The Integrated Characterization of Energy, Clouds, Atmospheric state and Precipitation at Summit (ICECAPS) project collected continuous observations of the atmosphere above Summit from 2010 to 2021 . At the highest point of the Greenland Ice Sheet (-38.45∘ E, 72.58∘ N, 3250 m a.s.l.), the atmosphere above Summit is extremely dry, and temperatures are rarely above freezing . The ice sheet surface is homogeneous in all directions so that the atmospheric conditions at Summit are minimally influenced by local topography. During the summer (JJAS), freezing fog (defined as fog that reduces visibility to less than 1000 m) was reported by on-site observers 10 % of the time (2010–2020). These fogs can occur when surface temperatures are as low as -35 ∘C and almost always contain supercooled liquid droplets , presumably due to a lack of ice-nucleating particles (near-surface aerosol concentrations at Summit are exceptionally low, ).

The Aerosol Cloud Experiment (ACE) was added to the ICECAPS project in 2019 and included the addition of temperature and humidity sensors and sonic anemometers at four levels on a 15 m tower for high resolution monitoring of the near-surface turbulent and thermodynamic structure . For this study, we focus on fog events during the summer of 2019 for which time the multi-level temperature data from the tower are available. Figure 1 shows the experimental setup of the MWR and AERI at Summit, and Table 1 provides details of all the ICECAPS-ACE instrumentation used in this study.

We use the tower-mounted temperature probes (Vaisala HMP155, installed in aspirated shields) as “true” reference points to assess the performance of the surface temperature retrievals from the MWR and AERI. The instrument uncertainty for the HMP155 is <±0.3 ∘C. For this study, we define the “surface” as the height of the raised platform photographed in Fig. 1, where both the AERI and MWR windows are situated. This surface is aligned with the HMP155 sensor mounted on the tower at 4 m above the snow surface; measurements from this sensor are henceforth referred to as surface temperature. Measurements from the HMP155 sensor located 10 m higher on the tower are compared to the 10 m thermodynamic retrievals. The same height adjustment is applied to the radiosonde profiles prior to comparison (which are launched approximately 3 m below the platform “surface” or 1 m above the snow surface). The uncertainty in the radiosonde measurements is ±4 % relative humidity and ±0.3 ∘C .

For forecasting and nowcasting purposes, fog is usually defined by a threshold in horizontal visibility (typically <1000 m), which has important implications from a safety perspective . However, limiting the definition of fogs to those that reduce visibility to <1000 m encourages thinner fogs (or mists) to be ignored or incorrectly classified as clear-sky events. Being able to accurately measure thinner fogs is extremely important because (a) they form the precursor to thick fog, (b) they modify the surface moisture, aerosol, temperature, and radiative structure that might impact fog development further down the line , and (c) they can have important radiative and climatological impacts even without developing into a thick fog . Because both the MWR and AERI are directly sensitive to the radiative impact of fog (as opposed to visibility), for the purpose of this study, we define fog as the presence of near-surface liquid water that has a detectable radiative impact. Radiation fogs typically form under clear skies; as such, we only consider cases of fog under otherwise clear skies, which allows us to be certain that the LWP retrievals are a measure of fog LWP alone. The applicability of the results of this study to other types of fog is discussed in Sect. 4.

To identify case studies of radiation fog under otherwise clear skies, we only considered times when there were no clouds detected by the MMCR, which has a lowest range gate close to 200 m a.g.l. and is therefore insensitive to fog, and when there was no precipitation detected by the POSS, which is particularly sensitive to ice crystals. Of the times that these criteria were met, fog was provisionally identified when the 962 cm-1 downwelling radiance measured by the AERI was greater than a threshold of 1.7 RU (radiance units, 1 RU = 1 mW m-2 sr-1 cm-1). In the extremely dry atmosphere over Summit, the 962 cm-1 microwindow is almost completely transparent under clear skies and is therefore particularly sensitive to the presence of clouds (e.g. ). The threshold value of 1.7 RU was 3 standard deviations above the mean 962 cm-1 radiance during 179 verified clear-sky hours between June and September 2019 and therefore identified when the AERI window was obscured by cloud/fog with a detectable radiative impact. Ambiguous cases when there was evidence that something other than fog may have caused the 962 cm-1 radiance increase, such as clear-sky ice crystal precipitation, high cirrus clouds, or the plume from the station generator, were removed based on the observer log and photographs. Table 3 details the 12 cases that met the criteria above and were selected for the intercomparison. In each case, the fog formed in late evening or early morning and usually dissipated by midday, as is characteristic of radiation fog (Fig. 2). Note that for 11 of these cases, there was no cloud base height detected by the ceilometer during the event, indicating that the events were indeed fog as opposed to low cloud. The only exception is for case ID 11, during which the ceilometer detected a cloud base between 52 and 105 m intermittently between periods of obscured vertical visibility.

