Scientific Investigations Report 2008–5059
U.S. GEOLOGICAL SURVEY
Scientific Investigations Report 2008–5059
The preferred way to map the water-table configuration is to obtain one or more synoptic (collected simultaneously) sets of measurements of the depth to water in wells that encompass the entire area of interest with sufficient density to minimize uncertainty between measurement locations. However, to conduct such an intensive collection of measurements was beyond the scope of this study. Instead, the method of analysis used to determine the configuration of the water table in the Portland area relied primarily on three sources of readily available information: (1) existing water-level data from shallow wells; (2) locations of surface-water features that are directly hydraulically connected to and, thereby, representative of the water table; and (3) land-surface elevation. These sources of information were then combined and used with statistical methods to estimate the water-table configuration. Many methods have been developed for the analysis of these types of data to determine the water-table configuration. Data often are manually contoured, enabling additional hydrologic knowledge to be incorporated; however, this method is potentially prone to bias and error, especially where hydrologic knowledge is limited. The fundamental observation that the water table is a subdued replica of the land surface indicates that topographic data can be used to guide and constrain the mapping of the water-table configuration. A number of studies have used a regression analysis to define the relation between water-table and land-surface elevations (Williams and Williamson, 1989; Sepúlveda, 2002; Peck and Payne, 2003). The regression analysis appears to work well for areas where the topography and precipitation are consistent over a region and the hydraulic properties of the aquifers generally are homogeneous. However, Sepúlveda (2002, p. 18) noted that regression generally fails to provide reliable estimates in upland areas of low recharge or high permeability where land-surface elevation and water levels may not be correlated. Most importantly, regression ignores local variations, possibly resulting in large errors for areas where the features are not typical of the region or that are subject to additional hydrologic stresses (Rouhani, 1986, p. 213 and 215). Supplemental explanatory variables can be included in the regression that can improve the results but require additional data that may not be readily available. Therefore, regression has limitations for the determination of the water-table configuration for specific areas. In addition, neither manual contouring nor regression methods readily provide an objective measure of the reliability of the water-table position estimate at specific locations. Manual contouring and regression methods were not adopted for the purposes of this study for these reasons.
Kriging was the method of interpolation selected for use in this study. Kriging is based on a geostatistical theory predicated on the observation that values of spatially distributed data commonly are correlated—values at nearby locations are more highly correlated than values at distant locations (Alley, 1993, p. 87). Kriging produces a grid of regularly spaced estimates from irregularly spaced data (like well locations) from which contour maps and other depictions of the water table can be made. Kriging is particularly well suited to problems in the hydrosciences (Delhomme, 1978, p. 251) and has been widely used to map ground-water surfaces (Alley, 1993, p. 87). Kriging estimates have statistically optimal properties such as producing the minimum possible error variances of any linear-estimation method (Davis, 2002, p. 418). The kriging method also maximizes the use of available data, helps to compensate for the effects of clustered data, provides a map of uncertainty of the kriging estimates, and is an objective analysis (Davis, 1986, p. 383 and 386; Bossong and others, 1999, p. 17). Because the kriging method is not based on the physics of the ground-water flow system, the results should be scrutinized to ensure that the interpolation is reasonable and consistent with available hydrogeologic information.
A flow chart of the simplified development of the depth-to-water and water-table elevation maps is presented in figure 5. A depth-to-water dataset was derived from locations and depths to water measured at wells and the locations of surface-water features where the depth to the water table is zero. A water-table elevation dataset was derived by subtracting depth-to-water values from land-surface elevation that was determined by the use of a Digital Elevation Model (DEM). A semivariogram (a special type of graph) was determined for each dataset to obtain the parameters for the kriging analysis. Each dataset was interpolated separately using kriging that resulted in preliminary maps of depth to water and water-table elevation. Values from the preliminary water-table elevation map were subtracted from the land-surface elevation to create another version of a preliminary depth-to-water map. The two versions of the depth-to-water maps were averaged to create a final depth-to-water map. Values from the final depth-to-water map were subtracted from the land-surface elevation at each location to create a final map of the water-table elevation.
Seasonal water-table fluctuations were analyzed using summary statistics of data from shallow wells that had multiple water-level measurements. Care was taken to ensure that only wells with water-level measurements collected throughout the year were used and to remove measurements that may not have been representative of the static water level of the aquifer. Careful selection of wells and measurements ensured that the complete range of seasonal variation was observed and that spurious measurements did not interfere with the analysis. Spatial distribution of seasonal fluctuations was determined to be largely influenced by the effective porosity and was classified based on the hydrogeology in the range of fluctuation of the water table.
Three sources of water-level information from wells were used in the analysis of the water table. Information on water levels reported by well constructors at the time of new well installation is the largest source of available data for the Portland area. Data also are available for ground-water levels reported in previous USGS studies of the ground-water hydrology in the Portland area. Finally, additional wells were located and water levels were measured as part of this study. The unsaturated zone thickness in the Portland area generally is less than 300 ft; therefore, only water levels from wells with completed depths of 300 ft or less were considered for use in the analysis of the water table. Water levels in these shallow wells were assumed to represent the water table, although the open interval of the well is usually substantially below the water table.
