Approximate Entropy and Sample Entropy are two algorithms for determining the regularity of series of data based on the existence of patterns. Despite their similarities, the theoretical ideas behind those techniques are different but usually ignored. This paper aims to be a complete guideline of the theory and application of the algorithms, intended to explain their characteristics in detail to researchers from different fields. While initially developed for physiological applications, both algorithms have been used in other fields such as medicine, telecommunications, economics or Earth sciences. In this paper, we explain the theoretical aspects involving Information Theory and Chaos Theory, provide simple source codes for their computation, and illustrate the techniques with a step by step example of how to use the algorithms properly. This paper is not intended to be an exhaustive review of all previous applications of the algorithms but rather a comprehensive tutorial where no previous knowledge is required to understand the methodology.

The cloud droplet number concentration (N_d) is of central interest to improve the understanding of cloud physics and for quantifying the effective radiative forcing by aerosol‐cloud interactions. Current standard satellite retrievals do not operationally provide N_d, but it can be inferred from retrievals of cloud optical depth (τ_c) cloud droplet effective radius (r_e) and cloud top temperature. This review summarizes issues with this approach and quantifies uncertainties. A total relative uncertainty of 78% is inferred for pixel‐level retrievals for relatively homogeneous, optically thick and unobscured stratiform clouds with favorable viewing geometry. The uncertainty is even greater if these conditions are not met. For averages over 1° ×1° regions the uncertainty is reduced to 54% assuming random errors for instrument uncertainties. In contrast, the few evaluation studies against reference in situ observations suggest much better accuracy with little variability in the bias. More such studies are required for a better error characterization. N_d uncertainty is dominated by errors in r_e, and therefore, improvements in r_e retrievals would greatly improve the quality of the N_d retrievals. Recommendations are made for how this might be achieved. Some existing N_d data sets are compared and discussed, and best practices for the use of N_d data from current passive instruments (e.g., filtering criteria) are recommended. Emerging alternative N_d estimates are also considered. First, new ideas to use additional information from existing and upcoming spaceborne instruments are discussed, and second, approaches using high‐quality ground‐based observations are examined.

The National Oceanic and Atmospheric Administration (NOAA) Deep Space Climate Observatory (DSCOVR) spacecraft was launched on 11 February 2015 and in June 2015 achieved its orbit at the first Lagrange point (L1), 1.5 million km from Earth toward the sun. There are two National Aeronautics and Space Administration (NASA) Earth-observing instruments on board: the Earth Polychromatic Imaging Camera (EPIC) and the National Institute of Standards and Technology Advanced Radiometer (NISTAR). The purpose of this paper is to describe various capabilities of the DSCOVR EPIC instrument. EPIC views the entire sunlit Earth from sunrise to sunset at the backscattering direction (scattering angles between 168.5° and 175.5°) with 10 narrowband filters: 317, 325, 340, 388, 443, 552, 680, 688, 764, and 779 nm. We discuss a number of preprocessing steps necessary for EPIC calibration including the geolocation algorithm and the radiometric calibration for each wavelength channel in terms of EPIC counts per second for conversion to reflectance units. The principal EPIC products are total ozone (O₃) amount, scene reflectivity, erythemal irradiance, ultraviolet (UV) aerosol properties, sulfur dioxide (SO₂) for volcanic eruptions, surface spectral reflectance, vegetation properties, and cloud products including cloud height. Finally, we describe the observation of horizontally oriented ice crystals in clouds and the unexpected use of the O₂ B-band absorption for vegetation properties.