- Email: [email protected]
Dissipation rates of turbulent kinetic energy and temperature and humidity variances over different surfaces
Atmospheric Research 50 Ž1999. 37–51
Dissipation rates of turbulent kinetic energy and temperature and humidity variances over different surfaces Hong-sheng Zhang b
a,)
, Soon-Ung Park
b
a Department of Geophysics, Peking UniÕersity, Beijing, 100871, China Department of Atmospheric Sciences, Seoul National UniÕersity, Seoul, 151-742, South Korea
Received 30 April 1998; accepted 6 September 1998
Abstract Dissipation rates of turbulent kinetic energy, and temperature and humidity variances have been analyzed using turbulent data collected from the Gobi desert, grassland, and suburban and urban sites that have different physical conditions. Instrumentation was installed at heights of 4.9 m, 3.45 m, 75 m and 47 m over the Gobi desert, grassland, and suburban and urban sites, respectively. The dimensionless dissipation rates of turbulent w´ , kinetic energy, temperature variance w N , and humidity variance wg are found to be more than 20% less than that required to balance the production of energy by wind shear and the variances by temperature and humidity gradients. The deficits appear to increase with the increase of absolute stability parameter. Combining the results from previous and present studies, the non-dimensional dissipation rates of turbulent kinetic energy, and temperature and humidity variances are modified by using the stability parameter. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Roughness length; Observational methods; Dissipation rate; Temperature variance; Humidity variance
1. Introduction The exchanges of momentum, heat, and moisture between atmosphere and land surface that determine the formation and evolution of planetary boundary layer ŽPBL. ) Corresponding author. Department of Atmospheric Sciences, Seoul National University, Seoul, 151-742, South Korea. Tel.: q82-2-880-6715; fax: q82-2-880-6715 or q82-2-883-4972; e-mail: [email protected]
0169-8095r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 8 0 9 5 Ž 9 8 . 0 0 0 8 9 - 1
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
38
are affected by the various scales of atmospheric processes. Therefore, information on the interaction between atmosphere and land surface is useful in enhancing the understanding of climate and general circulation as well as in improving their modeling. Land-surface processes mainly control the transformation and exchange of energy and substances between the atmosphere and land surface. Turbulent kinetic energy is one of the most important variables in land-surface processes because it is a measure of the intensity of turbulence. It is directly related to the transport of momentum, heat, and moisture through the boundary layer. Some important dimensionless parameters and scalings are also based on turbulent kinetic energy budget equation. Dissipation of the turbulent flow of heat is characterized by turbulent kinetic energy dissipation rate ´ and temperature variance dissipation rate N in the turbulent kinetic energy budget equation, but it is very difficult to measure ´ and N directly ŽStull, 1988.. Kaimal et al. Ž1972. proposed the relationship between ´ and stability parameter zrL using data measured by the hot-wire anemometer. Using the Kansas data ŽKaimal and Wyngaard, 1990., Wyngaard and Cote Ž1971. fitted the dissipation rates as:
w´ s Ž 1 q b < zrL < 2r3 .
3r2
w´ s Ž 1 q 2.5 < zrL < 5r3 .
for zrL - 0, and
3r2
for zrL ) 0,
Ž 1. Ž 2.
and the relationship between w N and stability parameter zrL was written ŽKaimal et al., 1972. as:
w N s 0.74 Ž 1 y 9 zrL .
y1 r2
for zrL - 0, and
w N s 0.74 q 4.7zrL for zrL ) 0.
Ž 3. Ž 4.
b in Eq. Ž1. ranged 0.5 to 0.75 ŽWyngaard and Cote, 1971; Kaimal et al., 1972; Caughey and Wygnaard, 1979.. Hogstrom Ž1990. examined the normalized dissipation rate w´ in terms of turbulent kinetic energy budget and the second order moment budgets formed by the three velocity components and temperature based on an experiment on a grassland of Lovsta, South Sweden. Frenzen and Vogel Ž1992. conducted a set of experiment and suggested a constant dissipation deficit relation in the normalized dissipation rate w´ . Roth and Oke Ž1993. showed the relationship between the normalized rates Ž w´ , w N and wg . and stability zrL using the spectral curves of velocity, temperature, and humidity. The present paper will report the results on the functional relationship between dimensionless dissipation rate of turbulent kinetic energy ŽTKE., temperature variance ŽTV., and humidity variance ŽHV. and stability zrL using a series of observational data taken over the Gobi desert, grassland, and suburban and urban sites.
2. Theory In the atmospheric boundary layer, if we choose a coordinate system aligned with the mean wind with the assumptions of horizontal homogeneity, steady flow, and negligible
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
39
subsidence, then a special form of TKE equation can be written ŽHogstrom, 1990.: g
u
Ž wXu X . yuX wX A
Ew X e
EU Ez
y
B
Ez
y
C
1 E Ž wX pX .
Ez
r
y´ s0,
Ž 5.
E
D
X
where p is the fluctuating pressure, r the air density, g the acceleration of gravity, u the potential temperature, e TKE, ´ the dissipation rate of TKE, and z the observational height. The terms from ŽA. to ŽE. in Eq. Ž5. represent buoyancy production, shear production, turbulence transport, pressure transport, and dissipation, respectively. Normalizing each term by the rate of TKE production in neutral conditions, u 3) rk z, yields
w´ s wm y zrL q w T q wp ,
Ž 6.
where w´ Žs k z ´ru 3) . is the normalized dissipation rate of TKE, L
ž
sy
u 3)
k Ž g r u . w Xu X
/ the
kZ EU u) E z
. the normalized wind profile function, Monin–Obukhov length scaling, wmŽs X eX E w . the normalized divergence of TKE, and w P s yk Z E wX pX the normalized w T Žs yk Z u 3) E z
u 3) E z
divergence of pressure transport. Because the turbulence data were measured at one level over different sites and because of the inherent difficulties in obtaining pressure fluctuations, both the normalized divergence of turbulent transport w T and pressure transport w P will be discussed simultaneously. Eq. Ž6. can be written as:
w´ s wm y zrL q w D ,
Ž 7.
where w D s w T q w P . Similarly, the non-dimensional dissipation rates of TV and HV are written as:
w N s w h q w Du ,
Ž 8.
where w h and w Du are the normalized potential temperature gradient and the divergence term of vertical turbulent flux of the temperature fluctuation, respectively, and
wg s wq q w D q ,
Ž 9.
where wq and w D q are the normalized humidity gradient and the divergence term of vertical turbulent flux of the humidity fluctuation, respectively. According to the Kolmogorov theory for the inertial subrange, the spectral density S of the velocity components is given by ŽKaimal et al., 1972; Panofsky and Dutton, 1984.: nSu ,Õ ,w Ž n . ru 2) s A1,2 Ž 2pk .
y2 r3
w´2r3 f y2r3 ,
Ž 10 .
where k is the von-Karman constant, n the frequency, u ) the friction velocity, f Žs nzrU . the non-dimensional frequency, U the mean wind speed, and A1,2 is a universal constant for the inertial subrange ŽKolmogorov constant.. In the present study, A1 Žfor u component. and A 2 Žfor Õ and w components. are 0.50 and 0.68, respectively ŽRoth and Oke, 1993..
