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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6

Helicopter rotor wake geometry and its influence in forward flight. Volume 1: Generalized wake geometry and wake effect on rotor airloads and performance

An analytic investigation to generalize wake geometry of a helicopter rotor in steady level forward flight and to demonstrate the influence of wake deformation in the prediction of rotor airloads and performance is described. Volume 1 presents a first level generalized wake model based on theoretically predicted tip vortex geometries for a selected representative blade design. The tip vortex distortions are generalized in equation form as displacements from the classical undistorted tip vortex geometry in terms of vortex age, blade azimuth, rotor advance ratio, thrust coefficient, and number of blades. These equations were programmed to provide distorted wake coordinates at very low cost for use in rotor airflow and airloads prediction analyses. The sensitivity of predicted rotor airloads, performance, and blade bending moments to the modeling of the tip vortex distortion are demonstrated for low to moderately high advance ratios for a representative rotor and the H-34 rotor. Comparisons with H-34 rotor test data demonstrate the effects of the classical, predicted distorted, and the newly developed generalized wake models on airloads and blade bending moments. Use of distorted wake models results in the occurrence of numerous blade-vortex interactions on the forward and lateral sides of the rotor disk. The significance of these interactions is related to the number and degree of proximity to the blades of the tip vortices. The correlation obtained with the distorted wake models (generalized and predicted) is encouraging.

Egolf, T. A.↗

Dynamic Distribution System Restoration Strategy for Resilience Enhancement: Preprint

In electric power distribution systems, distributed energy re-sources (DERs) can act as controllable power sources and support utility operators to minimize power outages after ex-treme weather events (e.g., hurricane, earthquake, wildfire) and thus help enhance the grid's resilience. Meanwhile, the influ-ences of extreme events and the capabilities of DERs are dy-namic and difficult to predict. Hence, the desired distribution system restoration strategy should be able to evolve according to real-time fault/disturbance information and the availabil-ity of DERs. In this paper, we propose a new dynamic distribu-tion system restoration strategy to enhance system resilience against potential hazards. An efficient reconfiguration algo-rithm is developed to eliminate the use of integer variables to relieve the computational burden. Model predictive control is implemented to adjust the system topology and DER opera-tion setpoints based on the updated fault information and DER forecasts. The effectiveness of the proposed restoration model in enhancing distribution system resilience is validated through an IEEE 123-bus test system. Simulation results also validate that the proposed restoration model can mitigate the occurrence of unexpected events and the fluctuations of DERs.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Examples of Nonconservatism in the CARE 3 Program

This paper presents parameter regions in the CARE 3 (Computer-Aided Reliability Estimation version 3) computer program where the program overestimates the reliability of a modeled system without warning the user. Five simple models of fault-tolerant computer systems are analyzed; and, the parameter regions where reliability is overestimated are given. The source of the error in the reliability estimates for models which incorporate transient fault occurrences was not readily apparent. However, the source of much of the error for models with permanent and intermittent faults can be attributed to the choice of values for the run-time parameters of the program.

Dotson, Kelly J.↗

On the Importance of High Frequency Gravity Waves for Ice Nucleation in the Tropical Tropopause Layer

Recent investigations of the influence of atmospheric waves on ice nucleation in cirrus have identified a number of key processes and sensitivities: (1) ice concentrations produced by homogeneous freezing are strongly dependent on cooling rates, with gravity waves dominating upper tropospheric cooling rates; (2) rapid cooling driven by high-frequency waves are likely responsible for the rare occurrences of very high ice concentrations in cirrus; (3) sedimentation and entrainment tend to decrease ice concentrations as cirrus age; and (4) in some situations, changes in temperature tendency driven by high-frequency waves can quench ice nucleation events and limit ice concentrations. Here we use parcel-model simulations of ice nucleation driven by long-duration, constant-pressure balloon temperature time series, along with an extensive dataset of cold cirrus microphysical properties from the recent ATTREX high-altitude aircraft campaign, to statistically examine the importance of high-frequency waves as well as the consistency between our theoretical understanding of ice nucleation and observed ice concentrations. The parcel-model simulations indicate common occurrence of peak ice concentrations exceeding several hundred per liter. Sedimentation and entrainment would reduce ice concentrations as clouds age, but 1-D simulations using a wave parameterization (which underestimates rapid cooling events) still produce ice concentrations higher than indicated by observations. We find that quenching of nucleation events by high-frequency waves occurs infrequently and does not prevent occurrences of large ice concentrations in parcel simulations of homogeneous freezing. In fact, the high-frequency variability in the balloon temperature data is entirely responsible for production of these high ice concentrations in the simulations.

