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Erick R. Burns

Publications and source records attributed to Erick R. Burns.

46 records · Page 3Linked to original sources
USGS2017

Thermal effect of climate change on groundwater-fed ecosystems

Groundwater temperature changes will lag surface temperature changes from a changing climate. Steady state solutions of the heat-transport equations are used to identify key processes that control the long-term thermal response of springs and other groundwater discharge to climate change, in particular changes in (1) groundwater recharge rate and temperature and (2) land-surface temperature transmitted through the vadose zone. Transient solutions are developed to estimate the time required for new thermal signals to arrive at ecosystems. The solution is applied to the volcanic Medicine Lake highlands, California, USA, and associated springs complexes that host groundwater-dependent ecosystems. In this system, upper basin groundwater temperatures are strongly affected only by recharge conditions. However, as the vadose zone thins away from the highlands, changes in the average annual land-surface temperature also influence groundwater temperatures. Transient response to temperature change depends on both the conductive time scale and the rate at which recharge delivers heat. Most of the thermal response of groundwater at high elevations will occur within 20 years of a shift in recharge temperatures, but the large lower elevation springs will respond more slowly, with about half of the conductive response occurring within the first 20 years and about half of the advective response to higher recharge temperatures occurring in approximately 60 years.

California↗
USGS2017

Geothermal implications of a refined composition-age geologic map for the volcanic terrains of southeast Oregon, northeast California, and southwest Idaho, USA

Sufficient temperatures to generate steam likely exist under most of the dominantly volcanic terrains of southeast Oregon, northeast California, and southeast Idaho, USA, but finding sufficient permeability to allow efficient advective heat exchange is an outstanding challenge. A new thematic interpretation of existing state-level geologic maps provides an updated and refined distribution of the composition and age of geologic units for the purposes of assessing the implications for measurement and development of geothermal resources. This interpretation has been developed to better understand geothermal and hydrologic resources of the region. Comparison of the new geologic categories with available hydrologic data shows that younger volcanogenic terrains tend to have higher primary permeability than older terrains. Decrease in primary permeability with age is attributable to weathering and hydrothermal alteration of volcanogenic deposits to pore-filling clays and deposition of secondary deposits (e.g., zeolites). Spring density as a function of geology and precipitation can be used to infer groundwater flow path length within the upper aquifers. Beneath the upper aquifers, we postulate that, due to accelerated hydrothermal alteration at temperatures ~>30 °C, primary permeability at depths of geothermal interest will be limited, and that secondary permeability is a more viable target for hydrothermal fluid withdrawal. Because open fractures resulting from tensile stresses will affect all geologic layers, regions with a significant amount of groundwater flow through shallow, structurally controlled secondary permeability may overlay zones of deep secondary permeability. Regardless of whether the shallow permeability is connected with the deep permeability, shallow groundwater flow can mask the presence of deep hydrothermal flow, resulting in blind geothermal systems. Ideally, hydraulic connectivity between shallow and deep secondary permeability is limited, so that shallow groundwater does not cool potential geothermal reservoirs.

Conference Paper↗
USGS2016

Evaluating geothermal and hydrogeologic controls on regional groundwater temperature distribution

A one-dimensional (1-D) analytic solution is developed for heat transport through an aquifer system where the vertical temperature profile in the aquifer is nearly uniform. The general anisotropic form of the viscous heat generation term is developed for use in groundwater flow simulations. The 1-D solution is extended to more complex geometries by solving the equation for piece-wise linear or uniform properties and boundary conditions. A moderately complex example, the Eastern Snake River Plain (ESRP), is analyzed to demonstrate the use of the analytic solution for identifying important physical processes. For example, it is shown that viscous heating is variably important and that heat conduction to the land surface is a primary control on the distribution of aquifer and spring temperatures. Use of published values for all aquifer and thermal properties results in a reasonable match between simulated and measured groundwater temperatures over most of the 300 km length of the ESRP, except for geothermal heat flow into the base of the aquifer within 20 km of the Yellowstone hotspot. Previous basal heat flow measurements (∼110 mW/m 2 ) made beneath the ESRP aquifer were collected at distances of >50 km from the Yellowstone Plateau, but a higher basal heat flow of 150 mW/m 2 is required to match groundwater temperatures near the Plateau. The ESRP example demonstrates how the new tool can be used during preliminary analysis of a groundwater system, allowing efficient identification of the important physical processes that must be represented during more-complex 2-D and 3-D simulations of combined groundwater and heat flow.

