Inundated lakes in the Sahara are presently a rare, mostly undocumented, transient phenomenon. As a consequence of the lack of rainfall (; ; ), the extent of surface waterbodies and vegetation in the Sahara is limited, and the region is considered to be mostly uninhabitable. Yet, ample geological evidence indicates that, during a relatively warm period in the mid-Holocene called the African Humid Period (AHP), the Sahara used to be wetter and greener e.g.. Although debated, one major line of evidence for a wetter Sahara during this period, as well as of previous AHPs, is the reported presence of Saharan (mega-) lakes e.g.. Such lakes, or even smaller-scale wetlands rather than mega-lakes, as was recently suggested by , point to increased precipitation during such AHPs. When Saharan lakes get filled, they can alter the regional atmospheric circulation and enhance precipitation, therefore locally triggering positive land surface feedbacks e.g.. However, currently, the mechanisms involved in both the initial filling and persistence of Saharan lakes are de facto unclear.

The interest in the processes leading to lake-filling episodes (LFEs) is raised not only because of paleo-environmental proxies indicating wetter conditions but also due to current climate warming. While, in many regions, present-day anthropogenically induced climate change decreases surface water availability e.g., intriguingly, some desert regions may exhibit increased water availability with climate warming. For example, in the Indian deserts, boosted food production was recently linked to climate-change-induced modifications of the hydrological regime due to a rise in precipitation . For the Sahara, climate model projections show a pronounced increase in precipitation throughout most of the desert (mean annual precipitation increase of 41.5 % with warming of 4°C under an SSP5-8.5 scenario, compared with the period 1850–1900) and a decrease in precipitation for the northwestern Sahara $\sim$ $-$10 % to $-$30 %;. Very large uncertainties, 1 order of magnitude larger than the projected change, are associated with these precipitation projections, especially in the northwestern part of the Sahara. Thus, the future of surface water resources in the Sahara is unclear.

In deserts, precipitation matters not only as a key component of the freshwater mass balance but also as a potentially high-impact hazard. Despite the vast uninhabited areas, there are several large urban centres bordering the Sahara. Storm Daniel, which affected northern Libya in September 2023, is a recent example of how deadly and devastating heavy-precipitation events (HPEs) can be in a desert area . This storm induced flash floods in ephemeral streams draining south into the Sahara and led to the filling of Saharan lakes that have been empty since the start of Landsat observations i.e. 1984;. While some studies previously addressed specific HPEs in the Sahara and their link with floods e.g., to the best of our knowledge, only one study thoroughly analysed the climatology of HPEs in this region , but it does not include the link to LFEs. The study of recent LFEs in the Sahara is fairly limited and outdated and is mainly based on observations collected by until the 1950s.

To better understand the processes involved in such potentially devastating rainstorms; their capacity to fill Saharan lakes under past, present, and future climates; and to clarify the impact of projected precipitation changes on water availability, we need a better quantitative understanding of the relationship between the atmospheric processes triggering rainfall in the Sahara and the desert hydrology leading to lake filling in the present-day climate.

Studies focusing on precipitation in the Sahara are scarce, particularly with respect to heavy precipitation . A few studies have investigated regional-scale precipitation events in the Sahara to identify the synoptic systems which can lead to Saharan precipitation, but they focused mainly on the periphery of the desert e.g..

Nevertheless, the processes leading to the dryness of the Sahara are generally well known: a year-round subsidence over the Sahara prevents strong and deep convection e.g.. During winter, the subsidence is established by the down-branches of the Hadley and Ferrel cells, which induce the subtropical high-pressure systems e.g.. An anticyclonic flow is established over the Sahara at the surface, creating dry northeasterly trades – the Harmattan e.g.. During summer, the heating of the surface induces a low-level heat low Fig. a;. Nevertheless, even in summer, several factors reinforce the weak subsidence from the Hadley cell and suppress the ascent of air needed for precipitation formation: (i) the compensating downward motion from the Asian Monsoon, (ii) the ageostrophic descending force at the right exit of the African Easterly Jet, and (iii) the surface cooling along the western coast of the Sahara through cold coastal upwelling of the Canary Current and maritime stratus cooling . However, given the strong subsidence aloft in all seasons, how can precipitation still occur in the Sahara?

