Amaro A., Reed D., Soares P. (editors) Modelling Forest Systems
Подождите немного. Документ загружается.
05Amaro Forests - Chap 04 25/7/03 11:04 am Page 46
46 G. Chirici et al.
(a)
0.60
0.50
0.40
0.30
0.20
0.10
0.00
r
r
RMSE
K
120
105
100
95
90
85
80
RMSE (m
3
/ha)
3456789 10 11 12 13 14 15 16 17 18 19 20
115
110
(b)
0.60
0.50
0.40
0.30
0.20
0.10
0.00
r
r
RMSE
K
4000
3900
3700
3600
3500
3300
3200
3100
3000
RMSE (n/ha)
3800
3400
3456789 10 11 12 13 14 15 16 17 18 19 20
Fig. 4.3. Accuracy statistics (r and RMSE) obtained by the leave-one-out application of the k-NN classifier
for the estimation of stemwood volume (a) and stem density (b).
medium numbers of points considered; specifically 13 for stemwood volume and 18
for stem density. These numbers are of the same order as those reported in the litera-
ture from the Finnish and Swedish investigations (Fazakas et al., 1999; Katila and
Tomppo, 2001). The prediction accuracy achieved with the final parameter choice is
actually not high, as testified by a correlation coefficient < 0.5. Thanks to the high
number of sample plots, however, these correlations are statistically significant for
both parameters (P < 0.01). Similar indications are provided by the root mean square
errors (RMSEs), which are actually medium-high with respect to the observed vari-
ability of the two forest attributes.
Fuzzy classifier
As regards the fuzzy classifier, its best configurations were found with very small
values of
R
d
(2 and 3 digital counts for stemwood volume and stem density, respec-
tively; Fig. 4.4). This indicates that the most influential plots are spectrally very close
to each estimation point. The best prediction accuracy (correlation and RMSE)
achieved with the fuzzy classifier was very similar to what could be achieved with
the k-NN. As before, the highest achieved correlation was statistically significant for
both study attributes (P < 0.01).
05Amaro Forests - Chap 04 25/7/03 11:04 am Page 47
47 Spatial Distribution Modelling
(a)
0.60
120
11
5
0.50
110
0.40
105
0.30
100
95
0.20
r
RMSE (n/ha) RMSE (m
3
/ha)
r
90
0.10
RMSE
0.00
1234567 8 9 10 11 12 13 14 15 16 17 18
Range (DC)
(b)
0.60
85
80
4000
3900
0.50
0.40
3800
3700
3600
0.30
3500
3400
r
r
0.20
3300
3200
0.10
RMSE
0.00
1234567 8 9 10 11 12 13 14 15 16 17 18
Range (DC)
3100
3000
Fig. 4.4. Accur
acy statistics (r and RMSE) obtained by the leave-one-out application of the fuzzy classifier
for the estimation of stemwood volume (a) and stem density (b).
Spatial predictions of stemwood volume
Spatial predictions of stemwood volume for the forested locations not included in
the inventory sample ar
e shown in Fig. 4.5. In these maps, all non-forest pixels are
masked out by the application of a threshold to the band subset considered (
ETM+
bands 3, 4 and 5). The two stemwood volume maps are quite similar, and differ-
ences in stemwood volume estimates are hardly visible.
Discussion and Conclusions
The current investigation presented the results obtained by applying two non-
parametric classification procedures to Landsat 7
ETM+ data for modelling the spatial
distribution of two major forest attributes; stemwood volume and tree stem density.
The tested modelling techniques are ‘transparent’ and easy to understand, while
allowing flexibility in the incorporation of ancillary information. In addition, a num-
ber of forest variables can be estimated at the same time. Both techniques can easily
be integrated into existing forest monitoring programmes, with the added potential
for combining different sources of information not only from outside a region of
interest, but even from different forest inventory designs.
