Retrieval of vegetation properties from satellite and airborne optical data usually takes place after atmospheric correction, yet it is also possible to develop retrieval algorithms directly from top-of-atmosphere (TOA) radiance data. One of the key vegetation variables that can be retrieved from at-sensor TOA radiance data is leaf area index (LAI) if algorithms account for variability in atmosphere. We demonstrate the feasibility of LAI retrieval from Sentinel-2 (S2) TOA radiance data (L1C product) in a hybrid machine learning framework. To achieve this, the coupled leaf-canopy-atmosphere radiative transfer models PROSAIL-6SV were used to simulate a look-up table (LUT) of TOA radiance data and associated input variables. This LUT was then used to train the Bayesian machine learning algorithms Gaussian processes regression (GPR) and variational heteroscedastic GPR (VHGPR). PROSAIL simulations were also used to train GPR and VHGPR models for LAI retrieval from S2 images at bottom-of-atmosphere (BOA) level (L2A product) for comparison purposes. The BOA and TOA LAI products were consistently validated against a field dataset with GPR ($R^2$ of 0.78) and with VHGPR ($R^2$ of 0.80) and for both cases a slightly lower RMSE for the TOA LAI product (about 10% reduction). Because of delivering superior accuracies and lower uncertainties, the VHGPR models were further applied for LAI mapping using S2 acquisitions over the agricultural sites Marchfeld (Austria) and Barrax (Spain). The models led to consistent LAI maps at BOA and TOA scale. The LAI maps were also compared against LAI maps as generated by the SNAP toolbox, which is based on a neural network (NN). Maps were again consistent, however the SNAP NN model tends to overestimate over dense vegetation cover. Overall, this study demonstrated that hybrid LAI retrieval algorithms can be developed from TOA radiance data given a cloud-free sky, thus without the need of atmospheric correction. To the benefit of the community, the development of such hybrid models for the retrieval vegetation properties from BOA or TOA images has been streamlined in the freely downloadable ALG-ARTMO software framework.

从卫星和机载光学数据中检索植被属性通常在大气校正之后进行，但也可以直接从大气层顶部（TOA）辐射数据开发检索算法。如果算法考虑了大气的变化，则可以从传感器 TOA 辐射数据中检索的关键植被变量之一是叶面积指数 (LAI)。我们演示了在混合机器学习框架中从 Sentinel-2 (S2) TOA 辐射数据（L1C 产品）检索 LAI 的可行性。为了实现这一目标，使用耦合的叶-冠层-大气辐射传输模型 PROSAIL-6SV 来模拟 TOA 辐射数据和相关输入变量的查找表 (LUT)。然后，该 LUT 用于训练贝叶斯机器学习算法高斯过程回归 (GPR) 和变分异方差 GPR (VHGPR)。 PROSAIL 模拟还用于训练 GPR 和 VHGPR 模型，以便从大气底部 (BOA) 水平的 S2 图像（L2A 产品）进行 LAI 检索，以进行比较。 BOA 和 TOA LAI 产品经过 GPR 现场数据集的一致验证（${\mathrm{<span\; data-immersive-translate-walked="b478b790-477e-4748-845c-6fac9b9caffc">右</span>}}^{\mathrm{<span\; data-immersive-translate-walked="b478b790-477e-4748-845c-6fac9b9caffc">2</span>}}$ 0.78）和 VHGPR（${\mathrm{<span\; data-immersive-translate-walked="b478b790-477e-4748-845c-6fac9b9caffc">右</span>}}^{\mathrm{<span\; data-immersive-translate-walked="b478b790-477e-4748-845c-6fac9b9caffc">2</span>}}$ 0.80），对于这两种情况，TOA LAI 产品的 RMSE 均略低（约降低 10%）。由于 VHGPR 模型具有较高的精度和较低的不确定性，因此通过在 Marchfeld（奥地利）和 Barrax（西班牙）农业地点采集 S2，进一步将 VHGPR 模型应用于 LAI 测绘。 这些模型生成了 BOA 和 TOA 比例尺的一致 LAI 地图。还将 LAI 地图与 SNAP 工具箱生成的 LAI 地图进行比较，SNAP 工具箱基于神经网络 (NN)。地图再次保持一致，但 SNAP NN 模型往往会高估茂密的植被覆盖。总的来说，这项研究表明，在无云天空的情况下，可以根据 TOA 辐射数据开发混合 LAI 反演算法，因此不需要大气校正。为了社区的利益，用于从 BOA 或 TOA 图像检索植被属性的混合模型的开发已在可免费下载的 ALG-ARTMO 软件框架中得到简化。