As the Sahara marks the subtropical transition region between extratropical and tropical weather systems, the northern Sahara receives most precipitation during winter from extratropical cyclones or fronts connected to upper-level troughs, dominantly reaching the northern regions of the Sahara, through the equatorward shift of the westerly jet stream e.g.. In the southern Sahara, most precipitation falls during summer due to tropical depressions, cloud clusters, or squall lines, originating from African easterly waves and potentially developing into mesoscale convective systems e.g. as the intertropical convergence zone (ITCZ) moves northward e.g.. During transition seasons, the interaction of the extratropical upper-level forcing and tropical systems creates precipitation over the Sahara, mainly at the eastern and western boundaries of the desert e.g.. A prominent feature associated with this rainfall is tropical plumes, i.e. elongated cloud bands stretching from southeast to northwest, or features similar to these tropical moisture excursions .

While different systems potentially cause Saharan precipitation, it is unclear whether similar systems are the cause of wetter periods in the past. Various mechanisms have been associated with increased frequency and intensity of precipitation and the filling of lakes in the geological past. The simplest, most discussed one is the invigoration and poleward migration of the African Monsoon in response to increased summer insolation during the early Holocene, contributing to increased rainfall throughout the Sahara e.g.. In addition to changes in heating and insolation, increased tropical-plume activity was suggested to be associated with larger rainfall input throughout the Sahara during past glacial periods e.g. based on the isotopic analysis of fossil groundwater or toward the end of the AHP in the northwestern Sahara . However, even collectively, these mechanisms cannot explain the reported amounts of precipitation needed to maintain proposed Saharan lakes e.g..

Despite these studies relating atmospheric conditions with lake filling in the geological past, no study relates present-day lake filling in the Sahara with atmospheric circulation features. Therefore, this study investigates the conditions associated with the filling of Sebkha el Melah (Fig. ) – a normally dry lake in the northwestern Sahara, filled, on average, only every few years . We combine present-day precipitation and lake-filling remote sensing observations from satellites with meteorological reanalysis data and trajectory-based atmospheric transport diagnostics to explore questions relevant to the hydrometeorology of desert lakes. What are the necessary meteorological ingredients to produce LFEs in the northwestern Sahara? What triggers the ascent of air, what are the origins of the precipitated moisture, and how do these properties differ between HPEs that trigger LFEs and “normal” HPEs? What portion of rainfall is converted into runoff and effectively contributes to lake filling? In other words, what is the ratio between catchment precipitation and lake-filling volume, known as the runoff coefficient e.g. ? What is the role of below-cloud precipitation evaporation in producing HPEs in the Sahara?

After presenting the study area (Sect. ) and the methods applied (Sect. ), we first identify HPEs and LFEs over the catchment area of the lake (Sect. ). Then, we investigate the atmospheric conditions prevailing during an exemplary case of an especially large LFE (Sect. ) and finally take on a climatological perspective, highlighting the differences in meteorological conditions associated with LFEs and more common HPEs (Sect. ). In the end, we discuss the ingredients leading to HPEs (Sect. ), the unique characteristics of LFEs (Sect. ), and the relevance of runoff coefficient values to understanding paleo- and future-climate impacts on surface water availability in the Sahara (Sect. ).

During the study period (June 2000–May 2021), 250 HPEs occurred in the catchment of Sebkha el Melah over 356 d in total (see Fig. a and the Supplement), with an average of 1.4 events per month. Events are not distributed evenly throughout the year (Fig. ): autumn is when events are most frequent (2.6 events per month), followed by spring (1.7 events per month), winter (0.9 events per month), and summer (0.4 events per month). Precipitation during HPEs varies between 0.5 and 60.8 mm, averaged over the catchment, with a mean value of 6.8 mm (Table ).

