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These authors contributed equally to this work.

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (

The ultimate goal of this multi-article series is to develop a methodology to generate continuous fields of tree height and biomass. The first paper demonstrated the need for Allometric Scaling and Resource Limitation (ASRL) model optimization and its ability to generate spatially continuous fields of tree heights over the continental USA at coarse (1 km) spatial resolution. The objective of this second paper is to provide an assessment of that approach at site scale, specifically at 12 FLUXNET sites where more accurate data are available. Estimates of tree heights from the Geoscience Laser Altimeter System (GLAS) waveform data are used for model optimization. Amongst the five possible GLAS metrics that are representative of tree heights, the best metric is selected based on how closely the metric resembles field-measured and Laser Vegetation Imaging Sensor tree heights. In the optimization process, three parameters of the ASRL model (area of single leaf, α; exponent for canopy radius, η; and root absorption efficiency, γ) are simultaneously adjusted to minimize the difference between model predictions and observations at the study sites (distances to valid GLAS footprints ≤ 10 km). Performance of the optimized ASRL model was evaluated through comparisons to the best GLAS metric of tree height using a two-fold cross validation approach (R^{2} = 0.85; RMSE = 1.81 m) and a bootstrapping approach (R^{2} = 0.66; RMSE = 2.60 m). The optimized model satisfactorily performed at the site scale, thus corroborating results presented in part one of this series. Future investigations will focus on generalizing these results and extending the model formulation using similar allometric concepts for the estimation of woody biomass.

Forest height and biomass are important attributes required for quantifying the dynamics of the terrestrial carbon cycle [

The extrapolation methods well estimate forest structural attributes by exploiting advancements in remote sensing. Small footprint lidar, Terrestrial Laser Scanners [

Therefore, the parametric optimization of the ASRL model possibly brings significant progress in mapping tree heights and biomass by incorporating actual observations (

In this study, we used four different sources of field-measured tree heights. Data from 82 plots were assembled from seven field sites (

LVIS is an airborne laser altimeter sensor that records the intensity of returned signals from a target surface [

LVIS datasets used in this study were categorized into two groups. The first dataset was used to compare LVIS heights with concurrent field-measured tree heights in seven different locations (

The latest release of GLAS laser altimetry data (Release 33) available from the National Snow and Ice Data Center was used in this study. GLAS waveform data provide information on land elevation and vegetation cover within its ellipsoidal footprints at ∼170 m spaced intervals [

The ASRL model predicts potential tree heights. The model combines statistical allometric scaling laws with local energy budgets constrained by resource limitations such as water, radiation, wind and air temperature [

The analysis in this paper is focused on sites from the FLUXNET network [

The FLUXNET datasets do not contain all the input climatic variables required by the ASRL model. Annual incoming solar radiation, annual average wind speed and annual average vapor pressure were therefore obtained from the DAYMET database [

The ASRL model requires two ancillary variables: (a) LAI and (b) DEM. Several Landsat TM scenes (

Prior to the optimization of the ASRL model with GLAS tree heights, we perform an exercise finding the best GLAS metric that closely corresponds to field-measured and LVIS derived tree heights. This analysis is based on two premises: (a) canopy height derived from LVIS data is related to field-measured tree height as reported in previous studies [

The root mean square error (RMSE) and R^{2} (from the linear-regression) are used to determine how well tree heights are related to each other in the inter-comparisons among field-measured, LVIS, and GLAS derived tree heights. Systematic errors related to biases in measurements are additionally considered in the interpretation of results.