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
40
Similarly, the one-dimensional spectra of temperature and humidity can be represented in the forms: nSu Ž n . ru)2 s Bu Ž 2pk .
y2 r3
w N w´y1r3 f y2r3 , and
Ž 11 .
rq)2 s Bq
y2 r3
wg w´y1r3 f y2r3 ,
Ž 12 .
nS q Ž n .
Ž 2pk .
where Bu and Bq are universal constants for the inertial subrange. The value of Bu and Bq are not well established. They are usually taken to be constants of 0.78 to 0.8 for both temperature and humidity ŽPanofsky and Dutton, 1984; Roth and Oke, 1993.. In the present study, Bu s Bq s 0.78. In the present study, the dissipation measurements were not made directly over all observational sites. Therefore, the normalized dissipation rates of TKE, TV and HV will be estimated using the velocity, temperature, and humidity spectral densities Su,Õ,w , Su Ž n., and S q Ž n. in the inertial subrange, respectively. From Eqs. Ž10. – Ž12., the normalized dissipation rates are
w´ s Ž 2pk . f w N s Ž 2pk . wg s Ž 2pk .
ž
nSu ,Õ ,w Ž n .
2r3
2r3
A1,2 u 2) f 2r3 f 2r3
ž ž
3r2
/
nSu Ž n . Bu u)2 nS q Ž n . Bq q)2
,
/ /
Ž 13 . w´1r3 ,
Ž 14 .
w´1r3 .
Ž 15 .
3. Experiment The detailed experimental sites, instrumentation, and data processing systems over the Gobi desert, grassland, and suburban and urban sites are described in detail in other reports ŽZhang et al., 1991; Wang and Mitsuta, 1992; Pan et al., 1996; Zhang and Chen, 1998.. For convenience, a brief summary of the experiments is given here. The data over the flat uniform Gobi desert were obtained during August 1992. The site is located in the northwestern part of Heihe river basin at 100806X E, 39809X N, over the dry area in Gan Su Province that is located to the northwestern part of China, approximately 20 km to the northwest of the foot of Qi Lian Mountain and about 1.2 km from the edge of the oasis lying along the north to northeast sector. A small farmland plot with a few trees is situated about 1.5 km to the northwest. The terrain around the site is flat arid Gobi desert consisting of sand grains and pebbles ŽMitsuta, 1988; Wang and Mitsuta, 1992.. The surface roughness is about 1.2 = 10y3 m ŽChen et al., 1991.. The experiment for the grassland site was conducted during August 1993. The site is located at the Bai Yin Xi Le livestock farm to the south of Xin Lin Hot City in the middle of Inner Mongolia steppe and covers the area extending from 43826X N to 44808X N and 116804X N to 117805X E with the mean elevation of 1187 m. The Xi Lin river flows from southwest to northwest. The surrounding area of the site is flat grass land. The surface roughness is about 2.8 = 10y2 m ŽPan et al., 1996..
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
41
The measurement for the suburban site was made on September 1994 in a suburban area of Fangshan in Beijing, China. The site is located to the 37 km southwest of Beijing city center. Yangshan Mountain is located at 10 km southwest of the tower. There are buildings lower than 15 m high standing to the north and northeast of the observational tower and farm land in the flat terrain in other directions. The surface roughness length is 0.37 m within the range of the wind direction in which the data were analyzed ŽZhang and Chen, 1998. The observational program for the urban site was conducted in Beijing, China with a 325-m meteorological tower. The tower is located to the 5 km north of Tian An Men Square. New building complexes with heights of 30–40 m are located to 1 km northeast, southeast, south and southwest of the tower. Single-story houses and markets are within 1 km. The surface roughness is about 1 m within the range of the wind direction in which the data were used ŽZhang et al., 1991.. Turbulent data were measured at the four sites with the same instrumentation, but the observational periods and measurement heights are different. The three-dimensional sonic anemometer–thermometer with the sound path length of 20 cm produced by Kaiji Denki of Japan Žmodel DAT-300 and sensor model TR-61C., the fast-response platinum wire thermometer Ža diameter of 20 mm and the total length of 48 cm platinum wire with the total resistance of 150 V ., the Lyman-a hygrometer Žmodel ERC-BL, made by Table 1 List of runs over the four sites Site
Date
Gobi desert Aug. 6–17, 1992
Grassland
Suburban
Urban
Instrumentation Variable Sonic anemometer Platinum thermometer Lyman-a hygrometer
Aug. 13–19, Sonic 1993 anemometer Platinum thermometer Lyman-a hygrometer Sept. 2–14, 1994
May 13–27, 1993
Sonic anemometer Platinum thermometer Lyman-a hygrometer Sonic anemometer Platinum thermometer
X
X
Observational Roughness height z Žm. z 0 Žm.
z r z0
Frequency ŽHz.
X
u, Õ,w
uX q
4.9
0.0012
4083.3 16
3.45
0.028
123.2 16
0.37
202.7 16
X
X
X
X
u, Õ,w
uX q
X
X
X
X
u, Õ,w X
u
q
75.0
X
X
X
X
u, Õ,w
uX
47.0
;1
47.0 16
42
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
ERC of America, and ror AIR-LA-1, made by AIR of America. were used for this study. All instruments have been checked in a laboratory before and after field experiments. Turbulent data recording and processing were carried out on a PCr486 with the same data acquisition system at each site. Signals were sampled at a rate of 160 Hz; 10 points were averaged to produce 16 Hz data which was recorded into the computer. The record periods were about 45–55 min; only 45-min record periods were used for this study. Recorded data were rejected according to the following criteria: the runs with more than 608 of horizontal wind direction from the coordinate system of sonic anemometer, the slope angle between the vertical and horizontal component winds ) 58, mean wind speed - 0.3 m sy1 , the friction velocity u ) - 0.02 m sy1 , the heat flux - 0.002 K m sy1 , the runs of day–night transition time and unreasonable data due to measurement errors. The characteristics of spectral analysis of wind components, temperature, and humidity are basically same as the standard case ŽHaugen, 1973; Panofsky and Dutton, 1984.. The spectra of the selected runs show strong similarities in shape with Eqs. Ž10. – Ž12. in the high frequency region. The normalized dissipation rates of TKE, TV, and HV were calculated using Eqs. Ž13. – Ž15. with the spectral densities determined by the average
Fig. 1. Non-dimensional dissipation rate of TKE Ž w´ . calculated by using w-component of spectral density against stability z r L over Ža. the Gobi desert, Žb. grassland, and Žc. suburban and Žd. urban sites. The dashed line is from Eqs. Ž1. and Ž2. with b s 0.5. The solid line is from Eq. Ž16. using different coefficients of a and b in Table 2.
