• Acevedo, O. C., , and D. R. Fitzjarrald, 2001: The early evening surface-layer transition: Temporal and special variability. J. Atmos. Sci., 58, 26502667, doi:10.1175/1520-0469(2001)058<2650:TEESLT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Banta, R. M., , Y. L. Pichugina, , and R. K. Newsom, 2003: Relationship between low-level jet properties and turbulence kinetic energy in the nocturnal stable boundary layer. J. Atmos. Sci., 60, 25492555, doi:10.1175/1520-0469(2003)060<2549:RBLJPA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Banta, R. M., , L. Mahrt, , D. Vickers, , J. Sun, , B. B. Balsley, , Y. L. Pichugina, , and E. J. Williams, 2007: The very stable boundary layer on nights with weak low-level jets. J. Atmos. Sci., 64, 30683089, doi:10.1175/JAS4002.1.

    • Search Google Scholar
    • Export Citation
  • Basu, S., , and F. Porte-Agel, 2006: Large-eddy simulation of stably stratified atmospheric boundary layer turbulence: A scale-dependent dynamic modeling approach. J. Atmos. Sci., 63, 20742091, doi:10.1175/JAS3734.1.

    • Search Google Scholar
    • Export Citation
  • Beare, R. J., and et al. , 2006: An intercomparison of large-eddy simulations of the stable boundary layer. Bound.-Layer Meteor., 118, 247272, doi:10.1007/s10546-004-2820-6.

    • Search Google Scholar
    • Export Citation
  • Betts, A. K., , S. Hong, , and H.-L. Pan, 1996: Comparison of NCEP–NCAR reanalysis with 1987 FIFE data. Mon. Wea. Rev., 124, 14801498, doi:10.1175/1520-0493(1996)124<1480:CONNRW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bougeault, P., , and P. LaCarrere, 1989: Parameterization of orography-induced turbulence in a mesobeta-scale model. Mon. Wea. Rev., 117, 18721890, doi:10.1175/1520-0493(1989)117<1872:POOITI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Caughey, S. J., , J. C. Wyngaard, , and J. C. Kaimal, 1979: Turbulence in the evolving stable boundary layer. J. Atmos. Sci., 36, 10411052.

    • Search Google Scholar
    • Export Citation
  • Chen, F., , and J. Dudhia, 2001a: Coupling an advanced land surface–hydrology model with the Penn State–NCAR MM5 modeling system. Part I: Model implementation and sensitivity. Mon. Wea. Rev., 129, 569585, doi:10.1175/1520-0493(2001)129<0569:CAALSH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Chen, F., , and J. Dudhia, 2001b: Coupling an advanced land surface–hydrology model with the Penn State–NCAR MM5 modeling system. Part II: Preliminary model validation. Mon. Wea. Rev., 129, 587604, doi:10.1175/1520-0493(2001)129<0587:CAALSH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Detering, H. W., , and D. Etling, 1985: Application of the E-ε turbulence model to the atmospheric boundary layer. Bound.-Layer Meteor., 33, 113133, doi:10.1007/BF00123386.

    • Search Google Scholar
    • Export Citation
  • Dudhia, J., 1989: Numerical study of convection observed during the winter monsoon experiment using a mesoscale two-dimensional model. J. Atmos. Sci., 46, 30773107, doi:10.1175/1520-0469(1989)046<3077:NSOCOD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Ek, M. B., , K. E. Mitchell, , Y. Lin, , E. Rogers, , P. Grummann, , V. Koren, , G. Gayno, , and J. D. Tarplay, 2003: Implementation of the Noah land surface model advances in the National Centers for Environmental Predication operational mesoscale Eta model. J. Geophys. Res., 108, 8851, doi:10.1029/2002JD003296.

    • Search Google Scholar
    • Export Citation
  • Fiebrich, C. A., , and K. C. Crawford, 2001: The impact of unique meteorological phenomena detected by the Oklahoma Mesonet and ARS Micronet on automated quality control. Bull. Amer. Meteor. Soc., 82, 21732187, doi:10.1175/1520-0477(2001)082<2173:TIOUMP>2.3.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gallice, Q., , F. G. Wienhold, , C. R. Hoyle, , F. Immler, , and T. Peter, 2011: Modeling the ascent of sounding balloons: Derivation of the vertical air motion. Atmos. Meas. Tech., 4, 22352253, doi:10.5194/amt-4-2235-2011.

    • Search Google Scholar
    • Export Citation
  • Grachev, A. A., , E. L. Andreas, , C. W. Fairall, , P. S. Guest, , and P. O. G. Persson, 2007: On the turbulent Prandtl number in the stable boundary layer. Bound.-Layer Meteor., 125, 329341, doi:10.1007/s10546-007-9192-7.

    • Search Google Scholar
    • Export Citation
  • Hacker, J. P., , and W. M. Angevine, 2013: Ensemble data assimilation to characterize surface-layer errors in numerical weather prediction models. Mon. Wea. Rev., 141, 18041821, doi:10.1175/MWR-D-12-00280.1.

    • Search Google Scholar
    • Export Citation
  • Hong, S.-Y., , Y. Noh, , and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 23182341, doi:10.1175/MWR3199.1.

    • Search Google Scholar
    • Export Citation
  • Janjic, Z. I., 2001: Nonsingular implementation of the Mellor-Yamada level 2.5 scheme in the NCEP Meso Model. NOAA/NWS/NCEP Office Note 437, 61 pp.

  • Johansson, C., , and H. Bergstrom, 2005: An auxiliary tool to determine the height of the boundary layer. Bound.-Layer Meteor.,115, 423–432, doi:10.1007/s10546-004-1424-5.

  • Kaimal, J. C., , and J. J. Finnigan, 1994: Atmospheric Boundary Layer Flows: Their Structure and Measurement. Oxford University Press, 289 pp.

    • Search Google Scholar
    • Export Citation
  • Kosovic, B., , and J. A. Curry, 2000: A large eddy simulation study of a quasi-steady, stably stratified atmospheric boundary layer. J. Atmos. Sci., 57, 10521068, doi:10.1175/1520-0469(2000)057<1052:ALESSO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kustas, W. P., , J. H. Prueger, , J. I. MacPherson, , M. Wolde, , and F. Li, 2005: Effects of land use and meteorological conditions on Midwestern cropping systems. J. Hydrometeor., 6, 825839, doi:10.1175/JHM460.1.

    • Search Google Scholar
    • Export Citation
  • LeMone, M. A., and et al. , 2000: Land–atmosphere interaction research, early results, and opportunities in the Walnut River Watershed in southeast Kansas: CASES and ABLE. Bull. Amer. Meteor. Soc., 81, 757779, doi:10.1175/1520-0477(2000)081<0757:LIRERA>2.3.CO;2.

    • Search Google Scholar
    • Export Citation
  • LeMone, M. A., , K. Ikeda, , R. L. Grossman, , and M. W. Rotach, 2003: Horizontal variability of 2-m temperature at night during CASES-97. J. Atmos. Sci., 60, 24312449, doi:10.1175/1520-0469(2003)060<2431:HVOMTA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • LeMone, M. A., , M. Tewari, , F. Chen, , and J. Dudhia, 2013: Objectively determined fair-weather CBL depths in the ARW-WRF model and their comparison to CASES-97 observations. Mon. Wea. Rev., 141, 3054, doi:10.1175/MWR-D-12-00106.1.

    • Search Google Scholar
    • Export Citation
  • Lenschow, D. H., , X. S. Li, , C. J. Zhu, , and B. B. Stankov, 1988: The stably stratified boundary layer over the Great Plains. Bound.-Layer Meteor., 42, 95121, doi:10.1007/BF00119877.

    • Search Google Scholar
    • Export Citation
  • Lin, Y.-L., , R. D. Farley, , and H. D. Orville, 1983: Bulk parameterization of the snow field in a cloud model. J. Climate Appl. Meteor., 22, 10651092, doi:10.1175/1520-0450(1983)022<1065:BPOTSF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Louis, J. F., 1979: A parametric model of vertical eddy fluxes in the atmosphere. Bound.-Layer Meteor., 17, 187202, doi:10.1007/BF00117978.

    • Search Google Scholar
    • Export Citation
  • MacCready, P. B., 1965: Comparison of some balloon techniques. J. Appl. Meteor., 4, 504508, doi:10.1175/1520-0450(1965)004<0504:COSBT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Mahrt, L., , and D. Vickers, 2006: Extremely weak mixing in stable conditions. Bound.-Layer Meteor., 119, 1939, doi:10.1007/s10546-005-9017-5.

    • Search Google Scholar
    • Export Citation
  • Melgarejo, J. W., , and J. W. Deardorff, 1974: Stability functions for the boundary-layer resistance laws based upon observed boundary-layer heights. J. Atmos. Sci., 31, 13241333, doi:10.1175/1520-0469(1974)031<1324:SFFTBL>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., , and T. Yamada, 1974: A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci., 31, 17911806, doi:10.1175/1520-0469(1974)031<1791:AHOTCM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., , and T. Yamada, 1982: Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys. Space Phys., 20, 851875, doi:10.1029/RG020i004p00851.

    • Search Google Scholar
    • Export Citation
  • Mlawer, E. J., , S. J. Taubman, , P. D. Brown, , M. J. Iacono, , and S. A. Clough, 1997: Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave. J. Geophys. Res., 102, 16 66316 682, doi:10.1029/97JD00237.

    • Search Google Scholar
    • Export Citation
  • Monti, P., , H. J. S. Fernando, , M. Princevac, , W. C. Chan, , T. A. Kowalewski, , and E. R. Pardyjak, 2002: Observations of flow and turbulence in the nocturnal boundary layer over a slope. J. Atmos. Sci., 59, 25132534, doi:10.1175/1520-0469(2002)059<2513:OOFATI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Noh, Y., , W. Chen, , S. Hone, , and S. Raasch, 2003: Improvement of the K-profile model for the planetary boundary layer based on large-eddy simulation data. Bound.-Layer Meteor., 107, 401427, doi:10.1023/A:1022146015946.

    • Search Google Scholar
    • Export Citation
  • Pichugina, Y. L., , and R. M. Banta, 2010: Stable boundary layer depth from high-resolution measurements of the mean wind profile. J. Appl. Meteor. Climate,49, 20–35, doi:10.1175/2009JAMC2168.1.

  • Poulos, G. S., and et al. , 2002: CASES-99: A comprehensive investigation of the stable nocturnal boundary layer. Bull. Amer. Meteor. Soc., 83, 555581, doi:10.1175/1520-0477(2002)083<0555:CACIOT>2.3.CO;2.

    • Search Google Scholar
    • Export Citation
  • Richardson, H., , S. Basu, , and A. A. M. Holtslag, 2013: Improving stable boundary-layer height estimation using a stability-dependent critical bulk Richardson number. Bound.-Layer Meteor., 148, 93–109, doi:10.1007/s10546-013-9812-3.

    • Search Google Scholar
    • Export Citation
  • Shin, H. H., , S.-Y. Hong, , and Y. Noh, 2013: Derivation of turbulent kinetic energy from a first-order nonlocal planetary boundary layer parameterization. J. Atmos. Sci., 70, 17951805, doi:10.1175/JAS-D-12-0150.1.

    • Search Google Scholar
    • Export Citation
  • Steeneveld, G. J., , B. J. H. Van de Wiel, , and A. A. M. Holtslag, 2007: Diagnostic equations for the stable boundary layer height: Evaluation and dimensional analysis. J. Appl. Meteor. Climatol., 46, 212225, doi:10.1175/JAM2454.1.

