A data assimilation method for using low‐resolution Earth
observation data in heterogeneous ecosystems
T. C. Hill,1 T. Quaife,2 and M. Williams1
Received 29 October 2010; revised 4 February 2011; accepted 8 February 2011; published 29 April 2011.
[1] We present an approach for dealing with coarse‐resolution Earth observations (EO) in
terrestrial ecosystem data assimilation schemes. The use of coarse‐scale observations in
ecological data assimilation schemes is complicated by spatial heterogeneity and nonlinear
processes in natural ecosystems. If these complications are not appropriately dealt with,
then the data assimilation will produce biased results. The “disaggregation” approach that
we describe in this paper combines frequent coarse‐resolution observations with
temporally sparse fine‐resolution measurements. We demonstrate the approach using a
demonstration data set based on measurements of an Arctic ecosystem. In this example,
normalized difference vegetation index observations are assimilated into a “zero‐order”
model of leaf area index and carbon uptake. The disaggregation approach conserves key
ecosystem characteristics regardless of the observation resolution and estimates the carbon
uptake to within 1% of the demonstration data set “truth.” Assimilating the same data in
the normal manner, but without the disaggregation approach, results in carbon uptake
being underestimated by 58% at an observation resolution of 250 m. The disaggregation
method allows the combination of multiresolution EO and improves in spatial resolution if
observations are located on a grid that shifts from one observation time to the next.
Additionally, the approach is not tied to a particular data assimilation scheme, model, or
EO product and can cope with complex observation distributions, as it makes no implicit
assumptions of normality.
Citation: Hill, T. C., T. Quaife, and M. Williams (2011), A data assimilation method for using low‐resolution Earth observation
data in heterogeneous ecosystems, J. Geophys. Res., 116, D08117, doi:10.1029/2010JD015268.
1. Introduction
[2] Understanding the spatial and temporal variability of
terrestrial ecosystem states and processes remains an
important challenge. Complexity in the Earth system derives
in large part from the interactions between ecological and
environmental processes over a range of temporal and spa-
tial scales. Naturally occurring ecosystems systems often
tend to vary continuously rather than discretely [Fletcher et
al., 2009] and the length scales for these variations do not
necessarily match the scales of observation. Furthermore,
because interactions are nonlinear in many biophysical
systems [Jarvis, 1995], the use of mean states can lead to
large biases in expected ecosystem response [Chen et al.,
2007; Kimball et al., 1999]. Chen et al. [2007] showed
differences of up to 25% (5% to 15% average) in simula-
tions of Canada’s surface carbon fluxes based on averaged
remotely sensed parameter versus “fine scale” (1 km2)
parameters. Stoy et al. [2009] showed that by spatially
averaging ecosystem properties, rather than preserving a
probability density function (PDF), the resulting biases will
change the predicted response from a moderate sink of
carbon into a source of equal magnitude.
[3] Thus our current understanding of ecosystem
dynamics and land‐atmosphere interactions is at least par-
tially limited by data availability and resolution. This is
largely because critical processes operate on a range of
spatial and temporal scales [Jarvis, 1995]. Land surfaces
tend to be highly heterogeneous and so direct measurements
frequently undersample, or average out, the variability.
Additionally, biophysical interactions are nonlinear and
require complex monitoring. Satellite observations can help
address many of these issues, but have temporal/spatial
resolution trade‐offs. Inherently, satellites with global cov-
erage have either, fine spatial resolution observations and a
lower return frequency (e.g., Landsat and IKONOS); or
frequent observations and a coarse spatial resolution (e.g.,
MODIS and AVHRR). It should also be noted that, satellite
derived reflectance does not scale linearly with many of the
ecosystem properties it is used to measure, for example, the
relationship between normalized difference vegetation index
(NDVI) and leaf area index (LAI) [Chen, 1999; van Wijk
1School of GeoSciences and NERC National Centre for Earth
Observation, University of Edinburgh, Edinburgh, UK.
2School of Geography and NERC National Centre for Earth
Observation, University of Exeter, Cornwall, UK.
Copyright 2011 by the American Geophysical Union.
0148‐0227/11/2010JD015268
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, D08117, doi:10.1029/2010JD015268, 2011
D08117 1 of 12

and Williams, 2005]. Therefore, we must properly account
for scaling issues if we are to make use of satellite observa-
tions and avoid introducing biases.
[4] Work has been done to combine plot studies with
multisatellite data, for example to extrapolate biomass esti-
mates over the Amazon basin at 1 km [Saatchi et al., 2007].
The technique combines the accurate measurements of the
plots with the spatial coverage of remote sensing to provide
a snap shot of biomass with uncertainty. However, the
approach presented by Saatchi et al. [2007] ignored infor-
mation formalized in process based ecosystem models. Both
Demarty et al. [2007] and Tang and Zhuang [2008] use data
assimilation to improve the simulation of spatially explicit
biosphere processes, though neither study deals with the
critical issue of biased data assimilation analyses due to
scaling problems.
