Cloud detection physical methods are based on fixed or dynamic multispectral threshold tests. Many cloud detection algorithms have been developed over the last 60/70 years, for different instruments and considering different channels or channel combinations. As previously noted, the first cloud detection methods utilized a single test for the presence of cloud: the pixel was declared cloud if the satellite measured radiance was above or below some reference value representing clear condition. For instance, the author in [
14] set the visible threshold value by visual inspection of the satellite images, and all the pixels with value higher than the fixed threshold were declared cloudy. Subsequently, many single test methods have been proposed [
15,
16,
17], based on the assumption that some parameters must remain below a predetermined threshold. Besides, different cloud detection schemes have been developed exploiting infrared (IR) and visible (Vis) window bands [
18,
19,
20], within the International Satellite Cloud Climatology Project (ISCCP). Radiance measured in many narrow spectral bands represented a major improvement in cloud detection research. The AVHRR was the first sensor featuring two split windows, allowing a series of threshold tests. The AVHRR consists of five different channels: two in the visible range at 0.6 and 0.9 μm, one at 3.6 μm and the last two channels at 11 and 12 μm. In [
21] two parameters have been used to classify clouds, i.e., the BT in channel 5 and the BT difference in channels 3 and 4. The authors in [
22] used simultaneously the Medium Resolution Infrared Radiometer (MRIR) (Nimbus II) channel 1 (6.4-6.9μm) and channel 2 (10-11μm) to infer cloud distribution. In [
23] a method is presented to discriminate clouds over snow using the channel at 3.7μm, with the solar contribution deducted via data simulation. In [
24] the authors proposed AVHRR channel at 1.6 μm to discriminate cloudy from snow/ice. A cloud detection scheme, using a sequence of the spatial coherence method at 11μm and different dynamic visible/infrared threshold tests for daytime and nighttime respectively, has been proposed in [
25]. The algorithm provided good results except for cirrus and cloud over complex surfaces that were not correctly identified. Successively, different AVHRR operational cloud detections have been developed based on threshold test series: i) the AVHRR Processing Scheme Over cLouds, Land and Ocean (APOLLO) package [
13] implemented in several operational centres, ii) the NOAA operative cloud detection called CLAVR [
26,
27,
28], used to cloud detection in the Global 1 km Land Cover Project, and iii) the operational cloud mask for the AVHRR and the Spinning Enhanced Visible and InfraRed Imager (SEVIRI) instrument on-board the Meteosat Second Generation (MSG) implemented at the Centre de Météorologie Spatiale (CMS) in Lannion [
29]. Furthermore, in [
29] some new tests have been implemented, i.e., the infrared threshold test at 11 μm based on the surface temperature (Ts) monthly sea climatology and on Numerical Weather Prediction (NWP) air temperature forecast over sea and over land respectively, and a test series to detect cloud edge and pixels partially cloudy over land during daytime. In [
30] the authors presented the Separation of Pixels Using Aggregated Rating over Canada (SPARC) algorithm based on all AVHRR channels and surface temperature map tests. The author in [
31] proposed the SMHI Cloud ANalysis model using Digital Avhrr data (SCANDIA) cloud detection where the test thresholds consider the sun elevations. The MetOffice SEVIRI cloud detection used simulated clear-sky brightness temperatures based on NWP forecast fields in addition to the classic tests [
32]. The cloud mask algorithm implemented in the Satellite Application Facility on support to Nowcasting (SAFNWC/MSG) software package has been described in [
33]: here a series of threshold tests has been used, where most thresholds are not fixed but estimated on the basis of climatology and forecast data. An improvement and a validation of this algorithm have been showed in [
34]. A cloudiness statistic comparison over Europe based on Surface Synoptic Observations (SYNOP) reported a non-detected cloudy pixels reduction by 50%. The MODIS cloud mask algorithm was able to benefit from high spatial resolution and large spectral coverage, as it uses 22 channels in the visible and infrared regions. For the development of this algorithm, the researchers were able to take advantage of all the previous studies and, therefore, they tried to solve the difficulties encountered by previous algorithms to detect thin cirrus, fog and low cloud layers overnight, and small cumulus due to insufficient contrast with the surface radiance [