    • Search Google Scholar
    • Export Citation
  • Strang, E. J., , and H. J. S. Fernando, 2001: Vertical mixing and transports through a stratified shear layer. J. Phys. Oceanogr., 31, 20262048, doi:10.1175/1520-0485(2001)031<2026:VMATTA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Strassberg, D., , M. LeMone, , T. Warner, , and J. Alfieri, 2008: Comparison of 10-m observed wind speeds to those based on Monin–Obukhov similarity theory using IHOP_2002 aircraft and surface data. Mon. Wea. Rev., 136, 964972, doi:10.1175/2007MWR2203.1.

    • Search Google Scholar
    • Export Citation
  • Sukoriansky, S., , and B. Galperin, 2008: Anisotropic turbulence and internal waves in stable stratified flows (QNSE theory). Phys. Scr., 132, 014036, doi:10.1088/0031-8949/2008/T132/014036.

    • Search Google Scholar
    • Export Citation
  • Sukoriansky, S., , B. Galperin, , and V. Perov, 2005: Application of a new spectral theory of stably stratified turbulence to the atmospheric boundary layer over ice. Bound.-Layer Meteor., 117, 231257, doi:10.1007/s10546-004-6848-4.

    • Search Google Scholar
    • Export Citation
  • Sukoriansky, S., , B. Galperin, , and V. Perov, 2006: A quasi-normal scale elimination model of turbulence and its application to stably stratified flows. Nonlinear Processes Geophys., 13, 922, doi:10.5194/npg-13-9-2006.

    • Search Google Scholar
    • Export Citation
  • Sun, J., and et al. , 2004: Atmospheric disturbances that generate intermittent turbulence in nocturnal boundary layers. Bound.-Layer Meteor., 110, 255279, doi:10.1023/A:1026097926169.

    • Search Google Scholar
    • Export Citation
  • Sun, J., , L. Mahrt, , R. M. Banta, , and Y. L. Pichugina, 2012: Turbulence regimes and turbulent intermittency in the stable boundary layer during CASES-99. J. Atmos. Sci., 69, 338351, doi:10.1175/JAS-D-11-082.1.

    • Search Google Scholar
    • Export Citation
  • Therry, G., , and P. LaCarrere, 1983: Improving the eddy kinetic energy model for planetary boundary layer description. Bound.-Layer Meteor., 25, 6388, doi:10.1007/BF00122098.

    • Search Google Scholar
    • Export Citation
  • Van de Wiel, B. J. H., , R. J. Ronda, , A. F. Moene, , H. A. R. De Bruin, , and A. A. M. Holtslag, 2002: Intermittent turbulence and oscillations in the stable boundary layer over land. Part I: A bulk model. J. Atmos. Sci., 59, 942958, doi:10.1175/1520-0469(2002)059<0942:ITAOIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Van de Wiel, B. J. H., , A. F. Moene, , O. K. Hartogenesis, , H. A. R. De Bruin, , and A. A. M. Holtslag, 2003: Intermittent turbulence in the stable boundary layer over land. Part III: A classification for observations during CASES-99. J. Atmos. Sci., 60, 25092522, doi:10.1175/1520-0469(2003)060<2509:ITITSB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Van de Wiel, B. J. H., , A. F. Moene, , H. J. J. Jonker, , P. Baas, , S. Basu, , J. M. M. Donda, , J. Sun, , and A. A. M. Holtslag, 2012: The minimum wind speed for sustainable turbulence in the nocturnal boundary layer. J. Atmos. Sci., 69, 31163127, doi:10.1175/JAS-D-12-0107.1.

    • Search Google Scholar
    • Export Citation
  • Vickers, D., , and L. Mahrt, 2004: Evaluating formulations of stable boundary layer height. J. Appl. Meteor., 43, 1736–1749, doi:10.1175/JAM2160.1.

    • Search Google Scholar
    • Export Citation
  • Vickers, D., , and L. Mahrt, 2006: A solution for flux contamination by mesoscale motions with very weak turbulence. Bound.-Layer Meteor., 118, 431447, doi:10.1007/s10546-005-9003-y.

    • Search Google Scholar
    • Export Citation
  • Vogelezang, D. H. P., , and A. A. M. Holtslag, 1996: Evaluation and model impacts of alternative boundary-layer height formulations. Bound.-Layer Meteor., 81, 245269, doi:10.1007/BF02430331.

    • Search Google Scholar
    • Export Citation
  • Wang, J., , J. Bian, , W. O. Brown, , H. Cole, , V. Grubisic, , and K. Young, 2009: Vertical air motion from T-REX radiosonde and dropsonde data. J. Atmos. Oceanic Technol., 26, 928942, doi:10.1175/2008JTECHA1240.1.

    • Search Google Scholar
    • Export Citation
  • Yamada, T., 1979: Prediction of the nocturnal surface inversion height. J. Appl. Meteor., 18, 526531, doi:10.1175/1520-0450(1979)018<0526:POTNSI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • View in gallery

    Steady-state LES TKE profiles for the weakly stable (L > 100 m) Arctic SBL. Black refers to Kosovic and Curry (2000), red refers to Basu and Porte-Agel (2006), and SGS is the subgrid scale.

  • View in gallery

    CASES-97 observational array. Numbers indicate surface flux sites. At the vertices of the triangle lie 915-MHz RWP/MS sites BEA (elevation 478 m), OXF (360 m), and WHI (430 m), with collocated radiosonde releases. Solid lines indicate flight tracks. Terrain contour interval is 20 m.

  • View in gallery

    Illustration of how hSmax, hTmax, hRiloc, h1wsonde, and h2wsonde are estimated from radiosonde data.

  • View in gallery

    Comparison of PBL scheme h (solid lines) for MYJ, QNSE, and YSU to subjective values based on TKE or Kh profiles (dashed lines). No h value is defined for BouLac in stable conditions. Squares are the full grid levels (zf) for MYJ, QNSE, and YSU and half grid levels (zh) for BouLac.

  • View in gallery

    For MYJ at Beaumont on 5 May 1997, the evaluation of h criteria based on TKE profiles (shifted 2 m2 s−2 each 2 h); “1M” in upper left of the first panel indicates that criterion 1 failed to identify h. Sunset was around 0130 UTC (1930 CST).

  • View in gallery

    For Beaumont, evaluation of eight potential h criteria based on comparisons to series of TKE profiles like those in Fig. 5 for nights of 4–5, 10–11, and 20–21 May. Labels refer to dates in UTC and M signifies May.

  • View in gallery

    Observed NBL features: hTmax (red circles), hSmax (blue circles for radiosondes, green squares for RWP + MS), h1wsonde (tan upside down triangles), and h2wsonde (tan triangles). Heights of minimum wind profile curvature (if it differs from hSmax sometime during the night): radiosonde (small turquoise dots) and RWP + MS (small light green squares). For Whitewater 5 May, smaller dots and the dashed blue line indicate heights of secondary maxima in Tυ and S.

  • View in gallery

    Time series of radiosonde depths of NBL features Smax and Tmax (symbols), minimum h1wsonde, and maximum h2wsonde (lines) after compositing using values at 0930 UTC as described in text. For the few times that minimum curvature in the wind profile did not correspond to Smax (see Fig. 7) the corresponding height was used rather than the height of Smax. Symbols represent location: Beaumont (squares), Whitewater (upside down triangles), and Oxford (circles).

  • View in gallery

    (left) Four patterns in hSmax and hTvmax evolution, along with h estimates and hMYJ (light blue line, top frame only). Top three panels show averages of Beaumont, Oxford, and Whitewater heights; the bottom panel is for one location/date. (right) Approximate grid height zh.

  • View in gallery

    For the three TKE schemes, frequency of times for which hTvmax increases with time, until it follows hSmax as observed, compared to too-low hTvmax (<50 m AGL) and too-high hTvmax (more than a grid point higher than hSmax) leading to patterns in Fig. 9.

  • View in gallery

    As in Fig. 10, but for YSU 3.2 and YSU 3.4.1. Number of samples are in parentheses.

  • View in gallery

    For a case of too-low hTvmax at Beaumont, 4–5 May 1997. (left) Evolution of hTvmax and hSmax. (right) Profiles of Θυ − 0.0098z (same shape as Tυ) and S at 0500 UTC.

  • View in gallery

    As in Fig. 12, but for turbulence variables for BouLac, QNSE, YSU 3.2, YSU 3.4.1, MYJ, and MYJ2 (MYJ rerun to extract KM but on a different computer). (top left) KH and (top right) KM; (bottom left) TKE, and (bottom right) Lmix. MYJ2 denoted by dashed line.

  • View in gallery

    (top) For 5 May Beaumont, inverse Prandtl number KH/KM as a function of height for hourly profiles from 0200 to 1000 UTC. (bottom) Relationship between KH/KM and local Richardson number, superposed on plot from Monti et al. (2002). For the bottom plot, the field data were collected in nocturnal downslope flows during the Vertical Transport and Mixing Experiment. Laboratory data are from Strang and Fernando (2001). The dashed line extending QNSE to higher Riloc is based on Fig. 4 of Sukoriansky et al. (2006).

  • View in gallery

    For 21 May Whitewater, observed and modeled time series of NBL profile features. Observations: Red with hSmax from both radiosondes (circles) and RWP + MS (squares), and h zone based on h1wsonde (upside down triangles) and h2wsonde (triangles). For PBL schemes: BouLac (green), MYJ (turquoise), QNSE (blue), and YSU 3.4.1 (purple). For BouLac, QNSE, and MYJ, h = ; for YSU, h = hYSU. Also shown is h = hMYJ (light turquoise). (right) Indicates grid heights for (top),(middle) zh and (bottom) zf.

  • View in gallery

    For Whitewater 0800 UTC 21 May, profiles of observed and modeled mean and turbulence parameters. Red and oranges represent observations. For PBL schemes, green is BouLac, turquoise is MYJ, blue is QNSE, and purple is YSU 3.4.1.

  • View in gallery

    Comparison of modeled to observed hTvmax, hSmax, and h. Model hTvmax represented by hυ,z = 10 K km−1); observed hTvmax represented by hTmax. For the model, h = for BouLac, QNSE, and MYJ (left value) and h = hYSU for YSU. Right h value for MYJ = hMYJ. Observed h bounded by h1wsonde and h2wsonde. Table cells not filled in represent departures that are consistently too high (or too low) by ~1–2 grid points. Averaging intervals (in parentheses) are from either 0200–1000 UTC or over times for which there are observed values.

  • View in gallery

    For YSU 3.4.1, profiles of K and Riloc. (top) Weaker wind night and (bottom) stronger wind night and time corresponding to Figs. 12 and 13.

  • View in gallery

    Observed (sites 1 and 2) and modeled (Beaumont) time series of and . For observations, vertical flux of sonic anemometer temperature is used. Symbols: for observations, orange triangles are for site 2 in Fig. 1; red upside down triangles are for site 1. Model results for Beaumont: circles (green is BouLac, turquoise is MYJ, blue is QNSE, and purple is YSU 3.4.1.).

  • View in gallery

    As in Fig. 19, but comparing modeled fluxes using MYJ at Beaumont, site 1, and site 2 to observations at sites 1 and 2.

  • View in gallery

    As in Fig. 20, but for 10-m wind speed, with model wind interpolated linearly between level 1 (~5 m) and level 2 (~14 m).