The similar results obtained by the two tested non-parametric classifiers are in
accor
dance with their substantially similar nature: both of them use Euclidean dis-
tances to compute spectral weights for the final parameter estimation. Some differ-
ences are, however, evident in the trends of the classifiers on the k numbers and
05Amaro Forests - Chap 04 25/7/03 11:04 am Page 48
48 G. Chirici et al.
Fig. 4.5. Maps of stemwood volume obtained by the k-NN (a) and the fuzzy (b) classifiers (non-forest pixels
are masked out). The white line delineates the study site.
05Amaro Forests - Chap 04 25/7/03 11:04 am Page 49
49 Spatial Distribution Modelling
ranges considered. While the sensitivity of the k-NN to the number of points consid-
ered is rather low, the fuzzy classifier presents a very clear accuracy maximum in
correspondence to very small R
d
values (2–4 digital counts).
The quality of the estimation by the two classifiers relies on the correlation
among the variables and the image featur
es. The key to success is therefore having
spectral data correlated to the examined forest attributes and enough ground sam-
ples to cover all relevant variations in the study area (Franco-Lopez et al., 2001;
Maselli et al., 2001). Similar procedures are being tested in northern Europe and the
USA, where the spatial variability in forest composition and structure are frequently
lower. The results obtained from this experimentation are therefore significant in
showing that non-parametric spatial smoothers may produce useful per-pixel esti-
mates of forest attributes even in complex Mediterranean environments.
In this regard, the statistical significance of the correlations found is a first indi-
cation that the ETM+ data consider
ed are actually informative on the two forest
attributes and that the two non-parametric classifiers are capable of extracting at
least part of this information. It must, however, be remembered that the accuracies
achieved were not high. This can be explained, in part, by considering the complex-
ity of the study environments – especially the fragmentation and heterogeneity of
local forest coverage – as well as the difficulty in estimating the forest attributes con-
sidered, which are probably only indirectly linked to relevant spectral responses.
Furthermore, when assessing the low correlation coefficients, it should be kept in
mind that they should not be compared with those of ideal cases but with correla-
tions that could be expected from conventional methods (i.e. estimating stand vol-
ume by photo-interpretation). In this respect, even the relatively low accuracies
currently achieved can improve operational forest monitoring and management in
complex Mediterranean areas.
From a methodological viewpoint, it can be expected that notable improve-
ments could be obtained by further investigations using both the curr
ent and other
data sets. First, only a subset of TM bands was used for this analysis, and some
improvement could be expected by the utilization of all
ETM+ bands, and, even
more, of multi-temporal satellite acquisitions. Different spectral distances, such as
that of Mahalanobis, which accounts for the intercorrelations of the satellite sensor
bands but not for the spatial intra-cluster correlations, should also be tested.
Modified forms of such distances could be defined for each considered attribute in
order to give more importance to the most informative bands (Maselli, 2001).
Another option to consider is the effect of differential thresholding and weight-
ing. These factors could assume a particular r
elevance in relation to the spatial struc-
ture of ground sampling design. The accuracy assessment based on the leave-one-out
strategy is in fact sensitive to the presence of autocorrelated ground attributes when
some reference points are spatially close, as in cluster sampling. In these cases the
presence of spectrally similar plots within the same cluster leads to the preferential
inclusion of plots within the same cluster. This fact could partly explain the previ-
ously mentioned different sensitivities of the two classifiers to changes in the k and
R
d
values. The implications of both these behaviours must be quantified in order to
progress further with these spatialization methods.
Acknowledgements
The work, carried out with equal contributions by the authors, was partially sup-
ported by the Italian Ministero delle Politiche Agricole e Forestali – RISELVITALIA
funds. We are grateful to two anonymous reviewers for their helpful comments.
05Amaro Forests - Chap 04 25/7/03 11:04 am Page 50
50 G. Chirici et al.
References
Barbati, A., Corona, P., De Natale, F., Marchetti, M. and Tosi, V. (2000) Forest remote sensing in
Italy in the framework of FRA2000. In: Zawila-Niedzwiecki, T. and Brach, M. (eds) Remote
Sensing and Forest Monitoring, EUR 19530. Office for Official Publications of the European
Communities, Luxemburg, pp. 284–299.
