282
Results of spatial models may be tested against
either field data (Costanza et al. 1990) or remotely
sensed data (Burke et al. 1991). Testing simulated
patterns against actual patterns is not a simple statistical procedure (Constanza et al. 1990), particularly since the spatial resolutions of simulated and
observed data often differ. Constanza et al. (1990)
apply goodness-of-fit tests to simulated results that
are aggregated to multiple resolutions. This approach not only allows one to assess how well the
spatial model performed at the simulated resolution, but also provides opportunities to test the most
appropriate scale of application for the model.
Extrapolating to the Regional
or Landscape Scale
Field Analysis
Many of the important questions associated with
biogeochemistry today involve extrapolating our
knowledge of biogeochemistry to landscape or regional scales (Walker 1994; Groffman and Wagenet
1994; Levin et al. 1997). For instance, we might
ask what the large-scale impacts of human activities
are on trace gas flux or soil C, or wish to know the
level of primary productivity associated with a
sociopolitical unit such as a county, state, or
geographic region. Such estimates are critical for
understanding the large-scale interactions of biogeochemical processes and atmospheric dynamics
(Matson et al. 1989; Schimel et al. 1988) and their
impacts on socioeconomic processes (Riebsame et
al. 1994).
In all cases, the best large-scale value is one that
is measured at the largest scale. Thus, gaseous exchange with the atmosphere is probably best estimated using either eddy correlation or eddy accumulation techniques (Chapter 11) or measurements
from aircraft (Matson and Harriss 1988) which
have footprints that correspond roughly to the landscape scale (hundreds of meters to kilometers).
Similarly, hydrologic fluxes of elements may be estimated at relatively large scales, through the watershed approach, which can be nested to estimate
efflux from small land areas to quite large regions
(e.g., Howarth et al. 1996).
For many of the variables with which we work,
however, such as net primary productivity and soil
Ingrid C. Burke
nutrient dynamics, it is not possible to directly estimate pools and fluxes at landscape to regional
scales. The actual processes are generally measured
in the field, at scales that correspond with < 1 to 10
m in plot size (e.g., see Chapters 2, 4, 5, and 7).
The key issues for landscape and regional studies
are the processes by which we scale this information up to larger scales, or extrapolate, and by
which we estimate the error of our estimates.
(I distinguish here between extrapolation, or using
small-scale measurements to assess large-scale
fluxes and pools, and interpolation, the process of
estimating values for places that were not
measured.)
If stratified sampling has taken place, as described above, and an average value is available for
each landscape or regional unit (e.g., soil type,
land-use type, vegetation type), these averages can
be aggregated based upon the known area of each
unit and a weighted sum:
n
~ Pi * Ai = Poolsize
i=1
(18.1)
where Pi is the pool per unit area within landscape
unit i, and Ai is the area of landscape unit i. If it is
a flux that is being estimated, the value must be
extrapolated to the appropriate time interval, then
scaled as above. Land area of the units may be provided from remotely sensed or other digital data.
The approach has been used to a large extent by
scientists studying trace gas flux (e.g., Robertson
and Rosswall1986; Matthews and Fung 1987; Reiners et al. 1989; reviewed by Matson et al. 1989;
Groffman et al. 1992), and by those studying smallscale soil nutrient variation associated with individual plants (e.g., Vinton and Burke 1995; Robles and
Burke 1997). The method of extrapolation is logical
and closely tied to the most common type of field
sampling, as described above. However, it is riddled with sources of error that ecologists have not
yet been successful at quantifying in an aggregate
sense (O'Neill et al. 1979; Jeffers 1988; Rastetter
et al. 1992). There is a significant literature on estimating error for scaling up temporal data (see Jeffers 1988), and for estimating error associated with
maps (e.g., A in Equation 18.1) (Maling 1989).
