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

Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005)

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Typical temporal scales in water-related modeling