Environmental Risk Assessment and Management from a Landscape Perspective (Kapustka/Environmental Risk) || Relevance of Spatial and Temporal Scales to Ecological Risk Assessment

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<ul><li><p>4RELEVANCE OF SPATIAL AND</p><p>TEMPORAL SCALES TOECOLOGICAL RISK</p><p>ASSESSMENTAlan R. Johnson and Sandra J. Turner</p><p>Monk: All is reduced to One. What is this One reduced to?Bassui: One inch long, one hundred meters short.</p><p>Monk: I cant understand.Bassui: Go and take some tea.</p><p>Stryk and Ikemoto (1981, p. 38)</p><p>As this dialogue between Bassui and an unnamed monk illustrates, discussions ofscale can be confusing. Is one inch long? Is 100 meters short? Its all relative, ofcourse. Perhaps the best course is simply to retreat and enjoy a cup of tea. However,scientists in many disciplines grapple with issues of scale in both space and time. Wesummarize some of the resulting literature, with an emphasis on ideas from landscapeecology, and discuss their relevance to ecological risk assessment.</p><p>The world can look very different depending upon the scale of observation. Theprocesses relevant to our description are often scale-dependent. In the macroscopicworld, describing the dynamics of planetary motion requires only one physical force:gravity. But among the forces recognized in modern physics, gravity is the weakest,and its effects are only apparent over relatively large distances. Descriptions of phe-nomena at the increasingly microscopic scales of molecules, atoms, and subatomicparticles requires stronger, but shorter-range, forces to be invoked, and gravity canessentially be ignored.</p><p>Environmental Risk and Management from a Landscape Perspective, edited by Kapustka and LandisCopyright 2010 John Wiley &amp; Sons, Inc.</p></li><li><p>56 RELEVANCE OF SPATIAL AND TEMPORAL SCALES TO ECOLOGICAL RISK ASSESSMENT</p><p>On the other hand, sometimes things look rather similar across a range of scales.As Benoit Mandelbrot, the inventor of fractal geometry, has observed, when one exam-ines a cloud or a coastline closely, it doesnt become smooth, but reveals irregularitiesat many scales. Understanding what changes, and what stays the same, across varyingscales of observation is one of the foundations of clear thinking about scale.</p><p>The concept that natural phenomena and anthropogenic change have characteristictemporal and spatial scales is critically important if we are to narrow any risk assess-ment to those things that specifically and coherently address the focal question of theassessment. We should incorporate these concepts explicitly into the design and imple-mentation of ecological risk assessments. Identifying the appropriate observation andmeasurement criteria and the appropriate temporal and spatial scales for measurementsis crucial. Investigations must consider interactions across multiple scales to quantifyprobable effects of environmental stressors on the chosen risk assessment endpoints.But before we can examine that issue, we must introduce some terminology that willallow for a more precise discussion.</p><p>A TYPOLOGY OF SCALE</p><p>Wu (2007) has systematized concepts of scale by distinguishing between dimensions,kinds of scale, and components of scale. Dungan et al. (2002) also discuss the ter-minology used to describe various aspects of scale in ecology. We present our owntreatment of the subject (Table 4.1) that borrows heavily from these two sources.</p><p>Dimensions of Scale</p><p>The dimensions that scale can refer to are either temporal or spatial. Time is inherentlyone-dimensional. Space, at least in our ordinary experience, is three-dimensional,although for the sake of analysis we sometimes restrict our attention to two-, one-,or zero-dimensional subspaces. That is, we live a world with volume, but sometimestalk about surfaces, lines, or points (embedded in three-dimensional space). So thefirst issue in discussing scale is to state the dimensions under consideration. Are wereferring to temporal scale, spatial scale, or both? And, if space is involved, are wemeasuring scale in terms of length, area, volume, or some combination?</p><p>Wu (2007) also identifies levels of hierarchical organization as a dimensionof scale. We do not follow this part of his scheme, because we view hierarchicalstructure as being conceptually different from dimension or scale. The tendency,prevalent in the literature, to equate hierarchical levels with scale has caused muchconfusion. However, as has been persuasively argued elsewhere, scales and levelsare conceptually different things and should not be confused (Ahl and Allen 1996,Allen and Hoekstra 1992, King 2005).