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Abstract
The evolution of a gust front to bore to solitary wave transition, and comprehensive information on the evolving nocturnal boundary layer (NBL) associated with this change, are described with analysis of radar and profiler measurements. The observations were obtained on 21 June 2002 in the Oklahoma panhandle during the International H2O Project. The evolution of this system, from a strong bore (initiated by a vigorous gust front) to a solitary wave, was observed over a 4-h period with Doppler radar and surface measurements. Detailed information on the mature bore structure was obtained by a cluster of profiling instruments including two boundary layer wind profilers, a lidar ceilometer, and a microwave profiling radiometer.
A strong bore was initiated by an extensive gust front that perturbed an incipient NBL whose development (prior to sunset) was enhanced by shading from the parent mesoscale convective system. At the time of bore formation, the NBL was about 300 m deep and exhibited a surface temperature about 4 K less than the afternoon maximum. Initially, the bore assumed kinematic properties similar to those of a gust front. As the NBL stabilized, the bore matured and exhibited undular formations over 30–60-km segments along the bore axis. A 30-km-wide cloud field accompanied the mature bore system within three hours of its formation. System-relative airflow within the cloud field was front-to-rear and exhibited a primary hydraulic jump updraft (4–5 m s−1 magnitude) within the bore core. The bore core exhibited a low, smooth cloud base, a cloud depth of 2.5 km, nearly adiabatic liquid water content, and pronounced turbulence. The maximum parcel displacements within the bore were about 2 km (sufficient for marginal convective initiation), and the net parcel displacement from before to after bore passage was 0.6–0.9 km.
Abstract
The evolution of a gust front to bore to solitary wave transition, and comprehensive information on the evolving nocturnal boundary layer (NBL) associated with this change, are described with analysis of radar and profiler measurements. The observations were obtained on 21 June 2002 in the Oklahoma panhandle during the International H2O Project. The evolution of this system, from a strong bore (initiated by a vigorous gust front) to a solitary wave, was observed over a 4-h period with Doppler radar and surface measurements. Detailed information on the mature bore structure was obtained by a cluster of profiling instruments including two boundary layer wind profilers, a lidar ceilometer, and a microwave profiling radiometer.
A strong bore was initiated by an extensive gust front that perturbed an incipient NBL whose development (prior to sunset) was enhanced by shading from the parent mesoscale convective system. At the time of bore formation, the NBL was about 300 m deep and exhibited a surface temperature about 4 K less than the afternoon maximum. Initially, the bore assumed kinematic properties similar to those of a gust front. As the NBL stabilized, the bore matured and exhibited undular formations over 30–60-km segments along the bore axis. A 30-km-wide cloud field accompanied the mature bore system within three hours of its formation. System-relative airflow within the cloud field was front-to-rear and exhibited a primary hydraulic jump updraft (4–5 m s−1 magnitude) within the bore core. The bore core exhibited a low, smooth cloud base, a cloud depth of 2.5 km, nearly adiabatic liquid water content, and pronounced turbulence. The maximum parcel displacements within the bore were about 2 km (sufficient for marginal convective initiation), and the net parcel displacement from before to after bore passage was 0.6–0.9 km.
Abstract
Characteristics of convergent boundary zones (CBZs) sampled by the Mobile Integrated Profiling System (MIPS) during the 2002 International H2O Project (IHOP_2002) are presented. The MIPS sensors (915-MHz wind profiler, 12-channel microwave profiling radiometer, ceilometer, and surface instrumentation) provide very fine temporal kinematic and thermodynamic profiles of the atmospheric boundary layer and CBZ properties, including enhanced 915-MHz backscatter within the CBZ updraft (equivalent to the radar fine line), a general increase in integrated water vapor within the updrafts of the CBZ, an increase in the convective boundary layer (CBL) depth, and changes in ceilometer backscatter that are typically coincident with arrival of cooler, moister air (the case for density current CBZ).
Three contrasting CBZs are analyzed. Convective initiation was associated with a slow-moving dryline as it passed over the MIPS on 19 June. Updrafts up to 6 m s−1 were measured, and the CBL attained its greatest depth within the CBZ. The CBZ in the other two cases were quite similar to density currents. The retrograding dryline of 18 June produced an enhancement in preexisting convection within 30 km of the MIPS. On 24 May, a shallow cold front, about 800 m deep, was sampled.
