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At least 127 records · Page 7Linked to original sources

USGS2020

Partly cloudy with a chance of lava flows: Forecasting volcanic eruptions in the 21st century

A primary goal of volcanology is forecasting hazardous eruptive activity. Despite much progress over the last century, however, volcanoes still erupt with no detected precursors, lives and livelihoods are lost to eruptive activity, and forecasting the onsets of eruptions remains fraught with uncertainty. Long‐term forecasts are generally derived from the geological and historical records, from which recurrence intervals and styles of activity can be inferred, while shorter‐term forecasts are derived from patterns in monitoring data. Information from geology and monitoring data can be evaluated and combined using statistical analysis, expert elicitation, and conceptual and or mathematical models. Integrative frameworks, such as event trees, combine this diversity of information to produce probabilistic forecasts that can inform the style and scale of the societal response to a potential future eruption. Several developments show promise to revolutionize the utility and accuracy of these forecasts. These include growth in the quantity and quality of multidisciplinary monitoring data, coupled with increases in computing power; machine learning algorithms, which will allow far better utilization of this growing volume of data; and new physiochemical volcano models and data assimilation algorithms, which take advantage of a wide range of monitoring data and realistic physics to better predict the evolution of a given physical state. Although eruption forecasts may never be as generally reliable as weather forecasts, and great caution must be exercised when attempting to predict highly complex volcanic behavior, these and other innovations—particularly when combined in integrative, fully probabilistic forecasting frameworks—should help volcanologists to better issue warnings of volcanic activity on societally relevant time frames.

Hawaii↗

USGS2020

Dimensional effects of inter-phase mass transfer on attenuation of structurally trapped gaseous carbon dioxide in shallow aquifers

Based on experimental evidence and using mathematical modeling, inter-phase mass transfer processes of CO 2 exsolving from and dissolving into water in heterogeneous porous media are investigated under two fundamentally different flow conditions: in a quasi one dimensional vertical column and in a two-dimensional tank with a lateral background water flow, both at laboratory scale. In both cases, the CO 2 dissolved in water under a given overpressure is injected for a certain period at the bottom of the tank, exsolves, and migrates upwards. A layer of fine sand is present in the tanks designed to mimic geological scenarios of accumulation and trapping of exsolved CO 2 in shallow aquifers. Then, clean water is injected and the accumulated CO 2 is dissolved back into the flowing water. The study aims to point out the differences in the mass transfer processes between the quasi-1D and 2D cases using a mathematical model of two-phase compositional flow in heterogeneous porous media calibrated to the experimental datasets, and expose strategies that should be explored in future research. Additionally, temperature variations observed during the 2D experiments allow for analysis of isothermal versus non-isothermal effects on the processes of multiphase CO 2 evolution. The mathematical model is discretized and solved using the mixed hybrid finite element method in 2D that allows for the simulation of both advection- and diffusion-dominated processes accurately.

Journal of Computational Physics↗

USGS1996

Earthquake mechanisms from linear-programming inversion of seismic-wave amplitude ratios

The amplitudes of radiated seismic waves contain far more information about earthquake source mechanisms than do first-motion polarities, but amplitudes are severely distorted by the effects of heterogeneity in the Earth. This distortion can be reduced greatly by using the ratios of amplitudes of appropriately chosen seismic phases, rather than simple amplitudes, but existing methods for inverting amplitude ratios are severely nonlinear and require computationally intensive searching methods to ensure that solutions are globally optimal. Searching methods are particularly costly if general (moment tensor) mechanisms are allowed. Efficient linear-programming methods, which do not suffer from these problems, have previously been applied to inverting polarities and wave amplitudes. We extend these methods to amplitude ratios, in which formulation on inequality constraint for an amplitude ratio takes the same mathematical form as a polarity observation. Three-component digital data for an earthquake at the Hengill-Grensdalur geothermal area in southwestern Iceland illustrate the power of the method. Polarities of P , SH , and SV waves, unusually well distributed on the focal sphere, cannot distinguish between diverse mechanisms, including a double couple. Amplitude ratios, on the other hand, clearly rule out the double-couple solution and require a large explosive isotropic component.

