Topography distorts the angular distribution of the canopy gap fraction (GF). Path length (PL) correction is a simple and effective method to harmonize this distortion and improve canopy reflectance modelling andin situleaf area index measurements for vegetation, including both continuous (e.g., grass and crop) and discrete (e.g., forests) canopies, over sloping terrains. The rigorously theoretical derivation of PL correction for continuous canopies has been implemented. However, for discrete canopies, the PL show a serious heterogeneity, making it nearly impossible to be calculated. In this regard, there is still a need to develop theoretical derivation to evaluate and improve PL correction for forests over sloping terrains. In this study, (1) PL correction is proven to be equivalent to the correction of the canopy GF over sloping terrains, and our strategy concerns the canopy GF as a proxy of PL. (2) PL correction is first proven to be completely valid for forests with the Poisson trees distribution; yet it may produce uncertainty in certain directions for forests with tree distribution deviating from the Poisson model, especially for forests with regular tree distribution. (3) An improved model based on a Nilson and Peterson’s GF model for correcting PL for forests is given in this study. The results show that error produced by the PL correction for some forests can be effectively decreased by the improved model. The variation of directional tree distribution parameter cB(θ) with slope is the main cause of error produced by PL correction for forests. The study is of importance for better understanding and more accurate application of PL theory in topographic corrections andin situleaf area index measurements for forest canopies over sloping terrains.

Canopy clumping index (CI) characterizes the extent of the nonrandom spatial distribution of foliage elements within a canopy and is critical for determining the radiative transfer, photosynthesis, and transpiration processes in the canopy. It is widely perceived that CI increases with zenith angle (θ), because between-crown gaps decrease in size and number with increasing θ. In this study, we demonstrate that this is not always true. Analytical equations between CI and θ are first developed based on widely-used forest canopy gap fraction theories. The results show that the zenith angular variation of CI is closely related to crown projected area or crown shapes (i.e., the ratio of the crown height to its diameter, RHD): CI increases with θ for canopies with “tower” crowns (RHD > 1), but decreases with θ for “umbrella” crowns (RHDin-situmeasurements and multi-angular remote sensing.

Many studies have confirmed that the microwave radiation of rock materials will change with compressive stress and pore water. However, how the presence of pore water in rock volume influences the stress-induced change in microwave radiation ($\Delta T_{B}$) is not clear. In this study, both the air-dry and humid (partially saturated) sandstone specimens were loaded compressively and the C-band (6.9 GHz) microwave radiometer was used to investigate the change of$T_{B}$and the differences of$\Delta T_{B}$. The experimental results illustrated that the presence of pore water in sandstone promotes significantly the relationship between the positive$\Delta T_{B}$and the applied compressive load. On the basis of radiative transfer theory and effective dielectric constant model of multiple-phase media, we found that$\Delta T_{B}$of sandstone mainly results from the compressive stress distributed on mineral grains, which is able to reduce the dielectric constant of minerals and lead to the increase of microwave radiation. For dry sandstone, the distribution of compressive stress on minerals is mainly controlled by grain contact, while for humid sandstone, the pore water plays an important role in applying uniform pressure on grain surface and reducing the dielectric constant of grains; thus, the effective dielectric constant of rock volume is sensitive to the applied loads on partially saturated specimen. This study is important for understanding the positive$T_{B}$anomalies prior to large tectonic earthquakes in condition of ground surface rock partially saturated and is valuable to uncover potential$T_{B}$anomaly related to seismic activities.

Incidence angles ( θ) and polarization modes ( p) are the essential factors for detecting earthquake (EQ)-related microwave radiation anomalies. However, their influences are still not well studied. In this article, research was carried out to simulate the observation of satellite on EQ under different θ and p. The microwave observation experiments were performed on granite samples pressed with θ from 0° to 30°, as well as vertical (v) to horizontal (h) polarizations under weak radiation environment. It was found that the stress-induced changes ( ΔTB) in the samples' microwave brightness temperature ( TB) are anisotropic and polarized. It was observed that the trends of ΔTBmay be reversed under different θ ( p), with a probability of 57.14% (14.29%). The magnitude of ΔTBat h is also prone to greater changes than that at v, with a probability of 67.86%. Theoretical analysis was performed based on crystal optics, Fresnel formulas, and dielectric physics. This phenomenon may relate to the combined action of piezoelectric effect, extension and contraction of ionic bonds, and turning-direction polarization. The sensitivity of TBto the change in permittivity was analyzed by theoretical simulation in order to reveal the effects of modification in θ and p on the TBchange in stress of rock. For rocks with permittivity ε = 7 - i0.3, the most and least sensitive θ are near 52° at h polarization and 69° at v polarization, respectively. Finally, the significance of these results was discussed.

