We investigate several lidar-type instruments and methodologies for boundary layer height (BLH) estimation during 2 days at a coastal site for winds that experience marine upstream flow conditions. Wavelet and profile fitting procedures on the aerosol backscatter signals from a ceilometer and an aerosol lidar reveal similar BLHs, but their agreement depends on the presence of clouds and the instrument signal, among others. BLHs derived by a threshold on the carrier-to-noise profiles of a wind lidar agree well with those derived by using a threshold on the backscatter profile of the ceilometer and are used as reference for a 10 day BLH intercomparison. Furthermore, the BLHs from the aerosol analysis are comparable to those derived from wind speed and direction profiles from combined mast/wind lidar measurements. The BLH derived from simulations performed with the Weather Research and Forecasting (WRF) model shows similar behavior compared to the lidar observations. The seasonal diurnal variation of the BLH for 2010, derived from the wind lidar and ceilometer thresholds, shows similar BLHs but generally higher values compared to that from WRF. No clear BLH diurnal variation is observed neither from the observations nor from the WRF model outputs, except in summer for the latter. Both observations and WRF model simulations reveal higher BLHs during autumn compared to spring time. These BLHs are used to evaluate the intra-annual variation and show high peaks in September, November, and February.
 The boundary layer height (BLH) determines the depth of the troposphere directly influenced by the Earth's surface (Stull, 1988). As pointed out by Beyrich and Leps , this “simple” definition does not reflect the complexity of the BLH estimation because the variables used to detect the BLH behave differently in the planetary boundary layer (PBL) and are differently influenced by the processes within it. In the dispersion community, the related term mixing height (MH) is commonly employed and refers to that “height of the layer adjacent to the ground over which pollutants or any constituents emitted within this layer or entrained into it become vertically dispersed by convection or mechanical turbulence within a time scale of about an hour” [Seibert et al., 2000]. In our study, the methods used for BLH estimation are nearly the same as those for MH detection and we will here be using the term BLH. It is also important to mention that the MH often coincides with another commonly used term, the mixed layer height, but the first is preferred since under stable conditions complete mixing might not be reached.
 The BLH influences the flow characteristics of the PBL, becoming more significant the higher we observe above ground level (AGL). With the advancement in boundary layer and wind power meteorology, and with the growth of wind turbines and structures, the need to estimate and measure meteorological parameters, other than wind speed and direction, has become more important. However, the effect of the BLH has not yet been fully investigated neither in the wind energy community nor in the meteorological one.
 The BLH has a significant impact on the shape of the vertical wind speed profile already at heights around 100 m [Gryning et al., 2007; Peña et al., 2010b] and even lower when the atmospheric stratification becomes stable [Peña et al., 2008] or when low-level jets occur [Källstrand, 1998; Banta et al., 2002]. In such conditions, the vertical wind shear might jump from being positive to negative within a few meters of height, which has a strong impact on the loading on structures. Analytical models of the vertical wind speed profile, which take into account the BLH and are consistent with the commonly used logarithmic wind profile within the first tens of meters AGL, have already been developed and are in good agreement with observations from tall meteorological masts and combined mast/remote-sensing measurements [Gryning et al., 2007; Peña et al., 2008, 2010b]. However, there is still a lack of simultaneous wind speed, turbulence, and BLH measurements for better wind speed prediction and model verification. A problem of using models involving the BLH in wind power meteorology, for example, is that it is not observed when performing wind resource assessments in which 10 min averaging periods are normally used. Accurate and long-term BLH measurements are performed with soundings launched every hour in the best of the cases. However, this is not optimal because the BLH might fluctuate in much shorter periods [Beyrich and Gryning, 1998].
 The BLH is also interpreted in different fashions and estimated using different techniques, which increases its uncertainty and the reluctance of its implementation in models. Common sources for the derivation of the BLH are surface turbulence measurements [Seibert et al., 2000], turbulence profiles [Frehlich et al., 2006; Lothon et al., 2009], temperature and humidity profiles [Seidel et al., 2010], spectral characteristics [Højstrup et al., 1997], remote-sensing instrumentation such as sodars, aerosol lidars, ceilometers, RASS, wind-profiling radars, and soundings [Cohn and Angevine, 2000; Münkel et al., 2007; Emeis et al., 2008], GPS occultation [Xie et al., 2012], and numerical models [Gryning and Batchvarova, 2002] that give different estimates, since aerosols, turbulence, temperature, and fluxes do not have the same dynamic behavior in the atmosphere. Further, vertical profiles, and their derivatives, of atmospheric properties and variables that are used to derive the BLH such as aerosols and temperature show different characteristics such as maxima, minima, and inflection points, which give different estimates of the BLH.
 Here, we illustrate 2 days in which the BLH has been estimated using different instruments and techniques at a coastal site in western Denmark under marine upstream conditions: (1) a long-range wind lidar, which measures wind speed and direction up to 2 km and that can be used to derive the BLH by analyzing the vertical profiles of wind speed, direction and carrier-to-noise ratio (CNR); (2) an aerosol lidar, which measures aerosol concentration profiles allowing BLH estimation by using different retrieval methodologies; (3) a ceilometer, which under conditions of high atmospheric aerosol concentration can measure the aerosol profile; and (4) numerical weather prediction (NWP) model simulations. Based on measurements of these 2 days, we intercompare a number of BLH estimates and analyze which instruments and methodologies show the best agreement under the given conditions for 10 days. The robustness of the ceilometer and wind lidar units allows us to study long-term observations of the diurnal, monthly, and seasonal variation of the BLH at this coastal site and their agreement with long-term NWP model simulations.
