Satellite-derived land surface temperature (LST) is a directional variable and has significant angular anisotropy. This characteristic contributes to enhance the differences among different satellite-derived LST products, and therefore increases the challenge of using multi-sensor and multi-decadal data to provide a long-term and angleconsistent LST climate data record. The kernel-driven model can balance the interpretability and operability well, so that it is suitable for angular normalization of LST products. The calibration of the kernel-driven model depends on multi-angle data which is difficult to obtain due to the spatial-temporal heterogeneity of LST. In this study, a novel LST angular normalization method based on the kernel-driven model was proposed to correct the angular effect of satellite-derived LST product by constructing multi-angle LST dataset from one geostationary satellite (GOES-R/ABI) and four polar-orbiting satellites (Terra/MODIS, Aqua/MODIS, Metop/AVHRR, and SNPP/VIIRS). The dataset gathered more abundant angle information, i.e., LSTs from three different observation geometries for the same pixel. The kernel-driven model was calibrated using the multi-angle LST dataset in the Continental United States (CONUS) during the year 2020. The discrepancies of the root mean square difference between LST before and after angular normalization range from 0.14 K to 1.10 K over nine land cover types in the four seasons. Similar results are obtained when the calibrated kernel-driven model was further expanded to other years and areas (i.e., the CONUS in 2021 and East Asia in 2020). The LST angular normalization method was applied to correct the angular effect of MODIS LST product. The results indicate that there is a strong correlation between the spatial distribution of LST differences (LST before and after angular normalization) and view zenith angle (VZA). MODIS LSTs before and after angular normalization were compared with Landsat 8 LST and Sentinel-3 A LST in near-nadir viewing for January, April, July, and October 2020. The angular normalization reduced the root mean square error (RMSE) between MODIS LST and Landsat 8 LST by 0.94-2.06 K in different months and by 0.13-2.61 K over various land cover types. For Sentinel-3 A, the RMSE decreased by 0.30-0.64 K in different months. The accuracies of MODIS LST before and after angular normalization were further validated using in situ measurements at the six SURFRAD sites. There are large discrepancies between the RMSE of MODIS LST before and after angular normalization versus in situ LST for VZA >= 45 degrees. The largest discrepancy is up to approximately 1.3 K at the GWN site. The LST angular normalization method has the potential to provide an angle-consistent LST climate data record.

Land surface temperature (LST) is an essential climate variable (ECV) which can be estimated from appropriate measurements of the surface thermal infrared (TIR) radiance. LST varies on a very short time scale and closely depends on the illumination and scan angles considered. To fully exploit LST products, a method for reconstructing the temporal profile and the angular dependence at the same time is proposed here. A combined visible- thermal envelope method (VT-KDTC) is built using kernel-driven (KD) and diurnal temperature cycle (DTC) models, referring to the surface structure and thermal factors, respectively. To demonstrate the reliability of the approach, TIR data from the geostationary satellite Himawari 8 are combined with visible and near-infrared (VNIR) data from the polar orbit satellite Sentinel-3A/3B. In addition to satellite observations, a synthetic dataset from the Soil Canopy Observation, Photochemistry and Energy Fluxes (SCOPE) model is also generated. Considering an anisotropy model in addition to the DTC model leads to a method displaying a better ability to simulate LSTs with a root mean squared error (RMSE) of 0.48 K against the original satellite results, compared to only the DTC model up to 1.44 K. By utilizing the field measurements as a reference, the reconstructed results are improved with a total bias of 0.72K and an RMSE of 2.58 K. Compared to the original results without correction, approximately 41% and 10% decreases are obtained in bias and RMSE, respectively. Our proposed method can also achieve LST downscaling supported by the higher spatial resolution of VNIR data when the temperature difference is assumed to be homogeneous within the coarse pixels. Thus, a simple achievable solution can be used for temperature reconstruction to enhance the quality of the LST product.

An approach based on a Physics-Informed Neural Network (PINN) is introduced to tackle the two-dimensional (2D) rheological consolidation problem in the soil surrounding twin tunnels with different cross-sections, under exponentially time-growing drainage boundary. The rheological properties of the soil are modelled using a generalized viscoelastic Voigt model. An enhanced PINN-based solution is proposed to overcome the limitation of traditional PINNs in solving integral-differential equations (IDEs) equations. In particular, two key elements are introduced. First, a normalization method is employed for the spatio-temporal coordinates, to convert the IDEs governing the consolidation problem into conditions characterized by unit-duration time and unit-area geometric domain. Second, a conversion method for integral operators containing function derivatives is devised to further transform the IDEs into a set of second-order constant-coefficient homogeneous linear partial differential equations (PDEs). By using the TensorFlow framework, a series of PINN-based models is developed, incorporating the residual adaptive sampling method to address the 2D consolidation equations of soft soils surrounding tunnels with different burial depths and cross-sections. Comparative analyses between the PINNbased solutions, and either finite element or analytical solutions highlight that the aforementioned normalization stage empowers PINNs to solve the PDEs across different spatial and temporal scales. The integral operator transformation method facilitates the utilization of PINNs for solving intricate IDEs.

In southwest China, red mudstone fill material (RMF) is widely used in constructing railway subgrades to substitute the conventional unbound granular materials (UGMs). Besides the strain-level dependent dynamic properties, RMF significantly depends on loading cycles. However, such an effect has yet to be incorporated into the current design method, which would lead to a considerable misprediction in dynamic responses of the RMF subgrade during the operation period. This paper presents a comprehensive study of long-term dynamic properties of RMF (a silty clay) over a range of water contents and cyclic stresses. The objective is to establish a normalization framework of dynamic properties that considers the effect of large numbers of cyclic loading. With this emphasis, 40 cyclic triaxial tests with 50000 loading cycles were conducted on RMF specimens compacted at various water contents. Two-stage behavior has been identified in equivalent Young's modulus and damping ratio evolutions. An exponential model is thus proposed to capture the two-stage pattern. The proposed normalization procedure showed a competent availability for the characterization of equivalent Young's modulus and damping ratio at different loading cycles. Soil fabric also played a decisive role in evaluating RMF's dynamic responses. Evidence of microfabric effect on the dynamic responses of RMF was strengthened by the Mercury intrusion porosimetry (MIP) and scanning electron microscope (SEM) analysis.

The loading intermittence duo to the time interval between adjacent passing trains is conducive to improving the dynamic stability of railway subgrade, but this intermittence effect is always ignored in existing experimental studies on the dynamic characteristics of subgrade fillers in which a continuous cyclic loading method was adopted to simulate the long-term train-induced loading on subgrade. This paper aims to study the backbone curves of subgrade silty filler under intermittent train-induced loading, considering the time interval between adjacent passing trains. By conducting a series of intermittent cyclic triaxial tests on silty filler, the backbone curves of each loading stage were constructed, and the effects of loading intermittence on the backbone curves were elaborated. The experiment results indicate that the loading intermittence enhances the resistance of subgrade silty filler to the dynamic loading and is conducive to the upward deviation of the backbone curves. The loading intermittence could effectively increase the ultimate value of dynamic stress amplitude that the silty filler could bear under cyclic loading, but has little effect on the maximum/initial resilient modulus. The backbone curves increase approximately linear under the states of plastic shakedown and plastic creep, but show significant nonlinearity after including the incremental collapse samples. Hyperbolic models for backbone curves such as H-D model and its improvement model could be adopted to characterize the backbone curves of silty filler under intermittent loading, and the normalization of H-D model was also discussed to integrate the influencing factors (i.e., moisture content and confining pressure) of the backbone curves.