Cloud forcing of surface energy balance from in-situ measurements in diverse mountain glacier environments

. Clouds are an important component of the climate system, yet our understanding of how they directly and indirectly 25 affect glacier melt in different climates is incomplete. Here we analyse high-quality datasets from 16 mountain glaciers in diverse climates around the globe to better conditions and others decreased melt energy. The complex association of clouds with melt energy is not amenable to simple relationships due to many interacting physical processes (direct radiative forcing, surface albedo, co-variance with temperature, humidity, and wind)varies with latitude, average melt-season air temperature, continentality, season, and elevation) but is most closely related to the effect of clouds on net radiation. These results motivate the use of physics-based surface energy balance models for representing glacier-climate relationships in regional- and global-scale assessments of glacier response to climate 40 change.

as temperature index or enhanced temperature index melt models (Huybrechts and Oerlemans, 1990;Hock, 2003;Pellicciotti et al., 2005) 70 While we know that glaciers are sensitive to changes in local climate, the extent to which cloud cover will amplify or reduce the melting of a glacier in response to future atmospheric warming is uncertain. Clouds alter the incoming shortwave (SWin) and longwave (LWin) radiation, which are generally the largest sources of energy at the glacier surface Pellicciotti et al., 2011;Cullen and Conway, 2015). Over highly reflective glacier surfaces (e.g.clean snow), a 'radiation paradox' can occur, where net radiation (Rnet) increases during cloudy conditions (Ambach, 75 1974). Clouds can also enhance or dampen the influence of near-surface meteorology, albedo feedbacks and subsurface processes (e.g. refreezing) on SEB and melt Giesen et al., 2014;Conway and Cullen, 2016;Van Tricht et al., 2016;Mandal et al., 2022). As a result, clouds have been associated with both increased and decreased melt rate depending on the climate Conway and Cullen, 2016;Chen et al., 2021). In the maritime Southern Alps of New Zealand, cloudy conditions have been shown to increase the sensitivity of melt to changes in air temperature (Conway 80 and , due to: (i) more frequent melt in cloudy compared to clear-sky conditions, (ii) increased (positive) LWnet and QL in cloudy conditions that enable a similar daily melt rate as clear-sky conditions, and (iii) a change in precipitation phase (from snow to rain) that enhances a positive snowdepth -albedo feedback. The higher sensitivity in cloudy conditions implies that, in the Southern Alps, the response of glacier melt (as well as accumulation) to past and future atmospheric warming will be modulated by atmospheric moisture (in the form of vapour/cloud/precipitation). How these processes interact 85 in different mountain glacier environments and climate regimes has not been well established.
One challenge has been the lack of direct measurements of cloud amount or type (from e.g. human observer, all-sky camera, or ceilometer) in mountain areas, which has required the derivation of cloud metrics from surface radiation measurements.
Studies have employed a variety of methods to derive cloudiness from surface radiation measurements, which limits the ability 90 to directly compare results from studies in different regions Conway and Cullen, 2016;Sicart et al., 2016;Chen et al., 2021).
The key question of this paper is, therefore: how does cloudiness and its relationships with near-surface meteorology, radiation, and energy balance vary in different mountain glacier environments? The objective is to use a common framework to assess 95 these relationships at a diverse set of sites where high-quality observations and modelling are available. To guide the analyses, a set of questions was posed: i.
How often do different cloud conditions occur at each site? ii.
What is the direct effect of clouds on surface radiation at each site?
iii. How does near-surface meteorology vary with cloudiness? 100 iv.
How do the characteristics of melt (e.g. frequency, amount and source of energy) vary in different cloud conditions? Section 2 sets out the methods used to collate and analyse data sets from 16 glacier automatic weather station (AWS) sites, including the calculation of cloudiness from LWin, the definition of melting periods and melt season, and analysis of cloud effects. Section 3 presents results that address the four questions posed above. Section 4 discusses commonalities and 105 differences in cloudmeteorology -SEBmelt relationships, uncertainties and implications for glacier melt modelling.