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
43
Table 2 List of coefficients in Eq. Ž16. over the four sites Site
Observational height z Žm.
Roughness z 0 Žm.
z r z0
z r L-y0.1 a b
Gobi desert Grassland Suburban Urban
4.9 3.45 75.0 47.0
0.0012 0.028 0.37 ;1
4083.3 123.2 202.7 47.0
y0.19 y0.19 y0.19 y0.19
0.56 0.56 0.76 0.37
0.1- z r L- 0 a b
z r L) 0 a b
y0.42 y0.42 y0.42 y0.42
y0.42 y0.42 y0.42 y0.42
y1.74 y1.74 y1.54 y1.93
y2.57 y3.53 y3.21 y1.00
taken in the inertial subrange spectral region. In the present study, the range of 1.5 - n - 3.5 were used subjectively. A summary of each run is given in Table 1.
4. The normalized TKE dissipation rate w ´ The normalized dissipation rate of TKE Ž w´ . was evaluated from Eq. Ž13. from w-component spectra in the inertial subrange over the four sites. A plot of w´ vs. stability zrL is shown in Fig. 1 over the four sites. The dashed line represents the
Fig. 2. The same as in Fig. 1 except for using u-component of spectral density.
44
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
Kansas data from Eq. Ž1. with b of 0.5 while the solid line is obtained from Eq. Ž16.. The coefficients a and b in Eq. Ž16. appear to depend on roughness length and observational height, but it is difficult to find the functional form Žsee Table 2..
ww s wm y zrL q a q b Ž zrL . .
Ž 16 .
The flux–gradient relationships are given as ŽDyer, 1974.:
wm s Ž 1 y a zrL . wm s 1 y b zrL
y1 r4
for zrL - 0, and for zrL ) 0,
Ž 17 .
where a and b are constants. In general, the range of a is from 15 to 28 and b from 4 to 7 ŽZhang et al., 1993.. A sensitivity analysis using Eq. Ž17. indicated that the different value of constants resulted in less than 20% error for the turbulent fluxes. In the present study, we have used a s 28 and b s 5. The present results in Fig. 1 differ markedly from those of Kansas but are similar with the results obtained from studies of St. Louis by Clarke and a suburban area of Vancouver by Roth ŽRoth and Oke, 1993.. The trends are similar to the Eq. Ž1. with the increase of the absolute value of stability zrL. Figs. 2 and 3 show the value of w´ obtained from the horizontal wind component of u and Õ, respectively. They are similar
Fig. 3. The same as in Fig. 1 except for using Õ-component of spectral density.
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
45
to the results for the w-component with some scatters. There are several possible different mechanisms that could produce the differences between the result of Kaimal and the present analysis as seen in Fig. 1. Roth and Oke Ž1993. concluded that under near-neutral conditions, lower dissipation values are associated with lower value of wm . But the result of the flux–gradient relationships studied over the desert site shows wm s 1 during the near-neutral condition, implying that lower dissipation values are not due to the lower value of wm ŽZhang et al., 1993.. Fig. 4 shows the variations of different components in TKE budget Žsee Eq. Ž7.. as a function of stability zrL over the four sites. It is seen that under weakly unstable to the near-neutral conditions, the sum of turbulent transport and pressure transport terms w D is small. The local production of TKE is balanced by local dissipation. As the absolute value of zrL increases under unstable conditions, the heat production term and the
Fig. 4. The components of TKE budget as a function of stability z r L over Ža. the Gobi desert, Žb. grassland, and Žc. suburban and Žd. urban sites.
46
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
Fig. 5. Non-dimensional dissipation rate of TV Ž w N . calculated by using temperature spectral density against stability z r L over Ža. the Gobi desert, Žb. grassland, and Žc. suburban and Žd. urban sites. The dashed line is from Eqs. Ž3. and Ž4., the solid line from Eqs. Ž18. and Ž19..
dissipation rate term Ž w´ . increase while the mechanical production term Ž wm . decreases. Because the local energy production is less than the local dissipation in the energy balance, the effect of the turbulent flux divergence should be larger to compensate for the local energy production. Another important term in the energy balance in Eq. Ž7. is the pressure transport term. Neglecting this divergence term would result in a noticeable error in the calculation of dissipation rate under unstable conditions ŽWyngaard and Cote, 1971..
5. The non-dimensional TV dissipation rates w N The non-dimensional dissipation rate of TV Ž w N . over the four sites are compared with the result of the Kansas experiment. The dashed line in Fig. 5 is from Eqs. Ž3. and Ž4., and the solid curve from the present study in the functional form of stability as:
wn s w h y 0.19 y 0.057 < zrL < 3r5 for zrL - 0, and
Ž 18 .
w N s w h y w 0.19 q 4.3 < zrL < x for zrL ) 0,
Ž 19 .
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
47
with the temperature gradient as ŽZhang et al., 1993.:
w h s Ž 1 y 20 zrL . w h s Ž 1 q 5 zrL .
y1 r2
for zrL - 0, and for zrL ) 0.
Ž 20 .
The presently derived curve follows the curve obtained from the Kansas data, but the value of w N is usually smaller than that of Kaimal, especially over the desert site. This may be caused by an underestimate of w´ . The components of TV budget as a function of zrL over the four sites are plotted in Fig. 6. Because there is no pressure transport term in the TV budget equation, the budget is much simpler than that of TKE. The local production w h and dissipation rate w N of TV are basically in balance with the change of stability over the suburban and urban sites. In the unstable range, the present results also agree well with those from Roth and Oke Ž1993. for his suburban site. Because the experimental data are widely scattered in the stable condition, it is hard to find a suitable dissipation rate curve with zrL. However, Eq. Ž2. is well satisfied over the urban site ŽFig. 5..
Fig. 6. The components of TV budget as a function of stability z r L over Ža. the Gobi desert, Žb. grassland, and Žc. suburban and Žd. urban sites.
48
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
6. The non-dimensional HV dissipation rates w g The non-dimensional dissipation rate of HV Ž wg . over the desert, grassland, and suburban sites is compared with the result of Kansas temperature data. The dashed curve in Fig. 7 is obtained from Eqs. Ž3. and Ž4. using Kansas temperature data while the solid curve is obtained from the present study in the functional form of stability as:
wg s w h y 0.19 y 0.057 < zrL < 3r5 for zrL - 0, and
Ž 21 .
wg s w h y w 0.19 q 4.3 < zrL < x for zrL ) 0,
Ž 22 .
