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- Author or Editor: Shuguang Wang x
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Abstract
Characteristic patterns of precipitation-associated tropical intraseasonal oscillations, including the Madden–Julian oscillation (MJO) and boreal summer intraseasonal oscillation (BSISO), are identified using local empirical orthogonal function (EOF) analysis of the Tropical Rainfall Measuring Mission (TRMM) precipitation data as a function of the day of the year. The explained variances of the EOF analysis show two peaks across the year: one in the middle of the boreal winter corresponding to the MJO and the other in the middle of summer corresponding to the BSISO. Comparing the fractional variance indicates that the BSISO is more coherent than the MJO during the TRMM period. Similar EOF analyses with the outgoing longwave radiation (OLR) confirm this result and indicate that the BSISO is less coherent before the TRMM era (1979–98). In contrast, the MJO exhibits much less decadal variability. A precipitation-based index for tropical intraseasonal oscillation (PII) is derived by projecting bandpass-filtered precipitation anomalies to the two leading EOFs as a function of day of the year. A real-time version that approximates the PII is further developed using precipitation anomalies without any bandpass filtering. It is further shown that this real-time PII index may be used to diagnose precipitation in the subseasonal forecasts.
Abstract
Characteristic patterns of precipitation-associated tropical intraseasonal oscillations, including the Madden–Julian oscillation (MJO) and boreal summer intraseasonal oscillation (BSISO), are identified using local empirical orthogonal function (EOF) analysis of the Tropical Rainfall Measuring Mission (TRMM) precipitation data as a function of the day of the year. The explained variances of the EOF analysis show two peaks across the year: one in the middle of the boreal winter corresponding to the MJO and the other in the middle of summer corresponding to the BSISO. Comparing the fractional variance indicates that the BSISO is more coherent than the MJO during the TRMM period. Similar EOF analyses with the outgoing longwave radiation (OLR) confirm this result and indicate that the BSISO is less coherent before the TRMM era (1979–98). In contrast, the MJO exhibits much less decadal variability. A precipitation-based index for tropical intraseasonal oscillation (PII) is derived by projecting bandpass-filtered precipitation anomalies to the two leading EOFs as a function of day of the year. A real-time version that approximates the PII is further developed using precipitation anomalies without any bandpass filtering. It is further shown that this real-time PII index may be used to diagnose precipitation in the subseasonal forecasts.
Abstract
This study develops a linear numerical model to address the source mechanism of the gravity waves generated within a vortex dipole simulated in a fully nonlinear nonhydrostatic mesoscale model. The background flow for this linear model is obtained from potential vorticity inversion constrained by the nonlinear balance equation. The forcing imposed in the linear model is derived from an imbalance in the large-scale flow—that is, the forcing or imbalance in the vorticity, divergence, and thermodynamic equations, respectively. The response from the sum of these imbalanced forcings obtained from the linear dynamics shows well-defined gravity wave signals, which compare reasonably well in terms of location, phase, and amplitude with the gravity waves simulated in a fully nonlinear nonhydrostatic mesoscale model. It is found that the vorticity forcing, largely due to the advection of balanced relative vorticity, is the leading contributor to the gravity waves in the exit region of the vortex-dipole jet.
Abstract
This study develops a linear numerical model to address the source mechanism of the gravity waves generated within a vortex dipole simulated in a fully nonlinear nonhydrostatic mesoscale model. The background flow for this linear model is obtained from potential vorticity inversion constrained by the nonlinear balance equation. The forcing imposed in the linear model is derived from an imbalance in the large-scale flow—that is, the forcing or imbalance in the vorticity, divergence, and thermodynamic equations, respectively. The response from the sum of these imbalanced forcings obtained from the linear dynamics shows well-defined gravity wave signals, which compare reasonably well in terms of location, phase, and amplitude with the gravity waves simulated in a fully nonlinear nonhydrostatic mesoscale model. It is found that the vorticity forcing, largely due to the advection of balanced relative vorticity, is the leading contributor to the gravity waves in the exit region of the vortex-dipole jet.