Generally, ground stress accumulates in the process of earthquake (EQ) preparation. The change trend of microwave brightness temperature (TB) of rock with stress change is an important factor for the understanding of the microwave anomalies associated with EQs. However, it is not yet clear whether the downtrend of rocks' TB is associated with increased stress. To confirm this, in this article, the instantaneous field of view of the microwave radiometer was identified first. Then, the microwave observation experiments were conducted on granite samples at 6.6 GHz under cyclic loading and outdoor conditions with weak background radiation. It was found that besides uptrend and fluctuation, the downtrend of granite samples' TB also correlates with stress, with an occurrence probability of 47.62% and a maximum rate of -0.038 K/MPa. The variation trends of TB with stress are not uniform across different areas of the same sample. To reveal the cause of this phenomenon, the permittivity of single-crystal quartz, one of the main mineral compositions of granite, was measured when it was under compassion loading at the direction perpendicular or parallel to the optical axis. For quartz, the real part of the permittivity rises (falls) when the two directions are perpendicular (parallel), causing the TB to fall (rise). The optic axes of minerals are randomly distributed in granite samples, which make the variation in the permittivity of minerals also random, thereby resulting in the nonuniformity of stress-induced TB variation in granite samples. Finally, the implications of these results were discussed.

The additional microwave radiation from underground rock mass (lithosphere) that is caused by tectonic activity and alternating crustal stress has been shown to be a detectable electromagnetic signal via satellite remote sensing. However, the emission of microwave radiation produced inside the lithosphere will be affected by its overburden matter, such as sand, soil, water, and vegetation, and this effect is unknown. In this article, we use a C-band microwave radiometer to detect the variations in the microwave brightness temperature (TB) of rock samples in the process of axial loading. For the rock samples, the surface was bare and covered with dry sand or humid sand. The experimental detection illustrates that the dry sand unexpectedly allows more stress-associated additional radiation (ATB) to be received by the radiometer, while humid sand shows significant extinction of ATB. Both the radiative transfer theory and the stress-activated positive hole hypothesis are applied to interpret the mechanisms of the effect of dry and humid sand layers on ATB. The outflow of stress-activated positive holes is from inside the loaded rock, and hence their accumulation beneath the surface of the sand layer is expected to reduce the local dielectric permittivity of sand, thereby making the detected ATB by the microwave radiometer to be larger than that extrapolated theoretically in accordance with radiative transfer theory. This article is valuable for understanding the diverse TB anomalies that have been observed prior to tectonic earthquakes, and it facilitates the evaluation of the potential application of ATB to seismic monitoring and earthquake prediction.

At present, the earth surface stress monitoring mainly relies on the ground drilling method. Affected by test conditions and cost, the large-scale and regional stress measurement cannot be realized by traditional methods in the actual measurement. As the ground information at the large scale can be observation by satellite in all-weather condition, it is possible for detecting the stress information via the satellite remote sensing. In this paper, the experimental studies on the microwave and thermal infrared spectrum of loaded rock were carried out. Based on the experimental results, the possibility for detecting the earth surface stress condition via remote sensing was discussed. This study demonstrates the potential ability to use satellite remote sensing to observe ground stress condition and earthquakes.

To simulate the actual satellite observation situation of crust rock on the land surface, the thermal infrared spectrum observation experiment of loaded quartz sandstone was carried out in the cold sky background. In order to analysis the mechanism of radiation variation due to stress, the spectrum observation comparison experiment of the sample in the heating process is conducted as well. The experimental results indicate that the spectral radiance variation features in the loading process is different from that in the heating process. The trend of the two variation curves are opposite in the range of 8.0-9.7μm, which is corresponding to the wave range of reststrahlen features (RF) of the spectral emissivity. The factors affecting the radiance variation are analyzed. It can be concluded that the radiance increase in the compressed loading process is caused by both the temperature and the emissivity change. The results indicate that it is probable to establish a relationship between the emissivity and stress and provide an experimental basis for the observation of the stress by means of the infrared remote sensing.

Previous studies have shown that thermal infrared anomalies can be detected in the crust rocks in satellite infrared images before an earthquake. However, thermal infrared remote sensing is easily affected by weather conditions because of the short wavelength of infrared radiation. In this paper, instead of infrared radiation, we focus on the microwave radiation characteristics of loaded rock. First, a microwave observation system was built to observe the loading process of rocks in an outdoor environment with a cold sky background. Then, the microwave radiation changes in the loaded granite samples during elastic deformation and fracturing stages were analyzed. The experiments yielded the following results. First, the microwave brightness temperature has a linear positive correlation with the load in the elastic deformation stage of the granite samples, and lateral pressure accelerates the changes in the microwave radiation. Second, the microwave brightness temperature usually decreases as the rock develops layered fractures but increases as the rock develops surface fractures, which significantly alter the surface morphology and roughness. The mechanisms responsible for the changes in microwave radiation during the rock deformation and fracturing processes are discussed. This study demonstrates the potential ability to use microwave-sensing satellites to observe seismogenic processes and earthquakes.