The trend of the two curves is similar to each other, especially for the unstable stratification. Comparison of dissipation rate for TV and that for HV, shows that the characteristics of the humidity fluctuations are quite similar to those of the temperature fluctuations. However, humidity fluctuations are more scattered, and the wg value is higher than w N value over the desert site. The components of HV budget as a function of zrL over the desert, grassland, and suburban sites are plotted in Fig. 8. The budget components of HV are quite similar to those of temperature ŽFig. 6. in all range of stability over the grassland and suburban sites. However, over the desert site those are quite similar each other for the stable
Fig. 7. Non-dimensional dissipation rate of HV Ž wg . calculated by using humidity spectra density against stability z r L over Ža. the Gobi desert, Žb. grassland and Žc. suburban sites. The dashed line is from Eqs. Ž3. and Ž4., the solid line from Eqs. Ž21. and Ž22..
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
49
Fig. 8. The components of HV budget as a function of stability z r L over the Ža. Gobi desert, Žb. grassland, and Žc. suburban sites.
condition but for the unstable case the absolute value of the normalized dissipation rate of HV is larger than that of temperature. Therefore, the divergence term w Dg should be large to balance with wg . This is presumably due to strong evaporation and larger dissipation rate of HV over the desert site during the observation period and due to several assumptions, such as homogeneity, steady flow and negligible subsidence made to derive Eq. Ž9. with the exclusion of the advection of humidity variance. The result ŽFig. 8a. suggests that the moisture flux in a dry region such as the desert is largely dependent on the transport of the horizontal moisture flux.
7. Summary and conclusions The dissipation rates of TKE, and TV and HV using turbulent data collected from the Gobi desert, grassland, and suburban and urban sites are examined. The instrumentation was installed at heights of 4.9 m, 3.45 m, 75 m, and 47 m over the Gobi desert, grassland, and suburban and urban sites, respectively. The dimensionless dissipation
50
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
Fig. 9. Non-dimensional dissipation rate of TKE Ž w´ . calculated by using the w-component spectra density against stability z r L over an urban site in winter of 1993. The dashed line is from Eqs. Ž1. and Ž2. with b s 0.5. The solid line from Eq. Ž16. with the different coefficients of a and b in Table 2.
rates of TKE Ž w´ ., TV Ž w N ., and HV Ž wg . are found to be smaller by 20% than that necessary to balance the production of energy by the observed wind shear, temperature, and humidity gradients. The deficit appears to increase with an increase in the absolute stability parameter. The present results differ markedly from those of the Kansas experiment but are similar to the results obtained by Roth and Oke Ž1993.. The net effect of turbulent transport and pressure transport is to remove energy from all stability ranges in proportion to the absolute value of zrL but not at a constant rate ŽFrenzen and Vogel, 1992.. Combining the results of previous and present studies, the non-dimensional dissipation rates of TKE, TV, and HV are modified as a function of stability with some empirical constants. The empirical coefficients in TKE, TV, and HV equations depend largely upon roughness length and observational height. Fig. 9 shows the non-dimensional dissipation rate of TKE calculated using the w-component spectral density against stability zrL over the same urban site and at the same observational height Ž47 m., but the experimental date are different. It was taken in winter for the period from December 1993 to February 1994. The result in Fig. 9 shows the same pattern in Fig. 1. The dissipation rate of TKE calculated with the data obtained in winter agrees well with the empirical curve Žsolid line. in Eq. Ž16., suggesting that the presently derived empirical equation of TKE dissipation rate can be used more usefully for the urban site. Acknowledgements This work was supported by the National Natural Science Foundation of China and the Korea Science and Engineering Foundation. References Caughey, S.J., Wygnaard, J.C., 1979. The turbulent kinetic energy budget in convective conditions. Q. J. R. Meteorol. Soc. 105, 231–239.
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
51
Chen, J.Y., Wang, J.M., Mitsuta, Y., 1991. An independent method to determine the surface roughness parameter. Reprinted from Bulletin of the Disaster Prevention Research Institute Kyoto University 41, pp. 121–127. Dyer, A.J., 1974. A review of flux–profile relationship. Boundary-Layer Meteorol. 7, 363–372. Frenzen, P., Vogel, C.A., 1992. The turbulent kinetic energy budget in the atmospheric surface layer: a review and an experimental reexamination in The Filed. Boundary-Layer Meteorol. 60, 49–76. Haugen, D.A., 1973. Workshop on Micrometeorology. Am. Meteorol. Soc., 45 Beacon St., Boston, MA 02108, pp. 34–47. Hogstrom, U., 1990. Analysis of turbulence structure in the surface layer with a modified similarity formulation for near neutral conditions. J. Atmos. Sci. 47, 1949–1972. Kaimal, J.C., Wyngaard, J.C., 1990. The kansas and minnesota experiments. Boundary-Layer Meteorol. 50, 31–47. Kaimal, J.C., Wyngaard, J.C., Izumi, Y., Cote, O.R., 1972. Spectral characteristics of surface-layer turbulence. Q. J. R. Meteorol. Soc. 98, 563–589. Mitsuta, Y., 1988. Sino–Japanese cooperation program on the atmosphere—land surface processes. TENKI 35, 501–505. Pan, L.L., Chen, J.Y., Zhang, H.S., Zhang, A.C., 1996. A one-dimensional model of land surface, canopy and atmosphere system and its using in research of interaction between grassland and atmosphere. Atmos. Sci. Sinica 20, 195–206. Panofsky, H.A., Dutton, J.A., 1984. Atmospheric Turbulence. Wiley-Interscience, Wiley, New York, pp. 174–211. Roth, M., Oke, T.R., 1993. Turbulent transfer relationships over an urban surface: I. Spectral characteristics. Q. J. R. Meteorol. Soc. 119, 1071–1104. Stull, R.B., 1988. An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers, Dordrecht, pp. 151–195. Wang, J.M., Mitsuta, Y., 1992. Evaporation from the desert: some preliminary results of HEIFE. BoundaryLayer Meteorol. 61, 413–418. Wyngaard, J.C., Cote, O.R., 1971. The budgets of turbulent kinetic energy and temperature variance in the atmospheric surface layer. J. Atoms. Sci. 28, 190–211. Zhang, H.S., Chen, J.Y., 1998. Correction of temperature measurement with sonic anemometer–thermometer. Atmos. Sci. Sinica 22, 11–17, Žin Chinese with English Abstract.. Zhang, A.C., Lu, J., Zhang, B., Liu, S.H., 1991. The atmospheric turbulence characteristic over Beijing suburban and city rim Žbrim, verge.. Atmos. Sci. Sinica 15, 88–96. Zhang, H.S., Chen, J.Y., Zhang, A.C., Wang, J.M., Mitsuta, Y., 1993. An Experiment and The Results on Flux–Gradient Relationships in The Atmospheric Surface Over Gobi Desert Surface. Proceedings of International Symposium on HEIFE, Kyoto, Japan, IV-12, pp. 349–362.
