Geophysical Research Letters

On the surface wind speed probability density function over complex terrain



[1] The physical mechanisms determining the shape of the surface wind speed probability density function over complex terrain are investigated using observations from a dense mesoscale network and a high spatial resolution mesoscale simulation for the 1992 to 2005 period. Results indicate that the atmospheric stability plays a major role in controlling the shape of the wind speed distribution but its effects are strongly modulated by the contribution of different atmospheric scales of motion such as the mesoscale or synoptic scale. The local topographic features further modulate the relative contribution of each mechanism. As a consequence of the complicated interaction of these atmospheric processes the surface wind speed distribution can present a complicated shape that is not always expected to fit a unimodal Weibull type distribution over complex terrain regions.

1. Introduction

[2] Understanding the surface wind speed probability density function (PDF) is important for quite different purposes. The surface fluxes of heat, moisture and momentum are ultimately related to the intensity of the near-surface wind, and thus the shape of the surface wind speed PDF largely conditions the land-atmosphere interactions. The increasing number of wind energy facilities can also benefit from an improved understanding due to the strong dependence of the electricity production on the surface wind resource [e.g., García-Bustamante et al., 2009]. Indeed, the first studies oriented to analyze the shape of the wind speed PDF were performed for wind energy applications [e.g., Hennessey, 1977; Stewart and Essenwanger, 1978; García et al., 1998]. Special emphasis was given to find the mathematical function that best fits observed wind distributions. The unimodal Weibull distribution is generally accepted to provide the best fit [Carta et al., 2009].

[3] The physical mechanisms responsible for the characteristics of the surface wind speed PDF have received less attention. Crawford and Hudson [1973] indirectly showed that the surface wind speed PDF over flat terrain should reflect the influence of two regimes associated with the atmospheric stability. The wind speed is higher during the day due to the downward transport of momentum associated with convective mixing, whereas it is lower during the night since this transport ceases with the suppression of convection. Hence, one should expect the existence of two regimes in the surface wind speed PDF, one associated with stable nighttime conditions and the other with unstable daytime conditions. Only recently, this expected behavior has been confirmed and the shape of the PDFs under the different regimes examined [He et al., 2010]. The wind speed PDF is more positively skewed during the night than during the day which has been attributed by Monahan et al. [2011] to the effects of nocturnal intermittent turbulence. During the day, the PDF shows a more Weibull like behavior [He et al., 2010; Monahan et al., 2011].

[4] Our current understanding of the surface wind speed PDF is therefore limited to physical processes operating in an unidimensional atmosphere. This provides us with a basic knowledge over homogeneous terrain. Considering the surface heterogeneity is expected to generate additional physical processes which may produce impacts on the shape of the wind speed distribution. For instance, the differential heating of the ground that occurs over complex terrain regions is able to generate thermally driven circulations [Whiteman, 2000]. No attempt has been previously made to evaluate the impacts that these kinds of mesoscale circulations exert over the surface wind speed PDF.

[5] Here we use surface wind observations from a dense mesoscale network with records available form 1992 to 2005 [Jiménez et al., 2010b] combined with long term fine spatial scale, 2 km, regional modelling to inspect the characteristics of the surface wind speed PDF over complex terrain. The target of the investigation is to understand the impacts that the different physical mechanisms produce on the PDF. Our results indicate that atmospheric stability plays a major role controlling the shape of the PDF but its effects are strongly modulated by the contribution of the different atmospheric scales of motions. The specific topographic features further modulate the relative contribution of each physical mechanism.

2. Data

[6] The surface wind observations were acquired from 1992 to 2005 over a complex terrain region located in the Northeast of the Iberian Peninsula (IP, Figure 1a). The original observations were quality-controlled [Jiménez et al., 2010b] and the 34 locations with the wind sensor located at 10 m above ground level (AGL) selected for this investigation. The quality-controlled observations consist of averaged samples every 10-min or 30-min but hourly averaged values are used herein. A large portion of the stations are located in the southern plains of the broad Ebro valley or in the narrower valleys in the more complicated areas of the North (circles in Figure 1a). In addition, there are a couple of stations installed over hills (diamonds in Figure 1a) and a total of six on mountain tops (triangles in Figure 1a), places wherein wind observations are not usually available.

Figure 1.

