Currents, sea waves, and climate changes are generated by air-sea interaction. Oceans cover more than 70 percent of the earth and play a significant role in the ecological environment. Therefore, various countries are researching oceans. A wide range of substances are present in oceans, of which phytoplankton are important primary producers in the marine ecosystem and are linked to a variety of oceanic processes. Chlorophyll a is an indicator to characterize the phytoplankton amount and plays an indispensable part in ocean research. Meanwhile, bio-optical parameters can be employed in various fields of oceanographic research and contribute to the rapid development of marine research. Chlorophyll concentration is an important prerequisite for the inversion of bio-optical parameters, and it directly affects the results of the bio-optical parameters. Active remote sensors with outstanding advantages have become one of the most rapidly growing and most effective remote sensors in recent years. Since active remote sensing technology does not depend on solar rays, it can obtain profile information with few detection limitations. As active remote sensing, oceanographic lidar can be mounted on a variety of platforms and obtain the profile concentration of chlorophyll. However, the traditional methods of inverting chlorophyll from lidar signals have poor accuracy, because they are susceptible to multiple scattering. Therefore, high-precision chlorophyll inversion algorithms are essential for marine research. Since the echo signal and chlorophyll concentration have a complex nonlinear relationship, deep learning can be adopted to filter multiple scattering noises, extract the backward scattering signal features, and build a high-precision chlorophyll inversion model.

Four steps are conducted as follows. Firstly, a dataset is built with two parts of label and feature. The label consisting of chlorophyll concentration profiles comes from BGC-Argo and the chlorophyll optical parameters are calculated by empirical relations. The lidar echo signals are simulated by a semi-analytic Monte Carlo algorithm and random sample consensus (RANSAC) algorithm is utilized to distinguish noises. Secondly, a network structure is constructed by Python. We build a lidar inversion model for chlorophyll based on backward propagation neural network (LIMC-BPNN) to solve the problem of multiple scattering effects degrading the accuracy. During the training, ReLU (linear rectification function) is adopted as the activation function, Adam (adaptive moment estimation) as the optimizer, and the epoch is 32. Python is an implementation language. Thirdly, chlorophyll concentration by PR-Chla is calculated to conduct a comparison between the two models. The perturbation retrieval (PR) proposed by Churnside can compute the lidar backscatter coefficient. Finally, relative error (RE), root mean square error (RMSE), correlation coefficient (R), and mean error (ME) are leveraged to quantify the results. The models are evaluated separately through three perspectives, including the average validation set, the validation set divided by water depth, and the set divided by chlorophyll concentration.

First, a network structure of LIMC-BPNN is built to extract lidar echo features (Fig. 2), and its parameters are determined by experiments. Next, a feature of the dataset covers the five oceans, which is around twenty thousand. The label is created from the dataset by empirical formulations of chlorophyll optics and a semi-analytic Monte Carlo (Table 3). The data in Table 3 exhibit lidar echoes containing chlorophyll information (Fig. 4), and then a comparison before and after noise rejection is shown using RANSAC (Fig. 5). After training, the average errors of the validation set are shown (Table 5). Additionally, two cases are presented (Fig. 6), the results in various chlorophyll concentrations and depths are demonstrated (Fig. 7), and the error variation at different depths (Fig. 8) is discussed.

The results of semi-analytic Monte Carlo can bring chlorophyll features, and RANSAC can filter outliers to enhance the dataset quality. In the ME of the validation dataset, LIMC-BPNN declines 34.22%, 0.363, and 0.213 in relative error, root mean square error, and mean error. The correlation coefficient is increased by 0.18, which indicates better credibility and stability of LIMC-BPNN to provide smaller data variances. Meanwhile, the error of LIMC-BPNN is lower than that of PR-Chla at different depths, which verifies the above findings. Additionally, in low concentration ranges, three errors of LIMC-BPNN are small. In 0-20 m, the traditional PR method performs well, but in 20-50 m RMSE and ME gradually grow larger. In medium and high concentration ranges, RE, RMSE, and ME are greater than those in low concentration ranges, with unchanged stability. Nevertheless, the PR-Chla is stable in 0-10 m and its error increased rapidly below 10 m. In conclusion, LIMC-BPNN is better than the PR-Chla for chlorophyll concentration. However, as the depth increases, errors of the two models are accumulated to demonstrate that the attenuation characteristics of the laser in water affect the accuracy.