simulation↗

Shock dynamics of phase diagrams

A thermodynamic phase transition denotes a drastic change of state of a physical system due to a continuous change of thermodynamic variables, as for instance pressure and temperature. The classical van der Waals equation of state is the simplest model that predicts the occurrence of a critical point associated with the gas–liquid phase transition. Nevertheless, below the critical temperature theoretical predictions of the van der Waals theory significantly depart from the observed physical behaviour. We develop a novel approach to classical thermodynamics based on the solution of Maxwell relations for a generalised family of nonlocal entropy functions. This theory provides an exact mathematical description of discontinuities of the order parameter within the phase transition region, it explains the universal form of the equations of state and the occurrence of triple points in terms of the dynamics of nonlinear shock wave fronts. -- Highlights: •A new generalisation of van der Waals equation of state. •Description of phase transitions in terms of shock dynamics of state curves. •Proof of the universality of equations of state for a general class of models. •Interpretation of triple points as confluence of classical shock waves. •Correspondence table between thermodynamics and nonlinear conservation laws.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Impact of Global Warming on U.S. Summertime Mesoscale Convective Systems: A Simple Lagrangian Parcel Model Perspective

Abstract Mesoscale convective systems (MCSs) are the dominant rainfall producer over the United States during the warm season, causing natural disasters and severe weather every year. Global climate models have large uncertainty in projecting precipitation changes in the future climate. Here, a simple Lagrangian parcel model is used to investigate the impact of global warming on MCS initiation and growth. The single-column parcel model projects a mean precipitation decrease over the central United States and an increase to its east, in agreement with the CMIP5 model projection. It also highlights the crucial role of current climate mean-state model bias in exaggerating the change in future mean precipitation projection by 25%. As for convective population, the model captures the decreased occurrence frequency of weak to moderate convection and increased frequency of strong convection due to the increased CAPE and CIN, in agreement with convection-permitting regional simulations. Novel parameterizations of gust-front propagation speed and subsidence strength are developed as guided by cloud-resolving simulations. The multicolumn parcel model employing those parameterizations captures readily the cold pool–induced upscale growth feature. It simulates smaller mesoscale clusters over the central United States under global warming due to gust-front slowdown and subsidence strength enhancement, which are further attributed to land aridity–induced weakening of initial accumulated precipitation and strengthening of updraft speed, respectively. That said, mesoscale clusters could become bigger under more favorable conditions in future climate, including boundary layer moistening, convection lifetime lengthening, and cold pool mechanical-lifting enhancement, which require further investigations to improve mechanistic understanding of future MCS changes.

54 ENVIRONMENTAL SCIENCES↗

Projecting Large Fires in the Western US With an Interpretable and Accurate Hybrid Machine Learning Method

More frequent and widespread large fires are occurring in the western United States (US), yet reliable methods for predicting these fires, particularly with extended lead times and a high spatial resolution, remain challenging. In this study, we proposed an interpretable and accurate hybrid machine learning (ML) model, that explicitly represented the controls of fuel flammability, fuel availability, and human suppression effects on fires. The model demonstrated notable accuracy with a F 1 -score of 0.846 ± 0.012, surpassing process-driven fire danger indices and four commonly used ML models by up to 40% and 9%, respectively. More importantly, the ML model showed remarkably higher interpretability relative to other ML models. Specifically, by demystifying the “black box” of each ML model using the explainable AI techniques, we identified substantial structural differences across ML fire models, even among those with similar accuracy. The relationships between fires and their drivers, identified by our model, were aligned closer with established fire physical principles. The ML structural discrepancy led to diverse fire predictions and our model predictions exhibited greater consistency with actual fire occurrence. With the highly interpretable and accurate model, we revealed the strong compound effects from multiple climate variables related to evaporative demand, energy release component, temperature, and wind speed, on the dynamics of large fires and megafires in the western US. Our findings highlight the importance of assessing the structural integrity of models in addition to their accuracy. They also underscore the critical need to address the rise in compound climate extremes linked to large wildfires.

