Abstract
Entrainment is a key process that can modulate the intensity of supercells, and a better understanding of its impact could help improve forecasts of thunderstorms and the precipitation they produce. In Part III of this series, the three distinct mechanisms of entrainment identified during the mature stage of idealized supercell thunderstorms in Part I (overturning “ribbons” of horizontal vorticity, “disorganized turbulent eddies,” and the “storm-relative airstream”) are examined as the absolute humidity of the environment is decreased. The existence of these mechanisms in a more realistic simulated storm environment is also established. Entrainment is calculated as fluxes of air across the storm core surface; passive fluid tracers help determine the resulting dilution of the storm updraft. Model microphysical rates are used to examine the direct impacts of entrainment on hydrometeors within the storm updraft as well as precipitation that falls to the ground. Results show that as mixed-layer humidity decreases, the “ribbons” and turbulent eddy mechanisms decrease in intensity, but their effects on precipitation production change little. With decreasing humidity in the 3–4 km AGL layer, the storm-relative airstream entrains less humid low-level air into the storm core, decreasing the vertical mass flux, and therefore the precipitation produced by the storm. When the humidity in the mid- to upper troposphere (4–20 km AGL) is decreased, precipitation is significantly reduced, but not due to the effects of the entrained air. Rather, enhanced evaporation and sublimation of falling precipitation decreases the overall precipitation efficiency of the storm.
Abstract
Entrainment is a key process that can modulate the intensity of supercells, and a better understanding of its impact could help improve forecasts of thunderstorms and the precipitation they produce. In Part III of this series, the three distinct mechanisms of entrainment identified during the mature stage of idealized supercell thunderstorms in Part I (overturning “ribbons” of horizontal vorticity, “disorganized turbulent eddies,” and the “storm-relative airstream”) are examined as the absolute humidity of the environment is decreased. The existence of these mechanisms in a more realistic simulated storm environment is also established. Entrainment is calculated as fluxes of air across the storm core surface; passive fluid tracers help determine the resulting dilution of the storm updraft. Model microphysical rates are used to examine the direct impacts of entrainment on hydrometeors within the storm updraft as well as precipitation that falls to the ground. Results show that as mixed-layer humidity decreases, the “ribbons” and turbulent eddy mechanisms decrease in intensity, but their effects on precipitation production change little. With decreasing humidity in the 3–4 km AGL layer, the storm-relative airstream entrains less humid low-level air into the storm core, decreasing the vertical mass flux, and therefore the precipitation produced by the storm. When the humidity in the mid- to upper troposphere (4–20 km AGL) is decreased, precipitation is significantly reduced, but not due to the effects of the entrained air. Rather, enhanced evaporation and sublimation of falling precipitation decreases the overall precipitation efficiency of the storm.
Abstract
The interaction between Typhoon Nepartak (2016) and the upper-tropospheric cold low (UTCL) is simulated to better understand the impact of UTCL on the structural and intensity change of tropical cyclones (TCs). An experiment without UTCL is also performed to highlight the quantitative impacts of UTCL. Furthermore, idealized sensitivity experiments are carried out to further investigate the specific TC–UTCL configurations leading to different interactions. It is shown that a TC interacting with the UTCL is associated with a more axisymmetric inner-core structure and an earlier rapid intensification. Three plausible mechanisms related to the causality between a UTCL and the intensity change of TC are addressed. First, the lower energy expenditure on outflow expansion leads to higher net heat energy and intensification rate. Second, the external eddy forcing reinforces the secondary circulation and promotes further TC development. Ultimately, the shear-induced downward and radial ventilation of the low-entropy air is unexpectedly reduced despite the presence of UTCL, leading to stronger inner-core convections in the upshear quadrants. In general, the TC–UTCL interaction process of Nepartak is favorable for TC intensification owing to the additional positive effect and the reduced negative effect. In addition, results from sensitivity experiments indicate that the most favorable interaction would occur when the UTCL is located to the north or northwest of the TC at a stable and proper distance of about one Rossby radius of deformation of the UTCL.
