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This study explores the feasibility of applying single-scan airborne, static terrestrial and mobile laser scanning for improving the accuracy of tree height growth measurement. Specifically, compared to the traditional works on forest growth inventory with airborne laser scanning, two issues are regarded: “Can the new technique characterize the height growth for each individual tree?” and “Can this technique refine the minimum growth-discernable temporal interval further?” To solve these two puzzles, the sampling principles of the three laser scanning modes were first examined, and their error sources against the task of tree-top capturing were also analyzed. Next, the three-year growths of 58 Nordic maple trees (

The knowledge of tree height growths is increasingly required in a variety of domains, which range from forest harvest prediction for land-use planning [

Apart from further enhancement of the efficiencies of the photogrammetric methods, laser scanning proved to be another effective plan [

A large amount of new terrestrial laser scanning modes have been attempted in the last decade. Two typical kinds are static terrestrial laser scanning (TLS) and mobile laser scanning (MLS), and both can generally perform with high sampling densities. With this advantage, TLS has been widely applied for acquiring forest properties in the fine scales [

With better efficiency than TLS, MLS serves as a state-of-the-art survey technology [

Based on literature review, it seems that the above-mentioned three kinds of laser scanning modes can be combined to improve the performance of tree height growth measurement. The cost-effective frame can be figured out as follows: First, ALS surveys the tree-covered area of interest, and this is aimed at constructing the basic database of tree height distributions. Then, MLS measures several strips of the same area later, and their height differences compared to the corresponding ALS data can be used to derive the associated tree height growth models. At the same time, TLS measures sample trees to calibrate the deduced models. Finally, tree height growths across the whole target area can be imputed. To fulfill this solution frame, the effectiveness of the integration of these three laser scanning modes must be in prior verified. Hence, the objective of this study is to testify the feasibility of using single-scan ALS, TLS and MLS to improve the accuracies of tree height growth measurements. Note that single-scan is emphasized here in favor of the cost-effective demands in practice. Before testing the whole objective, two sub-questions need to be answered: (1) Can this new technique characterize the height growth of each single tree? (2) Can this technique refine the minimum growth-discernable temporal interval further less than two years? The following works will be expanded aimed at the two specific puzzles and the objective of this study.

The test site is located in a rectangular block of the Espoonlahti region, Southern Finland (60°15′N, 24°65′E). This area has served as the experimental field for evaluating the contributions of multiple cooperative projects. 58 broadleaved Nordic maples (

The campaigns for data collection were deployed in six separate days, entirely spanning three years. First, the ALS survey was conducted using a Topeye MK-II scanner (Topeye, Helsinki, Finland) on 18 December 2006. This day was chosen according to the inference that ALS-based single tree inventory generally performs better in terms of tree height during the leaf-off phases [

After data collection, any two datasets cannot be directly overlaid to explore tree height growths by differencing tree heights. The reason is that the inconsistency of their initial parameter specifications, e.g., different precisions of their altitude/position modules, different shadowing effects and different scanning geometry are unavoidable. Thus, the first step of data preprocessing was to put all of the independently-georeferenced point clouds together for registration. Here, the registration was fulfilled as follows. The control points were manually picked up from the feature points surrounding the target trees, and then, the rotation matrix and shift vector were solved. The detailed solution was to calculate the associated six parameters for rigid body transformation by means of the iterative closest point algorithm [

Automatic algorithms for isolation of single trees in scattered point clouds have been developed in regard to the ALS mode [

Generally with high sampling densities, TLS and MLS tend to represent tree tops more steadily than ALS. Accordingly, the heights of the highest laser hits amidst the point clusters were directly deemed as the heights of the corresponding target trees. This strategy is evidenced by the previous derivations [

The substantial goal of the analyses of tree-top scan principles was to pre-estimate the error ranges of the associated laser-derived tree heights. This is instructive for choosing appropriate laser scanning systems and for predicting tree height growths. In

The estimation of tree-top capturing errors as above indicates that the case of underestimating tree heights is inevitable, even in TLS surveys. Theoretically, this situation has given a negative answer to the first question posed in Section 1. That is, tree-level features do not mean accurate tree-level height growth measurements. Of course, the confirmative answer needs to be concluded from the test results later. Anyhow, the planned approach for investigation of tree height growths was to assume statistical analysis accordingly. In detail, the average height variations regarding a certain number of trees were calculated to characterize their height growths, and this can overcome the errors of laser scanning to some extent. Histogram was employed to depict of the frequency distributions of tree height growths. Gaussian regression was deployed on the histogram to characterize the average height growths, and the fitting was calculated in accordance to
_{m}), and