Davis, J.C. (1973) Statistics and Data Analysis in Geology. Wiley, New York.
Fazakas, Z., Nilsson, M. and Olsson, H. (1999) Regional forest biomass and wood volume esti-
mation using satellite data and ancillary data. Agricultural and Forest Meteorology 98–99,
417–425.
Franco-Lopez, H., Ek, A.R. and Bauer, M.E. (2001) Estimation and mapping of forest stand den-
sity, volume, and cover type using the k-nearest neighbours method. Remote Sensing of
Environment 77, 251–274.
Horler, D.N.H. and Ahern, F.J. (1986) Forestry information content of Thematic Mapper data.
International Journal of Remote Sensing 8, 1785–1796.
Katila, M. and Tomppo, E. (2001) Selecting estimation parameters for the Finnish multisource
National Forest Inventory. Remote Sensing of Environment 76, 16–32.
Maselli, F. (2001) Extension of environmental parameters over the land surface by improved
fuzzy classification of remotely sensed data. International Journal of Remote Sensing 22,
3597–3610.
Maselli, F., Bonora, L. and Battista, P. (2001) Integration of spatial analysis and fuzzy classifica-
tion for the estimation of forest parameters in Mediterranean areas. Remote Sensing
Reviews 20, 71–88.
Richards, J.A. (1993) Remote Sensing Digital Image Analysis: an Introduction, 2nd edn. Springer-
Verlag, Heidelberg, Germany.
06Amaro Forests - Chap 05 25/7/03 11:05 am Page 51
5 Algorithmic and Interactive
Approaches to Stand Growth
Modelling
Michael Hauhs,
1
Falk-Juri Knauft
1
and Holger Lange
1
Abstract
The rationale for stand growth modelling is often grounded either in a search for improved sci-
entific understanding or in support for management decisions. The ultimate goal under the
first task is seen in mechanistic models, i.e. models that represent the stand structure realisti-
cally and predict future growth as a function of the current status of the stand. Such mechanis-
tic models tend to be over-parameterized with respect to the data actually available for a given
stand. Calibration of these models may lead to non-unique representations and unreliable pre-
dictions. Empirical models, the second major line of growth modelling, typically match avail-
able data sets as well as process-based models do. They have fewer degrees of freedom, and
thus mitigate the problem of non-unique calibration results, but they often employ parameters
without physiological or physical meaning. That is why empirical models cannot be extrapo-
lated beyond the existing conditions of observations. Here we argue that this widespread
dilemma can be overcome by using interactive models as an alternative approach to mechanis-
tic (algorithmic) models. Interactive models can be used at two levels: (i) the interactions
among trees of a species or ecosystem and (ii) the interactions between forest management and
a stand structure, for instance in thinning trials. In such a model, data from a range of sources
(scientific, administrative, empirical) can be incorporated into consistent growth reconstruc-
tions. Interactive selection among such growth reconstructions may be theoretically more pow-
erful than algorithmic automatic selection. We suggest a modelling approach in which this
theoretical conjecture can be put to a practical test. To this end, growth models need to be
equipped with interactive visualization interfaces in order to be utilized as input devices for
silvicultural expertise. Interactive models will not affect the difficulties of predicting forest
growth, but may be at their best in documenting and disseminating silvicultural competence in
forestry.
Introduction
Modern information technology (IT) has made modelling of many real world sys-
tems possible that were not long ago thought to be too complicated for the applica-
tion of formal methods of prediction. Distributed workstations and PC-based
1
BITÖK, University of Bayreuth, Germany
Correspondence to: michael.hauhs@bitoek.uni-bayreuth.de
© CAB International 2003. Modelling Forest Systems (eds A. Amaro, D. Reed and P. Soares) 51
06Amaro Forests - Chap 05 25/7/03 11:05 am Page 52
52 M. Hauhs et al.
computing extended modelling also to managed ecosystems, including the assess-
ment of forest growth. Yet the predictive power of growth models has not lived up
to the often high expectations derived from other applications (Vanclay and
Skovsgaard, 1997). Forest growth modelling is one example that may even be typical
of the general difficulty in linking and integrating research and management of (for-
est) ecosystems. In an exhaustive poll among German foresters in public service, sci-
ence and research came last when they were asked to rank external factors
potentially significant for sustainable forest management (Schanz, 1995). Scepticism
of managers towards models seems to be related to the generally low reputation of
formal methods and reasoning in silviculture practice.
