Convective Scale Research Articles

Ordering of time scales predicts applicability of quasilinear theory in unstable flows

We discuss the applicability of quasilinear-type approximations for a turbulent system with a large range of spatial and temporal scales. We consider a paradigm fluid system of rotating convection with vertical and horizontal temperature gradients. In particular, the interaction of rotation with the horizontal temperature gradient drives a ‘thermal wind’ shear flow whose strength is controlled by the horizontal temperature gradient. Varying this parameter therefore systematically alters the ordering of the shearing time scale, the convective time scale and the correlation time scale. We demonstrate that quasilinear-type approximations work well when the shearing time scale or the correlation time scale is sufficiently short. In all cases, the generalised quasilinear approximation systematically outperforms the quasilinear approximation. We discuss the consequences for statistical theories of turbulence interacting with mean gradients.

Separating urban heat island circulation and convective cells through dynamic mode decomposition

AbstractThis study applies dynamic mode decomposition (DMD) to three‐dimensional simulation results of urban heat island circulation (UHIC, which is horizontal circulation) and thermals (vertical convections). The aim of this study is to revisit how these phenomena coexist based on the characteristics of temporal changes in the flow field. We used DMD to obtain the dominant spatial patterns and information on temporal changes. One of the modes of horizontal wind, which does not change temporally (no oscillation or amplification), exhibits a spatial UHIC pattern. The unique feature of this UHIC mode is that there are small‐scale striated structures (150–200 m) and large‐scale convergence. The other modes are time‐varying (oscillating and decaying) and represent smaller spatial‐scale phenomena (150–250 m), such as thermals. The frequency of each mode takes various values, some of which are lower than the lifetime of thermals in accordance with the Deardorff convective scale (~10 min). These low‐frequency modes showed striated structures similar to that observed in the UHIC modes. These results suggest that UHIC and thermals deform each other through components that vary in long temporal scales.

Towards a 2DEnVar surface data assimilation approach within the convective scale numerical weather prediction model AROME‐France

AbstractSurface data assimilation (DA) plays a key role in the initialisation of soil variables in coupled surface–atmosphere numerical weather prediction (NWP) models. Météo‐France, as many other NWP centres, uses an operational surface DA method based on an optimal interpolation (OI), implemented more than 30 years ago. The current surface DA system implemented at Météo‐France in the operational limited‐area AROME‐France model operates in two steps. First, a two‐dimensional OI method analyses the diagnostic screen‐level parameters, which are then used to initialise the prognostic soil variables according to a one‐dimensional OI method. This article presents the implementation and the results of a new two‐dimensional ensemble‐based variational (2DEnVar) system, using the object‐oriented prediction system framework, for the diagnostic screen‐level variable analyses (2‐m temperature and 2‐m relative humidity) within the AROME‐France model. These analysed variables are then used to initialise the soil temperature and soil moisture of the first and second soil layers. A two‐dimensional variational system is initially implemented and compared with an equivalent system that uses an OI surface analysis. The comparison of 2‐m temperature increments shows that the two systems behave in a similar way. From this two‐dimensional variational approach, a 2DEnVar scheme is developed and compared with the OI screen‐level analysis used operationally (reference system). The results are encouraging even though a degradation in forecast quality is noticed at short ranges for 2‐m temperature and 2‐m relative humidity. This is mainly due to a low spread near the surface in the ensemble‐based data assimilation that is used to compute background‐error covariances in 2DEnVar. Sensitivity tests have been performed to improve the initial version of the 2DEnVar scheme. A positive and significant impact is noticed when a multiplicative inflation is applied to the background perturbations coming from the ensemble‐based data assimilation for the computation of 2‐m temperature and 2‐m relative humidity background‐error covariances. Finally, when comparing the inflated 2DEnVar system with the reference, the two systems behave similarly. This suggests that the 2DEnVar scheme, based on ensemble statistics, is capable of properly reconstructing background‐error structures derived from the empirical correlations described in OI.