35,
36,
37,
38,
39]. In [
39] some new tests based on 7.2 μm water vapor band and 14.2 μm carbon dioxide band and some modified old tests have been proposed. The main reason for these changes is to improve the cloud detection over polar areas especially in nighttime. Further changes in polar region during nighttime, in polar region over ice and snow surfaces, over ocean and land during the nighttime, and sun-glint have been reported in [
40]. In [
41] some operative MODIS cloud mask (MYD35/MOD35) threshold tests have been modified and the clear confidence level has been estimated in order to obtain a more neutral cloud mask (CLAUDIA), i.e., a cloud detection without clear or cloudy bias. The channels used in the algorithm is similar to MOD35, but with different threshold tests and a new reflectance ratio test over bright desert. In [
42] an unbiased cloud detection algorithm for daytime based on CLAUDIA has been proposed. The algorithm has been applied to FY-3A/VIRR data on board the Chinese FengYun-3A, the thresholds have been estimated on the basis of data acquired during four months. In [
43] a method that uses the SEVIRI/MSG information to explore the pixels identified as uncertain by MODIS operative cloud detection has been proposed. In [
44] the MODIS 6 collection cloud mask was compared against 267 million cloud profiles derived from CloudSat, Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) and Infrared Pathfinder Satellite Observations (C-C) products. MODIS and C-C showed a concordance of 77.8%, composed of 20.9% clear pixels and 56.9% cloudy pixels, while 9.1% of the pixels was identified as clear and 1.8% as cloudy only by MODIS. The cloud detection algorithm of the Royal Netherlands Meteorological Institute (KNMI) [
45] utilized NWP surface temperature and synoptic data to correct the surface temperatures in order to estimate clear satellite brightness temperatures accurately. The validation has been carried out with two million synoptic observations, correctly clear detected pixels were 92% during the day and 90% during the night over land and 94% during the day and 90% during the night over sea. The threshold test critical problem is to define the values to optimize the discrimination between clear and cloudy pixels. It is generally very complicated to find thresholds suitable for all Earth surfaces and in addition, a problem with thresholds also arises from the fact that pixels might be only partially covered by clouds. The thresholds can be static, if they are estimated on the basis of climatological or empirical data, or dynamic, if they are estimated using radiative transfer models and auxiliary data (e.g., atmospheric profiles, solar and satellite angles, surface temperatures). Unfortunately, dynamic thresholds are also subject to atmospheric composition uncertainties and surface emissivity variations [
46,
47]. The use of dynamic thresholds has been proposed by numerous researchers [
25,
48,
49,
50] with the aim of improving satellite cloud detection. Over the years, in addition to new thresholds, new tests have also been proposed. In the framework of the EUMETSAT Satellite Application Facility, in [
51] new tests to identify and classify satellite pixels at medium ad high latitude have been proposed; the tests are based on a combined threshold, estimated using simulated clear-sky brightness radiances. Validation metrics for different surface and area have been reported in [
52]. In addition to the threshold methods, there are other satellite cloud detection approaches, and numerous researchers used different statistical procedures to detect clouds. In the spatial coherence methods proposed in [
53] the under-examination pixel characteristics are compared with the surrounding pixel feature statistics, and the pixel is classified as cloudy if the difference is outside a fixed threshold. In [
54] the author used a two-step procedure to distinguish clouds, first the threshold tests based on temperature and albedo have been used to perform cloud screening, after a criterion based on the standard deviation derived from the images has been used. The authors in [
55] proposed an Atmospheric Infrared Sounder (AIRS) cloud detection algorithm using an adjacent-pixel approach. The spatial coherence tests work well on uniform surfaces, such as oceans, but fail on regions with highly variable spectral signatures, such as land [