(a) Location of the observational network [Jiménez et al., 2010b] within the IP. The red stars highlight the location of Santander and Tortosa whereas the blue square the location of Pamplona-Etsia. The number of peaks in the surface wind speed PDF for different samples of the observations are also shown: (b) the complete series, (c) daytime hours, (d) nighttime hours, (e) daytime hours under strong and weak synoptic situations, and (f) nighttime hours under strong and weak synoptic situations. A small (large) circle indicates the presence of one (two) peak(s) in the PDF whereas a medium circle indicates an intermediate behavior. The colors in Figures 1e and 1f highlight the contribution of strong or weak synoptic situations at those sites where the two PDFs present different shapes (see legend in Figure 1e). Sites located over mountain (hill) tops are represented in black (gray) whereas locations in plains or valleys are represented in white.

[7] In spite of the good sampling of the wind over the area, the observations are complemented with a high spatial resolution, 2 km, numerical simulation performed with the Weather Research and Forecasting model (WRF) [Skamarock et al., 2008]. The numerical experiment follows [Jiménez et al., 2010a]. The simulation spans the complete observational period (1992–2005) with the output recorded every hour in order to mimic the observational data set. Data from the ERA-Interim reanalysis project [Dee et al., 2011] was used as initial and boundary conditions. The ability of the WRF model to reproduce the daily wind variability over the region has been shown by Jiménez et al. [2010a] where the interested reader is referred to for further details on the dynamical and physical settings.

3. Results

[8] The surface wind speed PDFs reveal a clear influence of the topographic features. Sites located at plains and valleys can present either a clear unimodal (27%) or bimodal (46%) PDF (white circles in Figure 1b). On the contrary, mountain sites tend to present a unimodal PDF and hills a less clear structure (black and gray circles in Figure 1b). Some representative PDFs are shown in Figure 2 (black lines). The mountain station El Perdón (16) clearly shows a unimodal distribution (Figure 2a). Five of the six mountain sites show a similar wind distribution, the only exception being Ujué (37) that seems to present two maxima in a similar way as the stations located on hills. Bardenas-Loma negra (7) is a clear example of the hill behavior (Figure 2c). The PDF shows a flatter peak which indicates the presence of two wind regimes. The valley station at Doneztebe (15) shows an unimodal PDF (Figure 2b) whereas Pamplona-Noain (28), also located in a valley, shows a bimodal distribution (Figure 2d).

Figure 2.

Wind speed PDF at station (a) El Perdón (16), (b) Doneztebe (15), (c) Bardenas-Loma negra (7) and (d) Pamplona-Noain (28) for the complete observational period, the diurnal hours as well as the nocturnal hours (see legend). The wind speed bin is 0.1 m s−1.

[9] The presence of two maxima in some of the PDFs logically poses the question of identifying the physical mechanisms responsible for each circulation regime. The following subsections analyze the influence produced by the atmospheric stability (section 3.1) and different atmospheric scales of motion (section 3.2).

3.1. Stability Effects

[10] A potential explanation for the bimodality of the PDFs could lie in the different stability regimes that occur during the day and the night [Crawford and Hudson, 1973; He et al., 2010; Monahan et al., 2011]. It could be argued that the more intense regime is associated with the daytime convection and its downward transport of momentum, and the weaker one with the nocturnal stable regime dominated by the damping of turbulence. In order to explore this possibility, the wind speed observations at a given location are split into diurnal hours (8 to 15 UTC) and nocturnal hours (20 to 4 UTC). The nocturnal and diurnal hours were defined using observations of the solar insolation in order to guarantee the validity of the definitions for the whole year. In general, the subdivision into stable and unstable regimes does not discriminate the two peaks of the PDFs since many stations still show a bimodal distribution during the day (46%, Figure 1c) and/or during the night (35%, Figure 1d).

[11] However, important effects become evident in the PDFs of both stability regimes. Figure 2 also shows the PDFs calculated with the diurnal and nocturnal periods for the set of representative locations (red and blue lines, respectively). The mountain station shows unimodal distributions in relatively good agreement with each other (Figure 2a). A closer examination reveals that the distribution associated with daytime observations is somewhat displaced towards lower wind speeds. The other stations located at mountain tops also share this characteristic which becomes clearer at the stations located on hills (e.g., Figure 2c). The plain and valley stations show the opposite behavior with stronger winds during the day (e.g., Figures 2b and 2d). This differentiated behavior is ultimately related to the mixing that occurs during the day that tries to homogenize the PBL properties being responsible for an increase (decrease) of momentum at the less (more) windy sites [Yu et al., 2009]. Hence, topography is responsible for an important modulation of the effects produced by the atmospheric stability in the surface wind speed PDF.