</p><p>Kinds of Scale</p><p>The concept of scale can be applied to different aspects of reality (or our understandingof it). The kinds of scale considered here reflect those with particular relevance to</p></li><li><p>A TYPOLOGY OF SCALE 57</p><p>Table 4.1. A Typology of Scale, Adapted from Wu (2007) and Dungan et al. (2002), withSome Modifications</p><p>Dimensions of ScaleSpace Dimensions that allow for characterizing the size and location of objects</p><p>and phenomenaTime Dimensions that allow for characterizing the sequence, duration, and</p><p>frequency of events</p><p>Kinds ScaleIntrinsic The spatial or temporal scale at which a pattern or process occursObservational The spatial or temporal scale of measurements or other data used to study</p><p>a pattern or processExperimental The spatial or temporal scale of manipulations or treatments used in the</p><p>scientific investigation of a pattern or processAnalysis or</p><p>modelingThe spatial or temporal scale imposed or assumed in data analysis or</p><p>model constructionPolicy The spatial or temporal scale at which policies or management activities</p><p>affect the system</p><p>Components of ScaleLength, period,</p><p>or frequencyAn estimate of the intrinsic scale of a pattern or process</p><p>Grain The finest level of spatial or temporal resolution allowed by theobservational, analysis or modeling scale</p><p>Extent The greatest spatial or temporal span captured by the observational,analysis, or modeling scale</p><p>Coverage Proportion of the spatial or temporal extent actually sampled; related tosampling density or intensity</p><p>ecology and environmental risk assessment. For any phenomenon in the materialworld, we can imagine an intrinsic scale. What is the intrinsic scale of a hurricane?For a single event, we can discuss spatial scale in terms of the instantaneous size ofthe storm or the cumulative area affected by its passage. The temporal scale is set bythe storms duration. For hurricanes as a class of disturbance events, the frequency ofrecurrence is a component of temporal scale.</p><p>The concept of intrinsic scale (Table 4.1) can be applied widely to physical,chemical, biological, ecological, and social phenomena. The combined effect of set-tling rates and turbulent mixing rates determine how long particulates emitted froma stack will remain in the atmosphere. When the advection rate is included, the spa-tial scale of the particle fallout is determined. The dispersal rate of organisms placesa constraint on the rate of spread of an invasive species. The intrinsic populationgrowth rate constrains the time scale required for recovery of a population subsequentto intense harvesting or massive mortality from an oil spill. Human settlements grow,and sometimes decline, at various rates. New technologies, with concomitant benefitsand risks, diffuse through society at rates affected by economic and cultural factors.</p></li><li><p>58 RELEVANCE OF SPATIAL AND TEMPORAL SCALES TO ECOLOGICAL RISK ASSESSMENT</p><p>Although it is often convenient to talk about intrinsic rates of phenomena, we infact have no direct knowledge of any intrinsic properties of nature. What we, asscientists, can obtain are observations, which we analyze in various ways and fromwhich we build models or construct theories to account for the observed phenomena.Any set of observations can be characterized by its spatial and temporal scale. If theobservations come from a manipulative experiment, our experimental treatments occurat a particular spatial and temporal scale. As we analyze the data, we may subset it,or pool observations, or compute averages, or do other manipulations that have theeffect of changing the spatial or temporal scale. If we build a model, or elaboratea quantitative theory, this too has an associated scale, although sometimes the scaleis implicit (and perhaps obscure) rather than explicitly recognized. We may use ourmodels or theories to make inferences at spatial or temporal scales different than theexperimental or observational scales associated with our data. For example, responsesof plants in the laboratory or small-scale field plots to ozone may be used to modelchanges in regional forest productivity (Laurence et al. 2000). This approach requiresextrapolation of effects across scales, which is difficult and risky (Woodbury 2003),but is often demanded to generate policy. Policies are a product of human institutionsand operate at particular temporal and spatial scales. Discussions of scale must becareful to distinguish the kind of scale under consideration (Table 4.1).</p><p>Components of Scale</p><p>So far our typology of scale has focused on qualitative features. We turn now tocomponents of scale, which address quantitative aspects of scale (Table 4.1).</p><p>When we seek to quantify the intrinsic scale of a phenomenon in space, weusually do so in terms of a characteristic size or range of sizes. Size in space is oftenrepresented in terms of a length scale (e.g., a radius or diameter), but area, volume, ormass units may also be used. Thus, nanoparticles can be characterized by a distributionof particle sizes, usually log-normal, which may be related to the physical processesof their formation (Kiss et al. 1999). Similarly, in aquatic ecosystems, the biomassspectrum has frequently been studied, with bioenergetic and ecological interpretationsgiven to the positions and temporal changes in the modes (peaks) in the observeddistribution of organism sizes (e.g., Kerr and Dickie 2001). In landscape ecology,metrics such as area-weighted average patch size are used to characterize the scale ofheterogeneity in patchy landscapes (e.g., Gardner et al. 2008).