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Search indexed USGS publications on groundwater, aquifers, geologic maps, mineral resources and earthquakes. Explore source records by subject and place.

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At least 523 records · Page 29Linked to original sources
USGS2023

The 2018 eruption of Kīlauea: Insights, puzzles, and opportunities for volcano science

The science of volcanology advances disproportionately during exceptionally large or well-observed eruptions. The 2018 eruption of Kīlauea Volcano (Hawai‘i) was its most impactful in centuries, involving an outpouring of more than one cubic kilometer of basalt, a magnitude 7 flank earthquake, and the volcano’s largest summit collapse since at least the nineteenth century. Eruptive activity was documented in detail, yielding new insights into large caldera-rift eruptions; the geometry of a shallow magma storage-transport system and its interaction with rift zone tectonics; mechanisms of basaltic tephra-producing explosions; caldera collapse mechanics; and the dynamics of fissure eruptions and high-volume lava flows. Insights are broadly applicable to a range of volcanic systems and should reduce risk from future eruptions. Multidisciplinary collaboration will be required to fully leverage the diversity of monitoring data to address many of the most important outstanding questions.

Hawai‘i↗
USGS2014

Antecedent flow conditions and nitrate concentrations in the Mississippi River basin

The relationship between antecedent flow conditions and nitrate concentrations was explored at eight sites in the 2.9 million square kilometers (km 2 ) Mississippi River basin, USA. Antecedent flow conditions were quantified as the ratio between the mean daily flow of the previous year and the mean daily flow from the period of record (Qratio), and the Qratio was statistically related to nitrate anomalies (the unexplained variability in nitrate concentration after filtering out season, long-term trend, and contemporaneous flow effects) at each site. Nitrate anomaly and Qratio were negatively related at three of the four major tributary sites and upstream in the Mississippi River, indicating that when mean daily streamflow during the previous year was lower than average, nitrate concentrations were higher than expected. The strength of these relationships increased when data were subdivided by contemporaneous flow conditions. Five of the eight sites had significant negative relationships ( p ≤ 0.05) at high or moderately high contemporaneous flows, suggesting nitrate that accumulates in these basins during a drought is flushed during subsequent high flows. At half of the sites, when mean daily flow during the previous year was 50 percent lower than average, nitrate concentration can be from 9 to 27 percent higher than nitrate concentrations that follow a year with average mean daily flow. Conversely, nitrate concentration can be from 8 to 21 percent lower than expected when flow during the previous year was 50 percent higher than average. Previously documented for small, relatively homogenous basins, our results suggest that relationships between antecedent flows and nitrate concentrations are also observable at a regional scale. Relationships were not observed (using all contemporaneous flow data together) for basins larger than 1 million km 2 , suggesting that above this limit the overall size and diversity within these basins may necessitate the use of more complicated statistical approaches or that there may be no discernible basin-wide relationship with antecedent flow. The relationships between nitrate concentration and Qratio identified in this study serve as the basis for future studies that can better define specific hydrologic processes occurring during and after a drought (or high flow period) which influence nitrate concentration, such as the duration or magnitude of low flows, and the timing of low and high flows.

Mississippi River Basin↗
USGS2011

Shifting species interactions in terrestrial dryland ecosystems under altered water availability and climate change

Species interactions play key roles in linking the responses of populations, communities, and ecosystems to environmental change. For instance, species interactions are an important determinant of the complexity of changes in trophic biomass with variation in resources. Water resources are a major driver of terrestrial ecology and climate change is expected to greatly alter the distribution of this critical resource. While previous studies have documented strong effects of global environmental change on species interactions in general, responses can vary from region to region. Dryland ecosystems occupy more than one-third of the Earth's land mass, are greatly affected by changes in water availability, and are predicted to be hotspots of climate change. Thus, it is imperative to understand the effects of environmental change on these globally significant ecosystems. Here, we review studies of the responses of population-level plant-plant, plant-herbivore, and predator-prey interactions to changes in water availability in dryland environments in order to develop new hypotheses and predictions to guide future research. To help explain patterns of interaction outcomes, we developed a conceptual model that views interaction outcomes as shifting between (1) competition and facilitation (plant-plant), (2) herbivory, neutralism, or mutualism (plant-herbivore), or (3) neutralism and predation (predator-prey), as water availability crosses physiological, behavioural, or population-density thresholds. We link our conceptual model to hypothetical scenarios of current and future water availability to make testable predictions about the influence of changes in water availability on species interactions. We also examine potential implications of our conceptual model for the relative importance of top-down effects and the linearity of patterns of change in trophic biomass with changes in water availability. Finally, we highlight key research needs and some possible broader impacts of our findings. Overall, we hope to stimulate and guide future research that links changes in water availability to patterns of species interactions and the dynamics of populations and communities in dryland ecosystems.

