IEEE Geoscience and Remote Sensing Magazine - December 2020 - 12

2l
= 0; j ! " 1, 2, f, p ,.(3)
2b j

The solution to (3) is obtained by the iterative method of
Newton-Raphson [29]. The estimated parameters are denoted by bt = _ bt 1, bt 2, f, bt p i .
APPLICATION TO THE GEOSUD SPATIAL DATA
INFRASTRUCTURE
To apply this approach to the survey's observations, we created four dummy variables for the five different activity sectors of users: D 1 = NGOs and various organizations, D 2 =
local authorities, D 3 = state services, and D 4 = nonscientific
public institutions; we considered research and education organizations as the reference level. The choice of the reference
level had no impact on the quality of the model, and the effect of this sector is implicit within the intercept coefficient.
In addition, we considered the variables B = the proposed
price amount, V = the annual average volume of requested
images, and the four created dummy variables as independent variables. On the other hand, the response to the WTP
question was considered as a dependent variable. The annual
average volume of requested images represents an additional
variable resulting from the information registered for every respondent via the GEOSUD SDI: the global volume of images
requested by each group divided by the overall period during
which that group was a member of GEOSUD. This variable
was chosen instead of the global volume of images requested
because it represents the reality of satellite-image demand. We
noticed several gaps in the demand of some adherent groups,
which may request a many images in one year but none in the
next several years. Hence, we chose to use the average volume,
which gives a better representation of the images requested
since the registration date.
Therefore, an explicit expression of the logistic model is

Yi = F (b 0 + b 1 B i + b 2Vi + b 3 D 1i + b 4 D 2i + b 5 D 3i + b 6 D 4i)+ f i ;
i ! " 1, f, N ,,

where b 0 represents the intercept coefficient. After estimating
all of the coefficients of the model and considering the statistically significant ones, we could compute the probability
that a particular user would agree to pay a proposed charge. In
addition, by varying the amounts and applying (1), we could
also generate, for every sector, a probabilistic demand function for the imagery and, therefore, a global demand function
that respects the weights of each sector. Furthermore, to generate the demand function for each sector, the variable V was
fixed and represented by the mean of all Vi users within the
considered sector.
With demand functions, it was straightforward to find the
precise amount that a predefined percentage, p, of users is
willing to pay for an image. Analytically, the amount that corresponds to a probability of acceptance p is given by
4

p=
12

e b0 + b1 B i + b2 Vi + k/= 1 bk + 2 Dki
4

1 + e b0 + b1 B i + b2 Vi + k/= 1 bk + 2 Dki

Then,
p -level WTP =

4
p
1
ln c 1 - p m - d b 0 + b 2Vi + / b k + 2 D ki nG.
b1 =
k=1

(4)
Therefore, at the p-level WTP, when charged, p% of the users
are expected to accept paying, and ^1- p h % will turn down
the proposed amount.
Based on the WTP probabilistic distribution, the expected
WTP value was computed by applying a classical result for
continuous random variables:
∞

E[WTP] =

[1 - F (WTP 1 x)] dx,(5)

where F ($) is the CDF of the WTP distribution. Finally, to
solve the integral in (5), we applied numerical integration
methods [22], in which we considered the lowest and highest proposed prices as the lower and the upper boundaries,
respectively, of the integral.
RESULTS
DESCRIPTIVE RESULTS
The majority of respondents were from the research and education sector, with 179 responses (51% of 351 fully recorded
answers), followed by local authorities, with 60 responses
(17.1%). With respect to the usage category of HR satellite
images, we accounted for five different main uses. Two additional uses were recorded for the " Other " option. We can see
that the observation activity accounts for the highest percentage of use and that almost half of users acquire the images
for research activity (Table 1). The choice of the segmentation
between operational (e.g., monitoring) and nonoperational
(e.g., R&D) use was guided by the fact that scientists and operational public users do not have the same needs and do not
evaluate the satellite imagery on the same criteria due to the nature of their jobs. The researchers-direct users of G
- EOSUD,
the majority of whom are remote sensing experts-rely on the
usefulness of images to generate new knowledge and develop transferable methods. They are also used to benefit from
support programs for partial or total free access to images
[e.g., through the French Centre National d'Etudes Spatiales
(CNES) Incitation à l'utilisation Scientifique des images SPOT
program, European Space Agency (ESA), and so on]. On the
other hand, the operational users-often nonspecialists in the
remote sensing domain-react differently to satellite images
or image-based products (manufactured themselves or by expert providers) in their professional fields.
In sections 4 and 5, respondents were limited to a single
choice. In terms of payment, we noticed that a relatively high
percentage of users preferred to pay a membership fee for a
pool that allowed them free access to HR satellite images. The
offer of a number of images for free before the imposition
of price came second, with 35% of users choosing this option. (Our discussion of the answers to the section 3 question provides more details and elements of the analysis of
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

DECEMBER 2020

IEEE Geoscience and Remote Sensing Magazine - December 2020

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