Bouzidi, Sonia 
  
e N, is the number of land covers, 
RF (t) the reflectance of a NOAA pixel 4 in channel k (k — 1 or 2), at date t, 
RE (t) the individual reflectance of the land cover type 7 in channel k (k = 1 or 2), at date t, 
pij the proportion of the land cover j within a NOAA pixel 7. 
We first use this model within a learning process to estimate the individual temporal reflectances R^ (t) for each land 
cover type in the visible and near infrared channels. For this purpose, we consider a small learning area for which ground 
truthing and high spatial resolution remote sensing data are simultaneously available. A precise land cover thematic 
classification image is obtained for this area from the remote sensing and the ground truthing (Flügel, 1998). Then, 
after geometrical registration, we superpose the Landsat classification image and the NOAA images. Consequently, for 
each NOAA pixel, its composition in terms of percentage of land cover can be obtained by directly counting pixels on 
the Landsat classification image. We then obtain the pij Values for this learning area. At each date t, we consider the 
linear model (1) for several pixels 3; knowing the p;;, the inversion of the obtained linear system allows the estimation of 
individual values RE for this date. By repeating this process for all the dates, the temporal profiles RE (t) are computed. 
This method and its results are detailed in (Bouzidi et al., 1997a, Bouzidi et al., 1997b). 
In this paper, we use the hypothesis that these temporal profiles are spatially constant. At each pixel i, we consider the 
linear model (1) for several dates 1; knowing the R^(t) from the NOAA image and the individual temporal profiles RE (t) 
from the learning process, the inversion of the obtained linear system allows the estimation of the proportions p; j of each 
land cover j within the pixel. This point is described in the next section. 
3 LAND COVER PROPORTIONS ESTIMATION 
Our task is to estimate for each pixel i in the NOAA image the proportion p;; of land cover j. We then consider, for this 
given pixel 4, its reflectance in the visible and near infra-red channels for a number of dates. These dates are selected to 
avoid bad quality acquisitions and only images containing at least 80% of free clouds pixels are considered. Moreover, the 
acquisitions are constraint to cover an important part of the vegetative cycle in order to discriminate at best the different 
land covers. An over-determined system (S) of M linear equations (M denotes the number of dates) and NN. unknown 
variables (p;;,j = 1,..., N,) is then obtained: 
Ne 
(8) ROS uRKD GSLX (-L SM) Q) 
je 
with the following constraints: 
Ne 
S m nu G) 
j=1 
To solve these equations, we formulate the problem as an optimization problem. We aim to minimize, for a given pixel 
à, the difference between the different observed reflectance and that estimated by the linear model. This leads to the 
minimization of a set of functions for each pixel 2: 
N. 
i=l 
under the constraints (3) and (4). This minimization is performed using an algorithm based on sequential quadratic 
programming described in (Zhou and Tits, 1993). This process, that we call “NOAA unmixing process” outputs, for 
each pixel, N. values corresponding to the proportions: percentage of each land cover type. This process allows the 
generation of N. images, each one having the size of the original NOAA image and giving for the studied land cover type 
its proportion within each pixel. 
4 RESULTS AND VALIDATION 
The test area chosen to evaluate the results is the Mkomazi catchment in Kwazulu-Natal (South Africa). The data available 
for this site are obtained within the context of the European INCO-PED IWRMS project (Integrated Water Resources 
Management System). The available images are the following: 
  
206 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000.