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.radiative effect | spurious regression | plant ecology | carbon cycle

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.

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 k Ϫ5/3 , but from there down to the smallest observable scales (50-100 m) follows another k Ϫ␤ law with ␤ Ͼ 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 ⌬ z of the cloud, or with the ''transport'' mean free path l t ϭ [(1 Ϫ g)] Ϫ1 , which incorporates the effect of forward scattering ( is extinction and g the asymmetry factor of the phase function). The smoothing scale is found to be approximately l t ⌬ z at cloud top; this is the prediction of diffusion ͙ theory which applies when (1 Ϫ g) ϭ ⌬ z /l t տ 1 ( is optical thickness). Since the scale break is a tangible effect of net horizontal radiative fluxes excited by the fluctuations of , 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.

An international Intercomparison of 3D Radiation Codes (I3RC) underscores the vast progress of recent years, but also highlights the challenges ahead for routine implementation in remote sensing and global climate modeling applications. Modeling atmospheric and oceanic processes is one of the most important methods of the earth sciences for understanding the interactions of the various components of the surface-atmosphere system and predicting future weather and climate states. Great leaps in the availability of computing power at continuously decreasing costs have led to widespread popularity of computer models for research and operational applications. As part of routine scientific work, output from models built for AFFILIATIONS: CAHALAN-NASA

Abstract. Spectral and structure function analyses are used to study the smoothness properties of the radiation fields for stratiform clouds whose horizontally fluctuating extinction fields are modeled with multiplicative cascades. Models of this type are "scale invariant," meaning that their two-point statistics obey power laws in the scale parameter. The independent pixel approximation (IPA) treats each pixel as a plane-parallel layer and yields scale-invariant albedo and radiance fields with the same exponents as the associated optical depth field. This is not the case with exact Monte Carlo (MC) results for which we confirm the existence of a characteristic "radiative smoothing" scale q. For scales larger than 7, IPA and MC reflectance fields fluctuate together, and the IPA can be invoked to infer optical depths from measured radiances.We use a multifractal characterization of structure functions to assess the performance of such retrievals.For scales smaller than TJ, MC fields are much smoother than their IPA counterparts, and IPA-based retrievals of the tihderlying optical depth field are unreliable.The scale break location TJ has been found to be closely related to the characteristic size (p) of the "spot" of multiply scattered light excited by illumination with a narrow beam, the random variable p being the horizontal distance between photon entry and exit points. New analytical arguments are presented forgiven the cloud's optical (2) and geometrical (h) thicknesses (g is the asymmetry factor); this result is shown to hold numerically for fractal cloud models too. An improved "nonlocal" IPA is defined as the convolution product of the IPA field with a gamma-type smoothing kernel dependent on (p).