Lawrence Livermore National Laboratory, Livermore, CA, 94550

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1 4.9 TURBULENCE KINETIC ENERGY BUDGETS AND DISSIPATION RATES IN DISTURBED STABLE BOUNDARY LAYERS Jule K. Lundqust* 1, Mark Pper 2, and Branko Kosov 1 1 Atmospherc Scence Dvson Lawrence Lvermore Natonal Laboratory, Lvermore, CA, Program n Atmospherc and Oceanc Scence, Unversty of Colorado at Boulder 1. INTRODUCTION An mportant parameter n the numercal smulaton of atmospherc boundary layers s the dsspaton length scale, l ε. It s especally mportant n weakly to moderately stable condtons, n whch a tenuous balance between shear producton of turbulence, buoyant destructon of turbulence, and turbulent dsspaton s mantaned. In large-scale models, the dsspaton rate s often parameterzed usng a dagnostc equaton based on the producton of turbulent knetc energy (TKE) and an estmate of the dsspaton length scale. Proper parameterzaton of the dsspaton length scale from expermental data requres accurate estmaton of the rate of dsspaton of TKE from expermental data. Usng data from the MICROFRONTS and CASES-99 feld programs, we evaluate turbulent knetc energy (TKE), TKE dsspaton rate ε, and dsspaton length l ε over a range of stablty regmes represented by a stable boundary layer (SBL), a destablzng ntruson (by frst a cold front and second a densty current) and recovery. These data may be utlzed to test recent parameterzatons of dsspaton rate ε and l ε n order to determne the sutablty of these models for ncluson n mesoscale models for numercal weather predcton or polluton dsperson predcton. 2. DATA SOURCES Data from the MICROFRONTS and CASES-99 feld programs are used n ths study. The data from each experment are descrbed n the subsectons below. 2.1 MICROFRONTS (The cold front) The MICROFRONTS feld experment was conducted from 1 March 1995 through 30 March 1995 at a ste approxmately 75~km northeast of Wchta, near De Graff, Kansas. The feld ste was stuated n gently rollng farmland n eastern Kansas, wth a homogeneous fetch to the northwest. The ASTER faclty, operated by the Natonal Center for Atmospherc Research (NCAR) Atmospherc Technology Dvson, was deployed to collect turbulence data. The ASTER sonc anemometers were used to compute turbulence statstcs for the three velocty components and used to estmate dsspaton rate. A dry Arctc cold front passed the MICROFRONTS ste at approxmately 0237 UTC (2037 LST) 20 March 1995, two hours after local sunset at 1839 LST. Tme seres spannng the perod UTC are shown n Fgure 1.The 6-hr tme perod was chosen because t allows tme for the front to completely pass the nstrumented tower, wth tme on ether sde to vew the state of the surface layer. The top two panels show wnd speed and wnd drecton from the 10m south tower sonc anemometer, at a rate of 10 samples s -1. The next panel shows dry bulb temperature from the 10m south tower platnum resstance thermometer, also at 10 samples s -1. The last panel shows two surface layer scalng parameters, the local frcton velocty u* and the Monn-Obukhov scalng parameter ζ = z/l, where L s a local Obukhov length. Both u* and ζ are calculated from fluxes from the sonc anemometer at the 3m level. These scalng parameters are calculated usng 900-s averagng ntervals, centered on the tme of the frontal passage. The dotted lnes n Fgure 1 delmt the frontal zone. Note, vsually, the sharp ncrease n wnd speed varance wth the passng of the front. After the front passes, the wnd speed and speed varance decay to near prefrontal values. The wnd has a southwesterly component n the prefrontal perod. The temperature trace n panel 3 shows that there was a 2 o C rse n temperature startng at 0200 UTC, possbly due to advecton of warmer ar from the southwest or ncreased mxng n the surface layer. After the frontal passage, temperature decreased steadly due to radatonal coolng and cold ar advecton. The wnd shft and temperature drop were not concdent n ths front, wth the

