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Within the atmospheric modelling community, a large focus in recent years has been on the concept of Convective Self-Aggregation (CSA): In an environment of radiative convective equilibrium, with homogeneous initial conditions and a constant-temperature tropical sea surface, convection can spontaneously aggregate into domain-wide patterns of persistent dry areas and constrained rainy areas over a temporal timescale of weeks to months. CSA, albeit still a modeling paradigm, could reveal the mechanisms behind some of the convective organization observed in the tropics.This process of forming domain-wide structure can be accelerated to the order of days by imposing oscillating surface temperatures with a large enough amplitude [1]. The ‘diurnally aggregated’ cloud field is similar to CSA as it also constrains the surface rain field to certain parts of the domain. Further, pattern formation was found to initiate first as persistent dry patches in the uppermost layers of the simulated atmosphere. The dry patches subsequently penetrate through to the subcloud layer [2].In this work we investigate how diurnal surface temperature amplitudes, typical of tropical land, affect the formation of persistent dry patches and the spatio-temporal extent of the emergent mesoscale convective systems. We run a set of cloud resolving simulations initialized with typical profiles of temperature and humidity. We impose a large-amplitude diurnally oscillating surface temperature, which we then set to constant at different times, to see the effect on the diurnally aggregated cloud field. We present the results of this study, which show a strong dependence on the degree of aggregation over ‘land’, in determining the aggregation over ‘sea’, and a form of hysteresis arises. 1. Haerter, Jan O., Bettina Meyer, and Silas Boye Nissen. ‘Diurnal Self-Aggregation’. Npj Climate and Atmospheric Science 3, no. 1 (30 July 2020): 1–11. https://doi.org/10.1038/s41612-020-00132-z.2. Jensen, Gorm G., Romain Fiévet, and Jan O. Haerter. ‘The Diurnal Path to Persistent Convective Self-Aggregation’. Journal of Advances in Modeling Earth Systems 14, no. 5 (2022): e2021MS002923. https://doi.org/10.1029/2021MS002923.

Tropical convective rainfall is known to vary with the diurnal cycle, yet it is also influenced by large scale convergence. In a suite of idealized cloud-resolving numerical experiments, we mimic Earth's Hadley cell to probe the interactions between oscillations in rainfall inherent to the large-scale circulation and the rainfall oscillation caused by the convective diurnal cycle. The model tropics are thereby caricatured by a rectangular domain that is periodic in both the meridional and zonal dimensions. Surface temperature TS is spatially constant in the "zonal" direction and decreases when moving "meridionally" away from the model equator. We contrast temporally constant TS with a TS that varies harmonically in time. By design, a large scale circulation develops with an intrinsic mode of oscillation of period ω0~Ly, i.e., proportional to the meridional domain size Ly --- thus generally differing from the diurnal period of one day. Interestingly, the diurnal forcing by no means shapes the precipitation power spectrum. Rather, the intrinsic circulation period dominates the precipitation power spectrum for large and small domains. At intermediate 𝐿𝑦 ≈ 2, 000 km, where intrinsic frequencies approximately match the diurnal one, the diurnal period prevails, the intrinsic frequency is suppressed, and the precipitation amplitude is amplified. We explain the complex dynamics as a type of resonance using a highly simplified forced and kicked harmonic oscillator.

Mesoscale Convective Systems (MCS) are common over Europe and can produce severe weather, including extreme precipitation, which can lead to flash floods.The few studies analyzing the climatological characteristics of MCS over Europe are either based on only few years of data or focus on limited sub-areas.Using the recent Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (IMERG) satellite precipitation climatology, we identify and track MCS for 16 years over Europe.We devise a spatial filter and track cells according to the overlap of filtered rain patches between consecutive time steps.By fitting an ellipse to these patches, we determine their overall shape and orientation.To distinguish convective rain patches we condition on lightning data, thus reducing potential identification errors.We analyze this new European MCS climatology to characterize MCS rainfall properties:MCS overall occur most frequently over the Mediterranean and Atlantic during fall and winter, whereas during summer, they concentrate over the continent.Typically, more than half of seasonal precipitation can be attributed to MCS, andtheir contribution to extreme precipitation is even greater, often exceeding 70\%.MCS over the continent display a clear diurnal cycle peaking during the afternoon, and some continental areas even show a second, nocturnal peak.The MCS diurnal cycle for coastal and oceanic regions is more variable.Selecting sub-areas, we find that the spatio-temporal distribution of MCS precipitation throughout the year can be well explained by the spatio-temporal distribution of specific environmental variables, namely (sea) surface temperature, fronts occurrence and convective instability.

We investigate the development of cooperative behavior in networks over time. In our controlled laboratory experiment, subjects can cooperate by sending costly messages that contain valuable information for the receiver or other subjects in the network. Any message sent can increase the chance that subjects find the information they are looking for and consequently their profit. We find that cooperation emerges spontaneously and remains stable over time. In an additional treatment, we provide a non-binding suggestion about who to contact at the beginning of the experiment. We find that subjects partially follow our recommendation, and this increases their own and others’ profit. Despite the removal of suggestions, subjects build long-lasting relationships with the suggested contacts.

Cold pools are known to mediate the interactions between convective rain cells. Cold pool dynamics thus constitutes an important organizing mechanism for thunderstorms, in particular mesoscale convective systems and extreme rainfall events. Unfortunately, the observational detection of cold pools on a large scale has so far been hampered by the lack of relevant large-scale near-surface data. Unlike in numerical studies, where high-resolution near-surface fields of relevant quantities such as virtual temperature and winds are available and frequently used to detect cold pools, in observational studies cold pools are mainly identified based on surface time series. Since research vessels or weather stations measure these time series locally, the characterization of cold pools from observations is limited to regional or station-based studies. To eventually enable studies on a global scale, we here develop and evaluate a methodology for the detection of cold pools that relies only on data that (i) is globally available and (ii) has high spatio-temporal resolution. We trained convolutional neural networks to segment cold pools in cloud and rainfall fields from high-resolution cloud resolving simulation output. Such data is not only available from simulations, but also from geostationary satellites that fulfill both (i) and (ii). The networks feature a U-Net architecture, a common choice for image segmentation due to its strength in learning spatial correlations at different scales. Based on cloud and rainfall fields only, the trained networks systematically identify cold pool pixels in the simulation output. Our methodology may thus open for reliable global cold pool detection from space-borne sensors. As it also provides information on the spatial extent and the relative positioning of cold pools over time, our method may offer new insight into the role of cold pools in convective organization.