Since in situ rain measurements in the Sahara are scarce, it is difficult to validate precipitation data from both the satellite and reanalysis datasets. While ERA5-based precipitation is consistently lower compared to IMERG precipitation ($-$43 %, on average; Table ), high correlation values between the two datasets (${\mathit{\rho }}_{\mathrm{Pearson}}=\mathrm{0.87}$) and similar rankings for the events (${\mathit{\rho }}_{\mathrm{Spearman}}=\mathrm{0.72}$) suggest that both can capture HPEs in the catchment (Table ). However, because of the coarser resolution and parameterised convection in ERA5 (Sect. ), convective rainfall – which is an important contributor to the majority of HPEs in desert areas e.g. – is not well represented in the ERA5 data, and precipitation rates are probably too low, as was recently observed over the entire Sahara .

Rarely, HPEs trigger enough runoff to (partially) fill Sebkha el Melah. During the study period, LFEs occurred only six times, partially filling the lake with water volumes of $\le$ 0.8 km³, amounting to about 90 % of its capacity (Figs. b and and Table ). Clearly, LFEs originate from the largest HPEs; each of the LFEs is associated with at least one of the 10 largest HPEs by HPE magnitude (Sect. ), mostly coinciding with longer event durations (typically 3 d; Fig. a). Two of these LFEs resulted from two sequential HPEs, and the other four are a result of single HPEs (Table ). Hereafter, we number these LFEs chronologically and use the same numbers to describe the corresponding HPEs, such that the first LFE during the study period is termed LFE1, and its associated HPE is termed HPE1. LFE-generating HPEs are characterised by event magnitudes $>$ 1.4 km³ (14.7 mm when averaged over the catchment), while strong HPEs have magnitudes of $\ge$ 0.66 km³ (6.8 mm), and medium HPEs range between 0.66 and 0.01 km³ (6.7 and 0.1 mm, respectively).

While the HPEs that lead to LFEs are characterised by high rainfall values, runoff varies greatly between events. Mean catchment precipitation during these HPEs, when accumulating rainfall during consecutive HPEs if only one LFE eventuated, is between 20 and 93 mm. Effective runoff coefficients, which represent the portion of rainfall that actually reaches the lake by surface runoff, are computed for each of the LFEs based on the two end-member scenarios in the third point in Sect. 3.2.2. Scenario (a), in which precipitation is considered during HPEs only, is represented by the red symbols in Fig. b, and scenario (b), in which precipitation is accumulated until the Landsat observation time, is represented by the blue symbols. The calculated effective runoff coefficients of the LFEs vary by 5 orders of magnitude ($<$ 0.001 % – $\sim$ 10 %). While, in general, higher coefficients are exhibited when higher precipitation amounts occur, while relatively high coefficient values ($>$ 1 %) are exhibited in LFE1 (and potentially in LFE3; Fig. b). Still, the highest effective runoff coefficients are exhibited for the largest events (LFE2 and LFE5), where average precipitation over the catchment reaches nearly 100 mm during the event duration.

To better understand the synoptic ingredients involved in the filling of Sebkha el Melah, we focus now on a specific case study – LFE5 in November 2014 (Fig. b, Table ). This LFE is associated with two consecutive HPEs (event nos. 5.1 and 5.2 in Fig. a), which contributed a combined volume of 0.32 km³ to the lake, ending a 3-year period during which the lake was almost completely empty, with the exception of a small LFE in October 2012 (LFE4; Fig. ). Precipitation during HPE5.1 and HPE5.2 was extremely intense, summing to 93 mm averaged over the catchment, with values locally exceeding 140 mm over the central part of the catchment (Fig. ). In both sub-events of HPE5, two distinct peaks of precipitation appear: HPE5.1 on 22 November 2014 and from 23 to 24 November 2014 and HPE5.2 on 27 November 2014 and from 28 to 29 November 2014. Both IMERG- and ERA5-based precipitation data are remarkably similar in terms of the timing of precipitation, with ERA5 showing a $-$22 % bias compared to IMERG for catchment mean precipitation and slightly lower precipitation intensities.