Biological Reviews↗
USGS2012

Future opportunities and challenges in remote sensing of drought

The value of satellite remote sensing for drought monitoring was first realized more than two decades ago with the application of Normalized Difference Index (NDVI) data from the Advanced Very High Resolution Radiometer (AVHRR) for assessing the effect of drought on vegetation. Other indices such as the Vegetation Health Index (VHI) were also developed during this time period, and applied to AVHRR NDVI and brightness temperature data for routine global monitoring of drought conditions. These early efforts demonstrated the unique perspective that global imagers such as AVHRR could provide for operational drought monitoring through their near-daily, global observations of Earth's land surface. However, the advancement of satellite remote sensing of drought was limited by the relatively few spectral bands of operational global sensors such as AVHRR, along with a relatively short period of observational record. Remote sensing advancements are of paramount importance given the increasing demand for tools that can provide accurate, timely, and integrated information on drought conditions to facilitate proactive decision making (NIDIS, 2007). Satellite-based approaches are key to addressing significant gaps in the spatial and temporal coverage of current surface station instrument networks providing key moisture observations (e.g., rainfall, snow, soil moisture, ground water, and ET) over the United States and globally (NIDIS, 2007). Improved monitoring capabilities will be particularly important given increases in spatial extent, intensity, and duration of drought events observed in some regions of the world, as reported in the International Panel on Climate Change (IPCC) report (IPCC, 2007). The risk of drought is anticipated to further increase in some regions in response to climatic changes in the hydrologic cycle related to evaporation, precipitation, air temperature, and snow cover (Burke et al., 2006; IPCC, 2007; USGCRP, 2009). Numerous national, regional, and global efforts such as the Famine and Early Warning System (FEWS), National Integrated Drought Information System (NIDIS), and Group on Earth Observations (GEO), as well as the establishment of regional drought centers (e.g., European Drought Observatory) and geospatial visualization and monitoring systems (e.g, NASA SERVIR) have been undertaken to improve drought monitoring and early warning systems throughout the world. The suite of innovative remote sensing tools that have recently emerged will be looked upon to fill important data and knowledge gaps (NIDIS, 2007; NRC, 2007) to address a wide range of drought-related issues including food security, water scarcity, and human health.

Book chapter↗
USGS1985

New horizons in remote sensing for forest and range resource management

Forest and range resource scientists were among the first to recognize the potential of aircraft and satellite remote sensing for management of timber, forage, water, and wildlife resource. Today, data from a variety of sensor systems are being put to practical use for inventorying, monitoring, and assessing forest and range resources. In the future, improved sensor systems providing new kinds of data will be available. Likewise, new types of data handling and processing systems can be anticipated. Among the new or anticipated aircraft and satellite systems and/or data are National High-Altitude Photograph II, U. S. Geological Survey-acquired Side-Looking Airborne Radar, the Landsat thematic mapper, the National Oceanic Resolution Radiometer, the French Systeme Probatoire d'Observation de la Terre (SPOT) satellite, the European Space Agency Earth Resources Satellite, the National Aeronautics and Space Administration Large Format Camera and Shuttle Imaging Radar (SIR-A, -B, and -C), and a variety of other systems in existence or planned by the Soviets, Japanese, Canadians, Chinese, Brazilians, Indonesians, and other. Application examples are presented that illustrate uses of 1-kilometer-resolution AVHRR data, 80-meter Landsat multispectral scanner data, 30-meter Landsat thematic mapper data, and 10-meter SPOT-simulator data. These examples address fire fuel monitoring, land cover mapping, rangeland assessment, and soils landscape mapping.

