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Denoising Autoencoder for Reconstructing Sensor Observation Data and Predicting Evapotranspiration: Noisy and Missing Values Repair and Uncertainty Quantification

Abstract Machine learning (ML) methods applied in scientific research often deal with interrelated features in high‐dimensional data. Reducing data noise and redundancy is needed to increase prediction accuracy and efficiency especially when dealing with data from field sensors. We explored an unsupervised learning method, the denoising autoencoder (DAE), to extract the underlying data structure from noisy raw data in the context of predicting hydrologic quantities from multiple field sensors. These sensors have intrinsic instrumental noise and occasional malfunctions that cause missing values. Our DAE neural network reconstructed meteorological sensor data containing noise and missing values to predict evapotranspiration in a mountainous watershed. The DAE reconstructed the sensor variables with a mean coefficient of determination value of 0.77 across 15 dimensions representing individual sensors. It reduced variance and bias uncertainties compared to a classical autoencoder model. The reconstruction quality varied across dimensions depending on their cross‐correlation and alignment with the underlying data structure. Uncertainties arising from the model structure were overall higher than those resulting from data corruption. We attached the DAE structure to a downstream ET‐prediction neural network in three formats and achieved reasonably accurate ET predictions . The use of the DAE notably reduced variance uncertainty in ET prediction. However, excessive variance reduction may be accompanied by an increase in bias due to the intrinsic bias‐variance tradeoff. Our method of evaluating and reducing uncertainties in aggregated data from different sources can be used to improve predictive models, process understanding, and uncertainty quantification for better water resource management. Plain Language Summary We present a machine learning method, namely the denoising autoencoder, which reduces the effects of data noise and missing values typically present in scientific data sets collected through sensor measurements. This method selects the most relevant information from noisy raw data collected by the instruments and fills in missing values. To demonstrate the effectiveness of our method, we applied it to predict evapotranspiration, a hydrologic variable that represents the water moved from the land surface to the atmosphere through a combination of evaporation and plant water use (transpiration). We also used a random sampling technique (the Monte Carlo method) to compare the uncertainty in the predictions when using the raw and noisy data versus the reconstructed data. The denoising process produced more accurate predictions of evapotranspiration with less uncertainty. Improved predictions of evapotranspiration can lead to a better understanding and accounting of water budgets. This ML approach is broadly suitable for a wide variety of applications that involve noisy sensor data with missing values. Key Points We used a denoising autoencoder (DAE) neural network to reduce noise in meteorological and soil sensor observations by on average We used Monte Carlo sampling to estimate the bias and variance of all model outputs, including uncertainty sources from data and the model We attached the DAE component to a downstream neural network to predict ET with the variance reduced by , compared to that without the DAE

denoising autoencoder↗

Electric transmission value and its drivers in United States power markets

Electric transmission infrastructure plays a vital role during extreme weather and supply disruptions and can enable low-cost electricity systems. This paper contributes to a more complete understanding of the value and cost-effectiveness of transmission, as well as barriers to its development. By studying wholesale energy market prices in the United States between 2012 and 2022, we find that additional transfer capacity between regions would have been especially valuable, with a median value of $116 million per GW per year. This capacity would often have provided balanced benefits to each region. The market value of transmission was highly influenced by a small fraction of time: 5% of hours typically captured at least 45% of the total value. These peak periods were primarily driven by unforeseen changes in conditions within one day of operations. Annualized transmission infrastructure cost estimates were lower than the average market value for most locations, including all links crossing regional seams, where the value-to-cost ratio was often greater than 4. This suggests that there are barriers to developing valuable grid infrastructure. These results complement forward-looking modeling studies and support efforts to improve modeling practices.

