# Early-Morning Flow Transition in a Valley in Low-Mountain Terrain Under Clear-Sky Conditions

## Abstract

We investigate the evolution of the early-morning boundary layer in a low-mountain valley in south-western Germany during COPS (convective and orographically induced precipitation study) in summer 2007. The term *low-mountain* refers to a mountainous region with a relief of gentle slopes and with an absolute altitude that remains under a specified height (usually 1,500 m a.s.l.). A subset of 23 fair weather days from the campaign was selected to study the transition of the boundary-layer flow in the early morning. The typical valley atmosphere in the morning hours was characterized by a stable temperature stratification and a pronounced valley wind system. During the reversal period—called the low wind period—of the valley wind system (duration of 1–2 h), the horizontal flow was very weak and the conditions for free convection were fulfilled close to the ground. Ground-based sodar observations of the vertical wind show enhanced values of upward motion, and the corresponding statistical properties differ from those observed under windless convective conditions over flat terrain. Large-eddy simulations of the boundary-layer transition in the valley were conducted, and statistical properties of the simulated flow agree with the observed quantities. Spatially coherent turbulence structures are present in the temporal as well as in the ensemble mean analysis. Thus, the complex orography induces coherent convective structures at predictable, specific locations during the early-morning low wind situations. These coherent updrafts, found in both the sodar observations and the simulation, lead to a flux counter to the gradient of the stably stratified valley atmosphere and reach up to the heights of the surrounding ridges. Furthermore, the energy balance in the surface layer during the low wind periods is closed. However, it becomes unclosed after the onset of the valley wind. The partition into the sensible and the latent heat fluxes indicates that missing flux components of sensible heat are the main reason for the unclosed energy balance in the considered situations. This result supports previously published investigations on the energy balance closure.

## Keywords

Coherent structures Convection in a valley Energy balance closure Large-eddy simulation## 1 Introduction

Turbulent fluxes of heat, moisture, and momentum in the atmospheric boundary layer are of key importance both for the evolution of the boundary layer itself and for the overlying free atmosphere. The accurate knowledge of the magnitude and the vertical profiles of these fluxes and their reliable parametrization are essential for both numerical weather prediction and climate simulations. Sophisticated micrometeorological instrumentation and analysis techniques have successfully been applied in order to determine fluxes over flat and homogeneous terrain.

However, the determination of these fluxes above complex terrain, i.e. mountainous and/or with heterogeneity in land use, remains a challenging task (Foken 2008; Mahrt 2010). The boundary layer in complex terrain is characterized by orographically (Defant 1949; Whiteman 1990, 2000; Zardi and Whiteman 2013) or thermally induced (Segal and Arritt 1992) wind systems. In a convective boundary layer over flat surfaces quasi-stationary turbulence structures evolve (Schmidt and Schumann 1989). Over heterogeneous surfaces (Walko et al. 1992; Dörnbrack and Schumann 1993) coherent structures with surface-scale dependent length scales develop, especially in the lower part of the boundary layer. These flow structures can potentially modify the turbulent fluxes from valleys, thus potentially modifying the evolution of the mountainous boundary layer as a whole. Weigel et al. (2007) and Rotach et al. (2008) investigated the exchange processes in an alpine valley and found strong dependencies of the turbulent fluxes on orography and stratification in the mountainous boundary layer. Mayer et al. (2008) investigated an observed anomaly in the chemical composition of air at a mountain station. This anomaly was traced back to fluxes through the stably stratified valley atmosphere during the reversal of the thermally driven wind system in the morning.

