Estimates of turbulent parameters in the lower stratosphere-upper troposphere by radar observations' A novel twist

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Estimates of turbulent parameters in the lower

stratosphere-upper troposphere by radar observations’

A novel twist

Juliette Dole, Richard Wilson

To cite this version:

Juliette Dole, Richard Wilson. Estimates of turbulent parameters in the lower stratosphere-upper

tro-posphere by radar observations’ A novel twist. Geophysical Research Letters, American Geophysical

Union, 2000, 27 (17), pp.2625-2628. �10.1029/1999GL010766�. �hal-02925704�

GEOPHYSICAL RESEARCH LETTERS, VOL. 27, NO. 17, PAGES 2625-2628, SEPTEMBER 1, 2000

Estimates of turbulent parameters in the lower

stratosphere-

upper troposphere by radar

observations'

A novel

twist

J. Dole and R. Wilson

Service d'A•ronomie du C.N.R.S., Paris, France

Abstract. The turbulence parameters in the upper tropo- sphere- lower stratosphere are estimated from the backscat- tered power of a VHF radar located at the Observatoire de

Haute-Provence (OHP). Under the classical framework of

locally homogeneous and isotropic turbulence, we propose a slightly different method for estimating the turbulent diffu- sivity from radar measurements. The temperature structure

parameter,

C}, and the vertical

heat diffusivity,

Ko, are ex-

pressed as a function of the dissipation rate of the tempera-

ture variance, e0 (and not from the dissipation rate of kinetic energy). This parameter appears weakly dependent on un- known quantities such as the mixing efficiency Rf/(1 - Rf) (RI is the flux Richardson number) and the vertical stratifi- cation O0/Oz. Our estimations of e0 are of the same order as

in situ measurements. The inferred diffusivity Ko appears

considerably

weaker (one order of magnitude) than radar

estimates using the bandwidth of the Doppler spectrum.

1. Introduction

Mesosphere-stratosphere-troposphere (MST) and stra- tosphere-troposphere (ST) radars have provided a power-

ful measurement technique for determination of turbulence parameters over a quite broad altitude range with better temporal resolution and continuity than afforded by other

techniques

(balloons, aircraft). Two approaches

may be

used to estimate turbulence parameters from radar obser- vations. One relies on the measurement of Doppler spec-

tral width. Turbulent kinetic energy (KE) dissipation rate,

ek, is inferred under the classical hypothesis of locally ho- mogeneous and stationary fluctuations within the inertial subrange. The other one, under the same hypothesis, re-

lates the backscattered

power intensity to C•

2, the struc-

ture constant of refractive index. Additional data are

needed

to express

C}, the structure

constant

of temper-

ature fluctuations

from C• and then, ek is inferred from

C}. The turbulent diffusivity

is usually expressed,

from

both methods, as a function of e•. The purpose of this pa- per is to present a novel twist to the last above-mentioned

method in order to estimate turbulent parameters (dissi- pation rate, eddy diffusivity). The temperature structure

parameter,

C•, is expressed

as a function

of the dissipa-

tion rate of temperature variance, co, instead of e• as usu- ally done. The eo estimation is less dependent on supple-

mentary data (not provided by radar measurements) than

the e• estimation. Then Ko is directly estimated from co.

Copyright 2000 by the American Geophysical Union. Paper number 1999GL010766.

0094-8276/00/1999GL010766505.00

The organization of the paper is as follows: the method is presented in section 2. The main characteristics of the OHP radar and data processing are described in section 3. Results are presented and discussed in section 4.

2. Method

For a 15 ø off-vertical line of sight, the refractive index irregularities at the considered scale (• 2 m for the OHP radar) are assumed to be due to the isotropic turbulence. This assumption, though usual in the literature [Hocking

and Mu, 1997], will sometimes

not be valid [Worthington,

1999]. In some

cases,

aspect

sensitive

scatterers

are observed

and Palmer et al. [1998] suggest

that, in most cases, this

basic hypothesis holds, even if not always valid. The struc-

ture constant

of refractive

index C•

2 is related to the radar

reflectivity r/by [Ottersten,

1969]'

C•

2 -(r//0.38)A

x/3

(1)

where A is the electromagnetic wavelength.