Satellite based analysis of rapid intensification of Super Cyclone Amphan

Tropical Cyclones (TCs) are formidable natural hazards with destructive impacts on life and property along the tropical belt. TCs are responsible for multiple hazards such as riverine and urban floods, extreme winds, and lightning, storm surge significantly amplifying the threats they pose. Rapid Intensification (RI), defined as a sudden increase in Maximum Sustained Winds (MSWs) by 30 kt or more in 24 h, has been a growing concern. These events, characterized by a swift escalation in MSW are challenging to the forecasters and remain a considerable operational challenge, amplifying risks for coastal communities. Numerical modeling also struggles to predict RI, with limitations in describing inner core convective scale processes cited as a major limitation. Monitoring and assessing TCs heavily rely on satellite-based observations due to the absence of adequate in-situ measurements over the ocean. In the present study, we examine Super Cyclonic Storm (SuCS) Amphan, the first Super Cyclone of this century, that formed over the Bay of Bengal in 2020 using satellite imagery and derived products available in near-real time to monitor and identify the early signatures for the RI. It is observed that the intensification is intricately tied to substantial expansions in both the outer and inner core sizes along with its symmetricity before the RI. Notably, no significant alterations in size are observed between the very severe cyclonic storm (VSCS) and SuCS stages. The convection characteristics of TCs are found to provide crucial markers of their intensification, with a particular emphasis on polar satellite-based passive microwave imagery for analyzing embedded convection and early eye detection. Key observations indicate that inner convective ring patterns, identified through 37Ghz microwave imagery in lower-level convection, act as precursors to rapid intensification. Concurrently, the outer ring pattern observed during the mid-life course is found to permit further intensification of the system.

Unified framework for laser-induced transient bubble dynamics within microchannels

Oscillatory flow in confined spaces is central to understanding physiological flows and rational design of synthetic periodic-actuation based micromachines. Using theory and experiments on oscillating flows generated through a laser-induced cavitation bubble, we associate the dynamic bubble size (fluid velocity) and bubble lifetime to the laser energy supplied—a control parameter in experiments. Employing different channel cross-section shapes, sizes and lengths, we demonstrate the characteristic scales for velocity, time and energy to depend solely on the channel geometry. Contrary to the generally assumed absence of instability in low Reynolds number flows (<1000\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$<1000$$\\end{document}), we report a momentary flow distortion that originates due to the boundary layer separation near channel walls during flow deceleration. The emergence of distorted laminar states is characterized using two stages. First the conditions for the onset of instabilities is analyzed using the Reynolds number and Womersley number for oscillating flows. Second the growth and the ability of an instability to prevail is analyzed using the convective time scale of the flow. Our findings inform rational design of microsystems leveraging pulsatile flows via cavitation-powered microactuation.

Near‐surface wind profiles from numerical model predictions. Part II: Verifications against Australia‐wide surface wind observations

AbstractThe new scheme for deriving the near‐surface wind profiles discussed in Ma (in review) is applied to an Australian Bureau of Meteorology operational convective scale model over various domains. Both the new and conventional schemes' diagnostic 10‐m winds are then verified against Australia‐wide automatic weather station observations. Analyses of bulk statistics reveal that the new scheme's 10‐m wind forecasts have generally better accuracy than the current conventional scheme with a consistent reduction of biases over all domains. A widely recognised diurnal bias pattern of surface wind speed over the land is substantially reduced, and the inclusion of Ekman spiral effect on the 10‐m wind marginally improves statistics of the wind direction during the nighttime. The new scheme introduces no systemic bias, given the histogram of a bulk mean bias is analogiased to a Gaussian distribution, and moves the distribution of diagnostic wind speed closer to that observed.

Effect of Hot Air Drying Temperature on Drying Kinetics, Physico-Chemical Properties, and Energy Consumption of Culture Asparagus (Asparagus officinalis L.)

Influences of drying air temperatures on drying time, specific energy consumption as well as product quality of culture asparagus were investigated in hot-air drying. The drying properties of asparagus samples were performed in a laboratory scale convection dryer at three different temperatures. The drying times of asparagus samples were found as 1200, 630 and 510 min for 50, 60 and 70 °C, respectively. In regard to the data obtained, Midilli et al. model is superior to other models to describe drying behavior of asparagus samples. The effective moisture diffusivity values of asparagus samples were calculated between 6.32 ∙ 10−9−1.62 ∙ 10−8 m2/s and the activation energy was estimated as 43.59 kJ/mol. The highest rehydration content and the least total color change were found in asparagus slices dried at 50 °C. Energy consumption values for asparagus samples dried at 50, 60 and 70 °C temperatures were obtained as 10.14, 5.32 and 4.31 kWh, respectively. In terms of energy consumption values, the best efficiency among all drying temperatures was obtained at 70 °C. It has been determined that the specific energy consumption decreased with increasing temperature.

