The UV lidar onboard the ULA looks downward close to nadir (see Figure 1). It is built around a compact 355 nm tripled Nd-YAG laser that provides 16 mJ with 5 ns pulse duration at 20 Hz pulse repetition frequency (see Table 1). Eye safety conditions are met at the exit of the optical head (Figure 1(a)). The full waveform lidar signal is digitized at a 100 MHz sampling frequency or 1.5 m sampling resolution along the lidar line-of-sight. The lidar signal acquisitions are recorded during 1 s (20 consecutive shots) and then the data are stored on an on-board portable computer for 1 s. The shot to shot separation at ground is about 1 m for an ULA horizontal velocity of 20 m s⁻¹. The laser footprint at ground level has a nearly circular shape of 2.4 m diameter for a 300 m flying altitude above ground level (agl) and nadir pointing. Depending on the ULA attitude while in the air, the successive laser footprints move randomly within 10 to 40 m around the ULA ground track (see Section 3.4). A global positioning system (GPS) tracks the ULA position with an accuracy of 5 m. The three angles (yaw, pitch and roll) between the actual lidar line-of-sight and nadir direction are recorded with a 0.5° accuracy (i.e., 2.6 m at the ground from an altitude of 300 agl) to locate the lidar shot. Considering the root-mean-square errors of the GPS and the three line-of-sight angles, we estimate the overall absolute precision of ∼7 m.

The ULA carrying the LAUVAC system is a Tanarg 912-S manufactured by Air Création (http://www.aircreation.fr). It is highly maneuverable (see Table 1) and it only requires a 200 m long path for take off and landing. The maximal payload is 250 kg (including the pilot) and the flying endurance is 3 to 4 hours (here the canopy flights lasted for 2 hours). The lidar optical head is installed on an axis perpendicular to the ULA displacement direction so as to change the pointing angle before the flight.

The field experiments were conducted in September 2008 over three test areas located in the Landes forest region near the towns of Bray (test area #B) and Mimizan in southwestern France (two test areas referenced as #M1 and #M2; see satellite pictures in Figure 2(a,b,c)). The selected areas are mainly flat and populated with stands of Maritime pines (see example in Figure 1(b)) spanning a range of ages and either planted or naturally regenerated. These trees may reach a maximum height of 25 m in their mature stage, mostly corresponding to a trunk without living branches roughly 15 m high and a crown with branches and needles of nearly 10 m high and 5 to 8 m wide (e.g., [16]). The Bray area (#B, Figure 2(a)) is populated by regularly planted 28-year-old trees with a total tree height (TTH) of 20–25 m. The Mimizan #M1 area (Figure 2(b)) is composed of two sub-areas: the southeastern half of the area is composed of a 55-year-old naturally regenerated stand with TTH around 20 m and a northwestern sub-area of young 10-year-old plantation of 10 m height. The Mimizan #M2 area (Figure 2(c)) has several stands of different tree types and heights. From west to east, a quarter of the area is covered by sparse trees and bare ground, a quarter with semi-natural 50-year-old trees with TTH of 20–22 m, a quarter with planted younger 35-year-old slightly higher trees (with TTH ∼23 m) and a quarter of 19-year-old trees with TTH of 15–16 m. Density and height of undergrowth vegetation vary according to the species composition and the management of the stands (particularly dense for young tree sectors and up to ∼2 m for fern patches in the #M2 area).

Most of the airborne lidar measurements were conducted with the lidar beam pointing at nadir at an approximately constant altitude agl (300 m ± 30 m). The ULA sampled the test areas according to a grid pattern for Bray (#B) or longitudinal pattern for Mimizan #M1 and #M2 (see Figure 2(d,e,f)). For two-hour flights, the resulting spacing between lidar tracks was in average 6 to 7 m. To test the sensitivity of the lidar system retrievals to ULA altitude and beam pointing, the Bray #B area was overflown at 500 m agl with the lidar looking at nadir (i.e., it results in a 4 m laser footprint) and at 300 m agl with a beam at 20° from nadir (see Section 4.2).