Field-measured datasets used in this study differed in their sampling methodologies and plot designs. Also, the coordinates of individual trees were not recorded in every measurement campaign/census. This precluded a footprint-level comparison between field-measured and LVIS tree heights, unlike in some previous studies [_{field-measured}_{LVIS}

Three standard altimetry variables are available from the GLA14 product based on the Gaussian decomposition approach [_{A–E}

The spatial correspondence between LVIS and GLAS footprints was determined using the maximum distance from the center of a GLAS footprint to any LVIS footprint (within ∼45 m; _{LVIS}_{GLAS}

The result analyses were stratified into three groups, based on topographic conditions over the GLAS footprint, as low (slope ≤ 5°), intermediate (5° < slope ≤ 10°) and high (10° < slope ≤ 20°). All outliers were removed in this comparison exercise, _{A–E}

The initial model runs are driven by input datasets and result in potential tree heights at each study site. Key climate input data (temperature and precipitation) are derived from FLUXNET sites. DAYMET, LAI, and DEM grids nearest to the study sites provide other climatic variables and ancillary data for the model runs. The unoptimized ASRL model predicts only potential tree heights considering hydraulic limits to tree growth. These differ from observations due to the fact that the unoptimized model applies homogeneous steady-state allometric scaling laws across different environmental conditions and forest types with varying age classes [

Remote sensing based altimetry data, which provide actual tree heights, can alleviate the limitation of the unoptimized ASRL model related to different growing conditions and forest types with varying age classes. The model optimization is detailed in the first paper of this series [

Three model parameters are iteratively adjusted during optimization: (a) area of single leaf, α, (b) exponent for canopy radius, η, and (c) root absorption efficiency, γ. The respective initial values are 13 cm^{2}, 1.14, and 0.33 [^{2} ≤ α < 100 cm^{2}, 0.8 ≤ η < 1.5, and 0.1 ≤ γ < 0.8 (as in the TRY database [

Our approach has constraints due to a limited number of scaling parameters (α, η, and γ) explored in the model optimization and an assumption that allometric scaling laws at individual tree level are applicable at larger scales. In addition, a limitation of this study is that the model does not directly account for variation in forest stand age in the optimization process. Tree heights and growth rates are clearly related to forest stand ages [

The performance of the optimized ASRL model is evaluated through comparisons against GLAS tree heights in this study. The two-fold cross validation technique is a common statistical approach that randomly divides original samples into two equal sets of training and test data. The first half of GLAS tree heights was used as a training dataset to optimize the model at a site. The test dataset was prepared by averaging the remaining half of GLAS tree heights at the same site. Training and test GLAS data are completely separated in the cross validation (^{2} from the linear regression.
_{opt ASRL training}_{GLAS test}

A second evaluation of the optimized ASRL model was performed at the eco-climatic zone scale [

A bootstrapping approach [^{2} from the linear regression is additionally provided for the interpretation. Two groups of subsamples (training and test) also have no overlaps in each other.
_{opt ASRL training}_{GLAS test}

We first performed a plot-level comparison between LVIS tree heights and field measurements (^{2} = 0.76 and RMSE = 4.13 m) is comparable to previous reports (footprint-level comparison [

The average tree growth rates in study regions can be approximated using an equation of Shugart

Relatively large deviation is found in the results of Barro-Colorado Island. Two plausible reasons are associated with (a) tree growth rates of tropical forest and (b) terrain features and densely vegetated environment of the study area. Tropical forests increase more in size [

Subsequent analysis was focused on comparison of five metrics derived from GLAS waveform data (_{A–E}_{C}^{2} of 0.70 and RMSE of 4.42 m (P < 0.01)). This metric was derived from the distance between the last Gaussian peak and signal beginning of the GLAS waveform and incorporated topographic effect correction. Overestimations are related to both topographic gradient effects and GLAS waveform parameters. The bias increased with increasing tree heights (_{A}_{B}_{B}_{D}

Similarly, for regions with intermediate slope condition (_{C}^{2} and larger RMSE as compared to the low slope condition. In the case of high topographic gradients (_{D}

The ASRL model was optimized using tree heights derived from the best GLAS height metric (_{C}^{2} = 0.85; RMSE = 1.81 m; P < 0.01) was obtained when comparing the optimized model predictions with the average of test GLAS tree heights (

The optimized values of allometric parameters for the study sites are listed in ^{2}). It varied from 14.0 cm^{2} for the US-MMS site to 56.0 cm^{2} for the US-Ha2 site. This supports the relative significance of selecting α as an additional allometric parameter in model optimization. The other two allometric parameters, exponent for canopy radius, η (initial value: 1.14) and root absorption efficiency, γ (initial value: 0.33), were also adjusted in the optimization with η values ranging from 0.94 for the US-MOz site to 1.24 for the US-Ha1 site and γ ranging from 0.19 for the US-Ho1 site to 0.38 for the US-SP3 site. These parameters were relatively stable compared to α, as previously reported by Kempes

Optimizing three parameters clearly improved model performance.

