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  • View in gallery

    Kernel density estimates of the joint PDFs of mean(w)/std(w) and skew(w) for (top) daytime and (bottom) nighttime weather station data over global land in the summer season during 1979–99. The contour intervals are logarithmically spaced. The solid line is the theoretical curve for a Weibull variable, and the white square corresponds to a Rayleigh variable (a special case of the Weibull distribution arising when the vector wind components are Gaussian, isotropic, and uncorrelated with mean zero).

  • View in gallery

    The observed diurnal variation of potential temperature; mean, standard deviation, and skewness of boundary layer wind speed, and diurnal ratio of theoretical wind power in JJA at the Caubauw site during the period from 2000 to 2009. The skewness is defined as the difference between the observed skewness and that of a best-fit Weibull variable.

  • View in gallery

    The observed daily mean wind power density (m3 s−3) in the JJA season at the Cabauw site during the period from 2000 to 2009.

  • View in gallery

    Histograms of geostrophic wind speeds from 2 yr of hourly sampled stochastically varying geostrophic winds with mean values of (top) 3, (middle) 6, and (bottom) 9 m s−1. The wind speed range for all bins is 2 m s−1.

  • View in gallery

    One week of simulated variables from the equilibrium run. (from top to bottom) Bottom-level wind speed (m s−1); incoming clear-sky solar radiation reaching top of atmosphere (W m−2); surface sensible heat flux (W m−2); bottom-level air temperature (°C); near-surface stability (K), defined as the difference between ground temperature and bottom-level temperature; and boundary layer height (m).

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    Simulated diurnal cycle of potential temperature, vector wind components, and wind speed from the surface to 200 m in the equilibrium run with the background geostrophic wind speed of 3 m s−1.

  • View in gallery

    As in Fig. 2, but for the baseline SCM experiment with large-scale weather variability, intermittent mixing in the boundary layer inversion, and .

  • View in gallery

    Scatterplots of the relationship between bottom-level wind speed and wind speed at 200 m in (left) unstable ( < 0.0 ), (middle) near-neutral (: [−0.0 , 0.5 ]), and (right) stable stratification ( > 0.5 ) for simulations (top) with and (bottom) without enhanced intermittent mixing at the boundary layer inversion.

  • View in gallery

    As in Fig. 7, but without the enhanced intermittent mixing at the boundary layer inversion.

  • View in gallery

    As in Fig. 7, but without large-scale weather variability.

  • View in gallery

    The simulated PDF of (top) near-surface stability and (bottom) bottom-level wind speed with no enhanced intermittent mixing in the inversion layer (dashed line), with the FBN parameterization (solid line), and with the FWN parameterization(dashed–dotted line) at (left) midnight and (right) noon. In this simulation .

  • View in gallery

    The simulated PDF of (top) near-surface stability and (bottom) bottom-level wind speed with set as 0.25 (solid line), 0.35 (dashed line), 0.5 (dotted line), and 1.0 (dashed–dotted line) at (left) evening (2000 LT) and (right) early morning (0400 LT).

  • View in gallery

    As in Fig. 7, but using the standard vertical resolution in the SCM.

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The Influence of Boundary Layer Processes on the Diurnal Variation of the Climatological Near-Surface Wind Speed Probability Distribution over Land

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  • 1 School of Earth and Ocean Sciences, University of Victoria, Victoria, British Columbia, Canada
  • 2 Canadian Centre for Climate Modelling and Analysis, University of Victoria, Victoria, British Columbia, Canada
  • 3 School of Earth and Ocean Sciences, University of Victoria, Victoria, British Columbia, Canada
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Abstract

Knowledge of the diurnally varying land surface wind speed probability distribution is essential for surface flux estimation and wind power management. Global observations indicate that the surface wind speed probability density function (PDF) is characterized by a Weibull-like PDF during the day and a nighttime PDF with considerably greater skewness. Consideration of long-term tower observations at Cabauw, the Netherlands, indicates that this nighttime skewness is a shallow feature connected to the formation of a stably stratified nocturnal boundary layer. The observed diurnally varying vertical structure of the leading three climatological moments of near-surface wind speed (mean, standard deviation, and skewness) and the wind power density at the Cabauw site can be successfully simulated using the single-column version of the Canadian Centre for Climate Modelling and Analysis (CCCma) fourth-generation atmospheric general circulation model (CanAM4) with a new semiempirical diagnostic turbulent kinetic energy (TKE) scheme representing downgradient turbulent transfer processes for cloud-free conditions. This model also includes a simple stochastic representation of intermittent turbulence at the boundary layer inversion. It is found that the mean and the standard deviation of wind speed are most influenced by large-scale “weather” variability, while the shape of the PDF is influenced by the intermittent mixing process. This effect is quantitatively dependent on the asymptotic flux Richardson number, which determines the Prandtl number in stable flows. High vertical resolution near the land surface is also necessary for realistic simulation of the observed fine vertical structure of wind speed distribution.

Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/JCLI-D-11-00321.s1.