Over homogeneous terrain a strong influence of coherent turbulent structures, i.e. persistent quasi-stationary patterns of turbulent motion, on the turbulent fluxes was shown in several studies (Raasch and Harbusch 2001; Kanda et al. 2004; Inagaki et al. 2006). In particular, the interpretation of micrometeorological measurements in complex terrain requires the comprehensive knowledge of how turbulence is organized at the observational site and its surroundings. This leads to the guiding questions for this study: (i) How does the convective boundary layer in a typical low-mountain valley become organized in the early morning hours after sunrise? (ii) How does an along-valley flow in the morning change the convective structures? (iii) To what extent is the vertical transport in the valley affected? (iv) How are micrometeorological flux measurements at a specific location affected by complex terrain? To address these questions, large-eddy simulations (LES) were conducted, and compared to observations.

A micrometeorological dataset obtained during the field phase of the convective and orographically induced precipitation study (COPS) constitutes the basis of this study (see Eigenmann et al. 2009). The field campaign of summer 2007 in the low-mountain region of south-western Germany and eastern France, i.e. Black Forest and Vosges mountains, is well described in the literature (e.g. Wulfmeyer et al. 2011). The valley in which the observational site is located has a width of approximately 1,300 m and a depth of approximately 300 m, which are typical values for a low-mountain terrain. The objective of the campaign is to understand the influence of the orography of a low-mountain range on precipitation. Several surface flux measurement stations were installed throughout the respective region during the campaign (Eigenmann et al. 2011; Kalthoff et al. 2011). In addition, ground-based sodar^{1}/RASS^{2} instruments were installed at several of these stations. Our study uses data from one of these sites where a full energy balance station and a sodar/RASS operated simultaneously. The site Fußbach is located in the Kinzig valley, which is a typical low-mountain valley of the region with a pronounced valley wind system developing on fair weather days in summer.

In micrometeorological field experiments the energy balance is often not closed (e.g. Oncley et al. 2007; Foken et al. 2010). Although many uncertainties are connected with the determination of the components of the energy balance (Mahrt 2010), strong indications exist that the residual occurs due to transport by large-scale eddies or secondary circulations that are not captured by the eddy-covariance method (e.g. Mauder and Foken 2006; Foken 2008; Foken et al. 2010, 2011, Stoy et al. 2013). As these secondary circulations are mainly associated with the sensible heat flux (Foken et al. 2012b), the common approach of distributing the residual according to the Bowen ratio Twine et al. (2000) seems not to be appropriate. However, because the density effect of moisture cannot be excluded, a distribution of the residual according to the buoyancy flux ratio appears to be appropriate. The relative contributions of the sensible and latent heat fluxes to the buoyancy flux are described in Kaimal and Gaynor (1991). Also the COPS energy balance site Fußbach used herein shows an average residual of 21 % during the entire field campaign (see Eigenmann et al. 2011).

The remainder of this article is organized as follows. Sect. 2 describes the data and the methods applied, in particular the numerical model and its set-up. Sect. 3 presents the results and the discussion of them, while conclusions are given in Sect. 4.

## 2 Methods and Data

### 2.1 Observational Data

The observations used herein were obtained during the COPS experiment in the low-mountain terrain of the Kinzig valley. Turbulence data were measured at a height of 2 m above the valley surface and friction velocity \(u_{*}\), sensible heat \(Q_{H}\) and latent heat \(Q_{E}\) were calculated with the eddy-covariance method (EC) (Foken et al. 2012), using an averaging time of 30 min. Contributions to the fluxes with a time scale exceeding these 30 min cannot be captured. The geographical location of the site Fußbach is 48\(^\circ \)22\('\)7.8\(''\)N, 8\(^\circ \)1\('\)21.2\(''\)E, 178 m a.s.l. (the position is marked in Fig. 3) and local time is UTC+1 h. Details about the site and the measurement set-up can be found in Metzger et al. (2007) and Eigenmann et al. (2009, 2011). Close to the turbulence station, a sodar/RASS system measured vertical profiles of wind components and virtual temperature. Moreover, the remaining components of the energy balance, net radiation \(Q_{S}^{*}\), and soil heat flux \(Q_{G}\), were measured at the EC site. An overview of the data processing, quality control, and flux characteristics of the turbulent data as well as the calculation of the energy balance is given in Eigenmann et al. (2011). In this article the sign convention for the fluxes is used according to Stull (1988) modified by an opposite sign for the ground heat flux according to Garratt (1992), consequently with the opposite sign in the energy balance equation. See also Foken (2008).