25,
56]. Some cloud detection methods are based on time-series analyses: for instance, the method presented in [
57] detected a cloudy pixel on the basis of the comparison between the measurement and the clear sky composite reference value. In [
58] this procedure has been modified by using the visible albedo standard deviation minimum estimated during a one month for each pixel and adding an value that depends on the standard deviation minimum. In [
59] the author used some threshold combinations for the spatial variability test, assuming that the near-infrared and visible reflectance ratio absolute value is correlated to surface temperature negatively. In [
60] a clear-sky algorithm based on high covariance with a reference clear-sky image has been proposed. An initial comparison showed that the algorithm offered the potential to perform better than the MODIS/MOD35 and MODIS/MYD35 cloud mask in cases where the land surface is changing rapidly and over regions covered by snow and ice. The authors in [
61] developed a cloud detection for the Interferometric monitor for greenhouse gases (IMG) over sea surface that uses a cross-correlation between the real and a synthetic spectrum. In [
62] a method to derive thresholds based on data from days between the current day and the most recent clear sky day has been proposed. Infrared radiances in the carbon dioxide band (CO
2 slicing method) to distinguish clouds and clear sky has been used in many studies [
63,
64,
65,
66]. Also, in [
67] the authors used the CO
2 or the H
2O-sensitive spectral bands to detect the High resolution Infrared Radiation Sounder (HIRS) cloudy pixels. A comparison with collocated CALIOP cloud products shows that in 80% of the pixels, the CO
2 test detects clouds correctively. In [
68] the authors proposed a method for cloud detection using Group Thresholds: the tests inside each group are applied to each pixel at the same time, the pixel was identified as cloudy depending on the results of the different tests at both fixed and dynamic thresholds. Dynamic thresholds are estimated on the basis of clear sky radiance generated using a method similar to that showed in [
57] and [
69]. The method applied to two complex cases showed that some tests work well for some types of clouds, normally difficult to be identified with traditional tests. In [
70] the authors proposed an algorithm that detected cloud pixels according to two conditions: 1) sea surface temperature lower than 1°C, and 2) the gradient of the temperature larger than a defined threshold. In [
71] the authors proposed a cloud detection based on a combination of the Geostationary Operational Environmental Satellite (GOES) visible reflectance data and a bi-spectral composite threshold method based on GOES bands at 3.7 µm and 11 µm. The authors in [
72] proposed to use the Digital Elevation Model (DEM) data in order to correct some thresholds for the Advanced Himawari Imager (AHI) aboard Himawari-8. In [
73] a non-parametric threshold algorithm has been proposed, based on surface reflectance blue band time series and the visible/short-wave infrared ratio from the MODIS/MOD09 products. In [
74] a Universal Dynamic Threshold Cloud Detection Algorithm (UDTCDA) based on a monthly surface reflectance has been proposed. Its validation compared to the MOD35/MYD35 product showed some improvements but still leaving several open questions. In [
75] a cloud detection algorithm (SCDA), with only one editable threshold and few input parameters, derived from a radiative transfer model has been proposed. Compared with Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) vertical feature cloud mask data, the percentage of SCDA cloud pixels detected was 86.08%, slightly higher than Himawari-8 cloud products (85.71%). The correct SCDA clear-sky detection percentage was 88.33%, lower than Himawari-8 clear-sky products (90.54%). The authors in [
76] proposed a MODIS cloud detection over the Yellow Sea and Bohai Sea, based on a relationship between the Normalized Difference Water Index (NDWI) (estimated at 0.56 and 0.86 μm) and the reflectance at 0.56 μm as well as the radiance at 1.38 and 1.61 μm to identify thin clouds. The comparison with different products (MOD35/MYD35, Caliop and Infrared Pathfinder Satellite Observation) showed a detection probability of 0.933% and a false alarm of 0.086. In [