Corresponding author address: Norman A. McFarlane, Canadian Centre for Climate Modelling and Analysis, University of Victoria, P.O. Box 3065 STN CSC, Victoria BC V8W 3V6, Canada. E-mail: norm.mcfarlane@ec.gc.ca

Abstract

Knowledge of the diurnally varying land surface wind speed probability distribution is essential for surface flux estimation and wind power management. Global observations indicate that the surface wind speed probability density function (PDF) is characterized by a Weibull-like PDF during the day and a nighttime PDF with considerably greater skewness. Consideration of long-term tower observations at Cabauw, the Netherlands, indicates that this nighttime skewness is a shallow feature connected to the formation of a stably stratified nocturnal boundary layer. The observed diurnally varying vertical structure of the leading three climatological moments of near-surface wind speed (mean, standard deviation, and skewness) and the wind power density at the Cabauw site can be successfully simulated using the single-column version of the Canadian Centre for Climate Modelling and Analysis (CCCma) fourth-generation atmospheric general circulation model (CanAM4) with a new semiempirical diagnostic turbulent kinetic energy (TKE) scheme representing downgradient turbulent transfer processes for cloud-free conditions. This model also includes a simple stochastic representation of intermittent turbulence at the boundary layer inversion. It is found that the mean and the standard deviation of wind speed are most influenced by large-scale “weather” variability, while the shape of the PDF is influenced by the intermittent mixing process. This effect is quantitatively dependent on the asymptotic flux Richardson number, which determines the Prandtl number in stable flows. High vertical resolution near the land surface is also necessary for realistic simulation of the observed fine vertical structure of wind speed distribution.

Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/JCLI-D-11-00321.s1.

Corresponding author address: Norman A. McFarlane, Canadian Centre for Climate Modelling and Analysis, University of Victoria, P.O. Box 3065 STN CSC, Victoria BC V8W 3V6, Canada. E-mail: norm.mcfarlane@ec.gc.ca

1. Introduction

The horizontal wind near the surface (surface wind) is a fundamental observed meteorological variable, driven by pressure gradients, the Coriolis force, buoyancy effects, and surface friction. Knowledge of the land surface wind speed (SWS) probability density function (PDF) is important for many applications in wind power climatology (Petersen et al. 1998; Burton et al. 2001) and surface flux estimation (Cakmur et al. 2004; Monahan 2006). In particular, wind power density is proportional to the third power of wind speed. The wind power density demonstrates significant diurnal variation (Lazarus and Bewley 2005), which can be sufficiently characterized by the diurnal variation of the leading three statistical moments of wind speed (mean, standard deviation, and skewness; Hennessey 1977; He et al. 2010).

The diurnal variation of surface wind speed has been investigated in a number of previous studies. For example, the role of stability and surface roughness changes in generating a diurnal cycle of mean wind speed offshore was studied in Barthelmie et al. (1996), while the relationship of large-scale divergence and afternoon downward turbulent momentum entrainment on diurnal and semidiurnal varying wind speed was examined in Dai and Deser (1999). The mean surface wind speed and its physical controls were the focus of these previous studies. Relatively little attention has been given to higher-order moments of surface wind speed and the associated physical mechanisms until recently (e.g., He et al. 2010; Monahan et al. 2011). In particular, He et al. (2010) noted that although the daytime surface wind speed PDF is broadly consistent with the widely used Weibull distribution (Hennessey 1977; Justus et al. 1978; Conradsen et al. 1984; Pavia and O’Brien 1986; Monahan 2006), away from open water the skewness of nighttime winds is larger than that predicted by the Weibull PDF. In other words, the Weibull distribution generally underestimates the high-speed tail of the surface wind speed PDF at night. A number of regional climate models (RCMs) considered in this earlier study were not able to reproduce this diurnal cycle in the SWS PDF. This diurnal variation of SWS PDF is also observed at a large number of global surface stations and at two tall tower sites, as shown in Monahan et al. (2011). The tower observations demonstrate that wind speeds become more positively skewed than the corresponding Weibull distribution only in the shallow (~50 m) nocturnal boundary layer. Using an idealized two-layer model of the boundary layer momentum budget, Monahan et al. (2011) demonstrated that the observed variability of the daytime and nighttime surface wind speeds can be accounted for through a stochastic representation of intermittent turbulent mixing at the nocturnal boundary layer inversion.

The present study extends the findings of He et al. (2010) and Monahan et al. (2011) to consider the physical mechanisms controlling the SWS PDF using a single-column model with a more comprehensive representation of boundary layer processes. The observed diurnal variations of the leading three moments of SWS and the wind power density are reviewed in section 2. Basic descriptions of the single-column model (SCM) version of the Canadian Centre for Climate Modelling and Analysis (CCCma) fourth-generation atmospheric general circulation model (CanAM4), the stochastic model of the large-scale “weather” forcing, and of the experimental design are introduced in section 3. Equilibrium runs without weather variability and simulations, including weather, are presented and discussed in section 4; the relationship among near-surface wind speed distribution, boundary layer processes, and the near-surface thermal stability is investigated in section 5. A discussion and conclusions follow in section 6. The basic physics and key equations of the new turbulence diffusion scheme used in the SCM are presented in the online supplement (available at the Journals Online website: http://dx.doi.org/10.1175/JCLI-D-11-00321.s1). Note that throughout this study (excluding the online supplement), the variable “w” is used to denote wind speed unless otherwise noted. As well, for simplicity the cube of the wind speed is referred to as the “wind power density” (neglecting the contribution from air density).

2. Observations

The Weibull distribution is commonly used in empirical studies of the SWS PDF (cf. Monahan 2006; He et al. 2010). One feature of this PDF is that the skewness is a unique function of the ratio of the mean to the standard deviation. Observations taken from 3734 weather station wind records from around the world show that the observed relationship between moments of daytime SWS is consistent with the Weibull distribution [Fig. 1, top panel; details of these data are presented in He et al. (2010)]. In contrast, the nighttime SWS PDF is consistently more positively skewed than the Weibull PDF with the same mean and variance over most of the land surface (Fig. 1, bottom panel). This diurnal cycle in the shape of the SWS PDF is a common feature over all seasons, with the strongest diurnal amplitude in summer (He et al. 2010; Monahan et al. 2011).

Fig. 1.
Fig. 1.

