Optimum Strategies for Mapping Vegetation using Multiple Endmember Spectral Mixture Models

Dar A. Roberts^a, Meg Gardner^a, Rick Church^a, Susan L. Ustin^b, and Robert O. Green^a

^aDepartment of Geography and Institute for Computational Earth System Science, University of California, Santa Barbara, CA 93106 ^bDepartment of Land, Air and Water Resources, University of California, Davis, CA 95616

Further author information:
D.A.R.: Email: dar@geog.ucsb.edu; Telephone: 805-893-2276; Fax: 805-893-2276.
M.G.: Email: gardner@geog.ucsb.edu:
R.C.: Email: church@geog.ucsb.edu; Telephone: 805-893-4217.
S.L.U.: Email: slustin@ucdavis.edu; Telephone: 530-752-0621; Fax: 530-752-5262

Abstract

Improved vegetation maps are required for fire management and biodiversity assessment, form critical inputs for hydrological and biogeochemical models and represent a means for scaling-up point measurements. At scales greater than 10 meters, vegetation communities are typically mixed consisting of leaves, branches, exposed soil and shadows. To map mixed vegetation, many researchers employ spectral mixture analysis (SMA). In most SMA applications, a single set of spectra consisting of green vegetation, soil, non-photosynthetic vegetation and shade are used to "unmix" images. However, because most scenes contain more than four components, this simple approach leads to fraction errors and may fail to differentiate many vegetation types. In this work, we apply a new approach called multiple endmember spectral mixture analysis (MESMA), in which the number and types of endmembers vary per-pixel. Using this approach, hundreds of unique models are generated that account for community specific differences in plant chemistry, physical attributes and phenology. Additionally, we describe a new strategy for developing and organizing regionally specific spectral libraries. We present results from a study in the Santa Monica Mountains using AVIRIS data, in which we map grassland and chaparral communities, mapping species dominance in some cases to a high degree of accuracy.

1. INTRODUCTION

Accurate maps of land-cover are required for a wide variety of applications in hydrology, climatology, biogeochemistry and ecology¹. To date, most remote sensing applications for land-cover have focused on either classification of vegetation, or on direct or indirect estimation of vegetation biophysical or structural attributes independent of taxonomic information². Direct identification of species or species assemblages has been difficult due to limitations in the ability of most current remote sensing systems to discriminate subtle differences between species that arise through chemical and anatomical differences in leaves and structural differences in canopies.

Imaging spectrometry offers the potential of improved vegetation mapping while providing direct links to plant chemical and physical attributes. Discrimination to the species or generic level has wide potential application. For example, species may differ in photosynthetic light responses, respiration rates, stomata! conductance or other physiological processes that influence carbon and water exchange and plant environmental interactions. Accurate knowledge of the distribution of plant species can form a critical component for managing ecosystems and preserving biological diversity. In chaparral ecosystems, species-level differences influence biomass accumulation and fuels characteristics that are critical to the prediction and management of wildland fires. For example, Regelbrugge and Conard³ note significant differences in above ground biomass and fine fuels characteristics between several chaparral dominants including Adenostomo fasciculatum, Arctostaphylos glandulosa and several species of the genus Ceanothus. Differences in fuel characteristics might produce significantly different fire behavior and thus be critically important for fire hazard prediction and fire management.

In this study, we describe a new approach for analyzing imaging spectrometry data and mapping vegetation through the use of multiple endmember spectral mixture models. We describe a strategy for organizing a regionally specific spectral library that provides optimal discrimination of vegetation. We apply this approach to AVIRIS data collected in the Santa Monica Mountains as part of a larger on-going collaborative study with the Los Angeles County Fire Department (LACFD) and United States Forest Service to improve chaparral maps for fire prediction and preventive management.

