DRAFT: SUBMITTED TO PHOTOGRAMMETRIC ENGINEERING AND REMOTE SENSING.

Airborne Video Sampling Effort For Accuracy Assessment of Thematic Maps: A Simulation Experiment

Driese, Kenneth L., and William A Reiners

Simulated air videography transects are used with GAP statewide land cover maps to explore the relationships between transect length, sample size and map characteristics and to reduce unproductive sampling.

Abstract

The number of land cover types intersected by video transects is positively related to total transect length, but the relationship is not linear. Three statewide land cover maps (Wyoming, Colorado and Arkansas) from the Gap Analysis Program were used to generate sets of transects in 3 orientations (E-W, N-S, random) and 2 configurations (systematic and random). For all three states a "level of diminishing returns" was reached, beyond which additional transect length added few new cover types to the sample. Transect orientation (East -West vs. North - South vs. Random) had little effect on the number of cover types encountered, although vegetation zonation added small advantage to systematic vs. random transects. Mean proportional area per cover type and mean number of polygons per type influenced the rate of capture of new types. Diminishing returns were achieved at 2495 km, 3355 km and 1769 km for Wyoming, Colorado and Arkansas, respectively.

Introduction

The specter of global change resulting from changes in land use and from greenhouse gas-induced climate change has shifted the focus of scientists and land managers towards broader domains but with finer spatial resolution (Copeland et al. 1996, Oleson et al. 1997). Remote sensing provides an ideal tool for such studies (Townshend et al. 1991), but traditional ground-based collection of data for training and accuracy assessment is impractical for entire states, regions or continents due to their size and because of inaccessibility resulting from rugged terrain or private land access issues. Airborne videography provides an alternative for the collection of ground control because coverage is continuous along flight lines, media and equipment are not expensive, and multiple video cameras allow simultaneous resolution of features as fine as individual plants and as coarse as landscape settings to capture context (Mausel et al. 1992, Marsh et al. 1994, Slaymaker et al. 1996).

The Gap Analysis Program (GAP) of the US Geological Survey - Biological Resources Division (USGS-BRD) has been particularly active in promoting airborne videography as a tool for classification and accuracy assessment (Graham 1993, Slaymaker et al. 1996). The GAP program uses a "coarse-filter" approach for biodiversity protection by creating statewide maps of potential animal species richness (Scott et al. 1990, 1993). GAP researchers use Landsat TM data to map existing land cover, and then combine this with other spatial data (i.e. elevation, species occurrence) in a GIS to map potential vertebrate species habitat. These habitat maps are combined to provide a spatially distributed measure of potential species richness which is in turn compared to land status with regard to management for biodiversity. In this way areas of high potential vertebrate species richness that are not currently protected are identified, providing a decision-tool for land managers and policy makers (Davis et al. 1990).

The creation of statewide spatial data for this program has stimulated research in remote sensing, classification and accuracy assessment for large areas (e.g. Stoms and Estes 1993, Stoms et al. 1998). Early projects in Arizona and New England identified airborne videography as a useful tool at these scales (Graham 1993, Slaymaker et al. 1996) and video data were collected and used for training and future accuracy assessment of the GAP land cover maps for these states.

Currently, we are using airborne videography to assess the thematic accuracy of statewide GAP land cover maps for Wyoming and Colorado. In addition to overall map accuracy, the assessments will provide information on the types of confusion that occur for individual cover types, a pursuit that requires "ground control" samples for as many of these types as possible. This paper describes a sampling efficiency estimation scheme for this effort. Our objective here is to determine a minimum total video transect length for each state that intersects a maximum number of land cover types while remaining unbiased from a statistical perspective. Specifically, we want to provide a means of maximizing the success of video transect sampling while minimizing unnecessary or unproductive sampling expense.

