How does humidity and precipitation occur in a region? What factors affect a good rainfall? Why are some rainfalls torrential, some continuous, and sometimes storms?

The flash flood forecasting remains one of the most difficult tasks in the operative hydrology worldwide. The torrential rainfalls bring high uncertainty included in both forecasted and measured part of the input rainfall data. The hydrological models must be capable to deal with such amount of uncertainty. The artificial intelligence methods work on the principles of adaptability and could represent a proper solution. The application of different methods, approaches, hydrological models and usage of various input data is necessary. The tool for real-time evaluation of the flash flood occurrence was assembled on the bases of the fuzzy logic. The model covers whole area of the Czech Republic and the nearest surroundings. The domain is divided into 3245 small catchments of the average size of 30 km2 . Real flood episodes were used for the calibration and future flood events can be used for recalibration (principle of adaptability). The model consists of two fuzzy inference systems (FIS). The catchment predisposition for the flash flood occurrence is evaluated by the first FIS. The geomorphological characteristics and long-term meteorological statistics serve as the inputs. The second FIS evaluates real-time data. The inputs are: The predisposition for flash flood occurrence (gained from the first FIS), the rainfall intensity, the rainfall duration and the antecedent precipitation index. The meteorological radar measurement and the precipitation nowcasting serve as the precipitation data source. Various precipitation nowcasting methods are considered. The risk of the flash flood occurrence is evaluated for each small catchment every 5 or 10 minutes (the time step depends on the precipitation nowcasting method). The Fuzzy Flash Flood model is implemented in the Czech Hydrometeorological Institute (CHMI) – Brno Regional Office. The results are available for all forecasters at CHMI via web application for testing. The huge uncertainty inherent in the flash flood forecasting causes that fuzzy model outputs based on different nowcasting methods could vary significantly. The storms development is very dynamic and hydrological forecast could change a lot every 5 minutes. That is why the fuzzy model estimates are intended to be used by experts only. The Fuzzy Flash Flood model is an alternative tool for the flash flood forecasting. It can provide the first hints of danger of flash flood occurrence within the whole territory of the Czech Republic. Its main advantage is very fast calculation and possibility of variant approach using various precipitation nowcasting inputs. However, the system produces large number of false alarms, therefore the long-term testing in operation is necessary and the warning releasing rules must be set. Keywords: Fuzzy Logic, Flash Flood, Operative Hydrology.The flash flood forecasting has always represented a major challenge for hydrologists. A causal torrential rainfall has substantial dynamics in both space and time and it brings high amount of uncertainty, which we will probably not be able to eliminate sufficiently in the near future. Mentioned uncertainty must be taken into account in the process of forecasting as well as when interpreting the results. The Czech hydrometeorologic institute (CHMI) is the national service for meteorology, hydrology and air quality and ensures the flood forecasting service (FFS) in the Czech Republic. Standard hydrological forecast based on outputs from numerical prediction models is issued for more than one hundred forecasting profiles but in the case of flash floods it is not sufficient and a different approach is needed. A prime product of CHMI for flash flood forecasting is Flash Flood Guidance (Daňhelka et al., 2015) and output from this model is published in CHMI web site. Simultaneously, attention to a development of other tools is being paid. For example the distributive hydrological models used for flood forecasting on bigger catchments can be applied but it requires very detailed schematization and calculation is time-consuming. Currently this approach is tested only on selected small catchments and it doesn’t cover whole area of the Czech Republic (Daňhelka et al., 2015). The artificial intelligence based methods are also tested in the CHMI, the Fuzzy Flash Flood model is introduced in following text. Its advantage consists particularly of very fast calculation, which enables us to evaluate the most up-to-date input data in more variants.

Moreover, the adaptability principle becomes more and more important in the current climate change context. The fuzzy model assembly comes from the real flash flood episodes (2009-2019) and the new episodes are being added constantly. The model is so able to reflect possible changes in the rainfall-runoff processes. The difficulty of flash flood forecasting requires the usage of more tools and that is why the variety in the modeling approaches will be always beneficial. METHODS AND DATA In general, a process of a hydrological forecast could be divided into the three elementary steps: 1. An input data preparation. 2. A calculation of a hydrological model. 3. A results evaluation and publication. Let us compare a standard hydrological forecast (it means forecast for a catchments of size of hundreds of square kilometres, usually based on outputs from numerical weather prediction models) and flash flood forecast in each mentioned step. In the case of a standard hydrological forecast, the first step (input data preparation) enables checking input data both automatically and manually. Time-resolution of input data is usually 1 hour. Measured precipitation ordinarily consists of a merged product calculated as radar estimates combined with rain gauge measurements. More variants of weather forecast could be considered, according available numerical weather prediction (NWP) models. Through the consultation with meteorologists, the most probable future weather development could be determined. In contrast, a flash flood forecasting requires the most frequent updating as possible (5-10 minutes). A manual checking or editing of input data is unrealistic. The whole process must be fully automated. Time-resolution of input data should be 5-10 minutes. Measured precipitation is being derived from radar measurement and should be significantly under/overestimated. The precipitation forecast comes from the extrapolation of radar echo (nowcasting) and includes a huge amount of uncertainty. For example, extrapolation methods do not involve the life cycle of storm cells. It is possible to consider more variants of precipitation nowcasting methods. In the second step, a calculation of a hydrological model is carried out. When calculating a standard hydrological forecast, hydrologist’s main work lies in the adaptation of the hydrological model to the current rainfall-runoff situation. Parameters of the hydrological model could be adjusted to achieve the best possible matching of measured and simulated discharges. The estimation of the future discharge development follows. The flash flood forecasting does not enable any real-time adjustment of the hydrological model especially because of the lack of time and high uncertainties included in the input data. Hydrologists are reliant on the automated results only. The hydrological model can be recalibrated additionally (for example according hit/miss/false analyses). It needs to be pointed out, that flash floods occur randomly and mostly hit an unobserved catchments. That means that there is the lack of relevant data for the calibration of the hydrological model. There are differences also in the publishing options. Within the FFS provided by CHMI, the standard hydrological forecast is published on the internet and usually it is updated twice a day and during the flood situation, the updates can be done more frequently (every hour if needed). The flood reports with a verbal description of the current state and the further development are issued. The publishing of the flash flood forecast still remains a subject for discussion, in particular because of huge uncertainty of the results and the necessity of more complex interpretation. Currently, the presentation of forecast from the Flash flood guidance model is tested on CHMI website. The outputs from the Fuzzy Flash Flood model are not available for public and are used only internally

