Investigation of Turbulence Parametrization Schemes with Reference to the Atmospheric Boundary Layer Over the Aegean Sea During Etesian Winds

Abstract

The spatial structure of the marine atmospheric boundary layer (MABL) over the Aegean Sea is investigated using the Weather Research and Forecasting (WRF) mesoscale model. Two ‘first-order’ non-local and five ‘1.5-order’ local planetary boundary-layer (PBL) parametrization schemes are used. The predictions from the WRF model are evaluated against airborne observations obtained by the UK Facility for Airborne Atmospheric Measurements BAe-14 research aircraft during the Aegean-GAME field campaign. Statistical analysis shows good agreement between measurements and simulations especially at low altitude. Despite the differences between the predicted and measured wind speeds, they reach an agreement index of 0.76. The simulated wind-speed fields close to the surface differ substantially among the schemes (maximum values range from 13 to \(18\hbox { m s}^{-1}\) at 150-m height), but the differences become marginal at higher levels. In contrast, all schemes show similar spatial variation patterns in potential temperature fields. A warmer (1–2 K) and drier (2–3\(\hbox { g kg}^{-1})\) layer than is observed, is predicted by almost all schemes under stable conditions (eastern Aegean Sea), whereas a cooler (up to 2 K) and moister (1–2\(\hbox { g kg}^{-1})\) layer is simulated under near-neutral to nearly unstable conditions (western Aegean Sea). Almost all schemes reproduce the vertical structure of the PBL and the shallow MABL (up to 300 m) well, including the low-level jet in the eastern Aegean Sea, with non-local schemes being closer to observations. The simulated PBL depths diverge (up to 500 m) due to the different criteria applied by the schemes for their calculation. Under stable conditions, the observed MABL depth corresponds to the height above the sea surface where the simulated eddy viscosity reaches a minimum; under neutral to slightly unstable conditions this is close to the top of the simulated entrainment layer. The observed sensible heat fluxes vary from −40 to \(25\hbox { W m}^{-2}\), while the simulated fluxes range from −40 to \(40\hbox { W m}^{-2}\); however, all of the schemes’ predictions are close to the observations under unstable conditions. Finally, all schemes overestimate the friction velocity, although the simulated range (from 0.2 to \(0.5\hbox { m s}^{-1})\) is narrower than that observed (from 0.1 to \(0.7\hbox { m s}^{-1})\).

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References

  1. Balzarini A, Angelini F, Ferrero L, Moscatelli M, Perrone MG, Pirovano G, Riva GM, Sangiorgi G, Toppetti AM, Gobbi GP, Bolzacchini E (2014) Sensitivity analysis of PBL schemes by comparing WRF model and experimental data. Geosci Model Dev Discuss 7:6133–6171

    Article  Google Scholar 

  2. Banks RF, Tiana-Alsina J, Baldasano JM, Rocadenbosch F, Papayannis A, Solomos S, Tzanis CG (2016) Sensitivity of boundary-layer variables to PBL schemes in the WRF model based on surface meteorological observations, lidar, and radiosondes during the HygrA-CD campaign. Atmos Res 176–177:185–201

    Article  Google Scholar 

  3. Bezantakos S, Barmpounis K, Giamarelou M, Bossioli E, Tombrou M, Mihalopoulos N, Eleftheriadis K, Kalogiros J, Allan JD, Bacak A, Percival CJ, Coe H, Biskos G (2013) Chemical composition and hygroscopic properties of aerosol particles over the Aegean Sea. Atmos Chem Phys 12(22):11595–11608

    Article  Google Scholar 

  4. Borge R, Alexandrov V, del Vas JJ, Lumbreras J, Rodrıguez E (2008) A comprehensive sensitivity analysis of the WRF model for air quality applications over the Iberian Peninsula. Atmos Environ 42:8560–8574

    Article  Google Scholar 

  5. Bossioli E, Tombrou M, Kalogiros J, Allan J, Bacak A, Bezantakos S, Biskos S, Coe H, Jones BT, Kouvarakis G, Mihalopoulos N, Percival CJ (2016) Atmospheric composition in the Eastern Mediterranean: Influence of biomass burning during summertime using the WRF-Chem model. Atmos Environ 132:317–331

    Article  Google Scholar 

  6. Bougeault P, Lacarrére P (1989) Parameterization of orography-induced turbulence in a mesobeta-scale model. Mon Weather Rev 117:1872–1890