Laser emission of energetic pulses (16 mJ) and the relatively low flying heights (∼300 m) of LAUVAC provide much higher canopy and ground return signals than shot noise fluctuations, i.e., typical SNR ranges from 300 to 800. Within the length of the laser pulses (1.5 m), only one signal sample is available and we expect no correlation induced by the laser pulse width between consecutive waveform points. Considering these remarks, we presume that no pre-processing is needed for deconvolving the laser pulse shape (e.g., [17]) nor improving the accuracy for detecting canopy signal peaks (e.g., [18]), as widely done for other systems [17,18]. In order to test these assumptions, we performed numerical simulations of waveform decomposition into Gaussian functions (following [18]) for different instrumental configurations.

First, we considered a power signal S by convolving a synthetic tree attenuated backscatter profile by a Gaussian laser pulse shape of 1.5 m of length (Figure 3(a)). We sampled S and added random noise according to two lidar configurations: (i) 1.5 m vertical resolution and SNR up to 800 as for LAUVAC and (ii) 0.3 m vertical resolution and SNR from 20 to 50 as obtained by other systems such as LVIS (see e.g., [18]). For the LVIS-like configuration (Figure 3(b)), spurious fluctuations are removed and the actual SNR is increased by ∼10 in the waveform retrieved by fitting four Gaussian functions (gray shade). However, in the case of the LAUVAC-like waveform (Figure 3(c)), no significant difference is apparent between the waveforms with (gray shade) and without (red line) the Gaussian fitting procedure. Moreover, the limited number of points for constraining the Gaussian curves induces errors greater than the random noise fluctuations, which degrade the SNR after the fitting procedure (gray line in right panel of Figure 3(c)). Besides, as the central point of the Gaussian functions (black small triangles in Figure 3(b,c)) indicates the center of the canopy reflecting surfaces [18], no additional information is provided about tops and bases of tree crowns (which are retrieved in the present paper, see Section 3.2). For these previous reasons, we have chosen a threshold method as describe hereafter.

Four significant ranges are extracted from the full waveform lidar signals (see Figure 4(a)): (i) the ground range (G) as indicated by the last return, (ii) the canopy top height (CT) by subtracting G from the first return range, (iii) the crown base height (CB) as the last return after propagation in the tree foliage and (iv) the undergrowth height (U) when the ground return is broader than the 1.5 m sampling resolution (see Figure 4(a)). Then, we derive an apparent tree top height (AT) from the CT distribution: AT are the local maxima of the 2D horizontal distribution of CT, as adjacent lidar profiles sample in detail the shape of tree crowns (see Figure 4(b)). Among all local maxima, we only keep the highest ones within a proximity radius equivalent to the horizontal size of the tree crowns. In practice, a 2.5 m radius is used, which is the average of the in situ measurements performed in the test areas (for trees from 10 to 55 years old).

We use a threshold method to estimate automatically G, CT, CB and U from each single-shot lidar signal profile. Lidar power signal S is used to avoid multiplication of noise by the squared range. Reliable vegetation canopy signals are identified as all return signals exceeding a detection threshold t at ranges above G (taken as the maximum value of the ground signal peak). A false alarm occurs when the signal noise exceeds t and no detection occurs when the return signal of the canopy top CT (or CB, U, G) is below t. The value of t is chosen to minimize the total probability of error p_T on a given profile. This probability depends on p_F and p_N, respectively the probabilities of false alarm and no detection. Their product p_F p_N is the probability that for a profile both errors occur simultaneously. To calculate p_T, we subtract p_F p_N from the sum p_F + p_N in order not to account for it twice. Hence we write p_T as (e.g., [20,21]): (1) p T = p F + p N − p F   p N

To estimate p_F and p_N, we first use the lidar signal histogram in the detection range to identify and calculate the noise and canopy signals probability functions after normalization i.e., F_N (S) and F_S (S), respectively.

