1. Introduction
The structure of turbulence over flat, homogeneous terrain and under various atmospheric boundary layer (ABL) conditions has been investigated extensively (e.g., Wyngaard and Cote 1971; Kaimal et al. 1972, 1976; Oncley et al. 1996; Albertson et al. 1997; Piper and Lundquist 2004). These measurements and analyses have led to similarity theories that describe the flow over flat, homogeneous terrain very well. Although the need for the adaptation of the existing theory or the development of a new theoretical framework applicable to complex terrain has been recognized, the structure of turbulence in complex terrain remains relatively unexplored. Among a few papers devoted to this subject are those of Rotach et al. (2004), Weigel and Rotach (2004), and Rotach and Zardi (2007). Rotach et al. (2004) point out that, because turbulence parameterization schemes in atmospheric numerical models are based on measurements conducted over flat and horizontally homogeneous terrain, numerical models may have problems when dealing with complex terrain. Weigel and Rotach (2004) indicate that the turbulence structure is greatly influenced by the configuration of the underlying terrain. Rotach and Zardi (2007) argue that an extension and/or modification of the classical scaling for turbulence variables is required for which measurements in complex terrain are needed.
A correct parameterization of boundary layer turbulence is important for a variety of applications, such as air pollution dispersion and wind energy. In these applications, turbulence parameters are used as an input to atmospheric dispersion models and wind energy efficiency. Turbulent kinetic energy (TKE) is one of those parameters that describe the turbulence intensity in the ABL. In high-resolution numerical modeling, turbulent mixing is often parameterized using TKE. To advance the development of turbulence parameterization schemes, it is therefore important to investigate and document the temporal evolution and spatial structure of TKE in complex terrain.
The overall evolution of TKE depends on the TKE production and destruction processes described by various terms in Eq. (3). Calculating these terms is nontrivial. For example, extremely high data sampling frequency is required for direct calculation of ε (e.g., Piper and Lundquist 2004). Nevertheless, there are some alternative methods for the evaluation of ε that are not as demanding, one of which will be described later in the text. In turbulence parameterizations used in atmospheric numerical models, ε is typically parameterized using TKE (e.g., Mellor and Yamada 1974). By quantifying the terms in the TKE budget Eq. (3) that determine the magnitude of TKE, turbulence parameterization schemes could therefore be evaluated. Moreover, ε provides insight into the local turbulence strength. This finds a variety of applications such as turbulence nowcasting at airports related to the presence of aircraft wake vortices (e.g., Frech 2007).
The objectives of this paper are to investigate the spatial and temporal variability of TKE, to investigate the applicability of a one-dimensional model of the TKE budget described by Eq. (3) during a mountain-wave event over complex terrain, and to obtain a dataset that can be used in the evaluation of turbulence parameterization schemes. The event took place during the first intensive observing period (IOP 1) of T-REX. This event was well documented by a scanning aerosol backscatter lidar (De Wekker and Mayor 2009) and a dense network of weather stations (Grubišić and Xiao 2006). In section 2, we briefly describe the T-REX field campaign and the data used to study the IOP 1 mountain-wave event described in section 3. This is followed by a detailed investigation of turbulence characteristics in section 4 and spatial and temporal characteristics of the TKE budget during this event in section 5. Section 6 summarizes the conclusions of this study.
2. Data
This study uses data collected during T-REX, which took place in Owens Valley, California, in March and April of 2006 in an effort to explore the structure and evolution of atmospheric rotors (Grubišić et al. 2008). Owens Valley lies east of the southern Sierra Nevada, which is the tallest, steepest, quasi-two-dimensional topographic barrier in the contiguous United States. Mountain waves and rotors are known to reach particularly striking amplitude and strength there. Climatological studies have shown that in the Sierra Nevada the months of March and April have the highest frequency of mountain-wave events (Grubišić and Billings 2007). Ground-based and airborne in situ and remote sensing measurements were conducted in Owens Valley during the 2-month period [for details, see Grubišić et al. (2008)].
In this paper, we primarily use data from the T-REX network of 16 automatic weather stations (TAWS) installed across Owens Valley by the Desert Research Institute (Grubišić and Xiao 2006), from three 30-m towers from the National Center for Atmospheric Research (NCAR) Integrated Surface Flux Facility (ISFF), and from the scanning Raman-Shifted Eye-Safe Aerosol Lidar (REAL; De Wekker and Mayor 2009). The location of the TAWS, the ISFF towers, and the REAL are shown in Fig. 1. The location and height of the three ISFF towers and REAL are listed in Table 1. The western tower (WT) was located on the western side of the valley, on an alluvial fan in the lee of the Sierra Nevada. The central tower (CT) and the southern tower (ST) were located along the valley’s central axis extending from north-northwest to south-southeast. The WT and CT were aligned across the valley. Between these two towers, REAL was positioned on the western slope, providing an undisrupted view in all directions within its range.
Map of the central portion of Owens Valley showing the locations of the TAWS network (black squares), ISFF towers (black triangles), and REAL (black circle). See text for details.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
Map of the central portion of Owens Valley showing the locations of the TAWS network (black squares), ISFF towers (black triangles), and REAL (black circle). See text for details.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
Map of the central portion of Owens Valley showing the locations of the TAWS network (black squares), ISFF towers (black triangles), and REAL (black circle). See text for details.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
NCAR ISFF towers and REAL locations in Owens Valley during T-REX.
