Abstract
It is well known that the sum of the turbulent sensible and latent heat fluxes as measured by the eddy-covariance method is systematically lower than the available energy (i.e., the net radiation minus the ground heat flux). We examine the separate and joint effects of diurnal and spatial variations of surface temperature on this flux imbalance in a dry convective boundary layer using the Weather Research and Forecasting model. Results show that, over homogeneous surfaces, the flux due to turbulent-organized structures is responsible for the imbalance, whereas over heterogeneous surfaces, the flux due to mesoscale or secondary circulations is the main contributor to the imbalance. Over homogeneous surfaces, the flux imbalance in free convective conditions exhibits a clear diurnal cycle, showing that the flux-imbalance magnitude slowly decreases during the morning period and rapidly increases during the afternoon period. However, in shear convective conditions, the flux-imbalance magnitude is much smaller, but slightly increases with time. The flux imbalance over heterogeneous surfaces exhibits a diurnal cycle under both free and shear convective conditions, which is similar to that over homogeneous surfaces in free convective conditions, and is also consistent with the general trend in the global observations. The rapid increase in the flux-imbalance magnitude during the afternoon period is mainly caused by the afternoon decay of the turbulent kinetic energy (TKE). Interestingly, over heterogeneous surfaces, the flux imbalance is linearly related to the TKE and the difference between the potential temperature and surface temperature, ΔT; the larger the TKE and ΔT values, the smaller the flux-imbalance magnitude.
Similar content being viewed by others
References
Aubinet M, Vesala T, Papale D (eds) (2012) Eddy covariance: a practical guide to measurement and data analysis. Springer, Dordrecht
Beare RJ, Cortes MAJ, Cuxart J, Esau I, Golaz C, Holtslag AAM, Khairoutdinov M, Kosovic B, Lewellen D, Lund T, Lundquist J, McCabe A, Macvean MK, Moene A, Noh Y, Poulos G, Raasch S, Sullivan PP (2006) An intercomparison of large-eddy simulations of the stable boundary-layer. Boundary-Layer Meteorol 118:247–272
Cheng GD, Li X, Zhao WZ, Xu ZM, Feng Q, Xiao SC, Xiao HL (2014) Integrated study of the water–ecosystem–economy in the Heihe River Basin. Nat Sci Rev 1(3):413–428
Crosman ET, Horel JD (2010) Sea and lake breezes: a review of numerical studies. Boundary-Layer Meteorol 137:1–29
Darbieu C, Lohou F, Lothon M, Vilà-Guerau de Arellano J, Couvreux F, Durand P, Pino D, Patton EG, Nilsson E, Blay-Carreras E, Gioli B (2015) Turbulence vertical structure of the boundary layer during the afternoon transition. Atmos Chem Phys 15:10071–10086
De Roo F, Mauder M (2017) The influence of idealized surface heterogeneity on virtual turbulent flux measurements. Atmos Chem Phys Discuss. https://doi.org/10.5194/acp-2017-498
Eder F, De Roo F, Kohnert K, Desjardins RL, Schmid HP, Mauder M (2014) Evaluation of two energy balance closure parametrizations. Boundary-Layer Meteorol 151:195–219
Eder F, Schmidt M, Damian T, Traumner K, Mauder M (2015a) Mesoscale eddies affect near-surface turbulent exchange: evidence from lidar and tower measurements. J Appl Meteorol 54:189–206
Eder F, De Roo F, Rotenberg E, Yakir D, Schmid HP, Mauder M (2015b) Secondary circulations at a solitary forest surrounded by semi-arid shrubland and their impact on eddy-covariance measurements. Agric For Meteorol 211–212:115–127
Finnigan JJ (2000) Turbulence in plant canopies. Annu Rev Fluid Mech 32:519–571
