Predicting the Metro Scenario-based Spatiotemporal Evolution of Land Use Using CA- Kalman Filter Model: a Case Study of Nanjing City, China

Jialing Dai (  jialingdai@163.com ) NJU-ECE Institute for Underground Space and Geo-environment, Nanjing University Xiaozhao Li Chinese Academy of Geological Sciences Wei Zhang NJU-ECE Institute for Underground Space and Geo-environment, Nanjing University Ke Liao NJU-ECE Institute for Underground Space and Geo-environment, Nanjing University Tao Liu NJU-ECE Institute for Underground Space and Geo-environment, Nanjing University Peng Zhao NJU-ECE Institute for Underground Space and Geo-environment, Nanjing University Wentao Xu NJU-ECE Institute for Underground Space and Geo-environment, Nanjing University

(1) 128 Where i x is the i th neuron in the input layer. The signal received by neuron j in the hidden 129 layer on cell p at time t is estimated as an adaptive weight based equation:  The inertia coefficient can be altered with the dynamic trend of developing contradiction: (1) 166 If the macro demand for the specific land use type k equals to the current allocated amount, 167 then the inertia coefficient at iteration time t will stay unchanged; (2) If the macro demand 168 for the specific land use type k is less than the current allocated amount, then the inertia 169 coefficient at iteration time t will decrease slightly by multiplying the previous coefficient by (3) If the macro demand for the specific land use type k is greater than the current 171 allocated amount, then the inertia coefficient at iteration time t will increase slightly by 172 multiplying the previous coefficient by Besides, the model takes in the conversion cost from the perspective of nature of land, i.e.

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the intrinsic difficulty to convert land use type. It is determined based on expert experience, 175 works the same as the inertia to promote or inhabit the growing trend of current land use type.

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For each land use pair c and k , the cost of the land use change from c to k is denoted as The commonly utilized methods are Markov chain and system dynamics, both of which are 207 from macro-level perspective. System dynamics (SD) is another tool originated from complex 208 system, could have been an optimal choice to be integrated. However, SD requires a variety of 209 massive data across time, which would be a hurdle for pooling data, let alone complex processes 210 of adjusting parameters 16,31 . As to Markov chain, it is an incidence-based method commonly

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It begins by assuming the random process to be estimated in the form: Where x k is a n 1 process state vector at time k t ; +1 x k is a n 1 process state vector at x k  in the absence of a forcing function; 246 w k is a n 1 vector assumed to be a white sequence with known covariance structure. It is 247 the input white noise contribution to the state vector for the time interval ( k t , 1 k t  ).

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The measurement of the process is assumed to occur at discrete time points in accordance 249 with the linear relationship: Where z k is a m 1 vector measurement at time k t ; H k is a mn  matrix giving the ideal 252 (noiseless) connection between the measurement and the state vector at time k t ; v k is a m 253 1 measurement error assumed to be a white sequence with known covariance structure.

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The covariance matrices for w k and v k vectors are given by: We assume we have an initial estimate of the process at the point k t , and it is based on all 260 our knowledge about the process prior to k t . This a priori estimate will be denoted as x k  261 where the "hat" denotes estimation, and the "super minus" is a reminder that this is our best 262 estimate prior to assimilating the measurement at k t . We also assume that we know the error 263 covariance matrix associated with x k  . That is, we define the estimation error to be: In addition, the associated error covariance matrix is: With the assumption of a priori estimate x k  , we now seek to use the measurement z k to 268 improve it. We choose a linear blending of the noisy measurement and the a priori estimate in 269 accordance with the equation optimal because it minimizes the trace of a posteriori error covariance P k .
Next, we substitute the resulting expression for x k into Eq. (16) We proceed to differentiate the trace of P k with respect to K k : The updated estimated x k is easily projected ahead via the transition matrix. We are 280 justified in ignoring the contribution of w k in Eq. (16) because it has zero mean and is not 281 correlated with any of the previous w's. Thus, we have The error covariance matrix associated with 1 x k   is obtained by first forming the expression 284 for the a priori error 286 We now note that w k and e k have zero cross correlation, because w k is the process 287 noise for the step ahead of k t . Thus, we can write the expression for Equations (15)  Note: (1) The planned extensions of existing lines are not considered in this paper.
(2) For trans-provincial lines, the length of which beyond Nanjing is excluded.
Remotely sensed data have drawn considerable attention in the analysis and modelling of  sampling of naked eye that demands prior experience and knowledge for each land use type.

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Then an amount of samples are trained according to maximum likelihood of bands combination, 386 thus all cells find their own categories thanks to special spectrum feature, as is depicted in Fig.   387 4.  Table   421 3 shows. When one type of land use is able to convert to another type, the cost coefficient would      Table 4 479 The comparison of image indicators for model simulation accuracy  In order to find out the transition mechanism of urban expansion, four transition matrices for 558 land use change in four periods are obtained (Table 5,   In the four phases, the augmented urban land mainly comes from construction land and In effect, when using the Kalman filter to predict the amount of future land use, it is found 590 that in 2050 or so, urban land parcels will become saturated, as will construction land. Perhaps 591 a small amount of construction land (for industry, tourism) will contribute to urban land 592 continually, and this balance will not be broken in the short run. On the basis of the land use in Assuming that the predicted amount under the metro scenario is 0.7 times the actual amount, 601 then the rate of 0.08 will be converted to 0.11, which is still less than the ideal value 0.3. In 602 other words, taking into account the forecast errors, the growth rate of urban brought by the 603 metro from 2019 to 2035 is still less than the expected value, which has a lot to do with the 604 upper limit of urban parcels mentioned above.

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The main conclusions of this study are as follows:

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(1) Comparing the two scenarios in the future 2035 (with/without new metro lines), it shows 616 that the newly expanded urban patches in the metro scenario are mostly scattered on the 617 edge of existing urban land, such that promote patch connectivity and personnel mobility.

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The amount of urban parcel is predicted to reach saturation in 2050, which approximate that