The problem lies in the fact that we probably cannot enhance the accuracy of the input data significantly in the near future. That is the main motivation for using the artificial intelligence methods. The theory of the fuzzy logic could be found for example in (Jang, 1993). The principles of the Fuzzy model assemblage are described in (Janál, Starý, 2012). In following text, a description of the current version of the Fuzzy model with the emphases on its operation is provided. The whole area of the Czech Republic and certain surroundings is covered by the model. The area of interest is divided into the small catchments of the size of 30 km2 on average. There are 3245 small catchments in total and for each the input variables are considered as an average values. Many different structures of the model were tested in the past. The current version consists of two fuzzy interference systems (FIS). The first FIS was developed by dr. Ježik (Ježík, 2015) and it serves to the determination of the predisposition to the occurrence of the flash flood for each mentioned small catchment. Input variables are the catchments characteristics like the area, forest cover, slope, soil type and others. The second FIS forms an operative part of the model and has 4 input variables: Potential predisposition to the occurrence of the flash flood (gained from the first FIS) Average precipitation intensity Duration of the rain Antecedent precipitation index (calculated for 14 days) The values of the first input (Potential predisposition to the occurrence of the flash flood) are calculated in advance by the first FIS for the whole set of the small catchments and they are fixed. These values could be updated by new calculation of the first FIS when the more relevant catchments characteristics are available or in terms of the analyses of the success of the model. The remaining three input variables (a precipitation characteristics) are computed operatively for the whole set of the small catchments in each time step. More variants of the precipitation forecast are considered based on different precipitation nowcasting methods. The time step (updating frequency) of the Fuzzy model is 5 or 10 minutes, according to the used precipitation nowcasting product. The time interval of 5 hours is considered in each time step, 2 hours of history and 3 hours of nowcasting. The detailed description could be found in (Janál, Starý, 2012). Currently, three precipitation nowcasting products are used as inputs for the Fuzzy model (Haiden at al., 2011), (Novák, 2007): COTREC (time step 5 minutes) CELLTRACK (time step 10 minutes) INCA (time step 10 minutes) Additionally, the Fuzzy model is calculated in the variant when no precipitation nowcasting is taken into account and only measured precipitation is considered. In this variant, the uncertainty of input data is significantly lower, but the time for the warning is reduced. The antecedent precipitation index is also updated in each time step (moving method). The output variable of the Fuzzy model is the flash flood endangerment degree and it is determined for each catchment (3245 values in each time step). The modeled catchments are interlinked in the meaning that the endangerment is propagated downstream while it is reduced gradually. The exact time of the culmination is not the subject of the forecast. The interpretation is so, that flash flood could occur in the nearest future (in oncoming hours or minutes). The output variable ranges from 0 to 1, when 0 means no endangerment and 1 means the endangerment of flood with the return period of 100 years or more. This interval is divided into 5 levels represented by different colors, which are used for the operative presentation of the results through the Fuzzy Flash Flood application created by J. Brzezina, see figure 1.Through the application, the hydrological response based on different precipitation nowcasting methods can be compared in the form of the maps of endangered areas. Hydrologists can get a primary information about oncoming situation almost immediately after data from the meteorological radar are available. It means that the time for warning or some reaction is maximized. An easier interpretation could be achieved by merging the results into the bigger areas, which reflects the areas for standard warnings of CHMI (lower right map on the figure 1). All results are stored in relation database and are available for the retrospective analyses. RESULTS AND DISCUSSION The fuzzy model is in the testing operation in Brno regional office of CHMI and results are shared with the other offices of CHMI for internal use. Contemporary development is focused mainly on the validation of the model. This part is very demanding because of the character of flash floods. There is often not sufficient feedback and we can hardly detect all events, which have happened. Alongside the local case studies the more robust validation method is being developed. The validation method should be able to evaluate continuous time period and should be automatized. The essential requirement for such method is the reliable source of the impacts caused by the torrential rainfalls. Since CHMI closely cooperates with firefighters, the database of the firefighter actions was used for this purpose. This source of impact data has advantages that it is covering the whole territory of the Czech Republic and the events are localized by GPS coordinates. However, we must be aware of weaknesses of this data source. The time of the firefighter action does not always correspond with the time of flash flood. The reason of firefighter action is described by the specific code, it enables us to select only the situations that concern the flooding, for example the flooded cellars. But not all such events are caused by torrential rainfalls. The cellars could be for example flooded by the water pipe breakdown. The algorithm of evaluation method was compiled taking into account all mentioned features of the firefighter actions database. Flash flood warnings were evaluated for the same areas as in the case of the standard warnings of CHMI (lower right map on the figure 1) and hit-miss-false statistic was processed. The goal of evaluation was to find an adequate sensitivity of the Fuzzy model. Since the evaluation method is still under development, the results published in this paper only cover a short period from May 26 to June 1, 2018, but they can nevertheless demonstrate the potential of the model. Seven different levels of model sensitivity were tested, meaning that alerts were issued after seven different thresholds were crossed, while the model sensitivity decreased from the first to the seventh type. The error-to-error ratio for the seven mentioned types of model sensitivity is shown in Figure 2. Probably due to the high uncertainty of the input data, a high rate of false alarms will always exist, but it can be reduced by appropriately setting the alarm threshold. This depends on deciding which alarm threshold is most appropriate for action. A high number of false alarms can lead to a decrease in the predictive value in the eyes of users. On the other hand, issuing a false alarm may not be associated with the same risk as in the case of the false alarm might not be connected with the same risk as in the case of the missed flood. CONCLUSIONS The aspiration for the flash flood forecasting comes from the possibilities that are currently available in CHMI. Fifteen years ago, the flash flood forecast seemed to be almost impossible. The major progress in the meteorological radar measurement and precipitation nowcasting brought certain ways to predict even such fast natural disasters. The successfulness of the forecast is directly dependent on the accuracy of the precipitation estimates. The error of the precipitation measurement during the convective precipitation event could be dozens of percent and the error of the precipitation nowcasting could be even higher. We cannot rely on the specific values of the precipitation inputs since they are “always wrong”. The essence of the flash flood forecast lies in the real-time evaluation of all the data we have. The artificial intelligence methods enable the very fast calculation and the ability to work with the uncertain data. The question of the form of warning remains open. The publishing of the forecast through the websites might not by sufficient. If we were able to warn the residents of endangered municipality directly, the reaction strategy would have to be clearly specified. In the extreme cases it is not about the flooded cellars but about saving lives. Early warning may provide a few minutes for leaving the zones around watercourses.