2. BACKGROUND

California chaparral, is widely distributed along coastal Southern California⁴. It represents a significant source of species diversity⁵, and, through a unique fire ecology, is a major contributor to regional ecosystem dynamics⁶. Seasonal drought coupled with the presence of chaparral communities in the urbanized wildlands California make wildfire one of the most serious economic and life-threatening natural disasters faced by the region⁷. Urban encroachment into the canyons and mountain wildlands have increased fire hazard to critical levels. Additionally, the steep fire-burned hillsides are subject to erosion, slumpage, and mud slides during the winter rains. More than 70 years of fire suppression⁸, and an extensive die back during the 1987-1993 drought, has produced an impressive accumulated fuel load in these communities, of up to 118 Mg/ha⁹.

Remote sensing represents a viable means for rapid, regional mapping of chaparral. However, steep topographic gradients, harsh edaphic conditions and variable fire-histories complicate mapping by creating a complex mosaic of chaparral dominants that vary in age, successional status and canopy characteristics (e.g. moisture content, biomass, fuel load). Limitations in spatial and spectral resolution have restricted the success of previous efforts. For example, Nichols¹⁰ and Estes et al.¹¹ found poor separation of shrub communities using the Landsat Multispectral Scanner (MSS). More recently Franklin and Swenson¹² mapped chaparral to the series level in the Holland classification system using a combination of unsupervised classification of Landsat TM and aerial photography to identify clusters. However, the minimum mapping unit was 5 acres in areas where variation within the vegetation occurs at a finer scale. In this study, we apply imaging spectrometry to map species dominants at a 20 meter resolution.

3. METHODS

3.1 Study site

The study was conducted in the Santa Monica Mountains, an east-west trending range along the coast of western Los Angeles County and eastern Ventura County, California. Climate in the region is Mediterranean, typified by low annual precipitation and moderate temperatures that vary seasonally between hot, dry summers and cool wet winters. Vegetation is diverse, consisting of at least four distinct types of hard chaparral, wetlands, riparian habitats, woodlands, and coastal sage scrub and a range in successional states following fire. Land-ownership is complex within the region creating a mosaic of public and private lands. In addition to a complex land cover and history of frequent fires, the region has been the focus of a large number of studies and thus has a wealth of supporting geographic and field data, making it an ideal site for evaluating new mapping algorithms and applying them to the problem of fire hazard prediction.

3.2 Image Data and Preprocessing

Analysis presented here focuses on AVIRIS data collected on October 19, 1994. For a description of AVIRIS data characteristics see Vane et al.¹³. Two east-west flight lines were acquired, consisting of a total of 12 scenes. Results will only be presented for one scene centered over Point Dume, California, covering an area of approximately 11 x 9 km with an IFOV of 20 m. (Fig. 1). Areas labeled as Zuma and Castro on the figure show the location of two field sites, one consisting of coastal sage scrub (Zuma) and the other chemise (Castro), where plant samples and canopy scale field spectra were measured. Apparent reflectance was generated using an algorithm coupled with the Modtran3 radiative transfer code¹⁴.

3.3 Spectral Mixture Analysis

Once converted to apparent reflectance, the AVIRIS data were modeled as spectral mixtures of field and laboratory measured spectra of soil, non-photosynthetic vegetation (NPV), green leaves and shade^15,16. Spectral mixture analysis (SMA) was performed using a multiple endmember spectral mixture analysis (MESMA), in which the number of endmembers and types of endmembers are varied across the image¹⁷.

As described by Roberts et al.¹⁷, MESMA is an extension of a simple mixture model in which a mixed spectrum is modeled as a combination of pure spectra, called endmembers¹⁵. MESMA assumes linear spectral mixing, in which photons interact with a single component within the field of view. Linear SMA is based on the fundamental equation:

(1)

Where a spectral mixture, P_il' from pixel i is modeled as the sum of N reference endmembers, P_kleach weighted by fraction f_ki. Spectral variation that is not accounted for by the linear model is expressed in a wavelength specific residual term, e _il. In this analysis, fractions were derived using modified Gram-Schmidt orthogonalization¹⁵. Model fit can be assessed using the residual term, e _il, or by the Root-Mean Squared Error (RMS) (Eq. 2):

(2)

