Search NASA⌕ Search

SEARCH · Search NASA

Results for “climate change projections”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5

Inhomogeneous Forcing and Transient Climate Sensitivity

Understanding climate sensitivity is critical to projecting climate change in response to a given forcing scenario. Recent analyses have suggested that transient climate sensitivity is at the low end of the present model range taking into account the reduced warming rates during the past 10-15 years during which forcing has increased markedly. In contrast, comparisons of modelled feedback processes with observations indicate that the most realistic models have higher sensitivities. Here I analyse results from recent climate modelling intercomparison projects to demonstrate that transient climate sensitivity to historical aerosols and ozone is substantially greater than the transient climate sensitivity to CO2. This enhanced sensitivity is primarily caused by more of the forcing being located at Northern Hemisphere middle to high latitudes where it triggers more rapid land responses and stronger feedbacks. I find that accounting for this enhancement largely reconciles the two sets of results, and I conclude that the lowest end of the range of transient climate response to CO2 in present models and assessments (less than 1.3 C) is very unlikely.

sensitivity↗

Projecting Changes in the Frequency and Magnitude of Ozone Pollution Events Under Uncertain Climate Sensitivity

Abstract Climate change is projected to worsen ozone pollution over many populated regions, with larger impacts at higher concentrations. More intense and frequent ozone episodes risk setbacks to human health and environmental policy achievements. However, assessing these changes is complicated by uncertain climate sensitivity, closely related to climate model response, and internal variability in simulations projecting climate's influence on air quality. Here, leveraging a global modeling framework that one‐way couples a human activity model, an Earth system model of intermediate complexity, and an atmospheric chemistry model, we investigate the role of climate sensitivity in climate‐induced changes to high ozone pollution episodes in the United States using multiple greenhouse gas emissions scenarios, representations of climate sensitivity, and initial condition members. We bias correct and evaluate historical model simulations, identifying modeled and observed O 3 episodes using extreme value theory, and extend the approach to projections of mid‐ and end‐century climate impacts. Results show that the influence of climate sensitivity can be as significant as that of greenhouse gas emissions scenario absent precursor emissions changes. Climate change is projected to increase the magnitude of the highest annually occurring O 3 concentrations by over 2.3 ppb on average across the U.S. at mid‐century under a high climate sensitivity and moderate emissions scenario, but the increase is limited to less than 0.3 ppb under lower climate sensitivity. Further, we show that areas in the U.S. currently meeting air quality standards risk being pushed into non‐compliance due to a climate‐induced increase in frequency of high ozone days.

Environmental Sciences & Ecology↗

2016 International Land Model Benchmarking (ILAMB) Workshop Report

As earth system models (ESMs) become increasingly complex, there is a growing need for comprehensive and multi-faceted evaluation of model projections. To advance understanding of terrestrial biogeochemical processes and their interactions with hydrology and climate under conditions of increasing atmospheric carbon dioxide, new analysis methods are required that use observations to constrain model predictions, inform model development, and identify needed measurements and field experiments. Better representations of biogeochemistryclimate feedbacks and ecosystem processes in these models are essential for reducing the acknowledged substantial uncertainties in 21st century climate change projections.

earth system models (ESMs)↗

The climate change mitigation potential of annual grasslands under future climates