Given the different precipitation forcing mechanisms that appear to play a role for just one exemplary LFE, as well as the observation of precipitation appearing dominantly during afternoon and nighttime hours, in the following section, we explore whether these are general characteristics of HPEs and LFEs in Sebkha el Melah.

LFE-generating HPEs have distinct characteristics compared to other HPEs and the mean climatology. To show these differences, we divided the identified HPEs into three categories based on their HPE magnitude (Sect. ): (a) LFE-generating HPEs, (b) strong HPEs, and (c) medium HPEs (Fig. a).

First, we examine the daily cycle of precipitation; it shows a clear diurnal pattern in all seasons (Fig. ), albeit one that is less pronounced in winter. Precipitation intensity rises in the afternoon, peaks in the late evening (18:00 to 21:00 UTC+1), and then drops back to lower values during the night and morning. This daily cycle indicates a major convective influence on total rainfall due to the strong heating of the surface in the Sahara. During winter, though, the precipitation intensity varies more throughout the day, suggesting that the convective influence is smaller, and the large-scale forcing from extratropical systems is more prominent.

Rain intensity during LFE-generating HPEs is higher compared to the intensity during strong and medium events while exhibiting the same general daily cycle. In autumn, the difference in the mean catchment intensity of LFE-generating HPEs compared to other HPEs diminishes slightly, with LFEs situated at roughly the 65th quantile (Fig. ). We hypothesise that this smaller difference might be related to the typical area of rain cells, which is smaller in autumn because of a larger contribution of convective precipitation caused by the smaller-scale forcing for precipitation; more isolated convective cells forced by surface heating show typically higher rain intensities, smaller areal coverage, shorter lifetimes, and smaller vertical velocities e.g. . Despite the small area covered by convective storms, those events may create LFEs if they are situated over the areas contributing efficiently to the lake filling (i.e. the rockier and/or downstream part of the catchment). Yet, their precipitation intensity will be small when averaged over the catchment within the daily cycle.

In general, all three HPE categories exhibit the same type of synoptic-scale anomalies but with an increased anomaly for higher HPE intensities (Fig. ). The upper-level geopotential height anomaly during HPEs shows a major negative signal centred toward the northwest of the catchment over the western Atlas Mountains and the western coast of Morocco, accompanied by an upper-level cyclonic wind anomaly and increased atmospheric moisture contents. These anomalies become larger for the strong HPEs and are the deepest for LFE-generating HPEs. The structure of these anomalies indicates the presence of an upper-level low or a trough, which are chiefly associated with PV features such as streamers and cut-off lows (Fig. ) and a more meandering jet stream . These upper-level anomalies tend to destabilise the low levels and increase the potential of a surface cyclone formation, which is usually present along the western coast of Morocco (Fig. ) during precipitation events in the catchment.

An upper-level wind anomaly on the western side of the catchment changes from west-southwest during medium HPEs (Fig. d) to southwest during strong HPEs (Fig. c) to south-southwest during LFE-generating HPEs. Similar patterns are exhibited at the surface as well, although with a lower intensity (Fig. ). The normal westerlies (Fig. a) and the southwesterlies during medium HPEs impinge on the Atlas Mountains, which may lead to increased precipitation on the windward side of the mountains and decreased precipitation on the lee-side e.g.. In contrast, during strong HPEs and LFEs, the stronger winds clearly blow around the Atlas Mountains, leading to decreased orographically induced rain-out. Thus, larger amounts of moisture can reach the catchment and the southern side of the Atlas Mountains, enabling increased precipitation in the “rain shadow” of the mountains.

Atmospheric moisture content also shows clear anomaly signals during HPEs. Total column water increases over the catchment and upwind (southwest) of it, with larger anomaly amplitudes during strong and LFE-generating HPEs (Fig. ). During LFE-generating HPEs, higher moisture values are seen near the Moroccan coastline and over the Atlantic Ocean as well. This emphasises the importance of moisture presence over both the Sahara (to the southwest of the catchment) and the North Atlantic.