REFERENCES:

Daňhelka. J, Janál, P., Šercl, P. a kol. Možnosti predikce přívalových povodní v podmínkách České Republiky, Edice Sborník prací Českého hydrometeorologického ústavu, 2015, Praha, 50 s., ISBN 978-80-87577-27-1, ISSN 0232- 0401. Haiden et al. The Integrated Nowcasting through Comprehensive Analysis (INCA) system and its validation over the Eastern Alpine region. Weather Forecasting, 26, 2011. Janál, P., Starý, M. Fuzzy model used for the prediction of a state of emergency for a river basin in the case of a flash flood – part 2, J. Hydrol. Hydromech., 2012, Vol. 60, No. 3, p. 162–173. Jang, J.R. ANFIS: Adaptive-Network-Based Fuzzy Inference System, IEEE Transactions on Systems, Man, and Cybernetics, 1993, Vol. 23, No. 3 Ježík, P. (2015): Využití vybraných metod umělé inteligence pro nalezení malých povodí nejvíce ohrožených povodněmi z přívalových dešťů. Brno, 2015, Ph.D. thesis. Brno University of Technology, Faculty of civil engineering, Institute of landscape water management. Novák, P. The Czech Hydrometeorological Institute’s Severe Storm Nowcasting System. Atmospheric Research, 2007, 83, pp. 450–457.

Cutoff lows are upper-level cold-core cyclones that become detached from the mid-latitude westerlies, drifting slowly toward lower latitudes. In southwestern South America, they frequently appear near 30°S and play a significant role in driving rainfall, sometimes bringing intense precipitation to areas that are normally very dry. Because these systems are often convective and move slowly, forecasting their precipitation remains challenging, yet they are a major cause of extreme rainfall and floods in northern and central Chile. Despite their frequent occurrence, many of these storms fail to produce heavy rainfall unless they tap into sufficient moisture. A recurring factor in major flood events is the presence of a coastally trapped moisture plume that pushes water vapor southward from warmer waters near the Peru–Chile border. When these plumes intersect the topography of the Andes, the resulting uplift can trigger deep convection, causing significant precipitation and sometimes devastating floods and landslides. Looking ahead, changing climatic conditions, including increases in sea surface temperature and atmospheric moisture, may affect both the frequency and intensity of cutoff lows. Even moderate cyclonic disturbances can lead to major precipitation extremes when there is ample moisture available. As a result, understanding the interplay between large-scale dynamics, moisture supply, and mountain uplift is crucial for improving rainfall forecasts and anticipating the impacts of future storms on one of the driest regions on Earth. Keywords: Cutoff lows, Rossby wave breaking, Atacama Desert, Orographic precipitation, Moisture transport, Upper-level cyclones, Extreme rainfall, Climate change. Introduction: Cutoff lows have only been recognized as an important feature of the synoptic meteorology of southwestern South America during this century (Pizarro & Montecinos, 2000). For example, more than 50% of precipitation in the hyperarid core of Atacama and its surroundings can be explained by cutoff lows (Aceituno et al., 2021). In fact, some major extreme rainfall events in the region between 20°S and 35°S are associated with cutoff lows (Bozkurt et al., 2016; Mu˜noz & Schultz, 2021). Some historical accounts from the nineteenth century seem to confirm that cutoff lows have, from time to time, produced rainfall in the arid and semi-arid northern Chile. Vicu˜na-Mackenna (1877) refers to a storm in July 1877: ”But what constitutes the most remarkable peculiarity of the rainstorm on July 10 in Atacama is not that it rained in these regions when in the south it had completely cleared, nor that each of its rain showers lasted more than twelve hours, but that its movement was reversed, from north to south, as if its generating nucleus had been in the desert, that is, in latitudes where it never rains.”The Atacama flood of 2015 is perhaps the most extreme modern example of these storms. During March 24 and 25, 2015, a cutoff low caused significant damage and tens of deaths in hyperarid northern Chile (blueish region in Figure 1), due to landslides and major flooding experienced in all basins of the region (Barrett et al., 2016; Bozkurt et al., 2016; Reboita & Veiga, 2017; Wilcox et al., 2016). This has led to renewed interest in understanding the physical and dynamical characteristics of cutoff lows in this region, as well as exploring changes in frequency and intensity during historical and past periods (e.g. Reyers & Shao, 2019). Not only is it interesting to understand the processes that control the existence of the driest desert on Earth, it is also interesting to understand how these processes can break under current climatic conditions. Considering that climate projections for this century include a robust signal of moistening along Northwestern South America (e.g. Belmadani et al., 2014; Oerder et al., 2015), understanding the interaction of cutoff lows and atmospheric water vapor sources has become a major research priority. Dynamical Features Cutoff lows are closed cyclonic circulation in the mid- and upper levels of the troposphere that have been segregated from the mean westerly flow towards the equator (Palm´en, 1949). This segregation from the mid-latitude storm track makes cutoff lows more likely to impact lower latitudes than usual baroclinic disturbances. Cutoff lows also tend to drift slowly westward because of the absence of a strong background mean flow. They are a cold-core vortex (as opposed to hurricanes which have a warm-core), and this explains some of the names they receive in Spanish such as ”gota fr´ıa” (cold droplet) or ”n´ucleo fr´ıo en altura” (upper level cold-core). Although cutoff lows are a relatively common feature of the synoptic meteorology of southwestern South America, their impacts, especially with respect to precipitation, remain challenging to forecast mainly due to the convective nature of rainfall in these episodes. We illustrate several aspects of the typical development of cutoff lows in the southwestern Pacific using a case study of a cutoff low during April 2024. This particular cutoff low produced rainfall over Central and Northern Chile during the period between April 12th to 15th. This cutoff low can be considered representative of precipitating cutoff lows during fall in Northern Chile. Although not an extreme case, we can see in Figure 1.b, that this particular event was able to produce rainfall in many arid and hyperarid regions. Some stations recorded near 40 mm of accumulated rainfall during this event, competing with the annual accumulation in some cases. Potential Vorticity view From a large-scale perspective, cutoff lows can be thought of as disturbances