Abstract Composted manure and green waste amendments have been shown to increase net carbon (C) sequestration in rangeland soils and have been proposed as a means to help lower atmospheric CO 2 concentrations. However, the effect of climate change on soil organic C (SOC) stocks and greenhouse gas emissions in rangelands is not well understood, and the viability of climate change mitigation strategies under future conditions is even less certain. We used a process‐based biogeochemical model (DayCent) at a daily time step to explore the long‐term effects of potential future climate changes on C and greenhouse gas dynamics in annual grassland ecosystems. We then used the model to explore how the same ecosystems might respond to climate change following compost amendments to soils and determined the long‐term viability of net SOC sequestration under changing climates. We simulated net primary productivity (NPP), SOC, and greenhouse gas fluxes across seven California annual grasslands with and without compost amendments. We drove the DayCent simulations with field data and with site‐specific daily climate data from two Earth system models (CanESM2 and HadGEM‐ES) and two representative concentration pathways (RCP4.5 and RCP8.5) through 2100. NPP and SOC stocks in unamended and amended ecosystems were surprisingly insensitive to projected climate changes. A one‐time amendment of compost to rangeland acted as a slow‐release organic fertilizer and increased NPP by up to 390–814 kg C ha −1 year −1 across sites. The amendment effect on NPP was not sensitive to Earth system model or emissions scenario and endured through the end of the century. Net SOC sequestration amounted to 1.96 ± 0.02 Mg C ha −1 relative to unamended soils at the maximum amendment effect. Averaged across sites and scenarios, SOC sequestration peaked 22 ± 1 years after amendment and declined but remained positive throughout the century. Though compost stimulated nitrous oxide (N 2 O) emissions, the cumulative net emissions (in CO 2 equivalents) due to compost were far less than the amount of SOC sequestered. Compost amendments resulted in a net climate benefit of 69.6 ± 0.5 Tg CO 2 e 20 ± 1 years after amendment if applied to similar ecosystems across the state, amounting to 39% of California's rangeland. These results suggest that the biogeochemical benefits of a single amendment of compost to rangelands in California are insensitive to climate change and could contribute to decadal‐scale climate change mitigation goals alongside emissions reductions.

Mayer, Allegra↗

The Potential for Snow to Supply Human Water Demand in the Present and Future

Runoff from snowmelt is regarded as a vital water source for people and ecosystems throughout the Northern Hemisphere (NH). Numerous studies point to the threat global warming poses to the timing and magnitude of snow accumulation and melt. But analyses focused on snow supply do not show where changes to snowmelt runoff are likely to present the most pressing adaptation challenges, given sub-annual patterns of human water consumption and water availability from rainfall. We identify the NH basins where present spring and summer snowmelt has the greatest potential to supply the human water demand that would otherwise be unmet by instantaneous rainfall runoff. Using a multi-model ensemble of climate change projections, we find that these basins - which together have a present population of approx. 2 billion people - are exposed to a 67% risk of decreased snow supply this coming century. Further, in the multi-model mean, 68 basins (with a present population of more than 300 million people) transition from having sufficient rainfall runoff to meet all present human water demand to having insufficient rainfall runoff. However, internal climate variability creates irreducible uncertainty in the projected future trends in snow resource potential, with about 90% of snow-sensitive basins showing potential for either increases or decreases over the near-term decades. Our results emphasize the importance of snow for fulfilling human water demand in many NH basins, and highlight the need to account for the full range of internal climate variability in developing robust climate risk management decisions.

Mankin, Justin S.↗

Satellite imaging reveals increased proportion of population exposed to floods

Flooding affects more people than any other environmental hazard and hinders sustainable development. Investing in flood adaptation strategies may reduce the loss of life and livelihood caused by floods. Where and how floods occur and who is exposed are changing as a result of rapid urbanization4, flood mitigation infrastructure and increasing settlements in floodplains6. Previous estimates of the global flood-exposed population have been limited by a lack of observational data, relying instead on models, which have high uncertainty. Here we use daily satellite imagery at 250-metre resolution to estimate flood extent and population exposure for 913 large flood events from 2000 to 2018. We determine a total inundation area of 2.23 million square kilometres, with 255–290 million people directly affected by floods. We estimate that the total population in locations with satellite-observed inundation grew by 58–86 million from 2000 to 2015. This represents an increase of 20 to 24 per cent in the proportion of the global population exposed to floods, ten times higher than previous estimates. Climate change projections for 2030 indicate that the proportion of the population exposed to floods will increase further. The high spatial and temporal resolution of the satellite observations will improve our understanding of where floods are changing and how best to adapt. The global flood database generated from these observations will help to improve vulnerability assessments, the accuracy of global and local flood models, the efficacy of adaptation interventions and our understanding of the interactions between landcover change, climate and floods.

