Mixing at the extratropical tropopause as characterized by collocated airborne H₂O and O₃ lidar observations

The composition of the extratropical transition layer (ExTL), which is the transition zone between the stratosphere and the troposphere in the midlatitudes, largely depends on dynamical processes fostering the exchange of air masses. The Wave-driven ISentropic Exchange (WISE) field campaign in 2017 aimed for a better characterization of the ExTL in relation to the dynamic situation. This study investigates the potential of the first-ever collocated airborne lidar observations of ozone (O3) and water vapor (H2O) across the tropopause to depict the complex trace gas distributions and mixing in the ExTL. A case study of a perpendicular jet stream crossing with a coinciding strongly sloping tropopause is presented that was observed during a research flight over the North Atlantic on 1 October 2017. The collocated and range-resolved lidar data that are applied to established tracer–tracer (T–T) space diagnostics prove to be suitable to identify the ExTL and to reveal distinct mixing regimes that enabled a subdivision of mixed and tropospheric air. A back projection of this information to geometrical space shows remarkably coherent structures of these air mass classes along the cross section. This represents the first almost complete observation-based two-dimensional (2D) illustration of the shape and composition of the ExTL and a confirmation of established conceptual models. The trace gas distributions that represent typical H2O and O3 values for the season reveal tropospheric transport pathways from the tropics and extratropics that have influenced the ExTL. Although the combined view of T–T and geometrical space does not inform about the process, location and time of the mixing event, it gives insight into the formation and interpretation of mixing lines. A mixing factor diagnostic and a consideration of data subsets show that recent quasi-instantaneous isentropic mixing processes impacted the ExTL above and below the jet stream which is a confirmation of the well-established concept of turbulence-induced mixing in strong wind shear regions. At the level of maximum winds reduced mixing is reflected in jumps in T–T space that occurred over small horizontal distances along the cross section. For a better understanding of the dynamical and chemical discontinuities at the tropopause, the lidar data are illustrated in isentropic coordinates. The strongest gradients of H2O and O3 are found to be better represented by a potential vorticity-gradient-based tropopause compared to traditional dynamical tropopause definitions using constant potential vorticity values. The presented 2D lidar data are considered to be of relevance for the investigation of further meteorological situations leading to mixing across the tropopause and for future validation of chemistry and numerical weather prediction models.

Meningkatkan Pemahaman Konsep Bangun Ruang Mahasiswa Calon Guru Sekolah Dasar Menggunakan Game Android

This study aims to improve the conceptual understanding of prospective elementary school teacher students on the concept of geometrical space which includes the relationship between lines and planes as well as lines and lines in geometrical space using Android games. The Android game used was XSection. This research is a quasi-experimental study with a pretest-posttest control group design. The sample in this study was taken using a cluster random sampling technique and obtained class 3C as an experimental class, namely the class that learns using Android-based educational games and 3D class as the control class, namely the class that learns without using Android-based educational games. Data regarding conceptual understanding were obtained by the multiple-choice tests and data were analyzed using independent sample t-test and normalized gain test. The results showed that the experimental class showed a significant increase in understanding the concept of geometrical space compared to the control class. The post-test average score of students' conceptual understanding in the experimental class was higher than the control class so that the Android-based education game was effective in improving students' understanding of the concept of geometrical space for prospective elementary school teachers.

Assessment of a Takagi–Sugeno-Kang fuzzy model assembly for examination of polyphasic loglinear allometry

