Examining relationships between entrainment-driven scalar dissimilarity and surface energy balance underclosure in a semiarid valley

Highlights

• Surface energy budget underclosure coupled with scalar dissimilarity.

• Budget underclosure in a dry valley comparable to that over flat terrain.

• Spectral analysis used to extract low-frequency, large-scale convection effects.

• Quadrant analysis clarified impacts of counter-gradient motions on dissimilarity.

• Hectometre-scale horizontal advection likely the main driver of budget underclosure.

Abstract

A surface energy budget underclosure, equivalent to an undersampling of sensible and latent heat fluxes at the surface, is commonly observed in the daytime convective boundary layer over land. The two mechanisms currently held responsible for such underclosure are, on one hand, entrainment-induced reduction of heat fluxes due to low-frequency circulations spanning the depth of the convective boundary layer, and on the other hand, horizontal advection effects induced by surface horizontal heterogeneity. Given the involvement of both heat fluxes in the budget equation, it is expected that the turbulent perturbations of variables involved in these fluxes (potential temperature ${\theta }^{\prime }$ and specific humidity $q^{\prime }$) contain the signature of both mechanisms. Here, we assess to what extent non-local entrainment effects contribute to the budget underclosure in complex terrain using a quadrant analysis and multiresolution flux decomposition approach.

We use data collected in the semi-arid Owens Valley, CA, USA, during the Terrain-Induced Rotor Experiment (T-REX) campaign. The budget components are sampled near the surface of the valley floor and the adjacent slope, with turbulence flux measurements, pyranometers, pyrgeometers, as well as ground heat flux measurements. We found that the budget underclosure was within the range of underclosures reported in past studies, with a systematically poorer closure over the valley slope. Although quadrant analysis revealed a dominance of scalar-similar events, associated with convective boundary layer overturning, a high degree of disagreement was found between the scalar-dissimilar quadrants which represent the counter-gradient motions. Specifically, those turbulent motions associated with entrainment of free tropospheric air to the surface, were found to be of minor importance in degrading scalar similarity. Instead, we postulate that local horizontal advection and hectometre-scale land-use heterogeneity in the vicinity of both the valley floor and slope sites, are the major factors in controlling the relationship between the budget underclosure and scalar similarity.

Introduction

Governed by the first law of thermodynamics, in the atmospheric surface layer (ASL) over horizontally homogeneous and flat (HHF) terrain the provided energy input (composed of the net radiation $R_{net}$ and ground heat flux $G_0$) should balance the energy output (composed of the sensible $H$ and latent $LE$ heat fluxes). Assuming negligible contributions from terms associated with various sources and sinks, storage terms and advection terms (Cuxart et al., 2016), the energy balance ratio ($EBR$) over HHF terrain should be unity:

$$EBR=\frac{H+LE}{R_{net}-G_0}$$

Many applications assume a fully closed surface energy balance (SEB), i.e. $EBR=1$. For instance, land-surface models simulate a fully closed SEB while the validation and calibration of these models heavily depends on the quality of measured SEB components (e.g. Williams, Richardson, Reichstein, Stoy, Peylin, Verbeeck, Carvalhais, Jung, Hollinger, Kattge, et al., 2009, Foken, Aubinet, Finnigan, Leclerc, Mauder, Paw U, 2011). To estimate evapotranspiration at the surface using satellite remote sensing, the Surface Energy Balance Algorithm for Land framework (Long and Singh, 2010) invokes SEB closure by attributing the SEB residual to the latent heat flux $LE$. However, as indicated in many experiments and review studies (e.g. Foken, 2008, Leuning, Van Gorsel, Massman, Isaac, 2012), SEB closure is seldom achieved in the daytime ASL. Specifically for the FLUXNET network, Baldocchi et al. (2001) and Wilson et al. (2002) show that the average $EBR$ ranges between 0.7 and 0.9. Studies have revealed a number of factors that can explain such underclosure (Foken, 2008, Leuning, Van Gorsel, Massman, Isaac, 2012). Instrumental errors and sensor deficiencies have been dismissed as crucial factors (Foken et al., 2011). Instead, studies agree that the traditional eddy covariance (EC) methodology (Swinbank, 1951), with its 30-min temporal averaging, may miss a substantial portion of the heat fluxes $H$ and $LE$. These flux portions are carried by low-frequency motions, commonly referred to as turbulent organized structures (hereafter TOS).

TOS may be classified into two distinct forms of convection organization in the CBL: cellular convection characterized by low wind speed situations, and horizontal convective rolls characterized by high wind speed situations (Atkinson, Zhang, 1996, Babić, De Wekker, 2019, hereafter B19). In low wind speed situations, the low-frequency component of ASL fluxes will be biased since either a quasi-stationary updraft or downdraft will preferentially be sampled (Sakai et al., 2001). During high-wind speed conditions, this is not the case and several studies have reported better or even complete SEB closure (Wilson, Goldstein, Falge, Aubinet, Baldocchi, Berbigier, Bernhofer, Ceulemans, Dolman, Field, et al., 2002, Kanda, Inagaki, Letzel, Raasch, Watanabe, 2004, Franssen, Stöckli, Lehner, Rotenberg, Seneviratne, 2010, Anderson, Wang, 2014). Improved SEB closure in these studies has been ascribed to pronounced mechanical mixing, quantified traditionally with the friction velocity $u_{*},$ and a larger number of eddies sampled within 30 min. TOS have also been recognized by De Bruin et al. (2005), Lamaud and Irvine (2006) and Gao, Liu, Katul, Foken, 2017, Gao, Liu, Li, Katul, Blanken, 2018 to affect SEB via entrainment of warmer and drier free tropospheric air. This is quantified with the temperature-humidity correlation coefficient:

