Figure 1 provides a schematic drawing of radiative transfer processes in the atmosphere. Non-learning approaches to AC use physical modeling and empirical relationships to retrieve surface reflectance from observations contaminated by atmospheric scattering and absorption processes that occur in the paths between the sun, the Earth's surface, and the satellite sensor.

The algorithm used to derive MOD09GA, the daily SR product from NASA's Moderate Resolution Imaging Spectroradiometer (MODIS) corrects for gases, aerosols and Raleigh scattering. Due to prohibitive computational complexity, MOD09GA relies on look-up tables for aerosol retrieval and for precomputed SR retrieved according to atmospheric conditions (Vermote and Kotchenova, 2008). MAIAC is a newer algorithm that uses time series and spatial analysis to detect clouds, retrieve aerosol thickness and retrieve SR (Lyapustin et al., 2011a,b, 2012). MAIAC uses two algorithms, depending on whether the observation area is stable or undergoing rapid change, as classified by the change detection algorithm (Lyapustin et al., 2012). These approaches, and other state-of the art approaches including Fast Line-of-sight Atmospheric Analysis of Spectral Hypercubes (FLAASH) rely on sensor calibration and retrieval of accurate atmospheric conditions (Cooley et al., 2002).

ML techniques have been applied to remote sensing with results that enhance upon non-learning methods. ML has been used to implement empirical bias corrections to MODIS measurements (Lary et al., 2009). In atmospheric correction, a Support Vector Machine (SVM) has been used to predict SR from TOA reflectance with good agreement between reflectance products retrieved from the ML method and from two radiative transfer models (Zhu et al., 2018). This approach trains a separate model for each band.

Prior work also has blended data produced by multiple satellites to obtain synthetic images with enhanced spatial or temporal resolution (Gao et al., 2006). Convolutional Neural Networks (CNN) have been used in remote sensing for tasks such as land cover classification, object detection and precipitation downscaling, which make use of local correlation structures (Castelluccio et al., 2015; Long et al., 2017; Mou et al., 2017; Vandal et al., 2017).

Outside of the remote sensing domain, CNNs have been used for style transfer, where image content is preserved and image texture is modified (Gatys et al., 2016). This problem has similarities to the problem of atmospheric correction, in which we wish to preserve semantic structure of the image while applying some effect. In atmospheric correction, this includes reversing the blue shift and reducing the blurring caused by passage through the atmosphere.

Deep CNNs can reach an accuracy saturation, where increasing depth is associated with decreasing training accuracy (He et al., 2015). It is understood that a stack of nonlinear layers has a difficult time learning an identity mapping, thus a difficult time preserving the resolution of images. He et al. introduced deep residual nets (ResNets) in 2015. ResNets outperform state of the art methods in several image recognition competitions and are believed to be generalizable to vision and non-vision tasks.

To prepare TOA reflectance, raw scans from Himawari-8 are georeferenced and assembled into a gridded format. Pixel values are converted to TOA reflectance according to the Himawari-8/9 Himawari Standard Data User's Guide, Version 1.2 (Japan Meteorological Agency, 2015). The resulting full disk TOA is reprojected into geographic (latitude-longitude) projection with a 120° by 120° extent and 0.01° resolution. The domain, extending from 85°E to 155°W and 60°N to 60°S, is divided into 6° by 6° tiles. Full disk observations are repeated every 10 min. This gridded product (HM08_AHI05) is publicly available (https://www.geonex.org/). Four bands—blue, green, red, and near infrared (NIR)—are selected from AHI TOA data (Table 1). The data is treated as a multi-channel image, concatenated with two additional channels of solar zenith and solar azimuth angles.

MOD09GA is a seven-band surface reflectance product computed from Terra MODIS sensor (Vermote and Kotchenova, 2008). This MODIS SR product, which is validated with ground observations, provides a standard for the calibration of other atmospheric correction algorithms (Liang et al., 2002). Four bands from MOD09GA, corresponding to four AHI bands, are selected based on available spatial resolution (Table 1). MOD09GA is resampled from the distributed 1km x 1km sinusoidal projection to a 0.01° geographic projection, described above, using GIS tools.