To test the efficiency of video transect sampling for statewide data, we explore several research questions. First, what is the "level of diminishing returns" for video sampling in terms of total transect length? Does the number of cover types intersected by video transects "flatten" after a critical total transect length is achieved? Second, if there is a characteristic curve relating transect length to the number of cover types intersected, are there features of the land cover map that predict the shape of this curve? Third, does the orientation of the transects affect the shape of the curve or alter the position of the point where additional sampling yields little additional capture of previously unsampled types? Are there characteristics of maps of different areas that suggest optimal orientation of transects? Finally, are results different for randomly placed transects than for systematically arranged transects? To explore these questions we analyzed hypothetical video transects on three actual statewide land cover maps (Wyoming, Colorado, and Arkansas) produced by the GAP program.

Methods

Test Maps

The Wyoming and Colorado land cover maps were created using similar classification methodology (Driese et al. 1997), but the land cover differs, offering contrasting spatial configurations of polygon size and thematic diversity for testing video sampling efficiency. A third land cover map, created for Arkansas (Dzur et al. 1996, Smith et al. 1998) provides a different spatial pattern and a contrasting mapping methodology than that used for the two Rocky Mountain states. Analysis of these three maps offers the opportunity to search for general principles that may apply to transect sampling efficiency.

To create the Wyoming and Colorado maps, Landsat TM data provided an on-screen basis for photointerpretation. Both the Wyoming and Colorado maps have minimum mapping units (MMUs) of 100 ha, although most polygons are much larger than this. Details of mapping methodology are provided by Driese et al. (1997). The Wyoming land cover map depicts 41 cover types in 14,732 polygons, although some types are rare in the state and others are disproportionately important in total area and number of polygons (Table 1, Figure 1a). The Colorado land cover map depicts 61 cover types in 16,610 polygons although, as in the Wyoming map, many types are rare (Table 1, Figure 1b). Colorado differs from Wyoming physiognomically in that the eastern third of the state is dominated by relatively unbroken Great Plains land cover types (grasslands and agriculture) while the western two-thirds is dominated by mountain ranges and valleys with high cover diversity. The resulting vegetation zonation is more pronounced in Colorado than in either of the other two states used in this study. The physiognomy of Wyoming includes widely scattered mountain ranges separated by broad, rolling basins (Knight 1994).

The Arkansas Gap land cover map was created by performing an unsupervised classification on enhanced and stratified TM data (Smith et al. 1998). An initial raster-based classification was aggregated and converted to vector format to produce a map of 36 land cover classes in 19,749 polygons with the same MMU (100 ha) as Wyoming and Colorado (Table 1, Figure 1c). In addition to different mapping methodology, the physiognomy and vegetation of Arkansas differ from that of Wyoming and Colorado, where the climate is more continental and elevations are higher (Arkansass maximum elevation is 839 m). Arkansas is divided between highlands (the Oachita Province and Ozark Plateau) in the north and west and lowlands (the Mississippi Alluvial Plain and Gulf Coastal Plain) in the south and east. The east-west zonation in vegetation associated with these physiographic zones is, however, less pronounced than that in Colorado, where the Rocky Mountain front provides an abrupt physiognomic boundary between the plains of the east and the mountains of the west.

Together, these three maps represent a range of cover types, configurations and mapping methodologies, but depict land cover at similar scales and extents. As such they provide a test set for examining the effects of map characters on video sampling effort.

Video Transect Simulations

For each map, sets of simulated video transects were generated for each of a variety of configurations (Table 2). For each transect orientation, placement was either random or systematic. Randomly placed transects were oriented east-west, north-south, or randomly within each state map. Systematically placed transects were either east-west or north-south. For each combination of transect spacing and orientation, sets containing one to ten transects each were generated to simulate increasing sampling effort. Finally, for the randomly placed transects, 10 sets of each orientation and transect number were generated to allow characterization of variability. Because the systematic transects were placed in a regular pattern across the extent of each land cover map, only one set per scenario of these transects was generated.