Abstract
This study investigates the sensitivity of mesoscale gravity waves to the baroclinicity of the background jet-front systems by simulating different life cycles of baroclinic waves with a high-resolution mesoscale model. Four simulations are made starting from two-dimensional baroclinic jets having different static stability and wind shear in order to obtain baroclinic waves with significantly different growth rates. In all experiments, vertically propagating mesoscale gravity waves are simulated in the exit region of upper-tropospheric jet streaks. A two-dimensional spectral analysis demonstrates that these gravity waves have multiple components with different wave characteristics. The short-scale wave components that are preserved by a high-pass filter with a cutoff wavelength of 200 km have horizontal wavelengths of 85–161 km and intrinsic frequencies of 3–11 times the Coriolis parameter. The medium-scale waves that are preserved by a bandpass filter (with 200- and 600-km cutoff wavelengths) have horizontal wavelengths of 250–350 km and intrinsic frequencies less than 3 times the Coriolis parameter. The intrinsic frequencies of these gravity waves tend to increase with the growth rate of the baroclinic waves; gravity waves with similar frequency are found in the experiments with similar average baroclinic wave growth rate but with significantly different initial tropospheric static stability and tropopause geometry. The residuals of the nonlinear balance equation are used to assess the flow imbalance. In all experiments, the developing background baroclinic waves evolve from an initially balanced state to the strongly unbalanced state especially near the exit region of upper-level jet fronts before mature mesoscale gravity waves are generated. It is found that the growth rate of flow imbalance also correlates well to the growth rate of baroclinic waves and thus correlates to the frequency of gravity waves.
Abstract
This study investigates the sensitivity of mesoscale gravity waves to the baroclinicity of the background jet-front systems by simulating different life cycles of baroclinic waves with a high-resolution mesoscale model. Four simulations are made starting from two-dimensional baroclinic jets having different static stability and wind shear in order to obtain baroclinic waves with significantly different growth rates. In all experiments, vertically propagating mesoscale gravity waves are simulated in the exit region of upper-tropospheric jet streaks. A two-dimensional spectral analysis demonstrates that these gravity waves have multiple components with different wave characteristics. The short-scale wave components that are preserved by a high-pass filter with a cutoff wavelength of 200 km have horizontal wavelengths of 85–161 km and intrinsic frequencies of 3–11 times the Coriolis parameter. The medium-scale waves that are preserved by a bandpass filter (with 200- and 600-km cutoff wavelengths) have horizontal wavelengths of 250–350 km and intrinsic frequencies less than 3 times the Coriolis parameter. The intrinsic frequencies of these gravity waves tend to increase with the growth rate of the baroclinic waves; gravity waves with similar frequency are found in the experiments with similar average baroclinic wave growth rate but with significantly different initial tropospheric static stability and tropopause geometry. The residuals of the nonlinear balance equation are used to assess the flow imbalance. In all experiments, the developing background baroclinic waves evolve from an initially balanced state to the strongly unbalanced state especially near the exit region of upper-level jet fronts before mature mesoscale gravity waves are generated. It is found that the growth rate of flow imbalance also correlates well to the growth rate of baroclinic waves and thus correlates to the frequency of gravity waves.
Abstract
A set of idealized cloud-permitting simulations is performed to explore the influence of small islands on precipitating convection as a function of large-scale wind speed. The islands are situated in a long narrow ocean domain that is in radiative–convective equilibrium (RCE) as a whole, constraining the domain-average precipitation. The island occupies a small part of the domain, so that significant precipitation variations over the island can occur, compensated by smaller variations over the larger surrounding oceanic area.
While the prevailing wind speeds vary over flat islands, three distinct flow regimes occur. Rainfall is greatly enhanced, and a local symmetric circulation is formed in the time mean around the island, when the prevailing large-scale wind speed is small. The rainfall enhancement over the island is much reduced when the wind speed is increased to a moderate value. This difference is characterized by a change in the mechanisms by which convection is forced. A thermally forced sea breeze due to surface heating dominates when the large-scale wind is weak. Mechanically forced convection, on the other hand, is favored when the large-scale wind is moderately strong, and horizontal advection of temperature reduces the land–sea thermal contrast that drives the sea breeze. Further increases of the prevailing wind speed lead to strong asymmetry between the windward and leeward sides of the island, owing to gravity waves that result from the land–sea contrast in surface roughness as well as upward deflection of the horizontal flow by elevated diurnal heating. Small-amplitude topography (up to 800-m elevation is considered) has a quantitative impact but does not qualitatively alter the flow regimes or their dependence on wind speed.