Kernel density estimates of the joint PDFs of mean(w)/std(w) and skew(w) for (top) daytime and (bottom) nighttime weather station data over global land in the summer season during 1979–99. The contour intervals are logarithmically spaced. The solid line is the theoretical curve for a Weibull variable, and the white square corresponds to a Rayleigh variable (a special case of the Weibull distribution arising when the vector wind components are Gaussian, isotropic, and uncorrelated with mean zero).

Citation: Journal of Climate 25, 18; 10.1175/JCLI-D-11-00321.1

Using long records of high-resolution observations from tall towers, Monahan et al. (2011) demonstrated that the diurnal cycle in the midlatitude SWS PDF is a shallow feature confined to the bottom tens of meters of the atmosphere. Diurnal variations of potential temperature, the leading three moments of boundary layer wind speed, and the diurnal ratio of wind power density from the surface to 200 m at Cabouw (52°N, 4.9°E) in the western Netherlands in June–August (JJA) are illustrated in Fig. 2. The diurnal ratio of wind power density is defined as the ratio of its hourly value to its daily mean value (Fig. 3). These quantities are computed from hourly averages of 10-min observations from January 2000 to December 2009 [these data are described in detail in Monahan et al. (2011)]. The tower is located in open, flat land with few nearby windbreaks, such as houses or trees.

Fig. 2.
Fig. 2.

The observed diurnal variation of potential temperature; mean, standard deviation, and skewness of boundary layer wind speed, and diurnal ratio of theoretical wind power in JJA at the Caubauw site during the period from 2000 to 2009. The skewness is defined as the difference between the observed skewness and that of a best-fit Weibull variable.

Citation: Journal of Climate 25, 18; 10.1175/JCLI-D-11-00321.1

Fig. 3.
Fig. 3.

The observed daily mean wind power density (m3 s−3) in the JJA season at the Cabauw site during the period from 2000 to 2009.

Citation: Journal of Climate 25, 18; 10.1175/JCLI-D-11-00321.1

It is evident from Fig. 2 that the diurnal variation of thermal structure is similar to that characterized by fair-weather boundary layer evolution (Stull 1997): potential temperature is well mixed within an actively turbulent boundary layer during the day, and a strong temperature inversion is developed around 1900 LT and maintained until about 0700 LT. The mean and standard deviation of wind speed also demonstrate the canonical pattern (Dai and Deser 1999), with the largest values within the actively turbulent daytime unstable PBL and the smallest values within the statically stable shallow nighttime stable PBL (Monahan et al. 2011). During the day, the SWS skewness is consistent with that of a Weibull distributed variable having the same mean and variance. The SWS PDF becomes more skewed relative to a Weibull distribution when the near-surface temperature inversion is developed in the evening. This super-Weibull skewness takes a maximum between 1900 and 2200 LT, gradually decreases until midnight, and maintains a positive value till early morning, when the stable temperature inversion breaks down. The region of negative skewness anomaly aloft during the night is predominantly above the nocturnal inversion and corresponds to a shortening of the high wind speed tail of the observed distribution relative to that for the corresponding Weibull distribution. The diurnal variation of the near-surface wind speed skewness is qualitatively consistent with the global estimates from weather station wind observations shown in Fig. 1. The Cabauw data demonstrate that this diurnal evolution in skewness is concentrated within the nocturnal stable boundary layer. As this is a very shallow feature, it is not surprising that it is not well captured by global or regional climate models (e.g. He et al. 2010).

The wind power density is proportional to the third power of wind speed, and it has a large vertical gradient in the mean (Fig. 3) and a strong diurnal cycle (Fig. 2) at Cabauw. The wind power density normalized to its daily-mean value generally follows the evolution of the leading two moments of wind speed near the surface, reaching its daily maximum between 1200 and 1600 LT and its daily minimum at night in the lowest 100 m. Over this range of altitudes, the daytime maximum is up to 4 times as large as the nighttime minimum. Between 150 and 200 m, the diurnal ratio of wind power reaches its maximum from midnight until early morning, likely due to the development of a low-level jet.

3. Single-column model description and experimental design

a. SCM basic design

The SCM used here is based on CanAM4 (von Salzen et al. 2011, manuscript submitted to Atmos.–Ocean). This single column model is designed to simulate the effects of unresolved (parameterized) physical processes on the large-scale flow that is resolved in the GCM. The typical horizontal scales resolved by the GCM are of the order of 100 km or larger, and the typical temporal scales are on the order of hours. The corresponding SCM does not include a representation of processes such as horizontal advection, which depends on the horizontal discretization in the GCM, but it includes a full range of physical processes that are typically included in the GCM and implemented in a columnwise manner. These include the Canadian Land Surface Scheme (CLASS) (Verseghy 1991; Verseghy et al. 1993; Verseghy 2000), the surface flux formulation of Abdella and McFarlane (1996), radiative transfer and heating (Li and Barker 2005), and cloud physics as used in von Salzen et al. (2005). However, to simplify the analysis, the experiments reported here are designed to be cloud free.

