Geology Reports⌕ Search
Home/Archive/USGS

USGS · ofr84459

The principle of superposition and its application in ground-water hydraulics

T. E. Reilly·O.L. Franke·G.D. Bennett
View original source ↗Read source document ↗Export metadata ↓

Abstract

The principle of superposition, a powerful methematical technique for analyzing certain types of complex problems in many areas of science and technology, has important application in ground-water hydraulics and modeling of ground-water systems. The principle of superposition states that solutions to individual problems can be added together to obtain solutions to complex problems. This principle applies to linear systems governed by linear differential equations. This report introduces the principle of superposition as it applies to groundwater hydrology and provides background information, discussion, illustrative problems with solutions, and problems to be solved by the reader. (USGS)

Explore related subjects

Open-File ReportReport

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

T. E. Reilly, O.L. Franke, G.D. Bennett. 1984. The principle of superposition and its application in ground-water hydraulics. https://doi.org/10.3133/ofr84459

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related USGS reports

USGS2026

Estimating aftershock risk for entry into earthquake-damaged buildings

We present a simple method to estimate the risk of experiencing strong shaking from aftershocks during entry into earthquake-damaged buildings. We compute wait times until the probability of strong ground shaking from aftershocks reaches a predefined risk threshold; for example, a 0.4 percent probability of experiencing Modified Mercalli Intensity 7 or greater shaking during the planned building entry. We also develop a relation between aftershock probability and the probability of strong shaking, so that users can reference the U.S. Geological Survey aftershock forecast during an ongoing aftershock sequence to determine if the risk threshold has been met. We apply our method to active continental regions (for example, the Western United States), stable continental regions (for example, the Central and Eastern United States), and subduction zones (for example, Cascadia or Alaska).

Open-File Report↗
USGS2026

End-user needs for remote sensing wetlands of the Prairie Pothole Region of North America

The Prairie Pothole Region (PPR) of North America comprises globally important grassland and wetland ecosystems critical for numerous populations of migratory birds. Due to the importance of this region for migratory birds, and particularly waterfowl, and the threats of habitat loss due to intensifying agriculture, there is a mature and diverse system of conservation organizations, agencies, and partnerships that spends hundreds of millions of dollars annually on habitat conservation to support migratory bird populations. Remote sensing can be a powerful tool for observing and evaluating global change at large scales as well as expanding inferences from field studies to the broader landscape with statistical models. However, development and utilization of these tools has lagged behind their demand for several reasons, including concerns over spatial and temporal resolution and accuracy of products; perception of a misalignment with decision-maker needs; technological barriers such as skill sets of conservation professionals, computing resources, data access, and usability. In this report, we summarize the needs of conservation professionals and scientists who use or want to use remote sensing data products to inform science about wetland change and conservation of wetlands in the PPR. We assembled this information through several methods leading up to, during, and following a January 2026 PPR Wetland Remote Sensing Workshop. The workshop included United States and Canadian scientists, conservation professionals, and policy experts. Our goal was to bring together end-users and remote sensing product developers jointly to explore reducing the lag between product development and utilization of products to inform science and conservation. Specifically, we aimed to identify gaps in wetland remote sensing that limit effective monitoring, management, and conservation in the PPR, and to develop a framework that outlines pathways to address these gaps by fostering collaboration, improving communication networks, encouraging discussion, and building on existing and ongoing efforts. This report summarizes our participants’ descriptions of end-user needs and the outcomes of the workshop.

Prairie Pothole region↗
USGS2026

Bathymetric survey and storage capacity of Upper Lake Mary near Flagstaff, Arizona in 2024

The U.S. Geological Survey (USGS), in cooperation with the city of Flagstaff, collected bathymetric, light detection and ranging (lidar), and land-survey data of Upper Lake Mary in Arizona during the months of April and October 2024. The city of Flagstaff uses a combination of groundwater from well fields throughout the Flagstaff area and surface water, mainly from Upper Lake Mary, for its potable water supply. The purpose of the survey is to update previous surveys using new technology and compare the results to previous surveys to determine if there was a decrease in storage capacity that could affect the city’s water supply. The lakebed was mapped in April 2024 using a vessel equipped with a multibeam echosounder (MBES) and mobile lidar scanner with positioning captured using a real-time kinematic global navigation satellite system (RTK GNSS) base and receivers. In October 2024, areas of the reservoir that were too shallow for the boat and shoreline that were not captured by the vessel-based lidar were surveyed on foot using hand-held RTK GNSS receivers. At full pool (spillway elevation of 6,831.82 feet above NAVD 88 [2,082.34 meters (m)], Upper Lake Mary has a storage capacity of 16,449.80 acre-feet (20,290,611.73 cubic meters) and a surface area of 953.57 acres (3,860,926.075 square meters). The reservoir is 5.7 miles (9.7 kilometers) long and varies in width from 326 feet (99.36 m) near the central, narrow portion of the reservoir to 2,613 feet (796.44 m) in the upper portion. Comparisons between this survey and the previous two surveys from the 1950s and 2006 indicate no apparent decrease in reservoir area or storage capacity. Results of the 2024 survey indicate that Upper Lake Mary’s storage capacity increased by 0.9 percent from the 2006 survey and a 1.6 percent increase in surface area from the 2006 survey.

Arizona↗