Dissipation rates of turbulent kinetic energy and temperature and humidity variances over different surfaces Hong-sheng Zhang b
a,)
, Soon-Ung Park
b
a Department of Geophysics, Peking UniÕersity, Beijing, 100871, China Department of Atmospheric Sciences, Seoul National UniÕersity, Seoul, 151-742, South Korea
Received 30 April 1998; accepted 6 September 1998
Abstract Dissipation rates of turbulent kinetic energy, and temperature and humidity variances have been analyzed using turbulent data collected from the Gobi desert, grassland, and suburban and urban sites that have different physical conditions. Instrumentation was installed at heights of 4.9 m, 3.45 m, 75 m and 47 m over the Gobi desert, grassland, and suburban and urban sites, respectively. The dimensionless dissipation rates of turbulent w´ , kinetic energy, temperature variance w N , and humidity variance wg are found to be more than 20% less than that required to balance the production of energy by wind shear and the variances by temperature and humidity gradients. The deficits appear to increase with the increase of absolute stability parameter. Combining the results from previous and present studies, the non-dimensional dissipation rates of turbulent kinetic energy, and temperature and humidity variances are modified by using the stability parameter. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Roughness length; Observational methods; Dissipation rate; Temperature variance; Humidity variance
1. Introduction The exchanges of momentum, heat, and moisture between atmosphere and land surface that determine the formation and evolution of planetary boundary layer ŽPBL. ) Corresponding author. Department of Atmospheric Sciences, Seoul National University, Seoul, 151-742, South Korea. Tel.: q82-2-880-6715; fax: q82-2-880-6715 or q82-2-883-4972; e-mail: [email protected]
0169-8095r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 8 0 9 5 Ž 9 8 . 0 0 0 8 9 - 1
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
38
are affected by the various scales of atmospheric processes. Therefore, information on the interaction between atmosphere and land surface is useful in enhancing the understanding of climate and general circulation as well as in improving their modeling. Land-surface processes mainly control the transformation and exchange of energy and substances between the atmosphere and land surface. Turbulent kinetic energy is one of the most important variables in land-surface processes because it is a measure of the intensity of turbulence. It is directly related to the transport of momentum, heat, and moisture through the boundary layer. Some important dimensionless parameters and scalings are also based on turbulent kinetic energy budget equation. Dissipation of the turbulent flow of heat is characterized by turbulent kinetic energy dissipation rate ´ and temperature variance dissipation rate N in the turbulent kinetic energy budget equation, but it is very difficult to measure ´ and N directly ŽStull, 1988.. Kaimal et al. Ž1972. proposed the relationship between ´ and stability parameter zrL using data measured by the hot-wire anemometer. Using the Kansas data ŽKaimal and Wyngaard, 1990., Wyngaard and Cote Ž1971. fitted the dissipation rates as:
w´ s Ž 1 q b < zrL < 2r3 .
3r2
w´ s Ž 1 q 2.5 < zrL < 5r3 .
for zrL - 0, and
3r2
for zrL ) 0,
Ž 1. Ž 2.
and the relationship between w N and stability parameter zrL was written ŽKaimal et al., 1972. as:
w N s 0.74 Ž 1 y 9 zrL .
y1 r2
for zrL - 0, and
w N s 0.74 q 4.7zrL for zrL ) 0.
Ž 3. Ž 4.
b in Eq. Ž1. ranged 0.5 to 0.75 ŽWyngaard and Cote, 1971; Kaimal et al., 1972; Caughey and Wygnaard, 1979.. Hogstrom Ž1990. examined the normalized dissipation rate w´ in terms of turbulent kinetic energy budget and the second order moment budgets formed by the three velocity components and temperature based on an experiment on a grassland of Lovsta, South Sweden. Frenzen and Vogel Ž1992. conducted a set of experiment and suggested a constant dissipation deficit relation in the normalized dissipation rate w´ . Roth and Oke Ž1993. showed the relationship between the normalized rates Ž w´ , w N and wg . and stability zrL using the spectral curves of velocity, temperature, and humidity. The present paper will report the results on the functional relationship between dimensionless dissipation rate of turbulent kinetic energy ŽTKE., temperature variance ŽTV., and humidity variance ŽHV. and stability zrL using a series of observational data taken over the Gobi desert, grassland, and suburban and urban sites.
2. Theory In the atmospheric boundary layer, if we choose a coordinate system aligned with the mean wind with the assumptions of horizontal homogeneity, steady flow, and negligible
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
39
subsidence, then a special form of TKE equation can be written ŽHogstrom, 1990.: g
u
Ž wXu X . yuX wX A
Ew X e
EU Ez
y
B
Ez
y
C
1 E Ž wX pX .
Ez
r
y´ s0,
Ž 5.
E
D
X
where p is the fluctuating pressure, r the air density, g the acceleration of gravity, u the potential temperature, e TKE, ´ the dissipation rate of TKE, and z the observational height. The terms from ŽA. to ŽE. in Eq. Ž5. represent buoyancy production, shear production, turbulence transport, pressure transport, and dissipation, respectively. Normalizing each term by the rate of TKE production in neutral conditions, u 3) rk z, yields
w´ s wm y zrL q w T q wp ,
Ž 6.
where w´ Žs k z ´ru 3) . is the normalized dissipation rate of TKE, L
ž
sy
u 3)
k Ž g r u . w Xu X
/ the
kZ EU u) E z
. the normalized wind profile function, Monin–Obukhov length scaling, wmŽs X eX E w . the normalized divergence of TKE, and w P s yk Z E wX pX the normalized w T Žs yk Z u 3) E z
u 3) E z
divergence of pressure transport. Because the turbulence data were measured at one level over different sites and because of the inherent difficulties in obtaining pressure fluctuations, both the normalized divergence of turbulent transport w T and pressure transport w P will be discussed simultaneously. Eq. Ž6. can be written as:
w´ s wm y zrL q w D ,
Ž 7.
where w D s w T q w P . Similarly, the non-dimensional dissipation rates of TV and HV are written as:
w N s w h q w Du ,
Ž 8.
where w h and w Du are the normalized potential temperature gradient and the divergence term of vertical turbulent flux of the temperature fluctuation, respectively, and
wg s wq q w D q ,
Ž 9.
where wq and w D q are the normalized humidity gradient and the divergence term of vertical turbulent flux of the humidity fluctuation, respectively. According to the Kolmogorov theory for the inertial subrange, the spectral density S of the velocity components is given by ŽKaimal et al., 1972; Panofsky and Dutton, 1984.: nSu ,Õ ,w Ž n . ru 2) s A1,2 Ž 2pk .
y2 r3
w´2r3 f y2r3 ,
Ž 10 .
where k is the von-Karman constant, n the frequency, u ) the friction velocity, f Žs nzrU . the non-dimensional frequency, U the mean wind speed, and A1,2 is a universal constant for the inertial subrange ŽKolmogorov constant.. In the present study, A1 Žfor u component. and A 2 Žfor Õ and w components. are 0.50 and 0.68, respectively ŽRoth and Oke, 1993..
