2 Simplicity versus Efficiency
2.1 Simplicity, Efficiency, and Economy in Forest Surveys
Wayne L. Myers, Ganapati P. Patil
Abstract
Forest inventory must ensure that comprehensive information on forest ecosystems is obtained and presented to decision makers in a manner that is comprehensible.
Acquisition of comprehensive information must also be preceived as being straightforward by the field forester, otherwise the information will be wrongly obtained or the wrong information obtained. It is misleading, however, to be simplistic in dealing with com
plexity. Forest ecosystems are inherently complex and must be treated accordingly.
In a multi-resource or ecosystem-oriented forestry context, information requirements transcend status of individual components. Need for information on relations among components is the norm rather than the exception. Trends are often equally or more important than current status. Growing concern with landscape issues places emphasis on spatial specificity and vicinity effects that were heretofore largely ignored. Contemporary reality is that new issues will continue to arise which require responsiveness from the information system. The ability to prespecify information needs is eroding under environ - mental activism. Forestry information systems must be able to accommodate tracking of additional ecosystem elements as new issues arise.
Computerized knowledge-based systems have emerged for providing easily used and understandable interfaces for field foresters and decision makers. Innovative statistical approaches such as meta-analysis, weighted distributions with encountered data, ranked set sampling, and composite sampling offer observational economy. Geographic infor
mation systems are rapidly becoming essential platforms for integrating synoptic spatial data with sample-based field observations. Consideration should be given to new para
digms which will maximize the joint functionality of the several information sciences and technologies.
Keywords: Composite sampling, Ranked set sampling, Encounter sampling, Encoun
tered data, Meta-analysis, Weighted distributions.
2.1.1 Perspectives
Since trees are among the longer-lived organisms of our planet, forestry necessarily has a long-term perspective. Companion to this long-term perspective has been a reluctance toward fundamental shifts of paradigms. The trajectory of forestry is well captured by the theme for a national convention of the Society of American Foresters which was phrased as "Forestry - An Evolving Tradition". Forest survey as the informational arm of forestry has moved forward through time in this same inertial manner. As new informational strategies and technologies appear, they are treated as optional enhancements to existing
forestry information vehicles rather than as opportunities for new vehicle designs. Using a garden cultivator as an analogy, one adds a motor, then an electric start, then inter
changeable tilling blades, and so on. Irrespective of the enhancements, however, the cultivator still plays its traditional role in gardening. In forest survey, the computer still plays much the same role as mechanical calculators of a half-century past. As the new millenium approaches, it is perhaps appropriate to consider different information system paradigms to accompany the emerging ecosystem orientation of forestry.
We begin by examining questions of simplicity, efficiency, and economy in forest surveys. We next consider some statistical innovations which have proven advantageous in environmental contexts having counterparts in forest ecosystems. These statistical strategies can contribute directly to continuing incremental evolution of forest survey designs and inference therefrom, particularly in multi-resource settings. We then proceed to explore potentials for next-generation integrated forest ecosystem information systems which couple such strategies directly with emerging computer-based spatial technologies in the context of knowledge-based systems.
Simplicity vs. Simplification
Forestry practitioners have long treasured survey designs that simplify field work and procedures for arriving at estimates from the data thus collected. In the USA, for example, 10% systematic "cruises" were long a part of the forestry tradition, and remain fondly regarded by many of the elder foresters. When it has been necessary for the field forester to perform immediate analysis, considerable effort has gone into ingenious design of recording forms and formulation of "factors" that make the analysis highly mechanical.
The basic nature of this simplicity syndrome is revealed by that the ultimate universal acceptance of variable radius or point sampling methods. Although having much greater inherent complexity than fixed size plots, the variable radius approach has been made Easy to Apply. Prisms and relaskops facilitate selection of sample trees in the field, and "basal area factors" allow counts to be translated immediately into estimates. The fact that most field foresters would be hard pressed to explain the direct derivation of basal area factors does not seem to be of great concern. For this, one will be referred to inventory specialists and textbooks. Field foresters are content with being able to consider this as just a different sort of plot. Conversely, ingenious designs such as 3P sampling have been introduced with much fanfare by inventory specialists and then faded quietly into operational oblivion because the inherent complexity was not substantially concealed for purposes of application.