Diagnostics for Imbalance on the Convective Scale

Abstract The analyses produced by a data assimilation system may be unbalanced, that is dynamically inconsistent with the forecasting model, leading to noisy forecasts and reduced skill. While there are effective procedures to reduce synoptic-scale imbalance, the situation on the convective scale is less clear because the flowon this scale is strongly divergent and non-hydrostatic. In this studywe compare three measures of imbalance relevant to convective-scale data assimilation: (i) surface pressure tendencies, (ii) vertical velocity variance in the vicinity of convective clouds, and (iii) departures from the vertical velocity prescribed by the weak temperature gradient (WTG) approximation. These are applied in a numerical weather prediction system, with three different data assimilation algorithms: 1. Latent Heat Nudging (LHN), 2. Local Ensemble Transform Kalman Filter (LETKF), and 3. LETKF in combination with incremental analysis updates (IAU). Results indicate that surface pressure tendency diagnoses a different type of imbalance than the vertical velocity variance and theWTG departure. The LETKF induces a spike in surface pressure tendencies, with a large-scale spatial pattern that is not clearly related to the precipitation pattern. This anomaly is notably reduced by the IAU. LHN does not generate a pronounced signal in the surface pressure, but produces the most imbalance in the other two measures. The imbalances measured by the partitioned vertical velocity variance andWTG departures are similar, and closely coupled to the convective precipitation. Between these two measures, the WTG departure has the advantage of being simpler and more economical to compute.

Laminar separation bubble formation and bursting on a finite wing

The transient processes of laminar separation bubble (LSB) formation and bursting on a rectangular NACA 0018 wing are studied experimentally. A two-dimensional airfoil model is used as a baseline for the assessment of finite wing effects. The models are subjected to ramp changes in free-stream velocity causing the flow to switch between a state where an LSB forms and a state without reattachment. Lift force and particle image velocimetry measurements are used to relate the flow development to the aerodynamic loading. The lift coefficient of the airfoil exhibits substantial hysteresis, and the duration of the lift transients range from $10$ to $22$ convective time scales for bubble formation and $22$ to $30$ convective time scales for bursting. In contrast, the transient lift coefficients of the wing change gradually, with less hysteresis. The wing tip causes greater three-dimensionality in the separation bubble, whose thickness increases near the midspan where bursting is initiated. During bubble formation, the region of separated flow contracts towards the midspan. The gradual change in lift of the wing is linked to slower spanwise expansion and contraction of the separated flow region relative to the airfoil. On both models, the wavenumbers and amplitudes of disturbances in the separated shear layer rapidly change when reattachment initiates or ceases. Applying the bursting criterion of Gaster (Tech. Rep. Reports and Memoranda 3595. Aeronautical Research Council, London, 1967) to the bubble on the wing shows that bursting of the bubble at a single spanwise location is insufficient to cause complete spanwise failure of reattachment, and that the relationship between bursting parameters depends on spanwise position.

High resolution Tibetan Plateau regional reanalysis 1961-present

With the rapid global warming in recent decades, the Tibetan Plateau (TP) has suffered severe impacts, such as glacier retreat, glacial lake expansion, and permafrost degradation, which threaten the lives and properties of the local and downstream populations. Regional Reanalysis (RR) is vital for TP due to the limitations of observations. In this work, a 62-year (1961–2022) long atmospheric regional reanalysis with spatial resolution of 9 km (convective gray-zone scale) and temporal resolution of 1 hour over the TP (TPRR) was developed using the Weather Research and Forecasting (WRF) model, combined with re-initialization method, spectral nudging (SN), and several optimizations. TPRR is forced by ERA5 at hourly intervals. TPRR outperforms ERA5, realistically capturing climatological characteristics and seasonal variations of precipitation and T2m (air temperature at 2m above ground level). Moreover, TPRR better reproduces the frequency and intensity of precipitation, as well as the diurnal cycle of precipitation. This study also quantifies the wetting trend of 0.0071 mm/year over the TP amid global warming using TPRR.

