November 28, 2001
Note: This page details the methodology for an early version of FRAP's projection of development model using 1990 Census data. FRAP has since updated this model with 2000 Census data and made minor corrections and improvements. While the methodology detailed here is essentially the same as our current method, it is nevertheless out of date. An updated document will be available soon. However, current maps and model are online.
The land use impacts of population growth affect a number of responsibilities of the California Department of Forestry and Fire Protection. Expanded residential use of wildlands changes the fire protection needs in terms of public safety, assets at risk, patterns of fire ignitions, and the deployment of new state and local fire service resources. Expanded residential use within forest and woodland areas also affects a variety of resource management activities, such as forest management, prescribed burning, and other forms of vegetation management and watershed protection activities. Changing residential use patterns also change the overall stresses on many wildlife species that depend on a matrix of reserved, managed, and developed land and water areas; local definitions of important open space; and local and regional tax bases, and other factors.
To effectively assess trends and potential responses, it is useful to have a systematic approach towards projecting land use impacts of population growth. The Fire and Resource Assessment Program (FRAP) of the California Department of Forestry and Fire Protection has developed a method for mapping the historical and a scenario for the future progression of development with a common framework across all lands in California over the period 1940-2040. The primary purpose is to produce estimates with a low level of error in the acreage that are projected to attain at least a dispersed level of residential land use.
The underlying model is described in the Methods Description section below. It essentially allocates Department of Finance county population projections, after first converting populations to houses, to 9.6 square mile grid cells based on their share of the 1980-1990 housing growth. Other more specific projection approaches often have goals of predicting the number of new people in specific locations or changes to specific high value land parcels (Landis' California Urban Futures (CUF) model and Johnston's application of the MEPLAN model, for example). The CDF-FRAP technique is not as detailed as the Farmlands Mapping Program of the Department of Conservation or detailed historic analyses that have been done around major metropolitan areas. However, it has the advantage of providing a consistent scenario for the whole state that can be analyzed at any scale from a ten square mile area, a county, a region, to the entire state.
The core of the approach is based on mapping historic and current residences identified in the 1990 Census onto a base map of 1940-era forest, range, and agricultural land use. The analysis is initially done for the state as a whole and for the nine major bioregions. The base map for vegetation is from the Vegetation Type Map (VTM) Survey, conducted between 1929 and 1934 by the U.S. Forest and Range Experiment Station, Berkeley and updated in 1945. This map is referred to as Weislander after A.E. Weislander, the Survey's director and senior map author. The original Weislander maps were approximately 1:64,000 scale.
The four broad vegetation classifications-forest, range, agriculture, and barren-are different than current ecological or land use categories and reflect the historical perspective towards potential land uses. Current vegetation mapping systems such as the California Gap Analysis Project, CALVEG, and California Wildlife Habitat Relationships System, provide more ecologically based categories of vegetation. For this analysis, with its relatively large 9.6 square mile units, we continue to use the coarser 4-vegetation type scheme of Weislander. Further analyses could be done by mapping the Census-based population density coverages at this or other scales onto any type of ecological or land use categorization scheme.
This project maps both developed and mixed interface across most private ownership lands. The selected housing density of one house per 20 acres is a lower bound for mixed interface - essentially the beginning of a rural residential land use pattern. This is an estimated threshold beyond which there are progressive constraints on ecosystem management as well as increases in the potential for housing losses due to wildfire. Within this footprint of development opportunities exist to design corridors, best management practices, and favorable spatial layouts to sustain desired landscape functions. Whether the practices will be successful will have to be assessed empirically through after-the-fact monitoring or with apriori risk-based modeling.
The following digital photographs from San Bernardino County taken in 1994 illustrate some of the residential housing patterns of grid cells that cross the residential land use threshold used in the FRAP modeling exercise. Each photo represents one grid cell that is approximately three miles by three miles. In both Yucaipa and Redlands, the areas that crossed the residential land use threshold in the 1950s have experienced continuous infill. The areas developed in the 1980s, on the other hand, had only a fraction of the total cell in residential land use.Yucaipa
The model is complementary to other urban growth modeling efforts underway in California. For example, the developed and mixed interface footprint contains nearly all of the baseline 2020 urban footprint determined by John Landis at UC Berkeley for selected counties using the California Urban Futures Model (See Landis, John D. Imagining Land Use Futures: Applying the California Urban Futures Model. APA Journal, Autumn 1995.). The CUF model logically predicts growth around transportation routes that are not considered in the FRAP methodology. The FRAP coverage is designed to more accurately predict acres with some residential land use while the CUF model is designed to more accurately predict the higher density population areas.