While the traditional view of monsoons as continental sea breezes generated by land-sea contrasts was shown to have serious limitations, several competing alternative frameworks look promising. Within this debate, it remains unclear if the surface temperature contrast matters at all for the monsoon precipitation, and why there is a non-linear intensification of precipitation intensity with surface temperature forcing. Idealised studies such as aquaplanets often help improve our understanding of basic mechanisms. But there are very few idealised simulation studies of monsoons at high resolution. Therefore, to determine if monsoon non-linearities with surface forcing come from convective processes, dynamical feedbacks, or from non-linearities in the forcing themselves, we devise a modular framework to simulate idealised monsoons at convection-permitting resolution with the WRF model, in a domain based on an aquapatch (mini-aquaplanet), but in which we can gradually add more realistic components, such as an interactive land surface. The model is forced by a season-dependent meridional contrast of surface temperature, with comprehensive physics and rotation. We compare a series of aquapatch experiments with increasingly intense smooth sea surface temperature forcings with another series including land with increasingly sharp surface temperature contrasts at the land-ocean interface. By relating forcing to responses, we aim to describe the non-linearity of the relationship between surface temperature gradient (or surface Moist Static Energy (MSE) gradient, or low-level wind), and precipitation intensity (or monsoonal precipitation surface area, or monsoon onset timing). This should help clarify the actual role that surface temperature and MSE gradients play in controlling monsoon precipitation, and could potentially hint at the effect of climate change on monsoons.

Tropical deep convection is both driven by the large-scale circulation, such as the Hadley Cell, as well as by periodic heating, namely the diurnal cycle. In a suite of idealized cloud-resolving simulations we allow for an idealized Hadley Cell to evolve by imposing a spatial surface temperature gradient. In line with recent studies (O’Neill et al., 2017, Patrizio & Randall, 2019), we find that a large-scale oscillation of period TL self-organizes, visible in many quantities, especially precipitation. The period TL is found to depend approximately linearly on L, the meridional domain size. When we now impose a diurnal cycle at TD=1day, the timeseries of precipitation is modified. For small L, the power spectrum shows that TD dominates, whereas for large L the intrinsic mode TL prevails. At intermediate TL⋍TD a resonance occurs, which causes the amplitude to nearly double, leading to more extreme rainfall. To gain insight, we propose a simple damped harmonic oscillator model with a spatial energy source, mimicking convective latent heat release. We associate the “spring constant” with the meridional domain size L. The coupling to the diurnal cycle is then incorporated by a periodic drive. Results show that the model can mimic the resonance at intermediate periods and the dominance of large-scale modes at large system sizes. We further find an envelope period which may give insight into the observed meandering of the ITCZ (Mapes et al., 2018). Our results could help understanding of tropical extreme events, e.g. MCS, and how they could be invigorated by the large scale circulation.

For climate-change impact studies at the catchment scale, meteorological variables are typically extracted from ensem-ble simulations provided by global and regional climate models, which are then downscaled and bias-adjusted for eachstudy site. For bias adjustment, different statistical methods that re-scaleclimate model outputs have been suggested inthe scientific literature. They range from simple univariate methods that adjust each meteorological variable individ-ually, to more complex and more demanding multivariate methods that take existing relationships between meteoro-logical variables into consideration. Over the past decade, several attempts have been made to evaluate such methodsin various regions. There is, however, still no guidance for choosing appropriate bias adjustment methods for a study athand. In particular, the question whether the benefits of potentially improved adjustments outweigh the cost of in-creased complexity, remains unanswered.This paper presents a comprehensive evaluation of the performance of two commonly used univariate and two multi-variate bias adjustment methods in reproducing numerous univariate, multivariate and temporal features of precipita-tion and temperature series in different catchments in Sweden. The paper culminates in a discussion on trade-offs between the potential benefits (i.e., skills and added value) and disadvantages (complexity and computational de-mand) of each method to offer plausible, defensible and actionable insights from the standpoint of climate-change im-pact studies in high latitudes.We concluded that all selected bias adjustment methods generally improved the raw climate model simulations, but that not a single method consistently outperformed the other methods. There were, however, differences in the methods' performance for particular statistical features, indicating that other practical aspects such as computationaltime and heavy theoretical requirements should also be taken into consideration when choosing an appropriate biasadjustment method

In radiative-convective equilibrium simulations, convective self-aggregation (CSA) is the spontaneous organization into segregated cloudy and cloud-free regions. Evidence exists for how CSA is stabilized, but how it arises favorably on large domains is not settled. Using large-eddy simulations, we link the spatial organization emerging from the interaction of cold pools (CPs) to CSA. We systematically weaken simulated rain evaporation to reduce maximal CP radii, R_{max}, and find reducing R_{max} causes CSA to occur earlier. We further identify a typical rain cell generation time and a minimum radius, R_{min}, around a given rain cell, within which the formation of subsequent rain cells is suppressed. Incorporating R_{min} and R_{max}, we propose a toy model that captures how CSA arises earlier on large domains: when two CPs of radii r_i,r_j ∈ [R_{min}, R_{max}] collide, they form a new convective event. These findings imply that interactions between CPs may explain the initial stages of CSA. In radiative-convective equilibrium simulations, convective self-aggregation (CSA) is the spontaneous organization into segregated cloudy and cloud-free regions. Evidence exists for how CSA is stabilized, but how it arises favorably on large domains is not settled. Using large-eddy simulations, we link the spatial organization emerging from the interaction of cold pools (CPs) to CSA. We systematically weaken simulated rain evaporation to reduce maximal CP radii, R_{max}, and find reducing R_{max} causes CSA to occur earlier. We further identify a typical rain cell generation time and a minimum radius, R_{min}, around a given rain cell, within which the formation of subsequent rain cells is suppressed. Incorporating R_{min} and R_{max}, we propose a toy model that captures how CSA arises earlier on large domains: when two CPs of radii r_i,r_j ∈ [R_{min}, R_{max}] collide, they form a new convective event. These findings imply that interactions between CPs may explain the initial stages of CSA.

