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Abstract In a previous paper, we identified a “notch” in unstable layers at Koror (7.3°N, 134.5°E), where there was a relative deficiency in thin unstable layers and a corresponding relative excess in thicker layers, at altitudes centered at 12 km. We hypothesized that this feature was associated with the previously identified stability minimum in the tropics at that same altitude. In this paper, we extend our studies of this notch and its association with the tropical stability minimum by examining other stations in the deep tropics and also some stations at higher latitudes within the tropics. We find that this notch feature is found at all the other radiosonde stations in the deep tropics that we examined. We also find that the annual variations in unstable layer occurrences at stations at higher latitudes within the tropics show variations consistent with our hypothesis that this notch is associated with the region of minimum stability in the tropics at altitudes centered around 12 km, in that the annual variation in this notch feature is consistent with the annual variation of minimum stability in this region. Two factors contribute to the notch feature. One is that the data quality control procedure of the analysis rejects many thin layers due to the small trend-to-noise ratio in the region of minimum stability. The other is that the cloud-top outflow, which was previously identified with the stability minimum, advects thicker unstable layers throughout the deep tropics at the altitudes of the notch. Significance StatementPrevious papers have separately identified a stability minimum in the tropics and a “notch” feature in the thicknesses of unstable atmospheric layers where there are less thin unstable layers and a corresponding excess of thicker unstable layers, both at altitudes around 12 km. We previously hypothesized that these two features were associated with one another. In this paper, we examine this notch feature and the minimum in atmospheric stability at both deep tropical radiosonde stations and stations located at higher latitudes in the tropics, and we find that the annual variation of this notch feature is consistent with the latitudinal migration of the latitudes of the stability minimum. Turbulence associated with this notch feature might be significant for aircraft operations. 

Abstract One-second U.S. high vertical-resolution radiosonde data (HVRRD) contain two different sets of temperature data—the raw data and the processed data. The processed data have been subject to radiation corrections, which have been well documented, and smoothing, the details of which are proprietary to the radiosonde manufacturers. We have tried to characterize this smoothing by computing the root-mean-square (rms) of normalized temperature perturbations derived from removing a second-degree polynomial fit for altitude segments (Δz) from 100 m to 5 km. We find that for Δz= 100 m, rms values are larger at higher altitudes, are larger in the raw data than in the processed data, and are larger during daytime than during nighttime, for both the raw and processed data. The rms values and their daytime to nighttime differences are larger in the raw data than in the processed data. As Δzincreases toward 5 km, the geographical patterns of rms over the contiguous United States from both the raw and processed data start resembling previously published gravity wave total energy patterns obtained from the older 6-s U.S. radiosonde data. An example is shown of a discontinuity in the small-scale rms values when radiosonde instrumentation is changed, so it is concluded that small-scale temperature fluctuations will be different for different radiosonde instruments. Examples are shown of enhanced small-scale rms temperature values indicative of turbulence resulting from gravity wave critical levels and from enhanced gravity waves due to seasonal maxima in convection. Significance StatementWe have characterized the variability of the raw and processed temperature profiles of the U.S. high vertical resolution radiosonde data for various vertical scales. We have argued that sources of small-scale fluctuations in the processed data include turbulence and the radiation effects which have not been accounted for in the current derivation of the processed data. Temperature fluctuations of larger scales correspond to those from gravity waves. We have shown an example of a discontinuity in small-scale fluctuations at a radiosonde station when the instrumentation was changed. These results suggest that temperature fluctuations resulting from varying amounts of solar radiation falling on the temperature sensor as the radiosonde instrumentation swings and rotates should be evaluated for each radiosonde system. 

Abstract We have published a recent paper on differences between temperature fluctuations of various vertical scales in raw and processed U.S. high vertical resolution radiosonde data (HVRRD). In that paper, we note that the small-scale temperature fluctuations in the raw U.S. HVRRD are significantly larger than those in the processed U.S. HVRRD and that those small-scale temperature fluctuations are much larger during daytime that during nighttime. We believe that this is due to the varying amount of solar radiation falling on the radiosonde temperature sensor as the radiosonde instrument swings and rotates. In light of these new results, we present revisions to some of our conclusions about the climatology of atmospheric unstable layers. When we repeat our calculations of atmospheric unstable layers using the processed U.S. HVRRD, we find the following. 1) The 0000/1200 UTC differences in unstable layer occurrences in the lower stratosphere that were noted in our earlier paper essentially disappear. 2) The “notch” in the deep tropics where there is a relative deficiency of thin unstable layers and a corresponding excess of thicker layers is still a feature when processed data are analyzed, but the daytime notch is less marked when the processed data were used. 3) The discontinuity in unstable layer occurrences, when there was a change in radiosonde instrumentation, is still present when processed data are analyzed, but is diminished from what it was when the raw data were analyzed. Significance StatementIn a previous paper deriving the climatology of atmospheric unstable layers, we emphasized several findings. We reexamine three of the main points of that paper when processed U.S. high vertical resolution radiosonde data are analyzed instead of the raw data used in that previous paper. We find the 0000/1200 UTC differences virtually disappear in the new analysis. We find that the “notch” feature previously noted at Koror still exists, and we find that the discontinuity in unstable layers, when radiosonde instrumentation is changed, is diminished, but is still present in the new analysis. 