Scaling regimes in rapidly rotating thermal convection at extreme Rayleigh numbers

The geostrophic turbulence in rapidly rotating thermal convection exhibits characteristics shared by many highly turbulent geophysical and astrophysical flows. In this regime, the convective length and velocity scales and heat flux are all diffusion-free, i.e. independent of the viscosity and thermal diffusivity. Our direct numerical simulations (DNS) of rotating Rayleigh–Bénard convection in domains with no-slip top and bottom and periodic lateral boundary conditions for a fluid with the Prandtl number $Pr=1$ and extreme buoyancy and rotation parameters (the Rayleigh number up to $Ra=3\times 10^{13}$ and the Ekman number down to $Ek=5\times 10^{-9}$ ) indeed demonstrate all these diffusion-free scaling relations, in particular, that the dimensionless convective heat transport scales with the supercriticality parameter $\widetilde {Ra}\equiv Ra\, Ek^{4/3}$ as $Nu-1\propto \widetilde {Ra}^{3/2}$ , where $Nu$ is the Nusselt number. We further derive and verify in the DNS that with the decreasing $\widetilde {Ra}$ , the geostrophic turbulence regime undergoes a transition into another geostrophic regime, the convective heat transport in this regime is characterized by a very steep $\widetilde {Ra}$ -dependence, $Nu-1\propto \widetilde {Ra}^{3}$ .

Simulating small-scale dynamo action in cool main-sequence stars

Context. The origin of the ubiquitous small-scale magnetic field observed on the solar surface can be attributed to the presence of a small-scale dynamo (SSD) operating in the sub-surface layers of the Sun. It is expected that a similar process could self-sustain a considerable amount of magnetic energy also in the near-surface layers of cool main-sequence stars other than the Sun. Aims. In this paper the properties of the magnetic field resulting from SSD action operating in the near-surface layers of four cool main-sequence stars and its self-organization into magnetic flux concentrations are investigated numerically. Methods. Three-dimensional radiative magnetohydrodynamic simulations of SSD action in the near-surface layers of four cool main-sequence stars of spectral types K8V, K2V, G2V, and F5V are carried out with the CO5BOLD code. The simulations are set up to have approximately the same Reynolds and magnetic Reynolds numbers, and to disentangle the impact of the effective temperature and the surface gravity on the SSD action from numerical effects. Results. It is found that the SSD growth rates in SI units differ for the four stellar models; the highest and lowest growth rate is for the K2V and F5V model, respectively. This is due to the different turnover times in the four simulations. Even so, the SSD field strengths reached in the saturation phases are similar in all models, with the same amount of kinetic energy converted into magnetic energy. If the magnetic energy that is pumped out from the computational domain across the bottom boundary is partially replenished from outside of the computational domain, we find that the SSD action leads to a sufficient reduction in the convective velocities to reduce the convective horizontal length scales in the convection zone by 5–10%, vanishing towards the optical depth unity level. In this case, strong kilogauss magnetic flux concentrations emerge at the surface, leading to magnetic bright features, which are more numerous and conspicuous for the K2V and G2V models than for the K8V and F5V models. Their vertical magnetic field component on the surface of optical depth unity increases from 1 kG to 1.6 kG with decreasing effective temperature from F5V to K8V. However, more than 90% of the magnetic flux through any of these stellar surfaces has a field strength of less than 1 kG.