A simple mixing model has an advantage in that it is relatively simple and provides a physically meaningful measure of abundance that is portable across sensors and through time^18,19. However, it is limited because it fails to account for the fact that the number of materials within the field view and the spectral contrast between those materials may vary. When combined with atmospheric contamination and natural variability in spectra, the simple model may produce fraction errors resulting in physically unrealistic fractions²⁰. Even with 224 channels, high correlation between bands results in fairly low dimensionality for any given pixel. For example, a scene may consist of tens to hundreds of components, yet 98% or more of the spectral variation may be accounted for by only three to four endmembers¹⁶. As a result, simple mixing models fail to account for subtle spectral differences within a class of endmembers (e.g., green vegetation) and thus may not be capable of discriminating species or similar materials such as some soils and senesced grass¹⁶.

MESMA¹⁷ overcomes many of these limitations, recognizing that a spectrum for any given pixel can be modeled with few endmembers, while allowing, the number of endmembers, and types to vary in each pixel in the image. Thus, potentially hundreds of endmembers can be used across the image, while applying the optimal subset to each pixel. Roberts et al.¹⁷ describe a technique in which sets of candidate models from field or laboratory spectra are used to develop sets of two-endmember models that are then evaluated for each pixel based on three selection criteria: 1) a fraction criterion, in which a candidate model must produce fractions between -1% and 101%; 2) an RMS criterion, in which the model must meet a minimum RMS threshold and 3) a residual criterion, where residuals must remain within some critical threshold over a minimum number of contiguous bands. Criteria used in Roberts et al.¹⁷ and in this study included an RMS and residual threshold of 0.025 and a residual count (maximum number of residuals exceeding the threshold in contiguous bands) of 7. Each AVIRIS pixel is evaluated separately by every candidate model. If a candidate model fulfills all three criteria, the model is flagged as a candidate for that pixel. After all two-endmember models have been evaluated for each pixel, pixels that remain unmodeled (e.g., require three endmembers or more) are evaluated with models consisting of progressively more endmembers.

In this paper we extend the MESMA approach of Roberts et al.¹⁷ to include optimized selection of a single model based on RMS and model prioritization based on spectral separability of field and laboratory spectra. We develop a regionally specific library for the Santa Monica Mountains that includes all shrub dominants and common rocks and soils in the area. and a strategy for selecting the optimal model from a suite of candidates. In the previous study described by Roberts et al.¹⁷, the spectral library used in the analysis consisted of materials from large geographic region. Furthermore, a different approach for model selection, based on maximal areal coverage²¹ was employed. In the following two sections we describe development of a regionally specific library for the Santa Monica Mountains and the development of a hierarchical strategy for selecting the optimal model.

3.4 Field sampling and spectral libraries

A regionally specific spectral library of green leaves, non-photosynthetic vegetation and soils was developed using field samples measured in the laboratory and field spectra measured from ground level, a ladder and a bucket truck on loan from the Los Angeles County Fire Department. Spectra were collected for all dominants in the area in the fall and spring of 1995 and 1996. Hemispherical reflectance spectra were measured at the University of California, Davis using a Cary-5E (Varian, Inc. Sunnyvale, CA) standardized to halon. Canopy level spectra were measured between 1 and 4 meters above each plant using an Analytical Spectral Devices (Analytical Spectral Devices, Boulder' CO) full range spectrometer on loan from the Jet Propulsion Laboratory. Field spectra were standardized using a 100% reflectant spectralon plate. All spectra were converted to absolute reflectance using the reflectance spectrum for each standard. Initial canopy level spectra were measured in the spring and fall of 1995 using the bucket truck to sample 5-7 shrubs at three sites in the Santa Monica Mountains. Follow-up spectra were collected in the spring and fall of 1996 using a ladder to obtain spectra from shrubs that were poorly represented in the initial collection in 1995. A total list of spectra is provided in Table 1. To capture the spectral variability inherent in most species, multiple spectra were collected for each. Example mean spectra and a plot of one standard deviation is shown for twelve canopies in Figure 2.

