Cumulus Research Articles

Identifying optimal cloud cover for enhanced forest carbon uptake: Periodic-case NEE-overshoot modelling

On certain kinds of cloudy days, many forested ecosystems exhibit enhanced carbon uptake and water-use efficiency-the cloudy-day forest flux anomaly. Using ensemble methods to analyze eddy-covariance fluxes, we have diagnosed net ecosystem exchange (NEE) and water-use efficiency (WUE) of a temperate broadleaf forest and a tropical evergreen forest as they responded to natural fluctuating-light regimes. Here we apply average NEE and evapotranspiration solutions of a first-order dynamic model to describe the observed whole-canopy sensitivity to periodic light. On partly-cloudy days, maximum overall NEE enhancements over conventional steady-state equilibrium estimates are ≈ 25% for a midlatitude deciduous forest and ≈ 15% for a tropical evergreen forest. This finding supports our conclusion that in many cases the cloudy-day anomaly is a consequence of a dynamic response by the trees responding to fluctuating-light regimes occasioned by passing cumulus clouds.

Combining observations and simulations to investigate the small-scale variability of surface solar irradiance under continental cumulus clouds

Abstract. The amount of solar radiation reaching the Earth surface (surface solar irradiance, SSI) is critical for a variety of applications, ranging from surface–atmosphere interactions to solar energy. SSI is characterized by a large spatiotemporal variability, in particular in the presence of cumulus clouds. This results in complex spatial patterns of shadows and sunlight directly related to clouds' geometry and physical properties. Although key in many respects, the instantaneous spatial distribution of SSI remains largely unexplored. Here, we use unique observations from a dense network of pyranometers deployed during the HOPE field campaign to investigate the SSI spatial distribution. For cumulus scenes, bimodal distributions are found, with one mode corresponding to cloud shadows and the other to sunlit areas with enhanced SSI exceeding clear-sky values. Combining large-eddy simulations of cumulus clouds with Monte Carlo ray tracing, we demonstrate the capability of advanced numerical tools to reproduce the observed distributions and quantify the impact of cloud geometrical and physical properties on both modes. In particular, cloud cover strongly modulates their amplitudes, in addition to their position and width, which are also sensitive to cloud height, geometrical depth, and liquid water content. Combining observations and simulations, we also explore sampling strategies to estimate the SSI spatial distribution with a limited number of sensors, suggesting that 10 pyranometers integrated over 10 min can capture most details of the full distribution. Such a strategy could be used for future campaigns to further investigate SSI distributions and their impact on land–atmosphere exchanges or photovoltaic farm management.

Aircraft Observations Reveal the Relationship Between Cumulus Entrainment Rate and Aerosol Loading

AbstractThe influence of entrainment, a key process characterized by the entrainment rate in cumulus parameterization, on aerosol‐cloud interactions has been widely recognized. However, despite qualitative links established between entrainment and aerosol loading, a quantitative relationship based on observational evidence remains elusive. This study utilizes aircraft observations of cumulus clouds during two field campaigns to determine the quantitative relationship between entrainment rate and aerosol loading. In both campaigns, the entrainment rate is negatively correlated with aerosol loading. It is speculated that increased aerosol loading enhances cloud edge droplet evaporation, which leads to increased buoyancy and vertical velocity within the cloud, thereby reducing the entrainment rate. Further analysis shows that the response of entrainment rate to aerosol perturbations is more significant in smaller cumulus clouds with weak buoyancy and less pronounced under opposite conditions. These findings shed new light on improving the description of aerosol‐cloud interactions in cumulus parameterizations.

Connections Between Sub‐Cloud Coherent Updrafts and the Life Cycle of Maritime Shallow Cumulus Clouds in Large Eddy Simulation

