Turbulent kinetic energy in the atmospheric surface layer during the summer monsoon

Transcription

1 Meteorol. Appl. 9, (2002) DOI: /S Turbulent kinetic energy in the atmospheric surface layer during the summer monsoon Manoj K Srivastava, Department of Geophysics, Banaras Hindu University, Varanasi , India P Parth Sarthi, Centre for Atmospheric Sciences, Indian Institute of Technology, Hauz Khas, New Delhi , India The turbulent kinetic energy (TKE) in the atmospheric surface layer (ASL) gives a measure of the intensity of turbulence that could be altered or brought about by mechanical generation, by thermal generation, through vertical transport into or away, and through dissipation. TKE is mainly responsible for the transportation of pollutants suspended in the air. In this paper, TKE evolution in the ASL is studied for Kharagpur (22.20 N, E) during the summer monsoon by making use of data from a 0 m micrometeorological tower set up as part of the Monsoon Trough Boundary Layer Experiment (MONTBLEX). Under steady state and homogeneous conditions the various terms in the TKE equation are studied for active and non-active phases of the monsoon in Their day-to-day variations and the budgets are studied at the 8 m and 15 m levels. The study reveals strong day-to-day variation and significant vertical variations within the ASL. Despite being a tropical station, the buoyancy term is much less than the contribution by mechanical generation ostensibly due to the monsoon. There are also differences between active and non-active phases of the monsoon. Mechanical generation by wind shear has been found to be the dominating production term, while dissipation dominates the magnitude of all other terms. 1. Introduction The turbulent exchange processes between the earth and the atmosphere take place through the atmospheric surface layer (ASL), the depth of which is around few tens of metres. This layer acquires prominence partly because most human activities are confined to this layer. Incidentally, this is the layer that has been probed the most through fixed micrometeorological towers. The evolution of turbulence in this layer, therefore, assumes special importance. Turbulent kinetic energy (TKE) has sources as well as sinks but it is not a conserved quantity. The source could be associated with wind shear, buoyancy, redistribution of TKE from one level to the other and redistribution by pressure forces. Except for production due to wind shear, all the other sources mentioned could also be sinks, with dissipation by molecular processes being the most important sink of TKE. The following studies have been carried out into various aspects of the TKE budget. (a) Panofsky (1962) and Record & Cramer (1966) reported TKE evolution in the ASL and showed that the divergence of TKE flux was important under steady-state conditions. Busch & Panofsky (1968) in their spectral study of atmospheric turbulence contested the importance of divergence of TKE flux and showed that dissipation compensates shear and buoyancy productions. (b) Wyngaard & Cote (1971) reported that shear and buoyancy productions were lower than the dissipation rate, thereby making the role of divergence of TKE flux and redistribution by pressure forces significant. Garrat (1972) also described the occasional importance of divergence. (c) McBean & Miyake (1972) discussed the TKE transfer in the surface layer and McBean & Elliott (1975) showed that the pressure transport is larger than the vertical transport by flux divergence. They further reported a negative transport by pressure forces. (d) Lenschow (1974) and Caughey & Wyngaard (1979) studied the TKE budget under unstable conditions and convective conditions respectively. Actually, the TKE itself is a measure of total energy present in the air parcel. The budget of the TKE, which includes various causes generating the TKE due to speed and temperature of the parcel, distinguishes the various causes separately and is very useful for understanding the distribution of various pollution particles suspended in the air. The diffusive property of the flow is responsible for the efficient diffusion of the momentum, heat and mass (e.g. water vapour, CO 2 and various pollutants) in the turbulent flow. The turbulence diffusivity is largely responsible for the evaporation in the 29

