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## Mathematical Modelling in Geography: II

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### Where do EO datasets fit into this ? Show how the data can be used, and what are the ... Monochrome (i.e. single wavelength in the microwave spectrum) ... – PowerPoint PPT presentation

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Title: Mathematical Modelling in Geography: II

1
Mathematical Modelling in Geography II
• GEOG2021
• Environmental Remote Sensing

2
EO data in Environmental Models
• Introduction to Extended Practical
• Hydrological model of a tropical wetland
• motivation
• constructing a model
• Why ? How ? What is it used for ?
• Where do EO datasets fit into this ?
• Show how the data can be used, and what are the
implications of the model

3
EO data in Environmental Models
• to gain experience in
• undertaking a (collaborative or individual)
integrated science research project
• computer-based environmental modelling and
methods of analysis
• presenting your findings in written and verbal
form

4
Bau Sau wetland Cat Tien National Park
Cat Tien
5
Landsat TM image (March 1992)
6
Hydrological Modelling
• Why develop a hydrological model ?
• understanding
• prediction
• management tool
• investigating scenarios
• (sensitivity analysis)

7
Components of a hydrological model
• What things might / should appear in such a
model ?
• Since we are interested in flows of water in a
system, then think in terms of-
• rainfall
• river / catchment flows
• efficiencies? (of flows from catchment) - why ??
• Floods

8
Data requirements
• Why do we need to bother with data ?
• model development
• model validation / verification
• and what sorts of data do we need ?
• met data (rainfall, evapotranspiration,...)
• hydrological data (flow rates, wetland areas,
flooded areas, catchment areas, run-off)

9
Why use EO data ?
• Can EO data help ?
• spatial coverage (and / or sampling) compared
with in-situ data collection
• temporal repeat
• And if so, how ?
• detecting and monitoring...
• And if so, what sort of EO data ?
• Optical, microwave, anything else,...
• What are the relative advantages and
disadvantages of different sorts of EO data ?

10
Model parameterisation
• How do we pose the model ?
• What are the model variables / parameters ?
• Are they measurables (and if not all, then
which ones, and what do we do with the other
ones) ?
• Model will be a combination of empirical and
physically-based

11
Basic data
• Topography
• (Daily) Precipitation throughout the year
• wet / dry season
• Evapotranspiration
• Outflow data

12
Basic EO data ERS SAR
• Basic EO dataset is a series of radar
(microwave) images acquired with the ERS
satellite
• where radar microwave (i.e. microwave part
of the EM spectrum) and aperture synthesis is a
technique for getting high (i.e. good) spatial
resolution
• The images cover a time period from Jan 1999 to
Feb 2000

13
Distortions as SAR is a side-looking sensor
Bau Sau wetlands
Tiger Hill
14
Properties of SAR data
• Monochrome (i.e. single wavelength in the
microwave spectrum)
• ERS microwave images acquired at wavelength of
5cm (very different to optical images which are
at microns)
• As they are only at a single wavelength, we often
try to use multi-temporal data
• gives extra information
• colour composites, ...

15
Properties of SAR data
• The images are apparently noisy (variations in
brightness of pixels) so sometime we have to
smooth (filter) them in order to detect features
• If we do smoothing, what effects does this have
on the data?

16
hydroModel
• A hydrological model is already constructed. You
will be able to operate it on the UNIX
• You will also be able to modify it (by
introducing new input and output variables) and
changing other details of the model if you wish

17
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18
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19
How do we verify this ? How do we re-run the
model to get better agreement ?
20
EO data in Environmental Models
• 1 Definition of the problem Define, in
quantifiable terms, what it is you want to
monitor (and if possible, to what degree of
accuracy)
• 2 Assessment of resources What data do you have
available to achieve this? What sort of model is
appropriate to the task? Is what you propose
feasible in the time/other constraints available?
• 3 Preliminary study and sensitivity analysis
have a first pass attempts at defining the method
and models and gain an understanding of the
nature and sensitivities of both model and data.

21
EO data in Environmental Models
• 4 Refinement After this initial investigation,
does your model or the way you are using it need
any refinement? If so, refine it and re-run the
previous analysis.
• 5 Calibration Assuming you are working with an
empirical model, once you are happy with the
basic approach, apply the model to a calibration
dataset to parameterise it for the environment
you are working in.
• 6 Validation Apply the model with the calibrated
parameterisation to an independent dataset to
tests its ability to provide accurate
predictions.
• 7 Write up Write up and present your findings,
discussing and presenting the method, model
results, providing an indication of how (far) you
have met your aims and where the work could go
from this point.

22
Remember...
• Distinctions between different types of model
• empirical / theoretical
• which do you think hydroModel is ?
• Testing / validating / verifying models
• Understanding, and if possible quantification of
uncertainty

23
Suggestions...
• Have a look at the practical
• get a feel for what is involved
• Go back to the earlier practicals to revise and