Tiffany Vance and Ronald Doel have traced the history of the Stommel diagram from physical oceanography into biology, in their 2010 paper Graphical Methods and Cold War Scientific Practice: The Stommel Diagram’s Intriguing Journey from the Physical to the Biological Environmental Sciences in Historical Studies in the Natural Sciences (DOI: 10.1525/hsns.2010.40.1.1.)

The paper provides an rich history of how the innovative oceanographer Henry Stommel created his diagrams to emphasize the cross-scale dynamics of the ocean (See figure below), and how his diagram was adapted by biological oceanographers. However, they miss how Stommel diagrrams moved into ecosystem ecology and sustainability science.

Below I present a series of Stommel diagrams.  The first three figures are reproduced in Vance and Doel’s paper, the later three are from sustainability science.

First, Stommel’s original figure, which was designed to show how oceanic processes varied across scales, and that sampling efforts had to be planned with a consideration of these.

Schematic diagram of the spectral distribution of sea level (From Stommel 1963. Varieties of Oceanographic Experience. Science)

The first appearance of the Stommel Diagram in a new discipline was in a 1978 book chapter in John Steele‘s influential edited book Spatial Pattern in Plankton Communities (Loren R. Haury, John A. McGowan, and Peter H. Wiebe, Patterns and Processes in the Time-Space Scales of Plankton Distribution, pages 277−327.).  They adopted Stommel’s method to show processes influencing biological productivity.

The marine biology version of 1978, by Haury et al. The graph retains the same form as the Stommel's, but now emphasizes factors in marine biology, with an emphasis on biological productivity, here labeled “biomass variability.

Vance and Doel then show how this figure was simplified and coloured to show sampling scales in a textbook.

The biological version of the Stommel Diagram used in teaching: The first known textbook version, produced in 2005, and one of the first originally done in color. In this version, the authors added relevant scales for the main sources of data (ships, moored stations, and satellites). Source:M. J. Kaiser, et al, 2005. Marine Ecology Processes, Systems and Impacts. Oxford University Press)

Stommel diagrams were adopted by sustainability scientist William Clark to illustrate the cross scale impacts of climate change in William C. Clark 1985 Scales of Climate Impacts. Climatic Change 7(1):5-27.

Scales of climatic phenomena. Characteristic time and length scales for selected events.

This type of approach was used in the influential book Sustainable Development of the Biosphere edited by Clark and RE Munn. It has after this carried on in ecological science, particularly through Buzz Holling’s focus on cross-scale pattern, for example in Cross-scale Morphology, geometry, and dynamics of ecosystems (Ecol. Mon. 62(4): 447-502).  Buzz Holling, Craig Allen and I used this approach to illustrate how biodiversity studies need to more fully consider scale in this figure from Peterson, Allen, and Holling’s Ecological Resilience, Biodiversity, and Scale (Ecosystems 1998 1(1): 6–18), which builds upon Clark’s 1985 figure and a figure from Holling’s 1992 paper.

Time and space scales of the boreal forest and their relationship to some of the processes that structure the forest. These processes include insect outbreaks, fire, atmospheric processes, and the rapid carbon dioxide increase in modern times. Contagious mesoscale disturbance processes provide a linkage between macroscale atmospheric processes and microscale landscape processes. Scales at which deer mouse, beaver, and moose choose food items, occupy a home range, and disperse to locate suitable home ranges vary with their body size.

Modified Stommel diagrams were used throughout the 2002 book Panarchy: Understanding Transformations in Systems of Humans and Nature, to illustrate the cross-scale dynamics of social ecological systems.   For example, in the chapter Why Systems of People and Nature are not just Social and Ecological Systems co-authors Frances Westley, Steve Carpenter, Buz Brock, Lance Gunderson, and Buzz Holling modified the Stommel diagram by replacing the spatial scale with the log of number people involved in an institution in order to illustrate a possible cross-scale structure of social processes.

Institutional hierarchy of rule sets. In contrast to ecological hierarchies, this one is structured along dimensions of the number of people involved in rule set and approximate turnover time.

Another recent ecological adaptation of the Stommel diagram is found in my 2008 paper, Agricultural modifications of hydrological flows create ecological surprises (doi:10.1016/j.tree.2007.11.011).  There Line Gordon, Elena Bennett and I simplified the spatial axis into a number of broad catagories to plot the time and space scales at which a number of different hydrologically mediated agricultural regime shifts operate.

Estimates of the spatial and temporal scales at which regime shifts operate. Blue indicates agriculture and aquatic systems, white indicates agriculture and soil, and green indicates agriculture and atmosphere regime shifts.