Since 1955, well drillers in Oregon have been required by the State to file a well report (log) documenting the well installation with information describing the well location, type of subsurface materials encountered, well depth, construction, and the depth to water. These records are available from the Oregon Water Resources Department (OWRD) at http://www.wrd.state.or.us. OWRD has more than 20,000 wells on file that have completed depths of less than 300 ft in the Portland area; this extensive dataset was first investigated as a source of depth-to-water information for interpolation of the water table. Locations of many wells (especially older wells) generally are not accurately known. Commonly, the locations are reported only to the nearest mile or quarter mile. This large number of wells was initially assumed to provide a robust dataset for estimating the water-table position even though the locations are not always accurate. Wells in the same geographic area were grouped and a measure of the central value of the depth to water was used to represent the position of the water table for that location.
The values of depth to water recorded in well logs were grouped by sections (1 mi2). The median value (the central value of the distribution of all water-level measurements when the data are ranked in order of magnitude, also known as the 50th percentile) of depth to water for each section was then calculated. The median was selected as the summary value instead of the mean because, unlike the mean, the median is a “resistant measure” that is not strongly influenced by a few extreme measurements (Helsel and Hirsch, 2002, p. 5). This resistance to the presence of outlying measurements was considered a desirable property for characterizing depth to water.
Each of the 220 points in figure 6A represents a single 1 mi2 section in the study area where depth-to-water measurements have been documented from well-construction records and the USGS for one or more wells with depths less than or equal to 300 ft (although the measurements were not necessarily from the same wells in the section). If the water levels measured at the time of well construction are good representations of the depth to the water table, then there should be a close correspondence with the water levels measured in wells by the USGS in the same section, and the values would be expected to plot along a straight line with a slope of 1, referred to as the “line of agreement” in figure 6A. However, the plot reveals a cloud of points, rather than a line indicating only a modest relation between water levels measured at the time of well construction and water levels measured by the USGS over the last several decades in the same 1 mi2 section. The points in figures 6A and the histogram in figure 6B are skewed toward shallow values of depth to water as reported in the well logs, indicating that the measurements at the time of construction generally appear to be shallower than the measurements by the USGS. Magnitudes of differences in depth to water from the two sources of data range from -119 to 156 ft with a mean of the absolute value of the differences of 36 ft. The magnitude of the differences far exceeded what might be expected due to seasonal fluctuations or long-term trends as a result of measurements at the time of construction and those measured by the USGS on different dates. The large scatter and skew in depth-to-water data from the well reports indicated that the data would be unsuitable for the purpose of estimating depth to the water table in the present study.
Differences between median values for depths to water reported in well-construction records and those measured by the USGS could be a result of variations in land-surface relief in the 1-mi2 sections if different sets of wells were used. To determine if bias exists in the measurements reported at the time of well construction, a direct comparison was made for those wells with measurements subsequently made by the USGS. More than 4,400 water levels measured or recorded by the USGS were analyzed for 145 wells that had 10 or more measurements, including the measurement in the well-construction record to examine whether the measurements at the time of well construction were representative of the typical measurements for individual wells. The probability that the measurement at the time of construction represents an end-member observation (either the minimum or maximum depth to water) for an individual well, assuming a typical and unbiased measurement, is 2/n, where n is the number of measurements for the well. Using n equal to 20 measurements (the median value of the number of measurements for the 145 wells), the probability that a measurement at the time of construction represents an end-member observation is 2/20 or 10 percent. The number of wells that would be expected to have the measurement at the time of construction represent an end-member observation is N * 2/n where N is the number of wells. Therefore, if the measurements reported in well logs are typical and unbiased those measurements would be expected to represent an end-member observation in 145 * 2/20, or about 15 of the 145 wells. However, measurements reported in well logs represented an end-member observation for 62 of the 145 wells (43 percent of the wells). The probability of this occurring by chance alone is extremely unlikely, less than 1 in 1 billion. For these 62 wells, 65 percent of the measurements at the time of construction represented the shallowest depth to water recorded and 35 percent represented the deepest depth to water recorded. This is a clear indication that the measurements at the time of construction frequently are not representative of the static water-level conditions in a well and more likely are to be shallower than the actual depth to water.
Many factors can cause these departures from agreement; and may be related particularly to the differences in timing of when the well was constructed and measured and when the USGS made measurements, and may include short-term effects, seasonal variations, or long-term trends. However, the timing of the measurement reported in a well-construction record is important, especially if the measurements were made when water levels in the wells were not at equilibrium. Measurements at the time of well construction that appear to be shallow relative to measurements by the USGS may be the result of measurements that were made soon after well construction, when water levels in the wells were temporarily shallower as a result of incorporation of drilling fluids or well completion activities (development of well by surging and pumping of water). Other causes could include misidentification of a wetting front as the water table, or the encountering of perched aquifers due to the presence of local confining layers. Departures from agreement also may result from measurements at the time of well construction that generally appear to be deeper than measurements by the USGS. These may be a consequence of measurements that were taken soon after well construction while a well was undergoing recovery following heavy pumping during well completion activities in aquifers with lower permeabilities. Finally, strong vertical gradients, wrongly located wells, database errors, and variations in topographic relief also could contribute to discrepancies between water-level measurements from the well reports and USGS datasets. Therefore, water levels measured at the time of well construction should be used with caution, especially for wells that have locations that are not precisely known and have little information regarding their topographic position. Water-level measurements reported on well construction records as a result of these findings were deemed unsuitable for the purposes of determining the depth to the water table to the accuracy required for this study without the use of additional information regarding the well location or the measurement conditions.