Idaho↗
USGS2016

Are the Columbia River Basalts, Columbia Plateau, Idaho, Oregon, and Washington, USA, a viable geothermal target? A preliminary analysis

The successful development of a geothermal electric power generation facility relies on (1) the identification of sufficiently high temperatures at an economically viable depth and (2) the existence of or potential to create and maintain a permeable zone (permeability >10 -14 m 2 ) of sufficient size to allow efficient long-term extraction of heat from the reservoir host rock. If both occur at depth under the Columbia Plateau, development of geothermal resources there has the potential to expand both the magnitude and spatial extent of geothermal energy production. However, a number of scientific and technical issues must be resolved in order to evaluate the likelihood that the Columbia River Basalts, or deeper geologic units under the Columbia Plateau, are viable geothermal targets. Recent research has demonstrated that heat flow beneath the Columbia Plateau Regional Aquifer System may be higher than previously measured in relatively shallow (<600 m depth) wells, indicating that sufficient temperatures for electricity generation occur at depths 5 km. The remaining consideration is evaluating the likelihood that naturally high permeability exists, or that it is possible to replicate the high average permeability (approximately 10 -14 to 10 -12 m 2 ) characteristic of natural hydrothermal reservoirs. From a hydraulic perspective, Columbia River Basalts are typically divided into dense, impermeable flow interiors and interflow zones comprising the top of one flow, the bottom of the overlying flow, and any sedimentary interbed. Interflow zones are highly variable in texture but, at depths <600 m, some of them form highly permeable regional aquifers with connectivity over many tens of kilometers. Below depths of ~600 m, permeability reduction occurs in many interflow zones, caused by the formation of low-temperature hydrothermal alteration minerals (corresponding to temperatures above ~35 °C). However, some high permeability (>10-14 m 2 ) interflows are documented at depths up to ~1,400 m. If the elevated permeability in these zones persists to greater depths, they may provide natural permeability of sufficient magnitude to allow their exploitation as conventional geothermal reservoirs. Alternatively, if the permeability in these interflow zones is less than 10-14 m 2 at depth, it may be possible to use hydraulic and thermal stimulation to enhance the permeability of both the interflow zones and the natural jointing within the low-permeability interior portions of individual basalt flows in order to develop Enhanced/Engineered Geothermal System (EGS) reservoirs. The key challenge for an improved Columbia Plateau geothermal assessment is acquiring and interpreting comprehensive field data that can provide quantitative constraints on the recovery of heat from the Columbia River Basalts at depths greater than those currently tested by deep boreholes.

Idaho, Oregon, Washington↗
USGS2014

Understanding heat and groundwater flow through continental flood basalt provinces: insights gained from alternative models of permeability/depth relationships for the Columbia Plateau, USA

Heat-flow mapping of the western USA has identified an apparent low-heat-flow anomaly coincident with the Columbia Plateau Regional Aquifer System, a thick sequence of basalt aquifers within the Columbia River Basalt Group (CRBG). A heat and mass transport model (SUTRA) was used to evaluate the potential impact of groundwater flow on heat flow along two different regional groundwater flow paths. Limited in situ permeability (k) data from the CRBG are compatible with a steep permeability decrease (approximately 3.5 orders of magnitude) at 600&ndash;900 m depth and approximately 40&deg;C. Numerical simulations incorporating this permeability decrease demonstrate that regional groundwater flow can explain lower-than-expected heat flow in these highly anisotropic (k x /k z ~ 10 4 ) continental flood basalts. Simulation results indicate that the abrupt reduction in permeability at approximately 600 m depth results in an equivalently abrupt transition from a shallow region where heat flow is affected by groundwater flow to a deeper region of conduction-dominated heat flow. Most existing heat-flow measurements within the CRBG are from shallower than 600 m depth or near regional groundwater discharge zones, so that heat-flow maps generated using these data are likely influenced by groundwater flow. Substantial k decreases at similar temperatures have also been observed in the volcanic rocks of the adjacent Cascade Range volcanic arc and at Kilauea Volcano, Hawaii, where they result from low-temperature hydrothermal alteration.

