Effective water management in agriculture requires a comprehensive understanding of the distribution of water content throughout the soil profile to the root zone. This knowledge empowers farmers and water managers to make informed decisions regarding irrigation timing and quantity for optimizing crop growth. To estimate the soil moisture profile, this study utilized combined L- and P-band radiometry with four incoherent radiative transfer models, including three multi-layer models based on a zero-order (IZ), first order (IF) and incoherent solution (IS) approximation, and a uniform model (UM) model, as well as the stratified coherent Njoku model (NM). The impact of vegetation was considered through the conventional tau-omega model. Linear (Li) and second-order polynomial (Pn2) functions were used to represent the shape of the soil moisture profile. Observations from a tower-based experiment under various land cover conditions, including bare, bare-weed, grass, wheat and corn, were used. The root mean square error (RMSE) was calculated between the observed and estimated soil moisture profiles. The results revealed comparable RMSE values for all five radiative transfer models, with the Pn2 function outperforming the Li function in estimating the soil moisture of deeper layers. Regardless of the employed radiative transfer model, utilizing combined L- and P-band radiometry and employing the Pn2 function yielded RMSEs of 0.03 m/m, 0.08 m/m, and 0.1 m/m over depths of 0–5 cm, 0–30 cm, and 0–60 cm, respectively. A comparison between the incoherent and stratified coherent Njoku radiative transfer models indicated that the latter slightly outperformed the former under the dry bare soil conditions, exhibiting a 0.003 m/m lower RMSE at the surface while nearly equal performance at the bottom of the profile. Furthermore, the multi-layer incoherent radiative transfer models provided only a slightly better estimate than the UM model, especially for shallow layers, with the average RMSE over the entire profile being 0.002 m/m lower. Consequently, the complexity of the multi-layer incoherent and coherent radiative transfer models is not justified for this small gain in performance. The depth for which the UM model provided a reasonable soil moisture estimate ranged from 1 cm (under wet corn) to 39 cm (under dry bare), and depended on the soil moisture profile gradient and soil moisture content values in the shallow layers. These important findings pave the way for estimating soil moisture profile on a global scale using combined L- and P-band radiometry from future satellite missions.

中文翻译：

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使用组合的 L 波段和 P 波段辐射计观测来估计裸土和植被土壤下的土壤湿度剖面：一种不相干的建模方法

农业中有效的水资源管理需要全面了解从整个土壤剖面到根区的水分分布。这些知识使农民和水管理者能够就灌溉时间和数量做出明智的决定，以优化作物生长。为了估计土壤湿度剖面，本研究结合了 L 和 P 波段辐射测量以及四个非相干辐射传输模型，包括基于零阶 (IZ)、一阶 (IF) 和非相干解的三个多层模型 ( IS）近似，以及均匀模型（UM）模型，以及分层相干Njoku模型（NM）。通过传统的 tau-omega 模型考虑植被的影响。线性 (Li) 和二阶多项式 (Pn2) 函数用于表示土壤湿度剖面的形状。使用了在各种土地覆盖条件下（包括裸露、裸露杂草、草地、小麦和玉米）的塔式实验的观测结果。计算观测到的和估计的土壤湿度剖面之间的均方根误差（RMSE）。结果显示，所有五种辐射传输模型的 RMSE 值相当，其中 Pn2 函数在估计深层土壤湿度方面优于 Li 函数。无论采用何种辐射传输模型，利用组合的 L 和 P 波段辐射测量并采用 Pn2 函数，在 0–5 cm、0– 深度上产生的 RMSE 为 0.03 m/m、0.08 m/m 和 0.1 m/m。分别为 30 厘米和 0-60 厘米。非相干辐射传输模型和分层相干 Njoku 辐射传输模型之间的比较表明，后者在干燥裸土条件下略优于前者，表面 RMSE 低 0.003 m/m，而剖面底部的性能几乎相同。此外，多层非相干辐射传输模型仅提供了比 UM 模型稍好的估计，特别是对于浅层，整个剖面的平均 RMSE 低 0.002 m/m。因此，多层非相干和相干辐射传输模型的复杂性并不能证明这种微小的性能增益是合理的。 UM 模型提供合理土壤湿度估计的深度范围为 1 厘米（湿玉米下）到 39 厘米（干燥裸露下），并取决于土壤湿度剖面梯度和浅层土壤湿度值。这些重要发现为利用未来卫星任务的 L 和 P 波段辐射测量相结合来估计全球范围内的土壤湿度剖面铺平了道路。