Because of problems associated with the use of the water-level measurements reported in well-construction records, the use of these data was discontinued in favor of water-level data published in USGS reports, archived in the USGS National Water Information System (NWIS) database, or other USGS files (Piper, 1942; Griffin and others, 1956; Brown, 1963; Hart and Newcomb, 1965; Hogenson and Foxworthy, 1965; Leonard and Collins, 1983; McCarthy and Anderson, 1990; Hinkle, 1997; Woodward and others, 1998; Orzol and others, 2000; Lee, 2002; Conlon and others, 2005). This dataset has far fewer wells than the dataset of water levels recorded in well logs but contains verified well information and water-level measurements that are more substantiated. Wells that had artesian water levels (above land surface) or that were flowing, possibly indicating confined conditions, or that had completed depths greater than 300 ft were eliminated from the analysis. Otherwise, wells were assumed to be open to the water-table zone. When one or more wells were located within 100 ft of each other, a single well was selected for use in the analysis. The well selected generally was the shallowest well or the well with the greatest number of water-level measurements unless information was available to indicate that water levels in the well were not representative of the water table.
The period of record for the archived water-level data used extended from 1929 to 2004. The longest period of record for water-level measurements at an individual well was 67 years. The median water level calculated from all reliable water-level measurements was used to represent the water level for wells with multiple measurements. Individual measurements that indicated the well was dry, obstructed, or influenced by pumping were removed from consideration. Initial water-level measurements that were signified as “reported” or “by driller” were removed from the calculation of the median with the exception of wells with only a single water-level measurement. These single measurements that were probably obtained from well-construction reports were retained because much of the well information had been previously reviewed and evaluated for use; locations and land-surface elevations of these wells generally are more precisely known; and use of these measurements helped to constrain the position of the water table in areas of limited information.
Minimum elevation of the water table throughout the study area, referred to as the base water-table elevation, is expected to be equal to the elevation of the water table at the regional discharge areas unless the water level is being influenced by some type of local stress, such as pumping. The mean stage of the Columbia River at Vancouver, Washington (USGS site number 14144700), for the 5-year period from 1998 through 2002 was about 11 ft NAVD 88, which was selected to represent the base elevation of the water table. Median water-table elevations in wells that were lower than the base water-table elevation were evaluated. Most of these 66 wells are adjacent to the Columbia or Willamette Rivers. Stage in these rivers can vary widely as a result of seasonal fluctuations, tidal influences, or flow regulation by dams. The minimum stage at the Columbia River during the 5-year period used to establish the base water-table elevation was about 4 ft NAVD 88. Shallow wells adjacent to either of these rivers with median water-table elevations between 4 and 11 ft NAVD 88 were assumed to be strongly influenced by the river at the time of measurement. The 47 wells that met these criteria were retained in the analysis; however, the median water-table elevation at each well was set to 11 ft NAVD 88 and the depth to water adjusted accordingly. Wells with water levels between 4 and 11 ft NAVD 88 that were not adjacent to the rivers or that had median water-table elevations less than 4 ft NAVD 88 were assumed to have been influenced by pumping or to have been assigned inaccurate land-surface elevations for the determination of water-table elevation. There were 19 wells in this category that subsequently were eliminated from the analysis.
Median water levels used at each well, the USGS site number (a unique identifier), the USGS Portland Basin well-identification number, the station name, the location of the well, and other useful information are shown in appendix A, table A1. Figure 7 shows the location of wells used in previous USGS studies. Water-level and well-construction data for most wells can be retrieved from the USGS NWIS database through NWISWeb at http://waterdata.usgs.gov/or/nwis/gw using the USGS site number. Data for the remainder of the wells may be obtained online from the USGS Portland Basin Ground-Water Study data archive (U.S. Geological Survey, 2006) using the USGS Portland Basin well-identification number to access specific well information.
Available data from the USGS indicated that several areas in the study area were underrepresented by wells having useful information. The gaps in the distribution of available data would produce areas with high uncertainty. Some of these areas were located in regions where a substantial need exists to refine the position of the water table for use with regard to UIC systems and other ground-water resource issues. Additional ground-water level data were collected in these areas for use in the analysis.
Existing water-level information from wells was supplemented in areas of sparse data by identifying candidate wells in the OWRD database that were situated in areas of interest and conducting a field effort to locate and measure these wells. The criteria for selection included permanent water wells with characteristics that would indicate that the well was completed in the water table and water levels were representative of unconfined or water-table conditions. Wells with completed depths greater than 300 ft, wells with a substantial thickness of potential confining layers such as silt or clay above the open interval, or wells with water-level measurements above land surface (indicating artesian conditions) were not used to avoid water levels that could represent confined conditions. Wells that were relatively shallow (300 feet or less) and recently constructed, and that had complete location information were given priority during the field effort to locate and measure wells.
More than 75 wells were visited, but after on-site evaluation, only 20 wells met the criteria for inclusion in the current study (fig. 7). Well locations were determined by use of a Global Positioning System (GPS), well-construction details were documented, and water levels were measured based on standard USGS methods (U.S. Geological Survey, 1980, p. 2-8). Well information including location, construction, and depth to water were entered into the USGS NWIS database.
The resulting dataset of wells used in previous USGS investigations and wells located and measured for this study consisted of 582 wells. However, some areas remained where no suitable wells could be located or measured. The location of surface-water features representative of the water table was used to supplement information on the water-table position for these areas.