In addition to anomalous wind, pressure, and humidity, HPEs are characterised by a negative surface temperature anomaly. Anomalously low surface temperatures ($T$ at 2 m) are evident through all HPE classes, with a larger deviation for strong HPEs and even larger deviations for LFE-generating HPEs when compared to the yearly climatology (Fig. ). Compared to the wet-season (September–May) climatology (Fig. ), the negative anomaly is accentuated over the southwest of the catchment. This negative anomaly may represent below-cloud evaporative cooling, consistent with the evaporation of precipitation along the trajectory toward the catchment described in Sect. , advection of cold air from the ocean, or decreased surface warming due to the presence of clouds. However, taken together, evaporative cooling and the positive moisture anomaly upwind and over the catchment suggest that the repeated recycling of moisture through below-cloud evaporation (Sect. ) is likely to be essential in the generation of strong HPEs and LFEs.

To investigate the importance of the domino process in more detail we compiled a composite of the moisture sources of all medium HPEs, strong HPEs, and LFE-generating HPEs using our trajectory-based MSD results. Thereby, we can show that the importance of moisture recycling through this domino process is likely to be considerable and intensifies with increased event magnitude. The origin of more than 60 % of the moisture throughout all HPEs is classified as coming from the desert (Fig. , orange-yellow colours). While the largest moisture-contributing region to HPEs is the Sahara and the vicinity of the Sebkha el Melah catchment, during LFE-generating HPEs, the role of the farther Sahara and even the Sahel is clearly more important than for strong and medium HPEs. During these non-lake-filling HPEs, the moisture originates from regions closer to the catchment, and higher contributions from the Atlantic and the Mediterranean are observed.

However, given the normally dry conditions over the surface of the Sahara, we can assume that mechanisms other than surface evaporation are involved in triggering such HPEs. Based on the evaporation of precipitation upwind (Fig. ) and before the HPE starts (Fig. ), we suggest that a pre-moistening of the atmosphere in the vicinity of the catchment is important for precipitation formation over Sebkha el Melah and that recycling of moisture in a domino-like way throughout the upstream region within the Sahara is significant for HPEs. We term this moisture-recycling mechanism the “domino effect”. Moisture from the tropics forms clouds and precipitates along the tropical plume. A large part of this precipitation evaporates or sublimates when falling into the relatively dry lower and middle troposphere (possibly forming virgae). Thereby, a vertical connection between the upper-level clouds transporting moisture of tropical origin and the lower-level dry airstream from the Sahel is established. This moisture thus gets recycled and transported further north into the catchment in a domino-like process, which may repeat itself several times along the transport pathway from the tropics into the Sahara and finally into the catchment. This recycling process likely contributes to destabilising the lower to middle troposphere, which, together with the large-scale convergence of moisture from different tropical sources from the tropical North Atlantic and from the Sahel, Fig. ; similar observations were made by and the forcing for ascent due to topography upon arrival in the catchment, leads to the formation of a large-scale deep convective system forming intense precipitation. Since, during the evaporation phase, no precipitation is detected by IMERG, it is difficult to estimate the magnitude of this domino effect. To confirm the significance of this process, in situ or ground observations, such as from rain gauges or weather radar, would be needed. Nevertheless, because of this process, the Sahara can be described as a moisture source induced by precipitation evaporation and not due to contributions from surface evaporation. This domino process should be further investigated in the future by numerical tracer experiments that allow us to follow the moisture from surface evaporation in specific regions e.g. forward in time with model integration.

The MSD analysis reinforces the synoptic climatology observations (e.g. Fig. ), which indicates that the domino effect is more important for LFEs. Smaller events receive moisture mainly from local moisture recycling over the nearby desert region, with supplemental moisture originating from the Atlantic and the Mediterranean regions. However, to generate enough precipitation to fill the lake, moisture recycled from farther away is necessary, brought from the tropics and recycled over the Sahel and the Sahara. With the MSD approach used in this study, it is not possible to identify the sources of the recycled moisture underway; however, in a future study, we plan to use a regional climate model with numerical tracers as in, which will allow us to identify the tropical regions from which the moisture from the mid- to upper-level cloud layers originates.