    Article  Google Scholar 

  7. Bretherton C, Park S (2009) A new moist turbulence parameterization in the community atmosphere model. J Clim 22:3422–3448

    Article  Google Scholar 

  8. Chen F, Dudhia J (2001) Coupling an advanced land surface-hydrology model with the penn state-NCAR MM5 modeling system. Part I. Model implementation and sensitivity. Mon Weather Rev 129:569–585

    Article  Google Scholar 

  9. Cohen AE, Cavallo SM, Coniglio MC, Brooks HE (2015) A review of planetary boundary layer parameterization schemes and their sensitivity in simulating southeastern U.S. cold season severe weather environments. Wea Forecast 30:591–612

    Article  Google Scholar 

  10. Coniglio MC, Correia JRJ, Marsh PT, Kong F (2013) Verification of convection-allowing WRF model forecasts of the planetary boundary layer using sounding observations. Wea Forecast 28:842–862

    Article  Google Scholar 

  11. Colle BA, Olson JB, Tongue JS (2003) Multiseason verification of the MM5. Part I: comparison with the eta model over the central and eastern United States and impact of MM5 resolution. Wea Forecast 18:431–457

    Article  Google Scholar 

  12. Dandou A, Tombrou M, Schäfer K, Emeis S, Soulakellis N, Protonotariou A, Bossioli E, Suppan P (2009) A comparison between modelled and measured mixing height over Munich. Boundary-Layer Meteorol 131(3):425–440

    Article  Google Scholar 

  13. Dudhia J (1989) Numerical study of convection observed during the winter monsoon experiment using a mesoscale two-dimensional model. J Atmos Sci 46:3077–3107

    Article  Google Scholar 

  14. Dudhia J, Hong S-Y, Lim K-S (2008) A new method for representing mixed-phase particle fall speeds in bulk microphysics parameterizations. J Met Soc Japan 86A:33–44

    Article  Google Scholar 

  15. Emeis S (2011) Surface-Based Remote Sensing of the atmospheric boundary layer. Series: atmospheric and oceanographic sciences library 40. Springer, Heidelberg, 174 pp

  16. Emery C, Tai E, Yarwood G (2001) Enhanced meteorological modeling and performance evaluation for two Texas Ozone Episodes. Report to the Texas Natural Resources Conservation Commission, prepared by ENVIRON, International Corp Novato CA

  17. Fairall CW, Bradley EF, Rogers DP, Edson JB, Young GS (1996) Bulk parameterization of air-sea fluxes for tropical ocean-global atmosphere coupled-ocean atmosphere response experiment. J Geophys Res 101:3747–3764

    Article  Google Scholar 

  18. Fairall CW, Bradley EF, Hare JE, Grachev AA, Edson JB (2003) Bulk parameterization of air-sea fluxes: Updates and verification for COARE algorithm. J Clim 16:571–591

    Article  Google Scholar 

  19. Fast JD, Gustafson WI, Easter RC, Zaveri RA, Barnard JC, Chapman EG, Grell GA, Peckham SE (2006) Evolution of ozone, particulates, and aerosol direct radiative forcing in the vicinity of Houston using a fully coupled meteorology-chemistry-aerosol model. J Geophys Res–Atmos 111(D21):21305

    Article  Google Scholar 

  20. Giannakopoulou EA, Nhili R (2014) WRF model methodology for offshore wind energy applications. Adv Meteorol 2014:1–14

    Article  Google Scholar 

  21. Gibbs JA, Fedorovich E, van Eijk AMJ (2011) Evaluating weather research and forecasting (WRF) model predictions of turbulent flow parameters in a dry convective boundary layer. J Appl Meteorol Climatol 50:2429–2444

    Article  Google Scholar 

  22. Giorgi F (2006) Climate change hot-spots. Geophys Res Lett 33(8):L08707

    Article  Google Scholar 

  23. Huang H-Y, Hall A, Teixeira J (2013) Evaluation of the WRF PBL parameterizations for marine boundary layer clouds: cumulus and stratocumulus. Mon Weather Rev 141:2265–2271

    Article  Google Scholar 

  24. Hong S-Y, Pan H-L (1996) Nonlocal boundary layer vertical diffusion in a medium-range forecast model. Mon Weather Rev 124:2322–2339

    Article  Google Scholar 

  25. Hong S-Y, Dudhia J, Chen S-H (2004) A revised approach to ice microphysical processes for the bulk parameterization of clouds and precipitation. Mon Weather Rev 132:103–120