The following charts illustrate the historic and projected trends for the state as a whole and the nine bioregions. To simplify comparisons among regions, the trends all show the percentages of 1945 coverages that have, or are projected to have, some level of residential land use.
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Here you will find a discussion of the methods FRAP uses to map historical housing density, create a development scenario for the future, and estimate the intersection of development and vegetation over time.
Phase 1: Map Historical Housing Density
In his work for the Sierra Nevada Ecosystem Project, Tim Duane of the University of California at Berkeley pioneered a methodology for mapping historical housing density using information from the 1990 U.S. Census of Population and Housing long form question Year Structure Built. The census unit is the private ownership Block Group part. Block Groups are designed to average 250-550 housing units (Block Groups are "split" to allow for separate tabulations for parts within cities, etc.) FRAP expanded upon his work, which comprised USDA Forest Service lands in the Sierra Nevada bioregion to create a Progression of Development Map (block groups) for the entire State of California.
Development exerts pressure on surrounding lands. Therefore, FRAP defined "developed" at a somewhat low urban density of one house per 20 acres (32+ houses per square mile). In this way, areas are included that absorb some of the economic and environmental effects of urbanization even in the absence of pavement.
Phase 2: Translate Historical Housing Density Map to Grid for Future Scenarios
Due to the higher error levels with smaller analysis cells, relatively large analysis units are used. The Progression of Development Map - with Projections (5 X 5 Km or 3.1 X 3.1 Mi grid) was created using a trend extrapolation method called Share of Growth (Smith, et al., 2001), also called the apportionment method (Pittenger, 1976; White, 1954). Block group data are first aggregated to a larger scale (i.e., 5000 by 5000 meter square cells; 9.65 square miles) to reduce inter-decadal variability caused by land availability constraints, economic conditions, urban growth policies, and other factors. At this scale, the fraction of countywide housing growth in any cell is approximately constant. FRAP calls this the expected "share" of county growth.
Smith, et al. concluded that because of irreducible uncertainty regarding the future, complex methods such as structural, times series, and cohort-component models do not produce more accurate forecasts of total population than simple extrapolation methods (p.312).
Click here for an animation depicting the progression of development from 1940 to 2040. Data for the 1940-1990 period is provided by applying the methods in Phase 1 to the 9.6 square mile grid cells. The projection methods of Phase 2 supply the data for the period 2000-2040.
Forecasts of housing increases beyond 1990 reflect historical growth patterns within each county. Using population forecasts for counties in their entirety provided by the California Department of Finance (DOF), FRAP makes housing estimates, and distributes housing change within each county using a three-step process:
- Convert county population growth estimates into county housing growth estimates (using ratio of houses to people in 1990).
- Determine the growth factor, i.e., historical proportions of county growth or loss in each census or other spatial unit.
- Allocate county housing growth estimates according to historical proportions.
This analysis uses the 1980-90 period as the basis for the growth factors (an update using the 1990/00 period is planned). To forecast a cell's housing count for the year 2000 that cell's expected share of county growth for the period 1990-2000 is calculated by multiplying the cell's growth factor by number of DOF projected additional houses in county between 1990 and 2000. To forecast expected housing counts for subsequent decades, the same growth factor is applied to DOF county growth expectations for 2000-2010 and adds the results to the cell's expected housing count for 2000. These steps are repeated for calculations of 2020, 2030, and 2040 housing counts.
Subsequent to the analyses reported in this web presentation, we now split zones by county boundaries and/or public ownership to more accurately apportion county allocations and to better represent lands that can develop through private actions. Where possible, split zones smaller than 1600 hectares (6.2 square miles) are aggregated into adjacent zones. Projections are not made for zones less than 775 hectares (3.0 square miles) in area, although historical data are maintained.
Pittenger, D. (1976). Projecting state and local populations. Cambridge, MA: Ballinger.
Smith, S.K., Tayman, J. & Swanson, D. (2001). State and Local Population Projections. New York: Kluwer Academic/Plenum Publishers.
White, H. (1954). Empirical study of the accuracy of selected methods of projecting state population. Journal of the American Statistical Association, 49, 480-498.
FRAP demonstrates the general model using block groups, tracts, and 5000-meter grid cell data. Each analysis compares the actual growth of housing from 1980 to1990 in a map polygon or grid cell (the dependant variable) with housing counts calculated using the expected share as the independent variable.