B.Tellman↗

Evaluation of native Earth system model output with ESMValTool v2.6.0

Earth system models (ESMs) are state-of-the-art climate models that allow numerical simulations of the past, present-day, and future climate. To extend our understanding of the Earth system and improve climate change projections, the complexity of ESMs heavily increased over the last decades. As a consequence, the amount and volume of data provided by ESMs has increased considerably. Innovative tools for a comprehensive model evaluation and analysis are required to assess the performance of these increasingly complex ESMs against observations or reanalyses. One of these tools is the Earth System Model Evaluation Tool (ESMValTool), a community diagnostic and performance metrics tool for the evaluation of ESMs. Input data for ESMValTool needs to be formatted according to the CMOR (Climate Model Output Rewriter) standard, a process that is usually referred to as “CMORization”. While this is a quasi-standard for large model intercomparison projects like the Coupled Model Intercomparison Project (CMIP), this complicates the application of ESMValTool to non-CMOR-compliant climate model output. In this paper, we describe an extension of ESMValTool introduced in v2.6.0 that allows seamless reading and processing of “native” climate model output, i.e., operational output produced by running the climate model through the standard workflow of the corresponding modeling institute. This is achieved by an extension of ESMValTool's preprocessing pipeline that performs a CMOR-like reformatting of the native model output during runtime. Thus, the rich collection of diagnostics provided by ESMValTool is now fully available for these models. For models that use unstructured grids, a further preprocessing step required to apply many common diagnostics is regridding to a regular latitude–longitude grid. Extensions to ESMValTool's regridding functions described here allow for more flexible interpolation schemes that can be used on unstructured grids. Currently, ESMValTool supports nearest-neighbor, bilinear, and first-order conservative regridding from unstructured grids to regular grids. Example applications of this new native model support are the evaluation of new model setups against predecessor versions, assessing of the performance of different simulations against observations, CMORization of native model data for contributions to model intercomparison projects, and monitoring of running climate model simulations. For the latter, new general-purpose diagnostics have been added to ESMValTool that are able to plot a wide range of variable types. Currently, five climate models are supported: CESM2 (experimental; at the moment, only surface variables are available), EC-Earth3, EMAC, ICON, and IPSL-CM6. As the framework for the CMOR-like reformatting of native model output described here is implemented in a general way, support for other climate models can be easily added.

58 GEOSCIENCES↗

Drivers of coupled climate model biases in representing Labrador Sea convection

Abstract This study investigates the representation of ocean convection in the Labrador Sea in seven Earth System Models (ESMs) from the Coupled Model Intercomparison Project Phase 5 and 6 datasets. The relative role of the oceanic and atmospheric biases in the subpolar North Atlantic gyre are explored using regional ocean simulations where the atmospheric forcing or the ocean initial and boundary conditions are replaced by reanalysis data in the absence of interactive air-sea coupling. Commonalities and differences among model behaviors are discussed with the objective of finding a pathway forward to improve the representation of the ocean mean state and variability in a region of fundamental importance for climate variability and change. Results highlight that an improved representation of ocean stratification in the North Atlantic subpolar gyre is urgently needed to constrain future climate change projections. While improving the ocean model resolution in the North Atlantic alone may contribute a better representation of both boundary currents and propagation of heat and freshwater anomalies into the Labrador Sea, it may not be sufficient. Addressing the atmospheric heat flux bias with better resolution in the atmosphere and land topography may allow for deep convection to occur in the Labrador Sea in some of the models that miss it entirely, but the greatest priority remains improving the representation of ocean stratification.

Liu, Guangpeng↗

Planting miscanthus instead of row crops may increase the productivity and economic performance of farmed potholes

Abstract Climate change projections indicate that precipitation events in the central United States are expected to become more intense, more frequent in the spring, and less frequent in the summer. Such a precipitation shift could adversely impact crop yields, especially in subfield areas known as farmed potholes, which are highly susceptible to flooding and ponding, and crop death is more likely to occur, particularly early in the growing season. This suggests that planting alternative crops, such as more flood tolerant perennials, in these areas may be a more profitable option. Using observations of crop growth and yield along with ponding depth of a specific field and farmed pothole in the central United States, we developed a spatially explicit version of the agroecosystem model Agro‐IBIS to estimate water depth and crop yield. After evaluating the model, we conducted a case study for a specific farmed pothole with a range of future precipitation scenarios with Agro‐IBIS to simulate the effects of contemporary (2002–2016) and future precipitation on a conventional corn/soybean ( Zea mays L. and Glycine max Merr.) rotation and an alternative perennial miscanthus ( Miscanthus × giganteus Greef et Deu.) cropping system. The depth and frequency of ponding increased under most future precipitation scenarios. The corn/soybean rotation had greater total loss (i.e., no yield) on average (>30%) for all scenarios in comparison to miscanthus (<10%). Under one future precipitation scenario with increased spring precipitation, both the corn/soybean rotation and miscanthus simulations showed an increase in yield. A simple budget analysis indicated that it is more profitable to plant miscanthus instead of corn or soybeans where yields in farmed potholes are consistently poor. Our findings show that potholes can be individually modeled, and their influence on yield can be quantified for use in future management decisions dictated by change in climate.

