Mountain wave and downslope winds impact on wind power production

Solbakken, Kine; Samuelsen, Eirik Mikal; Birkelund, Yngve

doi:https://doi.org/10.5194/wes-2025-95

Preprints

https://doi.org/10.5194/wes-2025-95

Preprints

11 Jul 2025

| 11 Jul 2025

Status: this preprint is currently under review for the journal WES.

Mountain wave and downslope winds impact on wind power production

Kine Solbakken, Eirik Mikal Samuelsen, and Yngve Birkelund

Abstract. Vertically propagating mountain waves, accompanied by strong downslope winds, occur frequently along the coast of Norway and cause accelerated surface winds on the lee side and downstream of the mountain. Mountain waves form when stably stratified air flows over a mountain and can potentially impact the power production in wind parks located in complex terrains. Although mountain waves and downslope windstorms have received significant attention within the meteorology community, they have received less focus within the wind energy industry. Taking advantage of wind and power production data from a grid of 67 wind turbines spread across two nearby mountains, this study documents accelerated wind speeds and enhanced power production on the lee side of the mountains compared to at the mountain crest. The result of this study suggests that considering mountain waves in the planning phase of future wind parks may allow for an optimal layout of the wind turbines and improve the profitability. The non-dimensional mountain height Ĥ, is a key parameter for describing the development of mountain waves, and this study finds a strong relationship between Ĥ and the accelerated downslope winds. The results of this study suggest that mountain-wave-induced accelerated downslope winds tend to occur in the wind park when Ĥ < 3, above this value, the airflow is more likely to be blocked and diverted around the barrier. Finally, the Weather Research and Forecasting model reproduces the spatial variations in the wind speeds within the two wind parks relatively well during periods of strong downslope winds and blocking. However, the differences in the wind speeds at the windward side, the mountain top, and the lee side, are not as pronounced as in the observations.

Received: 26 May 2025 – Discussion started: 11 Jul 2025

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Kine Solbakken, Eirik Mikal Samuelsen, and Yngve Birkelund

Status: final response (author comments only)

RC1:
'Comment on wes-2025-95', Anonymous Referee #1, 27 Jul 2025
General considerations
In this paper, the authors elaborate on the impact of downslope wind storms on wind speed at hub height and power production downwind of a hill or small mountain of some 550 m height. The results are based on two (close) wind parks with a total of 67 turbines in northern Norway. From a mountain wave perspective, this is not entirely new (and also not intended to be by the authors) but from a wind power perspective, this additional aspect for site selection certainly will add added value. The problem with the paper is, that the authors do not have ‘good’ data (the nacelle wind speed is certainly good for operational purposes, but of course constitutes a perturbed measurement per se (one places the instrument into the perturbation that one wants to observe…). So, basically the analysis has to rely on the modeling, the essential features of which are hard to validate (what really counts is the upwind stability (no observations available), the Scorer parameter as a function of height, the upwind topography (for different flow situations), i.e., the compatibility of the flow configuration with theoretical framework, of mountain waves. So, when relying on the model simulations (or having to rely) it would be desirable to see some more sensitivity analysis rather than demonstration of the occurrence at this particular site.
I have added some suggestions (major comments 1-3) how to possibly enhance the value of the existing simulations and also a major comment on which sensitivities could possibly be explored in more detail (major comment 4). All together, since there are quite numerous detailed comments and one or the other major comment needs to be properly addressed, I call this ‘major revisions required’.

Major comment
The SE events are selected (which is fine in principle). The WD sector, however, consists of a range (from about 165 to 140 degrees) where indeed the approach flow rises from sea level to the 550 m high ‘hill top’ (so, non-dimensional mountain height is certainly appropriate), while for the WD range 140-120 degrees, the flow is in fact descending from a much higher mountain (cluster of peaks) to zero (only a few km horizontal distance), then rising over an even higher area. From idealized (e.g.doi:10.3390/atmos8010013 ) (but also real) studies we know that in this situation wave interference may play a crucial role. Did the authors consider a distinction according to wind direction within the SE sector (I perfectly realize that wind direction variability may not allow for such a fine distinction – but maybe a tendency will be visible)?