Energy economics↗

Ultrafast Bragg coherent diffraction imaging of epitaxial thin films using deep complex-valued neural networks

Abstract Domain wall structures form spontaneously due to epitaxial misfit during thin film growth. Imaging the dynamics of domains and domain walls at ultrafast timescales can provide fundamental clues to features that impact electrical transport in electronic devices. Recently, deep learning based methods showed promising phase retrieval (PR) performance, allowing intensity-only measurements to be transformed into snapshot real space images. While the Fourier imaging model involves complex-valued quantities, most existing deep learning based methods solve the PR problem with real-valued based models, where the connection between amplitude and phase is ignored. To this end, we involve complex numbers operation in the neural network to preserve the amplitude and phase connection. Therefore, we employ the complex-valued neural network for solving the PR problem and evaluate it on Bragg coherent diffraction data streams collected from an epitaxial La 2-x Sr x CuO 4 (LSCO) thin film using an X-ray Free Electron Laser (XFEL). Our proposed complex-valued neural network based approach outperforms the traditional real-valued neural network methods in both supervised and unsupervised learning manner. Phase domains are also observed from the LSCO thin film at an ultrafast timescale using the complex-valued neural network.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Infrared Optical Constants from Pressed Pellets of Powders: I. Improved n and k Values of (NH4)(2)SO(4)from Single-Angle Reflectance

In combination with other parameters, the real, n(?), and imaginary, k(?), components of the complex refractive index, = n + ik, can be used to simulate the optical properties of a material in different forms, e.g. its infrared spectra. But obtaining reliable values of the optical constants n/k for solid materials is challenging due to the lack of optical quality specimens, usually crystals, large enough to measure. An alternative to crystals is to press the powder into a uniform disk. We have produced pellets from ammonium sulfate, (NH4)2SO4, powder and derived the pellets’ n and k values via single-angle reflectance using a specular reflectance device in combination with a Fourier transform infrared spectrometer. The single-angle technique measures amplitude of light reflected from the material as a function of wavelength over a wide spectral domain; the optical constants are determined from the reflectance data using the Kramers-Kronig relationship. We investigate several parameters associated with the pellets and pellet formation and their effects upon delivering the most reliable n/k values. Parameters studied include pellet diameter, mass and density (void space), drying, grinding, sieving and particle size in the pellet formation, as well as pressing pressure and duration. Of these parameters, using size-selected mixtures of dried, small (< 100 µm) particles and pressing at = 10 tons for at least 30 minutes were found key to forming highly reflective samples. Comparison to two sets of previous literature n(?) and k(?) values obtained from crystalline (NH4)2SO4 both as crystal reflectance as well as extinction spectra of aerosols measured in a flow tube show reasonable agreement, but suggests the present values, as confirmed from two independent techniques, represent a substantial improvement for n/k values for (NH4)2SO4, also demonstrating promise to measure the optical constants of other materials.

Optical constants, index of refraction, single-ang↗

Business Models for Scaling Demand Flexibility Volume I – Value proposition characteristics, challenges, and lessons learned from U.S. programs

Load growth at the grid edge is driving increased attention to the distribution system and its ability to enable customer technology adoption in an affordable and timely manner. Key industry stakeholders, including electric utilities and regulators, can benefit from strategies to manage and balance customer needs with infrastructure investments, such as demand flexibility. This report focuses on demand flexibility—the ability to reduce, shift, shed, generate, or modulate loads in response to building and grid needs—to reduce the need for costly grid upgrades by deferring investment needs and increase system reliability by shifting electricity usage during periods of high risk. Specifically, we focus on the emerging characteristics of business models for demand flexibility as a framework to understand how demand flexibility programs generate value. In this report, we focus on demand flexibility value propositions, which provide information on value creation and describe how programs deliver clear benefits that address customer and grid needs. This report discusses the role of value propositions in demand flexibility programs, provides an overview of value propositions for a range of demand flexibility stakeholders, identifies existing challenges to establishing an effective value proposition, and describes lessons learned. This report is part of a series that includes reports on customer relationship management strategies, stakeholder ecosystem management, and program life cycle.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Utility-Scale Solar, 2024 Edition: Empirical Trends in Deployment, Technology, Cost, Performance, PPA Pricing, and Value in the United States [Slides]