It is the responsibility of inventory specialists to ensure that comprehensive information on forest ecosystems is obtained and presented to decision makers in a form that is comprehensible. Information that is not understood does not inform, but instead fosters confusion where clarity is needed. Acquisition of comprehensive information must likewise be perceived as being straightforward by the field forester, otherwise it will be wrongly obtained or the wrong information obtained. It is, however, a social wrong to be simplistic in dealing with complexity. Forest ecosystems are inherently complex and must be dealt with accordingly.
To borrow some computer jargon, forest inventory systems must be made "user
friendly". This does not imply that they should be inherently simple. Statistical and spatial sciences are generating ways of handling complexity faster than they can be implemented under traditional paradigms. Fortunately, knowledge-based systems have emerged for providing easily used and understandable interfaces for both field foresters and decision makers. It is inventory specialists who now face the issues of complexity in configuring appropriate systems for acquistion and delivery of comprehensive information regarding
forest ecosystems. Unless super intellect arises mystically, the Inventory Specialist is predestined to individual inadequacy.
The obvious solution is interdisciplinary inventory design teams with the former inventory specialist serving as coordinator of further specialized team members, each of which is fully cognizant relative to a particular branch of information science and technology. This is our approach at The Pennsylvania State University where the Center for Statistical Ecology and Environmental Statistics, the School of Forest Resources, and the Office for Remote Sensing of Earth Resources are collaborating.
Efficiency as Efficacy
The basic criterion of effectiveness for a forest inventory system is provision of adequate information for decision making at a suitable level of detail and in timely manner. Failure is evident when the inventory system itself becomes an issue in decision making. Further determinations of efficiency are probably better made in terms of the decision maker's time than in statistical terms of relative variance. Relative variance of alternative estimators has more to do with economy since it concerns the extent of data collection needed to achieve a given precision.
There are several considerations relative to efficiency of decision making. Time and effort expended by the decision maker(s) in accessing the system are primary considerations which could be quite readily and objectively assessed. Very important but more subjective is the degree of decision uncertainty that is attributable to the information system. This is perhaps best assessed retrospectively in questionnaire format by inquiring whether a decision would have carried less uncertainty if information had been available differently from the system. Where group decision making or constituencies are involved, it becomes necessary that the system be capable of casting information in a form suitable for participation/presentation. There is universal need for information systems to be anticipatory, since postponing decisions to accommodate supplemental field data collection is often problematic.
In a multi-resource or ecosystem-oriented forestry context, information requirements usually transcend status of individual components. Need for information on relations among components is the norm rather than the exception. Likewise, trends are often equally or more important than current status. Growing concern with landscape issues places emphasis on spatial specificity and vicinity effects that were heretofore largely ignored. Finally, a contemporary reality is that new issues will continue to arise which require responsiveness from the information system. The ability to prespecify information needs is eroding under environmental activism. Forestry information systems must be able to accommodate tracking of additional ecosystem elements as new issues emerge.
Economy of Scale
Economy concerns affordability and cost/benefit. Economy is highly dependent on scale and scope of organizational purview. Despite the foregoing and ensuing, it is prudent to resist temptation to fix what is not broken. Restructuring always places additional demands on personnel and finances, as well as requiring acclimation on the part of decision makers to the unfamiliar. Furthermore, a "proving period" is usually needed to ensure that new systems are functioning according to expectations. One should be aware of potential advantages in new approaches and should move aggressively when opportunity arises to achieve greater capability at less cost. More generally, costs and benefits of change must be weighed carefully under the realization that technological investments carry the prospect of rapid obsolesence. Concerns for information decay pertain primarily when trends are not of interest.
Having duly set forth the previous cautions, we venture to suggest that many, if not most, forestry organizations with substantial land areas have inventory infrastructure that is incipiently or already obsolete relative to current information science/technology and/or societal appetite for information regarding forest ecosystems. Evidence of organizational handicap in operating with obsolete infrastructure is globally abundant across many sectors, repeatedly proving to be uneconomical. Regrettably for the near term and fortunately for the long term, information sciences and technologies are in tremendous flux. Challenges of configuration and integration are formidable. Attempting to stay at the informational forefront is almost certain to prove uneconomical as well. The latest generation of computer hardware and software carries a large price premium relative to the immediate predecessor. Furthermore, experiential precedent for application is generally lacking at the developmental margin.
