I've been enjoying the discussion on integrating models and remote sensing,
and the message from Maurits van den Berg was particularly interesting to
me. While we are this topic, I would like to extend the discussion of the
last message to ask if anyone has good ideas on how to decide when to adjust
a model based on remotely sensed estimate.
Keeping with the example of LAI, there are really several options on how to
adjust the model (many already mentioned on the list - but to briefly
summarize):
1. Adjust some initial condition in the model so the LAI predictions from
the model is in better agreement with the remotely sensed estimates. As
noted in the last message, it is important to have some hypothesis as to why
the model is not in agreement so the appropriate condition is altered. For
example, if soil texture varies yet water holding capacity is not known for
every area, adjustment of related parameters could be appropriate.
2. Similarly, a model cultivar parameter could be adjusted. For example, in
the case several varieties of wheat are present and detailed calibration
data on each variety is not available.
3. Input LAI directly to the model (will likely require time-based
interpolation between RS observations).
A more complete review of various approaches is given by:
Moulin, S., A. Bondeau, and R. Delecolle. 1998. combining agricultural crop
models and satellite observations: from field to regional scales.
International Journal of Remote Sensing 19(6): 1021-1036.
However, Maurits raised an important point and that is remotely sensed (RS)
estimates are ESTIMATES and thus have a certain amount of error. In most of
the cases presented in the literature, the RS estimates are considered to be
"correct" and the model in error. One of the few studies I am aware of that
even considers this issue is:
Moulin, S. and M. Guerif. 1999. impacts of model parameter uncertainties on
crop reflectance estimates: a regional case study on wheat. International
Journal of Remote Sensing 20(1): 213-218.
So when considering "adjustment" of the model based on RS data, the
uncertainty in both estimates should be considered. Now I am finally
getting to my question. If we have two estimates of the same state variable
(in this example, LAI), how do we decide which is better?
I can think of a few ideas (but would like to hear more):
Monte Carlo Simulation, First Order Analysis, statistical prediction
intervals, and fuzzy number theory are all ways to get some estimate of the
uncertainty in both estimates (often harder in the case of the model
prediction), so we could either:
a. Not adjust the model if it is within the uncertainty limits of the RS
estimate,
b. If uncertainty estimates are available from both the model and RS data,
they could be used to arrive at a "combined" estimate by some weighted
average based on the uncertainty levels in each or use some ideas from fuzzy
number theory where "centroids" are used to change fuzzy numbers back to
crisp?
Often we resort to RS data because we do not know if the model is right or
wrong, thus may have no uncertainty estimate on the model prediction. I am
just starting to learn about "Bootstrap" statistics and it seems like a
similar concept could be used here? For example, in a simple case, if we
have an RS estimate at time t and t+1. Compare the model's prediction at
time t+1 with and without adjustment at time t. If the model agrees with
the RS estimate at time t+1 without adjustment, but disagrees with
adjustment, we may have cause to question our RS estimate at time t. I have
figured out away to formalize this idea or if it corresponds to an existing
statistical procedure - anyone have suggestions?
I am planning to pose this same question at the Biological Simulation Group
Meeting next week at MSU, but have had to readjust my presentation so I will
not be focusing on the details I had planned. So this list discussion is
timely for me.
There are a few papers available on some initial work we have done to use RS
data with CERES wheat available in PDF format from our web site at:
http://www.uswcl.ars.ag.gov/EPD/remsen/rspdfs.htm
I'd appreciate any feedback (including constructive criticism) on these
ideas.
Thanks,
Ed Barnes
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Edward M. Barnes, Ph.D.
Agricultural Engineer
USDA, ARS, US Water Conservation Laboratory
4331 E. Broadway Rd.
Phoenix, AZ 85040
Phone: 602-437-1702 x 268
Fax: 602-437-5291
email: [log in to unmask]
web: www.uswcl.ars.ag.gov
USWCL Remote Sensing Page: http://www.uswcl.ars.ag.gov/EPD/remsen/rsmiss.htm
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