Clustering of tropical thunderstorms constitutes an important climate feedback because it influences the heat radiated to space. Convective self-aggregation (CSA) is a profound modelling paradigm for explaining the clustering of tropical oceanic thunderstorms. However, CSA is hampered in the realistic limit of fine model resolution when cold pools -- dense air masses beneath thunderstorm clouds -- are well-resolved. Studies on CSA usually assume the surface temperature to be constant, despite realistic surface temperatures varying significantly between night and day, even over the sea. Here we mimic oscillating surface temperatures in cloud resolving numerical experiments and show that, in the presence of a diurnal cycle, CSA is enabled by high resolutions. We attribute this finding to vigorous combined cold pools emerging in symbiosis with mesoscale convective systems. Such cold pools suppress buoyancy in extended regions ($\mathbf{\sim 100}$ km) and enable the formation of persistent dry patches. Our findings help clarify how the tropical cloud field forms sustained clusters under realistic conditions and may have implications for the origin of extreme thunderstorm rainfall and tropical cyclones., 12 pages, 4 figures, 1 table + 5 supplementary take up one additional page each

Under radiative convective equilibrium (RCE), cloud populations simulated by large-eddy simulations (LES) can spontaneously segregate into cloudy and cloud-free subregions. This process is well-known as convective self-aggregation (CSA) [4]. But how initially randomly distributed raincells compete and merge until only one prevails, is not well-understood. We remove cold pools (CPs) in LES by suppressing the re-evaporation of rain, which leads to qualitatively different dynamics. This extreme case helps to understand the role of CPs in the formation of CSA and further has relevance when humidity is very high in the boundary layer, so very little rainfall evaporates.When convection starts, patterns of high and low moisture develop, which increase in scale over time. In contrast to CSA with CPs, individual rain events and convection cells persist up to tens of hours in the course of this modified CSA [1]. For the long lasting individual rain clusters, we observe interesting oscillations in rain intensity and spatial extent. We define an algorithm, that tracks the tree-like merging behavior of initially many individual small raincells to a final, single, raincell of large area and precipitation yield. We conceptualize the LES behavior in a simple model, that assumes different rain events to compete for buoyancy. This hypothesis is justified when viewing rain events as linked to local maxima of relative humidity around cloud base. The clusters‘ dynamics seem to be dominated by merging with other events and ’stealing’ from smaller events, whereas splitting and emerging of new rain events seem neglectable after a build-up time. In each step, the conceptual model chooses two adjacent clusters. Initially, each cluster is attributed a ‘mass’ parameter of similar magnitude and a fraction (p) of the smaller ’mass’ (m2) is transferred to the bigger event (m1).m1new = m1 + p(m1 − m2)m2new = m2 - p(m1 − m2)An event is removed, when its mass parameter is diminished to zero. In contrast to field based approaches [3], this approach implements discrete rich gets richer dynamics, to capture how individual cells grow. This conceptual model could be combined with existing models, where CP suppress the rain cells, but trigger new updrafts through the CP gust fronts [2]. Bringing together these two limits could further elucidate how CP dynamics can be made compatible with convective self-aggregation.References:[1] Nadir Jeevanjee and David M Romps. Convective self-aggregation, cold pools, and domain size. Geophysical Research Letters, 40(5):994–998, 2013.[2] Silas Boye Nissen and Jan O. Haerter. How weakened cold pools open for convective self-aggregation, 2020, arXiv:1911.12849v3.[3] Julia M. Windmiller and George C. Craig. Universality in the spatial evolution of self-aggregation of tropical convection. Journal of the Atmospheric Sciences, 76(6):1677 – 1696, 01 Jun. 2019.[4] Allison A Wing, Kerry Emanuel, Christopher E Holloway, and Caroline Muller. Convective self-aggregation in numerical simulations: A review. In Shallow Clouds, Water Vapor, Circulation, and Climate Sensitivity, pages 1–25. Springer, 2017.

Convective self-aggregation (CSA) is an established modelling paradigm for large-scale thunderstorm clusters, as they form in mesoscale convective systems, the Madden-JulianOscillation or tropical cyclo-genesis [1]. The onset of CSA is characterized by the spontaneous formation of persistently dry patches with suppressed deep convective rainfall. Recently another type of spatio-temporal pattern formation was observed in simulations where the diurnal cycle was mimicked by a sinusoidally varying surface temperature [2]. This diurnal aggregation (DA) is characterized by clusters of intense rain that correlate negatively from one day to the next. Here we demonstrate that the diurnal cycle can also act as a trigger of persistently dry patches resembling the early stages of CSA. When the surface temperature is held constant, CSA has been shown to occur within simulations of coarse horizontal model resolution, but not when the resolution was increased [3]. We show that, when a temporally periodic surface temperature forcing is imposed, persistently convection free patches occur even faster when the spatial resolution is increased. The failure to achieve CSA at high horizontal resolution has so far been attributed to the more pronounced cold pool effects at such resolution. In our simulations these cold pools in fact play a key role in promoting CSA. Our results have implications for the origin of persistent convective organization over continents and the sea — and point a path towards achieving such clustering under realistic conditions.[1] Christopher S Bretherton, Peter N Blossey, and Marat Khairoutdinov. An energy-balance analysisof deep convective self-aggregation above uniform SST.Journal of the Atmospheric Sciences, 62(12):4273–4292, 2005.[2] J. O. Haerter, B. Meyer, and S. B. Nissen. Diurnal self-aggregation.npj Climate and AtmosphericScience, 3:30, 2020.[3] Caroline Muller and Sandrine Bony. What favors convective aggregation and why?GeophysicalResearch Letters, 42(13):5626–5634, 2015. doi: https://doi.org/10.1002/2015GL064260.

