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Full disclosure: HydroLight was developed by web book author Curtis Mobley and is a commercial software product of Numerical Optics, Ltd. HydroLight is a radiative transfer numerical model that computes radiance distributions and derived quantities (irradiances, reflectances, K functions, etc.) for natural water bodies. It is designed to solve a wide range of problems in optical oceanography and ocean color remote sensing. In brief, HydroLight solves the 1D timeindependent radiative transfer equation to compute the radiance distribution within and leaving any planeparallel water body. The spectral radiance distribution is computed as a function of depth, direction, and wavelength within the water. The upwelling radiance just above the sea surface includes both the waterleaving radiance and that part of the incident direct and diffuse sky radiance that is reflected upward by the windblown sea surface. The waterleaving and reflectedsky radiances are computed separately in order to isolate the waterleaving radiance, which is the quantity of interest in most remote sensing applications. Input to the model consists of the absorbing and scattering properties of the water body, the nature of the windblown sea surface and of the bottom of the water column, and the sun and sky radiance incident on the sea surface. Output consists both of archival printout and of files of digital data from which graphical, spreadsheet, or other analyses can be performed. The input absorbing and scattering properties of the water body can vary arbitrarily with depth and wavelength. These IOPs can be obtained from actual measurements or from analytical models, which can build up the IOPs from contributions by any number of components. The software comes with various biooptical models for Case 1 and 2 waters, which are based on historical and recent publications on absorption and scattering by various water constituents. The user can also write subroutines to define the IOPs in any chosen way. The input sky radiance distribution can be completely arbitrary in the directional and wavelength distribution of the solar and diffuse sky light. HydroLight does not solve the RTE for the atmosphere to obtain the radiance incident onto the sea surface. However, it does include default sky radiance and irradiance models based on published atmospheric radiative transfer models. In its most general solution mode, HydroLight includes the effects of inelastic scatter by chlorophyll fluorescence, by colored dissolved organic matter (CDOM) fluorescence, and by Raman scattering by the water itself. The model also can simulate internal layers of bioluminescing microorganisms. HydroLight employs mathematically sophisticated invariant imbedding techniques to solve the radiative transfer equation. Details of this solution method are given in Light and Water (1994). When computing the full radiance distribution, invariant imbedding is computationally extremely fast compared to other solution methods such as discrete ordinates and Monte Carlo simulation. Computation time is almost independent of the depth variability of the inherent optical properties (whereas a discrete ordinates model, which resolves the depth structure as N homogeneous layers, takes N times as long to run for stratified water as for homogeneous water). Computation time depends linearly on the depth to which the radiance is desired (whereas Monte Carlo computation times increase exponentially with depth). All radiance directions are computed with equal accuracy. There is no statistical noise caused by the invariant imbedding inwater RTE solution (although there can be a small amount of statistical noise resulting from HydroLight's Monte Carlo treatment of windblown water surfaces). Monte Carlo models suffer from statistical noise, and quantities such as radiance contain more statistical noise than quantities such as irradiance, because the simulated photons must be partitioned into smaller directional bins when computing radiances. The waterleaving radiancethe fundamental quantity in remote sensing studiesis very time consuming to compute with Monte Carlo simulations because so few incident photons are backscattered into upward directions. HydroLight has been under development for over 20 years, with its first published description in Mobley (1989). It has been extensively compared with independent numerical models, e.g., in Mobley et al. (1993, wherein HydroLight version 3.0 is referred to as "Invariant Imbedding"). The literature contains many comparisons between HydroLight predictions and measurements. Representative examples are seen in Mobley et al. (2002), Chang et al. (2003), and Tzortziou et al. (2006). Although several researchers have developed excellent numerical codes for solving the RTE in the oceanographic setting, their codes are not readily available. HydroLight is commercially available and therefore is widely used.