Convective scale and subadiabatic layers in simulations of rotating compressible convection

Context. Rotation is thought to influence the size of convective eddies and the efficiency of convective energy transport in the deep convection zones of stars. Rotationally constrained convection has been invoked to explain the lack of large-scale power in observations of solar flows. Aims. Our main aims are to quantify the effects of rotation on the scale of convective eddies and velocity as well as the depths of convective overshoot and subadiabatic Deardorff layers. Methods. We ran moderately turbulent three-dimensional hydrodynamic simulations of rotating convection in local Cartesian domains. The rotation rate and luminosity of the simulations were varied in order to probe the dependency of the results on Coriolis, Mach, and Richardson numbers measuring the influences of rotation, compressibility, and stiffness of the radiative layer. The results were compared with theoretical scaling results that assume a balance between Coriolis, inertial, and buoyancy (Archimedean) forces, also referred to as the CIA balance. Results. The horizontal scale of convective eddies decreases as rotation increases, and it ultimately reaches a rotationally constrained regime consistent with the CIA balance. Using a new measure of the rotational influence on the system, we found that even the deep parts of the solar convection zone are not in the rotationally constrained regime. The simulations captured the slowly and rapidly rotating scaling laws predicted by theory, and the Sun appears to be in between these two regimes. Both the overshooting depth and the extent of the Deardorff layer decrease as rotation becomes more rapid. For sufficiently rapid rotation, the Deardorff layer is absent due to the symmetrisation of upflows and downflows. However, for the most rapidly rotating cases, the overshooting increases again due to unrealistically large Richardson numbers that allow convective columns to penetrate deep into the radiative layer. Conclusions. Relating the simulations with the Sun suggests that the convective scale, even in the deep parts of the Sun, is only mildly affected by rotation and that some other mechanism is needed to explain the lack of strong large-scale flows in the Sun. Taking the current results at face value, the overshoot and Deardorff layers are estimated to span roughly 5% of the pressure scale height at the base of the convection zone in the Sun.

Self-similarity of the dipole–multipole transition in rapidly rotating dynamos

The dipole–multipole transition in rapidly rotating dynamos is investigated through the analysis of forced magnetohydrodynamic waves in an unstably stratified fluid. The focus of this study is on the inertia-free limit applicable to planetary cores, where the Rossby number is small not only on the core depth but also on the length scale of columnar convection. By progressively increasing the buoyant forcing in a linear magnetoconvection model, the slow magnetic–Archimedean–Coriolis (MAC) waves are significantly attenuated so that their kinetic helicity decreases to zero; the fast MAC wave helicity, on the other hand, is practically unaffected. In turn, polarity reversals in low-inertia spherical dynamos are shown to occur when the slow MAC waves disappear under strong forcing. Two dynamically similar regimes are identified – the suppression of slow waves in a strongly forced dynamo and the excitation of slow waves in a moderately forced dynamo starting from a small seed field. While the former regime results in polarity reversals, the latter regime produces the axial dipole from a chaotic multipolar state. For either polarity transition, a local Rayleigh number based on the mean wavenumber of the energy-containing scales bears the same linear relationship with the square of the peak magnetic field measured at the transition. The self-similarity of the dipole–multipole transition can place a constraint on the Rayleigh number for polarity reversals in the Earth.

Effect of tip speed ratio on coherent dynamics in the near wake of a model wind turbine

The near wake of a small-scale wind turbine is investigated using particle image velocimetry experiments at different tip speed ratios ( $\lambda$ ). The wind turbine model had a nacelle and a tower mimicking real-scale wind turbines. The near wake is found to be dominated by multiple coherent structures, including the tip vortices, distinct vortex sheddings from the nacelle and tower, and wake meandering. The merging of the tip vortices is found to be strongly dependent on $\lambda$ . A convective length scale ( $L_c$ ) related to the pitch of the tip vortices is defined that is shown to be a better length scale than turbine diameter ( $D$ ) to demarcate the near wake from the far wake. The tower induced strong vertical asymmetry in the flow by destabilising the tip vortices and promoting mixing in the lower (below the nacelle) plane. The nacelle's shedding is found to be important in ‘seeding’ wake meandering, which, although not potent, exists close to the nacelle, and it becomes important only after a certain distance downstream ( $x&gt;3L_c$ ). A link between the ‘effective porosity’ of the turbine and $\lambda$ is established, and the strength and frequency of wake meandering are found to be dependent on $\lambda$ . In fact, a decreasing trend of wake meandering frequency with $\lambda$ is observed, similar to vortex shedding from a porous plate at varying porosity. Such similarity upholds the notion of wake meandering being a global instability of the turbine, which can be considered as a ‘porous’ bluff body of diameter $D$ .