Bulletin of the Seismological Society of America↗

USGS1986

Evaluation of six methods for estimating magnitude and frequency of peak discharges on urban streams in New York

Six methods of estimating peak discharges of urban streams were compared and evaluated for applicability to urban streams in New York. Discharge and frequency values developed from a series of synthesized annual flood records were compared with values obtained from the six methods. The synthesized flood records were computed from rainfall-runoff models of 11 urban basins in three counties across the State. Four of these basins had a sufficient period of record to enable rainfall-runoff modeling of two different 5-year periods so that increases in peak flow due to increased urbanization could also be used for comparison of the six methods. A graphical analysis and three types of mathematical analyses were made to evaluate the closeness of fit and bias of the methods. All methods showed a tendency to overestimate synthetic urban flood-magnitude values, but the two adjust rural flood-frequency estimates on a nationwide basis showed smallest standard errors of estimate and bias. The standard errors for these two methods ranged from 44 to 57 percent over the six recurrence intervals (2, 5, 10, 25, 50, and 100 year), and the bias ranged from +28 to +53 percent. The bias , however, is probably due to errors inherent in using synthetic records and in applying the New York rural flood-frequency equations to urban basins with small drainage areas. (USGS)

Water-Resources Investigations Report↗

USGS1979

Mathematical model for simulating discharges on the Sabine River between Tatum and Ruliff, Texas

A mathematical model for simulating discharges on the Sabine River between Tatum and Ruliff, TX., was developed to evaluate the effects of release schedules on discharges from the Toledo Bend Reservoir compared to discharges under natural conditions. Using the discharge at Tatum, TX., the rainfall over the basin, and the discharge release schedule for the reservoir, discharge hydrographs for the natural and reservoir-controlled conditions can be computed.

Texas↗

USGS1977

Fluorite solubility equilibria in selected geothermal waters

Calculation of chemical equilibria in 351 hot springs and surface waters from selected geothermal areas in the western United States indicate that the solubility of the mineral fluorite, CaF 2 , provides an equilibrium control on dissolved fluoride activity. Waters that are undersaturated have undergone dilution by non-thermal waters as shown by decreased conductivity and temperature values, and only 2% of the samples are supersaturated by more than the expected error. Calculations also demonstrate that simultaneous chemical equilibria between the thermal waters and calcite as well as fluorite minerals exist under a variety of conditions. Testing for fluorite solubility required a critical review of the thermodynamic data for fluorite. By applying multiple regression of a mathematical model to selected published data we have obtained revised estimates of the p K (10,96), ΔG o f (−280.08 kcal/mole), ΔH o f (−292.59 kcal/mole), S° (16.39 cal/deg/mole) and C o P (16.16 cal/deg/mole) for CaF 2 at 25°C and 1 atm. Association constants and reaction enthalpies for fluoride complexes with boron, calcium and iron are included in this review. The excellent agreement between the computer-based activity products and the revised p K suggests that the chemistry of geothermal waters may also be a guide to evaluating mineral solubility data where major discrepancies are evident.

Geochimica et Cosmochimica Acta↗

USGS1981

Modeling natural gas reservoirs: A simple model

A mathematical model is developed and tested for the production of natural gas with water encroachment and gas entrapment. The model is built on the material and volumetric balance relations, the Schilthuis water drive model, and a gas entrapment mechanism which assumes that the rate of gas entrapment is proportional to the volumetric rate of water influx. This model represents an alternative to the large grid models because of its low computer, maintenance, and manpower costs.