The HydroLight Physical ModelThe version of the RTE solved by HydroLight is describes the following physical conditions:
These conditions are appropriate for many (but not all) oceanographic simulations. HydroLight cannot, for example, simulate timedependent wave focusing by surface waves because its sea surface treatment describes the spatially or temporally averaged effects of surface waves. It cannot be user for pulsed Lidar bathymetry simulation, which is an inherently timedependent problem. It cannot simulate sloping bottoms or the radiance reflected by an object in the water, which are inherently 3D problems. Probably the most limiting simplification of the physics of HydroLight is that it solves the scalar, or unpolarized, RTE. It thus cannot be used for studies where the state of polarization is of interest.
The HydroLight Computational ModelAny radiance sensor actually measures an average of taken over some finite solid angle , which is determined by the field of view of the instrument, and over some finite bandwidth , which is determined by the wavelength response of the instrument. Likewise, in order to solve the RTE numerically, it must be discretized (or otherwise simplified) by averaging over direction and wavelength to obtain a finite number of values that must be computed. In HydroLight, this directional averaging is performed by first partitioning the set of all directions , into regions bounded by lines of constant (like lines of constant latitude) and constant (constant longitude), plus two polar caps. These quadrilateral regions and polar caps are collectively called "quads." The individual quads are labeled by discrete indices and to show their and positions, respectively. The standard (default) quad layout is shown in Figure 1. In this layout, which has and , the polar caps have a 5 deg half angle and the boundaries lie at 5, 15, 25, ...,75, 85, 90, 95, 105, ..., 175 deg. For mathematical reasons there is no quad centered on the "equator" at . However, the radiances computed for the 8590 and 9095 deg quads can be averaged to get the "horizontal" radiance at a nominal angle of . Thus the HydroLight standard quad layout essentially gives 10 deg resolution in and 15 deg in . This is adequate for most oceanographic simulations.
Similarly, the wavelength region of interest is partitioned into a number of contiguous wavelength bands of width . The need not be the same size for different j values. The fundamental quantities computed by HydroLight are then the quad and bandaveraged radiances at any selected set of depths :
The quads "homogenize" or average the radiance within each quad, just like a diffuser does in an instrument. Thus, in the quad layout of Fig. 1, it is not possible to resolve the difference in the radiance for polar angles and , because they both lie in the same quad extending from and . However, there is a difference in and , because those angles lie in different quads and thus are represented by (probably) different quadaveraged radiances. This same sort of directional averaging of radiances occurs in Monte Carlo models, which collect photons in directional "bins." If it is necessary to have greater angular resolution in the radiance distribution, a different quad layout can be created. However, the computer storage and run time are proportional to the square of the number of quads, so increasing the angular resolution comes with increased computational cost, just as for other solution techniques.
Ways in Which HydroLight Can Be UsedHydroLight has been used in numerous published studies on topics as diverse as biological primary production, ecosystem modeling, remote sensing, underwater visibility, mixedlayer thermodynamics, and the generation of large synthetic data sets needed for neural network training, spectrummatching libraries, and design of ocean color satellite sensors and retrieval algorithms. These studies have used HydroLight in various ways:
Inputs to HydroLightIn order to run HydroLight to predict the spectral radiance distribution within and leaving a particular body of water, during particular environmental (sky and surface wave) conditions, the user supplies the core model with the following information (via builtin submodels, or usersupplied subroutines or data files):
The absorption and scattering properties of the water body can be provided to HydroLight in various ways. For example, if actual measurements of the total absorption and scattering are available at selected depths and wavelengths, then these values can be read from files provided at run time. Interpolation is used to define values for those depths and wavelengths not contained in the data set. In the absence of actual measurements, the IOPs of the water body can be modeled in terms of contributions by any number of components. Thus the total absorption can be built up as the absorption by water itself, plus the absorption by chlorophyllbearing microbial particles, plus that by CDOM, by detritus, by mineral particles, and so on. In order to specify the absorption by chlorophyllbearing particles, for example, the user can specify the chlorophyll profile of the water column and then use a biooptical model to convert the chlorophyll concentration to the needed absorption coefficient. The chlorophyll profile also provides information needed for the computation of chlorophyll