[5] Data assimilation has been successfully used to com-
bine ecosystem models with time series satellite observa-
tions at particular sites [Quaife et al., 2008; Tang and
Zhuang, 2009; Zobitz et al., 2008]. However, a general-
ized approach for combining direct measurements and sat-
ellite observations with arbitrary spatial resolutions is still
missing [Raupach et al., 2005]. Tang and Zhuang [2008]
call for an integrated model‐data fusion scheme to reduce
the impact of “equifinality” in ill‐posed problems. Implicit
to the approach of reducing equifinality with multiple
orthogonal data, is the issue of scaling. Clearly, if the
effects of scaling outlined in multiple studies [Chen et al.,
2007; Chen, 1999; Kimball et al., 1999; Stoy et al., 2009] are
not accounted for, then using multiresolution observations in
non linear systems will lead to confused results, and will not
help address the equifinality of ill‐posed inversions.
[6] In this manuscript we present a new and flexible
approach to spatial data assimilation. We avoid the pro-
blems of scaling by combining coarse‐resolution EO with a
probability distribution function (PDF) which describes the
subpixel spatial heterogeneity. This PDF must capture the
natural heterogeneity at a sufficiently fine resolution to
preserve critical ecosystem states and processes. The coarse
EO is disaggregated so it maintains the high‐resolution
spatial information from the model state, the mean prop-
erties of the coarse observation and is combined with an
estimate of the observation’s PDF to create a new, fine‐
resolution observation. This new disaggregated observation
can then be assimilated normally, and thus can be applied
easily to most sequential data assimilation approaches. The
approach allows great flexibility in combining both high
and low, spatial and temporal resolution observations
within a data assimilation scheme to provide an unbiased
estimate of ecosystem states and processes. Using a dem-
onstration set of normalized difference vegetation index
(NDVI) observations we demonstrate the potential of this
approach to constrain estimates of carbon uptake over a
512 m by 512 m area. To do this we address a number of
questions: (1) To what degree does the standard data
assimilation of coarse observations introduce bias? (2) Does
the disaggregation approach perform better than the stan-
dard data assimilation? (3) How does the disaggregation
perform with more complex observations: First, with com-
binations of coarse spatial resolution (high frequency) and
fine spatial resolution (infrequent) observations? Second,
with observation aligned on a grid that moves between
observations times?
2. Methods
2.1. Sequential Data Assimilation and the Particle
Filter
[7] Sequential data assimilation approaches are particu-
larly useful in ecological applications, where they have been
successfully applied to both state and parameter estimation
[Quaife et al., 2008; Williams et al., 2005]. In common with
other data assimilation schemes, sequential filters and
smoothers are based on the application of Bayes [1763]
theory. However, unlike variational data assimilation
methods that rely on gradient descent algorithms for effi-
ciency, most sequential methods do not require a model
adjoint (the Extended Kalman Filter being a notable
exception to this), so the implementation of sequential
methods with an arbitrary ecosystem model is typically far
simpler. However, the relative merits of each approach are
often situation dependent and have been much discussed in
the literature [Raupach et al., 2005; Williams et al., 2009].
The approach that we describe in this paper is independent
of the specific data assimilation implementation chosen.
[8] In this study we implement a Monte Carlo Metropolis‐
Hastings sequential particle filter [Dowd, 2007]. This par-
ticle filter was chosen for its simple implementation and
numerical efficiency and ability to use a nonlinear model
operator. van Leeuwen [2009] provides a detailed review of
the different particle filtering approaches. The Ensemble
Kalman Filter (EnKF) [Evensen, 2003, 2009] is another
common sequential data assimilation approach used in
ecological studies. For the purposes of this study it is a
somewhat arbitrary choice between the two approaches, and
we would not expect using the EnKF to alter the conclusions
of this study. However, while the EnKF has been applied
with considerable success in a wide range of nonlinear
systems, it should be noted that the EnKF does not explicitly
allow for nonlinear model operators. The ability of the
particle filter to explicitly deal with nonlinear models and
arbitrary model operators is highly beneficial when con-
sidering the complex and nonlinear processes of terrestrial
ecosystems.
2.2. Disaggregation Approach
[9] Satellite observations with good spatial coverage and
regular sampling are an obvious data stream for use in
ecological data assimilation schemes. However, the spatial
resolution of temporally frequent satellite observations can
be coarse (e.g., MODIS has a resolution of 250 to 1000 m)
in comparison to the critical scales (on the order of meters)
of many terrestrial ecosystem processes [Spadavecchia
et al., 2008]. This disparity in scales creates problems for
data assimilation schemes. Stoy et al. [2009] showed that
merely preserving the mean state of an ecosystem parameter
was not sufficient to preserve an accurate representation of
the processes within an ecosystem model. Indeed to pre-
serve the response the mean, variance and skew need to be
preserved. The approach that we describe in this manuscript
provides a general framework for consistently combining
observations with a wide range of spatial and temporal
resolutions and extents, while preserving the PDF of the
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