Society of Petroleum Engineers journal↗

USGS2017

Documentation for the “XT3D” option in the Node Property Flow (NPF) Package of MODFLOW 6

This report describes the “XT3D” option in the Node Property Flow (NPF) Package of MODFLOW 6. The XT3D option extends the capabilities of MODFLOW by enabling simulation of fully three-dimensional anisotropy on regular or irregular grids in a way that properly takes into account the full, three-dimensional conductivity tensor. It can also improve the accuracy of groundwater-flow simulations in cases in which the model grid violates certain geometric requirements. Three example problems demonstrate the use of the XT3D option to simulate groundwater flow on irregular grids and through three-dimensional porous media with anisotropic hydraulic conductivity. Conceptually, the XT3D method of estimating flow between two MODFLOW 6 model cells can be viewed in terms of three main mathematical steps: construction of head-gradient estimates by interpolation; construction of fluid-flux estimates by application of the full, three-dimensional form of Darcy’s Law, in which the conductivity tensor can be heterogeneous and anisotropic; and construction of the flow expression by enforcement of continuity of flow across the cell interface. The resulting XT3D flow expression, which relates the flow across the cell interface to the values of heads computed at neighboring nodes, is the sum of terms in which conductance-like coefficients multiply head differences, as in the conductance-based flow expression the NPF Package uses by default. However, the XT3D flow expression contains terms that involve “neighbors of neighbors” of the two cells for which the flow is being calculated. These additional terms have no analog in the conductance-based formulation. When assembled into matrix form, the XT3D formulation results in a larger stencil than the conductance-based formulation; that is, each row of the coefficient matrix generally contains more nonzero elements. The “RHS” suboption can be used to avoid expanding the stencil by placing the additional terms on the right-hand side of the matrix equation and evaluating them at the previous iteration or time step. The XT3D option can be an alternative to the Ghost-Node Correction (GNC) Package. However, the XT3D formulation is typically more computationally intensive than the conductance-based formulation the NPF Package uses by default, either with or without ghost nodes. Before deciding whether to use the GNC Package or XT3D option for production runs, the user should consider whether the conductance-based formulation alone can provide acceptable accuracy for the particular problem being solved.

Techniques and Methods↗

USGS1973

Mathematical simulation of temperatures in deep impoundments: verification tests of the Water Resources Engineers, Inc. model - Horsetooth and Flaming Gorge Reservoirs

Successful use of predictive mathematical models requires verification of the accuracy of the models by applying them to existing situations where the prediction can be compared with reality. A Corps of Engineers' modification of a deep reservoir thermal stratification model developed by Water Resources Engineers, Inc., was applied to two existing Bureau of Reclamation reservoirs for verification. Diffusion coefficients used for the Corps' Detroit Reservoir were found to apply to Horsetooth Reservoir in Colorado, for which very food computer input data were available. The Detroit diffusion coefficients gave a reasonable simulation of Flaming Gorge Reservoir in Wyoming and Utah, which has very complex and variable physical characteristics and for which only average-quality computer input data were available.