The vertical diffusion scheme used in this version of the SCM differs from that in the standard version of CanAM4. It is discussed in more detail in the online supplement of this paper. Furthermore, the standard CanAM4 levels are such that there are three layers from the surface to 300 m. As has been seen for the observed winds at the Cabauw site, fluctuations of the boundary layer wind speed are most pronounced within the shallow nocturnal boundary layer. To better simulate these features of the boundary layer wind speed distribution and the associated vertical distribution of turbulent kinetic energy (TKE), a higher vertical resolution version of the SCM is implemented with seven layers in the bottom 300 m.

b. Wind forcing configurations

Large-scale winds in the boundary layer are driven by large-scale horizontal pressure gradients, the Coriolis force, boundary layer mixing, surface drag, and horizontal advection. More precisely, the tendency of the specific large-scale momentum can be expressed in terms of large-scale “ageostropic” forcing [], vertical diffusion of momentum, and other physical processes represented here by a small relaxation term :
e1
e2
where the primed quantities are horizontal () and vertical () components of the unresolved part of the velocity field (here assumed to be associated predominantly with small-scale turbulence), and the overbar denotes an appropriate average over unresolved small scales. The quadratic products appearing in Eqs. (1) and (2) correspond to the vertical momentum fluxes associated with unresolved processes. These quantities do not vanish under the averaging and therefore must be parameterized appropriately. The relaxation process, which parameterizes horizontal advection, nudges toward the geostrophic wind over a time scale that is very long in the lower troposphere (250 days at the surface) and decreases to ~1 day above 700 mb. This simplification ignores processes that may make the wind deviate significantly from geostrophic balance in the free atmosphere above the boundary layer.

A number of studies have explored the sensitivity of simulations to the magnitude of the geostrophic wind in the context of simplified single-column boundary layer models. It is now well known that the magnitude of the geostrophic wind is of importance in controlling the intensity of turbulent mixing in nocturnal boundary layers. When the geostrophic wind is relatively strong during the night, the associated enhanced turbulent mixing tends to inhibit thickening of the shallow stable layer that may develop near the surface due to the strong vertical gradiant of radiative cooling in the nocturnal boundary layer (Estournal and Guedalia 1985; Gopalakrishnan et al. 1998). Revelle (1993) and McNider et al. (1995) have studied the role of the geostrophic wind in the development of chaotic behavior in the nocturnal boundary layer characterized by intermittent breakdown of the stable layer near the surface in association with the turbulent mixing. Multiple equilibrium solutions are found to exist for these simple models, such that the air temperature in the nocturnal boundary layer either becomes disconnected from the surface temperature or remains connected with it, for some values of the gesotrophic wind. This internally generated intermittency has also been studied more recently by Costa et al. (2011), also with a relatively simple boundary layer model in which the magnitude of geostrophic wind is a specified external parameter but with a more realistic representation of the turbulent transfer processes in terms of the turbulent kinetic energy. This study shows that nonperiodic intermittent periods of turbulent mixing may occur in the nocturnal boundary layer in circumstances where the geostrophic wind is large enough to sustain the generation of turbulent kinetic energy through shear production.

The above-mentioned studies examined sensitivity to the gesotrophic wind in the context of it being imposed as a single specified quantity. Also, where intermittent mixing occurs, it arises in association with the explicitly resolved dynamics. In reality, of course, the geostrophic wind undergoes temporal variability, a prominent midlatitude source that is due to weather systems. An assumption fundamental to this study is that to understand the statistics of observed synoptic-scale wind speed variability, what is important is the existence of variability in the associated pressure gradient (the weather), rather than the precise details of its evolution. Accordingly, the geostropic winds are modeled as a vertically invariant Gaussian red-noise process with a constant mean and isotropic standard deviation (, ), and an autocorrelation time scale = 2 days, characteristic of the time scale associated with fluctuations of synoptic-scale pressure patterns in the midlatitudes. Specifically, we take
e3
e4
where and do not vary in the vertical and are mean zero, uncorrelated random variables that are each described by the stochastic differential equation
e5
In Eq. (5), is a white-noise process. Introductions to stochastic differential equations are presented in Gardiner (1997) and Penland (2003). Solutions to Eq. (5) can be simulated numerically using the forward-Euler recursion, given as
e6
where is a mean zero, unit variance Gaussian random variable. For the simulations in this study, we use a time step of 1 h.

We have carried out tests for choices of the time scale ranging from two to seven days and found that the results are not strongly sensitive to the choices of time scales in this range. Although this weather representation is introduced here for the sake of simplicity in the context of the SCM application, in practice it would be expected that large-scale weather variability would be reasonably well simulated in modern GCMs. For the results shown in this work, we have taken () = (3, 0) m s−1 and () = (6, 6) m s−1. The simple specification used here, although ignoring the effects of baroclinicity in the geostrophic wind, produces simulations of the actual wind speeds within the lower part of the boundary layer that are realistic, for example, qualitatively similar in magnitude and vertical structure to those observed at Cabouw, as discussed further in section 4. It is important to note that, because of the magnitude of the variance, a range of geostrophic wind speeds is produced even for the weak mean vector geostrophic wind used in the present study. In fact the most frequently occurring geostrophic wind speeds that result from the red-noise process are in the range of 6–10 m s−1 and not strongly dependent on the specified vector mean geostrophic wind. This is illustrated in Fig. 4, which shows the distributions of wind speeds that are produced by the red-noise process using vector mean geaostrophic winds of (3, 0), (6, 0), and (9, 0) m s−1 for the top, middle, and bottom panels but with the same variance (6 m s−1 standard deviation for both components). A thorough discussion of why the mean wind speed should depend more on the standard deviation of the vector wind than on its mean for the chosen variance and range of the mean vector wind is presented in Monahan (2012).

Fig. 4.
Fig. 4.

Histograms of geostrophic wind speeds from 2 yr of hourly sampled stochastically varying geostrophic winds with mean values of (top) 3, (middle) 6, and (bottom) 9 m s−1. The wind speed range for all bins is 2 m s−1.

Citation: Journal of Climate 25, 18; 10.1175/JCLI-D-11-00321.1

It is evident that higher geostrophic wind speeds, in excess of 10 m s−1, are more frequent for higher magnitudes of the mean geostrophic wind. However, the range of geostrophic wind speeds associated with the choice of m s−1 is realistic and, for example, in reasonable in accord with the geostrophic wind speeds observed at the Cabauw site in association with the incidence of low-level jets in the boundary layer (Baas et al. 2009).

