1. Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005) 1 Issues of Scale Mark Grismer Donald DeAngelis Laurel Saito

2. Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005) 2 Definitions scale Characteristic time or space used to define a process, observation, or model - Bloschl and Sivalpan (1995)

3. Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005) 3 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

4. Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005) 4 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:

5. Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005) 5 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)

6. Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005) 6 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)

7. Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005) 7 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)

8. Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005) 8 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

9. Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005) 9 Definitions aggregation disaggregation Smaller scales are combined to create properties at larger scales Larger scales are taken apart to create properties at smaller scales

10. Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005) 10 Typical spatial scales in water- related modeling

11. Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005) 11 Typical organismal scales in water-related modeling

12. Interdisciplinary Modeling for Aquatic Ecosystems Curriculum Development Workshop (July 2005) 12 Typical temporal scales in water- related modeling