that originate from the polar reservoir of planetary cyclonic vorticity as a result of the Rossby wave breaking along the polar front. The Ertel-Rossby potential vorticity (PV) on an isentropic surface (e.g. McIntyre, 2003) is defined as P V = −g(ζθ + f) ∂θ ∂p, (1) where g is gravity, ζθ is the relative vorticity on an isentropic surface, f is the planetary vorticity and θ is the potential temperature. Given that PV is materially conserved on an isentropic surface in the absence of friction and diabatic processes, cutoff lows appear as blobs of cyclonic vorticity abandoning the polar reservoir when seen in a PV map on an isentropic surface (Hoskins et al., 1985). Figure 2 shows one of such cases using isentropic maps on the 330 K surface from the period between April 11 and April 17, 2024. During April 11, a strong anticyclone centered around 105°W advected polar PV towards lower latitudes at around 90°W (Fig.2.a). At this point, a large region at the mid-latitudes showed a reversed gradient of PV (that is, more negative values toward the Figure 2: Isentropic potential vorticity maps from the period April 11 2024 to April 17 2024. PV is in colors and wind is in vectors over the 330 K isentropic surface. Data is from ERA5 reanalysis. equator), between 90°to 50°W (Fig. 2.a-b), which is the telltale sign of a Rossby wave breaking event. According to Ndarana and Waugh (2010), about 90% of the cases of cutoff low formation occur associated with the breaking of Rossby waves in the Southern Hemisphere. The low values of PV associated with the anticyclone reach approximately 60°S and the intrusion of cyclonic PV into the subtropics continues to amplify. The original cyclonic PV trough, that gave origin to the cutoff low, has now advanced eastward and is located at about 40°W (Fig.2.c). As the wave continues to amplify, we observe that the region connecting the main cyclonic circulation in the subtropics (centered approximately 80°W, 35°S in Figure 2.d) becomes elongated and thinner. During the following 24 hours, the main cyclonic PV blob remains almost completely stationary off the coast, a feature that is typical of other cases. For instance, Godoy et al. (2011) show that the so-called ’stagnation’ of the cutoff low windward of the Andes ocurrs associated to a balance between the divergence and the horizontal vorticity advection terms of the vorticity equation. By April 14th, 00 UTC, a filament is clearly visible along 45°S (Figure 2.f), connecting the cutoff low to the original source of cyclonic PV, which has shifted to 30°W by this time. As Figure 3: (a) A close-up view of the filament in Figure 2.h from ERA5 reanalysis(b) The corresponding mid-level water vapor channel (6.9 µm) image of the filament during April 15th, 00 UTC from GOES-16. the filament becomes thinner, it begins to erode due to diabatic and frictional processes (e.g. Appenzeller et al., 1996), effectively isolating the cutoff low from its polar PV reservoir (Figure 2.i). An interesting example of these irreversible processes can be seen immediately before the filament breaks on April 15th, 00 UTC (Fig. 2.h). The vorticity filament develops elipsoidal vorticity centers similar to those found in the barotropic instability (Figure 3.a, Appenzeller et al. (see e.g. 1996, and references therein)). In fact, the wavelength of this feature is about 1000 km, which, using the Rayleigh relation between the width of the vorticity region δ and the most unstable wavelength of in the barotropic instability λ ∼ 8δ (e.g. Reinaud, 2020), suggests a vorticity region width of about 135 km, closely matching the observed width of the filament. Also, the water vapor image at the same time confirms the existence of the barotropic instability in the observations, where the dry region in the image bears a striking resemblance to the solution of the non-linear barotropic equation for a parallel shear flow (see e.g. Figure 6.6 in Vallis, 2006). As the vortices grow at the expense of the horizontal shear of the flow —which is the source of the vertical vorticity of the filament— turbulence and irreversible mixing will develop. (Figure 2.i). Between April 15th, 12:00 and April 16th, 00:00 (Figures 2 i-j), the cutoff low crosses the Andes, losing part of its original intensity but conserving its shape. Once the cutoff low crosses the Andes, the system can tap water vapor from the Atlantic and the Amazon, and sometimes a rapid intensification of the storms associated with the system resulting in the demise of the upper-level cyclone due to diabatic heating, although in other cases the cut-off low can be intensified by the interaction with the stationary trough induced by the Andes and give rise to baroclinic development Funatsu et al. (2004). In this case, we see a rapid desintegration of the PV blob east of the Andes (Fig. 2.k). Finally, the remains of cyclonic PV near the La Plata basin begin to be mixed with PV of a subsequent wave breaking. In addition, a new meridional PV feature near 100°W appears to form of a new wave breaking in the Pacific (Figure 2.l) The advantages of this PV-view should be evident. We can see just from looking at one single field the formation of the cutoff low and its evolution as it segregates from the polar PV reservoir, in a way that is completely analogous to ink in a tank experiment of fluid dynamics.However, many aspects of the evolution of the cutoff low need further exploration. First, since we are looking at a single isentropic level, which is usually in the lower stratosphere, no major information on the coupling with the surface circulation is available from this field. If one considers the cutoff low as an upper-level cyclonic PV perturbation (e.g. Holton, 2004), the vertical extent of the perturbation can be theoretically quantified using the Rossby scale height H = fL N , where f is the Coriolis parameter, L is the horizontal scale of the perturbation and N is the Brunt-V¨ais¨al¨a frequency, a measure of static stratification. A peculiarity of the southeastern Pacific is that it is the coldest ocean at subtropical latitudes, which means it has a higher value of N compared to other regions of the planet at about the same latitude. This would result in lower values for H, and therefore the upper-level perturbations are relatively uncoupled from the surface west of the Andes. However, the decoupling of the upper-level perturbation is in some sense non-linear, given that the existence of stability precludes the development of surface and mid-level circulations and, therefore, might act as to ”protect” the upper-level cyclone from their demise through diabatic heating (Garreaud & Fuenzalida, 2007). As the cutoff low approaches the Andes, the possibility of the release of potential instability through ascent becomes more likely, and therefore diabatic