cycles and handle the unique behaviour of some species. 
The problems introduced by the different temporal 
sampling for the different years (the cloud shrouded days 
are different in different years) also have to be coped 
with. The cloud cover also behaves irregularly on a given 
image above different areas. A mathematical method was 
needed which deals with these irregularities and makes 
the data unified. 
The results showed that in Hungary the method can be 
applied in flat lands (the Great Plain) without 
stratification, so the regional yield averages can be 
estimated. For corn the greatest deviation between the 
estimated yield and the official statistical data is 0.68 t/ha 
(1991 Bäcs-Kiskun county), for wheat it is 0.55 t/ha 
(1993 Bács-Kiskun county). The average deviation is 
0.37 t/ha for corn and 0.32 t/ha for wheat. The question 
has arisen, whether it is possible to give an estimation for 
the whole country based on the estimations acquired in 
the flat counties. If the answer is ’yes’ then in practice 
the ratio of the flat land yield average to the whole 
country average is the same for every year. That is 
unfortunately not true, for example for corn in the period 
of 1991-93 the ratios are: 1.06, 1.01, 0.98: for wheat 
they are: 1.05, 0.89, 0.96. So one can see that the 
estimation for the whole country is not that simple as 
that. 
From the previous paragraph it is evident, that to get an 
accurate yield forecast for the whole country the 
examination of the data for other counties is necessary. 
But there are several problems arising. First of all one 
crop can behave quite differently in regions of different 
characteristics. This question is thoroughly discussed in 
literature. The subregions with irregular behaviour are 
called strata and there are still no theories to handle 
them. Moreover, even if the different strata behaved 
uniformly, there is the problem of the sloping surfaces. 
If there is a hilly, rugged terrain, the diffuse radiation 
reaching the satellite sensor is not simply related to 
canopy reflectance as a consequence of anisotropic 
backscattering. It is not even a simple question to handle 
it theoretically. In practice it amounts to an increased 
noise of the data. 
4. EXTENDING THE ROBUST METHOD TO THE 
WHOLE COUNTRY 
To eliminate the effects of the terrain there is two 
methods. The terrain correction can be done on a 
pixel-by-pixel basis, or one can use an averaging method. 
The first method is theoretically more correct, but 
unfortunately cannot be carried out in practice (as it is 
already mentioned, the ambiguity of the geographical 
correction of pixels makes it impossible with the half 
pixel uncertainty). Therefore our decision was to use a. 
method with a kind of an average relief correction. In the 
future, if there is a high-resolution study, then the 
pixel-by-pixel correction becomes inevitable. 
For the relief correction a digital elevation database 
(DTM) for Hungary was used. With this the data related 
to any county could be brought to a common reference 
base and so the robust method could be extended to the 
whole area of the country. For all of the 19 counties the 
modified GYURRI values were obtained. So there were 
19 points for each year on the plots, 57 overall for the 
three years. With the help of these points the linear 
relationship between the GYURRI and yield average 
values was established for each crops. Also the relief 
corrected GYURRI was calculated for the whole country, 
and using the established relationship the national average 
yields were estimated. 
The above data were obtained by applying the robust 
method with relief correction for every county of 
Hungary. The results show the method could be used as 
an operational method on national and regional level. 
More detailed study of the data showed that some of the 
points deviate more then it was expected. For example, 
see corn, on the left side of the Figure 3., there are 3 
points separated from the main band of points in a 
roughly perpendicular direction from the line. These are 
turned out to be the points of counties Gyór-Sopron, Zala 
and Vas in 1993. This means that there appeared a 
transient stratum at the western side of the country. The 
reason can be — as the meteorological data suggest 
— that the atmospherical parameters behaved strangely, 
not showing the usual characteristics of the area, 
modifying therefore the satellite data through 
atmospherical correction effects. The problem of the 
temporal transient strata is still an open question, but the 
above example shows that they cannot be neglected in the 
future. It is important to note, that the temporal transient 
didn't affect the estimation for the whole country average 
yield. 
The fact that the relief correction is necessary is clearly 
shown on Figures 2-5., where both the uncorrected and 
the corrected data is plotted for corn and wheat. The 
former shows a scattered cloud of points while the latter 
shows considerably more correlation with a linear 
relationship. Figures 6-9. show the results obtained by 
using the relief correction for the 4 remaining crops. The 
results can be considered good in all cases, and in the 
case of corn the 95.7% correlation value is exceptionally 
good. On the figures the squares denote the national 
average estimations, their y coordinate is the official 
statistical yield data, the y distance of the square to the 
line shows the error of the estimation in a given year. 
(To be exact the official statistical yield values are also 
only estimations achieved through some classical method 
of theirs, so the deviation from them can be other than 
the true errors.) Table 1. shows these deviations for the 
three years and for the 6 species of plant. 
The main task of satellite yield estimations is to tell 
accurately the maximum yield expectable in the year 
before harvesting. The estimation is certainly for 
maximum yield, because in the last moments the yield 
can be changed only in negative direction by 
unpredictable events (e.g. fires, droughts etc.). The 
basics of the method is, that knowing the remotely sensed 
data until a certain day, we try to predict a next value 
assuming that no stress event happens. For the moment 
we used only corn data, and found that in 1991 when 
there was not any late summer drought, already in the 
210th day (end of July) a good estimation could be given 
for the final yield.