Sites and dataset requirements
Datasets of near-surface meteorology and glacier SEBsurface energy balance were collated from a diverse set of sites where high-quality observations and modelling were available. The sites were required to have a published SEB record calculated 110 from automatic weather station (AWS) data collected over a glacier surface during melt seasons at hourly or smaller timestep.
The AWS data needed to include measurements of all four components of the radiation balance, incoming (SWin) and outgoing shortwave (SWout), incoming (LWin) and outgoing longwave (LWout), all in W m -2 . In addition, other SEB components needed to be calculated using accepted best-practice methods (e.g. turbulent fluxes were to be calculated using bulk aerodynamic methods) and avoiding potentially inaccurate assumptions (e.g. surface temperature fixed at 0 °C regardless of SEB). Note that 115 published values of surface melt and SEB fluxes are used in these analyses rather than being recalculated from near-surface meteorology and radiation. Thus, differences in the methods used to calculate SEB may introduce some uncertainty (mainly in the calculation of sub-surface fluxes), but the values are congruent with previous studies, and no additional validation is needed. A call for datasets was made on Cryolist in January 2020, and data from over 30 sites was offered. After assessing each dataset against the criteria above, 16 sites were selected for analysis ( Figure 1 and Table 1). These sites covered many of 120 the mountain glacier regions including continental North America, the European Alps, Norway, Greenland, the Himalaya, tropical glaciers in Africa and the Andes, the arid region of central Chile and the Southern Alps of New Zealand. It is worth noting that no suitable datasets were made available from some large regions of mountain glaciers including Alaska, Patagonia and Asia outside of the Himalaya.

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As most AWS sites are in ablation areas, they follow a broad pattern of decreasing altitude with distance from the equator ( Figure 2). Note that two locations have observations in both the ablation and accumulation area -Conrad Glacier (CABL, CACC) and Mera Summit (MERA) / Naulek (NAUL, an ablation area of Mera Glacier). Records from the same site in different years were also joined into continuous records (CABL and NAUL). Records from CABL, CACC and NORD cover only summer periods and CHHO has three two-month periods throughout the year, otherwise the records span all months of the 130 year and range from 46 to 3231 days in length (See Table 1 for site name abbreviations). Figures A1 and A2 show monthly average meteorology and SEB fluxes for each site used in the analysis. A few broad groupings of sites (listed in Table 1) can be identified through seasonal trends in near-surface air-temperature (Ta; °C) or relative humidity (RH) in Figure A1: mid-and high-latitude maritime and continental sites with strong seasonal cycles of Ta but small variations in RH; Himalayan sites with strong cycles of Ta, and distinct wet and dry seasons; tropical sites with small variations in Ta and distinct wet and dry seasons; 135 and a mid-latitude arid site (GUAN) with low RH. Table 1 Cullen et al. (2016) 150

Data processing
Data from each site were taken through several processing steps as outlined in Figure 3. After basic quality control and homogenisation (described below), a timeseries of cloudiness was generated for each site (Section 2.3), melting periods and the main melt season were defined (Section 2.4), after which cloud effects on melt were analysed (Section 2.5).
155 Figure 3: Steps used to process and analyse data, annotated with relevant sections of the methods.
Basic quality control and homogenisation involved the following steps: -Sub-hourly data resampled to hourly time steps 160 -Times converted to local solar time using longitude rounded to nearest full hour offset from UTC.
-Data cut to full days only (no days with partial missing data) Monthly statistics (averages, frequencies by bin etc.) were only calculated when at least 10 days of data from a given month 175 were available. Figures A1 and A2 show monthly average meteorology and SEB fluxes for each site used in the analysis.

Defining clear-sky and cloudy periods using incoming longwave radiation
For each site, timeseries of cloudiness were derived from measured LWin, ea and near-surface air temperature (Ta,K; K) following Konzelmann et al. (1994) and Conway et al. (2015). First, the effective sky emissivity (εeff) was calculated using: where σ is the Stefan-Boltzmann constant (5.67 ×10 8 ). While LWin is influenced by emission from surrounding terrain, the sky-view factor at all sites is close to 1 and horizons at all sites are below the limit of the sensor field of view, so no corrections were needed here. 185 Timeseries of theoretical clear-sky emissivity (εcs) at each site were defined using the Brutsaert (1975)  For each site, Equation 4 was fitted to the lowest 10% of LWin in each of 30 ea/Ta.K bins ( Figure A3) by finding the value of b (in 0.001 steps) that gave the smallest root mean square error (RMSE). This step used only hours with valid LWin, ea and Ta.K values and RH < 80%. Optimised values of b and RMSE are given in Table A1. 200 Timeseries of longwave equivalent cloudiness (Nε) were then derived by fitting hourly measured εeff between theoretical clearsky (εcs) and overcast ( = 1) emissivity values, limiting Nε to a range 0 to 1 : Following Giesen et al. (2008), clear-sky conditions are defined as <= 0.2, partialy -cloudy as 0.2 > < <> 0.8 and overcast as >= 0.8. Daily average, rather than hourly average, Nε was used to define cloudiness to reduce noise, limit the influence of diurnal cycles in variables and focus on synoptic scale (daily) variability in cloud -SEB relationships. Note that 210 moderate values of daily average cloudiness can indicate either patchy cloud cover and/or a mix of overcast and clear-sky conditions during a day. Cloudiness can be derived from SWin (e.g. Greuell et al., 1997;Sicart et al., 2006;Mölg et al., 2009a;Kuipers Munneke et al., 2011) but was considered a less appropriate metric here as its calculation relies onsetting a typical cloud extinction coefficient that differs between sites (Pellicciotti et al., 2011). In addition, cloudiness cannot be derived from SWin during the night and terrain shading of SWin introduces further uncertainty, especially in winter. and SWin does not 215 provide meaningful values during the night time. .