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 50 50 3
PDF Downloads 24 24 2

Objectively Determined Fair-Weather NBL Features in ARW-WRF and Their Comparison to CASES-97 Observations

View More View Less
  • 1 National Center for Atmospheric Research,* Boulder, Colorado
© Get Permissions
Full access

Abstract

Heights of nocturnal boundary layer (NBL) features are determined using vertical profiles from the Advanced Research Weather Research and Forecasting Model (ARW-WRF), and then compared to data for three moderately windy fair-weather nights during the April–May 1997 Kansas-based Cooperative Atmosphere–Surface Exchange Study (CASES-97) to evaluate the success of four PBL schemes in replicating observations. The schemes are Bougeault–LaCarrere (BouLac), Mellor–Yamada–Janjić (MYJ), quasi-normal scale elimination (QNSE), and Yonsei University (YSU) versions 3.2 and 3.4.1. This study’s chosen objectively determined model NBL height h estimate uses a turbulence kinetic energy (TKE) threshold equal to 5% , where TKE′ is relative to its background (free atmosphere) value. The YSU- and MYJ-determined h could not be improved upon. Observed heights of the virtual temperature maximum hTvmax and wind speed maximum hSmax, and the heights h1wsonde and h2wsonde, between which the radiosonde slows from ~5 to ~3 m s−1 as it rises from turbulent to nonturbulent air, and thus brackets h, were used for comparison to model results. The observations revealed a general pattern: hTvmax increased through the night, and hTvmax and hSmax converged with time, and the two mostly lay between h1wsonde and h2wsonde after several hours. Clear failure to adhere to this pattern and large excursions from observations or other PBL schemes revealed excess mixing for BouLac and YSU version 3.2 (but not version 3.4.1) and excess thermal mixing for QNSE under windy conditions. Observed friction velocity was much smaller than model values, with differences consistent with the observations reflecting local skin drag and the model reflecting regional form drag + skin drag.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: Margaret A. LeMone, National Center for Atmospheric Research, 3090 Center Green Dr., Boulder, CO 80301. E-mail: lemone@ucar.edu

Abstract

Heights of nocturnal boundary layer (NBL) features are determined using vertical profiles from the Advanced Research Weather Research and Forecasting Model (ARW-WRF), and then compared to data for three moderately windy fair-weather nights during the April–May 1997 Kansas-based Cooperative Atmosphere–Surface Exchange Study (CASES-97) to evaluate the success of four PBL schemes in replicating observations. The schemes are Bougeault–LaCarrere (BouLac), Mellor–Yamada–Janjić (MYJ), quasi-normal scale elimination (QNSE), and Yonsei University (YSU) versions 3.2 and 3.4.1. This study’s chosen objectively determined model NBL height h estimate uses a turbulence kinetic energy (TKE) threshold equal to 5% , where TKE′ is relative to its background (free atmosphere) value. The YSU- and MYJ-determined h could not be improved upon. Observed heights of the virtual temperature maximum hTvmax and wind speed maximum hSmax, and the heights h1wsonde and h2wsonde, between which the radiosonde slows from ~5 to ~3 m s−1 as it rises from turbulent to nonturbulent air, and thus brackets h, were used for comparison to model results. The observations revealed a general pattern: hTvmax increased through the night, and hTvmax and hSmax converged with time, and the two mostly lay between h1wsonde and h2wsonde after several hours. Clear failure to adhere to this pattern and large excursions from observations or other PBL schemes revealed excess mixing for BouLac and YSU version 3.2 (but not version 3.4.1) and excess thermal mixing for QNSE under windy conditions. Observed friction velocity was much smaller than model values, with differences consistent with the observations reflecting local skin drag and the model reflecting regional form drag + skin drag.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: Margaret A. LeMone, National Center for Atmospheric Research, 3090 Center Green Dr., Boulder, CO 80301. E-mail: lemone@ucar.edu

1. Introduction

The objectives of this paper are to evaluate the heights of significant nocturnal boundary layer (NBL) features using observed and model profiles and then use them to evaluate four planetary boundary layer (PBL) schemes in high-resolution (1-km innermost grid) simulations using the Advanced Research version of the Weather Research and Forecasting Model (ARW-WRF, hereafter referred to as WRF). As in its companion paper, LeMone et al. (2013), which examined the convective boundary layer (CBL), we focus on the Yonsei University (YSU; Hong et al. 2006), Mellor–Yamada–Janjić (MYJ; Janjić 2001), Bougeault–LaCarrere (BouLac; Bougeault and LaCarrere 1989), and quasi-normal scale elimination (QNSE; Sukoriansky and Galperin 2008; Sukoriansky et al. 2005) and use data from three fair-weather nights with mostly moderate winds during the April–May 1997 Kansas-based Cooperative Atmosphere–Surface Exchange Study (CASES-97; LeMone et al. 2000) field program. After identifying a good criterion for objectively determining NBL depth h, we explore PBL-scheme strengths and shortcomings by comparing the behavior and magnitudes of h, hTvmax, and hSmax, respectively the heights of the virtual temperature Tυ and wind speed S maxima, to observations.

While the CBL has a well-defined mixed-layer top, the NBL h can be difficult to identify. Numerous methods have been tried (Table 1). Diagnosis of h using mean or instantaneous vertical profiles has had mixed success. Using Doppler lidar data, Pichugina and Banta (2010) found a strong correspondence of hSmax to h as defined by profiles of the variance of the radial velocity for a subset of wind profiles (one maximum, wind in lowest 200 m greater than 5 m s−1), with minimum curvature in the S profiles yielding even better results. However, in a large-eddy simulation (LES) of a weakly stable NBL (Obukhov length L > 100 m) by Kosovic and Curry (2000), hSmax and hTvmax coincided with h only under steady-state conditions, after about one inertial period of simulation. Similarly, observations show that hTvmax does not necessarily coincide with hSmax or h in moderately to very stable conditions (e.g., Figs. 6 and 7 of Mahrt and Vickers 2006). Indeed, as illustrated in Banta et al. (2007) and Sun et al. (2004) and elsewhere, the NBL often has a complex structure that varies with time.

Table 1.

Selected potential criteria for NBL depth h from vertical profiles.

Table 1.

Bulk Richardson numbers (e.g., Vogelezang and Holtslag 1996) and more complex formulations (e.g., Vickers and Mahrt 2004; Steeneveld et al. 2007) have also been used, with varying degrees of success. A significant shortcoming of such approaches is that radiosonde data need to be smoothed for reliable estimates. Also, magnitudes of criteria using vertical gradients, including Richardson numbers, tend to vary with the vertical spacing used.

When turbulence data are available, the height at which a second-moment variable decreases to a specific fraction of its surface or near-surface maximum provides a useful estimate of h. Examples of such parameters are buoyancy flux (Caughey et al. 1979), vertical velocity variance (Vickers and Mahrt 2004), vertical flux of the component of the horizontal momentum along the surface wind direction (Kosovic and Curry 2000), and the turbulence kinetic energy (TKE; Lenschow et al. 1988). Fortunately, such parameters tend to be internally consistent, at least for weakly stable NBLs [e.g., see LES of Kosovic and Curry (2000), Basu and Porte-Agel (2006), and simulations summarized in Beare et al. (2006); compare to http://gabls.metoffice.com/variance_625.html and follow the menu for profiles of fluxes and means].

Since TKE profiles are available from WRF runs, we use them to determine subjective h (hsubj) for BouLac, MYJ, and QNSE and use the profiles and resulting hsubj to judge the model h metrics in Table 1. For YSU, we use the eddy exchange coefficient K, noting its relationship to TKE (Shin et al. 2013). The LES-generated TKE profiles of Kosovic and Curry (2000) and Basu and Porte-Agel (2006) in Fig. 1 illustrate what we can expect for weakly stable conditions. The two profiles in the figure have weakly concave-up, almost linear shapes, with a maximum at the lowest grid level (10 m). The authors found h by dividing by 0.95 the height at which , where the wind component up is parallel to the surface wind, w is the vertical wind, the overbars indicate an average, and the primes indicate a deviation from that average. In the figure, their h is roughly the height at which TKE(h) = 0.045TKE(10 m). However, we recognize that the TKE profile can depart significantly from this ideal. For example, Pichugina and Banta (2010) are forced to define their h in terms of the first significant minimum in their radial velocity variance profiles since there can be significant turbulence higher up.

Fig. 1.
Fig. 1.

Steady-state LES TKE profiles for the weakly stable (L > 100 m) Arctic SBL. Black refers to Kosovic and Curry (2000), red refers to Basu and Porte-Agel (2006), and SGS is the subgrid scale.

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

Here, we estimate h, hTvmax, and hSmax for observed NBLs that are deep enough for analysis using radiosondes, radar wind profilers, and minisodars, perform the same exercise for corresponding model profiles, and use model–observation comparisons to evaluate the behavior of the four PBL schemes. Observations, data analysis, and stability regimes are described in section 2. In section 3, we describe the model setup and PBL schemes and then explain how model TKE profiles are used to select from Table 1 the best h criterion for comparison to observations. In section 4, we evaluate the PBL schemes in terms of how well they replicate observed NBL evolution patterns and how predicted and modeled heights compare from day to day and make suggestions for future improvements, and we compare surface fluxes and discuss the origins and implications of their differences. We summarize the results and suggest future work in section 5.

a. The observational array

A major objective of CASES-97 was to examine the diurnal evolution of the fair-weather PBL. Radiosondes, released at 90-min intervals for four 24-h periods (1100 to 0930 UTC the following day), radar wind profilers (RWP), and minisodars (MS) at Beaumont (BEA), Whitewater (WHI), and Oxford (OXF) provided PBL profiles (Fig. 2). We used the “blended” RWP + MS data, which are simply combined from the two sources (R. Coulter, Argonne National Laboratory, 2014, personal communication). Surface mean and flux data from the sites numbered from 1 to 8 were used for comparison and defining stability. (The radiosonde data are available from http://data.eol.ucar.edu/codiac/ds_proj?CASES-97, the RWP and MS data are available from http://gonzalo.er.anl.gov/ABLE/, and the surface data are available from http://www.eol.ucar.edu/isf/projects/cases97/asciiDownload30min.jsp.)

Fig. 2.
Fig. 2.

CASES-97 observational array. Numbers indicate surface flux sites. At the vertices of the triangle lie 915-MHz RWP/MS sites BEA (elevation 478 m), OXF (360 m), and WHI (430 m), with collocated radiosonde releases. Solid lines indicate flight tracks. Terrain contour interval is 20 m.

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

Comparisons to radiosonde data indicated that the MS winds were good (MS data at Whitewater were only available for 10 and 20 May). As for the RWP, Beaumont winds were of good quality for all four nights, with Whitewater data totally absent on 29 April, of poor quality on 5 May, good for 10–11 and 20–21 May, and Oxford winds were of marginal quality. Radiosonde data were missing after 0500 UTC at Whitewater on 11 May (see Fig. 7).

b. Determination of NBL depth from observations

Figure 3 illustrates how the heights of the NBL features listed in Table 1 are identified subjectively from observations. Temperature T profiles were smooth enough to make hTmax easy to determine, with an uncertainty of the order of the radiosonde data spacing, 30–50 m, while scatter in the wind profile can increase uncertainty for hSmax to ~50 m. Heights at which the increase of wind with height suddenly slows down without reaching a maximum [a rough correspondence to Pichugina and Banta (2010)’s minimum curvature in the speed profile] were also documented, but this situation was rare (see Fig. 7). Evaluation of hSmax from the blended RWP + MS data was sometimes complicated by a jump in speed in the transition from RWP to MS measurements at about 150 m, likely a result of ground clutter contamination of the RWP data. Vertical spacing is 60 m for the RWP data at Whitewater and Beaumont and 5 m for the MS data. Scatter and coarse data spacing in the radiosonde data made Richardson numbers unreliable on most days.

Fig. 3.
Fig. 3.

Illustration of how hSmax, hTmax, hRiloc, h1wsonde, and h2wsonde are estimated from radiosonde data.

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

In the final technique, h is based on the rapid decrease in sonde vertical velocity wsonde as the balloon travels from turbulent to nonturbulent air (Johansson and Bergstrom 2005), which results from an increase in drag on the balloon once it enters laminar flow (MacCready 1965; Gallice et al. 2011; Wang et al. 2009). This method is appealing because it directly relates to our TKE-based NBL definition. In contrast to the one PBL depth chosen by Johannson and Bergstrom, we used two depths, h1wsonde and h2wsonde, to identify the lower and upper limits of the height interval through which wsonde falls from its “turbulent” to “nonturbulent” value. A low bias for hwsonde of up to 30 m results from the fact that the balloon responds to the turbulence, while the sonde, which collects the data, is attached to the balloon by a 30-m string. The angle of the string to the vertical is unknown, so we do not correct for this bias.

