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A Neural Network Correction to the Scalar Approximation in Radiative Transferaerosol optical properties. In this paper we present a method for correcting TOA radiances calculated with the scalar approximation, and we will focus on forward RT calculations in the UV-Vis, where the scalar error is significant. The approach utilizes a machine learning algorithm, specifically, an artificial neural network. The neural network is used as a data transformer that maps RTM input parameters to the difference between a scalar- and vector-calculated TOA radiance. Neural networks provide
aerosol optical properties. In this paper we present a method for correcting TOA radiances calculated with the scalar approximation, and we will focus on forward RT calculations in the UV-Vis, where the scalar error is significant. The approach utilizes a machine learning algorithm, specifically, an artificial neural network. The neural network is used as a data transformer that maps RTM input parameters to the difference between a scalar- and vector-calculated TOA radiance. Neural networks provide
statistical model does not prevent it from capturing linear relations as well. For example, temperature forecasts from the Advanced Regional Prediction System have been postprocessed via neural networks, displaying a reduction in bias and error variance of the forecasts ( Marzban 2003 ). There, it is found that the optimal neural network is indeed nonlinear. As such, the nonlinear statistical postprocessing yields temperature forecasts that are more accurate than the model forecasts as well as MOS
statistical model does not prevent it from capturing linear relations as well. For example, temperature forecasts from the Advanced Regional Prediction System have been postprocessed via neural networks, displaying a reduction in bias and error variance of the forecasts ( Marzban 2003 ). There, it is found that the optimal neural network is indeed nonlinear. As such, the nonlinear statistical postprocessing yields temperature forecasts that are more accurate than the model forecasts as well as MOS
; Hsu et al. 1997 ; Roebeling and Holleman 2009 ). One well-known algorithm and product is Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks (PERSIANN) which relates cloud-top temperature data obtained from IR imagery to the precipitation rate ( Hsu et al. 1997 ). PERSIANN is a near-real-time dataset with 0.25° (i.e., 25 km) spatial and hourly temporal resolutions ( Sorooshian et al. 2000 ). PERSIANN–Cloud Classification System (PERSIANN-CCS; Hong et al
; Hsu et al. 1997 ; Roebeling and Holleman 2009 ). One well-known algorithm and product is Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks (PERSIANN) which relates cloud-top temperature data obtained from IR imagery to the precipitation rate ( Hsu et al. 1997 ). PERSIANN is a near-real-time dataset with 0.25° (i.e., 25 km) spatial and hourly temporal resolutions ( Sorooshian et al. 2000 ). PERSIANN–Cloud Classification System (PERSIANN-CCS; Hong et al
estimating the thickness and volume of glaciers. The aim of the present contribution is to explore the potential of artificial neural networks (e.g., Bishop 1995 ; Reed and Marks 1999 ) as a tool for estimating ice thickness. In the next section we introduce artificial neural networks (ANNs), review their applications in climate science and glaciology, and describe how they are trained and used in the present study. In section 3 , we describe the construction of test datasets using a numerical ice
estimating the thickness and volume of glaciers. The aim of the present contribution is to explore the potential of artificial neural networks (e.g., Bishop 1995 ; Reed and Marks 1999 ) as a tool for estimating ice thickness. In the next section we introduce artificial neural networks (ANNs), review their applications in climate science and glaciology, and describe how they are trained and used in the present study. In section 3 , we describe the construction of test datasets using a numerical ice
, low- to midlevel relative humidity, midlevel relative humidity, upper-level relative humidity, and external compaction, as measured by surface wind speed and liquid equivalent precipitation amount. They then constructed 10-member ensembles of artificial neural networks 1 that substantially improved the diagnosis of snow-ratio class compared with the then-existing techniques [10:1 ratio, sample climatology, and National Weather Service (NWS) new-snowfall-to-estimated-meltwater conversion table
, low- to midlevel relative humidity, midlevel relative humidity, upper-level relative humidity, and external compaction, as measured by surface wind speed and liquid equivalent precipitation amount. They then constructed 10-member ensembles of artificial neural networks 1 that substantially improved the diagnosis of snow-ratio class compared with the then-existing techniques [10:1 ratio, sample climatology, and National Weather Service (NWS) new-snowfall-to-estimated-meltwater conversion table