Locations of surface-water features such as major rivers, streams, lakes, wetlands, and springs that are in direct hydraulic contact and interact with ground water can be used to constrain the estimate of the water-table position in these areas. These features indicate where the water table is at land surface, and the elevations of these features represent the elevation of the water table.
All reaches of the Columbia, Willamette, and Clackamas Rivers in the study area were assumed to be representative of the water table throughout the lengths and widths of the rivers. Other rivers and streams were selected on the basis of a previous USGS study (McFarland and Morgan, 1996, p. 8 and 27) in which streamflow measurements were made in downstream order during low-flow conditions following an extended dry period. Streams that showed gains in flow of greater than 0.5 ft3/s per river mile, after accounting for inflows from tributaries and outflows to diversions, were assumed to be gaining water from ground-water discharge and thus, representative of the water table. The following gaining reaches were identified and used in determining the water-table position (fig. 7): Clackamas River basin: Kellogg Creek, Rock Creek, parts of Deep Creek and Tickle Creek; Columbia River basin: Columbia Slough, Fairview Creek, Sandy River, Bull Run River; Willamette River basin: parts of Johnson Creek (pl. 1).
The elevations of 22 springs with discharges generally greater than 0.1 ft3/s reported by McFarland and Morgan (1996, p. 8, and 24-27) and McCarthy and Anderson (1990, p. 31) provide additional constraints of the water-table position (appendix A, table A2). The two primary areas of spring discharge are at Crystal Springs in southeast Portland and near the cities Troutdale and Wood Village (pl. 1). Other surface-water features, such as major lakes and wetlands, were reviewed and included if judged to be hydraulically connected to the ground-water flow system.
Information on land-surface and surface-water elevations is needed to determine the accurate elevations of wells and surface-water features so that the water-table elevation can be calculated from depth-to-water information. A 2-meter lateral resolution Digital Elevation Model (DEM) was obtained from Metro, a regional government agency serving the Portland metropolitan area. The 2-meter DEM covers most of the Portland metropolitan area and was developed from 5-foot-interval contours interpreted with the use of aerial orthophotography from 2001 (Metro, 2002). A 10-meter lateral resolution DEM from the USGS was used for areas not covered by the 2-meter DEM (U.S. Geological Survey, 1999). The 10-meter DEM was resampled at a 2-meter lateral spacing by use of a bilinear interpolation to match the spacing of the 2-meter DEM from Metro. These two DEMs were combined into a single 2-meter DEM for the entire study area. River reaches for the Columbia and Willamette Rivers were smoothed to remove structures such as bridges and to ensure that the river reaches remained lower than adjacent land-surface areas. The mean stage of the Columbia River, calculated as 11 ft NAVD 88, was used to represent the lowest river elevation throughout the study area. The vertical resolution of the 2-meter and 10-meter DEMs is reported as about 0.3 and 21 ft, respectively (U.S. Geological Survey, 2000; Metro, 2002). The land-surface elevations for wells and springs used in the study were estimated by using the revised 2-meter DEM and calculated as the median land-surface elevation within a 100-foot radius of the reported locations. The 100-foot buffer for determination of land-surface elevation was used because the locations of wells and springs often are known only to an accuracy of 100 ft, depending on the method of determination.
The method of depiction of surface-water features considered characteristic of the water table at land surface was dependent on the form of the feature represented: point, linear, or areal. Single points were used to represent individual features such as springs or small water bodies including small wetlands or lakes. Linear features such as streams and small or narrow rivers were represented by points spaced every 1,000 ft along the length of the reaches that were considered to be in connection with the ground-water system. Areal features, such as large rivers with substantial width or lakes having large areas, were discretized by placing points in each 1,000 × 1,000-ft2 area. Depth to water for all points representing surface-water features was set to zero. The water-table elevation was set equal to the lowest land-surface or surface-water elevation near the point on the basis of the 2-meter DEM developed for the study area. About 4,000 points were used to represent surface-water features representative of the water table at land surface (fig. 7).
Limitations in the dataset used for analysis can lead to increased errors and, therefore, larger uncertainty in the results. These include uncertainty in the spatial distribution of the data points (lateral and vertical), bias introduced as a result of the temporal distribution of the measurements, and errors resulting from the presence of perched or confined aquifers. Uncertainty resulting from the lateral spatial distribution of available data is a function of the number and location of data consisting of available wells and surface-water features used for analysis, and is discussed further in section, “Assumptions and Assessment of Errors.” The vertical spatial distribution is dependent on the construction characteristics of available wells. Water-level measurements used in this study are from wells with various open intervals in the saturated and unsaturated zones. Although these wells may have different open intervals, the measured water levels were assumed to reasonably represent the water-table depth. The criteria to use only wells less than 300 ft in depth may result in greater error in areas where the actual depth to water may be greater than 300 ft, although for the Portland Basin, this is restricted to a limited number of relatively well-defined areas. The accuracy of the land-surface elevation associated with each well and surface-water feature is dependent on the precision and accuracy of the lateral position of the well or surface-water feature and the accuracy of the 2-meter DEM used to represent the land-surface elevation. Use of the median land-surface elevation within a 100-foot radius of the reported position of the well or spring and the lowest elevation near the remaining surface-water features helped to provide a robust estimate of the land-surface elevation.