Abstract
The interaction between Typhoon Nepartak (2016) and the upper-tropospheric cold low (UTCL) is simulated to better understand the impact of UTCL on the structural and intensity change of tropical cyclones (TCs). An experiment without UTCL is also performed to highlight the quantitative impacts of UTCL. Furthermore, idealized sensitivity experiments are carried out to further investigate the specific TC–UTCL configurations leading to different interactions. It is shown that a TC interacting with the UTCL is associated with a more axisymmetric inner-core structure and an earlier rapid intensification. Three plausible mechanisms related to the causality between a UTCL and the intensity change of TC are addressed. First, the lower energy expenditure on outflow expansion leads to higher net heat energy and intensification rate. Second, the external eddy forcing reinforces the secondary circulation and promotes further TC development. Ultimately, the shear-induced downward and radial ventilation of the low-entropy air is unexpectedly reduced despite the presence of UTCL, leading to stronger inner-core convections in the upshear quadrants. In general, the TC–UTCL interaction process of Nepartak is favorable for TC intensification owing to the additional positive effect and the reduced negative effect. In addition, results from sensitivity experiments indicate that the most favorable interaction would occur when the UTCL is located to the north or northwest of the TC at a stable and proper distance of about one Rossby radius of deformation of the UTCL.
Abstract
We explore the effect of aerosol perturbations on stratocumulus clouds in the context of marine cloud brightening (MCB) using high-resolution large-eddy simulations. We use a Lagrangian cloud microphysical model with very detailed treatment of aerosol activation and droplet growth. The aerosol forcing is represented as a finite-width rectangular pulse in time (uniform in space). We analyze three stratocumulus cloud systems differing in their surface precipitation rate, namely – non-precipitating, intermediate, and precipitating. We report on the diurnal evolution of these cloud systems subjected to a range of perturbations characterized by varying the amplitude and duration of the aerosol forcing pulse. Our simulations show that in the non-precipitating system, the clouds are relatively insensitive to duration and amplitude, and are sensitive only to the total number concentration of the injected aerosol. In contrast, the precipitating cloud system is affected by the duration and the amplitude of the forcing, with the sensitivity conditional on the state of the cloud system before the injection of aerosol particles. We use these case studies to assess the efficacy of potential MCB spraying strategies. Our analysis shows that negative LWP adjustments offset a substantial fraction of the Twomey induced brightening in all three cloud systems. This is countered by substantial cloud brightening obtained through precipitation suppression induced cloud-fraction adjustments.
Abstract
We explore the effect of aerosol perturbations on stratocumulus clouds in the context of marine cloud brightening (MCB) using high-resolution large-eddy simulations. We use a Lagrangian cloud microphysical model with very detailed treatment of aerosol activation and droplet growth. The aerosol forcing is represented as a finite-width rectangular pulse in time (uniform in space). We analyze three stratocumulus cloud systems differing in their surface precipitation rate, namely – non-precipitating, intermediate, and precipitating. We report on the diurnal evolution of these cloud systems subjected to a range of perturbations characterized by varying the amplitude and duration of the aerosol forcing pulse. Our simulations show that in the non-precipitating system, the clouds are relatively insensitive to duration and amplitude, and are sensitive only to the total number concentration of the injected aerosol. In contrast, the precipitating cloud system is affected by the duration and the amplitude of the forcing, with the sensitivity conditional on the state of the cloud system before the injection of aerosol particles. We use these case studies to assess the efficacy of potential MCB spraying strategies. Our analysis shows that negative LWP adjustments offset a substantial fraction of the Twomey induced brightening in all three cloud systems. This is countered by substantial cloud brightening obtained through precipitation suppression induced cloud-fraction adjustments.