We performed a second evaluation of the optimized ASRL model at the eco-climatic zone scale (

As shown by the bootstrapping evaluation approach (^{2} = 0.66; RMSE = 2.60 m; P < 0.01). The model’s error variance decreased from 0.60 to 0.02 after optimization (

The Allometric Scaling and Resource Limitations (ASRL) model optimized with the Geoscience Laser Altimeter System (GLAS) waveform data was tested at site scale (12 FLUXNET sites over the continental USA) in this second of a multi-article series. The model predicts potential tree heights based on local energy budgets limited by water, radiation, wind and air temperature. Predicted potential tree heights differ from observations due to homogeneous scaling parameters and exponents across different eco-climatic zones and forest types with varying age classes. Model optimization in this study is aimed at minimizing the difference between model predictions and observations (

Amongst the five GLAS metrics (_{A–E}_{C}^{2} = 0.76; RMSE = 4.13 m) and (b) the five GLAS metrics of tree heights and LVIS tree heights (R^{2} = 0.70; RMSE = 4.42 m for _{C}_{C}

The optimized model prediction was evaluated using two-fold cross validation and bootstrapping exercises. Predicted tree heights explained 85% of the variability in GLAS tree heights and on average showed an estimation error of 1.81 units of height from the two-fold cross validation approach at the studied sites. The variance of model errors to observation decreased from 0.53 to 0.01 after model optimization. In the case of bootstrapping, the study sites were stratified into five eco-climatic zones based on dominant forest type, annual total precipitation and annual average temperature. This exercise also resulted in a satisfactory prediction of GLAS tree heights by the optimized model (R^{2} = 0.66; RMSE = 2.60 m) and a decrease in model error variance from 0.60 to 0.02 after optimization.

This investigation at site scale provides evidence corroborating our initial study [

Forthcoming investigations will focus on extending the model formulation using similar concepts for the estimation of woody biomass (next two articles in preparation). Also, our approach will be tested over different study locations (e.g., China and Amazon Basin) to generalize the results for mapping global tree heights and biomass. A future research will be conducted over Amazon Basin where eco-climatic regimes and forest types are quite different from the CONUS. The availability of input climate data with good quality is certainly a challenge in this study region. Additionally, eco-climatic regimes and forest types of some regions in China may resemble those of the CONUS, but scaling parameters of the ASRL model are not necessarily identical. Hence, we will investigate the feasibility of the ASRL model in various regions by obtaining the appropriate scaling parameters.

This study was partially funded by the National Natural Science Foundation of China (grants no. 40801139 and 41175077), China Scholarship Council and the Fulbright Foundation.

Preprocessing/filtering steps for determining valid GLAS waveform data. Ancillary datasets required include National Land Cover Database (NLCD) Landcover, Moderate Resolution Imaging Spectroradiometer (MODIS) Vegetation Continuous Fields (VCF) and National Elevation Dataset (NED)-derived Digital Elevation Model (DEM).

(

Diagram showing ASRL model optimization. The model predicts potential tree heights (initial prediction) using climatic and ancillary data. Three allometric scaling parameters of the model (area of single leaf, α; exponent for canopy radius, η; and root absorption efficiency, γ) are simultaneously adjusted to find the minimum of the difference between GLAS tree heights and model predictions. GLAS tree heights are estimated using the best GLAS metric that closely resembles field-measured and LVIS tree heights amongst five GLAS height metrics (

Comparison of LVIS tree heights with field measurements. A total of 82 plots from seven different sites are considered in this analysis. Regression analysis indicates a statistically significant relationship between LVIS tree heights and field measurements (p < 0.01). ^{#} In Sierra National Forest, there is one extremely influential observation due to old growth forests (ages > 150; [

Comparison of five GLAS-derived metrics (_{A–E}

Comparison of the optimized ASRL model predictions with the best GLAS metric of tree height (_{C}

Distributions of tree heights over 12 FLUXNET sites: (

Bootstrapping evaluation of the optimized ASRL model. The optimized model used the best GLAS tree height metric (_{C}

Datasets for inter-comparisons between field measured and Laser Vegetation Imaging Sensor (LVIS) waveform derived heights. There are 82 measurement plots spanning seven field sites in this study.

