vertical subsynoptic momentum flux in the atmosphere over ...€¦ · using the synoptic alpex...

Q. J . R. Meteorol. SOC. (1989), 115, pp. 1355-1372 551.551.8:551.515.11(4)

Vertical subsynoptic momentum flux in the atmosphere over central Europe

By YAPING SHAO* and MICHAEL HANTELt Meteorologisches Institut, Universitat Bonn, F. R. Germany

(Received 18 November 1987: revised 23 March 1989)

SUMMARY Using the synoptic ALPEX (Alpine Experiment) data, a diagnostic study of vertical SSMF (subsynoptic

momentum flux) is presented. The errors in the data are partially eliminated by the diagnostic model. It is found that the vertical SSMF has the order of magnitude of 1 N/m2 in the troposphere with its maximum at about 600 to 400 hPa. In the synoptic momentum budgets, SSMF is closely related to ageostrophic components. Systematic distributions and changes with time of the SSFM in a cyclogenesis process are found. Slant convective activity is a possible mechanism responsible for the intensive SSMF found in the cold area of the cyclone.

1. INTRODUCTION

Momentum fluxes are a quantitative description of interactions between different motions. In the case of global angular momentum balance, synoptic horizontal and vertical eddy momentum fluxes are found to be of fundamental importance (Oort and Peixoto 1983; Hantel and Hacker 1978). On a smaller scale, the SSMF (subsynoptic momentum flux), which is generated by mesoscale eddies, such as convective complexes, cloud clusters and internal gravity waves, embedded in synoptic systems, in turn influences the momentum budgets of such systems. The original incentive for investigating SSMF was the eventual need for its parametrization in numerical models on the synoptic scale, especially in mountainous areas. However, little is known about the interaction between the SSMF and synoptic systems, its magnitude, structure and development, as well as the responsible mechanisms. An important reason for the lack of understanding is that the SSMF is very difficult to measure.

In principle, there are two possible ways of determining the SSMF. The first is based on experimental meteorology, where the high-resolution wind components are directly determined (for instance, by airborne measurements), so that the SSMFcan be calculated using the eddy-correlation method. Of course, such experiments can be performed only in small regions and over short periods, so the studies are mostly concentrated on some special phenomenon (for example, lee waves). It therefore follows that understanding of the spatial structure and variation of the SSMF with time is limited.

Diagnostic modelling provides the second possibility. Wooldridge (1972), Godbole (1977) and more recently Miura (1987) have given examples of this approach, using a residual method (Riehl and Malkus 1958) in which it is supposed that the SSMF is a residual of the synoptic momentum budget. Unfortunately, the residual method does not take the errors of the synoptic data into account, so the results often cannot be trusted. Especially when dealing with the SSMF, errors of the resolved data in the residual can be as large as the signals and the residual method is then certainly not effective.

In this work an improved diagnostic model is introduced, the main ingredients of

* Present affiliation: Flinders Institute for Atmospheric and Marine Sciences, Bedford Park, 5042 South Australia. t Present affiliation: Institut fur Meteorologie und Geophysik der Universitat Wien, Hohe Warte 38, A-1 190 Wien, Austria.

1355

1356 Y. SHAO and M. HANTEL

which are an estimate of the magnitude of the error in synoptic data and a separation of this error from the signal. A similar method has been used in computing subsynoptic heat fluxes, which has proved effective (Emeis and Hantell984; Hantell987). From the diagnostic results, information on the spatial distribution and variation with time of SSMF has been obtained. Apart from statistical evaluation of signal and error, attempts have been made to investigate possible effects of the SSMF on the synoptic systems by presenting a case study associated with a cyclogenesis process.

2. DIAGNOSTIC MODEL

The starting point of the present diagnostic model is the vector equation of motion. In (A, 9,p) coordinates, the horizontal scalar equations can be written in the form

a t acosq, dA a all aP a cos Q, aA

+- -+--

- 0 (1) a u 1 auu I ~ U U C O S ~ , auw 1 a@ -+-- + - +--fu+---

(2) a u 1 auu iauucosq, auw cos cp a@ + - + fu + -- - 0 - a t acosq, aA a all aP a all

where A is longitude, r,~ is sin q,, q~ is latitude, p is pressure, a denotes the earth’s radius and f is the Coriolis parameter.