Abstract
A set of idealized cloud-permitting simulations is performed to explore the influence of small islands on precipitating convection as a function of large-scale wind speed. The islands are situated in a long narrow ocean domain that is in radiative–convective equilibrium (RCE) as a whole, constraining the domain-average precipitation. The island occupies a small part of the domain, so that significant precipitation variations over the island can occur, compensated by smaller variations over the larger surrounding oceanic area.
While the prevailing wind speeds vary over flat islands, three distinct flow regimes occur. Rainfall is greatly enhanced, and a local symmetric circulation is formed in the time mean around the island, when the prevailing large-scale wind speed is small. The rainfall enhancement over the island is much reduced when the wind speed is increased to a moderate value. This difference is characterized by a change in the mechanisms by which convection is forced. A thermally forced sea breeze due to surface heating dominates when the large-scale wind is weak. Mechanically forced convection, on the other hand, is favored when the large-scale wind is moderately strong, and horizontal advection of temperature reduces the land–sea thermal contrast that drives the sea breeze. Further increases of the prevailing wind speed lead to strong asymmetry between the windward and leeward sides of the island, owing to gravity waves that result from the land–sea contrast in surface roughness as well as upward deflection of the horizontal flow by elevated diurnal heating. Small-amplitude topography (up to 800-m elevation is considered) has a quantitative impact but does not qualitatively alter the flow regimes or their dependence on wind speed.
Abstract
The Madden–Julian oscillation (MJO) and the boreal summer intraseasonal oscillation (BSISO) are fundamental modes of variability in the tropical atmosphere on the intraseasonal time scale. A linear model, using a moist shallow water equation set on an equatorial beta plane, is developed to provide a unified treatment of the two modes and to understand their growth and propagation over the Indian Ocean. Moisture is assumed to increase linearly with longitude and to decrease quadratically with latitude. Solutions are obtained through linear stability analysis, considering the gravest (n = 1) meridional mode with nonzero meridional velocity. Anomalies in zonal moisture advection and surface fluxes are both proportional to those in zonal wind, but of opposite sign. With observation-based estimates for both effects, the zonal advection dominates, and drives the planetary-scale instability. With a sufficiently small meridional moisture gradient, the horizontal structure exhibits oscillations with latitude and a northwest–southeast horizontal tilt in the Northern Hemisphere, qualitatively resembling the observed BSISO. As the meridional moisture gradient increases, the horizontal tilt decreases and the spatial pattern transforms toward the “swallowtail” structure associated with the MJO, with cyclonic gyres in both hemispheres straddling the equatorial precipitation maximum. These results suggest that the magnitude of the meridional moisture gradient shapes the horizontal structures, leading to the transformation from the BSISO-like tilted horizontal structure to the MJO-like neutral wave structure as the meridional moisture gradient changes with the seasons. The existence and behavior of these intraseasonal modes can be understood as a consequence of phase speed matching between the equatorial mode with zero meridional velocity (analogous to the dry Kelvin wave) and a local off-equatorial component that is characterized by considering an otherwise similar system on an f plane.
Abstract
The Madden–Julian oscillation (MJO) and the boreal summer intraseasonal oscillation (BSISO) are fundamental modes of variability in the tropical atmosphere on the intraseasonal time scale. A linear model, using a moist shallow water equation set on an equatorial beta plane, is developed to provide a unified treatment of the two modes and to understand their growth and propagation over the Indian Ocean. Moisture is assumed to increase linearly with longitude and to decrease quadratically with latitude. Solutions are obtained through linear stability analysis, considering the gravest (n = 1) meridional mode with nonzero meridional velocity. Anomalies in zonal moisture advection and surface fluxes are both proportional to those in zonal wind, but of opposite sign. With observation-based estimates for both effects, the zonal advection dominates, and drives the planetary-scale instability. With a sufficiently small meridional moisture gradient, the horizontal structure exhibits oscillations with latitude and a northwest–southeast horizontal tilt in the Northern Hemisphere, qualitatively resembling the observed BSISO. As the meridional moisture gradient increases, the horizontal tilt decreases and the spatial pattern transforms toward the “swallowtail” structure associated with the MJO, with cyclonic gyres in both hemispheres straddling the equatorial precipitation maximum. These results suggest that the magnitude of the meridional moisture gradient shapes the horizontal structures, leading to the transformation from the BSISO-like tilted horizontal structure to the MJO-like neutral wave structure as the meridional moisture gradient changes with the seasons. The existence and behavior of these intraseasonal modes can be understood as a consequence of phase speed matching between the equatorial mode with zero meridional velocity (analogous to the dry Kelvin wave) and a local off-equatorial component that is characterized by considering an otherwise similar system on an f plane.