2 Manoj K Srivastava and P Parth Sarthi atmosphere and spread of pollutants released in the ABL (Arya, 1988). This gives the primary estimate about the subsidence of the polluting particles. However, no studies of this kind have been made in the tropics particularly in monsoon climates. Viswanadham et al. (1997) attempted a study of the TKE budget over Varanasi (roughly 25 N, 8 E) in India and reported the variations with stability. In the present paper we have made an attempt to study the TKE budget at a typical tropical station, namely Kharagpur (22.20 N, E), which lies close to the head of the Bay of Bengal where the monsoon trough also originates during the monsoon season and extends in a north-westerly direction (see Figure 1). This station is chosen to represent the area of deep moist convection which occurs whenever a monsoon depression develops near the head of the Bay of Bengal during the active phase of the monsoon. The studies are made during the active phase (i.e. when the monsoon trough is to the north of its normal position) as well as non-active or break phases (i.e. when the monsoon trough is to the south of its normal position), and the differences are described. In addition, the day-to-day variations of each of the parameters in the TKE equation under steady-state and homogeneous conditions are studied. Figure 1. Normal location of the monsoon trough during the summer monsoon over India. 2. Experiment and data The monsoon trough boundary layer experiment (MONTBLEX) was conducted from June to September 1990, primarily to understand the interaction between the boundary layer and monsoon trough whose position varies in time and space. The movement of the trough results in active or non-active spells of the summer monsoon, with the former resulting in overcast skies and occasional or continuous spells of rainfall, while the latter results in a break in the monsoon with scattered rainfall. As a part of the experiment, a 0 m micrometeorological tower was installed on farmland belonging to the Indian Institute of Technology Kharagpur, with sensors fixed at six levels: 1, 2, 4, 8, 15, 0 m. Table 1 provides information about the sensors and where they were mounted. Two types of data were collected from the tower: slow response data (SRD) (1 Hz) and fast response data (FRD) ( 8 Hz). The data used for the present study were collected between 17 and 25 July The SRD and FRD averaged for 10 min duration have been used in the present study and a total of 22 runs are used. Of the 22 cases examined, only in 17 cases were both FRD/SRD and weather parameters available for comparative studies. These weather parameters are given in Table 2. The measurements of tower data for the computation of TKE have been utilised from 17 July The tower site is flat and grassy. The wind has an uninterrupted fetch of half a kilometre in the prevailing south-southwesterly direction, beyond which mature 240 trees are present. The roughness length, although showing directional variations, is mostly confined to less than 2 cm throughout the experiment. Table 2 depicts the prevailing weather over Kharagpur for the period of data considered in the present study. Based on Table 2 the following active and non-active phases are delineated: July, 1990 is the active phase and July, 1990 is considered the non-active phase.. Methodology All the FRD were subjected to quality checks before being used in the final analysis. The following steps are used for quality checks. (a) A physical check of the raw data was made. (b) Any individual value falling within mean ± standard deviations (SD) only were retained and the rest were replaced by the limiting values of mean ± SD. Step (b) is necessary because the peaks could be due to instrumental or recording error, or could be due to real atmospheric variation that is difficult to discern. Therefore some criterion such as this is normally used. The data were then subjected to spectral analysis to check on conformity with the universal laws (Kolmogorov, 1941). Only those datasets that display

3 Turbulent kinetic energy in the atmospheric surface layer during the summer monsoon Table 1. Information about the sensors and the levels at which they are mounted. The levels are as follows: Level 1 = 1 m; Level 2 = 2 m; Level = 4 m; Level 4 = 8 m; Level 5 = 15 m; Level 6 = 0 m. Instrument Levels Percentage of time working Slow response sensors Cup anemometer (wind speed) 1, 2,, 4, 5, 6 9.2% Wind wave (wind direction) 1, 2,, 4, 5, 6 9.2% Platinum wire thermometer (temperature) 1,, 5, 6 9.2% Humi cap (relative humidity) 1,, 4, 6 9.2% Fast response sensors Platinum wire thermometer (fast temperature) 2, % Sonic Anemometer (-D wind speed) 4 4.8% Hot-wire anemometer (-D wind speed) % Lyman-alpha (absolute humidity) 2 4.4% Gill propeller (-D wind speed) % Table 2. Weather over Kharagpur during July Date, Time (LST) Pressure (hpa) Wind speed Cloud 18 July 1990, Low to medium Thunderstorms 19 July 1990, 110 Cloudy 19 July 1990, Low to medium Overcast 19 July 1990, 1745 Raining 20 July 1990, Low Overcast 20 July 1990, Low Overcast 21 July 1990, Very low Overcast 21 July 1990, Low Overcast 22 July 1990, Medium 5 oktas 22 July 1990, Medium 4 oktas 2 July 1990, High 5 oktas 2 July 1990, High 4 oktas 2 July 1990, Strong 5 oktas 24 July 1990, Low 7 oktas 25 July 1990, Low 4 oktas 25 July 1990, High 7 oktas 25 July 1990, Low 7 oktas the 5/ power law have been retained. The retained data sets were then subjected to high pass filter to remove any low frequency long waves following Meyer & Rao (1995). This process did not result in any significant changes to the data, which could perhaps be due to the short sampling time of 10 min. There is a small possibility of suppressing low frequency waves in such a short sampling time (for further details see Viswanadham et al., 1997). Accordingly 22 runs for the main phase are utilised for the study. For a steady-state homogeneous condition, the TKE equation can be written as follows (Stull, 1988) if the coordinate system is aligned with the mean wind (u ): g u we ( w θ v ) w u θ ( ) z 1 z ρ v ( wp ) ε = 0 z where u, v, w, p and θ v are the turbulent parts of the three wind component, pressure and virtual potential temperature, z is the log mean height, ρ and θ v are the mean density and mean virtual potential temperature, g is the acceleration due to gravity, ε is the dissipation, and the TKE is given by: 1 e= u + v + w 2 The terms in the TKE equation are as follows. (a) The first term is the buoyancy term (BT) which acts as source or sink respectively, for day or night time. (b) The second term is the shear production term (ST) which is normally a source. (c) The third term is the flux divergence term (FT) of vertical TKE flux, which may act as a source or sink depending upon whether the energy flows into or away from the layer. (d) The fourth term is the turbulent transport of TKE by pressure fluctuations, also referred to as the 241