Each ISFF tower was instrumented with Campbell Scientific, Inc., model CSAT3 three-dimensional ultrasonic anemometers collecting data with a sampling rate of 60 Hz at heights of 5, 10, 15, 20, 25, and 30 m. Consecutive blocks of 6 data points were averaged to create a 10-Hz database. This averaging reduces the effects of aliasing in the calculation of the turbulence spectra (section 4).
Besides anemometers, pressure sensors were installed at a height of 1 m and temperature/relative humidity sensors were installed at heights of 5, 15, and 30 m. There were some additional instruments on the towers such as radiometers, but the data from these instruments are not used in this study. A detailed description of the ISFF towers in T-REX can be found in Grubišić et al. (2008) and online (http://www.eol.ucar.edu).
3. Mountain-wave event
During T-REX, 15 IOPs and 5 enhanced observing periods (EOPs) were performed (Grubišić et al. 2008). Our period of interest is IOP 1, which took place from 0000 UTC 2 March to 1500 UTC 3 March 2006 (local standard time is UTC − 8 h). IOP 1 was characterized by significant mountain-wave activity with strong surface winds. Satellite images indicate the presence of trapped lee waves over the study area (not shown). Before the onset of the strong surface winds, a convective boundary layer (CBL) developed in the valley (De Wekker and Mayor 2009) with thermally driven upvalley and upslope flows (Fig. 2a). A transition from a quiescent valley atmosphere to a valley atmosphere affected by mountain-wave activity occurred during midafternoon between 2300 and 0000 UTC (Fig. 2b). While southeasterly flow prevailed in the valley center the flow on the western slope became more irregular with downslope winds replacing the upslope winds and colliding with the upvalley flow (Fig. 2c). Southeasterly winds up to 15 m s−1 in a layer between 400 and 1500 m in the valley center and a sudden transition to northwesterly winds were also observed by a network of radar wind profilers in Owens Valley (not shown).
The TAWS-network 10-m winds in the central portion of Owens Valley at (a) 2238 UTC 2 Mar, (b) 2321 UTC 2 Mar, and (c) 0039 UTC 3 Mar. A reference wind speed vector (m s−1) is located at the bottom-right corner of (c), and the TAWS network, ISFF towers, and REAL are denoted as in Fig. 1.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
The TAWS-network 10-m winds in the central portion of Owens Valley at (a) 2238 UTC 2 Mar, (b) 2321 UTC 2 Mar, and (c) 0039 UTC 3 Mar. A reference wind speed vector (m s−1) is located at the bottom-right corner of (c), and the TAWS network, ISFF towers, and REAL are denoted as in Fig. 1.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
The TAWS-network 10-m winds in the central portion of Owens Valley at (a) 2238 UTC 2 Mar, (b) 2321 UTC 2 Mar, and (c) 0039 UTC 3 Mar. A reference wind speed vector (m s−1) is located at the bottom-right corner of (c), and the TAWS network, ISFF towers, and REAL are denoted as in Fig. 1.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
The transition from a quiescent period with a developing CBL to a disturbed ABL was accompanied by large spatial inhomogeneities in the aerosol backscatter detected by the REAL. Downslope-directed flows to the west of the REAL carried clean air with low backscatter intensity to central regions of the valley, where it collided with aerosol-laden air transported by the channeled upvalley flows. The resulting aerosol structures suggest highly turbulent conditions around the location of the REAL (Fig. 3; see also Fig. 6d in De Wekker and Mayor 2009). These turbulent conditions are confirmed by the raw 10-m data of east (ux) and north (uy) wind speed components from the three ISFF towers, which show large fluctuations around the 5-min means (Fig. 4) and will be further explored in section 4b. Although at the CT and ST a mostly steady southwesterly (upvalley) flow is observed, the wind at the WT appears more irregular with rapidly changing wind direction from upslope to downslope flows around 2300 UTC. The change in wind direction at the WT is also apparent from the aerosol backscatter data in Fig. 3. A detailed analysis of the turbulence characteristics using data in Fig. 4 is presented in section 4.