The statistical methods used for tree height growth characterization are helpful from the perspective of overcoming the inevitable tree-top capturing errors, but do not mean everything. ALS tended to underestimate tree heights [

_{ALS} = S_{A_L} − S_{A_I}, wherein S means the height of surface, the subscript A_I refers to the initial height measured by ALS, and the subscript A_L notes the height measured by ALS at last) can equally embody the real height growths (G_{R}), although tree tops are mostly missed by this scanning mode. This presents the theoretical basis for ALS-based height growth predictions in the previous works [

The above-derived relationships between tree heights and height growths have biases, when height growths are achieved by differentiating two tree heights derived from different kinds of laser scanning. For instance, the sum of the ALS-derived average height and the experience-dependent annual height growth is unnecessarily equal to the TLS-inferred average height in the next year. This suggests that it is requisite to further exploit the underlying relationships between tree heights and height growths of the same trees surveyed by different modes of laser scanning. In view of the goal frame for integration of laser scanning emphasized in this study, the exploitation is equivalently to explore the relationships between tree heights surveyed by TLS, MLS, and ALS at the same time. Then, the above-mentioned biases can be relatively sought and revised. Specifically, according to the indications in _{T_I}) and the ALS-derived surface (S_{A_I}), and the second bias is the height gap between the TLS-derived surface (S_{T_I}) and the MLS-derived surface (S_{M_I}). Regression analysis by linear fitting is used here to exploit the underlying relationships between tree heights derived from different laser scanning data. The fitted formula can be employed to make revisions of tree height derivations from ALS and MLS relative to TLS, and then, the accuracies of tree height growth calculations can be improved.

The reference height growths over one year were derived from the RoT and RiM data. In order to maintain the conditions consistent with the following comparisons, 48 trees also covered by ToA were considered. After statistics, the distributions of height growths compared to the related tree heights are displayed in the boxplots (_{m}) is 0.32 m, the standard deviation of height growth (G_{std}) is 0.40 m, and the mean height pertaining to the surveying day of 7 May 2009 (H_{m (RoT-48)}) is 6.97 m. In

The investigation of tree height growths over two years was deployed on the ToA and RoT surveys, and the latter was used as the reference data. The same 48 trees as mentioned above were processed. The frequencies of tree height growths in multiple height divisions are demonstrated in the histogram (_{m (ToA-48)}) is 6.18 m. It can be further realized that the annual growths of these same trees are inconsistent, compared to the reference data. Namely, the derived average height growth over two years in this case is larger than the twice of the average height growth over one year retrieved in the reference case. The cause is that the ALS-derived canopy surfaces are overall lower than the real ones. In other words, ALS tends to result in tree height underestimations. This is evidenced by the results that the H_{RoT} is less than the H_{ToA} to some extent. Specifically, those GN cases are the samples that are definitely underestimated.

The investigation of tree height growths over three years was executed on the ToA and RiM surveys, and the latter was used as the reference data. The same 48 trees were again involved in statistics. The relevant frequencies of tree height growths in multiple height divisions are likewise manifested in the histogram (

The Subsection 4.1 has primarily validated the integration of ALS, TLS and MLS for measurement of tree height growths spanning two or three years. However, the year-level interval is unnecessarily the minimum growth-discernable temporal span for this integrated survey technique. It is noticed that the reference data corresponds to the one-year height growths. So, whether the integration of terrestrial laser scanning can distinguish height growths in shorter periods is worth exploring further.

The investigation of tree height growths over one month was implemented on the RoM and RoT surveys, and the latter was used as the reference data. All of the 58 trees were involved in statistics. The related frequencies of tree height growths in multiple height divisions are manifested in the histogram (_{m (RoT-58)}) is 7.29 m, which is different from the opposite value in

The investigation of tree height growths over one month was also conducted by twice using Sensei, which features the medium sampling densities. The same 58 trees were regarded. The frequencies of tree height growths in different height divisions are demonstrated in the histogram (

The first case of seeking the quantitative rules for relative revision of tree height derivations refers to the SeMM data. The reference data is the point set collected almost synchronously by Roamer in TLS mode on 7 May 2009. The relationships of height pairs are displayed by scatterplots (^{2} value indicates that the Roamer and Sensei surveys are positively correlated in this case. Then, this function can be used to revise the tree heights in other plots in the same Sensei campaign.

