Remote Sensing Based Piosphere Analysis

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136

Robert A. Washington-Allen

1

Department of Forestry, Range and Wildlife Science, Utah State University, Logan, Utah 84322-5230

Thomas G. Van Niel

CSIRO Land and Water, Private Bag No. 5, Wembley, WA 6913, Australia

R. Douglas Ramsey and Neil E. West

Department of Forestry, Range and Wildlife Science, Utah State University, Logan, Utah 84322-5230

Abstract: The term piosphere was orginially defined as an indicator of the localized impact of grazing on vegetation and soils. It is a radiating zone of attenuating animal impact away from a concentrator, e.g, water, mineral licks, bedding grounds, etc. Over time there may be increased soil erosion, reductions in vegetation cover and changes in soil chemistry within piospheres. This paper expands this definition to include any concentrated animal or anthropogenic impact that radiates from an area of concentration. Satellite remote sensing instruments are capable of detecting both broad-scale climatic effects and small-scale localized impacts. A remote sensing– based tool for conducting piospheric analysis was developed to help evaluate areas of landscape impact caused by livestock or other concentrators. The program charac-terizes a piospheric response using three GIS layers: a boundary (e.g., a paddock); a concentrator (e.g., a water source); and a response index (e.g., a remotely sensed vegetation index). Piospheric analysis was demonstrated within a grazing paddock that had obvious piospheres. The objectives of the analysis were to: (1) use a time series of dry-season vegetation index imagery from 1972 to 1997 to characterize the historical vegetation response and relate it to climate and grazing at the paddock spa-tial scale; (2) characterize vegetation response at water points and streams; (3) deter-mine if piospheres can be detected in sagebrush steppe; and (4) demonstrate the utility of the piospheric analysis program. Evidence of persistent degradation at water sources was detected but not at streams. This type of analysis could be quite useful to land managers for separating the effects of climate from persistent degrada-tion induced by localized disturbances.

INTRODUCTION

The National Research Council (NRC) and the Western Regional Research Coor-dinating Committee-40 on Rangeland Research (WRRCC-RR) recommended that

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REMOTESENSING–BASEDPIOSPHEREANALYSIS 137

research be conducted that developed the use of Geographic Information System (GIS) and remote sensing (RS) technologies for monitoring and assessment of range-lands at sub-regional to regional scales (NRC, 1994; West et al., 1994). This paper addresses this concern by providing a GIS-based algorithm to land managers and researchers that can be used to determine the local impact of land management activi-ties on their landscapes. The main objectives of this paper are to utilize a GIS applica-tion of a piosphere model to identify impacts on a landscape by characterizing the vegetation response at the paddock spatial scale and relating this response to climate and grazing. Further, the paper provides background information about piospheres and describes the developed piosphere analysis algorithm and its requirements.

Piospheres are the result of the impact of a disturbance (e.g., livestock grazing) at an environmental resource patch such as water, shade, mineral licks, etc. (Forman and Godron, 1981). The disturbance’s impact is highest at the center of a resource patch and attenuates radially with increased distance from the patch center (Andrew, 1988). Lange (1969), researching the effects of sheep grazing at water points, coined the term piosphere, where “pios” is the Greek word for drink and “sphere” is representa-tive of the weakening impact of the disturbance equally distant from the resource patch center. Piosphere analysis is important to land managers because environmental monitoring programs in drylands have had the problem of separating grazing impacts from climatic effects (Pickup et al., 1994). The distribution of resources and thus the impacts of disturbances like herbivory are spatially heterogenous (Coughenour, 1991). Piosphere analysis exploits a manager’s knowledge of resources for which a disturbance has high geographic fidelity (e.g., livestock require water). Piospheres have been used as indicators of desertification and land degradation (Glantz, 1977; Dregne, 1983; Pickup et al., 1998).