I wonder whether the argument could not be turned around, by also selecting a number of NW flows (the upwind ERA5 grid point is also available, for the Scorer parameter and non-dimensional mountain height. Wouldn’t then A3 be the upwind and A1 the downwind site?

The case studies. These are presented and discussed in a way to demonstrate their point (which, by the way, is not so clearly worked out, especially for case study two…. Is the intention to demonstrate that ‘it is complicated’?). However, case study 1, for example, could possibly be used to elucidate some wind direction sensitivity. At about 2 pm on the 25^th (Fig. 8), the observed WD abruptly changes, but does only go to about 150 degrees, while the modelled WD also changes but reaches some 130-140 degrees). Thus, the observed flow seems to clearly come through the fjord, while the modeled flow, at least for some 3 hours, seems to be modified by the high mountains possibly interacting (also with wave activity). Maybe another cross-section (as Fig. 8d) could help to understand some of the flow behavior.

Sensitivity studies: more than the question, whether downslope windstorms occur (and hence must have an impact on with energy and power production), it will b of interest, how this can appropriately be modelled with a model like WRF. The authors have made a number of choices: 1) location of P1 (or: determine the background flow characteristics from an ERA5 grid point (and if so, which), or from an average of WRF grid points (and if so, which); 2) levels from which N is diagnosed; 3) depth of what I assume is meant to be the boundary layer; 4) neglection of the non-linear term in determining the Scorer parameter; 5) definition of the variability across the chosen WD sector. It is not that I would doubt the authors’ actual choices (they are at least not unreasonable), but there would be considerable added value from an sensitivity analysis (how sensitive are the results on this or the other choice?).