Averaging Eqs. (1) and (2), we obtain -

b, + au‘w’/ap + imbu = 0 -

b, + a d d / a p + imbu = 0 (3)

(4)

where

aii 1 aiiii ~ ~ U U C O S ~ , aUZ 1 aT +-- fU+-- a t acosq, a A a all aP a cos q, dA

a; 1 aUU ~ ~ U U C O S ~ , aUE cos ~1 a3 + ~ +fii + -- a t acosq, aA a as aP a all‘

Overbars denote the synoptically observable and objectively analysed fields, repre- sented through grid point data, and primes the subgrid deviations which remained unresolved in the data - set. In (3) and (4), the horizontal components of the SSMF in the form of (l/acos q)au’d/aA are neglected. imbu and imbu are the imbalances, which include all possible errors arising from the synoptic data and the neglected terms. Mathematically speaking imbu and imbu are two further unknowns. The separation of imbalances from the SSMF can be achieved through two steps.

(a) Vertical integration of imbalances: This integration provides the total imbalance in an atmospheric column. That is

b, = - + -- + -

b, =-+-- + -

I, = Jops imbudp = - b,dp - u)wIps lS I, = /ops imbudp = - loPs b,dp - u)wIps (6)

where ps is the surface pressure. The SSMF at the upper - boundary of the atmosphere is assumed to be zero. At the lower boundary, U ’ W ’ ~ , and U ‘ W ’ , , ~ are parametrized by

VERTICAL MOMENTUM FLUX 1357

mp, = gpCDUgo v(u;o + u&J where the air density p is set to be 1-29kg/m3 and the gravitational acceleration g = 9-81 m/s2. The surface geostrophic wind components Ugo and Ugo are approximated by the geostrophic wind at 850 hPa following Baumgartner and Mayer (1977). Values of the drag coefficient CD for various regions over central Europe (including the North Atlantic) have also been obtained from Baumgartner and Mayer. Over central Europe CD is 1-225 x

(b) Vertical partition of imbalances: The vertical profiles of imbalances are specified after I, and I, have been determined. Although there are many possible ways, only three of them merit consideration. (1): Partition according to the momentum of the geostrophic wind. This assumes that the imbalances have the same vertical distribution as the geostrophic wind and can be formulated as

to 2.205 X and over water CD is 0-625 X

imbudp = I , I” d(?ii + Ui)dp / lps v(Gi + Ui)dp I” P I P I 0

imbu dp = I, I” v(i; + E;) dp/IPs v(Z; + Ui) dp P I P I 0

(9)

(2): Partition according to the momentum of the synoptic wind. (3): Imbalances constant in the vertical.

In this study, the first is preferred. The other two are used for sensitivity studies. The imbalances cannot be expected to be perfectly separated from the SSMF signal by this method but the calculated results and sensitivity studies demonstrate that the influence of the imbalances upon the signal is indeed limited (see section 4).

After the imbalance in layerp2-pl has been determined, the calculation of the SSMF is straightforward. Integrating (3) and (4) from p = 0 we obtain

P m p / g = -(l/g) I (b, + imbu)dp

0

m p / g = -(l/g) 1’ (b, + imbu)dp. 0

Using (1 1) and (12), the SSMF at any level can be determined. Owing to the division of the above integrals by g, the SSMF has dimensions N/rn2.

3. DATA, AREA OF INVESTIGATION AND NUMERICAL MESH

The ALPEX data used in this study are the objective numerical analyses provided by Dr Reimer of the Free University in Berlin. Methods used in the numerical analysis are described in various studies (Emeis 1986; Hantel 1987). Only the most important points are repeated here.

(a) Data and area of investigation The ALPEX data from the experiment carried out from March to April 1982 in

central Europe, contain the following 4 meteorological elements: egeopo ten t i a l (and


pressure at the earth's surface); u-longitudinal wind component; u-meridional wind component; e v e r t i c a l wind component in p coordinates; w is determined with the quasigeostrophic omega equation in p coordinates (Haltiner and Williams 1980, p. 66). After modification, the ALPEX data obey the continuity equation in p coordinates exactly (Emeis 1985). The period of investigation, from OOGMT 1 March to OOGMT 7 March, 1982, is divided into 11 diagnostic intervals. Each diagnostic interval contains three synoptic times, so 00 GMT and 12 GMT on the 1st with OOGMT on the 2nd make up one diagnostic interval and 12 GMT, 00 GMT, 12 GMT another. The area under investigation is the same as that of Hantel (1987), which is limited by the following boundaries (Fig. 1): west: A = 12"W; east: A = 24"E; north: rp = 54.1"N ( q = sin rp = 0.87); south: rp = 34.8"N ( q = sin rp = 0.57).

(b ) Numerical mesh Figure 1 also shows the numerical mesh. The part of the atmosphere considered is

divided into 16 x 16 = 256 diagnostic locations, with the basic surfaces covering about (156 km)*. In the vertical, a column is divided into 5 layers: 0-200 hPa, 200-400 hPa, 400-600 hPa, 600-800 hPa, 800-p,. Thus the number of diagnostic boxes totals 1280, all of which contain the same mass, except the lowest ones. To describe the mass difference, we introduce y , which is defined by y(z, j ) = {p,(i,j) - 800}/200. For the data set used, y varies between 0.13 (in the Alps region) and 1.1. In the numerical evaluation, terms in the budget equations related to mass are modified by multiplying by y (see Shao and Hantel 1986).