Berkeley Lab’s “Utility-Scale Solar, 2024 Edition” presents analysis of empirical plant-level data from the U.S. fleet of ground-mounted photovoltaic (PV), PV+battery, and concentrating solar-thermal power (CSP) plants with capacities exceeding 5 MWAC (PV plants of 5 MWAC or less, including residential rooftop systems, are covered separately in Berkeley Lab’s companion annual report, Tracking the Sun). Key findings from this year’s report include: -18.5 GWAC of new utility-scale PV capacity came online in 2023, bringing cumulative installed capacity to more than 80.2 GWAC across 47 states. Installed costs continued to fall in 2023. Relative to 2022, capacity-weighted averages decreased by 8% to -$\$1.43$/WAC (or $\$1.08$/WDC). Costs, based on a 7.1 GWAC sample of 76 plants completed in 2023, have fallen by 75% (averaging 10% annually) since 2010. Plant-level capacity factors vary widely, from 6% to 36% (on an AC basis), with a sample median of 24%. -Levelized cost of energy (LCOE) of new 2023 projects increased slightly to $\$46$/MWh prior to the application of tax credits but continued to fall to $\$31$/MWh when accounting for federal incentives. PPA prices have largely followed the decline in solar’s LCOE over time, but newly signed longer-term PPA prices have increased since 2021, to an average of $\$35$/MWh (levelized, in 2023 dollars). -Solar’s average energy and capacity value (i.e., ability to offset costs of other power generation sources) across the U.S. was $\$45$/MWh in 2023. Solar’s average market value was lowest in CAISO ($\$27$/MWh), the market with the greatest solar generation share, and highest in ERCOT ($\$67$/MWh). -Newer solar projects had greater market value in 2023 than their generation costs, yielding $\$1.1$ billion in benefits. Projects built in 2022 delivered on average $\$15$/MWh more market value than their costs in 2023. -Solar’s combined value from wholesale electricity markets, public health and climate damage reduction were greater than generation costs and incentives, yielding $\$13.7$ billion in net benefits in 2023. We estimate U.S. health benefits of $\$24$/MWh and reduced global climate damages of $\$101$/MWh. -Adding battery storage is one way to increase the value of solar. Deployment of 52 new PV+battery hybrid plants set a record with 5.3 GW installed in 2023. Our public data file tracks metadata and PPA prices from more than 100 PV+battery hybrid projects that are already online or that have secured offtake arrangements. -Looking ahead, a massive pipeline of at least 1,085 GW of solar capacity dominates the nation’s interconnection queues at the end of 2023. Nearly 571 GW, or 53%, of that total was paired with a battery – in CAISO it was a staggering 98%. Historically only 10% of the requested solar capacity is built. -For more information, and to explore related interactive data visualizations, go to utilityscalesolar.lbl.gov.

14 SOLAR ENERGY↗

Value of Geothermal Energy Storage for Supply-Side and Demand-Side Applications

This report presents the results of a study examining the value potential for geothermal energy storage (GES), a long-duration energy storage resource that stores thermal and/or geomechanical energy in the subsurface. GES could benefit the overall U.S. power system by temporally shifting electricity generation (supply-side) or meeting building heating and cooling load (demand-side). This report analyzes supply-side and demand-side opportunities independently because of differences in applications and models. Currently there is significant uncertainty about the development costs for GES, with only a limited number of demonstration plants for electric energy storage and building heating and cooling storage developments. In this report, we estimate the value of supply-side and demand-side GES to the bulk power system in the contiguous United States. Because of the significant uncertainty about GES development costs, this analysis does not consider GES deployment costs but instead focuses on the value of GES to the U.S. electricity system. The estimated values of GES provide reference points for economically competitive commercial cost targets. Supply-side GES is modeled as part of an enhanced geothermal system (EGS) generation plant in NREL's Regional Energy Deployment System (ReEDS) capacity expansion model (Ho et al. 2021). In contrast to conventional geothermal plants, which generate constant power, EGS plants have unique features that may allow for in-reservoir energy storage for flexible generation. Demand-side GES for heating and cooling, including seasonal hot and cold storage and short-duration heat pump storage, is incorporated into a price-taker model using Cambium electricity marginal cost projections. To establish an upper bound for the value of GES, analysis focused on favorable scenarios for storage with high generation from zero marginal cost, variable renewable energy resources. High penetrations of variable renewable energy generation can increase hourly electricity price variability, which increases the value of temporal energy arbitrage for storage technologies like GES.

