The Geographical Meaning About The Modifiable Areal Unit Problem In The Population Density Scaling

Scale was paid much attention in studies of geography and landscapes. Most works are focused on scale effects, scale transform and scale selections. Population density, as a common-used index of population distribution, was an ideal view point in study of multi-scale relations between human and environment.There are three groups in geography paying attentions to the population density:(1) is in the group of population geography. They focuse on natural environment, social economy, population policy and history to discuss the cause and factor of population density, and to reveal the regional difference of population distribution. The statistic of population density was usually based on the unit of county or upper district. (2) is in the group of cartology. They fasten on the population density based on longitude-latitude grid in recent works. (3) is in the group of Geographical Information System. They think much of making population density models.Reviewing all population density studies of native or foreigners, the scale of population density was not paid much attention in population geography. Despite multi-scale population density was started to be considered in research works of Geographical Information System, and geographical factors were also thought of in modeling. But, the geographical mechanism of controlling multi-scale population distribution was always ignored. Single-scale population density maps were more than multi-scale ones and the relationship between population density and geographical environments were disregarded in cartology. These limited the understanding and application of the real meaning of multi-scale population density.There were two opinions for the Modifiable Areal Unit Problem(MAUP) in academic field. (1) Geographical information system thought MAUP is a statistical or ecological error and being one of the eighth obstacles in space analysis. (2) Ecologists thought MAUP was unignorable in order to realize geographical pattern and ecological process more accurately and comprehensively. They suggested that MAUP should include scale effect and zoning effect. Openshaw and Taylor thought MAUP shouldn’t be considered pure statistical or mathematical problem, its geographical meaning should be thought much of and MAUP were the breakthrough point in studying spatial pattern. But for the constraint of speciality background, ecologists couldn’t find the quantized index and restricted the development of MAUP study. Native population geographical researchers all selected the index of population density in discussing the MAUP, which meant that population density was feasible quantized index, but the geographical problem implied behind was concerned little.In this paper, a case in Shijiazhuang district, multi-scales population densities were obtained basing on the scale effect and zoning effect of population MAUP. The cooperation relationship between multi-scale population densities were defined using multiple statistic analysis, the major factors controlling population densities were determined by selecting characteristic scales, and the impacting factors of characteristic scale population density and its relationship to the human actions were shown in grading framework system of population density. Finally, the geographical rule behind in the MAUP of population density was found out.Dominant database and multiple statistic analysis were used to study multi-scale population density quantitatively. Population density dominant database included two main technique steps:(1)compilating minimum grain map of population density (2) compilating calculation model of population density. During the course of compilating minimum grain map of population density, population density maps of county, township, village and district were compiled successively and minimum grain population density map was gained by means of district population density (R=0). There were only 12 grids whose population density were more than 200 000/km2 in the grid of 100m×100m map, which means that spatial statistic error was slight and the error wasn’t spread in scaling of population density. Minimum grain population density map supplied credible data basis to study of multi-scale population density. Focalmean Function was applied to formal description of population density. Circular and rectangle filtering operator were used to compile up-scaling model and two series of multi-scale population density maps from R=0 to R=99 and from 1 X 1 to 199X199. Basing on the multi-scale population density, the characteristic scales were selected quatitatively by optimal coefficient, Sheffield index and standard Sheffield index programme. CI index could be used as quantitative model of characteristic scale selection, in which parameter P was the key in characteristic scale selection. Basing on CI index, combining scale correlation analysis and with the aid of visual interpretation, five characteristic scales were selected (R=0, R=3, R=12, R=29,R=99) and impact factors of characteristic scale population density were analyzed initially.Comparison of multi-scale population density showed that the calculation model basing on circular filtering wave was better than that on rectangle filtering wave. These two up-scaling models all could ensure the consistency of multi-scale population density and as the scale expanding, the standard error of both series of