Abstract
Characteristics of convergent boundary zones (CBZs) sampled by the Mobile Integrated Profiling System (MIPS) during the 2002 International H2O Project (IHOP_2002) are presented. The MIPS sensors (915-MHz wind profiler, 12-channel microwave profiling radiometer, ceilometer, and surface instrumentation) provide very fine temporal kinematic and thermodynamic profiles of the atmospheric boundary layer and CBZ properties, including enhanced 915-MHz backscatter within the CBZ updraft (equivalent to the radar fine line), a general increase in integrated water vapor within the updrafts of the CBZ, an increase in the convective boundary layer (CBL) depth, and changes in ceilometer backscatter that are typically coincident with arrival of cooler, moister air (the case for density current CBZ).
Three contrasting CBZs are analyzed. Convective initiation was associated with a slow-moving dryline as it passed over the MIPS on 19 June. Updrafts up to 6 m s−1 were measured, and the CBL attained its greatest depth within the CBZ. The CBZ in the other two cases were quite similar to density currents. The retrograding dryline of 18 June produced an enhancement in preexisting convection within 30 km of the MIPS. On 24 May, a shallow cold front, about 800 m deep, was sampled.
Abstract
This paper describes an analysis of a long-lived, microburst-producing storm that evolved within a relatively dry environment having a relatively low CAPE value of 450 J kg−1. The storm displayed a variety of kinematic and echo formations over its 2.5-h lifetime, including 1) a near equality in the strength (∼10 m s−1) of updrafts and downdrafts, 2) strong downdrafts over an extended time period of greater than 60 min, 3) a prevalence of up-down-type downdraft trajectories associated with the strong downdrafts, 4) a prominent echo overhang during the early mature stage, 5) a spearhead-like echo protrusion during the mature storm phase that was indirectly associated with strong downdrafts, and 6) a narrow bow echo and associated weak inflow jet at midlevels during the latter storm stage.
An elongated ascending branch of the up-down downdraft circulation was associated with the echo protrusion. The prominence of the up-down trajectory is corroborated by surface data and 3D numerical simulations, both of which reveal comparable values of equivalent potential temperature in the low-level inflow and downdraft outflow air. Time series plots of saturation point reveal an evaporation line structure typical of evaporation of precipitation into the subcloud boundary layer. Thus, in this case there is little evidence to indicate that significant amounts of downdraft air originated above the atmospheric boundary layer during the sustained mature to dissipating stages.
Abstract
This paper describes an analysis of a long-lived, microburst-producing storm that evolved within a relatively dry environment having a relatively low CAPE value of 450 J kg−1. The storm displayed a variety of kinematic and echo formations over its 2.5-h lifetime, including 1) a near equality in the strength (∼10 m s−1) of updrafts and downdrafts, 2) strong downdrafts over an extended time period of greater than 60 min, 3) a prevalence of up-down-type downdraft trajectories associated with the strong downdrafts, 4) a prominent echo overhang during the early mature stage, 5) a spearhead-like echo protrusion during the mature storm phase that was indirectly associated with strong downdrafts, and 6) a narrow bow echo and associated weak inflow jet at midlevels during the latter storm stage.
An elongated ascending branch of the up-down downdraft circulation was associated with the echo protrusion. The prominence of the up-down trajectory is corroborated by surface data and 3D numerical simulations, both of which reveal comparable values of equivalent potential temperature in the low-level inflow and downdraft outflow air. Time series plots of saturation point reveal an evaporation line structure typical of evaporation of precipitation into the subcloud boundary layer. Thus, in this case there is little evidence to indicate that significant amounts of downdraft air originated above the atmospheric boundary layer during the sustained mature to dissipating stages.