The second most important moisture source for HPEs is the Atlantic Ocean (Fig. , blue-green colours). Extratropical cyclones from the (North) Atlantic control the wind fields and bring moisture around the Atlas Mountains, especially during strong (non-LFE) HPEs (middle column in Fig. ). The strong northerly winds over the North Atlantic (Fig. ) advect dry midlatitude air over the relatively warmer subtropical ocean surface, thus increasing oceanic surface evaporation .

Two meteorological features are responsible for generating heavy precipitation in the northwestern Sahara. These features are normally absent, thus keeping the region generally dry. However, when present, generally for durations of more than 1 d (Fig. a), LFEs may occur. These features are (i) synoptic-scale promotion and (ii) mesoscale reinforcement for the ascent of air, in combination with abundant moisture.

Ascent induced by synoptic-scale and mesoscale systems. Processes at various scales are involved in the HPEs in the northwestern Sahara, ranging from the synoptic scale to the local scale. At the synoptic scale, we have shown the importance of PV structures and low-level extratropical cyclones (Sect. –), which were previously also found to be important for different parts of Morocco . Upper-level PV structures destabilise the lower atmosphere and give rise to ascent. Furthermore, both the upper-level PV structures and low-level extratropical cyclones induce winds, which favour the advection of moist air from the Atlantic, the lifting of air parcels, and the formation of deep clouds due to low-level convergence and the advection of moist air toward the topography of the Atlas Mountains.

Climatological analyses of upper-level PV cut-offs and low-level extratropical cyclones show that the formation of such systems along the Atlantic coast of Morocco is rather exceptional. The frequency of both upper-level PV cut-offs and surface cyclones near the Atlantic coast of Morocco is roughly $<$ 5 % to 10 %, with the highest frequencies during winter and autumn . However, these two features do not necessarily co-occur, which highlights the exceptional situation needed for the formation of HPEs over the northwestern Sahara in today's climate. This finding may help to investigate past and future projections of HPEs over the southwestern Sahara, particularly in relation to shifts in the jet stream, Rossby wave breaking leading to the occurrence of upper-level PV cut-offs and surface cyclones e.g. . Additionally, the presence of upper-level PV features and low-level cyclones does not warrant the formation of a HPE, and further studies are needed to determine the frequency of these features without HPE formation.

On smaller scales, lifting mechanisms are connected to the wind field induced by the cyclone along the western coast of Morocco. Southerly to southwesterly winds force air parcels to travel over the Atlas Mountain chain. This either directly lifts air parcels enough to generate orographic precipitation or helps to overcome the convective inhibition that suppresses free convection. Furthermore, wind convergence can reinforce this ascent of air parcels. When convergence occurs upwind of the catchment (e.g. Fig. ), it can support the formation of precipitation, inducing the moisture recycling process described above as a domino effect.

On the smallest scale, the daily cycle of HPEs (Fig. ) indicates a contribution of free convection to the precipitation formation, with peak intensities observed in the evening in all seasons. However, it must be noted that convective precipitation is probably not sufficient to generate significant HPEs and LFEs; no LFEs are identified when the surface is warmest, i.e. in summer and in the other seasons convection happens mainly in connection with a synoptic-scale system (e.g. Fig. ). Therefore, while short-lived deep convection is important for HPEs, triggering and enhancing precipitation in the northwestern Sahara, it requires larger-scale forcing as well.

Moisture abundance. The most important moisture sources for precipitation in the region are (1) local sources from precipitation recycling within the catchment and its surroundings ($\sim$ 65 %) and (2) remote sources such as the North Atlantic, the Sahel, or the Mediterranean ($\sim$ 30 % combined; Fig. ).