Conference Paper↗
USGS2006

The future of imaging spectroscopy - Prospective technologies and applications

Spectroscopy has existed for more than three centuries now. Nonetheless, significant scientific advances have been achieved. We discuss the history of spectroscopy in relation to emerging technologies and applications. Advanced focal plane arrays, optical design, and intelligent on-board logic are prime prospective technologies. Scalable approaches in pre-processing of imaging spectrometer data will receive additional focus. Finally, we focus on new applications monitoring transitional ecological zones, where human impact and disturbance have highest impact as well as in monitoring changes in our natural resources and environment We conclude that imaging spectroscopy enables mapping of biophysical and biochemical variables of the Earth's surface and atmospheric composition with unprecedented accuracy.

Conference Paper↗
USGS2007

Analysis of continuous GPS measurements from southern Victoria Land, Antarctica

Several years of continuous data have been collected at remote bedrock Global Positioning System (GPS) sites in southern Victoria Land, Antarctica. Annual to sub-annual variations are observed in the position time-series. An atmospheric pressure loading (APL) effect is calculated from pressure field anomalies supplied by the European Centre for Medium-Range Weather Forecasts (ECMWF) model loading an elastic Earth model. The predicted APL signal has a moderate correlation with the vertical position time-series at McMurdo, Ross Island (International Global Navigation Satellite System Service (IGS) station MCM4), produced using a global solution. In contrast, a local solution in which MCM4 is the fiducial site generates a vertical time series for a remote site in Victoria Land (Cape Roberts, ROB4) which exhibits a low, inverse correlation with the predicted atmospheric pressure loading signal. If, in the future, known and well modeled geophysical loads can be separated from the time-series, then local hydrological loading, of interest for glaciological and climate applications, can potentially be extracted from the GPS time-series.

Open-File Report↗
USGS2013

A conceptual prototype for the next-generation national elevation dataset

In 2012 the U.S. Geological Survey's (USGS) National Geospatial Program (NGP) funded a study to develop a conceptual prototype for a new National Elevation Dataset (NED) design with expanded capabilities to generate and deliver a suite of bare earth and above ground feature information over the United States. This report details the research on identifying operational requirements based on prior research, evaluation of what is needed for the USGS to meet these requirements, and development of a possible conceptual framework that could potentially deliver the kinds of information that are needed to support NGP's partners and constituents. This report provides an initial proof-of-concept demonstration using an existing dataset, and recommendations for the future, to inform NGP's ongoing and future elevation program planning and management decisions. The demonstration shows that this type of functional process can robustly create derivatives from lidar point cloud data; however, more research needs to be done to see how well it extends to multiple datasets.

Open-File Report↗
USGS2022

Forecasting and communicating the dispersion and fallout of ash during volcanic eruptions: lessons from the September 20, 2020 eruptive pulse at Sangay volcano, Ecuador

Volcanic ash is a hazard to human health and activities. Accurate and timely forecasts coupled with effective communication about the dispersion and fallout of volcanic ash during explosive events are essential to reduce impacts on local communities and limit economic losses. In this study, we present the first detailed description of an eruptive pulse at Sangay volcano and its eruption source parameters. The eruptive pulse on September 20, 2020, started at about 9:20 UTC and lasted between 90 and 100 min, producing an eruptive column that rapidly separated into (1) a higher (15.2 km above sea level, asl), gas-rich cloud moving east-southeast and (2) a lower (12.2 km asl), ash-rich cloud moving west and causing ash fallout up to 280 km from the volcano. Field data collected immediately after the event allow estimating the volume of bulk tephra to be between 1.5 and 5.0 × 10 6 m 3 , corresponding to a volcanic explosivity index of 2. The eruptive pulse, identified as violent Strombolian, emitted andesitic ash that was more mafic than products ejected by Sangay volcano in recent decades. Component analysis and glass chemistry of juvenile particles support the hypothesis that this event excavated deeper into the upper conduit compared to typical Strombolian activity at Sangay volcano, while grain-size analysis allows reconstruction of the total grain-size distribution of the fallout deposit. The discrepancies between the ash fallout simulations performed with the Ash3D online tool and the actual deposit are mainly the result of inaccurate pre- and syn-eruptive configurations and highlight the importance of additional processes such as aggregation. Communication products issued during the event included (1) several standard short reports, (2) volcano observatory notices for aviation, (3) social media posts, and (4) a special report providing the results of the ash fallout simulation. Although communication was effective with the authorities and the connected population, an effort must be made to reach the most vulnerable isolated communities for future events. This study shows that forecasting ash dispersion and fallout during volcanic eruptions can guide early warnings and trigger humanitarian actions, and should become a standard in volcano observatories worldwide.