Each diagnostic box consists of 3 x 3 x 4 = 36 elementary boxes (shown sche- matically in Fig. 1). In the objective numerical analysis the observed data are available at grid points or interpolated to these grid points.

4. SYNOPTIC MOMENTUM BUDGETS AND THE SSMF In the numerical evaluation, each individual term in (3) and (4) is to be averaged

over a diagnostic box and diagnostic time interval (see section 3). The following notation has been used:

UTM = t(aii/at)Ap/g UXM = t{(l/a cos y)aii*/an}Ap/g UYM = l{(l/a)duE cos q/dq}Ap/g UPM = t(aiiSj/ap)Ap/g

POU = t{(i/a cos q)ai$/aA}Ap/g UPE = t(auw/ap)Ap/g

AGU = t{ -fu -k + (l/a cos rp)a$/aA}Ap/g

~~~

IMBU = t(imbu)Ap/g - B , = t( -b,)Ap/g = UPE -I- IMBU

UMOM = M(i iw) /g - UEOE = M(u'w')/g

VTM = t(aE/at)Ap/g VXM = t{(l/a cos rp)aiiE/aA}Ap/g VYM = t{( l/a)aE2 cos rp/d q}Ap/g VPM = t(aUZ/ap)Ap/g AGV = tcfii + (COS rp/a)a$/aq}Ap/g

POV = I{(cos rp/a)a$/aq}Ap/g VPE = t(adw'/ap)Ap/g

IMBV = t(imbu)Ap/g - B , = I(-b,)Ap/g = VPE -I- IMBV

VMOM = M ( u w ) / g - VEOE = M(U'U')/g

where the operator I denotes the averaging over the diagnostic box and diagnostic interval, while the operator M denotes the averaging over the horizontal surface of the diagnostic box and over the diagnostic interval. A detailed description of the numerical evaluation technique has been given in Shao and Hantel (1986).

An example of numerical evaluation of the diagnosis is shown in Fig. 2. A few characteristics of momentum budgets deserve some brief discussion.

54.1

48.3

743.

6

9- 39

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N 34

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9 8 7 6

A- 12

w

3w

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15E

24 E

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7 8

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RY

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Figu

re 1

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he a

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pher

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er E

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ertic

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ns w

ith a

hor

izon

tal s

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ce a

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of

(156

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ch c

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ded

into

5 d

iagn

ostic

box

es e

ach

200h

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ick

(with

exc

eptio

n in

the

low

est l

ayer

, see

text

) yi

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ng a

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tem

of.1

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ch d

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c.

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7"fip . t 0 0 0 0 II 0 0 0

0 0 S W

0 0

;' I 0 0 0 0 0 s m

n d 4 / d

a I I I a :F0 W I

' 0 0 0 0 0 0 0 0 = v m 0 0 = r m

Dd' l /d

a . X

' 0 0 0 0 0 9 m


(1) The ageostrophic components are of most significance in the momentum budget, while the total variation of momentum is relatively small. The latter consists of four terms: take dZ/dt as example

Z(dZ/dt)Ap/g = VTM -k VXM -k W M -I- VPM.

Generally speaking, the first three terms are equally large, although they often have different signs, while VPM is much smaller. This results in the total momentum variation contributing little to the residual of' the synoptic momentum budgets. This can be recognized by studying the vertical profiles of these 4 terms (Fig. 2). Since B, = AGU and B, = AGV (compare AGU and - B,, AGV and - B, in Fig. 2) but on the other hand - B, = IMBU + UPE and - B , = IMBV + VPE, it follows that the imbalances can be identified with the errors in the ageostrophic components and the vertical divergence of the SSMF with the true physical ageostrophic components. Very similar results have been reported by Miura (1987).

This determination provides a justification for the more or less arbitrary imbalance partition described in section 3. Evidently, the vertical imbalance partition according to the momentum of the geostrophic wind is reasonable.