54 ENVIRONMENTAL SCIENCES↗

A Spatially Explicit Individual-Based Modeling Approach to Evaluate the Cumulative Effects of Wind Energy Development on the Greater Sage-Grouse: Sensitivity Analysis and Validation of Key Parameters

To address the need for an approach to evaluate cumulative ecological impacts of wind energy development, particularly those on critical wildlife habitats and species, the authors developed a proof-of-concept, landscape-based, spatially explicit individual-based modeling (IBM) framework for populations of the greater sage-grouse (Centrocercus urophasianus) in Albany County, Wyoming, based on published and other available information on the life history of the species. This sage-grouse IBM estimates the spatial and temporal movements of sage-grouse based on modeled effects of habitat characteristics and developments on sage-grouse condition, survivorship, and reproduction. After completing the initial version of the model, we conducted a series of sensitivity analyses of key model parameters and validation of lek occurrences and spatial distributions to better understand performance of the model relative to observed values of important life history characteristics. The parameter sensitivity analysis was conducted as a series of one-factor-at-a-time tests in which the values of selected parameters were individually varied to evaluate the corresponding effects on model output. We examined the model’s response to changes in parameter values to gain insight into the overall robustness of the model, identify key driver parameters, and initiate qualitative validation. Five functions selected for sensitivity analyses were (1) the rate of change in body condition in relationship to habitat suitability index (HSI) of occupied habitat (condition change rate), (2) the effect of competition between individuals with overlapping home ranges expressed as a percentage reduction in HSI (competition factor), (3) value of condition at which survivorship probability is equal to zero (zero survivorship condition), (4) the relationship between female body condition and clutch size, and (5) the relationship between female body condition and nest success. We varied the parameter values to be tested for the sensitivity analysis around the original value used in the model (i.e., tested values were higher and lower than the model’s original value) to examine the effect of this variation on the predicted output of the model. Model outputs evaluated in the sensitivity analysis included (1) predicted age-class distribution (as measured by the percentage of immature individuals within the population); (2) predicted sex ratio; (3) predicted age-sex class distribution (percent of population in each of six age-sex classes, i.e., male and female juveniles, yearlings, and adults); (4) lifespan; (5) population size; and (6) spatial distribution. Of the five parameters analyzed, condition change rate, survivorship, clutch size, and nest success did not substantially affect any of the evaluated model outputs. For the predicted age-class distribution, the percentage of immature individuals predicted by the model for these four parameters ranged from 61.9% to 65.0%, which was reasonable with respect to the reference values of 51.4 to 57.8% in published studies. The ratio of females to males ranged from 1.09 to 1.14, which was comparable to the reference values of 1.2 to 3.0 presented in an existing study. The predicted mean lifespan ranged from 1.62 to 1.74 years, which appears to be reasonable with respect to the reference values of 0.9 to 1.1 years for sharp-tail grouse and greater prairie chickens presented by published studies. The predicted population size ranged from 1,877 to 3,140. This prediction would be reasonable with respect to our estimate of 5,000 yearlings and adults, which was based on the USFWS estimate for the state of Wyoming scaled to the number of leks in the county. The predicted spatial distribution was not substantially affected by the parameter values examined. In our sensitivity analyses, the only tested parameter that had a noticeable effect on model output was competition factor. Over the range of values tested for this parameter, predicted population size exhibited the largest range (from 1,833 to 4,737) of all parameters tested. As the competition factor increased, the predicted population size decreased. This reflects the effect competition had on the number of individuals that could co occur in high-quality habitat patches. Despite this apparently significant effect, the range of values appears to be reasonable with respect to our estimate of 5,000 yearlings and adults, which was based on the USFWS estimate for the state of Wyoming scaled to the number of leks in the county.

