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

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

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

The possible indirect aerosol effect on climate is examined. First, the spatial relationship is checked between cloud droplet radii and cloud albedo in different areas where aerosol concentration are known to differ significantly. Second, the temporal relationship between r(sub e) and cloud albedo is explored for each 2.5 deg x 2.5 deg grid box to reveal in which regions of the globe the variations of cloud albedo are correlated with changes in r(sub e) consistent with the indirect aerosol effect hypothesis

Frequency and Angular Variations of Land Surface Microwave Emissivities: Can we Estimate SSM/T and AMSU Emissivities from SSM/I Emissivities?

To retrieve temperature and humidity profiles from SSM/T and AMSU, it is important to quantify the contribution of the Earth surface emission. So far, no global estimates of the land surface emissivities are available at SSM/T and AMSU frequencies and scanning conditions. The land surface emissivities have been previously calculated for the globe from the SSM/I conical scanner between 19 and 85 GHz. To analyze the feasibility of deriving SSM/T and AMSU land surface emissivities from SSM/I emissivities, the spectral and angular variations of the emissivities are studied, with the help of ground-based measurements, models and satellite estimates. Up to 100 GHz, for snow and ice free areas, the SSM/T and AMSU emissivities can be derived with useful accuracy from the SSM/I emissivities- The emissivities can be linearly interpolated in frequency. Based on ground-based emissivity measurements of various surface types, a simple model is proposed to estimate SSM/T and AMSU emissivities for all zenith angles knowing only the emissivities for the vertical and horizontal polarizations at 53 deg zenith angle. The method is tested on the SSM/T-2 91.655 GHz channels. The mean difference between the SSM/T-2 and SSM/I-derived emissivities is less than or equal to 0.01 for all zenith angles with an r.m.s. difference of approx. = 0.02. Above 100 GHz, preliminary results are presented at 150 GHz, based on SSM/T-2 observations and are compared with the very few estimations available in the literature