Aerosol backscatter ratio in a vertical cross section across Owens Valley obtained by REAL at 0015 UTC 3 Mar 2006 during T-REX IOP 1 [adapted from De Wekker and Mayor (2009)]. Dashed range circles are shown every 2 km, and the location of REAL is in the center. The solid arrow indicates advection of relatively clear air from the west.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
Aerosol backscatter ratio in a vertical cross section across Owens Valley obtained by REAL at 0015 UTC 3 Mar 2006 during T-REX IOP 1 [adapted from De Wekker and Mayor (2009)]. Dashed range circles are shown every 2 km, and the location of REAL is in the center. The solid arrow indicates advection of relatively clear air from the west.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
Aerosol backscatter ratio in a vertical cross section across Owens Valley obtained by REAL at 0015 UTC 3 Mar 2006 during T-REX IOP 1 [adapted from De Wekker and Mayor (2009)]. Dashed range circles are shown every 2 km, and the location of REAL is in the center. The solid arrow indicates advection of relatively clear air from the west.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
The 10-Hz (left) east (ux) and (right) north (uy) wind speed components at 10 m for the selected 6-h interval (black curves) between 2100 UTC 2 Mar and 0300 UTC 3 Mar for the (a),(b) WT; (c),(d) CT; and (e),(f) ST. The gray curve is the 5-min moving average. Vertical dotted lines denote the 1-h period selected for detailed spectral analysis.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
The 10-Hz (left) east (ux) and (right) north (uy) wind speed components at 10 m for the selected 6-h interval (black curves) between 2100 UTC 2 Mar and 0300 UTC 3 Mar for the (a),(b) WT; (c),(d) CT; and (e),(f) ST. The gray curve is the 5-min moving average. Vertical dotted lines denote the 1-h period selected for detailed spectral analysis.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
The 10-Hz (left) east (ux) and (right) north (uy) wind speed components at 10 m for the selected 6-h interval (black curves) between 2100 UTC 2 Mar and 0300 UTC 3 Mar for the (a),(b) WT; (c),(d) CT; and (e),(f) ST. The gray curve is the 5-min moving average. Vertical dotted lines denote the 1-h period selected for detailed spectral analysis.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
The turbulence structure near the surface during and after transition periods from a convective to a stable boundary layer is poorly known and is potentially important for the modification of mountain-wave activity and the generation of rotors and subrotors on the lee side of mountains. To investigate the spatial and temporal characteristics of TKE and the terms in the TKE budget equation [Eq. (3)] surrounding the event, we investigate in detail a 6-h period from 2100 UTC 2 March to 0300 UTC 3 March. At the beginning of this period, approximately 29 min of data are missing at the WT and approximately 14 min of data are missing at the ST at all six levels. At the CT the time series are complete, but anemometers at 15 and 30 m did not operate properly, and data from these two levels could not be used. Turbulence characteristics during the transition period and the mountain-wave event will be discussed in detail in the next sections.
4. Estimation of turbulence from ISSF tower data
a. Determination of the averaging time
For the analysis of near-surface turbulence, it is necessary to separate turbulence from the mean flow. This is a nontrivial task, especially in complex terrain and for a flow situation such as presented here. A separation between the turbulent scales and synoptic scales is typically defined by the presence of a spectral energy gap at the mesoscale (e.g., Metzger and Holmes 2008; Vickers and Mahrt 2003). This gap is not always obvious, however. In our case, spectra of the 6-h streamwise component u at all three towers and all levels do not show the gap (not shown here), which is not surprising because this is a single realization over complex terrain during a mountain-wave event. Therefore, we have to use another method that is more suitable for determination of the turbulent scales. Our task is to find a proper averaging interval for our dataset, which will be used for the definition of turbulent perturbations that are necessary for estimation of turbulent properties.
(a) A log–linear representation of the mean power spectrum of the u component on all three towers for the 6-h period of interest (between 2100 and 0300 UTC). The solid line is for WT, the dashed line is for CT, and the dotted line is for ST. The vertical solid line denotes 15-min period. Ogives of kinematic heat flux for 1-h periods between 2100 and 0300 UTC on (b) WT, (c) CT, and (d) ST. Black solid, dashed, and dotted lines are for periods 2100–2200 UTC, 2200–2300 UTC, and 2300–0000 UTC, respectively, and gray solid, dashed, and dotted lines are for periods 0000–0100 UTC, 0100–0200 UTC, and 0200–0300 UTC, respectively. The vertical black solid line denotes 15-min period. Heights of levels are indicated on the right y axis of (b)–(d).
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
(a) A log–linear representation of the mean power spectrum of the u component on all three towers for the 6-h period of interest (between 2100 and 0300 UTC). The solid line is for WT, the dashed line is for CT, and the dotted line is for ST. The vertical solid line denotes 15-min period. Ogives of kinematic heat flux for 1-h periods between 2100 and 0300 UTC on (b) WT, (c) CT, and (d) ST. Black solid, dashed, and dotted lines are for periods 2100–2200 UTC, 2200–2300 UTC, and 2300–0000 UTC, respectively, and gray solid, dashed, and dotted lines are for periods 0000–0100 UTC, 0100–0200 UTC, and 0200–0300 UTC, respectively. The vertical black solid line denotes 15-min period. Heights of levels are indicated on the right y axis of (b)–(d).
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
(a) A log–linear representation of the mean power spectrum of the u component on all three towers for the 6-h period of interest (between 2100 and 0300 UTC). The solid line is for WT, the dashed line is for CT, and the dotted line is for ST. The vertical solid line denotes 15-min period. Ogives of kinematic heat flux for 1-h periods between 2100 and 0300 UTC on (b) WT, (c) CT, and (d) ST. Black solid, dashed, and dotted lines are for periods 2100–2200 UTC, 2200–2300 UTC, and 2300–0000 UTC, respectively, and gray solid, dashed, and dotted lines are for periods 0000–0100 UTC, 0100–0200 UTC, and 0200–0300 UTC, respectively. The vertical black solid line denotes 15-min period. Heights of levels are indicated on the right y axis of (b)–(d).