 The paper first presents the site, measurements, and model data in section 2. The methods for BLH estimation are explained in section 3. Section 4 presents the results for the BLH estimations for both days, as well as the intercomparison between instruments/methodologies for the 10 days and the diurnal, monthly, and seasonal BLH variation. Discussion and conclusions are given in the last two sections.
2 Site, Measurements, and Model Data
 The measurements were performed at the National Test Station for Wind Turbines at Høvsøre, Denmark, close to the west coast of Jutland (Figure 1). The station is located at 2 m above mean sea level (AMSL). Høvsøre is a flat and homogeneous farm area with the largest flow perturbations given by the change of roughness at the coastline.
 From the point of view of the test station (illustrated in a circle in Figure 1), the dominant wind direction is west, i.e., winds come directly from the North Sea, which we restrict to the range 225°–315° for capturing the coastal flow. The meteorological mast at the test station is located 1.7 km east of the coastline. Therefore, within the first ∼ 20 m AGL at the station (hereafter all heights are referenced to as AGL unless stated otherwise), westerly winds are in equilibrium with the land surface; at ∼ 70 m, the wind speed profile shows a distinct kink from the combined sea-land transition layer and above the offshore wind profile prevails. These numbers are characteristic for atmospheric neutral conditions; an overview of the flow modification due to the internal boundary layer (IBL) at Høvsøre is given in Floors et al. . Because of the sea-land transition, the west sector relative to the mast is considered as inhomogeneous whereas the east sector as homogenous (there are only few scattered trees and houses on this farm area).
 In this study, measurements and estimates of the BLH come from two different types of sources: (1) wind speed and direction measurements, where combined mast and wind lidar 10 min mean data are used to analyze vertical profiles of wind speed and direction; and (2) aerosol measurements from three different types of lidars, where a wind lidar, an aerosol lidar, and a ceilometer are used to analyze the 10 min mean aerosol profile.
2.2.1 Meteorological Mast
 A 116 m height tall meteorological mast is heavily instrumented at the Høvsøre test station and provides observations of wind speed, temperature, and turbulent fluxes at different levels since its erection in 2004. Here we use wind speed and direction observations from Risø cup anemometers at 10, 40, 60, 80, 100, and 116.5 m and wind vanes at 10, 60, and 100 m, with both types recorded at 10 Hz. Other details about the mast and its instrumentation can be found in Jørgensen et al.  and Peña . The mast is mostly within the IBL generated by the coastline for westerly winds.
2.2.2 Wind Lidar
 A wind lidar (a WLS70 WindCube from the company Leosphere) was installed ∼ 10 m away from the meteorological mast at Høvsøre and operated during the period April 2010 to March 2011. The WLS70 is a pulsed system, which measures the line-of-sight or radial velocity for four azimuthal positions separated by 90° in the horizontal plane and 15° with the zenith. The laser is operated at a wavelength of 1.5 μm, and due to its relative long pulse length (400 ns with a pulse energy of 20 μJ), it can reach up to 2 km, depending on the aerosol content in the atmosphere. Reported values depend on the threshold set for the CNR, which was left equal to the default value ( − 35 dB). The instrument measures near-simultaneously at all heights from 100 m, every 50 m at an acquisition rate of ∼ 10 s for each azimuthal position. The measurement volume at each height extends ∼ 60 m in the line-of-sight.
 Although the wind lidar is programmed to measure wind speeds at different heights, as a “traditional” lidar, its capabilities depend on the amount of aerosols in the atmosphere. In this study, we use the CNR outputs of the system as a measure of the aerosol backscatter at each height.
2.2.3 Aerosol Lidar
 An aerosol lidar (an ALS300 system also from the company Leosphere) was installed next to the wind lidar at Høvsøre and operated during the period April to June 2010 only. The ALS300 is also a pulsed system operating at a wavelength of 355 nm, retrieving aerosol backscatter every 15 m, from 15 up to 9990 m with a temporal resolution between 10 and 30 s. It has a cross-polarization detection channel, so two range and sky background-corrected parallel and perpendicular signals are delivered from the instrument's software. As a secondary product, the software computes the total backscatter coefficient. However, during the period of operation, we have not found a full day in which this has been performed successfully (large gaps are found in the time series).
 A ceilometer (a CL31 system from the company Vaisala) has been continuously operating at Høvsøre since January 2007 and is also located a few meters from the mast. The CL31 is also a pulsed lidar system operating at a wavelength of 910 nm and retrieves the volume aerosol backscatter coefficient every 20 m from 20 up to 7700 m with a temporal resolution of ∼ 10 s. This has a typical uncertainty of ± 20% for 30 min averaging periods [Tsaknakis et al., 2011].
 The CL31 was designed to estimate the cloud base and thickness. However, under certain conditions with high aerosol concentration and relatively cloud-free boundary layers, the CL31 is able to observe the BLH from profiles of the aerosol backscatter coefficient [Peña et al., 2010b].
2.3 WRF Model Data
 Simulations using the advanced Weather Research and Forecasting (WRF) model [Skamarock et al., 2008] were performed using the technique developed in Hahmann et al.,  for dynamical downscaling atmospheric reanalysis but with Newtonian relaxation terms toward the large-scale analysis (also known as grid nudging). This technique was successfully used in other wind atlas studies [Peña et al., 2011]. The model was run with two model domains with 41 vertical levels (model top at 50 hPa, 13 levels in the lowest 1000 m, and lowest model levels at ∼ 21, 76, 127, and 168 m), with the outer domain covering Europe with a horizontal grid spacing of 45 km and a nested inner one covering a larger area than that shown in Figure 1 (left) with 15 km between grid points (the model inner domain grid is shown in grey lines in Figure 1 (right)). The simulations cover the period from 1 January 1999 to present, were forced by NCAR/NCEP II reanalysis fields [Kanamitsu et al., 2002], and provide hourly outputs. Sea surface temperatures (SSTs) for the WRF simulations are derived from the data of Reynolds et al.  at 0.25° × 0.25° grid spacing and are updated daily. The model setup uses the Yonsei University (YSU) PBL scheme [Hong et al., 2006], MM5 similarity scheme, Noah land surface model, and the Thompson microphysics scheme. These physics options are described in detail in Wang et al. . More specific details on the simulations are given in Peña and Hahmann .