$$r_{\theta q}=\overline{{\theta }^{\prime }{q}^{\prime }}/\left({\sigma }_{\theta }{\sigma }_q\right),$$

which exhibits negative values in the entrainment zone and positive values in the daytime ASL (Detto et al., 2008). Scalar dissimilarity, expressed as a departure of $r_{\theta q}$ from unity, invalidates approaches to close SEB with traditional Bowen ratio-based methods (Twine, Kustas, Norman, Cook, Houser, Meyers, Prueger, Starks, Wesely, 2000, Asanuma, Tamagawa, Ishikawa, Ma, Hayashi, Qi, Wang, 2007), and violates Monin-Obukhov similarity theory which assumes perfect scalar similarity (Andreas, Hill, Gosz, Moore, Otto, Sarma, 1998, Van de Boer, Moene, Graf, Schüttemeyer, Simmer, 2014). However, a detailed quantification of the relationship between $r_{\theta q}$ and $EBR$ does not exist. Since TOS are CBL-spanning eddies, they are capable of transporting scalar-dissimilar air from the entrainment zone down into the ASL. However, the relative contribution of the two forms of TOS in this non-local violation of near-surface scalar similarity, and ultimately, the SEB underclosure, is unknown.

With the increasing effects of climate change worldwide through aridification, processes such as desertification become increasingly pronounced and widespread (D’Odorico et al., 2013). One might argue that the feedbacks between desertification and other global change drivers (Maestre et al., 2016) are even more emphasized in mountainous regions. In mountainous regions, also affected by elevation dependent warming (Gobiet, Kotlarski, Beniston, Heinrich, Rajczak, Stoffel, 2014, Pepin, Bradley, Diaz, Baraër, Caceres, Forsythe, Fowler, Greenwood, Hashmi, Liu, et al., 2015), the climate change impacts on land-atmosphere might be even more pronounced. As a result, for reliable future climate projections over mountains, proper validation and calibration of land-surface models with measured heat fluxes is paramount (Williams et al., 2009). Because half of the FLUXNET stations are sited in complex terrain (Rotach et al., 2014), the need to better our understanding of the SEB underclosure in such environments is obvious. Examining SEB underclosure in complex terrain requires consideration of additional factors compared to HHF terrain. Over sloping terrain, the orientation (gravity-parallel versus slope-normal) of the radiation measuring system affects $R_{net}$ (Matzinger, Andretta, Gorsel, Vogt, Ohmura, Rotach, 2003, Hiller, Zeeman, Eugster, 2008, Serrano-Ortiz, Sánchez-Cañete, Olmo, Metzger, Pérez-Priego, Carrara, Alados-Arboledas, Kowalski, 2016, Georg, Albin, Georg, Katharina, Enrico, Peng, 2016). The choice of the optimal post-processing treatment of EC-derived heat fluxes is essential (Večenaj, De Wekker, 2015, Stiperski, Rotach, 2016), particularly concerning coordinate rotation. Studies conducted over hilly terrain (Serrano-Ortiz, Sánchez-Cañete, Olmo, Metzger, Pérez-Priego, Carrara, Alados-Arboledas, Kowalski, 2016, McGloin, Šigut, Havránková, Dušek, Pavelka, Sedlák, 2018) and in mountain valleys (Hammerle, Haslwanter, Schmitt, Bahn, Tappeiner, Cernusca, Wohlfahrt, 2007, Hiller, Zeeman, Eugster, 2008, Rotach, Andretta, Calanca, Weigel, Weiss, 2008, Stiperski, Rotach, 2016, Nadeau, Oldroyd, Pardyjak, Sommer, Hoch, Parlange, 2018), have concluded that the observed SEB underclosure is typically worse than the average underclosure from FLUXNET.

The goals of the present study are (1) to establish the degree to which SEB departs from closure at the valley floor and slope given a prevalent along-valley flow, (2) to determine the contribution of all possible combinations of ${\theta }^{\prime }$ and $q^{\prime }$ to scalar similarity (expressed via $r_{\theta q}$) using quadrant analysis, and (3) to quantify the actual extent to which TOS-induced entrainment effects impact scalar similarity and hence SEB. To address these goals, we use data collected in the semi-arid Owens Valley (CA, USA). This particular valley is ideal for our investigations for several reasons. As pointed out by Mahrt (1991) and Lamaud and Irvine (2006), an arid environment, characterized by low rates of evapotranspiration and a Bowen ratio ($Bo=H/LE$) exceeding unity, is subject to pronounced entrainment impacts on scalar similarity. We expect this feature to facilitate the quantification of TOS effects on $EBR$. Furthermore, valley flows experience significant channeling by the neighbouring sidewalls (Zhong et al., 2008), resulting in bimodality of the along-valley flow which minimizes the degrees of freedom concerning the upwind fetch conditions. This is essential for reducing uncertainties when investigating the SEB underclosure in complex terrain.