15 GEOTHERMAL ENERGY↗

Effects of initial delamination on CIc and GIth values from glass/epoxy double cantilever beam tests

The effect of insert thickness and method of precracking on mode I interlaminar fracture toughness, GIc, and delamination fatigue threshold, GIth, values were determined for a glass/epoxy double cantilever beam specimen. The results of the static tests showed that precracking in tension would cause fiber bridging and thus may yield unconservative values of GIc and GIth. Precracking in shear yields suitable values of GIc but overly conservative values of GIth. For the glass/epoxy composite used, an insert thickness of 0.5 mil was most suitable for determining GIc and GIth values, although an insert thickness up to 3 mil was acceptable. Inserts thicker than 3 mil were not acceptable for determining GIc and GIth values.

Martin, Roderick H.↗

Decision theory for computing variable and value ordering decisions for scheduling problems

Heuristics that guide search are critical when solving large planning and scheduling problems, but most variable and value ordering heuristics are sensitive to only one feature of the search state. One wants to combine evidence from all features of the search state into a subjective probability that a value choice is best, but there has been no solid semantics for merging evidence when it is conceived in these terms. Instead, variable and value ordering decisions should be viewed as problems in decision theory. This led to two key insights: (1) The fundamental concept that allows heuristic evidence to be merged is the net incremental utility that will be achieved by assigning a value to a variable. Probability distributions about net incremental utility can merge evidence from the utility function, binary constraints, resource constraints, and other problem features. The subjective probability that a value is the best choice is then derived from probability distributions about net incremental utility. (2) The methods used for rumor control in Bayesian Networks are the primary way to prevent cycling in the computation of probable net incremental utility. These insights lead to semantically justifiable ways to compute heuristic variable and value ordering decisions that merge evidence from all available features of the search state.

Linden, Theodore A.↗

Effects of expected-value information and display format on recognition of aircraft subsystem abnormalities

This study identifies improved methods to present system parameter information for detecting abnormal conditions and to identify system status. Two workstation experiments were conducted. The first experiment determined if including expected-value-range information in traditional parameter display formats affected subject performance. The second experiment determined if using a nontraditional parameter display format, which presented relative deviation from expected value, was better than traditional formats with expected-value ranges included. The inclusion of expected-value-range information onto traditional parameter formats was found to have essentially no effect. However, subjective results indicated support for including this information. The nontraditional column deviation parameter display format resulted in significantly fewer errors compared with traditional formats with expected-value-ranges included. In addition, error rates for the column deviation parameter display format remained stable as the scenario complexity increased, whereas error rates for the traditional parameter display formats with expected-value ranges increased. Subjective results also indicated that the subjects preferred this new format and thought that their performance was better with it. The column deviation parameter display format is recommended for display applications that require rapid recognition of out-of-tolerance conditions, especially for a large number of parameters.

Palmer, Michael T.↗

NASA/DOD Aerospace Knowledge Diffusion Research Project. Paper 48: Valuing information in an interactive environment

Consideration effort has been devoted over the past 30 years to developing methods and means of assessing the value of information. Two approaches - value in exchange and value in use - dominate; however, neither approach enjoys much practical application because validation schema for decision-making is missing. The approaches fail to measure objectively the real costs of acquiring information and the real benefits that information will yield. Moreover, these approaches collectively fail to provide economic justification to build and/or continue to support an information product or service. In addition, the impact of Cyberspace adds a new dimension to the problem. A new paradigm is required to make economic sense in this revolutionary information environment. In previous work, the authors explored the various approaches to measuring the value of information and concluded that, in large measure, these methods were unworkable concepts and constructs. Instead, they proposed several axioms for valuing information. Most particularly they concluded that the 'value of information cannot be measured in the absence of a specific task, objective, or goal.' This paper builds on those axioms and describes under which circumstances information can be measured in objective and actionable terms. This paper also proposes a methodology for undertaking such measures and validating the results.