Definition of melt season and periods with surface melt
For each site, a melt season was defined as the months in which monthly-average QM at the site was greater than 20% of the maximum monthly-average QM for the same site ( Figure A2; A4). This proved a simple method to retain months with substantial melt but exclude winter months where melt is infrequent. The sensitivity of this choice was assessed by replicating 220 key results using only months with monthly-average QM greater than 80% of the maximum monthly-average QM for that site.
Rather than only selecting individual melt events for analysis, averages over all timesteps in the melt season were used to better understand the relationships between cloudiness, surface radiation and near-surface meteorology, without skewing the data towards melt episodes that may have atypical meteorology. To identify the times surface melt occurred and to quantify the contributions of SEB components to QM, periods with surface melt were defined as hourly timesteps with QM > 0. 225

Analysis of cloud effects
The relationship between cloudiness, meteorology, SEB and melt is assessed by binning the timeseries of different variables by daily average cloudiness. Five evenly sized bins were used with bin centres at = 0.1, 0.3, 0.5, 0.7 and 0.9, with the top and bottom bins corresponding to clear-sky and overcast conditions, respectively. Data within each bin were then averaged 230 across all days within the main melt season to demonstrate the average relationships between cloudiness and different variables.
In sections 3.2, 3.3 and 3.4, we use the term cloud effects to describe the change in a variable during cloudy conditions with respect to clear-sky conditions. In studies of net radiation, the cloud effect (CE) is defined as the difference between average and clear-sky conditions (e.g. Ambach, 1973;. Here we extend the concept to QM in order to 235 describe the average change in melt related to clouds, even though clouds are not the only meteorological forcing responsible for changes in QM. We calculate CE for all net radiation components (SWnet, LWnet, Rnet) and QM. Here, we calculate CE by subtracting the average value in the clear-sky bin ( <= 0.2) from the average value equally weighted across all cloudiness bins. Equally weighting each cloudiness bin ensures that differences in the frequency of different cloud conditions do not skew the data between sites. 240

Effective sky emissivity and fitted clear-sky curve
The derivation of clear-sky emissivity from LWin highlighted substantial variations in the relationship between near-surface meteorology and LWin between the sites. On an hourly basis, most sites show a preference for either clear-sky or overcast 245 conditions, as shown by the darker colours around the clear-sky and overcast emissivity ( Figure 4). Sites in the Himalaya (CHHO, YALA, NAUL, MERA) showed a distinct seasonality with predominately warm/wet/overcast or cold/dry/clear-sky conditions. Tropical and arid glacier sites (KERS, GUAN) show a much lower εcs for the same surface vapour pressure, in part due to the high elevation (therefore low εad), but also due to the low value of b (Equation 4; Table A1), which indicates a thinner atmospheric water vapour profile above the surface compared to Himalayan sites at similar altitudes. Mid-latitude sites 250 with records covering the full annual cycle in Europe (LANG, MIDT, MORT, STOR) and New Zealand (BREW) show a similar preference for cold/dry/clear-sky or warm/wet/overcast conditions, while QASI shows a greater frequency of cloud at lower temperature/vapour pressure. Sites in the Western Cordillera of Canada (NORD, CABL, CACC) and Europe (MIDT, MORT, STOR) show more frequent partial cloud than many other sites. Note that the short summertime records from Canada (NORD, CABL, CACC) do not capture the full spectrum of conditions at these sites. 255

Monthly cloud frequency
The frequency of clear-sky, partial-cloud and overcast conditions also shows distinct regional and seasonal variations ( Figure   5 for daily average, Figure A4 for hourly periods). Mid-latitude glaciers in maritime locations show very limited seasonality 265 (BREW, STOR, MIDT) and a high percentage of overcast conditions, except for LANG that displays more frequent overcast conditions during the melt season and QASI that shows a tendency towards more frequent clear-sky conditions during its melt season. Mid-latitude sites in continental locations (NORD, CABL, CACC, MORT) show less frequent overcast and more frequent partial-cloud conditions than the mid-latitude maritime sites, with MORT showing more frequent partial-cloud conditions during the melt season and more frequent clear-sky conditions in the winter. Most Himalayan sites (YALA, MERA, 270 NAUL) show much stronger seasonality, with more frequent overcast conditions during the melt season. The , exception is CHHO, which shows weaker monsoon influence (fewer overcast conditions) being on the transition zone between monsoon and arid regions (Azam et al., 2021), though the fraction of partial-cloud conditions still increases in July and August. While ZONG experiences melt most of the year, melt rates are higher during the cloudier months from September through April corresponding with marked seasonal changes in cloud and SEB caused by the tropical climate ( Figure A2). KERS experiences 275 less cloud from June through October, with low melt rates year-round. GUAN experiences the least cloud, with predominately clear-sky conditions and only sporadic melt during austral summer.

