Landscape Ecology 13: 381–395, 1998. © 1998 Kluwer Academic Publishers. Printed in the Netherlands.

381

Hierarchical relationships between landscape structure and temperature in a managed forest landscape Sari C. Saunders1,∗ , Jiquan Chen1 , Thomas R. Crow2 and Kimberley D. Brosofske1 1 School

of Forestry and Wood Products, Michigan Technological University, Houghton, Michigan, 49931, USA;

2 USDA Forest Service, North Central Experiment Station, Rhinelander, WI, 54501, USA; ∗ (Corresponding author:

E-mail: [email protected]; phone: (906)487–3417; fax: (906) 487–2915 (Received 4 June 1997; Revised 22 October 1997; Accepted 24 January 1998)

Key words: hierarchy, landscape structure, microclimate, pattern-process, scale, wavelet analysis

Abstract Management may influence abiotic environments differently across time and spatial scale, greatly influencing perceptions of fragmentation of the landscape. It is vital to consider a priori the spatial scales that are most relevant to an investigation, and to reflect on the influence that scale may have on conclusions. While the importance of scale in understanding ecological patterns and processes has been widely recognized, few researchers have investigated how the relationships between pattern and process change across spatial and temporal scales. We used wavelet analysis to examine the multiscale structure of surface and soil temperature, measured every 5 m across a 3820 m transect within a national forest in northern Wisconsin. Temperature functioned as an indicator – or end product – of processes associated with energy budget dynamics, such as radiative inputs, evapotranspiration and convective losses across the landscape. We hoped to determine whether functional relationships between landscape structure and temperature could be generalized, by examining patterns and relationships at multiple spatial scales and time periods during the day. The pattern of temperature varied between surface and soil temperature and among daily time periods. Wavelet variances indicated that no single scale dominated the pattern in temperature at any time, though values were highest at finest scales and at midday. Using general linear models, we explained 38% to 60% of the variation in temperature along the transect. Broad categorical variables describing the vegetation patch in which a point was located and the closest vegetation patch of a different type (landscape context) were important in models of both surface and soil temperature across time periods. Variables associated with slope and microtopography were more commonly incorporated into models explaining variation in soil temperature, whereas variables associated with vegetation or ground cover explained more variation in surface temperature. We examined correlations between wavelet transforms of temperature and vegetation (i.e., structural) pattern to determine whether these associations occurred at predictable scales or were consistent across time. Correlations between transforms characteristically had two peaks; one at finer scales of 100 to 150 m and one at broader scales of >300 m. These scales differed among times of day and between surface and soil temperatures. Our results indicate that temperature structure is distinct from vegetation structure and is spatially and temporally dynamic. There did not appear to be any single scale at which it was more relevant to study temperature or this patternprocess relationship, although the strongest relationships between vegetation structure and temperature occurred within a predictable range of scales. Forest managers and conservation biologists must recognize the dynamic relationship between temperature and structure across landscapes and incorporate the landscape elements created by temperature-structure interactions into management decisions.

382 Introduction The processes which structure ecosystems occur at a hierarchy of spatial and temporal scales (Allen and Starr 1982). Understanding the relationship between pattern and process is a central challenge in ecological research (Holling 1992). Knowledge of how process, pattern and their relationship change with scale is also of interest both in theoretical (Levin 1992) and applied ecology (Christensen et al. 1996; Franklin 1997). One school of thought contends that the existence of an inherent scale for ecological phenomena is a primary scaling law. Structure is created by a limited number of abiotic and biotic processes that drive all other functions of an ecosystem across time and space, and occur at discrete temporal frequencies (Holling 1992). Domains, or ranges, of scale exist within which patterns and dominant processes do not change (Wiens 1989). Alternatively, ecological relationships between pattern and process may occur along a continuum of scales. Particular scales of study would be more informative when investigating a system, but there would be no single, correct scale of analysis (Levin 1992; Hansen et al. 1993). In either case, we must understand how the description of a system changes with scale of observation (Hutchinson 1953), and how the pattern-process relationship alters across scales. Variation in ecosystem structure, such as vertical canopy layering or the horizontal arrangement of stand types, affects the spread of disturbances and influences the flow of energy, matter, and species within and among systems (Forman and Godron 1986). The resulting landscape heterogeneity affects many aspects of ecological dynamics, such as foraging behavior (Pearson et al. 1995), population structure (Gilpin and Hanski 1991), and the dynamics of communities and ecosystems (Pickett and White 1985; Wiens et al. 1993). Management may introduce processes that operate at scales of space and time that are exotic to an ecosystem. These practices may alter both patterns (e.g., in vegetation (Turner 1987) or microclimate (Chen et al. 1993)) and other ecosystem processes (e.g., litter decomposition or wildlife movement (Doak et al. 1992)). Understanding of heterogeneity across scale can only be achieved through identification of the dominant scales at which processes are expressed, and the associations of processes with variables describing landscape structure. Empirical data collected at multiple scales are required to substantiate theoretical studies on cross-scale extrapolation of process-