La Selva Biological Station, Costa Rica | 30 | 2006 | 10 × 100 | [ |
2005 |

Barro Colorado Island, Panama | 20 | 2000 | 100 × 100 | [ |
1998 |

Penobscot Experimental Forest, Maine, USA | 12 | 2009 | 50 × 200 | [ |
2003 |

Sierra National Forest, California, USA | 8 | 2008 | 100 × 100 | [ |
2008 |

Harvard Forest, Massachusetts, USA | 2 | 2007 | 100 × 100 | 2003 | |

2 | 2009 | 50 × 50 | |||

Howland Research Forest, Maine, USA | 2 | 2007 | 100 × 100 | 2003 | |

2 | 2009 | 50 × 50 | |||

Bartlett Experimental Forest, New Hampshire, USA | 2 | 2007 | 100 × 100 | 2003 | |

2 | 2009 | 50 × 50 |

Datasets for inter-comparisons between LVIS derived heights and Geoscience Laser Altimeter System (GLAS) height metrics (six different sites used in this study).

| ||
---|---|---|

White River Wildlife Refuge, AR, USA | 2006 | 2003–2006 |

Sierra Nevada, CA, USA | 2008 | 2003–2006 |

Harvard Forest, MA, USA | 2003 | 2003–2006 |

Patapsco Forest, MD, USA | 2003 | 2003–2006 |

Howland Research Forest and Penobscot Experimental Forest, ME, USA | 2003 | 2003–2006 |

Bartlett Experimental Forest, NH, USA | 2003 | 2003–2006 |

The 12 FLUXNET sites selected for analysis in this study based on the distance between a site and valid GLAS footprints (≤10 km radius). The three dominant forest types at these sites are Evergreen Needleleaf Forest (ENF), Deciduous Broadleaf Forest (DBF), and Mixed Forests (MF). Percent tree cover values were derived from the MODIS VCF product.

US-Me1 | Metolius Eyerly Burn | OR, USA | 2004–2005 | ENF | 63 | 29 |

US-Syv | Sylvania Wilderness Area | MI, USA | 2001–2006 | MF | 52 | 33 |

US-Ha1 | Harvard Forest EMS Tower | MA, USA | 1992–2006 | DBF | 74 | 68 |

US-Ho1 | Howland Forest (main tower) | ME, USA | 1996–2004 | ENF | 73 | 33 |

US-MMS | Morgan Monroe State Forest | IN, USA | 1999–2006 | DBF | 70 | 18 |

US-Bar | Bartlett Experimental Forest | NH, USA | 2004–2006 | DBF | 93 | 12 |

US-Ha2 | Harvard Forest Hemlock Site | MA, USA | 2004 | ENF | 74 | 67 |

US-MOz | Missouri Ozark Site | MO, USA | 2004–2007 | DBF | 51 | 64 |

US-Ho2 | Howland Forest (west tower) | ME, USA | 1999–2004 | ENF | 74 | 31 |

US-LPH | Little Prospect Hill | MA, USA | 2003–2005 | DBF | 73 | 68 |

US-SP3 | Slashpine-Donaldson-mid-rot-12yrs | FL, USA | 2008 | ENF | 51 | 30 |

US-WCr | Willow Creek | WI, USA | 1999–2006 | DBF | 51 | 9 |

Five possible GLAS height metrics based on Gaussian decomposition approach and topographic effect correction. Statistical analysis examining the full GLAS waveform extents [

_{A} |
No | [ | |

_{B} |
SigBegOff − |
No | [ |

_{C} |
Yes | [ | |

_{D} |
Yes | - | |

_{E} |
No | - |