C•

2 is proportional

to the structure

parameter

of tempera-

ture fluctuations,

C}, through

[Tatarski,

1961]'

a/az

(2)

where M is the vertical gradient of generalized potential refractive index.

P q O0 Oq

M = -70

x 10-6

•-• 1

q-

15600- - 7800 (3)

0

q being the specific

humidity (g/g), P is the pressure

(mb),

0 is the generalized

potential

temperature

(K). C} is defined

as[ Tatarski, 1961]'

C• - a 2 e0

•}/3

(4)

where a is a universal dimensionless constant characteris-

tic of the turbulence spectra of passive additives[Obukhov,

1949].

The dissipation rate of half the temperature variance e•

is:

--d9

e• - -w'•'-- _dz (5)

Using the following relation derived from the balance equa- tion of kinetic and available potential energy under the clas- sical hypothesis of local homogeneity and stationarity,

(½)

ek

2626 DOLE AND WILSON: ESTIMATION OF ATMOSPHERIC TURBULENT PARAMETERS 8 --6 --4 AT= 60min .•. . . . --2 --1 0 1 :::Log• 0 (r•Z s )

Figure 1. Vertical profiles at 1000 UTC 12 November 1998 of C• 2 (a), ½0 (b) and /(0 (c) by using balloon borne measurements

(solid line) or climatological values of 9 and d9/dz (dashed line). The integrating period of the radar data is 60 min.

where 3' is the so-called mixing efficiency:

ep Ry

v - - - (7)

ek i - Rf

where ep is the dissipation rate of available potential energy.

C•, may be expressed

either

as a function

of ek [Gage

et al.,

1980; Hocking and Mu, 1997]'

=

(8)

or as a function of e0 (as we suggest)'

C•. '•2

=

-

r21/3"2/3

(9)

The fi term is a function of a priori unknown parameters. 0

and O0/Oz can be evaluated from additional measurements (balloon borne or lidar) and the mixing efficiency 3' may be

estimated indirectly. In the literature [McEvan, 1983; Tay-

a value of 0.15 according

to Alisse and Sidi [1999]

who found

3' to be in the range 0.1-0.2. However, the fi term appears

in formula (9) at the power 1/3 whereas at the power 1 in formula (8). Therefore e0 estimation is less dependent than

e• estimation on supplementary data.

The heat diffusivity Ko, defined as minus the heat flux di- vided by the temperature gradient, is obtained from eq. 5'

Ko -

eo

(10)

(0OlOz)

3. Data description and processing

The ST radar of the Observatoire de Haute-Provence (44 ø N, 6 ø E), is a pulsed VHF radar, operating at 72 MHz.

Radar measurements consist of wind velocities and reflec- tivity in the 2-17 km range. Three antenna beams are used,

one vertical and two obliques, 15 ø off zenith, in two orthogo- nal planes. The antenna is a network of 16 coaxial-collinear antennas. The radar has been calibrated using sky noise

maps [Dole et al., 1998]. The main characteristics

of the

instrument are summarized in Table 1.

(a) log • (K2/S )

10 20 30 40 50 60 70

27Nov98 Time (h) 29Nov98

0.05

•(•/s

Figure 2. (a) Hourly-vertical variations of half temperature

variance dissipation rate deduced from radar measurements and climatological values. The shadings are labeled in log scale next

to the right axis. (b) Mean value of Ko as a function of altitude,

obtained from an averaged value of the radar reflectivity (C• 2)

DOLE AND WILSON: ESTIMATION OF ATMOSPHERIC TURBULENT PARAMETERS 2627

Table 1. OHP Radar Parameters

Symbol Parameter Value f Radar frequency 72 MHz

X Wavelength 4 m

Pt Peak power 3.6 kW 1 Loss term 0.5

Ae Antenna area 1260 m 2

r Pulse length 20 •us

rp Coded pulse length 2.5 •us

Ar Range resolution 375 m F• Pulse repetition frequency 6.4 kHz r Altitude range 2-17 km

X Zenith angle 15 ø

T•p Interpulse period 156/•s

Nj•j, FFT points number 128

Neon Coherent integrations 512

Ncode Number of code elements 8

Ni,•o Incoherent integrations 3 B Bandwidth of the receiving filter 280 MHz Afd Doppler frequency resolution 0.1 Hz

Ava

Radial velocity resolution

0.2 ms

-x

Assuming the observed volume filled with homogeneous

isotropic scatterers, the signal-to-noise ratio (SNR) is ex-

pressed

as a function of radar volume reflectivity r/[Gage et

al., 1980]:

S 2 12ptA•cosx

(__•)2

• ----

OTr ckT,•

NconNcoa•rl

(11)

where c is the velocity of light, T,• is the noise temperature. The other quantities are listed in table 1.