Building on the idealized model considered in Monahan et al. (2011), the SCM includes a simple parameterization of enhanced intermittent turbulence at the nocturnal boundary layer inversion. It has been observed that turbulent intensity in strongly stratified boundary layers is intermittent, with extended quiescent periods broken by episodes of intense turbulent stirring (e.g., Mahrt 1989, 1999; Van de Wiel et al. 2003; Meillier et al. 2008). These periods of enhanced turbulence may result from one or more of a broad range of “submeso” processes (e.g., Mahrt 2010), including internal gravity waves (e.g., Meillier et al. 2008), density currents, and local feedbacks between boundary layer and radiative processes (e.g., Van de Wiel et al. 2002). A representation of this intermittent turbulence is included in the eddy diffusivity of momentum and the corresponding value for heat within the top inversion layer [as formulated in Eq. (A2) in the online supplement] as , where is the diffusivity in the absence of intermittent turbulence. The contribution from intermittent turbulence is coupled to the TKE budget as an additional shear production source (as detailed in the online supplement of this paper). To assess the sensitivity of the results to the specification of this intermittently enhanced turbulence, we consider two forms: episodic fluctuations (FBN) or “white noise” fluctuations (FWN). Mathematically, FBN and FWN (in units of m2 s−1) are described by
e7
e8

In Eq. (7), are mean zero, uncorrelated random variables that are described by the stochastic differential equation Eq. (5) with an autocorrelation time scale, , of 6 h and a standard deviation of 1 m s−1. In Eq. 8, is a mean zero unit variance random number generated every hour. The episodic mixing FBN has a mean and standard deviation close to 3.0 m2 s−1, and a skewness of about 2. In contrast, the white-noise forcing FWN also has a mean and standard deviation close to 3.0 m2 s−1 and its skewness is close to zero.

We have not extensively examined the sensitivity of simulations to the choice of time scale for the episodic mixing parameterization but, as will be seen below, the simulations with episodic and white-noise parameterizations are qualitatively similar to each other. From our reading of the available literature on the range of processes that may contribute to episodic bursts of turbulence in the inversion, the choice of 6 h seemed reasonable to represent the effects of episodic events that actually produce significant amounts of mixing as opposed to shorter duration events that may not be so effective in mixing.

c. Idealized dry case: Design

It was shown in He et al. (2010) that a suite of state-of-the-art RCMs and GCMs fail to simulate the observed diurnal variation of land SWS PDF in the current climate. To simplify our analysis and to assess if the main features of the observed diurnal variability, such as that at the Cabauw site, can be understood to a first approximation without consideration of moist processes, we consider idealized SCM experiments for cloud-free dry-land-only cases.

In all of the following analyses, the model is driven by constant summertime diurnally varying incoming solar radiation at the top of the atmosphere. Air temperature is initialized with a constant temperature lapse rate at 6.5 from the surface to 150 hPa and then maintained at a constant value from 150 to 50 hPa; the specific humidity is initialized as a very dry clear-sky profile. Both air temperature and specific humidity are relaxed with a relaxation time scale of 1 day to their initial vertical profiles during the entire simulation period. Surface soil properties are set to those of the closest AGCM grid box to the Cabauw site with a surface roughness of 0.1 m. Surface fluxes and ground temperature are fully coupled with the atmosphere by the CLASS 2.7 land surface scheme (Verseghy 1991; Verseghy et al.1993; Verseghy 2000). The duration of each simulation is 2 yr and 3 months, with the first 3 months as a spinup period and the last 2-yr period for analysis of wind statistics.

The vertical resolution of the SCM was also increased from the standard configuration to one that is closer to that of the vertical sampling array of the observed winds at the Cabauw tower, which has seven levels from the surface to 300 m. The motivation for doing this is that the standard vertical resolution does not capture the typical fine vertical structure of the nocturnal wind in the observations, as discussed further in section 5c.

4. Simulation results

a. Equilibrium simulations

The surface momentum budget involves contributions from large-scale wind forcing, vertical diffusion within the boundary layer, and surface drag. In the absence of large-scale weather variability and fluctuating intermittent turbulence at the boundary layer inversion (the “equilibrium run”), the simulated surface conditions and boundary layer structure settle into periodic diurnal cycles. Although the presence of weather variability in the geostrophic wind is necessary to produce realistic simulations, we briefly discuss the equilibrium run to illustrate that the model is physically sensible.

Figure 5 displays one week of diurnal variations of simulated surface variables in the equilibrium run. The land surface is driven by constant incoming solar radiation, with its maximum clear-sky solar radiation at the top of the atmosphere reaching 900 W m−2 around noon; the resulting surface sensible heat flux has a strong diurnal cycle with its maximum value at 400 W m−2 around 1400 LT and a slightly negative minimum value at night. With a constant weak geostrophic wind of 3 m s−1 and the strong diurnal cycle of surface heat flux over dry land, the resulting SWS demonstrates typical fair-weather diurnal variations with a daytime maximum reaching 2 m s−1, a nighttime minimum close to zero, and a small early morning peak due to the influence of the nocturnal jet. The bottom-level (around 10 m) air temperature has a 10-K diurnal cycle ranging from 7°C in the early morning to 17°C in the early afternoon. The surface stability (defined here as the difference between ground temperature and the bottom-level air temperature) has a very large diurnal variation of around 30°C, which is significantly larger than a typical summertime diurnal amplitude value because our idealized experiment is designed as a completely dry clear-sky simulation over a dry land surface in the presence of a weak horizontal pressure gradient. In fact, when weather variability is included in the geostrophic wind, the mean diurnal cycle in surface stability is considerably reduced. The diurnally varying boundary layer depth is characterized by a daytime deep unstable layer extending to an altitude of 2000 m and a nighttime shallow stable layer with an inversion at about 12 m above the surface.

