Geology topics

William H. Farmer

Publications and source records attributed to William H. Farmer.

31 records · Page 2Linked to original sources

USGS2018

Quantifying uncertainty in simulated streamflow and runoff from a continental-scale monthly water balance model

One important component of continental-scale hydrologic modeling is quantifying the level of uncertainty in long-term hydrologic simulations and providing a range of possible simulated streamflow and/or runoff values for gaged and ungaged locations. In this paper, uncertainty was quantified for simulated streamflow and runoff generated from a monthly water balance model (MWBM) at 1575 streamgages and 109,951 hydrologic response units (HRUs), which span the conterminous United States (CONUS). A stochastic-approach, which incorporated the properties of modeled streamflow residuals back into the simulated model output, was used to create time series of upper and lower uncertainty intervals (UIs) around the simulated monthly time series. This approach was applied to an existing hydrologic regionalization implementation. Metrics used to evaluate the UIs across the CONUS (the coverage ratio, average width index, and interval skill score) indicated that on average the UIs were reliable, skillful, and sharp in being able to both contain measured streamflow observations and reduce estimates of uncertainty based on expected model predictions. These uncertainty evaluation metrics can complement each other in characterizing model skill and uncertainty over large-scale domains.

Advances in Water Resources↗

USGS2018

Improving predictions of hydrological low-flow indices in ungaged basins using machine learning

We compare the ability of eight machine-learning models (elastic net, gradient boosting, kernel-k-nearest neighbors, two variants of support vector machines , M5-cubist, random forest, and a meta-learning ensemble M5-cubist model) and four baseline models (ordinary kriging , a unit area discharge model, and two variants of censored regression) to generate estimates of the annual minimum 7-day mean streamflow with an annual exceedance probability of 90% (7Q10) at 224 unregulated sites in South Carolina, Georgia, and Alabama, USA. The machine-learning models produced substantially lower cross validation errors compared to the baseline models. The meta-learning M5-cubist model had the lowest root-mean-squared-error of 26.72 cubic feet per second. Partial dependence plots show that 7Q10s are likely moderated by late summer and early fall precipitation and the infiltration capacity of basin soils.

Alabama, Georgia, South Carolina↗

USGS2018

Computing under-ice discharge: A proof-of-concept using hydroacoustics and the Probability Concept

Under-ice discharge is estimated using open-water reference hydrographs; however, the ratings for ice-affected sites are generally qualified as poor. The U.S. Geological Survey (USGS), in collaboration with the Colorado Water Conservation Board, conducted a proof-of-concept to develop an alternative method for computing under-ice discharge using hydroacoustics and the Probability Concept. The study site was located south of Minturn, Colorado (CO), USA, and was selected because of (1) its proximity to the existing USGS streamgage 09064600 Eagle River near Minturn, CO, and (2) its ease-of-access to verify discharge using a variety of conventional methods. From late September 2014 to early March 2015, hydraulic conditions varied from open water to under ice. These temporal changes led to variations in water depth and velocity. Hydroacoustics (tethered and uplooking acoustic Doppler current profilers and acoustic Doppler velocimeters) were deployed to measure the vertical-velocity profile at a singularly important vertical of the channel-cross section. Because the velocity profile was non-standard and cannot be characterized using a Power Law or Log Law, velocity data were analyzed using the Probability Concept, which is a probabilistic formulation of the velocity distribution. The Probability Concept-derived discharge was compared to conventional methods including stage-discharge and index-velocity ratings and concurrent field measurements; each is complicated by the dynamics of ice formation, pressure influences on stage measurements, and variations in cross-sectional area due to ice formation. No particular discharge method was assigned as truth. Rather one statistical metric (Kolmogorov-Smirnov; KS), agreement plots, and concurrent measurements provided a measure of comparability between various methods. Regardless of the method employed, comparisons between each method revealed encouraging results depending on the flow conditions and the absence or presence of ice cover. For example, during lower discharges dominated by under-ice and transition (intermittent open-water and under-ice) conditions, the KS metric suggests there is not sufficient information to reject the null hypothesis and implies that the Probability Concept and index-velocity rating represent similar distributions. During high-flow, open-water conditions, the comparisons are less definitive; therefore, it is important that the appropriate analytical method and instrumentation be selected. Six conventional discharge measurements were collected concurrently with Probability Concept-derived discharges with percent differences (%) of −9.0%, −21%, −8.6%, 17.8%, 3.6%, and −2.3%. This proof-of-concept demonstrates that riverine discharges can be computed using the Probability Concept for a range of hydraulic extremes (variations in discharge, open-water and under-ice conditions) immediately after the siting phase is complete, which typically requires one day. Computing real-time discharges is particularly important at sites, where (1) new streamgages are planned, (2) river hydraulics are complex, and (3) shifts in the stage-discharge rating are needed to correct the streamflow record. Use of the Probability Concept does not preclude the need to maintain a stage-area relation. Both the Probability Concept and index-velocity rating offer water-resource managers and decision makers alternatives for computing real-time discharge for open-water and under-ice conditions.

