### Abstract

A toy model of large-scale deep convection variations is constructed around a radiative-convective equilibrium climate, with an observed mean sounding as its thermodynamic basic state. Vertical structure is truncated at two modes, excited by convective (one-signed) and stratiform (two-signed) heating processes in tropical deep convection. Separate treatments of deep and shallow convection are justified by observations that deep convection is more variable. Deep convection intensity is assumed to be modulated by convective available potential energy (CAPE), while occurrence frequency is modulated by the ratio of convective inhibition (CIN) to 'triggering energy' K, a scalar representing the intensity of subgrid-scale fluctuations. Deep convective downdrafts cool and dry the boundary layer but also increase K. Variations of K make the relationship between convection and thermodynamic variables (CAPE, CIN, θ(e)) nonunique and amplify the deep convective response to temperature waves of small (~1°C) amplitude. For a parameter set in which CAPE variations control convection, moist convective damping destroys all variability. When CIN/K variations have dominant importance (the 'inhibition-controlled' regime), a mechanism termed 'stratiform instability' generates large-scale waves. This mechanism involves lower-tropospheric cooling by stratiform precipitation, which preferentially occurs where the already cool lower troposphere favors deep convection, via smaller CIN. Stratiform instability has two subregimes, based on the relative importance of the two opposite effects of downdrafts: When boundary layer θ(e) reduction (a local negative feedback) is stronger, small-scale waves with frequency based on the boundary layer recovery time are preferred. When the K-generation effect (positive feedback) is stronger, very large scales (low wavenumbers of the domain) develop. A mixture of these scales occurs for parameter choices based on observations. Model waves resemble observed waves, with a phase speed ~20 m s^{-1} (near the dry wave speed of the second internal mode), and a 'cold boomerang' vertical temperature structure. Although K exhibits 'quasi-equilibrium' with other convection variables (correlations > 0.99), replacing the prognostic K equation with diagnostic equations based on these relationships can put the model into wildly different regimes, if small time lags indicative of causality are distorted. The response of model convection to climatological spatial anomalies of θ(e) (proxy for SST) and K (proxy for orographic and coastal triggering) is considered. Higher SST tends broadly to favor convection under either CAPE-controlled or inhibition-controlled regimes, but there are dynamical embellishments in the inhibition-controlled regime. The Kelvin wave seems to be the preferred structure when the model is run on a uniform equatorial β plane.

Original language | English (US) |
---|---|

Pages (from-to) | 1515-1535 |

Number of pages | 21 |

Journal | Journal of the Atmospheric Sciences |

Volume | 57 |

Issue number | 10 |

State | Published - May 15 2000 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atmospheric Science

### Cite this

**Convective inhibition, subgrid-scale triggering energy, and stratiform instability in a toy tropical wave model.** / Mapes, Brian E.

Research output: Contribution to journal › Article

*Journal of the Atmospheric Sciences*, vol. 57, no. 10, pp. 1515-1535.

}

TY - JOUR

T1 - Convective inhibition, subgrid-scale triggering energy, and stratiform instability in a toy tropical wave model