Cloud effects on melt-season surface radiation
An estimate of the direct effect of clouds on the SEB is gained by examining the variation of incoming radiation (SWin and LWin) with cloudiness ( Figure 6). At most sites the average direct effect of clouds on incoming radiation is negative, steadily 285 decreasing with increasing cloud cover to between -60 and -170 W m -2 (Figure 6f). The exceptions are low-latitude and highaltitude sites KERS, MERA, and ZONG, where comparatively small decreases in SWin with cloudiness ( Figure 6d) are compensated by large increases in LWin (Figure 6e). The large variation in SWin and LWin cloud effects between sites suggests that different cloud types and cloud properties play a role in determining radiative forcing and this should be investigated in future work. We note that changes in the profile of water vapour and air temperature (estimated by ea and Ta) also influence 290 LWin (and to a much lesser extent SWin). Hence, the direct cloud effects shown here represent the combined effects of direct radiative forcing and changes to atmospheric profiles of water vapour and temperature, in contrast to analyses of cloud radiative forcing that consider the changes in incoming radiation with respect to calculated clear-sky values (e.g. Sicart et al., 2016). LWnet effect at higher values of Nε, but much more negative SWnet effects cancel these out. For most sites, the Rnet cloud effect is small and negative (0 to -20 W m -2 ). Many of these sites show a decrease in Rnet only at higher values of Nε, while 3 sites (MIDT, MORT, CHHO) show the highest Rnet in partial-cloud conditions, emphasising that the relationship between 305 Rnet and cloudiness is not always linear. NORD, CABL, QASI, and CHHO all show a strong negative Rnet cloud effect, driven by strong negative SWnet effect and weak LWnet cloud effect. For the two sites with measurements from both the accumulation and the ablation areas, accumulation sites exhibit more positive and/or less negative Rnet cloud effectmuch more positive response to cloud compared with their ablation area counterparts, driven by the change in SWnet cloud effect (surface albedo) rather than a large change in LWnet cloud effect. 310

Variation of near-surface meteorology with cloudiness
Alongside radiative changes, differences in near-surface meteorology are also an important driver of SEB and melt variations with cloudiness, particularly QS, QL and LWin. Air temperature shows a divergent relationship to cloudiness; at sites with average melt-season Ta >> 0 °C, increasing cloudiness is associated with lower temperatures, while at sites with average meltseason Ta < 0 °C (KERS, MERA, NAUL, YALA), cloudiness isare generally associated with higher temperatures (Figure 8a). 320 Average Ta varies little with cloud cover at ZONG and CHHO. At most sites, wind speed decreases with increasing cloudiness (Figure 8b). The exceptions are BREW and STOR, which show moderate increases (< 1 m s -1 ), LANG and MIDT, which show larger increases (1.6 and 2.9 m s -1 , respectively), and QASI, which shows no large change cloudiness and and CACC, which shows peak wind speed at moderate cloudinesswhere the relationship is weak and non-linear. We note that sSites where wind speed increases with cloudiness (particularly MIDT and LANG) have a wind climate that is mainly influenced by the large-325 scale circulation, while other sites may have a more local wind climate where local or meso-scale katabatic or convective circulations prevail (e.g. Mölg et al., 2020;Conway et al., 2021). Stronger radiative cooling during clear-sky periods may promote higher katabatic wind speeds in clear-sky conditions, though the relationship is not simple; at ZONG, strong winds during clear-sky conditions are related to large-scale forcing during the dry season (Litt et al., 2014). As expected, ea and RH increase with cloudiness, however some sites with ea around the saturation vapour pressure of melting surface show a weak 330 relationship to cloudiness (e.g. QASI, CACC). The wide variation of RH in clear-sky conditions (~30 to ~70%) implies that care should be taken when using RH to model cloud cover using empirical parameterisations developed for particular study areas, or even at different altitudes (e.g. NAUL vs MERA).