 We use outputs of the PBL height from the model, which is estimated in the PBL parametrization. For the YSU-PBL scheme, the BLH is numerically obtained by two steps. First, it is estimated as a function of the ratio of the critical to the bulk Richardson number at the boundary layer top. Second, it is enhanced by adding a thermal excess of temperature near the surface [Hong et al., 2006].
3 Methods for BLH Estimation
 There are numerous ways to estimate the BLH based on the type of measurements we have at Høvsøre. The ceilometer and the aerosol lidar provide vertical profiles of quantities related to the amount of aerosols in the atmosphere (the backscatter intensity). Thus, peaks, inflections, and maximum and minimum gradients of these profiles are normally used as estimates of the BLH [Emeis and Schäfer, 2006; Emeis et al., 2008]. However, the signals from these instruments are very noisy (generally less noisy for the ALS300 than for the CL31 instrument).
 At Høvsøre, particularly, the concentration of aerosols is higher for westerly than for easterly winds because of sea spray due to high wind speeds from the sea. Easterly winds at Høvsøre are relatively “clean,” due partly to the low density of villages around the area. Most of the time, neither the CL31 nor the ALS300 shows a distinct aerosol backscatter profile for easterly wind directions. Furthermore, there are many precipitation, fog, and cloud events in this area, which “contaminate” the aerosol profiles by adding multiple peaks and drops to the signal. The effect of these events is normally attenuated by time and vertical averaging of the instantaneous profiles, but at Høvsøre, such events occur at low levels in the atmosphere, very often, and last for long periods, so the average profiles normally end up showing similar peaks and drops as in the “instantaneous” profiles.
 In Peña et al. [2010b], 10 min mean aerosol backscatter coefficient profiles of the CL31 unit measured at Høvsøre were classified into different atmospheric stability classes to estimate the BLH. Although the “individual” profiles are rather noisy (for the sector in analysis, i.e., the east), the average profile for each stability class showed a shape similar to that of the ideal backscatter profile in Steyn et al. , so Steyn's profile was used to estimate both the BLH and the entrainment depth. In this particular case, classifying the profiles in different stabilities helped for the BLH estimation because the upwind conditions were restricted to the homogeneous sector and there the BLH is related to the surface stability, which is observed at the meteorological mast. However, the analysis in this study is restricted to the west sector and therefore the atmospheric stability near the surface at the mast is not the main driver of the BLH.
 Here we use three main methodologies to derive the BLH from the observations. All of them are applied to each of the 10 min profiles of the instruments, i.e., either the variation of aerosol backscatter intensity, backscatter coefficient, or CNR with height (depending on the unit).
 The first method derives the BLH as the height where the maximum gradient is found, within the range 100–2000 m of the detailed coefficients that result from a single-level discrete wavelet decomposition using the Haar wavelet. By applying the wavelet decomposition, we basically locate the gradients of the original profile. This method has been already used to estimate the BLH from lidar profiles [Davies et al., 2000; Brooks, 2003]. We also use the results of the wavelet analysis to find the heights where the first five gradient maxima are. Once located, another BLH estimate is also produced (hereon referred to as “highest peak”) by selecting the position where the original signal is highest.
 The second estimates the BLH by fitting the profile of Steyn et al.  to the original signal. This idealized profile has the form:
where β is the backscatter coefficient with Ba and Bu as its values above and below the entrainment layer of depth 2d, respectively, z is the height, and zi the BLH. The method requires first guesses of zi, d, Ba, and Bu; for these we use 400 m, 100 m, and 50 × 10 − 5 and 20 × 10 − 5 m − 1 sr − 1 (for the CL31) and 500 and 200 V m2 (for the ALS300), for Bu and Ba, respectively.
 The third estimates the BLH by applying a threshold value to the signal. This threshold is based on previous attempts to derive the BLH from different instruments at Høvsøre. Here we specifically find the first height from the surface where the WLS70 CNR is − 22 dB and the CL31 backscatter coefficient is 50 × 10 − 5 m − 1 sr − 1.
 Although westerly flow at Høvsøre reveals high aerosol content, clouds are very often present and represent a challenge for the BLH methods, particularly for the CL31 and ALS300 signals. Since our purpose is to derive the BLH under all conditions and study its climatology, we cannot simply filter out cloud-affected profiles. Therefore, we also estimate the BLH (applying the above three type of methods) on a “smoothed” profile of the CL31 and ALS300 signals. Here we perform a local regression which uses weighted linear least squares and a first-degree polynomial order with a data span of 15%. To the outliers (normally clouds), it is assigned a lower weight in the regression.
Table 1. Overview of the Days Selected for BLH Detection Where Marine Upstream Flow Conditions Are Observed at Høvsøre During 2 Months in 2010
Results for the CL31 signal using Steyn's profile (first row) and threshold methods (second row), for the ALS300 using the highest peak (first row) and maximum gradient (second row) of the wavelet, and for the WLS70 signal using the threshold method.
