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Results for “Nonlinear Processes in Geophysics”

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28 records · Page 2Linked to original sources
USGS2017

Terrestrial ecosystem model performance in simulating productivity and its vulnerability to climate change in the northern permafrost region

Realistic projection of future climate-carbon (C) cycle feedbacks requires better understanding and an improved representation of the C cycle in permafrost regions in the current generation of Earth system models. Here we evaluated 10 terrestrial ecosystem models for their estimates of net primary productivity (NPP) and responses to historical climate change in permafrost regions in the Northern Hemisphere. In comparison with the satellite estimate from the Moderate Resolution Imaging Spectroradiometer (MODIS; 246 ± 6 g C m −2 yr −1 ), most models produced higher NPP (309 ± 12 g C m −2 yr −1 ) over the permafrost region during 2000–2009. By comparing the simulated gross primary productivity (GPP) with a flux tower-based database, we found that although mean GPP among the models was only overestimated by 10% over 1982–2009, there was a twofold discrepancy among models (380 to 800 g C m −2 yr −1 ), which mainly resulted from differences in simulated maximum monthly GPP (GPP max ). Most models overestimated C use efficiency (CUE) as compared to observations at both regional and site levels. Further analysis shows that model variability of GPP and CUE are nonlinearly correlated to variability in specific leaf area and the maximum rate of carboxylation by the enzyme Rubisco at 25°C ( V c max_25 ), respectively. The models also varied in their sensitivities of NPP, GPP, and CUE to historical changes in climate and atmospheric CO 2 concentration. These results indicate that model predictive ability of the C cycle in permafrost regions can be improved by better representation of the processes controlling CUE and GPP max as well as their sensitivity to climate change.

Journal of Geophysical Research: Biogeosciences↗
USGS2011

The significance of turbulent flow representation in single-continuum models

Karst aquifers exhibit highly conductive features caused from rock dissolution processes. Flow within these structures can become turbulent and therefore can be expressed by nonlinear gradient functions. One way to account for these effects is by coupling a continuum model with a conduit network. Alternatively, turbulent flow can be considered by adapting the hydraulic conductivity within the continuum model. Consequently, the significance of turbulent flow on the dynamic behavior of karst springs is investigated by an enhanced single-continuum model that results in conduit-type flow in continuum cells (CTFC). The single-continuum approach CTFC represents laminar and turbulent flow as well as more complex hybrid models that require additional programming and numerical efforts. A parameter study is conducted to investigate the effects of turbulent flow on the response of karst springs to recharge events using the new CTFC approach, existing hybrid models, and MODFLOW-2005. Results reflect the importance of representing (1) turbulent flow in karst conduits and (2) the exchange between conduits and continuum cells. More specifically, laminar models overestimate maximum spring discharge and underestimate hydraulic gradients within the conduit. It follows that aquifer properties inferred from spring hydrographs are potentially impaired by ignoring flow effects due to turbulence. The exchange factor used for hybrid models is necessary to account for the scale dependency between hydraulic properties of the matrix continuum and conduits. This functionality, which is not included in CTFC, can be mimicked by appropriate use of the Horizontal Flow Barrier package for MODFLOW. Copyright 2011 by the American Geophysical Union.

Water Resources Research↗
USGS2007

Tidal asymmetry and residual circulation over linear sandbanks and their implication on sediment transport: a process-oriented numerical study

A series of process-oriented numerical simulations is carried out in order to evaluate the relative role of locally generated residual flow and overtides on net sediment transport over linear sandbanks. The idealized bathymetry and forcing are similar to those present in the Norfolk Sandbanks, North Sea. The importance of bottom drag parameterization and bank orientation with respect to the ambient flow is examined in terms of residual flow and overtide generation, and subsequent sediment transport implications are discussed. The results show that although the magnitudes of residual flow and overtides are sensitive to bottom roughness parameterization and bank orientation, the magnitude of the generated residual flow is always larger than that of the locally generated overtides. Also, net sediment transport is always dominated by the nonlinear interaction of the residual flow and the semidiurnal tidal currents, although cross-bank sediment transport can occur even in the absence of a cross-shore residual flow. On the other hand, net sediment divergence/convergence increases as the bottom drag decreases and as bank orientation increases. The sediment erosion/deposition is not symmetric about the crest of the bank, suggesting that originally symmetric banks would have the tendency to become asymmetric.