3.5 Optimal Model Selection

Given multiple solutions for each pixel, it becomes necessary to select from a list of candidate models the optimal set. Painter et al.²², utilized minimum RMS as the primary selection criterion when using AVIRIS to map snow grain size. In this paper we combine the minimum RMS approach of Painter et al.²² with MESMA to select the optimal model from a suite of multiple endmember models. Furthermore, we incorporate a two stage approach, starting by applying two-endmember multiple endmember models to spectral libraries to develop a hierarchical strategy for their application to image data. In this fashion we are able to determine apriori whether two species can be discriminated in image data based on their field or laboratory spectra. In addition, we are able to determine at which point in the analysis two species can be separated. For example, two species may be readily separated from each other, yet difficult to separate from a third. We employ this approach by first arranging the regionally specific library so that all members of a species or like materials (e.g. soils) occur within the same region of the library (e.g., the first 20 spectra are soils, followed by beach sands, chemise etc). Next, we apply MESMA, using the same criteria used for images to a library of target spectra, in this case the same library used to generate the models. In the two-endmember case, we can then generate an image, in which model number forms the x axis and target number forms the y (Fig. 3). When a model meets the selection criteria, it's associated pixel is assigned a value of 1, 0 otherwise. Because each candidate spectrum, when combined with shade must unmodel itself, at a minimum we will generate a diagonal consisting of ones. Groups of similar spectra, arranged within the same region of the library, should form square clusters in the image. Ideally, each set of spectra from a species will form a unique cluster. Based on the resulting spatial pattern in the image, it becomes possible to determine which spectra are most unique to a species, which are readily modeled by the wrong materials, and which tend to fit too many models. The first might be considered specialists, the last, generalists. In terms of image analysis, specialists would be given the highest priority followed by generalists. Spectra that are easily confused with other materials, but do not tend to be generalists, might also be given a high priority. A more detailed example for the Santa Monica data set follows in the results. To date, we have only applied the first stage of analysis to two-endmember models. To apply the concepts to three endmembers, we have used categorizations based on two endmembers to assign priorities to the three-endmember cases.

Once members of a spectral library are placed into specialist or generalist categories, each candidate model can be given a priority as it is evaluated in the image. Candidate spectra that are specialist and thus should be readily separated are evaluated first and selected on the basis of a minimum RMS. Generalists would be given a lower priority and evaluated only after specialists have been evaluated. Once the optimal model has been selected for each pixel, it can be used to generate a vegetation map showing which species provided the best model for each pixel based on minimum RMS, and the fraction and residual criteria. A three-endmember prioritized list was built from the two-endmember models, placing models that included specialists at a higher priority than models generated from generalists.

4. RESULTS/DISCUSSION

4.1 Model Selection

The first stage image, showing spectra within the library that fit target spectra using MESMA provides a useful means for evaluating the separability of species and establishing an order for model selection when applied to the full AVIRIS image (Fig. 3). One way to view this result is that it provides a road map allowing a user to navigate and organize a potentially large spectral library. The following interpretation can be applied to the library developed for the Santa Monica Mountains. Each endmember unmixes itself, producing a white diagonal down the image. Specialists, which primarily unmix only like materials form clusters in the image. A good example is provided by spectra from Zuma Beach, which form a cluster in the upper left portion of the image, indicating that these spectra primarily unmix white sands at Zuma Beach, but are confused with few other materials in the library. A similar, less pronounced block marks many of the soil spectra, indicating that each soil spectrum is more unique than the beach spectra, but overall that most of the soils spectra are distinct from other materials in the library. Good examples of square clusters of vegetation spectra include Adenostoma fasciculatum (Adfa) and Arctostaphylos (Arglc and Argld). Generalists should be represented by clusters in the image that form along a vertical column, meaning a single set of models unmixes many target spectra. These types of models would tend to be over represented in the image. Good examples are provided by a large number of spectra, including Cercocarpus betuloides (Cebe), Heteromeles arbutifolia (Hear), Malosma laurina (Mala), Quercus dumosa (Qudu) and Rhus ovata (Rhov). These canopies typically consist primarily of green leaves, and thus may lack distinctive spectral features associated with vegetation structure and the presence of variable amounts of NPV. Horizontal white lines indicate target spectra that are easily modeled by a large number of models. A good example of this type of target is Ceanothus megacarpus (Ceme) and Ceanothus oliganthus (Ceol). Because many models will work for these targets, it would be necessary to give their respective models a higher priority over other models if they are to be successfully mapped. In all cases, laboratory spectra of NPV tend to be highly specific whereas most canopy) level spectra measured from the bucket truck that consisted of mixtures of several species form horizontal lines.

