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The definitions below are from the US Global Change Research Program glossary unless otherwise noted.

Adaptation: Adjustment in natural or human systems to a new or changing environment that exploits beneficial opportunities or moderates negative effects. 

Climate change: Changes in average weather conditions that persist over multiple decades or longer. Climate change encompasses both increases and decreases in temperature, as well as shifts in precipitation, changing risk of certain types of severe weather events, and changes to other features of the climate system.

Greenhouse gases: Gases that absorb heat in the atmosphere near the Earth's surface, preventing it from escaping into space. If the atmospheric concentrations of these gases rise, the average temperature of the lower atmosphere will gradually increase, a phenomenon known as the greenhouse effect. Greenhouse gases include, for example, carbon dioxide, water vapor, and methane.

Mitigation: Measures to reduce the amount and speed of future climate change by reducing emissions of heat-trapping gases or removing carbon dioxide from the atmosphere.

Natural Infrastructure: Infrastructure that uses, restores, or emulates natural ecological processes and— (A) is created through the action of natural physical, geological, biological, and chemical processes over time; (B) is created by human design, engineering, and construction to emulate or act in concert with natural processes; or (C) involves the use of plants, soils, and other natural features, including through the creation, restoration, or preservation of vegetated areas using materials appropriate to the region to manage stormwater and runoff, to attenuate flooding and storm surges, and for other related purposes. (Source: Public Law 117-58, also known as Bipartisan Infrastructure Law)

Nature-based solutions: sustainable planning, design, environmental management and engineering practices that weave natural features or processes into the built environment to promote adaptation and resilience. (Source: FEMA)  (Often used synonymously with natural infrastructure.)

Resilience: A capability to anticipate, prepare for, respond to, and recover from significant multi-hazard threats with minimum damage to social well-being, the economy, and the environment. 

Resilience with respect to a project: a project with the ability to anticipate, prepare for, or adapt to conditions or withstand, respond to, or recover rapidly from disruptions, including the ability—
    (A)(i) to resist hazards or withstand impacts from weather events and natural disasters; or(ii) to reduce the magnitude or duration of impacts of a disruptive weather event or natural disaster on a project; and
    (B) to have the absorptive capacity, adaptive capacity, and recoverability to decrease project vulnerability to weather events or other natural disasters. 
(Source: Public Law 117-58, also known as Bipartisan Infrastructure Law)

For definitions of additional climate change related terms, please see the US Global Change Research Program glossary.