A new data aggregation technique to improve ...

Landscape Ecol (2014) 29:1261–1276 DOI 10.1007/s10980-014-0066-3

RESEARCH ARTICLE

A new data aggregation technique to improve landscape metric downscaling Amy E. Frazier

Received: 26 October 2013 / Accepted: 30 June 2014 / Published online: 14 July 2014  Springer Science+Business Media Dordrecht 2014

Abstract Scale is a fundamental concept in landscape ecology and considerable attention has been given to the scale-dependent relationships of landscape metrics. Many metrics have been found to exhibit very consistent scaling relationships as map resolution (i.e., pixel or grain size) is increased. However, these scaling relationships tend to break down when attempting to ‘downscale’ them, and the scaling function is often unable to accurately predict metric values for finer resolutions than the original data. The reasons for this breakdown are not well understood. This research examines the downscaling behavior of metrics using various data aggregation techniques in an attempt to better understand the characteristics of metric scaling behavior. First, downscaling performance is examined using the traditional method of aggregation known as ‘majority rules’. Second, a new data aggregation technique is introduced that utilizes fractional land cover abundances obtained from sub-pixel remote sensing classifications in order to capture a greater amount of the spatial heterogeneity present in the landscape. The goal of this new aggregation technique is to produce a Electronic supplementary material The online version of this article (doi:10.1007/s10980-014-0066-3) contains supplementary material, which is available to authorized users. A. E. Frazier (&) Department of Geography, Oklahoma State University, 337 Murray Hall, Stillwater, OK 74078, USA e-mail: [email protected]

more accurate scaling relationship that can be downscaled to predict metric values at fine resolutions. Results indicate that sub-pixel classifications have the potential to transform data aggregation to allow more accurate downscaling for certain landscapes, but accuracy is linked to the spatial heterogeneity of the landscape. Keywords Modifiable areal unit problem (MAUP)  Spectral unmixing  Landscape metrics  Aggregation  Pattern  Classification  Population weighting  Power law

Introduction Scale is one of the most fundamental concepts in landscape ecology (Wu 2007, 2013). It has become a primary focus of many studies in landscape ecology, and the discipline has become widely recognized in both the natural and social sciences for its leading role in studying scale issues (McBratney 1998; Marceau 1999; Gibson et al. 2000; Sayre 2005). While the term scale encompasses many concepts and definitions (Wu and Li 2006; Wu 2007), it is most often examined in landscape ecology with respect to grain size, which is analogous to spatial resolution or pixel size. In particular, the scale-dependency of landscape metrics across grain size has received considerable attention (Turner et al. 1989; Milne 1991; Benson and MacKenzie 1995; Wickham and Riitters 1995; Jelinski and

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Wu 1996; O’Neill et al. 1996; Cain et al. 1997; Neel et al. 2004; Uuemaa et al. 2005; Na and Li 2013), and many researchers have demonstrated that certain metrics exhibit very consistent scaling relationships as map resolution changes (Wu et al. 2002; Shen et al. 2004; Wu 2004; Saura 2004; Castilla et al. 2009; Alhamad et al. 2011; Li et al. 2011). A major interest of investigating these scaling relationships is to estimate metrics at a finer (i.e., higher) resolution than the original data were collected (Saura and Castro 2007). Since high-resolution data acquisitions are costly and field observations often unfeasible, downscaling techniques are needed to enable detailed, local interpretations (Riitters 2005). The term downscaling describes when a statistical relationship (i.e., scaling function) is established from coarse resolution variables in order to predict values at finer resolutions. In recent years, researchers have begun to exploit the statistical relationships of landscape metrics in an attempt to downscale them (Riitters 2005; Gardner et al. 2008; Garcia-Gigorro and Saura 2005; Saura and Castro 2007; Arganaraz and Entraigas 2014). However, despite strong scaling relationships, downscaling results have been inconsistent (Arganaraz and Entraigas 2014). A possible reason for the inconsistent results when computing downscaled metrics in the manner described above stems from the aggregation of categorical data. Remote sensing images must first be classified as a categorical map before metrics can be computed. During classification, each pixel is assigned a single land cover class, which is known in remote sensing as ‘pixel-based’ or ‘hard’ classification. In order to build a scaling relationship, the hard classified map is degraded to multiple coarser resolutions (i.e., larger pixel sizes) through aggregation to generate a set of maps that cover the same extent but have varying resolutions. During aggregation, a large number of smaller units (pixels) are combined into a smaller number of larger units, often through a process known as ‘majority rules’. Using majority rules, the new, larger pixels are assigned a land cover class based on the class of the majority of the contributing pixels (Benson and Mackenzie 1995). Metrics can then be computed for each map and the values used to build a scaling relationship. Maps created in this fashion using majority rules have been found to

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Fig. 1 Loss/gain of land cover information that occurs with majority rules aggregation

exhibit scaled patterns across multiple resolutions for certain metrics (Wu et al. 2002; Shen et al. 2004; Wu 2004; Saura 2004; Castilla et al. 2009; Alhamad et al. 2011; Li et al. 2011). The drawback is that majority rules aggregation often leads to a significant loss/gain of land cover information (Fig. 1). This information loss/gain is likely the reason that metric scaling functions produce inconsistent results when downscaled. The downscaled metrics will almost always under- or over-project the true value, depending on the particular metric. These adverse effects of aggregation and scaling on spatial analyses form the basis of the theoretical foundation in geography known as the modifiable areal unit problem (MAUP; Openshaw and Taylor 1979; Openshaw 1984). The impact of MAUP and the associated ecological fallacy problem have been examined in detail as they relate to landscape ecology (Jelinski and Wu 1996; Wu 2007), and the well-known scale issue of MAUP, which is the variability of results that occurs when data are aggregated into larger aerial units, is known to be equivalent to changing the grain size or pixel resolution in landscape ecology (Turner et al. 1989; Wu 2007). If landscape metric scaling functions are to be accurately downscaled, the MAUP scaling issue must be addressed in order to minimize the loss of spatial heterogeneity that occurs (1) when remote sensing reflectance measurements are coded into categorical land cover classes, and (2) when the categorical classes are aggregated from a larger number of smaller units into a smaller number of larger units. For the first issue, categorical maps derived from pixel-based classifications present a problem because thematic