(2) The SSMF (UEOE, VEOE) are significantly larger than the synoptic momentum fluxes (UMOM, VMOM) as can be seen in Fig. 2. A statistical comparison is given in Table 1, where ,u is the linear mean, (J the standard deviation, I) the r.m.s. value. ,u of UEOE and VEOE have very small values which are determined by surface friction parametrizations given by (7) and (8). Because of the values obtained for I), it is reasonable to deduce the magnitude of the SSMF to be 1N/m2 and the absolute value of the array (UEOE, VEOE) to be 1.5 N/m2, although in individual cases the SSMF may be larger. In extreme cases, the values of UEOE and VEOE can reach 4 N/m2, this nearly matches a momentum flux of 4.7 N/m2 for the layer between 7 and 9 km during the Boulder storm on 11 January 1972 reported by Klemp and Lilly (1978). In a diagnostic study of cumulus activity in the Indian monsoon, Godbole (1977) reported a momentum flux of about 3N/m2 in the middle atmosphere (the profiles are similar to those of the SSMF in the present study), while Wooldridge (1972) reported momentum flux up to 6.2 N/m2 in a diagnostic study of the internal gravity waves over a mountain terrain. There seems to be agreement in the magnitude of the SSMF between these studies despite the differences in purposes, methods and data material.

(3) The imbalance is of the same order of magnitude as the vertical divergence of SSMF. Complete statistical evaluations of the three terms: budget, signal (the vertical divergence of SSMF) and imbalance, along with the vector statistics, are presented in Table 2. For instance, the vector r.m.s. mean of the budget IB( over the entire period is 1.99N/m2, that of signal 1st is 1.15N/m2 while that of the imbalance 111 is 1.56N/m2. The imbalance is larger than the signal. The overall r.m.s. imbalance, 111 = 1.56N/m2, to some extent arises from a relatively high mean component p(l1l) = 1.18 N/m2, while the mean signal p(lS1) = 0.04N/m2 is close to zero, thus one should compare the individual variance values a(lII), which are smaller than a(lSl) values in most cases.

In order to investigate the influence of vertical partitions of imbalances on the computed SSMF, sensitivity tests on the three different imbalance partitions described in section 3 have been carried out. Four examples of resulting profiles of IMBU specified by 1V.J and IV( together with the corresponding UEOE are shown in Fig. 3. It can be seen that in all cases the UEOE are qualitatively the same, although they differ in magnitude. It has been concluded that the relative uncertainty between the three partitions lies between 20% and 25% and the calculated values of the SSMF are qualitatively identical.

TAB

LE 1

. M

ASS

-AV

ER

AG

ED

C

OM

PON

ENTS

OF

VE

RT

ICA

L S

UB

SYN

OF-

TIC

(UE

OE

. V

EO

E) A

ND

SY

NO

~C

M

OM

ENTU

M

FLU

X (

UM

OM

. VM

OM

). ST

RA

TIF

IED

FOR

EA

CH

DA

TE

IN

VE

STIG

AT

ED

Stat

istic

al

Qua

ntity

co

mpo

nent

1/

12

2/00

2/

12

3/00

3/

12

4/00

4/

12

5/00

5/

12

6/00

6/

12

Mea

n

P -0

.03

-0.0

4 -0

.03

0.05

0.

18

0.00

0.00

0.09

0.12

0-

18

0.09

0.06

UEOE

U

0.65

0.

61

0.63

0.

72

0.84

0.

62

0.66

0.61

0.

76

0.69

0.

87

0.71

I

0.65

0-

61

0.63

0.

72

0.86

0.

62

0.66

0.61

0:7

8 0.

72

0.88

0.

71

P 0.

20

-0.3

7 -0

.56

-0.40

0.04

0.

05

-0.3

0 -0

-40

-0.3

8 -0

.24

-0.0

5 -0

.22

VEO

E U

0.91

1.

09

1.24

1.

36

1.11

1.

25

1.14

0.

95

1.05

0.

69

0.77

1.

10

* 0-

93

1.16

1.

36

1.42

1.

11

1.25

1-

18

1.03

1.

12

0.73

0.

78

1.12

P 0.

14

0-22

0-

02

0.02

-0

.02

0.06

0.

04

0.00

0-00

-0.0

1 0.

00

0.04

UMOM

U

0.31

0.

43

0-17

0.

23

0.58

0.

36

0.29

0.

28

0.17

0.

09

0-13

0.

32

* 0.

34

0.49

0.

17

0.23

0.

58

0.36

0.

29

0.28

0.

17

0.09

0.

13

0.32

P 0-09

0.04

0.

02

0.00

0.05

0.

03

0.02

-0

.01

-0-0

4 -0

.04

-0.0

4 0.

01

VM

OM

U

0.16

0-

15

0.17

0.

19

0.19

0.

14

0.12

0.

13

0.14

0.

10

0.10

0.

15

I 0.

18

0.16

0.

17

0-19

0.

20

0.14

0.

12

0.13

0.

14

0.10

0.

11

0.15

Uni

ts N

/m2.

p =

line

ar m

ean,

u =

stan

dard

dev

iatio

n, I =

root

mea

n sq

uare

TA

BL

E 2

. ST

AT

IST

ICS

OF

BUD

GET

B

= (

Bu,

BJ,

SIG

NA

L S

= (

UP

E,

VPE

) A

ND

IM

BA

LA

NC

ES

I =

(IM

BU, I

MB

V)

FOR

AL

L 1

1 D

AT

ES

INV

EST

IGA

TE

D

Stat

istic

al

Qua

ntity

co

mpo

nent

1/

12

2/00

2/

12

3/00

3/

12

4/00

4/

12

5/00

5/

12

6/00

6/

12

Mea

n

BU

BV

IBI

UPE

VPE

IS1

IMBU

IMB

V

III

-0.0

8 0.

75

0.75

0.44

0.

88

0.98

0-

45

1-15

1.

24

0.05

0.

54

0.55

0-02

0.

76

0.76

0.05

0.

93

0.94

0.02

0.

41

0.41

-0.46

0.55

0.

72

0.46

0.

69

0.83

0.29

0.

79