54 ENVIRONMENTAL SCIENCES↗

A Growing Freshwater Lens in the Arctic Ocean With Sustained Climate Warming Disrupts Marine Ecosystem Function

One of the most robust changes in the hydrological cycle predicted by Earth System Models (ESMs) during the remainder of 21st century is an increase in the difference between precipitation and evapotranspiration (P-E) in arctic and boreal regions. We explore the long-term consequences of this change for marine ecosystems in the Arctic Ocean using the Community Earth System Model forced with a business as usual scenario of future greenhouse gas concentrations. We find that by the year 2300 increases in freshwater delivery considerably reduce Arctic Ocean surface salinity, creating a freshwater lens that has far-reaching impacts on marine biogeochemistry. The expanding freshwater lens limits vertical nutrient supply into the euphotic zone by enhancing vertical stratification and accelerating surface lateral mixing with surface waters in the North Atlantic, which become increasingly nutrient depleted from weakening of the Atlantic Meridional Overturning Circulation (AMOC). The resulting increase in nutrient stress reduces marine export production in the Arctic Ocean by 53% in 2300 relative to the 1990s and triggers a shift in community composition with small phytoplankton replacing diatoms. At the same time, the seasonal timing of export production undergoes a 2-month forward shift, with the peak advancing from July to May. This suggests that the threat to food webs and higher trophic levels may intensify after the year 2100 as gains in productivity from sea ice loss saturate and freshwater impacts on nutrient stress continue to strengthen. Our analysis highlights the critical importance of changing terrestrial hydrology and land-ocean coupling as drivers of long-term biogeochemical change in the Arctic Ocean and the necessity of multi-century climate change projections.

54 ENVIRONMENTAL SCIENCES↗

Dual Impacts of Space Heating Electrification and Climate Change Increase Uncertainties in Peak Load Behavior and Grid Capacity Requirements in Texas

Around 60% of households in Texas currently rely on electricity for space heating. As decarbonization efforts increase, non‐electrified households could adopt electric heat pumps, significantly increasing peak (highest) electricity demand in winter. Simultaneously, anthropogenic climate change is expected to increase temperatures, the potential for summer heat waves, and associated electricity demand for cooling. Uncertainty regarding the timing and magnitude of these concurrent changes raises questions about how they will jointly affect the seasonality of peak demand, firm capacity requirements, and grid reliability. This study investigates the net effects of residential space heating electrification and climate change on long‐term demand patterns and load shedding potential, using climate change projections, a predictive load model, and a direct current optimal power flow (DCOPF) model of the Texas grid. Results show that full electrification of residential space heating by replacing existing fossil fuel use with higher efficiency heat pumps could significantly improve reliability under hotter futures. Less efficient heat pumps may result in more severe winter peaking events and increased reliability risks. As heating electrification intensifies, system planners will need to balance the potential for greater resource adequacy risk caused by shifts in seasonal peaking behavior alongside the benefits (improved efficiency and reductions in emissions).

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Ubiquity and Causes of Soil Water Preferential Flow Across 17 Ecoregions