heating over the Andes due to the precipitation produced by orographic lifting might contribute to the lysis of the cyclone. Presumably, turbulent mixing produced by the interaction between the perturbation and the topography also plays a role in destroying the cutoff low. We will explore some of these features in the following sections. Vertical Structure If we take a cross section of the low during April 13th 2024, 00 UTC along 80°S (Fig. 4) we can see that the PV anomaly can penetrate to mid levels of the atmosphere. High values of static stability are evident in the cyclonic PV region, where the isentropes are closely packed in the vertical. In contrast, the region immediately below the PV anomaly is a region of low static stability, consistent with the fact that the cutoff low corresponds to an upper-level cold core. This implies that cold air in the mid to upper levels of the atmosphere replaces otherwise warmer subtropical air, which tends to increase the static stability of the lower stratosphere and decrease the static stability of the lower troposphere. For example, during a case study in 2012, Rahn (2014) reported an increase in the height of the marine boundary layer from about 2 km to 4 km (and a complete disappearance of the subsidence temperature inversion) during the passage of a cutoff low. However, a decrease in static stability is usually not enough to produce deep convection over the ocean on the cold Pacific coast of Southeastern South America. Even if convective towers develop, the small values of shear below the center of the upper-level low, prevent mesoscale organization (Rahn, 2014). We see that in this particular case, the cyclonic circulation is confined to levels above 700 hPa where the horizontal winds are higher than 10 m/s ( Figure 4.b). On the equatorward side of the cyclone, an upper level front is evident (marked as a blue line in Fig. 4.b)). Along the front low values of specific humidity and cyclonic PV indicate a tropopause folding that occurs associated with the secondary circulation associated with the cutoff low (see e.g. Pinheiro et al., 2020; Rondanelli, Gallardo, et al., 2002). To understand the stability of the cutoff low, we look at a single vertical profile at 30°S and 80°W at April 13, 2024 00 UTC in a SkewT-logp diagram (Figure 5.a). It shows that a parcel on the surface is slightly unstable and exhibits some positive CAPE values (∼ 20 J/kg/K). However, these positive CAPE values are capped by a strong convective inhibition of magnitude similar to that of the CAPE. The lower positive CAPE values are confined to a shallow layer between 900 and 850 hPa. A nearly isothermal layer between 800 and 750 hPa suggests the usual effect of subsidence warming over this region of the Pacific. Above the isothermal region, the temperature profile is absolutely stable. Considering the sounding as a whole, surface parcels might develop much larger levels of CAPE through an increase in temperature or humidity, which could be relevant for the fate of the cutoff low on the eastward side of the Andes. Here, we have considered a vertical profile in Figure 4: Cross section along 80°W of potential vorticity (colors) during April 13th 2024, 00UTC. The black contours show the wind speed in the eastward (solid) and westward directions (dashed). Specific humidity (g kg-1) is show in blue contours. Potential temperature is shown in thin black contours (K). The thick red line shows the 330 K isentrope. The blue slanted line indicates the approximate location of the upper level front and the J marks the position of jet stream. the equatorial region of the low. This air column will be carried by the circulation and probably forced to ascend orographically over the steep coast of Northern Chile. In this case, examining the stability of a layer, rather than a single parcel, is more appropriate (Iribarne & Godson, 1981). In Figure 5.b, we see that an initial layer of a depth of 150 hPa between points A (900 hPa) and B (750 hPa), which includes the stable inversion layer, has a lapse rate lower than moist adiabatic and is therefore absolutely stable. When we consider the ascent of this finite layer by 200 hPa (which is roughly the height of the topography near the coast in Northern Chile), the lower part of the layer becomes saturated, reaching point A′ at 700 hPa. The B point never reaches saturation, so the ascent occurs along a dry-adiabat. As a result, the ascent of the layer results in a lapse rate which is between a dry-adiabat and a moist-adiabat, leading us to conclude that the profile is potentially unstable to this ascent. The potential instability of the profile has great explanatory power. If the profile were unstable over the ocean, deep convection would be released there and the demise of the cutoff low would occur rapidly due to latent heating release and convective overturning. However, if the profile were absolutely stable, no convection would be expected to occur on the windward side of the Andes as a result of topographical ascent. Potential instability is therefore ’just right’ to explain the behavior of most precipitating cutoff lows as they approach the Andes. However, Mu˜noz et al. (2020) studied the potential instability of the profiles, and they emphasize the role of the quasi-geostrophic ascent of the upper level cyclone as a major contributor to the release of potential instability, rather than the effect of the mostly blocked orographic ascent. Given the distribution of precipitation in individual cases and in the climatology (as we will see in the following sections), we tend to favor the view that even moderate orographic ascent contributes to the release of the potential instability, probably acting in combination with the synoptic-scale forcing. This is mainly due to the fact that precipitation from the cutoff low rarely peaks over the ocean, and therefore the potential instability is released when the system faces the Andes. However, more research is needed to understand the precise mechanism of release of the potential instability. Another interesting aspect is the ability of upper-level perturbations to induce a surface cyclone. This is an important consideration, as the vertical extent of the upper-level cyclone affects near-surface weather impacts and influences the system’s ability to transport water vapor. For example, in the 2015 Atacama storm, a distinct near-surface cyclone was observed, confirmed by scatterometer data (Bozkurt et al., 2016). In contrast, our case study only reaches around 700 hPa with substantial horizontal circulation (see Fig. 4.b). Nieto et al. (2005) found that approximately 50% of cutoff lows produce a surface cyclone, with even lower numbers reported for South America by Reboita and Veiga (2017). Furthermore, Barahona (2016) examined this