Nearly cloud-free within first 2000 m
North-western flow, warm front to the south
Low-level clouds in the morning (following BLH) and precipitation
( ∘ -cyan)
episodes. North-western flow, occluded front over the North Sea
and low pressure area over Norway
Partly clouded in the morning (following BLH) and precipitation
episode at noon. Northern flow, stationary front over the Baltic Sea
High aerosol content close to surface and high-level clouds (above
( ◇ -green)
1600 m). Northern flow, warm front approaching from northeast
High aerosol content close to the surface in the afternoon
Weak northern flow, high pressure area over the British Isles
Cloud-covered (following BLH).
( ⊳ -red)
Strong high pressure area over the North Sea
Partly clouded in the morning and cloud-covered in the afternoon
( ⊲ -black)
(following BLH). Northwestern flow, high pressure area over the
Clouds (following BLH) and high-level clouds in the morning with
( × -cyan)
rain episodes. Northwestern flow, high pressure area over central
Cloud-covered after 03:00 (following BLH).
( ▽ -blue)
Weak northern flow, high pressure area over the British Isles
Cloud-covered and precipitation episodes.
( ડ -green)
Strong northern flow, cold front approaching from the northwest
 Results are shown for days where westerly winds are predominant, i.e., during nearly the entire day the upstream conditions are marine. Around 10 days registered such conditions for the 2 month period where all instruments were available at Høvsøre (in some days in May and June, the ALS300 and WLS70 units did not operate due to heating-related issues). Here we present results of these 10 days and Table 1 gives an overview of their main characteristics.
Sections 4.1 and 4.2 present detailed results for 2 days where we apply all the methodologies described in the previous Section. These days are selected because (1) they correspond to periods where westerly winds are mainly observed and (2) they represent two different atmospheric conditions for BLH detection: the first one shows nearly no low-level clouds and the second shows both high- and low-level clouds. Section 4.3 shows an intercomparison of the BLH estimates from different instruments and methodologies for the 10 days described in Table 1. The diurnal, seasonal, and monthly analysis in sections 4.4 and 4.5 is focused on the results of the CL31 and WLS70 from which we have at least 1 year of data.
4.1 First Case Study: 24 April 2010
 This day coincided with the last part of the period where ash traces from the Eyjafjallajökull volcano were detected at Høvsøre at 4000–6000 m [Peña et al., 2010a]. During this day, winds blow constantly from the west ( ∼ 270°) until about 20:00 local standard time (LST)—all time references are hereafter LST—where the wind direction rapidly changes to east ( ∼ 100°). This means that the measurements at the mast are mostly affected by the land-sea interaction and thus not appropriate to characterize the whole PBL when this is higher than the mast.
 Figure 2 shows a number of 10 min wind speed profiles recorded at the mast combined with the wind lidar throughout this day. The range of the wind lidar measurements is limited to heights where CNR ≥ − 22 dB and where all instantaneous CNR values within the 10 min averaging period are above − 35 dB. These filters are based on wind speed comparisons against the cup at 100 m; with CNR values lower than − 22 dB, the mean bias highly increases and the linear correlation decreases, whereas above this value the mean bias is about 2% and the Pearson's linear correlation coefficient squared (R2) is 0.99, increasing and decreasing slowly, respectively, with increasing CNR (the latter however considerably reduces the amount of values for comparison). At the beginning of the day (00:00–04:50), the mean wind speed, , is high (at 116.5 m m s − 1) and the wind profile shows the same type of behavior: the wind speed increases up to ∼ 100 m where it then becomes rather constant up to ∼ 700 m. Then, the wind speed increases rapidly with height and this feature is commonly associated with the BLH [Seibert et al., 1998].
 Between 06:30 and 19:50, the wind speed decreases (at all heights) until it nearly reaches a zero value. During this period, the wind does not clearly speed up at a certain height (in fact the wind clearly slows down at ∼ 700 m between 06:30 and 08:10). The lower the wind speed, the more meandering the wind speed profile. It is difficult to identify the BLH, and the wind lidar measurements are not always aligned with the mast profile. The misalignment is mainly due to the difference in the nature of the measurements. This wind lidar assumes flow homogeneity within the measurement volume to estimate the wind speed components, which is quite large for this instrument due to the pulse length and scanning configuration. This assumption is most of the time violated at Høvsøre under westerly winds because of the IBL from the sea-land transition, which is about the height where both wind lidar and cup measurements meet, and the flow deceleration downstream the coastline. Contributing to this, one has the uncertainty of the cup wind speed, which is about 0.1 m s − 1 but that increases once mounted on a mast, and that of the wind lidar velocity measurement, which is 0.3 m s − 1. Later, the wind speed slightly increases but no clear BLH can be distinguished from the profiles.
 Figure 3 is similar to Figure 2 but for a number of 10 min wind direction profiles. Between 00:00 and 03:10 and at 08:10, the wind slightly turns counterclockwise with height up to ∼ 500 m where it highly turns counterclockwise. Between 04:50 and 06:30, it also turns counterclockwise up to ∼ 500 m but highly veers clockwise upward. The height where the rate of change in direction is the highest (counter or clockwise), i.e., ∼ 700 m, is associated with the BLH [Brown et al., 2005].
 Between 09:50 and 14:50, the wind generally veers clockwise and, although it meanders, a large increase in the veer is noticed at ∼ 400–500 m (e.g., at 11:30). Between 16:30 and 18:10, it is difficult to observe any clear peak in the profile and the wind speed does not change much with height. At 19:50 where the wind speed is the lowest, part of the atmosphere seems to be decoupled from the surface layer between 60 and 100 m, where the wind direction changes ∼ 180° (it actually occurs within a 30 min period). Such decoupling marks the BLH but it should be noted that this sudden direction change might be due to erratic wind directions caused by low wind speeds. Later from 21:30 onward with slightly increasing wind speed, the wind veer is very high; it changes ∼ 100° within the range 10–250 m (the highest veer is found between 100 and 150 m).