Finnigan JJ, Clement R, Malhi Y, Leuning R, Cleugh H (2003) A re-evaluation of long-term flux measurement techniques part I: averaging and coordinate rotation. Boundary-Layer Meteorol 107:1–48
Foken T (2008) The energy balance closure problem: an overview. Ecol Appl 18:1351–1367
Foken T, Wimmer F, Mauder M, Thomas C, Liebethal C (2006) Some aspects of the energy balance closure problem. Atmos Chem Phys 6:4395–4402
Foken T, Aubinet M, Finnigan JJ, Leclerc MY, Mauder M, Paw UKT (2011) Results of a panel discussion about the energy balance closure correction for trace gases. Bull Am Meteorol Soc 92(4):ES13–ES18
Gao ZQ, Horton R, Liu HP (2010) Impact of wave phase difference between soil surface heat flux and soil surface temperature on soil surface energy balance closure. J Geophys Res 115:D16112. https://doi.org/10.1029/2009JD013278
Gao ZM, Liu HP, Katul GK, Foken T (2017) Non-closure of the surface energy balance explained by phase difference between vertical velocity and scalars of large atmospheric eddies. Environ Res Lett 12(3):034025
Goulart A, Degrazia G, Rizza U, Anfossi D (2003) A theoretical model for the study of convective turbulence decay and comparison with large-eddy simulation data. Boundary-Layer Meteorol 107:143–155
He Y, Monahan AH, McFarlane NA (2013) Diurnal variations of land surface wind speed probability distributions under clear-sky and low-cloud conditions. Geophys Res Lett 40:3308–3314
Huang J, Lee X, Patton EG (2008) A modelling study of flux imbalance and the influence of entrainment in the convective boundary layer. Boundary-Layer Meteorol 127(2):273–292
Inagaki A, Letzel MO, Raasch S, Kanda M (2006) Impact of surface heterogeneity on energy imbalance: a study using LES. J Meteorol Soc Jpn 84:187–198
Kanda M, Inagaki A, Letzel MO, Raasch S, Watanabe T (2004) LES study of the energy imbalance problem with eddy covariance fluxes. Boundary-Layer Meteorol 110:381–404
Kristensen L, Mann J, Oncley SP, Wyngaard JC (1997) How close is close enough when measuring scalar fluxes with displaced sensors. J Atmos Ocean Technol 14:814–821
Lee X (1998) On micrometeorological observations of surface-air exchange over tall vegetation. Agric For Meteorol 91:39–49
Leuning R, van Gorsel E, Massman WJ, Isaac PR (2012) Reflections on the surface energy imbalance problem. Agric For Meteorol 156:65–74
Li X, Cheng GD, Liu SM, Xiao Q, Ma MG, Jin R, Che T, Liu QH, Wang WZ, Qi Y, Wen JG, Li HY, Zhu GF, Guo JW, Ran YH, Wang SG, Zhu ZL, Zhou J, Hu XL, Xu ZW (2013) Heihe Watershed Allied Telemetry Experimental Research (HiWATER): scientific objectives and experimental design. Bull Am Meteorol Soc 94:1145–1160
Li X, Yang K, Zhou YZ (2016) Progress in the study of oasis-desert interactions. Agric For Meteorol 230–231:1–7
Liu SM, Xu ZW, Song LS, Zhao QY, Ge Y, Xu TR, Ma YF, Zhu ZL, Jia ZZ, Zhang F (2016) Upscaling evapotranspiration measurements from multi-site to the satellite pixel scale over heterogeneous land surfaces. Agric For Meteorol 230–231:97–113
Mahrt L (1998) Flux sampling errors for aircraft and towers. J Atmos Ocean Technol 15:416–429
Mahrt L (2010) Computing turbulent fluxes near the surface: needed improvements. Agric For Meteorol 150(4):501–509
Moeng C, Dudhia J, Klemp J, Sullivan P (2007) Examining two-way grid nesting for large eddy simulation of the PBL using the WRF model. Mon Weather Rev 135(6):2295–2311
Nadeau DF, Pardyjak ER, Higgins CW, Fernando HJS, Parlange MB (2011) A simple model for the afternoon and early evening decay of convective turbulence over different land surfaces. Boundary-Layer Meteorol 141:301–324
