Information-Theoretic Methods for Identifying Relationships among Climate Variables

Information-theoretic quantities, such as entropy, are used to quantify the amount of information a given variable provides. Entropies can be used together to compute the mutual information, which quantifies the amount of information two variables share. However, accurately estimating these quantities from data is extremely challenging. We have developed a set of computational techniques that allow one to accurately compute marginal and joint entropies. These algorithms are probabilistic in nature and thus provide information on the uncertainty in our estimates, which enable us to establish statistical significance of our findings. We demonstrate these methods by identifying relations between cloud data from the International Satellite Cloud Climatology Project (ISCCP) and data from other sources, such as equatorial pacific sea surface temperatures (SST).Comment: Presented at the Earth-Sun System Technology Conference (ESTC 2008), Adelphi, MD. http://esto.nasa.gov/conferences/estc2008/ 3 pages, 3 figures. Appears in the Proceedings of the Earth-Sun System Technology Conference (ESTC 2008), Adelphi, M

Determination and impact of surface radiative processes for TOGA COARE

Experiments using atmospheric general circulation models have shown that the atmospheric circulation is very sensitive to small changes in sea surface temperature in the tropical western Pacific Ocean warm pool region. The mutual sensitivity of the ocean and the atmosphere in the warm pool region places stringent requirements on models of the coupled ocean atmosphere system. At present, the situation is such that diagnostic studies using available data sets have been unable to balance the surface energy budget in the warm pool region to better than 50 to 80 W/sq m. The Tropical Ocean Global Atmosphere (TOGA) Coupled Ocean Atmosphere Response Experiment (COARE) is an observation and modelling program that aims specifically at the elucidation of the physical process which determine the mean and transient state of the warm pool region and the manner in which the warm pool interacts with the global ocean and atmosphere. This project focuses on one very important aspect of the ocean atmosphere interface component of TOGA COARE, namely the temporal and spatial variability of surface radiative fluxes in the warm pool region

ISCCP CX observations during the FIRE/SRB Wisconsin Experiment from October 14 through November 2, 1986

Maps and tables are presented which show 45 satellite derived physical, radiation, or cloud parameters from ISCCP CX tapes during the FIRE/SRB Wisconsin experiment region from October 14 through November 2, 1986. Pixel locations selected for presentation are for an area which coincided with a 100 x 100 km array of evenly spaced ground truth sites. Area-averaged parameters derived from the ISSCP data should be consistent with area averages from the groundtruth stations

A Recipe for the Estimation of Information Flow in a Dynamical System

Information-theoretic quantities, such as entropy and mutual information (MI), can be used to quantify the amount of information needed to describe a dataset or the information shared between two datasets. In the case of a dynamical system, the behavior of the relevant variables can be tightly coupled, such that information about one variable at a given instance in time may provide information about other variables at later instances in time. This is often viewed as a flow of information, and tracking such a flow can reveal relationships among the system variables. Since the MI is a symmetric quantity; an asymmetric quantity, called Transfer Entropy (TE), has been proposed to estimate the directionality of the coupling. However, accurate estimation of entropy-based measures is notoriously difficult. Every method has its own free tuning parameter(s) and there is no consensus on an optimal way of estimating the TE from a dataset. We propose a new methodology to estimate TE and apply a set of methods together as an accuracy cross-check to provide a reliable mathematical tool for any given data set. We demonstrate both the variability in TE estimation across techniques as well as the benefits of the proposed methodology to reliably estimate the directionality of coupling among variables

A Recipe for the Estimation of Information Flow in a Dynamical System

Information-theoretic quantities, such as entropy and mutual information (MI), can be used to quantify the amount of information needed to describe a dataset or the information shared between two datasets. In the case of a dynamical system, the behavior of the relevant variables can be tightly coupled, such that information about one variable at a given instance in time may provide information about other variables at later instances in time. This is often viewed as a flow of information, and tracking such a flow can reveal relationships among the system variables. Since the MI is a symmetric quantity; an asymmetric quantity, called Transfer Entropy (TE), has been proposed to estimate the directionality of the coupling. However, accurate estimation of entropy-based measures is notoriously difficult. Every method has its own free tuning parameter(s) and there is no consensus on an optimal way of estimating the TE from a dataset. We propose a new methodology to estimate TE and apply a set of methods together as an accuracy cross-check to provide a reliable mathematical tool for any given data set. We demonstrate both the variability in TE estimation across techniques as well as the benefits of the proposed methodology to reliably estimate the directionality of coupling among variables