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land cover categories cannot be statistically combined (e.g., a forest and a wetland pixel cannot be averaged). However, sub-pixel classification may offer a solution. Sub-pixel (i.e., fuzzy or soft) classifications assign proportional values for every land cover present in the pixel instead of a single value. Because sub-pixel classifications can comprise proportions for multiple land covers, they are able to retain more of the inherent spatial heterogeneity of the landscape compared to hard classifications. Sub-pixel classifications have been used previously in landscape ecology to improve the accuracy of metrics (Li et al. 2011) and model landscape structure across a gradient (Frazier and Wang 2013), but their potential for ecological downscaling has not yet been explored (Wu 2007). Sub-pixel classifications may also help minimize the loss of spatial heterogeneity that occurs when pixels are aggregated to larger units. Since sub-pixel values are numerical not categorical, they can be statistically combined thereby allowing more spatial heterogeneity to be retained during aggregation compared to majority rules. Numerical aggregations still contain bias (Bian and Butler 1999), but they have been found to preserve class proportions better than majority rules for remote sensing data (Raj et al. 2013). Sub-pixel classifications thus offer a potential solution for building a new data aggregation scheme that can be used to improve the accuracy of metric downscaling. The objective of this study is two-fold. First, downscaling accuracy is examined for a set of metrics using traditional pixel-based classification with majority rules aggregation. Downscaling is tested across a variety of landscapes with varying levels of spatial heterogeneity in order to examine whether landscape structure impacts scaling. Second, this study introduces a new method for data aggregation based on sub-pixel remote sensing classifications. The new method utilizes the increased spatial heterogeneity available from sub-pixel classifications in order to retain a greater amount of land cover information in both the original classification as well as during aggregation. The new technique is used to compute metrics that are more representative of the actual landscape and thus build a more accurate scaling function. Because the new values more accurately represent the true landscape, they allow the scaling functions to be more accurately extrapolated to predict spatial patterns at finer spatial resolutions.

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Methods Study sites and data preprocessing Seven diverse landscapes containing a variety of land cover types were chosen to test scaling performance (Fig. 2). The sites include: (a) an urbanized landscape in Austin, TX (AUS) containing a heterogeneous mixture of impervious surfaces, grass/bare ground, and urban forest, (b) a primarily undisturbed, vegetated area in the Cross Timbers (TIM) region of the south-central U.S. in Oklahoma comprising an intermingled mixture of prairie/grassland and woodland forests containing two dominant species: native oaks and eastern red cedars, (c) a modified wetland agricultural region in the Sundarbans Reserve (SUN) in Bangladesh containing large, contiguous sections of mangrove forests and water, as well as wetland and dry agricultural areas, (d) an urbanized landscape in Buffalo, NY (BUF) consisting of impervious surfaces, bare ground, and vegetation, (e) a coastal landscape on Grophes Island (GRO) located in southwestern Louisiana, which is characterized by man-made water features (e.g., canals), freshwater and brackish marshes, and wetland vegetation, (f) a forested region in the Gallatin National Forest (GNF) near Bozeman, MT containing large agglomerations of mixed forest canopy and bare ground, with shaded and snowy areas, and (g) a wildland-urban interface (WUI) landscape in central Wisconsin that includes an urbanized area, rural/agricultural fields, and a temperate broadleaf and mixed forest where transitions between the three land cover classes are abrupt with little intermixing. Multispectral, high resolution images were obtained for each site from various sensors/platforms (e.g., QuickBird, Worldview-2, and Orbview-2,) depending on data availability. Since these sensors have varying ground spatial resolutions, each image was resampled to 5 m prior to classification using the built-in spectral and spatial resampling functionality in ENVI 4.8 (Excelis Visual Information Solutions). The 5 m images were then classified using maximum likelihood classification (MLC) to create categorical land cover maps for each study site (see Fig. 2). Ground reference GPS data for training samples were collected in situ for the Buffalo, Cross Timbers, Grophes Island, and WUI sites. For the sites where field observation was not possible (i.e., Austin, Gallatin, and Sundarbans), other resources including

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Fig. 2 Study sites

land use/land cover maps and GIS layers were used for reference. The lack of ground truth data in the testing stage should not adversely impact scaling results since the accuracy of the scaling and data aggregation techniques does not rely on the accuracy of the classification. However, it should be noted that gross misclassifications could potentially alter landscape

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heterogeneity, which may impact results as shown in the Discussion. Methodology The methodology consists of two separate phases to address the two objectives (Fig. 3). For the first

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Fig. 3 Methodology flowchart

objective, the 5 m classified maps were aggregated to a base resolution of 30 m using majority rules aggregation. This starting resolution mimics Landsat imagery in order to demonstrate that the methodology is repeatable with publicly available data. The 5 m maps will ultimately serve as validation data to assess the accuracy of downscaling. Since multiple resolutions are needed to build a scaling relationship, the 30 m classified maps were aggregated to 60, 90, and 120 m, also using majority rules. After aggregation, there were four maps/resolutions for each landscape from which landscape metrics can be computed and the scaling relationship constructed. The second objective is to introduce a new data aggregation technique constructed from sub-pixel, or ‘soft’ classifications. Sub-pixel classifications result from a process known as spectral unmixing whereby image pixels are decomposed into a set of land cover classes and the fractional proportion of each. There are a variety of spectral unmixing algorithms available, but for the purposes of this study, sub-pixel classifications were ‘synthesized’ from the 5 m classification.