Classification of Warm-Season Precipitation in High-Resolution Rapid Refresh (HRRR) Model Forecasts over the Contiguous United States

Abstract This study uses the convective adjustment time scale to identify the climatological frequency of equilibrium and nonequilibrium convection in different parts of the contiguous United States (CONUS) as modeled by the operational convection-allowing High-Resolution Rapid Refresh (HRRR) forecast system. We find a qualitatively different climatology in the northern and southern domains separated by the 40°N parallel. The convective adjustment time scale picks up the fact that convection over the northern domains is governed by synoptic flow (leading to equilibrium), while locally forced, nonequilibrium convection dominates over the southern domains. Using a machine learning algorithm, we demonstrate that the convective adjustment time-scale diagnostic provides a sensible classification that agrees with the underlying dynamics of equilibrium and nonequilibrium convection. Furthermore, the convective adjustment time scale can indicate the model quantitative precipitation forecast (QPF) quality, as it correctly reflects the higher QPF skill for precipitation under strong synoptic forcing. This diagnostic based on the strength of forcing for convection will be employed in future studies across different parts of CONUS to objectively distinguish different weather situations and explore the potential connection to warm-season precipitation predictability. Significance Statement An objective classification metric that can delineate a wide range of forecasts into distinct scenarios can serve as a valuable tool. This study represents a pioneering effort in utilizing the convective adjustment time scale to identify the climatological frequency of warm-season precipitation under varying levels of synoptic forcing in different parts of the contiguous United States (CONUS). The results demonstrate that the convective adjustment time scale is a robust metric for categorizing precipitation events and establishing a direct link to their predictability. Overall, this study provides a valuable framework for future studies focused on the CONUS domain, offering guidance on how to employ the convective adjustment time scale to classify weather regimes and explore the influence of environmental conditions on predictability of convection.

Mitigating thermoacoustic instabilities in premixed hydrogen flames using axial staging

In this paper we demonstrate how axial staging can be utilised to mitigate thermoacoustic instabilities in a combustion system by flame redistribution. This is achieved by moving flow to a second stage flame while keeping the combined thermal power and total flow fixed. The stability of the system was first characterised for premixed H2-CH4-air flames operated with hydrogen volume fraction in the range 80%–100%. As observed in recent work, increasing the hydrogen concentration led to the onset of strong self-excited instabilities. Increasing the flow velocity for a fixed hydrogen concentration was shown to have the same effect. Both of these are linked to a decrease in the convective time scale — causing the flame to become more convectively compact and responsive to higher frequencies. We then show that these instabilities could be reduced for all conditions, by distributing flow to the secondary flame. Two main driving mechanisms causing suppression were observed and analysed. Firstly, a reduction in the flow rate provided to the first stage flame, leading to a corresponding change in the flame structure. This leads to an increase in the convective time scale. This effect is quantified by a reduced gain at higher frequencies, and a change in the time delay of the flame transfer function. Secondly, introducing a second flame with a different convective time scale results in interference between the two flames. This acts to suppress or enhance the global fluctuations in heat release rate and hence, the amplitude of the pressure oscillations in the system.

Impact of Convection‐Permitting and Model Resolution on the Simulation of Mesoscale Convective System Properties Over East Asia

AbstractIn this study, two limited‐area convection‐permitting models (ICON‐CPMs) and convection‐parameterized models (ICON‐CParMs) covering the Asia monsoon region from ICOsahedral Nonhydrostatic model are conducted to investigate the sensitivities of Mesoscale Convective Systems (MCSs) to convection configurations and horizontal resolutions. We find that ICON‐CPMs outperform ICON‐CParMs and ERA5 in number, lifetime, size, shape, orientation, effective speed, and MCS‐mean precipitation. Compared to the satellite observation, MCSs in ICON‐CParMs and ERA5 are oversized (30%–66%) and have longer (21%–29%) lifetimes but occur less (37%–46%) frequently. When turning off the convection scheme, performances are improved to a large extent. The underestimation of MCS‐mean precipitation rates in ICON‐CParMs and ERA5 are improved in ICON‐CPMs. Moisture budgets show that low‐level winds rather than moisture determine the strength of MCS‐mean precipitation rate. The strong low‐level convergence produces strong updrafts in ICON‐CPMs and eventually results in strong MCS precipitation. The overly intense convective precipitation of MCSs in CPMs is an inherent problem since the scale of convection triggered at the gray zone grid spacing is larger than that in the real world. Although the MCS‐mean precipitation rate is closer to the satellite observation in ICON‐CPMs, it is actually a compensation for overly strong convective precipitation and overly weak stratiform precipitation. Upgrading resolution from 8 to 4 km in ICON‐CPMs has benefits in simulating MCS lifetime, size, shape, orientation, and precipitation but not in MCS number.