Journal of Geophysical Research C: Oceans↗
USGS2000

Estimation of wave phase speed and nearshore bathymetry from video imagery

A new remote sensing technique based on video image processing has been developed for the estimation of nearshore bathymetry. The shoreward propagation of waves is measured using pixel intensity time series collected at a cross-shore array of locations using remotely operated video cameras. The incident band is identified, and the cross-spectral matrix is calculated for this band. The cross-shore component of wavenumber is found as the gradient in phase of the first complex empirical orthogonal function of this matrix. Water depth is then inferred from linear wave theory's dispersion relationship. Full bathymetry maps may be measured by collecting data in a large array composed of both cross-shore and longshore lines. Data are collected hourly throughout the day, and a stable, daily estimate of bathymetry is calculated from the median of the hourly estimates. The technique was tested using 30 days of hourly data collected at the SandyDuck experiment in Duck, North Carolina, in October 1997. Errors calculated as the difference between estimated depth and ground truth data show a mean bias of −35 cm (rms error = 91 cm). Expressed as a fraction of the true water depth, the mean percent error was 13% (rms error = 34%). Excluding the region of known wave nonlinearities over the bar crest, the accuracy of the technique improved, and the mean (rms) error was −20 cm (75 cm). Additionally, under low-amplitude swells (wave height H ≤ 1 m), the performance of the technique across the entire profile improved to 6% (29%) of the true water depth with a mean (rms) error of −12 cm (71 cm).

North Carolina↗
USGS2018

Effect of dynamical phase on the resonant interaction among tsunami edge wave modes

Different modes of tsunami edge waves can interact through nonlinear resonance. During this process, edge waves that have very small initial amplitude can grow to be as large or larger than the initially dominant edge wave modes. In this study, the effects of dynamical phase are established for a single triad of edge waves that participate in resonant interactions. In previous studies, Jacobi elliptic functions were used to describe the slow variation in amplitude associated with the interaction. This analytical approach assumes that one of the edge waves in the triad has zero initial amplitude and that the combined phase of the three waves φ = θ 1 + θ 2 − θ 3 is constant at the value for maximum energy exchange ( φ = 0). To obtain a more general solution, dynamical phase effects and non-zero initial amplitudes for all three waves are incorporated using numerical methods for the governing differential equations. Results were obtained using initial conditions calculated from a subduction zone, inter-plate thrust fault geometry and a stochastic earthquake slip model. The effect of dynamical phase is most apparent when the initial amplitudes and frequencies of the three waves are within an order of magnitude. In this case, non-zero initial phase results in a marked decrease in energy exchange and a slight decrease in the period of the interaction. When there are large differences in frequency and/or initial amplitude, dynamical phase has less of an effect and typically one wave of the triad has very little energy exchange with the other two waves. Results from this study help elucidate under what conditions edge waves might be implicated in late, large-amplitude arrivals.

Pure and Applied Geophysics↗
USGS2007

A global search inversion for earthquake kinematic rupture history: Application to the 2000 western Tottori, Japan earthquake

[1] We present a two-stage nonlinear technique to invert strong motions records and geodetic data to retrieve the rupture history of an earthquake on a finite fault. To account for the actual rupture complexity, the fault parameters are spatially variable peak slip velocity, slip direction, rupture time and risetime. The unknown parameters are given at the nodes of the subfaults, whereas the parameters within a subfault are allowed to vary through a bilinear interpolation of the nodal values. The forward modeling is performed with a discrete wave number technique, whose Green's functions include the complete response of the vertically varying Earth structure. During the first stage, an algorithm based on the heat-bath simulated annealing generates an ensemble of models that efficiently sample the good data-fitting regions of parameter space. In the second stage (appraisal), the algorithm performs a statistical analysis of the model ensemble and computes a weighted mean model and its standard deviation. This technique, rather than simply looking at the best model, extracts the most stable features of the earthquake rupture that are consistent with the data and gives an estimate of the variability of each model parameter. We present some synthetic tests to show the effectiveness of the method and its robustness to uncertainty of the adopted crustal model. Finally, we apply this inverse technique to the well recorded 2000 western Tottori, Japan, earthquake ( Mw 6.6); we confirm that the rupture process is characterized by large slip (3-4 m) at very shallow depths but, differently from previous studies, we imaged a new slip patch (2-2.5 m) located deeper, between 14 and 18 km depth.