Sangay volcano↗
USGS1969

Satellite imagery of the earth

Photography of the Earth from spacecraft has application to both atmospheric and Earth sciences. Gemini and Apollo photographs have furnished information on sea surface roughness, areas of potential upwelling and oceanic current systems. Regional geologic structures and geomorphologic features are also recorded in orbital photographs. Infrared satellite imagery provides meteorological and hydrological data and is potentially useful for locating fresh water springs along coastal areas, sources of geothermal power and volcanic activity. Ground and airborne surveys are being undertaken to create a basis for the interpretation of data obtained from future satellite systems.

Photogrammetric Engineering↗
USGS2014

Pulverization provides a mechanism for the nucleation of earthquakes at low stress on strong faults

An earthquake occurs when rock that has been deformed under stress rebounds elastically along a fault plane ( Gilbert, 1884 ; Reid, 1911 ), radiating seismic waves through the surrounding earth. Rupture along the entire fault surface does not spontaneously occur at the same time, however. Rather the rupture starts in one tiny area, the rupture nucleation zone, and spreads sequentially along the fault. Like a row of dominoes, one bit of rebounding fault triggers the next. This triggering is understood to occur because of the large dynamic stresses at the tip of an active seismic rupture. The importance of these crack tip stresses is a central question in earthquake physics. The crack tip stresses are minimally important, for example, in the time predictable earthquake model ( Shimazaki and Nakata, 1980 ), which holds that prior to rupture stresses are comparable to fault strength in many locations on the future rupture plane, with bits of variation. The stress/strength ratio is highest at some point, which is where the earthquake nucleates. This model does not require any special conditions or processes at the nucleation site; the whole fault is essentially ready for rupture at the same time. The fault tip stresses ensure that the rupture occurs as a single rapid earthquake, but the fact that fault tip stresses are high is not particularly relevant since the stress at most points does not need to be raised by much. Under this model it should technically be possible to forecast earthquakes based on the stress-renewaql concept, or estimates of when the fault as a whole will reach the critical stress level, a practice used in official hazard mapping ( Field, 2008 ). This model also indicates that physical precursors may be present and detectable, since stresses are unusually high over a significant area before a large earthquake.

Frontiers in Earth Science↗
USGS2014

Agricultural conversion without external water and nutrient inputs reduces terrestrial vegetation productivity

Driven by global population and standard of living increases, humanity co-opts a growing share of the planet's natural resources resulting in many well-known environmental trade-offs. In this study, we explored the impact of agriculture on a resource fundamental to life on Earth: terrestrial vegetation growth (net primary production; NPP). We demonstrate that agricultural conversion has reduced terrestrial NPP by ~7.0%. Increases in NPP due to agricultural conversion were observed only in areas receiving external inputs (i.e., irrigation and/or fertilization). NPP reductions were found for ~88% of agricultural lands, with the largest reductions observed in areas formerly occupied by tropical forests and savannas (~71% and ~66% reductions, respectively). Without policies that explicitly consider the impact of agricultural conversion on primary production, future demand-driven increases in agricultural output will likely continue to drive net declines in global terrestrial productivity, with potential detrimental consequences for net ecosystem carbon storage and subsequent climate warming.

Geophysical Research Letters↗
USGS2014

Strong influence of El Niño Southern Oscillation on flood risk around the world

El Niño Southern Oscillation (ENSO) is the most dominant interannual signal of climate variability and has a strong influence on climate over large parts of the world. In turn, it strongly influences many natural hazards (such as hurricanes and droughts) and their resulting socioeconomic impacts, including economic damage and loss of life. However, although ENSO is known to influence hydrology in many regions of the world, little is known about its influence on the socioeconomic impacts of floods (i.e., flood risk). To address this, we developed a modeling framework to assess ENSO’s influence on flood risk at the global scale, expressed in terms of affected population and gross domestic product and economic damages. We show that ENSO exerts strong and widespread influences on both flood hazard and risk. Reliable anomalies of flood risk exist during El Niño or La Niña years, or both, in basins spanning almost half (44%) of Earth’s land surface. Our results show that climate variability, especially from ENSO, should be incorporated into disaster-risk analyses and policies. Because ENSO has some predictive skill with lead times of several seasons, the findings suggest the possibility to develop probabilistic flood-risk projections, which could be used for improved disaster planning. The findings are also relevant in the context of climate change. If the frequency and/or magnitude of ENSO events were to change in the future, this finding could imply changes in flood-risk variations across almost half of the world’s terrestrial regions.