Variation of melt frequency, melt amount and SEB with cloudiness
The percentage of hours with surface melt increases with cloudiness at all study sites (Figure 9), with the exception of GUAN, 340 which experiences very infrequent melt in all conditions. Colder sites across the Himalaya and tropical regions (except KERS) show the largest increases with respect to clear-sky conditions (up to 5 times more frequent), while BREW, MORT and LANG all show moderate increases up to 1.5 times more frequent in overcast conditions. Other European and North American sites show comparatively high melt frequency across all cloud conditions, indicative of the warm conditions where ea exceeds that of a melting ice/snow surface. Even in these conditions, periods with surface melt still become more common with increasing 345 cloudiness, with 100% of overcast periods at NORD experiencing melt (Figure 9a). While analysis of diurnal patterns of melt is beyond the scope of this paper, the higher percentage of hours with melt during overcast conditions indicates that it is likely    Figure A5) due to decreases in Ta (Figure 8a). The exceptions are BREW, MIDT, and QASI where the contribution from QS increases with cloudiness and ZONG where the contribution of QS decreases. Note that as Figure 11 presents averages for only periods with surface melt, LWout is constant and changes in LWnet are entirely due to LWin.

Relationships between QM cloud effect and site characteristics
While the average change in QM with cloudiness is small at some sites, it is instructive to assess whether the melt-season average QM cloud effect (CE) at the various sites can be related to geographic or climatic parameters. Figure 12a,b shows the relationship between average cloudiness and melt at the various sites does not directly relate to latitude or altitude. Average 395 near-surface air temperature is moderately correlated to QM CE (Figure 12c). Sites with lower Ta (e.g. MERA, KERS) generally have smaller QM CE than sites with higher high Ta (NORD, CABL, MORT), but with some notable exceptions (e.g. LANG has positive QM CE with relatively high Ta). Average cloudiness shows some association to QM CE with clearer sites tending to have more negative QM CE (Figure 12e), with the exception of tropical/arid sites with predominately clear-skies (KERS, GUAN) that show neutral QM CE. Neither, average wind speed or relative humidity show a clear relationships with the QM CE 400 (Figure 12d,f). Average turbulent heat fluxes and LWin are moderately correlated QM CE (Figure 12g,h,j), largely following the pattern of sites shown for Ta, while average SWin is not significantly correlated (Figure 12i).
Considering the association of radiative and melt cloud effects, average incoming radiation cloud effects explain some of the variance of QM CE, with LWin ( Figure 12l) showing a stronger association than SWin CE (Figure 12k). Combined, the incoming radiation cloud effects can explain over half (53%) of the variation in QM CE (Figure 12m). Surface albedo has a 405 similar correlation to QM CE (Figure 12n

Regional and elevational patterns 425
Two groups of sites with a broadly similar response emerge from the above analyses, largely split by latitude, but also air temperature and continentality. The first group (YALA, NAUL, MERA, KERS, ZONG) consists of high-altitude sites in tropical regions and the Himalaya (excluding CHHO) and tropical regions. These sites are comparatively cold, with negative QL and small QS during melt ( Figure A5d,e). During cloudy conditions, these sites experience warmer and calmer conditions (Figure 8a,b), reduced evaporation/sublimation (less negative or, at times, positive QL; Figure A5e) and a large increase in the 430 fraction of time that melt occurs (Figure 9), regardless of the seasonality of cloud or the typical cloud conditions (e.g. KERS vs MERA). These sites also generally experience greater QM in cloudy periods (except for NAUL; Figure 10 With a few exceptions (e.g. BREW, LANG), QM decreases with increased cloudiness, though the magnitude of decrease varies widely (from 20% to 60% less in overcast compared to clear-sky conditions; Figure 10). CHHO stands out from the other Himalayan sites in that it has a higher average Ta that does not vary greatly with cloudiness ( Figure 8a). Here also, low albedo drives a strong negative Rnet cloud effect (Figure 7f) that, in turn, drives a large decrease in QM during cloudy periods ( Figure   10).. At all these sites, QS is positive in all cloud conditions (Figure 11d), though the absolute magnitude is generally reduced 445 in cloudy periods due to decreased Ta ( Figure A5d). Cloud is associated with increased wind speed at most maritime sites (LANG, MIDT, STOR, BREW; Figure 8b) but does not show a consistent relationship to QM ( Figure 10); MIDT and STOR experience less QM in cloud conditions, whereas LANG and BREW experience greater QM due to increased wind speed and comparatively modest decreases in Ta that drive increased LWnet and more positive QL ( Figure A5e). In the case of LANG, increased QM during cloud is also due to a positive Rnet cloud effect (Figure 7f). 450 Locations with AWS at two elevations highlight more positive Rnet cloud effects at accumulation sites than ablation sites due to the higher albedo ( Figure A1) and larger difference between clear-sky and overcast emissivity (Figure 4). Differences in melt are stronger at the Himalayan pair (NAUL, MERA), where melt is decreased in cloudy conditions at the lower sites and increased during cloud at the upper site (Figure 10). At the pair in Canada (CABL, CACC),, both sites experience reduced 455 melt during cloudy conditions, though in absolute terms, the decrease is larger in the ablation area.