We retrieve boundary layer thermodynamic profiles (temperature, T, and water vapour mixing ratio, wv) and LWP at a 5 min temporal resolution using the TROPoe iterative optimal estimation physical retrieval algorithm that is detailed in and . TROPoe uses a forward model to calculate the observation vector from the current state vector, where the state vector is the retrieved thermodynamic profile and LWP, and the observation vector is the downwelling radiance observed by either the polar AERI or HATPRO MWR. Note that the observation vector from the MWR includes data from the elevation scans at 10.2, 16.2, and 19.2 degrees for the four most opaque V-band channels; including elevation scans in the retrieval has been shown to increase the accuracy of the retrieved temperature profile . The forward models are line-by-line radiative transfer models; the LBLRTM version 12.1 simulates the AERI spectral radiances, and the monochromatic MonoRTM simulates the MWR radiances. Note that the latter uses the improved temperature-dependent liquid water absorption coefficients . The state vector is incrementally adjusted to minimise the difference between the forward model calculation and the observation vector until the change between successive iterations is less than the uncertainty in the current state vector .

Due to the limited vertical resolution of the MWR, operational retrievals of thermodynamic profiles from MWRs are typically also constrained by an in-situ measurement of surface temperature, usually from a sensor that is integrated with the MWR (e.g. ). For this study, we run TROPoe in three physically consistent configurations: once using only the PAERI radiances as the observation vector (as in , henceforth named AERIoe), once using only the microwave brightness temperature observations from the HATPRO MWR (as in ) to provide a direct comparison of the relative sensitivity of the two instruments (henceforth named MWRoe), and lastly using the same configuration as the MWRoe but this time being additionally constrained by the in-situ surface temperature and water vapour observations from the HMP155, as it would be in an operational setting (henceforth named MWRoe-sfc).

Thermodynamic retrieval from passive spectral radiance observations is an ill-posed problem; hence the optimal-estimation retrieval is necessarily constrained by an a priori probability density function (the prior) that provides the first guess state vector that stabilises the retrieval . Typically, a location-specific prior can be derived from a database of historical observations (i.e. from radiosonde profiles) at or near the location of interest. The prior for Summit is computed from 1756 summer radiosonde launches (2010–2018). However, due to the rapid warming in the Arctic (e.g. ), this does not encapsulate the exceptionally warm and moist conditions at Summit during the summer of 2019 . To allow the retrievals more flexibility to account for the exceptional conditions, we have re-centred the prior using the mean of the three radiosondes closest to the retrieval date (whilst conserving relative humidity) and increased the wv variance in the prior by a factor of 4 at the surface (decreasing to 0 by 1 km a.g.l.).

Previous studies have used cloud base height (CBH) derived from a collocated ceilometer as an additional constraint on the retrieval, which allows the retrieval of below-cloud thermodynamic profiles from the AERI in the presence of thick clouds . Because we focus on radiation fogs under otherwise clear skies – which are, by definition, based at the surface – we initially assumed that the CBH is 5 m a.g.l. in all cases. However, large temperature biases (>5 K) in the AERIoe retrievals during fog illustrated that the TROPoe is highly sensitive to the CBH assumption when using AERI data as an input (see Sect. 3.1). For the final retrievals, we used CBH from the ceilometer to constrain the retrieval if the ceilometer detected a cloud base within 10 min of the retrieval time; if the ceilometer reported obscured vertical visibility, then the detected vertical visibility height was input as the CBH. If neither of these situations occurred, the CBH assumption defaulted to 5 m a.g.l. The sensitivity of the retrievals to this choice is discussed further in Sect. 3.1. We ran all retrievals for up to 3 h before and after each fog event to encapsulate the atmospheric conditions on either side of radiation fog formation. The retrieval algorithm outputs 1σ uncertainties for all variables that incorporate the random error from the observations, the correlated error propagated from the prior, and the sensitivity of the forward model. Errors related to the CBH assumption or phase assumption (when only liquid water is considered) are not included, and we discuss these below in Sects. 3.1 and 4.