The one thing which emerges as being certain in such an informational climate is that tradition loses its virtue. Any pronouncements regarding optimality must be highly conditional. What is advantageous at one scale may be deficient or unaffordable at a different scale. Simply acquiring the latest of each informational offering does not confer potential combinatorial advantage. Informational integration must be addressed explicitly, as in the recent release of linkage between S-Plus in the statistical software sector and Arc/Info in the geographic information systems (GIS) sector. Even this is only a beginning toward statistical penetration of the spatial domain.
2.1.2 Innovative Statistics
One can find either frustration or excitement in the contemporary information dynamic.
We advocate the latter view. In any case, complacency is imprudent. Accordingly, we turn next to some current realms of statistical innovation which have been explored in ecological and/or environmental contexts by the Center for Statistical Ecology and Environmental Statistics at The Pennsylvania State University. These topics are immediately relevant to multi-resource and ecosystem-oriented forest inventory. They further suggest alternative integrative views of forest inventory in spatial context that appeal to GIS and knowledge-based systems.
Meta-analysis, Encountered Data, and Weighted Distributions
Patil calls attention in numerous publications and presentations to a dismal cycle of no information, new information, and non-information. The essence of the message is that scientists and resource specialists, when confronted with a decision-making context, feel discomfort with a perceived inadequacy of data for addressing the question. Accordingly, they declare need to mount a new data acquisition effort. Assuming that the new data collection effort is sanctioned, and having proceeded to obtain the new data, they again perceive deficiencies so that the new data effectively becomes non-information since definitive direction for the pending decision is still not forthcoming. While this is perhaps more fundamentally a human psychological problem of anxiety concerning uncertainty, it nevertheless has a real impact in terms of the decision-making process. It also contributes to a negative view of investments in surveys from the decision maker's perspective.
Whereas the decision maker had reasonably expected to obtain solid quantitative guidance for administrative action, the support received is soft at best.
To the decision maker it appears that the value of past inventory investments has become negligible. It further appears that new inventory investments have questionable utility. The decision maker thus tends to overweight personal intuition and support
inventory operations only to the extent of having credible claim that inventory has been duly conducted. Clearly there is advantage to both decision makers and inventory specialists in breaking this cycle of negative feedback.
Although it may seem to be heresy, consider the scenario whereby inventory is obligated to render decision support on the basis of existing data, with new surveys only taking place when decision makers deem such guidance to be inadequate. Let there be a further inventory obligation to acquire supplemental data only to address particular deficiencies in existing data. Inventory must therefore combine evidence from disparate sampling operations in meeting its charge. This is known in statistical circles as Meta
Analysis, which now holds respectable stature in the discipline. PATIL (1991) provides a cogent view and review of meta-analysis in the context of statistical ecology and environmental statistics.
Since the area of present interest is unlikely to be framed exactly as in previous surveys, there is effectively no proper retrospective sampling frame. In searching the data archives, one will encounter some samples from each of several previous surveys having pertinence to the present problem. Part of the area may have been intensively sampled in one survey, and a different part lightly sampled in another survey. In some instances, the coverage of prior surveys will partially overlap. It is likewise inevitable that the prior surveys will have been made at different times, making some data more current than other data. It thus becomes necessary to weight available samples differentially in arriving at a combined estimate. This is a case of Encountered Data and the set of weights constitute a Weighting Function. The retrospective samples and their associated weights give rise to a Weighted Distribution.
In similar manner to the way unequal selection probabilities for a proper sampling frame are used inversely for estimation, so also the weights are used inversely with appropriate normalization in arriving at a combined meta-analytical estimator. Since it lends increased utility to past inventory investments, it would seem that inventory specialists should exhibit willingness to engage in meta-analysis even without managerial coercion.
Encountered data and weighted distributions have a unifying purview that extends well beyond meta-analysis. The unifying quality of weighted distributions was perceived early on by RAO (1965), and revisited by him two decades later (RAO 1985). Encounter sampling with elaborately conceived weighting (detectability) functions forms the basis of transect sampling for fauna as discussed by PATIL et al. (1993). They consider the possibility that encountered and biased data may be more informative under weighted distributions than designed counterparts. PATIL ( 1984) has discovered weighted distributions as stochastic models in the equilibrium study of populations subject to harvesting and predation. MAHFOUD and PATIL (1981) and PATIL et al. (1986) have identified a Bayesian analogue to the theory of weighted distributions through the relationship of the posterior distribution to prior distribution via the likelihood.