structure relationships. Due to technological and logistic constraints, examinations of pattern-process relationships are often conducted at coarse spatial resolutions (Turner et al. 1994; Donovan et al. 1995) or through simulation (Gardner et al. 1989; Gustafson and Gardner 1996; With et al. 1997). Thus, few broad-scale, empirical investigations have studied the connection between landscape structure and process at multiple scales (but see Lovejoy et al. 1986). Fine scale, abiotic features of a landscape are often ignored in studies of landscape heterogeneity (Chen et al. 1996). However, delineation of patch types based on abiotic aspects of the environment may be crucial to assess landscape connectivity for vegetation and wildlife management. We used temperature to assess the existence of predominant scales in ecosystem processes and in relationships between landscape structure and functional dynamics. Temperature forms a link between processes such as growth and energy flow and the landscape features that influence energy budget balance (Perry 1994). We used temperature to integrate effects of multiple processes associated with the vertical and horizontal movement of energy. At the stand level, vertical gradients in temperature are the result of effects of overstory structure on radiative input and latent heat loss (Chen et al. 1993). At the ecosystem and landscape scale, horizontal gradients in temperature are determined by the air transport of energy, which is influenced by landform and other aspects of landscape structure (Miller 1980; Swanson et al. 1988; Chen et al. 1995). These effects of the landscape mosaic on functional dynamics and patterns in physical variables such as temperature are temporally and spatially dynamic (Chen et al. 1996). We predicted that the relationships between vegetation structure and temperature would also be scale dependent. Our objectives in this study were to: (1) examine the patterns in surface and soil temperatures across a heterogeneous landscape created using multiple management techniques, (2) describe relationships between landscape structure and temperature; and (3) determine whether these functional relationships between landscape structure and temperature can be generalized across spatial scales and time periods during the day. We expected that patterns in temperature would be most defined at relatively fine spatial scales at which microtopography has a strong influence. At broader scales, we predicted that the vegetative structure produced by management activities, rather than natural processes, would have a dominant influence. We further anticipated that surface air temperature

383 would be less influenced at broad scales than soil temperature, due to the mixing of air masses across the heterogeneous landscape. Differing scales of structure were expected to produce distinct patterns in temperature at opposing ends of the range of scales examined, with relatively fine and relatively coarse spatial scales contributing most to the overall pattern in surface temperature. Intermediate scales were expected to show no strong relationship to landscape structure and contribute relatively little to the overall pattern in temperature.

Methods Field site This study was conducted in the Washburn District of the Chequamegon National Forest, northern Wisconsin, USA (46◦ 300 –46◦450 N, 91◦ 20 –91◦220 W). The study area lies within subsection X.1, Bayfield Barrens, of the Regional Landscape Ecosystems of Wisconsin (Albert 1995). Soils are deep (30–90 m), loamy, glacial outwash sands with little organic material, classified as Psamments and Orthods. Underlying bedrock is Precambrian basalt, lithic conglomerate, sandstone, shale, and feldspathic to quartzose sandstone. Topography in the area ranges from level terraces to pitted outwash, formed by the melting of masses of glacial ice on which the sediments were deposited (Chequamegon National Forest 1993; Albert 1995). Our research was conducted within the pine-small block (PSB) eco-unit of the forest. Each of the 10 eco-units in the Washburn District is defined by ‘desired future condition’ to provide a ‘healthy, functioning ecosystem’ as determined by current managers (Chequamegon National Forest 1993) based on an analysis of the pre-settlement vegetation, forest habitat types, and ownership of the surrounding land. Predominant overstory species are red pine (Pinus resinosa Ait.), planted during the 1940s, 1970s and 1980s, and jack pine (P. banksiana Lamb.), which has regenerated naturally. Species such as paper birch (Betula papyrifera Marsh.), red maple (Acer rubrum L.), trembling and big-toothed aspen (Populus tremuloides Michx. and P. grandidentata Michx.), and red and scrub oak (Quercus rubra L. and Q. ellipsoidalis E.J. Hill), occur due to natural successional dynamics and silvicultural activities. Historically, the PSB area was fragmented by frequent, naturally-occurring

fires and burning by native Americans and early European settlers (Heinselman 1981). Current management promotes early and mid-successional species through harvesting in small patches of approximately 16 ha. Clearcutting, while previously used to maximize timber output, is now considered an approximation of natural, catastrophic disturbance in jack pine forests and is performed every 40–70 years in the eco-unit. Thinning is conducted every 10–15 years to mimic historic frequencies of low intensity disturbances in this forest type. Shelterwood cutting or overstory removal occurs on a 100–150 year rotation and prescribed fire is used periodically to maintain specific, herbaceous species (Chequamegon National Forest 1993). We established a 3820 m linear, east-west transect within the PSB eco-unit. We defined 14 patch types along the transect based on perception of changes in overstory cover and species composition in the field, and examination of UDSA Forest Service compartment records of management status (Table 1). Average patch width along the transect was 219 m (std = 212 m, max = 635 m, min = 20 m; Table 2). Average slope along the transect was 7% (max = 34%, min = 0%). Temperature measurements We measured soil temperature at 5 cm depth (◦ C; Ts ) and surface air temperature (◦ C; Tsf ) every 5 m along the transect between June 12 (Julian day 163) and August 25 (Julian day 237) 1995. We used nine, mobile microclimate stations to concurrently measure both Tsf and Ts every 5 m over 760 m segments of the transect. Each station consisted of a Campbell Scientific CR10 datalogger coupled with an AM416 multiplexer (Campbell Scientific Inc., Logan, UT), both housed in a cooler, with the capability of recording temperatures over 80 m of the transect (40 m on each side of the cooler). Thermocouples were made from copperconstantan wire. Temperatures were measured every 20 s and averaged and recorded every 15 min. Data were downloaded in the field every 3–5 days using a portable laptop computer. We left stations in place from 10 days to two weeks in order to capture a representative sample of weather conditions during the growing season. Five, sequential time periods were used to sample the 3820 m over the growing season. Segments of the transect were measured successively. We maintained two reference stations throughout the sampling period, one in a closed canopy pine/oak stand in the Moquah Research Natural Area (REFC),

384 Table 1. Locations and descriptions of patch types along the pine small-block (PSB) transect in Chequamegon National Forest, WI, from 0 m (west end) to 3820 m (east end). Data on height, age and diameter at breast height (DBH) are based on trees within a circular, sample plot of 10 m radius (314m2 ).

