## 1 Introduction  
After entering water, sunlight is absorbed and scattered by constituents in the water, such as suspended particulate matter (SPM), phytoplankton, and colored dissolved organic matter (CDOM), and its downwelling irradiance attenuates nearly exponentially with increasing depth. The downwelling diffuse attenuation coefficient, \(K_{\mathrm{d}}\), is a main parameter that characterizes underwater light fields. \(K_{\mathrm{d}}\) is an apparent optical property that is determined collectively by factors such as absorption and backscattering by each constituent in the water, the incident light field, and the water depth [1; 2]. However, the effects of light fields are generally insignificant, and \(K_{\mathrm{d}}\) is therefore mainly determined by the inherent optical properties (e.g., absorption and scattering) of the water. Thus, \(K_{\mathrm{d}}\) is also often referred to as a \"quasi-inherent optical property\" [3]. In fact, the strength of a light field at a depth z is affected by the transfer of light radiation from the surface of the water to the depth z, rather than by only the attenuation of the light beam at the depth z. Therefore, the commonly used parameter \(K_{\mathrm{d}}\) is the vertical mean value of a certain layer of water [4]. \(K_{\mathrm{d}}\) is a basic parameter that characterizes underwater light fields [5] and plays a vital role in studying water turbidity [6], sediment transport and resuspension [7; 8], heat transfer within the upper water [9; 10], the photosynthesis of phytoplankton [11; 12], and the net primary productivity of natural waters [13; 14]. Satellite-based remote sensing is a more effective and rapid method for acquiring \(K_{\mathrm{d}}\) over large areas than conventional measurement methods. The \(K_{\mathrm{d}}\) value at the wavelength of 490 nm (\(K_{\mathrm{d}}\)(490)) is one of the most commonly used standard water color remote sensing products [15]. Extensive research has been conducted to develop algorithms for estimating \(K_{\mathrm{d}}\) for waters. Most of this research focuses on oceanic waters and can be classified into three types: (1) The type I research concerns the establishment of an empirical relationship between \(K_{\mathrm{d}}\) and the chlorophyll a (Chla) concentration [16] based on the observation that the optical properties of oceanic waters are mainly affected by phytoplankton; (2) The type II research focuses on the establishment of relationships between \(K_{\mathrm{d}}\)(490) and the inherent optical properties and boundary conditions (e.g., the solar elevation angle and water surface conditions) of water using the radiative transfer theory-based semi-analytical algorithm [4; 17; 18; 19; 20]; (3) The type III research involves the establishment of statistical relationships between \(K_{\mathrm{d}}\)(490) and the apparent optical properties (e.g., the water-leaving radiance, \(L_{\mathrm{w}}\), and remote sensing reflectance, \(R_{\mathrm{rs}}\)) [15; 20; 21; 22]. The algorithms developed in these three types of research are mainly applicable to open oceanic waters and slightly turbid coastal waters. Few studies have been conducted to estimate \(K_{\mathrm{d}}\)(490) for inland lakes, particularly turbid shallow lakes, based on remote sensing data. Research has demonstrated that the \(K_{\mathrm{d}}\) values for shallow lakes are one to two orders of magnitude greater than those for most oceanic or coastal waters [20; 23; 24]. The contributions of Chla, suspended particulate inorganic matter (SPIM), and CDOM to light attenuation can vary significantly, both spatially and seasonally [25]. Relatively significant uncertainties are also associated with the atmospheric correction for these waters [26]. Therefore, algorithms commonly used for estimating \(K_{\mathrm{d}}\)(490) for open oceanic waters and coastal waters cannot be used directly for highly turbid shallow lakes. The algorithms available for turbid inland waters are mostly empirical models. [PERSON] et al.