Alexander Marshak

The interpretation of spectral vegetation indexes

Empirical studies report several plausible correlations between transforms of spectral reflectance, called vegetation indexes, and parameters descriptive of vegetation leaf area, biomass and physiological functioning. However, most indexes can be generalized to show a derivative of surface reflectance with respect to wavelength. This derivative is a function of the optical properties of leaves and soil particles. In the case of optically dense vegetation, the spectral derivative, and thus the indexes, can be rigorously shown to be indicative of the abundance and activity of the absorbers in the leaves. Therefore, the widely used broad-band &near-infrared vegetation indexes are a measure of chlorophyll abundance and energy absorption.

Multifractal characterizations of nonstationarity and intermittency in geophysical fields: Observed, retrieved, or simulated

Geophysical data rarely show any smoothness at any scale, and this often makes comparison with theoretical model output difficult. However, highly fluctuating signals and fractal structures are typical of open dissipative systems with nonlinear dynamics, the focus of most geophysical research. High levels of variability are excited over a large range of scales by the combined actions of external forcing and internal instability. At very small scales we expect geophysical fields to be smooth, but these are rarely resolved with available instrumentation or simulation tools; nondifferentiable and even discontinuous models are therefore in order. We need methods of statistically analyzing geophysical data, whether measured in situ, remotely sensed or even generated by a computer model, that are adapted to these characteristics. An important preliminary task is to define statistically stationary features in generally nonstationary signals. We first discuss a simple criterion for stationarity in finite data streams that exhibit power law energy spectra and then, guided by developments in turbulence studies, we advocate the use of two ways of analyzing the scale dependence of statistical information: singular measures and qth order structure functions. In nonstationary situations, the approach based on singular measures seeks power law behavior in integrals over all possible scales of a nonnegative stationary field derived from the data, leading to a characterization of the intermittency in this (gradient-related) field. In contrast, the approach based on structure functions uses the signal itself, seeking power laws for the statistical moments of absolute increments over arbitrarily large scales, leading to a characterization of the prevailing nonstationarity in both quantitative and qualitative terms. We explain graphically, step by step, both multifractal statistics which are largely complementary to each other. The geometrical manifestations of nonstationarity and intermittency, “roughness” and “sparseness”, respectively, are illustrated and the associated analytical (differentiability and continuity) properties are discussed. As an example, the two techniques are applied to a series of recent measurements of liquid water distributions inside marine stratocumulus decks; these are found to be multifractal over scales ranging from ≈60 m to ≈60 km. Finally, we define the “mean multifractal plane” and show it to be a simple yet comprehensive tool with many applications including data intercomparison, (dynamical or stochastic) model and retrieval validations.

The Landsat Scale Break in Stratocumulus as a Three-Dimensional Radiative Transfer Effect: Implications for Cloud Remote Sensing

Several studies have uncovered a break in the scaling properties of Landsat cloud scenes at nonabsorbing wavelengths. For scales greater than 200‐400 m, the wavenumber spectrum is approximately power law in k25/3, but from there down to the smallest observable scales (50‐100 m) follows another k2b law with b . 3. This implies very smooth radiance fields. The authors reexamine the empirical evidence for this scale break and explain it using fractal cloud models, Monte Carlo simulations, and a Green function approach to multiple scattering theory. In particular, the authors define the ‘‘radiative smoothing scale’’ and relate it to the characteristic scale of horizontal photon transport. The scale break was originally thought to occur at a scale commensurate with either the geometrical thickness Dz of the cloud, or with the ‘‘transport’’ mean free path lt 5 [(1 2 g)s]21, which incorporates the effect of forward scattering (s is extinction and g the asymmetry factor of the phase function). The smoothing scale is found to be approximately ltDz at cloud top; this is the prediction of diffusion ˇ theory which applies when (1 2 g)t 5D z / l t * 1( tis optical thickness). Since the scale break is a tangible effect of net horizontal radiative fluxes excited by the fluctuations of t, the smoothing scale sets an absolute lower bound on the range where one can neglect these fluxes and use plane-parallel theory locally, even for stratiform clouds. In particular, this constrains the retrieval of cloud properties from remotely sensed data. Finally, the characterization of horizontal photon transport suggests a new lidar technique for joint measurements of optical and geometrical thicknesses at about 0.5-km resolution.

