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Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005)
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Issues of Scale
Mark Grismer
Donald DeAngelis
Laurel Saito
Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005)
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Definitions
• scaleCharacteristic time or space used to define a process, observation, or model
- Bloschl and Sivalpan (1995)
Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005)
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Definitions
• scale problem
• scaling problem
To determine requirements for correct estimation of process of concern at any scale
- Beven and Fisher (1996)
Gathering set of concepts to enable models developed at one scale to be used in making predictions at another
Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005)
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Definitions
• microscale
hydrology: pore scale
atmospheric: smallest scale of atmospheric motions (<2 km)
Smallest scale at which a system can be considered a continuum
- Wallender and Grismer (2002)
Examples:
Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005)
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Definitions
• macroscale
• megascale
Larger than microscale but smaller than the scale of the entire system
- Wallender and Grismer (2002)
Larger than macroscale where spatial variations are ignored and system is described by gross averages
- Wallender and Grismer (2002)
Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005)
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Definitions
• outer scale
• inner scale
Whole spatial scale over which one models a particular phenomenon
- DeAngelis et al. (2004)
Minimum scale resolvable by measurement; assumption of homogeneity
- DeAngelis et al. (2004)
Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005)
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Definitions
• spatially implicit models
• spatially explicit models
Focus on small spatial domain where exact spatial locations do not need to be modeled
Model characteristics and processes with space as a variable
- DeAngelis et al. (2004)
Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005)
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Definitions
• distributed models
• lumped models
Parameters are modeled with continuous distribution through time and/or space
Group representation of parameters over time and/or space
Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005)
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Definitions
• aggregation
• disaggregation
Smaller scales are combined to create properties at larger scales
Larger scales are taken apart to create properties at smaller scales
Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005)
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Typical spatial scales in water-related modeling
Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005)
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Typical organismal scales in water-related modeling