On the partition noise in chosen particle weighted methods and its consequences for weakly-compressible flow models

The Meshless Finite Volume (MFV) method, which is a member of the particle weighted methods (PWM) family, is analysed in the context of the so-called partition noise problem. This issue is inherent to PWM-type discretisation which is based on compact support kernel functions and particle sampling. The partition noise exhibits itself as spurious oscillations observed in the solution; they are caused by unphysical source terms in the discretised equations and approximate local volumes computation. Unfortunately, decreasing the discrete length scale which controls the spatial resolution reduces the partition noise only weakly (and never completely). When choosing numerical schemes, a special care is required since in naive implementations the partition noise may even lead to loss of stability. However, even when stability is assured, PWM does not fulfil the assumptions of the Lax equivalence theorem (i.e. the discretised equations are not consistent), therefore convergence in the classical meaning cannot be guaranteed.As an example of a problematic use of MFV, we investigate its application to the solution of fluid flow equations at low Mach numbers, aiming to mimic truly incompressible flow conditions. Taken here as isothermal Euler equations, they are the basis of the so-called weakly-compressible (WC) flow models. Such modelling does not involve any elliptic-type equation and, due to the algorithmic and computational reasons, seems to be well-suited for particle methods. The WC flow model imposes, however, a serious challenge for PWM since: (i) the method is not gauge invariant and the disparity between the speed of sound and the convective velocity scale causes a significant spurious source of momentum; (ii) the inaccuracy in the local volumes approximation leads to errors in the computed density which are comparable to physically relevant slight variations, inherent to the WC approach. We propose specific numerical and modelling measures: controlled relaxation of initial particle distribution, particle volumes computation using an optimal kernel function, a choice of gradient limiting techniques and a carefully chosen background pressure. Although these improvements significantly increase the accuracy (however at remarkably increased computational cost), the theoretical 2nd-order convergence is achieved only at lower spatial resolutions when the truncation errors dominate. The accuracy of mesh-based methods is achieved in PWM only for the pressure field; the errors in the velocity field are much larger and convergence is at most 1st-order. We point some contradictory requirements of the model equations and the numerical method. One of the conclusions is that it is doubtful to construct a convergent truly Lagrangean method of PWM type at reasonable computational cost. The present findings also apply to conservative variants of the weakly-compressible Smoothed Particle Hydrodynamics which, being first order consistent in the best case, suffers from the partition noise even more severely than the considered MFV approach which is theoretically second order consistent. The conclusions pose a question about a rationale for the use of WC-PWM approach in chosen applications, in particular free surface and interfacial flows.

Potential Predictability of the Madden‐Julian Oscillation in a Superparameterized Model

AbstractThe Madden‐Julian Oscillation (MJO) is a promising target for improving sub‐seasonal weather forecasts. Current forecast models struggle to simulate the MJO due to imperfect convective parameterizations and mean state biases, degrading their forecast skill. Previous studies have estimated a potential MJO predictability 5–15 days higher than current forecast skill, but these estimates also use models with parameterized convection. We perform a perfect‐model predictability experiment using a superparameterized global model in which the convective parameterization is replaced by a cloud resolving model. We add a second “silent” cloud resolving component to the control simulation that independently calculates convective‐scale processes using the same large‐scale forcings. The second set of convective states are used to initialize forecasts, representing uncertainty on the convective scale. We find a potential predictability of the MJO of 35–40 days in boreal winter using a single‐member ensemble forecast.