Using a hybrid demand-allocation algorithm to enable distributional analysis of land use change patterns

Abstract

Future land use projections are needed to inform long-term planning and policy. However, most projections require downscaling into spatially explicit projection rasters for ecosystem service analyses. Empirical demand-allocation algorithms input coarse-level transition quotas and convert cells across the raster, based on a modeled probability surface. Such algorithms typically employ contagious and/or random allocation approaches. We present a hybrid seeding approach designed to generate a stochastic collection of spatial realizations for distributional analysis, by 1) randomly selecting a seed cell from a sample of n cells, then 2) converting patches of neighboring cells based on transition probability and distance to the seed. We generated a collection of realizations from 2001-2011 for the conterminous USA at 90m resolution based on varying the value of n, then computed forest area by fragmentation class and compared the results with observed 2011 forest area by fragmentation class. We found that realizations based on values of n ≤ 256 generally covered observed forest fragmentation at regional scales, for approximately 70% of assessed cases. We also demonstrate the potential of the seeding algorithm for distributional analysis by generating 20 trajectories of realizations from 2020-2070 from a single example scenario. Generating a library of such trajectories from across multiple scenarios will enable analysis of projected patterns and downstream ecosystem services, as well as their variation.

Fig 1. Methodology framework.

Key components of the demand-allocation algorithm presented in this study.

Fig 2. Study area.

The conterminous United States (CONUS), as divided into the eight regions used by the Resource Planning Act (RPA) assessments. State boundaries are based on data freely available through the US Census Bureau (https://www.census.gov/geographies/mapping-files/time-series/geo/tiger-line-file.html).

Fig 3. Probability model groupings.

The conterminous United States (CONUS) was partitioned into 10 groupings of similar land use patterns for purposes of transition probability modeling. The groupings were derived from a k-means cluster analysis based on per-county land use distribution, elevation and slope, population and income, and geographic location. County feature data is freely available upon request from the USDA Forest Service Forest Inventory and Analysis program (https://data.fs.usda.gov/geodata/edw/datasets.php).

Fig 4. Distance modifier.

Distance modifier to pixel transition probabilities, as a function of distance to center and local standard deviation of transition probabilities. Note how as the standard deviation increases, the impact of the distance modifier is lessened.

Fig 5. Forest fragmentation classes.

(a) Land use around Charlotte, North Carolina, United States, and corresponding forest fragmentation classes for (b) 3x3, (c) 9x9, and (d) 27x27 pixel windows. See Table 3 for definitions for the specific classes.

Fig 6. Transition probability rasters.

Example probability rasters of transitions to the Developed land use class from Developed (red), Forest (green), and Agriculture (blue) land use classes. The probability of transitioning from Developed to Developed is set at 1, so the red pixels are intended here as a convenient reference to previously existing Developed area.

Fig 7. Coverage of observed forest patterns.

Differences between the total observed forest fragmentation and that derived from realizations, with respect to choice of the seeding size, n, and the scale of aggregation for results. Three example forest fragmentation classes (Table 3; Fig 5) are shown here. The green line represents a difference of 0 acres between the observed forest area and realized forest area, for forested pixels of the given fragmentation class at the given scale. Each boxplot represents six realizations per choice of n.

Fig 8. Coverage of forest patterns by RPA region.

Coverage of observed forest areas by fragmentation class, by window size (when determining percent forest) and RPA region. Values shown represent the minimum deviation of the forest area from the 48 realizations, as compared to the observed time 2 forest area. Values of 0 indicate that the observed time 2 forest area was contained within the distribution of the realized forest areas.

Fig 9. Forest pattern trajectories.

Projected change in forested area from 2020–2070, by forest fragmentation class (Table 3; Fig 5) and RPA subregion (Fig 2). Change is given as a percentage of the 2020 area. The lines represent the median value across 20 realizations; the polygons represent the corresponding inter-quartile ranges.