Limitations
The derivation of cloudiness from LWin also poses challenges. At some sites (e.g. LANG, and MORT), εcs shows a poor fit at higher vapour pressure, with incoming LWin during clear-sky periods being higher than that expected from the theoretical 460 curves (Figure 4). This mismatch between theoretical and observed εcs during periods of higher ea may cause some clear-sky periods to be misclassified as being in the first partial cloud bin (Nε ~ 0.3). Indeed, at both LANG and MORT, the Nε ~0.3 bin shows higher melt, indicating this may be the case. The reasons for this mismatch have not been investigated, but it may be due to a different method used to correct LWin data (Giesen et al, 2014) or changes in water vapour profiles in the atmospheric boundary layer. There is also some unavoidable degree of circularity in analysing longwave radiation fluxes (Figures 6 and 7) 465 that have also been used to derive cloudiness. However, as LWin does not solely depend on cloudiness, but also on variations in Ta and RH, the circularity is not complete. For instance, at Brewster Glacier, the increase in LWin between clear-sky and overcast conditions is approximately the same as the change in clear-sky LWin due to seasonal variations in Ta. Because the method used to calculate cloudiness accounts for the effect of Ta and RH on LWin, the effect of these variations in near-surface meteorology on LWin is retained in the analyses shown in Figures 6 and 7. 470 While efforts have been made to homogenise the datasets, it is possible that biases still affect the results. Interannual variability causes uncertainty, particularly for sites with only one or two seasons (e.g. NORD, ZONG). Giesen et al. (2008 Table 4) show that at MIDT, the contribution of SEB components to melt during clear-sky periods can vary up to 12% between years, while variability in overcast periods is less. The interannual variability is partly influenced by the seasonality of anomalies in 475 cloudiness, with strong anomalies in spring causing the importance of QS to melt to change markedly. Some sites also have discontinuous records (CABL, CACC, NORD, CHHO) that do not include periods with lower melt rate outside the peak melt season. Increased clear-sky solar radiation and Ta as well as decreased albedo during the peak melt season are likely to cause Rnet and QM cloud effects to be larger at these sites compared to those with longer records that include periods of more marginal melt. This effect is demonstrated by repeating the analysis but restricting the melt season to months with at least 80% of the 480 maximum monthly-average QM, 2-3 months at each site ( Figure A6). Figure 13 shows the relationship between average QM and Nε for the period with peak melt rates at each site. The previously large increase in QM with cloud at MERA and LANG becomes more variable, and QM is smaller in overcast conditions compared to clear-sky. This is primarily due to the removal of months with a high albedo snow surface in the early season where a strong radiation paradox drives an increase in melt during cloud periods. In clear-sky conditions, higher Ta and ea in the peak melt season creates generally positive QL at these 485 sites (not shown). BREW also now shows a moderate decrease in QM with cloud, while ZONG shows a much stronger decrease due to marked seasonal changes in the SEB terms driving melt (less negative LWnet and QL in austral spring and summer; Figure A2). Only one site (YALA) still shows its highest QM in overcast conditions, but the increase is small compared to the average for the longer melt season. In fact, at outer-tropical sites such as ZONG where melt can occur in most months alongside large seasonal variations in climate precipitation and cloudiness, the analysis here likely mixes cloud effects with seasonal 490 changes of other meteorological forcings (such as potential solar irradiance, humidity and air temperature).

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Seasonal changes in cloud effects on melt have been previously reported by some studies; Giesen et al. (2008) show that negative QM cloud effects at MIDT were restricted to July and August, with other months showing neutral or positive cloud effects; Conway and Cullen (2016) show only one month with negative QM cloud effect at BREW, with positive effects in 500 other months; Chen et al. (2021) report strong negative QM cloud effects in July and August for Laohugou Glacier No. 12 in the western Qilian Mountains of China, with weaker negative effects in May and June, and neutral effects in September. To elucidate spatial patterns of net melt cloud effect, future studies should investigate seasonal patterns of cloud effects, and establish the timing of transitions between periods of positive and negative QM CE and how these relate to Rnet CE and surface meteorology. It is likely that the timing of transition from positive to negative QM CE will therefore determine the melt-season 505 average cloud effects., caution is warranted in efforts to simplify or generalise these relationships.To this end, there is a The analysis does highlight the need to capture AWS records through the full annual cycle at study sites in order to fully understand the relationships between meteorological forcing and melt.