AbstractWe develop a novel approach to detect cloud‐subcloud coupling during the cloud life cycle and analyze a large eddy simulation of marine shallow cumulus based on the Barbados oceanographic and meteorological experiment campaign. Our results demonstrate how the activity of sub‐cloud coherent updrafts (SCUs) affect the evolution of shallow cloud properties during their life cycles, from triggering to development, and through to dissipation. Most clouds are related to SCUs during their lifetime but not every SCU ( for short‐lived ones) leads to cloud formation. The fastest growing SCUs in a relatively moist region are most likely to initiate clouds. The evolution of cloud base mass‐flux depends on cloud lifetime. Compared with short‐lived clouds, longer lived clouds have longer periods of development, even normalized by the full lifetime, and tend to increase their cloud base mass‐flux to a stronger maximum. This is consistent with the evolution of mass flux near the top of SCU, indicating that the development of clouds is closely related to the sub‐cloud activity. When the SCUs decay and detach from the lifting condensation level, the corresponding cloud base starts to rise, signifying the start of cloud dissipation, during which the cloud top lowers to approach the rising cloud base. Previous studies have described similar conceptual pieces of this relationship but here we provide a continuous framework to cover all the stages of cloud‐subcloud coupling. Our findings provide quantitative evidence to supplement the conceptual model of shallow cloud life cycle and is critical to improve the steady‐state assumption in parameterization.

Initiation and evolution of urban-induced precipitation under different background wind speeds: Roles of urban breeze circulation and cold pool

Urban-enhanced precipitation is often observed far downwind of cities, suggesting important roles of background wind. This study examines the impacts of background wind on the initiation and evolution of urban-induced precipitation through idealized ensemble large-eddy simulations with different initial background wind speeds of 0, 1, 2, 3, 4, and 5 m s−1. Without background wind, a strong urban breeze circulation (UBC) initiates a relatively large number of cumulus clouds in the urban area, which exhibit greater cloud top heights than those in the rural area. The early-initiated clouds do not produce precipitation but moisten the middle troposphere, assisting later-initiated clouds to develop into deep convective clouds and produce concentrated precipitation in the urban area. As the background wind speed increases, the UBC weakens. Also, the high-humidity area generated by early-initiated clouds is continuously advected away from the urban area. Consequently, the precipitation initiation is delayed as the background wind speed increases. Precipitating clouds are advected downwind and generate a cold pool, and updrafts are repeatedly produced at the downwind boundary of the cold pool. The downwind-advected clouds are fed by the newly produced updrafts, being a long-lived organized precipitation system that produces a considerable amount of precipitation in the downwind area. This feeding effect is most prominent for a moderate background wind (3 m s−1), causing the precipitation amount and duration to be maximized. For stronger background winds, precipitation is initiated by the mechanical lifting of the warm air of the urban boundary layer over the cool rural boundary layer around sunset.

The impact of coupled 3D shortwave radiative transfer on surface radiation and cumulus clouds over land

Abstract. Radiative transfer is a 3D process, but most atmospheric models consider radiation only in the vertical direction for computational efficiency. This results in inaccurate surface radiation fields, as the horizontal transport of radiation is neglected. Previous work on 3D radiative effects mainly used 3D radiative transfer uncoupled from the flow solver. In contrast, our current work uses 3D radiative transfer coupled to the flow solver to study its impact on the development of clouds and the resulting impact on the domain-averaged surface solar irradiance. To this end, we performed a series of realistic large-eddy simulations with MicroHH. To improve the level of realism of our radiation, we first included the direct effect of aerosols using aerosol data from the Copernicus Atmosphere Monitoring Service (CAMS) global reanalysis. Next, we performed simulations with 1D radiative transfer and with a coupled ray tracer for 12 d on which shallow cumulus clouds formed over Cabauw, the Netherlands. In general, simulations with the coupled ray tracer have a higher domain-averaged liquid water path, larger clouds, and similar cloud cover compared to simulations with 1D radiative transfer. Furthermore, the domain-averaged direct radiation is decreased with 3D radiative transfer, and the diffuse radiation is increased. However, the average difference in global radiation is less than 1 W m−2, as the increase in global radiation from uncoupled 3D radiative transfer is counterbalanced by a decrease in global radiation caused by changes in cloud properties.