Oncley SP, Foken T, Vogt R, Kohsiek W, DeBruin HAR, Bernhofer C, Christen A, van Gorsel E, Grantz D, Feigenwinter C, Lehner I, Liebethal C, Liu H, Mauder M, Pitacco A, Ribeiro L, Weidinger T (2007) The energy balance experiment EBEX-2000. Part I: overview and energy balance. Boundary-Layer Meteorol 123:1–28
Patton E, Sullivan P, Moeng C (2005) The influence of idealized heterogeneity on wet and dry planetary boundary layers coupled to the land surface. J Atmos Sci 62:2078–2097
Pino D, Jonker H, Vilà-Guerau De Arellano J, Dosio A (2006) Role of shear and the inversion strength during sunset turbulence over land: characteristic length scales. Boundary-Layer Meteorol 121:537–556
Rannik U, Vesala T (1999) Autoregressive filtering versus linear detrending in estimation of fluxes by the eddy covariance method. Boundary-Layer Meteorol 91(2):259–280
Raupach MR, Shaw RH (1982) Averaging procedures for flow within vegetation canopies. Boundary-Layer Meteorol 22:79–90
Rizza U, Miglietta M, Degrazia G, Acevedo O, Marques Filho E (2013) Sunset decay of the convective turbulence with large-eddy simulation under realistic conditions. Phys A 392:4481–4490
Schalkwijk J, Jonker HJJ, Siebesma AP (2016) An investigation of the eddy-covariance flux imbalance in a year-long large-eddy simulation of the weather at Cabauw. Boundary-Layer Meteorol 160:17–39
Sorbjan Z (1997) Decay of convective turbulence revisited. Boundary-Layer Meteorol 82:501–515
Steinfeld G, Letzel M, Raasch S, Kanda M, Inagaki A (2007) Spatial representativeness of single tower measurements and the imbalance problem with eddy-covariance fluxes: results of a large-eddy simulation study. Boundary-Layer Meteorol 123:77–98
Stoy PC, Mauder M, Foken T, Marcolla B, Boegh E, Ibrom A, Arain MA, Arneth A, Aurela M, Bernhofer C, Cescatti A, Dellwik E, Duce P, Gianelle D, van Gorsel E, Kiely G, Knohl A, Margolis H, McCaughey H, Merbold L, Montagnani L, Papale D, Reichstein M, Saunders M, Serrano-Ortiz P, Sottocornola M, Spano D, Vaccari F, Varlagin A (2013) A data-driven analysis of energy balance closure across FLUXNET research sites: the role of landscape scale heterogeneity. Agric For Meteorol 171–172:137–152
Talbot C, Bou-Zeid E, Smith J (2012) Nested mesoscale large-eddy simulations with WRF: performance in real test cases. J Hydrometeorol 13(5):1421–1441
Twine TE, Kustas WP, Norman JM, Cook DR, Houser PR, Meyers TP, Prueger JH, Starks PJ, Wesely ML (2000) Correcting eddy-covariance flux underestimates over a grassland. Agric For Meteorol 103:279–300
Wang JM, Wang WZ, Liu SM, Ma MG, Li X (2009) The problems of surface energy balance closure: an overview and case study. Adv Earth Sci 24:705–713 (in Chinese)
Wilson K, Goldstein A, Falge E, Aubinet M, Baldocchi D, Berbigier P, Bernhofer C, Ceulemans R, Dolman H, Field C, Grelle A, Ibrom A, Law BE, Kowalski A, Meyers T, Moncrieff J, Monson R, Oechel W, Tenhunen J, Valentini R, Verma S (2002) Energy balance closure at FLUXNET sites. Agric For Meteorol 113:223–243
Wohlfahrt G, Widmoser P (2013) Can an energy balance model provides additional constraints on how to close the energy imbalance? Agric For Meteorol 169:85–91
Xu ZW, Liu SM, Li X, Shi SJ, Wang JM, Zhu ZL, Xu TR, Wang WZ, Ma MG (2013) Intercomparison of surface energy flux measurement systems used during the HiWATER-MUSOEXE. J Geophys Res Atmos 118:13140–13157
Xu ZW, Ma YF, Liu SM, Shi WJ, Wang JM (2017) Assessment of the energy balance closure under advective conditions and its impact using remote sensing data. J Appl Meteorol 56(1):127–140
Zhang N, Wang XY, Peng Z (2014) Large-eddy simulation of mesoscale circulations forced by inhomogeneous urban heat island. Boundary-Layer Meteorol 151(1):179–194