a b c d

Code

Patch Name

Start (m)

End (m)

Patch Description

P1 P2 P3 P4 P5 P4 P5 P4 P6 P7 P8 P9 P10 P11 P12 P13 P14

6yr Red Pine 50yr Mixed Pine Open w/ Scrub 60yr Red Pine Clearing 60yr Red Pine Clearing 60yr Red Pine Retention Jack Pine 7yr Red Pine Clearcut w/ Slash 12 yr Red Pine Grassy Valley 60yr Red Pine2 Clearcut 50yr Red Pine2 50/30yr Mixed Pine

0 70 235 370 455 485 510 545 1125 1755 1880 2100 2570 2800 2925 3570 3675

65 230 365a 450 480 505 540 1115b 1745c 1875 2095 2565 2795 2920 3560d 3670 3820

originated 1989; height ≈1.5 m mixed jack and red pine; 50 yrs; height ≈20 m, mean dbh = 24.9 cm (n=17) associated with old access rights-of-way and road edges originated 1933; height ≈33 m , meanDBH = 29.6 cm (n= 10 dominants) associated with old landings and access roads as above as above as above cut 1995; residual tree height ≈24 m, meanDBH = 29 cm (average 2 trees/ plot) originated 1988; height ∼2 m red pine stand cut 1993 originated 1983; seedling-sapling > 70% stocked in 1990; height ≈3 m 100% grass cover, primarily Carex and Oryzopsis; scattered red pine ≈25 m height originated 1934; height ≈28 m, mean DBH = 31.6 cm (n=9 dominants) recently cut red pine sawtimber stand height ≈22.1 m, average dbh = 25.1 (n = 31) jack pine height ≈22.0 m, mean DBH = 13.1 cm, age ≈50 yr (n=8); red pine height ≈12 m, mean DBH = 10.1 cm, age ≈30 yr (n=27)

Sand road at m 255. ATV trail at m 780; atv trail at m 1085–1090; sand road at m 1120. ATV trail at m 1450; gravel road at m 1750. gravel road at m 3565. Table 2. Daily mean (standard error) temperature (◦ C) in patch types along the pine small-block (PSB) transect, Chequamegon National Forest, WI. Patch code

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14

Patch type

Temperature (◦ C) Surface (Tsf )

Total Length (m)

6 yr Red Pine 50 yr Mixed Pine Open w/ Scrub 60 yr Red Pine Clearing Retention Jack Pine 7 yr Red Pine Clearcut w/ Slash 12 yr Red Pine Grassy Valley 60 yr Red Pine2 Clearcut 50 yr Red Pine2 50/30 yr Mixed Pine

65 160 130 670a 60b 615 120 215 465 225 120 635 100 145

Mean Min Max

219 20 635

a Patch type consists of 3 patches of 20, 80 and 570 m. b Patch type consists of 2 patches of 25 and 30 m.

25.63 (0.20)

27.31

Soil (Ts )

23.66 (0.50) 23.36 (0.30) 24.89 (0.61) 24.33 (0.14) 25.09 (0.86) 26.22 (0.21) 27.31 (0.43) 26.08 (0.24) 24.44 (0.16) 24.32 (0.20) 25.09 (0.16) 25.82 (0.17) 17.66 (0.19) 25.34 (0.21)

16.86 (0.48) 14.23 (0.33) 16.90 (0.60) 16.89 (0.18) 17.91 (0.96) 18.29 (0.17) 18.73 (0.44) 17.82 (0.35) 16.55 (0.20) 17.14 (0.29) 17.37 (0.18) 19.13 (0.16)

25.11 23.36 19.13

17.39 14.23

18.02 (0.20)

385 and one in the open pine barrens (REFO). These stations provided microclimatic information for the two vegetative extremes encountered along the transect. We expected temperatures to show a maximum difference between these two stand types. These reference data were used to: (a) standardize temperature data collected at different time periods and (b) estimate missing data values in space or time. At both of these reference stations we measured soil temperatures (◦ C) at 0, 5, and 25 cm depths and air temperatures (◦ C) at 0, 0.5, 1.0, and 2.0 m above the ground. Landscape and vegetation structure assessment We assessed fine-scale and macro landscape structure at each point (every 5 m) along the transect. As measures of the finest-scale of landscape structure, we recorded microtopography (12 categories, Table 3), aspect (degrees), and slope (%) within a 1 m2 quadrat centered on each transect point. As measures of relatively coarse-scale landscape structure, we recorded patch type (Table 1), position of the quadrat on the dominant slope (7 categories, Table 3) and slope shape (3 categories, Table 3). To describe the context of a point in the landscape, we measured the closest distance and bearing from each point to any patch of a different type or distinct habitat edge within 85 m. We also recorded the aspect (◦ ) of the edges of these surrounding patches at their nearest locations. We considered this a further component of coarse-scale landscape heterogeneity. Vegetative structure was assessed every 5 m along the transect. Percent overstory cover was determined using a spherical canopy densiometer. The percentages of each 1 m2 quadrat covered by vegetation >0.5 m high (excluding overstory), vegetation <0.5 m high, litter, bare ground, moss and grass were estimated. We also measured depth of the undecomposed and decomposed litter (cm) at the center of each plot. Statistical analysis We initially searched the temperature measurements for missing data. These gaps resulted from equipment damage by animals (primarily bears and small mammals), equipment failure, data overwrite, or inability to measure temperature on active roads or ATV trails. For data gaps of a single time period or at a single location, we averaged temperatures from time periods or spatial locations on either side of the missing point. For larger spatial or temporal data gaps, we developed

Table 3. Categories of microtopography, slope position and slope shape used to classify landscape structure along the pine small-block transect in Chequamegon National Forest, WI. Categories Microtopography

