Fog is commonly perceived as a hazardous weather situation that can impact traffic systems as well as the economy . In arid environments like the Namib desert, fog can act as a critical source of water that enables life for diverse species and helps to sustain ecosystems e.g.,. As such, knowledge on the exact occurrence and spatiotemporal patterns of fog holds potential, ranging from socioeconomic benefits to a better understanding of fog processes and fog-driven ecosystems.

As previous studies e.g., have shown, geostationary satellites have the potential to draw a spatiotemporally coherent picture of the occurrence of fog and low clouds (FLCs). However, information on FLCs from satellites is typically inferred using separate daytime e.g., and night-time e.g., algorithms, disrupting our view of fog development at a critical time of its life cycle, as typically, shortwave radiative heating starts the dissipation of fog shortly after sunrise . This break in retrieval techniques has thus limited the applicability of satellite-based FLC observations for the analysis of entire fog life cycles. have developed an approach to continuously monitor fog from a geostationary satellite platform; however, their algorithm essentially consisted of three different modes, day, dusk/dawn and night, and cannot be described as stationary in time. While, for visualization purposes, 24 h false-color image products may be used in case studies, these images are not well suited for quantitative analyses. The overarching goal of this study is thus to develop and validate a single, diurnally stable satellite retrieval of FLCs over land to enable the exploration of currently untapped potentials of satellite-based analyses of FLCs.

Past satellite retrieval algorithms of FLCs have typically consisted of a sequential application of a number of spectral tests on the basis of individual pixels in the initial classification and a subsequent merging of FLC pixels to entities e.g.,. Using only spectral information, FLCs can be detected using a combination of brightness temperatures in the middle infrared (MIR) and thermal infrared (TIR) . As during daytime, the MIR has a solar component, separate daytime and night-time retrievals are needed. A stable and fully diurnal retrieval of FLCs would thus have to solely rely on observations in the TIR. However, as state, a purely TIR-based detection of FLCs is not possible, as the brightness temperatures of FLCs and land surfaces are too similar.

In the realm of image analysis and machine vision, the spatial context of a pixel is often exploited for its classification . In recent times, the utilization of contextual information has become more frequent in environmental remote-sensing techniques e.g.,. For FLCs, distinct spatial patterns that vary over time are to be expected due to the inversion-limited homogeneous cloud top and the coherent movement of FLC patches over the Earth surface. The guiding hypothesis of this study is as follows.

By a combination of spectral tests and contextual information, FLCs can be robustly detected using only satellite observations in the thermal infrared and enable new insights into the diurnal patterns of FLCs and their spatial variability.

In this study, FLCs are detected along the southwestern African coast with a specific focus on the central Namib desert, where fog is an important part of local ecosystems . Knowledge on the spatiotemporal occurrence of Namib-region fog is incomplete , and while it is commonly tied to the quasi-persistent stratiform clouds in the southeastern Atlantic , the processes that lead to the formation of fog are still controversially discussed, as recently, found indications of frequent water from freshwater sources in fog and related this to radiatively driven fog formation.

The data used and the novel FLC detection technique are described in Sect. 2, and a statistical evaluation of the algorithm is given in Sect. 3. Spatiotemporal patterns of fog and low clouds in the Namib are presented in Sect. 4, and conclusions and an outlook are given in Sect. 5.

Figure a summarizes validation results qualitatively and quantitatively. The red histogram line shows the bimodal distribution of the aggregated night-time net radiation measurements at the nine FogNet stations for the period of 2015–2017 (excluding high cloud and difficult observations), whereas the blue line represents the same station measurements, filtered for satellite-detected FLC situations. High clouds and difficult situations (grey line) are excluded from the validation as they cannot be clearly separated from clear or FLC situations with surface net radiation measurements. It is apparent that most of the ground-truth FLC situations are captured by the satellite product (POD of 0.94), with only a few false alarms (FAR of 0.12). The product features a high accuracy (PC of 0.97) with only a marginal positive bias (BS of 1.01). This leads to an overall high quality of the classification as expressed by a CSI of 0.83 and a HSS of 0.89. All in all, the validation is based on 325 836 co-located observations. As illustrated in Fig. b, there is relatively little variation in the validation results between the different FogNet stations. The most inland station Garnet Koppie (GK) accounts for all outliers in Fig. b and has the highest false-alarm rate. Here, FLC occurrence frequency is thus overestimated, leading to lower overall skill. This can be attributed to the rarity of the FLC occurrence in this region (cf. Fig. a), where a single, random misclassification has a higher relative impact. The overall accuracy of the product is considerably higher than current state-of-the-art algorithms for Europe e.g.,, probably in part due to the more complex and diverse terrain and cloud structures that have to be discriminated there, and comparable to the SEVIRI-based FLC product for this region by . However, the algorithm in is tailored to two specific times of the day and includes satellite observations in the visible and near-infrared spectrum. These comparisons with validation results from other studies are of an indicative nature, as differences could also be caused by the reference data used as ground truth or different periods considered.