Fig. 5.
Fig. 5.

One week of simulated variables from the equilibrium run. (from top to bottom) Bottom-level wind speed (m s−1); incoming clear-sky solar radiation reaching top of atmosphere (W m−2); surface sensible heat flux (W m−2); bottom-level air temperature (°C); near-surface stability (K), defined as the difference between ground temperature and bottom-level temperature; and boundary layer height (m).

Citation: Journal of Climate 25, 18; 10.1175/JCLI-D-11-00321.1

Figure 6 illustrates the diurnal evolution of the thermal structure and winds in the bottom 200 m of the atmosphere when the model reaches its equilibrium state. The simulated summertime diurnal cycle of temperature (top panel of Fig. 6) demonstrates a fair-weather boundary layer evolution characterized by a well-mixed active boundary layer with large surface warming in the day and a statically stable boundary layer capped by a strong temperature inversion from late afternoon to early morning. The diurnal evolution of wind speed (fourth panel in Fig. 6) is dominated by the evolution of the wind vector component along the mean wind (U; second panel in Fig. 6), and is characterized by a much different diurnal variation pattern compared to that at Cabauw (see Fig. 2). For example, the observed near-surface wind speed reaches its daily maximum during the day, while the model-simulated wind speed reaches its maximum from just past midnight until early morning, when the nocturnal jet is fully developed. The simulated daily maximum of the wind power density ratio also occurs at night (bottom panel in Fig. 6), while the observed daily maximum occurs between 1200 and 1600 LT in the bottom 100 m. As we will now show, realistic diurnal patterns of mean wind speed and wind power density can be achieved when large-scale weather and intermittent turbulence at the boundary layer inversion are included in the simulation.

Fig. 6.
Fig. 6.

Simulated diurnal cycle of potential temperature, vector wind components, and wind speed from the surface to 200 m in the equilibrium run with the background geostrophic wind speed of 3 m s−1.

Citation: Journal of Climate 25, 18; 10.1175/JCLI-D-11-00321.1

b. Simulations including weather variability

As discussed in section 3, the influence of large-scale weather processes is represented as stochastic variability in the geostrophic wind with isotropic, mutually uncorrelated fluctuations . The intermittent turbulence in the inversion layer is represented by another stochastic process.

The simulated diurnal evolution of boundary layer temperature and wind in the run with the FBN parameterization of intermittent turbulence (Fig. 7) shares many similarities to that observed at Cabauw. The diurnal cycles in mean potential temperature, mean wind speed, and wind speed standard deviation are similar to the observed cycles. Furthermore, the simulated near-surface wind speed skewness is close to the Weibull distribution value during the day, while it is more positively skewed than the Weibull distribution at night. The duration and vertical extent of the region of enhanced positive skewness correspond to those of the stably stratified nocturnal boundary layer. The diurnal ratio of wind power density is also well simulated, although there is an unrealistically large nighttime ratio of 2 at around 200 m above the surface due to the relatively strong nocturnal jet in the simulation. The observed features of diurnal variations in lower-tropospheric wind speed PDF and boundary layer thermal structure are also reproduced in simulations using the FWN parameterization of intermittent boundary layer top mixing (not shown).

Fig. 7.
Fig. 7.

As in Fig. 2, but for the baseline SCM experiment with large-scale weather variability, intermittent mixing in the boundary layer inversion, and .

Citation: Journal of Climate 25, 18; 10.1175/JCLI-D-11-00321.1

Figure 8 displays the relationship between the bottom-level wind speed (, around 10 m) and wind speed at 200 m () for unstable (defined as < ) near-neutral stratification (defined as : [−, ]) and stable stratification (defined as > ) with and without intermittent mixing. These plots have some qualitative similarity to those shown in Monahan et al. (2011, their Figs. 8, 9, and 13), wherein it is noted that the existence of two populations, one in which wind speeds are weakly correlated in the vertical and the other where they are strongly correlated, is consistent with observed winds. Simulations with their idealized model suggest that these populations are distinguished by the degree of mixing that occurs within the boundary layer. During the daytime hours, when the sensible heat flux at the surface is upward and the lower part of the boundary layer is unstable stratified, strong mixing results in wind speeds being well correlated with height in the boundary layer, with intermittent mixing at the top having a relatively small effect. However, in the evening and nighttime hours when buoyancy-driven mixing has died down, the effects of the intermittent mixing are more apparent. During periods of stronger mixing, and are more strongly correlated. This is seen in Fig. 8, where this correlation is more consistently apparent for the cases where the intermittent mixing parameterization is active.

Fig. 8.
Fig. 8.

Scatterplots of the relationship between bottom-level wind speed and wind speed at 200 m in (left) unstable ( < 0.0 ), (middle) near-neutral (: [−0.0 , 0.5 ]), and (right) stable stratification ( > 0.5 ) for simulations (top) with and (bottom) without enhanced intermittent mixing at the boundary layer inversion.

Citation: Journal of Climate 25, 18; 10.1175/JCLI-D-11-00321.1

5. Sensitivity tests

a. Weather variability and intermittent mixing at the boundary layer inversion

As discussed in section 4b, diurnal variations of the leading three moments of lower-tropospheric wind speed and wind power density at the Cabauw site are similar to those observed when both weather variability and intermittent turbulence in stably stratified conditions are considered in the basic perturbation simulations. The relative role of these two sources of variability on the diurnal evolution of the wind speed distributions are studied in two further simulations: the first, denoted the “weather only” simulation, considers only variability in the geostrophic wind; the other, denoted “intermittency only,” holds the geostrophic wind constant while allowing for intermittent turbulence at the boundary layer inversion.