Idaho;Oregon;Washington↗
USGS2014

Numerical simulation of groundwater flow in the Columbia Plateau Regional Aquifer System, Idaho, Oregon, and Washington

A three-dimensional numerical model of groundwater flow was constructed for the Columbia Plateau Regional Aquifer System (CPRAS), Idaho, Oregon, and Washington, to evaluate and test the conceptual model of the system and to evaluate groundwater availability. The model described in this report can be used as a tool by water-resource managers and other stakeholders to quantitatively evaluate proposed alternative management strategies and assess the long‑term availability of groundwater. The numerical simulation of groundwater flow in the CPRAS was completed with support from the Groundwater Resources Program of the U.S. Geological Survey Office of Groundwater. The model was constructed using the U.S. Geological Survey modular three-dimensional finite-difference groundwater-flow model, MODFLOW-NWT. The model uses 3-kilometer (9,842.5 feet) grid cells that subdivide the model domain by 126 rows and 131 columns. Vertically, the model domain was subdivided into six geologic model units. From youngest to oldest, the units are the Overburden, the Saddle Mountains Basalt, the Mabton Interbed, the Wanapum Basalt, the Vantage Interbed, and the Grande Ronde Basalt. Natural recharge was estimated using gridded historical estimates of annual precipitation for the period 1895&ndash;2007. Pre-development recharge was estimated to be the average natural recharge for this period. Irrigation recharge and irrigation pumping were estimated using a remote-sensing based soil-water balance model for the period 1985&ndash;2007. Pre-1985 irrigation recharge and pumping were estimated using previously published compilation maps and the history of large-scale irrigation projects. Pumping estimates for municipal, industrial, rural, residential, and all other uses were estimated using reported values and census data. Pumping was assumed to be negligible prior to 1920. Two models were constructed to simulate groundwater flow in the CPRAS: a steady-state predevelopment model representing conditions before large-scale pumping and irrigation altered the system, and a transient model representing the period 1900&ndash;2007. Automated parameter-estimation techniques (steady-state predevelopment model) and traditional trial-and-error (transient model) methods were used for calibration. To calibrate the steady-state and transient models, 10,525 and 46,460 water level measurements, respectively, and 50 base-flow estimates were used. The steady-state model simulated the shape, slope, and trends of a potentiometric surface that was generally consistent with mapped water levels. For the transient model, the mean and median difference between simulated and measured hydraulic heads is -10 and 4 ft, respectively, with a standard deviation of 164 ft over a 5,648 ft range of measured heads. The residuals for the simulation period show that 52 percent of the simulated heads exceeded measured heads with a median residual value of 43 ft, and 48 percent were less than measured heads with a median residual value of -76 ft. The CPRAS model was constructed to derive components of the groundwater budget and help understand the interactions of stresses, such as recharge, groundwater pumping, and commingling wells on the groundwater and surface-water system. Through these applications, the model can be used to identify trends in groundwater storage and use, and quantify groundwater availability. The annual groundwater budgets showed several patterns of change over the simulation period. Groundwater pumping was negligible until the 1950s and began to increase significantly during the 1970s and 1980s. Recharge was highly variable due to the interannual variability of precipitation, but began to increase in the late 1940s due to the increase in surface-water irrigation projects. Groundwater contributions to streamflow (base flow) followed recharge closely. However, in areas of significant groundwater-level decline, base flow is reduced. Groundwater pumping had the greatest effect on water levels, followed by irrigation enhanced recharge. Commingling was a larger factor in structurally complex upland areas where hydraulic-head gradients are naturally high. Groundwater pumping has increased substantially over the past 40&ndash;50 years; this increase resulted in declining water levels at depth and decreased base flows over much of the study area. The effects of pumping are mitigated somewhat by the increase of surface-water irrigation, especially in the shallow Overburden unit, and commingling wells in some areas. During dry to average years, groundwater pumping causes a net loss of groundwater in storage and current condition (2000&ndash;2007) groundwater pumping exceeds recharge in all but the wettest of years.