    Article  Google Scholar 

  26. Hong S-Y, Lim J-OJ (2006) The WRF single-moment 6-class microphysics scheme (WSM6). J Korean Meteor Soc 42(2):129–151

    Google Scholar 

  27. Hong S-Y, Noh Y, Dudhia J (2006) A new vertical diffusion package with an explicit treatment of entrainment processes. Mon Weather Rev 134:2318–2341

    Article  Google Scholar 

  28. Hu H-M, Nielsen-Gammon JW, Zhang F (2010) Evaluation of three planetary boundary layer schemes in the WRF model. J Appl Meteorol Clim 49:1831–1844

    Article  Google Scholar 

  29. Iacono MJ, Nehrkorn T (2010) Assessment of radiation options in the advanced research WRF weather forecast model. In: Proceedings, 1st atmospheric system research science team meeting, Bethesda, MD, 15–19 March, 2010. Office of Science, U.S. Department of Energy. http://www.arm.gov/publications/db

  30. Janjic ZI (1990) The step-mountain coordinate: physics package. Mon Weather Rev 118:1429–1443

    Article  Google Scholar 

  31. Janjic ZI (2002) Nonsingular implementation of the Mellor-Yamada level 2.5 scheme in the NCEP Meso model. NOAA/NWS/NCEP Office Note 437, 61 pp

  32. Jimenez PA, Dudhia J, Gonzalez-Rouco JF, Navarro J, Montavez JP, Garcia-Bustamente E (2012) A revised scheme for the WRF surface layer formulation. Mon Weather Rev 140:898–918

    Article  Google Scholar 

  33. Kain JS, Fritsch JM (1990) A one-dimensional entraining/detraining plume model and its application in convective parameterization. J Atmos Sci 47:2784–2802

    Article  Google Scholar 

  34. Kain JS, Fritsch JM (1993) Convective parameterization for mesoscale models: the 17 Kain–Fritsch scheme. The representation of cumulus convection in numerical models. Meteor Monogr No 24, Amer Meteor Soc 165–170

  35. Kalogiros J, Wang Q (2011) Aircraft observations of sea-surface turbulent fluxes near the California coast. Boundary-Layer Meteorol 139(2):283–306

    Article  Google Scholar 

  36. Kanakidou M, Mihalopoulos N, Kindap T, Im U, Vrekoussis M, Gerasopoulos E, Dermitzaki E, Unal A, Koçak M, Markakis K, Melas D, Kouvarakis G, Youssef AF, Richter A, Hatzianastassiou N, Hilboll A, Ebojie F, Wittrock F, von Savigny C, Burrows JP, Ladstaetter-Weissenmayer A, Moubasher H (2011) Megacities as hot spots of air pollution in the East Mediterranean. Atmos Environ 45(6):1223–35

    Article  Google Scholar 

  37. Kim SY, Matsuura T, Matsumi Y, Tom TH, Yasuda T, Mase H, Nishino H (2012) A study of sensitivity analysis of WRF parameters for meteorological predictions at the Sanin Coast. J Jpn Soc Civil Eng, Ser. B2 (Coast Eng) 68(2): I_1236-I_1240

  38. Kleczek MA, Steeneveld G-J, Holtslag AAM (2014) Evaluation of the weather research and forecasting mesoscale model for GABLS3: impact of boundary-layer schemes, boundary conditions and spin-up. Boundary-Layer Meteorol 152:213–243

    Article  Google Scholar 

  39. Kotroni V, Lagouvardos K, Lalas D (2001) The effect of the island of Crete on the Etesian winds over the Aegean Sea. Q J R Meteorol Soc 127(576):1917–37

    Article  Google Scholar 

  40. Kwun JH, Kim Y-K, Seo J-W, Jeong JH, You SH (2009) Sensitivity of MM5 and WRF mesoscale model predictions of surface winds in a typhoon to planetary boundary layer parameterizations. Nat Hazards 51:63–77

    Article  Google Scholar 

  41. Lelieveld J, Berresheim H, Borrmann S, Crutzen PJ, Dentener FJ, Fischer H, Feichter J, Flatau PJ, Heland J, Holzinger R, Korrmann R, Lawrence MG, Levin Z, Markowicz KM, Mihalopoulos N, Minikin A, Ramanathan V, de Reus M, Roelofs GJ, Scheeren HA, Sciare J, Schlager H, Schultz M, Siegmund P, Steil B, Stephanou EG, Stier P, Traub M, Warneke C, Williams J, Ziereis H (2002) Global air pollution crossroads over the mediterranean. Science 298(5594):794–799