Abstract Preferential flow (PF) in soil causes the rapid transport of water, nutrients, and contaminants into the subsurface, influencing groundwater recharge and streamflow. Data scarcity has hindered the quantification of PF occurrence and the identification of its drivers across diverse ecoregions. We address this gap by analyzing high‐frequency, multi‐depth soil moisture data across 17 ecoregions in the USA, using ∼1,500 sensors at 40 sites. We discovered that PF is widespread, with sites experiencing PF in up to 60% of rainfall events ≥2 mm. Multiple approaches consistently show that PF is more likely to occur with increased peak rainfall intensity, finer textured material, low soil moisture variability, humid climate, and higher net primary productivity. This suggests that PF patterns could shift with projected climate changes, increasing uncertainty in predictions of groundwater recharge, water quality, and streamflow generation. Plain Language Summary Water can bypass part of the soil's matrix through a process called preferential flow (PF). This quick transport of water through the soil brings with it nutrients and contaminants and eventually makes it to groundwater and streams. To ensure ample amounts of good quality groundwater and surface water we need to understand when and where PF occurs. We inferred when PF occurred at 40 different sites across 17 ecoregions in the USA using soil moisture and rainfall data. We found that PF happened at all sites and in up to 60% of rainfall events ≥2 mm. Preferential flow was most likely at sites with high rainfall intensities, high clay content in soils, low variability in soil moisture, and high vegetation productivity. As rainfall intensities are predicted to increase due to climate change and vegetation becomes more productive, PF occurrence becomes more important for predicting groundwater recharge, water quality, and streamflow generation. Key Points Preferential flow (PF) is ubiquitous across the USA and occurs in up to 60% of all rainfall events ≥2 mm Rainfall intensity, soil texture, and antecedent soil moisture emerge as critical in generating PF across diverse ecoregions Two different PF detection approaches show similar relationships between key drivers and occurrence of PF

Li, Bonan↗

Nutrients cause consolidation of soil carbon flux to small proportion of bacterial community

Nutrient amendment diminished bacterial functional diversity, consolidating carbon flow through fewer bacterial taxa. Here, we show strong differences in the bacterial taxa responsible for respiration from four ecosystems, indicating the potential for taxon-specific control over soil carbon cycling. Trends in functional diversity, defined as the richness of bacteria contributing to carbon flux and their equitability of carbon use, paralleled trends in taxonomic diversity although functional diversity was lower overall. Among genera common to all ecosystems, Bradyrhizobium, the Acidobacteria genus RB41, and Streptomyces together composed 45–57% of carbon flow through bacterial productivity and respiration. Bacteria that utilized the most carbon amendment (glucose) were also those that utilized the most native soil carbon, suggesting that the behavior of key soil taxa may influence carbon balance. Mapping carbon flow through different microbial taxa as demonstrated here is crucial in developing taxon-sensitive soil carbon models that may reduce the uncertainty in climate change projections.

59 BASIC BIOLOGICAL SCIENCES↗

Wildfire management decisions outweigh mechanical treatment as the keystone to forest landscape adaptation

Modern land management faces unprecedented uncertainty regarding future climates, novel disturbance regimes, and unanticipated ecological feedbacks. Mitigating this uncertainty requires a cohesive landscape management strategy that utilizes multiple methods to optimize benefits while hedging risks amidst uncertain futures. We used a process-based landscape simulation model (LANDIS-II) to forecast forest management, growth, climate effects, and future wildfire dynamics, and we distilled results using a decision support tool allowing us to examine tradeoffs between alternative management strategies. We developed plausible future management scenarios based on factorial combinations of restoration-oriented thinning prescriptions, prescribed fire, and wildland fire use. Results were assessed continuously for a 100-year simulation period, which provided a unique assessment of tradeoffs and benefits among seven primary topics representing social, ecological, and economic aspects of resilience. Projected climatic changes had a substantial impact on modeled wildfire activity. In the Wildfire Only scenario (no treatments, but including active wildfire and climate change), we observed an upwards inflection point in area burned around mid-century (2060) that had detrimental impacts on total landscape carbon storage. While simulated mechanical treatments (~ 3% area per year) reduced the incidence of high-severity fire, it did not eliminate this inflection completely. Scenarios involving wildland fire use resulted in greater reductions in high-severity fire and a more linear trend in cumulative area burned. Mechanical treatments were beneficial for subtopics under the economic topic given their positive financial return on investment, while wildland fire use scenarios were better for ecological subtopics, primarily due to a greater reduction in high-severity fire. Benefits among the social subtopics were mixed, reflecting the inevitability of tradeoffs in landscapes that we rely on for diverse and countervailing ecosystem services. This study provides evidence that optimal future scenarios will involve a mix of active and passive management strategies, allowing different management tactics to coexist within and among ownerships classes. Our results also emphasize the importance of wildfire management decisions as central to building more robust and resilient future landscapes.