As is illustrated in Fig. 9, the basic features of the mean and standard deviation of near-surface wind speed are well captured in the weather-only simulation, indicating that variability in the pressure gradient force associated with synoptic-scale processes plays a basic role in determining the first two moments of wind speed. While there is an enhancement of wind speed skewness in the nocturnal boundary layer relative to that for a Weibull distributed variable, the strength and spatial pattern of this structure differs considerably from that seen in observations. The quality of the simulation of mean wind power density is also reduced relative to the simulation, including the effects of intermittent mixing.

Fig. 9.
Fig. 9.

As in Fig. 7, but without the enhanced intermittent mixing at the boundary layer inversion.

Citation: Journal of Climate 25, 18; 10.1175/JCLI-D-11-00321.1

At this point we note that, although the default version of the SCM employs a background diffusivity for momentum, we have chosen to reduce the value of that quantity by an order of magnitude for the simulations presented here. The default value of the background diffusivity was chosen for GCM simulations to control development of episodes of vertical decoupling and strong vertical gradients that occasionally occur in statically stable conditions when gradient Richardson numbers are large. In the present work, implementing the intermittent mixing parameterization appears to provide sufficient mixing to control this behavior, but there is evidence (notably in Fig. 9) of its reappearance when this scheme is removed. We have done tests (not shown) that confirm that reintroducing a larger background diffusivity for momentum, instead of the intermittent mixing parameterization, produces qualitatively similar simulations of wind speed, variance, and power to that shown in Fig. 7. However, it tends to limit the development of the relatively high skewness periods shown in Fig. 7.

Effects of weather variability on the near-surface wind speed distribution can also be illustrated by comparing the equilibrium simulation results shown in Fig. 5 with the results of the weather-only simulation. Weather variability greatly increases the mean value of wind speed at all levels from the surface to 200 m. The diurnal phases of both the mean wind speed and the mean wind power density over the bottom 100 m are also significantly shifted through weather variability, such that daily maxima are reached not at the time of the nocturnal jet peak strength but rather between late morning and early afternoon due to strong downward momentum mixing in the convective boundary layer.

Simulation results from the intermittency-only run (Fig. 10) illustrate that in the absence of weather variability, the diurnal variations of lower-tropospheric mean wind speed and wind power density are essentially the same as in the equilibrium simulation. Variability in wind speed is weak, and the shape of the PDF (as measured by skewness) bears little resemblance to that of the observed winds. Again, we see that the presence of large-scale weather plays a fundamental role in determining the character of near-surface wind speed variability.

Fig. 10.
Fig. 10.

As in Fig. 7, but without large-scale weather variability.

Citation: Journal of Climate 25, 18; 10.1175/JCLI-D-11-00321.1

The simulated PDF of near-surface stability and in the three perturbation runs with or without intermittent mixing at 0000 and 1200 LT are illustrated in Fig. 11. Clearly, the daytime distributions of near-surface stability and are not sensitive to the presence of intermittent mixing; at night, both the near-surface stability PDF and the SWS PDF are influenced by this mixing. The elongated tail toward large wind speeds is maintained by occasional large wind bursts due to intermittent increases in the mixing of momentum at the boundary layer top. These effects of the presence of intermittent mixing at the top of the boundary layer are not sensitive to the choice of FBN or FWN parameterizations of this process.

Fig. 11.
Fig. 11.

The simulated PDF of (top) near-surface stability and (bottom) bottom-level wind speed with no enhanced intermittent mixing in the inversion layer (dashed line), with the FBN parameterization (solid line), and with the FWN parameterization(dashed–dotted line) at (left) midnight and (right) noon. In this simulation .

Citation: Journal of Climate 25, 18; 10.1175/JCLI-D-11-00321.1

b. Asymptotic flux Richardson number

In section 5a it was shown that intermittent turbulence at the inversion affects the shape of boundary layer wind speed distribution. This effect can be influenced to some extent by the specified value of the asymptotic flux Richardson number in the turbulence scheme due to its control on the Prandtl number () in stable flows (see the online supplement, which describes the turbulence scheme). This quantity cannot exceed unity on theoretical grounds, and theoretical studies (Canuto et al. 2008; Kantha and Carniel 2009; Zilitinkevich 2010; Ferrero et al. 2011) suggest values in the range of 0.2–0.3, although large-eddy simulations (LESs) and results from observations suggest a broader range (Esau and Grachev 2007). Since this quantity is a specified parameter in our turbulence scheme, is set to 0.25 as the operational value but we have tested the sensitivity of our simulations to values up to unity.

In the perturbation runs discussed in sections 4 and 5a, is set as 0.25. For these simulations the nocturnal boundary layer is very shallow (between 10 and 30 m). An intermittent turbulence source near the top of the inversion primarily reduces the vertical gradients in the wind speed and standard deviation (Figs. 7 and 9). Although qualitatively similar behavior occurs for other values of , there are modest quantitative differences. When is larger, the Prandtl number is relatively smaller and the turbulent transfer of heat is relatively less inhibited. The simulated boundary layer becomes deeper (greater than 40 m). The potential temperature is reduced near the inversion, and its vertical profile becomes less stably stratified within the boundary layer (not shown). The surface wind speed distribution is also less skewed near the surface during the nighttime, and there is a smaller diurnal variation of the ratio of the wind power density in the bottom 100 m.

