External factors affecting the processes of sprinkler irrigation water flow generation, flight, and landing have not been thoroughly considered in existing ballistic models. This result indicates that ballistic models with better prediction effects under specific conditions are not sufficient for extension to multi-factor coupled scenarios in large-scale farmlands. Therefore, wind, evaporation, surface slope, and tilted sprinkler riser factors were comprehensively considered in this study. Differential equations for jet and droplet motion under the influence of wind, differential equations of droplet evaporation, sprinkler riser deflection angle matrix, and surface slope angle matrix were constructed to establish a droplet distribution model for sprinkler irrigation considering multifactor coupling using MATLAB 2018a software. The results showed that, under different working conditions, the data points of the droplet landing diameter, velocity, and angle were distributed near the 1:1 line. The Nash efficiency coefficients (NSE) for the droplet landing diameter, velocity, and angle varied from 0.821 to 0.932, 0.616 to 0.931, and 0.770 to 0.911, respectively. The increase in slope resulted in droplets with diameters larger than 4.63 mm concentrating on the land in the reverse slope direction. When the ambient temperature increases from 10 to 45 degrees C and the total evaporation rate increases from 0.45 to 4.37%, the larger droplets have a larger area of contact with the air, and the higher the temperature, the greater the energy loss to the larger droplet diameters. The higher the wind speed, the more droplets in the downwind direction fall to the ground at a smaller landing angle, which can easily increase the risk of soil shear damage. If the sprinkler riser was tilted east, the droplets on both the east and west sides tended to be distributed centrally; the maximum droplet landing velocity occurred on the east side (tilted side), and the maximum droplet landing angle occurred on the west side. This study considers various factors that may affect the motion of sprinkler irrigation water flow, extends the application scenarios of the theoretical model, and improves the applicability of the theoretical model for sprinkler irrigation droplet motion in more complex and practical agricultural environments.

In an attempt to reduce the ambiguity on radar detection of water ice at the permanently shadowed regions near the lunar poles, radar echo strength and circular polarization ratio (CPR) of impact craters are analyzed using the Miniature Radio Frequency (Mini-RF) radar data from the Lunar Reconnaissance Orbiter mission. Eight typical craters, among over 70 craters, are selected and classified into four categories based on their locations and CPR characteristics: polar anomalous, polar fresh, nonpolar anomalous, and nonpolar fresh. The influences on CPR caused by surface slope, rocks, and dielectric constant are analyzed quantitatively using high-resolution topography data and optical images. A two-component mixed model for CPR that consists of a normal surface and a rocky surface is developed to study the effect of rocks that are perched on lunar surface and buried in regolith. Our analyses show that inner wall of a typical bowl-shaped crater can give rise to a change of about 30 degrees in local incidence angle of radar wave, which can further result in a CPR difference of about 0.2. There is a strong correlation between Mini-RF CPR and rock abundance that is obtained from high-resolution optical images, and predictions from the two-component mixed model match well with the observed CPRs and the estimated rock abundances. Statistical results show that there is almost no apparent difference in CPR characteristics between the polar and nonpolar anomalous craters, or between the polar and nonpolar fresh craters. The enhanced CPR in the interior of anomalous craters is most probably caused by rocks that are perched on lunar surface or buried in regolith, instead of ice deposits as suggested in previous studies.