We derive uniform asymptotic expansions for polynomials orthogonal with respect to a class of weight functions that are real analytic and behave asymptotically like the Freud weight at infinity. Although the limiting zero distributions are the same as in the Freud cases, the asymptotic expansions are different due to the fact that the weight functions may have a finite or infinite number of zeros on the imaginary axis. To resolve the singularities caused by these zeros, an auxiliary function is introduced in the Riemann-Hilbert analysis. Asymptotic formulas are established in several regions covering the whole complex plane. We take the continuous dual Hahn polynomials as an example to illustrate our main results. Some numerical verifications are also given. K E Y W O R D S asymptotic approximation, asymptotic Freud-like weight, continuous dual Hahn polynomials, Riemann-Hilbert problem ∑ =0 ( ) ( 2 ) ( + ) − ( − + ) − !( − )! , Stud Appl Math. 2020;144:133-163. wileyonlinelibrary.com/journal/sapm
Deadly humid heat conditions exceeding human thermoregulatory capacity have been reported; however, whether and where the deadly humid heat events occur consecutively across the land surface are largely unknown. We calculate the maximum consecutive days of deadly humid heat, defined as daily maximum wet-bulb temperature (TWmax) ≥35 C, for observations of 9,278 meteorological stations and for simulations of 14 global climate models. We further define short and long deadly humid heatwaves as a period of 3-4 and ≥5 consecutive days with daily TWmax ≥35 C, respectively. Our analyses show that six stations in some subtropical regions have experienced deadly humid heat with daily TWmax ≥35 C, but only occurs in individual days. Deadly humid heatwaves increase exponentially as the global mean temperature rising. When limiting global warming within 1.5 C, long deadly humid heatwaves will not occur across the land surface, and short deadly humid heatwaves will only emerge in some drylands but not in humid areas. Under 2 C warming, 0.09% of the global land, 0.42% of the human population, and 0.56% of the global centres of crop diversity are projected to be exposed to long deadly humid heatwaves. Meanwhile, 18% of the deadly humid heatwaves lasting ≥3 consecutive days will occur in humid areas; the fractions are projected to rapidly increase in humid areas as temperature rising further. At the end of the century, the percentage of land areas and human population exposed to deadly humid heatwaves lasting ≥3 consecutive days are expected to be 76-times higher than that under 1.5 C warming level.Our finding suggests that keeping global warming within 1.5 C will significantly constrain the emergence of prolonged deadly humid heatwaves and thus reduce the risk of the human population especially outdoor agricultural workers.climate warming, deadly humid heatwaves, exposure, wet bulb temperature | INTRODUCTIONExtreme humid heat is one of the most dangerous natural hazards (Wehner et al., 2016) and is recognized as an immediate threat to humans health and survivability (Meehl and Tebaldi, 2004;Sherwood and Huber, 2010;Mora et al., 2017; Mitchell, 2021). Compared with extreme dry heat, during extreme humid heatwaves, the threshold that temperature becomes deadly decreases with rising environment relative humidity (Pal and Eltahir, 2016;Xiang-Sheng Wang and Lei He are co-first authors.
Understanding the process of dryland degradation is crucial to combating desertification and maintaining land sustainability. To identify important indicators of dryland degradation, we conducted a field survey of 46 drylands spanning an aridity gradient across the Tibetan Plateau. Our random forest model suggested that soil sand content was the most important predictor of variation in soil fertility (carbon, nitrogen, and phosphorus). Most soil fertility showed a nonlinear and abrupt decline with increasing soil sand content, and displayed three sequential thresholds. First, soil organic carbon sharply decreased beyond a soil sand content threshold of 47%. Second, exceeding a subsequent threshold of 70%, the total nitrogen and light fraction carbon declined dramatically with increasing soil sand content. Finally, soil heavy fraction carbon, inorganic carbon, and total carbon were drastically reduced when the soil sand content exceeded 80%. The three soil fertility thresholds along the gradient of the soil sand content indicated a sequence of dryland degradation phases. Our findings provide an approach for detecting the severity of dryland degradation and suggest vulnerable areas of degradation on the Tibetan Plateau.
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