Thermal Land-surface Variables From METEOSAT-JR Data
287
alterations were implemented:
• The width of the cosine w is calculated from astronomical parameters (daylight
hours).
• The model is required to be differentiable at the boundary between the cosine and
the attenuation function. With this constraint the attenuation constant k can be
calculated.
• Furthermore, a robust estimator of the error function is used to reduce the effect
of outliers.
With these improvements the determination of the model parameters was stable
for all meaningful conditions. Furthermore, two parameters less have to be fitted.
The method is superior to minimum/maximum temperature schemes, because
theoretically no information is lost during parametrisation. Small gaps due to clouds
as well as outliers due to undetected clouds are smoothed by the modelling.
2.3 Maximum and Median Composites
Diurnal temperature waves of individual days are influenced by the current and the
previous synoptic situation, e.g. by the cloud situation and the surface-moisture. On
the other hand, more permanent surface properties, e.g. vegetation and soil type, are
to be derived from the temperature wave. The task now is to find a method to
separate the short term synoptic effects from these more permanent characteristics
of the surface. In principle two approaches are possible:
1 Calculation of the model parameters for a number of individual days and
subsequent averaging.
2 Generation of IR composites for a number of days and calculation of model
parameters for the composites.
Both approaches were applied to the vegetation period of 1996 with a
composition period of one month. In months with many clear sky situations both
approaches proved to be feasible, but for periods with moderate to high cloudiness
only the fitting of IR composites yields reasonable results. Good composites were
obtained using the maximum and the median:
1 Maximum composite: the maximum for each pixel location and slot in the
composi te-interval.
2 Median composite: the median for each pixel location and slot in the compositeinterval.
In order to exclude the maximum and minimum from the median the number
of cloud-screened values is required to be ?4; otherwise the median is marked as
missing. With this constraint, and because no averaging is performed, it is unlikely
that undetected clouds influence the median. Most pixel locations do not fulfil this
condition for all METEOSAT slots, but usually the remaining slots are sufficient to
model the missing values. In case of too many missing values, the modelled
287
alterations were implemented:
• The width of the cosine w is calculated from astronomical parameters (daylight
hours).
• The model is required to be differentiable at the boundary between the cosine and
the attenuation function. With this constraint the attenuation constant k can be
calculated.
• Furthermore, a robust estimator of the error function is used to reduce the effect
of outliers.
With these improvements the determination of the model parameters was stable
for all meaningful conditions. Furthermore, two parameters less have to be fitted.
The method is superior to minimum/maximum temperature schemes, because
theoretically no information is lost during parametrisation. Small gaps due to clouds
as well as outliers due to undetected clouds are smoothed by the modelling.
2.3 Maximum and Median Composites
Diurnal temperature waves of individual days are influenced by the current and the
previous synoptic situation, e.g. by the cloud situation and the surface-moisture. On
the other hand, more permanent surface properties, e.g. vegetation and soil type, are
to be derived from the temperature wave. The task now is to find a method to
separate the short term synoptic effects from these more permanent characteristics
of the surface. In principle two approaches are possible:
1 Calculation of the model parameters for a number of individual days and
subsequent averaging.
2 Generation of IR composites for a number of days and calculation of model
parameters for the composites.
Both approaches were applied to the vegetation period of 1996 with a
composition period of one month. In months with many clear sky situations both
approaches proved to be feasible, but for periods with moderate to high cloudiness
only the fitting of IR composites yields reasonable results. Good composites were
obtained using the maximum and the median:
1 Maximum composite: the maximum for each pixel location and slot in the
composi te-interval.
2 Median composite: the median for each pixel location and slot in the compositeinterval.
In order to exclude the maximum and minimum from the median the number
of cloud-screened values is required to be ?4; otherwise the median is marked as
missing. With this constraint, and because no averaging is performed, it is unlikely
that undetected clouds influence the median. Most pixel locations do not fulfil this
condition for all METEOSAT slots, but usually the remaining slots are sufficient to
model the missing values. In case of too many missing values, the modelled