The increasing availability of remotely sensed data has recently challenged the traditional way of performing forest inventories, and induced an interest in model-based inference. Like traditional design-based inference, model-based inference allows for regional estimates of totals and means, but in addition for wall-to-wall mapping of forest characteristics. Recently Light Detection and Ranging (LiDAR)-based maps of forest attributes have been developed in many countries and been well received by users due to their accurate spatial representation of forest resources. However, the correspondence between such mapping and model-based inference is seldom appreciated. In this study we applied hierarchical model-based inference to produce aboveground biomass maps as well as maps of the corresponding prediction uncertainties with the same spatial resolution. Further, an estimator of mean biomass at regional level, and its uncertainty, was developed to demonstrate how mapping and regional level assessment can be combined within the framework of model-based inference. Through a new version of hierarchical model-based estimation, allowing models to be nonlinear, we accounted for uncertainties in both the individual tree-level biomass models and the models linking plot level biomass predictions with LiDAR metrics. In a 5005 km2 large study area in south-central Sweden the predicted aboveground biomass at the level of 18 m ×18 m map units was found to range between 9 and 447 Mg ·ha−1. The corresponding root mean square errors ranged between 10 and 162 Mg ·ha−1. For the entire study region, the mean aboveground biomass was 55 Mg ·ha−1 and the corresponding relative root mean square error 8%. At this level 75% of the mean square error was due to the uncertainty associated with tree-level models. Through the proposed method it is possible to link mapping and estimation within the framework of model-based inference. Uncertainties in both tree-level biomass models and models linking plot level biomass with LiDAR data are accounted for, both for the uncertainty maps and the overall estimates. The development of hierarchical model-based inference to handle nonlinear models was an important prerequisite for the study.

中文翻译：

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使用LiDAR和野外数据绘制地上生物量及其预测不确定性，并解释了树级异度和LiDAR模型误差

遥感数据的可用性不断提高，最近对执行森林清单的传统方式提出了挑战，并引起了对基于模型的推理的兴趣。像传统的基于设计的推理一样，基于模型的推理允许对总量和均值进行区域估计，此外还可以进行森林特征的逐壁映射。最近，在许多国家已经开发了基于光检测和测距（LiDAR）的森林属性图，由于其精确的森林资源空间表示，受到了用户的好评。但是，这种映射和基于模型的推理之间的对应关系很少被理解。在这项研究中，我们应用了基于层次模型的推理，以生成地上生物量图以及具有相同空间分辨率的相应预测不确定性图。此外，开发了区域水平的平均生物量估计值及其不确定性，以说明如何在基于模型的推理框架内将地图绘制和区域水平评估相结合。通过基于模型的基于层次模型的估计的新版本，允许模型为非线性，我们考虑了单个树级生物量模型以及将样地级生物量预测与LiDAR指标链接的模型中的不确定性。在瑞典中南部的一个5005 km2的大研究区中，在18 m×18 m地图单位水平上预测的地上生物量被发现介于9到447 Mg·ha-1之间。相应的均方根误差在10到162 Mg·ha-1之间。在整个研究区域中，地上生物量平均为55 Mg·ha-1，相应的相对均方根误差为8％。在此级别，均方误差的75％是由于与树级模型相关的不确定性所致。通过提出的方法，可以在基于模型的推理框架内链接映射和估计。无论是不确定性图还是总体估计值，都考虑了树级生物量模型以及将样地级生物量与LiDAR数据关联的模型中的不确定性。开发基于层次模型的推理以处理非线性模型是该研究的重要前提。地上平均生物量为55 Mg·ha-1，相应的相对均方根误差为8％。在此级别，均方误差的75％是由于与树级模型相关的不确定性所致。通过提出的方法，可以在基于模型的推理框架内链接映射和估计。无论是不确定性图还是总体估计值，都考虑了树级生物量模型以及将样地级生物量与LiDAR数据关联的模型中的不确定性。开发基于层次模型的推理以处理非线性模型是该研究的重要前提。地上平均生物量为55 Mg·ha-1，相应的相对均方根误差为8％。在此级别，均方误差的75％是由于与树级模型相关的不确定性所致。通过提出的方法，可以在基于模型的推理框架内链接映射和估计。无论是不确定性图还是总体估计值，都考虑了树级生物量模型以及将样地级生物量与LiDAR数据关联的模型中的不确定性。开发基于层次模型的推理以处理非线性模型是该研究的重要前提。通过提出的方法，可以在基于模型的推理框架内链接映射和估计。无论是不确定性图还是总体估计值，都考虑了树级生物量模型以及将样地级生物量与LiDAR数据关联的模型中的不确定性。开发基于层次模型的推理以处理非线性模型是该研究的重要前提。通过提出的方法，可以在基于模型的推理框架内链接映射和估计。无论是不确定性图还是总体估计值，都考虑了树级生物量模型以及将样地级生物量与LiDAR数据关联的模型中的不确定性。开发基于层次模型的推理以处理非线性模型是该研究的重要前提。