 Figure 4 illustrates the aerosol range and sky background-corrected backscatter signal from the ALS300 aerosol lidar parallel channel. The intensity is higher close to the surface and between 06:00 and 18:00. The BLH estimations from the first two methodologies are also shown. The two methods generally show a similar BLH, although the highest peak of the wavelet analysis reveals a lower BLH compared to that found by fitting Steyn's profile and the maximum gradient overestimates the BLH when layers of high aerosol content are found at ∼ 1200–1600 m in the afternoon.
 Figure 5 illustrates the volume aerosol backscatter coefficient intensity from the CL31 ceilometer. As with the ALS300, the intensity is generally high close to the surface and a layer of high aerosol concentration is shown between ∼ 800 and 1700 m during the night. The BLH estimations from the three methodologies are also shown. The wavelet-based estimates overpredict the BLH (particularly those of the maximum gradient), whereas those based on fitting Steyn's profile follow the results obtained with the ALS300.
 Estimations of the BLH based on this instrument's signal threshold of 50 × 10 − 5 m − 1 sr − 1 follow the behavior of the Steyn's profile-based BLH estimates and those of the ALS300 signal well. The layer of high aerosol concentration in the night does not affect them and they “fluctuate” less than those from the other methods.
 Figure 6 illustrates the CNR from the WLS70 wind lidar. As with the ALS300 and the CL31, the CNR is generally high close to the surface. The resemblance with the CL31 signal is astounding and the instrument similarly detects the nighttime high aerosol concentrations at ∼ 800 m. It is difficult to obtain reliable BLH estimates using the signal of the WLS70 from the first two methods because the range of CNR values is small, high CNR gradients are found close to the highest CNR values, and the highest CNR in each profile is not found close to the ground but generally at the same height ( ∼ 400 m).
 Estimations of the BLH based on this instrument's signal threshold of − 22 dB nicely follow the behavior of the BLH estimates from the threshold and the Steyn's profile methods of the CL31 signal and the wavelet analysis performed on the ALS300 signal. The high aerosol concentration layer observed in the night seems to not have an effect on these estimates either.
 The BLH WRF outputs from the two grid points east and north-east of the meteorological mast at Høvsøre, illustrated in Figure 1 (right), are also shown in Figure 6. Both WRF estimates are similar and lower compared to those from the WLS70 in the early morning (until 06:00). They then match the BLH estimates from the WLS70 for a short period near 06:00. Those from the north-east grid point follow the decreasing behavior of those from the WLS70 until 12:00, showing in the afternoon and nighttimes a lower BLH than the WLS70. The results from the east grid point show an increasing BLH at 06:00, peaking at 12:00, and then rapidly decreasing in the afternoon. From 06:00 to 18:10, the BLH from this grid point is always higher than the observations and at 20:00 matches the BLH from the north-east point (not shown).
 The meteorological mast and the instruments are placed on land at Høvsøre. However, the land mask for these WRF model simulations is coarse and the grid point closest to the mast is a water point in the WRF model simulations used in this study. For this particular day, all grid points identified as water in the WRF model grid around the mast location show a much lower BLH compared to the observed values, except for the north-east point. The other land points around the mast show a much higher diurnal variation compared to the east point and therefore much higher BLHs compared to the observed values.
4.2 Second Case Study: 15 June 2010
 During this day, winds predominantly blow from the north west ( ∼ 330°) and only between 04:00–06:40 and 11:30–16:30, the winds turn completely north. As for the first case, the lidars observe the marine boundary and land-sea transition layers, whereas the mast is within the transition layer and only the first tens of meters are in the equilibrium layer of the land surface.
 Figure 7 shows a number of mast/wind lidar 10 min wind speed profiles recorded during this day. The range of the wind lidar measurements is also limited to heights where CNR ≥ − 22 dB. The wind speed is rather high throughout the day, except during the first period when the wind turns north (e.g., the profiles at 04:50 and at 06:30). Wind turbines with hub heights of ∼ 80 m are located north of the mast and their wakes appear visible during this period (wind speeds at 80 m are lower than those at 40 m). The wake also seems visible at 13:10 and 14:50 but this is a rather windy period anyway.
 At the beginning of the day (00:00–03:10), the wind speed is rather constant from 100 m up to ∼ 500–600 m, where the BLH is found. During the wake periods, it is difficult to estimate a BLH due to the distortion of the profile, although at 04:50 there is a sudden increase of wind speed at ∼ 450 m. Similarly at 09:50, the wind speed highly increases at ∼ 350 m. Between 11:30 and 16:30, the wind speed highly decreases at ∼ 400–500 m. In the night from 19:50 onward, the profile shows the same behavior: a rather logarithmic shape in the first 100 m, followed by a rather constant wind speed, which increases at ∼ 200–300 m.
 Figure 8 shows the mast/wind lidar 10 min wind direction profiles. During this day, the veering of the wind is generally small. The maximum veer is ∼ 40° between 100 and 600 m at 09:50. During a long part of the day (00:00–18:10), the wind slightly turns counterclockwise in the first tens of meters and higher up clockwise. Within this period, increasing veer is found at ∼ 600 m at 00:00 and ∼ 250 m at 08:10 and 09:50. The high veer at the two highest measuring levels at 01:30 and 03:10 is “artifacts” of the wind lidar, as under certain atmospheric conditions and CNR levels, the retrievals are not accurate (e.g., at 03:10 the wind speed at 550 m is unrealistically higher than 40 m s − 1). From 19:00 onward, it is difficult to define a BLH, except at 21:30 where the veer is clockwise and shows a high rate of change at 300 m.