Detailed comments
l.88           as follows?
Fig. 1        wouldn’t it make sense to indicate which of the two is ‘A’ and which is ’B’?
l.141 I think the Brunt-Väisälä frequency may not be well known to the audience of this journal and should therefore be defined (including its meaning).
l.144 the equal sign should be replaced by ‘approximately equal’
l.155         ‘It is assumed that the airflow that interacts directly with the mountain is spanning from the surface and up to a height of about 1 km’: based on what is this assumption being made? Can the authors elaborate?
l.156         In the EAR5 specifications (https://confluence.ecmwf.int/display/UDOC/L137+model+level+definitions) the first model level (which is labelled 137) is at 10 m – and the second (which the authors probably mean) at 31.0 m. The level closest to 1000 m (l. 157) would then be #118 (which is ‘number 19’ from the surface).
l.158         according to the same specification from above, the model level closest to about 550 m, would be #123, which is the 14^th level from the surface
Fig.3, caption ‘from sea level (green) to 1500 m asl (white)‘: the figure (and the color bar‘ suggest that the color convention is the other way around....
l.182         ‚boundary conditions‘: what is the type of boundary conditions? The vertical (if the top level is at 50 hPa) is of particular interest. Also, is there any Rayleigh damping layer invoked, as it is usually found necessary to absorb reflection of gravity waves (e.g., Klemp et al. 2008, https://doi.org/10.1175/2008MWR2596.1)? A damping layer is quite standard the numerical investigation of mountain flows – and if the topic is mountain waves it seems particularly apropriate.
l.228         ...is the dominant mechanism....
l.233         ‚....remaining consistent‘: usually we add ‘(not shown‘) when citing such a finding that is not demonstrated.
l.272         considerably higher.
Fig 6         according to what was stated before, I assume that this is the distribution for only the SE events, right? My ‘doubt’ seems to show that it might be good to explicitly state this again.
Tab 2, caption: the statistical measures have to be attributed to WRF simulations. Also Bias and MAE have units (which must be given in the title row). This would also make it clear whether they refer to the capacity factor or to wind speeds.
l.283         ….’produce 51% and 21% more…’: I am not familiar with the capacity factor, but these percentages seem to be based on the respective lower value (a well-known way to make your increase to look bigger). Assuming that the capacity factor is somehow based on a maximum achievable amount, I think a more appropriate way to characterize the production increase would be 25% and 13%, respectively.
l.404         ‘….while underestimating….’: wouldn’t this suggest that WRF is not perfectly reproducing the waves (or the effect of the waves)?
l.320         at the end of this ‘model evaluation paragraph’, I am a little disappointed to see only ‘mean biases’, etc. If the claim is that the velocity differences are due to the formation of downslope windstorm conditions, wouldn’t it be interesting to investigate whether the critical level has formed (we can get that from the model….) – maybe even with a distinction of different cases (e.g., wind direction sectors, see above, but also strong vs not so strong underestimation)?
Fig. 9 caption: ‘….the dotted contours….‘ should read ‘the gray solid contours. Also: ‘….indicated by the dotted line in the figure c)’ should read ‘indicated by the full line in panel c)’.
l.405         again the dashed grey contour lines…
l.407         the units for wind speed are m per seconds, not meters per seconds squared
l.413         not a dotted line….
l.415/417 again wrong units for wind speed
Fig.10, caption : please indicate which hours are displayed in panel a)
l.434         in a similar manner as ….
l.454         winds speed units…..also l.459, l.460
l.470         the amplitude of what is growing? And the sentence does not seem to be complete… what is ‘and upstream tilting’ referring to? The amplitude is tilting upstream?
Citation: https://doi.org/10.5194/wes-2025-95-RC1
RC2:
'Comment on wes-2025-95', Anonymous Referee #2, 29 Jul 2025
Introduction
This manuscript examines hub-height wind speed and power production data from two wind farms located in moderately complex terrain in Norway, and documents the link between lee-side wind acceleration and environmental properties supportive of mountain wave propagation. Some evidence of the match between observations and simplified linear mountain wave theory is presented: for instance, lee-side acceleration is often observed when the dimensionsless mountain height NH/U exceeds one. This is hardly a novelty from a mountain meteorology or mesoscale meteorology standpoint, but I might agree that the implications for wind energy harvesting went unnoticed so far. The manuscript also evaluates the ability of state-of-the-art hindcast simulations, performed with the WRF model at 750 m grid spacing, to resolve the lee-side acceleration. The model apparently captures the observed wind variability, but not entirely. For instance, lee-side acceleration in the simulations is less pronounced than in reality. The accuracy of numerical simulations is evaluated over a long hindcast run (about 4 months), and two day-long case studies are also presented.
Recommendation
The study contains a good initial review of literature on mountain waves (lines 27-48), which however contains some imprecise statements and misunderstandings, and lacks some fundamental concepts; accordingly, results based on the dimensionless mountain height NH/U and on the Scorer parameter are sometimes inappropriately discussed (see comments 1-8). The analysis of wind speeds and power production data is convincing, although some aspects could be improved (see comment 9). The global analysis of the accuracy of WRF simulations is thin (Figure 6b, Table 2), but the contents are seemingly solid. The purpose of the two case studies is not explained anywhere; they don’t really add much to the scientific content; most importantly, some statements in the case study discussions are gross misinterpretations (see comments 8-9). Finally, some technical aspects of the simulations are debatable (see comments 11-14). All considered, I would recommend requesting major revisions before considering publication.
Major Comments

NH/U is an important quantity, but in a specific context: it serves as a nonlinearity parameter for linearly stratified flow with uniform wind speed (constant U and N). Yes, the critical value above which upstream blocking and leeside acceleration are expected is of order 1, and somewhat dependent on the geometry of the orography; but this concept only applies to flows that match reasonably well the constant N-constant U assumption. Real-world flows over mountains display extreme horizontal and vertical variability of wind speed, direction and stratification, so NH/U is generally not such a good predictor as one might expect.