    Article  Google Scholar 

  42. LeMone MA, Tewari M, Chen F, Dudhia J (2013) Objectively determined fair-weather CBL depths in the ARW-WRF model and their comparison to CASES-97 observations. Mon Weather Rev 141(1):30–54

    Article  Google Scholar 

  43. Lin Y-L, Farley RD, Orville HD (1983) Bulk parameterization of the snow field in a cloud model. J Clim Appl Meteor 22:1065–1092

    Article  Google Scholar 

  44. Mlawer EJ, Taubman SI, Brown PD, Iacono MJ, Clough SA (1997) Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave. J Geophys Res 102:16663–16682

    Article  Google Scholar 

  45. Mavropoulou AM, Mantziafou A, Jarosz E, Sofianos S (2016) The influence of Black Sea Water inflow and its synoptic time-scale variability in the North Aegean Sea hydrodynamics. Ocean Dyn 66(2):195–206

    Article  Google Scholar 

  46. Misenis C, Zhang Y (2010) An examination of WRF/Chem: physical parameterizations, nesting options, and grid resolutions. Atmos Res 97:315–334

    Article  Google Scholar 

  47. Nakanishi M (2001) Improvement of the Mellor–Yamada turbulence closure model based on large-eddy simulation data. Boundary-Layer Meteorol 99(3):49–378

    Google Scholar 

  48. Nakanishi M, Niino H (2004) An improved Mellor–Yamada level-3 model with condensation physics: its design and verification. Boundary-Layer Meteorol 112:1–31

    Article  Google Scholar 

  49. Nakanishi M, Niino H (2006) An improved Mellor–Yamada level-3 model: its numerical stability and application to a regional prediction of advection fog. Boundary-Layer Meteorol 119:397–407

    Article  Google Scholar 

  50. Nakanishi M, Niino H (2009) Development of an improved turbulence closure model for the atmospheric boundary layer. J Meteorol Soc Jpn 87:895–912

    Article  Google Scholar 

  51. Nunalee C, Basu S (2014) Mesoscale modeling of low-level jets over the north Sea. In: Holling M, Peinke J, Ivanell S (eds) Wind energy-impact of turbulence. Research topics in wind energy, vol 2. Springer, Berlin, pp 197–202

    Google Scholar 

  52. Olson JB, Brown JM (2009) Comparison of two Mellor–Yamada-based PBL schemes in simulating a hybrid barrier jet. In: 23rd conference on weather analysis and forecasting/19th conference on numerical weather prediction, 31 May–5 June 2009

  53. Park S, Bretherton CS (2009) The university of washington shallow convection scheme and moist turbulence schemes and their impact on climate simulations with the community atmosphere model. J Clim 22:3449–3469

    Article  Google Scholar 

  54. Perlin N, de Szoeke SP, Chelton DB, Samelson RM, Skyllingstad ED, O’Neill LW (2013) Modeling the atmospheric boundary layer wind response to mesoscale sea surface temperature perturbations. Mon Weather Rev 142(11):4284–4307

    Article  Google Scholar 

  55. Pleim JE, Chang JS (1992) A non-local closure model for vertical mixing in the convective boundary layer. Atmos Environ 26A:965–981

    Article  Google Scholar 

  56. Pleim JE (2007a) A combined local and nonlocal closure model for the atmospheric boundary layer. Part I: model description and testing. J Appl Meteorol Clim 46:1383–1395

    Article  Google Scholar 

  57. Pleim JE (2007b) A combined local and nonlocal closure model for the atmospheric boundary layer. Part II: application and evaluation in a mesoscale meteorological model. J Appl Meteorol Clim 46:1396–1409

    Article  Google Scholar 

  58. Sempreviva A, Gryning S-E (1996) Humidity fluctuations in the marine boundary layer measured at a coastal site with an infrared humidity sensor. Boundary-Layer Meteorol 77:331–352

    Article  Google Scholar 

  59. Shin HH, Hong S-Y (2011) Intercomparison of planetary boundary-layer parameterizations in the WRF model for a single day from CASES-99. Boundary-Layer Meteorol 139:261–281