Brinberg, Herbert R.↗

Probability Distribution Estimated From the Minimum, Maximum, and Most Likely Values: Applied to Turbine Inlet Temperature Uncertainty

Modern engineering design practices are tending more toward the treatment of design parameters as random variables as opposed to fixed, or deterministic, values. The probabilistic design approach attempts to account for the uncertainty in design parameters by representing them as a distribution of values rather than as a single value. The motivations for this effort include preventing excessive overdesign as well as assessing and assuring reliability, both of which are important for aerospace applications. However, the determination of the probability distribution is a fundamental problem in reliability analysis. A random variable is often defined by the parameters of the theoretical distribution function that gives the best fit to experimental data. In many cases the distribution must be assumed from very limited information or data. Often the types of information that are available or reasonably estimated are the minimum, maximum, and most likely values of the design parameter. For these situations the beta distribution model is very convenient because the parameters that define the distribution can be easily determined from these three pieces of information. Widely used in the field of operations research, the beta model is very flexible and is also useful for estimating the mean and standard deviation of a random variable given only the aforementioned three values. However, an assumption is required to determine the four parameters of the beta distribution from only these three pieces of information (some of the more common distributions, like the normal, lognormal, gamma, and Weibull distributions, have two or three parameters). The conventional method assumes that the standard deviation is a certain fraction of the range. The beta parameters are then determined by solving a set of equations simultaneously. A new method developed in-house at the NASA Glenn Research Center assumes a value for one of the beta shape parameters based on an analogy with the normal distribution (ref.1). This new approach allows for a very simple and direct algebraic solution without restricting the standard deviation. The beta parameters obtained by the new method are comparable to the conventional method (and identical when the distribution is symmetrical). However, the proposed method generally produces a less peaked distribution with a slightly larger standard deviation (up to 7 percent) than the conventional method in cases where the distribution is asymmetric or skewed. The beta distribution model has now been implemented into the Fast Probability Integration (FPI) module used in the NESSUS computer code for probabilistic analyses of structures (ref. 2).

Holland, Frederic A., Jr.↗

The Impact of Different Absolute Solar Irradiance Values on Current Climate Model Simulations

Simulations of the preindustrial and doubled CO2 climates are made with the GISS Global Climate Middle Atmosphere Model 3 using two different estimates of the absolute solar irradiance value: a higher value measured by solar radiometers in the 1990s and a lower value measured recently by the Solar Radiation and Climate Experiment. Each of the model simulations is adjusted to achieve global energy balance; without this adjustment the difference in irradiance produces a global temperature change of 0.48C, comparable to the cooling estimated for the Maunder Minimum. The results indicate that by altering cloud cover the model properly compensates for the different absolute solar irradiance values on a global level when simulating both preindustrial and doubled CO2 climates. On a regional level, the preindustrial climate simulations and the patterns of change with doubled CO2 concentrations are again remarkably similar, but there are some differences. Using a higher absolute solar irradiance value and the requisite cloud cover affects the model's depictions of high-latitude surface air temperature, sea level pressure, and stratospheric ozone, as well as tropical precipitation. In the climate change experiments it leads to an underestimation of North Atlantic warming, reduced precipitation in the tropical western Pacific, and smaller total ozone growth at high northern latitudes. Although significant, these differences are typically modest compared with the magnitude of the regional changes expected for doubled greenhouse gas concentrations. Nevertheless, the model simulations demonstrate that achieving the highest possible fidelity when simulating regional climate change requires that climate models use as input the most accurate (lower) solar irradiance value.

climate change↗

System Value Model of a Launch Vehicle

System value provides a mathematical representation of stakeholder’s preferences for the system. System value represents the utility that the system provides to the stakeholders. For a launch vehicle, important values are revenue generated through successful payloads, mission reliability, and the ability to accommodate payloads without modification to the payload instruments or spacecraft bus. This paper considers the value provided by a heavy lift launch vehicle to the satellite industry and to human exploration. An estimate is developed for a generic launch vehicle value in terms of impact to the Gross Domestic Product. Thermo-economics are applied in the calculation of system value. Mission reliability considers both successful delivery and on time delivery (i.e., operational availability). Payload accommodation considers mainly the diameter of the payload fairing for various types of missions.