The study of Eigenmann et al. (2009) identified 23 days during the three-month COPS campaign with free convective conditions (mean duration: 85 min, standard deviation: approximately 1 h) based on EC measurements in the early morning hours. Free convective conditions were identified by the stability parameter \(\zeta = z/L\) for \(\zeta <-1\), where \(z\) is the height above the ground and \(L\) is the Obukhov length. These periods were characterized by low horizontal wind speeds due to the reversal of the valley wind system from downvalley flow to upvalley flow. The mean time for the occurrence of free convection on these 23 days is 0815 UTC with a standard deviation of 1 h, corresponding to 3.5 h after sunrise. No moist convection or significant clouds had been observed during the times selected.

The vertical wind speed \(w\) derived from the sodar observations was analyzed for the identified low wind periods. Hereafter this period of low winds is referred to as \(p_{1}\) and the subsequent 2 h of upvalley flow is referred to as \(p_{2}\). Both periods have comparable durations that leave the resulting datasets with comparable cardinalities. In order to make the individual days comparable, each sodar sample of \(w\) was normalized with the Deardorff convective velocity \(w_{*}\) (Deardorff 1970), and \(z\) was normalized with the height of the boundary layer \(z_{i}\). Surface buoyancy fluxes for the calculation of \(w_{*}\) were derived from the EC measurements and values of \(z_{i}\) were determined by a secondary maximum in the reflectivity profiles of the sodar measurements as described in Eigenmann et al. (2009) and suggested by Beyrich (1997). After that, histograms of \(w/w_{*}\) were calculated for three characteristic heights of \(z/z_{i} = 0.25, 0.50 \) and \(0.75\).

### 2.2 Simulations

#### 2.2.1 Numerical Model

In addition to the horizontally homogeneous basic state, a more general ambient (environmental) state is denoted by the subscript \(_e\). The corresponding variables may vary in the horizontal directions and they have to satisfy Eqs. 1–3; see Prusa et al. (2008) for a discussion of ambient state and its benefits. The primed variables \(\mathbf {v}^\prime \) and \(\Theta ^\prime \) appearing in Eqs. 2–3 correspond to deviations from the environmental variables \(\mathbf {v}_e\) and \(\Theta _e\); (\(\mathbf {v}^\prime =\mathbf {v}-\mathbf {v}_e\) and \(\mathbf {\Theta }^\prime =\mathbf {\Theta }-\mathbf {\Theta }_e\)). The quantity \(\pi ^\prime \) in the linearized pressure gradient term in Eq. 2 denotes a density normalized pressure deviation.

The terms proportional to \(\alpha \) and \(\beta \) denote wave-absorbing devices used at the upper boundary of the computational domain, see Smolarkiewicz and Margolin (1997). The coefficients \(\alpha \) and \(\beta \) are functions of the coordinates and are used to define the region and the intensity of the applied damping. The source terms \(\mathbf {D}\) and \(\mathcal {H}\) not explicitly stated in Eqs. 2 and 3 symbolize the viscous dissipation of momentum and the diffusion of heat, respectively. Via both of these terms, the subgrid-scale model enters the equations of motion. \(\mathbf {F}\) symbolizes an additional forcing for specified simulations, see below. The formulation of the TKE production and dissipation term hidden in \(\mathcal {S}\) and the applied parameters follow the description of Sorbjan (1996).

*MPDATA*

^{3}stands for the non-oscillatory forward-in-time (NFT) advection transport scheme described in Smolarkiewicz and Margolin (1998). The elliptic equation for pressure is solved iteratively with a Krylov-sub space solver, see Thomas et al. (2003). Both elements are integral parts of the EULAG and are fundamental to the stability of the code and the reliability of the results.