Abstract
A new autonomous turbulence profiling float has been designed, built and tested in field trials off Oregon. Flippin’
χ
SOLO (F
χ
S) employs a SOLO-II buoyancy engine that not only changes but also shifts ballast to move the center of mass to positions on either side of the center of buoyancy thus causing F
χ
S to flip. F
χ
S is outfitted with a full suite of turbulence sensors—two shear probes, two fast thermistors and pitot tube as well as a pressure sensor and 3-axis linear accelerometers. F
χ
S descends and ascends with turbulence sensors leading, thereby permitting measurement through the sea surface. The turbulence sensors are housed antipodal from communication antennae so as to eliminate flow disturbance. By flipping at the sea surface, antennae are exposed for communications. The mission of F
χ
S is to provide intensive profiling measurements of the upper ocean from 240m and through the sea surface, particularly during periods of extreme surface forcing. While surfaced, accelerometers provide estimates of wave height spectra and significant wave height. From
Abstract
A new autonomous turbulence profiling float has been designed, built and tested in field trials off Oregon. Flippin’
χ
SOLO (F
χ
S) employs a SOLO-II buoyancy engine that not only changes but also shifts ballast to move the center of mass to positions on either side of the center of buoyancy thus causing F
χ
S to flip. F
χ
S is outfitted with a full suite of turbulence sensors—two shear probes, two fast thermistors and pitot tube as well as a pressure sensor and 3-axis linear accelerometers. F
χ
S descends and ascends with turbulence sensors leading, thereby permitting measurement through the sea surface. The turbulence sensors are housed antipodal from communication antennae so as to eliminate flow disturbance. By flipping at the sea surface, antennae are exposed for communications. The mission of F
χ
S is to provide intensive profiling measurements of the upper ocean from 240m and through the sea surface, particularly during periods of extreme surface forcing. While surfaced, accelerometers provide estimates of wave height spectra and significant wave height. From
Abstract
Accurate and reliable precipitation product on regular grids is essential for understanding trends and variability within climate studies, for weather forecasting, and in hydrology and agrometeorology applications. However, the construction of high-resolution spatiotemporal precipitation grid product is challenging for complex terrain with sparse rain gauge networks and when only coarse spatial resolutions of satellite data are available. The objective of this study was to consequently provide a practical method to create grid precipitation product by merging accurate quantitative observations from weather stations with continuous spatial information and from satellite-based estimate product. The new gridded precipitation product exhibits a monthly temporal resolution and a spatial resolution of 0.01° for the Tianshan Mountains, while extending back to 1981. To overcome the limitation of low densities and sparse distributions of meteorological stations in the complex terrain of the Tianshan Mountains, a suitable interpolation of ANUSPLIN was used to interpolate grid precipitation based on in situ data. The interpolation grid precipitation was then merged with the satellite precipitation product developed by the U.S. Geological Survey and the Climate Hazards Group. After evaluation and validation using withheld stations and comparison to reference datasets, the result indicated that the merged product exhibit considerable promise for application in complex terrain. The method can be widely applied and is expected to construct precipitation product with high spatial and temporal resolution by merging multiple precipitation data sources.
Abstract
Accurate and reliable precipitation product on regular grids is essential for understanding trends and variability within climate studies, for weather forecasting, and in hydrology and agrometeorology applications. However, the construction of high-resolution spatiotemporal precipitation grid product is challenging for complex terrain with sparse rain gauge networks and when only coarse spatial resolutions of satellite data are available. The objective of this study was to consequently provide a practical method to create grid precipitation product by merging accurate quantitative observations from weather stations with continuous spatial information and from satellite-based estimate product. The new gridded precipitation product exhibits a monthly temporal resolution and a spatial resolution of 0.01° for the Tianshan Mountains, while extending back to 1981. To overcome the limitation of low densities and sparse distributions of meteorological stations in the complex terrain of the Tianshan Mountains, a suitable interpolation of ANUSPLIN was used to interpolate grid precipitation based on in situ data. The interpolation grid precipitation was then merged with the satellite precipitation product developed by the U.S. Geological Survey and the Climate Hazards Group. After evaluation and validation using withheld stations and comparison to reference datasets, the result indicated that the merged product exhibit considerable promise for application in complex terrain. The method can be widely applied and is expected to construct precipitation product with high spatial and temporal resolution by merging multiple precipitation data sources.
Abstract
Equatorial waves are a major driver of widespread convection in South East Asia and the tropics more widely, a region in which accurate heavy rainfall forecasts are still a challenge. Conditioning rainfall over land on local equatorial wave phases finds that heavy rainfall can be between two and four times more likely to occur in Indonesia, Malaysia, Vietnam, and the Philippines. Equatorial waves are identified in a global numerical weather prediction ensemble forecast (MOGREPS-G). Skill in the ensemble forecast of wave activity is highly dependent on region and time of year, although generally forecasts of equatorial Rossby waves and westward-moving mixed Rossby-gravity waves are substantially more skilful than for the eastward moving Kelvin wave. The observed statistical relationship between wave phases and rainfall is combined with ensemble forecasts of dynamicalwave fields to construct hybrid dynamical-statistical forecasts of rainfall probability using a Bayesian approach. The Brier Skill Score is used to assess the skill of forecasts of rainfall probability. Skill in the hybrid forecasts can exceed that of probabilistic rainfall forecasts taken directly from MOGREPS-G and can be linked to both the skill in forecasts of wave activity and the relationship between equatorial waves and heavy rainfall in the relevant region. The results show that there is potential for improvements of forecasts of high impact weather using this method as forecasts of large-scale waves improve.