Modelling is not only a method to bridge this gap between science and man-
agement, it can also help to analyse its causes.
Are growth models under-appreci-
ated by practitioners of silviculture or do models suffer from conceptual and
technical limitations that render them unsuitable for practical management? In any
modelling project, several aspects of the posed problem need to be reconciled: con-
ceptual, mathematical, engineering and ecological aspects. The sceptical attitude of
German foresters towards new growth models is the background for the question: Is
there anything that makes forestry qualitatively distinct from other application areas
of modern IT? In these other fields, weather prediction is such a case; computer
models have had a large and lasting impact on the routines of managers and the
reliability of services provided to customers. Historically, weather prediction mainly
rested on an empirical (and local) basis. Predictions were derived from past experi-
ences, rather than from the solution of well-understood equations describing non-
linear atmospheric transport processes. These days, such equations can be fed with
sufficiently accurate, actual data and solved computationally such that the corre-
sponding predictions now outcompete the crude empirical models of the past in
most cases. Limits in the time horizon of weather predictability are understood as
an inevitable feature of a complex dynamic system. In forestry, however, the yield
table, a form of ‘tabulated experience’, still dominates prediction under operational
conditions. Growth equations have a quite different character from transport equa-
tions; they are heuristic generalizations rather than applications of an underlying
theory. Practical management seems to work, yet often remains based on empirical
predictions that are sometimes outdated by the current context of forestry. Why is it
so hard for rigorous objective observations in forest ecosystems to provide knowl-
edge that is capable of substituting for empirical expertise? Here it is suggested that
the answer is interaction. Unlike the links to the weather system, any ecosystem
management includes interactive relationships at the scales relevant for managers.
The following discussion will show how it is technically possible to reflect interac-
tive relationships in modern software technology, and an application of a prototype
of such a model will be sketched out.
We use a specific task typical of German forestry, in order to analyse and dis-
cuss the challenges and opportunities that for
est growth modelling offers as an
application area of IT. The example is a series of thinning operations that typically
occur over the extended rotation periods for managed tree species of central Europe.
For Norway spruce, the economically most important species, the total timber yield
from such thinnings is about the same as the final harvest. Expertise in selective
thinning, the ability to regulate the growth competition among individual trees or
small groups of trees, can be regarded as a paradigmatic example of practical silvi-
cultural knowledge and expertise. Of course, the economic and ecological rationale
on which thinning decisions were based will have changed over the last rotation
period (80–120 years) due to the changing social, economic and environmental
boundary conditions of forestry. At the same time the regional, and sometimes even
06Amaro Forests - Chap 05 25/7/03 11:05 am Page 53
53 Algorithmic and Interactive Stand Growth Modelling
local, experience about growth responses to thinning has accumulated within
forestry. We will focus the following discussion on this knowledge about the per-
ceived technical choices that form the basis of each thinning from the perspective of
a forester. What are the silvicultural options, for example, when the task at hand is
the thinning of a 60-year-old spruce stand in southern Bavaria? In order to answer
this question, modelling forest growth has two options.
● Use the most recent and complete pool of relevant management experience, e.g.
the most appr
opriate yield table, local expertise, etc. (typically this approach is
currently used and organized within forestry); and/or
● use the best process-level understanding that is relevant to describe tree
gr
owth, e.g. from plant ecology, biogeochemistry of the nutrient turnover, etc.
(typically applied for regions or future scenarios where expertise is scarce).