Spontaneous aggregation of clouds is a puzzling phenomenon observed in field studies [Holloway et al. (2017)] and idealized simulations alike [Held et al. (1993), Bretherton et al. (2005)]. With its relevance to climate sensitivity and extreme events, aggregation continues to be heavily studied, [Wing et al., 2017 for a review], with radiative-convective feedbacks emerging as main drivers of simulated convective self-aggregation (CSA) [Mueller & Bony (2015)].In state-of-the art cloud-resolving models, CSA finds itself consistently hampered by finer horizontal resolutions [Muller & Held (2012), Yanase et al. (2020)]. This feature was ascribed to the effect of cold pool (CP) gust fronts in opposing the positive moisture feedback underlying CSA [Jeevanjee & Romps (2013)]. In contrast, recent numerical experiments [Haerter et al. (2020)] with diurnally oscillating surface temperature highlights an orthogonal effect: stronger CPs, driven by small-scale density gradients, promote cloud field self-organization into mesoscale convective systems (MCS). Interestingly, this upscale growth, which we here term diurnal self-organisation (DSO), differs from classical CSA as it is driven by CPs rather than large-scale radiative imbalances. In stark contrast to CSA, strengthening CPs promotes this organization effect.Hence, numerical simulations of CSA and DSO should go beyond the typical cloud-resolving paradigm and achieve cold pool-resolving capabilities. The current study systematically examines the impact of model resolution on CP effects. First, numerical convergence is probed in a 12km x 20km laterally periodic domain where a single CP propagates and self-collides at the domain's edges. As the spatial resolution is stepwise increased from 250 to 25m, it is shown that the initially coarsely resolved density current dissipates and collision and updraft effects are weak. As finer resolution is approached, we identify a cold pool resolving resolution D, which is deemed satisfactory for propagation and collision properties. Second, convergence for a (250km)2 domain under a diurnal radiative cycle is assessed at various spatial resolutions, including the scale D. This mesoscale configuration allows us to quantify the impact of resolution of cold pool dynamics on DSO.Together, this work systematically lays out the numerical requirements to study mesoscale clustering by means of explicit numerical simulations.

Convective cold pools (CPs) have been recognised as an important ingredient in the organization of convective cloud fields and the formation of intense rain events (Feng et al. 2015, Torria and Kuang 2019). To understand the life cycle of CPs and their mutual interaction, idealised large-eddy simulations (LES) of isolated or colliding CPs have become an important tool to develop simple theories about the propagation speed, the dissipation rate and the moisture distribution within the CP and the surrounding environment (Rooney 2015; Langhans et al. 2015; Romps and Jeevanjee 2016; Grant et al. 2016, 2018). On the contrary, the formation of CPs and specifically their relation to their parent rain events has so far not gained much attention in idealised studies. This is surprising, as the relation between the generating rain event and the CP strength is relevant for the theoretical understanding of the ‘rain – CP – rain’ cycle and the parameterization of CPs, which aims at adjusting for the enhanced convective triggering under the presence of CPs, where the triggering scales with the CP strength. In this study we thus examine the relation between rain intensity, duration and CP strength in an idealised setting. To this end, we include the temporal extent of the rain event that forms the CP through evaporative cooling by varying the duration, intensity and area of the air volume that is cooled and moistened to simulate the generation of a CP. This finite duration of the CP forcing has been neglected by most studies that initialise the CP by an instantaneous forcing alone (e.g., Rooney 2015, Grant 2016). Our simulations show that a continuous cooling, imitating persistent rainfall, affects the generated CP only over a period of approximately ten minutes. Shorter cooling leads to smaller and weaker CPs, while cooling occurring after 10mins does not substantially affect the CP properties, such as its radius and propagation speed, the internal circulation in the CP head. Consequently, the CP’s effect on the environment as measured in terms of the updraft strength ahead of the CP, increases for cooling times up to 10mins and converges thereafter. To imitate a change in precipitation intensity, we vary the cooling amplitude. As expected, stronger cooling leads to stronger CPs. However, this effect is surprisingly small and does not substantially alter the CPs’ internal structure. To test the extent to which these results can be translated to ‘real’ CPs generated by evaporative cooling of rainfall, we study the relation between rain intensity and CP strength in comprehensive LES of deep convection and observational data. Hereby, we hopefully can improve our understanding , how best to characterise rain events, e.g. by their instantaneous or time-integrated precipitation statistics, to determine the CP strength.

Climate models are primary tools to reconstruct past and predict future climates. It is common procedure to use general circulation models (GCMs) for large scale studies and regional climate models (RCMs), for impact studies at a finer spatial resolution. However, climate models face biases compared to observation. To overcome these biases, different statistical methods have been suggested in the scientific literature that employ a transformation algorithm to re-scale (or bias-correct) RCM outputs. Some of these methods (e.g. univariate methods that adjust only one RCM-simulated variable at a time) are comparatively easy to implement while others (e.g., multi-variate correction that guarantees consistency in spatiotemporal fields and different climate variables) that have been introduced lately to the field, are more complex and require advanced statistical knowledge and more computing power. Therefore, the need to further investigate the performance of the latest more complex bias-adjustment methods under different climatic conditions still exists and their added value still needs to be evaluated from different aspects.Thus, we assessed the skill of two commonly used multivariate methods, namely copula based bias adjustment methods and non-parametric n-dimensional multivariate bias correction (MBCn). We further compared them with widely used univariate methods, i.e. the parametric distribution mapping (DS) and the non-parametric quantile delta mapping (QDM), to adjust RCM-simulated temperature and precipitation. We evaluated these methods over 55 Swedish catchments varying in size and climatic features using an ensemble of 10 different RCMs under varying climate conditions to check multiple features that represent both probabilistic and temporal behavior. To evaluate how these methods, perform in nonstationary climate conditions, we performed the assessment over two periods of 22 years each, where the period 1961-1982 is used for calibration and 1983-2004 for validation. The adequacy of each bias adjustment method in reducing the biases varies depending on several factors such as the studied watershed, the applied RCM model, utilized climate variable and the statistical feature that is subjected to adjustment. We further discuss potential issues and trade-offs of each of the applied methods and present an evaluation of each bias-corrected climate variable in terms of its (1) statistical properties, (2) temporal behavior utilizing cross correlation and autocorrelation measures, and (3) dependence structure to the other variable with help of copula-based dependence measures. Finally, we also examined how the four bias-adjustment methods influence the Clausius Clapeyron relation, which serves as an important climatic illustration of the relationship between extreme precipitation and temperature.

