Subsurface chlorophyll maxima (SCMs), commonly occurring beneath the surface mixed layer in coastal seas and open oceans, account for main changes in depth-integrated primary production and hence significantly contribute to the global carbon cycle. To fill the gap of previous methods (in situ measurement, remote sensing, and the extrapolating function based on surface-ocean data) for obtaining SCM characteristics (intensity, depth, and thickness), we developed an improved deep neural network (IDNN) model using a Gaussian radial basis activation function to retrieve the vertical profile of chlorophyll a concentration (Chl a) and associated SCM characteristics from surface-ocean data. The annually averaged SCM depth was further incorporated into the bias term and the Gaussian activation function to improve the estimation accuracy of the IDNN model. Based on the Biogeochemical-Argo (BGC-Argo) data acquired for three regions in the northwestern Pacific Ocean, vertical Chl a profiles produced by our improved DNN model using sea surface Chl a and sea surface temperature (SST) were in good agreement with the observations, especially in regions with low surface Chl a. Compared to other neural-network-based models with one hidden layer and a sigmoid activation function, the IDNN model retrieved vertical Chl a profiles well in more eutrophic subpolar regions. Furthermore, the application of the IDNN model to infer vertical Chl a profiles from remote-sensing information was validated in the northwestern Pacific Ocean.

In this paper, a weighted k-shell method is proposed to further improve the distinction of node importance by taking advantage of the number of iterations and edge weights when the node is deleted. The weighted k-shell decomposition method is applied to simple networks and complex networks respectively. The simulation results show that the improved method has low computational complexity, high result resolution and high accuracy.