Tottori↗
USGS2012

Modification of wave-cut and faulting-controlled landforms

From a casual observation that the form of degraded fault scarps resembles the error function, this investigation proceeds through an elementary diffusion equation representation of landform evolution to the application of the resulting equations to the modern topography of scarplike landforms. The morphologic observations can be analyzed either in the form of one or more cross-strike elevation profiles or in the form of the slope-offset plot, a point plot of maximum scarp slope versus scarp offset. Working with either or both of these data representations for nine geologic structures, which range in age from 3 to 400 ka B.P. and in offset from 1 to 50 m, we apply analytical solutions for the vertical initial value scarp, the vertical continuous offset scarp, and the finite slope, initial value scarp. The model calculations are intrinsically ambiguous, yielding as the final answer only the product κ t (in the case of the initial value problem) or the product κ A −1 (in the case of the repeated faulting problem); here t is the age of a single scarp-forming event, 2 A is the vertical slip rate, and κ is the “mass diffusivity.” A single profile across three sea cliffs along the Santa Cruz, California, coast is analyzed as three separate initial value problems. A reasonably constrained age for the sea cliff standing above the Highway 1 platform returns κ = 11 GKG (1 GKG = 1 m 2 /ka). With this κ, we can date the two older sea cliffs. In fact, we do the converse: age estimates for these two older sea cliffs based on a uniform rate of uplift both yield the same κ as for the lower sea cliff. We treat a single profile of the Raymond fault in Pasadena/San Marino in terms of the repeated faulting problem; for it the uplift rate of R. Crook and others yields κ = 16 GKG. The very substantial preexisting offset across the Raymond fault must have been buried/leveled some 230 ka B.P., when the modern topography began to form. Our analysis of the Lake Bonneville shoreline scarps reveals a dependence of κ t on 2a, suggestive of nonlinear modification processes. This appearance is treated with the finite slope initial value scarp model to determine κ=1.1 GKG for the Lake Bonneville shoreline scarps. The suggestion of M. N. Machette that approximately 100,000-year-old, meter-high scarps are “unobservable” in weakly consolidated alluvial terranes of the Basin and Range and Rio Grande Rift Valley provinces can be formulated as κ ≳ 1 GKG. The coincidence between this inequality and the Lake Bonneville shoreline κ is striking, and it suggests that the value of κ = 1 GKG may be generally applicable, as a good first approximation, to the modification of alluvial terranes within the semiarid regions of the western United States. The Lake Bonneville shoreline κ is the basis for dating four sets of fault scarps in west-central Utah. The Drum Mountains fault scarps can be modeled in several different circumstances, but the most likely interpretation is that these fault scarps formed as the result of a single episode of normal faulting 3.6 to 5.7 ka B.P. The younger age is associated with quite low initial slope angles (25°). The other three sets of fault scarps show no evidence for finite initial value slopes. Fault scarps along the eastern base of the Fish Springs Range are very young, 3 ka B.P. We estimate the age of fault scarps along the western flank of the Oquirrh Mountains to be 32 ka B.P., which meets the weak geologic constraint that they be older than the Lake Bonneville shoreline. Fault scarps along the northeastern margin of the Sheeprock Mountains are even older, 53 ka B.P. An intriguing consequence of our single-event analysis of these scarps is that an 11.5-m offset occurred in a single earthquake.

Journal of Geophysical Research Solid Earth↗
USGS2015

Simulation of groundwater flow and analysis of the effects of water-management options in the North Platte Natural Resources District, Nebraska