Degrading a high resolution map to obtain exact land cover proportions at a coarser resolution is common practice in remote sensing because it allows sub-pixel classifications to be synthesized without introducing additional error from a spectral unmixing technique (Atkinson 2009). The original, high resolution map can also then provide reference data for assessing accuracy. To synthesize a 30 m sub-pixel classification, the fractional proportion of each land cover is derived directly from the thirty-six (36) 5 m pixels falling within the 30 m pixel. It is important to note that the 5 m maps are only used to synthesize subpixel classifications for the 30 m resolution and are not part of the operational methodology. From the 30 m sub-pixel classifications, coarser resolutions (i.e., 60, 90, and 120 m) can be generated by averaging the land cover fractions of the contributing pixels (Fig. 4). In this manner, each pixel at each resolution has a fractional value for every land cover class, thereby retaining much more information than a hard classification. The method was designed to be repeatable using spectrally unmixed Landsat (or similar)

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Fig. 4 Process to synthesize a sub-pixel classification from a high resolution map. The classified map (a) is aggregated to fractional values at 30 m resolution (b). The fractional values

for the entire image (c) can then be resampled (e.g., through averaging) to coarser resolutions (d)

Table 1 Metrics examined

resolutions (30, 60, 90, and 120 m) for each land cover class in each landscape. Metric values are plotted against resolution, and a power law scaling function is fit to the four points. The scaling function is then extrapolated backwards to predict the metric value at 5 m resolution (Fig. 5). Scaling computations were completed in Matlab 2010 using the Curve Fitting Toolbox (The Mathworks, Inc., 2010). Accuracy is assessed by comparing the predicted metric value at 5 m to the ‘true’ value computed directly from the original 5 m categorical map. Relative error is computed using Eq. 1:    Erel ð%Þ ¼ Mexp  Mtrue =Mtrue  100 ð1Þ

Category

Metric

Abbrev.

Aggregation metrics

Number of patches

NP

Area-edge metrics

Patch density

PD

Landscape shape index Total edge

LSI TE

Edge density

ED

imagery. However, the typical constraints of spectral unmixing would apply such as constraints on the number of endmembers/thematic classes based on the number of spectral bands, which can be a limitation in spectrally diverse landscapes. Additionally, while most studies assume linear unmixing, non-linear cases are possible and could also confound this approach. Landscape metrics

where Erel is the relative error for a particular metric, Mexp is the predicted metric based on the scaling function, and Mtrue is the true metric value calculated directly from the 5 m map. Low Erel values indicate

Five metrics were selected that consistently show strong scaling relationships with respect to grain size in order to test downscaling (Table 1). The five metrics are all considered ‘Type 1’ metrics and have been found to exhibit consistent power law scaling functions across various types of landscapes (Shen et al. 2004; Wu 2004; Alhamad et al. 2011). The metrics were computed at the class level, and metric calculations were completed using FRAGSTATS 4.1 (McGarigal et al. 2012). Examining majority rules downscaling Evaluating downscaling accuracy for majority aggregated data is straightforward. First, the five metrics are computed at the class level for each of the four

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Fig. 5 Downscaling metric values based on the scaling function built from coarser resolution maps

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Fig. 6 Threshold discretization for a sub-pixel classification

that the scaling function built from majority rules aggregated data accurately predicts the metric value at a finer resolution. A separate Erel value is computed for each metric for each of the land cover classes in each landscape. Erel values within 10 % of the true value will be considered accurate.

sub-pixel classification can be captured for metric analysis, which ultimately generates a greater amount of landscape information than traditional, single-value metrics (Frazier and Wang 2013).

Data aggregation using sub-pixel classifications

The threshold method produces multiple maps for each land cover class, and there is overlap between the pixels contained in each map (Fig. 6). The metric values for each map must therefore be weighted if all maps are to be considered in the analysis. Remote sensing images are often analyzed using weighting techniques (Jensen 2005), but these concepts have not yet been applied to sub-pixel classifications. This study adopts population weighting, which is widely used in applications such as political polling to make the sample population more representative of the population at large. If each threshold map is regarded as a sample of the entire population (i.e., landscape), then population weighting can be applied to correct for differences between the sampled proportion and the actual proportion of the population. These weighed values can then be used to produce a metric value that is more representative of the total population. The adaptation of a population weighting scheme for landscape metrics based on sub-pixel classifications is a key contribution of this paper. Derivation of the specific weights is discussed in detail below, but the new metric value calculation takes the general form of Eq. 2:

The new data aggregation technique utilizes sub-pixel classifications to retain and propagate a greater amount of spatial heterogeneity during aggregation. Since sub-pixel classifications are continuous, there are no discrete boundaries for each land cover class. Therefore, landscape metrics cannot be computed directly for sub-pixel classifications without discretizing them first. However, the process of discretization can eliminate much of the increased spatial heterogeneity. Several methods of discretization have been proposed to render sub-pixel classifications compatible with landscape metrics (Arnot et al. 2004; Frazier and Wang 2011, 2013; Rashed 2008; Walsh et al. 2008; Van de Voorde et al. 2011). Among those, the threshold continuum approach (Frazier and Wang 2011, 2013) has been found to retain a greater amount of spatial heterogeneity compared to other methods. In the threshold approach, the user sets thresholds at increments along the continuum of fractional cover (0.0–1.0) and discretizes all pixels with fractional cover amounts greater than or equal to the threshold (Fig. 6). The threshold is incrementally increased so a single sub-pixel classification will generate multiple categorical maps (i.e., one map for each threshold). In this way, the increased spatial heterogeneity from a