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
40
Similarly, the one-dimensional spectra of temperature and humidity can be represented in the forms: nSu Ž n . ru)2 s Bu Ž 2pk .
y2 r3
w N w´y1r3 f y2r3 , and
Ž 11 .
rq)2 s Bq
y2 r3
wg w´y1r3 f y2r3 ,
Ž 12 .
nS q Ž n .
Ž 2pk .
where Bu and Bq are universal constants for the inertial subrange. The value of Bu and Bq are not well established. They are usually taken to be constants of 0.78 to 0.8 for both temperature and humidity ŽPanofsky and Dutton, 1984; Roth and Oke, 1993.. In the present study, Bu s Bq s 0.78. In the present study, the dissipation measurements were not made directly over all observational sites. Therefore, the normalized dissipation rates of TKE, TV and HV will be estimated using the velocity, temperature, and humidity spectral densities Su,Õ,w , Su Ž n., and S q Ž n. in the inertial subrange, respectively. From Eqs. Ž10. – Ž12., the normalized dissipation rates are
w´ s Ž 2pk . f w N s Ž 2pk . wg s Ž 2pk .
ž
nSu ,Õ ,w Ž n .
2r3
2r3
A1,2 u 2) f 2r3 f 2r3
ž ž
3r2
/
nSu Ž n . Bu u)2 nS q Ž n . Bq q)2
,
/ /
Ž 13 . w´1r3 ,
Ž 14 .
w´1r3 .
Ž 15 .
3. Experiment The detailed experimental sites, instrumentation, and data processing systems over the Gobi desert, grassland, and suburban and urban sites are described in detail in other reports ŽZhang et al., 1991; Wang and Mitsuta, 1992; Pan et al., 1996; Zhang and Chen, 1998.. For convenience, a brief summary of the experiments is given here. The data over the flat uniform Gobi desert were obtained during August 1992. The site is located in the northwestern part of Heihe river basin at 100806X E, 39809X N, over the dry area in Gan Su Province that is located to the northwestern part of China, approximately 20 km to the northwest of the foot of Qi Lian Mountain and about 1.2 km from the edge of the oasis lying along the north to northeast sector. A small farmland plot with a few trees is situated about 1.5 km to the northwest. The terrain around the site is flat arid Gobi desert consisting of sand grains and pebbles ŽMitsuta, 1988; Wang and Mitsuta, 1992.. The surface roughness is about 1.2 = 10y3 m ŽChen et al., 1991.. The experiment for the grassland site was conducted during August 1993. The site is located at the Bai Yin Xi Le livestock farm to the south of Xin Lin Hot City in the middle of Inner Mongolia steppe and covers the area extending from 43826X N to 44808X N and 116804X N to 117805X E with the mean elevation of 1187 m. The Xi Lin river flows from southwest to northwest. The surrounding area of the site is flat grass land. The surface roughness is about 2.8 = 10y2 m ŽPan et al., 1996..
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
41
The measurement for the suburban site was made on September 1994 in a suburban area of Fangshan in Beijing, China. The site is located to the 37 km southwest of Beijing city center. Yangshan Mountain is located at 10 km southwest of the tower. There are buildings lower than 15 m high standing to the north and northeast of the observational tower and farm land in the flat terrain in other directions. The surface roughness length is 0.37 m within the range of the wind direction in which the data were analyzed ŽZhang and Chen, 1998. The observational program for the urban site was conducted in Beijing, China with a 325-m meteorological tower. The tower is located to the 5 km north of Tian An Men Square. New building complexes with heights of 30–40 m are located to 1 km northeast, southeast, south and southwest of the tower. Single-story houses and markets are within 1 km. The surface roughness is about 1 m within the range of the wind direction in which the data were used ŽZhang et al., 1991.. Turbulent data were measured at the four sites with the same instrumentation, but the observational periods and measurement heights are different. The three-dimensional sonic anemometer–thermometer with the sound path length of 20 cm produced by Kaiji Denki of Japan Žmodel DAT-300 and sensor model TR-61C., the fast-response platinum wire thermometer Ža diameter of 20 mm and the total length of 48 cm platinum wire with the total resistance of 150 V ., the Lyman-a hygrometer Žmodel ERC-BL, made by Table 1 List of runs over the four sites Site
Date
Gobi desert Aug. 6–17, 1992
Grassland
Suburban
Urban
Instrumentation Variable Sonic anemometer Platinum thermometer Lyman-a hygrometer
Aug. 13–19, Sonic 1993 anemometer Platinum thermometer Lyman-a hygrometer Sept. 2–14, 1994
May 13–27, 1993
Sonic anemometer Platinum thermometer Lyman-a hygrometer Sonic anemometer Platinum thermometer
X
X
Observational Roughness height z Žm. z 0 Žm.
z r z0
Frequency ŽHz.
X
u, Õ,w
uX q
4.9
0.0012
4083.3 16
3.45
0.028
123.2 16
0.37
202.7 16
X
X
X
X
u, Õ,w
uX q
X
X
X
X
u, Õ,w X
u
q
75.0
X
X
X
X
u, Õ,w
uX
47.0
;1
47.0 16
42
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
ERC of America, and ror AIR-LA-1, made by AIR of America. were used for this study. All instruments have been checked in a laboratory before and after field experiments. Turbulent data recording and processing were carried out on a PCr486 with the same data acquisition system at each site. Signals were sampled at a rate of 160 Hz; 10 points were averaged to produce 16 Hz data which was recorded into the computer. The record periods were about 45–55 min; only 45-min record periods were used for this study. Recorded data were rejected according to the following criteria: the runs with more than 608 of horizontal wind direction from the coordinate system of sonic anemometer, the slope angle between the vertical and horizontal component winds ) 58, mean wind speed - 0.3 m sy1 , the friction velocity u ) - 0.02 m sy1 , the heat flux - 0.002 K m sy1 , the runs of day–night transition time and unreasonable data due to measurement errors. The characteristics of spectral analysis of wind components, temperature, and humidity are basically same as the standard case ŽHaugen, 1973; Panofsky and Dutton, 1984.. The spectra of the selected runs show strong similarities in shape with Eqs. Ž10. – Ž12. in the high frequency region. The normalized dissipation rates of TKE, TV, and HV were calculated using Eqs. Ž13. – Ž15. with the spectral densities determined by the average
Fig. 1. Non-dimensional dissipation rate of TKE Ž w´ . calculated by using w-component of spectral density against stability z r L over Ža. the Gobi desert, Žb. grassland, and Žc. suburban and Žd. urban sites. The dashed line is from Eqs. Ž1. and Ž2. with b s 0.5. The solid line is from Eq. Ž16. using different coefficients of a and b in Table 2.
