Knowledge of cloud geometrical thickness (H) is of importance for the study of radiative balance and cloud microphysics. However, the retrieval of H remains challenging, especially for passive instruments. In this work, we derive a semi-analytical algorithm for retrieving H of single-layer liquid cloud based on oxygen A-band hyperspectral measurements from NASA's Orbiting Carbon Observatory-2 (OCO-2). In this algorithm, a high-order correction is introduced to the approximation formula to accurately calculate oxygen A-band hyperspectral cloud reflectance. The algorithm can retrieve H in real time as it does not require the use of the time-consuming radiative transfer model for radiation calculation during each retrieval. In addition, the algorithm currently requires cloud optical depth, cloud top height, and aerosol properties measured by other instruments as input. In idealized simulations using ten thousand A-band spectra spanning a range of cloud cases, the root mean squared error (RMSE) of the retrieval is approximately 2.0 hPa (for low clouds, 1 hPa is about 10 m). We also retrieve H based on millions of real OCO-2 observations and compare the retrieval results with the cloud product from CloudSat/CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations). After abnormal samples are removed, the correlation coefficient is 0.716, the average bias is −15.6 hPa, and the RMSE is 27.4 hPa. The statistical results show that the absolute bias increases systematically with the reference cloud geometrical thickness, which may be caused by the unrealistic vertical homogeneous cloud assumption. The similar phenomenon was also found in comparison with OCO2CLD-LIDAR-AUX, a joint retrieval product based on OCO-2, CALIPSO, and accurate radiative transfer model. The fast algorithm shows a similar distribution of retrieved cloud bottom pressure and a smaller bias on cloud geometrical thickness retrieval compared to the OCO2CLD-LIDAR-AUX products.

云的几何厚度（H）的知识对于辐射平衡和云微物理学的研究非常重要。但是，H的检索仍然具有挑战性，尤其是对于无源仪器而言。在这项工作中，我们根据美国航空航天局（NASA）的轨道碳观测站2（OCO-2）的氧气A波段高光谱测量结果，得出了用于检索单层液云H的半分析算法。在该算法中，将高阶校正引入到近似公式中，以准确计算氧气A波段高光谱云的反射率。该算法可以检索H由于不需要在每次检索过程中使用费时的辐射传递模型进行辐射计算，因此可以实时进行。另外，该算法当前需要由其他仪器测量的云光学深度，云顶高度和气溶胶特性作为输入。在使用一万个A波段频谱跨云情况的理想模拟中，反演的均方根误差（RMSE）约为2.0 hPa（对于低云，1 hPa约为10 m）。我们还检索H基于数百万个实际OCO-2观测值，并将检索结果与CloudSat / CALIPSO（云气溶胶激光雷达和红外探路者卫星观测）的云产品进行比较。去除异常样本后，相关系数为0.716，平均偏差为-15.6 hPa，RMSE为27.4 hPa。统计结果表明，绝对偏差随着参考云几何厚度的增加而系统地增加，这可能是由于不切实际的垂直均匀云假设所致。与基于OCO-2，CALIPSO和精确辐射传输模型的联合检索产品OCO2CLD-LIDAR-AUX相比，也发现了类似现象。