Revealing Relationships among Relevant Climate Variables with Information Theory

A primary objective of the NASA Earth-Sun Exploration Technology Office is to understand the observed Earth climate variability, thus enabling the determination and prediction of the climate's response to both natural and human-induced forcing. We are currently developing a suite of computational tools that will allow researchers to calculate, from data, a variety of information-theoretic quantities such as mutual information, which can be used to identify relationships among climate variables, and transfer entropy, which indicates the possibility of causal interactions. Our tools estimate these quantities along with their associated error bars, the latter of which is critical for describing the degree of uncertainty in the estimates. This work is based upon optimal binning techniques that we have developed for piecewise-constant, histogram-style models of the underlying density functions. Two useful side benefits have already been discovered. The first allows a researcher to determine whether there exist sufficient data to estimate the underlying probability density. The second permits one to determine an acceptable degree of round-off when compressing data for efficient transfer and storage. We also demonstrate how mutual information and transfer entropy can be applied so as to allow researchers not only to identify relations among climate variables, but also to characterize and quantify their possible causal interactions.Comment: 14 pages, 5 figures, Proceedings of the Earth-Sun System Technology Conference (ESTC 2005), Adelphi, M

Comparison of Different Global Information Sources Used in Surface Radiative Flux Calculation: Radiative Properties of the Surface

Direct estimates of surface radiative fluxes that resolve regional and weather-scale variabilty over the whole globe with reasonable accuracy have only become possible with the advent of extensive global, mostly satellite, datasets within the past couple of decades. The accuracy of these fluxes, estimated to be about 10-15 W per square meter is largely limited by the accuracy of the input datasets. The leading uncertainties in the surface fluxes are no longer predominantly induced by clouds but are now as much associated with uncertainties in the surface and near-surface atmospheric properties. This study presents a fuller, more quantitative evaluation of the uncertainties for the surface albedo and emissivity and surface skin temperatures by comparing the main available global datasets from the Moderate-Resolution Imaging Spectroradiometer product, the NASA Global Energy and Water Cycle Experiment Surface Radiation Budget project, the European Centre for Medium-Range Weather Forecasts, the National Aeronautics and Space Administration, the National Centers for Environmental Prediction, the International Satellite Cloud Climatology Project (ISCCP), the Laboratoire de Meteorologie Dynamique, NOAA/NASA Pathfinder Advanced Very High Resolution Radiometer project, NOAA Optimum Interpolation Sea Surface Temperature Analysis and the Tropical Rainfall Measuring Mission (TRMM) Microwave Image project. The datasets are, in practice, treated as an ensemble of realizations of the actual climate such that their differences represent an estimate of the uncertainty in their measurements because we do not possess global truth datasets for these quantities. The results are globally representative and may be taken as a generalization of our previous ISCCP-based uncertainty estimates for the input datasets. Surface properties have the primary role in determining the surface upward shortwave (SW) and longwave (LW) flux. From this study, the following conclusions are obtained. Although land surface albedos in the near near-infrared remain poorly constrained (highly uncertain), they do not cause too much error in total surface SW fluxes; the more subtle regional and seasonal variations associated with vegetation and snow are still on doubt. The uncertainty of the broadband black-sky SW albedo for land surface from this study is about 7%, which can easily induce 5-10 W per square meter uncertainty in (upwelling) surface SW flux estimates. Even though available surface (broadband) LW emissivity datasets differ significantly (3%-5% uncertainty), this disagreement is confined to wavelengths greater than 20 micrometers so that there is little practical effect (1-3 W per square meters) on the surface upwelling LW fluxes. The surface skin temperature is one of two leading factors that cause problems with surface LW fluxes. Even though the differences among the various datasets are generally only 2-4 K, this can easily cause 10-15 W per square meter uncertainty in calculated surface (upwelling) LW fluxes. Significant improvements could be obtained for surface LW flux calculations by improving the retrievals of (in order of decreasing importance): (1) surface skin temperature, (2) surface air and near-surface-layer temperature, (3) column precipitable water amount and (4) broadband emissivity. And for surface SW fluxes, improvements could be obtained (excluding improved cloud treatment) by improving the retrievals of (1) aerosols (from our sensitivity studies but not discussed in this work), and (2) surface (black-sky) albedo, of which, NIR part of the spectrum has much larger uncertainty

