Neural Networks Technique for Filling Gaps in Satellite Measurements: Application to Ocean Color Observations.

A neural network (NN) technique to fill gaps in satellite data is introduced, linking satellite-derived fields of interest with other satellites and in situ physical observations. Satellite-derived "ocean color" (OC) data are used in this study because OC variability is primarily driven by biological processes related and correlated in complex, nonlinear relationships with the physical processes of the upper ocean. Specifically, ocean color chlorophyll-a fields from NOAA's operational Visible Imaging Infrared Radiometer Suite (VIIRS) are used, as well as NOAA and NASA ocean surface and upper-ocean observations employed--signatures of upper-ocean dynamics. An NN transfer function is trained, using global data for two years (2012 and 2013), and tested on independent data for 2014. To reduce the impact of noise in the data and to calculate a stable NN Jacobian for sensitivity studies, an ensemble of NNs with different weights is constructed and compared with a single NN. The impact of the NN training period on the NN's generalization ability is evaluated. The NN technique provides an accurate and computationally cheap method for filling in gaps in satellite ocean color observation fields and time series.

Neural network approach for robust and fast calculation of physical processes in numerical environmental models: compound parameterization with a quality control of larger errors.

Development of neural network (NN) emulations for fast calculations of physical processes in numerical climate and weather prediction models depends significantly on our ability to generate a representative training set. Owing to the high dimensionality of the NN input vector which is of the order of several hundreds or more, it is rather difficult to cover the entire domain, especially its "far corners" associated with rare events, even when we use model simulated data for the NN training. Moreover the domain may evolve (e.g., due to climate change). In this situation the emulating NN may be forced to extrapolate beyond its generalization ability and may lead to larger errors in NN outputs. A new technique, a compound parameterization, has been developed to address this problem and to make the NN emulation approach more suitable for long-term climate prediction and climate change projections and other numerical modeling applications. Two different designs of the compound parameterization are presented and discussed.

Reducing uncertainties in neural network Jacobians and improving accuracy of neural network emulations with NN ensemble approaches.

A new application of the NN ensemble technique to improve the accuracy (reduce uncertainty) of NN emulation Jacobians is presented. It is shown that the introduced ensemble technique can be successfully applied to significantly reduce uncertainties in NN emulation Jacobians and to reach the accuracy of NN Jacobian calculations that is sufficient for the use in data assimilation systems. An NN ensemble approach is also applied to improve the accuracy of NN emulations themselves. Two ensembles linear (or conservative) and nonlinear (uses an additional averaging NN to calculate the ensemble average) were introduced and compared. The ensemble approaches: (a) significantly reduce the systematic and random error in NN emulation Jacobian, (b) significantly reduce the magnitudes of the extreme outliers and, (c) in general, significantly reduce the number of larger errors. It is also shown that the nonlinear ensemble is able to account for nonlinear correlations between ensemble members and to improve significantly the accuracy of the NN emulation as compared to the linear conservative ensemble in terms of systematic (bias), random, and larger errors.

Complex hybrid models combining deterministic and machine learning components for numerical climate modeling and weather prediction.

A new practical application of neural network (NN) techniques to environmental numerical modeling has been developed. Namely, a new type of numerical model, a complex hybrid environmental model based on a synergetic combination of deterministic and machine learning model components, has been introduced. Conceptual and practical possibilities of developing hybrid models are discussed in this paper for applications to climate modeling and weather prediction. The approach presented here uses NN as a statistical or machine learning technique to develop highly accurate and fast emulations for time consuming model physics components (model physics parameterizations). The NN emulations of the most time consuming model physics components, short and long wave radiation parameterizations or full model radiation, presented in this paper are combined with the remaining deterministic components (like model dynamics) of the original complex environmental model--a general circulation model or global climate model (GCM)--to constitute a hybrid GCM (HGCM). The parallel GCM and HGCM simulations produce very similar results but HGCM is significantly faster. The speed-up of model calculations opens the opportunity for model improvement. Examples of developed HGCMs illustrate the feasibility and efficiency of the new approach for modeling complex multidimensional interdisciplinary systems.

Some neural network applications in environmental sciences. Part I: forward and inverse problems in geophysical remote measurements.

A broad class of neural network (NN) applications dealing with the remote measurements of geophysical (physical, chemical, and biological) parameters of the oceans, atmosphere, and land surface is presented. In order to infer these parameters from remote sensing (RS) measurements, standard retrieval and variational techniques are applied. Both techniques require a data converter (transfer function or forward model) to convert satellite measurements into geophysical parameters or vice versa. In many cases, the transfer function and the forward model can be represented as a continuous nonlinear mapping. Because the NN technique is a generic technique for nonlinear mapping, it can be used beneficially for modeling transfer functions and forward models. These applications are introduced in a broader framework of solving forward and inverse problems in RS. In this broader context, we show that NN is an appropriate and efficient tool for solving forward and inverse problems in RS and for developing fast and accurate forward models and accurate and robust retrieval algorithms. Theoretical considerations are illustrated by several real-life examples-operational NN applications developed by the authors for SSM/I and medium resolution imaging spectrometer sensors.

Some neural network applications in environmental sciences. Part II: advancing computational efficiency of environmental numerical models.

A new generic neural network (NN) application-improving computational efficiency of certain processes in numerical environmental models-is considered. This approach can be used to accelerate the calculations and improve the accuracy of the parameterizations of several types of physical processes which generally require computations involving complex mathematical expressions, including differential and integral equations, rules, restrictions and highly nonlinear empirical relations based on physical or statistical models. It is shown that, from a mathematical point of view, such parameterizations can usually be considered as continuous mappings (continuous dependencies between two vectors) and, therefore, NNs can be used to replace primary parameterization algorithms. In addition to fast and accurate approximation of the primary parameterization, NN also provides the entire Jacobian for very little computation cost. Four particular real-life applications of the NN approach are presented here: for oceanic numerical models, a NN approximation of the UNESCO equation of state of the sea water (NN for the density of the seawater) and an inversion of this equation (NN for the salinity of the seawater); for atmospheric numerical models, a NN approximation for long wave radiative transfer code; and for wave models, a NN approximation for the nonlinear wave-wave interaction. In all considered applications a significant acceleration of numerical computations has been achieved. The first two of these NN applications have already been implemented in the multi-scale ocean forecast system at NCEP. The NN approach introduced in this paper can provide numerically efficient solutions to a wide range of problems in numerical models where lengthy, complicated calculations, which describe physical, chemical and/or biological processes, must be repeated frequently.