Convective self-aggregation is a well-studied atmospheric state, obtained in typically multi-week idealized numerical experiments, where boundary conditions are constant and spatially homogeneous. As radiative convective equilibrium is approached, the atmosphere develops a heavily precipitating moist patch, which is surrounded by subsiding, cloud-free regions. It was recently shown that a homogeneous, but temporally oscillating surface temperature can quickly lead to the emergence of so-called mesoscale convective systems (MCS, diameters of >100 km) - on temporal scales of only a few days. Furthermore, the patterns formed by these MCS remind of checkerboards, and alternate from day to day [1]. We here extend this finding further, to add realism to the otherwise preserved idealization: Mimicking a form of “miniature tropics” we retain a laterally periodic domain (Lx, Ly), but impose spatial variation in mean surface temperature along one dimension - reminiscent of a meridional reduction in mean surface temperature, when moving poleward from the equator. By making the wavelength of spatial variation commensurate with domain size, we retail double-periodic lateral boundary conditions. When the diurnal cycle is set to zero, the system quickly organizes to a forcefully aggregated caricature of the actual tropics - with heavy convection near the equator and pronounced subsidence and enhanced long-wave cooling in the subtropics. When the diurnal cycle is increased, bi-diurnal temporal oscillations appear, which lead to a single precipitation peak centered on the equator on one day, but a bimodal meridional pattern with precipitation away from the equator on the next.Our findings, obtained for a still idealized numerical experiment, may have implications for “edge intensifications” suggested from observations and numerical modeling of tropical precipitation patterns near the ITCZ [2,3].[1] Haerter, J.O., Meyer, B. & Nissen, S.B. Diurnal self-aggregation. npj Clim Atmos Sci 3, 30 (2020). https://doi.org/10.1038/s41612-020-00132-z[2] Mapes, B. E., E.-S. Chung, W. M. Hannah, H. Masunaga, A. J. Wimmers and C. S. Velden, 2018: The meandering margin of the meteorological moist Tropics, Geophys. Res. Lett., 45, 1177-1184. doi:10.1002/2017GL076440[3] Windmiller, J. M., & Hohenegger, C. 2019: Convection on the edge. J. Adv. Model. Earth Syst., 11, 3959-3972, 10.1029/2019MS001820

Short-duration (1–3 h) rainfall extremes can cause serious damage to societies through rapidly developing (flash) flooding and are determined by complex, multifaceted processes that are altering as Earth’s climate warms. In this Review, we examine evidence from observational, theoretical and modelling studies for the intensification of these rainfall extremes, the drivers and the impact on flash flooding. Both short-duration and long-duration (>1 day) rainfall extremes are intensifying with warming at a rate consistent with the increase in atmospheric moisture (~7% K−1), while in some regions, increases in short-duration extreme rainfall intensities are stronger than expected from moisture increases alone. These stronger local increases are related to feedbacks in convective clouds, but their exact role is uncertain because of the very small scales involved. Future extreme rainfall intensification is also modulated by changes to temperature stratification and large-scale atmospheric circulation. The latter remains a major source of uncertainty. Intensification of short-duration extremes has likely increased the incidence of flash flooding at local scales, and this can further compound with an increase in storm spatial footprint to considerably increase total event rainfall. These findings call for urgent climate change adaptation measures to manage increasing flood risks. Short-duration rainfall extremes are determined by complex processes that are affected by the warming climate. This Review assesses the evidence for the intensification of short-duration rainfall extremes, the associated drivers and the implications for flood risks.

For most hydroclimatic applications, precipitation and temperature are of particular interest as they strongly affect the water cycle, can easily be measured and are often readily available from many meteorological stations worldwide. To account for precipitation and temperature variability, their co-dependence and their correlation, several multivariate analysis methods have been adopted in the hydroclimatic literature in recent years. In line with the steadily rising number of publications on this topic, the notion of copula-based probability distribution has also attracted tremendous interest to deal with the complexity of compound events in the multidimensional context. A copula is a function that connects a multivariate distribution to its one-dimensional margins, which allows for a joint distribution of random variables with great flexibility for the marginal distribution. However, there seems to be a lack of comprehensive understanding of the fundamental requirements of the copula concept such as the strength and significance of correlation between variables, autocorrelation effects and the choice of representative copula families, which potentially compromises the robustness of projections of future environmental processes and natural hazards. Therefore, by combining a systematic literature review with a specific hydroclimatic case study in Sweden, we illustrate a practical approach to copula-based modeling, which (1) provides end-users with an overview of necessary requirements, statistical assumptions and consequential limitations of copulas, (2) highlights possible pitfalls and misconceptions, and (3) offers a decision support framework for the application of copulas to support researchers and decision makers in addressing climatological hazards and sustainable development, thereby demystifying what is currently an area of great confusion.

To study the diurnal evolution of the convective cloud field, we develop a precipitation cell tracking algorithm which records the merging and fragmentation of convective cells during their life cycles, and apply it on large eddy simulation (LES) data. Conditioning on the area covered by each cell, our algorithm is capable of analyzing an arbitrary number of auxiliary fields, such as the anomalies of temperature and moisture, convective available potential energy (CAPE) and convective inhibition (CIN). For tracks that do not merge or split (termed "solitary"), many of these quantities show generic, often nearly linear relations that hardly depend on the forcing conditions of the simulations, such as surface temperature. This finding allows us to propose a highly idealized model of rain events, where the surface precipitation area is circular and a cell's precipitation intensity falls off linearly with the distance from the respective cell center. The drop-off gradient is nearly independent of track duration and cell size, which allows for a generic description of such solitary tracks, with the only remaining parameter the peak intensity. In contrast to the simple and robust behavior of solitary tracks, tracks that result from merging of two or more cells show a much more complicated behavior. The most intense, long lasting and largest tracks indeed stem from multi-mergers - tracks involved in repeated merging. Another interesting finding is that the precipitation intensity of tracks does not strongly depend on the absolute amount of local initial CAPE, which is only partially consumed by most rain events. Rather, our results speak to boundary layer cooling, induced by rain re-evaporation, as the cause for CAPE reduction, CIN increase and shutdown of precipitation cells., Manuscript under review in Journal of Advances in Modeling Earth Systems