0.84

0.

54

1.27

1.

38

0-61

1 .s

o 1-

61

0.06

0.

51

0.52

0.01

1.

02

1.02

0.06

1.

14

1.14

0.22

0.

46

0.51

0.54

0.

83

0.99

0.

59

0.95

1.

12

-0.3

0 0.

78

0.83

0.70

1.

52

1.67

0.

76

1.71

1.

87

0.05

0.

55

0.56

0.00

1.

10

1.10

0.05

1.

23

1.23

0.24

0.

48

0.54

-0.6

9 0.

95

1.17

0.73

1.

06

1.29

-0.1

1 0

44

0-

85

0-93

1-

56

1.82

0.

94

1.77

2.

01

0.07

0.

61

0.61

0.01

1.

24

1.24

0.

07

1.38

1.

38

0.05

0.44

0.44

-0.9

4 0.

82

1.25

0.94

0.

94

1.33

-0.0

8 1.

06

1.06

1.33

1.

31

1.86

1.

33

1.68

2.

14

0.06

0.

68

0.68

0.02

1.

12

1.13

0.06

1.

31

1.32

0.02

0.

62

0.62

-1.3

5 0.

82

1.58

1.35

1.

03

1.67

-0.5

7 0.

91

1.07

1.70

1 -

22

2-09

1.

79

1.52

2.

35

0.06

0.

52

0.53

0.02

1.

14

1.14

0.06

1.

25

1.25

0.51

0.

60

0.79

-1.7

1 0.

50

1.78

1.79

0.

78

1.95

-1.2

8 0.

83

1.56

1.70

1.

34

2.16

2.12

1.

60

2.67

0.04

0.

62

0.62

0.00

1.11

1.

11

0.04

1.

27

1.27

1.24

0.

60

1.38

-

1.69

0.

51

1.77

2.10

0.

79

2.24

- 1.

62

0.90

1.

85

1.48

1.

12

1.86

2.

19

1.44

2.

62

0.02

0.

57

0.57

-0.0

1 0.

88

0.88

0.

03

1.05

1.

05

1.59

0.

50

1.67

-1.4

6 0.

45

1.53

2.16

0.

67

2.26

-0.9

1 0.

83

1.23

1.

24

1.03

1.

62

1.54

1.

33

2.03

0.01

0.66

0.66

-0.0

2 0.

84

0.84

0.

02

1.07

1.

07

0.90

0.

40

0.98

- 1.

22

0.54

1.

33

1.51

0.

67

1.65

-0.3

1 0.

71

0.78

0.

72

0.68

0.

99

0.78

0.

98

1.26

0.00

0.

56

0.56

-0.0

2 0.

62

0.62

0.02

0.

84

0.84

0.31

0.40

0.51

-0.7

0 0.

35

0.78

0.77

0.

53

0.93

0.13

1.

02

1.02

0.56

0.

89

1.06

0.58

1.

35

1.47

0.00

0.

76

0.76

-0.0

1 0.

71

0.71

0.01

1.

04

1.04

-0.1

2 0-

64

0.65

-0.5

5 0.

55

0.78

0.56

0.

84

1.01

-0.44

1.04

1.

13

1.03

1.

28

1.64

1.

19

1.59

1.

99

0.04

0.

61

0.61

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IMBU UEOE

(a, f u o : m 1 -1 eoo

i u o : T J 4

(b) ; 800

Figure 3. Sensitivity test with respect to imbalance partition. Imbalance (IMBU) partitions according to IVJ, (a) and IVI, (b), together with the corresponding SSMF (UEOE) in 4 adjacent diagnostic locations: 1: ( i = 10,

j = l l ) , 2: (i = 10, j = lo), 3: ( i = 11, j = 11) and 4: ( i = 11 , j = 10) on 2 March 12GMT are displayed.

Statistically, the imbalance and signal are independent. The correlations between budget B, signal S and imbalance I have been computed. It has been found that the correlation coefficients r ( B , I ) = -0.7 and r ( B , S ) A -0.7 and r ( S , I ) = 0 within significance limits (see Shao and Hantel 1986). This seems to indicate that I has been separated from S on the average.

(4) Both frictional drag and subgrid mountain drag have influences on the synoptic momentum budgets. As mentioned in the previous section, the frictional drag is parametrized by (7) and (8). Since the SSMF is much larger than the frictional drag, the uncertainty in this parametrization has little effect on the accuracy of the calculated SSMF. Sensitivity studies show that by changing the drag coefficient C, by a factor of two to three, no clear difference in the SSMF can be determined. More severe errors arise from the underestimation of the subgrid mountain drag, the force exerted on the atmosphere by small mountains. In the present study the subgrid mountain drag has not been considered, a simplification causing errors in the gradient force term in the budget equations. Davies and Phillips (1985) pointed out that the subgrid mountain drag on this scale varies on the order 5 N/m2 with a mean of 0.78N/m2. This is of the same order of magnitude as the SSMF. There is thus a large uncertainty in the results obtained in mountain areas. Unless the subgrid mountain drag is correctly parametrized, little can


be said about the SSMF. However, in areas where the subgrid mountain drag does not exist, the results are reliable.

5 . THE SSMF DURING A CYCLOGENESIS PROCESS-,

During the period of investigation there was one typical process of cyclogenesis in the region of the Mediterranean Sea. The subsynoptic energy fluxes during this process have been discussed by Emeis (1986) and Hantel(l987). The development of the cyclone from 4 March ~ ~ G M T to 6 March OOGMT is depicted in Fig. 4 and Fig. 5 , where in Fig. 5 the surface pressure field is shown together with the corresponding SSMF at 600 hPa. On the first date there was a flat trough moving south-east over France and the Alps. It