Slope position

Slope shape

Flat Mounded Convex Concave Sloped Convex on slash Concave on slash Flat on slash Stump or log Pitted Furrowed Pit and mound

crest upper middle lower toe depression level

straight convex concave

simple linear regression equations based on temperatures measured at adjacent or nearby points, or at the reference stations. In general, models used to replace missing data had an r 2 ≥ 0.90. When highly predictive relationships could not initially be found using data measured over all times of the day, we subdivided the data into successively finer temporal periods to develop regressions. We determined average temperature (x 1 ) at each 5 m point along the transect during four time periods: morning (05:00–10:45 hr) midday (11:00–16:45 hr), evening (17:00–22:45 hr), and night (23:00, dayt−1 – 04:45 hr, dayt). These divisions were considered representative of daily temperature behavior based on graphical analysis of the data. We then standardized these averages in order to allow examination of temperature across the transect as though the entire 3820 m transect had been measured concurrently. We used the first time period (June 12–June 28), during which meters 0–760 had been sampled, as our reference time period (Figure 1A). We determined overall morning, midday, evening, and night time averages within a 760 m section (x 760a) and standard deviations of soil and surface temperatures within the same section (s760), and calculated normalized values (Tn ; Figure 1B) for each point as: Tn = (x − x 760a )/s760

(1)

We computed linear regressions to determine the relationships between average temperature within each

386 To examine the patterns of temperature across the landscape, we performed wavelet analysis of surface (Tsf ) and soil (Ts ) temperatures during each time period. Wavelet analysis quantifies the influence of pattern at each scale within the data series as a function of location along a transect. This technique allows the analyst to assess pattern in the data at multiple scales concurrently (Graps 1995). The discrete form of the wavelet transform can be defined as:   1X x−b W (a, b) = f (x) ∗ g , (3) a a

Figure 1. Standardization to one reference time period of temperatures along the pine small-block transect, illustrated using morning surface temperature. Original temperatures were recorded during five different time periods (A). Normalized values were determined for each point along the transect (B) and then added to mean temperatures, determined by regression for each point as though it were measured in time period one, to yield standardized temperatures (C). See text for details.

760 m section of the transect, over the period it was actually sampled, and temperature at the open canopy reference station (REFO) during the same period. Each day was used as an independent sample point. Models were independently developed for soil and surface temperature in all four time periods. Using the temperatures at REFO during the reference time period and the linear models developed above, we predicted the overall average soil and surface temperatures (x 760p) during morning, midday, evening, and night within the other four sections of the transect for the same time period. We calculated the standardized temperature at each point and time of the day as: Tst = (Tn · s760 ) + x 760p

(2)

(Figure 1C). The assumptions for the above transformations were: (a) the relationship between transect temperature and temperature at REFO remained the same over the field season, and (b) the standard deviation within a section of the transect was stationary. We used these standardized data for all subsequent analyses.

where the shape (i.e., the dimension of the window of analysis) of the analyzing wavelet, g(x), changes with scale, a, and the analyzing wavelet moves along the data series, f (x), centered at each point, b, along the transect (Bradshaw and Spies 1992; Gao and Li 1993). Relatively extreme values of the wavelet transform, W (a, b), indicate similarity between the patterns in the analyzing wavelet and in the data being analyzed, reflecting patch structure and locations of ‘edges’ in the data. Analysis is not restricted to data sets that have stationary statistical properties (ie., properties that are similar regardless of location along the transect) as with related techniques such as Fourier analysis (Bradshaw 1991). Because information on location along the transect is retained for the wavelet transform, we were able to examine our data post hoc for features in the landscape which might have influenced patterns in temperature. Different analyzing wavelets (with different forms) can be chosen based on the type of data and the objectives of the study (Bradshaw 1991). We performed wavelet analysis with the program of Gao and Li (1992) which utilizes a Mexican hat analyzing wavelet to detect peak and trough morphology, as opposed to using the Haar function which highlights edge events (see Bradshaw 1991). Our analysis was restricted to scale values of a = 5, 10..., 750 in a ≤ b ≤ n − a, for x = 0, 5, ...n, n = 3820. Patterns in the wavelet transforms at different scales were compared with the distribution of vegetation and management patches on the landscape, to identify the relationship between vegetation structure and temperature. We also calculated the wavelet variance, V (a): 1X 2 W (a, b), (4) V (a) = n associated with each wavelet analysis, to assess whether there were any dominant scales contributing to the overall pattern of temperature across this landscape. The wavelet variance quantifies the average

387 contribution of n values along the transect (b) to the wavelet transform at each scale, a (Bradshaw 1991). We developed general linear models relating landscape and vegetation structure to Ts and Tsf during each time period, in order to determine which features on the landscape contributed most to patterns in temperature at a fine scale. We used this model-building process as an exploratory procedure to investigate which structural or compositional features of the landscape might be most influential on temperature, rather than to develop robust statistical models, recognizing the high degree of spatial autocorrelation among data points. The following variables initially were entered into the models: aspect (transformed as cos (θ 45◦)*slope (%/100) (Stage 1976)), slope, slope shape, slope position, microtopography, patch type, patch transition type, distance to nearest patch of a different type, bearing to nearest patch of a different type, edge aspect of the nearest different patch at that bearing, overstory (% cover), vegetation <0.5 m high (% cover), vegetation >0.5 m high (% cover), bare ground (% cover), litter (% cover), moss (% cover), grass (% cover), undecomposed duff (depth, cm), and decomposed duff (depth, cm). Patch transition type was a categorical variable assigned to each adjacency of two patch types. We made no a priori predictions regarding the effects of adjacency of different patch types on temperature, and thus gave each adjacency a separate category, for a total of 24 transition types. Variables were sequentially removed after examination of Type I and Type III sums of squares and consideration of model parsimony. Based on the results of the general linear modeling procedure, we also performed wavelet analysis on the data for percent cover of vegetation >0.5 m in height and depth of the decomposed duff layer along the transect. We used Pearson correlations of the wavelet transforms to examine associations between these two landscape variables and soil and surface temperatures at scales from 10 to 750 m, every 10 m. Correlations were calculated for each period during the day. We also calculated correlations between the wavelet transforms of Tsf and Ts for each of these time periods and spatial scales, to determine whether this relationship was consistent and could be used for predictive purposes. To clarify the influence of patch type on this association, we calculated Pearson correlations between the nontransformed data for Tsf and Ts by patch type and time of day.