Mechanisms influencing SEB changes with cloud 510
In addition to the key role that surface albedo plays in determining Rnet, there are three key mechanisms that drive temporal changes in SEB with cloudiness i) direct forcing of incoming radiation (decreased SWin and increased LWin), ii) changes to near-surface meteorology that alter turbulent heat fluxes iii) surface and subsurface temperature feedbacks that alter net radiative and turbulent fluxes 515 Here we demonstrate that direct forcing of incoming radiation and surface albedo explains much of the net effect of clouds on on Mt Everest are due to increased Rnet as well as lower wind speeds that drive smaller losses to QL, and Conway et al. (2016) who found changes to QL contributed to increased melt during cloudy periods. Future work should also assess the mechanisms driving the observed covariance between cloudiness and near-surface meteorology at different sites, e.g. Do large-scale 530 changes in airmass or local/meso-scale processes drive changes in Ta with cloud? How well are these processes represented in the datasets used to force glacier melt models on regional scales? Seasonal changes in the relative magnitudes of turbulent and radiative cloud effects also deserve further scrutiny.
Surface temperature responds quickly to changes in SEB, and here we show that during cloudy periods, a melting state is 535 observed more frequently, in line with previous research on maritime glaciers . We have not attempted to analyse further surface and sub-surface temperature feedbacks here as not all datasets contain these variables and a detailed analysis is more suited to sensitivity experiments that allow the transient response of sub-surface temperature, humidity and refreezing to be resolved.

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The increased frequency of melt during cloudy conditions, especially at higher elevations, raises the question of how glacierwide melt is altered by clouds, along with how glacier-wide surface mass balance is altered by refreezing. Van Tricht et al., (2016) show increased runoff from the Greenland Ice Sheet during cloudy periods due to increased melt extent and decreased refreezing of melt water, while Niwano et al. (2019) found clouds increase melt extent but reduce total melt due to feedbacks between cloudiness and near-surface humidity. These studies are in line with the findings herethat clouds enhance the 545 possibility of melt at a given site, by removing large negative LWnet and QL fluxes to precondition the surface to melt, but do not necessarily cause greater melt unless albedo is high enough to cause a radiation paradox or unless increased near-surface air temperature, humidity and/or wind speed causes an increase in net turbulent fluxes.

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Future work should also assess the mechanisms driving the observed covariance between cloudiness and near-surface meteorology, e.g. Do large-scale changes in airmass or local/meso-scale processes drive changes in Ta with cloud? How well are these processes represented in the datasets used to force glacier melt models on regional scales?

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The derivation of cloudiness from LWin also poses challenges. At some sites (e.g. LANG, and MORT), εcs shows a poor fit at higher vapour pressure, with incoming LWin during clear-sky periods being higher than that expected from the theoretical curves ( Figure 4). This mismatch between theoretical and observed εcs during periods of higher ea may cause some clear-sky periods to be misclassified as being in first partial cloud bin (Nε ~ 0.3). Indeed, at both LANG and MORT, the Nε ~0.3 bin shows higher melt, indicating this may be the case. The reasons for this mismatch have not been investigated, but it may be 560 due to a different method use to correct LWin data (Giesen et al, 2014) or changes in water vapour profiles in the atmospheric boundary layer.

Implications for glacier melt modelling
Previous research that identified a higher sensitivity to warming associated with cloud at BREW , showed this occurred without increased melt during cloud periods. The effect was primarily due to increased melt frequency 565 and temperature-dependent fluxes during cloudy periods as well as accumulation-albedo feedbacks. All sites analysed here show increased melt frequency and temperature-dependent fluxes during cloudy periods, suggesting more sites may also experience a higher sensitivity to warming associated with cloud. While a formal analysis is beyond the scope of this paper, we may therefore expect that the response of melt to past and future temperature change will be modified by changes to atmospheric moisture in the form of clouds and vapour fluxes. The simplified temperature-index models that are generally 570 used to predict future glacier change on global and regional levels (e.g. Marzeion et al., 2018;Huss and Hock, 2018;Zekollari et al., 2019) do not account for these effects. Enhanced temperature-index models that can account for changes in cloudiness through solar radiation (e.g. Pellicciotti et al., 2005) If they do include the effects of clouds, they generally only include the opposite effecta reduction in solar radiation by cloudsand therefore may underestimate future melt at sites where cloud cover is not universally associated with reduced melt (e.g. high altitude and maritime glacier sites). Furthermore, any increase 575 in clouds and atmospheric moisture accompanying future warming may result in greater melting than predicted. Given the positive effect of clouds on net radiation at snow covered and high-altitude sites, future increases in cloud cover may promote further melt, especially during marginal melt seasons and especially at high elevations. However, caution is warranted in making generalisations as the analysis here shows that even in this set of 16 glaciers, we find variability in the links between clouds and melt, and it seems that some processes are site specific even in this small sample. 580 The non-linear relationships between clouds and melt motivates the use of SEB models in regional and global assessments of glacier response to climate change. To aid in the development of globally and regionally applicable SEB models and parameter sets, the research community should investigate creating a central open-source repository for glacier AWS and SEB datasets along with supporting meta data. Such a repository would facilitate the easy transfer of data between researchers, streamline 585 processing by establishing data format and meta data standards, as well as motivating best-practice in data collection and quality control. Alongside this, careful assessments of SWin and LWin and their relationship to near-surface meteorology from global, regional and meso-scale meteorological models should be undertaken to ensure uncertainties in model input data are reduced and to assess the need for downscaling to account for local-scale processes. As many glacier SEB models rely on empirical relationships between SWin and LWin to modify these variables to account for local-scale changes in near-surface 590 meteorology topography(e.g. Mölg et al., 2009a;Conway et al., 2015), globally applicable parameterisations of SWin and LWin should be tested.

