taken at a particular instant of time and at a particular location. This information should
be recorded as it can be used for post-stratification or for building models based on the
sample. It is almost certainly true that the sample will not be at the right spatial or
temporal scales when it is used for future studies, and this misalignment can be handled
using spatio-temporal statistical methodology (sometimes referred to as change-of-
support). Optimal sampling design has a large literature, but here it makes just as much
sense to use near-optimal designs that capture the various sources of variability.
Dynamical designs exploit the temporal statistical dependence of the variable under
study by choosing fewer sample locations per time period without sacrificing the size of
estimation variances (Wikle and Royle, 1999).
A common thread in sustainability assessment is the quantification of baselines.
Sustainability assessments are generally conducted by estimating trends expressed as
changes from baseline estimates. Data for estimating baselines from probability
sampling designs are preferable because they lend themselves to analysis using familiar
sampling theory. Spatially explicit baseline estimates may be necessary in which case
interpolation techniques may be used or sample data may be combined with spatially
explicit ancillary data such as satellite imagery. Of non-trivial importance, efficient
sampling designs for estimating baselines, for estimating trends and/or change, and for
calibrating models using ancillary data may differ considerably.
Regardless of how one defines sustainability, the fact that there is a time-
invariance component to it is generally accepted. Thus presence of (or lack of) changes
in a system over time scales of sufficient duration to avoid confounding with inherent and
natural short-term fluctuations are key barometers of sustainability (or lack thereof). For
example, because climate is defined over time scales of 30+ years, looking for evidence
of changes in climate requires data over much longer periods of time. The same is true
of many other key ecological processes or systems. Thus for data-based investigations
of sustainability, reliance on existing historical data is essential and will always be. This
creates challenges because measurement technology evolves faster than climate-paced
processes, usually in the direction of greater information content (more and extensive
measurements of higher quality), although not always as evidenced by policy- and
funding-induced cessation of data collection efforts.
The unavoidable reliance on data collected over relatively long periods of time (or
combining historical and current data) results in challenging problems of: 1) uncertainty
analysis (information from the past often has greater uncertainty than contemporary
data); 2) temporal data fusion (changes in measurement technology or protocol often
necessitates calibration of one data stream to another); and 3) sampling design (optimal
augmentation of existing sampling sites/technology with new sites/technology). These
problems will persist as long as measurement technology and protocol evolve at a faster
rate than the processes they are designed to measure.
2.3 Models for synthesizing data and forecasting
The word model has many different meanings to many people. For example,
statisticians often think of models as empirical models estimated based on observed
data. Mathematicians tend to think of models in terms of theoretical constructions, or
process models. In this document, one of our goals is to discuss how sustainability
science can be advanced by combining theoretical process models with observed data.
Two major advantages of this approach are that it allows for the predictions beyond the