Results The overall mean temperature across the transect was 25.11 ◦ C for surface and 17.39 ◦ C for soil temperature (Table 2). The lowest mean temperatures for any one patch type were 23.36 ◦ C (SE = 0.30) at the surface and 14.23 ◦ C (SE = 0.33) in the soil, both recorded in the 50 yr Mixed Pine stand (P2). Highest mean temperatures for a patch type were measured in the 7 yr Red Pine stand (P7) for surface (27.31 ◦ C, SE = 0.43) and in the Clearcut (P12) for soil (19.13 ◦ C, SE = 0.16). Temperature patterns were different across scales and at each of the four time periods; however, certain features were common to all wavelet transforms of temperature (Figures 2 and 3). Continuous regions of similar shading in the wavelets indicated a relatively homogeneous thermal environment, whereas abrupt transitions in color indicated gradients in temperature and thus edges between patches of thermal habitat. At the finest scale of analysis (5 m), temperature pattern consisted of patches of 30 to 50 m in length along the entire transect. Many of the vegetation patches that were defined in the field could be detected in images of the transforms of temperature. However, not all vegetation patches corresponded to temperature patches at the same scale of analysis. Some of the vegetation patches did not appear to resolve into single temperature patches, regardless of scale. Lastly, the effects of features such as roads and all terrain vehicle (ATV) trails on temperature environment could be observed across a wide range of scales in the wavelet transform. The wavelet transform for morning surface temperature (Figure 2a) resolved some of the smaller (< 200 m) patches, such as patches 2 and 3 at scales of approximately 5 to 100 m. However, some of these small patches, such as patch 10, were only apparent at scales of 400–600 m. Edge environment created by the road at m 255 was visible from the relatively high values of the transform (darker image) across a wide range of scales, from 5 to 200 m (Figures 2a, b, and d). Similarly, though only 5 m wide, the ATV trail at 780 m appeared to influence temperature at scales of 200 to 600 m. Larger patch types identified in the field were not resolved into single temperature patches at any scale. For example, patch 6 (P6) appeared to be composed of three broad, temperature patches in the morning (Figure 2a), even at scales above 400 m. This structure may have been induced by the roads which bisect and mark the beginning and end points of this patch.

388

Figure 2. Wavelet transforms of surface temperature at morning (a) midday (b) evening (c) and night time (d) through 14 patch types (e) along the pine small-block transect, Chequamegon National Forest, WI. Darker shades indicate higher values of the wavelet transform and of temperature. Positions of roads and ATV trails are indicated by arrows in (e). See Table 1 for description of management patch types.

Figure 3. Wavelet transforms of soil temperature at morning (a) midday (b) evening (c) and night time (d) through 14 patch types (e) along the pine small-block transect, Chequamegon National Forest, WI. Darker shades indicate higher values of the wavelet transform and temperature. Positions of roads and ATV trails are indicated by arrows in (e). See Table 1 for description of management patch types.

389 The patterns of surface temperature were most similar in the morning and midday (Figures 2a and b). However, there was a noticeable difference in the resolution of P12 which, at midday and at scales > 400 m, existed as a single patch in the image of the wavelet transform. In the morning, this clearcut appeared as a minimum of three patches, possibly consisting of edge environment at either end of the patch and some ‘interior’ temperature habitat from ∼3000–3400 m, even at relatively coarse scales. Similarly, there was a more noticeable effect at midday of the ATV routes at meters 1085 and 1120. These trails created edges which persisted over a broader range of scales (<100 to ∼500 m). Overall, temperature structure was less complex in the evening than at morning or midday, particularly at broader scales (Figure 2c). For example, the larger sections of 60 yr Red Pine (P 4) from 545 to 780 m and 785 to 1115 m, were clear in the transform from scales of ∼220 through 750 m. At earlier periods of the day, this cover type appeared to consist of greater than two temperature patches, even at the broadest scales. The patterns in surface temperature and correspondence with vegetation patch types were most distinctive at night (Figure 2d). Edges between patch types were most obvious at this time of day. For example, there were bands of distinct temperature conditions created by the edges between P7 and P8 (at scales of 100 to 200 m), P8 and P9 (at scales >200 m), and P9 and P10 (at scales of 250 to 550 m). Edges delineating thermal patches were more distinct at relatively broad scales (> 100 m) for soil than surface temperature (Figure 3). Soil temperature was less variable than surface temperature at the finest scales. As with surface temperature, the pattern of soil temperature was more easily defined by areas around roads and the transitions zones between patches than by vegetation patches themselves. For example, a distinct temperature zone was observable around the ATV trail at 1750 m. This was one of the most noticeable patches in the transforms for both soil and surface temperatures in the morning and at midday, and influenced structure of both variables at scales from <100 to 750 m. Similarly, P9 appeared as ≥ 3 regions of soil temperature even at scales over 100 m; an edge zone on each end of this 465 m patch, and an ‘interior’ temperature environment only 200 m long. The patterns of evening and night time soil temperature were similar (Figures 3c and d). The most obvious edges and patches were not around roads and edges at 1750 m (as earlier in the day), but at both