population density declined sharply by the means of exponential function, which meant that as the scale enlarging, the spatial heterogeneity of population density decreased gradually. Correlation analysis showed that the relationship among all scales of R≥30 enhanced obviously, while the population density of R=99 appeared regional conjugation.Analysis of impact factors of characteristic scale population density shown that (1) there was scale-dependent correlation between population density, population pattern and population process, in which artificial factors played dominant roles in population distribution on small scale(R=0), for example, the population density of new business-inhabitant district was greater than 80000 person/km2, developers were fulfiled with gain and consumers were acceptable life cost; (2) there was close correlation between human habitant and official, enterprise and institution distributions, population densities were high in adjacent areas of province, city and district officials, where population densities were 50 000 to 80 000 persons per square kilometer. Population densities were different evidently in habitant districts of factory, there are 50 000 to 60 000 persons per square kilometer around the areas of Huabei pharmaceutical factory, while 30 000 to 50 000 persons per square kilometer around the areas of the 3th and the 4th cotton mills. All these population distribution were the characteristics in the planning economy system. The area along the Beijing-Guangzhou Railway (between Zhonghua and Pingan street) was the main commercial center, but the population density was only 10 000 to 20 000 persons per square kilometer. Population in this area was higher as massive flowed population in daytime, and was evident contrast to low population in nighttime, which shown that registered population only reflected habitant pattern, didn’t reflect employ pattern. At present, resident areas are forward to separate with working places. Working places are forward to select in the areas of convenient matters and informations, while residential area prefered to choose good property, low cost and graceful environment. (3)Each population pattern was controlled by natural and location factors, e. g. the population of middle and small scale(R=3、11) were influenced by rivers, and the population of large scale(R=29、99) was controlled landforms. (4)The impacts of river and landform on population distribution embodied in different scales. (5) The historical data of population density in Hebei province showed that the Yuan Dynasty was a start of present population pattern. Human marks to the environment couldn’t be found in modern population patterns before the Yuan Dynasty. (6) Characteristic scale population density embodied the scale effect of human and environment, and was the result of historical development. Contradiction balance was the basic reason causing scale-dependence of population density, pattern and process, which was also the basic reason forming MAUP of population density. The impacting factors analysis of population density in Shijiazhuang city revealed that MAUP included not only the natural characters, but also included the human behavior.This paper discussed the population MAUP preliminaryly and many problems remained to study further.(1) Mathematics base in scaling model need improvement. Hypothesis of present scaling was based on the points and the directions homogeneous in Euclid space and on the scales equilibrium. This hypothesis could be approximately tenable in small region and low precision, but it was incorrect in nation and continent scale. Any object corresponded to an integer dimension in Euclid space, which meant that the scaling was reversible in Euclid space. But the real world was fractional dimensions; scaling description of geographic space with euclid space couldn’t realize the simple reversion. The progress in map algebra, sphere disperse grid, fractal geometry and zoning effect would improve the mathematics base of scaling.(2) Up-scaling of population density belonged to adjacent-scale scaling, whether it could be used to cross-scale scaling was a problem in suspense, and the application scope need to be discussed.(3) Up-scaling was the process from complex to simple, so the up-scaling model of population density was easy to construct. But it was difficult to infer complex small-scale information from simple large-scale information, so down-scaling was a difficult problem to be solved. Up-scaling of population density realized the variable-focus observation of population distribution, but population density scaling couldn’t realize automatic focusing. Further research of controlling mechanism of down-scaling was important to reveal key-point variation mechanism of scaling. Trying to combine the pattern and process of environment into down-scaling model would promote modern geography innovation and its application greatly.(4) Basing on characteristic scale, if large, medium and small scale could be endowed special scale meaning in different factors of human-environment correlation system, providing uniform level and standard scale template? This need research progress of different subject.(5) Up-scaling of population density in lager-scale (Hebei province of Huabei region) need to be carried out, probing into the scale-dependent correlation of population density and macroscopic factors such as atmospheric flow field, temperature and precipitation in the monsoon background.