Assuming that the Bragg scale is within the inertial isotropic

subrange

(eq. 1), C•

2 can be expressed

as a function of the

SNR:

ckTnA

•/a (r)2 S

C•2

= 37'212ptA•cosxN•onN•oa•

•rr •

(12)

where C• 2 is averaged over the observation volume. 4. Results

An example

of C•

2 profile,

estimated

from (12), is shown

in Figure la. The averaged refractive index structure con- stant is estimated assuming that the turbulent layer fills the observation volume during the integration time. This as- sumption is clearly not valid for our vertical and temporal

resolution

(360 m and one hour). The estimated C•

2 and

related e0 and Ko are therefore averaged quantities taking into account the time-space intermittency of the turbulent layers.

From the C• 2 estimates, the parameters e0 and Ko are evalu- ated by using either climatological values of 0 and O0/Oz or

in situ balloon measurements of pressure, temperature and humidity. Comparisons of the resulting profiles are shown in Figures lbc.

The discrepancy between the two estimates of e0 is large

(up to three orders of magnitude) in the troposphere, clearly showing that additional data of humidity are necessary (this is well known). However, in the stratosphere, both estima-

tions of e0 show a weak bias (less than a factor of two).

The reason lies in the weak dependence of the e0 estimation

on O0/Oz. Discrepancies are observed between both estima- tions of Ko (up to one order of magnitude) when the vertical

temperature gradient becomes very small.

On Figure 2a, e0 is displayed as a function of altitude and

time using climatological values of 0 and O0/Oz. We ob-

serve

a large time-altitude

variability,

e0 ranging

from 10

-7

to 3 x 10 -4 K2s -x.

The mean value of Ko as a function of altitude, obtained

from an averaged

value of the radar reflectivity

(C•

2) over

3 days, is also shown in Figure 2b. We observe rather

weak

values

of the turbulent

diffusivity

(2 x 10

-2 < Ko <

6 x 10

-2 m2s-X).

Our estimations

of e0, are of the same

or-

der as balloon measurements

[Alisse and Sidi, 1999]. The

few 10

-2 m2s

-x) agrees

fairly well with aircraft measure-

ments [Lilly et al., 1974] and indirect estimates using air-

Haynes, 1993]. However, our Ko estimate is roughly one

order of magnitude smaller than previously published esti-

mations from radar data [Fukao et al., 1994; Nastrom and

to the KE dissipation rate estimated from the widths of the Doppler spectra. One possible reason than may explain the discrepancy between both Ko estimations is that the spec-

tral width (second moment of the Doppler spectrum) does

not depend on the space-time intermittency. The inferred Ko characterizes the diffusivity within turbulent layers. On the other hand, the quantities inferred from backscattered

power

(C•

2 , e0 and Ko) represent

averaged

quantities

over

the observation volume taking into account the intermit- tency of the turbulent layers.

5. Conclusion

The presented method yields a robust estimation of the dissipation rate of temperature variance e0. Precise values

of 0 and O0/Oz are not necessary in the stratosphere and our

estimate is weakly dependent on not well known parameters, such as the mixing efficiency, unlike previous approaches. The turbulent diffusivity Ko is directly expressed from e0.

Our estimations of e0 and Ko are of the same order as in situ

measurements and considerably weaker than radar measure- ments using the bandwidth of the Doppler spectrum.

Acknowledgments. The authors are grateful to the staff

of the O.H.P. radar facility, G. Kaczmarek and G. Velghe. Thanks also to J-L. Conrad, C. Bourdier, C. Laqui and C. Blaize for their precious help in the development and good working order of the O.H.P radar. We also thank an anonymous reviewer for helpful suggestions and comments. This study was partly supported by the "Institut National des Sciences de l'Univers".

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(Received November 18, 1999; revised July 3, 2000; accepted July 7, 2000.)