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
To get detailed insight into the temporal variability of TKE within the 6-h period, we create 15-min intervals shifted by 1 min. A maximum of 346 intervals is available for each sonic anemometer. For each of these intervals, the coordinate system is rotated into the mean wind direction. Turbulent perturbations of the u, υ, and w velocity components are calculated as the residuals between the instantaneous velocity component and its mean value during each 15-min interval.
b. Nature of turbulence during IOP 1
Time series of bulk Richardson number RB in the layer between 5 and 30 m (between 5 and 25 m at the WT) from 1200 UTC 2 Mar to 1200 UTC 3 Mar 2006 at the (a) WT, (b) CT, and (c) ST. Vertical dashed lines denote the 6-h period of interest, and the 1-h period selected for detailed spectral analysis is indicated by vertical dotted lines.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
Time series of bulk Richardson number RB in the layer between 5 and 30 m (between 5 and 25 m at the WT) from 1200 UTC 2 Mar to 1200 UTC 3 Mar 2006 at the (a) WT, (b) CT, and (c) ST. Vertical dashed lines denote the 6-h period of interest, and the 1-h period selected for detailed spectral analysis is indicated by vertical dotted lines.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
Time series of bulk Richardson number RB in the layer between 5 and 30 m (between 5 and 25 m at the WT) from 1200 UTC 2 Mar to 1200 UTC 3 Mar 2006 at the (a) WT, (b) CT, and (c) ST. Vertical dashed lines denote the 6-h period of interest, and the 1-h period selected for detailed spectral analysis is indicated by vertical dotted lines.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
The terms in Eq. (3) can be directly calculated with high-frequency measurements from the ISFF towers. Terms II, IV, and V contain vertical derivatives that are approximated using the measured values at two consecutive levels. The center of these levels, or midlevel, is the location at which all turbulent quantities calculated in the next sections will be specified. We start our investigation of the TKE budget with the calculation of the eddy dissipation rate ε. Estimation of this term relies on spectral analysis.
c. Evaluation of eddy dissipation rate and spectral analysis
We will now apply a basic spectral analysis to the 10-Hz wind speed data at all three towers. For this purpose a 1-h interval is chosen in which the time series of horizontal wind speed components at the WT (Figs. 4a,b) are most stationary (between 2221 and 2321 UTC 2 March). It is shown in Table 2 that the TH criterion is satisfied for all three towers in this interval. During this particular hour, a transition from unstable to stable conditions occurs at the WT while strong shear accompanied by weak stratification prevails at the CT and ST (Fig. 6). After rotating the coordinate system into the mean wind for each tower, the streamwise u and transverse υ velocity components are defined, and their corresponding spectra Su and Sυ as well as vertical Sw are calculated as a function of frequency. Figure 7 shows the Sυ/Su and Sw/Su ratios over the chosen 1-h interval for all three towers at heights of 10 (Fig. 7a) and 25 (Fig. 7b) m. The Sυ/Su ratios at the CT and ST approach
Taylor’s-hypothesis criterion σM/M for the 1-h interval (2221–2321 UTC 2 Mar) at 10-m height. The terms σM and M are the standard deviation and mean horizontal wind speed, respectively.
Ratios between transverse (υ) and streamwise (u) velocity spectra (black markers) and between vertical (w) and streamwise (u) spectra (gray markers) at the height of (a) 10 and (b) 25 m showing the approach to the 
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
Ratios between transverse (υ) and streamwise (u) velocity spectra (black markers) and between vertical (w) and streamwise (u) spectra (gray markers) at the height of (a) 10 and (b) 25 m showing the approach to the
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
Ratios between transverse (υ) and streamwise (u) velocity spectra (black markers) and between vertical (w) and streamwise (u) spectra (gray markers) at the height of (a) 10 and (b) 25 m showing the approach to the
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
Power spectra of streamwise [Su(f); thin solid line], transverse [Sυ(f); thin dashed line], and vertical [Sw(f); thin dotted line] velocity fluctuations for the 1-h segment of IOP 1 (2221–2321 UTC 2 Mar). Thick dashed lines denote 
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
Power spectra of streamwise [Su(f); thin solid line], transverse [Sυ(f); thin dashed line], and vertical [Sw(f); thin dotted line] velocity fluctuations for the 1-h segment of IOP 1 (2221–2321 UTC 2 Mar). Thick dashed lines denote
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
Power spectra of streamwise [Su(f); thin solid line], transverse [Sυ(f); thin dashed line], and vertical [Sw(f); thin dotted line] velocity fluctuations for the 1-h segment of IOP 1 (2221–2321 UTC 2 Mar). Thick dashed lines denote
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
The test of the TH criterion [Eq. (7)], which is required for the estimation of ε, is applied to all 346 of the 15-min intervals. This test resulted in the removal of a significant number of intervals from further analysis at the WT and removal of some intervals at the CT. More detailed information about the number of excluded 15-min intervals is given in Table 3. Only the perturbations of streamwise velocity component are used for the calculation of ε, because this component is least contaminated by self-induced distortion by the anemometer (e.g., Piper and Lundquist 2004).
Number of 15-min intervals that do not satisfy the Taylor’s-hypothesis criterion during the 6-h period from 2100 UTC 2 Mar to 0300 UTC 3 Mar. Data were not available at 15 and 30 m at the CT.