A GIS (Arc/Info, ESRI, Redlands, CA) allowed tabulation of the total transect length within the corresponding land cover map for each of the scenarios. The number of land cover types intersected by each set of transects was determined by overlaying the transects on the land cover maps. These two quantities allowed construction of characteristic curves describing the change in total number of intersected types as sampling effort (total transect length) increased.

Data Analysis

Total transect length was plotted against the number of cover types intersected by each set of transects for each scenario and 2-parameter exponential curves were fit to the resulting scatter plot. Curve-fitting with additional parameters improved the fit slightly, but at the expense of interpretability and so was not used. All curve-fitting was done using SigmaPlot 4.0 (SPSS, Inc., Chicago, IL). The resulting exponential curves are of the form:

(1) y = a(1 - e-bx)

where y is the number of land cover types intersected, x is the total transect length (km), and a and b are model parameters unique for each transect scenario and determined empirically by iteration to achieve a best fit curve for each scenario.

The exponential curves describing the relationship between total transect length and the number of cover types encountered were analyzed to identify 1) the transect length beyond which increasing length provided little increase in the number of cover types intersected (the level of diminishing returns), 2) map characters that might explain the shape of the exponential response curves, particularly with regard to the rate of rise to an asymptote, 3) differences within each state for the various curve orientations, and 4) differences in curve shape and asymptote between systematic and random placement of video transects.

To provide a consistent basis for comparison, we define the level of diminishing returns as the point on the mean exponential curve for each state where its slope reaches 0.001. In physical terms, this is the level where 1000 km of transect is required to add 1 land cover type to the sample. To calculate this, we computed the first derivative of equation (1):

(2) dy/dx = abe-bx

where a, b, y and x are as defined for equation (1). Setting dy/dx = 0.001 and solving for x provides the transect length (km) at the level of diminishing returns, which is used in equation (1) to calculate the number of sampled cover types at that level.

Curve parameters were compared with the distribution of proportional statewide area occupied by each of the cover types to explore their relationship with map characters. The proportional area per cover type for each map was calculated by dividing total state area (km) by the number of types in each map and expressing this value as a proportion of the state area. Skewness in the distribution of proportional area for the land cover types was calculated as:

(3) skew = (n/(n-1)(n-2)) * S ((xj-xavg)/s))3

where n is the number of cover types for a map, xj is the area occupied by type j, xavg is the mean area for all mapped cover types, and s is the standard deviation of the mean area. Additionally, the curves were evaluated qualitatively to identify possible relationships between curve orientation (e.g. E-W vs. N-S) and broad differences in the distribution of land cover across each of the three states (i.e. the orientation of vegetation zones).

Results and Discussion

Diminishing Returns

Parameter a from equation (1) represents the asymptotic number of land cover types encountered along the video transects and approached by the exponential curves fit to our simulation data (Table 3, Figure 2). Imposing these exponential curves onto the data scatter is artificial in the sense that sufficient line length would eventually capture all mapped types in a particular state (e.g., 41 for Wyoming), but for the maps analyzed here, the asymptote of the fitted curves is an index of the level of diminishing returns, beyond which additional sampling produces only small gains in the number of types encountered. Because many mapped types in these states are rare (Figure 1), long transect lengths are required on average before these types are encountered.

For Wyoming, diminishing returns defined by our slope criterion of 0.001 types/km occurs at capture of 33 cover types (Table 3, Figure 2) representing 80% of all mapped types. This level is achieved at a total transect length of 2495 km. For Colorado, diminishing returns occurs at 46 land cover types (75%), corresponding to a total transect length of 3355 km. Arkansas reaches diminishing returns at 25 cover types (70%) and 1769 km of transect. These differences between states are substantial, and suggest that simulation exercises like the ones described here are worthwhile for planning sampling strategies for any large accuracy assessment project. Beyond the level of diminishing returns, extension of airborne videography transects adds little to the sample size, at least in the number of sampled cover types (though additional samples are added for already visited types).