It was not possible to estimate h from wsonde if the NBL was much less than ~100 m deep. It takes time for the sonde to unreel from the balloon and for the balloon–sonde system to accelerate to a typical speed of ~5 m s−1, and there were typically only 3–4 points below 100 m at the 10-s data rate. Given the general association of deeper NBLs with larger (e.g., Caughey et al. 1979; Steeneveld et al. 2007), we limited our analysis to windier nights. Even so, the balloon rise rate method did not always work, because balloon inflation was not optimum or vertical air motions modified balloon rise rate.

c. NBL classification

The data used for this study were gathered in rolling terrain (Fig. 2) with varying land cover (Table 2); both cause wind and turbulence to vary horizontally. Indeed, according to Acevedo and Fitzjarrald (2001), Fiebrich and Crawford (2001), Van de Wiel et al. (2002), and others, the turbulent near-surface flow sometimes detaches from the surface, especially in lower-lying areas. With this in mind, we characterize the NBL in a regional sense.

Table 2.

Conditions for days examined (time in UTC). B is Beaumont (open grassland), O is Oxford (some trees), and W is Whitewater (grassland). Figure 2 shows site locations. Italics indicate data that are from the radiosonde.

Table 2.

According to LeMone et al. (2003), NBLs regionally vary from being continuously turbulent and fully coupled to the surface, with air trajectories following the terrain along the synoptic wind direction, to having only weak turbulence driven by drainage winds. In the former case, the 2-m T changes with the elevation, T2m,el ~ −9.8 K km−1, following the adiabatic lapse rate, while T2m,el > +40 K km−1 for the latter case (their Fig. 5), with a magnitude that increases with the vertical T gradient; low-lying locations where radiative cooling is not offset by downslope winds or turbulent mixing also increase T2m,el. From Table 2, T2m,el = −11 K km−1 (based on a least squares straight line for T2m as a function of elevation for sites 1–8), and the wind direction varies little spatially, indicating that the synoptic flow on 4–5 May is continuously coupled to the surface at 0930 UTC. On the other hand, intermediate T2m,el and more variation in wind direction on the nights of 10–11 May and 20–21 May suggest some influence by drainage flow, with possible occasional decoupling and associated cooling, especially for the low-lying stations.

A similar picture emerges from the local classification scheme of Van de Wiel et al. (2003), who use net radiation Rnet and , where the friction velocity and u′ and υ′ are the horizontal wind components, to identify three regimes: “continuous turbulent,” “intermittent,” and “radiative.” To identify the regimes for CASES-97, we plotted on their Fig. 8 our best estimates of h along with three sets of flux averages (for sites 1–8, the two highest grassland sites 1 and 2, and the two floodplain sites 3 and 6). Assuming that the regimes in the figure apply (reasonable since CASES-97 was in the same location), we found that 4–5 May falls in the continuous turbulence regime for all three averages at 0930 UTC and a mix of intermittent and continuous turbulence at 0200 UTC. The other 2 days fall mostly in the intermittent regime, consistent with the evaluation based on T2m,el. The fourth night, 28–29 April (not shown), falls in the radiative regime for all three averages and thus was considered too stable to be included here.

Following Van de Wiel et al. (2012) and Sun et al. (2012), classifying the days according to whether the wind speed at a given height is capable of sustaining turbulence beneath also reveals a similar picture. Based on Cabauw data, Van de Wiel et al. found that continuous turbulence is maintained when the wind at 40 m exceeds ~5 m s−1, with the threshold increasing with |Rnet|. Using data from the 55-m CASES-99 tower, Sun et al. found that threshold speeds increase with height, with values of ~7 m s−1 at 40 m and ~8 m s−1 at 50 m. The CASES-99 thresholds are larger than for Cabauw at least partially because of larger |Rnet| [cf. Fig. 4 of Van de Wiel et al. (2012) for Cabauw to Table 2 of Van de Wiel et al. (2003) for CASES-99]. Since |Rnet| in our Table 3 is close to that during CASES-99, 7.5–8 m s−1 is a good threshold speed at 48 m for CASES-97 as well as CASES-99. Based on this criterion, turbulence below 48 m can be sustained on 4–5 May, at Beaumont and Whitewater at 0930 UTC 10–11 May, for Beaumont on 20–21 May, and for Oxford at 0930 UTC 21 May.

Table 3.

Net radiation (W m−2) at surface flux sites 1–8.

Table 3.

2. Model setup and analysis

a. WRF runs

The model results analyzed are from WRF version 3.2 runs described in LeMone et al. (2013) for 4–5 May, 10–11 May, and 20–21 May, with an additional set performed using WRF version 3.4 with YSU version 3.4.1. Each simulation was run for 24 h, starting at 1200 UTC (0600 LST), using four two-way interacting nested grids with spacing of 27, 9, 3, and 1 km, respectively. The 2128 × 2547 km2 outer domain (Fig. 4; LeMone et al. 2013) extends across most of the continental United States, and the inner 127 × 107 km2 grid is centered on the CASES array. The vertical grid has 44 sigma levels, with the lowest half model level just below 5 m, spacing increasing with height (e.g., Fig. 4), and the top level at about 16 km. Initial and boundary conditions for WRF are from the 3-h North American Regional Reanalysis (NARR; http://rda.ucar.edu/datasets/ds608.0/) data on a 32-km grid.

Fig. 4.
Fig. 4.

Comparison of PBL scheme h (solid lines) for MYJ, QNSE, and YSU to subjective values based on TKE or Kh profiles (dashed lines). No h value is defined for BouLac in stable conditions. Squares are the full grid levels (zf) for MYJ, QNSE, and YSU and half grid levels (zh) for BouLac.

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

The physical parameterizations include the Noah land surface model (Chen and Dudhia 2001a,b; Ek et al. 2003), the Rapid Radiative Transfer Model (RRTM) long-wave parameterization scheme (Mlawer et al. 1997), the Dudhia (1989) shortwave radiation scheme, and the Lin et al. (1983) bulk microphysics scheme. Three PBL schemes (described in more detail in the next section) were linked to their default surface layer options (option 1 for YSU, option 2 for MYJ, and option 4 for QNSE); BouLac uses the same option as MYJ. Surface characteristics are based on the Moderate Resolution Imaging Spectroradiometer (MODIS) VEGPARM Table version 3.1.1, with modified surface roughness values zo (see Table 3; LeMone et al. 2013). Land use types over the CASES-97 array are mainly crop- and grassland, with the latter increasing eastward. All three grassland sites used for model observation comparisons (Beaumont, site 1, and site 2) correspond to grassland grid cells in WRF.

b. PBL schemes in stable conditions

The four PBL schemes, BouLac, MYJ, QNSE, and YSU, are outlined in Table 4, along with references. The first three, henceforth called TKE schemes, solve various forms of the equation for TKE (represented here by e), given by
e1
where the wind components (u, υ, w) are in a right-handed coordinate system with u positive east, and each component is the sum of the resolved (upper case) and unresolved/parameterized (primed) component. For Tυ and air density ρ the resolved portion is indicated with an overbar. The first two terms on the right-hand side are the vertical divergence of vertical energy transport and vertical pressure transport by w′,1 the third and fourth terms are shear production, the fifth term is buoyancy production, and the sixth term is dissipation. Note that the three TKE schemes allow neither TKE transport by the resolved flow nor horizontal TKE transport by turbulence.
Table 4.

Characteristics of PBL schemes for stable conditions. N is the Brunt−Väisälä frequency. TKE units are m2 s−2.

Table 4.
For all four PBL schemes (including YSU, for which the nonlocal terms are zero for stable conditions), the tendency for a quantity C due to subgrid fluxes is found using an eddy diffusivity Kc from
e2
The eddy viscosity KM for the TKE schemes is given by
e3
In (3), K is the eddy diffusivity, and the subscripts M and H refer to momentum and heat, respectively. The master length scale Lmix and the function FM,H varies with the scheme (Table 4) as does the Prandtl number Pr, given by the ratio KM/KH. Note that Pr = 1 for BouLac. Also, Lmix for BouLac is the maximum vertical distance traveled by a frictionless air parcel with initial vertical velocity (2e)1/2, against unfavorable thermal stratification. This simplification, which ignores the decrease with stability of the fractional contribution of to e, is expected to overestimate Lmix (Therry and LaCarrere 1983).
For YSU, KH,M for a stable boundary layer is calculated from the YSU NBL depth hYSU via
e4
where the von Kármán constant k = 0.4 and ws is essentially equal to the friction velocity in YSU version 3.2 and in YSU version 3.4.1.

c. Evaluation of model NBL depth and selection of the 5% criterion

The model output h values, hMYJ, hQNSE, and hYSU, based on the criteria listed in Table 4 and shown as solid lines in Fig. 4, diverge much more than implied by the actual profiles of TKE or, for YSU, K (hsubj indicated by dashed lines). Also, TKE falls with height to a different “background” value for each scheme. Thus, we defined a candidate NBL depth as the height satisfying
e5
where TKEb is the background value and f = 0.05 (~ the value in Fig. 1) or 0.10. For BouLac, TKEmax was always at half grid level zh2 (~5 m). For MYJ and QNSE, TKEmax tended to occur at the surface (full grid level zf1) but not always; so TKEmax was determined for the lowest kilometer. We also considered the same TKE thresholds as in LeMone et al. (2013), namely, 0.101 and 0.2 m2 s−2.

The candidate h criteria based on the mean profiles and Richardson numbers are listed in Table 1. Note that the altitude at which the vertical gradient of virtual potential temperature Θυ,z = 10 K km−1 is within ~10 m of hTvmax. This is not surprising, as can be shown by subtracting the adiabatic lapse rate from to obtain a profile with the same shape as Tυ. Thus, we use hTvmax in the text for the sake of brevity, while using or Θυ,z = 10 K km−1 in the figures for the sake of accuracy. We do not evaluate minimum curvature objectively but discuss it in section 4.

To describe the bulk Richardson number Ri criteria, we start with the expression
e6
where the subscripts b and t denote the bottom and top of the layer for which Ri is calculated. Thus, for the local Richardson number Riloc in Table 1, the subscripts b and t refer to adjacent grid points. For the Richardson number Rilayer, the two subscripts refer to the top grid point of the layer and the lowest grid point above the surface (level 1 at height zh1). The Rilayer used to find hYSU (RiYSU) is based on (6) with Ub and Vb set to zero. The layer Ris are assigned to the layer top; Riloc is assigned to the layer midpoint.

All thresholds are examined moving upward until their value is bracketed and interpolation can take place to determine the corresponding h.

The eight candidate h indicators were plotted on TKE (or for YSU, K) profiles for each night and location for subjective assessment, as illustrated in Fig. 5.2 The TKE only slightly above the background (0.1 m2 s−2) in the upper part of the profiles at 0000 and 0200 UTC is associated with decaying CBL turbulence. After 0200 UTC, the two hRi are close to or slightly higher than hsubj, the top of the enhanced TKE profile. The TKE-based criteria 5, 7, and 8 do well through the night, but hTKE from criterion 6 (TKE = 0.101 m2 s−2) is initially greater than hsubj by two grid points, changing to one grid point later on. Finally, hTvmax and hSmax are different from one another and from hsubj at the beginning of the night, but converge by 0500 UTC, after which they correspond to within one grid point.

Fig. 5.
Fig. 5.

For MYJ at Beaumont on 5 May 1997, the evaluation of h criteria based on TKE profiles (shifted 2 m2 s−2 each 2 h); “1M” in upper left of the first panel indicates that criterion 1 failed to identify h. Sunset was around 0130 UTC (1930 CST).