Numerical Investigation of Track and Intensity Evolution of Typhoon Doksuri (2023)

This study utilized the WRF model to investigate the track evolution and rapid intensification (RI) of Typhoon Doksuri (2023) as it moved across the Luzon Strait and through the South China Sea (SCS). The simulation results indicate that Doksuri has a smaller track sensitivity to the use of different physics schemes, while having a greater intensity sensitivity. Sensitivity numerical experiments with different physics schemes can well capture its northwestward movement in the first two days, but they predict less westward track deflection as the typhoon moves across the Luzon Strait and through the SCS. Moreover, all the experiments successfully simulated Doksuri’s RI, albeit with quite different rates and a time lag of 12 h. Among different combinations of physics schemes, there exists an optimal set of cumulus parameterization and cloud microphysics schemes for track and intensity predictions. Doksuri’s track changes as the typhoon moved across the Luzon Strait and through the SCS were influenced by the topographic effects of the terrain of the Philippines and Taiwan, to different extents. The track changes of Doksuri are explained by the wavenumber-one potential vorticity (PV) tendency budget from different physical processes, highlighting that the horizontal PV advection dominates the PV tendency throughout most of the simulation time due to the offset of vertical PV advection and differential diabatic heating. In addition, this study applies the extended Sawyer–Eliassen (SE) equation to compare the transverse circulations of the typhoon induced by various forcing sources. The SE solution indicates that radial inflow was largely driven in the lower-tropospheric vortex by strong diabatic heating, while being significantly enhanced in the lower boundary layer due to turbulent friction. All other physical forcing terms were relatively insignificant for the induced transverse circulation. The coordinated radial inflow at low levels may have led to the eyewall development in unbalanced dynamics. Intense diabatic heating thus was vital to the severe RI of Doksuri under a weak vertical wind shear.

On Climate Change and Trade Cumulus Organization

AbstractWe investigate the role of mesoscale organization for the response of trade cumulus (Tc) clouds to climate change. Among four recently identified states of Tc organization, the “Sugar” state has the lowest and the “Flower” state the highest cloud fraction and cloud radiative effect. Using large‐eddy simulations, we find that the Flower Tc state is more sensitive to climate change than the Sugar Tc state. In the considered case, the short‐wave cloud radiative effect weakens by 0.28 W m−2 in the Sugar state and by 1.5 W m−2 in the Flower state over the course of 21st century under the RCP8.5 emissions scenario. This is accompanied by a reduction of the short‐wave cloud radiative effect variance on the mesoscale. The primary mechanism is stabilization of the boundary layer by stronger long‐wave radiative heating at the inversion associated with higher greenhouse gas levels. This weakens the boundary layer mesoscale circulation that is responsible for aggregation of moisture and formation of the Flower Tc state. Thus, in the considered case, organization on the mesoscale amplifies the positive feedback of Tc clouds to climate change. Owing to the widespread occurrence of boundary layer mesoscale circulations in the Tc regime, this mechanism could modulate the Tc response to climate change in general.

Lev Gutman—A Pioneer in Theoretical Mesoscale Meteorology

Abstract On 5 March 2023, Professor Lev Gutman would have been 100 years old. This article describes Professor Gutman’s legacy in the field of dynamic mesoscale meteorology and numerical weather prediction. Gutman developed his career as a mathematician and meteorologist in the Soviet Union, where he built a school of specialists in mesoscale meteorology from the 1950s through the 1970s. He primarily worked on analytical methods to solve complex nonlinear problems, such as the structure of sea breezes, mountain–valley circulations, and thermal convection over heated terrain. Gutman pioneered the development of theories of cumulus clouds, tornadoes, and other atmospheric phenomena. In the 1960s, he carried out numerous research investigations on these topics with his doctoral students and collaborators at the High-Altitude Geophysical Institute in Nalchik in the northern Caucasus and later at the Siberian Scientific Center near Novosibirsk. Gutman compiled the results from these studies into a monograph titled “Introduction to the Nonlinear Theory of Mesoscale Meteorological Processes,” which was published in Russian in 1969 and later translated into English, Chinese, and Japanese. This monograph became a major textbook for specialists in mesoscale meteorology, remaining relevant to this day. After Professor Gutman immigrated to Israel in 1978, his collaborations expanded to include Israeli and western scientists from Europe and the United States. Gutman did not receive the recognition he deserved due to the political realities of the time. His book and his seminal analytical solutions should still be useful for early career scientists in mesoscale meteorology and atmospheric dynamics.