Weighting scheme

Pn Mexp ¼

t¼1

wi wj Mt n

ð2Þ

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where Mexp is the refined expected metric value at each resolution, Mt is the actual metric value computed at threshold t, wi is a weight to adjust for the proportion of pixels included at each threshold, and wj is a weight to adjust for the average fractional value of the pixels at each threshold. Mexp is the average of the set of weighted metric values and can be computed for any threshold increment. For this study, four different threshold increments are tested (i.e., 0.05, 0.1, 0.2, and 0.5) to determine whether there is a trade-off between increased information and computational/labor costs. For example, a threshold increment of 0.05 would consist of 19 maps created from thresholds set at fractional proportions of 0.0, 0.05, 0.1, 0.15…0.95, while a threshold increment of 0.2 would consist of five maps created from thresholds set at 0.0, 0.2, 0.4, 0.6, and 0.8. A separate Mexp is computed for the subpixel classification at each of the four resolutions, and the scaling function is fit to the four Mexp values. Proportional weights Proportional weighting is applied in population studies where there are differences between the sample size and the population size (Maletta 2007). Since each threshold includes a different number of pixels, the metric computed at each threshold represents a different proportion of the landscape. Therefore, metrics must be weighted according to the proportion of the landscape they represent. The first weighting term in Eq. 2 adjusts the metric value at each threshold depending on whether the threshold over-represents (w \ 1), under-represents (w [ 1), or adequately represents (w = 1) the entire population. The following example illustrates this concept. Consider the case where a threshold is set at 0.5. All pixels containing 50 % or more of a land cover class would be discretized into a map. This map is identical to the map that results from majority rules aggregation of a sub-pixel classification. If we accept that majority rules represents the ‘standard population’, which is the current practice for most studies, then all thresholds below 0.5 (e.g., 0.1, 0.2) would be over-sampling the landscape, because pixels are being included in the metric analysis that have less than 50 % land cover. Similarly, all thresholds over 0.5 are under-sampling the landscape because there may be pixels containing more than 50 % of the land cover that are being excluded from

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the analysis. For example, an ‘over 0.7’ threshold would omit all pixels containing 0–69 % of a particular land cover, thereby under-sampling the population. This type of proportional sampling bias can be corrected by applying the following weight to the metric value computed for each threshold: wi ¼

N nt

ð3Þ

where N is the number of pixels in the standard population (i.e., the number of pixels at threshold 0.5), and nt is the number of pixels in a class at threshold t. A second weighting term is also needed to account for the ‘hardening’ of pixels that occurs when pixels with fractional abundances are discretized into hard pixels with boundaries. Currently, there are no alternatives for assessing sub-pixel classifications through traditional landscape metrics other than discretizing pixels. Since pixels rarely contain 100 % of any land cover, particularly as resolution becomes coarser, the process of discretization almost always over-samples the amount of land cover in each pixel. This bias can be corrected by applying the following weight: wj ¼

F ft

ð4Þ

where F is the average fractional value for all pixels included in the standard population (i.e. the threshold over 0.5 case), and ft is the average fractional weight of the pixels at each threshold, t. Substituting Eqs. 3 and 4 into Eq. 2, the final equation for computing the expected metric value becomes: Pn N F  t¼1 nt ft M t Mexp ¼ ð5Þ n Downscaling Mexp is computed for each land cover class at each of the four resolutions, and a power-law function is fit to the four values using Matlab’s Curve Fitting Toolbox. The scaling function is then extrapolated to 5 m to determine how well the new function is able to predict the true landscape value at a finer resolution than the original data. By averaging metric values from multiple configurations of the same landscape, it is hypothesized that a more accurate metric value for the landscape can be computed.

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The improvement of the new data aggregation method is compared against majority rules aggregation using the accuracy improvement percentage (Saura and Castro 2007):     Mmaj  Mobs   Mexp  Mobs     AI ð%Þ ¼ 100  ð6Þ Mmaj  Mobs  þ Mexp  Mobs  where Mmaj is the estimated value of the metric at 5 m based on majority aggregation, Mexp is the estimated metric value at 5 m using the new data aggregation technique, and Mobs is the observed or true metric value at 5 m resolution computed directly from the high resolution maps. Positive AI values indicate that the new method improves downscaling accuracy compared to majority aggregation, while negative AI values indicate that majority aggregation outperformed the new method at predicting the metric value at 5 m. The larger the magnitude of a positive AI value, the greater the improvement of the new method over majority aggregation. For example, an AI value of 100 % indicates that the new method exactly predicted the true metric value at 5 m while an AI value of 3 % indicates only marginal improvement over majority aggregation. Similarly, large, negative AI values indicate that the new method performed significantly worse than majority aggregation.

Results

Fig. 7 Accuracy of majority aggregation downscaling using relative error values (Erel). Low Erel values indicate higher accuracies

Table 2 Relative error (Erel) for the majority aggregated downscaling results for the WUI landscape compared to the true value at 5 m Metric

Class

Maj. agg.

True

Erel (%)

NP

Rural

29,905

49,129

39.13

Urban

33,671

33,069

1.82

Wildland

31,791

29,448

7.96

Rural

461.19

758.16

39.17

Urban

519.16

510.32

1.73

Wildland

491.49

454.44

8.15

Rural

139.55

181.65

23.18

Urban

173.86

169.82

2.37

Wildland

91.32

142.67

35.99

Rural

2,682,840

3,641,780

26.33

Urban Wildland

1,596,200 1,894,350

1,816,465 3,098,810

12.13 38.87

Rural

413.96

562.00

26.34

Urban

246.48

280.32

12.07

Wildland

292.32

478.21

38.87

PD

LSI

TE

Performance of majority aggregation ED

The scaling function built from majority rules aggregated data was only able to predict the metric value at 5 m with an Erel of less than 10 % in 18 of 120 attempts, or 15 % of the time. When the range of Erel was increased to 20 %, accuracy improved to 35 of 120 (*29 %). Overall Erel values across all landscapes/classes were poor though, with many values above 50 % and several values greater than 300 % (Fig. 7). Due to space constraints, full results are shown only for WUI, which had the best performance of all landscapes (Table 2). Results for the remaining six landscapes are provided in Appendix 1—Electronic Supplemental Materials. Erel values for WUI ranged from 1.82 to 39.17 % with five of the 15 metrics having Erel values below 10 % and seven below 20 %. However, even for WUI, majority

Bolded values indicate relative errors less than 10 %

aggregation wasn’t able to predict more than half of the metrics within 20 % of the true value. The other six landscapes performed worse, and two landscapes (e.g., BUF and TIM) didn’t have a single metric predicted within 20 % of the true value. Overall, majority aggregation performed poorly in most cases. Performance of new aggregation technique Since the new aggregation technique produces a new set of metric values, it is necessary to first report on how well the scaling functions fit the new values. The

