Thermal Land-surface Variables From METEOSAT-IR Data
281
using the Stuttgart Neural Network Simulator (SNNS). The training of neural
networks is equivalent to finding the minimum error E given by equation 3. This
task can be performed by several algorithms, e.g. Back-propagation, Quick-prop, or
Resilient Propagation (Rprop). Here, Rprop with weight-decay (Riedmiller, 1993)
was used because it converges reliably and is robust in respect to the choice of its
parameters. The best network-architecture was determined during training and
validation. This is a time-consuming approach and chances are small that the global
optimum is found. Therefore, the evolutionary optimisation scheme "Evolutionarer
Netzwerkoptimierer (ENZO)" was utilised to determine a NN which is closer to the
global optimum (Braun and Ragg, 1996). More information on neural networks and
SNNS can be found in Zell (1994). The simulator, a user manual and information
about ENZO can be downloaded from the SNNS homepage at the University of
Ttibingen: http://www-ra.informatik.uni-tuebingen.de/forsch ung/ snns/.
1.5 Training and Validation Data for Atmospheric Correction
The first step in designing any neural network is to obtain adequate data sets for
training and validation. The data has to cover the whole bandwidth of situations
which might be encountered during the application phase of the neural network -
otherwise it will produce unpredictable results. Here, the atmospheric situations are
described by 84 profiles from the TOVS Initial Guess Retrieval (TIGR) library. The
profiles were chosen in Eurasia between 45.0 Nand 55.0 N latitude. The number of
pressure levels of the profiles was reduced to 14 to match ECMWF re-analyses
(ERA-IS). In order to take into account the influence of atmospheric path-length
and the variability of surface temperature, MODTRAN-3 calculations were
performed for variations of surface temperature (4), surface elevation (4), and scan
angle (3) for all 84 profiles. Then brightness temperatures corresponding to
METEOSAT-IR measurements were derived. The generated data was split into
training data (68 profiles, 3264 input patterns), which are actually used for the
teaching of the network, and validation data (16 profiles, 768 input patterns), which
are used to detect over-fitting (Zell, 1994). The structure of the data determines the
number of neurones in the input layer and the output layer (Table I).
In order to avoid problems associated with neuron saturation all data were
linearly mapped to the interval (0,1). According to an neural network heuristic the
optimum network is the one which has the fewest neurones and the smallest error
for the validation data - if more neurons are added the networks ability to
generalise, i.e. to produce good results for the validation data, deteriorates, because
it starts to memorise the training data rather than to approximate underlying
relationships (over-fitting). Starting with one hiden layer and with 5 neurons,
Vollmer et al. (2000) determined a suitable network architecture by successively
adding neurons or layers. During the training phase the quality of a network can be
281
using the Stuttgart Neural Network Simulator (SNNS). The training of neural
networks is equivalent to finding the minimum error E given by equation 3. This
task can be performed by several algorithms, e.g. Back-propagation, Quick-prop, or
Resilient Propagation (Rprop). Here, Rprop with weight-decay (Riedmiller, 1993)
was used because it converges reliably and is robust in respect to the choice of its
parameters. The best network-architecture was determined during training and
validation. This is a time-consuming approach and chances are small that the global
optimum is found. Therefore, the evolutionary optimisation scheme "Evolutionarer
Netzwerkoptimierer (ENZO)" was utilised to determine a NN which is closer to the
global optimum (Braun and Ragg, 1996). More information on neural networks and
SNNS can be found in Zell (1994). The simulator, a user manual and information
about ENZO can be downloaded from the SNNS homepage at the University of
Ttibingen: http://www-ra.informatik.uni-tuebingen.de/forsch ung/ snns/.
1.5 Training and Validation Data for Atmospheric Correction
The first step in designing any neural network is to obtain adequate data sets for
training and validation. The data has to cover the whole bandwidth of situations
which might be encountered during the application phase of the neural network -
otherwise it will produce unpredictable results. Here, the atmospheric situations are
described by 84 profiles from the TOVS Initial Guess Retrieval (TIGR) library. The
profiles were chosen in Eurasia between 45.0 Nand 55.0 N latitude. The number of
pressure levels of the profiles was reduced to 14 to match ECMWF re-analyses
(ERA-IS). In order to take into account the influence of atmospheric path-length
and the variability of surface temperature, MODTRAN-3 calculations were
performed for variations of surface temperature (4), surface elevation (4), and scan
angle (3) for all 84 profiles. Then brightness temperatures corresponding to
METEOSAT-IR measurements were derived. The generated data was split into
training data (68 profiles, 3264 input patterns), which are actually used for the
teaching of the network, and validation data (16 profiles, 768 input patterns), which
are used to detect over-fitting (Zell, 1994). The structure of the data determines the
number of neurones in the input layer and the output layer (Table I).
In order to avoid problems associated with neuron saturation all data were
linearly mapped to the interval (0,1). According to an neural network heuristic the
optimum network is the one which has the fewest neurones and the smallest error
for the validation data - if more neurons are added the networks ability to
generalise, i.e. to produce good results for the validation data, deteriorates, because
it starts to memorise the training data rather than to approximate underlying
relationships (over-fitting). Starting with one hiden layer and with 5 neurons,
Vollmer et al. (2000) determined a suitable network architecture by successively
adding neurons or layers. During the training phase the quality of a network can be