Latent heat fluxes during stably stratified conditions

Stephan de Roode

with contributions from Fred Bosveld and Reinder Ronda

Turbulent transport: Turbulent kinetic energy E > 0

For very stable conditions shear generation of TKE is not sufficient(?)

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buoyancy shear production turbulent transport dissipation

TKE production requires

Write

and if KH = KM then TKE production for the following criterion

Bulk critical Richardson number

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Stable boundary layers

Cabauw data 2000-2006

Data selection:

weak winds: Utot (z=10 m) < 3 m/s

clear skies: LWnet,sfc > 40 W/m2

nighttime: SWnet,sfc = 0 W/m2

7.1% of all data points satisfy these criteria

Stable boundary layers

Cabauw data 2000-2006

Further data selection:

Latent, sensible and ground heat flow at 5 cm

are available

weak winds: Utot (z=10 m) < 3 m/s

clear skies: LWnet,sfc > 40 W/m2

nighttime: SWnet,sfc = 0 W/m2

3.5% of all data points

Surface energy balance during the night

-G = SW + LW + H + LE

G = energy flow into the ground

SW = net shortwave radiation

LW = net longwave radiation

H = sensible heat flux

LE = latent heat flux (evaporation)

night-time

Low wind speeds during stable nights:

turbulent fluxes H and LE become very small.

Cabauw Monthly Mean Surface Energy Balance results

for stable boundary layers

month N10mins G|10 cm G|05 cm LWnet H LE

Jan 536 -6.6 -9.7 50.4 -4.7 -1.4

Feb 751 -6.6 -10.0 54.9 -6.8 -0.1

Mar 1478 -3.0 -8.4 52.1 -5.9 0.4

Apr 1620 -0.9 -7.8 49.6 -6.2 0.8

May 1291 0.3 -7.4 48.5 -6.5 0.3

Jun 867 -0.0 -8.0 48.0 -7.9 2.1

Jul 798 0.0 -7.3 46.5 -8.7 1.1

Aug 1333 -1.8 -7.4 46.9 -9.8 1.5

Sep 1557 -3.9 -9.9 46.5 -8.5 -0.3

Oct 1098 -3.9 -7.6 47.7 -9.8 -0.9

Nov 723 -7.1 -10.2 48.4 -6.0 -2.1

Dec 1122 -8.7 -11.9 50.7 -5.7 -1.4

[W/m2]

Is it possible to close the surface energy balance from observations?

Dew formation in Wageningen

Results based on modeling and observations

from Jacobs et al. (2006)

Percentage of monthly dew nights in Wageningen

Energy equivalence of dew formation

Evaporation of 1 kg (= 1mm) of water:

2.5·106 J

In Wageningen monthly mean dew formation:

3.5 mm/month = 0.12 mm/day

Rough estimation: Assume that dew formation takes place during 12 hours

(half a day) then the typical heat production due to dew formation amounts

2.5·106 x 0.12 / 12 / 3600 = 7 W/m2

A few examples from Cabauw

• Select clear nights with low wind speeds

• Select negative humidity tendencies

• In the examples that will be shown the observed latent heat flux ~ 0 W/m2

Moisture tendencies: weak wind velocities

z=2m

z=10m

z=80m

z=200m

qsat,sfc

Moisture tendencies: weak wind velocities

z=2m

z=10m

z=80m

z=200m

qsat,sfc

Moisture tendencies: weak wind velocities

z=2mz=10m

z=80m

z=200m

qsat,sfc

Moisture tendencies: very weak wind velocities

z=2mz=10m

z=80m

z=200m

qsat,sfc

Moisture tendencies: very weak wind velocities

z=2m

z=10m

z=80mz=200m

qsat,sfc

Add selection criterion: humidity tendency < 0.02 g/kg/hour at

z=20m

Monthly mean humidity tendencies

z=2m

z=10m

z=80m

z=200m

Conclusions from observations

• Specific humidity in the lower part of the atmosphere follows surface

saturation specific humidity rather well

• It is difficult to assess the magnitude of the large-scale horizontal advection

of moisture

Diagnose the latent heat flux from the humidity budget equation

x

qU

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ii

Latent heat fluxes diagnosed from the humidity budget equation

Monthly mean values

I

II

I. Neglect large-scale advection term

II. Large-scale (ls) tendency correction.

Assume that the tendency at 200 m is

representative for the ls-tendency at every

height.

Can we possibly explain transport for stable conditions?

Prognostic equations

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Turbulent potential energy TPE

Total turbulent energy TTE (Zilitinkevich, 2007)

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1ETPETKETTE

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TTE

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shear production turbulent transport total dissipation

Prognostic equations

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Stable <0 always >0 ! transport dissipation radiation

Unstable > 0

Large eddy simulation

• Initial (very) stable lapse rate:

• No fluxes at the surface, no moisture present

• No horizontal winds: U=V=0.001 m/s

• nr of grid points Nx=Ny=64 , Nz=80

• x=y=z=5m

• sinusoidal initial perturbation at layers between 50 and 150 m

• amplitude of perturbation AMPL =0.5 K

What will happen?