Colorado↗

USGS1961

Graphic and algebraic solutions of the discordant lead-uranium age problem

Uranium-bearing minerals that give lead-uranium and lead—lead ages that are essentially in agreement, i.e. concordant, generally are considered to have had a relatively simple geologic history and to have been unaltered since their deposition. The concordant ages obtained on such materials are, therefore, assumed to approach closely the actual age of the minerals. Many uranium-bearing samples, particularly uranium ores, give the following discordant age sequences; Pb 206 U 238 < Pb 207 U 235 ⪡ Pb 207 Pb 206 "> Pb 206 U 238 <Pb 207 U 235 ⪡Pb 207 Pb 206 or, less frequently, Pb 207 Pb 206 ⪡ Pb 207 U 235 < Pb 206 U 238 "> Pb 207 Pb 206 ⪡Pb 207 U 235 <Pb 206 U 238 . These discordant age sequences have been attributed most often to uncertainties in the common lead correction, selective loss of radio-active daughter products, loss or gain of lead or uranium, or contamination by an older generation of radiogenic lead. The evaluation of discordant lead isotope age data may be separated into two operations. The first operation, with which this paper is concerned, is mechanical in nature and involves the calculation of the different possible concordant ages corresponding to the various processes assumed to have produced the discordant ages. The second operation is more difficult to define and requires, in part, some personal judgement. It includes a synthesis of the possible concordant age solutions with other independent geologic and isotopic evidence. The concordant age ultimately chosen as most acceptable should be consistent not only with the known events in the geologic history of the area, the age relations of the enclosing rocks, and the mineralogic and paragenetic evidence, but also with other independent age measurements and the isotopic data obtained on the lead in related or associated non-radioactive minerals. The calculation of the possible concordant ages from discordant age data has been greatly simplified by Wetherill's graphical method of plotting the mole ratios of radiogenic Pb 206 U 238 "> Pb 206 U 238 ( N 206 N 238 "> N 206 N 238 ) vs. radiogenic Pb 207 U 235 "> Pb 207 U 235 ( N 207 N 235 "> N 207 N 235 ) after correcting for the contaminating common Pb 206 and Pb 207 . The linear relationships noted in this graphical procedure have been extended to plots of the mole ratios of total Pb 206 U 238 "> Pb 206 U 238 ( t N 206 N 238 "> t N 206 N 238 ) vs. total Pb 207 U 235 "> Pb 207 U 235 ( t N 207 N 235 "> t N 207 N 235 ). This modification permits the calculation of concordant ages for unaltered samples using only the Pb 207 Pb 206 "> Pb 207 Pb 206 ratio of the contaminating common lead. If isotopic data are available for two samples of the same age, x and y , from the same or related deposits or outcrops, graphs of the normalized difference ratios [ ( N 206 N 204 )x − ( N 206 N 204 )y ( N 238 N 204 )x −( N 238 N 204 )y ] vs. [ ( N 207 N 204 )x − ( N 207 N 204 )y ( N 235 N 204 )x −( N 235 N 204 )y ] "> [(N 206 N 204 )x − (N 206 N 204 )y(N 238 N 204 )x −(N 238 N 204 )y] vs. [(N 207 N 204 )x − (N 207 N 204 )y(N 235 N 204 )x −(N 235 N 204 )y] can give concordant ages corrected for unknown amounts of a common lead with an unknown Pb 207 / Pb 206 ratio. (If thorium is absent the difference ratios may be normalized with the more abundant index isotope, Pb 208 .) Similar plots of tho normalized, difference ratios for three genetically related samples ( x − y ) and( x − z ), will give concordant ages corrected, in addition, for either one unknown period of past alteration or initial contamination by an older generation of radiogenic lead of unknown Pb 207 /Pb 206 ratio. Practical numerical solutions for many of tho concordant age calculations are not currently available. However, the algebraic equivalents of these new graphical methods give equations which may be programmed for computing machines. For geologically probable parameters the equations of higher order have two positive real roots that rapidly converge on the exact concordant ages corrected for original radiogenic lead and for loss or gain of lead or uranium. Modifications of these general age equations expanded only to the second degree have been derived for use with desk calculators. These graphical and algebraic methods clearly suggest both the type and minimum number of samples necessary for adequate mathematical analysis of discordant lead isotope age data. This mathematical treatment also makes it clear that discordant lead isotope data alone cannot provide the basis for the choice of one of the possible concordant age solutions. The new equations, in particular, provide an incentive to improve our physical constants, analytical techniques and sampling methods in order that we may derive all of the useful geologic information that is available in a comprehensive lead isotope age study.

Geochimica et Cosmochimica Acta↗

USGS1994

Data requirements for simulation of hydrogeologic effects of liquid waste injection, Harrison and Jackson Counties, Mississippi

Available literature and data were reviewed to quantify data requirements for computer simulation of hydrogeologic effects of liquid waste injection in southeastern Mississippi. Emphasis of each review was placed on quantifying physical properties of current Class I injection zones in Harrison and Jackson Counties. Class I injection zones are zones that are used for injection of hazardous or non-hazardous liquid waste below a formation containing the lowermost underground source of drinking water located within one-quarter of a mile of the injection well. Several mathematical models have been developed to simulate injection effects. The Basic Plume Method was selected because it is commonly used in permit applications, and the Intercomp model was selected because it is generally accepted and used in injection-related research. The input data requirements of the two models were combined into a single data requirement list inclusive of physical properties of injection zones only; injected waste and well properties are not included because such information is site-specific by industry, which is beyond the scope of this report. Results of the reviews of available literature and data indicated that Class I permit applications and standard-reference chemistry and physics texts were the primary sources of information to quantify physical properties of injection zones in Harrison and Jackson Counties. With the exception of a few reports and supplementary data for one injection zone in Jackson County, very little additional information pertaining to physical properties of the injection zones was available in sources other than permit applications and standard-reference texts.