17 WIND ENERGY↗

Data-Efficient Dimensionality Reduction and Surrogate Modeling of High-Dimensional Stress Fields

Tensor datatypes representing field variables like stress, displacement, velocity, etc., have increasingly become a common occurrence in data-driven modeling and analysis of simulations. Numerous methods [such as convolutional neural networks (CNNs)] exist to address the meta-modeling of field data from simulations. As the complexity of the simulation increases, so does the cost of acquisition, leading to limited data scenarios. Modeling of tensor datatypes under limited data scenarios remains a hindrance for engineering applications. Here, in this article, we introduce a direct image-to-image modeling framework of convolutional autoencoders enhanced by information bottleneck loss function to tackle the tensor data types with limited data. The information bottleneck method penalizes the nuisance information in the latent space while maximizing relevant information making it robust for limited data scenarios. The entire neural network framework is further combined with robust hyperparameter optimization. We perform numerical studies to compare the predictive performance of the proposed method with a dimensionality reduction-based surrogate modeling framework on a representative linear elastic ellipsoidal void problem with uniaxial loading. The data structure focuses on the low-data regime (fewer than 100 data points) and includes the parameterized geometry of the ellipsoidal void as the input and the predicted stress field as the output. The results of the numerical studies show that the information bottleneck approach yields improved overall accuracy and more precise prediction of the extremes of the stress field. Additionally, an in-depth analysis is carried out to elucidate the information compression behavior of the proposed framework.

artificial intelligence↗

The formation of compact groups of galaxies. I: Optical properties

The small crossing time of compact groups of galaxies (t(sub cr)H(sub 0) approximately less than 0.02) makes it hard to understand why they are observable at all. Our dissipationless N-body simulations show that within a single rich collapsing group compact groups of galaxies continually form. The mean lifetime of a particular compact configuration if approximately 1 Gyr. On this time scale, members may merge and/or other galaxies in the loose group may join the compact configuration. In other words, compact configurations are continually replaced by new systems. The frequency of this process explains the observability of compact groups. Our model produces compact configurations (compact groups (CG's) with optical properties remarkably similar to Hickson's (1982) compact groups (HCG's): (1) CG's have a frequency distribution of members similar to that of HCG's; (2) CG's are approximately equals 10 times as dense as loose groups; (3) CG's have dynamical properties remarkably similar to those of HCG's; (4) most of the galaxy members of CG's are not merger remnants. The crucial aspect of the model is the relationship between CG's and the surrounding rich loose group. Our model predicts the frequency of occurrence of CG's. A preliminary analysis of 18 rich loose groups is consistent with the model prediction. We suggest further observational tests of the model.

Diaferio, Antonaldo↗

Numerical Issues Associated with Compensating and Competing Processes in Climate Models: an Example from ECHAM-HAM

The purpose of this paper is to draw attention to the need for appropriate numerical techniques to represent process interactions in climate models. In two versions of the ECHAM-HAM model, different time integration methods are used to solve the sulfuric acid (H2SO4) gas evolution equation, which lead to substantially different results in the H2SO4 gas concentration and the aerosol nucleation rate. Using convergence tests and sensitivity simulations performed with various time stepping schemes, it is confirmed that numerical errors in the second model version are significantly smaller than those in version one. The use of sequential operator splitting in combination with long time step is identified as the main reason for the large systematic biases in the old model. The remaining errors in version two in the nucleation rate, related to the competition between condensation and nucleation, have a clear impact on the simulated concentration of cloud condensation nuclei in the lower troposphere. These errors can be significantly reduced by employing an implicit solver that handles production, condensation and nucleation at the same time. Lessons learned in this work underline the need for more caution when treating multi-time-scale problems involving compensating and competing processes, a common occurrence in current climate models.

climate↗

Estimation of polar stratospheric cloud infrared extinction climatology using visible satellite observations

Polar stratospheric clouds (PSC's) provide surfaces for heterogeneous processes which can dramatically alter the normal partitioning of odd nitrogen and chlorine families in the winter polar stratospheres, setting up conditions for significant ozone depletion as manifested in the springtime Antarctic ozone hole. The spatial and temporal distribution of PSC's is important for parameterizing PSC occurrence in multidimensional photochemical models whose use is essential for fully understanding observed Antarctic ozone losses as well as for accessing the possibility of a similar phemonenon occurring in the future in the Arctic. The Stratospheric Aerosol Measurement (SAM) 2 sensor, a single-channel (1mu m) photometer launched into a Sun-synchronous orbit aboard the Nimbus 7 satellite in October 1978, provided a unique database to establish the climatology of PSC's. Poole and Pitts (1994) used the record of high-latitude aerosol extinction obtained by SAM II from 1979-1989 to establish the climatology of PSC occurrences in the Arctic and Antarctic. Unfortunately, little information about PSC composition or type was detectable from the single-wavelength SAM II data.