Idaho, Oregon, Washington↗
USGS2014

Simulation of groundwater flow and the interaction of groundwater and surface water in the Willamette Basin and Central Willamette subbasin, Oregon

Full appropriation of tributary streamflow during summer, a growing population, and agricultural needs are increasing the demand for groundwater in the Willamette Basin. Greater groundwater use could diminish streamflow and create seasonal and long-term declines in groundwater levels. The U.S. Geological Survey (USGS) and the Oregon Water Resources Department (OWRD) cooperated in a study to develop a conceptual and quantitative understanding of the groundwater-flow system of the Willamette Basin with an emphasis on the Central Willamette subbasin. This final report from the cooperative study describes numerical models of the regional and local groundwater-flow systems and evaluates the effects of pumping on groundwater and surface‑water resources. The models described in this report can be used to evaluate spatial and temporal effects of pumping on groundwater, base flow, and stream capture. The regional model covers about 6,700 square miles of the 12,000-square mile Willamette and Sandy River drainage basins in northwestern Oregon—referred to as the Willamette Basin in this report. The Willamette Basin is a topographic and structural trough that lies between the Coast Range and the Cascade Range and is divided into five sedimentary subbasins underlain and separated by basalts of the Columbia River Basalt Group (Columbia River basalt) that crop out as local uplands. From north to south, these five subbasins are the Portland subbasin, the Tualatin subbasin, the Central Willamette subbasin, the Stayton subbasin, and the Southern Willamette subbasin. Recharge in the Willamette Basin is primarily from precipitation in the uplands of the Cascade Range, Coast Range, and western Cascades areas. Groundwater moves downward and laterally through sedimentary or basalt units until it discharges locally to wells, evapotranspiration, or streams. Mean annual groundwater withdrawal for water years 1995 and 1996 was about 400 cubic feet per second; irrigation withdrawals accounted for about 80 percent of that total. The upper 180 feet of productive aquifers in the Central Willamette and Southern Willamette subbasins produced about 70 percent of the total pumped volume. In this study, the USGS constructed a three-dimensional numerical finite-difference groundwater-flow model of the Willamette Basin representing the six hydrogeologic units, defined in previous investigations, as six model layers. From youngest to oldest, and [generally] uppermost to lowermost they are the: upper sedimentary unit, Willamette silt unit, middle sedimentary unit, lower sedimentary unit, Columbia River basalt unit, and basement confining unit. The high Cascade unit is not included in the groundwater-flow model because it is not present within the model boundaries. Geographic boundaries are simulated as no-flow (no water flowing in or out of the model), except where the Columbia River is simulated as a constant hydraulic head boundary. Streams are designated as head-dependent-flux boundaries, in which the flux depends on the elevation of the stream surface. Groundwater recharge from precipitation was estimated using the Precipitation-Runoff Modeling System (PRMS), a watershed model that accounts for evapotranspiration from the unsaturated zone. Evapotranspiration from the saturated zone was not considered an important component of groundwater discharge. Well pumping was simulated as specified flux and included public supply, irrigation, and industrial pumping. Hydraulic conductivity values were estimated from previous studies through aquifer slug and permeameter tests, specific capacity data, core analysis, and modeling. Upper, middle and lower sedimentary unit horizontal hydraulic conductivity values were differentiated between the Portland subbasin and the Tualatin, Central Willamette, and Southern Willamette subbasins based on preliminary model results.

Oregon↗
USGS2012

Evaluation of long-term water-level declines in basalt aquifers near Mosier, Oregon