[12] It is interesting to notice that the unimodal PDF recorded at station Doneztebe (15) is actually the composition of two unimodal distributions associated with each stability regime (Figure 2b). The nocturnal PDF is more positively skewed than the diurnal one in agreement with the findings of He et al. [2010] and Monahan et al. [2011]. This is a characteristic of other valley/plain sites that showed a unimodal distribution of the wind speed (Figure 1b). However, many sites still show bimodality of the PDFs during the day and/or night; there being a clear example the PDFs at station Pamplona-Noain (28) shown in Figure 2d. The two regimes are not associated with changes in atmospheric stability, which indicates that other physical mechanisms are playing a significant role in determining the wind regimes at these sites.

3.2. Contribution of Different Atmospheric Scales

[13] A potential explanation for the bimodality of the PDFs (Figures 1b, 1c, and 1d) could be associated with the contribution of different atmospheric scales of motion. The relative importance of the synoptic scale over the region can be quantified in terms of the pressure gradient over the broad Ebro valley [Jiménez et al., 2009]. A strong positive (negative) pressure gradient, higher (lower) pressures in the headlands in the Atlantic ocean (A in Figure 1a) than at the valley mouth in the Mediterranean sea (M in Figure 1a), intensifies the northwestern (southeastern) circulations. Positive gradients are more frequent than negative ones leading to northwestern climatological flows [Jiménez et al., 2009]. On the contrary, a low pressure gradient indicates a weak synoptic situation that allows for the development of other kinds of circulations associated with the mesoscale.

[14] In order to investigate the relative contribution of these atmospheric scales, sea level pressure observations at Santander and Tortosa (red stars in Figure 1a) are used to compute the pressure difference (Δp) over the Ebro valley which is indicative of the intensity of the surface pressure gradient. Then, the daytime and nighttime wind speeds are split into two additional groups, one associated with weak synoptic conditions (∣Δp∣ < 3 hPa, 38% of the time) and the other with strong conditions (∣Δp∣ > 6 hPa, 30%). Figure 1e shows that there is not any site with two clear peaks in the daytime PDFs after the splitting. This indicates that the separation into strong and weak synoptic regimes is able to discriminate the two wind regimes of the PDFs. Except for a few observational locations, this is also true for the separation of the nocturnal PDFs into weak and strong synoptic conditions (Figure 1f). The one related to weak synoptic conditions is associated with a gap effect due to local topography. However, the sites showing a bimodal PDF during strong synoptic conditions show a certain spatial structure. These sites tend to be distributed in the narrow valley with a northwest to southeast orientation in the center of the region (Figure 1f). The origin of this behavior is inspected with observations at station Pamplona-Etsia (blue square in Figure 1a), located in this valley nearby station Pamplona-Noain (28). Pamplona-Etsia has been selected in spite of the shorter, and different, temporal coverage of the observations (2004–2009) due to the availability of temperature records at 20 cm AGL as well as 10 m AGL, that allows one to compute the Richardson number (Ri = equation image Δzequation imageequation image Δzequation image) in order to determine the stability within the atmospheric layer between the ground and the wind sensor (10 m AGL).

[15] The wind speed PDF at Pamplona-Etsia is shown in the inset of Figure 3a. Results from the WRF simulation (1992–2005) are also shown (inset in Figure 3e). The observed PDF shows a clear bimodal distribution (black line). These peaks are still present in the PDF of the unstable atmosphere (red line). The PDF associated with stable situations is more positively skewed (blue line). The WRF simulation is able to reproduce these characteristics although the PDF associated with stable situations is not as sharp as observations reveal. The wind speed PDF as a function of the synoptic situation and certain degrees of stability are also shown in Figure 3. For weak synoptic situations, both the unstable and stable observational PDFs show contributions to the weak wind speed regime (Figures 3a and 3b, respectively). The one associated with unstable situations shows higher wind speeds and a higher variance (Figure 3a) than the contribution of the stable situations (Figure 3b). The more unstable/stable the near-surface layer the weaker the wind speeds. For the case of strong synoptic situations there is a clear isolation of the more intense wind speed regime under unstable situations (Figure 3c). However, under stable situations both the weak and strong regimes are present (Figure 3d). This is in agreement with the tendency of the locations in the central valley, wherein Pamplona-Etsia is located (Figure 1a), to show a bimodal distribution under stable situations with strong synoptic conditions (Figure 1f). Figure 3d shows that the contributions to the regime associated with low wind speeds are related to very stable situations (Ri > 0.5), whereas the contribution to the stronger regimes are related to weak stability dominated by mechanical turbulence (Ri < 0.1) where the wind behaves more like the unstable counterpart (Figure 3c). This result indicates that for some strong synoptic conditions the surface wind speed can be weak due to a decoupling of the flow from upper levels associated with the strong enough stability near the ground. The WRF simulation is in a general agreement with the observations (Figures 3e3h) but tends to overestimate the wind especially under stable situations.