Ranked-Set Sampling
Ranked-set sampling (RSS) fills a void in the repertoire of surveys by offering opportunity for direct exploitation of capability for ordination. Its history also underscores the importance of recognizing generality of concepts that may be introduced in limited context. The Center for Statistical Ecology and Environmental Statistics at The Pennsylvania State University has played a substantial role in solidifying theory for this approach and calling attention to breadth of applicability.
RSS originated with MCI NTYRE (1952) for estimation of pasture yields. After some years of inattention, it was similarly applied to forage under forest (HALLS and D ELL
1966) and forest regeneration (EVANS 1967). These early explorations shared the narrow context of ranking to select one among a set of locally clustered plots for measurement.
This particular context is affected by spatial autocorrelation among the members of local clusters.
RSS is conveniently viewed as a nonparametric sort of double sampling with sets. The first phase determination is a ranking, and the second phase determination is quanti
fication of a subsample selected on the basis of rank. The scenario begins with choice of a set size (M) such that the M members of a set can be ranked with some degree of consistency. Although limited ranking errors do not obviate the method, increasing numbers of such errors will progressively degrade efficiency. The first phase sample is a series of sets, with each member of a set being individually selected (at random) from the population. When M sets of size M have been identified, the members are ranked within each set. One member of each set is then designated for quantification. The highest ranking member is designated from the first set, the second ranking member from the second set, and so on. Such a cycle of selection activity yields M samples for quantification in the second phase. The second phase sample size can be augmented in steps of M by repeating the selection cycle. Repeating the cycle R times will yield an ultimate sample of size MR.
The mean is estimated as for a simple random sample of size MR. Multiple cycles are required for estimating the variance of the mean and each sample value must be rank
tagged, since squared deviations are computed about the respective rank means. The divisor for the sum of squared deviations is then MMR(R-1). Estimates of the mean and its variance are unbiased, even in the presence of possible ranking error. The nonparametric character of the RSS involves no restrictive assumptions concerning underlying dis
tributions.
In terms of relative efficiency as variance ratio for estimators, RSS performs at least as well as simple random sampling with size MR. Since T AKA HAS I and W AKIMOTO (1968) have showed that (M+l)/2 constitutes an upper bound on efficiency for all continuous distributions with finite variance, large set size is advantageous if it does not impair ranking ability. It seems that ranking errors should generally increase with set size for many ecology/forestry applications, if only as number of ties that must be arbitrarily or randomly broken. Such increases in ranking error tend to counter the advantage of larger set size.
As discussed later, remote sensing and GIS provide a huge pool of opportunity for ranking in forest inventory. Ranking from these sources is, however, not without cost.
While unit cost of ranking has been considered under certain conditions, GIS and remote sensing will often involve fixed cost for the first set with much smaller variable cost for additional sets. Additional research is needed to improve designability of RSS with fixed cost for ranking.
JOHNSON et al. (1993) have reviewed RSS for vegetation. PATIL, SI NHA and TAILLI E (1992) have compared RSS with the regression estimator in double sampling. GO RE, et al.
(1993) have explored some multivariate issues in RSS. PATIL et al. (1993) provide a general framework for RSS with reference to encounter sampling and weighted distributions which were introduced in the previous section.
Composite Sampling
Ranked set sampling effectively increases sample representation while avoiding the more costly determinations for many samples. The same sort of observational economy can be achieved by composite sampling for some types of environmental variables, particularly compositional aspects of soil and some other substrates. Since soils will become
increasingly important for ecosystem-oriented forestry, this approach has potential relevance to forestry.
The composite sampling approach involves removing samples to the laboratory and mixing aliquots according to certain schemes for joint analysis. Considerable research in application of composite sampling for analysis of soil contaminants has been conducted in the Center for Statistical Ecology and Environmental Statistics (PATIL, G ORE and SINHA 1992). This work includes schemes for detecting more localized concentrations of contaminants/constituents. GORE et al. (1993) consider compositing in conjunction with rank set samples. This latter combination of approaches provides opportunities for exploiting GIS that remain to be explored.
2.1.3 Spatially Framed and Object-Oriented Forest Inventory
As indicated earlier, conventional approaches to forest inventory pose difficulties in combining information from different surveys. Posing an even greater problem is the increasingly important issue of integrating information across multiple ecosystem components that demand to be addressed differently for purposes of data acquistion. Still more problematic is growing need to account for vicinity effects so that management can better recognize landscape structure in its husbandry of resources. Contemporary foresters are expected to manage "standscapes" rather than stands.