From a modelling perspective, it has been customary to separate the dynamics
of for
est growth from the occasional evaluation and (thinning) interference imposed
by the forester. The former is represented as an autonomous set of algorithms that
can be run on a computer, the second can either be represented as an extra (goal)
function acting upon the growth simulation or by a real forester acting through an
appropriate (visual) interface (see Knauft, Chapter 30, this volume). In order to be
useful in an economic (or ecological) evaluation of thinning operations, the human
decisions are provided to the growth model through a visual interface in the form of
an external actor.
Interaction in Information Science
Among the various aspects of IT, the vastly increased possibility of interacting with
computer programs is one of most fascinating and relevant issues for the (cultural)
impact and theoretical foundations of IT (Wegner, 1997; Stein, 1999; Wegner and
Goldin, 2003). Based on our hypothesis that silviculture is an interactive enterprise
at its core, we regard forest growth modelling as particularly well suited to exploit-
ing the interactive character of today’s IT techniques. The technical aspects of devel-
oping interactive growth models through visualization is the topic of a companion
study (Knauft, Chapter 30, this volume); the example of applying an interactive
growth simulator to data from a thinning trial in Bavaria is presented elsewhere
(Hauhs et al., 2001). An interactive version of this reconstruction will be used as a
demonstration of the concept and is available from our website (www.bitoek.
uni-bayreuth.de/mod/html/webapps).
Interaction is a widely used (technical) term in scientific writing. A number of
systems fr
om basic sciences (interacting elementary particles), engineering (interac-
tive software) to sociology (‘true’ interaction among humans) might be character-
ized as interactive. In order to discuss links between the notions of interaction useful
for growth modelling and used in information science, we use a definition that is
based on the relationship between just two actors, i.e. systems that have choices and
make decisions. In these sequential interactions, two decision-making systems are
brought into mutual and sequential dependence for their respective choices, such as
in a two-person game. We use choice as a purely phenomenological description
attached to systems for their external behaviour. It does not relate to any internal
feature or organization inside the system displaying choice in a given situation (see
the chess example below, where a computer actually makes choices about the next
move). Choice is hence attributed to a system, whereas interaction is an attribute of
the relationship between two (or several) systems.
06Amaro Forests - Chap 05 25/7/03 11:05 am Page 54
54 M. Hauhs et al.
In computer networks, more powerful (non-sequential) forms of interaction
have been implemented, but there are few theoretical tools available yet to study
them. However, in information science the sequential form of interaction is already
regarded as more powerful than algorithmic computing. ‘Interactive computing can
be broken into algorithmic steps, but viewing it as nothing more than that would
“miss the forest for the trees”’ (Goldin et al., 2001).
A further difference is related to the perspective under which choices or inter-
action can be further classified: a decision or choice for a system can be assessed by
an external observer of its behaviour who may want to analyse the choice-making
system for internal mechanisms, i.e. finding out whether the choice is ‘r
eal’ or vir-
tual. For example, in the case of a chess computer, an observer might be informed
about the implemented algorithm and the conditions upon which it stops and
decides about the next move. However, with the quality of today’s chess computer,
there is no way to discover this just by playing against such an algorithm.
Knowledge about the internal organization of such an actor comes from the engi-
neers who build chess computers (Levy and Newborn, 1991). As long as we do not
have the engineers who build living systems from non-living ones, any question
about the nature of the choices displayed by biota remains open to speculation. It is
sufficient to note that all behaviour of living entities is currently history-dependent
and its memory is not fully accessible to an external observer. However, the above
definition of interaction is phenomenological, including, for example, interaction
with a telephone-answering machine. That is why we do not need a more sophisti-
cated discussion about the ‘true nature’ of the various types of choices occurring
within the systems that interact.
The notion of interaction as introduced here is actor-dependent and needs to be
posed in the context of the computational and memory r
esources of the respective
actor. This implies that asking whether any external relationship between two actors
is interactive or not has to be asked and answered separately for each of them.