Barth, Andrew↗

Assessing the Added Value of Miniature X-Ray in the Setting of Portable Ultrasound in Spaceflight

INTRODUCTION: Point-of-care ultrasound (POCUS) has become the standard of care for imaging diagnosis and management in low-Earth Orbit (LEO) spaceflight and it has long been hypothesized that POCUS will also be the standard of care for exploration spaceflight. However, like the trajectory for which ultrasound became more portable and user-friendly, the mass, volume, and power requirements of radiography devices for both diagnostic and therapeutic applications have also been dramatically reduced. This study seeks to determine the clinical utility and added value of miniature x-ray (XR) for the diagnosis and management of each of the 119 conditions within NASA Exploration Medical Capability’s IMPACT Condition List (ICL) given that the medical system is presumed to already be carrying a handheld portable POCUS device. METHODS: For each condition, a team of reviewers performed a rapid systematic literature review seeking sensitivity and specificity data for both handheld portable ultrasound and miniature XR. When there was a paucity of data, subject matter expertise and clinical experience was added to semi-quantitatively score the added value of miniature XR, given an US was already available for both diagnosis and management. Diagnostic utility of a modality for a condition was evaluated in the setting of both the best- and worst-case scenario definitions included and defined by the ICL. Evidence tracing and quality of evidence scores were also recorded. RESULTS/DISCUSSION: Conditions for which it was determined that miniature XR added diagnostic or therapeutic value are provided in this presentation. Previously presented work by our team has demonstrated that XR provides diagnostic and management capabilities that are hypothesized to complement or surpass ultrasound for over one-third of medical conditions that may arise during exploration spaceflight (i.e., diagnosis of injuries to the axial skeleton, teeth, and lungs as well as management of orthopedic reductions, endotracheal tube placement, and drain placement confirmation). In the setting of known inclusion of a handheld portable POCUS device, there remains significant added value of portable miniature XR. Whether or not this added clinical benefit is worth the mass, volume, and power requirements of the radiography system remains yet unknown and is the focus of future work. LEARNING OBJECTIVES: 1) Understand the value of ultrasound and radiography in the diagnosis and management of medical comorbidities that may arise in exploration spaceflight; 2) Understand the medical conditions of highest concern on exploration class missions for which miniature x-ray may provide added value to portable ultrasound.

J G Steller↗

Assessing the Added Value of Miniature X-Ray in the Setting of US in Spaceflight

INTRODUCTION: Point-of-care ultrasound (POCUS) has become the standard of care for imaging diagnosis and management in lowEarth Orbit (LEO) spaceflight and it has long been hypothesized that POCUS will also be the standard of care for exploration spaceflight. However, like the trajectory for which ultrasound became more portable and user-friendly, the mass, volume, and power requirements of radiography devices for both diagnostic and therapeutic applications have also been dramatically reduced. This study seeks to determine the clinical utility and added value of miniature x-ray (XR) for the diagnosis and management of each of the 119 conditions within NASA Exploration Medical Capability’s IMPACT Condition List (ICL) given that the medical system is presumed to already be carrying a handheld portable POCUS device. METHODS: For each condition, a team of reviewers performed a rapid systematic literature review seeking sensitivity and specificity data for both handheld portable ultrasound and miniature XR. When there was a paucity of data, subject matter expertise and clinical experience was added to semi-quantitatively score the added value of miniature XR, given an US was already available for both diagnosis and management. Diagnostic utility of a modality for a condition was evaluated in the setting of both the best- and worst-case scenario definitions included and defined by the ICL. Evidence tracing and quality of evidence scores were also recorded. RESULTS/DISCUSSION: Conditions for which it was determined that miniature XR added diagnostic or therapeutic value are provided in this presentation. Previously presented work by our team has demonstrated that XR provides diagnostic and management capabilities that are hypothesized to complement or surpass ultrasound for over one-third of medical conditions that may arise during exploration spaceflight (i.e., diagnosis of injuries to the axial skeleton, teeth, and lungs as well as management of orthopedic reductions, endotracheal tube placement, and drain placement confirmation). In the setting of known inclusion of a handheld portable POCUS device, there remains significant added value of portable miniature XR. Whether or not this added clinical benefit is worth the mass, volume, and power requirements of the radiography system remains yet unknown and is the focus of future work. LEARNING OBJECTIVES: 1) Understand the value of ultrasound and radiography in the diagnosis and management of medical comorbidities that may arise in exploration spaceflight; 2) Understand the medical conditions of highest concern on exploration class missions for which miniature x-ray may provide added value to portable ultrasound.