Background The traditional allometric analysis relies on log- transformation to contemplate linear regression in geometrical space then retransforming to get Huxley’s model of simple allometry. Views assert this induces bias endorsing multi-parameter complex allometry forms and nonlinear regression in arithmetical scales. Defenders of traditional approach deem it necessary since generally organismal growth is essentially multiplicative. Then keeping allometry as originally envisioned by Huxley requires a paradigm of polyphasic loglinear allometry. A Takagi-Sugeno-Kang fuzzy model assembles a mixture of weighted sub models. This allows direct identification of break points for transition between phases. Then, this paradigm is seamlessly appropriate for efficient allometric examination of polyphasic loglinear allometry patterns. Here, we explore its suitability. Methods Present fuzzy model embraces firing strength weights from Gaussian membership functions and linear consequents. Weights are identified by subtractive clustering and consequents through recursive least squares or maximum likelihood. Intersection of firing strength factors set criterion to estimate breakpoints. A multi-parameter complex allometry model follows by adapting firing strengths by composite membership functions and linear consequents in arithmetical space. Results Takagi-Sugeno-Kang surrogates adapted complexity depending on analyzed data set. Retransformation results conveyed reproducibility strength of similar proxies identified in arithmetical space. Breakpoints were straightforwardly identified. Retransformed form implies complex allometry as a generalization of Huxley’s power model involving covariate depending parameters. Huxley reported a breakpoint in the log–log plot of chela mass vs. body mass of fiddler crabs (Uca pugnax), attributed to a sudden change in relative growth of the chela approximately when crabs reach sexual maturity. G.C. Packard implied this breakpoint as putative. However, according to present fuzzy methods existence of a break point in Huxley’s data could be validated. Conclusions Offered scheme bears reliable analysis of zero intercept allometries based on geometrical space protocols. Endorsed affine structure accommodates either polyphasic or simple allometry if whatever turns required. Interpretation of break points characterizing heterogeneity is intuitive. Analysis can be achieved in an interactive way. This could not have been obtained by relying on customary approaches. Besides, identification of break points in arithmetical scale is straightforward. Present Takagi-Sugeno-Kang arrangement offers a way to overcome the controversy between a school considering a log-transformation necessary and their critics claiming that consistent results can be only obtained through complex allometry models fitted by direct nonlinear regression in the original scales.

A Generalized Model of Complex Allometry I: Formal Setup, Identification Procedures and Applications to Non-Destructive Estimation of Plant Biomass Units

(1) Background: We previously demonstrated that customary regression protocols for curvature in geometrical space all derive from a generalized model of complex allometry combining scaling parameters expressing as continuous functions of covariate. Results highlighted the relevance of addressing suitable complexity in enhancing the accuracy of allometric surrogates of plant biomass units. Nevertheless, examination was circumscribed to particular characterizations of the generalized model. Here we address the general identification problem. (2) Methods: We first suggest a log-scales protocol composing a mixture of linear models weighted by exponential powers. Alternatively, adopting an operating regime-based modeling slant we offer mixture regression or Takagi–Sugeno–Kang arrangements. This last approach allows polyphasic identification in direct scales. A derived index measures the extent on what complexity in arithmetic space drives curvature in arithmetical space. (3) Results: Fits on real and simulated data produced proxies of outstanding reproducibility strength indistinctly of data scales. (4) Conclusions: Presented analytical constructs are expected to grant efficient allometric projection of plant biomass units and also for the general settings of allometric examination. A traditional perspective deems log-transformation and allometry inseparable. Recent views assert that this leads to biased results. The present examination suggests this controversy can be resolved by addressing adequately the complexity of geometrical space protocols

Examination of the Effects of Curvature in Geometrical Space on Accuracy of Scaling Derived Projections of Plant Biomass Units: Applications to the Assessment of Average Leaf Biomass in Eelgrass Shoots

Conservation of eelgrass relies on transplants and evaluation of success depends on nondestructive measurements of average leaf biomass in shoots among other variables. Allometric proxies offer a convenient way to assessments. Identifying surrogates via log transformation and linear regression can set biased results. Views conceive this approach to be meaningful, asserting that curvature in geometrical space explains bias. Inappropriateness of correction factor of retransformation bias could also explain inconsistencies. Accounting for nonlinearity of the log transformed response relied on a generalized allometric model. Scaling parameters depend continuously on the descriptor. Joining correction factor is conceived as the partial sum of series expansion of mean retransformed residuals leading to highest reproducibility strength. Fits of particular characterizations of the generalized curvature model conveyed outstanding reproducibility of average eelgrass leaf biomass in shoots. Although nonlinear heteroscedastic regression resulted also to be suitable, only log transformation approaches can unmask a size related differentiation in growth form of the leaf. Generally, whenever structure of regression error is undetermined, choosing a suitable form of retransformation correction factor becomes elusive. Compared to customary nonparametric characterizations of this correction factor, present form proved more efficient. We expect that offered generalized allometric model along with proposed correction factor form provides a suitable analytical arrangement for the general settings of allometric examination.