Research papers
A new free-convection form to estimate sensible heat and latent heat fluxes for unstable cases

https://doi.org/10.1016/j.jhydrol.2020.124917Get rights and content

Highlights

  • New Free Convection Limit approaches (FCL) are developed for turbulent fluxes.

  • FCL are tested over three surfaces of major interest in agriculture.

  • Similar surface energy balance closures obtained using FCL and reference methods.

Abstract

Free convection limit (FCL) approaches to estimate surface fluxes are of interest given the evidence that they may extend up to near neutral stability conditions. For measurements taken in the inertial sublayer, the formulation based on surface renewal theory and the analysis of small eddies (SRSE) to estimate the sensible heat flux (H) was extended to latent heat flux (LE) with the aim to derive their FCL approaches. For sensible heat flux (HFCL), the input requirements are traces of the fast-response (such as 10–20 Hz) air temperature and the zero-plane displacement. For latent heat flux (LEFCL), input requirements are fast response traces of water vapor density, mean temperature of the air, the available net surface energy (Rn-G, where Rn and G are the net radiation and soil heat flux, respectively) and the zero-plane displacement. Taking eddy covariance (EC) as a reference method, the performance of the FCL method was tested over a growing cotton field that involved three contrasting surfaces: partly mulched bare soil, a sparse canopy and a homogeneous canopy. Using traces at 10 Hz and 20 Hz, HFCL overestimated and underestimated the EC sensible heat flux (HEC), respectively. In general, LEFCL tended to slightly underestimate LEEC. The surface energy balance closure show that (HEC + LEEC) underestimated (Rn-G) in a range of 19% (homogeneous canopy) and 8% (sparse canopy). Given that, in general (HFCL + LEFCL) was closer to (Rn-G) than (HEC + LEEC), the FCL method may be recommended for field applications, especially when the wind speed is not available.

Introduction

The latent heat flux (LE) is involved in two fundamental equations, the surface energy-balance equation and the water-balance equation. Given that the main drivers for LE are the supply of water (including water content in topsoil) and the available net surface energy, (Rn – G) where Rn is the net radiation and G is the soil heat flux, it links hydrological, agricultural and climatological features (Dominguez et al., 2008, Li and Wang, 2019, Robles-Morua et al., 2012, Stagl et al., 2014, Yang and Wang, 2014). In particular, its knowledge is crucial for irrigation planning, to perform weather forecasting, climate modelling, to determine the risk of fire, among others (Brutsaert, 1982, Fang et al., 2018, Silva et al., 2010).

Direct measurements of LE by means of the eddy covariance (EC) method and large weighing lysimeters are preferred for scientific studies in agricultural landscapes. However, the required instrumentation and maintenance are expensive. When the sensible heat flux (H), LE and the available net surface energy are measured independently they allow calculating the simplified surface energy balance (Rn – G = H + LE), which can be used as a conventional quality control, to indirectly check the measurement reliability of H and LE (Aubinet et al., 2000). In general, the instrumentation required for monitoring LE over large areas involving different surfaces is not always affordable or applicable (Haymann et al., 2019) and, on the other hand, flow distortion and windy conditions (among others) are problems when using, respectively, the EC method and a weighing lysimeter (Alfieri et al., 2012, Brutsaert, 1982, Burba, 2013, Noltz et al., 2013). Thus, techniques and approaches to estimate LE are of interest to overcome some shortcomings in measurement scaling and cost that are inherent in the EC method and weighing lysimeters (Albertson et al., 1995, Castellví, 2004, Drexler et al., 2004, Drexler et al., 2008, French et al., 2012, Haymann et al., 2019, Li and Wang, 2019, Paw U et al., 1995, Snyder et al., 1996, Suvočarev et al., 2019, Yang and Wang, 2014, Zhao et al., 2010).

To minimize costs, in moderately tall canopies LE has often been estimated indirectly using the simplified energy balance residual method (i.e., LE = Rn – G – H) because the instrumentation required to estimate H, G and Rn is more affordable. A major (potential) issue involved in the residual method to estimate LE half-hourly is that accurate measurements of all the energy terms involved in the surface energy balance (SEB) equation do not guarantee its closure. On a half-hourly basis, in general, even on extended homogeneous surfaces, the sum of turbulent fluxes is smaller than the available net surface energy (Foken, 2008, Foken et al., 2011, Twine et al., 2000, Wilson et al., 2002). Thus, often the residual method adds unexplained energy to LE. There is an ongoing scientific debate about the role of low frequency circulations in the lack of closure of the SEB equation (Cuxart et al., 2015; Eder et al., 2014, Foken, 2008, Huang et al., 2008, Kanda et al., 2004, Stoy et al., 2013, Steinfeld et al., 2007). While some studies have suggested that large circulations appear to be more efficient in transporting sensible heat than latent heat (Charuchittipan et al., 2014, Stoy et al., 2006, Stoy et al., 2013), other studies have shown that this role depends on the surface heterogeneity, type of terrain, and its uses (Brunsell et al., 2011; Cuxart et al., 2015). These issues may affect the uncertainty when the residual method to estimate LE is used. In fact, at some sites the residual method may be preferred to estimate H (i.e., H = Rn – G – LE) than LE (Castellví and Oliphant, 2017).