54 ENVIRONMENTAL SCIENCES↗

Data from: “Significant stream chemistry response to temperature variations in a high-elevation mountain watershed”

High-elevation mountain regions, central to global freshwater supply, are experiencing more rapid warming than low-elevation locations. High-elevation streams are therefore potentially critical indicators for earth system and water chemistry response to warming. Here we present concerted hydroclimatic and biogeochemical data from Coal Creek, Colorado in the central Rocky Mountains at elevations of 2700 to 3700 m, where air temperatures have increased by about 2 °C since 1980. We analyzed water chemistry every other day from 2016 to 2019. Water chemistry data indicate distinct responses of different solutes to inter-annual hydroclimatic variations. Specifically, the concentrations of solutes from rock weathering are stable inter-annually. Solutes that are active in soils, including dissolved organic carbon, vary dramatically, with double to triple peak concentrations occurring during snowmelt and in warm years. We advocate for consistent and persistent monitoring of high elevation streams to record early glimpse of earth surface response to warming.1) Coal Creek stream were sampled and measured to answer the question if there is a significant stream chemistry response to climate change in high-elevation watershed2) The file contains data regarding discharge, water temperature and stream chemistry data for 2016-2019 year. Stream chemistry includes dissolved organic and inorganic carbon, chloride, nutrients, cations. The data collection efforts were carried out by the DOE-funded "Advancing a Watershed Hydro-Biogeochemical Theory: Linking Water Travel Time and Reaction Rates Under Changing Climate" project and Watershed Function SFA.

54 ENVIRONMENTAL SCIENCES↗

Soil fertility and drought interact to determine large variations in wood production for a hyperdominant Amazonian tree species

The productivity of the Amazon Rainforest is related to climate and soil fertility. However, the degrees to which these interactions influence multiannual to decadal variations in tree diameter growth are still poorly explored. To fill this gap, we used radiocarbon measurements to evaluate the variation in tree growth rates over the past decades in an important hyperdominant species, Eschweilera coriacea (Lecythidaceae), from six sites in the Brazilian Amazon that span a range of soil properties and climate. Using linear mixed-effects models, we show that temporal variations in mean annual diameter increment evaluated over a specific time period reflect interactions between soil fertility and the drought index (SPEI-Standardized Precipitation and Evapotranspiration Index). Our results indicate that the growth response of trees to drought is strongly dependent on soil conditions, a facet of forest productivity that is still underexplored, and which has great potential for improving predictions of future tropical tree growth in the face of projected climate change.

54 ENVIRONMENTAL SCIENCES↗

Driving terrestrial ecosystem models from space

Regional air pollution, land-use conversion, and projected climate change all affect ecosystem processes at large scales. Changes in vegetation cover and growth dynamics can impact the functioning of ecosystems, carbon fluxes, and climate. As a result, there is a need to assess and monitor vegetation structure and function comprehensively at regional to global scales. To provide a test of our present understanding of how ecosystems operate at large scales we can compare model predictions of CO2, O2, and methane exchange with the atmosphere against regional measurements of interannual variation in the atmospheric concentration of these gases. Recent advances in remote sensing of the Earth's surface are beginning to provide methods for estimating important ecosystem variables at large scales. Ecologists attempting to generalize across landscapes have made extensive use of models and remote sensing technology. The success of such ventures is dependent on merging insights and expertise from two distinct fields. Ecologists must provide the understanding of how well models emulate important biological variables and their interactions; experts in remote sensing must provide the biophysical interpretation of complex optical reflectance and radar backscatter data.

Waring, R. H.↗

Cloud Coverage Enhancement and Nocturnal Drizzle Suppression in Stratocumulus by Aerosols

Recent satellite observations of ship tracks surprisingly indicate that cloud water decreases with increasing droplet concentrations. However, we find by analyzing detailed simulations of stratocumulus that the reported trend is likely an artifact of sampling, only overcast clouds. The simulations instead show cloud coverage increasing with droplet concentrations, accounting for 25% of cloud albedo increase at moderate droplet concentrations. Our simulations also show that increases in cloud water from drizzle suppression (by increasing droplet concentrations) are favored only at night or at extremely low droplet concentrations, suggesting that the indirect aerosol forcing is overestimated in climate change projections by many general circulation models.

Ackerman, Andrew S.↗