Abstract
Equatorial waves are a major driver of widespread convection in South East Asia and the tropics more widely, a region in which accurate heavy rainfall forecasts are still a challenge. Conditioning rainfall over land on local equatorial wave phases finds that heavy rainfall can be between two and four times more likely to occur in Indonesia, Malaysia, Vietnam, and the Philippines. Equatorial waves are identified in a global numerical weather prediction ensemble forecast (MOGREPS-G). Skill in the ensemble forecast of wave activity is highly dependent on region and time of year, although generally forecasts of equatorial Rossby waves and westward-moving mixed Rossby-gravity waves are substantially more skilful than for the eastward moving Kelvin wave. The observed statistical relationship between wave phases and rainfall is combined with ensemble forecasts of dynamicalwave fields to construct hybrid dynamical-statistical forecasts of rainfall probability using a Bayesian approach. The Brier Skill Score is used to assess the skill of forecasts of rainfall probability. Skill in the hybrid forecasts can exceed that of probabilistic rainfall forecasts taken directly from MOGREPS-G and can be linked to both the skill in forecasts of wave activity and the relationship between equatorial waves and heavy rainfall in the relevant region. The results show that there is potential for improvements of forecasts of high impact weather using this method as forecasts of large-scale waves improve.
Abstract
The Southern Annular Mode (SAM) describes the annular or zonal component of the large-scale atmospheric circulation in the Southern Hemisphere (SH) extratropics and influences surface climate across the SH. Although this annular flow is dominant in austral summer, in other seasons considerable zonal asymmetries are evident, reflecting a zonal wave 3 (ZW3) pattern. We define an index representing asymmetric flow using the first two leading modes of meridional wind variability in the SH. Two orthogonal ZW3 indices are used together to capture longitudinal shifts in the wave train and their connection to tropical convection. We compare the impacts of SAM and ZW3 on surface climate by examining composites of temperature and precipitation fields during each season. Impacts on mean and extreme surface climate are assessed. We find that SAM and ZW3 are not clearly separated modes, but rather, ZW3 modulates the impact of SAM across the midlatitudes. The SAM influence on regional temperature and precipitation is similar for both mean impacts and extremes. The ZW3 influence on extremes is more varied across indices and does not always reflect the ZW3 impact on mean fields. Notably, amplified ZW3 activity has a significant influence on the number of midlatitude fronts and frontal rainfall highlighting the importance of considering ZW3 when exploring the surface climate impacts of large-scale SH circulation states, particularly for non-summer seasons.
Abstract
The Southern Annular Mode (SAM) describes the annular or zonal component of the large-scale atmospheric circulation in the Southern Hemisphere (SH) extratropics and influences surface climate across the SH. Although this annular flow is dominant in austral summer, in other seasons considerable zonal asymmetries are evident, reflecting a zonal wave 3 (ZW3) pattern. We define an index representing asymmetric flow using the first two leading modes of meridional wind variability in the SH. Two orthogonal ZW3 indices are used together to capture longitudinal shifts in the wave train and their connection to tropical convection. We compare the impacts of SAM and ZW3 on surface climate by examining composites of temperature and precipitation fields during each season. Impacts on mean and extreme surface climate are assessed. We find that SAM and ZW3 are not clearly separated modes, but rather, ZW3 modulates the impact of SAM across the midlatitudes. The SAM influence on regional temperature and precipitation is similar for both mean impacts and extremes. The ZW3 influence on extremes is more varied across indices and does not always reflect the ZW3 impact on mean fields. Notably, amplified ZW3 activity has a significant influence on the number of midlatitude fronts and frontal rainfall highlighting the importance of considering ZW3 when exploring the surface climate impacts of large-scale SH circulation states, particularly for non-summer seasons.
