Construction of Cubic Timmer Triangular Patches and its Application in Scattered Data Interpolation

This paper discusses scattered data interpolation by using cubic Timmer triangular patches. In order to achieve C1 continuity everywhere, we impose a rational corrected scheme that results from convex combination between three local schemes. The final interpolant has the form quintic numerator and quadratic denominator. We test the scheme by considering the established dataset as well as visualizing the rainfall data and digital elevation in Malaysia. We compare the performance between the proposed scheme and some well-known schemes. Numerical and graphical results are presented by using Mathematica and MATLAB. From all numerical results, the proposed scheme is better in terms of smaller root mean square error (RMSE) and higher coefficient of determination (R2). The higher R2 value indicates that the proposed scheme can reconstruct the surface with excellent fit that is in line with the standard set by Renka and Brown’s validation.

Asymptotically optimal minimizers schemes

MotivationThe minimizers technique is a method to sample k-mers that is used in many bioinformatics software to reduce computation, memory usage and run time. The number of applications using minimizers keeps on growing steadily. Despite its many uses, the theoretical understanding of minimizers is still very limited. In many applications, selecting as few k-mers as possible (i.e. having a low density) is beneficial. The density is highly dependent on the choice of the order on the k-mers. Different applications use different orders, but none of these orders are optimal. A better understanding of minimizers schemes, and the related local and forward schemes, will allow designing schemes with lower density, and thereby making existing and future bioinformatics tools even more efficient.ResultsFrom the analysis of the asymptotic behavior of minimizers, forward and local schemes, we show that the previously believed lower bound on minimizers schemes does not hold, and that schemes with density lower than thought possible actually exist. The proof is constructive and leads to an efficient algorithm to compare k-mers. These orders are the first known orders that are asymptotically optimal. Additionally, we give improved bounds on the density achievable by the 3 type of [email protected]@cs.cmu.edu

Evaluation of Multiple Planetary Boundary Layer Parameterization Schemes in Southeast U.S. Cold Season Severe Thunderstorm Environments

Southeast U.S. cold season severe weather events can be difficult to predict because of the marginality of the supporting thermodynamic instability in this regime. The sensitivity of this environment to prognoses of instability encourages additional research on ways in which mesoscale models represent turbulent processes within the lower atmosphere that directly influence thermodynamic profiles and forecasts of instability. This work summarizes characteristics of the southeast U.S. cold season severe weather environment and planetary boundary layer (PBL) parameterization schemes used in mesoscale modeling and proceeds with a focused investigation of the performance of nine different representations of the PBL in this environment by comparing simulated thermodynamic and kinematic profiles to observationally influenced ones. It is demonstrated that simultaneous representation of both nonlocal and local mixing in the Asymmetric Convective Model, version 2 (ACM2), scheme has the lowest overall errors for the southeast U.S. cold season tornado regime. For storm-relative helicity, strictly nonlocal schemes provide the largest overall differences from observationally influenced datasets (underforecast). Meanwhile, strictly local schemes yield the most extreme differences from these observationally influenced datasets (underforecast) in a mean sense for the low-level lapse rate and depth of the PBL, on average. A hybrid local–nonlocal scheme is found to mitigate these mean difference extremes. These findings are traced to a tendency for local schemes to incompletely mix the PBL while nonlocal schemes overmix the PBL, whereas the hybrid schemes represent more intermediate mixing in a regime where vertical shear enhances mixing and limited instability suppresses mixing.

A Review of Planetary Boundary Layer Parameterization Schemes and Their Sensitivity in Simulating Southeastern U.S. Cold Season Severe Weather Environments

The representation of turbulent mixing within the lower troposphere is needed to accurately portray the vertical thermodynamic and kinematic profiles of the atmosphere in mesoscale model forecasts. For mesoscale models, turbulence is mostly a subgrid-scale process, but its presence in the planetary boundary layer (PBL) can directly modulate a simulation’s depiction of mass fields relevant for forecast problems. The primary goal of this work is to review the various parameterization schemes that the Weather Research and Forecasting Model employs in its depiction of turbulent mixing (PBL schemes) in general, and is followed by an application to a severe weather environment. Each scheme represents mixing on a local and/or nonlocal basis. Local schemes only consider immediately adjacent vertical levels in the model, whereas nonlocal schemes can consider a deeper layer covering multiple levels in representing the effects of vertical mixing through the PBL. As an application, a pair of cold season severe weather events that occurred in the southeastern United States are examined. Such cases highlight the ambiguities of classically defined PBL schemes in a cold season severe weather environment, though characteristics of the PBL schemes are apparent in this case. Low-level lapse rates and storm-relative helicity are typically steeper and slightly smaller for nonlocal than local schemes, respectively. Nonlocal mixing is necessary to more accurately forecast the lower-tropospheric lapse rates within the warm sector of these events. While all schemes yield overestimations of mixed-layer convective available potential energy (MLCAPE), nonlocal schemes more strongly overestimate MLCAPE than do local schemes.

Verification of Convection-Allowing WRF Model Forecasts of the Planetary Boundary Layer Using Sounding Observations

This study evaluates forecasts of thermodynamic variables from five convection-allowing configurations of the Weather Research and Forecasting Model (WRF) with the Advanced Research core (WRF-ARW). The forecasts vary only in their planetary boundary layer (PBL) scheme, including three “local” schemes [Mellor–Yamada–Janjić (MYJ), quasi-normal scale elimination (QNSE), and Mellor–Yamada–Nakanishi–Niino (MYNN)] and two schemes that include “nonlocal” mixing [the asymmetric cloud model version 2 (ACM2) and the Yonei University (YSU) scheme]. The forecasts are compared to springtime radiosonde observations upstream from deep convection to gain a better understanding of the thermodynamic characteristics of these PBL schemes in this regime. The morning PBLs are all too cool and dry despite having little bias in PBL depth (except for YSU). In the evening, the local schemes produce shallower PBLs that are often too shallow and too moist compared to nonlocal schemes. However, MYNN is nearly unbiased in PBL depth, moisture, and potential temperature, which is comparable to the background North American Mesoscale model (NAM) forecasts. This result gives confidence in the use of the MYNN scheme in convection-allowing configurations of WRF-ARW to alleviate the typical cool, moist bias of the MYJ scheme in convective boundary layers upstream from convection. The morning cool and dry biases lead to an underprediction of mixed-layer CAPE (MLCAPE) and an overprediction of mixed-layer convective inhibition (MLCIN) at that time in all schemes. MLCAPE and MLCIN forecasts improve in the evening, with MYJ, QNSE, and MYNN having small mean errors, but ACM2 and YSU having a somewhat low bias. Strong observed capping inversions tend to be associated with an underprediction of MLCIN in the evening, as the model profiles are too smooth. MLCAPE tends to be overpredicted (underpredicted) by MYJ and QNSE (MYNN, ACM2, and YSU) when the observed MLCAPE is relatively small (large).