These are inherently spatial issues, and much of the difficulty in resolving them is attributable to the pseudo-spatial nature of conventional forest inventory parameters and their estimators. Means are stated in apparent spatial density form using "per unit area"
scalars. While such scaling is interpretively appealing to the natural human spatial sense, it is completely lacking in multidimensional congruence with the physical space that provides the integral fabric of landscapes. We should not be surprised that there is difficulty in capturing the structural integrity of physical space in a statistical parameter space which makes no such provision.
We therefore propose that planimetric position must be directly associated with all informational elements in forest inventory, with positional uncertainty being explicitly recognized. We further propose a shift in paradigm toward conceptionalization, represen
tation, and estimation of informational structures as spatial fields in the sense of physics and/or objects with definite planimetric configuration existing in geometric coordinate space. Dual representation will be appropriate in many cases.
In field mode, we would recognize three major types of field variables. We would characterize the first type of field variable as an occupancy field, generating expectation of particle frequency when volumetrically integrated over a planimetric region. We would characterize the second type of field variable as a mass field, with the volumetric integral operating on a spatial attribute which may permeate or be attached to particles. We would characterize the third type of field variable as an influence field, being a polarized directional effect over space. Elevational and/or temporal effects can be represented as bivariate or multivariate fields.
In this new view, plot-based data would generate synoptically estimated fields through the geostatistical approach to be stored as rasters and analyzed or portrayed with geographic information systems. Unlike the conventional situation, associations among information elements induced by spatial proximity thus become subject to direct modeling and/or empirical investigation. Synoptically mapped or remotely sensed information as currently incorporated in GIS become directly conformant with other information
elements. It should be highly informative to study, for instance, estimated tree occupancy fields or canopy height fields through the lens of remotely sensed data.
Objects constitute the natural complement of fields, and object-oriented approaches to software coupled with vector GIS provide a natural way of representing them. The object - oriented rendition is nevertheless quite different from the traditional program and data file version. The objects are software entities having an appropriate suite of attributes and a complement of methods by which they become active. An object-oriented approach to conventional plot-based estimation would have plot objects passing informational mess
ages to a formative estimate object. Future augmentation of objects with artificial intelli
gence will eventually give rise to INFORmation ORGANISMS (INFORGANISMS).
Computer intelligence of the present flows from knowledge-based systems (KBS), which have reached a level of maturity sufficient to support the new forest inventory paradigms outlined above. It would be folly to undertake construction of a monolithic program for implementing such scenarios. A very workable architecture, however, has platoons of knowledge-based subsystems responding to direction from higher level (sub)systems and giving direction in turn to lower level subsystems, with capability for
"firing" an external software system as a "demon" at any level. When modifications are needed or new capabilities appear in external software packages, new demons replace old demons or join the growing host. Knowledge of system intricacies and structure is imbedded directly in the systems so that users need not be bothered. Even manuals could easily become an artifact of the past. Myers and Foster at The Pennsylvania State University have built an operational and publicly available, but as yet unpublished, shell called GNOSIS for configuring such systems within the somewhat limited capacity of PC
DOS computers.
It is not expected that the paradigm shifts sketched in these seeming flights of fancy will be embraced by a traditionally conservative forestry profession in the immediate future.
Mounting such a hypersystem in the near term would, in fact, be a rather heroic undertaking. Nevertheless, all necessary elements of information science and technology are essentially available or rapidly emerging ( MYERS 1993). The rates of evolution in GIS and KBS are particularly impressive, and both of these technologies will inevitably be integral to future forest inventory. There is an abundance of opportunity and considerable challenge in effecting the merger of statistics with GIS. We are focusing our joint efforts on innovative sampling with GIS, using ranked set sampling as a point of departure.
Suitability and sensitivity indices are a mainstay of GIS, and these can serve for ranking.
The major labor is in using macros and toolkits to build support for rule-based set selection with visual or algorithmic ranking.
Prepared with partial support from the Statistical Analysis and computing Branch, Environmental Statistics and Information Division, Office of Policy, Planning, and Evaluation, United States Environmental Protection Agency, Washington, DC under a Cooperative Agreement Number CR-821531. The contents have not been subjected to Agency review and therefore do not necessarily reflect the views of the Agency and no official endorsement should be inferred.
2.1.4 References
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HALLS , L.S.; DELL, T.R., 1966: Trial of ranked set sampling for foraged yields. For. Sci. 12, 22-26.
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