Derivation of relations between urbanization level and velocity from logistic growth model

New relations on urbanization level and velocity are derived from logistic equation of urbanization process:(1) Z_(max(V))=max(Z_(t))/2,and(2) max(V_(t))=kmax(Z_(t))/4,where max(Z_(t)) denotes percentage of capacity at end of terminal stage,max(V_(t)) denotes maximum of urbanization velocity on the trend line and k denotes urban-rural growth difference.The first formula implies that urbanization velocity becomes a maximum when urbanization level becomes half of the saturation value,and the second formula means that the maximum velocity of urbanization equals the product of urban-rural growth difference and the saturation value of urbanization level.The US urban and rural population data by census from 1790 to 1960 are applied to validating/verifying the above-mentioned theoretical relations. We can predict the saturated level of urbanization by means of the maximum velocity of urbanization;meanwhile,we can also achieve the goal of expected saturated value by control of urbanization velocity.As the relations are derived from logistic growth model,the precondition of applying the formulae is that urbanization process in a region follows logistic rule.In addition,the maximum velocity of urbanization should be estimated by trend line instead of observed data because of random stochastic disturbance. The formulae are applied to China's data of urbanization level from 1978 to 2000.Conclusions are drawn as follows:(1) Saturation value of China's urbanization level is predicted as around 79.26%.China's level of urbanization reaches the peak value round about 2005,when level of urbanization is 39.63% or so.(2) Urbanization of China should be decelerated from 2005 forth/onwards.Population of China is more than 13 hundred million nowadays.It is hard for such a large country of population to make its urbanization level exceed 80%.According to China Statistical Yearbook 2005,the urbanization level of China is about 41.76%.If the current urbanization velocity holds the line,it might lead to grave consequences,such as over-urbanization,pollution of the environment,ecological disturbance,and various urban problems.