Abstract
The kinematics of a head-on collision between two gust fronts, followed by a secondary collision between a third gust front and a bore generated by the initial collision, are described using analyses of Weather Surveillance Radar-1988 Doppler (WSR-88D) and Mobile Integrated Profiling System (MIPS) data. Each gust front involved in the initial collision exhibited a nearly north–south orientation and an east–west movement. The eastward-moving boundary was 2°C colder and moved 7 m s−1 faster than the westward-moving boundary. Two-dimensional wind retrievals reveal contrasting flows within each gravity current. One exhibited a typical gravity current flow structure, while the other assumed the form of a gravity wave/current hybrid with multiple vortices atop the outflow. One of the after-collision boundaries exhibited multiple radar finelines resembling a solitary wave shortly after the collision. About 1 h after the initial collision, a vigorous gust front intersected the eastward-moving bore several minutes before both circulations were sampled by the MIPS. The MIPS measurements indicate that the gust front displaced the bore upward into a neutral residual layer. The bore apparently propagated upward even farther to the next stable layer between 2 and 3 km AGL. MIPS measurements show that the elevated turbulent bore consisted of an initial vigorous wave, with updraft/downdraft magnitudes of 3 and −6 m s−1, respectively, followed by several (elevated) waves of decreasing amplitude.
Abstract
The kinematics of a head-on collision between two gust fronts, followed by a secondary collision between a third gust front and a bore generated by the initial collision, are described using analyses of Weather Surveillance Radar-1988 Doppler (WSR-88D) and Mobile Integrated Profiling System (MIPS) data. Each gust front involved in the initial collision exhibited a nearly north–south orientation and an east–west movement. The eastward-moving boundary was 2°C colder and moved 7 m s−1 faster than the westward-moving boundary. Two-dimensional wind retrievals reveal contrasting flows within each gravity current. One exhibited a typical gravity current flow structure, while the other assumed the form of a gravity wave/current hybrid with multiple vortices atop the outflow. One of the after-collision boundaries exhibited multiple radar finelines resembling a solitary wave shortly after the collision. About 1 h after the initial collision, a vigorous gust front intersected the eastward-moving bore several minutes before both circulations were sampled by the MIPS. The MIPS measurements indicate that the gust front displaced the bore upward into a neutral residual layer. The bore apparently propagated upward even farther to the next stable layer between 2 and 3 km AGL. MIPS measurements show that the elevated turbulent bore consisted of an initial vigorous wave, with updraft/downdraft magnitudes of 3 and −6 m s−1, respectively, followed by several (elevated) waves of decreasing amplitude.
Abstract
The dynamical and thermodynamical properties of precipitation-associated downdrafts are examined using a Lagrangian trajectory analysis approach applied to parcels passing through the low-level downdraft of precipitating convection. Both observations and three-dimensional cloud model results for one particular case presented in Part I are included. For this case, negative buoyancy within the low-level downdraft is very rapidly produced over the lowest 2 km by melting and evaporation of precipitation. Cooling profiles from the melting and evaporation cooling components show a significant overlap in the case considered. Both diagnosed and modeled low perturbation pressure located near the 2 km level appear to be generated by the rapid onset of negative buoyancy.
The diagnosed and modeled behavior along two low-level downdraft branches defined in Part I are examined for this particular case. It is found that the low-level downdraft is forced in varying amounts by condensate loading, negative buoyancy produced by precipitation evaporation and melting, and pressure forces. The relative role of cooling by evaporation and melting varies according to trajectory type. Along midlevel trajectories, evaporation is most significant, whereas along up–down trajectories melting is more important. For the particular case examined, the maximum amplitude in downward acceleration was found in the 1–2 km layer, where effects of loading, melting, evaporation/sublimation and negative vertical pressure gradient contributed to downward acceleration.
Abstract
The dynamical and thermodynamical properties of precipitation-associated downdrafts are examined using a Lagrangian trajectory analysis approach applied to parcels passing through the low-level downdraft of precipitating convection. Both observations and three-dimensional cloud model results for one particular case presented in Part I are included. For this case, negative buoyancy within the low-level downdraft is very rapidly produced over the lowest 2 km by melting and evaporation of precipitation. Cooling profiles from the melting and evaporation cooling components show a significant overlap in the case considered. Both diagnosed and modeled low perturbation pressure located near the 2 km level appear to be generated by the rapid onset of negative buoyancy.
The diagnosed and modeled behavior along two low-level downdraft branches defined in Part I are examined for this particular case. It is found that the low-level downdraft is forced in varying amounts by condensate loading, negative buoyancy produced by precipitation evaporation and melting, and pressure forces. The relative role of cooling by evaporation and melting varies according to trajectory type. Along midlevel trajectories, evaporation is most significant, whereas along up–down trajectories melting is more important. For the particular case examined, the maximum amplitude in downward acceleration was found in the 1–2 km layer, where effects of loading, melting, evaporation/sublimation and negative vertical pressure gradient contributed to downward acceleration.
