Research papersPhysical connection of sensible and ground heat flux
Introduction
Net solar radiation at the land surface (Rn) is partitioned into the latent (E) and sensible heat fluxes into the ground (G) and ambient air (H). Understanding this partitioning is of paramount importance in studying the global energy, water, and carbon cycles (Wong et al., 1979, Schimel et al., 1997, Katul et al., 2012, Fisher et al., 2017) and has motivated numerous studies in the past century (Wang and Dickinson, 2012). The Bowen (1926) ratio method and the Penman (1948) eddy diffusion-energy balance combination approach are two classical examples.
These fluxes are measurable locally at field scales using ground-based sensors. The ground heat flux is often more readily measurable, for example, using heat flux plates (Mayocchi and Bristow, 1995, Sauer et al., 2007), while direct measurements of H and E are more challenging. High-precision weighing lysimeters are the most direct means to measure E, but they are costly to build and operate (Howell et al., 1991, Moorhead et al., 2019). The eddy covariance systems based on sonic anemometry are widely used to estimate H (E) as the covariance of air temperature (specific humidity) and vertical wind velocity (Swinbank, 1951, Baldocchi et al., 2001).
Direct measurement of these surface fluxes is not feasible at large spatial scales, where remote sensing offers a promising alternative (Fisher et al., 2008, Zhang et al., 2016). Remote sensing inference of these fluxes often relies on their physical connections with surface skin temperature, which can be obtained from air- or space-borne observations of upwelling surface radiances in thermal infrared wavelengths (Prata et al., 1995, Jiménez-Muñoz and Sobrino, 2003). Such an inference is often under-constrained and thus requires additional information. For example, in addition to surface temperature, remote sensing retrieval of H requires an estimate of air temperature, wind velocity, and bulk transfer coefficient of heat (Su, 2002, Jia et al., 2003). To reduce the uncertainty of inference, land surface energy balance equation and interrelations between its components provide additional information (Bastiaanssen et al., 1998, Allen et al., 2007). The motivation is that if at least two interrelations between fluxes are characterized accurately, based on the remote sensing observations, the surface energy balance equation can be solved with reduced uncertainty.
Bowen (1926) was one of the first to study the H-E physical connection based on an analogy between the diffusive transfer of heat and water vapor in the ambient air. Relying on more readily measurable variables such as air temperature and vapor pressure, the Bowen ratio adds a constraint to the energy balance equation. Yet, the problem of inferring surface fluxes remains ill-posed with two equations and three unknowns. Wang and Bras, 2009, Wang and Bras, 2011 demonstrated that G and H are strongly linked as the partition of net radiation based on the theory of maximum entropy production. While a third relationship between G and H is highly desirable, such a relationship is poorly understood due to the fundamental difference between the timescale of dominant transport mechanisms of heat in the atmosphere and soil. In effect, while temperature in soil depth changes diurnally, turbulent transport mechanisms of heat in atmosphere operate in sub-hourly scales. This paper attempts to narrow down this knowledge gap. Here, we propose a new relationship between G and H at the daily timescale. This relationship is theoretically derived for bare soil and is evaluated for a variety of bare to vegetated sites.
Section snippets
Ground and sensible heat flux relationship
Conductive and advective flux of heat in unsaturated zone, through molecular diffusion and laminar flow of liquid water, may be expressed as (Sakai et al., 2011):
In Eq. (1) and following equations, the subscripts ‘s’, ‘a’, and ‘w’ denote ‘soil’, ‘air’, and ‘water’, respectively. When the subscripts are dropped for brevity, the corresponding variables can represent either ‘soil’ or ‘air’ media. Note that ‘soil’ is here referred to the bulk soil including all its
Results and Discussion
Fig. 1 presents the estimates of ground heat flux from time series of land surface temperature using the analytical solution (Sadeghi et al., 2019) of the linear advection–diffusion equation (Eq. (15)), with constant advection velocity and thermal diffusion coefficient. The results reaffirm that the assumed linear transport mechanism adequately explains the seasonal dynamics of daily ground heat flux solely based on surface temperature variations. The results confirm previous findings (Wang and
Concluding remarks
The provided analyses and discussions demonstrate that the land surface temperature contains essential information to infer temporal variations of ground and sensible heat flux at daily timescale. Based on a bulk heat transfer parameterization of turbulent fluxes of heat in atmospheric boundary layer in the context of a linear advection–diffusion equation, a new relationship is derived linking daily mean sensible and ground heat flux. The proposed relationship combined with Bowen ratio provides
CRediT authorship contribution statement
M. Sadeghi: Conceptualization, Methodology, Data curation, Formal analysis, Writing – original draft. A. Ebtehaj: Funding acquisition, Conceptualization, Methodology, Writing - review & editing. M. Guala: Methodology, Writing - review & editing. J. Wang: Methodology, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
We gratefully acknowledge support from the NASA Terrestrial Hydrology Program (THP, #80NSSC18K152) through Dr. J. Entin and the New (Early Career) Investigator Program (NIP, #80NSSC18K0742) through Dr. T. Lee and Dr. A. Leidner. Partial support of this study is provided by the NASA NEWS Program (NNX15AT41G) and NSF CZO Program (EAR-1331846). Data used in this study were acquired from the AmeriFlux stations and are available at https://ameriflux.lbl.gov/.
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