In the desert, the importance of nearby moisture sources may seem surprising as actual evaporation from the surface is close to zero. However, we suggest that this moisture is actually mostly recycled; moisture diagnosed here as being taken up over the Sahara does not come from direct surface evaporation but rather from moistening through precipitation evaporation and sublimation and mixing due to the convergence of air parcels and convection . This means that this moisture might have originally come from other sources compared to the ones identified here, most likely from the tropics and the North Atlantic – upwind of the identified moisture sources. Cloud formation in squall lines or other mesoscale convective systems and tropical plumes is a potential candidate which fuels moisture transport into the southwestern outskirts of the Sahara, where it can precipitate, be recycled, and be transported deeper into the desert by the southerly flow. This sequence is repeated in a domino-like manner until the catchment region is reached, thus contributing “Saharan-flagged” moisture to the HPEs in our applied moisture source diagnostic approach. In addition, this aerial precipitation recycling process is supplemented by continental recycling and, thus, surface evaporation of the moisture remaining from recent precipitation events, which is common mainly in autumn (see, for example, the November 2014 case study (Sect. ), Figs.  and ). It is important to note that moisture sources in this study are analysed using one reanalysis product, as commonly done in MSD studies e.g.; however, if another reanalysis is used, results may slightly differ. In this regard, we do not expect the result to differ drastically between datasets because of the relatively good representation of synoptic-scale flows in modern reanalyses, even over the in situ-data-scarce region of North Africa .

While several types of synoptic or mesoscale systems can contribute to cloud formation upwind of the Sahara, to transport this moisture deep into the desert, persistent southwesterly flows are needed. These flows occur in the middle to upper levels of the troposphere whenever a southward-intruding upper-level trough is present at the edge of the northwestern Sahara or over the Atlantic coast, which is indeed the case during the identified HPEs (Fig. ). The related cyclones accumulate moisture from the Atlantic Ocean over their life cycle and precipitate during their passage into the Sahara and the catchment of Sebkha el Melah. This type of tropical–extratropical interaction was previously associated with tropical plumes .

Three conditions seemingly determine LFEs. These are the (a) lifting mechanism, (b) wind conditions, and (c) moisture source, which are described below.

LFEs need a strong and long-lasting lifting mechanism, which is maintained by the coupling of large-scale forcing and the mesoscale convective forcing. Persistence of upper-level conditions conducive to air lifting can happen, for example, when a strong, northward-extending, blocking high is situated upwind in the central North Atlantic Ocean. An example of this is given by the November 2014 case study (Sect. ), where PV structures appear repeatedly in the vicinity of the catchment and a high persists over the central North Atlantic. At the same time, the persistent conditions allow for increased moisture transport from the southwest e.g. and continuous formation of rain cells and, therefore, also for a longer rainfall duration and larger areal coverage, which are needed to generate intense desert floods e.g.. These conditions lead to relatively long-duration HPEs, with typical durations of 3 d for the LFE-triggering HPEs.

The wind conditions are related to the large-scale forcing. Orographic lifting only appears when the wind is strong enough and directed close to perpendicular toward the Atlas Mountains (i.e. southerly winds, similar to what was shown by for heavy precipitation in the Alps), such that the air parcels are forced to rise, making it possible to overcome the typical subsidence aloft. However, it seems that the essential ingredient is not the south-to-southwesterly wind within the catchment but actually the southwesterly flow that circumvents most of the High Atlas Mountains from the south such that the moisture is not lost to precipitation beforehand. These winds blow with higher velocities when the low-level cyclone is relatively deep and situated close to the western coast of Morocco (Fig. ).

Lastly, to obtain enough moisture for creating heavy precipitation, it needs to be transported not only from the surrounding regions but also from faraway, specifically from tropical Africa and the midlatitude North Atlantic, being transported and recycled by the domino effect once it has reached the edge of the Sahara. Favourable conditions for such long-range-transport events are also obtained when the winds are stronger and blow from the southwest. The non-lake-filling HPEs show a less pronounced recycling process of moisture in the Sahara. The major part of the moisture for these events originates from the nearby upstream region, and the moisture uptake is, in general, weaker than for LFEs (Figs. , ).

When all the above conditions are met, the precipitation that falls in the catchment of Sebkha el Melah has a higher potential to fill the lake. Namely, events are generally longer (2–5 d compared with 1 d on average for the non-lake-filling HPEs) and have high precipitation volumes. While the volume itself may not be sufficient to determine whether the lake gets filled (since few of the heaviest precipitation events did not fill the lake), the HPE magnitude (Sect. ) is quite a good determinant for lake filling. Out of the 10 highest flood magnitude HPEs, 8 produced LFEs. This means that high-intensity precipitation needs to be rather spatially focused and located over the runoff-contributing areas of the catchment (Sect. ) to overcome infiltration rates and generate high-magnitude surface runoff and flows in the streams.

