Thermal Land-surface Variables From METEOSAT-IR Data
283
reference for the creation of the initial population ofNNs. Due to ENZO's ability to
identify redundant input parameters the 14 input neurons representing the altitudes
of the atmospheric pressure levels (Table 1) could be removed from the input data
(Gottsche and Olesen, 2002). This can be understood when taking into account that
the pressure levels are intrinsically coded in the neurons for the atmospheric
temperature and humidity values. The final NN determined by ENZO for a desired
rms. error of 0.3 K ("ENZO-NN" in Table 2) has 58% fewer hidden neurons and ca.
90% fewer weights than the manually determined NN. The rms. validation error
(untrained TIGR data) ofENZO-NN is 0.25 K, which is slightly higher than for the
Manual-NN.
1.6 Verification of the Trained Neural Network
Finally, the developed network is verified (tested) with data which were generated
analogously to the training and validation data, but using cloud-free atmospheric
profiles from ECMWF analyses. These are available globally for more than 10 years
and have a spatial resolution of 1.1 degree. The profiles were selected from within
the rectangle given by (5
e
E, 54'N) and (20E, 46'N). The rectangle is contained in
the geographic area from which the TIGR profiles used for training were selected.
The profiles were taken from 6 ECMWF analyses: 10.03.96 - 12 hours, 12.04.9606 hours, 15.06.96 - 06 hours, 20.07.96 - 18 hours, 18.09.96 - 00 hours, and
26.10.96 - 12 hours. By varying the surface parameters of Table 1, a verification
data set of 1200 situations was generated for each analysis. Cloud-free grid cells
were identified using cloud-masks derived from METEOSAT data (Schadlich et aI.,
2001).
For the cloud-free verification data the average error between MODTRAN-3 and
the Manual-NN is 0.33 K; the mean temperature errors for the six individual data
sets range from 0.16 K to 0.68 K. The corresponding mean errors for all grid cells
(includes clouded ones) range from 0.34 K to 1.03 K. ENZO-NN proved to be
superior to the Manual-NN: for the cloud-free situations the rms. error ranges from
0.26 K to 0.44 K and for the corresponding rms. errors for all grid cells (no cloudclearing) the rms. error ranges from 0.31 K to 0.69 K. The rms. verification error
(cloud-free ECMWF analyses) ofENZO-NN is 0.31 K, which is slightly lower than
for the Manual-NN. This underlines the better generalisation of the impressively
smaller ENZO-NN (Gottsche and Olesen, 2002). Furthermore, in spite of the
different structure of the ECMWF analyses compared to the TIGRradio-soundings,
which were used to train the network, the errors are smaller than the intrinsic
maximum error of MODTRAN-3. Taking into account these results, the higher rms.
validation error ofENZO-NN compared to the Manual-NN is interpreted as a hint
that the latter was over-fitted. A practical advantage of ENZO is the fast
development of the NNs (6 days without user interaction). Radiative transfer
283
reference for the creation of the initial population ofNNs. Due to ENZO's ability to
identify redundant input parameters the 14 input neurons representing the altitudes
of the atmospheric pressure levels (Table 1) could be removed from the input data
(Gottsche and Olesen, 2002). This can be understood when taking into account that
the pressure levels are intrinsically coded in the neurons for the atmospheric
temperature and humidity values. The final NN determined by ENZO for a desired
rms. error of 0.3 K ("ENZO-NN" in Table 2) has 58% fewer hidden neurons and ca.
90% fewer weights than the manually determined NN. The rms. validation error
(untrained TIGR data) ofENZO-NN is 0.25 K, which is slightly higher than for the
Manual-NN.
1.6 Verification of the Trained Neural Network
Finally, the developed network is verified (tested) with data which were generated
analogously to the training and validation data, but using cloud-free atmospheric
profiles from ECMWF analyses. These are available globally for more than 10 years
and have a spatial resolution of 1.1 degree. The profiles were selected from within
the rectangle given by (5
e
E, 54'N) and (20E, 46'N). The rectangle is contained in
the geographic area from which the TIGR profiles used for training were selected.
The profiles were taken from 6 ECMWF analyses: 10.03.96 - 12 hours, 12.04.9606 hours, 15.06.96 - 06 hours, 20.07.96 - 18 hours, 18.09.96 - 00 hours, and
26.10.96 - 12 hours. By varying the surface parameters of Table 1, a verification
data set of 1200 situations was generated for each analysis. Cloud-free grid cells
were identified using cloud-masks derived from METEOSAT data (Schadlich et aI.,
2001).
For the cloud-free verification data the average error between MODTRAN-3 and
the Manual-NN is 0.33 K; the mean temperature errors for the six individual data
sets range from 0.16 K to 0.68 K. The corresponding mean errors for all grid cells
(includes clouded ones) range from 0.34 K to 1.03 K. ENZO-NN proved to be
superior to the Manual-NN: for the cloud-free situations the rms. error ranges from
0.26 K to 0.44 K and for the corresponding rms. errors for all grid cells (no cloudclearing) the rms. error ranges from 0.31 K to 0.69 K. The rms. verification error
(cloud-free ECMWF analyses) ofENZO-NN is 0.31 K, which is slightly lower than
for the Manual-NN. This underlines the better generalisation of the impressively
smaller ENZO-NN (Gottsche and Olesen, 2002). Furthermore, in spite of the
different structure of the ECMWF analyses compared to the TIGRradio-soundings,
which were used to train the network, the errors are smaller than the intrinsic
maximum error of MODTRAN-3. Taking into account these results, the higher rms.
validation error ofENZO-NN compared to the Manual-NN is interpreted as a hint
that the latter was over-fitted. A practical advantage of ENZO is the fast
development of the NNs (6 days without user interaction). Radiative transfer