Results of this classification will depend on the actor’s respective computational
capacity, as an example from chess will show. One could imagine that a powerful
computer or player discovers a (conditional) winning strategy at a given point in the
game and hence renders the remaining moves a simple choice problem whose out-
come will be fixed. To this actor, the remaining sequence of choices is no longer fully
interactive and will in fact no longer have the character of a game. An opponent
who has yet to discover the full picture still regards the same situation as truly inter-
active. Mathematically, chess is interesting as a fully deterministic game with a finite
number of simple rules, yet a game for which no winning strategy is known and
may not even exist. From a forestry perspective, a thinning trial can be abstracted as
a sequential game with predefined rules (at least for the forester) and the yield table
as an archive or crude look-up table of played out games.
Interaction in Biology
There have been different proposals in information science about how to formalize
(sequential) interaction (van Leeuwen and Wiedermann, 2001; Wegner and Goldin,
2003). For the purpose of this discussion it is sufficient to note that any capacity to
engage in an interaction among programs requires persistence of data (states)
between the individual decisions provided by the actor. Any of these individual
decisions may in itself be algorithmic, as in the example of a chess computer. The
memory on which an algorithmic decision is based is usually not available to the
partner in a sequential interaction such as a game, and that is why choice and deci-
06Amaro Forests - Chap 05 25/7/03 11:05 am Page 55
55 Algorithmic and Interactive Stand Growth Modelling
sion making seem to occur for an external observer. Different types of interactions
can be distinguished by the form of persistent data, i.e. the type of memory utilized
by the respective actor engaged in interaction. Here we need two versions of inter-
action, human interaction (i.e. interaction based on cultural forms of memory, such
as yield tables or growth equations) and biological interaction with a genetically
encoded memory.
Biological interaction describes the ability of organisms to engage in a mutu-
ally dependent r
elationship that has the character of a temporal chain of choices
(in our phenomenological sense). In these mutually dependent decisions, the
future choices for one organism are partly constrained by the past choices of the
others and its own decisions, similar to the character of a game. In ecosystems
this becomes a multi-player game in most cases. The possibility of biotic choices
is an expression of phenotypic plasticity, i.e. the property of a given genotype to
produce different phenotypes in response to distinct environmental conditions
(Pigliucci, 2001). The strategic aspects of height growth of trees, for example, can
be regarded as a behavioural phenotype evolved from past interactions with
competing species. A forester has to deduce this growth potential of a specific
stand from the actualized growth that can only resemble a subset of the potential
behaviour.
The key assumption for the proposed interactive approach to growth modelling
is to r
egard biological interaction as ‘irreducible’, i.e. at least for pragmatic reasons
we will not seek to reduce it to an algorithm, or engage in discussions about the
chances of doing so (Hauhs and Lange, 2003). It is important to note that the special
character of interaction does not derive from internal ‘mechanisms’ within the con-
sidered actors, but rather derives from the richness and responsiveness of their envi-
ronment. Given the computational and memory capacity of the actors involved, no
algorithmic prediction can be given for the environment under which forest growth
occurs.
Interaction in Silviculture
Modern forestry has to provide and manage a number of services, not just the goal
of a maximum (or economically optimal) rate of fibre production. This starting point
resembles the observation that ‘at the heart of the new computing paradigm is the
notion that a system’s job is not to transform a single static input to an output, but
rather to provide an ongoing service’ (Goldin et al., 2001, emphasis in original).
Silviculture is a repetitive interference with the growth processes under a specific
goal and in the face of several technical and biological options that act to influence
forest growth. However, in any particular stand, the silvicultural options with
respect to thinnings are not known at the time of planting or stand regeneration;
they have to be inferred and updated from actual growth. This reflects the history
dependence and unique character of each ecosystem (Lange, 1999). A common prin-
ciple for any specific thinning operation is therefore to make only those decisions
that are regarded as necessary at the current stage of growth and leave a maximum
number of potential choices for the next visit, e.g. after 10–20 years. In this respect,
thinning trials do resemble the chess example. Only the goals and the rules are
known at the beginning, decisions can only be made by assessing each actualized
situation. In information science, such a system of data supply, where each element
in a stream of data, which only becomes available after the preceding one has been
processed, is termed ‘lazy evaluation’. This distinguishes streams from strings, or
sequences that define the known and finite amount of input to ordinary algorithmic