[landuse.mod] Land-use models

Transcription

1 [landuse.mod] Land-use models V

2 Table of Contents for Land-use models I. Land-use models V - 1 A. Economic base and activity allocation V - 1 B. Forecasting air-base housing requirements V - 1 C. Iterative Lowry-model calculations V - 1 D. Traditional Lowry software V - 1 E. The Projective Land Use Model (PLUM) V - 4 F. Bifurcation in the Garin-Lowry model V - 4 G. Bifurcation in York V - 5 H. Kansai-Airport Econometric-Model V - 5

3 I. Land-use models A. Economic base and activity allocation (Chan & Rasmussen) Let us examine the Chan & Rasmussen study in terms of both the aggregate total-forecast and the subareal housing-distribution. This is to verify the soundness of the Economic-base Theory and the Gravity Spatialinteractance relationship--two of the basic building blocks of many urban-development models. The Chan & Rasmussen study appears to yield lower forecasts in general than the CRPC approach. This is attributed to the fact that the Chan & Rasmussen procedure considers not only the demand for housing, but also the economic base to support new residents in the area. Furthermore, the actual housing requirement is tempered by the availability of housing supply. The CRPC approach, on the other hand, does not seem to address the problem of land-holding capacity. It is a "statement of the need" for additional housing, whether or not land is actually available for new housing-development. The former can be view as the realizable demand while the latter can be interpreted as the gross demand. Commuting between home and the place of employment is recognized by the Chan & Rasmussen study as one of the major determinants of residential location. As such, spatial interaction is explicitly modelled by a gravity-type formulation that locates residents in relation to their place of employment. The CRPC study, on the other hand, is a good deal less specific in dealing with locational choice, where subareal housing is simply derived from its population projection. In other words, while the Chan & Rasmussen study recognizes the coupling relationship between transportation and land-use, less emphasis is given by the CRPC housing-forecast. It is not surprising, therefore, that the Chan & Rasmussen study projects (quite realistically) more clustering of high-density housing close to State College, which is by far the largest employment-center of the region. Both the CRPC and Chan/Rasmussen study assume that there are no substantial in or out migration, suggesting the student enrollment at Penn State would stabilize at by Both studies again assume the existing trends, including birth/death rates and other coefficients and ratios, will remain constant over time for each township. These assumptions, particularly the first two, did not hold true over the years. The scientific resources at Penn State University have attracted new industries (and therefore population) into the region. Defying the demographic projection, participation of a more mature studentbody broke the enrollment ceiling forecasted for the traditional, post-world-war-ii age-group. Over the ten years from 1975 to 1985, State College and its immediate environs have decidedly gotten more urban than anticipated. This is evidenced by the unexpected increase in multiple-family units in State College and all the townships in the Center Region. In State College, single-family units are replaced by multiple-family units. With the exception of a decline in State-College proper, single-family units also increase elsewhere to a level comparable to the CRPC forecast, which is above the Chan & Rasmussen study. In short, the observed housing-units are closer to the CRPC optimistic-forecast than the Chan & Rasmussen study. The significant in-migration makes the difference, suggesting that there are really other "basic industries" beyond higher education--a fact overlooked by Chan & Rasmussen. B. Forecasting air-base housing requirements C. Iterative Lowry-model calculations D. Traditional Lowry software (a) Preparing for the forecast. The only input which differs between the null alternative and the dosomething alternative was the travel time from zone to zone. The differences in the travel-time matrix are shown in Table I, where the extreme cases of increases and decreases are highlighted. Changes in the V - 1