Pitts, Michael C.↗

Textural remanence - A new model of lunar rock magnetism

In reexamining the accumulated magnetic data on lunar rocks, several common patterns of magnetic behavior are recognized. Their joint occurrence strongly suggests a new model of lunar rock magnetism, which is based on partial preferred textural alignment of the spontaneous moments of magnetic grains without requiring the existence of ancient lunar magnetic fields. This magnetic fabric, mimetic to locally oriented petrofabric, gives rise to an apparent 'textural remanent magnetization'. In order to account for the observed intensity of 'stable remanence' in lunar rocks, only a minute fraction (0.001 to 0.00001) of the single-domain iron grains present need be preferentially aligned. Several mechanisms operating on the lunar surface, including shock and diurnal thermal cycling, appear adequate for producing the required type and degree of magnetic alignment in all lunar rock classes. The model is supported by a wide variety of direct and indirect evidence, and its predictions (e.g., regarding anisotropic susceptibility and remanence acquisition) can be experimentally tested.

Brecher, A.↗

Modeling the behavioral substrates of associate learning and memory - Adaptive neural models

Three adaptive single-neuron models based on neural analogies of behavior modification episodes are proposed, which attempt to bridge the gap between psychology and neurophysiology. The proposed models capture the predictive nature of Pavlovian conditioning, which is essential to the theory of adaptive/learning systems. The models learn to anticipate the occurrence of a conditioned response before the presence of a reinforcing stimulus when training is complete. Furthermore, each model can find the most nonredundant and earliest predictor of reinforcement. The behavior of the models accounts for several aspects of basic animal learning phenomena in Pavlovian conditioning beyond previous related models. Computer simulations show how well the models fit empirical data from various animal learning paradigms.

Lee, Chuen-Chien↗

Kepler Planet Detection Metrics: Per-Target Detection Contours for Data Release 25

A necessary input to planet occurrence calculations is an accurate model for the pipeline completeness (Burke et al., 2015). This document describes the use of the Kepler planet occurrence rate products in order to calculate a per-target detection contour for the measured Data Release 25 (DR25) pipeline performance. A per-target detection contour measures for a given combination of orbital period, Porb, and planet radius, Rp, what fraction of transit signals are recoverable by the Kepler pipeline (Twicken et al., 2016; Jenkins et al., 2017). The steps for calculating a detection contour follow the procedure outlined in Burke et al. (2015), but have been updated to provide improved accuracy enabled by the substantially larger database of transit injection and recovery tests that were performed on the final version (i.e., SOC 9.3) of the Kepler pipeline (Christiansen, 2017; Burke Catanzarite, 2017a). In the following sections, we describe the main inputs to the per-target detection contour and provide a worked example of the python software released with this document (Kepler Planet Occurrence Rate Tools KeplerPORTs)1 that illustrates the generation of a detection contour in practice. As background material for this document and its nomenclature, we recommend the reader be familiar with the previous method of calculating a detection contour (Section 2 of Burke et al.,2015), input parameters relevant for describing the data quantity and quality of Kepler targets (Burke Catanzarite, 2017b), and the extensive new transit injection and recovery tests of the Kepler pipeline (Christiansen et al., 2016; Burke Catanzarite, 2017a; Christiansen, 2017).