The temporal distribution of the available water-level data used in the study covered the period from 1929 to 2004, with measurements collected during different months, seasons, and years. A synoptic dataset, which would have removed influences of long-term, seasonal, or short-term fluctuations, was impossible to obtain. Long-term fluctuations can result from climatic changes in temperature or the quantity and timing of precipitation, or may be due to anthropogenic influences such as the use of water resources or land-use changes that affect the quantity or timing of discharge including pumping, stream withdrawals, or recharge due to irrigation or changes in impervious areas. Seasonal fluctuations can result from precipitation, evapotranspiration, streamflow, and irrigation patterns. Short-term fluctuations can occur as a result of high intensity rainfall events, floods, or localized pumping. However, many of the wells have multiple measurements covering long periods of time, and the use of the median values of these measurements is intended to help reduce the uncertainty of the water-table position estimate. Additional discussion on temporal variations in water-level measurement is presented in the section, “Seasonal Water-Table Fluctuations.”
Perched ground-water zones may be present in the shallowest parts of surficial aquifers, though water wells rarely are open to these zones, as the source of water often is unreliable due to large seasonal variations (McFarland and Morgan, 1996, p. 20). Hogenson and Foxworthy (1965, p. 36 and 42) noted that in the eastern and northern parts of the city of Portland, area water levels in wells generally are representative of the regional water table. However, they also noted that perched conditions are more common in the more eastern and southeastern parts of the study area, especially in the area between the cities of Gresham and Sandy (pl. 1), in the aquifers of the Boring Lava in the Boring Hills area, or in areas covered by alluvial deposits adjacent to the Sandy and Clackamas Rivers (Hogenson and Foxworthy, 1965, p. 25, 29, 36, and 39). Some of the water-level measurements used in this study possibly could represent perched zones. Nonetheless, in most places, the measurements of depth to water are believed to reflect the depth to the water table. The use of water-level measurements representative of perched zones rather than the regional water table could result in estimating the water table to be shallower than the actual elevation.
Each water-level measurement from a well or location of a surface-water feature that was deemed to represent the water table at land surface was represented by a point (or set of points for some surface-water features) (fig. 7). These points represent the water table at these locations and can be used to interpolate the position of the water table between these points.
Two conventions typically are used to define the position of the water table, depth to water and water-table elevation (fig. 8). The choice of which convention to use (depth to water or water-table elevation) may not be obvious when interpolating the water table. The interpolation of the water table is unlike the interpolation of the potentiometric surface of a confined aquifer where only the elevation of the potentiometric surface above some datum such as sea level typically would be used. This is because the potentiometric surface generally is not influenced by surface topography and can be either above or below land surface (Fetter, 1994, p. 115). However, the water tables for some ground-water systems are expected to be related to land surface in that the water table is commonly a subdued replica of the land surface (Latham, 1878, p. 207-208; King, 1892, p. 15 and 18; Meinzer, 1923, p. 31; Heath, 1983, p. 20; Haitjema and Mitchell-Bruker, 2005, p. 781). This is particularly true for most parts of the Portland area, where much of the surficial aquifer consists of unconsolidated materials and the depth to water is relatively shallow. As a result, the influence of the land surface should be considered during the interpolation of the water table; however, the degree to which the land surface influences the water table depends on several factors. These factors have been discussed by many authors (Tóth, 1963; Freeze and Witherspoon, 1967, p. 634; Haitjema and Mitchell-Bruker, 2005, p. 784) and include wavelength of topographic features (steep versus gentle slopes), amplitude (magnitude) of topographic features (water levels generally are shallowest beneath valleys and deepest beneath hilltops [Low and others, 2002, p. 204]), hydraulic conductivity and storage of the surficial aquifer (aquifers with low hydraulic conductivity and storage more closely resemble topography than aquifers with high hydraulic conductivity and storage [Low and others, 2002, p. 204]); hydraulic conductivity of the underlying aquifer or confining unit (controls vertical flow), and spatial distribution and quantity of recharge and discharge.
The interpolation of the depth-to-water and water-table elevation datasets can produce substantially different results. The interpolations are expected to be exactly identical at the control points, such as observation wells or surface-water features representative of the water table, which act to constrain the interpolations (fig. 8). However, the interpolations may greatly diverge with increased distance from control points. For the hypothetical example presented in figure 8, the interpolation of the water table based on depth to water is too shallow under hills compared to the hypothetical water table, and under valleys the depth-to-water interpolation is too deep compared to the hypothetical water table. In contrast, the interpolation of the water table based on water-table elevation is too low under hills compared to the hypothetical water table, and under valleys the water-table elevation interpolation is too high compared to the hypothetical water table. Neither interpolation is entirely satisfactory for this hypothetical example; however, if the two interpolations are averaged by taking the mean of the values at each spatial position, the resulting surface (fig. 8) appears to be an improvement in the representation of the water table. This averaged interpolation retains many of the strengths of each interpolation with fewer of the weaknesses of either for the particular hypothetical example presented.
Averaging the interpolations of depth to water and water-table elevation incorporates the land-surface information into the interpolation. The interpolations of the water-table elevation and the depth to water represent the end members of a spectrum of possible interpolations depending on the conditions controlling the position of the water table previously described. These conditions change spatially across an area of interest as topography and hydrogeology change from place to place.
Both conventions of defining the water table initially were used to interpolate the water table for the Portland area. However, the conditions described for the hypothetical example were observed in each of the interpolations. As a result, the two interpolations were averaged by taking the mean of the values at each spatial position. This produced a water-table map that was realistic and reasonable based on our conceptualization of the ground-water flow system in the Portland area.