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

Figure 6 summarizes the height comparisons for Beaumont. From the figure, criteria 7 or 8 were closest to hsubj. Comparing results from all three profiler sites, we chose criterion 7, which we will call the 5% criterion, as our best estimate of h. Constant TKE thresholds did not work as well, with h high biases for large TKE changing to low biases for small TKE, and sometimes TKE maxima remained below the TKE threshold, implying “no” NBL when subjective or percentage-based assessments indicated there was one. Nor were Richardson number criteria a good match, with the relationship of hRi to hsubj varying from hour to hour and from day to day. Indeed, QNSE hRiloc (criterion 3) was both greater and less than hsubj on 5 May. As in Fig. 5, hTvmax (criterion 1) and hSmax (criterion 2) for MYJ and QNSE were different from hsubj right after sunset, but were mostly within one grid point of hsubj after several hours. The YSU h value hYSU was closer to hsubj than those based on the criteria in Fig. 6 and hence will be used here. This is not surprising, since hYSU is used to calculate K in (4).

Fig. 6.
Fig. 6.

For Beaumont, evaluation of eight potential h criteria based on comparisons to series of TKE profiles like those in Fig. 5 for nights of 4–5, 10–11, and 20–21 May. Labels refer to dates in UTC and M signifies May.

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

The 5% criterion has its drawbacks. For example, the logical choice of hsubj as the height at which the TKE decrease with height abruptly slows down can lead to a value quite different from . This problem was common for QNSE, since its TKE profile decreases asymptotically with height toward its background value; such profiles also occur in the early evening for the other TKE schemes due to decaying turbulence in the residual layer. Further, the TKE profiles sometimes depart significantly from Fig. 1, especially on weaker wind nights, with TKEmax several grid points above the surface. In such circumstances, can occur either above or below the height of , depending on where the criterion is first met.

d. Uncertainty in heights of NBL features in WRF output

Our analysis is limited by relatively coarse vertical grid spacing compared to h, which varied from ~100 m (resolved by 5 grid points) to ~500 m (resolved by 10 grid points). In addition, maps of 1-km domain w at 270 m (a “typical” NBL depth) indicate weak but noticeable resolved wave structures, which could displace h, hSmax, and hTvmax vertically. While their impact appears to be minor for the weaker wind nights, the structures reach an amplitude of ~0.1 m s−1 by 0900 UTC 5 May. With a northwest–southeast orientation and a 30-km wavelength along the north–south wind (20 m s−1) this translates to a worst-case displacement of features of up to ~24 m.

3. Comparison to observations

a. Relationship among observed NBL profile features

Since our sample is small, we look for repeatable behavior of hSmax, hTvmax, h1wsonde, and h2wsonde before comparison to model results. The observations are summarized in Fig. 7. Though there are considerable differences among the three heights for some of the cases, there is a close match between hTmax and hSmax by 0800 UTC (0200 LST), just as for the model results in Figs. 5 and 6. Note that Beaumont had the fewest clear estimates of h1wsonde and h2wsonde, perhaps due to air currents associated with nearby terrain.

Fig. 7.
Fig. 7.

Observed NBL features: hTmax (red circles), hSmax (blue circles for radiosondes, green squares for RWP + MS), h1wsonde (tan upside down triangles), and h2wsonde (tan triangles). Heights of minimum wind profile curvature (if it differs from hSmax sometime during the night): radiosonde (small turquoise dots) and RWP + MS (small light green squares). For Whitewater 5 May, smaller dots and the dashed blue line indicate heights of secondary maxima in Tυ and S.

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

The composited data (Fig. 8) show convergence of hTmax and hSmax with time, with hTmax starting out lower than hSmax but increasing fast enough to catch up with it by around 0800 UTC, at which time both lie within the h range bracketed by minimum h1wsonde and maximum h2wsonde. Composite time series of each height were estimated using its value at 0930 UTC. For example, for each night and location, (i) the time series hTmax(t) was divided by hTmax(t = 0930 UTC), (ii) the hTmax(t = 0930 UTC) values were averaged (for all cases in Fig. 7 except for 11 May/Whitewater, when soundings ended before 0930 UTC), and (iii) the normalized heights were multiplied by the average 0930 UTC value to obtain its composite value. The procedure was similar for hSmax, h1wsonde, and h2wsonde.

Fig. 8.
Fig. 8.

Time series of radiosonde depths of NBL features Smax and Tmax (symbols), minimum h1wsonde, and maximum h2wsonde (lines) after compositing using values at 0930 UTC as described in text. For the few times that minimum curvature in the wind profile did not correspond to Smax (see Fig. 7) the corresponding height was used rather than the height of Smax. Symbols represent location: Beaumont (squares), Whitewater (upside down triangles), and Oxford (circles).

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

Time convergence of hTmax and hSmax is supported by the closeness of average hTmax at 0930 UTC (279 m) to average hSmax from radiosondes (264 m) and blended RWP + MS data (265 m), using the four cases with good data from both sources (Fig. 7). Taking the seven cases for which 0930 UTC values can be determined without extrapolation, average hTmax = 377 m and average hSmax = 354 m, close to average h2wsonde (333–363 m) but greater than average h1wsonde (212–242 m), where the first number is the sonde height and the second number accounts for the maximum possible correction for the balloon–sonde separation.

b. Relationship among modeled NBL profile features and comparison to observations

Figure 9 shows four types of modeled behavior for hTvmax, hSmax, and h. The pattern in the top panel, that is, converging of hTvmax, hSmax, and hTKE with time, is most consistent with observations (Figs. 7, 8). In this case hMYJ overlaps with the heights of the two maxima, while is about a grid point lower. The second and third patterns involve very low hTvmax and do not correspond to observations. For the final pattern, the more rapidly growing hTvmax approaches hSmax, but then overtakes it, ending up several grid points higher. In this case, the evolution of hSmax follows observations, but hTvmax grows too rapidly (cf. Figs. 7 and 9), eventually exceeding observed values as well as hSmax. Since the last three patterns in the figure are not observed, we refer to these patterns as “pathological”3 for this dataset.

Fig. 9.
Fig. 9.

(left) Four patterns in hSmax and hTvmax evolution, along with h estimates and hMYJ (light blue line, top frame only). Top three panels show averages of Beaumont, Oxford, and Whitewater heights; the bottom panel is for one location/date. (right) Approximate grid height zh.

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

To trace the origins of the pathologies in Fig. 9, we plot their frequency as a function of stability (Obukhov length L) for three types of hTvmax behavior: “increasing,” “too low,” and “too high” in Figs. 10 and 11. Individual points were counted. Thus, all the hTvmax points showing an increase toward hSmax with time were counted in the increasing pattern; points for which hTvmax < 50 m were counted as too low, and points for which hTmax exceeds hSmax by more than a grid point were counted as too high. Thus, for example, BouLac 11 May in Fig. 9 has five increasing points and six too-low points. Similarly, only the last three points for the YSU 3.4.1 case on 5 May fall in the too-high category.

Fig. 10.
Fig. 10.

For the three TKE schemes, frequency of times for which hTvmax increases with time, until it follows hSmax as observed, compared to too-low hTvmax (<50 m AGL) and too-high hTvmax (more than a grid point higher than hSmax) leading to patterns in Fig. 9.

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

Fig. 11.
Fig. 11.

As in Fig. 10, but for YSU 3.2 and YSU 3.4.1. Number of samples are in parentheses.

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

From Figs. 10 and 11, the behavior of hTvmax varies with PBL scheme, with MYJ reproducing the observed increasing pattern most often (89% of the samples). YSU 3.2 (67%) and BouLac (55%) show too-low hTvmax most often and MYJ (7%) the least. The too-high values are the least common, with a few examples for YSU 3.4.1 (7%) and MYJ (4%). Both too-low and too-high hTvmax occurred more often for more near-neutral situations (larger L), although the association is not perfect. The lack of a sharp distinction is likely related to horizontal variation of wind, temperature, and L; so, any relationship reflects upstream as well as local behavior. Also, the TKE schemes from (1) respond to vertical gradients (and for QNSE, the bulk Richardson number; see Table 4) more directly than the surface flux–determined L.

The origins of too-low hTvmax become apparent when we examine the results for Beaumont on 5 May, the windiest night, in Fig. 12. In the time series (left side), MYJ and YSU 3.4.1 replicate observed hTmax to within about a grid interval until at least 0800 UTC, while BouLac, QNSE, and YSU 3.2 show hTvmax < 50 m AGL. The vertical profiles (right side) reveal the explanation: too-strong vertical mixing produces deep near-neutral layers for BouLac and YSU 3.2 and a more modestly well-mixed layer for QNSE; all result in low-level Tυ maxima. (The lower secondary maximum in the observed Tυ profile does not persist.) For the BouLac and YSU 3.2 wind profiles, a height of minimum curvature below 100 m and an hSmax much greater than observed roughly bracket the well-mixed thermal layer, while hSmax for QNSE, MYJ, and YSU 3.4.1 is close to the observed value.

Fig. 12.
Fig. 12.

For a case of too-low hTvmax at Beaumont, 4–5 May 1997. (left) Evolution of hTvmax and hSmax. (right) Profiles of Θυ − 0.0098z (same shape as Tυ) and S at 0500 UTC.

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

From Fig. 13, the excessive mixing for YSU 3.2 and BouLac can be traced to their K (=KH = KM) being much larger than for the other three PBL schemes. In the case of YSU 3.2, large KH results from setting the scaling velocity ws to its neutral stratification value ; the more reasonable K in YSU 3.4.1 results from accounting for stratification in the ws formulation (Table 4). In the case of BouLac, the large K results primarily from the too-large Lmix. The QNSE hTvmax collapse, like that for BouLac and YSU 3.2, is related to relatively large KH in the lowest 150 m. Unlike BouLac and YSU 3.2, QNSE produces a KM close to that of MYJ, leading to reasonable agreement with the observed S profile in Fig. 12. The final pathology, for which hTvmax > hSmax, is also associated with too-strong mixing that just happens not to be strong enough to form a low-level Tυ maximum.

Fig. 13.
Fig. 13.

As in Fig. 12, but for turbulence variables for BouLac, QNSE, YSU 3.2, YSU 3.4.1, MYJ, and MYJ2 (MYJ rerun to extract KM but on a different computer). (top left) KH and (top right) KM; (bottom left) TKE, and (bottom right) Lmix. MYJ2 denoted by dashed line.

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

The differences between QNSE and MYJ are related to differences in their Pr values. Figure 14 (top) compares Pr−1 = KH/KM for hourly profiles at Beaumont for the same night as Figs. 12 and 13. While KH/KM = 1.4 for QNSE [consistent with Sukoriansky et al. (2006)] near the surface where Riloc is closest to neutral, KH/KM = 1.0 for MYJ, a consequence of (A8) in Janjić (2001). If one accepts Pr = 1 for the surface layer (e.g., Kaimal and Finnigan 1994, their Fig. 1.8), the MYJ Prandtl number is closer to correct near the surface. Further, when Pr−1 is plotted against Riloc (Fig. 14, bottom), the MYJ points fit the Monti et al. (2002) data at least as well as the QNSE points [though Grachev et al. (2007) suggest that the relationship in such plots is contaminated by self-correlation and that Pr might actually increase with Riloc if self-correlation is eliminated]. Note that Riloc < 0.5 for all MYJ NBL output examined.4 However, Pr = 1 when TKE = 0.1 m2 s−2, its background value.

Fig. 14.
Fig. 14.

(top) For 5 May Beaumont, inverse Prandtl number KH/KM as a function of height for hourly profiles from 0200 to 1000 UTC. (bottom) Relationship between KH/KM and local Richardson number, superposed on plot from Monti et al. (2002). For the bottom plot, the field data were collected in nocturnal downslope flows during the Vertical Transport and Mixing Experiment. Laboratory data are from Strang and Fernando (2001). The dashed line extending QNSE to higher Riloc is based on Fig. 4 of Sukoriansky et al. (2006).