To evaluate the three TROPoe retrieval configurations (AERIoe, MWRoe, and MWRoe-sfc), we focus on three aspects that are crucial for making accurate fog forecasts with NWP models, for visibility nowcasting, and for understanding the climatic impact of fog:

accurate representation of the structure of the temperature and humidity profile in the lowest 1 km a.g.l.

To evaluate the accuracy of the temperature and humidity profile retrievals in the lowest 1 km a.g.l., we assess the performance of the MWRoe-sfc and AERIoe against 14 coincident radiosonde profiles by evaluating the mean bias and spread between the radiosonde profiles (truth) and the retrievals. We use modified Taylor diagrams to assess how well the retrieved profiles capture the shape of the true profiles by considering the Pearson's correlation coefficient and the ratio of the standard deviation of the retrieval to that of the truth profile. These results allow for a direct comparison with , who compare TROPoe retrievals based on MWR and AERI observations to a larger number of radiosonde profiles (127) in southwestern Germany (but only consider clear-sky days or clouds with bases >500 m a.g.l.).

To evaluate the ability of each retrieval to detect the occurrence and strength of surface-based temperature inversions, we compare the retrieved surface (0 m) and 10 m temperatures with measurements from in-situ temperature sensors (see Sect. 2.1). We define the inversion “strength” as the 10–0 m temperature and evaluate the Pearson's correlation coefficients and root-mean-squared error (RMSE) between the retrieved values and the “truth” (the in-situ temperature sensors). Although we are limited by a maximum sensor height on the tower, we expect the 10–0 m temperature difference to be a good indicator of whether or not the retrieval captures the surface-based temperature inversion, since most of the inversion during radiation fog often occurs in the lowest 10 m a.g.l. . We also compare the retrieved inversion strength over a deeper layer (100–10 m) with the 14 coincident radiosonde profiles.

Finally, in the absence of an independent method of determining LWP, we evaluate the ability of each retrieval to detect the initial increase in LWP, which is defined in this study as an indicator of fog formation that might lead to visibility reduction, with “fog onset” being defined as the point at which the retrieved LWP minus 2σ uncertainty (which is directly computed by TROPoe) increases above 0.1 g m-2 for at least 10 min. We then compare the difference in fog onset detection time between the MWRoe and the AERIoe for each case study. We use the ceilometer range-corrected attenuated backscatter as an independent indicator of fog onset time. This methodology allows us to compare the sensitivity of the two sets of retrievals to small increases in liquid water that can begin to reduce visibility and impact radiative energy fluxes at the surface.

All 2045 retrievals from each configuration of TROPoe converged, meaning that the retrieval algorithm was able to find a solution within the maximum number of iterations. The mean RMSE between the final forward model calculation and the observed PAERI radiance across all AERIoe retrievals was 0.54±0.09 RU, which is of the order of the instrument noise level . For the MWRoe retrievals the mean RMSE between the final forward model calculation and the MWR brightness temperatures was 0.38±0.12 K, again within the instrument noise level . The MWRoe and MWRoe-sfc are comparable in terms of RMSE, liquid water path retrieval and thermodynamic profile retrievals above 100 m a.g.l., so we only discuss the difference between the MWRoe and MWRoe-sfc when we consider the ability of each retrieval configuration to capture the strong surface-based temperature inversions associated with radiation fog in Sect. 3.3.

The AERIoe retrievals were very sensitive to the cloud base height (CBH) assumption. Because we are only considering cases of radiation fog under otherwise clear skies, the first iteration of retrievals assumed that, if liquid water was detected, the cloud base height was 5 m a.g.l., removing the requirement for additional instrumentation to detect CBH. Figure 3a demonstrates that, under this assumption, the AERIoe retrieved unrealistic temperature profiles in some cases when the fog was optically thick (i.e. ceilometer is obscured) or when the ceilometer detected a cloud with a base close to 1300 m a.g.l. prior to the start of the fog event. The unrealistic temperature profiles manifest as exceptionally warm temperatures just above the surface, indicated by red colours in Fig. 3.