HYPOTHESES

Piosphere analysis measures the effects of a disturbance’s radial attenuation on the condition of vegetation and soil resources. Pickup (1989), Stafford Smith and Pickup (1990), and Pickup et al. (1994, 1998) developed a general hypothesis of a remotely sensed vegetation index’s (VI) piospheric response (Fig. 1). Figure 1 is a conceptual model of the expected wet and dry period piospheric response, as mea-sured by a remotely sensed VI (the y-axis), originating from a water point within an arid landscape. The typical piospheric response is usually depicted as a sigmoidal response function (Graetz and Ludwig, 1978) and is accompanied by four diagnostic characteristics for which a persistent trend indicates degradation. These diagnostics are: (1) the development of a permanent grazing gradient in the area directly sur-rounding the resource patch, where vegetation cover is permanently reduced or non-existent during wet periods (Fig. 1A, dashed line); (2) a decrease of the wet-period response toward the dry period (Fig. 1B); (3) a decrease of the dry-period response toward plant extinction (Fig. 1C); and (4) an increase in the distance of either the inflection point (Fig. 1D) or asymptote (Fig. 1E) away from the resource patch. Alter-natively, Graetz and Ludwig (1978) found that a decrease in the slope of the line between the asymptote and the inflection points over time is an indicator of degrada-tion. An opposite trend to each of these responses is indicative of recovery at a water-point.

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Pickup et al. (1994) observed that there were three more types of gradient responses in addition to the “normal” response, which they termed, inverse, compos-ite, and complex (Fig. 2). An inverse piosphere (Fig. 2A) consists of a decrease in cover from the waterpoint, except in the vicinity of the waterpoint. This pattern sug-gests the presence of unpalatable species immediately surrounding the water source (ibid.). A composite gradient (Fig. 2B) is a combination of normal and inverse gradi-ents. In this case, cover decreases with distance from water and then begins to increase. Pickup et al. (1994) suggest either a woody plant increase or build-up of unpalatable species. If the gradient persists for a short time after a rain event, then it is probably indicative of an annual flush. Finally, a complex piosphere (Fig. 2C) is when the mean response of the index is not sufficiently robust to detect changes, but the index’s variance does detect the disturbance. Complex gradients appear in areas where reduced growth of vegetation in runoff and eroded areas is offset by increased growth in run-on and sediment sinks. The topographic mosaic of source and sinks average out the mean response of the index and a weak gradient is detected. However, the variance of the vegetation index is more robust where topographic effects are

Fig. 1. Conceptual piosphere model of the response to grazing of a remotely sensed vegetation

index at a water source. The response is measured during wet and dry periods in an arid landscape. Aspects of the model (A–E) are explained in the text. The model is adapted from Pickup et al. (1994).

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present (Pickup et al., 1994). For this paper, analyses of degradation features will focus on the formation of permanent gradients (Fig. 1A).

Disturbance processes associated with resource patches include grazing, military training and testing, recreation activities, and urbanization. Resource patches in rangelands used for animal production include water points (thus the term piosphere), riparian corridors, mineral blocks, obligate shade, and bedding grounds. Common resource patches in drylands managed by the military can include troop bivouac areas, weapon firing points, roads, and trails. To avoid confusion, we call piospheres developed by processes other than grazing (e.g., military activities) concentration areas.

STUDY SITE

The study site selected to demonstrate the application of the piosphere algorithm was a paddock within the Deseret Land & Livestock Ranch known as Negro Dan Paddock (Fig. 3). This paddock comprises 1198 ha and has a rolling topography of stream terraces, alluvial fans, and valley bottom flood plains. Deseret Land & Live-stock Company (DL&L) ranch is located in the northeastern part of the Utah panhan-dle and occupies 88,800 ha, including 6,800 ha of Department of Interior Bureau of

Fig. 2. Three types of piosphere responses of vegetation with distance from water, including the

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Land Management (BLM) and Utah state land (McMurrin, 1991). Mean annual pre-cipitation is 240 mm in the northeast and 440 mm in southwest. Mean monthly tem-peratures range from –17.1° to 27.3° C. Elevations range between 1889 and 2700 m. The DL&L is primarily covered by sagebrush steppe vegetation (West, 1989). Taxo-nomic soil orders present on the DL&L are Aridisols, Mollisols, Inceptisols, and Entisols. Negro Dan Paddock (NDP) contains 4 ecological sites: Semidesert Loam, Semidesert Clay, Upland Loam, and Upland Stony Loam (SCS, 1982). Primary land use on DL&L is a mixed commercial cow-calf ranching and wildlife hunting opera-tion.