A brief description of kriging is presented here—the method of interpolation used for this study. Davis (1986), Deutsch and Journel (1998), and Bossong and others (1999) provide a more complete discussion on geostatistical methods. Kriging can be described as a type of spatial moving average, where the value at an unsampled location is estimated as a weighted average of the known observations. The weights assigned to the known values are based on spatial trends and correlations that may be present (Bossong and others, 1999, p. 4). The weights are a function of distance, where nearby observations are given more influential weights than more distant observations (Davis, 1986, p. 384). Kriging automatically adjusts the weights for the effects of data clustering, reducing the overall weight of a group of observations that contain much of the same information (Bossong and others, 1999, p. 17).
Kriging weights are assigned through the use of semivariograms. A semivariogram is a graph of the semivariance, which is a measure of the average difference of the observed values for points a given distance apart. As the distance increases, the semivariance (or dissimilarity) in the water-table level increases. The interaction of distance and semivariance is represented graphically on the semivariogram. Separation distances between all possible pairings of the observed data in a semivariogram are computed and the results divided into bins (lags) of generally equal intervals of separation distance (Holtschlag and Koschik, 2004, p. 7). Squared differences between all measured water-table levels are computed in each lag, and one-half the mean squared differenced value, the semivariance, is plotted at the center of each lag. This graph is called the empirical semivariogram (also referred to as the experimental or sample semivariogram), and is based on the actual water-level data. The empirical semivariogram consists of a set of points from the observed data and is used to develop a theoretical semivariogram for use in the kriging analysis. The theoretical semivariogram generally consists of a smooth curve representing a mathematical expression or function that needs to be fit through the scattered empirical semivariogram points. A number of possible theoretical semivariograms (or models) can be tested through a trial-and-error process to determine the model that bests fits the measured data of the empirical semivariogram (Bossong and others, 1999, p. 5). The selected theoretical semivariogram model then is used in the kriging analysis to assign the optimal set of weights to the observations of the water-table level when interpolating a value of the water table between existing observation locations (Davis, 1986, p. 383).
Two types of kriging methods were used to analyze the data. One consideration in the selection of the kriging method is the absence or presence of a detectable spatial trend or “drift” in the data. Drift is often associated with land-surface or water-table elevation data that have a regional dip or trend (Bossong and others, 1999, p. 4 and 27; Desbarats and others, 2002, p. 25). The method of ordinary kriging is used for data with no drift; universal kriging should be considered for data when drift is present (Bossong and others, 1999, p. 6). The presence of spatial trends in the data is indicated by a parabolic empirical semivariogram shape (Bossong and others, 1999, p. 29, 42). Drift in the analysis of the empirical semivariogram typically is handled by estimating the spatial trend in the data by using a polynomial representation and then subtracting this from the data (Bossong and others, 1999, p. 29; Davis, 2002, p. 428-429 and 259-260). The residuals then are used to determine a new empirical semivariogram for the selection of a theoretical semivariogram model. The parameters of the model are used by universal kriging, the method subsequently used for the interpolation of the data.
Kriging can be used to interpolate values at points or over blocks. Point kriging is an exact interpolator, returning the value of the measurements at the observation locations. Block kriging is not an exact interpolator and returns the linear average of an attribute over some subarea (Alley, 1993, p. 99). Desbarats and others (2002, p. 33) describe block kriging as a compromise between spatial resolution and accuracy in measured water-table levels because water levels averaged over blocks of area can be estimated with less uncertainty than levels at a single point and can serve to mitigate the influence of erratic samples. Block kriging was used for the interpolation because of these considerations, and as a result estimates at observation locations may vary slightly from the measured values.
Kriging analysis was performed separately for the two conventions of depicting the water table, depth to water and water-table elevation. Semivariograms were developed individually for each convention and were used to determine the parameters for block kriging of each dataset. The interpolated values of water-table elevation then were subtracted from a DEM simulation of the land-surface elevation at each spatial position to transform the interpolated values of water-table elevation into values representing depth to water. The land-surface elevation DEM used was a resampled version of the 2-meter DEM developed for the study based on bilinear interpolation at a cell spacing of 250 ft to match the orientation, position, and spacing of the interpolation grid. The two interpolations of depth to water (direct and through transformation) then were averaged to produce a final interpolation of depth to water. A final interpolation of the water-table elevation then was created by subtracting the averaged depth-to-water interpolated values from the resampled DEM of the land-surface elevation. The maps and discussion of depth to water and water-table elevation use the average of the two interpolations.
Empirical and model semivariograms were determined for each kriging analysis (depth to water and water-table elevation). The semivariograms developed for this study were determined with the use of only the information from wells and springs to prevent the large number of data points representing the other types of surface-water features from overwhelming the well and spring data, which more directly represent the water table over land areas. The kriging method accounts for clustering of data, and, therefore, the surface-water data were used in addition to the well and spring data. The development of the semivariograms was accomplished through the use of several programs designed to aid in the display and selection of parameters. These programs facilitate identifying which of the many theoretical semivariogram models best fit the empirical semivariogram and help to optimize the parameters for the best fit. Empirical semivariogram analysis and modeling of theoretical semivariograms were performed by using VARIOWIN software (Pannatier, 1996). The theoretical semivariogram models were fitted manually to the empirical semivariograms and the fit assessed with the “Indicative Goodness of Fit” statistic, which provides a measure of how well a model matches the measured data (Pannatier, 1996, p. 56).