Previous AERIoe algorithms have used the ceilometer “first cloud base height field” (an output of the Vaisala proprietary software) to estimate CBH . Using this assumption rather than simply assuming the CBH to be 5 m a.g.l. reduced the temperature profile artefacts in some but not all cases (Fig. 3b). The ceilometer software also outputs a vertical visibility field (described in ) when the extinction profile is such that the atmosphere is obscured but no distinct cloud base can be determined, as often happens in the case of thick fog. The remaining artefacts in the example case study occur when the ceilometer reports a vertical visibility value (Fig. 3b). When we used the vertical visibility field in addition to the first cloud base height field to provide the CBH assumption in the AERIoe retrieval, the remaining artefacts were removed (Fig. 3c).

Even if the fog is reducing visibility at the surface, the cloud base height is the height at which the fog becomes optically thick to the PAERI, which is similar to when it becomes optically thick for the ceilometer (which uses radiation in the near-infrared, 905 nm). Figure 3 shows that a difference in CBH of just 30 m can make a significant difference to the retrieval when the cloud is close to the surface, demonstrating that accurate CBH measurements are a necessary input to the AERIoe for retrieving thermodynamic profiles in the presence of fog or near-surface clouds. In contrast, the MWRoe was not sensitive to the CBH assumption, because clouds are markedly more transparent at microwave frequencies. For the remainder of this study, all retrieval configurations derive CBH from both the first cloud base height and the vertical visibility field of the ceilometer.

The AERIoe temperature profiles (0–1 km a.g.l.) compared extremely well to the 14 radiosonde profiles considered, with a mean bias of -0.43 ∘C and a mean RMSE of 1.0 ∘C (Fig. 4a). The MWRoe temperature profiles exhibited a vertically consistent negative bias compared to the radiosonde profiles, with an average value of -1.5 ∘C and an average RMSE of 1.7 ∘C (Fig. 4a). Although investigating the source of the negative bias in the MWRoe temperature profile is outside the scope of this study, such systematic biases can often be corrected for, and the similar spread in bias magnitude between the AERIoe and the MWRoe temperature retrievals imply that the performance of the two sets of retrievals would be similar after an additional bias correction (Fig. 4a). For both sets of retrievals, the temperature RMSE is largest in the lowest 50 m a.g.l., where it approaches 2.0 ∘C (Fig. 4a); this is also the case for the MWRoe-sfc, which looks qualitatively similar (not shown).

For water vapour, the performance of the AERIoe and MWRoe retrievals compared to the radiosonde profiles was very similar (Fig. 4b). Neither set of retrievals exhibited a mean bias, and the RMSE of the AERIoe retrievals was slightly smaller than the MWRoe up to 800 m a.g.l., with a mean value of 0.39 g kg-1 (compared to 0.44 g kg-1 for the MWRoe).

Figure 4c and d show that both sets of temperature profile retrievals are better correlated with the radiosonde profiles (r>0.98, Fig. 4c,) than the water vapour profile retrievals, which in some cases have correlation coefficients <0.7 (Fig. 4d), and the spread in the standard deviation ratio is much smaller for the temperature retrievals (0.9–1.2) than for the water vapour profile retrievals (0.6–1.3). The AERIoe retrievals (for both temperature and water vapour) have a similar spread in correlation coefficients and standard deviation ratios than the MWRoe retrievals, indicating that the performance of the two retrievals was comparable across this subset of profiles.

The AERIoe temperature retrievals at 0 and 10 m a.g.l. are equally well correlated with observations (r=0.99, RMSE=1.1 ∘C), indicating that the AERIoe captures vertical temperature gradients in the lowest 10 m of the atmosphere well and retrieves surface temperatures with consistently high accuracy (Fig. 5). In comparison, the MWRoe retrievals perform worse than the AERIoe at both heights, with r=0.86, RMSE=4.2 ∘C at 0 m, and r=0.95, RMSE=2.1 ∘C at 10 m (Fig. 5). Notably, the performance of the MWRoe is worst at 0 m, where the MWRoe typically has a warm bias at colder temperatures (72 % of the time when T<-7 ∘C) and a cold bias at warmer temperatures (93 % of the time when T>-7 ∘C). This bias reduced at 10 m, implying that the temperature lapse rate between 0 and 10 m a.g.l. is often incorrect in the MWRoe retrieval (Fig. 5).

