## 1 Introduction  
Throughout the recent decades, satellite remote sensing of the world oceans became increasingly important in light of both the problem of global climate change and frequent deterioration of the aquatic ecology status, the latter being driven by ever increasing needs of growing populations for drinking water as well as for fish and other sea food.  
Satellite-based sensors operating in the visible are most suited for this mission as only the visible radiation penetrates appreciably into the water column and its backscattered component carries the desired information about the quality of water bodies under surveillance.  
Several satellite sensors, such as Sea-viewing Wide Field-of-view Sensor (SeaWiFS), Moderate Resolution Imaging Spectroradiometer (MODIS), and Medium Resolution Imaging Spectrometer (MERIS), operate in the visible and near infrared and provide global coverage. The main challenge resides in the retrieval of exact information about water quality parameters from the collected images.  
The approaches to the retrieval of water quality parameters from spaceborne data depend on the optical complexity of the target water body. According to [PERSON] [1], all natural waters are partitioned into case 1 and case 2 waters. In case 1 waters, variations of the aquatic medium optical properties (and hence water colour) are predominantly controlled by phytoplankton and co-varying products of their life cycle. Colour variations in case 2 waters are controlled not only by phytoplankton and their accompanying retinue, but also by other substances, notably terrigenous suspended minerals (_sm_) and allochthonous dissolved organic matter (_doc_) that vary independently of phytoplankton.  
In case 1 waters (mostly open ocean waters), algorithms for the retrieval of the desired water quality parameter, e.g. the phytoplankton abundance, are rather unsophisticated. For instance, the case 1 water OC4 algorithm currently used by the National Aeronautics and Space Administration (NASA) [2; 3] is based on a relationship between the concentration of phytoplankton chlorophyll, _chl_ (a proxy of the phytoplankton abundance) and the emerging radiance at two or more wavelengths normalized to the incident irradiance at the same wavelengths.  
In case 2 waters, this approach is untenable as the radiation emerging from beneath the water surface is affected at any wavelength not solely by phytoplankton, but other substances as well. Therefore, in order to retrieve one component, e.g. _chl_ it is necessary to infer simultaneously the content of other water constituents affecting the water colour, so called colour producing agents (CPAs), first and foremost, _sm_ and _doc_. Together with _chl_, _sm_, _doc_ and such substances as total organic carbon (_toc_) and total suspended sediments (_tss_) are traditionally categorized as water quality parameters (WQP).  
One of the possible solutions of the problem of WQP retrieval from satellite images collected over case 2 waters is the application of an algorithm based upon the Levenberg-Marquardt (LM) multivariate optimization procedure [4; 5]. The main advantage of the LM algorithm comparing to such algorithms as band ratio algorithms or neural networks is higher accuracy in inverse problem solution [6; 7; 8]. As our experience shows other multivariate optimization techniques (as genetic algorithms) prove to be at least twice more time consuming.  
In the \"Methods\" section we begin with a concise description of the basic principles of the LM technique, assessment of the algorithm efficiency. In the same section we also focus on the development and characteristics of hydro-optical models. The next section, \"The algorithmapplications\", is devoted to the assessment of the developed algorithm efficiency in some case studies. In \"Discussions\" we describe possible sources of errors and the favourable conditions for the algorithm application.