Mississippi↗

USGS1994

Development and application of generalized-least-squares regression models to estimate low-flow duration discharges in Massachusetts

Physically based mathematical models were developed by use of generalized-least-squares regression analyses to estimate long-term 95-, 98-, and 99-percent duration discharges for ungaged streams in Massachusetts. Duration discharges for 61 sites were used in the recession analyses; 37 sites were streamflow-gaging stations and 24 sites were low-flow partial-record stations. The duration discharges were related to basin chacteristics measured from digital data bases, by use of geographic information systems computer software. Significant chacterisfics used in the models were drainage area, area underlain by stratified-drift deposits per unit of stream length in the basin, and a surrogate for the effective head on the aquifer in the stratified-drift deposits, computed by subtracting the minimum basin elevation from the mean basin elevation. Standard errors of prediction were 57.5, 85.6, and 98.5 percent for models for the 95-, 98-, and 99-percent duration discharges, respectively. Model error variances were about 10 times the sampling error variances, indicating that the precision of future models are likely to be improved more by obtaining better measurements of basin characteristics or by adding new sites to the analyses than by collecting more streamflow data at the sites presently used in the analyses. The models were used to predict duration discharges for 35 selected sites in the Concord River, Noah Coastal, South Coastal, Narragansett and Tenmile River Basins. Ninety-perrcent prediction intervals were computed for the estimates at each of the sites, except at sites where values of the independent variables were outside the ranges of those for the sites used in the regression analyses.

Water-Resources Investigations Report↗

USGS1983

Computer routines for probability distributions, random numbers, and related functions

Use of previously coded and tested subroutines simplifies and speeds up program development and testing. This report presents routines that can be used to calculate various probability distributions and other functions of importance in statistical hydrology. The routines are designed as general-purpose Fortran subroutines and functions to be called from user-written main progress. The probability distributions provided include the beta, chi-square, gamma, Gaussian (normal), Pearson Type III (tables and approximation), and Weibull. Also provided are the distributions of the Grubbs-Beck outlier test, Kolmogorov 's and Smirnov 's D, Student 's t, noncentral t (approximate), and Snedecor F. Other mathematical functions include the Bessel function, I sub o, gamma and log-gamma functions, error functions, and exponential integral. Auxiliary services include sorting and printer-plotting. Random number generators for uniform and normal numbers are provided and may be used with some of the above routines to generate numbers from other distributions. (USGS)

Water-Resources Investigations Report↗

USGS2014

A suggestion for computing objective function in model calibration

A parameter-optimization process (model calibration) is usually required for numerical model applications, which involves the use of an objective function to determine the model cost (model-data errors). The sum of square errors (SSR) has been widely adopted as the objective function in various optimization procedures. However, ‘square error’ calculation was found to be more sensitive to extreme or high values. Thus, we proposed that the sum of absolute errors (SAR) may be a better option than SSR for model calibration. To test this hypothesis, we used two case studies—a hydrological model calibration and a biogeochemical model calibration—to investigate the behavior of a group of potential objective functions: SSR, SAR, sum of squared relative deviation (SSRD), and sum of absolute relative deviation (SARD). Mathematical evaluation of model performance demonstrates that ‘absolute error’ (SAR and SARD) are superior to ‘square error’ (SSR and SSRD) in calculating objective function for model calibration, and SAR behaved the best (with the least error and highest efficiency). This study suggests that SSR might be overly used in real applications, and SAR may be a reasonable choice in common optimization implementations without emphasizing either high or low values (e.g., modeling for supporting resources management).