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majority of R2 values were between 0.99 and 1.0, indicating the power law functions fit the Mexp values quite well. A few isolated cases had R2 values as low as 0.85, mainly for TE and ED, but even these low values indicate adequate fitting. Given that the five metrics tested have previously been found to be very consistent when fit with scaling functions across multiple resolutions (Wu 2004), it is not surprising that most R2 values were above 0.99. These goodnessof-fit results support the new data aggregation technique because they affirm that even though the new technique generates new metric values, the values still maintain the characteristic scaling relationships. Downscaling results Downscaling accuracy can be reported and discussed on several levels including: (1) overall downscaling performance across the various landscapes, (2) the performance of downscaling for individual classes within each landscape, and (3) the performance of downscaling for each of the threshold increments tested. Since the complete set of results is quite large and includes more than 1,200 data values, full results for just the AUS landscape are reported here, and results for all landscapes are provided in Appendix 2—Electronic Supplemental Materials. Overall results are generalized below for discussion purposes. The AUS results (Table 3) show downscaling results for majority aggregation as well as the new data aggregation technique at the four threshold increments for three land cover classes: bare ground (Bare), impervious surfaces (Imp), and vegetation (Veg). Positive AI values indicate improvement of the new technique compared to majority aggregation. For example, the true NP value at 5 m resolution for the ‘Bare’ class is 156,177. The value predicted by majority aggregated data is 287,168, nearly double the correct value. The value predicted using the new technique is 154,043 using a threshold increment of 0.5. The associated AI value is 96.79 %, indicating that the new technique was able to predict the value almost exactly. Not all classes/metrics performed as well, but the new technique improved over majority aggregation in all classes at all thresholds for both NP and PD in the AUS and BUF landscapes. This is a significant finding and indicates promise for the use of sub-pixel classifications for overcoming data aggregation biases. Results for the remaining metrics, LSI,

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TE, and ED, were mixed, but in all cases at least one threshold was able to outperform majority aggregation for each class, which is also a promising finding. In order to present generalized results for all seven landscapes, each metric was assigned a score for each landscape based on aggregated class performance (Table 4). To compute the score, the 12 or 16 metric values (depending on whether the landscape was classified with three or four classes) were assigned a value of 1 if the new technique improved over majority aggregation and 0 if it did not. The values were then averaged to produce a final score for each metric. A perfect score of 1.0 indicates positive AI values across all thresholds for all classes. Each landscape can receive a maximum total score of 5.0 (for the 5 metrics), and each metric can receive a maximum total score of 7.0 (for the 7 landscapes). AUS and BUF, which are both urban landscapes, displayed the best overall performance with high scores of 3.92/5.0 and 4.59/5.0, respectively. WUI and GRO had the lowest scores of 0.74/5.0 and 1.07/5.0, respectively. The results suggest that downscaling performance may be linked to landscape heterogeneity, particularly since the two urban landscapes, which contain close mixtures of land covers, outperformed all other landscapes. The TIM landscape, which also contains a heterogeneous mixture of vegetation types also performed well. The relationship between downscaling performance and spatial heterogeneity will be examined further in the Discussion. In terms of individual metrics, NP, PD, and LSI performed well overall. NP and PD performed particularly well for the AUS and BUF landscapes, improving over majority aggregation in all cases. LSI had the highest overall total (4.31/7.0) and performed well in the GNF and BUF landscapes. TE and ED performed moderately for most landscapes with the exception of BUF and AUS, where results were above average. The specific land cover classes vary across the seven landscapes both in category and hierarchy, which makes comparisons difficult (see Appendix 2—Electronic Supplemental Materials). However, some generalizations can be made. The ‘Vegetation’ classes performed well, particularly in the AUS and BUF landscapes, as well as GNF. ‘Water’ classes performed poorly at all thresholds for all metrics, as did the ‘Wetland’ classes. It is suspected that the configuration of different land covers may impact performance, and this hypothesis will be examined further in the Discussion.

696.59 516.08

534.25

Veg

13,404,540

Veg

Bare Imp

12,948,630

Imp

375.54

Veg

17,477,860

382.84

Bare

486.24

337.19

Veg

Imp

292.15

Imp

Bare

622.45

Bare

84,603

Veg

797.49

716.42 599.12

20,009,300

15,035,600

17,977,000

527.02

457.64

521.00

566.60

868.75

1146.85

142,260

164,319

287,168

Maj. agg.

715.61

659.93 565.60

17,957,900

14,192,300

16,557,600

360.69

284.40

379.56

481.89

280.13

498.54

121,027

70,448

125,252

TH (05)

701.39

677.99 562.08

17,599,100

14,102,600

17,010,700

368.19

294.12

387.39

476.90

265.15

487.12

119,787

66,567

122,256

TH (10)

723.79

720.19 558.99

18,159,300

14,024,700

18,067,000

380.13

316.31

399.68

477.19

269.11

491.83

119,680

65,790

122,752

TH (20)

772.76

938.17 608.07

19,388,500

15,255,000

23,542,100

433.29

378.68

458.44

410.49

532.41

613.68

102,609

103,441

154,043

TH (50)

18.42

-29.80 25.29

18.38

25.32

-29.67

82.14

-13.65

-50.86

22.64

95.91

61.77

22.57

93.92

61.80

AI (05)

22.33

3.18 28.70

22.32

28.79

3.31

90.74

-8.51

-47.98

24.30

91.05

58.97

24.21

86.22

58.86

AI (10)

16.28

-8.69 31.86

16.29

31.96

-8.27

94.12

5.85

-42.71

24.20

92.31

60.12

24.35

84.75

59.34

AI (20)

4.93

-84.83 -5.11

4.93

-4.99

-84.79

44.80

89.47

11.11

51.57

41.18

96.71

52.40

50.25

96.79

AI (50)

Bolded values indicate positive AI values

Downscaled values at 5 m are shown for majority aggregation (Maj. agg.) and for the four thresholds (TH), with the step increment in parentheses, using the new technique. Accuracy improvement values (AI) are in percent

ED

TE

LSI

PD

156,177

73,303

Bare

NP

True metric (5 m)