Abstract
The influence of mid-high latitude intraseasonal variability (ISV) on the occurrence frequency of Northeast China cold vortex (NCCV) in early summer was examined through statistical analysis and thermal-dynamical diagnostic. Multi-variable empirical orthogonal function (MVEOF) was employed to extract the thermal-pressure coupled ISV mode. Our results show that the geopotential height and air temperature over the NCCV active region exhibit a statistically significant intraseasonal periodicity of 20–60 day. The dominant ISV mode features a westward propagated zonal dipole pattern, which is generated over the Lake Baikal region and triggered by intraseasonal wave energy accumulation. By dividing the ISV cycle into 8 phases, it is found that more NCCVs with a large scope occur in phases 5 to 8 than those in phases 1 to 4. The positive (negative) geopotential height and air temperature tendencies in phases 1 to 4 (5 to 8) act to suppress (facilitate) the NCCV activity. The thermo-dynamical tendency budget and scale decomposition reveal that when an anomalous intraseasonal cyclonic circulation propagates westward from Lake Baikal to Ural Mountains, the anomalous southwesterly transports mean negative vorticity from the north side of the Tibetan Plateau to Northeast Asia, and transports mean warm air temperature from low latitude to high latitude, leading to the positive geopotential height and air temperature tendencies and thereby restraining the NCCV activity. The opposite is also true for the facilitation of NCCV modulated by the negative geopotential height and air temperature tendencies.
Abstract
The influence of mid-high latitude intraseasonal variability (ISV) on the occurrence frequency of Northeast China cold vortex (NCCV) in early summer was examined through statistical analysis and thermal-dynamical diagnostic. Multi-variable empirical orthogonal function (MVEOF) was employed to extract the thermal-pressure coupled ISV mode. Our results show that the geopotential height and air temperature over the NCCV active region exhibit a statistically significant intraseasonal periodicity of 20–60 day. The dominant ISV mode features a westward propagated zonal dipole pattern, which is generated over the Lake Baikal region and triggered by intraseasonal wave energy accumulation. By dividing the ISV cycle into 8 phases, it is found that more NCCVs with a large scope occur in phases 5 to 8 than those in phases 1 to 4. The positive (negative) geopotential height and air temperature tendencies in phases 1 to 4 (5 to 8) act to suppress (facilitate) the NCCV activity. The thermo-dynamical tendency budget and scale decomposition reveal that when an anomalous intraseasonal cyclonic circulation propagates westward from Lake Baikal to Ural Mountains, the anomalous southwesterly transports mean negative vorticity from the north side of the Tibetan Plateau to Northeast Asia, and transports mean warm air temperature from low latitude to high latitude, leading to the positive geopotential height and air temperature tendencies and thereby restraining the NCCV activity. The opposite is also true for the facilitation of NCCV modulated by the negative geopotential height and air temperature tendencies.
Abstract
The scattering properties of aggregates are studied herein. Early aggregates (<7 monomers) of branched planar crystals and mature aggregates (up to 100 monomers) of columns are randomly generated with varying assumptions about the monomer attachment processes and the orientation behavior during collection. The resulting physical properties of the aggregates correspond well with prior in situ and retrieved sizes and shapes. Assumed azimuthally uniform orientations during collection and monomer pivoting upon attachment resulted in flatter and denser aggregates. The column aggregates had lower density and more spherical shapes than the branched planar crystal aggregates. The scattering properties were calculated using the discrete dipole approximation for a set of orientation angles and transformed to spectral coefficients representing modes of orientation angle variability. The zeroth- and second-order coefficients dominate this variability, with the zeroth-order coefficients representing the scattering properties for randomly oriented particles. The second-order coefficients for backscatter showed differences between horizontal and vertical polarization increasing with density, and these coefficients for specific differential phase increase with both mass and density. Similarly, coefficients for the copolar covariance decreased with density. Rapid changes in the contributions to the radar moments from the second-order coefficients from low to moderate density were observed, likely due to the increasing presence of horizontally aligned monomers in the aggregate structure. Differences in how differential reflectivity and correlation coefficient evolve with the orientation distribution parameters suggest that these measurements, along with specific differential phase and reflectivity, provide complementary information about aggregate sizes, shapes, and orientation distributions.