Figure 4. Geopotential of 200 hPa surface in gpdm and temperature at 200 hPa in "C for 4 March 1982,12 GMT to 6 March 0 0 ~ m (after Emeis 1985).


Figure 5. Horizontal distribution of the SSMF vector r, at 600hPa in a cyclogenesis process together with the surface pressure field. The solid lines are isobars in hPa. The symbol ‘p’ indicates the position of the diagnostic column discussed in Fig. 7. (a): on 4 March 12GMT; (b): on 5 March MGMT; (c) on 5 March 12GMT and

(d): on 6 March OOGMT.

developed quickly into a cyclone from ~ ~ G M T on the 4th to WGMT on the 5th over the Gulf of Genoa, with associated warm and cold fronts. Aloft, a trough shifted over France and Spain before becoming stationary over Corsica and Sardinia. Following the development of this low pressure system, there was a systematic change in the SSMF.

In Fig. 5 the SSMF vectors T = (UEOE, VEOE) at 600 hPa for four successive diagnostic intervals have been displayed together with the corresponding synoptic situations. In z coordinates, the direction of the SSMF vector indicates the downward transport of momentum in the direction to which the T is pointing. For instance, T pointing to the east means a downward momentum flux of westerly wind.

At ~ ~ G M T on the 4th, the low pressure system was in the early stage of its development and the surface front separated the two different regions of the SSMF. Strong downward transport of the northerly wind component is concentrated behind the cold front, while on the warm side of the front system, there seems to be no systematic momentum transport on the subsynoptic scale. Along the front the SSMF is especially weak. Remarkable changes are found at the next diagnostic time. Corresponding to the formation of the south-westerly-moving cyclone, the region with strong SSMF moved in the same direction with the centre located in the cold region behind the cyclone, where the directions of the SSMF vectors diverged from north to south. Therefore, in the area


immediately behind the cold front, the downward transport of north-west wind prevailed, while there was a downward flux of north-east wind further away from the centre of the cyclone. This situation became more pronounced at 12 GMT on the 5th when the intensity of the fluxes increased. The SSMF vectors pointed away from the low pressure centre, except in the region north of the cyclone. A similar situation can be found at 00 GMT on the 6th. The effect of this distribution was to increase the divergent wind components in the lower atmosphere, which intensified the development of the low pressure system. This was an opposite effect to that of surface friction, which would generate convergence in the lower atmosphere. During the whole period, the location of strong SSMF tended to coincide with the warm centre at 200 hPa. It was also noted that in the region under the influence of the high pressure system, the SSMF were much weaker.

The asymmetry of the distribution of the SSMF is clear. Systematic and intensive momentum fluxes were concentrated in the cold areas of the cyclone, while in the warm areas they remained weak and unsystematic. This distribution of the SSMF has synoptic relevance. The strong downward transport of the north-west wind component would increase the north-west wind component in the lower layers. More precisely it can be seen that the strengthening of the north wind would mainly be on the western side of the cyclone, while the increase of the west wind would be mainly on the southern side. This can clearly intensify the cyclonic circulation in the lower atmosphere and reduce anticyclonic circulation in the upper atmosphere.

In the present study, the SSMF reached its maximum at 600 hPa. This can be seen in Fig. 6, where the SSMF is displayed in components for four different levels. Here the characteristics of the distribution of the SSMF can be seen more clearly. In the vertical, the structure of the SSMF was similar in the three lower levels, while a different distribution prevailed at 200 hPa. However, the detailed differences in the three lower levels can be seen in the intensity of the SSMF and the areas covered by positive or negative SSMF.

