## 2 Data and Methods
### Ecolight Simulation Data  
Ecolight (version 5, Sequoia Scientific, Inc., Bellevue, WA, USA) was used to simulate the underwater light field of waters with four types of constituents: Pure water, phytoplankton, mineral particles, and colored dissolved organic matter (CDOM). According to the field dataset of Lake Chaohu, China, details of the input parameters of Ecolight simulation are presented in Table 2. The specific inherent optical properties (SIOPs), phase functions, and backscattering ratio were same as those in the study of [PERSON] et al. [21] according to the field measurement of OACs and IOPs in Lake Chaohu. Water depth was set as 0-3.0 m with an interval of 0.1 m based on the mean water depth (-2.6 m) of Lake Chaohu. Furthermore, as penetration depth is evidently lower than water depth in Lake Chaohu, scattering signal from the bottom of water was not taken into consideration. The simulations were performed from 400 to 750 nm with an interval of 5 nm, and the solar zenith angle (\(\theta\)) was set as 30\({}^{\circ}\). Wind speed was set as 2.25 m/s to obtain the slope statistics of the air-water interface (refractive index = 1.34). Inelastic radiative processes, including Raman scattering by water molecules, fluorescence by CDOM, and fluorescence by Ch\(\lambda\)_a_, were also considered in the Ecolight simulation. Raman scattering was calculated for the Raman scattering coefficient at a reference wavelength of 488 nm using the default algorithm in Ecolight. For Ch\(\lambda\) fluorescence, the quantum efficiency of 0.02 was used, and it was assumed to be independent of excitation wavelength [23]. The RADTRAN-X subroutine of Ecolight was used to model the incident solar and sky irradiances the water surface under clear sky conditions [23]. There were total 1008 Ch\(\lambda\)(z) profiles: The range of C\({}_{0}\) is 0-40 with an interval of 5, that of h is 1-76 with an interval of 5, and that of \(\sigma\) is 0.2-1.4 with an interval of 0.2 (Table 2). The underwater light field of the 1008 vertical inhomogeneous of Ch\(\lambda\)(z) profiles and the corresponding homogeneous cases (N = 1008) with average Ch\(\lambda\)_a_ value in the water column were simulated using Ecolight. Moreover, six representative profiles (L1-L6, Figure 1a) with different vertical variations of Ch\(\lambda\)(z) and vertical homogeneous SPIM (=30 mg/L) and \(a_{g}\)(440) (=0.85 m\({}^{-1}\)) were selected to describe the effects of Ch\(\lambda\)_a_(z) vertical distribution on the underwater light field. Ch\(\lambda\)(z) profiles of L1 (C\({}_{0}\) = 5, h = 16, \(\sigma\) = 0.6) and L2 (C\({}_{0}\) = 10, h = 16, \(\sigma\) = 0.6) exhibited less variability, whereas L5 (C\({}_{0}\) = 10, h = 16, \(\sigma\) = 0.2) and L6 (C\({}_{0}\) = 10, h = 21, \(\sigma\) = 0.2) changed dramatically near the water surface. The associated _a_(z) and _b_(z) profiles at 550 nm presented a similar vertical tendency as Ch\(\lambda\)_a_(z) (Figure 1b,c). _b_(_a_ + _b_)(550) demonstrated an inverse distribution with Ch\(\lambda\)_a_(z), _a_(z), and _b_(z) profiles (Figure 1d). In addition, the six representative Ch\(\lambda\)_a_(z) profiles with varying SPIM (0-60 mg/L with an interval of 5 mg/L) and _a_g(440) (0-4.0 m\({}^{-1}\) with an interval of 0.5 m\({}^{-1}\)) were simulated to illustrate the effects of SPIM and _a_g(440) on underwater light field. After the Ecolight simulation, two AOP parameters, namely, subsurface remote sensing reflectance (\(r_{rs}\)(\(\lambda\), z)) and the diffuse attenuation coefficient (\(K_{x}\)(\(\lambda\), z)), were used to describe the spectral and vertical variations of the underwater light field.