The form of the model for forecasting growth from 1980 to 1990 (which can be verified from the map data) is as follows:"Share" Model (allocating 1980-90 growth):
In words: The increment of growth in cell i during the decade 1980 to 1990 equals its historical expected share of county growth, that is, the total county growth from 1980 to 1990 times the proportion of the 1970 to 1980 growth captured by cell i (i.e., the growth factor).
Ordinary Least Squares Regression provides an overall measure of the correspondence between the expected share and the actual share. Both variables are highly and positively skewed and are made approximately normal using logarithmic transformations. Regression results for transformed and non-transformed data follow:
R2 (percent of variation explained)
N (number of observations)
Census Block Groups
5000-meter grid cells
Ordinary least squares regression shows that the expected share for 1990 explains almost 71% of the variation in actual housing increase in 1990. An XY graph shows this relationship. Results are similar when predicting 1980, 1970, and 1960 in a similar manner. This relationship holds for prior decades as well (i.e., predicting 1970's growth using 1960's share; predicting 1960's growth using 1950's share). Regression on random samples of as few as 10% returns significant models with R square in the high 60%. These results are similar to that found when analyzing data aggregated to census tracts, which are larger than block groups.
Note on use of statistics: The use of regression is intended to describe the fit of the share model and not to provide inferential information concerning a larger population (i.e., of census data). With such a large and arbitrary sampling scheme, most relevant variables will prove significant. In addition, no measures are taken to account for spatial autocorrelation in the data because FRAP is not trying to use these data as a sample of yet larger population.
To better visualize the fit, each cell is assigned to one of eight housing density classes, first using the actual 1990 housing count and again using the predicted 1990 housing count.
Less than 1 unit per 160 acres
1/160 acres to 1/40 acres
> 1/40 acres to 1/20 acres
> 1/20 acres to 1/10 acres
> 1/10 acres to 1/5 acres
> 1/5 acres to 1 per acre
> 1 per acre to 5 per acre
Greater than 5 per acre
A histogram comparing actual and modeled data shows a remarkably close correspondence.
If you have a VRML plug-in you can view a virtual world containing two maps of California. The lower map shows 1970's housing gain as heights (exaggerated for visibility) for comparing with the upper map showing 1980's housing gain. Manipulate the view to see the striking similarities.
With 30% of variability remaining unexplained, the model should be used to explore general patterns rather than to make site-specific predictions. At the zone level, even with perfect countywide DOF projections and continuation of past growth patterns, the typical difference between predicted and actual growth (in the test case) as measured by the median absolute percent error is 40%.
In the new method, to improve reliability, the data are reduced to three classes per decade, DEVELOPED (128+ units/sq. mi), INTERFACE, 32+ units/sq. mile) and UNDEVELOPED (< 128 units/sq. mi.). UNDEVELOPED is represented by a '0' in the DECADE_DEV item. The test case correctly labeled 94% of the 1990 UNDEVELOPED polygons, 84% of the 1990 INTERFACE polygons, and 77% of the 1990 DEVELOPED polygons. The user is cautioned that this map is but one possible realization of a complex underlying process and that forecasts are meant to provide an input to the process of policy-making and cannot predict the future.
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Phase 3: Estimate Vegetation Loss
An overlay of an historical vegetation map on the Progression of Development Map allows for calculation of acres subjected to the proximity of residential development.
Overlaying an historic vegetation map (Weislander, 1945) that shows the location of forests, rangelands, and agricultural areas shortly after World War II onto the progression of development map allows one to estimate the area of vegetation coming under the footprint of development over time. Because the Weislander vegetation map did not exclude urban areas, acres are subtracted under the 1945 development footprint to leave a base map of circa-1945 vegetation.
Two Weislander overlays are needed to produce the tables of 1945-era vegetation developed by decade: one using census block groups and the other using the 5 X 5 Km grid. The census block group overlay provides the data for 1950 through 1990 while decades 2000 through 2040 are based on the grid overlay with a calibration adjustment. The need for two different overlays arises because the two maps yield different results due to the effects of averaging. For example, the number of developed acres in 1990 (and earlier decades) differs because small areas of high housing density measured at the Block Group level result in a developed label on a grid cell of greater size. To deflate the grid-based results, a multiplier is used based on the ratio between the results in the two maps for 1990. This adjusts developed acres for 2000, 2010, 2020, 2030, and 2040 and makes them consistent with the historical (1990 and earlier) data.
Note that the number of acres of developed rangeland will catch up to the acres of developed agricultural land sometime around 2010 (table).
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