</p><p>Along the temporal dimension, the most straightforward analog of size is dura-tion. However, time scales are also often characterized according to frequency. Themotivation for this comes from statistical time-series analysis, in which a given timeseries, representing the fluctuations of some ecologically relevant quantity, can beconverted into a sum of sine and cosine functions via the Fourier transform (Platt andDenman 1975, Turner et al. 1991). For many environmental quantities, it is observedthat variation at certain frequencies contribute more heavily to the observed dynam-ics, as indicated by peaks in the frequency spectrum. These peaks may be said torepresent dominant or characteristic frequencies for the phenomenon. For instance,in reconstructed regional dynamics spanning centuries, forest disturbance processes</p></li><li><p>A TYPOLOGY OF SCALE 59</p><p>such as fire and defoliating insect outbreaks exhibit quasi-periodic behavior that maybe related to climatic variability or other factors (Swetnam and Betancourt 1990,Swetnam and Lynch 1993).</p><p>Ecological phenomena can be said to have an intrinsic scale, expressed in termsof characteristic size and frequency along spatial and temporal dimensions, but ourknowledge of these scales ultimately rests on observational data. Two key componentsof observational scale are referred to by landscape ecologists as grain and extent. Theterm grain can be understood by analogy to grain in photographic film. In film, imagesare recorded by photochemical changes of a silver halide into actual grains of metallicsilver. In some situations, the grains become perceptible to the human eye, yielding acoarse texture to the image. Clearly, the photograph is unable to record details finerthan the size of the individual grains. Thus, landscape ecologists use the term grainto mean the finest level of spatial or temporal resolution of a pattern or dataset (Wu2007). In a digital image, the grain would be equivalent to the pixel size. The termresolution is often used to express a concept that is either equivalent to or closelyrelated to grain. For instance, it is often stated that Landsat-TM imagery has a spatialresolution of 30 m, which is the approximate linear distance represented by a singlepixel, a measure of grain as we have defined it.</p><p>Extent refers to the spatial or temporal span of an observation set. In space, thiswould be equivalent to the size of the area represented on a map or in a digital image,or the size of a study area from which environmental samples or data were collected.This may be expressed in units of area, or by a representative length scale (e.g., thelength of one side of a square image). In time, extent would be equivalent to theduration of the study or time span covered by the observations.</p><p>Consider a digital satellite image of a portion of the Earths surface. For conve-nience, assume a 1000- 1000-pixel image taken from a Landsat-TM scene. As notedabove, we can take the grain to be 30 m, the spatial resolution of an individual pixel.The extent can be calculated as 1000 30 m = 30,000 m = 30 km. Now, assumethat we apply some procedure to classify each pixel into a land cover category (e.g.,water, urban, cropland, forest). We may then want to ground-truth our classificationby visiting locations on the ground and determining whether the actual land covercorresponds with the prediction of our classified image. Visiting the location repre-sented by each individual pixel is an unrealistic proposition: There are 106 pixels inthe image, not to mention the difficulty of accurately locating a particular 30- 30-marea on the ground. Instead, we will visit selected locations scattered throughout thearea represented by the image, and gather land cover data at some spatial resolution.Thus, our ground-based data will have essentially the same extent as the image, but thegrain may be different. More noticeably, the classified pixels provide 100% coverageof the area in terms of predicted land cover (assuming no cloud cover in the originalimage), but our field data will provide substantially less coverage. The coverage willdepend upon how many field sites we visit. A related issue is the spacing of the fieldsites. The locations visited may be selected in a uniform grid pattern, or randomlyplaced, or selected by some other procedure. Generally, the more sites selected, thecloser they will be to each other, at least on average.</p></li><li><p>60 RELEVANCE OF SPATIAL AND TEMPORAL SCALES TO ECOLOGICAL RISK ASSESSMENT</p><p>The notions of grain, extent, and sample spacing are relevant to the temporaldimension as well. In time-series analysis, sampling frequency is a key feature of adataset. Sampling frequency is the number of observations per unit time and, thus,is inversely related to sample spacing (i.e., the time interval between observations).Observations are often treated as instantaneous (grain = zero), but sometimes thetime interval associated with individual measurements or observations is important.The extent (duration of the time series) sets limits on the low-frequency phenomenathat can be extracted by the analysis...</p></li></ul>


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