Heat-like and wave-like lifespan estimates for solutions of semilinear damped wave equations via a Kato's type lemma

In this work we consider several semilinear damped wave equations with “subcritical” nonlinearities, focusing on studying lifespan estimates for energy solutions. Our main concern is on equations with scale-invariant damping and mass. By imposing different assumptions on the initial data, we prove lifespan estimates from above, distinguishing between “wave-like” and “heat-like” behaviours. Furthermore, we conjecture logarithmic improvements for the estimates on the “transition surfaces” separating the two behaviours. As a direct consequence, we reorganize the blow-up results and lifespan estimates for the massless case, and we obtain in particular improved lifespan estimates for the one dimensional case, compared to the known results. We also study semilinear wave equations with scattering damping and negative mass term, finding that if the decay rate of the mass term equals to 2, the lifespan estimate coincides with the one in a special case of scale-invariant damped equation. The main tool employed in the proof is a Kato's type lemma, established by iteration argument

Development of a new data-processing method for SKYNET sky radiometer observations

In order to reduce uncertainty in the estimation of Direct Aerosol Radiative Forcing (DARF), it is important to improve the estimation of the single scattering albedo (SSA). In this study, we propose a new data processing method to improve SSA retrievals for the SKYNET sky radiometer network, which is one of the growing number of networks of sun-sky photometers, such as NASA AERONET and others. There are several reports that SSA values from SKYNET have a bias compared to those from AERONET, which is regarded to be the most accurate due to its rigorous calibration routines and data quality and cloud screening algorithms. We investigated possible causes of errors in SSA that might explain the known biases through sensitivity experiments using a numerical model, and also using real data at the SKYNET sites at Pune (18.616° N/73.800° E) in India and Beijing (39.586° N/116.229° E) in China. Sensitivity experiments showed that an uncertainty of the order of ±0.03 in the SSA value can be caused by a possible error in the ground surface albedo or solid view angle assumed for each observation site. Another candidate for possible error in the SSA was found in cirrus contamination generated by imperfect cloud screening in the SKYNET data processing. Therefore, we developed a new data quality control method to get rid of low quality or cloud contamination data, and we applied this method to the real observation data at the Pune site in SKYNET. After applying this method to the observation data, we were able to screen out a large amount of cirrus-contaminated data and to reduce the deviation in the SSA value from that of AERONET. We then estimated DARF using data screened by our new method. The result showed that the method significantly reduced the difference of 5 W m−2 that existed between the SKYNET and AERONET values of DARF before screening. The present study also suggests the necessity of preparing suitable a priori information on the distribution of coarse particles ranging in radius between 10 μm and 30 μm for the analysis of heavily dust-laden atmospheric case