Hyperspectral remote sensing of foliar nitrogen content

A strong positive correlation between vegetation canopy bidirectional reflectance factor (BRF) in the near infrared (NIR) spectral region and foliar mass-based nitrogen concentration (%N) has been reported in some temperate and boreal forests. This relationship, if true, would indicate an additional role for nitrogen in the climate system via its influence on surface albedo and may offer a simple approach for monitoring foliar nitrogen using satellite data. We report, however, that the previously reported correlation is an artifact—it is a consequence of variations in canopy structure, rather than of %N. The data underlying this relationship were collected at sites with varying proportions of foliar nitrogen-poor needleleaf and nitrogen-rich broadleaf species, whose canopy structure differs considerably. When the BRF data are corrected for canopy-structure effects, the residual reflectance variations are negatively related to %N at all wavelengths in the interval 423–855 nm. This suggests that the observed positive correlation between BRF and %N conveys no information about %N. We find that to infer leaf biochemical constituents, e.g., N content, from remotely sensed data, BRF spectra in the interval 710–790 nm provide critical information for correction of structural influences. Our analysis also suggests that surface characteristics of leaves impact remote sensing of its internal constituents. This further decreases the ability to remotely sense canopy foliar nitrogen. Finally, the analysis presented here is generic to the problem of remote sensing of leaf-tissue constituents and is therefore not a specific critique of articles espousing remote sensing of foliar %N.

3D Radiative Transfer in Cloudy Atmospheres

Preliminaries.- Scales, Tools and Reminiscences.- Observing Clouds and Their Optical Properties.- Fundamentals.- A Primer in 3D Radiative Transfer.- Numerical Methods.- Approximation Methods in Atmospheric 3D Radiative Transfer Part 1: Resolved Variability and Phenomenology.- Climate.- Approximation Methods in Atmospheric 3D Radiative Transfer Part 2: Unresolved Variability and Climate Applications.- 3D Radiative Transfer in Stochastic Media.- Effective Cloud Properties for Large-Scale Models.- Broadband Irradiances and Heating Rates for Cloudy Atmospheres.- Longwave Radiative Transfer in Inhomogeneous Cloud Layers.- Remote Sensing.- 3D Radiative Transfer in Satellite Remote Sensing of Cloud Properties.- Horizontal Fluxes and Radiative Smoothing.- Photon Paths and Cloud Heterogeneity: An Observational Strategy to Assess Effects of 3D Geometry on Radiative Transfer.- 3D Radiative Transfer in Vegetation Canopies and Cloud-Vegetation Interaction.

The ICESat-2 Laser Altimetry Mission

Satellite and aircraft observations have revealed that remarkable changes in the Earths polar ice cover have occurred in the last decade. The impacts of these changes, which include dramatic ice loss from ice sheets and rapid declines in Arctic sea ice, could be quite large in terms of sea level rise and global climate. NASAs Ice, Cloud and Land Elevation Satellite-2 (ICESat-2), currently planned for launch in 2015, is specifically intended to quantify the amount of change in ice sheets and sea ice and provide key insights into their behavior. It will achieve these objectives through the use of precise laser measurements of surface elevation, building on the groundbreaking capabilities of its predecessor, the Ice Cloud and Land Elevation Satellite (ICESat). In particular, ICESat-2 will measure the temporal and spatial character of ice sheet elevation change to enable assessment of ice sheet mass balance and examination of the underlying mechanisms that control it. The precision of ICESat-2s elevation measurement will also allow for accurate measurements of sea ice freeboard height, from which sea ice thickness and its temporal changes can be estimated. ICESat-2 will provide important information on other components of the Earth System as well, most notably large-scale vegetation biomass estimates through the measurement of vegetation canopy height. When combined with the original ICESat observations, ICESat-2 will provide ice change measurements across more than a 15-year time span. Its significantly improved laser system will also provide observations with much greater spatial resolution, temporal resolution, and accuracy than has ever been possible before.

