A Study on Potentiality for Breeding Communities in the Taipei Metropolitan Area
2. Background of the Study Case
Hsindan City is a breeding community on the fringes of the Taipei Metropolitan Area, in the Northern Taiwan. The population of the city is steadily growing from 210,942 in 1988 to 289,366 in 2006 (Fig. 1). The total area of the city is 120.23KM2, which can be divided into 5 sub-areas in terms of land use zoning plans (Fig. 2).
Area A has 16.75KM2and is the most developed and populated area with the city hall, densely commercial and residential areas. The city government announced a land zoning map and regulation in 1956. In 1976, the area of zoning plan was expanded to Area B of 7.81 KM2to accommodate the growing population in 1976.
However, a reservoir was built up within mountainous Area D in 1987 to supply drinking water for the Taipei Metropolitan area. Area B is on downstream location from Area D; thus, further development in Area B was prohibited by modifying the zoning regulation in 2001. Area D is of 56.5KM2and conserved as conservation zone with forest, rivers, a reservoir, and a few aboriginal settlements. Areas C (3405 KM2) and E (494 KM2) are rural, agricultural and slope areas. While population is growing, they are the most potential area for urban sprawl. While Area C has many newly development communities, Area E announced her land use zoning plan in 1997.
Figure 1. population of the Hsinden City, 1988-2006
Figure 2. topographical map of Hsinden City with different land use control sub-areas
topographical maps made in 1976, 1984 and 2000, respectively. A grid system of 100 meters by 100 meters is used to make four digital land use maps against the four spatial data sets. For each cell in the grid, built-up areas, roads, water bodies,
agricultural fields, forests, grass fields, bare lands, wet-lands, public facilities and offices are identified in terms of the ratio of coverage.
According to the result of the land use identification process, we found that the developed area, including built-up areas, roads, public facilities and offices, was expanded significantly between 1947 and 1984, but only a slightly growth between 1984 and 2000 (Figure 3). Recall that population was still steadily growing between 1984 and 2000 in Figure 1. That means population density was increasing without significantly expanding urban lands during 1980’s and 1990’s. On the other hand, the time interval between 1947 and 1976 is relatively longer than 8 years between 1976 to 1984. The information of urban development between 1947 and 1976 is also scarce. Therefore, we choose the time interval between 1976 to 1984 for case study in this research.
0
1940 1950 1960 1970 1980 1990 2000 2010 year KM2
developed area built-up area
Figure 3. developed and built-up areas, Hsinden City, 1947-2000
There are four categories of variables: (1) topography, including slope and water body; (2)land use, including built-up area, government office, school, power plant, temple, grave yard, farm, grass, and forest; (3) local proximity: including the
distance to a major road and the number of built-up area within the surrounding cells;
and (4) socio-economics: population auto-correlation, land ownership, land price.
We use two models, namely binary logistic model and multinomial logistic model, to study the land use change on the Hsinden City and its sub-areas. All the variables of 1976 are potential independent variables, while built-up area of 1984 is the dependent variable. The value of variables of binary logistic model with respect to each land use in each cell is 1 or 0, where 1 represents the ratio of its area coverage in a cell is above 10%; otherwise, 0 will be assigned. The value of variables of
multinomial logistic model is area coverage in terms of percentage of the corresponding land use.
The result of logistic model analysis can be organized in a tabular structure as shown in Table 1. Identified data are corresponding to information shown in the
topographical map of 1984, while predicted data are produced by logistic models based on information drawn from the topographical map of 1976. T denotes the total number of cells in the study area. By overlapping the identified data of 1984 to those of 1976 for every cell, we can find and calculate the new-developed (In), unchanged (Iu), and removed built-up (Ir) areas which are identified in 1984. Similarly, by overlapping the predicted data of 1984 to the identified data of 1976 for every cell, we can find and calculate the new-developed (Pn), unchanged (Pu), and removed built-up (Pr) areas which are predicted in 1984. By cross comparison, the number of new-developed, unchanged, and removed cells of predicted versus identified data can be calculated. For examples, Vnn denotes the number of cells which are predicted to be new developed built-up cells and truly identified as new developed built-up areas, while Vnu and Vnr are unchanged and removed built-up area which are mis-predicted to be developed. Similarly, new development built-up cells which are identified from the topographical map but mis-predicted as unchanged or removed built-up cells are denoted as Vun and Vrn, respectively.