The North Platte Natural Resources District (NPNRD) has been actively collecting data and studying groundwater resources because of concerns about the future availability of the highly inter-connected surface-water and groundwater resources. This report, prepared by the U.S. Geological Survey in cooperation with the North Platte Natural Resources District, describes a groundwater-flow model of the North Platte River valley from Bridgeport, Nebraska, extending west to 6 miles into Wyoming. The model was built to improve the understanding of the interaction of surface-water and groundwater resources, and as an optimization tool, the model is able to analyze the effects of water-management options on the simulated stream base flow of the North Platte River. The groundwater system and related sources and sinks of water were simulated using a newton formulation of the U.S. Geological Survey modular three-dimensional groundwater model, referred to as MODFLOW–NWT, which provided an improved ability to solve nonlinear unconfined aquifer simulations with wetting and drying of cells. Using previously published aquifer-base-altitude contours in conjunction with newer test-hole and geophysical data, a new base-of-aquifer altitude map was generated because of the strong effect of the aquifer-base topography on groundwater-flow direction and magnitude. The largest inflow to groundwater is recharge originating from water leaking from canals, which is much larger than recharge originating from infiltration of precipitation. The largest component of groundwater discharge from the study area is to the North Platte River and its tributaries, with smaller amounts of discharge to evapotranspiration and groundwater withdrawals for irrigation. Recharge from infiltration of precipitation was estimated with a daily soil-water-balance model. Annual recharge from canal seepage was estimated using available records from the Bureau of Reclamation and then modified with canal-seepage potentials estimated using geophysical data. Groundwater withdrawals were estimated using land-cover data, precipitation data, and published crop water-use data. For fields irrigated with surface water and groundwater, surface-water deliveries were subtracted from the estimated net irrigation requirement, and groundwater withdrawal was assumed to be equal to any demand unmet by surface water. The groundwater-flow model was calibrated to measured groundwater levels and stream base flows estimated using the base-flow index method. The model was calibrated through automated adjustments using statistical techniques through parameter estimation using the parameter estimation suite of software (PEST). PEST was used to adjust 273 parameters, grouped as hydraulic conductivity of the aquifer, spatial multipliers to recharge, temporal multipliers to recharge, and two specific recharge parameters. Base flow of the North Platte River at Bridgeport, Nebraska, streamgage near the eastern, downstream end of the model was one of the primary calibration targets. Simulated base flow reasonably matched estimated base flow for this streamgage during 1950–2008, with an average difference of 15 percent. Overall, 1950–2008 simulated base flow followed the trend of the estimated base flow reasonably well, in cases with generally increasing or decreasing base flow from the start of the simulation to the end. Simulated base flow also matched estimated base flow reasonably well for most of the North Platte River tributaries with estimated base flow. Average simulated groundwater budgets during 1989–2008 were nearly three times larger for irrigation seasons than for non-irrigation seasons. The calibrated groundwater-flow model was used with the Groundwater-Management Process for the 2005 version of the U.S. Geological Survey modular three-dimensional groundwater model, MODFLOW–2005, to provide a tool for the NPNRD to better understand how water-management decisions could affect stream base flows of the North Platte River at Bridgeport, Nebr., streamgage in a future period from 2008 to 2019 under varying climatic conditions. The simulation-optimization model was constructed to analyze the maximum increase in simulated stream base flow that could be obtained with the minimum amount of reductions in groundwater withdrawals for irrigation. A second analysis extended the first to analyze the simulated base-flow benefit of groundwater withdrawals along with application of intentional recharge, that is, water from canals being released into rangeland areas with sandy soils. With optimized groundwater withdrawals and intentional recharge, the maximum simulated stream base flow was 15–23 cubic feet per second (ft 3 /s) greater than with no management at all, or 10–15 ft 3 /s larger than with managed groundwater withdrawals only. These results indicate not only the amount that simulated stream base flow can be increased by these management options, but also the locations where the management options provide the most or least benefit to the simulated stream base flow. For the analyses in this report, simulated base flow was best optimized by reductions in groundwater withdrawals north of the North Platte River and in the western half of the area. Intentional recharge sites selected by the optimization had a complex distribution but were more likely to be closer to the North Platte River or its tributaries. Future users of the simulation-optimization model will be able to modify the input files as to type, location, and timing of constraints, decision variables of groundwater withdrawals by zone, and other variables to explore other feasible management scenarios that may yield different increases in simulated future base flow of the North Platte River.

Nebraska↗
USGS2026

Subsurface structure across the Tacoma Basin, Washington State, using trans-dimensional Bayesian inversion of fundamental mode spatial autocorrelation data