The use of fitted exponential curves does not quantify the rate at which the rare types not encountered early in transect sampling are added. Total transect lengths at the level of diminishing returns are approximately half of the maximum transect lengths generated in our simulation for each state (Figure 2). Doubling transect length in Wyoming from 2500 km to 5000 km increases the number of cover types encountered from 33 to about 35, an increase that might be better achieved by using other sampling strategies for rare types. Similar small increases after diminishing returns are observed in Colorado and Arkansas.

Map Characteristics and Curve Parameters

Our second research question concerns predicting the shape of the exponential curves for each state map using features of the maps themselves. Candidates for map characters that might alter the parameters from equation (1) include total map area, the distribution of proportional areas occupied by individual land cover types, the "skewness" of the distribution of area among cover types, and the spatial evenness of the distribution of cover types across the extent of the map. To quantify relationships (e.g., using regression analysis) between the equation parameters and the map characters would require many more than three maps, a task that we did not attempt due to the long processing time for the simulations, but results from Wyoming, Colorado and Arkansas suggest qualitative relationships that can be tested in future mapping projects.

As discussed in the previous section, parameter a from equation (1) corresponds to the number of cover types at the asymptote of the fitted exponential curves. Parameter b represents the rate at which this asymptote is approached. For larger b, the curve rises more steeply towards the asymptote, and reaches the level of diminishing returns at a shorter total transect length (Table 3, Figure 2). Together, the two parameters dictate the shape of the fitted curves and hint at map characters that influence the curve shapes.

The magnitude of parameter a is clearly related to the total number of cover types mapped in each state. Given similar distributions of cover types (Figure 3), one expects a to be larger for maps with more mapped cover types than for maps with less. This is supported by our data which show higher values of a for Colorado, where 61 types were mapped, than for Wyoming and Arkansas with 41 and 36 mapped covert types, respectively (Table 3).

The relationship between parameter b and map characteristics is more difficult to interpret. For the three maps, the mean value of b increases from Colorado to Wyoming to Arkansas. Intuitively, the chance of encountering a particular cover type depends upon the proportional area of the map occupied by that type. Comparison of mean parameter b from equation (1) for each state with proportional mean area/type shows a parallel increase in this quantity from Colorado to Wyoming to Arkansas (Table 3), providing qualitative evidence that mean typal area as a proportion of total state area influences the rate (b) at which new types are encountered by the video transects. Based on these three maps, the rate at which types are captured before reaching diminishing returns is higher for maps with larger mean proportional typal areas.

Although we hypothesized that the capture rate (b) would increase as the skewness of the distribution of average area for the cover types decreased, this was not supported by the data (Table 3). Instead, Colorado had the least skewed (most even) (skew = 2.87) distribution of typal areas among the three states but the lowest rate of capture with increasing transect length. This may be due to the zonality of the Colorado land cover compared to the other states, a spatial pattern not reflected in the skew value which describes only the non-spatial distribution of area among types. Wyoming had an intermediate capture rate (b) but the highest skew (4.53), reflecting the strong dominance of 2 cover types (Wyoming big sagebrush steppe and mixed grass prairie) (Figure 1), but with a relatively even spatial distribution of types.

There is a linear relationship between b and the mean number of polygons per cover type, although the constraint of a small (N = 3 maps) sample size limits extension of this relationship to other maps. For our maps, polygon frequency may vary fortuitously with spatial evenness, a characteristic that would be expected to increase capture rate with transect length. We place little importance on this result because there is not an evident physical explanation for the relationship.

Our sample size (3) is too small to make conclusive quantitative statements about the relationship between capture rate and map characteristics. Qualitative examination of the maps suggests that capture rate is higher (more types captured with smaller increases in transect length) for maps that 1) have a larger proportional average area per cover type, 2) have a more even distribution of types spatially, and 3) have a larger mean number of polygons per cover type. No area will have ideal distributional patterns, however, and empirical characterizations like the ones described in this paper are probably the most direct means of estimation of video transect distance requirements.