Abstract
This paper presents results from a comprehensive investigation in which observations from several case studies an integrated with three-dimensional cloud model results to examine the general kinematic structure of downdrafts associated with High Plains precipitating convection. One particular downdraft type, the low-level precipitation-associated downdraft, is the focus of this paper.
General airflow and trajectory patterns within low-level downdrafts are convergent from 0.8 km upwards to downdraft top, typically less than 5 km AGL. Observed mass flux profiles often increase rapidly with height as a result of strong buoyancy forcing below the melting level. Inflow to the low-level downdraft although vertically continuous, can be separated into two branches. The up-down branch originating within the planetary boundary layer initially rises up to 4 km and then descends within the main precipitation-associated downdraft. The midlevel branch, usually more pronounced during early downdraft stages, originates from above the PBL and transports low-valued θ e air to low levels.
The depth of the low-level downdraft can be approximated by the environmental sounding transition level, defined as the vertical height interval separating conditionally unstable to neutral air below from roughly stable air above. The low-level downdraft is most frequently located along the upshear storm flank relative to the updraft, although a downshear downdraft may become common under higher environmental wind shear.
Abstract
This paper presents results from a comprehensive investigation in which observations from several case studies an integrated with three-dimensional cloud model results to examine the general kinematic structure of downdrafts associated with High Plains precipitating convection. One particular downdraft type, the low-level precipitation-associated downdraft, is the focus of this paper.
General airflow and trajectory patterns within low-level downdrafts are convergent from 0.8 km upwards to downdraft top, typically less than 5 km AGL. Observed mass flux profiles often increase rapidly with height as a result of strong buoyancy forcing below the melting level. Inflow to the low-level downdraft although vertically continuous, can be separated into two branches. The up-down branch originating within the planetary boundary layer initially rises up to 4 km and then descends within the main precipitation-associated downdraft. The midlevel branch, usually more pronounced during early downdraft stages, originates from above the PBL and transports low-valued θ e air to low levels.
The depth of the low-level downdraft can be approximated by the environmental sounding transition level, defined as the vertical height interval separating conditionally unstable to neutral air below from roughly stable air above. The low-level downdraft is most frequently located along the upshear storm flank relative to the updraft, although a downshear downdraft may become common under higher environmental wind shear.
Abstract
The early-evening boundary layer transition has been defined in the past using a variety of criteria, the most popular of which is the onset of a negative surface heat flux. According to this definition, the transition is an almost-instantaneous event that occurs when the positive daytime heat flux switches to the negative nighttime heat flux. This definition is simplistic, however, because the stable boundary layer does not form instantaneously over a deep layer. Other factors are involved, and many changes occur aloft during the transition period that this definition does not account for—for example, a more gradual reduction in turbulence and an increase in wind speed. The combined use of sodar data, as well as 915-MHz wind profiler, surface temperature, dewpoint, and wind data, provides a more-comprehensive definition of the early-evening boundary layer transition. Sodar backscatter is sensitive to temperature fluctuations, and therefore as the heat flux decreases, the sodar return power exhibits changes from a time-varying convective structure to a more-stratified and steady structure. A relative minimum in intensity and height of the sodar backscatter is one indication that the transition is occurring. As the boundary layer evolves from the unstable convective afternoon conditions to the more stable nocturnal conditions, the finescale temporal variations in many parameters, including temperature, the 10–2-m temperature difference, dewpoint, and wind speed, decrease. There is often a distinct steplike shape in the temperature/wind decrease or dewpoint increase within 30 min of the sodar minimum. In this paper, an analysis of sodar and surface data is presented for low-wind cases to demonstrate the efficacy of this combined sensor technique, and to illustrate the average physical characteristics of the transition period for 21 cases during the summer months (June–August) and 9 cases during the autumn months (November–December) in Huntsville, Alabama.