Zhu X, Ni G, Cong Z, Sun T, Li D (2016) Impacts of surface heterogeneity on dry planetary boundary layers in an urban-rural setting. J Geophys Res Atmos 121:12164–121179
Acknowledgements
This work was jointly supported by the National Natural Science Foundation of China (Grant: 91425303 and 41630856) and the Strategic Priority Research Program of the Chinese Academy of Sciences, Grant: XDA19070100. H.L. acknowledges support by National Science Foundation AGS under Grants: 1419614. The major part of this work was conducted when the first author visited Boston University in 2017. We thank Professor Guido Salvucci and Dr. Angela Rigden at Boston University for their constructive comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Appendices
Appendix 1: The Effect of Numerical Error
As stated in Sect. 2.1, we treat \( \left[ w \right] \) as identically zero in case HO. However, when the surface is heterogeneous, we must use the \( \left[ {\bar{F}} \right] \) as the “true flux” or “representative flux” (Sect. 2.2). Therefore, one question remains to be answered: how does the numerical error in \( \left[ w \right] \) affect the imbalance in case HE? Figure 14 shows the mean and standard deviation of the vertical velocity component in the HO and HE cases at 28 m during the first hour. The inset shows the mean and standard deviation of the vertical velocity component in case HO because the value is too low. As the numerical error is clearly four orders of magnitude smaller than the simulated vertical velocity component over heterogeneous surfaces, the effects of numerical errors in case HE can be safely neglected.
Appendix 2: Sensitivity to Resolution and Vertical Stretching
To examine the sensitivity to the resolution, additional simulations were conducted at a finer horizontal grid resolution of 25 m × 25 m in the first hour of the HO and HE cases. Also, to examine the sensitivity to the vertical stretching, the additional simulations employed a constant vertical grid resolution of 25 m for the HE case, but a vertically-stretched grid for the HO case.
The FrTOS and FrTMC values in the HO and HE cases at different heights are shown in Fig. 15, where little difference between the simulated results from the two grids of different horizontal resolutions is evident, with a mean absolute difference of 1.2%. Similarly, the effects of vertical grid stretching on FrTOS and FrTMC values are also small, with a mean absolute difference of 1.27%. Therefore, a grid with a horizontal resolution of 50 m × 50 m, and stretched in the vertical direction is used.
Appendix 3: Sensitivity to Output Frequency
To examine the sensitivity to the output frequency, \( w \) and \( \theta \) values are produced every 1, 60, 300 and 600 s in the first hour of the HO case. The probability density function and statistics of the imbalance at different heights are shown in Fig. 16 and Table 2, where little difference in the results of 1-s and 1-min output frequencies is illustrated, with a mean absolute difference ratio of 2%. The difference is larger when the output frequency becomes larger than 60 s, with a mean absolute difference ratio of 22% at 300 s and 47% at 600 s. Therefore, outputs of \( w \) and \( \theta \) values are produced every minute to save storage space without affecting the final results.
Rights and permissions
About this article
Cite this article
Zhou, Y., Li, D., Liu, H. et al. Diurnal Variations of the Flux Imbalance Over Homogeneous and Heterogeneous Landscapes. Boundary-Layer Meteorol 168, 417–442 (2018). https://doi.org/10.1007/s10546-018-0358-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10546-018-0358-2