Within hierarchy theor y, a hiera rchically organized syst em can be visualize d as a
(three-tiered) nested system in which level s exhibi ting progressiv ely slower behavior
are at the top (leve l + 1), whi le those re flecti ng succes sively fast er behavi or are seen as
a lower level in the hiera rchy (level − 1). The level of inte rest is referr ed to as the focal
level (leve l 0) and it exists betw een the other tw o. From an ecological perspe ctive,
hierarchy theor y stat es that c omplex ecolog ical systems , such as lands capes, are
compo sed of loose ly couple d levels ( scale doma ins) which operat e wi thin a distinct
range of tem poral and spatial scale s. Intera ctions tend to be stronger and more
freque nt within a level than amon g level s, and scale threshold s separa te domai ns by
representi ng relativel y sharp trans itions or critical locations wher e shif ts occur in the
relative imp ortan ce of varia bles in fluencin g a proces s (Allen and Starr, 1982;
Meentemey er, 1989; W iens, 1989). These shifts then mani fest themselv es as changes
in spatia l patterns. This importan t respon se enables the perception and descripti on of
complex syst ems by decom posing them into their fundam ental parts and interpret ing
their interactions (Simon, 1962).
Building on these ideas , the hierarchic al patch dynam ics paradi gm (HPDP)
represents a n organi zational fram ework that attempt s to inte grate the vertical component s of hierarchy theory and the horiz ontal compo nents of patch dynamics theory
(PDT) to expres s the relat ionships among pattern, proces s, and scale expli citly within
the contex t of lands capes (Wu and Loucks, 1995). In the HPDP, the hiera rchica l
structure of a system is concept ualized as a “scaling ladder, ” wher e eac h rung
correspond s to a thres hold wi thin the scale continuum (Wu, 1999 ). Reference is made
to extra polating infor mation along a hiera rchic al scali ng ladder by varyi ng grain or
extent or both; howe ver, limited informat ion is provi ded on how to do so or wher e the
ladder or its rungs shoul d exist withi n the landscape or over what spati al resoluti on(s).
Conceptu ally, one woul d scale (i.e., trans fer infor mation) between dominant landscape p atches (i.e., inte rnally homog eneous image objects); however, de fining
meaningful patche s at different scales, the “correct ” met hod(s) for scaling between
them is not trivial (Hay et al., 1997; Hay and Marce au, 1998; Wu and Li, 2005) and
remains an acti ve body of resear ch in numer ous domai ns.
In more recen t HPDP w ork, Wu e t al. (20 03) d isc uss the conc ept of ecosystem
functiona l t ype s (EFTs) an d de scribe scaling between these entities. It is sugges te d tha t
EFTs pro vide a w ay of clu stering a l arge n umber of loc al ecosys te ms i n to a smalle r number
of catego rie s t ha t eac h h ave similar fu nctional prop erties i n t erms of biogeo chemica l
cycling (Reyn olds and W u, 199 9). Th us, EFTs e ffectively re presen t multisca le p atches
within the HPDP. One of the challenges of this approach is the necessity for detailed
information regarding biogeochemical cycling, which is seldom ubiquitously available.
In an effort to automate patch delineation from remote sensing imagery, new ideas
and methods are being developed and implemented by the GEOBIA (Geographic
Object-Based Image Analysis) community (Hay and Castilla, 2008; Dey et al., 2010;
Blaschke, 2010). Based on an integration of earlier definitions (Hay and Castilla,
2008; Hay and Blaschke, 2010), and the closing panel discussion of GEOBIA 2012,
3
GEOBIA may simply be described as “a sub-discipline of Geoinformatics devoted to
3 http://www.inpe.br/geobia2012/keynote.php.
144
VISUALIZING SCALE-DOMAIN MANIFOLDS
(three-tiered) nested system in which level s exhibi ting progressiv ely slower behavior
are at the top (leve l + 1), whi le those re flecti ng succes sively fast er behavi or are seen as
a lower level in the hiera rchy (level − 1). The level of inte rest is referr ed to as the focal
level (leve l 0) and it exists betw een the other tw o. From an ecological perspe ctive,
hierarchy theor y stat es that c omplex ecolog ical systems , such as lands capes, are
compo sed of loose ly couple d levels ( scale doma ins) which operat e wi thin a distinct
range of tem poral and spatial scale s. Intera ctions tend to be stronger and more
freque nt within a level than amon g level s, and scale threshold s separa te domai ns by
representi ng relativel y sharp trans itions or critical locations wher e shif ts occur in the
relative imp ortan ce of varia bles in fluencin g a proces s (Allen and Starr, 1982;
Meentemey er, 1989; W iens, 1989). These shifts then mani fest themselv es as changes
in spatia l patterns. This importan t respon se enables the perception and descripti on of
complex syst ems by decom posing them into their fundam ental parts and interpret ing
their interactions (Simon, 1962).
Building on these ideas , the hierarchic al patch dynam ics paradi gm (HPDP)
represents a n organi zational fram ework that attempt s to inte grate the vertical component s of hierarchy theory and the horiz ontal compo nents of patch dynamics theory
(PDT) to expres s the relat ionships among pattern, proces s, and scale expli citly within
the contex t of lands capes (Wu and Loucks, 1995). In the HPDP, the hiera rchica l
structure of a system is concept ualized as a “scaling ladder, ” wher e eac h rung
correspond s to a thres hold wi thin the scale continuum (Wu, 1999 ). Reference is made
to extra polating infor mation along a hiera rchic al scali ng ladder by varyi ng grain or
extent or both; howe ver, limited informat ion is provi ded on how to do so or wher e the
ladder or its rungs shoul d exist withi n the landscape or over what spati al resoluti on(s).
Conceptu ally, one woul d scale (i.e., trans fer infor mation) between dominant landscape p atches (i.e., inte rnally homog eneous image objects); however, de fining
meaningful patche s at different scales, the “correct ” met hod(s) for scaling between
them is not trivial (Hay et al., 1997; Hay and Marce au, 1998; Wu and Li, 2005) and
remains an acti ve body of resear ch in numer ous domai ns.
In more recen t HPDP w ork, Wu e t al. (20 03) d isc uss the conc ept of ecosystem
functiona l t ype s (EFTs) an d de scribe scaling between these entities. It is sugges te d tha t
EFTs pro vide a w ay of clu stering a l arge n umber of loc al ecosys te ms i n to a smalle r number
of catego rie s t ha t eac h h ave similar fu nctional prop erties i n t erms of biogeo chemica l
cycling (Reyn olds and W u, 199 9). Th us, EFTs e ffectively re presen t multisca le p atches
within the HPDP. One of the challenges of this approach is the necessity for detailed
information regarding biogeochemical cycling, which is seldom ubiquitously available.
In an effort to automate patch delineation from remote sensing imagery, new ideas
and methods are being developed and implemented by the GEOBIA (Geographic
Object-Based Image Analysis) community (Hay and Castilla, 2008; Dey et al., 2010;
Blaschke, 2010). Based on an integration of earlier definitions (Hay and Castilla,
2008; Hay and Blaschke, 2010), and the closing panel discussion of GEOBIA 2012,
3
GEOBIA may simply be described as “a sub-discipline of Geoinformatics devoted to
3 http://www.inpe.br/geobia2012/keynote.php.
144
VISUALIZING SCALE-DOMAIN MANIFOLDS