Abstract
The authors analyze the column-integrated moist static energy budget over the region of the tropical Indian Ocean covered by the sounding array during the Cooperative Indian Ocean Experiment on Intraseasonal Variability in the Year 2011 (CINDY2011)/Dynamics of the Madden–Julian Oscillation (DYNAMO) field experiment in late 2011. The analysis is performed using data from the sounding array complemented by additional observational datasets for surface turbulent fluxes and atmospheric radiative heating. The entire analysis is repeated using the ECMWF Interim Re-Analysis (ERA-Interim). The roles of surface turbulent fluxes, radiative heating, and advection are quantified for the two MJO events that occurred in October and November using the sounding data; a third event in December is also studied in the ERA-Interim data.
These results are consistent with the view that the MJO’s moist static energy anomalies grow and are sustained to a significant extent by the radiative feedbacks associated with MJO water vapor and cloud anomalies and that propagation of the MJO is associated with advection of moist static energy. Both horizontal and vertical advection appear to play significant roles in the events studied here. Horizontal advection strongly moistens the atmosphere during the buildup to the active phase of the October event when the low-level winds switch from westerly to easterly. Horizontal advection strongly dries the atmosphere in the wake of the active phases of the November and December events as the westerlies associated with off-equatorial cyclonic gyres bring subtropical dry air into the convective region from the west and north. Vertical advection provides relative moistening ahead of the active phase and drying behind it, associated with an increase of the normalized gross moist stability.
Abstract
The authors analyze the column-integrated moist static energy budget over the region of the tropical Indian Ocean covered by the sounding array during the Cooperative Indian Ocean Experiment on Intraseasonal Variability in the Year 2011 (CINDY2011)/Dynamics of the Madden–Julian Oscillation (DYNAMO) field experiment in late 2011. The analysis is performed using data from the sounding array complemented by additional observational datasets for surface turbulent fluxes and atmospheric radiative heating. The entire analysis is repeated using the ECMWF Interim Re-Analysis (ERA-Interim). The roles of surface turbulent fluxes, radiative heating, and advection are quantified for the two MJO events that occurred in October and November using the sounding data; a third event in December is also studied in the ERA-Interim data.
These results are consistent with the view that the MJO’s moist static energy anomalies grow and are sustained to a significant extent by the radiative feedbacks associated with MJO water vapor and cloud anomalies and that propagation of the MJO is associated with advection of moist static energy. Both horizontal and vertical advection appear to play significant roles in the events studied here. Horizontal advection strongly moistens the atmosphere during the buildup to the active phase of the October event when the low-level winds switch from westerly to easterly. Horizontal advection strongly dries the atmosphere in the wake of the active phases of the November and December events as the westerlies associated with off-equatorial cyclonic gyres bring subtropical dry air into the convective region from the west and north. Vertical advection provides relative moistening ahead of the active phase and drying behind it, associated with an increase of the normalized gross moist stability.
Abstract
It is well known that vertical wind shear can organize deep convective systems and greatly extend their lifetimes. Much less is known about the influence of shear on the bulk properties of tropical convection in statistical equilibrium. To address the latter question, the authors present a series of cloud-resolving simulations on a doubly periodic domain with parameterized large-scale dynamics based on the weak temperature gradient (WTG) approximation. The horizontal-mean horizontal wind is relaxed strongly in these simulations toward a simple unidirectional linear vertical shear profile in the troposphere. The strength and depth of the shear layer are varied as control parameters. Surface enthalpy fluxes are prescribed.
The results fall in two distinct regimes. For weak wind shear, time-averaged rainfall decreases with shear and convection remains disorganized. For larger wind shear, rainfall increases with shear, as convection becomes organized into linear mesoscale systems. This nonmonotonic dependence of rainfall on shear is observed when the imposed surface fluxes are moderate. For larger surface fluxes, convection in the unsheared basic state is already strongly organized, but increasing wind shear still leads to increasing rainfall. In addition to surface rainfall, the impacts of shear on the parameterized large-scale vertical velocity, convective mass fluxes, cloud fraction, and momentum transport are also discussed.
