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Clouds are a crucial component of the atmospheric energy system, particularly the radiative balance within, above, and below the troposphere. The vertical distribution of cloud mass and phase determines layer heating rates, the loss of radiation to space, and the amount of radiative heating at the surface. Thus, it is important to know how clouds are distributed both vertically and horizontally at all times of day. Satellite remote sensing is the only approach available to monitor clouds day and night around the globe. In this paper several artificial neural network (ANN) algorithms, employing several Aqua MODIS infrared channels, profiles of relative humidity and temperature from GMAO numerical weather analyses, and the retrieved total cloud visible optical depth, are trained to detect multilayer ice-over-water cloud systems and to retrieve some of their properties as identified by a year of 2008 Aqua MODIS data matched with CloudSat and CALIPSO (CC) cloud profiles. The CC lidar and radar profiles provide the vertical structure that serves as output truth for the multilayer algorithm. The neural networks were trained using one year (2008) of cloud top height data from the CC dataset, with correlation around 0.94 (0.95) and MAE as low as 0.82 (0.81) km for nonpolar regions during the day (night). Applying the trained ANN to independent year 2009 MODIS data resulted in a combined ML and single layer hit rate of 86.4% (85.1%) for nonpolar regions during the day (night). Since the ANN is trained using near-nadir MODIS pixels, infrared radiance corrections were developed as a function of view zenith angle from MODIS and applied to off-nadir pixels when processing MODIS swath data. The multilayer amount derived with the ANN is relatively invariant with increasing view zenith angle compared to the multilayer amount without the corrections.