Spatial autocorrelation (SPAC), the azimuthal average of the normalized cross-correlation between equidistant station pairs deployed in a 2-D array, is widely used to image the subsurface structure. However, the rigorous estimate of subsurface structure and its uncertainties as a function of depth using SPAC data is challenging due to the nonlinear relation between the SPAC data and Earth structure as well as the trade-off between depth and velocity. Additionally, data noise is strongly correlated due to data processing (e.g. filtering, stacking from multiple time segments and azimuthal averaging). Most studies do not account for the correlated noise and fix the ratio of compressional-wave velocity ( V P ) to shear-wave velocity ( V s ) (i.e. V P / V s ratio) and the number of layers, both of which are typically unknown. To address these challenges, we develop a hierarchical trans-dimensional Bayesian inversion of fundamental mode of SPAC data that properly accounts for the correlated data noise, samples the V P / V s ratio and relaxes the number of layers (i.e. model parametrization) to be unknown in the inversion. We further examine the limitation of using only fundamental modes in the inversion. Our synthetic experiments show that the inversion recovers an incorrect model unless we sample the correlated noise and V P / V s ratio in the inversion. The inversion is then applied to SPAC data acquired at 19 sites across the Tacoma basin in Washington State to characterize the V s and the time-averaged V s over 30-m depth ( V s 30 ). Our results show that the V s 30 varies from ∼200 to 800 m s −1 . The V s 30 within the basin is higher in the middle and lower on the east and west sides. We find that these V s 30 values vary with geologic unit. The uncertainties for V s 30 are within 20 m s −1 in average except for the most eastern site TB28. Additionally, the uncertainties are greater for deeper depths beneath most of the sites as the sensitivity decreases as a function of depth. The Vs structure as a function of depth is also complex beneath some sites, possibly because the SPAC curves are affected by higher order Rayleigh modes that are not considered in the inversion. To better constrain the deeper V s structure, V s 30 and/or other average measures of V s over depth, additional constraints from complementary data, such as ellipticity or geologic data are needed. Moreover, our synthetic experiments show that higher order modes can have significant effect in the inversion results, particularly when there is a low-velocity layer.

Washington↗
USGS2018

Santa Barbara and Foothill groundwater basins Geohydrology and optimal water resources management—Developed using density dependent solute transport and optimization models