Proceedings of the National Academy of Sciences↗
USGS2014

A new analysis of Mars "Special Regions": findings of the Second MEPAG Special Regions Science Analysis Group (SR-SAG2)

A committee of the Mars Exploration Program Analysis Group (MEPAG) has reviewed and updated the description of Special Regions on Mars as places where terrestrial organisms might replicate (per the COSPAR Planetary Protection Policy). This review and update was conducted by an international team (SR-SAG2) drawn from both the biological science and Mars exploration communities, focused on understanding when and where Special Regions could occur. The study applied recently available data about martian environments and about terrestrial organisms, building on a previous analysis of Mars Special Regions (2006) undertaken by a similar team. Since then, a new body of highly relevant information has been generated from the Mars Reconnaissance Orbiter (launched in 2005) and Phoenix (2007) and data from Mars Express and the twin Mars Exploration Rovers (all 2003). Results have also been gleaned from the Mars Science Laboratory (launched in 2011). In addition to Mars data, there is a considerable body of new data regarding the known environmental limits to life on Earth—including the potential for terrestrial microbial life to survive and replicate under martian environmental conditions. The SR-SAG2 analysis has included an examination of new Mars models relevant to natural environmental variation in water activity and temperature; a review and reconsideration of the current parameters used to define Special Regions; and updated maps and descriptions of the martian environments recommended for treatment as "Uncertain" or "Special" as natural features or those potentially formed by the influence of future landed spacecraft. Significant changes in our knowledge of the capabilities of terrestrial organisms and the existence of possibly habitable martian environments have led to a new appreciation of where Mars Special Regions may be identified and protected. The SR-SAG also considered the impact of Special Regions on potential future human missions to Mars, both as locations of potential resources and as places that should not be inadvertently contaminated by human activity.

Astrobiology↗
USGS2011

Process-based, morphodynamic hindcast of decadal deposition patterns in San Pablo Bay, California, 1856-1887

This study investigates the possibility of hindcasting-observed decadal-scale morphologic change in San Pablo Bay, a subembayment of the San Francisco Estuary, California, USA, by means of a 3-D numerical model (Delft3D). The hindcast period, 1856-1887, is characterized by upstream hydraulic mining that resulted in a high sediment input to the estuary. The model includes wind waves, salt water and fresh water interactions, and graded sediment transport, among others. Simplified initial conditions and hydrodynamic forcing were necessary because detailed historic descriptions were lacking. Model results show significant skill. The river discharge and sediment concentration have a strong positive influence on deposition volumes. Waves decrease deposition rates and have, together with tidal movement, the greatest effect on sediment distribution within San Pablo Bay. The applied process-based (or reductionist) modeling approach is valuable once reasonable values for model parameters and hydrodynamic forcing are obtained. Sensitivity analysis reveals the dominant forcing of the system and suggests that the model planform plays a dominant role in the morphodynamic development. A detailed physical explanation of the model outcomes is difficult because of the high nonlinearity of the processes. Process formulation refinement, a more detailed description of the forcing, or further model parameter variations may lead to an enhanced model performance, albeit to a limited extent. The approach potentially provides a sound basis for prediction of future developments. Parallel use of highly schematized box models and a process-based approach as described in the present work is probably the most valuable method to assess decadal morphodynamic development. Copyright ?? 2011 by the American Geophysical Union.