 Figure 9 illustrates the aerosol range and background-corrected backscatter signal from the ALS300 aerosol lidar parallel channel. Rain episodes and two cloud layers, a “low” one at the beginning of the day at 400–600 m and a “high” one at 1400–1800 m from 09:00 to 12:00, are observed. BLH estimations from the wavelet and Steyn's profile methods are similar during the low-cloud period, whereas during the high-cloud episodes most of the BLH estimates of the maximum gradient using the wavelet follow the clouds.
 Between 12:00 and 21:00, both wavelet-based results show rather distinct BLH estimates; the maximum gradient smoothly follows a layer where the backscatter intensity is low, matching well the results from Steyn's profile, and the highest peak estimates a more fluctuating BLH on layers of higher backscatter intensity. At 18:00, the highest peak BLH slowly starts to increase and matches the other two estimates from 21:00 onward. Attempts to estimate the BLH based on thresholds of this instrument's signals were also performed for this day but did not show any clear results.
 Figure 10 illustrates the volume aerosol backscatter coefficient intensity from the CL31 ceilometer. The rain episodes and the cloud layers are observed as for the ALS300 signal, but in this case they cover a larger range of heights. The cloud-free period (i.e., from 12:00 onward) shows a slightly different aerosol structure than that from the ALS300. The BLH estimations from the three methodologies are also shown. As for the first case, the wavelet-based BLH estimates tend to overpredict the BLH except during the low-cloud period, whereas Steyn's profile-BLH estimates agree with the results from the highest peak of the wavelet using the ALS300 signal. From 16:30 onward (a cloud-free period), both methods show a rather low and slowly increasing BLH ( ∼ 250–400 m), which matches with the highest peak of the wavelet-based BLH estimated using the ALS300 signal.
 Estimations of the BLH based on this instrument's signal threshold of 50 × 10 − 5 m − 1 srad − 1 follow the wavelet-based BLH estimates well during the first cloud period until 07:30. From that time onward, they follow the Steyn's profile-based BLH estimates rather well.
 Figure 11 illustrates the CNR from the WLS70 wind lidar. The resemblance with the CL31 signal is also astounding, particularly in the cloud-free period. The instrument detects the cloud layers at similar heights as the ALS300 and CL31 units and shows a much higher CNR during such episodes compared to the first test case. Estimations of the BLH based on this instrument's signal threshold of − 22 dB follow the behavior of the BLH estimates from the threshold and Steyn's profile methods on the CL31 signal very well.
 The WRF-derived BLH from the two grid points east and north-east of the meteorological mast at Høvsøre, illustrated in Figure 1-right, is also shown in Figure 11. Both WRF-based BLH estimates show a similar behavior; the BLH is low in the early morning, then increases during the daylight period (06:00–18:00) and finally decreases and stabilizes during the night. In the WRF simulations, there is no cloud cover during the whole day for both grid points and thus the WRF BLH behavior shows a clear diurnal variation and much lower BLHs during the low-cloud period in the morning (00:00–07:00). The diurnal variation is higher for the east grid point than for the north-east one, as expected, since the first is a land point.
 As for the first test case, the WRF-based BLH from the north-east point compares better to the BLH estimate from the WLS70 CNR threshold than that from the east point. The comparison is rather good in the relatively cloud-free period 08:00–18:00. After 18:00 onward (a 100% cloud-free period), the WRF BLH from the north-east point is much lower than the observed values from any instrument/methodology.
 Concerning the results on the smoothed CL31 and ALS300 signals (not shown in figures), for the first case smoothing does not have a significant effect on the CL31 when looking at the results of the threshold and Steyn's profile methods, but dramatically improves those of the maximum gradient and underpredicts the BLH using the highest peak of the wavelet. It similarly affects the results of the ALS300, although those from the maximum gradient are not improved. For the second case smoothing improves both wavelet-based results compared to the other methods on the CL31 signal, whereas it deteriorates the results for all methods on the ALS300 signal.
4.3 BLH Intercomparisons
 Based on the estimations of the BLH from the different instruments/methodologies and WRF simulations in sections 4.1 and 4.2, we intercompare the 10 min BLH observations from the ALS300 and the CL31 against the results from the WLS70. This is illustrated in Figure 12 for 10 days, which are described in Table 1. There we select to present the uncertainty on the methodologies which are better related to the nature of the signal (e.g., Steyn's profile was originally proposed to describe the behavior of the backscatter coefficient and although the signal from the ALS300 shows a clear drop, it does not follow the tails in the error function). This uncertainty is computed for each 10 min BLH estimate as the standard error of the 10 min BLH estimates within a period of ± 30 min (we therefore assume that the uncertainty in the method is given by the variation of the estimate within an hour). Thus, a time series of uncertainties is computed for each day and the table shows its maximum, mean, and minimum values. It can be seen that the threshold methods on the CL31 and ALS300 signals show the lowest uncertainties.
 For the 10 days, BLH estimations based on fitting Steyn's profile poorly correlate (R2) against those from the threshold, although the agreement is not poor; the slope of the linear correlation through origin is 0.81 (Figure 12 (top left)). The main issue is that the measurements split up in two sets of correlated data, one over the 1 : 1 line and one below it. The main reason for the latter relates to days with low-level clouds, in which the results from Steyn's profile are systematically lower than those using the threshold. The statistics are similar and slightly poorer when using the results of the wavelet on the ALS300 (Figure 12 (top right) shows those of the maximum gradient but similar statistics are found for the highest peak). Days with high-level clouds (higher than the BLH) contribute the most to the outliers.
