Spatial Modelling and Scaling Issues - Environmental Modelling: Finding Simplicity in Complexity - page 73

inclusion of such land-surface parameters into models is
thereby hindered or precluded. Second, various satellite
instruments over past decades have been used to derive
land-surface properties, which provides an opportunity
to generate long-term regional and global changes in
land-surface properties. However, these datasets have
drawbacks in continuity because of the uncertainties
among the satellite instruments.
An ecosystem-dependent temporal interpolation tech-
nique is effective in filling the missed data caused by
cloud cover or seasonally snow cover. Temporal infor-
mation from satellite data are potentially applicable for
gap-filling purposes giving the high frequency of satellite
observations, such as twice a day from Terra and Aqua
MODIS observations (Justice et al., 2002), and every 30
minutes from geostationary satellites (Prins et al ., 1998).
In most cases, a pixel has adequate temporal coverage to
be able to perform simple splines to fill missing temporal
data in a meaningful way. If the temporal observations are
limited in persistent cloud cover, the statistics gathered
from pixels of the same ecosystem class within a limited
region surrounding the pixel is likely to have the requisite
temporal coverage (Moody et al ., 2005). By assuming that
the temporal behaviour of an ecosystem class is similar,
this approach impose the shapes of the temporal curves
in the same ecosystem onto the valid temporal data of
the pixel by computing an average offset between pixel
data and the behavioural curves. The missing temporal
data in a pixel can then be filled from the pixel's temporal
curve or from one of the regional curves, depending on
what curve is deemed to provide the best information.
In this way, temporally and spatially continuous data can
be developed in seasonal and diurnal variations (Moody
et al ., 2005; Zhang et al ., 2008).
A seasonal trajectory model is effective in temporal
interpolation of vegetation-related parameters in order to
fill the gaps in the inputs. Specifically, time-series analysis
algorithms (see also Chapter 3), such as sigmoidal model
or asymmetric Gaussian functions, can realistically model
seasonal variation in vegetation growth parameters, such
as leaf-area index and vegetation greenness (Zhang et al .,
2003; Jonsson and Eklundh, 2004). These algorithms are
capable of removing frequent cloud contaminations and
generating temporally continuous data at given spatial
resolutions.
Data-calibration algorithms are developed to reduce
the data from different sensors, such as AVHRR, MODIS
and VIIRS, to generate long-term environmental model
inputs. Sensor-specific characteristics may quantify the
parameters with biases or uncertainties. It is complex

and not immediately practical to calibrate theoretically
remotely sensed products derived from different sensors,
because the data processing should include the calibra-
tions of spectral response functions, solar zenith angles,
atmospheric effects, bidirectional reference distribution
functions, geometric registrations, vegetation index com-
positing techniques, and sensor differences. Alternatively,
continuity of parameters (such as greenness) that are
available across multiple sensors, can be facilitated by
using the cross-sensor translation equations that are avail-
able for this purpose (Steven et al ., 2003). The empirical
translation models allowed us to create long-term time
series of surface properties that are independent of spe-
cific sensors (e.g. Steven et al ., 2003; Gallo et al ., 2004;
Fensholt and Sandholt, 2005; Miura et al ., 2006).

5.5 Methodology for scaling physically
based models

5.5.1 Incompatibilitiesbetweenscales

A major source of error in environmental modelling
comes from the incompatibilities between model scale,
input parameter (database) scale and the intended scale
of model outputs. The common issue is that the param-
eters measured at one scale (or several different scales)
are input into a model built up at another scale. When
we build an environmental model, at least two groups of
measurements at the same or a similar scale are required.
One is used to establish amodel while another is employed
to test the model. When changing measurement scales,
the models based on these measurements may vary con-
siderably. For example, Campbell et al . (1999) found that
effective dispersion values estimated using data from each
type of probe are systematically different when using dif-
ferent devices to obtain solute-transport parameters for
modelling. This difference may be a scale issue result-
ing from the probe sampling volumes. Even if a model
operates linearly across the range of model-input val-
ues, the aggregation of the model-parameter values with
increased scale still biases model predictions because of
the effects of the heterogeneity. Both the model constants
and the relationship significance between dependent and
independent variables are usually controlled by scale of
processing the model. For example, when investigating
a linear model between elevation and biomass index
using different spatial resolution of parameters, Bian
(1997) found the constants in the model and the corre-
lation coefficient between independent variables and the