Analysis of the empirical semivariogram for depth to water indicated that the data exhibited no discernible drift as determined from the shape of the empirical semivariogram (fig. 9A). Therefore, the parameters resulting from the semivariogram analysis could be used directly with ordinary kriging to interpolate the data. Parameters used for the theoretical semivariogram model for the kriging methods are listed in table 1.
The water-table elevation data exhibit drift, as determined from the parabolic shape of the empirical semivariogram (fig. 9B). The drift in the water-table elevation was estimated by using a quadratic least-squares regression, which was subtracted from the water-table elevation. The residuals were then used in a new semivariogram analysis to determine the parameters of the theoretical semivariogram model to be used in interpolation by using universal kriging (fig. 9C and table 1). For the water-table elevation dataset, the subtraction of the estimated drift, kriging of the residual values, and subsequent transformation back to water-table elevations by adding the estimated drift was carried out by the kriging software.
Kriging analysis was performed with the use of Surfer software (Golden Software, Inc., 2002) by using a rectangular grid oriented north-south/east-west with square blocks 250 ft on each side. The area of analysis was extended about 4 mi beyond the geographic extremes of the data to maximize the information made available by the data. The semivariogram and kriging parameters used for the depth-to-water and water-table elevation interpolations are listed in table 1.
A small number of blocks in the analysis of depth to water were interpolated to be negative (above land surface), especially in low-lying areas, where many surface-water features were used to represent the water table with a depth to water of 0 ft. These values were corrected to represent a depth to water of 0 ft for these blocks to be consistent with the definition of the water table based on hydrogeologic reasoning by using existing knowledge of these areas. Similarly, a small number of blocks in the analysis of the water-table elevation were interpolated with values less than 11 ft. These values were corrected to 11 ft, which is the elevation used to represent the base water-table elevation as determined by the mean stage of the Columbia River, which is the regional discharge area and lowest water-table elevation. Water-table elevations less than 11 ft are hydrogeologically unlikely unless the levels were being influenced by some type of local stress such as pumping or evapotranspiration. The averaged interpolations of depth to water and water-table elevation also were evaluated and modified as needed to ensure that the depth to water equals or exceeds 0 feet below land surface and that the water-table elevation equals or exceeds 11 ft.
The formation of maps of the standard deviations of the estimates of the water-table position is a product of the kriging analysis. These maps largely are based on the semivariogram model used and the geometric configuration of the available data (Delhomme, 1978, p. 257, 262; Bossong and others, 1999, p. 5 and 43). The maps provide a method to evaluate the reliability associated with the values of the water-table position and can be used as a measure of the uncertainty. However, the standard deviation values should be considered relative to one another and not in any absolute sense (Alley, 1993, p. 97).
Standard deviation maps were generated for the analyses of depth-to-water and water-table elevation. These maps are similar and were averaged to produce a single standard deviation map for the water-table position. The resulting standard deviation map was used to limit the extent of the analysis. Areas where the averaged standard deviation exceeded 100 ft were excluded from the results. These areas are on the perimeter of the study area, where few data are available to constrain the interpolation analysis and as such have unacceptably high uncertainty. The areas with standard deviation values less than 100 ft were rescaled to a dimensionless value that will be referred to as the “relative uncertainty.” The values of the relative uncertainty range between 0 and 1 where 0 represents a low relative uncertainty and 1 represents a high relative uncertainty. The resulting map (pl. 3) is intended to be used to determine relative uncertainty when evaluating the water-table configuration maps or estimating a value at a site-specific location. Locations with more nearby data sites that are less redundant (values on multiple sides are more useful than values on the same side) will exhibit a smaller relative uncertainty than locations with few or distant data sites, or with data sites that are less than optimally positioned (Davis, 1986, p. 388-389; Alley, 1993, p. 96). Note that the relative uncertainty map is a result of the statistical properties of the dataset and does not incorporate knowledge or uncertainty with regard to the hydrogeology of the study area.
The accuracy of the depth-to-water and water-table elevation maps depends on various factors pertaining to the data, the method of interpolation, and the hydrogeologic conditions of the surficial aquifers in the study area. Some of these factors have been discussed in the sections, “Data Limitations” and “Relative Uncertainty.” The following assumptions are made with regard to the well data used for interpolation:
The method of interpolation has a large influence on the accuracy of the water-table maps, which is influenced by the spatial distribution of data points, semivariogram modeling, the appropriate selection of the kriging parameters, the level of discretization (spatial resolution) used, and basic assumptions about the hydrogeology. The latter includes the assumption that the hydrogeologic conditions in the surficial aquifers were homogeneous and isotropic. The spatial discretization used in the interpolation can lead to errors when comparing to site-specific measurements of the water-table position, especially in areas of abrupt local change in hydrogeologic properties, steep land-surface relief, or steep water-table gradients, as the estimate from interpolation represents the water-table position for a 250-foot square block and also relied on the resampled DEM of land-surface elevation.
Some of the assumptions cannot be completely evaluated and may not have been fully met. The water-table configuration maps, however, generally are representative of the conditions in the study area. Nonetheless, the actual position of the water table may differ from the estimated position at site-specific locations, and short-term, seasonal, and long-term variations in the differences also should be expected. A measure of the accuracy of the estimation of the water-table configuration can be determined by evaluating the magnitude and the variability in the differences between measured and estimated values of the water-table position. The difference between the measured depth to water and the estimated depth to water based on the interpolation for the 582 wells and 22 springs ranged from -49 to 50 ft, with a median value of less than 1 ft and 95 percent of the estimated values within 18 ft of the measured value.