Figure 4. Wavelet variance for surface (A) and soil (B) temperatures at morning, midday, evening and night time along the pine small-block transect, Chequamegon National Forest, WI.

ends of P8, a clear-cut bordered by pine plantations of age 7 years (P7; west end) and 12 years (P9; east end). The interior environment of P9 only appeared distinct between 250 and 550 m scales. Most of the smaller patches of vegetation types (∼150–200 m length) were most evident in the transform as uniform soil temperature environments from scales of 150 to 400 m. Vegetation patches larger than this rarely appeared as a single patch within the wavelet transform. The highest wavelet variance was at midday across all scales for both surface and soil temperature (Figure 4). Wavelet variance was lowest in the evening for surface temperature and at night for soil temperature. Amplitudes of the wavelet variance were higher for surface temperature than for soil temperature at all times of the day and at all scales, except at night when amplitude was higher for soil temperature. Differences in wavelet variance among time periods were greater for surface temperature than soil, for which midday, evening and night time temperatures exhibited similar variance patterns. No one scale dominated the pattern in temperature for any time period, though amplitude was highest at the finest scales. Wavelet variance, and thus the contribution to overall pattern, declined linearly with increase in scale in all cases. General linear models explained between 38% (midday soil) and 60% (morning surface) of the varia-

390 tion in temperature (Table 4). Models explained more variation for surface temperature for all times of the day except evening. More variation could be explained in the morning than any other time of day for both variables. The most important explanatory variables were the broad categorical variables; patch transition (all eight models) and patch type (all surface temperature models, two soil temperature models). Finer scale variables associated with slope and topography were retained in more models for surface than soil temperature. Explanatory variables associated with vegetation and ground cover were more often associated with models of soil than surface temperature. However, the percent cover of vegetation >0.5 m height was important for explaining variation in both surface and soil temperatures in the morning and midday (and in the evening for soil). Litter cover (%) explained significant amounts of variation in surface and soil temperatures in the morning (also at night for soil). Duff depth (cm) was important for explaining variation in soil temperature in morning, midday and evening, but was not useful for explaining surface temperature at any time. Correlations between the wavelet transforms of temperature and vegetation cover varied with scale and time of day (Figures 5A, B, and C). There was a peak in correlation with vegetation cover at ∼130 m for both surface and soil temperatures (Figures 5A and B). At this scale, correlations were most extreme for morning (r = −0.42 at 130 m for surface, r = −0.35 at 100 m for soil) and midday (r = −0.31 at 150 m for surface, r = −0.26 at 130 m for soil) but relatively negligible for evening and night. Evening and night time correlations were slightly positive and morning and midday correlations negative at small scales for surface temperature. All correlations were negative for soil temperature below a 200 m scale. However, at broader scales, vegetation cover and soil temperature were positively associated during morning and midday. There was a second peak in correlations between transforms of vegetation cover and temperature at broader scales. This peak was most obvious for soil temperature (Figure 5B), occurring at a scale ∼340 m in the morning (r = 0.89) and midday (r = 0.27), and at a scale of ∼500 m in the evening (r = −0.41) and night (r = −0.55). At the surface, this second peak was less apparent, occurring at a scale of ∼400 m for midday and evening and at ∼500 m for morning temperatures; no second peak was evident for night time.

Figure 5. Correlations at scales from 5 to 750 m between the wavelet transforms of (A) vegetation > 0.5 m in height (% cover) and surface temperature (B) vegetation > 0.5 m in height (% cover) and soil temperature (◦ C) (C) duff depth (cm) and soil temperature (◦ C) and D) surface and soil temperatures (◦ C) at morning, midday, evening and night time. N = 763 at 5 m scale, 761 at 10 m scale, declining by 4 data points for every 10 m increase in scale, to n = 465 at a 750 m scale.

A similar structure was apparent in the relationship between duff depth and soil temperature (Figure 5C). Correlations showed an initial, smaller peak between scales of 100 and 200 m and a second peak at ≥750 m. These associations were relatively stronger and positive at this second peak in the morning and midday, and relatively weaker and negative in the evening and night time. Correlations between the wavelet transforms of soil and surface temperature followed a similar pattern to those between temperature and vegetation cover (Figure 5D). Temperatures were associated most

391 Table 4. Results of general linear models relating soil and surface temperature to landscape structure along the pine small-block transect. Values are probablility > F associated with Type I sums of squares for each variable. Empty cells indicate that the variable was not statistically significant in the model for that temperature or time of day (p > 0.01), or was removed from the model for simplicity. n = 679 for all models. Landscape structure Slope (%) Slope position Slope shape Microtop Patch type Patch trans Overstory (%) Veg <0.5 m (%) Veg >0.5 m (%) Litter (%) Moss (%) Grass (%) Bare Gr (%) Duff (cm) r2 MSE

Surface temperature (◦ C) Morning Midday

Evening

Night

Soil temperature (◦ C) Morning Midday

Evening

Night

0.0001 0.0001 0.0001 0.0001 0.0001 0.0001

0.0001

0.0001

0.0001 0.0001 0.0001 0.0001

0.0001 0.0001

0.0001 0.0001

0.0001

0.0001

0.0001 0.0001 0.0002

0.0001 0.0001 0.0001

0.0001

0.0001

0.0002

0.0023

0.0001 0.0006

0.0001 0.0001

0.0040 0.0002 0.0010

0.0001

0.0001

0.0003 0.0001

0.60 44.55

0.50 72.72

0.39 28.14

strongly at morning and midday, with peaks of correlation at ∼150 m (r = 0.72 for morning, r = 0.74 for midday) and 500 m scales. Soil and surface temperature transforms were positively associated except at night when the largest correlation occurs at the 500 m scale (r = −0.31). Examination of correlations among nontransformed (scale = 5 m) mean surface and soil temperatures showed no consistency of association among times of day within a patch or within times of day across patches (Table 5). Correlations ranged from r < 0.01 (for P4) to r = 0.88 (for P5), both in the evening. In summary, the wavelet variance suggests that no one scale contributed relatively more to the structure of temperature across this landscape. However, edge zones and transitions between temperature environments were most distinct at scales of 100–500 m (average of 300 m) for many times of the day. Definite transitions occurred between temperature patches at this scale even if not between vegetation patches. The relationships of vegetation cover and other structural layers (e.g., duff) to temperature occurred at specific scales or within predictable ranges of scales, although the exact scales at which these associations were strongest varied among times of day and between the temperature variables. These correlations