Whenever a low-level inversion is present, concepts based on shallow-water flow are usually a lot more useful than internal gravity wave theory with constant N-constant U. Sometimes, downslope windstorms are caused by the transition from subcritical to supercritical conditions in "hydraulic" flow, capped by a strong inversion which acts as a density discontinuity. Here, sub- and super-critical refer to the shallow-water Froude number, Fr=U/sqrt(g'H). See for instance Durran (1990).

Although the definition of NH/U seems straightforward, this parameter is not easily evaluated. See Reinecke and Durran (2008).

Another relevant aspect totally ignored in this manuscript is that, besides mountain height, mountain width matters too. In analogy to NH/U, it is possible to define a dimensionless mountain width NL/U, where L is the mountain half-width. Mountain wave response is known to be affected by NL/U as much as by NH/U (see for instance Sachsperger et al 2015). NL/U serves as a hydrostaticity parameter. By ignoring NL/U, this study implicitly assumes that waves always propagate nearly hydrostatically. This might not be true in general. Although, indeed, strongly stratified flow over a broad mountain is likely hydrostatic. The reason why NL/U and hydrostaticity are important is that, for sufficiently small NL/U, the maximum wind speed in cross-mountain flow occurs at mountain top, not on the lee slope.

Similarly to NH/U, the Scorer parameter is an important parameter in a specific context. It is relevant for the description of wave trapping, i.e., horizontal propagation of resonant gravity waves within a wave duct. The Scorer parameter is really useful if one wants to show that variable stratification, wind shear, or wind curvature, lead to lee wave trapping; but trapped lee waves are not discussed anywhere in this manuscript! Herein, the Scorer parameter seems to be used only as an indicator of the presence of a mean-state critical level in the wind profile (U=0, or unbounded Scorer parameter; Fig. 7 and 10). However, wave breaking in the two case studies is visibly not caused by a mean-state critical level. All in all, there seems to be no good reason to use the Scorer parameter in this study. Note also that, if wind shear and curvature are neglected, the Scorer parameter (N/U) and the dimensionless mountain height (NH/U) carry essentially the same information.

Lines 240-256 are rather speculative, and I would recommend reducing them. I think it is fine to say simply that real-world measurements are likely to deviate (even a lot) from expectations based on linear theory. If the environment is heterogeneous in terms of N and U, there's no reason why linear theory predictions should hold. For instance, a very stable surface layer leeward of the mountain (=strong vertical variability in N), might prevent a downslope windstorm from reaching the foothills.

The authors seem to interpret lee-side wind acceleration and blocking as distinct phenomena; instead, they are closely related. Dynamically, blocking is caused by a large pressure maximum upstream of the mountain, while lee-side acceleration is caused by a large pressure minimum downstream of it. In constant N-constant U flows, large pressure perturbations upstream and downstream of a mountain occur in the same conditions (NH/U>1). See for instance the introductory review by Serafin (2025).

Line 278 (“low wind speeds at A3 can be due to blocking of the air flow”) and the whole discussion in Sec. 3.3.2: Orographic blocking occurs upstream of a mountain, not downstream of it. More likely reasons for low wind speeds on the lee side are the presence of a shallow and very stable surface layer (which would impede the penetration of downslope winds down to the level of A3 turbines); or wake effects such as in atmospheric rotors. Superficially, the spatial distribution of wind speed in Fig 12 is reminiscent of the flow structure often observed in Bora flow, with weak winds leeward of the highest mountains. See for instance Fig 11 in Gohm et al 2008 or Fig 12 in Gohm and Mayr 2005.

Please describe the rationale for the choice of the case studies. It is really not clear. It looks like the dynamics are understandable based on simple theory in case 1, while they are not in case 2.

Figure 5 represents only data points from SE wind events. One might still argue that wind speeds at A3 could be higher than at A2 or A1 for reasons unrelated to leeside acceleration; so the normalized wind speeds A3/A2 and A3/A1 could be >1 even if the wind at P blows from directions other than SE. Does the distribution of normalized wind speed look substantially different for other directions? Could one check similar ratios for NW flow? I think the information could be easily added to this Figure.