. It is useful to develop an approach to predict water levels based on the recognition of the patterns of observed water-level variations rather than on the use of the environmental forcing information. It is often difficult to obtain good linear relationships of sea levels among different stations to represent the changes of their phase and amplitude. However, neural networks (NNs), which are able to approximate any nonlinear mathematical functions, have the ability to predict a complex system
. It is useful to develop an approach to predict water levels based on the recognition of the patterns of observed water-level variations rather than on the use of the environmental forcing information. It is often difficult to obtain good linear relationships of sea levels among different stations to represent the changes of their phase and amplitude. However, neural networks (NNs), which are able to approximate any nonlinear mathematical functions, have the ability to predict a complex system
output dewpoint temperature membership functions were expressed as low, medium, and high. The evaluation with 40 uniformly distributed days for all four seasons in 1994 resulted in absolute errors ranging to a maximum of 8°C with no mean error presented. An artificial neural network (ANN) is a robust computational technique modeled after biological neuron connections found in human brains ( Bose and Liang 1995 ; Haykin 1999 ). Like the human brain, ANNs are repeatedly exposed to inputs and vary the
output dewpoint temperature membership functions were expressed as low, medium, and high. The evaluation with 40 uniformly distributed days for all four seasons in 1994 resulted in absolute errors ranging to a maximum of 8°C with no mean error presented. An artificial neural network (ANN) is a robust computational technique modeled after biological neuron connections found in human brains ( Bose and Liang 1995 ; Haykin 1999 ). Like the human brain, ANNs are repeatedly exposed to inputs and vary the
1. Introduction The knowledge of wind wave characteristics is essential in many ocean engineering activities. In the past a number of models have been developed to simulate and forecast these characteristics. These simulations are predominantly based on approximated analytical models. An alternative approach is based on developing artificial neural networks (ANNs). ANNs have effectively been utilized in forecasting natural phenomena that are commonly characterized by uncertain
1. Introduction The knowledge of wind wave characteristics is essential in many ocean engineering activities. In the past a number of models have been developed to simulate and forecast these characteristics. These simulations are predominantly based on approximated analytical models. An alternative approach is based on developing artificial neural networks (ANNs). ANNs have effectively been utilized in forecasting natural phenomena that are commonly characterized by uncertain
uncertainties. To develop probabilistic error models that make the best possible use of available information, it is necessary to derive a procedure to estimate conditional distributions of rainfall with respect to multidimensional satellite input vectors. A number of multiplatform satellite rainfall algorithms are based on neural network techniques ( Bellerby et al. 2000 ; Bellerby 2004 ; Grimes et al. 2003 ; Hong et al. 2004 ; Hsu et al. 1999 ; Sorooshian et al. 2000 ; Tapiador et al. 2004 ; Zhang
uncertainties. To develop probabilistic error models that make the best possible use of available information, it is necessary to derive a procedure to estimate conditional distributions of rainfall with respect to multidimensional satellite input vectors. A number of multiplatform satellite rainfall algorithms are based on neural network techniques ( Bellerby et al. 2000 ; Bellerby 2004 ; Grimes et al. 2003 ; Hong et al. 2004 ; Hsu et al. 1999 ; Sorooshian et al. 2000 ; Tapiador et al. 2004 ; Zhang
, in the U.S. National Weather Service (NWS), the primary method for accomplishing this mapping is multiple linear regression [model output statistics (MOS; Glahn and Lowry 1972 ]. Many other methods are possible, such as neural networks (e.g., Rasp and Lerch 2018 ), random forests (e.g., Hill et al. 2020 ), support vector machines (e.g., Felker et al. 2011 ), quantile regression (e.g., Bremnes 2019 ), nearest neighbors (e.g., Kim et al. 2016 ), and analogs (e.g., Eckel and Delle Monache
, in the U.S. National Weather Service (NWS), the primary method for accomplishing this mapping is multiple linear regression [model output statistics (MOS; Glahn and Lowry 1972 ]. Many other methods are possible, such as neural networks (e.g., Rasp and Lerch 2018 ), random forests (e.g., Hill et al. 2020 ), support vector machines (e.g., Felker et al. 2011 ), quantile regression (e.g., Bremnes 2019 ), nearest neighbors (e.g., Kim et al. 2016 ), and analogs (e.g., Eckel and Delle Monache