0.54 21.56

0.54 36.44

0.38 70.74

0.0001 0.0009 0.53 40.37

0.39 34.90

were bimodal even in cases where the relationships were weak, showing a first peak at scales between 100 and 300 m and a second peak at scales >400 m.

Discussion Management and recreational activities, not natural processes, appeared to have a dominant influence on temperature patterns at broad scales across this landscape. Attributes of topography, such as slope position, steepness, aspect and elevation can influence landscape structure and functional characteristics, such as the microclimatic environment (Swanson et al. 1988; 1992); however, the study landscape was relatively flat to rolling. The recurrent scales of correlation between vegetation and temperature structure roughly corresponded to scales of within (i.e., approximately 100 m) and between (i.e., >300 m scales) vegetation patches. We believe, therefore, that landform was not a significant influence relative to management on temperature across this landscape. Given the east-west orientation of our transect, we expected the influences of topography and of abrupt, clearcut-forest edges to differ (a) between surface and soil temperatures; and (b) among times of day. When

392 Table 5. Correlations between surface and soil temperatures by patch type and time of day along the pine small-block transect. N = 679 for all correlations. Using a Bonferroni correction, a P < 0.001 indicates significance at α = 0.05. Patch Code

Patch Type

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14

6 yr Red Pine 50 yr Mixed Pine Open w/ Scrub 60yr Red Pine Clearing Retention Jack Pine 5–60 Pine Stand Clearcut w/Slash 10–120 Pine Stand Grassy Valley 50 yr Red Pine Clearcut 50 yr Red Pine2 50/30 yr Mixed Pine

N

14 33 26 135 13 124 25 44 94 46 25 128 21 30

Pearson Correlation (P>|R|) Morning Midday 0.38 0.50 0.70 0.34 −0.02 0.49 0.19 0.49 0.52 0.38 0.71 0.44 0.28 0.17

(0.174) (0.003) (<0.001) (<0.001) (0.936) (<0.001) (0.357) (<0.001) (<0.001) (0.009) (<0.001) (<0.001) (0.211) (0.359)

the sun is overhead at midday, features such as edges and roads were predicted to have less influence on the temperature pattern. Morning temperature was highly variable and rapidly changing, creating a relatively diverse pattern that was more strongly related to the vegetative and structural features we measured than at other times of the day. Structure of surface temperature was simpler at night, perhaps because surface temperature is most stable then and broad differences between areas of open and closed canopy become more obvious. This was supported by the close match between locations of vegetative patches and surface temperature patches at this time. In contrast, the more apparent structure of soil temperature at midday reflected the differential responses of soil and surface temperatures to diurnal changes in solar energy and wind. These differences in patterns of soil and surface temperatures and of their responses to (vegetation) patch-level structure were highlighted by the dynamics of the correlations between the variables’ transforms at different scales, and the difference in soil-surface associations among patch types. Soil and surface temperature were only closely related within a narrow range of spatial scales. Caution should be exercised when inferring either the pattern or the nature of the relationship to structure of one temperature variable from the other. The diurnal dynamics of the relationship between temperature and landscape structure suggested that

0.73 0.24 0.48 0.36 0.82 0.47 0.25 0.46 0.35 0.26 0.52 0.37 0.54 0.56

Evening (0.003) (0.184) (0.013) (<0.001) (0.001) (<0.001) (0.223) (<0.001) (<0.001) (0.078) (0.007) (<0.001) (0.021) (0.001)

−0.01 0.47 0.10 <0.01 0.88 0.42 −0.05 0.68 0.09 0.67 −0.36 0.67 −0.37 0.69

Night (0.977) (0.006) (0.627) (0.970) (<0.001) (<0.001) (0.81) (<0.001) (0.366) (<0.001) (0.073) (<0.001) (0.093) (<0.001)

−0.10 0.44 0.31 0.18 0.85 0.08 −0.66 0.52 −0.01 0.57 0.06 0.24 −0.33 0.53

(0.741) (0.011) (0.128) (0.040) (<0.001) (0.376) (<0.001) (<0.001) (0.886) (<0.001) (0.789) (0.007) (0.139) (0.003)

these interactions may also differ with temporal scales of analysis. Although our data were measured with fine temporal resolution, we investigated relationships at a relatively short extent of time (daily temperature) over a single growing season. Horne and Schneider (1995) suggest that, although both terrestrial and aquatic systems appear to have characteristic spatial scales of variance, these scale-dependent patterns occur over short temporal scales and often disappear when temporal scale is increased (Weber et al. 1986; Horne and Schneider 1994). Temperature structure and vegetation-temperature relationships may differ substantially at broader temporal scales, in the winter, or even among growing seasons in different years. Spatial distribution of patches based on abiotic features, such as temperature, can clearly differ from that based on dominant, biotic, structural features. Abiotic patches were found to differ from biotic patches (areas of clearcut and forest) and among themselves for modeled landscapes of old-growth Douglas-fir forest (Chen et al. 1996). For the case of checkerboard harvesting, which was widely used in the US Pacific Northwest beginning in the 1940s (see Franklin and Forman 1987), the amount of forest interior greatly decreased when measured using abiotic criteria, and this loss was offset by increases in area of edge influence across the landscape (Chen et al. 1996). Our results suggested a similar pattern for temperature patches compared to structural, vegetation patches. For al-