Jon Steller↗

Spatially quasi-periodic bifurcations from periodic traveling water waves and a method for detecting bifurcations using signed singular values

We present a method of detecting bifurcations by locating zeros of a signed version of the smallest singular value of the Jacobian. This enables the use of quadratically convergent root-bracketing techniques or Chebyshev interpolation to locate bifurcation points. Only positive singular values have to be computed, though the method relies on the existence of an analytic or smooth singular value decomposition (SVD). The sign of the determinant of the Jacobian, computed as part of the bidiagonal reduction in the SVD algorithm, eliminates slope discontinuities at the zeros of the smallest singular value. We use the method to search for spatially quasi-periodic traveling water waves that bifurcate from large-amplitude periodic waves. The water wave equations are formulated in a conformal mapping framework to facilitate the computation of the quasi-periodic Dirichlet-Neumann operator. We find examples of pure gravity waves with zero surface tension and overhanging gravity-capillary waves. In both cases, the waves have two spatial quasi-periods whose ratio is irrational. We follow the secondary branches via numerical continuation beyond the realm of linearization about solutions on the primary branch to obtain traveling water waves that extend over the real line with no two crests or troughs of exactly the same shape. The pure gravity wave problem is of relevance to ocean waves, where capillary effects can be neglected. Such waves can only exist through secondary bifurcation as they do not persist to zero amplitude. The gravity-capillary wave problem demonstrates the effectiveness of using the signed smallest singular value as a test function for multi-parameter bifurcation problems. This test function becomes mesh independent once the mesh is fine enough.

97 MATHEMATICS AND COMPUTING↗

Estimating biotic integrity to capture existence value of freshwater ecosystems

The US Environmental Protection Agency (EPA) uses a water quality index (WQI) to estimate benefits of proposed Clean Water Act regulations. The WQI is relevant to human use value, such as recreation, but may not fully capture aspects of nonuse value, such as existence value. Here, we identify an index of biological integrity to supplement the WQI in a forthcoming national stated preference survey that seeks to capture existence value of streams and lakes more accurately within the conterminous United States (CONUS). We used literature and focus group research to evaluate aquatic indices regularly reported by the EPA’s National Aquatic Resource Surveys. We chose an index that quantifies loss in biodiversity as the observed-to-expected (O/E) ratio of taxonomic composition because focus group participants easily understood its meaning and the environmental changes that would result in incremental improvements. However, available datasets of this index do not provide the spatial coverage to account for how conditions near survey respondents affect their willingness to pay for its improvement. Therefore, we modeled and interpolated the values of this index from sampled sites to 1.1 million stream segments and 297,071 lakes across the CONUS to provide the required coverage. The models explained 13 to 36% of the variation in O/E scores and demonstrate how modeling can provide data at the required density for benefits estimation. We close by discussing future work to improve performance of the models and to link biological condition with water quality and habitat models that will allow us to forecast changes resulting from regulatory options.

59 BASIC BIOLOGICAL SCIENCES↗