Transect Orientation

Our third research question addresses the orientation of the transect lines. The results (Table 3, Figure 2) reveal only small differences between the best fit exponential curves for each of the three states for the various transect orientations. E-W, N-S and randomly oriented curves all converge on approximately the same asymptotic number of types for each state, and within states all orientations reach this asymptote at approximately the same total transect length. Colorado, where zonation between the eastern plains and the western mountains is more distinct than zonation in the other two states, shows a faster initial increase in captured cover types for E-W transects than for N-S transects, but the curves converge at a transect length of about 4000 km (Figure 2), about the level of diminishing returns. For all three states, randomly oriented transects achieved a slightly lower level of diminishing returns than did E-W or N-S transects (Figure 2), but again differences are small.

Random vs. Systematic Transects

Systematic transects show a slightly higher rate of increase to the asymptotic level and, with the exception of Arkansas, achieve a small advantage in the number of captured types at the level of diminishing returns (Figure 2, Table 3). In Arkansas, randomly placed E-W transects reach the asymptotic level more slowly but eventually surpass the number of types captured by the systematically placed N-S transects. The advantage of systematic transects is probably due to increased probability that they will sample all broad land cover zones because the transects by design are spread across the latitudinal or longitudinal extent of each map. There is no guarantee that randomly placed transects will sample all zones, although at long transect lengths (longer than used in our simulations) the results should converge. Differences appear to be related to broad-scale zonality in land cover, but even in Colorado, where the differences between results for systematic and randomly placed transects are greatest, the difference in transect length between the most efficient and least efficient rates of capture represent only 1000 km of transect length in a state that requires 4000 km of video transect to achieve diminishing returns. These results, coupled with the practical considerations of planning flight lines, may dictate the use of systematic rather than random transects, but the advantages in terms of sampling efficiency are small and alternatives for particular sampling strategies should not be discarded.

Conclusions

Airborne videography provides a practical alternative to ground-based sampling for collection of "ground control" data to assess the accuracy of thematic maps in situations where thematic types are easily interpreted from low-level videography. Collection of video data for this purpose requires that transects capture a sufficient sample of cover types to satisfy statistical requirements, while simultaneously minimizing expense. The simulations described in this paper quantify a level of diminishing returns beyond which large increase in transect length adds few additional sampled types. For Wyoming 80% of all mapped cover types were captured at this level of diminishing return at a transect length of 2495 km. For Colorado and Arkansas, these levels were 75% at 3355 km and 70% at 1769 km respectively, as defined by the point on the fitted exponential curves where slope falls to 1 captured type per 1000 km of transect.

The relationship between total transect length and the number of cover types captured is exponential, and the shape of the curves reflecting this relationship for the three states is related in part to the total number of cover types found in the map, and in part to the mean proportional area per cover type, the mean number of polygons of each cover type, and the broad-scale zonality of the mapped land cover. Despite the small differences seen among these three states, for practical purposes, the orientation of the video transects (e.g. E-W, N-S, Random) has little effect on the outcome because all of the curves converge near the level of diminishing returns at approximately the same transect length. Systematically (vs. randomly) placed curves offered a small advantage, but perhaps not enough to overwhelm other sampling considerations.

These simulations are easy to perform within a GIS and are an efficient means of planning a sampling strategy for accuracy assessment using airborne videography transects. Thoughtful design of sample transects can eliminate unproductive sampling beyond the level of diminishing returns where additional flight time and expensed provides little benefit.

Acknowledgments

The work described here is supported by the USGS-BRD Gap Analysis Program (Cooperative Agreement 14-45-009-94-1512). Special thanks are due to Donald Schrupp, of the Colorado Division of Wildlife, who pioneered the video sampling effort used in both Colorado and Wyoming, and to Tom Thompson who was largely responsible for the Colorado Gap land cover map. Additionally, we would like to thank the Arkansas Gap team and Kimberly Smith and Rob Dzur in particular, for creating the Arkansas land cover map and for making it readily available on the World Wide Web. Kenneth Gerow provided statistical consultation.