    Article  Google Scholar 

  60. Sienkiewicz MJ, Colle BA (2014) Evaluation of WRF PBL schemes in the marine atmospheric boundary layer over the coastal waters of southern New England. In: Proceedings of the 26th conference on weather analysis and forecasting/22nd conference on numerical weather prediction 2–6 February 2014, Atlanta GA

  61. Skamarock WC, Klemp JB, Dudhia J, Gill DO, Barker DM, Duda MG, Huang X-Y, Wang W, Powers JG (2008) A description of the advanced research WRF version 3. NCAR TECHNICAL NOTE, NCAR/TN-475+STR, 113 pp

  62. Stull RB (1988) An introduction to boundary layer meteorology. Kluwer, Dordrecht, 666 pp

  63. Sukoriansky S, Galperin B, Perov V (2005) Application of a new spectral theory of stable stratified turbulence to the atmospheric boundary layer over sea ice. Boundary-Layer Meteorol 117:231–257

    Article  Google Scholar 

  64. Tesche TW, McNally DE, Emery CA, Tai E (2001) Evaluation of the MM5 model over the Midwestern U.S. for three 8-hr oxidant episodes. Prepared for the Kansas City Ozone Technical Work Group, prepared by Alpine Geophysics, LLC, Ft. Wright, KY and ENVIRON International Corp, Novato, CA

  65. Tombrou M, Dandou A, Helmis C, Akylas E, Aggelopoulos G, Flocas H, Assimakopoulos V, Soulakellis N (2007) Model evaluation of the atmospheric boundary layer and mixed-layer evolution. Boundary-Layer Meteorol 124:61–79

    Article  Google Scholar 

  66. Tombrou M, Bossioli E, Kalogiros J, Allan J, Bacak A, Biskos G, Coe H, Dandou A, Kouvarakis G, Mihalopoulos N, Percival CJ, Protonotariou AP, Szabó-Takács B (2015) Physical and chemical processes of air masses in the Aegean Sea during Etesians: Aegean-Game airborne campaign. Sci Total Environ 506–507:201–216

    Article  Google Scholar 

  67. Triantafyllou E, Giamarelou M, Bossioli E, Zarmpas P, Theodosi C, Matsoukas C, Tombrou M, Mihalopoulos N, Biskos G (2016) Particulate pollution transport episodes from Eurasia to a remote region of northeast Mediterranean. Atmos Environ 128:45–52

    Article  Google Scholar 

  68. Tyrlis E, Lelieveld J, Steil B (2013) The summer circulation in the eastern Mediterranean and the middle east: influence of the south Asian Monsoon and mid-latitude dynamics. In: Helmis CG, Nastos PT (eds) Advances in meteorology, climatology and atmospheric physics. Springer, Berlin, pp 793–802

    Google Scholar 

  69. Yver CE, Gravenm HD, Lucas DD, Cameron-Smith PJ, Keeling RF, Weiss RF (2013) Evaluating transport in the WRF model along the California coast. Atmos Chem Phys 13:1837–1852

    Article  Google Scholar 

  70. Wang LT, Jang C, Zhang Y, Wang K, Zhang Q, Streets DG, Fu J, Lei Y, Schreifels J, He K, Hao J, Lam Y-F, Lin J, Meskhidze N, Voorhees S, Evarts D, Phillips S (2010) Assessment of air quality benefits from national air pollution control policies in China. Part I: background, emission scenarios and evaluation of meteorological predictions. Atmos Environ 44:3442–3448

    Article  Google Scholar 

  71. Xie B, Fung J-CH, Chan A, Lau A (2012) Evaluation of nonlocal and local planetary boundary layer schemes in the WRF model. J Geophys Res 117:D12103

    Google Scholar 

  72. Zanis P, Hadjinicolaou P, Pozzer A, Tyrlis E, Dafka S, Mihalopoulos N, Lelieveld J (2014) Summertime free-tropospheric ozone pool over the eastern Mediterranean/Middle East. Atmos Chem Phys 4(1):115–32

    Article  Google Scholar 

  73. Zerefos CS, Kourtidis KA, Melas D, Balis D, Zanis P, Katsaros L, Mantis HT, Repapis C, Isaksen I, Sundet J, Herman J, Bhartia PK, Calpini B (2002) Photochemical activity and solar ultraviolet radiation (PAUR) modulation factors: an overview of the project. J Geophys Res 107(D18):8134