4 travel-time matrix caused different values to be input for the annular-ring matrix. This matrix is input into the LOWRY program as RING(I,J) where I is the zone from which the rings radiate and J is the number of travel-time minutes that the ring is from the zonal centroid I. The rings can be thought of as one-minute travel-contours from the centroid of zone I. RING(I,J) is the number of zones that fall within the limits of the ring. The RING matrix is used in calculating several variables in the LOWRY program and is input as a separate matrix. It is, however, completely dependent upon the travel-time matrix for its values. Table I - Difference in interzonal travel-time inputs There is no difference in the values input for the null alternative and the do-something alternative in the following variables: (a) Total land-area in the zone (b) Unusable land-area in the zone (c) Basic land-use-area in the zone (d)* Retail land-use-area in the zone (e)* Residential land-use-area in the zone (f) Basic employment in the zone (g) Retail employment in the zone (h) Number of households in the zone (i)* Residential density (j) Maximum residential-density. Note that the entries marked with an asterisk (*) are prepared, but not input into the program. The parameters controlling such items as the number of trade-classes, minimum-employment per zone in retail-trade, and number-of-households needed to supply one labor-force-member remain the same for both sets of input data. The Lowry Model lists 11 different elements in output. Five of the output elements remain constant from the base year to the forecast year. The five elements are: total land, unusable land, basic land, basic employment, and maximum residential-density. Six elements changed between the Null-alternative output and the PRT-alternative output. These are: the number of households, total employment, retail employment, housing land-use, retail land-use, and household density. Table II summarizes the difference in these output elements for only those zones where significant changes occurred, where "+"s are used to denote increases and "-"s used to denote decreases. The entries of the Table range from "++" to "--", showing the extreme cases of activity increase and decreases respectively. Table II - Zones showing significant changes from base to forecast year (b) Difference in development patterns. One basic difference in development occurs. Both residential and retail activities are more evenly distributed in the PRT-alternative than the Null-alternative. Since retail land-use takes priority over residential land-use in the Lowry Model, it is reasonable to expect the equation that distributes retail employment among the 42 zones to be key to the difference. The equation that allocates retail employment is employment, N i is the number of households, and where these terms are defined: E is is the Spatial-interaction function. Since V - 2

5 all factors remain constant for the two alternatives except C ij, it is quite logical that the employment distribution would be more uniform with the PRT-alternative than with the Null-alternative. (Please remember that accessibility is more uniform with the PRT alternative.) The effect is doubly reinforced in the population-allocation equation:, where both terms in the equation are more uniform for the PRT than for the Null alternative. The attached Figure 1 shows the differences that result by zone between the Null-alternative and the PRT-alternative. Notice that in the center-city zones, residential activity and land-use activity increase significantly while retail activity and land-use decrease from the Null alternative. In zones next to the center city (nos. 6, 8, 11, 14 and 16), the opposite change occur, i.e. retail increase while residential decreased. Finally, zones 34 and 41 have residential-activity decrease and retail-activity increase from the Null- to PRT-alternative forecasts. Figure 1 - Zonal difference between Null and PRT alternative (c) Accessibility. The projected development of the York area was made by use of the LOWRY model with the only input-data change being travel-time matrix. The travel-time matrix originally used to establish the base conditions was obtained by using actual driving-speeds along the transportation links to establish travel times. The travel-time matrix used to arrive at projected trends assume a constant travelspeed throughout the entire transportation network. The speed was somewhat lower than could be maintained by suburban traffic but higher than the speeds currently possible in the Central Business District (CBD). The lower travel-speeds are the cause of the changed development to the southwest. The decreased accessibility to this southwest area from the CBD caused the area to develop as a suburb. In the past, its close ties to the CBD afforded the area development opportunities (as the result of interchanges of activities). This development is lessened now by the decreased accessibility. Thus, the population decline is caused by the loss of accessibility with the York CBD. As the outlying areas experience decreased accessibility, the downtown area becomes a more attractive place to live. Since considerable basic employment exists in the city center, workers in the basic sector are located close to their work with decreased suburban accessibility. The demand for housing is greater than retail employment and the retail sector is forced from the CBD. The high opportunity-cost of a CBD location dictates that very dense housing-development must occur to provide an adequate return for the land investment. On the other hand, zone 32 reflects the typical suburban residential development and is close enough to the city to be affected least by the lack of accessibility. The zones to the north of the CBD (18, 19 and 20) remain relatively unchanged, showing both a saturated level of development and the general absence of significant accessibility changes. This juxtaposition of the Null-alternative and the PRT-alternative provides a very interesting policy study. Implementing a uniform speed-limit on the city is an attempt to influence future CBD-development. It is easily seen as one means of putting population back into the city core. Accessibility is the primary reason for the shift in population and employment. Development potential. As defined by Lowry, the developability of the different zones has not changes since the maximum-density constraint and the minimum-size of retail-activity have not changed. If we expand this concept to the developable land-area (at a specific density) we still do not find any change in the development potential. V - 3