393 most all structural patches greater than 200 m across, the wavelet transform showed distinctly different edge and interior temperature habitat, except at very broad scales and specific times of the day. Similarly, Fortin et al. (1996) demonstrated that boundary delineation was contingent on the nature of the variable (abiotic versus biotic) and the measurement used to quantify that variable (e.g., density versus presence-absence for species of vegetation; Fortin 1994). The spatial relationships and intensity of association between abiotic and biotic boundaries also depended on the variables used to define structure and the statistics used to measure overlap (Fortin et al. 1996). These results further highlight the importance of choosing the appropriate statistic and scale of observation for the ecological question under consideration.

Implications and Future Work The implications of these results for the theory of pattern-process relationships and for management of fragmented landscapes are broad. The dynamic nature of the wavelet transform and lack of dominance of the wavelet variance by any one scale support the contention that pattern has a continuous nature. However, the bimodal nature of the vegetation-temperature relationship supports the theory of discrete scales of pattern-process associations. Although we examined temperature as a functional response to structure, we expect that these relationships occur at multiple scales for other process variables. This highlights the importance examining ecological phenomena at a range of scales rather than a single scale. Whether these few (relatively fine and relatively coarse) scales of vegetation structure drove the continuous pattern in temperature or other structural variables, not measured in this study, produced the temperature patterns at intermediate scales should be examined in future studies. Further research is required to conclude definitively whether the bimodal nature of the structuretemperature relationship was due to management rather than other intrinsic characteristics of the landscape. Anthropogenic disturbances such as harvesting often differ from ‘natural’ disturbance regimes in their influences on structure from within- stand to landscape scales (Lertzman et al. 1997). These influences may have confounded any natural, intrinsic scales of structure. The dominant associations between temperature and the vegetative structure created by historic distur-

bance regimes may have occurred within an entirely different range of spatial scales. Measurements across similar, but undisturbed, ecosystems and areas with different management attributes, could provide insight regarding whether these temperature patterns are due to underlying physiography or soil conditions, or are just an artifact of management and locations of roads within the landscape. Habitat management and delineation of conservation areas based solely on vegetation characteristics may be insufficient (Chen et al. 1996). Temperature gradients may have a greater influence than vegetation composition or structure on the perceived connectivity of habitat patches within this landscape for ectothermic species of herptiles or invertebrates (Huey 1991; Wiens et al. 1993). Xu et al. (1997) also found that the distribution of plant species can be highly correlated (r2 =0.90) with temperature and its variability. Organisms will perceive and respond to the structure and fragmentation of their environment at different spatial scales, depending on factors such as dispersal ability and foraging behavior (Wiens 1989; Wiens et al. 1993; With et al. 1997). Our analysis of temperature suggests that thermal habitat will change throughout the day and will differ depending on the resolution at which a species recognizes habitat heterogeneity. From a human perspective, our study landscape is fragmented by management activities into vegetation patches of approximately 200 m in length. However, as the wavelet transform indicates, the temperature environment only parallels these management areas to a moderate degree. Depending on the spatial grain of an organism of interest (MacArthur and Levins 1964), this landscape may exist as up to 80 patches of approximately 50 m in length (at the finest scale of analysis) or as few as six patches approximately 600 m long (at the coarsest scale of analysis). Thus, the landscape may be much more or less fragmented than one could conclude from an examination of the distribution of silvicultural activities. Roads are an important structural element on the landscape. Distinct edge environments were created for both soil and surface pattern and were only detected by examination of the wavelet transform of the two variables across scales. Reed et al. (1996) found that the amount of edge created by roads could reach 1.98 times greater than that created by clearcuts alone. Our analysis suggests that impacts on the thermal environment of roads as narrow as 5 m persist up to broad analytical scales of >600 m. Roads only 10 m in width created patches of edge environment >100 m,

394 visible in the wavelet transforms of temperature along the transect. Thus, thermal habitat induced by roads could be up to 10 times greater than the distance along the transect occupied by the roads themselves, dependent on time of day and scale. Habitat biologists must recognize the dynamic relationship between temperature across landscapes and incorporate the unique landscape elements created by temperature-structure interactions into conservation planning. Further examination of the relationship between soil and surface temperature, and between temperature and biotic structure, at lagged temporal scales may improve the ability to predict thermal habitat with minimal field measurements. Current management on the Bayfield Barrens is modeled after the perceived historical disturbance regimes, with the constraint that timber production must be maintained. Although managers strive to mimic natural events, timber harvest rarely creates forest structure similar to that created by non-human disturbances (Lertzman et al. 1997). Even when the intensity, extent and distribution of management patches created across the landscape approximate the characteristics of natural disturbance regimes, important fine-scale, internal features are usually lost (Hansen et al. 1995). Future research should assess the effects of these differing scales of temperature structure on ecosystem functions such as decomposition rates, nutrient cycling, and animal movements. This will provide further insight into the impacts of management on relationships between processes and abiotic relative to biotic structure.

Conclusions No single spatial scale is dominant in defining pattern of temperature at any time of the day. Our results support the contention that there is more than one appropriate scale at which to study a process-pattern relationship (Levin 1992). Pattern will differ among abiotic and biotic variables and the relationships between these variables will differ across time and scale. It is exceptionally important to consider a priori the range of scales which should provide relevant information to any ecological study, and to reflect on the influence that scale will have on conclusions and management decisions.

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