Colorado↗

USGS2017

Characterizing uncertainty in daily streamflow estimates at ungauged locations for the Massachusetts sustainable yield estimator

Hydrologic characterization at ungauged locations is one of the quintessential challenges of hydrology. Beyond simulation of historical streamflows, it is similarly important to characterize the level of uncertainty in hydrologic estimates. In tandem with updates to Massachusetts Sustainable Yield Estimator, this work explores the application of global uncertainty estimates to daily streamflow simulations. Expanding on a method developed for deterministic modeling, this approach produces confidence intervals on daily streamflow developed through nonlinear spatial interpolation of daily streamflow using flow duration curves; the 95% confidence is examined. Archived cross‐validations of daily streamflows from 66 watersheds in and around Massachusetts are used to evaluate an approach to uncertainty characterization. Neighboring sites are treated as ungauged, producing relative errors that can be resampled and applied to target sites. The method, with some modification, is found to provide appropriately narrow confidence intervals that contain 95% of the observed streamflows in cross‐validation. Further characterizing uncertainty, multiday means of daily streamflow are evaluated. Working through cross‐validation in Massachusetts, two‐ to three‐month averages of daily streamflow show the best performance. These two approaches to uncertainty characterization inform how streamflow simulation produced for prediction in ungauged basins can be used for water resources management.

Massachusetts↗

USGS2017

Water-quality trends in the nation’s rivers and streams, 1972–2012—Data preparation, statistical methods, and trend results

Since passage of the Clean Water Act in 1972, Federal, State, and local governments have invested billions of dollars to reduce pollution entering rivers and streams. To understand the return on these investments and to effectively manage and protect the Nation’s water resources in the future, we need to know how and why water quality has been changing over time. As part of the National Water-Quality Assessment Project, of the U.S. Geological Survey’s National Water-Quality Program, data from the U.S. Geological Survey, along with multiple other Federal, State, Tribal, regional, and local agencies, have been used to support the most comprehensive assessment conducted to date of surface-water-quality trends in the United States. This report documents the methods used to determine trends in water quality and ecology because these methods are vital to ensuring the quality of the results. Specific objectives are to document (1) the data compilation and processing steps used to identify river and stream sites throughout the Nation suitable for water-quality, pesticide, and ecology trend analysis, (2) the statistical methods used to determine trends in target parameters, (3) considerations for water-quality, pesticide, and ecology data and streamflow data when modeling trends, (4) sensitivity analyses for selecting data and interpreting trend results with the Weighted Regressions on Time, Discharge, and Season method, and (5) the final trend results at each site. The scope of this study includes trends in water-quality concentrations and loads (nutrient, sediment, major ion, salinity, and carbon), pesticide concentrations and loads, and metrics for aquatic ecology (fish, invertebrates, and algae) for four time periods: (1) 1972–2012, (2) 1982–2012, (3) 1992–2012, and (4) 2002–12. In total, nearly 12,000 trends in concentration, load, and ecology metrics were evaluated in this study; there were 11,893 combinations of sites, parameters, and trend periods. The final trend results are presented with examples of how to interpret the results from each trend model. Interpretation of the trend results, such as causal analysis, is not included.

Scientific Investigations Report↗

USGS2017

Geospatial tools effectively estimate nonexceedance probabilities of daily streamflow at ungauged and intermittently gauged locations in Ohio

Study region The state of Ohio in the United States, a humid, continental climate. Study focus The estimation of nonexceedance probabilities of daily streamflows as an alternative means of establishing the relative magnitudes of streamflows associated with hydrologic and water-quality observations. New hydrological insights for the region Several methods for estimating nonexceedance probabilities of daily mean streamflows are explored, including single-index methodologies (nearest-neighboring index) and geospatial tools (kriging and topological kriging). These methods were evaluated by conducting leave-one-out cross-validations based on analyses of nearly 7 years of daily streamflow data from 79 unregulated streamgages in Ohio and neighboring states. The pooled, ordinary kriging model, with a median Nash–Sutcliffe performance of 0.87, was superior to the single-site index methods, though there was some bias in the tails of the probability distribution. Incorporating network structure through topological kriging did not improve performance. The pooled, ordinary kriging model was applied to 118 locations without systematic streamgaging across Ohio where instantaneous streamflow measurements had been made concurrent with water-quality sampling on at least 3 separate days. Spearman rank correlations between estimated nonexceedance probabilities and measured streamflows were high, with a median value of 0.76. In consideration of application, the degree of regulation in a set of sample sites helped to specify the streamgages required to implement kriging approaches successfully.