The second case involves the ALS Topeye MK-II scanner with a low sampling density. The related reference data was generated by using the point sets collected by Roamer in TLS mode on 7 May 2009 and by Riegl in MLS mode on 21 March 2010, since their accuracies are approximate to the accuracies of traditional tree height measurement equipments like clinometers. For each tree, its reference height was acquired by subtracting the twice of the difference between the RiM- and RoT-derived heights from the RoT-derived height. The scatterplots in _{Inv (RiM-RoT)}). According to the definitions of GE and GN, the calculations of reference heights here can be corrected by pre-cancelling the GE and GN samples in the step of differencing the RiM- and RoT-derived heights. The scatterplots after this correction are shown in ^{2} and standard deviation improved both. The related linear fitting function as the simplified rule can be utilized to relatively revise the tree heights derived from the ALS data in other stands. With the state-of-the-art full waveform laser scanner [

The evaluation shows that the height growth of each individual tree cannot be reliably characterized even by terrestrial laser scanning in the single-scan mode. Note that the limitation of single-scan is highlighted particularly in this study in favor of the demands of cost-effectiveness in practice. Height growths yet need to be assessed by measuring a certain number of sample trees. After statistics, the minimum temporal interval for single-scan terrestrial laser scanning to distinguish tree height growths can be refined into one month, and the related mean height growths can still be discerned. Moreover, it shows that the incorporation of terrestrial laser scanning modes can help revising the parameter of tree height generally underestimated by airborne laser scanning and even mobile laser scanning. The joint usage of the three categories of laser scanning modes can enhance the conventional airborne laser scanning approaches in terms of efficiency, accuracy and adaptability. Overall, the feasibility of the proposed new technique for characterizing tree height growths has been primarily validated.

The financial support from the Academy of Finland (“Science and technology towards precision forestry”) is gratefully appreciated.

Illustration of the point clusters pertinent to a same tree that is surveyed by laser scanning in multi-modes: (

Schematic diagrams of laser scanning mechanisms ((

Schematic relationships between the measurements of tree heights and height growths in different laser scanning modes. See text for the definition of symbols.

Boxplots (

Histogram of the height growths derived (

Histogram of the one-month height growths derived (

Scatterplots of the tree heights derived from the SeMM and RoT data. See text for the definition of symbols.

Scatterplots of the tree heights derived from the ToA data and the tree heights inversely derived by combining the RoT and RiM data before relative revision (

Descriptive statistics of the 58 sample trees for test in terms of tree height.

_{(7 May 2009) by TLS} (m) |
_{(21 Mar 2010) by MLS} (m) | |
---|---|---|

Min | 3.36 | 4.08 |

Max | 10.32 | 10.73 |

Mean | 7.29 | 7.61 |

Std | 1.81 | 1.83 |

The settings of the campaigns for test and the configurations of all of the pulsed laser scanning systems (time-of-flight (TF) and phase-shift (PS)) for data collection.

Topeye MK-II | Topeye MK-II | ALS (ToA) | 960 | TF | 1064 | 83 |

Roamer | Faro Photon 80 | TLS (RoT) | 76 | PS | 785 | 7937 |

Roamer | Faro Photon 80 | MLS (RoM) | 76 | PS | 785 | 9441 |

Sensei | Ibeo Lux | MLS (SeMM) | 200 | TF | 905 | 2020 |

Sensei | Ibeo Lux | MLS (SeMJ) | 200 | TF | 905 | 2272 |

Riegl VMX-250 | Riegl VQ-250 | MLS (RiM) | 500 | TF | 1550 | 9532 |

Note that the abbreviations for short ((MLS system name, e.g., Ro) & (Scan mode, e.g., T)) apply throughout the paper.

Parametric specifications of the used laser scanning systems and the related tree-top capturing error estimations.

ToA | 90 | 0 | - | - | 360 | 0.3 | _{1} |

RiM | 45 | 45 | - | 0.12 | 360 | 0.04 | _{2} |

RoM | 45 | 0 | - | 0.096 | 360 | 0.17 | _{2} |

SeM | 0 | 0 | - | 0.25 | 110 | 0.4 | _{1} |

RoT | 0 | 0 | 0.15 | 0.125 | 360 | _{1} |
_{1} |