Ecological Informatics↗

USGS2023

Source contributions to suspended sediment and particulate selenium export from the Loutsenhizer Arroyo and Sunflower Drain watersheds in Colorado

Selenium in aquatic ecosystems of the lower Gunnison River Basin in Colorado is affecting the recovery of populations of endangered, native fish species. Dietary exposure is the primary pathway for bioaccumulation of selenium in fish, and particulate selenium can be consumed directly by fish or by the invertebrates on which fish feed. Although selenium can be incorporated into particulate matter via biogeochemical processes, particulate selenium can also enter aquatic ecosystems of the lower Gunnison River Basin from sediments derived from the selenium-rich Mancos Shale. The U.S. Geological Survey, in cooperation with the Colorado Water Conservation Board, conducted this study during 2018–19 to identify sources of selenium-rich suspended sediments from two watersheds underlain by Mancos Shale: Loutsenhizer Arroyo and Sunflower Drain, which is a locally known agricultural drainage near the municipality of Delta, Colorado. A multipronged approach (fieldwork, laboratory work, and computer modeling) referred to as “sediment fingerprinting” was used to evaluate sources of suspended sediments in the streams flowing out of the two studied watersheds. Four potential source types for suspended sediments were identified and sampled (using soil plugs) within the watersheds: rangelands, agricultural fields, arroyo walls, and streambanks. The sediment fingerprinting approach used elemental concentrations and naturally occurring fallout radionuclides as tracers to apportion percent contributions from the four source types of suspended sediments found in streamflow from both watersheds. To determine the dominant sources of suspended sediment in streamflow from both watersheds, a mathematical “unmixing” model was used. Unmixing models apportion source percentages to samples of material in which those sources are mixed. These models used elemental and isotopic data in the suspended sediments to unmix them into proportional contributions from source types. The results indicated that arroyo walls and streambanks generally dominated as sources of the suspended sediment. Arroyo walls and streambanks were channel-adjacent sources, with sediments mobilized by water flowing within the stream channel. These sources accounted for greater than 50 percent of suspended sediment in all but one sample and accounted for 100 percent of suspended sediment in 5 of the 11 samples collected. Rangeland and agricultural field sources were located in uplands outside of stream channels and were detected more often during the non-irrigation season. Rangeland and agricultural field sources each were found in 5 of the 11 samples collected. Concentrations of selenium in sediment-source samples were comparatively greater in streambanks and lower in rangelands, with agricultural fields and arroyo walls being intermediate. As a result, source apportionments for particulate selenium skewed towards sources adjacent to stream channels more than for suspended sediments. Water imports for irrigation have changed the hydrology of the watersheds, and a notable fraction of imported water passes through the watersheds rapidly. The rapid flowthrough water during the irrigation season likely contributes heavily to sediment erosion and transport in Loutsenhizer Arroyo and Sunflower Drain, particularly from channel-adjacent sources of sediment. Decreases in irrigation season streamflow, at least in Loutsenhizer Arroyo, may have decreased sediment erosion and transport during the 2018–20 irrigation seasons compared to the 2015–17 seasons.

Colorado↗

USGS1975

Optimal exploitation strategies for an animal population in a Markovian environment: A theory and an example

Optimal exploitation strategies were studied for an animal population in a Markovian (stochastic, serially correlated) environment. This is a general case and encompasses a number of important special cases as simplifications. Extensive empirical data on the Mallard (Anas platyrhynchos) were used as an example of general theory. The number of small ponds on the central breeding grounds was used as an index to the state of the environment. A general mathematical model was formulated to provide a synthesis of the existing literature, estimates of parameters developed from an analysis of data, and hypotheses regarding the specific effect of exploitation on total survival. The literature and analysis of data were inconclusive concerning the effect of exploitation on survival. Therefore, two hypotheses were explored: (1) exploitation mortality represents a largely additive form of mortality, and (2) exploitation mortality is compensatory with other forms of mortality, at least to some threshold level. Models incorporating these two hypotheses were formulated as stochastic dynamic programming models and optimal exploitation strategies were derived numerically on a digital computer. Optimal exploitation strategies were found to exist under the rather general conditions. Direct feedback control was an integral component in the optimal decision—making process. Optimal exploitation was found to be substantially different depending upon the hypothesis regarding the effect of exploitation on the population. If we assume that exploitation is largely an additive force of mortality in Mallards, then optimal exploitation decisions are a convex function of the size of the breeding population and a linear or slight concave function of the environmental conditions. Under the hypothesis of compensatory mortality forces, optimal exploitation decisions are approximately linearly related to the size of the Mallard breeding population. Dynamic programming is suggested as a very general formulation for realistic solutions to the general optimal exploitation problem. The concepts of state vectors and stage transformations are completely general. Populations can be modeled stochastically and the objective function can include extra—biological factors. The optimal level of exploitation in year t must be based on the observed size of the population and the state of the environment in year t unless the dynamics of the population, the state of the environment, and the result of the exploitation decisions are completely deterministic. Exploitation based on an average harvest, or harvest rate, or designed to maintain a constant breeding population size is inefficient.

