Buoyancy driven turbulence in the atmosphere Stephan de Roode (TU Delft) Applied Physics Department Clouds, Climate and Air Quality s.r.deroode@tudelft.nl eastern Pacific island of Guadalupe. The rugged terrain of this volcanic Mexican island reaches a maximum elevation of 1.3 kilometers. The island is about 35 kilometers long

Clouds, Climate and Air Quality Harm Jonker, Pier Siebesma and Stephan de Roode cloud-climate feedback detailed numerical simulation N2O CH4 new methods for measuring emission rates atmospheric boundary layer in the laboratory

Length scales in the atmosphere Earth 103 km Landsat 60 km 65km LES 10 km ~1mm-100mm ~mm ~100m courtesy: Harm Jonker

Global mean turbulent heat fluxes source: Ruddiman, 2000

No single model can encompass all relevant processes mm 10 m 100 m 1 km 10 km 100 km 1000 km 10000 km Cloud microphysics  turbulence Cumulus clouds Cumulonimbus clouds Mesoscale Convective systems Extratropical Cyclones Planetary waves DNS Subgrid Large Eddy Simulation (LES) Model Cloud System Resolving Model (CSRM) Numerical Weather Prediction (NWP) Model Global Climate Model

DALES: Dutch Atmospheric Large-Eddy Simulation Model Dry LES code (prognostic subgrid TKE, stability dependent length scale) Frans Nieuwstadt (KNMI) and R. A. Brost (NOAA/NCAR, USA) Radiation and moist thermodynamics Hans Cuijpers and Peter Duynkerke (KNMI/TU Delft, Utrecht University) Parallellisation and Poisson solver Matthieu Pourquie and Bendiks Jan Boersma (TU Delft) Drizzle Margreet Van Zanten and Pier Siebesma (UCLA/KNMI) Atmospheric Chemistry Jordi Vila (Wageningen University) Land-surface interaction, advection schemes Chiel van Heerwaarden (Wageningen University) Particle dispersion, numerics Thijs Heus and Harm Jonker (TU Delft)

Contents Governing equations & static stability Observations, large-eddy simulations and parameterizations: - Clear convection - Latent heat release & shallow cumulus - Longwave radiative cooling & stratocumulus

z Temperature Static stability Q: what will happen with the air measured vertical temperature profile Q: what will happen with the air parcel if it is vertically displaced? z Temperature

First law of thermodynamics: Conservation of energy added heat internal energy work cv = specific heat of dry air at constant volume (718 J kg-1K-1 at 0 oC) T = temperature p = air pressure r = air density

Equation of state for dry air: gas law Combine gas law and energy conservation cp = specific heat of dry air at constant pressure (1005 J kg-1K-1 at 0 oC) Rd = gas constant for dry air (287 J kg-1K-1 )

Hydrostatic equilibrium Gas law, energy conservation and hydrostatic equilibrium Adiabatic process dq=0  dry adiabatic lapse rate

z T Atmospheric stability: dry air measured vertical temperature profile Atmospheric stability: dry air dry adiabatic lapse rate: –10K/km A dry air parcel, moved upwards, cools according to the dry adiabatic lapse rate. But now it is warmer than the environmental air, and experiences an upward force. A dry air parcel, moved downwards, warms according to the dry adiabatic lapse rate. But now it is cooler than the environmental air, and experiences a downward force. F z unstable situation for dry air F T

z T Atmospheric stability: dry air F F stable situation for dry air A dry air parcel, moved downwards, warms according to the dry adiabatic lapse rate. But now it is warmer than the environmental air, and experiences an upward force. A dry air parcel, moved upwards, cools according to the dry adiabatic lapse rate. But now it is cooler than the environmental air, and experiences a downward force. Atmospheric stability: dry air stable situation for dry air F F z dry adiabatic lapse rate: –10K/km measured environmental temperature profile unstable situation for dry air T

Harm Jonker's saline convective water tank Initial state: tank is filled with salt water Convection driven by a fresh water flux at the surface Schematic by Daniel Abrahams

Convective water tank Movie by Phillia Lijdsman

Adiabatic process dq=0  dry adiabatic lapse rate (2) The potential temperature q is the temperature if a parcel would be brought adiabatically to a reference pressure p0

Balloon observations at Cabauw during daytime Q: what makes this case challlenging for modeling?

LES results of a convective boundary layer: Buoyancy flux warm air going down entrainment of warm air warm air going up Q: what is sign of the mean tendency for qv?

LES results Buoyancy flux and vertical velocity variance

LES results of a convective boundary layer - resolved TKE budget

LES results Humidity flux Flux-jump relation: w'q'T = -weDq Dq H we and wls are of the order 1 cm s-1

Entrainment scaling Large-scale subsidence Entrainment atmospheric boundary layer Photograph: Adriaan Schuitmaker

Conservation of energy: saturated case heat released by condensation internal energy work ql = liquid water content Lv = enthalpy of vaporization of water (2.5x106 J kg-1 at 0 oC)

For a moist adiabatic process, the liquid water static energy (sl) is a conserved variable meteorologists sl

z T Atmospheric stability: conditional instability measured F wet adiabatic lapse rate measured environmental temperature profile F A moist air parcel, moved upwards, cools according to the wet adiabatic lapse rate. But now it is warmer than the environmental air, and experiences an upward force. A dry air parcel, moved upwards, cools according to the dry adiabatic lapse rate. But now it is cooler than the environmental air, and experiences a downward force. F dry adiabatic lapse rate F z T

z T Atmospheric stability: conditional instability stable for dry and moist air stable for dry air possibly unstable for moist air z T Q: why possibly unstable for moist air?

Convective transport in Shallow Cumulus: Characteristics Courtesy Bjorn Stevens LES Heus TU Delft

Shallow cumulus movie by Thijs Heus

Stratocumulus 1100 km

Longwave radiative flux (FL) profile in cloud Cloud top cooling!

Turbulence in stratocumulus: LES results and observations Nighttime Daytime

Standard transport parameterization approach: This unwanted situation can lead to: Double counting of processes Inconsistencies Problems with transitions between different regimes: dry pbl  shallow cu scu  shallow cu shallow cu deep cu

How to estimate updraft fields and mass flux? Betts 1974 JAS Arakawa&Schubert 1974 JAS Tiedtke 1988 MWR Gregory & Rowntree 1990 MWR Kain & Fritsch 1990 JAS And many more…….. The old working horse: Entraining plume model: M e d Plus boundary conditions at cloud base.

Downgradient-diffusion models

Downgradient-diffusion models Analytical solutions for stable stratifications see Baas et al. (2008)

Stable boundary layer solutions Nieuwstadt's (1984) z/L  ∞

Turbulence and clouds: do we care?

Climate Model Sensistivity estimates of GCM’s participating in IPCC AR4 Source: IPCC Chapter 8 2007 Spread in climate sensitivity: concern for many aspects of climate change research, assesment of climate extremes, design of mitigation scenarios. What is the origin of this spread? Radiative Forcing, Climate feedbacks,

Relative Contributions to the uncertainty in climate feedbacks Cloud feedback Surface albedo feedback Water vapor feedback Radiative effects only Source: Dufresne & Bony, Journal of Climate 2008 Uncertainty in climate sensitivity mainly due to (low) cloud feedbacks