Figure 5(a) shows an example of a histogram of lidar signal S (here between 9 and 25 m above the ground) which is modeled as the sum of two log-normal functions that account respectively for the contributions of noise and canopy returns. We first identify the noise histogram F_N (S) as the lower peak of the signal histogram and we fit a Gaussian curve by a classical method (e.g., [18]). We obtain the probability function of the useful signal F_S (S) from the remaining part of the histogram. Then, we calculate p_F and p_N as (e.g., [20]): (2) p N ( t ) = 1 − F S ( t ) (3) p F ( t ) = 1 − ( 1 − F F ( t ) ) Mwhere M is the number of independent points within the detection range. According to the example showed in Figure 5(b), canopy detections are expected in 95% of the cases (or equivalently 5% probability of error) when we use the optimum t value (which minimizes p_T). For this example, the mean ground return is approximately a factor 4 higher than the mean canopy returns (not shown). Then, the ground return probability distribution is less overlapped with the noise probability distributions and thus less sensitive to the choice of t (the minimum of p_T is mostly flat over a wider range of t values).

A horizontal transect of lidar profiles and the corresponding detected parameters are shown in Figure 6. Following the ULA attitude during flight, the lidar footprint (black circles in Figure 6(a)) moves around the flight track (gray dots).

Due to the vertical displacement of the ULA, we observe a progressive variation in range between the lidar and the ground return (detected in most profiles and displayed in red in Figure 6(b)). After the shot-to-shot ground detection, the coherence between adjacent information is verified. If they differ by more than 5 m (∼5% of cases), the ground range is determined by interpolation between the two closest lidar profiles. Lidar profiles are then projected in the vertical direction (gray shading in Figure 6(c)) according to the ULA attitude (i.e., pitch and roll). With a typical 5° deviation from nadir, the correction is negligible (Figure 6(c)). Canopy parameters CT, CB and U are then retrieved and AT is obtained from the CT horizontal distribution (Figure 6(c)).

Figure 7 displays the horizontal distribution of AT, CT, CB and U for Mimizan #M1 (Figure 7(a)) and #M2 (Figure 7(b)), as a function of local easting (LE) and local northing (LN).

The discontinuities between tall (AT ≥18 m) and short (AT ≤10 m) trees are clearly marked (at ∼500 m LE for #M1 and ∼1700 m LE for #M2) as shown by the color code transitions e.g., from light-blue/green to orange/red for CT. This agrees with the corresponding distribution of mature and young trees within the test areas (see Section 2.2). Figure 7(b) shows a more heterogeneous height distribution for mature trees of #M2 (from 500–1,500 m LE). This is related to differences in height between taller planted trees (500–1,000 m LE 0–500 m LN) and relatively shorter naturally regenerated trees (500–1,000 m LE 500–1,000 LN and also 1,000–1,500 LE). As expected, higher (respectively smaller) undergrowth is associated with the younger (respectively older) forest stand. Clear void zones without trees (see Figure 2(b,c)) are correctly identified (i.e., no canopy top and tree crown base information extracted from lidar signals; e.g., ∼1,200 m LE ∼0 m LN in Figure 7(a) and 100–300 m LE in Figure 7(b)).

Lidar retrievals for #B present good coherence of mostly homogeneous canopy top heights (not shown on the figures) for this uniformly planted forest stand. Mean CT and AT (see histograms in Figure 8(a,b)) of 19.5 m and 21.2 m, respectively, are observed. Tree crown bases are located on average 7.5 m below the tree tops. As confirmed by in situ information, only sparse undergrowth vegetation in the first meter above the ground was observed for #B.

We compare histograms of in situ-measured total tree heights TTH of 100 trees selected at random in the Bray #B area (1 forest stand) with AT retrieved by lidar and checked the consistency of the lidar retrieval for three different flight configurations: (i) nadir pointing, (ii) pointing at 20° from nadir pointing flying at 300 m agl as well as (iii) nadir pointing at 500 m agl. Tree top height histograms (Figure 8(a)) from in situ operator and lidar show a very good agreement (particularly for a flight altitude of 300 m agl and for AT ≥19 m).