2 temperature drop at 10m laggng the wnd shft by about 180s. Ths s also observed n Taylor et al. (1993) and Shapro et al. (1985), suggestng that ths front may have an elevated head, lke a densty current. Fgure 1: Tme seres from the 10m south tower nstruments on 20 Mar (A) Wnd speed from the sonc anemometer. (B) Wnd drecton from the sonc anemometer. (C) Temperature from the platnum resstance thermometer. (D) The frcton velocty u* (.) and the Monn-Obukhov scalng parameter ζ (squares). The dotted lnes gve the extent of the frontal zone. 2.2 CASES-99: the densty current The CASES-99 feld experment was conducted from 1 October 1999 through 30 October 1999 east of Wchta, near Leon, Kansas. An extensve array of nstrumentaton ncludng a 60m tower, the HRDL ldar, boundary-layer wnd proflers, radosondes, a tethered lftng system, and two arcraft probed the nocturnal boundary layer throughout the feld program (Poulos et al. 2002a). Local orographc relef dd not exceed 30m, and yet several densty currents were observed durng early evenngs throughout the feld campagn. A densty current passed the CASES-99 man tower at approxmately 0215 UTC (2115 LDT) 20 October 1999, two hours after local sunset at 1900 CDT and four hours after surface heat flux became negatve. Fgure 2 shows an 10 hour tme seres of wnd speed, wnd drecton, vrtual temperature T v, u*, and heat flux from the sonc anemometer located at the 10m level. In addton to the 0215 UTC ntal passage of the densty current, another mxng event occurs at 0315 UTC. The later event s not accompaned by coolng and lkely ndcates the tal end of the densty current. The top two panels show wnd speed and wnd drecton at a rate of 10 samples sec -1. The next panel shows vrtual temperature measured by the sonc anemometer, also at 10 samples sec -1. The bottom panel shows the frcton velocty u* and heat flux, also calculated wth sonc anemometer data. The fluxes are calculated as covarances of perturbatons from 720s mean values. The 0215 UTC densty current caused temperatures at 10m to drop from 10 o to 6 o C for a perod of about fve mnutes. Ths pool of cooler ar was confned to the regon between the surface and 20m; hgher levels (not shown) exhbted gradual coolng rather than an mpulse of cold ar. Whle the cold front was accompaned by a sharp ncrease n wnd speed, the densty current suppressed wnds: wnd speed decreases almost to zero momentarly, and the varance of wnd speed s reduced followng the passage of the densty current. The passage of the densty current s accompaned by an uplft-downdraft couplet (Blumen et al. 1999), as evdent n the local maxma of heat flux. The vertcal lnes on Fgure 2 mark the begnnng and the end of the densty current as defned by the temperature decrease and concurrent wnd shft at the 5m level. The 10m data, presented here, lag the 5m data, ndcatng that the head of the densty current s tlted. Ths tlted structure s also evdent n tme-heght cross sectons of temperature, as shown n Poulos et al. (2002b). 3. DISSIPATION RATE CALCULATIONS As descrbed, for example, n Champagne et al. (1977), f u ( f ) s the frequency spectrum of S velocty component u n the nertal range and α s the Kolmogorov constant for the velocty component, the dsspaton rate s gven by 2π f = U 5/3 S u ( f ) α 3/ 2 ε. Ths technque can be used by any hgh-frequency sensor that can measure veloctes n the nertal range (Oncley et al. 1996). Ths method s compared wth other methods of estmatng ε durng the MICROFRONTS experment n paper 7.5 ( Surface-layer turbulence durng a frontal passage, by Pper and Lundqust) of ths volume and n Pper and Lundqust (2004). Only the

3 streamwse component s used for the calculatons shown here. Values of ε are calculated n 300s ntervals, whereas 60s ntervals are presented n Pper and Lundqust (2004). The longer tme seres both smooths out small-scale fluctuatons and ncreases the confdence n the calculatons (Pper, 2001). Fgure 3 shows a tme seres of dsspaton rate at 10m calculated for the 6 hour nterval depcted n Fgure 1. At the tme of the frontal passage, dsspaton rates ncrease to a maxmum value of ~0.4 m 2 s -3, compared to prefrontal values of ~0.05 m 2 s -3. Dsspaton rate levels reman hgh even after the passage of the frontal zone. Note that the maxmum value here, at 10m heght usng 300s ntervals, s one-thrd of the maxmum value calculated usng data from 3m heght at 60s ntervals, presented n Pper & Lundqust (2004). The ncreased dsspaton rate n the frontal zone reflects the ncreased producton of TKE due to mxng n the frontal zone. Prevous work (Blumen et al. 1999) has suggested that the head of a densty current also nduces turbulent mxng. Fgure 4 depcts a tme seres of dsspaton rate at 10m calculated for the 10 hour nterval presented n Fgure 2. Pre-densty current values are ~ 0.1 m 2 s -3, twce those observed before the frontal passage n MICROFRONTS. Even more strkng, the passage of the densty current head s not marked by ncreased dsspaton, as seen n Blumen et al. (1999), and would be expected from the peak n momentum and heat flux seen n Fgure 2, but rather by a suppresson of dsspaton. Dsspaton rates are less than 0.01 m 2 s -3 from the tme of the passage of the head through untl ts end. Ths unque response could be a functon of the relatvely long nterval (300s) used for calculatng ε compared to the tme requred for the head of the densty current to pass; ths behavor wll be nvestgated n future work. 4. COMPARISONS OF OBSERVED DISSIPATION LENGTH WITH PROPOSED MODELS The calculatons presented above, as well as those from dfferent levels durng the same tme perods wll be compared wth several proposed models for dsspaton length. Dsspaton length l ε s typcally proposed to be a related to local stablty, ether through a gradent Rchardson number, a flux Rchardson number, or a local Froude number. The parameterzatons offered by Cheng & Canuto (1994) and Freedman and Jacobson (2003) wll be consdered. Fgure 2: Tme seres from the sonc anemometer mounted at 10m on the man 60m CASES-99 tower on 20 Oct (A) Wnd speed. (B) Wnd drecton. (C) Vrtual temperature. (D) Frcton velocty u* and heat flux wt. Dotted lnes mark the passage of the densty current as defned by the temperature shft at the 5m level; note that the 10m level (shown here) slghtly lags the 5m level, ndcatng a tlted structure to the head of the densty current. 5. SUMMARY Observatons of turbulent knetc energy dsspaton rate n dsturbed stable boundary layers exhbt great varablty. In the 20 March 1995 frontal passage, the dsspaton rate s found to ncrease by nearly an order of magntude to a maxmum value of ~0.4 m 2 s -3, compared to prefrontal values of ~0.05 m 2 s -3. Dsspaton rate levels reman hgh even after the passage of the frontal zone. In the 20 October 1999 densty current, the densty current suppresses TKE dsspaton, from pre-densty current values ~ 0.1 m 2 s -3 to less than 0.01 m 2 s -3. The broad range of

