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Diurnal Variations of the Flux Imbalance Over Homogeneous and Heterogeneous Landscapes

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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.

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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.

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Authors and Affiliations

  1. Key Laboratory of Remote Sensing of Gansu Province, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou, Gansu, China

    Yanzhao Zhou

  2. University of Chinese Academy of Sciences, Beijing, China

    Yanzhao Zhou

  3. Department of Earth and Environment, Boston University, Boston, MA, USA

    Dan Li

  4. Laboratory for Atmospheric Research, Department of Civil and Environmental Engineering, Washington State University, Pullman, WA, USA

    Heping Liu

  5. Institute of Tibetan Plateau Research, Chinese Academy of Sciences, Beijing, China

    Xin Li

  6. CAS Center for Excellence in Tibetan Plateau Earth Sciences, Chinese Academy of Sciences, Beijing, China

    Xin Li

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  1. Yanzhao Zhou
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Correspondence to Xin Li.

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.

Fig. 14
figure 14

The mean and standard deviation (std) of the vertical velocity component in the HO and HE cases at 28 m during the first hour. The inset is the mean and standard variation of the vertical velocity component in case HO

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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.

Fig. 15
figure 15

The FrTOS and FrTMC values at different heights with different horizontal and vertical resolutions

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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.

Fig. 16
figure 16

The probability density function (p.d.f.) of flux imbalance calculated with different output frequencies in case HO

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Table 2 The statistics of the flux imbalance in case HO with different output frequencies; std denotes the standard deviation
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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

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