The sensitivity of the relationship between the intermittent turbulence source and thermal stratification to the choice of is illustrated in Fig. 12, which shows the simulated PDF of near-surface thermal stability () and with set as 0.25, 0.35, 0.5, and 1.0 in the evening (2000 LT) and earlier morning (0400 LT). In the evening the surface sensible heat flux is near zero and near-surface temperature inversion just begins to develop, with the being near unity. The simulated near-surface stability and land surface wind speed PDF show small differences among the four cases. In the earlier morning, the ground temperature becomes much colder than that of the evening, when the temperature inversion is fully developed. When is larger, the simulated stable boundary layer is deeper and the potential temperature profile becomes more well mixed within the boundary layer, as illustrated by the reduced near-surface thermal stability in the top panel of Fig. 12. As a consequence, the bottom-level winds are more strongly coupled with free atmosphere winds above, and the resulting wind speed distribution is characterized by slightly larger mean, broader scale in the early morning.

Fig. 12.
Fig. 12.

The simulated PDF of (top) near-surface stability and (bottom) bottom-level wind speed with set as 0.25 (solid line), 0.35 (dashed line), 0.5 (dotted line), and 1.0 (dashed–dotted line) at (left) evening (2000 LT) and (right) early morning (0400 LT).

Citation: Journal of Climate 25, 18; 10.1175/JCLI-D-11-00321.1

c. Vertical resolution

As is illustrated in Fig. 2, the near-surface wind speed PDF at Cabauw displays fine vertical structure. In particular, both the wind speed skewness and wind power density display large vertical gradients near the surface. The high vertical resolution of our standard simulations (six layers in the modified SCM in the bottom 200 m) is capable of simulating this fine structure. However, the standard-resolution version of the SCM (with two layers from the surface to 200 m) fails to capture both the phase and amplitude of the diurnal cycle of mean and standard deviation of wind speed (Fig. 13). The simulated nighttime skewness is well below the Weibull distribution value, and the daily maximum of wind power density is shifted from midday to the nocturnal jet period. This result clearly demonstrates the importance of sufficiently high vertical resolution for the accurate simulation of surface wind variability at Cabauw.

Fig. 13.
Fig. 13.

As in Fig. 7, but using the standard vertical resolution in the SCM.

Citation: Journal of Climate 25, 18; 10.1175/JCLI-D-11-00321.1

6. Discussion and conclusions

Long-term observations from both a global network of weather stations from 1979 to 1999 and wind tower records at Cabauw, the Netherlands, from 2000 to 2009 suggest a strongly diurnally varying SWS–PDF characterized by a Weibull-like daytime PDF and more skewed (above Weibull) nighttime PDF at the land surface; the observed boundary layer wind speed distribution also varies vertically, with fine structure within the boundary layer (Monahan et al. 2011). The focus of this study has been to simulate the observed diurnal variations of near-surface wind speed distribution and to explore the underlying physical mechanisms in the framework of a single-column model. The study has reached the following conclusions:

  • The basic features of the observed diurnal variation of surface wind speed PDF at the Cabauw site can be realistically simulated with the CanAM4 SCM in an idealized dry experiment.
  • The mixing associated with unresolved physical processes within the PBL inversion layer (represented here by enhanced intermittent mixing at the inversion) plays an important role in determining the shape of the diurnally varying wind speed distribution and the wind power density. This effect is moderately influenced by the choice of the asymptotic flux Richardson number, a parameter controlling the Prandtl number in stable flows.
  • High vertical resolution is required to simulate the realistic vertical structure of wind speed distribution in the wind turbine height range between 20 and 200 m.

It is worth noting that the recent work of Monahan et al. (2011) clearly illustrates the importance of representing unresolved physical processes in the boundary layer top inversion for the diurnal variation of surface wind speed distribution (particularly skewness). The nature of intermittent turbulence is shown to be important when thermal stratification is fixed in their highly idealized two-layer model. In this more comprehensive SCM analysis, in which near-surface thermal stratification is not fixed, its relationship with intermittent mixing in the inversion is shown to also play an important role in generating positively skewed wind speed distribution in the nocturnal stable boundary layer. These results suggest that the parameterization of unresolved processes in the boundary layer top inversion are important to better simulate surface wind speeds, surface heat fluxes, and extreme wind events.

The shape of the near-surface wind speed distribution and the diurnal ratio of wind power have been shown to be moderately sensitive to the choice of asymptotic flux Richardson number in this SCM study. This quantity, in reality a property of the turbulent flow regimes under consideration, is a specified parameter in the SCM turbulence scheme.

An understanding and better simulation of diurnally varying land surface wind speed distributions is important for realistic simulations of surface fluxes of energy, momentum, moisture, and aerosols in GCMs, and for better wind power resource management and weather forecasts. This study presents a first effort to produce a realistic simulation of the diurnal variation of the near-surface wind speed distribution in a SCM that includes processes typically included in GCMs and to explore physical mechanisms underlying the observed basic features of higher-order moments of wind speed distributions and the diurnal evolution of wind power over land. The treatment of enhanced intermittent mixing at the inversion is highly simplified. As noted above and illustrated in Fig. 11, both versions of the stochastic parameterization for this process produce similar results. However, a more physically based representation of this apparently important process is desirable and this is now under investigation for future work.

Acknowledgments

The authors thank the two anonymous referees for their helpful comments regarding this manuscript. This research is supported by the Mathematics of Information Technology and Complex Systems (MITACS) project supported by Simon Fraser University and Ouranos, and the cloud–aerosol feedbacks and climate (CAFS) network supported by CFCAS. The global weather station data are kindly provided by Dr. Aiguo Dai of NCAR. N. McFarlane also acknowledges support from Environment Canada for his contribution to this work. A. Monahan gratefully acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada.

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