 When applying Steyn's profile method to the smoothed CL31 profile (Figure 12 (bottom left)), we considerably improve the overall statistics, since most of the low-level clouds are “removed.” However, it deteriorates the statistics for one particular day (21 May 2010) as during this entire day, the BLH is consistently low ( ∼ 200 m) and the smoothing sometimes removes the entire shallow boundary layer.
 The agreement between BLH estimates from the WLS70 and the backscatter threshold of the CL31 is excellent for the 10 days as shown by the statistics in Figure 12 (bottom right) (highest R2 and lowest root mean square error (RMSE)). This is the only one of the four comparisons presented where all the 1440 possible matches (N) are shown, which highlights the robustness of the method on the CL31 and WLS70 signals. Such agreement is interesting because the WLS70 was not designed to observe the BLH, but wind speed and direction. Since the two thresholds are fast and robust and have low uncertainty (mainly because they do not seem to be highly affected by the presence of clouds well above the BLH), we implement them in the 1 year analysis as the two BLH observations from the WLS70 and CL31 instruments.
4.4 Diurnal and Seasonal Variation of the Coastal BLH for Wind from the Sea
 The observations from the two instruments, the WLS31 and CL31, which robustly operated together nearly 1 year at Høvsøre, are used to derive the diurnal and seasonal variation of the BLH. Figure 13 illustrates this analysis together with the results from the two grid points from the WRF simulation. The plots show the mean within each hourly bin and for each of the seasons. Similar results are found when the median is used instead.
 There is no clear diurnal variation in the BLH estimates from the instruments. The highest diurnal variation by far (i.e., the variance in the 24 h cycle) is found in winter for both the CL31 and WLS70, which we expected, since high storm activity leading to a broad range of stabilities and atmospheric conditions is experienced in this period in Denmark. The BLHs are similar for both instruments during spring and winter, whereas they are lower and higher for the WLS70 compared to the CL31 in autumn and summer, respectively. For both instruments, the BLH is generally the highest in autumn and the lowest in spring.
 The values of BLH from the two WRF grid points show similar results to those from the instruments, generally highest BLHs in autumn and lowest in spring. The mean BLHs derived from WRF simulations are generally lower than those observed, particularly for the north-east grid point that is located on sea. SSTs are kept constant throughout the day in the model and thus can constrain PBL development. Strong diurnal variation is only noticed in summer for the east grid point located on land. Our results agree with those by Krogsæter , who found too low WRF BLHs compared to observations at the offshore research platform Fino1 in the North Sea and rather low BLHs during spring time. Similarly to us, Duda  found nearly no diurnal variation in the BLH during any season when investigating several PBL schemes in the WRF model for the Gulf of Mexico.
4.5 Intra-Annual Variation of the Coastal BLH
 The observations from the two instruments, CL31 and WLS70, are also used to derive the intra-annual or monthly variation of the BLH. Figure 14 illustrates the results of this analysis for the mean and median monthly values along with the results from the two WRF grid points.
 Both BLH observations show similar behavior; the BLH is lowest within the months of March–June and highest within September–November and in February. The September–November high BLHs are due to the relatively colder air compared to the sea, which often leads to convective conditions upstream from Høvsøre. The CL31-derived BLH is generally lower than that from the WLS70 for most months, except for November where the highest difference and values are found; the BLHs are nearly the same in September, October, and January–March. The highest peaks in BLH are located in the same months: September, November, and February.
 The monthly BLH behavior from the WRF results of the two grid points is very similar to that from the observations, especially for the east grid point (located on land), although both WRF simulation outputs show lower BLHs than the observations. The highest peaks in BLH are also located in the same months: September, November, and February (for the east grid point). The peak in November is not so well captured by the water grid point in the WRF simulations. This is partly because in November the WRF points on land experience the relatively warm marine conditions and, in addition, the heating of the surface (with cold air aloft).
 The features and possible BLH estimations derived from the wind speed and direction profiles are well correlated to those observed from the aerosol profiles of the lidars. For the first test case, the height where the wind starts to speed up/down with height is ∼ 700–800 m in the period 00:00–08:10, where the CL31 threshold method shows BLHs between 800 and 1200 m. For the second test case, similar wind speed ups/downs are found between 400 and 700 m from 00:00 to 04:50 which is nearly the same range of BLHs found from the CL31 threshold method in the same period. The relatively “low” BLHs found from the wind speed profile from 19:50 onward (200–300 m) match the BLH estimates from the highest peak of the wavelet analysis of the ALS300 signal and the CL31 threshold method rather well. Whenever the vertical wind shear is large, we generally find an increase in the wind veer as well.
 High turning of the wind is observed at heights far above 100 m at relatively high wind speeds during the first test case. The wind at those heights is marine and so one can relate the increase of turning with the increasing wind speed, since the roughness length also increases with wind speed over the sea.
 Here, we use 1-D methods for BLH estimation, i.e., we only use information of the actual 10 min mean profile with height of aerosol characteristics. Loaëc et al.  developed a 2-D BLH detection algorithm that uses the history and the time evolution of the aerosol profiles and their BLH estimations showed high correlation compared to those from 1-D wavelet and gradient methods. The details of such 2-D algorithm depend on the type of instrument used, since the outputs of the three lidars are not the same and do behave differently with time.
 Outputs from the nine closest WRF grid points to the meteorological mast (Figure 1 (right)) were also studied for the 2 days and the north-east and east ones show the closest agreement with the BLH observations. The north-east point (on water) agrees better with the observations for the two test cases, whereas the east point (on land) agrees with the observed long-term diurnal, monthly, and seasonal variations. The east and south grid points are the most geographically similar compared to the mast location, since they are both on land and equally separated from the sea-land change of roughness. For the two test cases, the WRF-derived BLHs from the south and east grid points show nearly the same results (not shown), except that for the first test case the south grid point BLH dramatically decreases around 06:00. The good agreement for the two test cases of the north-east point might be because it is surrounded by land and under convective and cloud-free conditions, for example, the BLH grows higher than the other points on water.