California↗
USGS2015

Urgent need for warming experiments in tropical forests

Although tropical forests account for only a fraction of the planet's terrestrial surface, they exchange more carbon dioxide with the atmosphere than any other biome on Earth, and thus play a disproportionate role in the global climate. In the next 20 years, the tropics will experience unprecedented warming, yet there is exceedingly high uncertainty about their potential responses to this imminent climatic change. Here, we prioritize research approaches given both funding and logistical constraints in order to resolve major uncertainties about how tropical forests function and also to improve predictive capacity of earth system models. We investigate overall model uncertainty of tropical latitudes and explore the scientific benefits and inevitable trade-offs inherent in large-scale manipulative field experiments. With a Coupled Model Intercomparison Project Phase 5 analysis, we found that model variability in projected net ecosystem production was nearly 3 times greater in the tropics than for any other latitude. Through a review of the most current literature, we concluded that manipulative warming experiments are vital to accurately predict future tropical forest carbon balance, and we further recommend the establishment of a network of comparable studies spanning gradients of precipitation, edaphic qualities, plant types, and/or land use change. We provide arguments for long-term, single-factor warming experiments that incorporate warming of the most biogeochemically active ecosystem components (i.e. leaves, roots, soil microbes). Hypothesis testing of underlying mechanisms should be a priority, along with improving model parameterization and constraints. No single tropical forest is representative of all tropical forests; therefore logistical feasibility should be the most important consideration for locating large-scale manipulative experiments. Above all, we advocate for multi-faceted research programs, and we offer arguments for what we consider the most powerful and urgent way forward in order to improve our understanding of tropical forest responses to climate change.

Global Change Biology↗
USGS2022

Comparisons of Coupled Model Intercomparison Project Phase 5 (CMIP5) and Coupled Model Intercomparison Project Phase 6 (CMIP6) sea-ice projections in polar bear (Ursus maritimus) ecoregions during the 21st century

Climate model projections are commonly used to assess potential impacts of global warming on a breadth of social, economic, and environmental topics. Modeling centers throughout the world coordinate to apply a consistent suite of radiative forcing experiments so that all model outputs can be collectively analyzed and compared. Three generations of model outputs have been produced and made available to the scientific community through the Coupled Model Intercomparison Project (CMIP): CMIP3 disseminated during the mid-2000s, CMIP5 during the early-2010s, and CMIP6 during the late-2010s. Twenty-first century sea-ice projections from CMIP3 and CMIP5 models have been used in Bayesian network assessments of how climate change could impact the future persistence of polar bears ( Ursus maritimus ) throughout their range. In this report, we compare sea-ice projections by CMIP6 models to those of CMIP5 models in each of four polar bear ecoregions over the 21st century. We evaluate differences between the two CMIP generations with respect to other sources of variability that affect uncertainties of the model projections: (1) variability from different models; (2) variability from different greenhouse gas emissions scenarios; and (3) natural (internal) variability in the earth’s climate system. We found that natural variability as well as that attributable to models dominated uncertainties in sea-ice projections in all months and ecoregions during the first half of the 21st century, while emissions scenarios dominated uncertainties during the late 21st century. By comparison, we found only slight differences between the CMIP6 and CMIP5 model projections of sea ice. Applying CMIP6 instead of CMIP5 sea-ice projections to the polar bear Bayesian network model developed in 2016, therefore, would not qualitatively change the population status outcomes published therein.

Open-File Report↗
USGS2017

Glaciological measurements and mass balances from Sperry Glacier, Montana, USA, years 2005–2015

Glacier mass balance measurements help to provide an understanding of the behavior of glaciers and their response to local and regional climate. In 2005 the United States Geological Survey established a surface mass balance monitoring program on Sperry Glacier, Montana, USA. This project is the first quantitative study of mass changes of a glacier in the US northern Rocky Mountains and continues to the present. The following paper describes the methods used during the first 11 years of measurements and reports the associated results. From 2005 to 2015, Sperry Glacier had a cumulative mean mass balance loss of 4.37 m w.e. (water equivalent). The mean winter, summer, and annual glacier-wide mass balances were 2.92, −3.41, and −0.40 m w.e. yr −1 respectively. We derive these cumulative and mean results from an expansive data set of snow depth, snow density, and ablation measurements taken at selected points on the glacier. These data allow for the determination of mass balance point values and a time series of seasonal and annual glacier-wide mass balances for all 11 measurement years. We also provide measurements of glacier extent and accumulation areas for select years. All data have been submitted to the World Glacier Monitoring Service and are available at doi:10.5904/wgms-fog-2016-08 . This foundational work provides valuable insight about Sperry Glacier and supplies additional data to the worldwide record of glaciers measured using the glaciological method. Future research will focus on the processes that control accumulation and ablation patterns across the glacier. Also we plan to examine the uncertainties related to our methods and eventually quantify a more robust estimate of error associated with our results.

Montana↗