Conclusions
Sixteen high-quality published datasets of near-surface meteorology, radiation, and surface energy balance from over glaciers in very different climate settings have been homogenised and analysed in a common framework. The analyses sought to assess 595 how the relationships between clouds, near-surface meteorology and surface energy balance vary in different mountain glacier environments. Distinct regional differences in the seasonality of cloudiness are demonstrated between different mountain glacier environments. On average, over the main period of melt at each site: -Near-surface humidity (both relative and absolute) is shown to universally increase in cloudy conditions. In contrast,, whereas a divergent relationship is found between near-surface air temperature and cloudiness; at colder sites (average 600 near-surface air temperature in melt season < 0 °C), air temperature is increased in cloudy conditions, while for warmer sites (average near-surface air temperature in melt season >> 0 °C), air temperature decreases in cloudy conditions. In essence, air temperature tends towards the melting point of ice in cloudy conditions. Wind speed shows a mixed association to cloudiness at different sites.
-Most sites, on average, show , on average, a modest to strong decrease in net radiation during cloudy conditions 605 during the melt season. A few sites show a clear increase in net radiation with cloud -aka 'radiation paradox'but this result is sensitive to the months used in the analysis due to seasonal changes in incoming radiation fluxes and albedo.
-At all sites, surface melt is more frequent in cloudy conditions compared to clear-skyies conditions.
-At all sites, temperature-dependent fluxes contribute a larger fraction of melt energy during cloudy conditions, 610 primarily due to increaseds in incoming longwave radiation and less negative and/or more positive turbulent latent heat fluxes. The contribution of turbulent sensible heat generally varies little with cloudiness.
-Cloud cover does not affect daily total melt in a universal way;, with some sites showing average increased melt energy increases in cloudy conditions while at other sites,and other decreased average melt energy decreases. The complex association of clouds and with melt energy is complex and not amenable to simple relationships due to many 615 the interaction of multiple ing physical processes (direct radiative forcing, surface albedo, co-variance with temperature, humidity, and wind) that force it to vary widely varies with latitude, average melt-season air temperature, degree of continentality, season, and elevation). OverallHowever, the association of clouds and melt is most closely related to net radiation cloud effect, with sites displaying a radiation paradox also showing an increase in energy for melt in cloudy conditions. 620 -It is likely that substantial seasonal variations in Rnet CE exert the primary control on the effect of clouds on glacier melt, through changes in surface albedo and the balance of incoming radiation fluxes. Changes in net turbulent fluxes also play a role, and the mechanisms driving co-variance between clouds and near-surface air temperature, humidity and wind speed should be more widely explored.

625
The non-linear relationships between clouds, near-surface meteorology and melt motivate the use of physics-based surface energy balance models for understanding future glacier response to climate change, particularly in areas where atmospheric moisture plays a key role both in accumulation and ablation processes (e.g. Himalaya, tropical glaciers, maritime glaciers).
Future work should also look to carefully assess shortwave and longwave radiation fluxes and their relationships with nearsurface meteorology in global, regional and meso-scale meteorological model analyses if we are to confidently use these tools 630 to better understand how future glacier melt will respond to changes in atmospheric temperature.

Data and code availability
AWS data is available from individual paper authors listed in Table 1. Analysis code can be accessed at https://github.com/jonoconway/cloud-glacier. 635 Author contributions JC conceptualized the study, curated the data, conducted the formal analyses, and wrote the manuscript. Other co-authors supplied data suitable for curation, aided in the investigation and reviewed/edited the manuscript.