, and the temporal confidence interval. This coefficient and the individual results of each analysis are used in evaluating the present network and determining future management decisions.

Florida↗

USGS2003

Development and calibration of a ground-water flow model for the Sparta Aquifer of southeastern Arkansas and north-central Louisiana and simulated response to withdrawals, 1998-2027

The Sparta aquifer, which consists of the Sparta Sand, in southeastern Arkansas and north-central Louisiana is a major water resource and provides water for municipal, industrial, and agricultural uses. In recent years, the demand in some areas has resulted in withdrawals from the Sparta aquifer that substantially exceed replenishment of the aquifer. Considerable drawdown has occurred in the potentiometric surface forming regional cones of depression as water is removed from storage by withdrawals. These cones of depression are centered beneath the Grand Prairie area and the cities of Pine Bluff and El Dorado in Arkansas, and Monroe in Louisiana. The rate of decline for hydraulic heads in the aquifer has been greater than 1 foot per year for more than a decade in much of southern Arkansas and northern Louisiana where hydraulic heads are now below the top of the Sparta Sand. Continued hydraulic-head declines have caused water users and managers alike to question the ability of the aquifer to supply water for the long term. Concern over protecting the Sparta aquifer as a sustainable resource has resulted in a continued, cooperative effort by the Arkansas Soil and Water Conservation Commission, U.S. Army Corps of Engineers, and the U.S. Geological Survey to develop, maintain, and utilize numerical ground-water flow models to manage and further analyze the ground-water system. The work presented in this report describes the development and calibration of a ground-water flow model representing the Sparta aquifer to simulate observed hydraulic heads, documents major differences in the current Sparta model compared to the previous Sparta model calibrated in the mid-1980's, and presents the results of three hypothetical future withdrawal scenarios. The current Sparta model-a regional scale, three-dimensional numerical ground-water flow model-was constructed and calibrated using available hydrogeologic, hydraulic, and water-use data from 1898 to 1997. Significant changes from the previous model include grid rediscretization of the aquifer, extension of the active model area northward beyond the Cane River Formation facies change, and representation of model boundaries. The current model was calibrated with the aid of parameter estimation, a nonlinear regression technique, combined with trial and error parameter adjustment using a total of 795 observations from 316 wells over 4 different years-1970, 1985, 1990, and 1997. The calibration data set provides broad spatial and temporal coverage of aquifer conditions. Analysis of the residual statistics, spatial distribution of residuals, simulated compared to observed hydrographs, and simulated compared to observed potentiometric surfaces were used to analyze the ability of the calibrated model to simulate aquifer conditions within acceptable error. The calibrated model has a root mean square error of 18 feet for all observations, an improvement of more than 12 feet from the previous model. The current Sparta model was used to predict the effects of three hypothetical withdrawal scenarios on hydraulic heads over the period 1998-2027 with one of those extended indefinitely until equilibrium conditions were attained, or steady state. In scenario 1a, withdrawals representing the time period from 1990 to 1997 was held constant for 30 years from 1998 to 2027. Hydraulic heads in the middle of the cone of depression centered on El Dorado decreased by 10 feet from the 1997 simulation to 222 feet below NGVD of 1929 in 2027. Hydraulic heads in the Pine Bluff cone of depression showed a greater decline from 61 feet below NGVD of 1929 to 78 feet below NGVD of 1929 in the center of the cone. With these same withdrawals extended to steady state (scenario 1b), hydraulic heads in the Pine Bluff cone of depression center declined an 2 Development and Calibration of a Ground-Water Flow Model for the Sparta Aquifer of Southeastern Arkansas and North-Central Louisiana and Simulated Response to Withdrawa

Water-Resources Investigations Report↗

USGS2013

Effects of sampling interval on spatial patterns and statistics of watershed nitrogen concentration

This study investigates how spatial patterns and statistics of a 30 m resolution, model-simulated, watershed nitrogen concentration surface change with sampling intervals from 30 m to 600 m for every 30 m increase for the Little River Watershed (Georgia, USA). The results indicate that the mean, standard deviation, and variogram sills do not have consistent trends with increasing sampling intervals, whereas the variogram ranges remain constant. A sampling interval smaller than or equal to 90 m is necessary to build a representative variogram. The interpolation accuracy, clustering level, and total hot spot areas show decreasing trends approximating a logarithmic function. The trends correspond to the nitrogen variogram and start to level at a sampling interval of 360 m, which is therefore regarded as a critical spatial scale of the Little River Watershed. Copyright ?? 2009 by Bellwether Publishing, Ltd. All right reserved.

GIScience and Remote Sensing↗