The momentum budgets show different properties at different times during the cyclogenesis. Again the ageostrophic components were the dominating terms. In Fig. 7 the budget terms for three occasions are compared (the location of the diagnostic box is indicated in Figs. 5(a), (b) and (c)). At 12GMT on the 4th, both UEOE and VEOE were insignificant with UEOE being negative and VEOE positive between 800 and 200 hPa. Twelve hours later the intensity of the SSMF increased and the direction of the flux changed, while the synoptic wind changed from west to south-west. The intensity of the SSMF increased again in the next period. The maximum of UEOE reached more than 3N/m2 at 600hPa, while that of VEOE reached over 2.5N/m2. It is to be noted that the magnitude and profile of the imbalances changed little, demonstrating the reliability of the results.

The advection terms varied over a considerable range, and can be large when considered separately, for instance, UXM, VXM and VYM at WGMT on the 5th. Since they compensated each other, their total contribution remained limited. The dominating contribution from the ageostrophic components becomes clear by comparing them with -B , and - B , respectively. It was found that the ageostrophic components were the important part in the momentum budget at all three diagnostic times, while certain influences of the advection terms can be seen in the upper atmosphere between 400 and 200 hPa. These represent the most frequent cases, although there might be some instances in which the advection terms must not be omitted. The ageostrophic components, indicating the relationship between the pressure field and the wind field, are balanced by the vertical divergences of the SSMF. Little can be said about the causality between the two; however, large ageostrophic components do not necessarily imply strong accel-

1368

UEOE

Y. SHAO and M. HANTEL

VEOE

Figure 6. UEOE and VEOE in 10-'N/mZ at 800, 600, 400 and 200mb on 5 March 12GMT together with the surface front system.


eration of the synoptic wind directly, but momentum redistribution in the vertical direction via the subsynoptic eddies.

While in the region influenced by the high pressure system the SSMF remained relatively weak, the deduced SSMF in the cyclone was quite large, corresponding to fluctuations of several m s-' in horizontal and vertical velocities with a high correlation between them. Furthermore, large SSMF extended up to 400 hPa and covered a large area behind the cold front. An inevitable question is, what might be the possible mechanism responsible? One is usually satisfied with a diagnostic model, that shows the SSMF can be determined and some characteristics can be described without having to discretize the physical processes involved; therefore no dynamic statements concerning the mechanism responsible for the SSMF are made. Lilly (1972) pointed out that tilted stationary internal gravity waves are capable of transporting momentum in the vertical. Moncrieff (1986) listed a variety of possible mechanisms, including convective activity on the cumulus scale and slant convection.

One mechanism, not yet quantitatively evaluated, has recently been suggested by Kuettner et al. (1987). It concerns gravity wave systems over convectively active boundary layers. The pertinent vertical subscale momentum flux can be as large as 5 Pa (Kuettner 1989, personal communication).

Organized slant convection on a small scale in the cold region of the Genoa cyclone is a possible mechanism responsible for the large SSMF. After the cold front passage the thermal structure of the atmosphere eventually became unstable to a certain height, which enabled the active development of convection. Penetrating convective clouds can often be seen well organized behind ceM fronts on satellite images. Most probably the convective cells were slanted because of the wind shear. These organized, slanting convection cells could transport momentum in the vertical direction very effectively. In the area influenced by the high pressure system, where convective activities had not been possible, the SSMF remained insignificant. Since 400 hPa was roughly the limit convection reached, this hypothesis seems also to explain why the distribution patterns of SSMF at 200 hPa were different from those at the lower levels.

6. CONCLUSIONS

In this study the inaccuracy of synoptic data has been separated by computing the vertical mean value of imbalance of a diagnostic column and specifying its vertical variation. It has been found necessary in diagnostic models of momentum to treat the inaccuracy of synoptic data cautiously, otherwise the diagnostic results can become erroneous, because the imbalances are as large as the vertical divergences of the SSMF. The vertical partition of imbalances in this study is based on an examination of the budget terms; while not being objective, this improves the results although the errors remaining in the SSMF can be as large as 25%, or more.