4.2 Building the Vegetation Map

Based on the first stage of analysis a prioritized list of six categories was developed (Table 2). Within each category, the model that generated the lowest RMS and fit the fraction and residual criteria is selected. After all models in the first category have been evaluated, the second category will be evaluated and so on. In developing this list, specialists, such as A. Fasciculatum and target spectra that formed horizontal lines in the spectral library map, such as Ceanothus megacarpus were placed in early categories. Generalists, such as Heteromeles arbutifolia, and Malosma laurina were placed in a low priority category. Senesced materials and soils were given intermediate priority, although the fact that many were specialists suggests that order was not important in this case. Note, most materials or species are represented by more than one spectrum, accounting for spectral variability within a class. The number of spectra used for each species is a rough indicator of species-level variation at the canopy level and within the scene.

Once all two endmember models were evaluated, three endmember models were generated using the two-endmember priorities to choose orders for three endmember models. An image generated by combining the two-endmember optimized models with the three-endmember case was generated for drought-deciduous vegetation and evergreen chaparral (Fig. 4). Initial accuracy assessment by Gardner²³, using a fuzzy approach showed high levels of accuracy based on distinguishing hard chaparral from soft chaparral, senesced grass and rock. Accuracy to the genus and species level remained high for several vegetation types including Ceanothus megacarpus, Artemisia californica and Salvia leucophylla. Lower accuracies were achieved for Adenosroma fasciculatum due to confusion between senesced crowns and Eriogonum cinereum. Quercus, Ceanothus spinosus, Salvia mellifera and Eriogonum fasciculatum showed low accuracies, in part due to known spectral ambiguities and in part due to very low abundance.

5. CONCLUSIONS

In this paper we describe three powerful new concepts, multiple endmember spectral mixture models, regionally specific spectral libraries and a hierarchical strategy for organizing spectral libraries and selecting models. We apply these strategies to AVIRIS dare collected over the Santa Monica Mountains, in southern California, generating vegetation maps that may prove invaluable for fire hazard prediction. Beyond the Santa Monica Mountains, the techniques should have broad applicability over a much larger geographic region. For example, we are currently extending the analysis to include arid ecosystems, forests of the Pacific Northwest, conifer forests in the Sierra Nevada and Boreal forests of Canada. We consider the techniques, as described, only the beginning of what should prove to be a fruitful direction of research. For example, the hierarchical strategy described was only applied to the two-endmember case. There is a clear need for developing similar approaches for three or more endmembers. Additional directions for research include the potential use or spectral weighting factors during model selection, and model dependent selection criteria (e.g. tightened constraints for materials that are difficult to separate).

ACKNOWLEDGEMENTS

Support for this research was provided in part by a grant from the National Aeronautics and Space Administration, Terrestrial Ecosystems and Biogeochemical Dynamics Branch, NAGW-4626-I, as a subcontract with U.C. Davis. Additional research support and computational equipment was provided through a University of California Directed Research and Development (UCDRD) grant for collaborative research with Los Alamos National Laboratory (Grant STB/UC:97-50). Original algorithm development and image processing was accomplished on computer equipment purchased through start-up funds from U.C. Santa Barbara Department of Geography. We thank LACFD for the loan of a bucket truck in 1995 and JPL for the loan of the ASD full range spectrometer.

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1998, Center for Spatial Technologies and Remote Sensing (CSTARS)
University of California, Davis