References

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Smith, K.G., R.S. Dzur, D.G. Gatanzaro, M.E. Garner, and W.F. Limp. 1998. State-wide biodiversity mapping for Arkansas. Final Report. Arkansas Cooperative Fish and Wildlife Research Unit, Center for Advanced Spatial Technologies (CAST), University of Arkansas, Fayatteville, AR. (http://www.cast.uark.edu - digital report available).

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Table 1. Selected map characteristics for the GAP land cover maps of Wyoming, Colorado and Arkansas.

State

Total Area (km2)

No. of

Cover Types

Mean # Polys/Type

Stdev Polys/Type

Mean Area/Type (km2)

Stdev Area/Type (km2)

Skewness of Typal Areas

Wyoming

254,346

41

359

683

6,203

14,600

4.53

Colorado

269,498

61

272

419

4,418

8,225

2.87

Arkansas

137,667

36

549

732

3,824

7,469

2.96

 

Table 2. Video transect scenarios used for modeling. For each combination of random transect placement and orientation, 10 sets of transects were generated for each of 1 to 10 transect lines per set, resulting in 100 total sets for the random transect placements. One set of from 1 to 10 transects was generated for each systematic orientation, resulting in 10 total transect sets for these simulations.

Placement

Orientation

Number of lines

Number of Sets per Scenario

Total Number of Sets

Random

East - West

1 - 10

10

100

Random

North - South

1 - 10

10

100

Random

Random

1 - 10

10

100

Systematic

East-West

1 - 10

1

10

Systematic

North-South

1 - 10

1

10

 

Table 3. Exponential curve parameters a and b from equation (1) (see text) from each state for each of the 5 simulated transect scenarios and the transect length, number of cover types and proportion of all cover types sampled at the level of diminishing returns (DR) for each state. Diminishing returns are based on the criterion of the exponential curves reaching a slope of 1 cover type per 1000 km of transect. Values are for the average parameters for each state. Curves for the randomly placed transects are based on 100 points each and for the systematically placed transects on 10 points each.

 

Transect

Parameter

Parameter

 

DR Transect

DR #

DR Proportion

State

Scenario

a

b

R2

Length (km)

Types

of Types (%)

Wyoming

E-W Rnd

33.9

.0017

.83

     
 

N-S Rnd

34.5

.0013

.82

     
 

Rnd-Rnd

32.1

.0018

.77

     
 

E-W Sys

34.8

.0016

.83

     
 

N-S Sys

34.4

.0016

.93

     

Mean

 

33.9

.0016

 

2,495

33

80

Stdev

 

1.1

.0002

       

Colorado

E-W Rnd

46.9

.0012

.85

     
 

N-S Rnd

47.3

.0009

.79

     
 

Rnd-Rnd

44.4

.0011

.81

     
 

E-W Sys

47.9

.0017

.70

     
 

N-S Sys

47.4

.0012

.88

     

Mean

 

46.7

.0012

 

3355

46

75

Stdev

 

1.4

.0003

       

Arkansas

E-W Rnd

25.9

.0015

.80

     
 

N-S Rnd

24.8

.0024

.78

     
 

Rnd-Rnd

23.5

.0028

.73

     
 

E-W Sys

27.5

.0021

.91

     
 

N-S Sys

25.0

.0028

.70

     

Mean

 

25.4

.0023

 

1769

25

70

Stdev

 

1.5

.0005

       

Figure captions

Figure 1. The distribution of land cover types in terms of proportional area of each type occurring in a) Wyoming, b) Colorado and c) Arkansas.

Figure 2. Best fit exponential curves representing the relationships between total transect length on the horizontal axis and the number of land cover types encountered on the vertical axis for a) Wyoming, b) Colorado and c) Arkansas. Each curve represents the average response for a particular orientation (E-W, N-S and Random) and configuration (systematic, random) of the simulated video transects.

 

Figure 1.a.

Figure 1.b.

 

Figure 1.c.

Figure 2.a.

Figure 2.b.Figure 2.c.