issue, finding that around 55% of cutoff lows reach the 850 hPa level and only 20% produce a closed cyclonic circulation at the surface. The spatial distribution of the depth of the cutoff lows presented by Barahona (2016) appears to be consistent with the concept that the stability of the mean flow controls the depth of cutoff lows to some extent: mid-latitudes exhibit deeper cutoff lows than the subtropics (as also shown by Barnes et al., 2021; Pinheiro et al., 2024). Moreover, deeper systems are more common in eastern than in western South America, although Pinheiro et al. (2024) observed the opposite pattern. Notably, since H = fL N may govern the depth of systems from the originating perturbation level, higher stability in the subtropics and Western South America would generally lead to shallower systems. Barnes et al. (2021) also identify fall as the season with deeper systems, aligning with lower environmental stability likely due to relatively warmer sea surface temperatures and cooler midtropospheric temperatures. Besides stability, the dynamical tropopause’s location is significant, as perturbations originate at higher levels during summer, when the dynamical tropopause reaches greater geometric heights (Barnes et al., 2021). Lastly, the baroclinicity of the mean flow may also affect the depth of the system, as upper-level perturbations can amplify and interact with surface disturbances via baroclinic instability (Pinheiro et al., 2024).Clouds and Precipitation distribution As we have discussed in previous sections, most of the precipitation activity of a cutoff low is expected to occur over the continent. Consistent with the release of potential instability, precipitation develops on the continent in part due to orographic ascent and predominantly over the poleward leading quadrant of the low (Barahona, 2016; Pinheiro et al., 2020). From a quasi-geostropic perspective the equatorial side of the low can be seen as a jet streak with cyclonic curvature (see the geopotential at 300 hPa in Fig. 6.a)). In such cases, the ascent is concentrated over the polar exit side of the jet streak (see e.g. Mu˜noz & Schultz, 2021). This coincides with the large area of clouds observed on the southeast of the center of the low. Also interesting is that deep convective clouds show cloud top temperatures near -40°C on the windward side of the Andes (∼ 300 hPa), but only appear on the continent. This was also the case, for example, during the strong cutoff low of March 2015, when satellite radar passages showed precipitation starting only within a few kilometers from the coast (Bozkurt et al., 2016). Figure 6.a shows that deep clouds are accompanied by lightning (marked with red crosses in the figure). There are isolated deep convective clouds near the center of the low; however, the main convective activity occurs over the diffluence region already identified. Deep convection directly associated with the cutoff low is concentrated on the windward side of the Andes. A passage of the GPM satellite around April 13th, 10 UTC, confirms that lightning occurs associated with precipitation bands with instantaneous rainfall values close to 10 mm/h (Figure 7). Spatial Distribution and Seasonality Many algorithms have been developed over the years to identify cutoff lows in reanalysis data in order to construct climatologies and to study the seasonality, spatial distribution, duration

Figure 5: (a) SkewT-log p thermodynamic diagram of from an ERA5 reanalysis vertical profile from 30°S and 78°W during April 13th 2024, 00 UTC. The red thick line is the temperature, the blue thick line is the dewpoint temperature and the dotted black line is the trajectory of a parcel from the surface. Red dotted lines are dry-adiabats, blue dotted lines are moist adiabats and green dotted lines are lines of constant saturation mixing ratio. Grey thick lines are isotherms (b) Close up of the region marked with a solid black rectangle in panel (a). The yellow lines show the mean lapse rate of the layers A-B and A′ -B′ . The thick dotted blue lines are the trajectories of the parcels A and B when they ascend 200 hPa.Figure 6: (a) Infrarred window channel brightness temperature during April 13th 2024, 12UTC. Lightning strikes are marked as red crosses from GOES Lightning Mapper. Geopotential height at 300 hPa is shown as white contours (b) Water vapor channel image (brightness temperature in greyscale)Figure 7: Infrarred window channel brightness temperature during April 13th 2024, 10UTC from GOES-16. On top of the infrared images are radar based surface precipitation estimates from the GPM satellite. Black lines show the width of the swath of the radar instrument.Figure 8: (a) Global climatology of the cutoff low frequency based on a climatology of cutoff lows using 300 hPa Geopotential following criteria by Barahona (2016). The climatology was constructed using ERA5 reanalysis from 1979 to 2023 (b) Monthly seasonality of cutoff lows over South America (140°W to 30°W, based on the same climatology. (c) Annual frequency (number/year/grid) of points at the beginning of a cutoff low trajectory (cyclogenesis) and (d) at the end of the cutoff low trajectory (cyclolysis) and location of the genesis and lysis of these systems (e.g. Barahona, 2016; Favre et al., 2012; Fuenzalida et al., 2005; Ndarana & Waugh, 2010; Pinheiro et al., 2017, 2019; Reboita et al., 2010). The first important thing to mention is that in all these climatologies, Southwestern South America is a region where a large frequency of cutoff lows occurs year-round, at about 30°S. In some of these climatologies, (e.g. Favre et al., 2012) this region represents the maximum cutoff low frequency in the southern hemisphere. Following the work by Barahona (2016), we constructed a climatology covering the period 1979 to 2023 using the ERA5 reanalysis (Hersbach et al., 2020). Our criteria for defining a cutoff low are as follows: (1) The first criterion is the presence of a relative minimum in the gradient of the geopotential height at 300 hPa. The gradient between the minimum and a square region of 4°×4° must be larger than 40 gpm. The second criterion is that the thickness between 300 hPa and 600 hPa must also exhibit a relative minimum, ensuring the existence of a cold core. The minimum in this case must have a similar gradient between the center and the 4°×4° perimeter region, with a thickness difference of at least 15 gpm. The third criterion is that the identified cold core must be equatorward of the mean position of the jet stream during a particular month, indicating that the low is segregated from the mid-latitude westerlies. Finally, a criterion on the duration of the cutoff low is also applied: the minimum duration of the cutoff low must be 24 hours. Cutoff low trajectories are then constructed