GEO surface reflectance is retrieved from AHI TOA reflectance using the MAIAC algorithm (henceforth referred to as MAIAC SR). MAIAC is a semi-empirical algorithm originally developed for MODIS and adapted to perform SR retrievals for Himwari-8 AHI. Performance of MAIAC is evaluated by comparison with MOD09GA. The projection and resolution are identical to AHI TOA reflectance, described above. This product (HM08_AHI12) is released as a provisional product and is available upon request (https://www.geonex.org/).

All data belongs to a 3 month period of December 2016 through February 2017. We use observations over the Australian continent. This landmass is chosen as it provides a large contiguous landmass with a variety of land cover classes with which to train a flexible emulator. Where satellite images are affected by missing pixels due to clouds, aerosols, and water bodies, we select images for training and testing only if they contain 80% valid pixels or greater. We create and apply a composite mask to standardize valid pixels between all images from the same date. Furthermore, all reflectances are normalized to intensity between 0 and 1.

We modify ResNets with long and short skip connections, as defined by He et al. and as depicted in Figure 1 (He et al., 2015). In this modified architecture, patch dimensions (width and height) are preserved throughout the network, as only relatively local information is necessary to retrieve pixelwise SR. Input patches are treated as six channel images, with four wavelength bands and two solar angle bands. Output images are four channel images with four wavelength bands.

ResNets and CNNs with varying numbers of residual blocks and hidden units are trained to determine the optimal architecture for this application. Models with partial convolutions (ResNet-P and CNN-P) and without partial convolutions (ResNet and CNN) are tested.

Missing pixel values pose a processing problem in CNNs. When they fall within the convolutional window centered around a neighboring pixel, missing values create anomalous output, or edge effects. Partial convolutions offer a semantically aware method for normalization of output values that performs well on irregularly shaped holes. In this method, a binary mask is used to calculate scaling factors that adjust outputs according to the number of valid inputs.

Given M, a binary mask denoting the positions of valid and invalid pixels, x, the values in the sliding convolution window, and W, the convolution window weights, the output of the partial convolution layer is defined as:

Convolutions with some or all valid pixels in the window are properly weighted and accepted as a valid response; convolutions with no valid pixels are not accepted. In each step, the binary mask is updated where a valid response was made, progressively shrinking holes. We adapt partial convolutions to prevent ill effects in processing satellite images with missing pixels due to clouds, cloud shadows and water bodies. Partial convolutions also have the desirable effect of eliminating edge effects in patches when used in combination with zero padding.

Partial convolutions are implemented in TensorFlow using the convolutional operation described by Liu et al. (2018). While partial convolutions shrink holes in images, our approach reapplies the original mask to the model output. This preserves the interpretability of the results, as ground truth surface reflectance values are not available for all missing pixels that are inferred through inpainting. We compare the results of both models with partial and regular convolutions.

The reflectance product generated by the emulator is validated by comparison with MODIS SR (MOD09GA). Reference to a comprehensively validated SR product is a standard assessment for new SR products (Feng et al., 2012). In addition to direct comparison with MOD09GA, performance of emulator SR retrieval is benchmarked by comparison with the MAIAC SR product, also generated from Himawari-8 TOA reflectance. This MAIAC algorithm has been calibrated using agreement with MODIS SR, and provides a comparison between the emulator and a physically based model using the same sensor.

We use root mean square error (RMSE) as a metric of distance between prediction and MODIS SR, and evaluate each spectral band individually. RMSE is computed on the dimensionless pixel reflectance, which takes values between 0 and 1. To further assess the goodness of fit, Pearson's r, and the related metric R², are statistical measures calculated to determine the amount of variation of data explained by the model. R² always falls between 0 and 1, with a higher R² value indicating better fit of the model to the data. Pearson's r and R² are common metrics in the remote sensing domain to measure the coherence between images for validation purposes (Vinukollu et al., 2011; Tang et al., 2014). Additionally, we compute mutual information (MI) as an image matching metric. Mutual information is a dimensionless quantity that expresses how much information one random variable gives us about another. MI here is calculated with respect to the MODIS SR product.