For the MWRoe-sfc, which includes the surface temperature as an additional constraint in the retrieval, the correlation with in-situ surface temperature measurement is perfect, suggesting that very little additional variability is introduced by the microwave radiance measurements. Despite this, the 10 m temperature retrievals from the MWRoe-sfc perform only marginally better than those of the MWRoe compared to the in-situ measurements and not as well as the AERIoe, which did not have the advantage of the extra information from the in-situ surface temperature probe (Fig. 5). This suggests that constraining the retrieval by the in-situ surface temperature does not translate to improvements in the temperature profile retrieval above that level.

Figure 6a confirms that the MWRoe is not able to capture the 0–10 m temperature lapse rate by demonstrating that there is no correlation between the measured surface-inversion strength (10–0 m T) and that retrieved by the MWRoe. In fact, the 10–0 m lapse rate is essentially constant in the MWRoe, implying that retrieved temperatures at 0 and 10 m are highly correlated. In contrast, the AERIoe surface-inversion strength is well correlated with in-situ measurements (r=0.80) with an RMSE of 1.9 ∘C (Fig. 6a), demonstrating that the AERIoe can accurately retrieve shallow surface temperature inversions with lapse rates of up to -1.2 ∘C m-1. When the in-situ surface temperatures are used to constrain the MWR retrieval (in the MWRoe-sfc), the ability of the retrieval to capture the shallow temperature inversions is considerably improved (Fig. 6a). Note that the correlation between the MWRoe-sfc near-surface temperature inversion and the in-situ measurements in Fig. 6a is not a fair assessment of performance, since the retrieval results are not independent from the in-situ measurements. Nonetheless, it highlights the importance of using accurate surface temperature measurements to constrain MWR temperature retrievals.

The radiosonde profiles provide an alternative independent measure of surface-inversion strength, allowing the comparison of the ability of each retrieval configuration to capture surface temperature inversions over a deeper layer. Figure 6b compares the 100–10 m retrieved inversion strength with that measured by the 14 coincident radiosonde profiles. Over this depth, the RMSE of the AERIoe and the MWRoe-sfc are comparable to the values for the 10–0 m comparison (1.65 and 1.83 ∘C m-1 respectively), but the MWRoe RMSE remains much larger (2.22 ∘C m-1), demonstrating that the MWRoe alone is not capable of accurate retrievals of surface temperature inversions even in this deeper layer. Only the AERIoe retrievals in this case are significantly correlated (r=0.46) with the radiosonde measurements, although the small number of radiosondes available for comparison makes it difficult to draw robust conclusions from this result. compared AERI-derived lapse rate 100–10 m against more than 200 radiosondes in Oklahoma (southern US) and found very good agreement with r2 values >0.93.

The reason that the AERIoe can accurately retrieve shallow surface-based temperature inversions but the MWRoe cannot is because the AERI infrared radiance measurements theoretically contain much more information about the near-surface temperature profile than the MWR brightness temperatures . Figure 7 supports this by illustrating that the degrees of freedom for signal for temperature from the AERIoe retrievals is greater than that from the MWRoe retrievals, especially at the surface. The degrees of freedom for signal is a measure of the number of independent pieces of information from the observation vector that the retrieval used to generate the solution . Figure 7 shows that the AERIoe has around 6 times as much information about the surface temperature than the MWRoe and twice as much at 10 m. The mean degrees of freedom for signal for the surface temperature retrieval is over 4 times higher for the MWRoe-sfc compared to the MWRoe due to the additional information about the surface temperature in the observation vector. However, above the surface, the AERIoe still contains more information about the temperature profile than the MWRoe-sfc in the lowest 500 m of the boundary layer, the region in which accurate temperature profiles in NWP models are critical for successful fog forecasts .

The LWP retrievals from the AERIoe and MWRoe were well correlated (r=0.88) and fell within ±5 g m-2 of each other in ∼90 % of all retrievals; however, on occasion, there were discrepancies of up to 10 g m-2 (Fig. 8), which can be equivalent to significant differences in horizontal visibility and net surface radiative forcing (see example in Sect. 1).

