A linear model to derive melt pond depth on Arctic sea ice from hyperspectral data

Melt ponds are key elements in the energy balance of Arctic sea ice. Observing their temporal evolution is crucial for understanding melt processes and predicting sea ice evolution. Remote sensing is the only technique that enables large-scale observations of Arctic sea ice. However, monitoring melt pond deepening in this way is challenging because most of the optical signal reflected by a pond is defined by the scattering characteristics of the underlying ice. Without knowing the influence of meltwater on the reflected signal, the water depth cannot be determined. To solve the problem, we simulated the way meltwater changes the reflected spectra of bare ice. We developed a model based on the slope of the log-scaled remote sensing reflectance at 710 nm as a function of depth that is widely independent from the bottom albedo and accounts for the influence of varying solar zenith angles. We validated the model using 49 in situ melt pond spectra and corresponding depths from shallow ponds on dark and bright ice. Retrieved pond depths are accurate (root mean square error, RMSE=2.81 cm; nRMSE=16 %) and highly correlated with in situ measurements (r=0.89; p=4.34×10-17). The model further explains a large portion of the variation in pond depth (R2=0.74). Our results indicate that our model enables the accurate retrieval of pond depth on Arctic sea ice from optical data under clear sky conditions without having to consider pond bottom albedo. This technique is potentially transferrable to hyperspectral remote sensors on unmanned aerial vehicles, aircraft and satellites.

Reflective properties of melt ponds on sea ice

Melt ponds occupy a large part of the Arctic sea ice in summer and strongly affect the radiative budget of the atmosphere–ice–ocean system. In this study, the melt pond reflectance is considered in the framework of radiative transfer theory. The melt pond is modeled as a plane-parallel layer of pure water upon a layer of sea ice (the pond bottom). We consider pond reflection as comprising Fresnel reflection by the water surface and multiple reflections between the pond surface and its bottom, which is assumed to be Lambertian. In order to give a description of how to find the pond bottom albedo, we investigate the inherent optical properties of sea ice. Using the Wentzel–Kramers–Brillouin approximation approach to light scattering by non-spherical particles (brine inclusions) and Mie solution for spherical particles (air bubbles), we conclude that the transport scattering coefficient in sea ice is a spectrally independent value. Then, within the two-stream approximation of the radiative transfer theory, we show that the under-pond ice spectral albedo is determined by two independent scalar values: the transport scattering coefficient and ice layer thickness. Given the pond depth and bottom albedo values, the bidirectional reflectance factor (BRF) and albedo of a pond can be calculated with analytical formulas. Thus, the main reflective properties of the melt pond, including their spectral dependence, are determined by only three independent parameters: pond depth z, ice layer thickness H, and transport scattering coefficient of ice σt.The effects of the incident conditions and the atmosphere state are examined. It is clearly shown that atmospheric correction is necessary even for in situ measurements. The atmospheric correction procedure has been used in the model verification. The optical model developed is verified with data from in situ measurements made during three field campaigns performed on landfast and pack ice in the Arctic. The measured pond albedo spectra were fitted with the modeled spectra by varying the pond parameters (z, H, and σt). The coincidence of the measured and fitted spectra demonstrates good performance of the model: it is able to reproduce the albedo spectrum in the visible range with RMSD that does not exceed 1.5 % for a wide variety of melt pond types observed in the Arctic.

In-situ multispectral and bathymetric measurements over a supraglacial lake in western Greenland using a remotely controlled watercraft

Supraglacial lakes form from meltwater on the Greenland ice sheet in topographic depressions on the surface, affecting both surface and sub-glacial processes. As the reflectance in the visible and near-infrared regions of a column of water is modulated by its height, retrieval techniques using spaceborne remote sensing data (e.g. Landsat, MODIS) have been proposed in the literature for the detection of lakes and estimation of their volume. These techniques require basic assumptions on the spectral properties of the water as well as the bottom of the lake, among other things. In this study, we report results obtained from the analysis of concurrent in-situ multi-spectral and depth measurements collected over a supraglacial lake during early July 2010 in West Greenland (Lake Olivia, 69°36'35" N, 49°29'40" W) and aim to assess some of the underlying hypotheses in remote sensing based bathymetric approaches. In particular, we focus our attention on the analysis of the lake bottom albedo and of the water attenuation coefficient. The analysis of in-situ data (collected by means of a remotely controlled boat equipped with a GPS, a sonar and a spectrometer) highlights the exponential trend of the water-leaving reflectance with lake depth. The values of the attenuation factor obtained from in-situ data are compared with those computed using approaches proposed in the literature. Also, the values of the lake bottom albedo from in-situ measurements are compared with those obtained from the analysis of reflectance of shallow waters. Finally, we quantify the error between in-situ measured and satellite-estimated lake depth values for the lake under study.

In-situ multispectral and bathymetric measurements over a supraglacial lake in western Greenland using a remotely controlled watercraft

We report concurrent in-situ multi-spectral and depth measurements over a supraglacial lake in West Greenland, collected by means of a remotely controlled boat equipped with a GPS, a sonar and a spectrometer. We focus our attention on the analysis of some of the key parameters widely used for multispectral spaceborne bathymetry, namely the lake bottom albedo and the water attenuation coefficient. The analysis of in-situ data highlights the exponential trend of the water-leaving reflectance with lake depth. The values of the attenuation factor are obtained from in-situ data and compared with those computed using approaches proposed in the literature. Also, the values of the lake bottom albedo from in-situ measurements are compared with those obtained from the analysis of reflectance of shallow-waters. Finally, we quantify the error between in-situ measured and satellite-estimated lake depth values for the lake under study.