When the Monin – Obukhov Similarity Theory (MOST) is used, through the stability parameter, the friction velocity (u) and the sensible heat flux are required as input to estimate the latent heat flux. Traditionally, to avoid measurement of the wind field, the wind log-law is implemented to estimate u, H and LE (Castellví and Snyder, 2010; De Bruin et al., 1993, Hsieh and Katul, 1996, Suvočarev et al., 2019). When convection dominates the turbulence in the atmospheric surface boundary layer, MOST similarity relationships were redone to best fit this limit case (termed free convection limit, FCL, approaches) (Stull, 1988). Implementing the FCL formulation, surface eddy flux estimates of scalars become independent of the friction velocity. Consequently, FCL approaches become simpler and, surprisingly, there is evidence that they performed rather reliably up to near-neutral conditions (Albertson et al., 1995; Högström , 1988; Kohsiek, 1982, Monin and Yaglom, 1971, Wang and Brass, 2010). For field applications, minimization of input requirements has special interest when surface flux estimates are desired at multiple sites, such as in the framework of remote sensing and estimation of crop coefficients (Drexler et al., 2008, French et al., 2012, Zapata and Martı́nez-Cob, 2001, Zhao et al., 2010).

The framework of Surface Renewal (SR) theory (Danckwerts, 1951; Harriott, 1962; Higbie, 1935, Seo and Lee, 1988), combined with the analysis of Small Eddies (SRSE) (Aminzadeh et al., 2017, Castellví, 2018, Haghighi and Or, 2013, Haghighi and Or, 2015), has shown potential to open new perspectives in micrometeorology. For instance, an SRSE approach was proposed to estimate u (alternative to the wind log-law) and H requiring as input measurements of the mean wind speed and the high-frequency trace of the air (or virtual) temperature in the roughness and inertial sub-layers (Castellví, 2018; Castellví et al., 2020). In the following, the SRSE formulation will refer to applications requiring measurements taken in the inertial sub-layer as input and it will be used to estimate LE. To our knowledge, the SRSE approach to estimate fluxes of scalars other than temperature, has never been tested. Here, given the benefits of developing approaches requiring minimum inputs, an SRSE-FCL expression was derived for estimating H and LE. It was shown that the inputs required to determine H as HFCL are fast-response traces of air temperature and the zero-plane displacement. Similarly, for LE, LEFCL may be determined using fast-response traces of water vapor concentration, the zero-plane displacement, the mean temperature of the air and the available net surface energy as input. Therefore, HFCL and LEFCL do not share instrumentation. This separation minimizes the probability to have simultaneous gaps in H and LE. In addition, HFCL and LEFCL are estimated independently which allows testing closure of the surface energy balance for an integral quality check. Here, the performance of HFCL and LEFCL were tested for a growing cotton field, which involved surfaces with different roughness.

Section snippets

The SRSE method with measurements in the inertial sub-layer

SRSE is a semi-empirical method, fully described in Castellví (2018), to estimate the friction velocity and eddy fluxes. To estimate the surface flux of a scalar, SRSE considers that downward flows (i.e., descending macro-parcels of air following a coherent motion) generate a narrow, highly turbulent, shear layer containing multiple small-scale vortices (Zhu et al., 2007). SRSE assumes: (1) the population of small eddies (which in the following are termed fluid elements) generated in the volume

The field campaign

From 13 May to 30 September 2016, an experiment was carried out on a cotton field in Manila, AR, US (35° 53′ 14″, −90° 8′ 15″) (Suvočarev et al., 2019, Fong et al., 2020). The field was on a flat terrain (0.1% slope), the crop was sprinkler irrigated, and the fetch, in practice, may be considered unlimited regardless of the wind direction because the flux tower was deployed between two fields of the same cotton crop (63 × 104 and 45 × 104 m2). From the beginning of the campaign up to 22 June,

Results

For each dataset, Table 1 shows the regression characteristics and model error terms to compare H and LE determined using traces of scalars sampled at 10 Hz against the corresponding EC reference fluxes, and (H + LE) against (Rn-G). The results obtained for H and LE determined using the sampling frequency of 20 Hz differed from the results obtained at 10 Hz are shown in parentheses. Though not shown in Table 1, for each half-hour scalar trace the number of fluid elements resolved at 20 Hz

Conclusions

Combining the frameworks of transilient and Surface Renewal theories with the analysis of Small fluctuations in scalar traces, Eddies (the SRSE method), the Free Convection Limit (FCL) approach for estimating the sensible and latent heat fluxes was derived to avoid measurement of the wind speed. Along a full cotton growing season and taking as a reference the EC method operating at 20 Hz, it was found that the EC and FCL methods performed similarly when taking measurements in the inertial

CRediT authorship contribution statement

Francesc Castellví: Conceptualization, Methodology, Funding acquisition, Visualization, Writing - original draft. Kosana Suvočarev: Data curation, Methodology, Writing - review & editing. Michele L. Reba: Resources, Investigation, Funding acquisition, Writing - review & editing. Benjamin R.K. Runkle: Resources, Investigation, Funding acquisition, 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

This work was supported under project RTI2018-098693-B-C31 Ministerio de Ciencia, Economía y Universidades of Spain. Data collection and analysis was partially funded through the U.S. Geological Survey (USGS) under Cooperative Agreements G11AP20066 and G16AP00040 administered by the Arkansas Water Resources Center at the University of Arkansas; the United States Department of Agriculture (USDA), Natural Resources Conservation Service under Cooperative Agreement 68-7103-17-119, and the United

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      Two soil heat flux plates (HFP01, Hukseflux, Netherlands) were buried at 0.08 m depth in the row and in the inter-row plants below the tower, each accompanied with a soil thermocouple and volumetric water content probes (TCAV and CS630 Campbell Scientific, respectively) placed above the plate (0.05 m below the ground). SRSE is a semi-empirical method to estimate the friction velocity and surface eddy fluxes that may operate in the roughness and inertial sublayers (Castellví, 2018; Castellví et al., 2020a, 2020b). To estimate the sensible heat flux SRSE requires the mean wind speed, traces of temperature of the air (measured at a frequency of 10 Hz–20 Hz) and the zero-plane displacement as input.

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