Combined refraction and diffraction models for sea waves over complicated topography and with currents in shallow water

-Combined refraction and diffraction models in the form of linear parabolic approximation are derived through smallparameter method. More strictly theoretical basis and more accuracy in the models than Lozano's (1980) are obtained. Some theoretical defects in Liu's model (1985) with consideration of current are not only found but also eliminated. More strict and accurate models are, therefore, presented in this paper.The calculation results and analysis in applying the models to actual wave field with consideration of bottom friction will be given in the following paper.

Observations and Modeling of Incoming Longwave Radiation to Snow Beneath Forest Canopies in the West Tianshan Mountains, China

Forest canopy reduces shortwave radiation and increases the incoming longwave radiation to snowpacks beneath forest canopies. Furthermore, the effect of forest canopy may be changed by complex topography. In this paper, we measured and simulated the incoming longwave radiation to snow beneath forest at different canopy openness in the west Tianshan Mountains, China(43°16'N, 84°24'E) during spring 2013. A sensitivity study was conducted to explore the way that terrain influenced the incoming longwave radiation to snow beneath forest canopies. In the simulation model, measurement datasets, including air temperature, incoming shortwave radiation above canopy, and longwave radiation enhanced by adjacent terrain, were applied to calculate the incoming longwave radiation to snow beneath forest canopy. The simulation results were consistent with the measurements on hourly scale and daily scale. The effect of longwave radiation enhanced by terrain was important than that of shortwave radiation above forest canopy with different openness except the 20% canopy openness. The longwave radiation enhanced due to adjacent terrain increases with the slope increase and temperature rise. When air temperature(or slope) is relatively low, thelongwave radiation enhanced by adjacent terrain is not sensitive to slope(or air temperature), but the sensitivity increases with the decrease of snow cover area on sunny slope. The effect of longwave radiation is especially sensitive when the snow cover on sunny slope melts completely. The effect of incoming shortwave radiation reflected by adjacent terrain on incoming longwave radiation to snow beneath forest canopies is more slight than that of the enhanced longwave radiation.

Mathematical analysis of corneal remodelling after intracorneal ring surgery in keratoconus

AIM：To represent mathematically the intersection between the ectatic corneal geometry and the plane of intracorneal ring implants（ICRS）in order to determine the corneal response to ICRS surgery in keratoconus（KC）.Thereafter,to present the concept and early results of a newly derived topography-guided nomogram for ICRS surgery for the treatment of keratectasia. METHODS：The corneal rings plane intersection was modelled to a conic section. Ring effect was the result of：the ring size,position（steep vs flat）,location（distance from the geometric centre of the cornea）,and the discrepancy between the ring＇s curvature and the tunnel＇s curvature.Femtosecond laser was used to create the tunnels and the incision sites were chosen according to the nomogram in order to place the thickest ring in the steepest portion of the cornea regardless of the astigmatism axis of refraction.RESULTS：The conic section had a more prolate shape in the steep area of the cornea than in the flat area,depending on the corneal sagittal curvature. Equal ring size had more flattening effect in the steep area than in the flat area. Thick segment should be implanted under the steep portion of the cornea regardless of the cylinder axis of refraction. Single segment in the steep area was sufficient in early and moderate cases of KC. The new nomogram provided more topographic regularity with significant reduction of astigmatism and better improvement in uncorrected visual acuity（UCVA）and best-corrected visual acuity（BCVA）than the conventional nomogram. CONCLUSION：The newly derived nomogram can produce better results than the conventional nomogram. Moreover,based on this concept,a new nomogram can be integrated into the femtosecond laser software to create topography-guided,customized,elliptical tunnels with modified focal asphericity that allows for customized focal flattening of the irregularly steepened ectatic cornea.