by considering that we are dealing with the same cutoff low if, during the next 6 hours, the cutoff low is within 10° of its previous position. We have also filtered out cutoff lows that remain stationary within 1°during their lifecycle, to avoid including perturbations that are exclusively related to topography (e.g. Wernli & Sprenger, 2007)Figure 9: (a) Histogram of the annual frequency of cutoff lows for each month based on the ERA5 climatology of cutoff lows at 300 hPa from 1979 to 2023. (b) Box plot of the distribution of cutoff low intensities, measured as the difference in 300 hpa geopotential height of the center and the geopentential height of the perimeter of a concentric 4°latitude-longitude square. We see in Figure 8.a that at 300 hPa the cutoff low area in southwestern South America shows prominent maxima with regions of about 4 cutoff lows per year or even more over the Andes. Looking closer 8.a, the region is composed of a maximum near the coast at around 30°S (e.g. Barnes et al., 2021; Favre et al., 2012; Fuenzalida et al., 2005) and a projection of this maximum towards the subtropical Pacific with a maximum at around 20°S, 100°W (Barnes et al., 2021; Portmann et al., 2021). It is interesting to note that early on these two ’modes’ in which cutoff lows can form in the Southeastern Pacific, namely the coastal cyclone and the south Pacific equatorward band, were recognized to have an impact in episodic spikes of ozone registered at mountain stations at 30°S (cases W and D, respectively in Rondanelli, Gallardo, et al., 2002). Another interesting aspect concerns cyclogenesis and cyclolysis. Figures 8.c-d illustrate the density of the start and end point of each identified cutoff trajectory, which we refer to as cyclogenesis and cyclolysis, respectively. Both maps exhibit minimal differences, closely resembling the overall distribution of cutoff lows. This suggests that all areas are potential regions where a cutoff low can form or dissipate. However, the coastal region near 30° S appears to be a preferred region for cyclogenesis, whereas the leeward side of the Andes at 30° S is a preferred region for cyclolysis, as noted by several authors (Fuenzalida et al., 2005; Pinheiro et al., 2017, 2022). Cyclolysis in the lee of the Andes has several possible explanations. The first is the increase in friction experienced by the system while crossing the Andes, especially north of 30°S, where the average height of the Andes exceeds 5000 m. A second possibility is the release of latent heat produced by precipitation as the low crosses the Andes. On the lee side, the upper-level perturbation induces southerly flow at the leading edge, rapidly transporting water vapor from tropical South America. This transport of water vapor induces precipitation and latent heat release, leading to upper-level divergence, which weakens the cyclonic perturbation at upper levels (e.g. Garreaud & Fuenzalida, 2007; Pinheiro et al., 2022). Finally, the interaction between the cutoff low and a stationary ridge induced by topography has also been proposed as a weakening mechanism for the low (Funatsu et al., 2004). Regarding the genesis mechanisms, Pinheiro et al. (2022) identify the coastal region as an area of significant convergence of ageostrophic flux during the stage of formation of the cutoff lows. One might consider the role of topography in this flux convergence, as the dominant westerly flow impinging on the Andes is blocked and diverted southward (Kalthoff, Bischoff-Gauß, et al., 2002), generating cyclonic relative vorticity and ageostrophic convergence poleward of the subtropical jet stream.From Table 1, we see that there is a wide range of approaches to define the climatology of cutoff lows. Therefore, some of the features of the climatologies are expected to be dependent on the particular definition of the systems, as well as the horizontal resolution of the reanalysis data and the main level of the atmosphere where perturbations are defined (Mu˜noz et al., 2020; Pinheiro et al., 2017; Reboita et al., 2010). However, some common characteristics arise, for example, where upper tropospheric levels are chosen, the seasonal maxima are found in summer early Autumm, while the minimum frequency of cutoff lows is found during winter (Barahona, 2016; Ndarana & Waugh, 2010; Pinheiro et al., 2017; Reboita et al., 2010). An almost opposite seasonality is found when the 500 hPa level is considered, where maxima occur during Autumn and Winter and minima during Summer (Fuenzalida et al., 2005; Mu˜noz et al., 2020). In the climatology we constructed, we detected only a third of the number of cutoff lows during the Winter minimum compared to the frequency found during the Summer maximum (Figure 9), consistent with previous work using a similar pressure level (Table 1). This level-dependent seasonality in the frequency of cutoff could be in part due to an artifact of selecting a single level for the analysis of the perturbations. In fact, Portmann et al. (2021) use a level-independent climatology in which they identify ’PV cutoffs’ at any isentropic level between 275 and 360 K. In their analysis, the South Pacific equatorward band shows a maximum frequency of cutoff lows of about 10% during summer and 3% during winter, whereas the coastal region shows a summer maximum as well of approximately 9% compared to the minimum 6% in winter. The summer minimum therefore found in climatologies using 500 hPa can be explained simply by the fact that during the summer the level of formation of the cutoff lows reaches higher levels (Barnes et al., 2021; Portmann et al., 2021; Wernli & Sprenger, 2007). This is also a warning for studies that attempt to look at trends in the frequency of these systems in the future and in the past, where changes in the level of formation of cutoff lows might be misinterpreted as changes in the frequency of these systems. The mean intensity of the cutoff lows also appears to have a seasonal cycle at 300 hPa, with a slight increase in the mean intensity of the systems during winter and a minimum during summer (Figure 8). Again, this behavior of the systems might be influenced by the single-level selection made in this case. During winter, the 300 hPa level is lower than during summer, possibly capturing more intense systems, although some outliers during summer display larger gradients. A complete understanding of the seasonality of cutoff lows is lacking at this time, as a complete 3D analysis of the formation of these systems is needed (e.g. Lakkis et al., 2019; Portmann et al., 2021). Presumably, even if no seasonality of upper-level formation was detected, seasonality of the tropospheric stability and the height of the perturbations will induce a different effect on the surface weather, a matter that needs further exploration.