Table 1. Structure of logistic model results with respect to built-up areas Identified
Sub-total New Unchanged Removed
Predicted
New Vnn Vnu Vnr Pn
Unchanged Vun Vuu Vur Pu
Removed Vrn Vru Vrr Pr
Sub-total In Iu Ir T
Based on Table1, the following indices in Table 2 can be calculated with respect to built-up areas.
indices Expression Meaning
T = Pn+Pu+Pr = In+Iu+Ir the total number of cells in the study area (1) Pn =Vnn+Vnu+Vnr the number of cells predicted to be new
developed build-up areas
(2) Pu =Vun+Vuu+Vur the number of cells predicted to be (3)
Iu =Vnu+Vuu+Vru the number of cells identified as truly unchanged build-up areas
(6) Ir =Vnr+Vur+Vrr the number of cells identified as truly
removed build-up areas
(7) Pb =Pn+Pu the number of cells predicted to be
built-up areas
(8) Pc =Pn+Pr the number of cells predicted to be
changed (i.e. new developed or removed built-up) areas
(9)
Ib =In+Iu the number of cells identified as built-up areas
(10) Ic =In+Ir the number of cells identified as changed
areas
(11) Mt =Vnn+Vuu+Vrr The number of correctly predicted cells (12) Mc =Vnn+Vrr The number of correctly predicted cells
which are changed (i.e. new developed or removed built-up) areas
(13)
q-crt-b =1 –[abs(Pb - Ib)/Ib] Quantitative correctness of built-up areas (14) s-crt-b =1 –[abs(Mt –T)/T] Spatial correctness of built-up areas (15) q-crt-c =1 –[abs(Pc –Ic)/Ic] Quantitative correctness of changed
built-up areas
(16) s-crt-c =1 –[abs(Mc –Pc)/Pc] Spatial correctness of changed built-up
areas
(17) s-cpt-c =1 –[abs(Mc –Ic)/Ic] Spatial completeness of changed built-up
areas
(18)
Kappa test (Cohen 1960) is commonly used to quantify the level of agreement. Hagen (2002) further proposes a fuzzy approach, which can be considered as the fuzzy equivalent of the Kappa statistic, to assessing the similarity between raster maps.
However, Uebersax (2002) has some critiques about this method, and suggest researchers to consider alternatives and make an informed choice. In this research, Equations 14-18 can be employed to evaluate the predictive power of mathematical models, which are logistic models in this article. Equation 14 measures how good the total number of predicted built-up cells can be close to that of identified ones. While equation 14 quantitatively measures the total number of correctly predicted built-up area only, equation 15 further considers their spatial correctness. Equations 14 and 15 take the whole study area, including changed and unchanged built-up areas, into account. Those who may be only interested in land use change can employ equations 16, 17 and 18 to evaluate the predictive power of models. Respectively like equations 14 and 15, equations 16 and 17 measure quantitative and spatial correctness for changed built-up areas. Equation 18 measures the completeness of correctly prediction for built-up land use change; in other words, the percentage of changed built-up areas that are correctly predicted with respect to identified. The results of equations 14-18 will be less than 1 (100%); however, a result with negative value,
which is meaningless, will be set to 0.
4. Results
To explore the land use change in terms of built-up area expansion, we choose the whole Hsinden City (including slope and mountainous areas), city center (sub-area A), new urbanized area (sub-area E), and a new developed community (Community F) as study cases. The area sizes of study cases are ranging from 120.23 to 0.81 KM2. After testing different logistic models and choosing different dependent variables upon these study cases, detailed analysis reveals some interesting results concerning with effective factors for accommodating new built-up areas and prediction powers.
4.1 Community F
Community F locates at western end of sub-area E. Figure 4 shows its topographical map in 1984 overlaid with a grid of 9 by 9 cells. Red areas are communities and black spots are scattered buildings. Major and secondary roads are shown as red lines. A valley, going from northeast to southwest, is gradually changed to built-up areas. Within each cell, there are black, red and without 1s. Black 1s show built-up cells which can be identified from the map. Red 1s is predicted built-up cells by binary logistic model. Cells without 1s are non-built-up ones. Therefore, it is very clear to see mis-predicted cells which are marked by blue boundaries.