 It is important to state that the uncertainty on the mean statistics of BLH estimates for the diurnal, monthly, and seasonal variation is rather high, mainly due to low-level clouds and fog events. The standard deviation of the diurnal variation ranges between 12–142 m and 39–184 m in winter, 1–87 m and 12–78 m in spring, 11–129 m and 33–103 m in summer, and 25–148 m and 30–137 m in autumn for the BLH estimates of the WLS70 and CL31, respectively. For the WRF east and north-east points, respectively, it ranges between 24–168 m and 27–173 m in winter, 7–140 m and 32–99 m in spring, 34–120 m and 43–96 m in summer, and 5–126 m and 13–124 m in autumn. The correspondence in ranges is very good for both instruments and WRF north-east results, which show largest variations in autumn and winter and consistently lowest in spring and summer.
 Although there is high variability in the BLH estimates, the seasonal trends are always the same: highest and lowest BLHs during autumn and spring, respectively. For the westerly flow conditions at Høvsøre, such trends are expected for this region of Denmark. The water west of Høvsøre is warmest at the end of summer and autumn, and in the middle of autumn, the air cools down and so most of the convective conditions are registered offshore from Høvsøre. In spring, the situation is the opposite; the air starts to warm up while the water is still cold from the winter period and so most of the stable conditions appear offshore from Høvsøre.
 The BLH estimates from WRF are generally lower than those from the lidar observations, since a good number of BLH observations are found at the top of the low clouds and fog layers. In the WRF formulation, the BLH is function of the bulk Richardson number, which depends on the temperature and wind speed profile. Thermal excess of surface temperature is added for the BLH computation, which partly explains the higher BLH estimations for the east point (on land) compared to the north-east point (on water). Also the amount of cloud cover which is parameterized in WRF is lower than that observed for the whole year of analysis at Høvsøre (clouds are detected by the ceilometer below 400 m 21% of the time, whereas WRF-derived maximum cloud cover is 15% for the model levels up to 400 m).
 From the authors knowledge, this is the first time that the CNR values of a wind lidar are systematically used for BLH estimation. Wind lidars (or Doppler lidars) are often used for BLH detection by looking at the profile of the variance of the vertical wind speed component, and fitting BLH-dependent parameterizations to such turbulence observations [Hogan et al., 2009]. Tucker et al.  further combined wind shear-, wind veer-, and -based BLH estimations from a high-resolution wind lidar and found good agreement with sonde-measured BLHs. Pearson et al.  concluded that profiles observed with a wind lidar over a tropical rain forest are easier to interpret than aerosol profiles, since the first ones directly give a measure of the PBL mixing process. With our particular wind lidar, such turbulence quantities are strongly influenced by the instrument's scanning pattern and the measurement volume (particularly its vertical extent), among others. Quantification of these effects (i.e., the systematic errors) depends on, e.g., the structure of atmospheric turbulence (the turbulence spectral tensor all the way up to the BLH), the height of observation, atmospheric stability, and wind lidar configuration and properties. Details of such effects can be found in Sathe et al.  and Sathe and Mann , where the errors are up to 90%, explaining why wind lidar and sonic turbulence measures are simply not equal, as also found in Barlow et al. . Further, we are here looking at westerly winds (the non-homogenous sector); thus, the wind lidar's values are inherently different for the four azimuthal positions and the flow homogeneity assumption to derive the wind speed components is violated, which increases the errors in the variances differently with height.
 The BLH observations at a coastal site in western Denmark (restricted to marine upstream conditions) are analyzed for 2 days using measurements of wind speed and direction from combined meteorological mast and wind lidar measurements, aerosol concentration profiles from a ceilometer and an aerosol lidar, and CNR profiles from the wind lidar. When the BLH can be determined from the wind speed and direction profiles, it is in agreement with that derived from the aerosol profiles.
 Different methodologies are applied for BLH estimation based on the aerosol structure observed by the lidars and are intercompared for 10 days. The wavelet analysis performed on both ceilometer and aerosol lidar signals shows similar BLHs compared to those derived by fitting the profile from Steyn et al.  to the aerosol backscatter profile. A threshold criterion applied to the ceilometer aerosol backscatter estimates BLHs, which are in excellent agreement with a threshold criterion used on the CNR profiles of the wind lidar.
 The BLHs estimated from WRF reanalysis simulations from different grid points close to the meteorological mast are compared with the BLH observations for the 2 days. They generally agree with the behavior of the observed BLHs, although they normally reveal lower BLHs during early morning and nighttimes and higher BLHs during daytime.
 No clear diurnal variation for the year 2010 is found from the BLH observations from the ceilometer and the wind lidar aerosol-related signals, when the analysis is performed for different seasons. Both observations reveal similar BLHs except for the autumn period, where the ceilometer-based BLH is higher than that of the wind lidar. Although the diurnal variations from the mean are rather high, the trends are the same from the observations and WRF: the BLH is higher and lower in the autumn and spring periods, respectively. WRF-derived BLHs are (generally) lower than those from the observations. Interannual variations are similar from the ceilometer and wind lidar signals and WRF outputs; low BLHs are observed in April–June and high peaks in September, November, and February.
 Funding from the Danish Council for Strategic Research Project 2104-08-0025 “Tall Wind” project is acknowledged. We would also like to thank the Test and Measurements section of DTU Wind Energy for the maintenance of the Høvsøre database.