fluorescence effects. Each such absorption component has its own depth and wavelength dependence. Similar modeling can be used for scattering. Phase function information can be provided by selecting (from a builtin library) a phase function for each IOP component, e.g., using a Rayleighlike phase function for scattering by the water itself, by using a Petzold type phase function for scattering by particles, and by assuming that dissolved substances like CDOM do not scatter. HydroLight can also generate phase functions that have a specified backscatter fraction. For example, if the user has both measured scattering coefficients (e.g., from a WETLabs ac9 instrument) and measured backscatter coefficients (e.g., from a WETLabs bb9 or HOBILabs HydroScat6 instrument), then HydroLight can use the ratio to generate a phase function that has the same backscatter fraction at each depth and wavelength. The individualcomponent phase functions are weighted by the respective scattering coefficients and summed in order to obtain the total phase function. HydroLight does not carry out radiative transfer calculations for the atmosphere per se. The sky radiance for either cloudfree or overcast skies can be obtained from simple analytical models or from a combination of semiempirical models. Such models are included in the HydroLight code. Alternatively, if the sky radiance is measured, that data can be used as input to HydroLight via a userwritten subroutine. It is also possible to run an independent atmospheric radiative transfer model (such as MODTRAN) in order to generate the sky radiance coming from each part of the sky hemisphere, and then give the modelgenerated values to HydroLight as input. The bottom boundary condition is applied at the deepest depth of interest in the simulation at hand. For a remote sensing simulation concerned only with the waterleaving radiance, it is usually sufficient to solve the radiative transfer equation only for the upper two optical depths, because almost all light leaving the water surface comes from this nearsurface region. In this case, the bottom boundary condition can be taken to describe an optically infinitely deep layer of water below two optical depths. In a biological study of primary productivity, it might be necessary to solve for the radiance down to five (or more) optical depths to reach the bottom of the euphotic zone, in which case the bottom boundary condition would be applied at that depth. In such cases, HydroLight computes the needed bottom boundary BRDF from the inherent optical properties at the deepest depth of interest. The bottom boundary condition also can describe a physical bottom at a given geometric depth. In that case, irradiance reflectance of the bottom must be specified (for a Lambertian bottom). In general, this reflectance is a function of wavelength and depends on the type of bottommud, sand, sea grass, etc. The user can also supply a subroutine to define a nonLambertian bottom BRDF.
Output from HydroLightHydroLight generates files of archival "printout," which are convenient for a quick examination of the results, and larger files of digital data. The digital files are designed for spreadsheet analysis of selected results and for graphical or numerical analysis of all output, including the full radiance distribution. The default printout gives a moderate amount of information to document the input to the run and to show selected results of interest to most oceanographers (such as various irradiances, reflectances, mean cosines, Kfunctions, and zenith and nadir radiances). This output is easily tailored to the user's requirements. A file of digital data contains the complete input and output for the run, including the full radiance distribution. This file is generally used as input to plotting routines that give graphical output of various quantities as functions of depth, direction, or wavelength. Macros are provided to convert selected digital output files into spreadsheets. All input and output files are in ASCII format to enable easy transfer between different computer systems.
DocumentationThe invariant imbedding algorithms used within HydroLight are described in detail in Light and Water (1994), in particular Chapters 4 and 8. The source code is extensively documented with comments referencing equations in Light and Water and other publications. There is a Users' Guide that describes how to run the code, and Technical Documentation that gives information about the included models for IOPs, bottom reflectances, sky radiances, and such. The latest versions of these documents can be downloaded from the references page. Finally, there is an online users' group that is open to all HydroLight users. That site is used to post questions and answers of general interest, share userwritten codes for plotting of HydroLight outputs, distribute updates, and make other announcements of interest to HydroLight users. caveat emptor: There are many "HydroLight" products on the market, including hydrogen powered lighting systems, hydroelectric power systems, underwater dive lights, lighting for irrigation systems, lighting for growing recreational plants in your basement hydroponics tank, and even skin care lotions, bicycles, sports drinks, and a toothbrush. However, none of those other HydroLights can solve the radiative transfer equation.