Groundwater has been a part of the city of Santa Barbara’s water-supply portfolio since the 1800s; however, since the 1960s, the majority of the city’s water has come from local surface water, and the remainder has come from groundwater, State Water Project, recycled water, increased water conservation, and as needed, seawater desalination. Although groundwater from the Santa Barbara and Foothill groundwater basins only accounts for a small percentage of the long-term supply, it is an important source of supplemental water during times of surface-water shortages. During the late 1980s and early 1990s, production wells extracted additional groundwater to compensate for drought related water-delivery shortfalls from other sources; in response, water levels declined substantially in the Santa Barbara and Foothill groundwater basins (below sea level in the Santa Barbara groundwater basin). In coastal basins that have groundwater extraction near shore, seawater intrusion is often a problem. Seawater intrusion in the Santa Barbara groundwater basin is thought to be more limited than in other coastal basins because of an offshore fault that acts as a partial barrier to groundwater flow. During the late 1980s and early 1990s, seawater intrusion was observed in the Santa Barbara groundwater basin, as indicated by increased chloride concentrations at several monitoring wells that ranged from 200 ft to 1,300 ft from the ocean and as close as 2,900 ft to the nearest pumping well. This demonstrated that seawater can intrude into the Santa Barbara groundwater basin when groundwater levels fall below sea level near the coast. The city of Santa Barbara is interested in developing a better understanding of the sustainability of its groundwater supplies. In 2014, California adopted historic legislation to manage its groundwater: the Sustainable Groundwater Management Act (SGMA). The SGMA requires the development and implementation of “Groundwater Sustainability Plans” in 127 priority groundwater basins; although Santa Barbara was not a designated priority basin, the city is taking steps to achieve sustainability. Sustainability was defined in the SGMA in terms of avoiding undesirable results: significant and unreasonable groundwater-level declines, reduction in groundwater storage, seawater intrusion, water-quality degradation, land subsidence, and surface-water depletion. In this project, a cooperative study between the U.S. Geological Survey (USGS) and the city of Santa Barbara, sustainable yield is defined as the volume of groundwater that can be pumped from storage without causing water-level drawdowns and the associated increases in seawater intrusion (as indicated by increases in measured chloride concentrations) at selected wells. In order to estimate the sustainability of Santa Barbara’s groundwater basins, a three-dimensional density-dependent groundwater-flow and solute-transport model (the Santa Barbara Flow and Transport Model, or SBFTM) was developed on the basis of an existing groundwater-flow model. To simulate seawater intrusion to the Santa Barbara Basin under various management strategies, the SBFTM uses the USGS code SEAWAT to simulate salinity transport and variable-density flow. The completed SBFTM was coupled with a management optimization tool, in this case a multi-objective evolutionary algorithm, to determine optimal pumping strategies that maximize the sustainable yield and at the same time satisfy user-defined drawdown and chloride-concentration constraints. As part of this study, a three-dimensional hydrogeologic framework model was developed to quantify the extent and hydrogeologic characteristics of the Santa Barbara and Foothill groundwater basins and to help define the discretization and hydraulic properties used in the SBFTM. The development of the hydrogeologic framework model required the collection and reconciliation of geologic and geophysical data from existing maps, reports, and databases, along with geologic and hydrologic data from recently drilled wells. These data were integrated into a three-dimensional hydrogeologic framework model that defines the stratigraphy and geometry of the aquifer zones and the major geologic structures in the basin. The hydrogeologic framework model also quantifies the variation in sediment grain size within each aquifer zone as the percentage of coarse-grained sediment. Previous studies indicated that there are two principal water-producing zones in the Santa Barbara groundwater basin, the upper and lower producing zones; an additional thin, productive zone was identified as part of this study. This “middle producing zone” is not as areally extensive as the upper and lower producing zones and only exists in the coastal part of Storage Unit I. These producing zones are bounded at depth by less productive shallow, middle, and deep zones. Two versions of the SBFTM were constructed: an initial-condition model and a modern transient model. The initial-condition model is a long-term transient model that simulates flow and solute-transport conditions during a period with limited anthropogenic influences preceeding the modern transient model. The simulation-transient model simulates flow and transport conditions from 1929 through 2013; however, because of data availability, the focus of the model calibration was 1972–2013. The SBFTM was calibrated to measured groundwater levels and drawdown, as well as measured chloride concentrations and change in concentrations, using a combination of automated and trial-and-error parameter-estimation techniques. A sensitivity analysis indicated that, in general, the SBFTM was most sensitive to recharge- and pumping-distribution parameters, specifically those controlling the amount of small-catchment recharge and the distribution of water extraction by hydrogeologic layer for production wells. The model was also sensitive to parameters controlling stream-recharge rates, horizontal and vertical hydraulic conductivity, and porosity. From 1929 to 1971, most of the water entering the area represented by the SBFTM was from creek and small-catchment recharge, and the majority of water leaving the SBFTM area was from pumping, discharge to creeks, and drains. In addition, about 37 percent of the total pumpage came from a net reduction in groundwater storage. From 1972 to 2013, the amount of water entering and leaving the SBFTM was fairly similar as that from 1929 to 1971, except the reduction in pumpage added about 17,000 acre-ft of water to storage. During this later period, there were also times of storage loss. For example, during July 1990, a month when approximately 705 acre-ft of groundwater was pumped in the study area, the pumpage was much greater than all sources of recharge combined, and about 382 acre-ft of water was removed from groundwater storage. Simulated hydraulic heads replicated the observed data to an acceptable matching of the measured water-level, flow direction, and vertical gradients. Simulated hydrographs for selected wells were in good agreement with the measured data, with an average residual of -2.7 ft and a standard deviation of 14.5 