#### 2.2.2 Simulation Strategy

Among the broad range of applications documented in the literature, EULAG has been successfully applied to atmospheric boundary-layer flows (see Smolarkiewicz et al. 2007; Piotrowski et al. 2009). For the present study, the set-up was chosen as follows.

The numerical simulations are conducted in a domain of (\(L_x\), \(L_y\), \(H\)) \(=\) (7680, 7680, 2430 m) with a regular grid size of \(\Delta x\) \(=\) \(\Delta y\) \(=\) \(\Delta z\) \(=\) 30 m. For a simulation of 2.5 h physical time, 30,000 timesteps with \(\Delta t\) \(=\) 0.3 s are necessary. The height \(h(x,y)\) of the lower boundary is taken from the advanced spaceborne thermal emission and reflection radiometer (ASTER) digital topographic dataset (NASA LP DAAC 2001) in a 30 m \(\times \) 30 m regular resolution. In all simulations shown here the computational domain is periodic in the horizontal directions. To enable this periodicity the topography was smoothly relaxed within a frame around the actual region of interest. Due to the complex orography and the low inversion layer height the width of the frame could be chosen to be 300 m.

For all simulations an anelastic basic state with a background stratification \(N\) \(=\) 0.01 s\(^{-1}\) is used according to Clark and Farley (1984), resulting in exponentially decreasing \(\rho _b\) and increasing \(\Theta _b\) profiles.

Set-up for the simulations in this study

Name | Terrain | Stratification below \(z_{i}\) | \(z_{i}\) (m) | Wind forcing | d\(x\) (m) |
---|---|---|---|---|---|

\(S1\) | Flat | Neutral | 800 | Off | 20 |

\(S2\) | Flat | – | 0 | Off | 20 |

\(R1\) | Complex | Neutral | 800 | Off | 30 |

\(R2\) | Complex | – | 0 | On (during p2) | 30 |

White noise with an amplitude of 0.001 m s\(^{-1}\) was added to the initial vertical wind field in order to initiate convective motions. For the ensemble runs analyzed in Sect. 3.2, eight independent realizations were simulated using the set-up \(R1\). For this purpose, the random generator was seeded differently at the initial time for each realization. Because the three wind components are zero before adding the noise, the random disturbance is 100 % of the absolute value of the wind vector. This ensures that the eight realizations are statistically independent. The numerical simulations were conducted for a dry atmosphere, and the surface kinematic sensible heat flux \(Q_H\) = 0.05 K m s\(^{-1}\) was specified in all runs. The homogeneous heating can be justified because flux differences between different types of land surfaces turned out to be negligible in the observed early-morning situations (see Eigenmann et al. 2011). The effect of orographic shading is not taken into account. Orographically-induced flows (valley winds, upslope flows, etc.) are expected to mainly dominate the properties of the CBL in the valley at this time of the day.

The along-valley winds are part of a mountain plain circulation between a mountain massif and an adjacent plane, in our case the Black Forest and the Upper Rhine Valley, respectively. Due to the small computational domain, the effect of this mesoscale circulation on the flow in the valley is modelled by an additional dynamical forcing \(\mathbf {F}\) \(=\) \((0,-v_{0}(z)\tau ^{-1},0)\) for the meridional wind component \(v\), where \(\tau \) \(=\) \(t_\mathrm{end}\) \(-\) \(t_\mathrm{beg}\) is the period when the forcing is applied. The reference profile for the horizontal wind speed \(v_0(z)\) was derived from the sodar observations, and in simulation \(R2\) the additional forcing \(\mathbf {F}\) is applied. The period from \(t\) \(=\) 0 to \(t_\mathrm{beg}\) represents the observed low wind period \(p_{1}\), and the period from \(t_\mathrm{beg}\) to the end of the simulation represents the up-valley wind period \(p_{2}\). In the remainder of the article two exemplary simulation times referred to as \(t_{1}\) for a specified time in \(p_{1}\) and \(t_{2}\) for a specified time in \(p_{2}\) are chosen in order to compare differences in the simulated periods \(p_{1}\) and \(p_{2}\).