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

c. Collapse of the NBL

A final behavior, “collapse” of h to near-zero values, occurs only for the most stable NBL encountered, on 21 May at Whitewater (Fig. 15), with hMYJ < 10 m for 11 h. For QNSE, is undefined at 0600 UTC (TKE = its background value) and small at 0800 UTC. Based on WRF simulations, the weak winds result from the deceleration of the easterly synoptic-scale wind by downslope forces on the west side of the watershed, consistent with observations (Table 2). In spite of small TKE, h1wsonde and h2wsonde are mostly close to observed hTvmax and hSmax, as well as for MYJ, QNSE, and YSU 3.4.1. Model success in replicating observations likely results from the momentum and temperature profiles (and thus the TKE they produce) bearing the effects of forces and stronger turbulence upstream.

Fig. 15.
Fig. 15.

For 21 May Whitewater, observed and modeled time series of NBL profile features. Observations: Red with hSmax from both radiosondes (circles) and RWP + MS (squares), and h zone based on h1wsonde (upside down triangles) and h2wsonde (triangles). For PBL schemes: BouLac (green), MYJ (turquoise), QNSE (blue), and YSU 3.4.1 (purple). For BouLac, QNSE, and MYJ, h = ; for YSU, h = hYSU. Also shown is h = hMYJ (light turquoise). (right) Indicates grid heights for (top),(middle) zh and (bottom) zf.

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

Figure 16 indicates that small hMYJ is associated with TKE hitting its lowest-allowed value, 0.1 m2 s−2 at the surface; is based on profiles of TKE′ < 0.05 m2 s−2, sometimes with double maxima, as illustrated in the figure. Given stronger modeled (not shown) and observed (Table 2) easterlies, greater model TKE upstream (near-surface TKE at Beaumont 0.3–0.5 m2 s−2 at 0500–0800 UTC), and the well-defined change in wsonde in Fig. 16, we suspect that model TKE at Whitewater was too small, something that could be remedied by allowing horizontal transport of TKE. As for YSU 3.4.1, K reverts to a function of vertical grid spacing since K from (4) is less than that value.

Fig. 16.
Fig. 16.

For Whitewater 0800 UTC 21 May, profiles of observed and modeled mean and turbulence parameters. Red and oranges represent observations. For PBL schemes, green is BouLac, turquoise is MYJ, blue is QNSE, and purple is YSU 3.4.1.

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

d. Daily model bias in depth of NBL profile features

Figure 17 compares modeled and observed hTvmax, hSmax, and h. The green-shaded cells, which indicate model heights within about one grid point of observed heights, show that the number of successful predictions so defined is about the same for MYJ (using ), QNSE, and YSU 3.4.1. The most obvious problem in the figure is the relatively large positive h and hSmax biases for all the PBL schemes on 5 May, the windiest day. Also evident are the previously discussed impacts of excess mixing on hTvmax, with unrealistically low values, especially on 5 May for BouLac and QNSE (light blue cells) and both too-high and too-low values for BouLac on the less windy days (red cells). Excess mixing on 5 May is also reflected in too-high hSmax for MYJ and to a lesser degree for QNSE and for all days for BouLac. The too-high hSmax for BouLac is commonly paired with a height of minimum curvature close to hTvmax (e.g., Fig. 12) or the minimum curvature height in the Tυ profile. The MYJ, QNSE, and YSU 3.4.1 S profiles rarely show similar behavior. Spikes in hSmax, most common for MYJ, are mostly associated with real shifts in Smax.

Fig. 17.
Fig. 17.

Comparison of modeled to observed hTvmax, hSmax, and h. Model hTvmax represented by hυ,z = 10 K km−1); observed hTvmax represented by hTmax. For the model, h = for BouLac, QNSE, and MYJ (left value) and h = hYSU for YSU. Right h value for MYJ = hMYJ. Observed h bounded by h1wsonde and h2wsonde. Table cells not filled in represent departures that are consistently too high (or too low) by ~1–2 grid points. Averaging intervals (in parentheses) are from either 0200–1000 UTC or over times for which there are observed values.

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

The assumption that KH = KM for z < hYSU does not seem to have had a negative impact on YSU 3.4.1. Why is this? As illustrated by Fig. 18, Riloc (and thus Pr, see Fig. 14, bottom) reaches a maximum above the height of the K maximum, keeping Pr closer to 1 where K is the largest. Furthermore, NBL Riloc reaches only ~0.5–1 in windy conditions. However, it should be noted that Pr > 1 for z > hYSU.

Fig. 18.
Fig. 18.

For YSU 3.4.1, profiles of K and Riloc. (top) Weaker wind night and (bottom) stronger wind night and time corresponding to Figs. 12 and 13.

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

Although often appears to be a better measure of h than hMYJ, the differences are not that large, except for around sunset (Fig. 5, noting that hMYJ > h from criterion 6). From Figs. 5, 9, and 17, the differences between the two estimates are mostly of the order of 1–1.5 grid points. Furthermore, hMYJ coincides with hTvmax and hSmax by 0700 UTC in Fig. 9, while lies a grid point lower. Finally, the collapse of hMYJ to near-zero values is a better indicator of the modeled very stable NBL (MYJ TKE excess over background is less than 0.01 m2 s−2). As noted previously, it is likely that the observed h bounded by h1wsonde and h2wsonde is strongly influenced by the advection of TKE from upstream. We speculate that the MYJ mean profiles, being partially shaped by the upstream effects of TKE, produce TKE profiles of much smaller magnitude relative to the background but with depths (hsubj and ) similar to observations.

e. Surface fluxes

Since surface fluxes influence NBL evolution, we compare model and to the observed values. We use Beaumont and grassland flux sites 1 and 2, since all three sites are only ~10 km from each other (Fig. 2) and correctly classified as grassland in WRF.

Figure 19 shows variation among model values at Beaumont to be small compared to their excess over observed values at the flux sites, while model observation differences in are only slightly larger than the spread among model values, with model values more negative. To remove the impact of horizontal variability, we plot observed and MYJ surface fluxes at sites 1 and 2 along with MYJ surface fluxes at Beaumont in Fig. 20. As expected, the modeled fluxes at sites 1 and 2 are mostly closer to observations than those for Beaumont, especially for on 11 and 21 May, but the discrepancy is still large. The small spread for model compared to observed values suggests the model observation differences are not due to differences in the PBL or associated surface schemes.

Fig. 19.
Fig. 19.

Observed (sites 1 and 2) and modeled (Beaumont) time series of and . For observations, vertical flux of sonic anemometer temperature is used. Symbols: for observations, orange triangles are for site 2 in Fig. 1; red upside down triangles are for site 1. Model results for Beaumont: circles (green is BouLac, turquoise is MYJ, blue is QNSE, and purple is YSU 3.4.1.).

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

Fig. 20.
Fig. 20.

As in Fig. 19, but comparing modeled fluxes using MYJ at Beaumont, site 1, and site 2 to observations at sites 1 and 2.

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

Nor does the discrepancy appear to be due to biases in the observed values, which are half-hour averages. Averaging fluxes over smaller time intervals has been suggested for stable conditions (e.g., Vickers and Mahrt 2006) in order to obtain internal consistency between turbulence and mean profile measurements and to avoid scatter associated with “mesoscale” motions. However, varies smoothly with time. Furthermore, given that averaging times should increase as stability decreases, the 30-min averaging times should work the best for the near-neutral 5 May case, when the discrepancy is largest. Finally, our objective is not to find consistency between measured fluxes and profiles, but rather to account for all unresolved fluxes.

Though the largest discrepancy for 5 May in Fig. 17 is consistent with the greatest model departures from observations, MYJ and the QNSE and YSU 3.4.1 hSmax values for Beaumont are close to observed values, and Fig. 12 shows close correspondence of the modeled and observed S profiles. Also, MYJ, QNSE, and YSU 3.4.1 perform rather well on the weaker wind days, despite significant discrepancies. Given this behavior, the poor correspondence of observed and modeled is somewhat surprising, particularly since there is some evidence (e.g., Table 1 of Caughey et al. 1979, their Eq. (4); Steeneveld et al. 2007, p. 222) for a linear relationship between h and , other things being equal.

In addition, MYJ 10-m winds are consistent with observations on all 3 days (Fig. 21). Based on averages of sites 1 and 2 between 0200 and 1100 UTC, the observed speed exceeds the linearly interpolated model results by 0.48, 0.14, and 0.58 m s−1 for 5, 11, and 21 May, respectively. Interpolation assuming a logarithmic profile reduces the differences by up to 0.2 m s−1, based on calculations for the day with the strongest winds (5 May). Thus, model underestimates are ~2%–3% for this day.

Fig. 21.
Fig. 21.

As in Fig. 20, but for 10-m wind speed, with model wind interpolated linearly between level 1 (~5 m) and level 2 (~14 m).

Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1

Moreover, a similar discrepancy emerges when we apply the h criterion of Richardson et al. (2013),5 namely, that
e7
where Ric is the layer Richardson number evaluated at h and α is a constant, to modeled and observed data. Both roughly satisfy (7). However, while observed α is within 40% of their α (0.045), the model yields α values a factor of up to 5 larger (Table 5), depending on how Ric is calculated. The large α discrepancy results primarily from differences between observed and modeled . For the observations, α was estimated from averaged data using times for which we had high confidence in h, while model α was calculated from the corresponding hourly L, hsubj, and Rilayer(hsubj) and then averaged.
Table 5.

Estimates of Richardson et al. (2013) constant α in (7) at Beaumont. For observations, Ric from (6) with h and lowest level above surface; L based on sites 1 and 2.

Table 5.
Drawing from Kustas et al. (2005) and Strassberg et al. (2008), we hypothesize that both values are correct, with the observed values representing (100) m fetches and the model value representing a much larger region. To demonstrate this, we assume that the model and observed wind are equal, but that the surface roughness length z0 values differ. Thus, assuming neutral stability, the wind speed S is related to model (M) and observed (O) and momentum roughness length z0, via
e8
Solving for z0,O by setting , we obtain
e9
The stability is closest to neutral on 5 May, when R = 1.5 (Fig. 20). Using z = 10 m and z0,M = 0.05 m (intermediate value for grass in our simulations; see Table 3 of LeMone et al. 2013), we obtain z0,O = 0.0035 m. This value is close to the approximate values tabulated online (at http://www.eol.ucar.edu/isf/projects/cases97/), namely, z0,O (site 1) ~ 0.006 m and z0,O (site 2) ~ 0.002 m.

4. Conclusions

Radiosonde, minisodar, radar wind profiler, and surface observations and WRF simulations for three moderately windy fair-weather nights during the CASES-97 field program are used to identify NBL depth h and the heights of maxima in wind speed hSmax and virtual temperature hTvmax, which are then used to evaluate four PBL schemes: BouLac, MYJ, QNSE, and YSU. Rather than simply focus on biases, we determine the observed coevolution pattern of h, hTmax ~ hTvmax, and hSmax and then evaluate the success of the four schemes in reproducing that pattern as a function of environmental conditions, as defined by the Obukhov length L.

To find h for BouLac, MYJ, and QNSE, we compared eight objectively determined h criteria (four TKE-based criteria, two Richardson number criteria, hTvmax, and hSmax; Table 1) to subjectively based values (hsubj) on plots of the model TKE profiles. Based on this comparison, we chose a threshold equal to 5% of the maximum TKE excess from its background value, where the maximum was found for the lowest kilometer. Fortuitously, the height so derived, , was consistent with Fig. 1. However, was not a significant improvement over the MYJ-derived value hMYJ. For YSU, we used its Richardson number–based hYSU, which was a close equivalent to the subjective NBL depth based on K, except under the most stable conditions, when K was proportional to the vertical grid spacing.