4 Manoj K Srivastava and P Parth Sarthi residual term (RT) for this work, which can be a source or a sink depending upon the situation. (e) The fifth term is the dissipation (DT) and is a sink. The intention of this paper is to examine the relative importance of the above-mentioned terms. The first two terms can be computed easily from the data, while the divergence term needs modification. Hence following McBean & Elliott (1975) we put: where k is von Karman s constant, u is the friction velocity and L is the Monin-Obukhov length scale. The term is w e/u a universal function of z/l, so we put: Consequently the divergence is: We have obtained the function F(z/L) from the data. The divergence of TKE flux for individual runs is obtained by differentiating F(z/L) and multiplying it with u /L. If the stability is not extreme, then dissipation can be obtained as a function of z/l following Wyngaard & Cote (1971) and Stull (1988). Unstable conditions Stable conditions In this study we have used this expression to compute dissipation, as the stability variation was found to be between (± 0.015). Finally, the pressure transportation term is obtained as a residual. 242 kz u z we kz weu / ( ) ( ) = L ( zl / ) we = FzL ( / ) u kz u z we kz ( FzL / ( ) = ( )) L ( zl / ) u z ε= kz L u z ε= kz L Results Figure 2 shows the day-to-day variation of the TKE budget parameters at 8 m and 15 m levels respectively. These results will be discussed in sections 4.1 and Day-to-day variations at 8 m height There is a significant variation of the BT ranging from near zero to about m 2 s. Sometimes this term has acted as a source term because it has positive values on several occasions. It was negative or near zero on very few occasions (i.e. from the evening hours of 18 July to 20 July 1990), which is mainly responsible for the negligible buoyancy. On other occasions the near zero values occurred in the evening hours as expected. From 21 July onwards, high values occurred around noon when the production of TKE due to buoyancy is expected to be maximum. The overall variation is on the expected trend as it should be based on the actual observed weather. The ST was at its maximum on 2 July with multiple secondary peaks. It shows a clear-cut variation from hour to hour, although not all the hourly data are available. During the rainy periods (i.e July) the value is relatively low and during the non-rainy periods values are relatively high. FT has acted as a sink of TKE almost continuously. This means that most of the TKE is transported away from the 8 m level. It is interesting to note that during the rainy period, the value is too small indicating very little vertical transport. During the non-active phase, the transport is higher. Incidentally, all the low values, except that during the rainy period, were around 170 LST. This shows that there is a clear upward transport of TKE from this layer during the daytime. Careful examination shows that when the BT is negative, the FT is positive. In other words, the negative BT results in downward transport of TKE into this level. The converse is true for positive BT which is associated with upward transport of TKE from the surface layer. This, we believe, is possible because the tendency of the BT is to have an upward turbulence and as a consequence along with heat, the TKE is transported vertically upward. The day-to-day variation of DT is almost opposite to that of shear production. The rainy period shows very little dissipation because the production itself is too low. The non-rainy days show relatively more dissipation because of the larger production of TKE. The RT shows both positive and negative values with little variation between 18 and 21 July and a considerably high variation thereafter. However, it is difficult to interpret this result because this term consists not only of the pressure-correlation term but also the cumula-