Grazing records from 1980 to 1997 indicated that NDP was grazed by cattle at a mean stocking rate of 12 ± 28 AUDHa-1 _{(Animal Unit Day per Hectare). For this}

period, 5 individual years of rest were provided over the 18-year span, with a maxi-mum stocking rate of 123 AUDHa-1_{when grazed in 1984.}

METHODS

The basic piosphere analysis algorithm (Fig. 4) relates a vector concentration layer to a raster response index layer that can be stratified by an optional boundary layer. The concentration layer can be representative of point, line, or polygon (area) surface features such as livestock water points. The response index layer can be repre-sentative of a static or variable surface attribute, such as vegetation cover, elevation,

Fig. 3. Negro Dan Paddock within the Deseret Land & Livestock Company Ranch in

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or a vegetation index. This paper used the soil-adjusted vegetation index (SAVI) (Huete, 1988) as the response index layer. SAVI was developed specifically for arid environments to reduce soil background noise on the vegetation signal (Huete, 1988). The SAVI was generated from a ratio of near-infrared (NIR) and red (R) radiances that are detected by either a field, airborne, or satellite-mounted spectroradiometer. SAVI is a measure of vegetation greenness, a variable that has been correlated with vegetation cover (Sellers, 1985). SAVI was calculated as:

SAVI = [(NIR – R)/(NIR + R + L)] · (1 + L),

where L varies between 0 and 1 and its weighting is dependent on vegetation cover or soil moisture conditions (Huete, 1988). The default L factor of 0.5 was used for all images (Huete, 1988). The boundary layer is a vector layer that represents different spatial extents of interest to the user, such as a grazing paddock area. The need for a boundary layer is dependant on the user’s needs.

The Piosphere Analysis Algorithm

The program first requires the user to specify in a dialog box a concentration layer. The concentration layer can be either a point, line, or polygon layer composed of individual or multiple features (e.g., one or many water points). The user has the choice of distinguishing individual features of a concentration layer by choosing a unique field from the layer’s feature attribute table. For example, the concentration layer may consist of a number of watering points where each point is distinguished in a feature attribute table that contains information on each waterpoint’s attributes,

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including an ID number, its name, and year of installation. If a field with unique val-ues is selected, statistics will be output for each waterpoint. The user chooses a field with identical values or ignores the field selection; statistics are summarized for all water points.

The user is prompted by a series of dialog boxes to specify: (1) the input response index layer; and (2) either a boundary layer that limits the generation of an annulus to a specific area or the annulus to a specified distance. An annulus is composed of indi-vidual annulus or concentric rings that radiate from a concentration point. The last dialog in this series prompts the user to specify the thickness of an annulus based on the pixel resolution of the response index layer (e.g., if the response layer’s pixel size is 60 × 60 m, then this is the minimum thickness of an annulus). This allows the user to scale (or smooth) the index response to the disturbances effect within an annulus. The extent of the annuli is chosen by assigning a desired number of annulus. The specification of distance (number of annuli) rather than a boundary is based on the user’s knowledge of the disturbance process. For example, cattle or sheep have vary-ing distances for their dependencies on water or minerals (Stuth, 1991). If the maxi-mum distance from water for cattle is 4 km, then the maximaxi-mum number of annuli is set according to this constraint. Once these parameters are set, the program generates an annulus around the concentration layer and each successive annulus using a Euclidean distance function. This process continues until either the response index layer or boundary layer extent, or the set number of annuli, or the annulus from another feature is reached. In the latter case, the annuli that meet will not overlap but will intersect. Finally, the program outputs an annuli GIS layer, a table that summa-rizes the descriptive statistics (minimum, maximum, mean, sum, and standard devia-tion) for each feature’s annuli, and a graph of the possible piospheric response for all the features selected (Fig. 3).

Data Set and Processing

The ranch manager identified 106 water sources with either a recorded year of use and/or a description of use on the ranch. These sources were confirmed using Global Positioning System (GPS) field surveys, 1976 and 1977 aerial orthophotos, the Rich County soil survey (SCS, 1982), USGS digital raster graphics and paper copy 7.5 minute quadrangle topographic maps, and interviews with the ranch’s man-agement. NDP contains five livestock watering points and the stream channel: Negro Dan Hollow. The five water points were used to test the point features of the pio-sphere algorithm and the stream channel was used to test the line feature. The five water points had been established prior to 1970 and had obvious piospheres that had been observed both on the ground and within aerial photographs (Fig. 5).