Next, a specific procedure was followed to calculate ε using IDM. As shown in Fig. 8, the
To evaluate the robustness of these ε estimates, we have used an alternative method to calculate ε that relies on the third-order structure function (e.g., Albertson et al. 1997). Results of the comparison of ε obtained by these two methods are given in appendix A, where a decent agreement between the methods is shown. The TKE from Eq. (1) as well as terms I–V in Eq. (3) are calculated in the next section.
d. Evaluation of TKE and terms I–V
The TKE values are calculated using Eq. (1) for each 15-min interval. As an example, the time evolution of TKE for the CT at the 10-m level is shown in Fig. 9a. In the 6-h period, TKE is high between 2200 UTC 2 March and 0100 UTC 3 March, which approximately corresponds to the period of the coherent aerosol structures observed by the REAL (De Wekker and Mayor 2009, their Fig. 6).
Time series over the selected 6-h period at the CT of (a) TKE at 10 m and (b) TKE budget equation terms at 7.5-m midlevel: vertical advection (II; gray dashed line), buoyancy (III; black dotted line), mechanical shear (IV; solid black line), vertical transport (V; black dashed line), and dissipation (ε; solid gray line). The values of ε are multiplied by −1 for presentation.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
Time series over the selected 6-h period at the CT of (a) TKE at 10 m and (b) TKE budget equation terms at 7.5-m midlevel: vertical advection (II; gray dashed line), buoyancy (III; black dotted line), mechanical shear (IV; solid black line), vertical transport (V; black dashed line), and dissipation (ε; solid gray line). The values of ε are multiplied by −1 for presentation.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
Time series over the selected 6-h period at the CT of (a) TKE at 10 m and (b) TKE budget equation terms at 7.5-m midlevel: vertical advection (II; gray dashed line), buoyancy (III; black dotted line), mechanical shear (IV; solid black line), vertical transport (V; black dashed line), and dissipation (ε; solid gray line). The values of ε are multiplied by −1 for presentation.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
The local storage term I from Eq. (3) is calculated for each level using the central-differencing method in time. It is found that this term is at least an order of magnitude smaller than any other calculated term and therefore can be considered to be negligible. According to Kaimal and Finnigan (1994), a balance between turbulence production and destruction (or local equilibrium) may occur in turbulent flows over complex terrain. Our estimations of term I indicate that this situation occurs for the period of interest.
The buoyancy term III is calculated as defined in Eq. (3) for each level. The calculation of the vertical advection term II, the mechanical term IV and the vertical transport term V from Eq. (3) requires two levels of data. These three terms are therefore calculated in the layer between the two consecutive levels using a second-order central-differencing method in height. The value of the terms in this layer is assigned to a height between the two levels or “midlevel.”
As an example, the results of the TKE budget analysis at the 7.5-m midlevel for the CT are shown in Fig. 9b. The mechanical term IV (black solid curve) and ε (gray solid curve) are largest and show a similar temporal variability. The two terms are highly correlated during the entire 6-h period, with a correlation coefficient squared r2 equal to 0.97. Therefore, in this particular case, the mechanical shear and molecular viscosity are the dominant physical mechanisms that determine the TKE. The mechanical term is governed by the vertical shear of the horizontal wind speed. The vertical wind convergence/divergence (third part of term IV) turns out to be negligible (in all of our cases presented later). Vertical advection, buoyancy, and the vertical transport term are denoted in Fig. 9b by the gray dashed, black dotted, and black dashed curves, respectively. Although vertical advection and buoyancy can be considered to be negligible during the observed period, the transport term fluctuates around zero, alternatively contributing to the TKE production and destruction. This example is consistent with the RB analysis in section 4b, which indicates shear-dominated turbulence at the CT.
Analysis of the uncertainty of the estimated TKE and different TKE budget terms shows that estimations of term V, the vertical transport term, show the largest uncertainty. This uncertainty analysis is presented in appendix B using a representation of the statistical characteristics of each budget term. The results from the TKE budget analysis presented above will be discussed for all different heights and towers in detail in section 5.
e. Sensitivity of the results to the choice of averaging interval
The optimal averaging time for the calculation of turbulence terms over complex terrain has been discussed in several papers but remains an open question (e.g., Sakai et al. 2001; Finnigan et al. 2003; Lee et al. 2004). To investigate the sensitivity of the TKE budget terms to the averaging interval, we compare the terms calculated using the 15-min averaging interval with the terms calculated using 1- and 30-min averaging intervals for the 6-h period of interest. The most sensitive variables appear to be TKE and the mechanical term (IV), and the least sensitive is ε. Figure 10 shows results of this analysis for TKE and ε at the 10-m level and for the mechanical production term IV at the 7.5-m midlevel. In Figs. 10d–f, term IV is positive and is placed in the first quadrant while ε is presented as negative and therefore is placed in the fourth quadrant. TKE values increase by using the 30-min averaging interval, especially at the WT and CT (Figs. 10a and 10b, respectively). This dependence of the TKE on the averaging interval is most likely due to the influence of mesoscale transport, which will be discussed in more detail in the next section. The mechanical term IV (first quadrant of Figs. 10d–f) is much smaller for the 1-min averaging interval than for the 15-min averaging interval, whereas the differences in the terms between the 30- and 15-min averaging intervals appear negligible. Dissipation rate ε (fourth quadrant of Figs. 10d–f) is least sensitive to the averaging time, with reduced scatter when larger averaging intervals are used.