5 Turbulent kinetic energy in the atmospheric surface layer during the summer monsoon this level. On several occasions the value is constant and very near to zero. Mostly negative values of RT are observed except on three to four occasions when it was positive. 4.. TKE budget The actual balance of the terms and their ratios are computed to arrive at the compensation of terms. Based on the rainfall and the cloud cover, the active and nonactive periods are identified and the balance is discussed separately for these periods. The means of the individual parameters for active and non-active phases and for the whole of the period are shown in Tables and 4 for 8 m and 15 m respectively. Figure 2. Variation of various terms in the TKE equation at a height of (a) 8 m and (b) 15 m. All quantities are given in units of 10 5 m 2 s. tive errors of all other terms computed, since it is computed as a residual Day-to-day variation at 15 m height There are some differences between values at the 15 m and 8 m levels. During the rainy period, BT almost vanishes but during non-rainy periods the value is also quite small. Except on a few occasions, the value oscillates around zero. The difference between both the levels is worth noting. The day-to-day variation of ST is significant but the pattern at the 8 m level differs with the pattern at this level, particularly in their peak values. The highest value is observed during the rainy period. However, there is an isolated peak which appears at a particular time when there is a temporary break in the rain. Generally the FT is low during the rainy period. The occasional positive values occurred when the BT was negative. The magnitudes are relatively small at this level compared with those at the 8 m level. The variation of DT is more or less similar to that found at the 8 m level with the exception of the maximum value which is observed during rainy period at The balance at 8 m during main phase shows DT as the dominating term followed by RT, ST, FT and BT. The source terms are ST, BT and RT. The FT and DT act as the sink of TKE, which means that TKE is lost from the ASL by molecular dissipation and vertical transport into the layer above. The balance for the active and non-active phases also shows a similar trend. As far as the magnitudes are concerned, generally the values during the non-active phase are high for all the terms. The active phase here represents raining and/or cloudy sky. Therefore, it is natural to expect less buoyancy and less vertical transport. The variation at the 15 m level (Table 4) is similar to that at 8 m, although it has reduced magnitude. It is rather surprising and intriguing that for the same period such a drastic difference of this parameter at 8 m and 15 m occurs within the ASL. The mean picture reveals that there is very little FT which is almost zero. It is only the DT which is more or less compensating all other terms including the RT. The active and nonactive phases show a similar balance but with varying magnitudes. As before, the non-active phase shows higher magnitudes, except for the RT. To get a better insight into the relative magnitudes, the ratios of all the terms to ST are considered. Tables 5 and 6 shows the ratio values for 8 m and 15 m respectively. It is interesting to note that the DT is 2 to times greater than the ST while the RT is 1.5 to 2 times greater. The BT is almost a quarter or less and the FT is negligible at the 15 m level, while it is half at the 8 m level. All these parameters except ST correlated significantly with cloud cover and to some extent with pressure. 5. Discussions and conclusions The BT, ST, FT and DT of the TKE budget are responsible for the upward moment, viscous resistance, 24

6 Manoj K Srivastava and P Parth Sarthi Table. Mean values for active, non-active phase and for total at 8 m level. Period Buoyancy Shear Flux Dissipation Residual ( 10 5 m 2 s ) production divergence ( 10 5 m 2 s ) ( 10 5 m 2 s ) ( 10 5 m 2 s ) ( 10 5 m 2 s ) Active phase Non-active phase Total Table 4. Mean values for active, non-active phase and for total at 15 m level. Period Buoyancy Shear Flux Dissipation Residual ( 10 5 m 2 s ) production divergence ( 10 5 m 2 s ) ( 10 5 m 2 s ) ( 10 5 m 2 s ) ( 10 5 m 2 s ) Active phase Non-active phase Total energy loss (gain) to (from) the adjacent atmosphere and estimate of energy available in the parcel. These terms of the TKE budget can give an estimate of the subsidence of the aerosols suspended in the parcel polluting the atmosphere. Some studies have been carried out to estimate these terms for the understanding of the kind of energy available in the ABL. (a) Viswanadham et al. (1997) discussed the budget of TKE under different stability stratification. A comparison with the present results reveals major differences in the magnitude and also the signs. For example DT is negligible at the 15 m level in the present case, while it shows a positive contribution at Varanasi. (b) McBean & Elliott (1975) found the same magnitude for BT and DT but with opposite signs. Our results at 8 m and 15 m levels also show BT and DT to be of opposite signs. (c) Wyngaard & Cote (1971) brought out the domination of RT based on the Kansas Experiment. The present study reveals the importance of DT particularly at the 8 m level. At the 15 m level, however, DT is negligible, while it is more than BT and less than half of ST in active phase, and less than half of ST in non-active phase. The DT dominates all Table 5. Ratio of TKE budget parameters to shear production term at 8 m height. Date Time (LST) Buoyancy Flux divergence Dissipation Residual July July July July July July July July July July July July July July July July July July July July July July