AU - Mapes, Brian E

PY - 2000/5/15

Y1 - 2000/5/15

N2 - A toy model of large-scale deep convection variations is constructed around a radiative-convective equilibrium climate, with an observed mean sounding as its thermodynamic basic state. Vertical structure is truncated at two modes, excited by convective (one-signed) and stratiform (two-signed) heating processes in tropical deep convection. Separate treatments of deep and shallow convection are justified by observations that deep convection is more variable. Deep convection intensity is assumed to be modulated by convective available potential energy (CAPE), while occurrence frequency is modulated by the ratio of convective inhibition (CIN) to 'triggering energy' K, a scalar representing the intensity of subgrid-scale fluctuations. Deep convective downdrafts cool and dry the boundary layer but also increase K. Variations of K make the relationship between convection and thermodynamic variables (CAPE, CIN, θ(e)) nonunique and amplify the deep convective response to temperature waves of small (~1°C) amplitude. For a parameter set in which CAPE variations control convection, moist convective damping destroys all variability. When CIN/K variations have dominant importance (the 'inhibition-controlled' regime), a mechanism termed 'stratiform instability' generates large-scale waves. This mechanism involves lower-tropospheric cooling by stratiform precipitation, which preferentially occurs where the already cool lower troposphere favors deep convection, via smaller CIN. Stratiform instability has two subregimes, based on the relative importance of the two opposite effects of downdrafts: When boundary layer θ(e) reduction (a local negative feedback) is stronger, small-scale waves with frequency based on the boundary layer recovery time are preferred. When the K-generation effect (positive feedback) is stronger, very large scales (low wavenumbers of the domain) develop. A mixture of these scales occurs for parameter choices based on observations. Model waves resemble observed waves, with a phase speed ~20 m s-1 (near the dry wave speed of the second internal mode), and a 'cold boomerang' vertical temperature structure. Although K exhibits 'quasi-equilibrium' with other convection variables (correlations > 0.99), replacing the prognostic K equation with diagnostic equations based on these relationships can put the model into wildly different regimes, if small time lags indicative of causality are distorted. The response of model convection to climatological spatial anomalies of θ(e) (proxy for SST) and K (proxy for orographic and coastal triggering) is considered. Higher SST tends broadly to favor convection under either CAPE-controlled or inhibition-controlled regimes, but there are dynamical embellishments in the inhibition-controlled regime. The Kelvin wave seems to be the preferred structure when the model is run on a uniform equatorial β plane.

AB - A toy model of large-scale deep convection variations is constructed around a radiative-convective equilibrium climate, with an observed mean sounding as its thermodynamic basic state. Vertical structure is truncated at two modes, excited by convective (one-signed) and stratiform (two-signed) heating processes in tropical deep convection. Separate treatments of deep and shallow convection are justified by observations that deep convection is more variable. Deep convection intensity is assumed to be modulated by convective available potential energy (CAPE), while occurrence frequency is modulated by the ratio of convective inhibition (CIN) to 'triggering energy' K, a scalar representing the intensity of subgrid-scale fluctuations. Deep convective downdrafts cool and dry the boundary layer but also increase K. Variations of K make the relationship between convection and thermodynamic variables (CAPE, CIN, θ(e)) nonunique and amplify the deep convective response to temperature waves of small (~1°C) amplitude. For a parameter set in which CAPE variations control convection, moist convective damping destroys all variability. When CIN/K variations have dominant importance (the 'inhibition-controlled' regime), a mechanism termed 'stratiform instability' generates large-scale waves. This mechanism involves lower-tropospheric cooling by stratiform precipitation, which preferentially occurs where the already cool lower troposphere favors deep convection, via smaller CIN. Stratiform instability has two subregimes, based on the relative importance of the two opposite effects of downdrafts: When boundary layer θ(e) reduction (a local negative feedback) is stronger, small-scale waves with frequency based on the boundary layer recovery time are preferred. When the K-generation effect (positive feedback) is stronger, very large scales (low wavenumbers of the domain) develop. A mixture of these scales occurs for parameter choices based on observations. Model waves resemble observed waves, with a phase speed ~20 m s-1 (near the dry wave speed of the second internal mode), and a 'cold boomerang' vertical temperature structure. Although K exhibits 'quasi-equilibrium' with other convection variables (correlations > 0.99), replacing the prognostic K equation with diagnostic equations based on these relationships can put the model into wildly different regimes, if small time lags indicative of causality are distorted. The response of model convection to climatological spatial anomalies of θ(e) (proxy for SST) and K (proxy for orographic and coastal triggering) is considered. Higher SST tends broadly to favor convection under either CAPE-controlled or inhibition-controlled regimes, but there are dynamical embellishments in the inhibition-controlled regime. The Kelvin wave seems to be the preferred structure when the model is run on a uniform equatorial β plane.

UR - http://www.scopus.com/inward/record.url?scp=0034193907&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034193907&partnerID=8YFLogxK

M3 - Article

VL - 57

SP - 1515

EP - 1535

JO - Journals of the Atmospheric Sciences

JF - Journals of the Atmospheric Sciences

SN - 0022-4928

IS - 10

ER -