Deep-learning-driven simulations of boundary layer clouds over the Southern Great Plains

Abstract. Based on long-term observations at the Southern Great Plains site by the Atmospheric Radiation Measurement (ARM) program for training and validation, a deep-learning model is developed to simulate the daytime evolution of boundary layer clouds (BLCs) from the perspective of land–atmosphere coupling. The model takes ARM measurements (including early-morning soundings and diurnally varying surface meteorological conditions and heat fluxes) as inputs and predicts hourly estimates (including cloud occurrence, the positions of cloud boundaries, and the vertical profile of the cloud fraction) as outputs. The deep-learning model offers good agreement with the observed cloud fields, especially in the accuracy with which cloud occurrence and base height are reproduced. When the inputs are substituted by reanalysis data from ERA5 and MERRA-2, the outputs of the deep-learning model provide a better agreement with observation than the cloud fields extracted from ERA5 and MERRA-2 themselves. Thus, the deep-learning model shows great potential to serve as a diagnostic tool for the performance of physics-based models in simulating stratiform and cumulus clouds. By quantifying biases in clouds and attributing them to the simulated atmospheric state variables versus the model-parameterized cloud processes, this observation-based deep-learning model may offer insights into the directions needed to improve the simulation of BLCs in physics-based models for weather forecasting and climate prediction.

Weather Research and Forecasting Model (WRF) Sensitivity to Choice of Parameterization Options over Ethiopia

Downscaling seasonal climate forecasts using regional climate models (RCMs) became an emerging area during the last decade owing to RCMs’ more comprehensive representation of the important physical processes at a finer resolution. However, it is crucial to test RCMs for the most appropriate model setup for a particular purpose over a given region through numerical experiments. Thus, this sensitivity study was aimed at identifying an optimum configuration in the Weather, Research, and Forecasting (WRF) model over Ethiopia. A total of 35 WRF simulations with different combinations of parameterization schemes for cumulus (CU), planetary boundary layer (PBL), cloud microphysics (MP), longwave (LW), and shortwave (SW) radiation were tested during the summer (June to August, JJA) season of 2002. The WRF simulations used a two-domain configuration with a 12 km nested domain covering Ethiopia. The initial and boundary forcing data for WRF were from the Climate Forecast System Reanalysis (CFSR). The simulations were compared with station and gridded observations to evaluate their ability to reproduce different aspects of JJA rainfall. An objective ranking method using an aggregate score of several statistics was used to select the best-performing model configuration. The JJA rainfall was found to be most sensitive to the choice of cumulus parameterization and least sensitive to cloud microphysics. All the simulations captured the spatial distribution of JJA rainfall with the pattern correlation coefficient (PCC) ranging from 0.89 to 0.94. However, all the simulations overestimated the JJA rainfall amount and the number of rainy days. Out of the 35 simulations, one that used the Grell CU, ACM2 PBL, LIN MP, RRTM LW, and Dudhia SW schemes performed the best in reproducing the amount and spatio-temporal distribution of JJA rainfall and was selected for downscaling the CFSv2 operational forecast.

Source Levels of In‐Cloud Air in Shallow Cumulus: Consistency Between Paluch Diagram and Lagrangian Particle Tracking

AbstractThe Paluch diagram is a widely used tool for interpreting aircraft measurements of shallow cumulus clouds. A prior study conducted by Heus et al. (2008, https://doi.org/10.1175/2008jas2572.1) concluded that the source levels of in‐cloud air inferred from the Paluch diagram exhibit biases, sometimes of several hundred meters, in comparison to those derived from Lagrangian particle tracking. In this short study we revisit this comparison. The results indicate that the upper source levels of in‐cloud air determined from the Lagrangian Particle Tracking and the Paluch diagram are consistent, and the choice of statistical methods is crucial. The significance of this research lies in confirming the reliability of the Paluch analysis, enabling its confident application to aircraft data.

Aerosol-Induced Invigoration of Cumulus Clouds—A Review

Aerosol-Induced Invigoration of Cumulus Clouds—A Review

Mesoscale and Large-Eddy Simulation of the Boundary-Layer Process of Cumulus Development over Naqu, Tibetan Plateau Part B: The Low-level Baroclinic Vortex and its Contribution to Cumulus Clouds Formation

Mesoscale and Large-Eddy Simulation of the Boundary-Layer Process of Cumulus Development over Naqu, Tibetan Plateau Part B: The Low-level Baroclinic Vortex and its Contribution to Cumulus Clouds Formation

Effect of current density and operating temperature on degradation of protonic ceramic fuel cells containing BaZr0.8Yb0.2O3-δ electrolyte during long-term operation