## 3 Results and Discussion

### 3.1 Modification of the Energy Balance by the Valley Flow

Regarding Fig. 1a, b, the relative flux contributions missing in period \(p_{2}\) compared to period \(p_{1}\) have exactly the proportions of the buoyancy flux ratio. The buoyancy flux ratio distributes about 85 % of the residual to \(Q_{H}\) and 15 % to \(Q_{E}\) for a typical Bowen ratio of about 0.45 in the observed early-morning situations. As such, Fig. 1 supports the assumption that the residual can be mainly associated with the missing flux components of \(Q_H\) (Foken et al. 2012b). The missing flux components in period \(p_{2}\) are assumed to exist within buoyancy-driven secondary circulations not captured by the EC measurements (e.g. Foken 2008). The transfer of the missing energy into the secondary circulation mainly occurs at significant surface heterogeneities that can be found over complex terrain. Advection-dominated processes (also not captured by EC) probably lead to the transport of the missing energy to these heterogeneities. As the horizontal wind speed becomes low in period \(p_{1}\), all fluxes are observed by the EC station and the energy balance is closed. However, the along-valley wind in period \(p_{2}\) leads to missing advective flux components and thus to the observed residual in this period.

The finding discussed above also supports the choice of a constant heat-flux forcing for the transient simulation \(R2\) (see Sect. 2.2). The same relative forcing by \(Q_{H}\) is achieved for both periods \(p_{1}\) and \(p_{2}\) by adding (for simplification) 100 % of the residual to \(Q_{H}\). In this way, the forcing of period \(p_{1}\) can also be used for period \(p_{2}\). Moreover, no significant relative flux differences of \(Q_{E}\) exist in both periods (see Fig. 1b). Thus, for the questions addressed herein, it appears to be appropriate to concentrate on dry model runs.

### 3.2 Coherent Structures in the Valley Imposed by Surrounding Orography

To gain confidence in the simulations the well known pdfs of the vertical wind in a CBL are calculated for the simulated data of set-up \(S1\). Very good agreement with the published values is found (not shown). Moreover, the simulation results show the well-known spoke patterns of coherent convective motions known from numerous numerical studies (e.g. Schmidt and Schumann 1989). The data from the simulation of set-up \(S2\) are then used to create the pdfs for a CBL with a growing mixed layer, see Fig. 2 (situation closer to the observation period \(p_{1}\)). In this set-up, spoke patterns evolve in the simulated boundary layer that grow slightly in size as the inversion layer height grows in time. A conditional sampling is applied to obtain the pdfs of the coherent updraft areas. The *updraft areas* are defined as follows: the vertical wind component at a height of 200 m is temporally averaged after a spin-up time of 45 min to the end of the simulation (150 min). All locations on that layer where the average exceeds a value of 0.05 m s\(^{-1}\) define the *updraft areas* for the entire boundary layer.

The resulting pdfs resemble the properties of the histograms from the sodar data (see Fig. 2). The maximum and the skewness of the pdfs of the conditionally sampled updraft areas match well with those of the histograms of the observational data for all heights. Only the absolute numbers of the probability density do not fully match. A possible explanation for this is that the sodar instrument averages over a specific volume, so that the spread of the resulting pdfs is reduced. This effect becomes larger with height.

We interpret these findings as follows: it is well known that coherent convective motions evolve in a CBL, and which remain quasi-stationary in space and time (see e.g. Stull 1988). This means that the location where a possible sodar instrument is located will remain under an updraft or a downdraft area for a long time. As a consequence, it is very likely that a sodar measurement captures only the statistical properties of a part of the velocity spectrum. The fact that the result from Fig. 2 stems from a composite over 23 periods with similar overall conditions suggests the hypothesis that the sodar instrument was preferentially located at an updraft region.