The Mosier area lies along the Columbia River in northwestern Wasco County between the cities of Hood River and The Dalles, Oregon. Major water uses in the area are irrigation, municipal supply for the city of Mosier, and domestic supply for rural residents. The primary source of water is groundwater from the Columbia River Basalt Group (CRBG) aquifers that underlie the area. Concerns regarding this supply of water arose in the mid-1970s, when groundwater levels in the orchard tract area began to steadily decline. In the 1980s, the Oregon Water Resources Department (OWRD) conducted a study of the aquifer system, which resulted in delineation of an administrative area where parts of the Pomona and Priest Rapids aquifers were withdrawn from further appropriations for any use other than domestic supply. Despite this action, water levels continued to drop at approximately the same, nearly constant annual rate of about 4 feet per year, resulting in a current total decline of between 150 and 200 feet in many wells with continued downward trends. In 2005, the Mosier Watershed Council and the Wasco Soil and Water Conservation District began a cooperative investigation of the groundwater system with the U.S. Geological Survey. The objectives of the study were to advance the scientific understanding of the hydrology of the basin, to assess the sustainability of the water supply, to evaluate the causes of persistent groundwater-level declines, and to evaluate potential management strategies. An additional U.S. Geological Survey objective was to advance the understanding of CRBG aquifers, which are the primary source of water across a large part of Oregon, Washington, and Idaho. In many areas, significant groundwater level declines have resulted as these aquifers were heavily developed for agricultural, municipal, and domestic water supplies. Three major factors were identified as possible contributors to the water-level declines in the study area: (1) pumping at rates that are not sustainable, (2) well construction practices that have resulted in leakage from aquifers into springs and streams, and (3) reduction in aquifer recharge resulting from long-term climate variations. Historical well construction practices, specifically open, unlined, uncased boreholes that result in cross-connecting (or commingling) multiple aquifers, allow water to flow between these aquifers. Water flowing along the path of least resistance, through commingled boreholes, allows the drainage of aquifers that previously stored water more efficiently. The study area is in the eastern foothills of the Cascade Range in north central Oregon in a transitional zone between the High Cascades to the west and the Columbia Plateau to the east. The 78-square mile (mi 2 ) area is defined by the drainages of three streams - Mosier Creek (51.8 mi 2 ), Rock Creek (13.9 mi 2 ), and Rowena Creek (6.9 mi 2 ) - plus a small area that drains directly to the Columbia River.The three major components of the study are: (1) a 2-year intensive data collection period to augment previous streamflow and groundwater-level measurements, (2) precipitation-runoff modeling of the watersheds to determine the amount of recharge to the aquifer system, and (3) groundwater-flow modeling and analysis to evaluate the cause of groundwater-level declines and to evaluate possible water resource management strategies. Data collection included the following: 1. Water-level measurements were made in 37 wells. Bi-monthly or quarterly measurements were made in 30 wells, and continuous water-level monitoring instruments were installed in 7 wells. The measurements principally were made to capture the seasonal patterns in the groundwater system, and to augment the available long-term record. 2. Groundwater pumping was measured, reported, or estimated from irrigation, municipal and domestic wells. Flowmeters were installed on 74 percent of all high-capacity irrigation wells in the study area. 3. Borehole geophysical data were collected from a known commingling well. These data measured geologic properties and vertical flow through the well. 4. Streamflow measurements were made in Rock, Rowena, and Mosier Creeks. A long-term recording stream-gaging station was reestablished on Mosier Creek to provide a continuous record of streamflow. Streamflow measurements also were made along the creeks periodically to evaluate seasonal patterns of exchange between streams and the groundwater system. Major findings from the study include: 1. Annual average precipitation ranges from 20 to 54 inches across the study area with an average value of about 30 inches. Based on rainfall-runoff modeling, about one-third of this water infiltrates into the aquifer system. 2. Currently, about 3 percent of the water infiltrated into the groundwater system is extracted for municipal, agricultural, and rural residential use. The remainder of the water flows through the aquifer system, discharging into local streams and the Columbia River. About 80 percent of recent pumping supports crop production. The city of Mosier public supply wells account for about 10 percent of total pumping, with the remaining 10 percent being pumped from the private wells of rural residents. 3. Groundwater-flow simulation results indicate that leakage through commingling wells is a significant and likely the dominant cause of water level declines. Leakage patterns can be complex, but most of the leaked water likely flows out the CRBG aquifer system through very permeable sediments into Mosier Creek and its tributary streams in the OWRD administrative area. Model-derived estimates attribute 80-90 percent of the declines to commingling, with pumping accounting for the remaining 10-20 percent. Although decadal trends in precipitation have occurred, associated changes in aquifer recharge are likely not a significant contributor to the current water level declines. 4. As many as 150 wells might be commingling. To evaluate whether or not the local combination of geology and well construction have resulted in aquifer commingling at a particular well, the well needs to be tested by measuring intraborehole flow. During geophysical testing of one known commingling well, the flow rate through the well between aquifers ranged between 70 and 135 gallons per minute (11-22 percent of total annual pumping in the study area). Historically, when aquifer water levels were 150-200 feet higher, this flow rate would have been correspondingly higher. 5. Because aquifer commingling through well boreholes is likely the dominant cause of aquifer declines, flow simulations were conducted to evaluate the benefit of repairing wells in specified locations and the benefit of recharging aquifers using diverted flow from study area creeks. As part of this analysis, maps were generated that show which areas are more vulnerable to commingling. These maps indicate that the value of repairing wells in the area generally coincident with the OWRD administrative area is higher than in areas farther upstream in the watershed. Simulation results also indicate that artificial recharge of the aquifers using diverted creek water will not significantly improve water levels in the aquifer system unless at least some commingling wells are repaired first. Repairs would entail construction of wells in a manner that prevents commingling of multiple aquifers. The value of artificially recharging the aquifers improves as more wells are repaired because the aquifer system more efficiently stores water.

