A deep learning method for estimating the atmospheric pollutants removal potential of the large-scale environmental strategy based on green roofs

Abstract

Rapid urbanization is responsible for local atmospheric pollution, which negatively affects the sustainability and human health. To offset the adverse effects, a new form of greening, termed as the green roof, is becoming one of the remedies. Previous studies and practice have validated the positive impacts of green roofs on atmospheric environment improvement, but the large-scale quantitative studies and the related urban planning still show that difficulties exist in obtaining the overall area and spatial morphological pattern of green roofs from the massive building stock. In this study, we presented a novel method based on deep learning to recognize the rooftops available and simulated the atmospheric pollutants removal potential (APRP) of green roofs in visualization. Compared with traditional methods, our method was more accurate and efficient. In this study, we recovered a trained neural network model and achieved a satisfactory 94.17% validation accuracy. According to our results, Shijiazhuang City offered great potential that if all the selected rooftops installed green roofs, 1.210465×10⁶ kg/year pollutants would be cleaned up with dry deposition. This study provides an intuitive basis for environment policy making and urban green system planning.

Appendix 1

Related work

Pooling, convolution, and up-convolution are the basic operations of a convolution neural network. Through the combination of the operations, networks realize different functions and cause dimensional changes. In the U-Net, the convolution layers and max pooling layers constitute the contracting path for feature downsampling. Similarly, the up-convolution layers and convolution layers constitute the expanding path for feature upsampling. We explain pooling, convolution, and up-convolution in details as following.

The pooling layer belongs to the downsampling layer, which mainly includes three functions: (1) extend the receptive field and improve the model performance; (2) reduce the dimension of the input and simplify the convolution neural network calculation; and (3) remain feature invariant during rotation, translation, and expansion. The U-Net adopts max pooling to connect the convolution layers in the contracting path. Max pooling layers divide the input into several rectangular regions and output the maximum value for each sub region. This type of pooling preserves the texture of features more easily. Figure 12 shows an example of this operation with specific numbers.

Fig. 12

Example of max pooling

Convolution is a many-to-one mapping process that also realizes feature downsampling and reduces the size of images but in a slightly more complicated way than the pooling. A convolution operation requires an input and a kernel and produces an output. Here, we give one element matrix with the size of 4×4 as the input.

$$ input=\left[\begin{array}{cccc}{x}_1& {x}_2& {x}_3& {x}_4\\ {}{x}_5& {x}_6& {x}_7& {x}_8\\ {}{x}_9& {x}_{10}& {x}_{11}& {x}_{12}\\ {}{x}_{13}& {x}_{14}& {x}_{15}& {x}_{16}\end{array}\right] $$

Then, we give another element matrix with a size of 3×3 as the kernel.

$$ kernel=\left[\begin{array}{ccc}{\omega}_{0,0}& {\omega}_{0,1}& {\omega}_{0,2}\\ {}{\omega}_{1,0}& {\omega}_{1,1}& {\omega}_{1,2}\\ {}{\omega}_{2,0}& {\omega}_{2,1}& {\omega}_{2,2}\end{array}\right] $$

According to the convolution formula, $o=\frac{i+2p-k}{s}+1$ (o, size of the output; i, size of the input, where i = 4; p, padding, where p = 0; s, stride, where s =1; and k:, kernel, where k = 3), it can be inferred that the output is a 2 × 2 matrix.

$$ output=\left[\begin{array}{cc}{y}_1& {y}_2\\ {}{y}_3& {y}_4\end{array}\right] $$

Furthermore, if we transform the element matrix of the input into a column vector X and transform the element matrix of the output into a column vector Y, the calculation process of the convolution can be expressed as Y = CX, where C is a deducible sparse matrix transformed from the kernel via Toeplitz matrix.

$$ C=\left[\begin{array}{cccccccccccccccc}{\omega}_{0,0}& {\omega}_{0,1}& {\omega}_{0,2}& 0& {\omega}_{1,0}& {\omega}_{1,1}& {\omega}_{1,2}& 0& {\omega}_{2,0}& {\omega}_{2,1}& {\omega}_{2,2}& 0& 0& 0& 0& 0\\ {}0& {\omega}_{0,0}& {\omega}_{0,1}& {\omega}_{0,2}& 0& {\omega}_{1,0}& {\omega}_{1,1}& {\omega}_{1,2}& 0& {\omega}_{2,0}& {\omega}_{2,1}& {\omega}_{2,2}& 0& 0& 0& 0\\ {}0& 0& 0& 0& {\omega}_{0,0}& {\omega}_{0,1}& {\omega}_{0,2}& 0& {\omega}_{1,0}& {\omega}_{1,1}& {\omega}_{1,2}& 0& {\omega}_{2,0}& {\omega}_{2,1}& {\omega}_{2,2}& 0\\ {}0& 0& 0& 0& 0& {\omega}_{0,0}& {\omega}_{0,1}& {\omega}_{0,2}& 0& {\omega}_{1,0}& {\omega}_{1,1}& {\omega}_{1,2}& 0& {\omega}_{2,0}& {\omega}_{2,1}& {\omega}_{2,2}\end{array}\right] $$

Intuitively, we fill in some specific numbers in the element to explain the operating process of the convolution in more detail in Fig. 13. The regular operating mode of the convolution can be seen: the kernel multiplies the selected region of the input, and all figures are summed to obtain the output.

Fig. 13

Example of convolution

Meanwhile, up-convolution is a one-to-many mapping process that recovers the size of images via upsampling, which can be regarded as the inverse operation of convolution like Fig. 14. According to the size of the input matrix and output matrix, we can easily obtain the calculation process of the up-convolution as X = C^TY.

However, it should be noted that the up-convolution searches C^T via network training rather than artificial setting. In addition, in actual operations, up-convolution can only recover the image size, not including the recovery of the original value (Dumoulin and Visin 2016; Odena et al. 2016). Accordingly, miscellaneous information is removed and key information is retained.