For the sake of completeness the histograms and the simulated pdfs for \(z/z_{i} = 0.5\) and \(z/z_{i} = 0.75\) are shown in Fig. 2. They show a less clear deviation from the “LES all points” pdfs of the simulation. But the difference between the “LES updraft area” pdfs and the “LES all points” pdfs themselves become also very small at these heights. This restricts the application of the method described in this section to the lower part of the CBL.

### 3.3 Vertical Transport in the Early-Morning Valley Atmosphere

Based on the same micrometeorological dataset as in this study, Eigenmann et al. (2009) discussed spectral analysis of the EC measurements. These analyses showed an increase of spectral power within turbulent scales of a few minutes during the low wind-speed period \(p_{1}\) in the morning (see Eigenmann et al. 2009). These time scales could be related to the presence of large coherent vertical structures (e.g. plumes or updrafts) with a spatial extent in the order of the boundary-layer height, which are known to be responsible for the majority of the transport within the CBL (see e.g. Stull 1988; Chandra et al. 2010). The occurrence of these turbulent scales in the ground-based EC data indicates that during the period \(p_{1}\), air very close to the ground is able to be transported upwards very efficiently by non-local large-eddy transport processes. The free convective conditions detected simultaneously by the EC measurements also support these findings. By the onset of the up-valley wind the spectral analysis of Eigenmann et al. (2009) does not show these turbulent scales any longer, indicating that the turbulent transport of near-ground air became less effective. The effective vertical transport in period \(p_{1}\) is important because air masses close to the valley bottom are humid, have a characteristic chemical composition, and may possibly be polluted. The effect of the free convective release of surface-layer air masses from the valley bottom on ozone measurements at a mountain-top station was reported by Mayer et al. (2008).

The profiles for the buoyancy term and the shear term of the TKE budget are plotted in Fig. 7 in the same manner as the profiles described above. During the transition from \(t_1\) to \(t_2\), the profile for buoyancy production of TKE remains positive below 0.7\(z_{i}\) and negative above. The major change here is that the maximum of the buoyant production of TKE is shifted upwards to 0.15\(z_{i}\). This shift is accompanied by an increased shear production of TKE below 0.2\(z_{i}\). The maximum in shear production of TKE at 0.7\(z_{i}\) and at time \(t_2\) derives from the imposed along-valley wind described in Sect. 2.2.2.

## 4 Conclusions

During the three months of the COPS campaign the surface energy balance at one site in the Kinzig valley was rarely closed, as is common for many energy balance measurements. However, the presented analysis gave the surprising result that the energy balance was closed on average for the low wind period in the morning hours on fair weather days. A closed energy balance indicates that all energy containing motions were captured by the instrumentation and that the assumptions for data processing, i.e. stationarity and homogeneity of the flow, were satisfied. It has to be assumed that due to the vanishing horizontal wind speed all flux components were captured by the EC system at the observational site. After the onset of the valley wind, advective flux components were missing and the desired closure was no longer met. The residual of the energy balance increased to values typical for the full dataset of this site. Our analysis indicates that the residual is mainly associated with the missing flux components of the sensible heat flux.

Large-eddy simulations of the atmosphere in the Kinzig valley were carried out. It was found that the convection in the valley becomes organized due to the surrounding ridges during the low-wind period, resulting in quasi-stationary patterns at preferred locations. This result leads to the conclusion that the sodar/RASS observed only a part of the vertical velocity spectrum. This has implications for future observational set-ups in complex terrain and interpretation of their data.

## Footnotes

## Notes

### Acknowledgments

This study was funded by the Deutsche Forschungsgesellschaft (DFG) within the special priority program SPP1167 (WI 1685/9-1, WI 1685/10-1, FO 226/19-1, FO 226/23-1). The numerical simulations made for this study were carried out at the high performance computing centre of the Deutsches Klima Rechenzentrum (DKRZ) in Hamburg, Germany. We thank Prof. Dr. Werner Eugster and two other anonymous reviewers for their helpful comments.

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