6 But following Hansen (1959) we can say that residential (and retail) development is related to accessibility, in that the greater the accessibility the greater the residential (or retail) development. According to this concept for development potential, which is really development 'opportunity,' one can say that as the accessibility has increased the opportunity has also increased. Overall interpretation. The provision for the PRT-alternative forecast does not include any difference in basic-employment input when compared with the Null alternative. They refer exclusively to changes in the travel time between the different zones and to transportation policies that cope with increasing-congestion downtown. These policies redistribute activities among the different zones--the most notable of which being the decentralization of retail employment and the allocation in zone 1 the maximum number of households, thus reversing the general trend of American cites toward suburbanization. Graphic plot. Computer graphics are used to represent the pair of Lowry York-forecasts. In all, 14 maps are included, with those showing activity variables display in contours and those showing landuse variables in the 'primal' format. In the key to the plots, 10 data-ranges are used. Sometimes manual definition for range size was used to accommodate extreme distributions of the data. The graphics make it much easier to see the changes that occur due to the PRT. Residential land-use increases in the CBD (as mentioned previously), while retail employment and land use decrease. Increased retail activities southeast of the CBD at zones 31 and 34 show that some retail will move out from the CBD to provide services to those living farther away. The additional service is needed due to the increased travel-time caused by the uniform-speed PRT to go from the suburb to the CBD. Retail also shifted to zone 11, close to the CBD, servicing the increase in CBD residents in zones 1 and 2. E. The Projective Land Use Model (PLUM). F. Bifurcation in the Garin-Lowry model (Yi 1986) (a) For all three groups, the inter-zonal spatial-cost matrix is In the Group-3 example, a and f in each zone are different (as in Groups 1 and 2). The areawide averages for a.f remain less than one (that is, and a w f w =0.745<1.) A review of the Yi-Chan subdirectory (folder) in the software disk would reveal that the computation shown in Group 3 of the given Table can in fact be replicated by the following two routines. AFTUCAL.EXE: This is the executable code to calculate disaggregate multipliers a and f and basic accessibility functions t and u. For this application, we simply replicate multipliers a j and obtain f j by division (200/40=5) from the given base-year data (and no time-oriented computation is warranted). The following variables are calculated in the program: the basic accessibility-functions t and u. DONOTHIN.EXE: This is the executable code for the forecasting program (with constraints) for both aggregate and disaggregate cases corresponding to the "do-nothing" alternative. In other words, it simply derives and allocates activities in the three-zone case over the forecast period. In this case, we choose to bypass the constraint part of the program (i.e., the follow-on Fibonacci-search technique is not necessary). We are dealing with an unconstrained forecast. V - 4

7 (b) The question is whether the stringent condition of (for all j) can be treated as the criterion for convergence. In other words, does the following geometric matrix-series reach a steady-state? (1) where [b ij ]=[t ij ][f j ][u ij ][a j ]. It has been shown that this deterministic approximation of the underlying stochastic equation may or may not converge under certain circumstances. Here we will investigate the circumstances where convergence is guaranteed. From the "Control" book-appendix, the spectral radius of matrix B, ρ(b), is defined as max k q' k where q' k s are eigenvalues of B. It can be shown that ρ(b) B for any eigenvalue. One can conclude thereof that B r =0 if ρ(b)<1. From what have been shown, the convergence criterion is ρ(b)< B =max i Σ j b ij <1 for b ij 0. Convergence is guaranteed since V1 for all i. This is confirmed by the row sums Σ j b ij : 0.9, 0.78 and The 'watershed' value of 1 for the spectral radius is referred to as a bifurcation point. G. Bifurcation in York H. Kansai-Airport Econometric-Model (Suzuki et al. 1989, Pak et al. 1988) (a) Denote the number of employees in the kth industrial-sector required for the operation of the new airport as E k a (k=1,..,12), which is assumed to be determined exogenous to the model. The induced increment of gross output and jobs which will be caused by the production activities of E k a can be estimated. Thus if we denote the per-capita output produced by E k a as g ka, then the gross output R a generated by the production activities of the new-airport employees can be estimated as where a k denotes a 12 1 vector whose ith element (i=1,...,12) is the input to the ith industrial-sector out of g ka. The gross output R a gives multiplier effects to all the industrial sectors through their interdependencies. Now denote the gross output induced by R a as R a I. Then R I a can be estimated by where R j a denotes the jth element of R a and likewise b jj is the jth element of B j --the jthcolumn vector of the Leontief inverse-matrix (I-r) -1. Denoting the increase-in-employment induced by production activities of the new-airport employees as E I a and utilizing the result of Y'= C'R, E I a can then be estimated by The increased gross-outputs R a and R a I induced by the operation of the new airport are considered to increase the income and the consumption in the region, and these in turn will increase the regional gross-output. Per-capita income is induced by direct and indirect increase in employment due to the new airport operation. If we denote per-capita income in the jth sector for E a and E a a I as w j and w Ija, respectively, then the increase in the regional income, denoted by Y, can be obtained as where w a and w a are 12 1 vectors whose ith elements are w I ia and w Iia, respectively. Let us denote the multiplier effect on production induced by this income-increase as R c. Then R c can be estimated by the concatenated relationship where C' denotes a 12 1 consumptioncoefficient-vector whose ith element is equal to the ratio of the purchased-amount-of-the-commodity-fromthe-ith-industrial-sector to the household-income--i.e. a input-output coefficient. a' denotes a 12 1 vector whose ith element is the ratio of the household-income to the gross-output-in-the-ith-industrial-sector. If the increase-in-employment induced by R c is denoted as E c, then E c can be estimated by using an equation a which can be obtained by replacing R I with R c in Equation (2). Once the employment level is determined, (2) V - 5