Abstract
The scattering properties of aggregates are studied herein. Early aggregates (<7 monomers) of branched planar crystals and mature aggregates (up to 100 monomers) of columns are randomly generated with varying assumptions about the monomer attachment processes and the orientation behavior during collection. The resulting physical properties of the aggregates correspond well with prior in situ and retrieved sizes and shapes. Assumed azimuthally uniform orientations during collection and monomer pivoting upon attachment resulted in flatter and denser aggregates. The column aggregates had lower density and more spherical shapes than the branched planar crystal aggregates. The scattering properties were calculated using the discrete dipole approximation for a set of orientation angles and transformed to spectral coefficients representing modes of orientation angle variability. The zeroth- and second-order coefficients dominate this variability, with the zeroth-order coefficients representing the scattering properties for randomly oriented particles. The second-order coefficients for backscatter showed differences between horizontal and vertical polarization increasing with density, and these coefficients for specific differential phase increase with both mass and density. Similarly, coefficients for the copolar covariance decreased with density. Rapid changes in the contributions to the radar moments from the second-order coefficients from low to moderate density were observed, likely due to the increasing presence of horizontally aligned monomers in the aggregate structure. Differences in how differential reflectivity and correlation coefficient evolve with the orientation distribution parameters suggest that these measurements, along with specific differential phase and reflectivity, provide complementary information about aggregate sizes, shapes, and orientation distributions.
Abstract
Summer precipitation in the middle and lower reaches of the Yangtze River (MLYR) has obvious characteristics of intraseasonal oscillation, but there are different inferences about its propagation. Based on observed precipitation and ERA5 reanalysis data, the propagation diversity of summer quasi-biweekly precipitation in MLYR is analyzed. The results show that summer precipitation in MLYR has obvious quasi-biweekly oscillation (QBWO) characteristics, and precipitation QBWO events can be classified into three categories: southward, northward, and local oscillation events. The frequency of southward events is significantly higher than that of northward or local oscillation events. For southward events, a wave train is observed in the mid-high latitudes and propagates southward in East Asia. The northward and local oscillation events are closely related to the QBWO of Northwest Pacific in low-latitude. Meridional asymmetry of quasi-biweekly divergence and background wind are responsible for the diversity of QBWO propagation. Quasi-biweekly convergence is usually located on the south of the quasi-biweekly cyclone, so the convergence interacts with geostrophic vorticity to guide the quasi-biweekly cyclone to move southward; in the southerly basic flow, north of the quasi-biweekly cyclone is positive relative vorticity advection, which leads the quasi-biweekly cyclone to move northward. Therefore, quasi-biweekly disturbance originating from north of MLYR, with weak basic wind, mainly moves southward under the influence of convergence. However, quasi-biweekly disturbances at low-latitudes move northward under the guidance of relative vorticity advection due to the strong basic flow. Disturbance originating from MLYR presents local oscillation under the co-action of quasi-biweekly relative vorticity advection and divergence.
Abstract
Summer precipitation in the middle and lower reaches of the Yangtze River (MLYR) has obvious characteristics of intraseasonal oscillation, but there are different inferences about its propagation. Based on observed precipitation and ERA5 reanalysis data, the propagation diversity of summer quasi-biweekly precipitation in MLYR is analyzed. The results show that summer precipitation in MLYR has obvious quasi-biweekly oscillation (QBWO) characteristics, and precipitation QBWO events can be classified into three categories: southward, northward, and local oscillation events. The frequency of southward events is significantly higher than that of northward or local oscillation events. For southward events, a wave train is observed in the mid-high latitudes and propagates southward in East Asia. The northward and local oscillation events are closely related to the QBWO of Northwest Pacific in low-latitude. Meridional asymmetry of quasi-biweekly divergence and background wind are responsible for the diversity of QBWO propagation. Quasi-biweekly convergence is usually located on the south of the quasi-biweekly cyclone, so the convergence interacts with geostrophic vorticity to guide the quasi-biweekly cyclone to move southward; in the southerly basic flow, north of the quasi-biweekly cyclone is positive relative vorticity advection, which leads the quasi-biweekly cyclone to move northward. Therefore, quasi-biweekly disturbance originating from north of MLYR, with weak basic wind, mainly moves southward under the influence of convergence. However, quasi-biweekly disturbances at low-latitudes move northward under the guidance of relative vorticity advection due to the strong basic flow. Disturbance originating from MLYR presents local oscillation under the co-action of quasi-biweekly relative vorticity advection and divergence.