4.2 effective factors
As mentioned above, we consider 16 variables of 4 categories in binary and multinomial logistic models. Based in statistical significances and odd ratios, each model adopts different effective factors as shown in Table 3. As a result, we find that existing and nearby built-up area, water body, and distance to major roads are most common factors. Factor of slope shows its influence in sub-area E and Community F where there are hills with a valley. It is also noted that, in Community F, factors of land ownership and price are significant, while distance to major roads and built-up areas nearby are not. A possible reason is that Community F is a large scale new community developed by a single developer. The site size and capital investment are so huge that they can construct their own road system connecting to without being
difficult the developer will encounter. Also, the land price in less developed area will be much lower. The factor will attract developers to choose a site away from existing built-up area for reducing capital investment.
Table 3
variables
topography Landuses Localproximity Socio-economic
Slope Waterbody Existingbuilt–uparea Governmentoffice School Powerplant Temple Graveyard Farmland Grassland Forest Distancetomajorroads Built-upareasnearby Populationauto-correlation Landownership Landprice
Hsinden City
BLR V V V V
MLR V V V
Sub-area A MLR V V V V V V
Sub-area E BLR V V V V V
CommunityF BLR V V V V V
4.3 tendencies
Table 4 shows 5 indices evaluating the correctness and completeness of logistic models upon four study areas. The preliminary result seems to reveal the following tendencies:
Being independent from the size of study area, qualitative correctness (q-crt-b) is higher than spatial correctness (s-crt-b). It implies that the work of
predicting spatial pattern is more difficult than that of total amount without considering location.
Being independent from the size of study area, the spatial correctness (s-crt-b) of the whole study area, including changed and unchanged built-up cells, is dramatically higher than that of changed area (q-crt-c) only. A possible reason is that a small portion of changed area (Ic/T) may bring a small quantitative correctness【???】. However, it is noticed that Community F has a high q-crt-c score while it has a relatively larger changed cells. This tendency implies that we may need to know the potential location of new community first for correctly predicting its spatial pattern.
Almost regardless of the size of study area, any cell which is predicted by binary logistic model to be changed (s-crt-c), either new developed or
removed, has a high possibility to be true with correctness above 0.5 to 0.8.
However, only a very small portion of changed cells (s-cpt-c) can be predicted.
It seems that the smaller a study area, the better prediction power the logistic models will have.
Table 4. Evaluative Indices against built-up areas in various study areas
indices Area
(KM2) Ic/T q-crt-b s-crt-b q-crt-c s-crt-c s-cpt-c Hsinden City
BLR
120.23 0.0195
0.998671 0.983994 0.082051 0.5625 0.046154 MLR 0.999169 0.977359 0.361702 0.270588 0.097872 Sub-area A MLR 16.75 0.0449 0.993369 0.954491 0.12 0.444444 0.053333 Sub-area E BLR 4.94 0.1667 1 0.849593 0.195122 0.75 0.146341
CommunityF BLR 0.81 0.1975 1 0.938272 0.933333 0.8125 0.866667
Figure 4. Predicted and identified built-up cells in Community F
5. Conclusions
This article takes Hsinden City, on the outskirt of Taipei Metropolitan Area, as a study case to explore geographical, urban development and economic conditions where land use changes may happen. Through this case study, we find that the significant and effective variables vary in different sizes of study areas. By proposing five evaluative indices, we can further judge the predictive power of logistic models. We find that spatial logistic regression models have less predictive power than those without spatial consideration. Predicting spatial pattern of
In the future, more cases with different community characteristics are needed to be explored. In the case of Hsinden City, we study the land use change models for places with flat lands, rivers, hillsides and mountains. New cases of seaside, natural disaster potential areas, or large scale urban development projects, such as
technopolis, should be further included.
As mentioned above, the population was still growing in 1990s; however, the built-up area was not expanded significantly. That implies many urban renewal projects were implemented to accommodate new residents, business, commercial and industrial activities. Thus, research interest may have to cover the phenomenon of urban renewal. Since compound, complex and mixed land uses are common in Taiwan, topographical maps and aerial photos alone are not sufficient. More socio-economic information, such as field investigation, company registration, population and economic census, is needed.
Acknowledgment
This research is supported by the National Science Council, Taiwan, under project number NSC 95-2621-Z-002 -015.
References