Figure 3.

Wind speed PDFs calculated with subsamples for stable/unstable and weak/strong synoptic situations of the (a–d) observations and (e–h) simulations at Pamplona-Etsia (blue square in Figure 1a). The stability is defined in terms of Ri. The colors represent additional sub-samples with different stabilities: the complete sub-sample (red), excluding weak situations (green, ∣Ri∣ < 0.1), excluding until moderate situations (dark blue, ∣Ri∣ < 0.2) and only including very stable/unstable situations (light blue, ∣Ri∣ > 0.5). The PDFs calculated with the complete series as well as stable and unstable situations in a similar way as in Figure 2 are also shown (inset in Figures 3a and 3e).

[16] The previous considerations indicate the existence of two wind regimes one associated with strong synoptic situations and the other with weak synoptic situations that modulate the effects of the atmospheric stability over the wind speed PDF. The higher spatial resolution of the WRF simulation is used to gain further insight of the physical mechanisms responsible for each regime. The wind field for those days with weak (∣Δp∣ < 3 hPa) and strong (∣Δp∣ > 6 hPa) synoptic conditions were averaged at the 00 UTC and 12 UTC and represented in Figure 4 (black arrows). The averaged observational fields are also shown (white arrows). The simulation is in a general good agreement with observations. This is especially the case for the strong situations, both 00 and 12 UTC, (Figures 4a and 4b). The pattern shows strong northwestern circulations as a consequence of the higher frequency of positive pressure gradients, the channeling of the flow that occurs over the Ebro valley and the intensification exerted by the strong gradient [Jiménez et al., 2009]. The flow shows a very different structure in the pattern associated with weak synoptic forcings (Figures 4c and 4d). The wind field at 00 UTC clearly shows the structure of thermally driven circulations (Figure 4c): down-slope winds in the different mountains that comprise the Ebro valley, the Pyrenees and other mountainous areas as well as down-valley wind in the Ebro valley. During the day (Figure 4d), the flow pattern reverses its direction and shows the mesoscale circulations associated with up-valley and up-slope wind in the Ebro valley as well as up-slope winds in the Pyrenees.

Figure 4.

Mean wind (arrows) at 00 UTC and 12 UTC for days with (a and b) strong and (c and d) weak pressure gradient during 1992 to 2005. The simulation (observations) are represented in black (white). For illustrative purposes, only one of every two (four) grid points of the WRF simulation are represented for the weak (strong) gradients. The topography is also shown (shaded).

4. Conclusions

[17] The combination of long term wind observations and a high spatial resolution numerical simulation have allowed us to investigate the influence that different physical mechanisms produce on the characteristics of the surface wind speed PDF over a complex terrain region. Both the effects of the atmospheric stability and the influence of the governing atmospheric scale of motion introduce noticeable impacts in the PDF. Strong synoptic situations, governed by large scale flow, tend to reduce the influence of stability effects over the surface wind circulations. However, the surface flow can be decoupled from upper levels under strong stable conditions, and the surface wind is weak in spite of the strong synoptic forcing. When the synoptic influence weakens, the motion is governed by mesoscale circulations induced by the heterogeneity of the terrain, being responsible for noticeable impacts in the surface wind speed PDF. Similar mechanisms are expected to operate in other complex terrain regions also characterized by important synoptic and mesoscale forcings [e.g., Bastin and Drobinski, 2006; Hughes and Hall, 2010].

[18] As a result of the complicated interaction between these atmospheric processes, the majority of the sites show a bimodal distribution, the only clear exception being those sites located at mountain tops well exposed to the large scale winds and therefore less affected by the surface physical processes. Hence, a unimodal Weibull type distribution should not be always expected to provide a good fit to surface wind speed PDFs over complex terrain areas. The two wind regimes can be present in both daytime and nighttime which indicates that the wind speed PDF over complex terrain departs from the broad consistency with a Weibull distribution that occurs during daytime at a global scale [Monahan et al., 2011]. The assumed shape of the PDF over complex terrain regions deserves special attention if it is to be used for wind resource applications, for example. Records from other mesoscale networks [e.g., Horel et al., 2002] can be used to further investigate these conclusions.


[19] The work was supported by projects CGL-2008-05093/CLI and CGL-2011-29677-C02 and was accomplished within the collaboration agreement 09/490 between CIEMAT and NCAR. NCAR is sponsored by the National Science Foundation. Special thanks to J. Vilà-Guerau de Arellano for his constructive comments.

[20] The Editor thanks the two anonymous reviewers for their assistance evaluating this paper.