The response index layers consisted of a SAVI time series that was generated from twenty-two (22) dry- season anniversary Landsat MSS and TM scenes from 1972 to 1997 that were acquired from the U.S. Geological Survey’s EROS Data Cen-ter (EDC) in Sioux Falls, South Dakota (Table 1). Landsat scenes from 1977, 1978, 1983, 1993, and 1994 were either not available or not suitable for this analysis due to cloud cover. Landsat image scenes were geometrically rectified using nearest neigh-bor resampling to a 60 × 60 m resolution of an August 7, 1972 Landsat MSS image, from the North American Landscape Characterization (NALC) data set (Lunetta and

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Sturdevant, 1993) using a RMSE between 0.25 and 0.50 pixel as recommended by Jensen (1996). The imagery were normalized to exo-atmospheric radiance from digi-tal numbers and then converted to reflectance values using Landsat MSS and TM post-launch calibration gains and biases from tables and formulae provided by Markham and Barker (1986). The dataset was then atmospherically corrected using a relative atmospheric correction procedure developed for multi-temporal imagery (Hall et al., 1991; Jensen, 1996; Callahan, 2002; Washington-Allen, 2003). The stan-dardized dataset was then converted to SAVI images and subset to the proportions of Negro Dan Paddock.

The NDP boundary was intersected with the Rich County SCS range site layer (SCS, 1982) to create a new boundary layer that stratified the paddock by fencelines and topography. Hosten (1995) suggested in his field studies of water points, in a sagebrush steppe-dominated landscape in southern Idaho, that non-detection of a pio-sphere was related to failure to stratify the landscape for topography and environmen-tal gradients represented by range sites.

Analysis

In this study, both space and time were analyzed where: (1) MATLAB (Hanselman and Littlefield, 1997) was used to fit a three-dimensional gridded mesh to the mean SAVI values for a particular number of annuli for each year (i.e., SAVI vs. distance

Fig. 5. An example of two of the piosphere’s (53 and 54) that were studied within Negro Dan

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from water vs. time); (2) the mean SAVI for each annulus for the 27-year period (i.e., SAVI vs. distance from water) was calculated for each water point and a polynomial was fit to discern the piospheric response in the manner of Graetz and Ludwig (1978); and (3) the mean SAVI was calculated for the annuli in each year and a polynomial was fit to determine the magnitude of the regression (i.e., SAVI vs. time). The magnitude of the regression is a measure of temporal trend (Yafee and McGhee, 2000).

RESULTS

An example of the annuli output for a single year is shown in Figure 6. The annuli are shown in relation to the concentration features: the five water points in NDP (A) and Negro Dan Hollow stream channel (B), and the boundary layer—the intersection of NDP boundary with the range site polygons within it. Annuli are

Table 1. The Dry Season Interannual Time series (1972–1997) of Landsat Multispectral Scanner (MSS) and Thematic Mapper (TM) Satellite Imagery Used in this Studya

Acquisition date Landsat Scanner and number Sun zenith angle RMSEb 08/07/1972 MSS 1 34 0.13 09/07/1973 MSS 1 42 0.19 08/15/1974 MSS 1 37 0.04 09/06/1975 MSS 2 43 0.04 09/09/1976 MSS 1 49 0.04 09/03/1979 MSS 1 42 0.06 08/28/1980 MSS 2 41 0.04 08/21/1981 MSS 2 40 0.05 08/09/1982 MSS 3 35 0.02 08/28/1984 MSS 5 40 0.16 09/16/1985 MSS 5 36 0.04 09/03/1986 MSS 5 42 0.04 09/06/1987 MSS 5 42 0.04 09/08/1988 MSS 5 42 0.08 08/28/1989 TM 5 39 0.06 08/29/1990 MSS 5 41 0.09 09/17/1991 TM 5 46 0.03 09/03/1992 MSS 5 42 0.37 09/09/1994 TM 5 44 0.02 08/27/1995 TM 5 33 0.08 08/29/1996 TM 5 41 0.04 09/01/1997 TM 5 40 0.01

a_{GCP = ground control points; RMSE = root mean square error.} b_{30 GCPs.}

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composed of an individual one pixel-thick (60 m) annulus, around the concentration features, i.e., the five water points (Fig. 6A) and Negro Dan Hollow stream channel (Fig. 6B). The extent of the set of annuli continues until the last annulus intersects either the boundary layer or another annulus. Each individual water point’s annuli stay constrained to the range site they are within (Fig. 6). However, Negro Dan Hollow stream occurs at the border between two range sites, and thus the annuli there are composed of two different range sites (Fig. 6B).