Abstract
The early-evening boundary layer transition has been defined in the past using a variety of criteria, the most popular of which is the onset of a negative surface heat flux. According to this definition, the transition is an almost-instantaneous event that occurs when the positive daytime heat flux switches to the negative nighttime heat flux. This definition is simplistic, however, because the stable boundary layer does not form instantaneously over a deep layer. Other factors are involved, and many changes occur aloft during the transition period that this definition does not account for—for example, a more gradual reduction in turbulence and an increase in wind speed. The combined use of sodar data, as well as 915-MHz wind profiler, surface temperature, dewpoint, and wind data, provides a more-comprehensive definition of the early-evening boundary layer transition. Sodar backscatter is sensitive to temperature fluctuations, and therefore as the heat flux decreases, the sodar return power exhibits changes from a time-varying convective structure to a more-stratified and steady structure. A relative minimum in intensity and height of the sodar backscatter is one indication that the transition is occurring. As the boundary layer evolves from the unstable convective afternoon conditions to the more stable nocturnal conditions, the finescale temporal variations in many parameters, including temperature, the 10–2-m temperature difference, dewpoint, and wind speed, decrease. There is often a distinct steplike shape in the temperature/wind decrease or dewpoint increase within 30 min of the sodar minimum. In this paper, an analysis of sodar and surface data is presented for low-wind cases to demonstrate the efficacy of this combined sensor technique, and to illustrate the average physical characteristics of the transition period for 21 cases during the summer months (June–August) and 9 cases during the autumn months (November–December) in Huntsville, Alabama.
Abstract
Two three-dimensional cloud model simulations are examined and compared in order to define some of the characteristics of the low-level downdraft initiation process within deep precipitating convection. The initial environment of each case displayed similar temperature profiles but different moisture profiles. In one case, relatively dry subcloud layers were capped by relatively moist middle levels, while the opposite moisture stratification existed for the second case. Although both simulations displayed peak low-level downdraft speeds of ∼12 m s−1, downdraft spatial and temporal behavior showed significant differences. These differences can be related to dissimilarities in the environment of each case. In the dry subcloud case (the microburst case), peak downdraft speeds occurred near the 0.8 km level shortly after precipitation arrived at low levels. Low-level downdraft developed very rapidly in this case. In the other moist subcloud case, the low-level downdraft developed less rapidly and exhibited a peak magnitude significantly higher at 1.8 km. In both case the downdraft initiation process occurred within the downshear flank. Downdrafts were forced primarily over the lowest 2 km (below the melting level), where melting and evaporation of precipitation generated negative buoyancy. The results demonstrate that low-level downdraft characteristics are closely controlled by arrival of precipitation at low levels.
Abstract
Two three-dimensional cloud model simulations are examined and compared in order to define some of the characteristics of the low-level downdraft initiation process within deep precipitating convection. The initial environment of each case displayed similar temperature profiles but different moisture profiles. In one case, relatively dry subcloud layers were capped by relatively moist middle levels, while the opposite moisture stratification existed for the second case. Although both simulations displayed peak low-level downdraft speeds of ∼12 m s−1, downdraft spatial and temporal behavior showed significant differences. These differences can be related to dissimilarities in the environment of each case. In the dry subcloud case (the microburst case), peak downdraft speeds occurred near the 0.8 km level shortly after precipitation arrived at low levels. Low-level downdraft developed very rapidly in this case. In the other moist subcloud case, the low-level downdraft developed less rapidly and exhibited a peak magnitude significantly higher at 1.8 km. In both case the downdraft initiation process occurred within the downshear flank. Downdrafts were forced primarily over the lowest 2 km (below the melting level), where melting and evaporation of precipitation generated negative buoyancy. The results demonstrate that low-level downdraft characteristics are closely controlled by arrival of precipitation at low levels.
Abstract
The effects of terrain on tornadoes are poorly understood. Efforts to understand terrain effects on tornadoes have been limited in scope, typically examining a small number of cases with limited observations or idealized numerical simulations. This study evaluates an apparent tornado activity maximum across the Sand Mountain and Lookout Mountain plateaus of northeastern Alabama. These plateaus, separated by the narrow Wills Valley, span ~5000 km2 and were impacted by 79 tornadoes from 1992 to 2016. This area represents a relative regional statistical maximum in tornadogenesis, with a particular tendency for tornadogenesis on the northwestern side of Sand Mountain. This exploratory paper investigates storm behavior and possible physical explanations for this density of tornadogenesis events and tornadoes. Long-term surface observation datasets indicate that surface winds tend to be stronger and more backed atop Sand Mountain than over the adjacent Tennessee Valley, potentially indicative of changes in the low-level wind profile supportive to storm rotation. The surface data additionally indicate potentially lower lifting condensation levels over the plateaus versus the adjacent valleys, an attribute previously shown to be favorable for tornadogenesis. Rapid Update Cycle and Rapid Refresh model output indicate that Froude numbers for the plateaus in tornadic environments are likely supportive of enhanced low-level flow over the plateaus, which further indicates the potential for favorable wind profile changes for tornado production. Examples of tornadic storms rapidly acquiring increased low-level rotation while reaching the plateaus of northeast Alabama are presented. The use of this background to inform the VORTEX-SE 2017 field campaign is discussed.