77] a dynamic threshold cloud detection method has been proposed, based on the FY-3E\MERSI-LL infrared channel and some additional data: the snow cover mask, the sea and land surface temperature and topography/elevation. The results show that at low-middle latitudes the correct and the false alarm percentages are 76.46% and 8.15%, respectively. The authors in [
78] proposed and evaluated a threshold cloud mask for the High Resolution Visible (HRV) channel of Meteosat SEVIRI. It was based on low resolution channels of SEVIRI EUMETSAT cloud mask. The aim is to detect sub-pixel convective clouds that are not identified by cloud mask EUMETSAT. The main contraindication of the cloud mask HRV is the minimum cloud optical thickness that can be distinguished. This cloud optical thickness was found to be around 0.8 and 2 over the ocean and land according to the surface albedo, respectively. In [
79] a daytime cloud detection has been proposed based on a combination of sun geometry, atmosphere top reflectance, near-infrared dynamic thresholds and normalized difference vegetation index, for the GEOstationary KOrea Multi-Purpose SATellite 2A (GEO-KOMPSAT-2A, GK-2A). This study [
80] explored the performance of the minimum residual (MR) algorithm [
81] for the Advanced Himawari Imager (AHI). The MR algorithm derives cloud top pressure and cloud fraction using a combination of two or more infrared channels [
81,
82,
83,
84]. Eleven tests (9 to detected clear pixels and 2 for thin cirrus) were added to the MR algorithm. The ACM cloud mask algorithm has been described in [
85,
86]: this was based on spatial, spectral and temporal signatures. Most thresholds were derived from space-borne Lidar and geostationary imager data analysis. In comparison with the CALIPSO products the algorithm presented a total Probability of Correct Detection Metric (POD) of 91.4%, a False Cloud of 3.7% and a False Clear of 4.9%. The authors in [
84] developed a cloud detection over ocean based on four channels (0.2–4.0μm, 6.5–7.0μm, 10–1μm and 20–23μm) and on atmospheric and humidity profiles for Nimbus-3 Medium Resolution Infrared Radiometer (MRIR). In [
87] the authors proposed a clustering cloud mask algorithm over land and a threshold adaptive cloud mask algorithm over ocean in [
88] for GOES data. Different improvements in VIIRS cloud detection have been discussed extensively in many publications [
89,
90,
91,
92,
93]. In [
90] the VCM dynamic threshold algorithm has been proposed, thresholds for all the reflectance tests vary with the scattering geometry of the sun-earth sensor, while the thresholds used in the IR bands vary with the integrated water vapor for the geometry of satellite sensor. Each VCM cloud detection test utilised three sets of thresholds: a high and a low cloud-free confidence, and a medium threshold [
90]. The final threshold sets selected for each VIIRS sensor are adjusted up or down without changing the shape of the set for each VIIRS sensor during post-launch tuning. In [
93] a new procedure using the channels at 12.0 μm, at 4.0 μm and 3.7 μm to remove many misclassifications between snow and clouds has been proposed. A further discussion of VIIRS cloud mask has been reported in [
94], which analyses the differences between MODIS and VIIRS in cloud detection. For instance, MODIS detected more clouds in the middle to high levels, while VIIRS detected more clouds in the upper troposphere. These results from the sensor bandwidth of the VIIRS band were made 50% more narrow than MODIS, which means that VIIRS reduces surface contaminations contained in the MODIS observations. The cloud detection algorithm developed in [
95] included five tests, threshold were estimated on the basis of one year of data, which takes into account the seasonal and climatic variations. The accuracy was greater than 93% based on 36 images acquired over Texas and Mexico. Cloud detection approaches that examine individual channels have also been explored. This is because, completely cloud-free soundings are rare (typically on the order of 10%) for a radiometer/interferometer with a footprint around 12 km [
64,
96]. However, the instruments often have channels that are not affected by the cloud presence, where weighting functions are above the cloud top. The detection of these channels permits to use the available data and avoid the removal of hypothetically useful information, for instance discarding all the channels, perhaps only for a few channels affected by the cloud. For example, in [
97] a method for high spectral resolution has been presented; the method attempts to identify clear channels, rather than completely clear spectra.