4 stablty condtons offered by these two cases creates an deal testbed for parameterzatons of TKE dsspaton and TKE dsspaton length l ε. Acknowledgements Support for MP has been provded by the Ar Force Offce of Scentfc Research under Grant F and under AASERT Grant F Support for MP and JKL at the Unversty of Colorado has been provded by the Atmospherc Scences Dvson, Mesoscale Dynamcs Program of the Natonal Scence Foundaton under Grant ATM MP also thanks Research Systems, Inc. for allowng a leave of absence. Ths work was performed under the auspces of the U.S. Department of Energy by the Unversty of Calforna, Lawrence Lvermore Natonal Laboratory under contract No. W-7405-Eng-48. References Blumen, W., R.L. Grossman, and M. Pper, 1999: Analyss of heat budget, dsspaton and frontogeness n a shallow densty current. Bound.-Layer Meteorol., 91, Fgure 3: Inertal dsspaton rate calculatons from the 10m sonc anemometer for the 20 Mar 1995 front. Values of ε are calculated n 300s ntervals. Error bars denote 95% confdence ntervals on the means. Champagne, F.H., C.A. Frehe, J.C. LaRue, and J.C. Wyngaard, 1977: Flux measurements, flux estmaton technques, and fne-scale turbulence measurements n the unstable surface layer over land. J. Atmos. Sc., 34, Cheng, Y. and V.M. Canuto, 1994: Stably stratfed shear turbulence: A new model for the energy dsspaton length scale. J. Atmos. Sc., 51, Freedman, F. R. and M. Z. Jacobson. 2003: Modfcaton of the standard ε-equaton for the stable ABL through enforced consstency wth Monn-Obukhov smlarty theory. Bound.-Layer Meteorol., 106, Oncley, S.P., C.A. Frehe, J.A. Busnger, E.C. Itswere, J. C. LaRue and S.S. Chang, 1996: Surface-layer fluxes, profles, and turbulence measurements over unform terran under near-neutral condtons. J. Atmos. Sc., 53, Fgure 4:. Inertal dsspaton rate calculatons from the 10m sonc anemometer for the 20 Oct 1999 densty current. Values of ε are calculated n 300s ntervals. Error bars denote 95% confdence ntervals on the means. Note the expanded ordnate, n comparson to that n Fgure 3.

5 Pper, M., 2001: The Effects of a Frontal Passage on Fne-Scale Nocturnal Boundary Layer Turbulence. Ph.D. dssertaton, Unversty of Colorado at Boulder, Dept. of Astrophyscal, Planetary, and Atmospherc Scences, 217 pp. Pper, M., and J. K. Lundqust, 2004: Surface- Layer Turbulence Measurements durng a Frontal Passage. J. Atmos. Sc., to appear. Poulos, G.S., and co-authors, 2002a: CASES-99: A comprehensve nvestgaton of the stable nocturnal boundary layer. Bull. Amer. Meteor. Soc., 83, Poulos, G.S., J.K. Lundqust, W. Blumen, and S. Neuvlle, 2002b: Shallow Slope Densty Currents durng CASES-99: Observatons and Modelng. 15 th Symposum on Boundary Layers and Turbulence, Wagenngen, The Netherlands, pp