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
43
Table 2 List of coefficients in Eq. Ž16. over the four sites Site
Observational height z Žm.
Roughness z 0 Žm.
z r z0
z r L-y0.1 a b
Gobi desert Grassland Suburban Urban
4.9 3.45 75.0 47.0
0.0012 0.028 0.37 ;1
4083.3 123.2 202.7 47.0
y0.19 y0.19 y0.19 y0.19
0.56 0.56 0.76 0.37
0.1- z r L- 0 a b
z r L) 0 a b
y0.42 y0.42 y0.42 y0.42
y0.42 y0.42 y0.42 y0.42
y1.74 y1.74 y1.54 y1.93
y2.57 y3.53 y3.21 y1.00
taken in the inertial subrange spectral region. In the present study, the range of 1.5 - n - 3.5 were used subjectively. A summary of each run is given in Table 1.
4. The normalized TKE dissipation rate w ´ The normalized dissipation rate of TKE Ž w´ . was evaluated from Eq. Ž13. from w-component spectra in the inertial subrange over the four sites. A plot of w´ vs. stability zrL is shown in Fig. 1 over the four sites. The dashed line represents the
Fig. 2. The same as in Fig. 1 except for using u-component of spectral density.
44
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
Kansas data from Eq. Ž1. with b of 0.5 while the solid line is obtained from Eq. Ž16.. The coefficients a and b in Eq. Ž16. appear to depend on roughness length and observational height, but it is difficult to find the functional form Žsee Table 2..
ww s wm y zrL q a q b Ž zrL . .
Ž 16 .
The flux–gradient relationships are given as ŽDyer, 1974.:
wm s Ž 1 y a zrL . wm s 1 y b zrL
y1 r4
for zrL - 0, and for zrL ) 0,
Ž 17 .
where a and b are constants. In general, the range of a is from 15 to 28 and b from 4 to 7 ŽZhang et al., 1993.. A sensitivity analysis using Eq. Ž17. indicated that the different value of constants resulted in less than 20% error for the turbulent fluxes. In the present study, we have used a s 28 and b s 5. The present results in Fig. 1 differ markedly from those of Kansas but are similar with the results obtained from studies of St. Louis by Clarke and a suburban area of Vancouver by Roth ŽRoth and Oke, 1993.. The trends are similar to the Eq. Ž1. with the increase of the absolute value of stability zrL. Figs. 2 and 3 show the value of w´ obtained from the horizontal wind component of u and Õ, respectively. They are similar
Fig. 3. The same as in Fig. 1 except for using Õ-component of spectral density.
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
45
to the results for the w-component with some scatters. There are several possible different mechanisms that could produce the differences between the result of Kaimal and the present analysis as seen in Fig. 1. Roth and Oke Ž1993. concluded that under near-neutral conditions, lower dissipation values are associated with lower value of wm . But the result of the flux–gradient relationships studied over the desert site shows wm s 1 during the near-neutral condition, implying that lower dissipation values are not due to the lower value of wm ŽZhang et al., 1993.. Fig. 4 shows the variations of different components in TKE budget Žsee Eq. Ž7.. as a function of stability zrL over the four sites. It is seen that under weakly unstable to the near-neutral conditions, the sum of turbulent transport and pressure transport terms w D is small. The local production of TKE is balanced by local dissipation. As the absolute value of zrL increases under unstable conditions, the heat production term and the
Fig. 4. The components of TKE budget as a function of stability z r L over Ža. the Gobi desert, Žb. grassland, and Žc. suburban and Žd. urban sites.
46
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
Fig. 5. Non-dimensional dissipation rate of TV Ž w N . calculated by using temperature spectral density against stability z r L over Ža. the Gobi desert, Žb. grassland, and Žc. suburban and Žd. urban sites. The dashed line is from Eqs. Ž3. and Ž4., the solid line from Eqs. Ž18. and Ž19..
dissipation rate term Ž w´ . increase while the mechanical production term Ž wm . decreases. Because the local energy production is less than the local dissipation in the energy balance, the effect of the turbulent flux divergence should be larger to compensate for the local energy production. Another important term in the energy balance in Eq. Ž7. is the pressure transport term. Neglecting this divergence term would result in a noticeable error in the calculation of dissipation rate under unstable conditions ŽWyngaard and Cote, 1971..
5. The non-dimensional TV dissipation rates w N The non-dimensional dissipation rate of TV Ž w N . over the four sites are compared with the result of the Kansas experiment. The dashed line in Fig. 5 is from Eqs. Ž3. and Ž4., and the solid curve from the present study in the functional form of stability as:
wn s w h y 0.19 y 0.057 < zrL < 3r5 for zrL - 0, and
Ž 18 .
w N s w h y w 0.19 q 4.3 < zrL < x for zrL ) 0,
Ž 19 .
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
47
with the temperature gradient as ŽZhang et al., 1993.:
w h s Ž 1 y 20 zrL . w h s Ž 1 q 5 zrL .
y1 r2
for zrL - 0, and for zrL ) 0.
Ž 20 .
The presently derived curve follows the curve obtained from the Kansas data, but the value of w N is usually smaller than that of Kaimal, especially over the desert site. This may be caused by an underestimate of w´ . The components of TV budget as a function of zrL over the four sites are plotted in Fig. 6. Because there is no pressure transport term in the TV budget equation, the budget is much simpler than that of TKE. The local production w h and dissipation rate w N of TV are basically in balance with the change of stability over the suburban and urban sites. In the unstable range, the present results also agree well with those from Roth and Oke Ž1993. for his suburban site. Because the experimental data are widely scattered in the stable condition, it is hard to find a suitable dissipation rate curve with zrL. However, Eq. Ž2. is well satisfied over the urban site ŽFig. 5..
Fig. 6. The components of TV budget as a function of stability z r L over Ža. the Gobi desert, Žb. grassland, and Žc. suburban and Žd. urban sites.
48
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
6. The non-dimensional HV dissipation rates w g The non-dimensional dissipation rate of HV Ž wg . over the desert, grassland, and suburban sites is compared with the result of Kansas temperature data. The dashed curve in Fig. 7 is obtained from Eqs. Ž3. and Ž4. using Kansas temperature data while the solid curve is obtained from the present study in the functional form of stability as:
wg s w h y 0.19 y 0.057 < zrL < 3r5 for zrL - 0, and
Ž 21 .
wg s w h y w 0.19 q 4.3 < zrL < x for zrL ) 0,
Ž 22 .