The observed TKE-based h was based on a decrease in balloon rise rate from ~5 to ~3 m s−1 going from turbulent to nonturbulent air (Johansson and Bergstrom 2005). Taking the heights at which the deceleration started (h1wsonde) and ended (h2wsonde) yielded reasonable bounds for h, given proper balloon launch procedure, the absence of large air vertical velocities, and h > ~100 m. This method worked least reliably at Beaumont, perhaps because of the currents associated with nearby terrain.

Summary plots of composite h1wsonde, h2wsonde, hSmax, and hTvmax revealed a general pattern: hTvmax increases gradually through the night, hSmax and hTvmax converge, and the two approach the h zone based on wsonde after several hours, after which all three occupy roughly the same altitude range until surface heating starts to form the CBL. On many nights hSmax followed h through most of the night to such a degree that hSmax was a good secondary measure of h, in agreement with the work of Banta et al. (2003) and Pichugina and Banta (2010). Kosovic and Curry (2000) produced such an evolution using LES, although they cautioned that it took an inertial period (about 20 h at this latitude) for the three heights to correspond.

The observed coevolution pattern provided metrics against which the NBL schemes could be judged. Of the PBL schemes examined, MYJ, QNSE, and YSU version 3.4.1 mostly reproduced the observed converging of hTvmax, hSmax, and h with time. However, BouLac (55% of the time) and YSU version 3.2 (67% of the time) produced unrealistically low hTvmax, a sign of too much vertical mixing. In both cases, hSmax tended to be too high compared to observations. The low hTvmax behavior occurred with intermediate frequency for QNSE (33%) and seemed to be associated with too low a Prandtl number (too large a KH) since QNSE wind profiles were simulated far better (KM about right). The low hTvmax behavior occurred least frequently for MYJ (7%) and YSU 3.4.1 (8%). In most cases, the excessive vertical mixing was associated with larger values of L (windier nights). However, the L dependence was not a clean one: a bulk Richardson number could be a better parameter, and upstream as well as local forcing determines the profiles of resolved parameters.

A final behavior, the collapse of the NBL (hMYJ ~ 0 for several hours; undefined 1 h each for MYJ and QNSE), occurred on 21 May (Whitewater), with TKEs for MYJ and QNSE sometimes pegged at background values. In this case, hTvmax, hSmax, and (surprisingly) were close to observed values, the presumed effect of forces and stronger turbulence upstream on the wind and temperature profiles and thus the model TKE profiles. Consistently well-defined h1wsonde and h2wsonde suggest model underestimates of TKE, a possible result of neglecting horizontal TKE advection.

There was a large mismatch between observed and modeled friction velocity near Beaumont even though the PBL schemes replicated NBL features at Beaumont reasonably well. The discrepancy appears to reflect a mismatch in model and observed roughness length z0. Indeed, using the modeled and measured and S at 10 m, and the model z0, we were able to reproduce the measured z0. Similarly, the observed and model results each produce internally consistent values of the constant α in Richardson et al. (2013) that relates h to Ri(h) and L [see (7)], but α for the model results is up to 5 times α for the observations, again a consequence of the discrepancy. We suggest that the observed z0, , and 10-m wind speed reflect skin drag over an (100) m grassland fetch, while the corresponding model values are consistent with a larger flux footprint that produces form drag as well as skin drag. Likewise, the modeled and observed NBL wind profiles likely reflect regional z0 values that include form drag. Similar conclusions were reached by Kustas et al. (2005) and Strassberg et al. (2008) for the CBL. Such discrepancies may also contribute to the surface flux inconsistencies noted by Hacker and Angevine (2013).

The conclusions should be generalized with caution. Because of data limitations, we limited ourselves to windier nights, during which we would expect deeper NBLs and more continuous coupling of the atmosphere to the surface. The 108 h and three locations analyzed thus mostly represent less stable conditions [intermittent to continuous turbulence regimes of Van de Wiel et al. (2003)]. Further, the TKE did not always simply decrease with height, sometimes reaching a maximum (or two maxima) above the surface. Finally, resolved mesoscale NBL structures could influence the results slightly.

The small number of nights sampled is compensated for by the completeness of the dataset, which along with the WRF runs, allows the examination of the impacts of upstream and surface conditions on the evolution of the NBL. This case study approach draws on the strengths of the simulations and observations to examine the coevolution of observed and modeled NBL profile features and TKE values, terrain effects on the flow, and vertical surface fluxes. Though we cannot quantify model biases, we can explore their sources.

As to PBL scheme improvements, the results suggest the following:

  • for BouLac, allowing for stability in converting TKE to vertical velocity in the expression for estimating Lmix, which could mitigate too much mixing at night [already recognized as a shortcoming by Therry and LaCarrere (1983)];
  • modifying QNSE to mitigate apparent excess mixing of the temperature profile;
  • using the stability-dependent form for ws in YSU (i.e., use YSU 3.4.1 rather than 3.2); and
  • including the advection of TKE by resolved winds.

As to the observations, the results suggest designing field measurements to better measure the relevant parameters in NBL evolution or using datasets that include a useful subset (e.g., CASES-99; Poulos et al. 2002):

  • For NBL depth, this would include radiosonde releases optimized to find h using balloon rise rate. Collocated tethersonde, tower, and lidar data could enable sampling a broader range of NBLs as well as comparison of techniques for determining h.
  • This would also involve designing flux measurements to include “regional” as well as “local” fluxes by adding measurements from a taller tower and/or aircraft or unmanned aerial vehicles to a traditional flux tower network. Analysis would include examination of averaging times.

Acknowledgments

The surface meteorology, surface flux, and radiosonde data were collected, processed, and archived by NCAR’s Earth Observations Laboratory and the RWP/MS data were collected, processed, and archived by the Argonne National Laboratory’s former Argonne Boundary Layer Experiments Facility. The authors are indebted to Tom Horst and Steven Oncley of NCAR and Richard Coulter of Argonne National Laboratory for help in data interpretation as needed. Valuable help in interpreting the PBL schemes was provided by Alberto Martilli (BouLac), Zavisa Janjić (MYJ), Esa-Matti Tastula (QNSE), and Songyu Hong (YSU). Xubin Zeng, Jeff Weil, Sukanta Basu, Jielun Sun, and Wayne Angevine provided useful insights, with the last two also helping to clarify figures. Finally, suggestions by Jun Zhang and an anonymous reviewer helped us clarify several points and improve the figures. This work was supported by the Air Force Weather Agency, the NCAR Water System Program, and NCAR base funding from the National Science Foundation.

REFERENCES

  • Acevedo, O. C., , and D. R. Fitzjarrald, 2001: The early evening surface-layer transition: Temporal and special variability. J. Atmos. Sci., 58, 26502667, doi:10.1175/1520-0469(2001)058<2650:TEESLT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Banta, R. M., , Y. L. Pichugina, , and R. K. Newsom, 2003: Relationship between low-level jet properties and turbulence kinetic energy in the nocturnal stable boundary layer. J. Atmos. Sci., 60, 25492555, doi:10.1175/1520-0469(2003)060<2549:RBLJPA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Banta, R. M., , L. Mahrt, , D. Vickers, , J. Sun, , B. B. Balsley, , Y. L. Pichugina, , and E. J. Williams, 2007: The very stable boundary layer on nights with weak low-level jets. J. Atmos. Sci., 64, 30683089, doi:10.1175/JAS4002.1.

    • Search Google Scholar
    • Export Citation
  • Basu, S., , and F. Porte-Agel, 2006: Large-eddy simulation of stably stratified atmospheric boundary layer turbulence: A scale-dependent dynamic modeling approach. J. Atmos. Sci., 63, 20742091, doi:10.1175/JAS3734.1.

    • Search Google Scholar
    • Export Citation
  • Beare, R. J., and et al. , 2006: An intercomparison of large-eddy simulations of the stable boundary layer. Bound.-Layer Meteor., 118, 247272, doi:10.1007/s10546-004-2820-6.

    • Search Google Scholar
    • Export Citation
  • Betts, A. K., , S. Hong, , and H.-L. Pan, 1996: Comparison of NCEP–NCAR reanalysis with 1987 FIFE data. Mon. Wea. Rev., 124, 14801498, doi:10.1175/1520-0493(1996)124<1480:CONNRW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bougeault, P., , and P. LaCarrere, 1989: Parameterization of orography-induced turbulence in a mesobeta-scale model. Mon. Wea. Rev., 117, 18721890, doi:10.1175/1520-0493(1989)117<1872:POOITI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Caughey, S. J., , J. C. Wyngaard, , and J. C. Kaimal, 1979: Turbulence in the evolving stable boundary layer. J. Atmos. Sci., 36, 10411052.

    • Search Google Scholar
    • Export Citation
  • Chen, F., , and J. Dudhia, 2001a: Coupling an advanced land surface–hydrology model with the Penn State–NCAR MM5 modeling system. Part I: Model implementation and sensitivity. Mon. Wea. Rev., 129, 569585, doi:10.1175/1520-0493(2001)129<0569:CAALSH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Chen, F., , and J. Dudhia, 2001b: Coupling an advanced land surface–hydrology model with the Penn State–NCAR MM5 modeling system. Part II: Preliminary model validation. Mon. Wea. Rev., 129, 587604, doi:10.1175/1520-0493(2001)129<0587:CAALSH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Detering, H. W., , and D. Etling, 1985: Application of the E-ε turbulence model to the atmospheric boundary layer. Bound.-Layer Meteor., 33, 113133, doi:10.1007/BF00123386.

    • Search Google Scholar
    • Export Citation
  • Dudhia, J., 1989: Numerical study of convection observed during the winter monsoon experiment using a mesoscale two-dimensional model. J. Atmos. Sci., 46, 30773107, doi:10.1175/1520-0469(1989)046<3077:NSOCOD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Ek, M. B., , K. E. Mitchell, , Y. Lin, , E. Rogers, , P. Grummann, , V. Koren, , G. Gayno, , and J. D. Tarplay, 2003: Implementation of the Noah land surface model advances in the National Centers for Environmental Predication operational mesoscale Eta model. J. Geophys. Res., 108, 8851, doi:10.1029/2002JD003296.

    • Search Google Scholar
    • Export Citation
  • Fiebrich, C. A., , and K. C. Crawford, 2001: The impact of unique meteorological phenomena detected by the Oklahoma Mesonet and ARS Micronet on automated quality control. Bull. Amer. Meteor. Soc., 82, 21732187, doi:10.1175/1520-0477(2001)082<2173:TIOUMP>2.3.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gallice, Q., , F. G. Wienhold, , C. R. Hoyle, , F. Immler, , and T. Peter, 2011: Modeling the ascent of sounding balloons: Derivation of the vertical air motion. Atmos. Meas. Tech., 4, 22352253, doi:10.5194/amt-4-2235-2011.

    • Search Google Scholar
    • Export Citation
  • Grachev, A. A., , E. L. Andreas, , C. W. Fairall, , P. S. Guest, , and P. O. G. Persson, 2007: On the turbulent Prandtl number in the stable boundary layer. Bound.-Layer Meteor., 125, 329341, doi:10.1007/s10546-007-9192-7.

    • Search Google Scholar
    • Export Citation
  • Hacker, J. P., , and W. M. Angevine, 2013: Ensemble data assimilation to characterize surface-layer errors in numerical weather prediction models. Mon. Wea. Rev., 141, 18041821, doi:10.1175/MWR-D-12-00280.1.

    • Search Google Scholar
    • Export Citation
  • Hong, S.-Y., , Y. Noh, , and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 23182341, doi:10.1175/MWR3199.1.

    • Search Google Scholar
    • Export Citation
  • Janjic, Z. I., 2001: Nonsingular implementation of the Mellor-Yamada level 2.5 scheme in the NCEP Meso Model. NOAA/NWS/NCEP Office Note 437, 61 pp.