Line 137: ERA5 profiles at point P. Judging from Fig. 3, point P is well within the highest-resolution WRF simulation domain D03. If the purpose is to evaluate the ability of WRF to reproduce downslope windstorms and their impact on power production, I really do not understand the reason why the properties of the upstream environment are drawn from ERA5 instead of WRF. Leeside flow properties in WRF simulations should be more closely linked to upstream profiles from the same simulations, than to ERA5 upstream profiles (a different model, with much coarser spatitial resolution).

Judging from Fig. 1, the area of the two wind parks is about 10 km across. At 750 m resolution, this means about 13 grid points. This is marginally adequate to resolve atmospheric variability within the area, especially considering that the effective resolution of a NWP model is usually at least 7dx. This means that all variability at shorter scales is severely damped by the dynamical core of the model, in order to preserve numerical stability (see e.g. Skamarock 2004). This likely explains why the simulations presented here do not resolve much the of observed variability in the wind.

The WRF orography is drawn from the GMTED digital elevation model. The maximum resolution of this DEM is 7.5 arc seconds (about 230 m), but I think the version available in the WRF pre-processing system is at 30 arc seconds (about 1 km). Again, this is marginally adequate.

Lines 182-184 explain that the hindcast simulations are actually 8 days long, and are connected by some kind of “interpolation”. What kind of interpolation is alluded to here? Is it a weighted average between the two simulations, with weights changing over time? Please specify better. I understand that the authors do this in order to ensure that the WRF simulations do not drift away from the ERA5 analysis fields over a 4-month long simulation. However, I have never seen a solution based on interpolation before. Weighted averages of different weather forecasts are notoriously rather unphysical. The state-of-the art technique to prevent drifting is spectral nudging (see e.g. Waldron et al 1996 and Liu et al 2012). I personally find this a severe shortcoming in experiment design, but I concede that it only affects about 7% of simulated period (12 hours every week).

Minor comments

Lines 34-35: Speaking of "fast propagating lee waves" is potentially very misleading. Mountain waves and lee wave fronts propagate opposite to the mean flow, and therefore they are generally stationary. Fast variations in local atmospheric properties near mountain or lee waves are most often not caused by wave "propagation", but by nonlinear wave interactions (Nance and Durran 1998), or by the transient phases (wave onset/demise) in non-stationary flow (Nance and Durran 1997, Grubisic et al 2015).

Line 41: More precisely, locally reversed air flow near the surface is typical of atmospheric rotors. These may or may not be connected with a hydraulic jump (e.g. Hertenstein and Kuettner 2015). Convective overturning and reversed flow connected with a hydraulic jump typically do not occur near the surface.

Line 60: This is strange wording. Static stability is a physical property of the atmosphere, so "various static atmospheric stabilities" sounds just as strange as "various atmospheric pressures".

Line 95: “Straits” instead of “straights”?

Line 98, and elsewhere: please add a blank space between “m” and “s”; “ms” means milliseconds.

Line 117: “Winds from SE are considered”. I presume this refers to hub-height winds. Wind direction changes with height, and the manuscript makes abundant use of concepts form 2D (x-z) mountain wave theory; so it would be important to make sure that the flow is reasonably 2D, that is, without large directional shear. Is this feasible, with the data at hand?

Line 166: Horizontal resolutions of 10.5 km, 3.5 km, and 750 m. Is this correct? Nesting ratios in WRF must be integer numbers, preferably odd integers. 10.5/3.5 = 3, which is fine. But 3500/750 is 4.6666, which is not fine. Could you please verify?

Line 204: “conditions in which both mountain waves might grow and break, as well as being dissipated at a critical level”. I don't understand this distinction. Mountain waves "grow" and "break" even at a critical level. Dissipation (deposition of the wave kinetic energy into the mean flow) is a consequence of breaking.

Line 272: “considerably” instead of “considerable”.