Ecology↗

USGS2015

PRMS-IV, the precipitation-runoff modeling system, version 4

Computer models that simulate the hydrologic cycle at a watershed scale facilitate assessment of variability in climate, biota, geology, and human activities on water availability and flow. This report describes an updated version of the Precipitation-Runoff Modeling System. The Precipitation-Runoff Modeling System is a deterministic, distributed-parameter, physical-process-based modeling system developed to evaluate the response of various combinations of climate and land use on streamflow and general watershed hydrology. Several new model components were developed, and all existing components were updated, to enhance performance and supportability. This report describes the history, application, concepts, organization, and mathematical formulation of the Precipitation-Runoff Modeling System and its model components. This updated version provides improvements in (1) system flexibility for integrated science, (2) verification of conservation of water during simulation, (3) methods for spatial distribution of climate boundary conditions, and (4) methods for simulation of soil-water flow and storage.

Techniques and Methods↗

USGS1974

Optimal exploitation strategies for an animal population in a stochastic serially correlated environment

Optimal exploitation strategies were studied for an animal population in a stochastic, serially correlated environment. This is a general case and encompasses a number of important cases as simplifications. Data on the mallard (Anas platyrhynchos) were used to explore the exploitation strategies and test several hypotheses because relatively much is known concerning the life history and general ecology of this species and extensive empirical data are available for analysis. The number of small ponds on the central breeding grounds was used as an index to the state of the environment. Desirable properties of an optimal exploitation strategy were defined. A mathematical model was formulated to provide a synthesis of the existing literature, estimates of parameters developed from an analysis of data, and hypotheses regarding the specific effect of exploitation on total survival. Both the literature and the analysis of data were inconclusive concerning the effect of exploitation on survival. Therefore, alternative hypotheses were formulated: (1) exploitation mortality represents a largely additive form of mortality, or (2 ) exploitation mortality is compensatory with other forms of mortality, at least to some threshold level. Models incorporating these two hypotheses were formulated as stochastic dynamic programming models and optimal exploitation strategies were derived numerically on a digital computer. Optimal exploitation strategies were found to exist under rather general conditions. Direct feedback control was an integral component in the optimal decision-making process. Optimal exploitation was found to be substantially different depending upon the hypothesis regarding the effect of exploitation on the population. Assuming that exploitation is largely an additive force of mortality, optimal exploitation decisions are a convex function of the size of the breeding population and a linear or slightly concave function of the environmental conditions. Optimal exploitation under this hypothesis tends to reduce the variance of the size of the population. Under the hypothesis of compensatory mortality forces, optimal exploitation decisions are approximately linearly related to the size of the breeding population. Environmental variables may be somewhat more important than the size of the breeding population to the production of young mallards. In contrast, the size of the breeding population appears to be more important in the exploitation process than is the state of the environment. The form of the exploitation strategy appears to be relatively insensitive to small changes in the production rate. In general, the relative importance of the size of the breeding population may decrease as fecundity increases. The optimal level of exploitation in year t must be based on the observed size of the population and the state of the environment in year t unless the dynamics of the population, the state of the environment, and the result of the exploitation decisions are completely deterministic. Exploitation based on an average harvest, harvest rate, or designed to maintain a constant breeding population size is inefficient.

Book↗