Abstract
It is well known that vertical wind shear can organize deep convective systems and greatly extend their lifetimes. Much less is known about the influence of shear on the bulk properties of tropical convection in statistical equilibrium. To address the latter question, the authors present a series of cloud-resolving simulations on a doubly periodic domain with parameterized large-scale dynamics based on the weak temperature gradient (WTG) approximation. The horizontal-mean horizontal wind is relaxed strongly in these simulations toward a simple unidirectional linear vertical shear profile in the troposphere. The strength and depth of the shear layer are varied as control parameters. Surface enthalpy fluxes are prescribed.
The results fall in two distinct regimes. For weak wind shear, time-averaged rainfall decreases with shear and convection remains disorganized. For larger wind shear, rainfall increases with shear, as convection becomes organized into linear mesoscale systems. This nonmonotonic dependence of rainfall on shear is observed when the imposed surface fluxes are moderate. For larger surface fluxes, convection in the unsheared basic state is already strongly organized, but increasing wind shear still leads to increasing rainfall. In addition to surface rainfall, the impacts of shear on the parameterized large-scale vertical velocity, convective mass fluxes, cloud fraction, and momentum transport are also discussed.
Abstract
This study investigates gravity wave generation and propagation from jets within idealized vortex dipoles using a nonhydrostatic mesoscale model. Two types of initially balanced and localized jets induced by vortex dipoles are examined here. These jets have their maximum strength either at the surface or in the middle levels of a uniformly stratified atmosphere. Within these dipoles, inertia–gravity waves with intrinsic frequencies 1–2 times the Coriolis parameter are simulated in the jet exit region. These gravity waves are nearly phase locked with the jets as shown in previous studies, suggesting spontaneous emission of the waves by the localized jets. A ray tracing technique is further employed to investigate the propagation effects of gravity waves. The ray tracing analysis reveals strong variation of wave characteristics along ray paths due to variations (particularly horizontal variations) in the propagating environment.
The dependence of wave amplitude on the jet strength (and thus on the Rossby number of the flow) is examined through experiments in which the two vortices are initially separated by a large distance but subsequently approach each other and form a vortex dipole with an associated amplifying localized jet. The amplitude of the stationary gravity waves in the simulations with 90-km grid spacing increases as the square of the Rossby number (Ro), when Ro falls in a small range of 0.05–0.15, but does so significantly more rapidly when a smaller grid spacing is used.
Abstract
This study investigates gravity wave generation and propagation from jets within idealized vortex dipoles using a nonhydrostatic mesoscale model. Two types of initially balanced and localized jets induced by vortex dipoles are examined here. These jets have their maximum strength either at the surface or in the middle levels of a uniformly stratified atmosphere. Within these dipoles, inertia–gravity waves with intrinsic frequencies 1–2 times the Coriolis parameter are simulated in the jet exit region. These gravity waves are nearly phase locked with the jets as shown in previous studies, suggesting spontaneous emission of the waves by the localized jets. A ray tracing technique is further employed to investigate the propagation effects of gravity waves. The ray tracing analysis reveals strong variation of wave characteristics along ray paths due to variations (particularly horizontal variations) in the propagating environment.
The dependence of wave amplitude on the jet strength (and thus on the Rossby number of the flow) is examined through experiments in which the two vortices are initially separated by a large distance but subsequently approach each other and form a vortex dipole with an associated amplifying localized jet. The amplitude of the stationary gravity waves in the simulations with 90-km grid spacing increases as the square of the Rossby number (Ro), when Ro falls in a small range of 0.05–0.15, but does so significantly more rapidly when a smaller grid spacing is used.
Abstract
The authors investigate the effects of cloud–radiation interaction and vertical wind shear on convective ensembles interacting with large-scale dynamics in cloud-resolving model simulations, with the large-scale circulation parameterized using the weak temperature gradient approximation. Numerical experiments with interactive radiation are conducted with imposed surface heat fluxes constant in space and time, an idealized lower boundary condition that prevents wind–evaporation feedback. Each simulation with interactive radiation is compared to a simulation in which the radiative heating profile is held constant in the horizontal and in time and is equal to the horizontal-mean profile from the interactive-radiation simulation with the same vertical shear profile and surface fluxes. Interactive radiation is found to reduce mean precipitation in all cases. The magnitude of the reduction is nearly independent of the vertical wind shear but increases with surface fluxes. Deep shear also reduces precipitation, though by approximately the same amount with or without interactive radiation. The reductions in precipitation due to either interactive radiation or deep shear are associated with strong large-scale ascent in the upper troposphere, which more strongly exports moist static energy and is quantified by a larger normalized gross moist stability.