Planet Detection Metrics↗

Assessing the cloud radiative bias at Macquarie Island in the ACCESS-AM2 model

Abstract. As a long-standing problem in climate models, large positive shortwave radiation biases exist at the surface over the Southern Ocean, impacting the accurate simulation of sea surface temperature, atmospheric circulation, and precipitation. Underestimations of low-level cloud fraction and liquid water content are suggested to predominantly contribute to these radiation biases. Most model evaluations for radiation focus on summer and rely on satellite products, which have their own limitations. In this work, we use surface-based observations at Macquarie Island to provide the first long-term, seasonal evaluation of both downwelling surface shortwave and longwave radiation in the Australian Community Climate and Earth System Simulator Atmosphere-only Model version 2 (ACCESS-AM2) over the Southern Ocean. The capacity of the Clouds and the Earth’s Radiant Energy System (CERES) product to simulate radiation is also investigated. We utilize the novel lidar simulator, the Automatic Lidar and Ceilometer Framework (ALCF), and all-sky cloud camera observations of cloud fraction to investigate how radiation biases are influenced by cloud properties. Overall, we find an overestimation of +9.5±33.5 W m−2 for downwelling surface shortwave radiation fluxes and an underestimation of -2.3±13.5 W m−2 for downwelling surface longwave radiation in ACCESS-AM2 in all-sky conditions, with more pronounced shortwave biases of +25.0±48.0 W m−2 occurring in summer. CERES presents an overestimation of +8.0±18.0 W m−2 for the shortwave and an underestimation of -12.1±12.2 W m−2 for the longwave in all-sky conditions. For the cloud radiative effect (CRE) biases, there is an overestimation of +4.8±28.0 W m−2 in ACCESS-AM2 and an underestimation of -7.9±20.9 W m−2 in CERES. An overestimation of downwelling surface shortwave radiation is associated with an underestimated cloud fraction and low-level cloud occurrence. We suggest that modeled cloud phase is also having an impact on the radiation biases. Our results show that the ACCESS-AM2 model and CERES product require further development to reduce these radiation biases not just in shortwave and in all-sky conditions, but also in longwave and in clear-sky conditions.

54 ENVIRONMENTAL SCIENCES↗

The Prevalence of Precipitation from Polar Supercooled Clouds

Supercooled clouds substantially impact polar surface energy budgets but large-scale models often underestimate their occurrence, which motivates accurately establishing metrics of basic processes. An analysis of long-term measurements at Utqiaġvik, Alaska, and McMurdo Station, Antarctica, combines lidar-validated use of soundings to identify supercooled cloud layers and colocated ground-based profiling radar measurements to quantify cloud base precipitation. We find that more than 85 % (75 %) of sampled supercooled layers are precipitating over the Arctic (Antarctic) site, with more than 75 % (50 %) precipitating continuously to the surface. Such high frequencies can be reconciled with substantially lesser spaceborne estimates by considering differences in radar hydrometeor detection sensitivity. While ice precipitation into supercooled clouds from aloft is common, we also find that the great majority of supercooled cloud layers without ice falling into them are themselves continuously generating precipitation. Such sustained primary ice formation is consistent with continuous activation of immersion-mode ice nucleating particles (INPs), suggesting that supercooled cloud formation is a principal gateway to ice formation at temperatures greater than ~ −38 °C over polar regions. The prevalence of weak precipitation fluxes is also consistent with supercooled cloud longevity, and with well-observed and widely simulated case studies. An analysis of colocated microwave radiometer retrievals suggests that weak precipitation fluxes can be nonetheless consequential to moisture budgets for supercooled clouds owing to small liquid water paths. Finally, we suggest that these ground-based precipitation rate statistics offer valuable guidance for improving the representation of polar cloud processes in large-scale models.

Polar clouds↗

Simulation of Avifauna Distributions Using Remote Sensing

Remote sensing has proved a fruitful tool for understanding the distribution and functioning of plant communities at multiple scales and to understand their coupling to bioclimatic and anthropogenic factors. But a similar approach to understanding the distribution and abundance of bird species as well as many other animal organisms is lacking. The increasing need for such understanding is evident with the recent examples of threats to human health via avian vector transmission and the increasing emphasis on global conservation biology. From experimental observations we know that species richness tends to track biological or environmental gradients. In this paper, we explore the fundamental idea that thermal and water-relation environments of birds, as estimated from satellite data and biophysical models, can define the constraints on their Occurrences and richness. We develop individual bird energy budget models and use these models to define the climate space niche of birds. Using satellite data assimilation products to drive our models, we disperse a distribution of virtual or actual bird species across the landscape in accordance to the limits expressed by their climate space niche. Here, we focus on the North American summer breeding season and give two examples to illustrate our approach. The first is a tundra loving bird, e.g. corresponding to the Culidris genus, and a second genus example, Myiurchus, that corresponds to arid or semi-arid regions. We define these birds in terms of their basic physiology and morphological characteristics, construct avian energetic simulations to predict their allowable metabolic ranges and climate space limits.

Smith, James A.↗