Abstract
The effects of terrain on tornadoes are poorly understood. Efforts to understand terrain effects on tornadoes have been limited in scope, typically examining a small number of cases with limited observations or idealized numerical simulations. This study evaluates an apparent tornado activity maximum across the Sand Mountain and Lookout Mountain plateaus of northeastern Alabama. These plateaus, separated by the narrow Wills Valley, span ~5000 km2 and were impacted by 79 tornadoes from 1992 to 2016. This area represents a relative regional statistical maximum in tornadogenesis, with a particular tendency for tornadogenesis on the northwestern side of Sand Mountain. This exploratory paper investigates storm behavior and possible physical explanations for this density of tornadogenesis events and tornadoes. Long-term surface observation datasets indicate that surface winds tend to be stronger and more backed atop Sand Mountain than over the adjacent Tennessee Valley, potentially indicative of changes in the low-level wind profile supportive to storm rotation. The surface data additionally indicate potentially lower lifting condensation levels over the plateaus versus the adjacent valleys, an attribute previously shown to be favorable for tornadogenesis. Rapid Update Cycle and Rapid Refresh model output indicate that Froude numbers for the plateaus in tornadic environments are likely supportive of enhanced low-level flow over the plateaus, which further indicates the potential for favorable wind profile changes for tornado production. Examples of tornadic storms rapidly acquiring increased low-level rotation while reaching the plateaus of northeast Alabama are presented. The use of this background to inform the VORTEX-SE 2017 field campaign is discussed.
Abstract
Apparent interactions between ducted gravity waves and preexisting mesocyclones are investigated. Preliminary analyses of Weather Surveillance Radar-1988 Doppler (WSR-88D) observations from several cases reveal that the intersection of fine lines, whose propagation speed is consistent with that of gravity waves, and existing mesocyclones leads to an increase in the rotational velocity of the mesocyclone. Utilizing simplified ducted wave kinematics and the vorticity equation, changes in vorticity associated with convergence–divergence and perturbation wind shear within the gravity wave are examined. Convergence ahead of wave ridges may be significant, causing mesocyclone intensification through vorticity stretching. It will also be shown that a wave may significantly change the vertical wind shear and streamwise vorticity in storm inflow. A simple one-dimensional model is presented, which shows that vorticity decreases temporarily ahead of the wave ridge, then increases rapidly behind the ridge as positive tilting and stretching act together. The mesocyclone vorticity reaches a peak just ahead of the wave ridge, then begins to rapidly decrease behind the ridge. Model results compared very well to actual measurements in a sample case in which a mesocyclone interacted with two gravity waves of different amplitudes.
Abstract
Apparent interactions between ducted gravity waves and preexisting mesocyclones are investigated. Preliminary analyses of Weather Surveillance Radar-1988 Doppler (WSR-88D) observations from several cases reveal that the intersection of fine lines, whose propagation speed is consistent with that of gravity waves, and existing mesocyclones leads to an increase in the rotational velocity of the mesocyclone. Utilizing simplified ducted wave kinematics and the vorticity equation, changes in vorticity associated with convergence–divergence and perturbation wind shear within the gravity wave are examined. Convergence ahead of wave ridges may be significant, causing mesocyclone intensification through vorticity stretching. It will also be shown that a wave may significantly change the vertical wind shear and streamwise vorticity in storm inflow. A simple one-dimensional model is presented, which shows that vorticity decreases temporarily ahead of the wave ridge, then increases rapidly behind the ridge as positive tilting and stretching act together. The mesocyclone vorticity reaches a peak just ahead of the wave ridge, then begins to rapidly decrease behind the ridge. Model results compared very well to actual measurements in a sample case in which a mesocyclone interacted with two gravity waves of different amplitudes.