The trend of the two curves is similar to each other, especially for the unstable stratification. Comparison of dissipation rate for TV and that for HV, shows that the characteristics of the humidity fluctuations are quite similar to those of the temperature fluctuations. However, humidity fluctuations are more scattered, and the wg value is higher than w N value over the desert site. The components of HV budget as a function of zrL over the desert, grassland, and suburban sites are plotted in Fig. 8. The budget components of HV are quite similar to those of temperature ŽFig. 6. in all range of stability over the grassland and suburban sites. However, over the desert site those are quite similar each other for the stable
Fig. 7. Non-dimensional dissipation rate of HV Ž wg . calculated by using humidity spectra density against stability z r L over Ža. the Gobi desert, Žb. grassland and Žc. suburban sites. The dashed line is from Eqs. Ž3. and Ž4., the solid line from Eqs. Ž21. and Ž22..
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
49
Fig. 8. The components of HV budget as a function of stability z r L over the Ža. Gobi desert, Žb. grassland, and Žc. suburban sites.
condition but for the unstable case the absolute value of the normalized dissipation rate of HV is larger than that of temperature. Therefore, the divergence term w Dg should be large to balance with wg . This is presumably due to strong evaporation and larger dissipation rate of HV over the desert site during the observation period and due to several assumptions, such as homogeneity, steady flow and negligible subsidence made to derive Eq. Ž9. with the exclusion of the advection of humidity variance. The result ŽFig. 8a. suggests that the moisture flux in a dry region such as the desert is largely dependent on the transport of the horizontal moisture flux.
7. Summary and conclusions The dissipation rates of TKE, and TV and HV using turbulent data collected from the Gobi desert, grassland, and suburban and urban sites are examined. The instrumentation was installed at heights of 4.9 m, 3.45 m, 75 m, and 47 m over the Gobi desert, grassland, and suburban and urban sites, respectively. The dimensionless dissipation
50
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
Fig. 9. Non-dimensional dissipation rate of TKE Ž w´ . calculated by using the w-component spectra density against stability z r L over an urban site in winter of 1993. The dashed line is from Eqs. Ž1. and Ž2. with b s 0.5. The solid line from Eq. Ž16. with the different coefficients of a and b in Table 2.
rates of TKE Ž w´ ., TV Ž w N ., and HV Ž wg . are found to be smaller by 20% than that necessary to balance the production of energy by the observed wind shear, temperature, and humidity gradients. The deficit appears to increase with an increase in the absolute stability parameter. The present results differ markedly from those of the Kansas experiment but are similar to the results obtained by Roth and Oke Ž1993.. The net effect of turbulent transport and pressure transport is to remove energy from all stability ranges in proportion to the absolute value of zrL but not at a constant rate ŽFrenzen and Vogel, 1992.. Combining the results of previous and present studies, the non-dimensional dissipation rates of TKE, TV, and HV are modified as a function of stability with some empirical constants. The empirical coefficients in TKE, TV, and HV equations depend largely upon roughness length and observational height. Fig. 9 shows the non-dimensional dissipation rate of TKE calculated using the w-component spectral density against stability zrL over the same urban site and at the same observational height Ž47 m., but the experimental date are different. It was taken in winter for the period from December 1993 to February 1994. The result in Fig. 9 shows the same pattern in Fig. 1. The dissipation rate of TKE calculated with the data obtained in winter agrees well with the empirical curve Žsolid line. in Eq. Ž16., suggesting that the presently derived empirical equation of TKE dissipation rate can be used more usefully for the urban site. Acknowledgements This work was supported by the National Natural Science Foundation of China and the Korea Science and Engineering Foundation. References Caughey, S.J., Wygnaard, J.C., 1979. The turbulent kinetic energy budget in convective conditions. Q. J. R. Meteorol. Soc. 105, 231–239.
H.-s. Zhang, S.-U. Park r Atmospheric Research 50 (1999) 37–51
51
Chen, J.Y., Wang, J.M., Mitsuta, Y., 1991. An independent method to determine the surface roughness parameter. Reprinted from Bulletin of the Disaster Prevention Research Institute Kyoto University 41, pp. 121–127. Dyer, A.J., 1974. A review of flux–profile relationship. Boundary-Layer Meteorol. 7, 363–372. Frenzen, P., Vogel, C.A., 1992. The turbulent kinetic energy budget in the atmospheric surface layer: a review and an experimental reexamination in The Filed. Boundary-Layer Meteorol. 60, 49–76. Haugen, D.A., 1973. Workshop on Micrometeorology. Am. Meteorol. Soc., 45 Beacon St., Boston, MA 02108, pp. 34–47. Hogstrom, U., 1990. Analysis of turbulence structure in the surface layer with a modified similarity formulation for near neutral conditions. J. Atmos. Sci. 47, 1949–1972. Kaimal, J.C., Wyngaard, J.C., 1990. The kansas and minnesota experiments. Boundary-Layer Meteorol. 50, 31–47. Kaimal, J.C., Wyngaard, J.C., Izumi, Y., Cote, O.R., 1972. Spectral characteristics of surface-layer turbulence. Q. J. R. Meteorol. Soc. 98, 563–589. Mitsuta, Y., 1988. Sino–Japanese cooperation program on the atmosphere—land surface processes. TENKI 35, 501–505. Pan, L.L., Chen, J.Y., Zhang, H.S., Zhang, A.C., 1996. A one-dimensional model of land surface, canopy and atmosphere system and its using in research of interaction between grassland and atmosphere. Atmos. Sci. Sinica 20, 195–206. Panofsky, H.A., Dutton, J.A., 1984. Atmospheric Turbulence. Wiley-Interscience, Wiley, New York, pp. 174–211. Roth, M., Oke, T.R., 1993. Turbulent transfer relationships over an urban surface: I. Spectral characteristics. Q. J. R. Meteorol. Soc. 119, 1071–1104. Stull, R.B., 1988. An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers, Dordrecht, pp. 151–195. Wang, J.M., Mitsuta, Y., 1992. Evaporation from the desert: some preliminary results of HEIFE. BoundaryLayer Meteorol. 61, 413–418. Wyngaard, J.C., Cote, O.R., 1971. The budgets of turbulent kinetic energy and temperature variance in the atmospheric surface layer. J. Atoms. Sci. 28, 190–211. Zhang, H.S., Chen, J.Y., 1998. Correction of temperature measurement with sonic anemometer–thermometer. Atmos. Sci. Sinica 22, 11–17, Žin Chinese with English Abstract.. Zhang, A.C., Lu, J., Zhang, B., Liu, S.H., 1991. The atmospheric turbulence characteristic over Beijing suburban and city rim Žbrim, verge.. Atmos. Sci. Sinica 15, 88–96. Zhang, H.S., Chen, J.Y., Zhang, A.C., Wang, J.M., Mitsuta, Y., 1993. An Experiment and The Results on Flux–Gradient Relationships in The Atmospheric Surface Over Gobi Desert Surface. Proceedings of International Symposium on HEIFE, Kyoto, Japan, IV-12, pp. 349–362.