In comparison with the vertical synoptic momentum flux UE/g, the SSMF is an order of magnitude larger, so that the importance of the SSMF in synoptic momentum budgets must not be ignored. The magnitude of the SSMF has been found to be about 1 N/m2, which is in agreement with some other experimental and diagnostic studies. In the synoptic momentum budget the convergence of the SSMF is mainly determined by ageostrophic components, while the total influence of advection remains small and limited in the upper atmosphere.

One source of error, implicit in a recent analysis of Sardeshmukh and Hoskins (1987), cannot be ruled out by our residual technique. Suppose the analysed omega field carries an error of, say, 30%. This would influence the vertical profiles of UPM, VPM but


UEOE/Pa UEOE I P a

BOO

4/12

u/ns-l m UXfl/Pa

i UYM/Pa

m UPfl/Pa

I I UXM/Pa

a 2 . ! I ,

UYM/Pa -u - 2 0 2 9

I 1 UPfl/Pa

1 . - 2 . 0 . 2 4 c .

Ulfl /Pn m AGU/Pa

m I flW/ Pa

m

5/12 Figure 7. Comparison of the u , (a), and u, (b), budget terms at three diagnostic times from 4 March 1 2 ~ ~

to 5 March 12GMT for the diagnostic column (i = 12, j = 5) (see also Fig. 5).

would not show up in the imbalance. It would nevertheless contaminate the ageostrophic components AGU, AGV, the budget components, the signal, and eventually 7, the SSMF vector.

This type of error is, however, of less consequence than might seem. Firstly, part of the erroneous ageostrophic component is accounted for in the imbalance profile (9), (lo), by the proportionality to the absolute geostrophic wind speed, assuming that the ageostrophic wind (and thus its error) tends to be proportional to the geostrophic wind. Secondly, this error type can hardly explain the large magnitude of our results. For example, from Figs. 2, 7 one can estimate that the profiles of UPM, VPM would be off by at most 0.1 Pa resulting in a maximum error of SSMF of about 0.5 Pa in the level 500 hPa. While this is clearly serious it does not change the principal results of this study.


I . uo;m 000

L A VXM/Pa

P \ ..:- 800

VYM/Pa

\ L 800

L I A VPM/Pa

C y 0 ; r / . . I llo:r/ \ : llo:m/ BOO ;uo;m

800 V T M l P a

*BOO A G V l P a

\

BOO I nsvi p a

. * 800

L I A VPM/Pa

C y 0 ; r / . . I llo:r/ 800

V T M l P a

*BOO A G V l P a

% 1100 4 BOO ;uo;m \

BOO

I nsvi p a

; . qo;rl * 800

4/12

L v Tf

I A

5/00

Figure 7 (continued).

During a cyclogenesis event, the SSMF shows systematic changes in its distribution. Downward transport of north wind momentum by subsynoptic activities is mainly concentrated in the eastern part, while west wind momentum is mainly in the southern part of the cyclone. This intensifies the cyclonic circulation in the lower atmosphere. In contrast, under the influence of high pressure systems, SSMF is small and its distribution is less regular. In the lower atmosphere, the SSMF seems to increase the divergent wind component of a cyclone. Opposed to surface friction, this effect is favourable for the development or maintenance of the Genoa cyclone. As one of the disadvantages of a diagnostic study, physical processes responsible for the SSMF remained unexplained. One possible mechanism for the large SSMF in the cold region of the Genoa cyclone is the organized slant convection.


ACKNOWLEDGEMENTS

This study benefitted from valuable discussions with Dr S. Emeis and other colleagues in our institute. Dr E. Reimer provided the objectively analysed data set. Comments by Prof. P. Schwerdtfeger on earlier versions of the manuscript are acknowledged. We are also grateful to the anonymous reviewers, who made helpful suggestions.

Baumgartner, A. and Mayer, H.

Davies, H. C. and Phillips, P. D.

Emeis, S .

Emeis, S. and Hantel, M.

Godbole, R. V.

Haltiner, G. J . and Williams, R. T.

Hantel, M.

Hantel, M. and Hacker, J . M.

Klemp, J . B. and Lilly, D. K.

Kuettner, J . P., Hildebrand, P. A. and Clark, T. L.

Lilly, D. K.

Miura, Y.

Moncrieff. M. W.

Oort, A. H. and Peix6t0, J . P.

Riehl, H. and Malkus, J . S .

Sardeshmukh, P. D. and Hoskins B. J .

Shao, Y. and Hantel, M.

Wooldridge, G. L.

1977

1985

1985

1986

1984

1977

1980

1987

1978

1978

1987

1972

1987

1986

1983

1958

1987

1986

1972

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vertical subsynoptic momentum flux in the atmosphere over ...€¦ · using the synoptic alpex...

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