Ohio↗

USGS2016

On the deterministic and stochastic use of hydrologic models

Environmental simulation models, such as precipitation-runoff watershed models, are increasingly used in a deterministic manner for environmental and water resources design, planning, and management. In operational hydrology, simulated responses are now routinely used to plan, design, and manage a very wide class of water resource systems. However, all such models are calibrated to existing data sets and retain some residual error. This residual, typically unknown in practice, is often ignored, implicitly trusting simulated responses as if they are deterministic quantities. In general, ignoring the residuals will result in simulated responses with distributional properties that do not mimic those of the observed responses. This discrepancy has major implications for the operational use of environmental simulation models as is shown here. Both a simple linear model and a distributed-parameter precipitation-runoff model are used to document the expected bias in the distributional properties of simulated responses when the residuals are ignored. The systematic reintroduction of residuals into simulated responses in a manner that produces stochastic output is shown to improve the distributional properties of the simulated responses. Every effort should be made to understand the distributional behavior of simulation residuals and to use environmental simulation models in a stochastic manner.

Water Resources Research↗

USGS2016

Ordinary kriging as a tool to estimate historical daily streamflow records

Efficient and responsible management of water resources relies on accurate streamflow records. However, many watersheds are ungaged, limiting the ability to assess and understand local hydrology. Several tools have been developed to alleviate this data scarcity, but few provide continuous daily streamflow records at individual streamgages within an entire region. Building on the history of hydrologic mapping, ordinary kriging was extended to predict daily streamflow time series on a regional basis. Pooling parameters to estimate a single, time-invariant characterization of spatial semivariance structure is shown to produce accurate reproduction of streamflow. This approach is contrasted with a time-varying series of variograms, representing the temporal evolution and behavior of the spatial semivariance structure. Furthermore, the ordinary kriging approach is shown to produce more accurate time series than more common, single-index hydrologic transfers. A comparison between topological kriging and ordinary kriging is less definitive, showing the ordinary kriging approach to be significantly inferior in terms of Nash–Sutcliffe model efficiencies while maintaining significantly superior performance measured by root mean squared errors. Given the similarity of performance and the computational efficiency of ordinary kriging, it is concluded that ordinary kriging is useful for first-order approximation of daily streamflow time series in ungaged watersheds.

Hydrology and Earth System Sciences↗

USGS2016

Regional flow duration curves: Geostatistical techniques versus multivariate regression

A period-of-record flow duration curve (FDC) represents the relationship between the magnitude and frequency of daily streamflows. Prediction of FDCs is of great importance for locations characterized by sparse or missing streamflow observations. We present a detailed comparison of two methods which are capable of predicting an FDC at ungauged basins: (1) an adaptation of the geostatistical method, Top-kriging, employing a linear weighted average of dimensionless empirical FDCs, standardised with a reference streamflow value; and (2) regional multiple linear regression of streamflow quantiles, perhaps the most common method for the prediction of FDCs at ungauged sites. In particular, Top-kriging relies on a metric for expressing the similarity between catchments computed as the negative deviation of the FDC from a reference streamflow value, which we termed total negative deviation (TND). Comparisons of these two methods are made in 182 largely unregulated river catchments in the southeastern U.S. using a three-fold cross-validation algorithm. Our results reveal that the two methods perform similarly throughout flow-regimes, with average Nash-Sutcliffe Efficiencies 0.566 and 0.662, (0.883 and 0.829 on log-transformed quantiles) for the geostatistical and the linear regression models, respectively. The differences between the reproduction of FDC's occurred mostly for low flows with exceedance probability (i.e. duration) above 0.98.

Advances in Water Resources↗

USGS2015

Accelerating advances in continental domain hydrologic modeling

In the past, hydrologic modeling of surface water resources has mainly focused on simulating the hydrologic cycle at local to regional catchment modeling domains. There now exists a level of maturity among the catchment, global water security, and land surface modeling communities such that these communities are converging toward continental domain hydrologic models. This commentary, written from a catchment hydrology community perspective, provides a review of progress in each community toward this achievement, identifies common challenges the communities face, and details immediate and specific areas in which these communities can mutually benefit one another from the convergence of their research perspectives. Those include: (1) creating new incentives and infrastructure to report and share model inputs, outputs, and parameters in data services and open access, machine-independent formats for model replication or reanalysis; (2) ensuring that hydrologic models have: sufficient complexity to represent the dominant physical processes and adequate representation of anthropogenic impacts on the terrestrial water cycle, a process-based approach to model parameter estimation, and appropriate parameterizations to represent large-scale fluxes and scaling behavior; (3) maintaining a balance between model complexity and data availability as well as uncertainties; and (4) quantifying and communicating significant advancements toward these modeling goals.