Barium zirconate doped with 20 mol% Yb (BaZr0.8Yb0.2O3-δ, BZYb20) is one of the most promising candidates for use as an electrolyte material in protonic ceramic fuel cells (PCFCs) due to its high proton conductivity and high chemical stability under CO2-containing fuel conditions. The long-term durabilities of PCFCs prepared using the BZYb20 electrolyte were evaluated as a function of the current density at 500 and 600 °C over a period of 1000 h. At 600 °C, the internal resistance of the cell increased even under open circuit voltage (OCV) condition. Comparing the voltage lowering rates at a current density of 0.172 A cm−2 based on the current density–voltage curves recorded during the durability tests, rates of 3.0, 5.3, and 9.0%/1000 h were achieved at the OCV, 0.047, and 0.172 A cm−2, respectively. A small amount of Ni elements diffused into the electrolyte from the anode to the cathode side, resulting in the formation of cumulus cloud shapes that corresponded to Ni element segregation at the grain boundaries in the electrolyte layer after long-term durability testing at 0.172 A cm−2. At current densities of 0.047–0.048 A cm−2, the voltage lowering rate at 500 °C was higher than that at 600 °C, with values of 6.0 and 2.6%/1000 h being recorded, respectively. This effect may be due to the higher resistance of the cell at 500 °C compared to that at 600 °C.

Diurnal Variation in Surface Incident Solar Radiation Retrieved by CERES and Himawari-8

The diurnal variation of surface incident solar radiation (Rs) has a significant impact on the Earth’s climate. Satellite-retrieved Rs datasets display good spatial and temporal continuity compared with ground-based observations and, more importantly, have higher accuracy than reanalysis datasets. Facilitated by these advantages, many scholars have evaluated satellite-retrieved Rs, especially based on monthly and annual data. However, there is a lack of evaluation on an hourly scale, which has a profound impact on sea–air interactions, climate change, agriculture, and prognostic models. This study evaluates Himawari-8 and Clouds and the Earth’s Radiant Energy System Synoptic (CERES)-retrieved hourly Rs data covering 60°S–60°N and 80°E–160°W based on ground-based observations from the Baseline Surface Radiation Network (BSRN). Hourly Rs were first standardized to remove the diurnal and seasonal cycles. Furthermore, the sensitivities of satellite-retrieved Rs products to clouds, aerosols, and land cover types were explored. It was found that Himawari-8-retrieved Rs was better than CERES-retrieved Rs at 8:00–16:00 and worse at 7:00 and 17:00. Both satellites performed better at continental sites than at island/coastal sites. The diurnal variations of statistical parameters of Himawari-8 satellite-retrieved Rs were stronger than those of CERES. Relatively larger MABs in the case of stratus and stratocumulus were exhibited for both hourly products. Smaller MAB values were found for CERES covered by deep convection and cumulus clouds and for Himawari-8 covered by deep convection and nimbostratus clouds. Larger MAB values at evergreen broadleaf forest sites and smaller MAB values at open shrubland sites were found for both products. In addition, Rs retrieved by Himawari-8 was more sensitive to AOD at 10:00–16:00, while that retrieved by CERES was more sensitive to COD at 9:00–15:00. The CERES product showed larger sensitivity to COD (at 9:00–15:00) and AOD (at 7:00–10:00) than Himawari-8. This work helps data producers know how to improve their future products and helps data users be aware of the uncertainties that exist in hourly satellite-retrieved Rs data.

The Role of the Toroidal Vortex in Cumulus Clouds' Entrainment and Mixing

AbstractShallow convective clouds play a crucial role in Earth's energy budget, as they modulate the radiative transfer in the atmosphere and participate in the vertical transport of aerosols, energy, and humidity. The parameterizations representing these complex, vital players in weather and climate models are mostly based on a description of steady‐state plumes and are a source of major uncertainty. Recently, several studies have shown that buoyant thermals are inherent in atmospheric convection and contain a toroidal (ring) vortex. This work studies those vortices in growing shallow cumulus (Cu) clouds using high‐resolution (10 m) Large Eddy Simulations that resolve these vortices in much detail. Recent analysis of such data showed that small‐scale turbulent diffusion is unable to explain the large diluted portion of the cloud. Here we advocate for the important role of the Cu toroidal vortex (TV) in cloud dilution and present the complex dynamics and structure of a Cu TV. Nevertheless, since the vortex dominates the cloud's dilution, simplicity emerges when considering the cloud's lateral mass flux profile. The cloud mixing is quantified using direct flux calculations and Eulerian tracers. In addition, Lagrangian tracers are used to identify the origin of the entrained air and its thermodynamic properties. It shows that most of the air entrained by the vortex is not recycled by the vortex, yet is significantly more humid than the environment. We suggest that the development of new models describing thermals, together with their toroidal vortices, might improve cloud parameterizations in weather and climate models.