Convective self-aggregation is a modelling paradigm for thunderstorm organisation over a constant-temperature tropical sea surface. This setup can give rise to cloud clusters over timescales of weeks. In reality, sea surface temperatures do oscillate diurnally, affecting the atmospheric state. Over land, surface temperatures vary more strongly, and rain rate is significantly influenced. Here, we carry out a substantial suite of cloud-resolving numerical experiments, and find that even weak surface temperature oscillations enable qualitatively different dynamics to emerge: the spatial distribution of rainfall is only homogeneous during the first day. Already on the second day, the rain field is firmly structured. In later days, the clustering becomes stronger and alternates from day-to-day. We show that these features are robust to changes in resolution, domain size, and surface temperature, but can be removed by a reduction of the amplitude of oscillation, suggesting a transition to a clustered state. Maximal clustering occurs at a scale of $\mathbf{l_{max}\approx 180\;km}$, a scale we relate to the emergence of mesoscale convective systems. At $\mathbf{l_{max}}$ rainfall is strongly enhanced and far exceeds the rainfall expected at random. We explain the transition to clustering using simple conceptual modelling. Our results may help clarify how continental extremes build up and how cloud clustering over the tropical ocean could emerge much faster than through conventional self-aggregation alone., 27 pages, 4 main figures, 7 supplementary figures, 2 main tables, 1 supplementary table

When precipitation evaporates in a sub-saturated boundary layer, it cools the air and produces dense downdrafts, which flow towards the surface and can spread horizontally as a gust front. These spreading “cold pools” (CPs) can trigger convection and thus new precipitation events due to dynamical and thermodynamical lifting mechanisms. Due to their role in the local organization of convection, CP properties are currently being studied with the use of high-resolution numerical simulations. Measurement campaigns have been conducted over the ocean to validate the models. However, fewer studies have specifically targeted cold pools over land.We use the observational network of the Netherlands (meteorological stations and radar) to study CPs developing from summer convection and their role in triggering new convective events over land. Detailed information about CP gust fronts in terms of temperature, wind speed, heat fluxes, moisture and pressure at high vertical resolution is obtained from time series, measured at the 213-meter Cabauw tower. We aim to create an algorithm that detects the passage of a CP from the tower time series to automatize the finding of CPs from a point measurement. To confirm the results, we have access to temperature time series from a spatially dense crowdsourcing weather station network (WOW-NL).The properties of the detected CPs are further studied with imagery from the Herwijnen Doppler radar, situated in proximity to the Cabauw tower. We can see clear signatures of spreading CPs in reflectivity plots, probably caused by the upwelling of dust and insects in the gust front. We currently explore how this can serve as a direct way of visualizing the dynamics of CPs and their collisions.With enough observations of CPs, we expect to learn more about the CP spreading velocity and lifetime in dependence of precipitation intensity of the generating precipitation cell and eventually triggered cell. This link will help gain more insight into the role of CPs in organizing convection over land.

The soil-moisture feedback describes how precipitation amount, timing and intensity react to spatial anomalies in surface moisture. For heterogeneous moisture distributions with moist/dry patches on the scale of 10− 50km, numerical studies supported by observations indicate a negative soil-moisture feedback, where it rains more over dry patches (Imamovic, 2018; Rieck et al., 2014). The circulation established by the heterogeneous soil-moisture patches not only modifies the spatial rain distribution but allows for more water to be extracted from the atmosphere, thereby increasing the domain mean precipitation. We here suggest that the negative soil-moisture feedback can be exploited when irrigating agricultural land: if farmers cooperate by following a spatially heterogeneous irrigation pattern, they can increase both their collective time-mean precipitation and thus the total water available for growing crops. However, the spatially non-local nature of the feedback allows individual farmers to exploit this strategy, thereby saving their own resources; a typical ‘tragedy of commons’ situation. We formulate this setup in terms of an optimisation problem and study its parameter phase space, both analytically and numerically, in order to understand optimal rules and the consequences of the players’ choice to cooperate vs. compete. Different constraints in terms of water availability (reservoir) and average soil moisture as defined by the evaporation timescale are explored. Reducing the details of the land-atmosphere interaction into simple feedback parameters helps to elucidate the complex interactions between the precipitation, soil moisture and the human intervention by irrigation. Taking into account the negative soil-moisture feedback in irrigation models opens up new strategies to optimise water management and thereby increase crop yield.

Self-aggregation of convective cloud activity has attracted a lot of attention due to its role in the emergence of large scale weather phenomena such as the formation of hurricanes. Simulations with uniform boundary conditions show self-aggregation ocurring on the time-scale of a few weeks [1]. Recently, numerical experiments demonstrated that spatial clustering can form withing a few days, when the system is driven by diurnal temperature oscillations [2]. These simulations indicate that there may be a discontinuous phase transition between the clustered and the non-clustered state, i.e. that a threshold for the amplitudes of diurnal temperature oscillations exist, below which clustering does not emerge. A conceptual model has been proposed, suggesting that the phase transition might give rise to hysteresis in the sense that clustering emerging at high temperature amplitudes might persist if the amplitude is subsequently reduced to a level below the critical threshold.Here we test the hysteresis–hypothesis explicitly by performing cloud-resolving simulations with a high-amplitude transient period followed by a period with a low diurnal temperature amplitude. In reality, diurnal temperature oscillations have significantly larger amplitudes over land than over the ocean. The existence of hysteresis effects in the convective cloud clustering could have profound implications: clusters formed over land, where diurnal temperature variations are large, could persist over the ocean when transported there by large-scale wind advection. Once present, the clusters could even intensify over the ocean—with possible implications for cyclogenesis.[1] CJ Muller and IM Held, Journal of the Atmospheric Sciences, 69(8):2551–2565, 2012.[2] arXiv:2001.04740 [physics.ao-ph]