7 Turbulent kinetic energy in the atmospheric surface layer during the summer monsoon Table 6. Ratio of TKE budget parameters to shear production term at 15 m height. Date Time (LST) Buoyancy Flux divergence Dissipation Residual July July July July July July July July July July July July July July July July July July July July July July other terms individually. DT and FT together compensate all terms during the main phase at both the levels. Unlike the result of Wyngaard & Cote (1971), we have found that ST is a significant term. The low BT and relatively high ST are the characteristic features of the monsoon particularly in its active phase. This is because the monsoon season brings in a lot of moisture over the land which obstructs the insolation through the cloud cover and produces a lowlevel wind shear due to the strong wind, all of which results in a low BT and high ST. In other words, the mechanically generated turbulence dominates the thermally induced turbulence. This is interesting because a typical tropical location during summer should naturally produce more free convective conditions (high BT) due to excess heat received at the surface. However, it is the monsoon which transforms the whole scenario to produce more mechanically generated turbulence, although the monsoon itself is a thermally driven large-scale system. We wish to argue here that only during the monsoon season do we have a low BT and high ST. For a premonsoon season, BT would naturally dominate. Very close to the ground we feel that FT is significant and more so during the non-active phase. Even during the active phase, the difference between the work done for the pilot phase of this experiment and the present work is worth noting, when the FT has opposite signs suggesting that the generalisation of FT being positive or negative during the monsoon season would be inappropriate but its magnitude is considerable. DT dominates at all levels in both phases. Acknowledgements This work was carried out as a part of the main project funded by the Department of Science and Technology, Government of India. We gratefully acknowledge the India Meteorology Department and Indian Institute of Tropical Meteorology, Pune for supplying the necessary data. We are thankful to anonymous referees for their valuable comments, suggestions and guidance. We also thank the Council of Scientific and Industrial Research, Government of India for providing the financial support. References Busch, N. E. & Panofsky, H. A. (1968). Recent spectra of atmospheric turbulence. Q. J. R. Meteorol. Soc., 94: Businger, J. A., Wyngaard, J. C., Izumi, Y. & Bradley, E. F. (1971). Flux Profile relationships in the atmospheric surface layer. J. Atmos. Sci., 28: Caughey, J. & Wyngaard, J. C. (1979). The turbulent kinetic energy budget in convective conditions. Q. J. R. Meteorol. Soc., 105: Garratt, J. R. (1972). Studies of turbulence in the surface layer over water (Lough Neagh) part II. Production and dissipation of velocity and temperature fluctuations. Q. J. R. Meteorol. Soc., 98: Kolmogorov, A. N. (1941). Energy dissipation in locally isotropic turbulence. Doklady AN SSSR, 2: No. 1, Lenschow, D. H. (1974). Model of the height variation of the turbulence kinetic energy budget in the unstable planetary boundary layer. J. Atmos. Sci., 1: Lumley, J. L. & Panofsky, H. A. (1964). The Structure of Atmospheric Turbulence. Interscience, New York. 245

8 Manoj K Srivastava and P Parth Sarthi McBean, G. A. & Elliott, J. A. (1975). The vertical transports of kinetic energy by turbulence and pressure in the boundary layer. J. Atmos. Sci., 2: McBean, G. A. & Miyake, M. (1972). Turbulent transfer mechanism in the atmospheric surface layer. Q. J. R. Meteorol. Soc., 98: Panofsky, H. A. (1962). The budget of turbulent energy in the lowest 100 meters. J. Geophys. Res., 67: Record, F. A. & Cramer, H. E. (1966). Turbulent energy dissipation rates and exchange processes above a non-homogeneous surface. Q. J. R. Meteorol. Soc., 92: Stull, R. B. (1988). An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers, The Netherlands. Viswanathan D. V., Satyanarayna, A. N. V., Stuti Mishra & Partha Sarthi, P. (1997). Turbulent kinetic energy budget parameter over Varanasi from MONTBLEX-90. Proc. Indian Natl. Sci. Acad., 6A: Wyngaard, J. C. & Cote, O. R. (1971). The budget of turbulent kinetic energy and temperature variance in the atmospheric surface layer. J. Atmos. Sci., 28: