Neural network uncertainty assessment using Bayesian statistics: a remote sensing application.

Neural network (NN) techniques have proved successful for many regression problems, in particular for remote sensing; however, uncertainty estimates are rarely provided. In this article, a Bayesian technique to evaluate uncertainties of the NN parameters (i.e., synaptic weights) is first presented. In contrast to more traditional approaches based on point estimation of the NN weights, we assess uncertainties on such estimates to monitor the robustness of the NN model. These theoretical developments are illustrated by applying them to the problem of retrieving surface skin temperature, microwave surface emissivities, and integrated water vapor content from a combined analysis of satellite microwave and infrared observations over land. The weight uncertainty estimates are then used to compute analytically the uncertainties in the network outputs (i.e., error bars and correlation structure of these errors). Such quantities are very important for evaluating any application of an NN model. The uncertainties on the NN Jacobians are then considered in the third part of this article. Used for regression fitting, NN models can be used effectively to represent highly nonlinear, multivariate functions. In this situation, most emphasis is put on estimating the output errors, but almost no attention has been given to errors associated with the internal structure of the regression model. The complex structure of dependency inside the NN is the essence of the model, and assessing its quality, coherency, and physical character makes all the difference between a blackbox model with small output errors and a reliable, robust, and physically coherent model. Such dependency structures are described to the first order by the NN Jacobians: they indicate the sensitivity of one output with respect to the inputs of the model for given input data. We use a Monte Carlo integration procedure to estimate the robustness of the NN Jacobians. A regularization strategy based on principal component analysis is proposed to suppress the multicollinearities in order to make these Jacobians robust and physically meaningful.

Aerosol retrievals over the ocean by use of channels 1 and 2 AVHRR data: sensitivity analysis and preliminary results.

We outline the methodology of interpreting channels 1 and 2 Advanced Very High Resolution Radiometer (AVHRR) radiance data over the oceans and describe a detailed analysis of the sensitivity of monthly averages of retrieved aerosol parameters to the assumptions made in different retrieval algorithms. The analysis is based on using real AVHRR data and exploiting accurate numerical techniques for computing single and multiple scattering and spectral absorption of light in the vertically inhomogeneous atmosphere-ocean system. We show that two-channel algorithms can be expected to provide significantly more accurate and less biased retrievals of the aerosol optical thickness than one-channel algorithms and that imperfect cloud screening and calibration uncertainties are by far the largest sources of errors in the retrieved aerosol parameters. Both underestimating and overestimating aerosol absorption as well as the potentially strong variability of the real part of the aerosol refractive index may lead to regional and/or seasonal biases in optical-thickness retrievals. The Angström exponent appears to be the aerosol size characteristic that is least sensitive to the choice of aerosol model and should be retrieved along with optical thickness as the second aerosol parameter.

Cloud feedback: a stabilizing effect for the early Earth?

The effect of variations in cloud cover, optical properties, and fractional distribution with altitude on the mean surface temperature of a model of the early earth has been investigated. In all cases examined, cloud-climate feedbacks result in temperatures greater than those in models with no cloud feedbacks. If the model of hydrospheric feedback effects is correct, then cloud feedbacks are as important to the climate as changes in solar luminosity and atmospheric composition during the earth's atmospheric evolution. In particular, the early earth need not become completely ice-covered if strong negative cloud feedbacks occur. However, until a proper understanding of cloud feedbacks is available, conclusions regarding conditions in the early atmosphere must remain in doubt.

Cloud images from the pioneer venus orbiter.

Ultraviolet images of Venus over a 3-month period show marked evolution of the planetary scale features in the cloud patterns. The dark horizontal Y feature recurs quasi-periodically, at intervals of about 4 days, but it has also been absent for periods of several weeks. Bow-shaped features observed in Pioneer Venus images are farther upstream from the subsolar point than those in Mariner 10 images.