Moisture dynamics and Precipitation During an early stage of the research on cutoff lows, at least until the work of Garreaud and Fuenzalida (2007), little was understood about the interaction of the cutoff low with the surrounding moisture field. In fact, emphasis on the dry dynamical features of these systems usually led to conflicting forecasts regarding the ability of the cutoff low to produce precipitation over the windward side of the Andes. Fuentes (2014) compared two mesoscale simulations of a case study of a cutoff low in Central Chile and —perhaps for the first time, identified the source of water vapor of the cutoff low as coming from a water vapor streamer originating in the coast of Peru and Northern Chile during March 2008. In particular, he used two different reanalysis datasets as boundary condition for the simulation, one reanalysis representing a slightly dryer condition along this streamer and therefore producing less precipitation in the corresponding simulation. In March 2015, we experienced one the major hydrometeorological disasters in Northern Chile when a cutoff low was able to tap water from the rather warm coastal waters of Peru at the beginning of El Ni˜no 2015-2016. It was then immediately clear to us that a similar mechanism as in the case study of Fuentes (2014) was at play in this case, namely the transport of water vapor in a water vapor streamer trapped along the coast, being fed by the strong southerly circulation in the leading edge of a cutoff low (Barrett et al., 2016; Bozkurt et al., 2016). To borrow from chemistry, the limiting reagent for this extreme storm was not circulation but water vapor. For instance, the 500 hPa anomaly for the March 2015 storm was only one standard deviation below climatology (Barrett et al., 2016), therefore many upper-level storms with a similar circulation anomaly would be expected over a period of several years; however, the peak discharge of the storm estimated for several basins in Northern Chile, was the largest documented over a period of several decades and without any precedent (Wilcox et al., 2016). Also the large sensitivity of the precipitation to the sea surface temperature over the Peruvian coast in the modeling study carried by Bozkurt et al. (2016) is also suggestive of the little relative importance of the dry dynamical anomaly with respect to the water vapor anomaly, in setting the extreme precipitation experienced during this event.With this knowledge in mind, Barahona (2016) classified cutoff lows in the Southern Hemisphere according to their precipitable water and gradient intensity based on the geopotential height of 300 hPa. From his composites, it is clear that even very strong circulation anomalies in 300 hPa (gradients of the order of 300 m/10 °) combined with precipitable water in the lower 20% percentile of the distribution, produce precipitation confined to a small sector at the poleward (difluent) leading edge of the cutoff low. However, low circulation gradients of even less than 100 m over 10°for systems in the upper 80 percentile of precipitable water produce a large region of precipitation that extends over most of the leading edge area (as in Fig. 6.a in our case study). Similarly, Mu˜noz and Schultz (2021) studied cutoff lows in the southeast Pacific based on surface precipitation at 94 surface stations. They classified systems from 1979 to 2017 into LOW25 and HIGH25 depending on whether precipitation was in the lower or higher quartiles of the precipitation distribution for cutoff lows based on surface station data. They found that synoptic vertical forcing in both cases was not significantly different and therefore could not explain the difference in precipitation found between these systems. They attributed the difference between these systems to a better defined and stronger ’moisture plume’ feeding the cutoff lows in the HIGH25 quartile cases, in line with previous research indicating the critical role of water vapor availability in the resulting precipitation. Figure 10 shows a cross section along 26°S for three of the cases already mentioned. The first corresponds to the case studied by Fuentes (2014), the second is the Atacama storm of March 2015, and the third is our case study. We see that in all three cases there is a noticeable presence of the coastally trapped moisture plume originating in front of the coast of Peru, and extending even to Southern Chile in the most extreme cases. This coastally trapped moisture plume is characteristic of precipitating cutoff lows. Presumably once the leading edge of the cutoff low begins to approach the continent, the southerly circulation at Figure 10: (a),(b) and (c) are maps of the precipitable water (colors) and integrated water vapor transport (vectors) for March, 7 2008, March 24 2015 and April 13, 2024 respectively. (d), (e) and (f) are cross sections of specific humidity (colors) and meridional wind component (solid and dashed contours for positive and negative values respectively) for the same dates as the upper panels. the leading edge reinforces the southerly barrier jet that results from the blocking of the flow by the Andes, and which is usually located between 2000 and 4000 m (Kalthoff, Bischoff-Gauß, et al., 2002). We see that in all three cases, meridional winds peak in the lower troposphere closer to the Andes barrier and in Fig.10.a and b, display a maximum of ∼ 15 m/s at around 750 hPa, and with relatively high humidity values up to at least the level of 600 hPa (For the Atacama storm which constitutes the most extreme member of this set . This relatively deep layer of water vapor is then effectively transported southward producing strong values of integrated vapor transport values (larger than 200 kg/m/s). Perhaps not coincidentally, all of our cases occur at the end of summer and beginning of fall, where sea surface waters in the coast of Peru reach their maximum annual temperature. Using the climatology of cutoff lows presented in the previous section, we have recalculated the distribution of rainfall due to cutoff lows and the fraction that this rainfall represents with respect to the total rainfall, as done in Aceituno et al. (2021). Despite the fact that our cutoff lows climatology closely followed that of Barahona (2016), we find a larger number of COLs, perhaps due to the use of a higher resolution reanalysis. We find that annual precipitation peaks at about 300 mm on the leeward side of the Andes (Figure 11.a). Many places along the Andes show precipitation larger than 100 mm from about 28°S to 38°S. The rainfall distribution due to cutoff lows has a very distinct orographic pattern with a minimum near the coast and a maximum over the leeward side of the southern Andes. Also notable is that most of the precipitation in the hyperarid core of Atacama is explained by cutoff lows (see Fig. 1.a and Fig. 11.b). The maximum percentage peaks at about 25°S. (Fig. 11.d) and is higher than 50% north of 30°S on the windward side. We also notice a large area of influence on the leeward side of the Andes Figure 11: Rainfall distribution due to cut-off lows from CR2Met database from 1979 to 2021 (Boisier, 2023; Boisier et al., 2018) (a) Annual precipitation due to cutoff lows (mm). (b) Percentage of cutoff low rainfall respect to total rainfall. (c) Latitude distribution of the mean annual precipitation due to cutoff lows. (d) Latitude distribution of the percentage rainfall due to cutoff lows where most of the annual precipitation appears associated with cutoff lows, presumably due to the modulation of cutoff lows on the convective activity during summer. Outlook Cutoff lows in Southwestern South America are significant because they are the main drivers of extreme precipitation events in this region. They represent the main mechanism through which the extreme dryness and stability of the Atacama Desert can break down, potentially bringing rain to this otherwise hyperarid desert. As we have discussed, cutoff lows are very frequent in this part of the world. The lack of precipitation due to these systems is often more associated with the relatively dry climatological water vapor over this region than with the absence of synoptic-scale perturbations. For example, Lagos-Z´u˜niga et al. (2024) have shown an increase of approximately 1.5 mm per decade in precipitable water over the source region of Peru during the fall, which is consistent with an increasing trend for daily precipitation extremes north of 30°S during the same season. Climate change is expected to increase the availability of water vapor in the region, which is considered the main source of moisture for these systems. Furthermore, Mu˜noz et al. (2020) documented an upward trend in the number of cutoff lows, attributing this to the poleward shift of the mid-latitude jet, which increases the likelihood of anticyclonic wave breaking (Rivi`ere, 2011), the primary mechanism for the formation of cutoff lows. Given the very low precipitation in the arid regions of northern Chile, even a few extreme cases can significantly influence the climatology of precipitation over decades. Therefore, a more detailed understanding of the mechanisms behind these specific events can provide insight into the future behavior of these systems. In particular, the future of arid northern Chile under climate change must be carefully considered. Modeling studies often do not focus on the specific processes that produce precipitation in various model projections. However, some studies indicate an increase in extreme rainfall in this region (e.g., Ortega et al., 2019). 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