Imp

Class

Metric

Table 3 Downscaling results for the Austin (AUS) landscape

Landscape Ecol (2014) 29:1261–1276 1271

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Landscape Ecol (2014) 29:1261–1276

Table 4 Generalized downscaling scores for all landscapes/metrics Metric

AUS

BUF

GNF

GRO

SUN

TIM

WUI

Total

NP

1.00

1.00

0.31

0.44

0.63

0.75

0.00

4.13

PD

1.00

1.00

0.31

0.44

0.63

0.75

0.00

4.13

LSI TE

0.58 0.67

0.75 0.92

1.00 0.44

0.19 0.00

0.63 0.44

0.58 0.25

0.58 0.08

4.31 2.80

ED

0.67

0.92

0.44

0.00

0.44

0.25

0.08

2.80

Total score

3.92

4.59

2.5

1.07

2.77

2.58

0.74

No consistent results emerged for threshold performance. Typically, if the new technique outperformed majority aggregation at one threshold increment, then it also outperformed for least one other threshold (see Appendix 2—Electronic Supplemental Materials). This is not unexpected since the threshold increments are simply different sampling frequencies of the same data. There is likely a correlation between sampling/ threshold increment and the inherent behavior of particular metrics that in turn affects how well a certain threshold increment performs. For example, when the threshold is set to 0, all pixels containing any fraction of land cover are included in the analysis. At this threshold, the land cover map often consists of a single, large, contiguous patch, whereby both NP and PD would have very small values. In contrast, for this same map MPS would have an extremely large value. If a threshold increment of 0.5 is used, only two values are comprised in the average (threshold ‘0’ and threshold ‘0.5’), so the metric value at threshold 0 (whether it is very large or very small depending on the metric) will have a significant influence on the computed Mexp value. In contrast, when a threshold increment of 0.05 is used, 19 total values are included in the Mexp computation, so the influence of a significantly large or small value at threshold ‘0’ is counterbalanced by 18 other values. Exposing the exact nature of this relationship is beyond the scope of this study, but an important finding of this study is that downscaling performance may rely on the behavioral characteristics of individual metrics.

Discussion Scale and heterogeneity are inherently linked (Wu 2007), so it is not surprising that the results indicate downscaling accuracy varies with heterogeneity. The

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landscapes that performed best (e.g., AUS and BUF), are comprised of heterogeneous mixtures of land cover classes (see Fig. 2). In contrast, the WUI landscape, which performed poorly, contains large, homogeneous areas of wildland and rural areas that do not intermingle. To further explore the relationship between landscape heterogeneity and downscaling accuracy, several landscape-level metrics computed at 30 m resolution were plotted against AI. The metrics included mean patch size (MPS), percent of like adjacencies (PLADJ), and contagion (CONTAG). In all three plots (Fig. 8), there is an obvious correlation between spatial heterogeneity and AI, with higher heterogeneity leading to higher downscaling accuracy improvement with the new method. For instance, as MPS increases, landscape heterogeneity decreases. Landscapes with small MPS (i.e., high spatial heterogeneity) had higher AI values than landscapes with large MPS. Similarly, PLADJ measures the frequency with which similar cover types are side-by-side in the landscape (McGarigal et al. 2012), and a high PLADJ indicates less heterogeneity in the landscape. As PLADJ increased for landscapes, AI decreased. Lastly, CONTAG measures the spatial aggregation of the landscape. It is high when a single class occupies a very large percentage of the landscape, indicating low spatial heterogeneity. As CONTAG increased across the landscapes, AI decreased, again showing a correlation between spatial heterogeneity and downscaling accuracy. These results support previous findings in the field regarding the relationship between scale and heterogeneity. A thorough investigation is needed to determine the exact nature of this relationship, but the findings are encouraging because they indicate the potential ability to predict which landscapes will perform well using the new data aggregation method. The poor performance of certain classes may be related to previous findings that scaling relationships are

Landscape Ecol (2014) 29:1261–1276

Fig. 8 Regressions for several landscape-level metrics indicating spatial heterogeneity versus accuracy improvement (AI) percentage

influenced by the relative abundance and dispersion of class patches (Saura and Martinez-Millan 2000; Shen et al. 2004) as well as by the thematic resolution, or the number of classes (Wu et al. 2002; Li and Wu 2004; Shen et al. 2004; Wu 2004; Buyantuyev and Wu 2007). With regard to relative abundance, the water class offers a compelling example for sub-pixels. Water is not typically found mixed with other land covers, and there are often abrupt boundaries rather than large transitional zones. Therefore, in sub-pixel classifications, water pixels often have fractional abundances of 0 or 100 %, and very few pixels have intermediate fractional proportions. While relative abundance at the sub-pixel level has not specifically been tested with respect to scaling, inferences from the results of this study along with knowledge from previous findings suggest it is likely an influencing factor. With regard to thematic resolution, this study tested only a single set of classes for each landscape.

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However the relationships between spatial heterogeneity and AI suggest that accuracy would improve with increasing thematic resolution. Changing the thematic resolution would also change the intrinsic spatial configuration and distribution of classes. For example, the structural configuration of water features is often regular and compact (e.g., circular ponds or lakes) or linear and complex (e.g., rivers or canals), and water is often unevenly dispersed throughout a landscape. These inherent characteristics likely impacted the downscaling accuracy for water, and while water itself is not always represented with a hierarchy of thematic classes, other land cover classes would most certainly experience changes in structural characteristics with changes in thematic resolution. The minimum mapping unit (MMU), as discussed by Castilla et al. (2009), is also likely impacting results. MMU is the minimum size a pattern must be in order to be detected. It is well known that problems can arise when sensor resolution is much larger than the MMU of the landscape patches (O’Neill et al. 1996). For downscaling, the opposite problem arises when the smallest pixel size (i.e., 30 m in this study) is much smaller than the patches being detected. If most patches are detectable at 30 m, then the number of patches will not change even when resolution is increased to 5 m. In these situations, downscaling is counterproductive and will only introduce error. The lower AI values for landscapes with larger patch sizes (e.g., WUI, GNF, SUN) are likely a result of the MMU issue. This study adopted a systematic approach by attempting to measure all class accuracies at 5 m resolution based on the same four course resolutions and did not test whether accuracy would improve using different resolutions. Thorough investigation of the intrinsic scale of the data, (i.e., the scale at which the pattern actually operates; Wu 2007), may provide additional insight into these factors and should be the focus of future investigation.