8 as described above, the total population of the region can be calculated by using the per-capita employment, which is also given exogenously to the model. (b) Spatial-distribution of economic-activities--or the concept of shares in EMPIRIC--can be modelled by the transition of state-variables in each subarea (defined here as a traffic zone). In the Kansai case, there are 120 zones, 46 economic sectors plus the population sector (47 sectors total) and seven land-use categories. Let us denote the pth state-variable in zone i at time k as x p i(k), and the qth state-variable in zone j at time k+1 as x jq (k+1) respectively. A linear state-transition-equation can be written: where the calibration coefficient represents the impact of x ip (k) on x jq (k+1). In order to calibrate these coefficients, let us separate the internal-zonal-impacts from impactsby-other-zones into two terms: (3) We then make the following assumptions. First, the local-impacts of industry p, x jp (k), on industry q, x jq (k+1), is the same in all the zones, or (4) For example, if employment is the state variable, this means the local effect of zonal employment is the same in all zones. Second, the value of (i j) is proportional to x jq (k). However, interzonal impact (i j) is inversely proportional to the b p th power of the average-trip-time between zones i and j. Thus (5) where c pq is a proportionality constant, and τ ij is the average travel-time between zones i and j. Combining Equations (3), (4) and (5), we have an equation-set similar to EMPIRIC: (6) where accessibility for activity p to zone j is defined as (7) Several submodels are used to calibrate the parameters exogenously to the model, as shown in the "Schematic diagram" in the "Kansai Airport" section of the "Spatial Econometric Models" Chapter. The accessibility expression above is estimated by a travel-time submodel. The other parameters in Equation (6) are calibrated by an employment submodel, which estimates the a pq s and c pq s. Then there is the population submedial and land-use submodel. These submodels are absolutely required to calibrate the Kansai econometric-model with its large number of parameters, many of which are determined exogenously. The readers can see by now the many parallels of this model to EMPIRIC. V - 6

9 Listing of Figures for Land-use models Figure 1 - Zonal difference between Null and PRT alternative V - 3

10 NUMBER OF HOUSEHOLDS NULL ALTERNATIVES NUMBER OF HOUSEHOLDS PRT ALTERNATIVES Figure 5-1(a). Zonal difference between Null and PRT alternative

11 RESIDENTIAL LAND USE NULL ALTERNATIVES RESIDENTIAL LAND USE PRT ALTERNATIVES Figure 5-1(b). Zonal difference between Null and PRT alternative (continued)

12 RETAIL EMPLOYMENT NULL ALTERNATIVES RETAIL EMPLOYMENT PRT ALTERNATIVES Figure 5-1. Zonal difference between Null and PRT alternative (continued)

13 RETAIL LAND USE NULL ALTERNATIVES RETAIL LAND USE PRT ALTERNATIVES Figure 5-1(d). Zonal difference between Null and PRT alternative (continued)

14 BASIC EMPLOYMENT NULL ALTERNATIVES BASIC EMPLOYMENT PRT ALTERNATIVES Figure 5-1(e). Zonal difference between Null and PRT alternative (continued)

15 BASIC LAND USE NULL ALTERNATIVES BASIC LAND USE PRT ALTERNATIVES Figure 5-1(f). Zonal difference between Null and PRT alternative (continued)

16 UNUSABLE LAND NULL ALTERNATIVES UNUSABLE LAND PRT ALTERNATIVES Figure 5-1(g). Zonal difference between Null and PRT alternative (continued)

17 Listing of Tables for Land-use models Table I - Difference in interzonal travel-time inputs V - 2 Table II - Zones showing significant changes from base to forecast year V - 2

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19 Table II - Zones showing significant changes from base to forecast year Zone Population distribution Total employment REtail employment Housing land-use Retail landuse Household density [l-change.tab]