Scale Invariance of Liquid Water Distributions in Marine Stratocumulus. Part I: Spectral Properties and Stationarity Issues

Abstract This study investigates the internal structure of marine stratocumulus (Sc) using the spatial fluctuations of liquid water content (LWC) measured along horizontal flights off the coast of southern California during the First ISCCP Regional Experiment (FIRE) in summer of 1987. The results of FIRE 87 data analyses are compared to similar ones for marine Sc probed during the Atlantic Stratocumulus Transition Experiment (ASTEX) in summer 1992 near the Azores. In this first of two parts, the authors use spectral analysis to determine the main scale-invariant regimes, defined by the ranges of scales where wavenumber spectra follow power laws; from there, they discuss stationary issues. Although crucial for obtaining meaningful spatial statistics (e.g., in climate diagnostics), the importance of establishing stationarity—statistical invariance under translation—is often overlooked. The sequel uses multifractal analysis techniques and addresses intermittency issues. By improving our understanding of both...

Thin Liquid Water Clouds: Their Importance and Our Challenge

Abstract Many of the clouds important to the Earths energy balance, from the Tropics to the Arctic, contain small amounts of liquid water. Longwave and shortwave radiative fluxes are very sensitive to small perturbations of the cloud liquid water path (LWP), when the LWP is small (i.e., < 100 g m−2; clouds with LWP less than this threshold will be referred to as “thin”). Thus, the radiative properties of these thin liquid water clouds must be well understood to capture them correctly in climate models. We review the importance of these thin clouds to the Earths energy balance, and explain the difficulties in observing them. In particular, because these clouds are thin, potentially mixed phase, and often broken (i.e., have large 3D variability), it is challenging to retrieve their microphysical properties accurately. We describe a retrieval algorithm intercomparison that was conducted to evaluate the issues involved. The intercomparison used data collected at the Atmospheric Radiation Measurement (ARM) S...

3-D aerosol-cloud radiative interaction observed in collocated MODIS and ASTER images of cumulus cloud fields

[1] Three-dimensional (3-D) aerosol-cloud interaction is examined by analyzing two images containing cumulus clouds in biomass-burning regions in Brazil. The research consists of two parts. The first part focuses on identifying 3-D cloud impacts on reflectances for the pixels selected for the MODIS aerosol retrieval based purely on observations. The second part of the research combines the observations with radiative transfer computations to identify key parameters in the 3-D aerosol-cloud interaction. We find that 3-D cloud-induced enhancement depends on the optical properties of nearby clouds as well as on wavelength. The enhancement is too large to be ignored. Associated bias error in one-dimensional (1-D) aerosol optical thickness retrieval ranges from 50 to 140% depending on wavelength and the optical depth of nearby clouds, as well as aerosol optical thickness. We caution the community to be prudent when applying 1-D approximations in computing solar radiation in clear regions adjacent to clouds or when using traditional retrieved aerosol optical thickness in aerosol indirect effect research.

Scale invariance in liquid water distributions in marine stratocumulus. Part II: Multifractal properties and intermittency issues

Abstract This is the second of two papers analyzing the internal liquid water content (LWC) structure of marine stratocumulus (Sc) based on observations taken during the First ICCP (International Commission on Cloud Physics) Regional Experiment (FIRE) 1987 and Atlantic Stratocumulus Transition Experiment (ASTEX) 1992 field programs. Part I examined wavenumber spectra and the three-decade scale range (tens of meters to tens of kilometers) over which scale invariance holds; the inability of spectral analysis to distinguish between different random processes was also underscored. This indetermination is removed in this part by applying multifractal analysis techniques to the LWC fields, leading to a characterization of the role of intermittency in marine Sc. Two multiscaling statistics are computed and associated nonincreasing hierarchies of exponents are obtained: structure functions and H(q), singular measures and D(q). The real variable q is the order of a statistical moment (e.g., q = 1.0 yields a mean);...