Scatterplots of TKE estimated using 1- and 30-min averaging intervals vs TKE estimated using a 15-min averaging interval at the 10-m level at the (a) WT, (b) CT, and (c) ST. Gray markers denote 1-min vs 15-min scatter, and black markers denote 30-min vs 15-min scatter. Scatterplots of mechanical term IV (first quadrant) at the 7.5-m midlevel and ε (third quadrant) at the 10-m level estimated using the same averaging intervals at the (d) WT, (e) CT, and (f) ST. The values of ε are multiplied by −1 for presentation.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
Scatterplots of TKE estimated using 1- and 30-min averaging intervals vs TKE estimated using a 15-min averaging interval at the 10-m level at the (a) WT, (b) CT, and (c) ST. Gray markers denote 1-min vs 15-min scatter, and black markers denote 30-min vs 15-min scatter. Scatterplots of mechanical term IV (first quadrant) at the 7.5-m midlevel and ε (third quadrant) at the 10-m level estimated using the same averaging intervals at the (d) WT, (e) CT, and (f) ST. The values of ε are multiplied by −1 for presentation.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
Scatterplots of TKE estimated using 1- and 30-min averaging intervals vs TKE estimated using a 15-min averaging interval at the 10-m level at the (a) WT, (b) CT, and (c) ST. Gray markers denote 1-min vs 15-min scatter, and black markers denote 30-min vs 15-min scatter. Scatterplots of mechanical term IV (first quadrant) at the 7.5-m midlevel and ε (third quadrant) at the 10-m level estimated using the same averaging intervals at the (d) WT, (e) CT, and (f) ST. The values of ε are multiplied by −1 for presentation.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
5. Turbulence structure in Owens Valley
a. Time evolution of the vertical turbulence structure
Time series of TKE from different levels within the selected 6-h period at all three towers are shown in Fig. 11. TKE at the WT (Fig. 11a) suddenly increases around 2315 UTC just around the time when downslope winds replace the former upslope winds (Figs. 2a,b). TKE increases with height at the WT with values from 9 m2 s−2 at 5 m to values of 16 m2 s−2 at 30 m. Along the valley axis [ST (Fig. 11c) and CT (Fig. 11b)], TKE is weaker and does not show a strong dependence on height, with a slight increase with height at the CT (from its maximum value of 6 m2 s−2 at 5 m to 7 m2 s−2 at 25 m) and a slight decrease with height at the ST (from its maximum value of 6 m2 s−2 at 5 m to 5 m2 s−2 at 30 m). A possible interpretation of these observations is that the TKE structure at the western alluvial slope is affected at the higher levels by mountain-wave activity whose influence is also felt by the higher levels at the CT (but not at the ST). Data obtained by the REAL show that mountain-wave-induced downslope advection of stable stratified air starts at the location of the WT around 2200 UTC 2 March (De Wekker and Mayor 2009, their Fig. 6b), with increased mixing aloft (above ~1 km). Time evolution of the aerosol structure indicates that this increased mixing is caused by the interaction of the downslope flow and the southeasterly flow along the valley, resulting in generation of coherent structures with a spatial scale of several hundred meters (De Wekker and Mayor 2009).
Temporal evolution of TKE at various levels at (a) WT, (b) CT, and (c) ST. The level heights are indicated on the right y axis in (c).
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
Temporal evolution of TKE at various levels at (a) WT, (b) CT, and (c) ST. The level heights are indicated on the right y axis in (c).
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
Temporal evolution of TKE at various levels at (a) WT, (b) CT, and (c) ST. The level heights are indicated on the right y axis in (c).
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
The time series of the TKE budget terms at different midlevels (Fig. 12) show that at the CT and ST the mechanical term and the dissipation rate ε are dominant mechanisms in TKE production/destruction at all levels. The mechanical term is considerably stronger than ε, however, especially at the lower levels (Figs. 12b,c). At the WT (Fig. 12a), the situation is considerably different. In general, the values of the budget terms are approximately one-half of those at the CT and ST, which contrasts with the stronger TKE at the WT when compared with the TKE at the CT and ST. Also, the vertical advection term (II) and the vertical transport term (V) play a significant role in the TKE budget at the WT. These observations confirm the different nature of turbulence at the western slope than along the valley axis.