In radiative-convective equilibrium (RCE) simulations, convective self-aggregation (CSA) is the spontaneous organization into segregated cloudy and cloud-free regions. Evidence exists for how CSA is stabilized, but how it arises favorably on large domains is not settled. Using large-eddy simulations (LES), we link the spatial organization emerging from the interaction of cold pools (CPs) to CSA. We systematically weaken simulated rain evaporation to reduce maximal CP radii, $R_{\text{max}}$, and find reducing $R_{\text{max}}$ causes CSA to occur earlier. We further identify a typical rain cell generation time and a minimum radius, $R_{\text{min}}$, around a given rain cell, within which the formation of subsequent rain cells is suppressed. Incorporating $R_{\text{min}}$ and $R_{\text{max}}$, we propose a toy model that captures how CSA arises earlier on large domains: when two CPs of radii $r_{i,j}\in[R_{\text{min}},R_{\text{max}}]$ collide, they form a new convective event. These findings imply that interactions between CPs may explain the initial stages of CSA., 17 pages, 5 main figures, 4 supplementary figures

Convective self-aggregation is when thunderstorm clouds cluster over a constant temperature surface in radiative convective equilibrium. Self-aggregation was implicated in the Madden-Julian Oscillation and hurricanes. Yet, numerical simulations succeed or fail at producing self-aggregation, depending on modeling choices. Common explanations for self-aggregation invoke radiative effects, acting to concentrate moisture in a sub-domain. Interaction between cold pools, caused by rain evaporation, drives reorganization of boundary layer moisture and triggers new updrafts. We propose a simple model for aggregation by cold pool interaction, assuming a local number density $\rho(\mathbf{r})$ of precipitation cells, and that interaction scales quadratically with $\rho(\mathbf{r})$. Our model mimics global energy constraints by limiting further cell production when many cells are present. The phase diagram shows a continuous phase transition between a continuum and an aggregated state. Strong cold pool-cold pool interaction gives a uniform convective phase, while weak interaction yields few and independent cells. Segregation results for intermediate interaction strength.

Strong social capital is increasingly recognized as an organizational advantage. Better knowledge sharing and reduced transaction costs increase work efficiency. To mimic the formation of the associated communication network, we propose the Expert Game, where each individual must find a specific expert and receive her help. Participants act in an impersonal environment and under time constraints that provide short-term incentives for noncooperative behavior. Despite these constraints, we observe cooperation between individuals and the self-organization of a sustained trust network, which facilitates efficient communication channels with increased information flow. We build a behavioral model that explains the experimental dynamics. Analysis of the model reveals an exploitation protection mechanism and measurable social capital, which quantitatively describe the economic utility of trust.

In a changing climate, a key role may be played by the response of convective-type cloud and precipitation to temperature changes. Yet, it is unclear if precipitation intensities will increase mainly due to modified thermodynamic forcing or due to stronger convective dynamics. In gradual self-organization, convective events produce highest intensities late in the day. Tracking rain cells throughout their life cycles, we find that interacting events respond strongly to changes in boundary conditions. Conversely, events without interaction remain unaffected. Increased surface temperature indeed leads to more interaction and higher precipitation extremes. However, a similar intensification occurs when leaving temperature unchanged but simply granting more time for self-organization.Our study implies that the convective field as a whole acquires a memory of past precipitation and inter-cloud dynamics, driving extremes. Our results implicate that the dynamical interaction between convective clouds must be incorporated in global climate models to describe convective extremes and the diurnal cycle more realistically., Comment: 25 pages, 10 figures; removed typo in abstract

In vertebrates, methylation of cytosine at CpG sequences is implicated in stable and heritable patterns of gene expression. The classical model for inheritance, in which individual CpG sites are independent, provides no explanation for the observed non-random patterns of methylation. We first investigate the exact topology of CpG clustering in the human genome associated to CpG islands. Then, by pooling genomic CpG clusters on the basis of short distances between CpGs within and long distances outside clusters, we show a strong dependence of methylation on the number and density of CpG organization. CpG clusters with fewer, or less densely spaced, CpGs are predominantly hyper-methylated, while larger clusters are predominantly hypo-methylated. Intermediate clusters, however, are either hyper- or hypo-methylated but are rarely found in intermediate methylation states. We develop a model for spatially-dependent collaboration between CpGs, where methylated CpGs recruit methylation enzymes that can act on CpGs over an extended local region, while unmethylated CpGs recruit demethylation enzymes that act more strongly on nearby CpGs. This model can reproduce the effects of CpG clustering on methylation and produces stable and heritable alternative methylation states of CpG clusters, thus providing a coherent model for methylation inheritance and methylation patterning.

When food webs are exposed to species invasion, secondary extinction cascades may be set off. Although much work has gone into characterizing the structure of food webs, systematic predictions on their evolutionary dynamics are still scarce. Here we present a theoretical framework that predicts extinctions in terms of an alternating sequence of two basic processes: resource depletion by or competitive exclusion between consumers. We first propose a conceptual invasion extinction model (IEM) involving random fitness coefficients. We bolster this IEM by an analytical, recursive procedure for calculating idealized extinction cascades after any species addition and simulate the long-time evolution. Our procedure describes minimal food webs where each species interacts with only a single resource through the generalized Lotka-Volterra equations. For such food webs ex- tinction cascades are determined uniquely and the system always relaxes to a stable steady state. The dynamics and scale invariant species life time resemble the behavior of the IEM, and correctly predict an upper limit for trophic levels as observed in the field.

DNA methylation of CpG sites is an important epigenetic mark in mammals. Active promoters are often associated with unmethylated CpG sites, whereas methylated CpG sites correlate with silenced promoters. Methylation of CpG sites must be generally described as a dynamical process that is mediated by methylation enzymes, such as DNMT1 and DNMT3a/b. However, there are several models of how CpG sites can be protected from methylation and thereby remain unmethylated. In this paper we examine the combination of both: the positive feedbacks of DNA methylation and a short range counterpart which in turn protects-and thereby maintains-the unmethylated state. The emergent dynamics is provided by collaborative, re-enforcing feedbacks in favor of methylated CpG islands and cooperative protection of one CpG site by another in favor of unmethylated CpG sites. Our results suggest that this synthesis of mechanisms provides equally robust maintenance of both the unmethylated and methylated states of CpG islands.