Abstract
The authors investigate the effects of cloud–radiation interaction and vertical wind shear on convective ensembles interacting with large-scale dynamics in cloud-resolving model simulations, with the large-scale circulation parameterized using the weak temperature gradient approximation. Numerical experiments with interactive radiation are conducted with imposed surface heat fluxes constant in space and time, an idealized lower boundary condition that prevents wind–evaporation feedback. Each simulation with interactive radiation is compared to a simulation in which the radiative heating profile is held constant in the horizontal and in time and is equal to the horizontal-mean profile from the interactive-radiation simulation with the same vertical shear profile and surface fluxes. Interactive radiation is found to reduce mean precipitation in all cases. The magnitude of the reduction is nearly independent of the vertical wind shear but increases with surface fluxes. Deep shear also reduces precipitation, though by approximately the same amount with or without interactive radiation. The reductions in precipitation due to either interactive radiation or deep shear are associated with strong large-scale ascent in the upper troposphere, which more strongly exports moist static energy and is quantified by a larger normalized gross moist stability.
Abstract
The effects of turbulent surface fluxes and radiative heating on tropical deep convection are compared in a series of idealized cloud-system-resolving simulations with parameterized large-scale dynamics. Two methods of parameterizing the large-scale dynamics are used: the weak temperature gradient (WTG) approximation and the damped gravity wave (DGW) method. Both surface fluxes and radiative heating are specified, with radiative heating taken as constant in the vertical in the troposphere. All simulations are run to statistical equilibrium.
In the precipitating equilibria, which result from sufficiently moist initial conditions, an increment in surface fluxes produces more precipitation than an equal increment of column-integrated radiative heating. This is straightforwardly understood in terms of the column-integrated moist static energy budget with constant normalized gross moist stability. Under both large-scale parameterizations, the gross moist stability does in fact remain close to constant over a wide range of forcings, and the small variations that occur are similar for equal increments of surface flux and radiative heating.
With completely dry initial conditions, the WTG simulations exhibit hysteresis, maintaining a dry state with no precipitation for a wide range of net energy inputs to the atmospheric column. The same boundary conditions and forcings admit a rainy state also (for moist initial conditions), and thus multiple equilibria exist under WTG. When the net forcing (surface fluxes minus radiative heating) is increased enough that simulations that begin dry eventually develop precipitation, the dry state persists longer after initialization when the surface fluxes are increased than when radiative heating is increased. The DGW method, however, shows no multiple equilibria in any of the simulations.
Abstract
The effects of turbulent surface fluxes and radiative heating on tropical deep convection are compared in a series of idealized cloud-system-resolving simulations with parameterized large-scale dynamics. Two methods of parameterizing the large-scale dynamics are used: the weak temperature gradient (WTG) approximation and the damped gravity wave (DGW) method. Both surface fluxes and radiative heating are specified, with radiative heating taken as constant in the vertical in the troposphere. All simulations are run to statistical equilibrium.
In the precipitating equilibria, which result from sufficiently moist initial conditions, an increment in surface fluxes produces more precipitation than an equal increment of column-integrated radiative heating. This is straightforwardly understood in terms of the column-integrated moist static energy budget with constant normalized gross moist stability. Under both large-scale parameterizations, the gross moist stability does in fact remain close to constant over a wide range of forcings, and the small variations that occur are similar for equal increments of surface flux and radiative heating.
With completely dry initial conditions, the WTG simulations exhibit hysteresis, maintaining a dry state with no precipitation for a wide range of net energy inputs to the atmospheric column. The same boundary conditions and forcings admit a rainy state also (for moist initial conditions), and thus multiple equilibria exist under WTG. When the net forcing (surface fluxes minus radiative heating) is increased enough that simulations that begin dry eventually develop precipitation, the dry state persists longer after initialization when the surface fluxes are increased than when radiative heating is increased. The DGW method, however, shows no multiple equilibria in any of the simulations.