Effective runoff coefficient, namely, the portion of precipitation that ends up in the lake, is one of the most important but non-resolved factors in relating paleo-lakes to paleo-climatic conditions e.g.. Runoff coefficients are generally not available for large desert catchments, especially at the event scale . At the annual scale, considering the fact that it rains every year but the lake remains empty most of the time, effective runoff coefficients are expected to be close to zero. The runoff coefficients presented here are, to the best of our knowledge, the first to be obtained over the Sahara which represent the actual ratio between event precipitation and lake volume. Annual runoff coefficients in AHP literature range from $\sim$ 10 % to $\sim$ 30 % annual values; e.g. . Here, we show that the event-based effective runoff coefficients in the basin range over about 5 orders of magnitude, from $\sim \mathrm{1}\times {\mathrm{10}}^{-\mathrm{4}}$ % to $\sim \mathrm{1}\times \mathrm{10}{}^{\mathrm{1}}$ % (Fig. b). The higher runoff coefficient values are presumably related to precipitation over the parts of the catchment where rocky surfaces are exposed in combination with higher rainfall intensities, as well as longer rainfall durations and shorter inter-event periods. All these aspects increase the runoff-contributing area and its contribution to flood discharge e.g.. The obtained runoff coefficient values are in line with the results of based on gridded rainfall data in Australia, but only a few of the catchments in their study are large, arid catchments. The construction of dams in the catchment is expected to lower the effective runoff coefficient. However, large HPEs are not expected to be heavily affected; the main dam in the catchment can only contain $\sim$ 0.25 km³ , which is $\sim$ 4 % of the mean catchment rainfall in the largest HPE (Fig. a).

Desert lakes are commonly relatively small compared to their catchment area; therefore, effective runoff coefficients control the filling of these lakes, with only a minor filling contribution from direct rainfall over the lake . Therefore, when reconstructing the water budget of a desert lake, slight shifts in the values of the effective runoff coefficient lead to large deviations in the estimation of lake volumes. With the 21 years of data, the largest effective runoff coefficient values we estimate here per event are on the order of 10 %, and most are well below (Fig. b). These are very low values compared to the ones used in estimating paleo-rainfall during the AHP based on hydrological and radiative budgets e.g.. Here, we showed that higher runoff coefficients seem to be related to higher rainfall event depths and shorter inter-event dry periods. Therefore, based on present-day observations, we suggest that the filling and maintaining of Saharan lakes can be related to the intensity of individual events and changes in their frequency. In other words, if high-magnitude events are more frequent, the annual runoff coefficient is expected to increase even if the mean annual rainfall remains the same. Since it could take years for lakes to empty out through evaporation (e.g. Fig. c), a higher frequency of years with such high-magnitude events can maintain filled lakes with no change in the mean annual rainfall. Moreover, given the presented modern observations, a large-scale northward shift of the African monsoon during AHPs may not be necessary. Rather, a higher tendency of extratropical cyclones could produce increased lake levels. Therefore, while climate models struggle in shifting the African monsoon as far north as in filling lakes in the northwestern Sahara, an increased frequency of southward-intruding extratropical cyclones can potentially produce a similar result. We do not mean to imply that no change in precipitation occurred during the AHP; rather, we suggest that the magnitude of the change might have been less important compared to changes in the intensity and frequency of HPEs or that the type of change needed was previously undervalued. One major implication of this suggestion is that, to effectively model precipitation changes during past (or future) periods in the Sahara, relatively small-scale changes in precipitation need to be accounted for, calling for high-resolution model simulations. Given that precipitation during Saharan HPEs is largely convective, as discussed in Sect. , in order to accurately simulate changes in both precipitation and runoff, models need to be able to resolve convective-scale processes, which reaffirms conclusions made by both and .