We study the solvability of singular Abreu equations which arise in the approximation of convex functionals subject to a convexity constraint. Previous works established the solvability of their second boundary value problems either in two dimensions, or in higher dimensions under either a smallness condition or a radial symmetry condition. Here, we solve the higher-dimensional case by transforming singular Abreu equations into linearized Monge–Ampère equations with drifts. We establish global Hölder estimates for linearized Monge–Ampère equations with drifts under suitable hypotheses, and then apply them to prove the regularity and solvability of the second boundary value problem for singular Abreu equations in higher dimensions. Many cases with general right-hand side are also discussed. 

Abstract A companion paper by Fritts et al. reviews extensive evidence for Kelvin–Helmholtz instability (KHI) “tube” and “knot” (T&K) dynamics at multiple altitudes in the atmosphere and in the oceans that reveal these dynamics to be widespread. A second companion paper by Fritts and Wang reveals KHI T&K events at larger and smaller scales to arise on multiple highly stratified sheets in a direct numerical simulation (DNS) of idealized, multiscale gravity wave–fine structure interactions. These studies reveal the diverse environments in which KHI T&K dynamics arise and suggest their potentially ubiquitous occurrence throughout the atmosphere and oceans. This paper describes a DNS of multiple KHI evolutions in wide and narrow domains enabling and excluding T&K dynamics. These DNSs employ common initial conditions but are performed for decreasing Reynolds numbers (Re) to explore whether T&K dynamics enable enhanced KHI-induced turbulence where it would be weaker or not otherwise occur. The major results are that KHI T&K dynamics extend elevated turbulence intensities and energy dissipation ratesεto smaller Re. We expect these results to have important implications for improving parameterizations of KHI-induced turbulence in the atmosphere and oceans. Significance StatementTurbulence due to small-scale shear flows plays important roles in the structure and variability of the atmosphere and oceans extending to large spatial and temporal scales. New modeling reveals that enhanced turbulence accompanies Kelvin–Helmholtz instabilities (KHIs) that arise on unstable shear layers and exhibit what were initially described as “tubes” and “knots” (T&K) when they were first observed in early laboratory experiments. We perform new modeling to explore two further aspects of these dynamics: 1) can KHI T&K dynamics increase turbulence intensities compared to KHI without T&K dynamics for the same initial fields and 2) can KHI T&K dynamics enable elevated turbulence and energy dissipation extending to more viscous flows? We show here that the answer to both questions is yes. 

Synopsis Predicting performance responses of insects to climate change is crucial for biodiversity conservation and pest management. While most projections on insects’ performance under climate change have used macro-scale weather station data, few incorporated the microclimates within vegetation that insects inhabit and their feeding behaviors (e.g., leaf-nesting: building leaf nests or feeding inside). Here, taking advantage of relatively homogenous vegetation structures in agricultural fields, we built microclimate models to examine fine-scale air temperatures within two important crop systems (maize and rice) and compared microclimate air temperatures to temperatures from weather stations. We deployed physical models of caterpillars and quantified effects of leaf-nesting behavior on operative temperatures of two Lepidoptera pests: Ostrinia furnacalis (Pyralidae) and Cnaphalocrocis medinalis (Crambidae). We built temperature-growth rate curves and predicted the growth rate of caterpillars with and without leaf-nesting behavior based on downscaled microclimate changes under different climate change scenarios. We identified widespread differences between microclimates in our crop systems and air temperatures reported by local weather stations. Leaf-nesting individuals in general had much lower body temperatures compared to non-leaf-nesting individuals. When considering microclimates, we predicted leaf-nesting individuals grow slower compared to non-leaf-nesting individuals with rising temperature. Our findings highlight the importance of considering microclimate and habitat-modifying behavior in predicting performance responses to climate change. Understanding the thermal biology of pests and other insects would allow us to make more accurate projections on crop yields and biodiversity responses to environmental changes. 

Abstract A companion paper by Fritts et al. reviews evidence for Kelvin–Helmholtz instability (KHI) “tube” and “knot” (T&K) dynamics that appear to be widespread throughout the atmosphere. Here we describe the results of an idealized direct numerical simulation of multiscale gravity wave dynamics that reveals multiple larger- and smaller-scale KHI T&K events. The results enable assessments of the environments in which these dynamics arise and their competition with concurrent gravity wave breaking in driving turbulence and energy dissipation. A larger-scale event is diagnosed in detail and reveals diverse and intense T&K dynamics driving more intense turbulence than occurs due to gravity wave breaking in the same environment. Smaller-scale events reveal that KHI T&K dynamics readily extend to weaker, smaller-scale, and increasingly viscous shear flows. Our results suggest that KHI T&K dynamics should be widespread, perhaps ubiquitous, wherever superposed gravity waves induce intensifying shear layers, because such layers are virtually always present. A second companion paper demonstrates that KHI T&K dynamics exhibit elevated turbulence generation and energy dissipation rates extending to smaller Reynolds numbers for relevant KHI scales wherever they arise. These dynamics are suggested to be significant sources of turbulence and mixing throughout the atmosphere that are currently ignored or underrepresented in turbulence parameterizations in regional and global models. Significance StatementAtmospheric observations reveal that Kelvin–Helmholtz instabilities (KHI) often exhibit complex interactions described as “tube” and “knot” (T&K) dynamics in the presence of larger-scale gravity waves (GWs). These dynamics may prove to make significant contributions to energy dissipation and mixing that are not presently accounted for in large-scale modeling and weather prediction. We explore here the occurrence of KHI T&K dynamics in an idealized model that describes their behavior and character arising at larger and smaller scales due to superposed, large-amplitude GWs. The results reveal that KHI T&K dynamics arise at larger and smaller scales, and that their turbulence intensities can be comparable to those of the GWs.