    Article  Google Scholar 

  74. Zhang H, Li J, Ying Q, Yu JZ, Wu D, Cheng Y et al (2012) Source apportionment of PM2.5 nitrate and sulfate in China using a source-oriented chemical transport model. Atmos Environ 62:228–242

    Article  Google Scholar 

  75. Zhang H, Chen G, Hu J, Chen S-H, Wiedinmyer C, Kleeman M, Ying Q (2014) Evaluation of a seven-year air quality simulation using the weather research and forecasting (WRF)/community multiscale air quality (CMAQ) models in the eastern United States. Sci Total Environ 473–474:275–285

    Google Scholar 

  76. Zhong S, In H, Clements C (2007) Impact of turbulence, land surface, and radiation parameterizations on simulated boundary layer properties in a coastal environment. J Geophys Res 112:D13110

    Google Scholar 

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Acknowledgements

This work is supported by the EUFAR Integrating Activity (227159) funded by the EC under FP7. Airborne data were obtained using the BAe-146-301 Atmospheric Research Aircraft (ARA) flown by Direct flight Ltd and managed by the Facility for Airborne Atmospheric Measurements (FAAM), which is a joint entity of NERC and the Met Office. We gratefully acknowledge the FAAM Team, Maureen Smith, Axel Wellpott and Angela Dean. Many thanks to Phil Brown and our mission scientists Dave Kindred and Steve Abel, all from the Met Office. This work was supported by the Cy-Tera Project (NEA YPODOMH/STRATH/0308/31), which is co-funded by the European Regional Development Fund and the Republic of Cyprus through the Research Promotion Foundation. The assistance of Thekla Loizou from the Cyprus Institute in achieving the technical requirements is gratefully acknowledged. Finally, we thank the two anonymous reviewers for their constructive criticism and suggestions.

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Appendix

Appendix

Mathematical formulations and statistical benchmarks for water vapour mixing ratio, air temperature, wind direction and wind speed, respectively according to Tesche et al. (2001) and Emery et al. (2001).

Metrics Formulae\(^{*}\) Benchmarks
Mean bias \(M{B}=\frac{1}{N}\mathop \sum \nolimits _{i=1}^N \left( {E_i -O_i } \right) \) \({\le } \pm 0.1\hbox {g kg}^{-1}\), \({\le } \pm 0.5\hbox { K}\), \({\le } \pm 10^{\circ }\), \({\le } \pm 0.5\hbox { m s}^{-1}\)
Mean absolute error \(MAE=\frac{1}{N}\mathop \sum \nolimits _{i=1}^N \left| {E_i -O_i } \right| \) \(< 2\hbox {g kg}^{-1}\), \({\le } 2\hbox { K}\), \({\le } 30^{\circ }\), -
Root-mean-square error \(RMSE=\sqrt{\frac{1}{N}\mathop \sum \nolimits _{i=1}^N \left| {E_i -O_i } \right| ^{2}}\) -, -, -, \({\le } 2\hbox { m s}^{-1}\)
Index of agreement \(IA=1-\left[ {\frac{N\cdot RMSE^{2}}{\mathop \sum \nolimits _{i=1}^N \left( {\left| {E_i -\bar{O}} \right| +\left| {O_i -\bar{O}} \right| } \right) ^{2}}} \right] \) \(\ge 0.6\), \(\ge 0.8\), -, \(\ge 0.6\)
Normalized mean bias \(NMB=\frac{\mathop \sum \nolimits _{i=1}^N \left( {E_i -O_i } \right) }{\mathop \sum \nolimits _{i=1}^N O_i }\times 100\% \)  
Normalized mean error \(NME=\frac{\mathop \sum \nolimits _{i=1}^N \left| {E_i -O_i } \right| }{\mathop \sum \nolimits _{i=1}^N O_i }\times 100\%\)  
  1. \(^{*}E\) is the estimated (modeled) and O is the observed value of each parameter, paired in space and time for each i of N data pairs. \(\bar{E}\) and \(\bar{O}\) are the mean values of estimations and observations, respectively

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Dandou, A., Tombrou, M., Kalogiros, J. et al. Investigation of Turbulence Parametrization Schemes with Reference to the Atmospheric Boundary Layer Over the Aegean Sea During Etesian Winds. Boundary-Layer Meteorol 164, 303–329 (2017). https://doi.org/10.1007/s10546-017-0255-0

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Keywords

  • Aegean-GAME
  • Aegean Sea
  • Etesian winds
  • Marine atmospheric boundary layer
  • Turbulent fluxes