Figure 7 shows the three-dimensional (3-D) piospheric response surfaces for each of the five water points within NDP. To detect whether a permanent gradient exists as defined in Pickup et al. (1994), the mean piospheric response for each annu-lus per water point from 1972 to 1997 was calculated. A polynomial was then fit to discern the type of piospheric response for each of the water points. The fits for the five water points were all cubic and significant at the p ≤ 0.10 level. Both water points 52 (inflection = 19 pixels, asymptote = 38 pixels, extent = 51 pixels) and 76 (inflec-tion = 6 pixels, asymptote = 11 pixels, extent = 13 pixels) have normal “permanent” gradients. Water point 53 has an inverse gradient (inflection = indeterminate, asymp-tote = 10 pixels, extent = 17 pixels). Water point 54 (permanent gradient trough at 5 pixels, asymptote at 10 pixels, and extent at 13 pixels) and 77 (permanent gradient trough at 10 pixels, asymptote at 26 pixels, and extent at 34 pixels) are composite “permanent” gradients (Fig. 8).

Figure 9 is the 3-D response surface for Negro Dan Hollow stream channel from 1972 to 1997 and Figure 10 is the SAVI mean and variance of each annulus’s values

Fig. 6. The annuli output from the five water points (A) and streams (B) within Negro Dan

Paddock on Deseret Land & Livestock Co. Ranch in northeastern Utah. The points and streams are shown in relation to the paddock and range site boundaries. The waterpoints at the center of each annuli are numbered 52 to 54 and 76 and 77 (A) and Negro Dan Hollow stream is labeled (B).

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for Negro Dan Hollow stream channel from 1972 to 1997. The mean response is a significant quadratic and has an asymptote of 7 pixels and an extent of 18 pixels.

DISCUSSION

The analysis demonstrated here took advantage of the historical Landsat archive (1972 to 1997) to derive the response index layers. It is envisaged that a land manger would use the program with a time series of response index layers to capture both natural historical variation and significant departures from reference conditions. Ref-erence conditions for piospheric analysis can be baseline, mean, minimum, or maxi-mum, or some management-preferred intermediate condition (Pickup et al., 1994). Knight (1995) recommended using either a neutral model where departure from ran-dom conditions indicates the action of constraints (disturbances) or a conceptual

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Fig. 7. The dry-season piospheric response surface for five waterpoints within Negro Dam

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model of reference conditions, e.g., the normal grazing gradient. Pickup et al. (1998) used a space-for-time substitution and a vegetation index/historical precipitation driven productivity model to establish good condition reference sites within different land units. The values for references sites were then ratioed against the observed values to standardize for precipitation effects. Departure from maximum predicted conditions was used to measure the trend of degradation (Pickup et al., 1998). Both Archer and Smeins (1991) and Pickup and Chewings (1994) have suggested that at least a 20-year monitoring record is required to detect a significant trend in an indica-tor of change in semi-arid and arid landscapes.

The mean piospheric response, a quadratic, observed in Negro Dan Hollow stream channel at first suggested a complex gradient. however, the response of the mean and variance are concordant and thus suggest there is no piospheric response from the riparian vegetation (Fig. 10).

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Fig. 8. The interannual mean dry season piospheric response for each of the five waterpoints

from 1973 to 1997. Polynomials, after Ludwig and Graetz (1978), were fit to detect the type of piospheric response.

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The mean piospheric response for water points 52, 54, and 77 were weakly expressed (r2_{< 0.50, though 54 is r}2_{= 0.53), but strongly expressed for water points}

53 and 76 (r2_{> 0.50). However, despite the high recovery from mean and drought}

conditions attributable to extremely wet periods (for example the 1995 and 1997

Fig. 9. The dry-season piospheric response surfaces for Negro Dan Hollow stream within

Negro Dan Paddock on Deseret Land & Livestock Co. Ranch from 1972 to 1997.

Fig. 10. The interannual (grand) mean and variance dry season piospheric response for Negro

Dan Hollow stream within Negro Dan Paddock on Deseret Land & Livestock Co. Ranch from 1972 to 1997. A quadratic, after Ludwig and Graetz (1978), was fit to detect the type of piospheric response.

