2.4.1. GeoSOS-FLUS Model

GeoSOS-FLUS was developed and improved by Li Xia et al. [37], based on the cellular automata (CA) principle. This model can be applied to simulate future land use change scenarios and is generally effective for geospatial simulation, spatial optimization, and decision making. GeoSOS-FLUS initially applies the artificial neural network (ANN) algorithm to estimate land conversion probability based on the driving factors of land use change, combines the land conversion probability, the interaction among cells, and the land change trends to calculate the overall probability of cell transformation, and then couples the Markov and CA models to improve the applicability and realize the simulation of land use change. GeoSOS-FLUS has an adaptive inertial competition mechanism based on roulette selection that can effectively cope with the uncertainty and complexity of the mutual transformation of various land use types under the joint influence of natural and human activities, thereby increasing its simulation accuracy and producing results that closely reflect actual land use distributions [38,39]. The main calculation modules are described as follows:

(1) Calculation of suitability probability based on neural network

ANN includes a prediction and training stage and comprises an input layer, a hidden layer, and an output layer. The suitability probability is calculated as:

where p (k, t, l) represents the suitability probability of the t type of land on raster k at time l, ω_j,k, t, and sigmoid are the weight and excitation functions between the hidden and output layers, and net_j (p, t) is the signal received by the j hidden layer grid p at time t:

where the suitability probability p (k, t, l) indicates that the sum of all suitability probabilities is 1 on grid k at time l.

(2) Adaptive inertial competition mechanism

The probability of land use conversion not only depends on the distribution probability of the neural network output but is also affected by certain factors, such as neighborhood density, inertia coefficient, conversion cost, and land competition. The gap between the current land quantity and land demand will be adjusted in an iterative process that determines the inertia coefficients of different land types. The adaptive inertia coefficient of the k land category at time t is:

where Dkt−1 and Dkt−2 are the differences between the demand and the number of grids in the k type of land at t − 1 and t − 2, respectively.

After calculating the probability of different grids, the CA model was used to determine the land types. At time t, the probability of transforming grid p into k land type can be expressed as

where sc_c→k is the cost of changing land type c to k, 1 − sc_c→k is the degree of difficulty in the conversion, and Ωp,tt is the neighborhood function, which is computed as:

where ∑N×Ncon(cpt−1=k) denotes the total number of grids of the k land after the last iteration in the Moore neighboring window of N × N. In this paper, N = 3, and ω_k denotes the neighboring effect weight of various land types.

The accuracy of the model was verified by observing three parameters, namely, OA, ROC, and Kappa. Parameter values closer to 1 indicate a higher accuracy. Previous studies have shown that the simulation accuracy of GeoSOS-FLUS is higher than that of commonly used models, such as CLUE-S and ANN-CA [37]. Therefore, this model was used in this study to simulate and predict the future ESV of Anyang under different scenarios.