As in Fig. 11, but for the terms of the TKE budget equation. The dashed gray, dotted black, solid black, dashed black, and solid gray lines denote the vertical advection (II), buoyancy (III), mechanical shear (IV), and vertical transport (V) terms and dissipation ε, respectively. The [X] in the y axis label of (a) substitutes for various terms of the TKE budget. The values of ε are multiplied by −1 for presentation.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
As in Fig. 11, but for the terms of the TKE budget equation. The dashed gray, dotted black, solid black, dashed black, and solid gray lines denote the vertical advection (II), buoyancy (III), mechanical shear (IV), and vertical transport (V) terms and dissipation ε, respectively. The [X] in the y axis label of (a) substitutes for various terms of the TKE budget. The values of ε are multiplied by −1 for presentation.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
As in Fig. 11, but for the terms of the TKE budget equation. The dashed gray, dotted black, solid black, dashed black, and solid gray lines denote the vertical advection (II), buoyancy (III), mechanical shear (IV), and vertical transport (V) terms and dissipation ε, respectively. The [X] in the y axis label of (a) substitutes for various terms of the TKE budget. The values of ε are multiplied by −1 for presentation.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
Term I is at least an order of magnitude smaller than any of the other calculated terms (a maximum value of 0.004 m2 s−3 is obtained at the 25-m level at the WT) and therefore might be considered to be negligible. The question that arises now is how well the simplified TKE budget in Eq. (3) is closed by the calculated terms at the different towers and the different midlevels. In Fig. 13, we have summarized all of the positive and negative contributions of the terms in Eq. (3) to the TKE budget for each 15-min interval. The difference between the TKE production and destruction is also shown in Fig. 13 and is significant at all three towers at midlevels. At the CT and ST (Figs. 13b and 13c, respectively), the difference is mainly positive, which means that we measure more production than dissipation of TKE, whereas at the WT the difference changes sign. Overall, it can be concluded that the simplified TKE budget in Eq. (3) is not closed. The pressure correlation term, the horizontal TKE advection terms, and the horizontal wind shear terms (terms that we cannot calculate with our dataset and that are summarized in the residual term Rs) obviously play important roles in the TKE budget during this event.
As in Fig. 12, but for the sum of the TKE production (black solid lines) and destruction (gray solid lines) terms and the difference between the two (black dashed lines).
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
As in Fig. 12, but for the sum of the TKE production (black solid lines) and destruction (gray solid lines) terms and the difference between the two (black dashed lines).
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
As in Fig. 12, but for the sum of the TKE production (black solid lines) and destruction (gray solid lines) terms and the difference between the two (black dashed lines).
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
The picture that emerges from these observations is that—in particular, at the WT, where TKE is strongest and the budget terms are smallest—TKE is not only produced locally but is also redistributed from layers aloft (where the turbulence activity was large) and advected from the area upslope of the WT toward the valley central axis. Snapshots and animations of the aerosol structure derived from the scanning backscatter lidar (Fig. 3 and De Wekker and Mayor 2009) along with the TKE behavior with height at the WT and CT support this picture.
b. Turbulent-length-scale parameter
(a) Vertical profiles of the length-scale parameter Λ at the WT (black triangles), CT (black squares), and ST (black circles). The correlation coefficients between fits provided by Eq. (11) and the data at all midlevels are plotted for the WT (gray asterisks), CT (gray plus signs), and ST (gray times signs). (b) Vertical profiles of the length-scale parameter Λ estimated from Eq. (11) (black curves) and from Eq. (12) (gray curves). Markers for Λ are as in (a).
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
(a) Vertical profiles of the length-scale parameter Λ at the WT (black triangles), CT (black squares), and ST (black circles). The correlation coefficients between fits provided by Eq. (11) and the data at all midlevels are plotted for the WT (gray asterisks), CT (gray plus signs), and ST (gray times signs). (b) Vertical profiles of the length-scale parameter Λ estimated from Eq. (11) (black curves) and from Eq. (12) (gray curves). Markers for Λ are as in (a).
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
(a) Vertical profiles of the length-scale parameter Λ at the WT (black triangles), CT (black squares), and ST (black circles). The correlation coefficients between fits provided by Eq. (11) and the data at all midlevels are plotted for the WT (gray asterisks), CT (gray plus signs), and ST (gray times signs). (b) Vertical profiles of the length-scale parameter Λ estimated from Eq. (11) (black curves) and from Eq. (12) (gray curves). Markers for Λ are as in (a).
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
The results presented above demonstrate the weakness in using a single turbulent-length-scale parameter to describe turbulence characteristics in complex terrain where nonlocal effects and mesoscale transport can become important.
6. Conclusions
In this study, data from T-REX IOP 1 are analyzed to investigate properties of the near-surface turbulence during a mountain-wave event. Temporal and spatial variability of the terms in the TKE budget are obtained from high-frequency data collected at multiple levels on three 30-m NCAR ISFF towers. A transition from a quiescent to a disturbed boundary layer is accompanied by large variability of TKE in space and time. Observations and analyses show that mesoscale transport associated with mountain-wave activity greatly enhances TKE on the western side of the valley. The contribution of the mesoscale transport becomes obvious when increasing the averaging interval for the turbulence calculations. In the central part of the valley, TKE is also strong but is mostly determined by local processes associated with the along-valley flow. Nevertheless, some evidence of the influence of scales that are larger than the local scale is still present at the highest levels on the tower that is located in the same cross-valley cross section as the western-slope tower.
We have shown that the TKE budget is poorly closed by the evaluated terms at all three locations. Possible reasons for this imbalance are the redistribution of TKE by the pressure fluctuations, the horizontal advection of TKE, and the horizontal wind shear—processes that we cannot estimate from our data.