K/km 10z

Turbulent kinetic energy (TKE) - Turbulent potential energy (TPE)

TKE

TPE (buoyancy variance term)

● TKE generation by TPE, their sum is not conserved (dissipation)

● Rapid oscillations (but not Brunt-Vaissala frequency)

● vertical integral buoyancy flux > 0 for d/dt TKE > 0 and vice versa

Lorenz, Available potential energy and the maintenance of the

general circulation, Tellus., 1955

Lorenz showed that available potential energy (APE) is given

approximately by the volume integral over the entire atmosphere of

the variance of potential temperature on isobaric surfaces:

As the potential temperature is conserved for adiabatic processes,

and as kinetic energy is produced, the enthalpy (cpT) of the

atmosphere should decrease (see also Holton 1992)

dV

'

V

1APE

2

2

Temperature evolution

t=0

t=1200 s

Enthalpy change

enthalpy

PKE

● Enthalpy in phase with PKE and TKE

TKE

Conclusions

● Surface energy balance does not close for Cabauw for strong stable conditions

Observations suggests the observed latent heat flux is underestimated

● Concept of 'total turbulent energy' is just a smart combination of the variance

equations for E and the virtual potential temperature. Note that Nieuwstadt also

uses these equations and gets identical solutions as from a simple TKE equation

(Baas et al., 2007)

● However, note that buoyancy fluctuations plane will trigger vertical motions

● The radiation term might be very important in generating temperature variance

Can we measure small latent heat fluxes?

Write the flux according to an updraft downdraft decomposition:

with = updraft fraction

wu (wd) = updraft (downdraft) vertical velocity

qu (qd) = updraft (downdraft) specific humidity

qqwqqww1'q'w uududu

Can we measure small latent heat fluxes?

Measure 7 W/m2:

Examples wu (m/s) qt' (g/kg)

1 0.0028

0.1 0.028

0.001 0.28

Li-Cor Li7500 RMS noise ± 0.0033 g/kg

m/sg/kg 108.2L

7'q'w 3

v

g/kg w

108.2

w

'q'wqq'q

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3

uut

Soil heat flux

Soil heat flux: soil heat flux plates.

The six plates are burried at the three vertices of an equilateral triangle with sides of 2 m at depths of 0.05 and 0.10 m. The measurements are averaged over the three plates at each depth.

To obtain the surface soil heat flux a Fourier decompostion method is used.

The instruments are manufactured by TNO-Delft. Type: WS31S, measuring principle: thermo-pile, diameter 0.11 m, thickness 5 mm, sensitive surface: central square of 25*25 mm2. Thermal conductivity of the sensor 0.2-0.3 W/m/K.

Temperature tendencies during stable, clear nights:

Monthly mean values [K/hour]

Month 2m 10m 20m 40m 80m 140 m 200m

Jan -0.874 -0.772 -0.710 -0.470 -0.214 -0.117 -0.048

Feb -0.714 -0.652 -0.610 -0.449 -0.322 -0.135 -0.053

Mar -0.871 -0.691 -0.679 -0.523 -0.336 -0.190 -0.113

Apr -0.775 -0.594 -0.492 -0.396 -0.287 -0.181 -0.163

May -0.833 -0.668 -0.618 -0.430 -0.282 -0.188 -0.166

Jun -0.820 -0.719 -0.651 -0.513 -0.406 -0.264 -0.218

Jul -0.966 -0.755 -0.695 -0.562 -0.363 -0.295 -0.254

Aug -0.883 -0.787 -0.752 -0.618 -0.443 -0.275 -0.118

Sep -0.843 -0.746 -0.694 -0.567 -0.380 -0.241 -0.165

Oct -0.815 -0.744 -0.717 -0.597 -0.380 -0.197 -0.141

Nov -0.941 -0.720 -0.696 -0.526 -0.316 -0.149 -0.059

Dec -0.692 -0.650 -0.658 -0.410 -0.204 -0.106 -0.035

Humidity tendencies during stable, clear nights:

Monthly mean values [g/kg/hour]

Month 2m 10m 20m 40m 80m 140 m 200m

Jan -0.176 -0.160 -0.167 -0.098 -0.050 0.002 -0.007

Feb -0.148 -0.130 -0.150 -0.093 -0.069 -0.044 -0.043

Mar -0.167 -0.147 -0.173 -0.104 -0.073 -0.052 -0.066

Apr -0.181 -0.189 -0.242 -0.146 -0.104 -0.089 -0.064

May -0.244 -0.194 -0.271 -0.158 -0.095 -0.074 -0.031

Jun -0.282 -0.241 -0.272 -0.186 -0.118 -0.104 -0.025

Jul -0.372 -0.283 -0.358 -0.204 -0.096 -0.051 -0.080

Aug -0.334 -0.272 -0.333 -0.191 -0.073 -0.086 -0.064

Sep -0.297 -0.274 -0.323 -0.152 -0.144 -0.110 -0.070

Oct -0.283 -0.231 -0.252 -0.171 -0.125 -0.103 -0.085

Nov -0.248 -0.197 -0.218 -0.134 -0.086 -0.062 -0.077

Dec -0.147 -0.139 -0.170 -0.092 -0.067 -0.057 -0.041

Humidity budget equation

I. Neglect large-scale advection term

II. Assume 200 m tendency is due to horizontal advection

month LE_I LE_II (advection correction)

Jan -7.32 -6.30

Feb -10.07 -4.15

Mar -11.64 -2.46

Apr -16.16 -7.22

May -15.37 -11.07

Jun -18.37 -14.83

Jul -18.43 -7.38

Aug -17.97 -9.13

Sep -20.52 -10.82

Oct -19.24 -7.44

Nov -14.49 -3.74

Dec -10.71 -5.02