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pulses), a permanent grazing gradient is indicated for each water point for the 27-year period (Fig. 8). The permanent gradient was likely formed due to grazing and tram-pling by herbivores (livestock and wildlife) at the water point or the zone beyond unpalatable plants. Research by Perkins and Thomas (1993) suggests that formation of a permanent gradient is an indication that changes in soil quality as well as quantity have occurred. Consequently, some aspects of land degradation may have occurred within NDP. However, Negro Dan Hollow stream channel shows no indication of a piospheric response and thus no indication of degradation. Finally, only the perma-nent gradient diagnostic feature of piospheres was used to detect degradation (Fig. 1). Although our purpose was to present a simple application and analysis of the model, we could have further explored the degree of degradation by comparing the other diagnostic features, particularly change in the inflection point, an indicator of expan-sion of a permanent gradient from a concentration feature (Fig. 1).

The analysis of NDP used here was an empirical study of an ecosystem measure of vegetation response to grazing. It is the first time a nearly continuous time series of satellite imagery has been used to conduct this type of analysis. Similar remote sens-ing studies by Pickup and others covered a similar time period, but utilized a limited number of images that tended to represent the mid- and endpoints of the time periods studied.

Hosten (1995) conducted a field-based piospheric analysis in the sagebrush steppe ecosystem of southern Idaho that failed to detect a piospheric response. Hosten attributed the non-detection to variable topography. Hosten’s data were collected dur-ing average to wet conditions that may have indicated a recovery period (Fig. 1). Ground truth of remote sensing–based piospheric response was conducted by Bastin et al. (1993). However, unlike Bastin’s, this study lacked both historical and contem-porary field-based surveys of the piospheres to confirm the interpretation of trends. This study reduced this problem somewhat by using established water points with obvious piospheres (Fig. 5).

Two possible improvements to this method of monitoring are to: (1) monitor cur-rent field conditions at selected water points in NDP, and (2) establish reference water points for ground-based monitoring and manipulation to calibrate and confirm persis-tent indicators of degradation detected by satellite imagery. Also, where continuous long-term field monitoring data are lacking, an alternative technique could be com-puter simulation models. For example, Jeltsch et al. (1997) examined vegetation change within a piosphere using a spatially explicit 30-year simulation model. The model tracked plant species composition changes within piospheres, with the most obvious change being an increase in shrub cover after 30 years. However, because it was a forecast it only provided a hypothesis of future events. Consequently, the time series analysis demonstrated here was developed to take advantage of the historical Landsat archive (1972 to 1997) from which the response index maps were derived. It is envisaged that a land manger would use this process with a similar time series of satellite images to capture natural historical variation, significant departures from ref-erence conditions, and the persistence of features diagnostic of disturbance impacts in locations where the disturbance’s distribution is known (e.g., a water source, drilling pad, or military firing point).

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CONCLUSIONS

This research documented a process for conducting piospheric analysis within a remote sensing and GIS environment. This piospheric analysis allows separation of the impact of a localized disturbance in semi-arid and arid landscapes from the effects of climate by distinguishing between (1) the recovery from disturbance facilitated by wet periods, and (2) the expected spatial and temporal persistence of degradation characteristics attributed to a localized disturbance.

Turner (1990, p. 385) observed that “the linkage of remote sensing and GIS tech-nologies with landscape ecological research, which integrates the spatial pattern of land-cover and ecological processes, can provide a sound basis for assessing broad-scale changes in the rural landscape and developing strategies for land management.” We feel this method will help fulfill this goal and the intent of the National Research Council (NRC, 1994) and West et al. (1994).

ACKNOWLEDGMENTS

This research was sponsored by the Strategic Environmental Research and Development Program (SERDP) under contract DE-AC05-000R22725 with Utah State University and to Oak Ridge National Laboratory, managed by UT-Battelle, LLC, the Utah Agricultural Experiment Station (Journal Paper No. 7231), and by the Environmental Protection Agency (EPA) through a Science to Achieve Results grant #GADR826112 (it has not been subjected to the Agency’s required peer and policy review and therefore does not necessarily reflect the views of the Agency and no offi-cial endorsement should be inferred). The submitted manuscript has been authorized by a contractor of the U.S. Government. Accordingly, the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so for U.S. Government purposes.

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