ft, indicating that the simulated heads, on average, underestimated the observed water levels. An examination of the model fit indicated that most of the discrepancies were lower simulated heads at wells proximal to production well sites. The simulated chloride concentrations reasonably matched the rising limbs of the measured breakthrough curves in terms of timing and magnitude; however, the simulation overestimated the chloride concentrations on the falling limbs. The overestimation of low chloride concentrations was attributed to the model overestimating the advance of the chloride front during periods of heavy pumping and underestimating the retreat of the chloride front during periods of low pumping. These simulation errors would result in a conservative response by local water managers to seawater intrusion. The SBFTM was used to develop a collection of predictive simulations optimized to produce pumping schedules that maximize yield, subject to a set of constraints and competing objectives. The simulations were grouped as scenarios that differed in their time horizon, initial conditions for groundwater levels and chloride concentrations, as well as precipitation, which was incorporated into the model through simulated recharge. Overall, five scenarios were developed in a multi-objective framework to obtain optimal pumping rates for all of the wells managed by the city, while minimizing excessive drawdown and seawater intrusion. For the current study, complexities in the simulation model and the optimization formulation required additional considerations. Incorporating the solute-transport equations to simulate chloride transport added a highly nonlinear process that is solved iteratively in each time step of the groundwater-flow model. These nonlinearities, coupled with the highly refined grid in the current model, creates challenges for many traditional optimization methods. Therefore, an optimization method was needed that could address nonlinear relationships as well as a very large problem size. Lastly, the optimization problem was reformulated to include multiple objectives without requiring convergence to a single solution. This approach, guided by the city’s objectives, allowed the maximum extraction of information from the complex simulation. Borg, a multi-objective evolutionary algorithm, was chosen as the optimization algorithm for this study for several reasons: (1) it is very computationally efficient; (2) it can run in parallel; (3) it requires little user input; and (4) it can solve for multiple competing objectives. The first three points allow the algorithm to proceed toward the optimal solutions at the fastest possible rate. The fourth point is advantageous for large, complex optimization problems because it is difficult to formulate the optimization problem in a way that produces only one optimal solution. The problem formulation consisted of four competing objectives and a constraint set in accordance with the main concerns of the city. The objectives were maximizing total pumpage, minimizing seawater intrusion, minimizing total drawdown in production wells, and minimizing the maximum drawdown. The constraints were pump capacity, meeting drinking-water standards for chloride, maintaining a specified minimum flowrate to a groundwater treatment plant, and maintaining minimum water levels in pumping wells. The decision variables either were quarterly pumpage by well or total pumpage by basin. Five optimization scenarios were developed that allow the decision makers to evaluate a range of optimal solutions for a variety of water levels and chloride concentrations as well as potential future climatic conditions. Three scenarios (1, 2, and 5) were multi-objective optimization formulations that allowed for variations in management preferences and climatic conditions. The other two scenarios (3 and 4) were designed to examine the optimization results to answer specific questions. Scenario 1 described the best-case sustainable yield assuming a “full” basin (that is, high initial water levels) and typical climate conditions for 10 years. Scenario 2 also started with a “full” basin; however, this was followed by a 10-year drought. Scenario 3 determined if an “empty” basin (that is, low initial water levels) would recover to full conditions (1998 conditions) given climate assumptions and optimal pumping schedules from scenarios 1 and 2. Scenario 4 was designed to produce decision rules that can be used by water managers to help choose an optimal pumping schedule based on measured water-level or chloride data. Scenario 5 identified future pumping schedules based on short-term climate variations during a 2-year management horizon. The results from scenarios 1 and 2 described the differences in maximum pumpage in the basin under typical and dry long-term climate projections, respectively. The scenario 1 results indicated the maximum 10-year pumpage of the basin was about 31,300 acre-ft under typical conditions and controlling simulated seawater intrusion and drawdowns. For scenario 2, less recharge over the 10-year dry climate produced a maximum pumpage estimate of 30,000 acre-ft to control seawater intrusion and drawdowns. The larger pumpage for scenario 1 resulted in more seawater intrusion, but less total drawdown, compared to that of scenario 2. Results for scenarios 3 and 4 showed the basin’s response to management actions combined with climate projections. Both scenarios used the optimal pumping schedules and the 10-year climates from scenarios 1 and 2. The scenario 3 results showed that under minimal pumping, the basin did not fully recover to 1998 water levels within 10 years under either climate scenario. The relatively larger recharge from the typical climate resulted in less drawdown at coastal monitoring wells after the 10-year recovery period than that from the dry climate. The location of the seawater intrusion front was not appreciably different between the scenarios, however. Scenario 4 used the optimal results from scenarios 1 and 2 to produce decision-rule curves that illustrated the pumpage for each basin, given measured levels of chloride concentration or drawdown. This allowed the use of additional measurements at monitoring wells to assess future management decisions on the basis of the sensitivity of observations of drawdown and seawater intrusion to various pumping rates. Scenario 5 allowed managers to investigate the effects of short-term climate variations on optimal pumping schedules. Three specific 2-year simulations were optimized: typical-to-dry (scenario 5A), dry-to-typical (scenario 5B), and dry-to-dry (scenario 5C). The most noteable result from scenario 5 was the overall reduction in optimal pumpage for most schedules in scenario 5C, when the climate is simulated as dry-to-dry. There are also many optimal pumping schedules that produced an overall increase in waterlevels over the two-year simulation period, regardless of climatic condition. Similar to scenario 2, the scenario 5C results represents conservative yield estimates under a minimal-precipitation climatic condition.

California↗