Even the detection of thin cirrus from satellite radiometric measurements in the visible and IR window region is rather difficult because of little contrast with respect to clear pixel, especially over snow- or ice-covered surfaces. A method [
133] has been proposed to derive the cirrus temperature and emissivity from measurements in the two infrared channels (5.7–7.1 μm, 10.5–12.5 μm). The authors in [
127] introduced a threshold test at 1.38 μm useful for separating thin cirrus clouds from clear sky and thick clouds. A case study that showed some errors in the detection of cirrus using channels 1.38 µm and 1.88 µm due to surface spectral signals has been showed in [
134]. According to the authors in any case the water vapor channel at 1.8498 µm was found to be more suitable for cirrus detection compared to 1.3827 µm. Using the data acquired from AVHRR, an algorithm for the retrieval of cirrus cloud optical depth and mean effective size has been developed [
134]. This algorithm is based on the correlation between the 3.7 µm and 0.63 µm radiances. In [
135] the 0.65 µm visible and 11.5 µm infrared channels have been used to derive cirrus optical depth using AVHRR data. In [
136] the authors proposed an algorithm to estimate daytime cirrus bidirectional reflectance by means of 0.66 µm and 1.38 µm channels. The algorithm is based on the relationship between these channels. To derive ice cloud properties both during the day and during the night, the infrared split window method has been developed on the basis of the ice different absorption properties at 11 µm and 12 µm [
12,
137,
138]. In [
139] the authors demonstrated that to obtain accurate results using the 1.38 μm channel it is necessary to estimate the dynamic threshold by using the albedo and the water vapor concentration. The authors in [
140] used three MODIS IR bands at 0.645, 1.64 and 2.13, and 3.75 μm to retrieve cirrus optical thickness and effective particle size. The study reported in [
141] described an optimal estimation algorithm to retrieval cirrus properties using three MODIS bands centred at 8.5, 11, and 12 μm. In [
142] an algorithm to retrieve the tropical cirrus optical thickness using the 1 and 26 MODIS bands has been proposed. A modification based on BT (11 μm) and a multiday average land surface to minimize low water vapor content effect and high elevation has been proposed in [
143]. The algorithm validated in the Tibetan Plateau using VIIRS and MODIS data provided better accuracy than using only MODIS 1.38 μm cirrus test. In [
101] the thin cirrus detection exploited the relationship between the reflectance at 1.6 or 2.1 µm and at 11 µm. The operative cirrus [
120] detection MODIS is combined of two algorithms, for day and night. The daytime algorithm is based on the radiance at 1.38 µm, this channel is located in an absorption band of H
2O and, therefore, no radiation reflected from the Earth’s surface reaches the sensor when there is a sufficient quantity of water vapor in the atmosphere. To separate thin cirrus clouds from thick ones, the water vapor absorption channel at 6.7 µm, the window channel at 11.0 µm and the 6.7-11.0 µm difference are used, and the difference technique is also applied during the night but with the channel difference between 3.7 µm and 11.0 µm. The 3.7 µm channel is sensitive to both solar energy and terrestrial radiation, this channel is very suitable for identifying hot surface emission. In [
144] a cirrus clouds algorithm (MeCiDA) that combines morphological and multi-spectral threshold tests has been proposed. The thresholds were estimated using radiative transfer simulations. An improvement of MeCiDA, MeCiDA2 was presented in [
145] which used seven thermal channels of the SEVIRI instrument, and it can be applied to the entire MSG/SEVIRI disc. The algorithm has been adapted to Terra/MODIS and compared with the MOD06 cloud phase operation; the difference in cirrus cloud cover between MOD06 products and MeCiDA2 was less than 0.1 except for latitudes above 50
o N. The authors in [
146,
147] determined cirrus occurrence with CO
2-slicing method using HIRS data. High spectral resolution instruments bring more information regarding cirrus compared to other old instruments. Synthetic data show that radiances in the 800–1130 cm-1 are suitably sensitive to variations in cirrus optical depth and ice crystal size and shape [
130,
148,
149,
150]. An approach to estimate optical thickness of semi-transparent ice clouds by using AIRS high spectral resolution radiances has been presented in [
151]. The retrievals use window channels which have greater sensitivity to the optical thickness of ice clouds and are not very sensitive to cloud particle size and atmospheric profile errors. The authors in [
152] proposed a method for the detection of cirrus during the night by using BT differences determined from a set of selected AIRS window channels and the Total Precipitable Water (TPW) measurements derived from AIRS and AMSU-A. The authors in [
153] developed a cloud detection algorithm based on the CO
2-slicing method for high-resolution Greenhouse gases Observing SATellite (GOSAT)/FTS thermal infrared observations and reported improved accuracy with respect to the traditional method by comparing the results with coincident CALIPSO observations.