Water Resources Research↗

USGS2015

Evaluation of statistical and rainfall-runoff models for predicting historical daily streamflow time series in the Des Moines and Iowa River watersheds

Daily records of streamflow are essential to understanding hydrologic systems and managing the interactions between human and natural systems. Many watersheds and locations lack streamgages to provide accurate and reliable records of daily streamflow. In such ungaged watersheds, statistical tools and rainfall-runoff models are used to estimate daily streamflow. Previous work compared 19 different techniques for predicting daily streamflow records in the southeastern United States. Here, five of the better-performing methods are compared in a different hydroclimatic region of the United States, in Iowa. The methods fall into three classes: (1) drainage-area ratio methods, (2) nonlinear spatial interpolations using flow duration curves, and (3) mechanistic rainfall-runoff models. The first two classes are each applied with nearest-neighbor and map-correlated index streamgages. Using a threefold validation and robust rank-based evaluation, the methods are assessed for overall goodness of fit of the hydrograph of daily streamflow, the ability to reproduce a daily, no-fail storage-yield curve, and the ability to reproduce key streamflow statistics. As in the Southeast study, a nonlinear spatial interpolation of daily streamflow using flow duration curves is found to be a method with the best predictive accuracy. Comparisons with previous work in Iowa show that the accuracy of mechanistic models with at-site calibration is substantially degraded in the ungaged framework.

Iowa, Minnesota↗

USGS2015

Multiple regression and inverse moments improve the characterization of the spatial scaling behavior of daily streamflows in the Southeast United States

Understanding the spatial structure of daily streamflow is essential for managing freshwater resources, especially in poorly-gaged regions. Spatial scaling assumptions are common in flood frequency prediction (e.g., index-flood method) and the prediction of continuous streamflow at ungaged sites (e.g. drainage-area ratio), with simple scaling by drainage area being the most common assumption. In this study, scaling analyses of daily streamflow from 173 streamgages in the southeastern US resulted in three important findings. First, the use of only positive integer moment orders, as has been done in most previous studies, captures only the probabilistic and spatial scaling behavior of flows above an exceedance probability near the median; negative moment orders (inverse moments) are needed for lower streamflows. Second, assessing scaling by using drainage area alone is shown to result in a high degree of omitted-variable bias, masking the true spatial scaling behavior. Multiple regression is shown to mitigate this bias, controlling for regional heterogeneity of basin attributes, especially those correlated with drainage area. Previous univariate scaling analyses have neglected the scaling of low-flow events and may have produced biased estimates of the spatial scaling exponent. Third, the multiple regression results show that mean flows scale with an exponent of one, low flows scale with spatial scaling exponents greater than one, and high flows scale with exponents less than one. The relationship between scaling exponents and exceedance probabilities may be a fundamental signature of regional streamflow. This signature may improve our understanding of the physical processes generating streamflow at different exceedance probabilities.

Water Resources Research↗

USGS2015

A comparison of methods to predict historical daily streamflow time series in the southeastern United States

Effective and responsible management of water resources relies on a thorough understanding of the quantity and quality of available water. Streamgages cannot be installed at every location where streamflow information is needed. As part of its National Water Census, the U.S. Geological Survey is planning to provide streamflow predictions for ungaged locations. In order to predict streamflow at a useful spatial and temporal resolution throughout the Nation, efficient methods need to be selected. This report examines several methods used for streamflow prediction in ungaged basins to determine the best methods for regional and national implementation. A pilot area in the southeastern United States was selected to apply 19 different streamflow prediction methods and evaluate each method by a wide set of performance metrics. Through these comparisons, two methods emerged as the most generally accurate streamflow prediction methods: the nearest-neighbor implementations of nonlinear spatial interpolation using flow duration curves (NN-QPPQ) and standardizing logarithms of streamflow by monthly means and standard deviations (NN-SMS12L). It was nearly impossible to distinguish between these two methods in terms of performance. Furthermore, neither of these methods requires significantly more parameterization in order to be applied: NN-SMS12L requires 24 regional regressions—12 for monthly means and 12 for monthly standard deviations. NN-QPPQ, in the application described in this study, required 27 regressions of particular quantiles along the flow duration curve. Despite this finding, the results suggest that an optimal streamflow prediction method depends on the intended application. Some methods are stronger overall, while some methods may be better at predicting particular statistics. The methods of analysis presented here reflect a possible framework for continued analysis and comprehensive multiple comparisons of methods of prediction in ungaged basins (PUB). Additional metrics of comparison can easily be incorporated into this type of analysis. By considering such a multifaceted approach, the top-performing models can easily be identified and considered for further research. The top-performing models can then provide a basis for future applications and explorations by scientists, engineers, managers, and practitioners to suit their own needs.

Scientific Investigations Report↗