**Area Frames for Land Cover Estimation: Improving the European LUCAS
Survey.**

**Javier Gallego.**

**JRC-IES, Ispra (Italy). <javier.gallego@jrc.it>**

**Abstract**

LUCAS (Land Use/Cover Area frame Survey) has been launched by the
European Union (EU) in 2001 based on an area frame of points with a
two-stage systematic sampling. We discuss some possible options to
improve LUCAS assuming that it could combine in the future an annual
survey focused on arable land with a general purpose survey. A test is
being carried in Greece out with a two-phase area frame of unclustered
points, following the current approach of the Italian AGRIT survey. The
high share of the variance coming from the first sasmpling stage
suggests that unclustered points can be better. The same conclusion is
reached considering the "equivalent number of points of a Primary
Sampling Unit". A simulation shows that a stratification based on
photo-interpretation is much more efficient with unclustered points
(single stage sampling) than with the current two-stage design if the
photo-interpretation is very accurate. The gain is debatable with a
moderate amount of photo-interpretation errors. A remark is made showing
that the current LUCAS two-stage sampling scheme can be seen as a
single-stage systematic sampling, which simplifies the estimation of
variances

# Area frame surveys of points: two-stage versus two-phase schemes. 

# 

We speak of an area frame survey when the sampling units are defined on
a cartographic representation of the surveyed territory. Area frames
generally match more precisely the population than list frames. The
units of an area frame can be points, transects (straight lines of a
certain length) or pieces of territory, often named segments. The LUCAS
(Land Use/Cover Area-frame Survey) was launched by the European Union
(EU) in 2001. LUCAS is based on a non-stratified, systematic, two-stage
sampling scheme, with Primary Sampling Units (PSUs) defined as a
rectangle of 1500 x 600 m following a grid of 18 km \[Delincé, 2001,
Bettio et al., 2002\]. In each PSU 10 points (SSUs) are selected
arranged on two rows of 5 points with a step of 300 m. The "point" (SSU)
is defined as a circle of 3 m to be consistent with ground survey
specifications. This two-stage systematic design can be described as a
single stage systematic sample if the PSU is defined as containing only
the 10 "square points" of 3 x 3 m, so that the 1500 x 600 m rectangle
contains 100x100=100000 PSUs. This scheme simplifies the problem of
variance computation.

An alternative is the current design of the Italian AGRIT survey
\[Consorvio ITA, 2003, Martino, 2003\]: single stage (unclustered
points) two-phase sampling: the first phase gives a systematic sample of
unclustered points that are photo-interpreted and subsampled (second
phase) with higher rates in agricultural strata. A similar approach
approach has tested in Greece in 2004: its data are being analysed at
the time of writing this paper, that focuses on the analysis of the
reasons why an imporvement can be obtained with this approach. For the
comparison of the two-stage scheme with the single-stage, two-phase
scheme, it is useful to estimate the part of variance coming from each
sampling stage. A good idea can be obtained using the formulae for
two-stage random sampling \[Cochran, 1977\]:

$$v\left( \overline{\overline{y}} \right) = \left( \frac{N - n}{N} \right)\frac{s_{1}^{2}}{n} + \frac{n}{N}\left( \frac{M - m}{M} \right)\frac{s_{2}^{2}}{\text{mn}} = \left( 1 - f_{1} \right)\frac{s_{1}^{2}}{n} + \left( 1 - f_{2} \right)\frac{s_{2}^{2}}{\text{mN}}$$

Some care is needed when estimating the contribution of each stage. The
proportion of variance coming from the first stage is estimated by
$\text{rb} = \frac{\left( 1 - f_{1} \right)}{n}\frac{\left( s_{1}^{2} - \frac{s_{2}^{2}\left( 1 - f_{2} \right)}{m} \right)}{v\left( \overline{\overline{y}} \right)}$

The share of the variance due to the first stage is between 70% and 85%
for major crops and even higher for forest, due to its higher spatial
auto-correlation. This means that improving the accuracy requires a
higher number of PSUs rather than increasing the number of SSUs per PSU.

A different way to compare both approaches is pretending that only 1 of
the 10 points in the PSU has been visited. For this approach we have
estimated variances with a slightly modified Matern formula \[Matern,
1986\], better adapted to systematic sampling. Comparing the estimated
variances leads to the "equivalent number of points of a PSU", with
values around 4 for main annual crops and around 3 for grassland and
forest. This means that 3-4 unclustered points give as much information,
in terms of variance, as the current cluster of 10 points.

An additional question is the possible improvement in the efficiency of
stratification. Let us assume that LUCAS becomes a set of two
co-ordinated surveys: a general land cover survey with a periodicity of
4-5 years and a specific survey for annual crops every year. For the
specific survey on annual crops, the efficiency of stratification needs
to be assessed. Classifying each point into one stratum may be more
efficient than classifying a whole PSU in the same stratum, because a
PSU contains points belonging to different categories. A simulation
using three types of information for stratification suggests that
unclustered points only give a clear advantage from this point of view
if the stratification is based on a very accurate photo-interpretation.
The question must be studied more in depth with real
photo-interpretation data.

**References**

Bettio M., Delincé J., Bruyas P., Croi W., Eiden G., (2002), Area frame
surveys: aim, principals and operational surveys. *Building
Agri-environmental indicators, focussing on the European Area frame
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<http://agrienv.jrc.it/publications/ECpubs/agri-ind/>

Cochran W., (1977), *Sampling Techniques, chapter 10*. New York: John
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Consorzio ITA (2003). *Bollettino finale di statistiche agricole
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Delincé J. (2001), A European approach to area frame survey.
*Proceedings of the Conference on Agricultural and Environmental
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<http://www.ec-gis.org:/>

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