Evaluation of a New Approach for Entrainment and Detrainment Rate Estimation

AbstractEntrainment and detrainment rates (ε and δ) constitute the most critical free parameters in mass flux schemes commonly employed for cumulus parameterizations. Recently, Zhu et al. (2021) introduced a new approach that utilizes aircraft observations to simultaneously estimate ε and δ for cumulus clouds, overcoming the limitation of other observation‐based approaches that solely yield ε without offering insights into δ. This study aims to comprehensively evaluate the reliability of this new approach. First, evaluation using an Explicit Mixing Parcel Model demonstrates the capability of the new approach to back‐calculate predetermined ε and δ based on the physical properties before and after the entrainment mixing. Second, evaluation using large‐eddy simulations illustrates that the new approach yields consistent ε and δ profiles compared to the traditional approach. Sensitivity tests indicate a weak sensitivity of the estimated δ with the new approach to the entrained air source. A decrease in the proportion of cloudy air in the assumed detrained air leads to a reduction in the estimated δ, while ε remains unaffected. Finally, the most appropriate assumptions for entrained and detrained air are discussed. Estimating ε for cumulus parameterizations involves acquiring ambient air more than 500 m away from the cloud edge as entrained air. Due to implicit mean field approximations in the traditional approach, determining the optimal assumption for detrained air properties proves challenging. This study confirms the reliability of the new approach in estimating ε and δ, providing confidence in its application to extensive observational data and advancement in parameterization.

Enabling Space-Based Computed Cloud Tomography with a Mixed Integer Linear Programming Scheduler

Cumuliform clouds in Earth’s lower atmosphere play important roles in the radiative balance and hydrological cycle of the climate system. Yet key processes unfolding in these clouds, such as aerosol interactions and precipitation initiation, are still poorly understood. Current space-based cloud observation methods are inadequate for inferring the internal structure of clouds outside of a narrow transect that is probed actively by radar and lidar. Cloud tomography is an emerging technique that uses passive imaging of a cloud target from multiple locations with a large angular range to infer internal cloud structure. Many low convective clouds only have a lifetime of 15–25 min, necessitating autonomous scheduling of observation targets as they appear. Onboard autonomous scheduling is formulated as a mixed-integer optimization problem (MILP) with a finite time horizon and a reward scheme designed to maximize the angular range of the observations. A finite time horizon MILP scheduler is well suited to this mission because the short lifetime of low convective clouds creates a natural time horizon. This MILP can solve for an optimal observation schedule in a maximum time of 15 ms on a desktop CPU. The MILP scheduler is able to observe nearly 60% more targets than a conventional push-broom camera configuration. This initial result is promising and demonstrates the need for continued research in this area.

Bulk Microphysics Schemes May Perform Better With a Unified Cloud‐Rain Category

AbstractBulk microphysics schemes continue to face challenges due in part to the necessary simplification of hydrometeor properties and processes that is inherent to any parameterization. In all operational bulk schemes, one such simplification is the division of liquid water into two subcategories (cloud and rain) when predicting the evolution of warm clouds. It was previously found that biases in collisional growth in a bulk scheme with these separate liquid water categories can be mitigated with a unified liquid water category in which cloud and rain are contained within the same category. In this study, we examine the effect of artificially separating the liquid water category on other microphysical processes and in more realistic settings. Both our idealized 1D and 3D results show that a unified category bulk scheme is fundamentally better at predicting the timing and intensity of rain from warm‐phase cumulus clouds compared to a traditional (separate) category bulk scheme. This is because a unified category bulk scheme allows a bimodal distribution to exist within one traditional “rain” category, whereas separate category bulk scheme only have one mode per category. This advantage allows the unified bulk scheme to retain the information of the largest droplets even as they fall through a layer of small raindrops. A separate category bulk scheme fails to represent this bimodal feature in comparison.