Apparent tree top heights retrieved by lidar between 15 m and 19 m do not correspond to actual tree tops, as shown by comparison to in situ measurements. In those cases (∼20%), the laser footprints sample the side and not the top of the trees (notice that false alarms are only 5% of the cases). Such effect produces a 1 m underestimation of mean tree top height (see Figure 8(a) and Table 2), which is smaller than the actual lidar sampling resolution of 1.5 m.

Provided that a proper detection threshold t is selected (see Section 3.3), the results on Figure 8 show good consistency between the canopy lidar retrievals for the different flight configurations. The resulting histograms are almost identical for all the parameters of interest (AT, CT and CB). Table 2 shows in more details the results, and especially for the 500 m agl data when they are processed using the same threshold as for the 300 m flights indicated as “1.5t” (it is 50% higher than the optimum value for the 500 m flight data using Equation 1 to 3).

For such a non-optimal threshold value, it results in 1.5 m underestimation of the canopy top (and AT). So, for too high threshold value the weak signal that marks the canopy top transition may be missed. However, this bias cancels when the optimum threshold is used (see Table 2 and Figure 8). For the crown bases heights (and ground returns), a robust detection is indicated by almost identical results for the three flights (Figure 8(c)), even using different thresholds (see Table 2). This is probably due to a higher density of the scattering volume (foliage and branches) for the crown bases.

For verification consistency at smaller scales, we have analyzed Bray #B area divided into 4 quadrants of equal area (see Figure 2(a)). Table 2 shows that similar results were also obtained for AT, CT and CB for each of these quadrants (with differences of about 1 m between quadrants) both in the comparisons between different lidar retrievals (different configurations and thresholds) and with in situ measurements.

Additional statistical comparisons between lidar and in situ information were conducted for smaller sample plots (of 30 × 30 m²) representative of different stands within the test areas #M1 (five plots #M1A to #M1F, see location in Figure 2(b)) and #M2 (three plots #M2A to #M2C, see Figure 2(c)). All sample plot comparisons are summarized in Table 3.

We compare both tree top and crown base heights as measured in situ (TTH and CB_IS, respectively) and by airborne canopy lidar (AT and CB respectively). Good consistency, within 0.5 to 1 m, is verified for tree top and crown base average heights for mature trees plots (i.e., #M1C, #M1D, #M1E and #M2A). Young tree sample plot comparisons show as well a good accuracy in the order of 1 m for the tree top retrievals. However, the crown bases estimations by lidar present a 2 m overestimation (#M1A and #M1B in Table 3). This could be related to a limited penetration of the laser beam into denser foliage of young trees.

Given the tree population and distribution densities in Mimizan #M1 and #M2 tests areas, the geo-location of the canopy lidar profiles were accurate enough to draw unambiguous one-to-one correlation with in situ measurements. This sub section presents the relevant comparisons between lidar and in situ observations. Two examples of coincidences for 14 and 17 trees, respectively, are displayed on Figures 9(a,b) (#M2B) and 9(c,d) (#M1B) for illustration.

Figure 9 shows a comparison of tree top and crown base heights as measured in situ (open bold squares) and by airborne canopy lidar (plain circles). Within the 7 m uncertainty on lidar footprint location at ground, very good agreement is found for measurements that are likely to correspond to the same trees in Figure 9(a,b) (e.g., for geo-location at 28 m LE, 18 m LN; 22 m LE, 13 m LN; and 13 m LE 26 m LN). Good measurements consistency is found for the histograms of tree top and crown base height measurements (to the right of Figure 9(a,b)).

Figure 9(c) indicates that for a young tree sample plot (#M2B) we obtain good matches (±1 m) for measurements of tree tops (e.g., at 15 m LE, 33 LN; 28 m LE, 8 LN; 21 m LE 3 m LN), but an overestimation of ∼2 m for the crown base (see histogram to the right of Figure 9(d); as mentioned from Table 3).