Line 346: “Several factors may impact the accuracy of the model simulations”. I find it awkward to begin this discussion with an impact of microphysics parameterizations. Yes, microphysical schemes might be relevant (especially if the flow is often saturated), but they are certainly not the primary factor that comes to mind. Besides the aforementioned marginally adequate resolution of the numerical grid, I report two more factors that are most likely a lot more relevant than microphysics: 1) Surface friction parameterization, e.g. Richard et al 1989; 2) Predictability; small changes in upstream conditions can cause very large deviations in leeside response, especially in nonlinear flow regimes e.g., Reinecke and Durran 2009.

Lines 404-421: A lot of text in this paragraph describes the graphical elements of Figure 9, and should therefore be reported in the figure caption.

Line 420: “This is in accordance with the Scorer parameter in point P”. It is really an excellent match with theory, but the description doesn't really explain why and could be more precise. Citing from Serafin 2025: “If N and U are nearly uniform and NH=U is supercritical, wave-breaking tends to occur at altitudes between 1/2 and 3/4 of the vertical wavelength (2piU/N in the hydrostatic limit)”. Neglecting the curvature term in the Scorer parameter, I roughly assume N/U=3*10^-3 (Figure 7a). This maps to a vertical wavelength of 2100 m. Therefore, wave-breaking is expected between 1000 and 1500 m, which matches Fig 9d very well.

Line 484: “Strong relationship”. I presume this statement alludes to Figure 5. It does not look like a "strong relationship". The Pearson correlation coefficient of the relationships between A3/A2, or A3/A1, and NH/U is not displayed, but is likely quite low (for good reasons, as extensively explained above).

Figure 1: Please add a latitude-longitude grid, to make it more comparable with Fig. 2 and 3

Figure 2: Please add a bar scale to the map, so that actual distances can be clearly understood. I would also recommend adding a second panel with the resolved model orography.

Figure 4: I would recommend showing also the variability of the profile, e.g. mean plus-minus standard deviation, or horizontal whiskers between 10th and 90th percentile. I presume the variability will be quite large.

References
Durran 1990: https://doi.org/10.1007/978-1-935704-25-6_4.

Gohm and Mayr 2005: https://doi.org/10.1256/qj.04.82

Gohm et al 2008: http://doi.wiley.com/10.1002/qj.206

Grubisic et al 2015: https://doi.org/10.1175/JAS-D-14-0381.1

Hertenstein and Kuettner 2015: https://doi.org/10.1111/j.1600-0870.2005.00099.x

Liu et al 2012: https://doi.org/10.5194/acp-12-3601-2012

Nance and Durran 1997: https://doi.org/10.1175/1520-0469(1997)054%3C2275:AMSONT%3E2.0.CO;2

Nance and Durran 1998: https://doi.org/10.1175/1520-0469(1998)055%3C1429:AMSONT%3E2.0.CO;2

Reinecke and Durran 2008: https://doi.org/10.1175/2007JAS2100.1

Reinecke and Durran 2009: https://doi.org/10.1175/2009JAS3023.1

Richard et al 1989 https://doi.org/10.1175/1520-0450(1989)028%3C0241:TROSFI%3E2.0.CO;2

Sachsperger et al 2015: https://doi.org/10.1002/qj.2746

Serafin 2025: https://doi.org/10.1016/B978-0-323-96026-7.00123-5

Skamarock 2004, https://doi.org/10.1175/MWR2830.1

Waldron et al 1996: https://doi.org/10.1175/1520-0493(1996)124%3C0529:soasfa%3E2.0.co;2
Citation: https://doi.org/10.5194/wes-2025-95-RC2

Kine Solbakken, Eirik Mikal Samuelsen, and Yngve Birkelund

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Short summary

Mountain waves can form when air passes over a large barrier and can cause strong winds on the lee side. Understanding how these strong downslope winds impact wind power production can help improve wind park efficiency. We have studied two wind parks in Norway and found that the turbines on the leeward side of the mountain produce more power than the turbines on the mountain top. This study also investigates how weather models can help predicting when and where strong downslope winds may occur.


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