Although we do not have an independent measure of the “true” LWP, Fig. 9 illustrates the difference in the sensitivity of the MWRoe and the AERIoe to LWP as a function of LWP magnitude. The PAERI radiance observations are very sensitive to changes in LWP when the LWP is small, and so the 1σ uncertainty in the retrieved LWP from the AERIoe is less than 1 g m-2 for LWP<20 g m-2 (or less than 10 %, Fig. 9). In contrast, the uncertainties in LWP derived from MWR brightness temperatures are related to absolute radiometric uncertainties that are approximately constant with respect to LWP, equating to at least 50 % uncertainty for LWP<10 g m-2 (Fig. 9). However, as the LWP approaches opacity in the infrared (>40 g m-2), the sensitivity of the PAERI radiance observations to changes in LWP decreases until the uncertainties in the LWP retrievals from the AERIoe become equivalent to those from the MWRoe (∼3 g m-2 or ∼6 % uncertainty at 50 g m-2).

The high sensitivity of the AERIoe to changes in LWP when LWP is small means that the increase in LWP associated with the development of radiation fog under clear skies is detected earlier in the AERIoe retrievals compared to the MWRoe retrievals (following our fog definition as the presence of near-surface liquid water that has a detectable radiative impact). The increased sensitivity of the infrared over the microwave to small LWP values was described in . This is illustrated in Fig. 10, which shows the development of LWP during the 15 July 2019 case study. Shortly after 23 h on 15 July, the AERIoe detected a significant LWP that continued to increase gradually at a rate of ∼1.4 g m-2 h-1, until 02:00 h on 16 July, after which it increased rapidly to ∼30 g m-2 at 03:00 h (Fig. 10). In contrast, due to the larger uncertainties in the MWRoe LWP retrieval, the MWRoe LWP did not increase to a value that was significantly different from the noise until the onset of the rapid LWP increase just after 02:00 h.

For independent verification, we also determine fog onset from the ceilometer range-corrected attenuated backscatter. We define the ceilometer fog onset as being where the 5 min mean total backscatter increases by more than 3 standard deviations from the mean clear-sky backscatter at Summit between 1 June and 30 September 2019 (the mean clear-sky backscatter is determined using the same subset of verified clear-sky hours used to identify fog events from the AERI radiance, Sect. 2.2). Ceilometer attenuated backscatter is sensitive to the scattering cross section of molecules and particles in the atmosphere and can be sensitive to the presence of atmospheric aerosols (e.g. ) and to the hygroscopic growth of aerosols prior to their activation into fog droplets , the latter of which can be a precursor to radiation fog formation . At Summit, the aerosol scattering cross section is usually extremely small (<2×10-6 m-1 at 550 nm, ), and any signal due to the presence of aerosols is incorporated into the calculation into the mean clear-sky backscatter. We do not distinguish between the detection of aerosol hygroscopic growth and droplet formation in the ceilometer backscatter.

For the 15 July 2019 case, the ceilometer detected fog onset shortly before 00:00 on 16 July, 40 min after the AERIoe (Fig. 10b). Despite the relatively low LWP, the visibility at 00:00 h was only 400 m, and the observer reported freezing fog, indicating that this signal was indeed due to the presence of liquid droplets. In this case, if the MWRoe LWP retrieval was used to detect fog or for visibility nowcasting, the fog at 00:00 h on 16 July would not have been detected, whereas if the AERIoe LWP retrieval was used instead, it would have been.

The ceilometer detects fog (or aerosol hygroscopic growth) for all cases, with the exception of case 7 (4 August). During this case, the fog was extremely thin (maximum LWP from the AERI only 2 g m-2), but the onsite observer logged the presence of a fog bow between 07:15 and 08:30, demonstrating that liquid water droplets were indeed present. This was a very marginal case that demonstrates the ability of the AERI to detect very small amounts of liquid water when even the ceilometer cannot. The MWRoe retrieval only detects fog for 6/12 cases (Fig. 11), and for those 6 cases, the AERIoe retrieval consistently detects the onset of fog (via the increase in LWP) before the MWRoe retrieval by 25 to 185 min (Fig. 11). For the 6 cases where the MWRoe does not detect the fog, the mean LWP detected by the AERIoe is very low (1.4 to 3.1 g m-2).