It should be noted that the comparison of station-level net radiation measurements with a binary satellite product is certainly not perfect. Two potential sources of error may specifically affect the validation results:

A large difference in spatial resolution of the two observations exists. While station measurements are temporally averaged with the intent of approximating spatial variation within the area covered by a SEVIRI pixel as in, the difference in field of view cannot be neglected. The difference in spatial resolution is expected to randomly lead to erroneous comparisons in both ways and thus not markedly affect the validation results. This may explain the overestimation of the FLC occurrence frequency at GK, as the effect of this small random error on the validation measures scales inversely with FLC occurrence.

In addition to the validation described here, considerable effort has gone into the systematic evaluation of classifications of individual scenes as illustrated in Fig. . In light of these arguments, the validation results give confidence in the skill of the novel algorithm and the derived FLC product, which is well suited for the purpose of characterizing the spatial and temporal patterns of FLCs in the Namib desert.

Figure a shows the average FLC occurrence frequency in the study area over the study period. FLCs most frequently occur in the plane regions along the coastline (cf. Fig. c). Three core regions of the FLC occurrence can be identified in the Angolan parts of the Namib at around 16–17∘ S, in a region stretching from Walvis Bay at 23∘ S northwards to about 18∘ S and at Alexander Bay at around 28∘ S. The patterns closely resemble those found by and qualitatively and quantitatively. As illustrated by Fig. b, in some regions a reliable retrieval of FLCs is often not possible. This can be related to frequent occurrences of high clouds in the tropical northern parts of the study area, too little spatial variance in the clear-sky composites, e.g., in the region of the Etendeka flood basalts at 20∘ S and 14∘ E , or where the monthly composites were not stationary in time in some northeastern parts of the study area.

Figure  illustrates the average diurnal cycle of FLCs at all FogNet stations as retrieved from the satellite. It is apparent that at stations close to the coast (purple-blue lines), FLCs occur much more frequently than further inland. The general diurnal behavior of FLCs is similar at all stations, with a distinct peak of the FLC occurrence at night between 03:30 UTC with 9 % relative occurrence frequency of FLCs at Garnet Koppie (GK) and 06:15 UTC with 64 % at SW, and typically a fairly fast dissipation shortly after sunrise. However, distinct features of the diurnal cycle of FLCs can be identified at some stations. At the station Saltworks (SW), located directly at the coastline (cf. Fig. ), FLCs tend to start to occur in the early afternoon, several hours before other stations are overcast. This could potentially be related to local land–sea winds that transport FLCs from the ocean over land during this time. In general, a time lag exists at the average start of the diurnal cycle, as well as in the time of the diurnal maximum occurrence frequency that seems to be dependent on the longitudinal position of the stations, which approximates their distance to the coastline. This time lag is indicative of a region that is generally dominated by FLCs that form at the coast or over the ocean and is then advected inland, as described by , and , contrasting more recent findings by . As FLCs are advected inland, locations close to the coastline are overcast first. At the coast, FLCs not only occur earlier in the day but typically also persists longer than further inland, where FLCs tend to start dissipating before sunrise. The dissipation rate (negative δ FLS occurrence / δ time in the morning hours) at inland stations is considerably lower than closer to the coast, which can probably be attributed to stronger solar irradiance later in the day. It should be noted that the figure represents highly aggregated information on the average diurnal cycle of FLCs and does not preclude other formation or dissipation processes.

As a detailed statistical analysis of the full life cycle of FLCs and their seasonal behavior is not within the scope of this paper, this example is intended to illustrate the potential of the novel algorithm for the analysis of spatiotemporal patterns of fog and low clouds over land.

The central aim of this study was to develop the first thermal-infrared-only and thereby diurnally stable satellite retrieval of fog and low clouds. The algorithm design uses a combination of spectral tests and contextual information in order to retrieve FLCs. A structural similarity index is computed, comparing each satellite scene with cloud-free composites to discriminate between land surfaces and FLCs. The novel algorithm is thereby relatively independent from exact spectral thresholds and thus has the potential to be easily applied to other regions and to generate climate data sets. An operational deployment is possible with small adjustments in algorithm design and holds potential for the prediction of FLC dissipation. In the future, the value of the derived FLC product may be further enhanced with a retrieval of cloud-base altitudes for the separation of low-level clouds from ground fog.

The algorithm was applied to detect spatial and temporal patterns of Namib-region FLCs and was validated against net radiation measurements at the FogNet station network located in the central Namib region. The algorithm shows good overall detection accuracy, with a few false alarms and a small positive bias, and relatively little station-to-station variation. FLCs most frequently occur close to the southwestern African coastline, with Walvis Bay among the core regions, confirming findings from and . The diurnal cycle of FLCs is described for the locations of the FogNet stations. Marked differences in the timing of the FLC occurrence and temporal persistence are found. The time lag of the FLC occurrence from the coast to inland regions may be attributed to the advection of FLCs from the coast inland, a typical feature of the region . FLCs persist longer in coastal regions than further inland and but then dissipates more rapidly after sunrise.

The study shows the potential of the diurnal FLC algorithm to study fog and low-cloud patterns, processes and life cycles. Future research efforts should focus on coherently mapping diurnal characteristics of FLCs; further understanding fog formation processes, specifically considering knowledge on the factors that drive low-level clouds in the southeastern Atlantic e.g.,, and potentially detecting changes in FLC occurrence. This may best be achieved by combining the satellite retrievals with numerical modeling and ground-based observations, and will be undertaken within the ongoing research project Namib Fog Life Cycle Analysis (NaFoLiCA).