A possible consequence of interpolation is that if features are used in the analysis (wells and (or) surface-water features representative of the water table) that are within close proximity to each other and have substantially different water levels, the resulting estimate of the water-table position will be intermediate to all values. This can result in a large difference between the measured and estimated water-table position. Differing water levels in adjacent features can result from the use of wells with dissimilar open-intervals, steep hydraulic gradients due to changes in lithology or structure of the aquifer, areas of high land-surface relief, proximity to recharge or discharge stresses, the use of wells with water-level measurements representative of different time periods, or the use of wells or surface-water features that are not representative of the water table (such as wells influenced by perched ground water or streams that are not gaining).
The relative uncertainty map (pl. 3) addresses some but not all possible errors associated with the analysis of the water-table position. For example, areas with estimated depths to water greater than 300 ft will have a high uncertainty because data for the analysis of the water table were restricted to wells with a maximum depth of 300 ft. Therefore, the relative uncertainty map is intended to be used as a guide with the understanding that all sources of uncertainty are not depicted.
The water table is not a stationary surface and is continually fluctuating in response to changes in recharge to or discharge from the aquifer. Seasonal fluctuations of the water table in the Portland area are related to seasonal changes in ground-water recharge from precipitation, losing streams, irrigation, or runoff to UIC systems, or from seasonal changes in discharge due to evapotranspiration or the pumping of wells (McFarland and Morgan, 1996, p. 30). Ground-water levels in the Portland area normally are highest during the spring following the winter period of high precipitation and low evapotranspiration. Water levels recede during the summer in response to less precipitation and high evapotranspiration and are lowest in the autumn. The position of the water table also can change as a result of long-term changes in precipitation; changes in the location, timing, or quantity of irrigation or pumping; creation of impervious surfaces from urban development; or installation or removal of UIC systems or on-site waste disposal systems (septic systems). However, the present analysis did not differentiate between seasonal fluctuations and long-term changes except for the exclusion of a small number of wells with hydrographs that exhibited obvious long-term influences. These changes, especially from pumping, can be severe in areas such as the Sandy-Boring or Damascus areas, where large declines in ground-water levels led to declaration of ground-water limited areas by the Oregon Water Resources Department (2006, p. 12-13). Limitations on withdrawals instituted by the OWRD have subsequently resulted in the substantial recovery of ground-water levels in these areas. These fluctuations may influence the analysis of seasonal water-table fluctuations but should have limited influence on the median water level used in the depth-to-water analysis.
The magnitude of seasonal water-table fluctuations depends on the quantity of recharge or discharge added or removed from the aquifer as well as on the effective porosity of the aquifer. The greater the effective porosity, the greater the storage available in the aquifer. An aquifer with a greater effective porosity will experience a smaller change in the water-table position due to a change in a given volume of water compared to an aquifer with a lesser effective porosity.
The 582 wells used in the analysis of the water-table position were evaluated for use in the analysis of seasonal water-table fluctuations. In addition, 20 wells not used in the analysis of the water-table position, primarily because of the proximity to other wells, were added to the pool of candidate wells for analysis of seasonal water-table fluctuations. Of these wells, 394 wells had 2 or more water-level measurements and had no depths to water above land-surface (depth to water less than 0 ft below land surface) that might indicate artesian or confined conditions. Water-level fluctuations for wells in this group for the period of record ranged from 0 to 138 ft, with a median of 7.5 ft.
Only water-level measurements in wells representative of all seasons were used to evaluate the seasonal-water level fluctuations. The data were inspected through various graphical and statistical techniques, such as by plotting the calendar date of measurements based on polar coordinates to identify the center of mass (mean measurement date) and by comparing the polygonal area defined by the measurement dates plotted based on polar coordinates to identify those wells that had suitable distributions of measurements throughout the year. Wells with 10 or more measurements substantially met these criteria and were used to develop the seasonal-water level fluctuation analysis. As a result, 147 wells were analyzed with the number of measurements ranging from 10 to 306 with a median of 20 measurements. Inspection of the data revealed possible anomalous measurements likely due to clerical errors or resulting from measurement of wells when water levels were not in equilibrium such as during recovery from pumping or well development following construction. To remove possible errant measurements the measurements for each well were ranked by depth to water and only the central 90 percent of the measurements for each well were used for analysis and will be referred to as the trimmed values. Although this will remove most of the effects of measurement errors, trimming also can reduce the full range of the actual water-level fluctuations for any single well, although this effect generally is expected to be small given the number of measurements for each well. Water-levels in wells that are indicative of unusually large ranges in fluctuations were reviewed for inclusion in the analysis. The hydrographs of wells with water-level fluctuations of 20 ft or greater were visually inspected. Twenty well records, with long-term trends indicating large declines or recoveries, or with an unusually large percentage of apparently erroneous measurements likely due to recent or nearby pumping at the time of measurement, were removed from the analysis. The locations and the values of the trimmed ranges of water-table fluctuations for the remaining 127 wells are presented in figure 10 and in table A3.
U.S. Department of the Interior | U.S. Geological Survey
URL: http://pubs.usgs.gov/sir/2008/5059
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