Turbulence parameterizations in atmospheric numerical models often use a turbulence-length-scale parameter whose value is not well known. Using our calculations of the dissipation rate and the turbulent kinetic energy, we obtained values of this length-scale parameter. The spatial variability of the length-scale parameter suggests the presence of larger turbulent eddies at the western alluvial slope than along the valley axis. This finding is in agreement with the observation of aerosol structures from the scanning lidar. Turbulence parameterizations need to take into account the spatial variability of turbulent length scales in situations in which mountain-wave activity is apparent. Because boundary layer effects are important in the forecasting of mountain waves (e.g., Doyle and Durran 2007), an appropriate turbulence parameterization in these situations is highly needed. The data and results from our case study can be used to develop and evaluate turbulence parameterizations for complex terrain.
Among the many observations made during T-REX IOP 1, scanning aerosol lidar data proved to be particularly helpful in interpreting the results of the TKE budget analysis and in providing a more complete understanding of temporal and spatial variability of turbulence in mountainous terrain.
Acknowledgments
This work was initiated while the first author, ŽV, was a visiting student at the University of Virginia (UVA). UVA is acknowledged for providing funding to ŽV to work on the T-REX dataset. The primary sponsor of T-REX is the U.S. National Science Foundation (NSF). This work was partially supported by the Croatian Ministry of Science, Education and Sports project BORA 119-1193086-1311, and by NSF Grant ATM-0524891 to the Desert Research Institute, which supported early stages of this work by VG. We thank Steve Oncley from NCAR for providing the raw turbulence data from the three ISFF towers, Tom Horst, Steve Oncley, and Branko Grisogono for helpful suggestions, and Ming Xiao from DRI for processing the TAWS data and generating Fig. 2. We also thank the three anonymous reviewers whose comments improved the quality of the manuscript.
APPENDIX A
Comparison of ε Estimated Using IDM and 3SF
We used Eq. (A2) to estimate ε for each 15-min interval. The smallest period τ from our data for using 3SF is 0.1 s. According to Kolmogorov’s ⅘ law given in Eq. (A2), linear dependence of 3SF on τ is expected within the inertial subrange. We found that for different levels and different towers this linear dependence occurs when τ is between 5 and 30 s. Figure A1 shows the results of ε obtained using both IDM and 3SF for the CT at the 10-m level, indicating close agreement between the two methods (Fig. A1a) but with a slight underestimation of ε obtained by 3SF at higher values (Fig. A1b). Similar results are obtained at all levels at all three towers.
(a) Time series of ε estimated by IDM (black curve) and by 3SF (gray curve). (b) Scatterplot between these two series.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
(a) Time series of ε estimated by IDM (black curve) and by 3SF (gray curve). (b) Scatterplot between these two series.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
(a) Time series of ε estimated by IDM (black curve) and by 3SF (gray curve). (b) Scatterplot between these two series.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
APPENDIX B
Variability of TKE and TKE Budget Equation Terms
The variability of the magnitude of each individual term in the TKE budget equation can provide some insight to the uncertainty in the calculation of the terms. To this end, we created normalized histograms of certain term samples and then fitted a suitable probability density function (PDF) on these normalized histograms. Values of all terms are calculated for 346 of the 15-min intervals, each of which contains 9000 data points (10-Hz data). For each interval, TKE and TKE budget equation terms from II to V are calculated and then averaged. For the eddy dissipation ε, samples are much shorter (not exceeding 257 points) as a consequence of the limited frequency band that exhibits the
Normalized histograms (dark gray rectangles) and correspondent probability density functions (black solid line) of (a) TKE with Weibull distribution; (b) vertical advection (II) with normal distribution; (c) buoyancy term (III) with normal distribution; (d) mechanical term (IV) with exponential distribution; (e) vertical distribution term (V) with normal distribution; and (f) dissipation ε estimated using IDM with lognormal distribution for the 15-min interval between 2352 UTC 2 Mar and 0007 UTC 3 Mar at the CT. In the background, probability density functions of all 345 other 15-min intervals are shown (light gray lines). TKE, term III, and ε are given for the 10-m level, and terms II, IV, and V are given for the 7.5-m midlevel.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
Normalized histograms (dark gray rectangles) and correspondent probability density functions (black solid line) of (a) TKE with Weibull distribution; (b) vertical advection (II) with normal distribution; (c) buoyancy term (III) with normal distribution; (d) mechanical term (IV) with exponential distribution; (e) vertical distribution term (V) with normal distribution; and (f) dissipation ε estimated using IDM with lognormal distribution for the 15-min interval between 2352 UTC 2 Mar and 0007 UTC 3 Mar at the CT. In the background, probability density functions of all 345 other 15-min intervals are shown (light gray lines). TKE, term III, and ε are given for the 10-m level, and terms II, IV, and V are given for the 7.5-m midlevel.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
Normalized histograms (dark gray rectangles) and correspondent probability density functions (black solid line) of (a) TKE with Weibull distribution; (b) vertical advection (II) with normal distribution; (c) buoyancy term (III) with normal distribution; (d) mechanical term (IV) with exponential distribution; (e) vertical distribution term (V) with normal distribution; and (f) dissipation ε estimated using IDM with lognormal distribution for the 15-min interval between 2352 UTC 2 Mar and 0007 UTC 3 Mar at the CT. In the background, probability density functions of all 345 other 15-min intervals are shown (light gray lines). TKE, term III, and ε are given for the 10-m level, and terms II, IV, and V are given for the 7.5-m midlevel.
Citation: Journal of Applied Meteorology and Climatology 50, 5; 10.1175/2010JAMC2450.1
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