Near promoters, both nucleosomes and CpG sites form characteristic spatial patterns. Previously, nucleosome depleted regions were observed upstream of transcription start sites and nucleosome occupancy was reported to correlate both with CpG density and the level of CpG methylation. Several studies imply a causal link where CpG methylation might induce nucleosome formation, whereas others argue the opposite, i.e., that nucleosome occupancy might influence CpG methylation. Correlations are indeed evident between nucleosomes, CpG density and CpG methylation-at least near promoter sites. It is however less established whether there is an immediate causal relation between nucleosome occupancy and the presence of CpG sites-or if nucleosome occupancy could be influenced by other factors. In this work, we test for such causality in human genomes by analyzing the three quantities both near and away from promoter sites. For data from the human genome we compare promoter regions with given CpG densities with genomic regions without promoters but of similar CpG densities. We find the observed correlation between nucleosome occupancy and CpG density, respectively CpG methylation, to be specific to promoter regions. In other regions along the genome nucleosome occupancy is statistically independent of the positioning of CpGs or their methylation levels. Anti-correlation between CpG density and methylation level is however similarly strong in both regions. On promoters, nucleosome occupancy is more strongly affected by the level of gene expression than CpG density or CpG methylation-calling into question any direct causal relation between nucleosome occupancy and CpG organization. Rather, our results suggest that for organisms with cytosine methylation nucleosome occupancy might be primarily linked to gene expression, with no strong impact on methylation.

In a dry convective boundary layer, convective patterns of typical scales spontaneously develop, qualitatively similar to those in a fluid which is placed between two horizontal plates and sufficiently heated from below. As soon as precipitating cumulus clouds form, this pattern is disturbed and a transition to a different state occurs. Here we use idealized large-eddy simulations to explore how the horizontal scale of convection is modified during this transition in the course of a diurnal cycle. Before onset of precipitation, cells with relatively constant diameter self-organize, with diameters roughly on the scale of the atmospheric boundary layer height. We find that the onset of precipitation then signals an approximately linear increase in horizontal scale with time. For our transient simulations, this scale increase progresses at a speed which is relatively insensitive to modifications in mean surface temperature, modifications in the rate at which surface temperature changes, or the initial lapse rate. When exploring the strength of the spatial correlations, we find that precipitation onset causes a sudden disruption of order and a subsequent decline of organization-until precipitation eventually ceases. We discuss possible implications for the development of extreme precipitation events. ©2017. American Geophysical Union.

The combination of bistability and noise is ubiquitous in complex systems, from biology to social interactions, and has important implications for their functioning and resilience. Here we use a simple three-state dynamical process, in which nodes go from one pole to another through an intermediate state, to show that noise can induce polarization switching in bistable systems if dynamical correlations are significant. In large, fully connected networks, where dynamical correlations can be neglected, increasing noise yields a collapse of bistability to an unpolarized configuration where the three possible states of the nodes are equally likely. In contrast, increased noise induces abrupt and irreversible polarization switching in sparsely connected networks. In multiplexes, where each layer can have a different polarization tendency, one layer is dominant and progressively imposes its polarization state on the other, offsetting or promoting the ability of noise to switch its polarization. Overall, we show that the interplay of noise and dynamical correlations can yield discontinuous transitions between extremes, which cannot be explained by a simple mean-field description.

Ecological diversity is ubiquitous despite the restrictions imposed by competitive exclusion and apparent competition. To explain the observed richness of species in a given habitat, food web theory has explored nonlinear functional responses, self-interaction or spatial structure and dispersal — model ingredients that have proven to promote stability and diversity. We here instead return to classical Lotka-Volterra equations, where species-species interaction is characterized by a simple product and spatial restrictions are ignored. We quantify how this idealization imposes constraints on coexistence and diversity for many species. To this end, we introduce the concept of free and controlled species and use this to demonstrate how stable food webs can be constructed by sequential addition of species. When we augment the resulting network by additional weak interactions we are able to show that it is possible to construct large food webs of arbitrary connectivity. Our model thus serves as a formal starting point for the study of sustainable interaction patterns between species.

In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show that this requirement is equivalent to demanding that each species be part of a non-overlapping pairing, which substantially constrains the food web structure. We demonstrate that a stable food web can always be obtained if a non-overlapping pairing exists. If it does not, the matrix rank can be used to quantify the lack of niches, corresponding to unpaired species. For the species richness at each trophic level, we derive the food web assembly rules, which specify sustainable combinations. In neighboring levels, these rules allow the higher level to avert competitive exclusion at the lower, thereby incorporating apparent competition. In agreement with data, the assembly rules predict high species numbers at intermediate levels and thinning at the top and bottom. Using comprehensive food web data, we demonstrate how omnivores or parasites with hosts at multiple trophic levels can loosen the constraints and help obtain coexistence in food webs. Hence, omnivory may be the glue that keeps communities intact even under extinction or ecological release of species., Author Summary Human impact currently induces rapid reductions in global biodiversity. Assessing the consequences of such modifications requires that ecological science better understand the conditions under which the species in a community can coexist and when not. Fundamentally, two species can not coexist indefinitely when they exclusively compete for the same prey—one must inevitably become extinct. This paradigm is known as the competitive exclusion principle. We consider communities of any number of species and multiple trophic levels, i.e. the average number of steps between a predator and basic nutrient, e.g. sunlight or sugars. We show that the extension of the competitive exclusion principle to such large systems means that each species must be part of a “non-overlapping pairing”. Such pairings are exclusive connections between two species, e.g. a predator and a prey. We demonstrate that a stable food web can always be obtained if a non-overlapping pairing exists. The food web assembly rules are explicit conditions that specify sustainable combinations of species at the different trophic levels. As also seen in field data, our rules imply high species numbers at intermediate levels and few at the top and bottom. We further show that omnivorous species—those with hosts at multiple trophic levels—may take a special role in stabilizing food webs, as they combine several trophic levels.