Oregon↗
USGS2012

Groundwater status and trends for the Columbia Plateau Regional Aquifer System, Washington, Oregon, and Idaho

Well information and groundwater-level measurements for the Columbia Plateau Regional Aquifer System in Washington, Oregon, and Idaho, were compiled from data provided by the U.S. Geological Survey and seven other organizations. From the full set of about 60,000 wells and 450,000 water-level measurements a subset of 761 wells within the aquifers of the Columbia River Basalt Group (CRBG) then was used to develop a simple linear groundwater-level trend map for 1968–2009. The mean of the trends was a decline of 1.9 feet per year (ft/yr), with 72 percent of the water levels in wells declining. Rates of declines greater than 1.0 ft/yr were measured in 50 percent of wells, declines greater than 2.0 ft/yr in 38 percent of wells, declines greater than 4.0 ft/yr in 29 percent of wells, and declines greater than 8.0 ft/yr in 4 percent of wells. Water-level data were used to identify groups of wells with similar hydraulic heads and temporal trends to delineate areas of overall similar groundwater conditions. Discontinuities in hydraulic head between well groups were used to help infer the presence of barriers to groundwater flow such as changes in lithology or the occurrence of folds and faults. In areas without flow barriers, dissimilarities in response of well groups over time resulted from the formation of groundwater mounds caused by recharge from irrigation or regions of decline caused by pumping. The areas of focus for this analysis included the Umatilla area, Oregon, and the Palouse Slope/eastern Yakima Fold Belt in the Columbia Basin Ground Water Management Area (GWMA) consisting of Adams, Franklin, Grant, and Lincoln Counties, Washington. In the Umatilla area, water levels from 286 wells were used to identify multiple areas of high hydraulic gradient that indicate vertical and horizontal barriers to groundwater flow. These barriers divide the groundwater-flow system into several compartments with varying degrees of interconnection. Horizontal flow barriers commonly correspond to mapped geologic structure and result in horizontal hydraulic gradients that progressively become steeper from north to south corresponding to an increase in structural complexity that may be impeding recharge from the uplands into the heavily developed areas. Most CRBG aquifers in the Umatilla area are declining and since 1970, cumulative declines range from about 100 to 300 feet. Significant vertical hydraulic gradients are documented for relatively small areas near Umatilla, and since the 1970s, downward vertical gradients in these areas have been increasing as hydraulic heads in the deeper units have declined. The absence of vertical gradients over much of the area may be a consequence of flow through commingling wells that results in the equilibration of the heads between aquifers. On the Palouse Slope in the central GWMA, large groundwater declines occurred during 1968–2009 along a north-south swath in the middle of the region. An analysis of 1,195 wells along major flow paths and through the area of persistent groundwater-level declines indicates that barriers to flow are not as evident in this area as in Umatilla. This is consistent with the geologic interpretation of the Palouse Slope as being a gently folded structure created by voluminous sheet flows of CRBG lavas. Groundwater discharge into the sediment-filled coulees, where the upper aquifers are intersected at land surface by incised canyons, is proposed as an alternative to explain local steepening of the hydraulic gradient along the Palouse Slope previously attributed to the presence of a groundwater dam. Comparison of generalized potentiometric surface maps developed for pre-development conditions and post-2000 conditions indicate that pre-development groundwater flow was from the uplands toward the Columbia and Snake River and that post-2000 flow patterns in the area are controlled by irrigation practices that have resulted in broad regions of elevated or depressed hydraulic head. In some cases, irrigation-related changes in head have reversed groundwater flow directions. Evidence of significant vertical hydraulic gradients exists, although much of the aquifer thickness is affected by commingling of wells. The effect of commingling and its relative contribution to problems related to groundwater-level declines remains unclear.

Washington, Oregon, Idaho↗