  • Johansson, C., , and H. Bergstrom, 2005: An auxiliary tool to determine the height of the boundary layer. Bound.-Layer Meteor.,115, 423–432, doi:10.1007/s10546-004-1424-5.

  • Kaimal, J. C., , and J. J. Finnigan, 1994: Atmospheric Boundary Layer Flows: Their Structure and Measurement. Oxford University Press, 289 pp.

    • Search Google Scholar
    • Export Citation
  • Kosovic, B., , and J. A. Curry, 2000: A large eddy simulation study of a quasi-steady, stably stratified atmospheric boundary layer. J. Atmos. Sci., 57, 10521068, doi:10.1175/1520-0469(2000)057<1052:ALESSO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kustas, W. P., , J. H. Prueger, , J. I. MacPherson, , M. Wolde, , and F. Li, 2005: Effects of land use and meteorological conditions on Midwestern cropping systems. J. Hydrometeor., 6, 825839, doi:10.1175/JHM460.1.

    • Search Google Scholar
    • Export Citation
  • LeMone, M. A., and et al. , 2000: Land–atmosphere interaction research, early results, and opportunities in the Walnut River Watershed in southeast Kansas: CASES and ABLE. Bull. Amer. Meteor. Soc., 81, 757779, doi:10.1175/1520-0477(2000)081<0757:LIRERA>2.3.CO;2.

    • Search Google Scholar
    • Export Citation
  • LeMone, M. A., , K. Ikeda, , R. L. Grossman, , and M. W. Rotach, 2003: Horizontal variability of 2-m temperature at night during CASES-97. J. Atmos. Sci., 60, 24312449, doi:10.1175/1520-0469(2003)060<2431:HVOMTA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • LeMone, M. A., , M. Tewari, , F. Chen, , and J. Dudhia, 2013: Objectively determined fair-weather CBL depths in the ARW-WRF model and their comparison to CASES-97 observations. Mon. Wea. Rev., 141, 3054, doi:10.1175/MWR-D-12-00106.1.

    • Search Google Scholar
    • Export Citation
  • Lenschow, D. H., , X. S. Li, , C. J. Zhu, , and B. B. Stankov, 1988: The stably stratified boundary layer over the Great Plains. Bound.-Layer Meteor., 42, 95121, doi:10.1007/BF00119877.

    • Search Google Scholar
    • Export Citation
  • Lin, Y.-L., , R. D. Farley, , and H. D. Orville, 1983: Bulk parameterization of the snow field in a cloud model. J. Climate Appl. Meteor., 22, 10651092, doi:10.1175/1520-0450(1983)022<1065:BPOTSF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Louis, J. F., 1979: A parametric model of vertical eddy fluxes in the atmosphere. Bound.-Layer Meteor., 17, 187202, doi:10.1007/BF00117978.

    • Search Google Scholar
    • Export Citation
  • MacCready, P. B., 1965: Comparison of some balloon techniques. J. Appl. Meteor., 4, 504508, doi:10.1175/1520-0450(1965)004<0504:COSBT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Mahrt, L., , and D. Vickers, 2006: Extremely weak mixing in stable conditions. Bound.-Layer Meteor., 119, 1939, doi:10.1007/s10546-005-9017-5.

    • Search Google Scholar
    • Export Citation
  • Melgarejo, J. W., , and J. W. Deardorff, 1974: Stability functions for the boundary-layer resistance laws based upon observed boundary-layer heights. J. Atmos. Sci., 31, 13241333, doi:10.1175/1520-0469(1974)031<1324:SFFTBL>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., , and T. Yamada, 1974: A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci., 31, 17911806, doi:10.1175/1520-0469(1974)031<1791:AHOTCM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., , and T. Yamada, 1982: Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys. Space Phys., 20, 851875, doi:10.1029/RG020i004p00851.

    • Search Google Scholar
    • Export Citation
  • Mlawer, E. J., , S. J. Taubman, , P. D. Brown, , M. J. Iacono, , and S. A. Clough, 1997: Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave. J. Geophys. Res., 102, 16 66316 682, doi:10.1029/97JD00237.

    • Search Google Scholar
    • Export Citation
  • Monti, P., , H. J. S. Fernando, , M. Princevac, , W. C. Chan, , T. A. Kowalewski, , and E. R. Pardyjak, 2002: Observations of flow and turbulence in the nocturnal boundary layer over a slope. J. Atmos. Sci., 59, 25132534, doi:10.1175/1520-0469(2002)059<2513:OOFATI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Noh, Y., , W. Chen, , S. Hone, , and S. Raasch, 2003: Improvement of the K-profile model for the planetary boundary layer based on large-eddy simulation data. Bound.-Layer Meteor., 107, 401427, doi:10.1023/A:1022146015946.

    • Search Google Scholar
    • Export Citation
  • Pichugina, Y. L., , and R. M. Banta, 2010: Stable boundary layer depth from high-resolution measurements of the mean wind profile. J. Appl. Meteor. Climate,49, 20–35, doi:10.1175/2009JAMC2168.1.

  • Poulos, G. S., and et al. , 2002: CASES-99: A comprehensive investigation of the stable nocturnal boundary layer. Bull. Amer. Meteor. Soc., 83, 555581, doi:10.1175/1520-0477(2002)083<0555:CACIOT>2.3.CO;2.

    • Search Google Scholar
    • Export Citation
  • Richardson, H., , S. Basu, , and A. A. M. Holtslag, 2013: Improving stable boundary-layer height estimation using a stability-dependent critical bulk Richardson number. Bound.-Layer Meteor., 148, 93–109, doi:10.1007/s10546-013-9812-3.

    • Search Google Scholar
    • Export Citation
  • Shin, H. H., , S.-Y. Hong, , and Y. Noh, 2013: Derivation of turbulent kinetic energy from a first-order nonlocal planetary boundary layer parameterization. J. Atmos. Sci., 70, 17951805, doi:10.1175/JAS-D-12-0150.1.

    • Search Google Scholar
    • Export Citation
  • Steeneveld, G. J., , B. J. H. Van de Wiel, , and A. A. M. Holtslag, 2007: Diagnostic equations for the stable boundary layer height: Evaluation and dimensional analysis. J. Appl. Meteor. Climatol., 46, 212225, doi:10.1175/JAM2454.1.

    • Search Google Scholar
    • Export Citation
  • Strang, E. J., , and H. J. S. Fernando, 2001: Vertical mixing and transports through a stratified shear layer. J. Phys. Oceanogr., 31, 20262048, doi:10.1175/1520-0485(2001)031<2026:VMATTA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Strassberg, D., , M. LeMone, , T. Warner, , and J. Alfieri, 2008: Comparison of 10-m observed wind speeds to those based on Monin–Obukhov similarity theory using IHOP_2002 aircraft and surface data. Mon. Wea. Rev., 136, 964972, doi:10.1175/2007MWR2203.1.

    • Search Google Scholar
    • Export Citation
  • Sukoriansky, S., , and B. Galperin, 2008: Anisotropic turbulence and internal waves in stable stratified flows (QNSE theory). Phys. Scr., 132, 014036, doi:10.1088/0031-8949/2008/T132/014036.

    • Search Google Scholar
    • Export Citation
  • Sukoriansky, S., , B. Galperin, , and V. Perov, 2005: Application of a new spectral theory of stably stratified turbulence to the atmospheric boundary layer over ice. Bound.-Layer Meteor., 117, 231257, doi:10.1007/s10546-004-6848-4.

    • Search Google Scholar
    • Export Citation
  • Sukoriansky, S., , B. Galperin, , and V. Perov, 2006: A quasi-normal scale elimination model of turbulence and its application to stably stratified flows. Nonlinear Processes Geophys., 13, 922, doi:10.5194/npg-13-9-2006.

    • Search Google Scholar
    • Export Citation
  • Sun, J., and et al. , 2004: Atmospheric disturbances that generate intermittent turbulence in nocturnal boundary layers. Bound.-Layer Meteor., 110, 255279, doi:10.1023/A:1026097926169.

    • Search Google Scholar
    • Export Citation
  • Sun, J., , L. Mahrt, , R. M. Banta, , and Y. L. Pichugina, 2012: Turbulence regimes and turbulent intermittency in the stable boundary layer during CASES-99. J. Atmos. Sci., 69, 338351, doi:10.1175/JAS-D-11-082.1.

    • Search Google Scholar
    • Export Citation
  • Therry, G., , and P. LaCarrere, 1983: Improving the eddy kinetic energy model for planetary boundary layer description. Bound.-Layer Meteor., 25, 6388, doi:10.1007/BF00122098.

    • Search Google Scholar
    • Export Citation
  • Van de Wiel, B. J. H., , R. J. Ronda, , A. F. Moene, , H. A. R. De Bruin, , and A. A. M. Holtslag, 2002: Intermittent turbulence and oscillations in the stable boundary layer over land. Part I: A bulk model. J. Atmos. Sci., 59, 942958, doi:10.1175/1520-0469(2002)059<0942:ITAOIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Van de Wiel, B. J. H., , A. F. Moene, , O. K. Hartogenesis, , H. A. R. De Bruin, , and A. A. M. Holtslag, 2003: Intermittent turbulence in the stable boundary layer over land. Part III: A classification for observations during CASES-99. J. Atmos. Sci., 60, 25092522, doi:10.1175/1520-0469(2003)060<2509:ITITSB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Van de Wiel, B. J. H., , A. F. Moene, , H. J. J. Jonker, , P. Baas, , S. Basu, , J. M. M. Donda, , J. Sun, , and A. A. M. Holtslag, 2012: The minimum wind speed for sustainable turbulence in the nocturnal boundary layer. J. Atmos. Sci., 69, 31163127, doi:10.1175/JAS-D-12-0107.1.

    • Search Google Scholar
    • Export Citation
  • Vickers, D., , and L. Mahrt, 2004: Evaluating formulations of stable boundary layer height. J. Appl. Meteor., 43, 1736–1749, doi:10.1175/JAM2160.1.

    • Search Google Scholar
    • Export Citation
  • Vickers, D., , and L. Mahrt, 2006: A solution for flux contamination by mesoscale motions with very weak turbulence. Bound.-Layer Meteor., 118, 431447, doi:10.1007/s10546-005-9003-y.

    • Search Google Scholar
    • Export Citation
  • Vogelezang, D. H. P., , and A. A. M. Holtslag, 1996: Evaluation and model impacts of alternative boundary-layer height formulations. Bound.-Layer Meteor., 81, 245269, doi:10.1007/BF02430331.

    • Search Google Scholar
    • Export Citation
  • Wang, J., , J. Bian, , W. O. Brown, , H. Cole, , V. Grubisic, , and K. Young, 2009: Vertical air motion from T-REX radiosonde and dropsonde data. J. Atmos. Oceanic Technol., 26, 928942, doi:10.1175/2008JTECHA1240.1.

    • Search Google Scholar
    • Export Citation
  • Yamada, T., 1979: Prediction of the nocturnal surface inversion height. J. Appl. Meteor., 18, 526531, doi:10.1175/1520-0450(1979)018<0526:POTNSI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
1

Both vertical divergence terms are much smaller than the other terms in (1), with the pressure transport contribution close to zero in the Kosovic and Curry (2000) LES of a weakly stable NBL.

2

Odd hours are omitted for readability.

3

A persistent (3 h) shallow S maximum occurs at ~50–100 m, which is sometimes linked to a Tυ maximum on 5 May at Whitewater (Fig. 7). A check of other observed sounding sequences showed this behavior to be unique.

4

This is consistent with Janjic (2001, p. 13) as well as our choice of Riloc = 0.5 as a potential NBL depth criterion (Table 1). On nights when it failed for MYJ, hRiloc > h.

5

The criterion of Richardson et al. is an improvement over a critical Richardson number for both model and observations: values of α vary far less than values of Ric, with time or between days.

Save