However, many of these errors must be aggregated
for the extrapolated value, and we do not at this
time have a simple set of equations for estimating
Results of spatial models may be tested against
either field data (Costanza et al. 1990) or remotely
sensed data (Burke et al. 1991). Testing simulated
patterns against actual patterns is not a simple statistical procedure (Constanza et al. 1990), particularly since the spatial resolutions of simulated and
observed data often differ. Constanza et al. (1990)
apply goodness-of-fit tests to simulated results that
are aggregated to multiple resolutions. This approach not only allows one to assess how well the
spatial model performed at the simulated resolution, but also provides opportunities to test the most
appropriate scale of application for the model.
Extrapolating to the Regional
or Landscape Scale
Field Analysis
Many of the important questions associated with
biogeochemistry today involve extrapolating our
knowledge of biogeochemistry to landscape or regional scales (Walker 1994; Groffman and Wagenet
1994; Levin et al. 1997). For instance, we might
ask what the large-scale impacts of human activities
are on trace gas flux or soil C, or wish to know the
level of primary productivity associated with a
sociopolitical unit such as a county, state, or
geographic region. Such estimates are critical for
understanding the large-scale interactions of biogeochemical processes and atmospheric dynamics
(Matson et al. 1989; Schimel et al. 1988) and their
impacts on socioeconomic processes (Riebsame et
al. 1994).
In all cases, the best large-scale value is one that
is measured at the largest scale. Thus, gaseous exchange with the atmosphere is probably best estimated using either eddy correlation or eddy accumulation techniques (Chapter 11) or measurements
from aircraft (Matson and Harriss 1988) which
have footprints that correspond roughly to the landscape scale (hundreds of meters to kilometers).
Similarly, hydrologic fluxes of elements may be estimated at relatively large scales, through the watershed approach, which can be nested to estimate
efflux from small land areas to quite large regions
(e.g., Howarth et al. 1996).
For many of the variables with which we work,
however, such as net primary productivity and soil
Ingrid C. Burke
nutrient dynamics, it is not possible to directly estimate pools and fluxes at landscape to regional
scales. The actual processes are generally measured
in the field, at scales that correspond with < 1 to 10
m in plot size (e.g., see Chapters 2, 4, 5, and 7).
The key issues for landscape and regional studies
are the processes by which we scale this information up to larger scales, or extrapolate, and by
which we estimate the error of our estimates.
(I distinguish here between extrapolation, or using
small-scale measurements to assess large-scale
fluxes and pools, and interpolation, the process of
estimating values for places that were not
measured.)
If stratified sampling has taken place, as described above, and an average value is available for
each landscape or regional unit (e.g., soil type,
land-use type, vegetation type), these averages can
be aggregated based upon the known area of each
unit and a weighted sum:
n
~ Pi * Ai = Poolsize
i=1
(18.1)
where Pi is the pool per unit area within landscape
unit i, and Ai is the area of landscape unit i. If it is
a flux that is being estimated, the value must be
extrapolated to the appropriate time interval, then
scaled as above. Land area of the units may be provided from remotely sensed or other digital data.
The approach has been used to a large extent by
scientists studying trace gas flux (e.g., Robertson
and Rosswall1986; Matthews and Fung 1987; Reiners et al. 1989; reviewed by Matson et al. 1989;
Groffman et al. 1992), and by those studying smallscale soil nutrient variation associated with individual plants (e.g., Vinton and Burke 1995; Robles and
Burke 1997). The method of extrapolation is logical
and closely tied to the most common type of field
sampling, as described above. However, it is riddled with sources of error that ecologists have not
yet been successful at quantifying in an aggregate
sense (O'Neill et al. 1979; Jeffers 1988; Rastetter
et al. 1992). There is a significant literature on estimating error for scaling up temporal data (see Jeffers 1988), and for estimating error associated with
maps (e.g., A in Equation 18.1) (Maling 1989).
However, many of these errors must be aggregated
for the extrapolated value, and we do not at this
time have a simple set of equations for estimating