Global Survey of the Relationship Between Cloud Droplet Size and Albedo Using ISCCP

Aerosols affect climate through direct and indirect effects. The direct effect of aerosols (e.g., sulfates) includes reflection of sunlight back toward space and for some aerosols (e.g., smoke particles), absorption in the atmosphere; both effects cool the Earth's surface. The indirect effect of aerosols refers to the modification of cloud microphysical properties, thereby affecting the radiation balance. Higher concentrations of Cloud Condensation Nuclei (CCN) generally produce higher concentrations of cloud droplets, which are also usually assumed to lead to decreased cloud droplet sizes. The result is an increase in cloud albedo, producing a net radiative cooling, opposite to the warming caused by greenhouse gases (Charlson et al. 1992). The change in clouds that is directly induced by an increase of aerosol concentration is an increase of cloud droplet number density, N; but is is usually assumed that cloud droplet size decreases as if the water mass density Liquid Water Content (LWC) were constant. There is actually no reason why this should be the case. Shifting the cloud droplet size distribution to more numerous smaller droplets can change the relative rates of condensational and coalescence growth, leading to different LWC (e.g., Rossow 1978). Moreover, the resulting change in cloud albedo is usually ascribed to more efficient scattering by smaller droplets, when in fact it is the increase in droplet number density (assuming constant LWC) that produces the most important change in cloud albedo: e.g., holding N constant and decreasing the droplet size would actually decrease the scattering cross-section and, thus, the albedo much more than it is increased by the increased scattering efficiency

Comparison of Ice Cloud Particle Sizes Retrieved from Satellite Data Derived from In Situ Measurements

Cloud microphysical parameterizations have attracted a great deal of attention in recent years due to their effect on cloud radiative properties and cloud-related hydrological processes in large-scale models. The parameterization of cirrus particle size has been demonstrated as an indispensable component in the climate feedback analysis. Therefore, global-scale, long-term observations of cirrus particle sizes are required both as a basis of and as a validation of parameterizations for climate models. While there is a global scale, long-term survey of water cloud droplet sizes (Han et al.), there is no comparable study for cirrus ice crystals. This study is an effort to supply such a data set

A Near-Global Survey of Cirrus Particle Size Using ISCCP

Cirrus is the most frequently occurring and widely distributed cloud type. The average annual frequency of occurrence for cirrus is 34% and its global coverage is about 20-30% (Warren et al. 1985). It strongly influences weather and climate processes through its effects on the radiation budget of the earth and the atmosphere (Liou 1986). Microphysics of cirrus is a critical component in understanding cloud-climate radiative interactions. For example, ice water content feedback is positive from a 1-D model study. But the feedback is substantially reduced upon the inclusion of small ice crystals (Sinha and Shine 1994). Due to the complexity caused by the non-spherical shape of ice crystals in cirrus, retrievals of cirrus properties are difficult. In recent years, advances have been made both in models and in case studies (e.g., Takano and Liou 1989, Young et al. 1994), but no global scale survey has been conducted. Similar to our previous near-global survey of droplet sizes of liquid water clouds (Han et al. 1994), a survey of cirrus ice crystal sizes is conducted over both continental and oceanic areas. We describe a method for retrieving cirrus particle size information on a near-global scale 50 deg S to 50 deg N using currently available satellite data from ISCCP. To retrieve cirrus particle size, we use a radiative transfer model that includes all major absorbing gases and cloud scattering/absorption to compute synthetic radiances as a function of satellite viewing geometry. Ice crystal shapes are assumed to be hexagonal columns and plates. The model results have been validated against clear sky observations and are consistent with the observed radiance range under cloudy conditions