Limitations The statistical method of aggregation (e.g., averaging, median, etc.) as well as the position of the aggregation window can impact results (Bian and Butler 1999). The images in this study were clipped to a size that yielded 60, 90, and 120 m aggregations exactly, but there is the possibility that surplus cells will be present

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along the edges that do not divide evenly into the aggregate resolution. A method for dealing with such edge pixels (e.g., discard them or include them despite edge influences) should be determined prior to starting the study. This study focused on the aggregation of remote sensing classifications to define scaling relationships, but it should be noted that remote sensing images cannot be disaggregated directly instead. Unfortunately there are currently no methods for disaggregation other than spectral unmixing or other soft classification techniques. And while unmixing is able to determine the fractions of each land cover class, it is currently unable to determine the physical locations of those fractions with certainty. There is a growing body of research known as super-resolution mapping focused on solving this sub-pixel location problem, but no universally accepted methods have been developed. It is hoped that the method introduced in this paper may aid development of super-resolution mapping techniques. Lastly, uncertainty analysis is an essential part of the scaling process (Wu 2007) and is particularly relevant for studies using remote sensing data (Lechner et al. 2012). This study used synthesized classifications to minimize classification error, but if the study were to be implemented using spectral unmixing, there would likely be error introduced from the unmixing procedure. While the propagation of pixelbased classification error has been examined for landscape metrics (Wickham et al. 1997; Fang et al. 2006; Peng et al. 2007; Shao and Wu 2008), it has not yet been examined for sub-pixel classifications and requires future investigation. To fully test these issues, the method should be tested using spectrally unmixed imagery instead of synthesized classifications.

(2)

(3)

the loss of spatial heterogeneity compared to hard classifications. This finding is significant for the future exploration of ‘soft’ classifications and their potential impact for alleviating MAUP and ecological fallacies in landscape ecology. Population weighting techniques can be applied to sub-pixel classifications to allow multiple threshold maps to be analyzed in tandem. The significance of this finding is that the spatial heterogeneity from sub-pixel classifications can be retained for metric analysis through the threshold approach without over- or undersampling the landscape. Findings indicate the potential for broad and repeatable use of the downscaling technique in the future, particularly in spatially heterogeneous landscapes. Furthermore, the results suggested several parallels between heterogeneity, thematic resolution, class behavior, and minimum mapping unit that can be explored further to improve accuracy.

The results of this research indicate that many of the same issues are present when downscaling with subpixel classifications that have been found when working with traditional, categorical scaling relationships, and this study will hopefully provide a platform for future investigations into the use of sub-pixel classifications for downscaling accuracy and behavior. Acknowledgments This research was made possible through an NSF Doctoral Dissertation Research Improvement (DDRI) grant to the author (Award No. 1303086). The author would also like to thank the Global Land Cover Facility (GLCF) for providing the QuickBird image of the Sundarbans Reserve, and the insightful comments from the anonymous reviewers, which helped improved the manuscript.

Conclusions The objectives of this study were to (1) examine downscaling accuracy using traditional majority rules aggregation methods, and (2) introduce a new method for data aggregation based on sub-pixel remote sensing classifications in order to construct a more accurate scaling function. Several key findings emerge from this research: (1)

Sub-pixel classifications can be used to build a new data aggregation technique that minimizes

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References Alhamad MN, Alrababah MA, Feagin RA, Gharaibeh A (2011) Mediterranean drylands: the effect of grain size and domain of scale on landscape metrics. Ecol Indic 11:611–621 Arganaraz JP, Entraigas I (2014) Scaling functions evaluation for estimation of landscape metrics at higher resolutions. Ecol Inform 22:1–12 Arnot C, Fisher PF, Wadsworth R, Wellens J (2004) Landscape metrics with ecotones: pattern under uncertainty. Landscape Ecol 19:181–195

Landscape Ecol (2014) 29:1261–1276 Atkinson PM (2009) Issues of uncertainty in super-resolution mappng and their implications for the design of an inter-comparison study. Int J Remote Sens 30(20): 5293–5308 Benson BJ, MacKenzie MD (1995) Effects of sensor spatial resolution on landscape structure parameters. Landscape Ecol 10(2):113–120 Bian L, Butler R (1999) Comparing effects of aggregation methods on statistical and spatial properties of simulated spatial data. Photogramm Eng Remote Sens 65(1):73–84 Buyantuyev A, Wu J (2007) Effects of thematic resolution on landscape pattern analysis. Landscape Ecol 22:7–13 Cain DH, Riitters K, Orvis K (1997) A multi-scale analysis of landscape statistics. Landscape Ecol 12(4):199–212 Castilla G, Larkin K, Linke J, Hay GJ (2009) The impact of thematic resolution on the patch-mosaic model of natural landscapes. Landscape Ecol 24:15–23 Fang S, Gertner G, Wang G, Anderson A (2006) The impact of misclassification in land use maps in the prediction of landscape dynamics. Landscape Ecol 21:233–242 Frazier AE, Wang L (2011) Evaluation of soft classifications for characterizing spatial patterns of invasive species. Remote Sens Environ 115:1997–2007 Frazier AE, Wang L (2013) Modeling landscape structure response across a gradient of land cover intensity. Landscape Ecol 28(2):233–246 Garcia-Gigorro S, Saura S (2005) Forest fragmentation estimated from remotely sensed data: is comparison across scales possible? Forest Sci 51(1):51–63 Gardner RH, Lookingbill TR, Townsend PA, Ferrari J (2008) A new approach for rescaling land cover data. Landscape Ecol 23:513–526 Gibson CC, Ostrom E, Ahn TK (2000) The concept of scale and the human dimensions of global change: a survey. Ecol Econ 32:217–239 Jelinski DE, Wu J (1996) The modifiable areal unit problem and implications for landscape ecology. Landscape Ecol 11(3):129–140 Jensen J (2005) Introductory digital image processing: a remote sensing perspective. Prentice Hall, Upper Saddle River Lechner AM, Langford WT, Bekessy SA, Jones SD (2012) Are landscape ecologists addressing uncertainty in their remote sensing data? Landscape Ecol 27(9):1249–1261 Li X, Du Y, Ling F, Wu S, Feng Q (2011) Using a sub-pixel mapping model to improve the accuracy of landscape pattern indices. Ecol Indic 11:1160–1170 Maletta H (2007) Weighting. Manuscript posted on spsstools.net. Retrieved from http://www.spsstools.net/ Tutorials/WEIGHTING.pdf. Accessed 31 May 2013 Marceau DJ (1999) The scale issue in social and natural sciences. Can J Remtoe Sens 25:347–356 McBratney AB (1998) Some considerations on methods for spatially aggregating and disaggregating soil information. Nutr Cycl Agroecosyst 50:51–62 McGarigal K, Cushman SA, Ene E (2012) FRAGSTATS v4: Spatial pattern analysis program for categorical and continuous maps. Computer software program produced by the authors at the University of Massachusetts, Amherst. Available at the following web site: http://www.umass. edu/landeco/research/fragstats/fragstats.html. Accessed 1 Feb 2012

1275 Milne BT (1991) Heterogeneity as a multiscale characteristic of landscapes. In: Kolasa J, Pickett TA (eds) Ecological heterogeneity. Springer, New York, pp 69–84 Na Z, Li H (2013) Sensitivity and effectiveness of landscape metric scalograms in determining characteristics scale of a hierarchically structured landscape. Landscape Ecol 28(2):343–363 Neel MC, McGarigal K, Cushman SA (2004) Behavior of classlevel landscape metrics across gradients of class aggregation and area. Landscape Ecol 19:435–455 O’Neill RV, Hunsaker CT, Timmins SP, Jackson BL, Jones KB, Riitters KH, Wickham JD (1996) Scale problems in reporting landscape patterns at the regional scale. Landscape Ecol 11(3):169–180 Openshaw S (1984) The modifiable areal unit problem. Geo Books, Norwich Openshaw S, Taylor P (1979) A million or so correlation coefficients: three experiments on the modifiable areal unit problem. In: Wrigley N (ed) Statistical applications in the spatial sciences. Pion, London, pp 127–144 Peng J, Wang Y, Ye M, Wu J, Zhang Y (2007) Effects of landuse categorization on landscape metrics: A case study in urban landscape of Shenzhen, China. Int J Remote Sens 28:4877–4895 Raj R, Hamm NAS, Kant Y (2013) Analysing the effect of different aggregation approaches on remotely sensed data. Int J Remote Sens 34(14):4900–4916 Rashed T (2008) Remote sensing of within-class change in urban neighborhood structures. Comput Environ Urban 32:343–354 Riitters KH (2005) Downscaling indicators of forest habitat structure from national assessments. Ecol Indic 5(4):273–279 Saura S (2004) Effects of remote sensor spatial resolution and data aggregation on selected fragmentation indices. Landscape Ecol 19:197–209 Saura S, Castro S (2007) Scaling functions for landscape pattern metrics derived from remotely sensed data: Are their subpixel estimates really accurate? Int J Photogramme 62:201–216 Saura S, Martinez-Millan J (2000) Landscape patterns simulation with a modified random clusters method. Landscape Ecol 15:661–678 Sayre NF (2005) Ecological and geographical scale: parallels and potential for integration. Prog Hum Geog 29(3):276–290 Shao G, Wu J (2008) On the accuracy of landscape pattern analysis using remote sensing data. Landscape Ecol 23:505–511 Shen W, Jenerette D, Wu J, Gardner RH (2004) Evaluating empirical scaling relations of pattern metrics with simulated landscapes. Ecography 27:459–469 Turner MG, O’Neill RV, Gardner RH, Milne BT (1989) Effects of changing spatial scale on the analysis of landscape pattern. Landscape Ecol 3:153–162 Uuemaa E, Roosaare J, Mander U (2005) Scale dependence of landscape metrics and their indicatory value for nutrient and organic matter losses from catchments. Ecol Indic 5:350–369 Van de Voorde T, Jacquet W, Canters F (2011) Mapping form and function in urban areas: an approach based on urban

123

1276 metrics and continuous impervious surface data. Landscape Urban Plan 102:143–155 Walsh S, McCleary A, Mena C, Shao Y, Tuttle J, Gonzalez A (2008) QuickBird and Hyperion data analysis of an invasive plant species in the. Galapagos Islands of Ecuador: Implications for control and land use management. Remote Sens Environ 112(5):1927–1941 Wickham JD, Riitters KH (1995) Sensitivity of landscape metrics to pixel size. Int J Remote Sens 17(18):3585–3594 Wickham JD, O’Neill RV, Ritters KH, Wade TG, Jones KB (1997) Sensitivity of selected landscape pattern metrics to land-cover misclassification and differences in land-cover composition. Photogramm Eng Remote Sens 63(4):397–402 Wu J (2004) Effects of changing scale on landscape pattern analysis: scaling relations. Landscape Ecol 19:125–138

123

Landscape Ecol (2014) 29:1261–1276 Wu J (2013) Key concepts and research topics in landscape ecology revisited: 30 years after the Allerton Park workshop. Landscape Ecol 28(1):1–11 Wu J (2007) Scale and scaling: a cross-disciplinary perspective. In: Wu J, Hobbs R (eds) Key topics in landscape ecology, Cambridge University Press, Cambridge, pp 115–142 Wu J, Li H (2006) Concepts of scale and scaling. In: Wu J, Jones KB, Li H, Loucks OL (eds) Scaling and uncertainty analysis in ecology: methods and applications. Springer, Dordrecht, pp 3–15 Wu J, Shen W, Sun W, Tueller PT (2002) Empirical patterns of the effects of changing scale on landscape metrics. Landscape Ecol 17:761–792

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