A comparative study of regression methods to predict forest structure and canopy fuel variables from LiDAR full-waveform data

In general, the application conditions of linear regression models could be met after the natural logarithmic transformation of data. From the practical perspective, this paper introduced the linear regression models with natural logarithmic transformation of independent variable, dependent variable, and both independent and dependent variables in detail. The paper illustrated why the equation and coefficients could not be directly explained after the natural logarithmic transformation of data. The percentage changes of X and/or Y were applied to elaborate the principle and method for the explanation of the equation and coefficients. Three examples were used to fit simple linear models with natural logarithmic transformation of independent, dependent, and both independent and dependent variables and the results of theses models were explained in detail.

For the generalized Rapoport-Leas equations, algebra of differential invariants is constructed with respect to point transformations, that is, transformations of independent and dependent variables. The finding of a general transformation of this type reduces to solving an extremely complicated functional equation. Therefore, following the approach of Sophus Lie, we restrict ourselves to the search for infinitesimal transformations which are generated by translations along the trajectories of vector fields. The problem of finding these vector fields reduces to the redefined system decision of linear differential equations with respect to their coefficients. The Rapoport-Leas equations arise in the study of nonlinear filtration processes in porous media, as well as in other areas of natural science: for example, these equations describe various physical phenomena: two-phase filtration in a porous medium, filtration of a polytropic gas, and propagation of heat at nuclear explosion. They are vital topic for research: in recent works of Bibikov, Lychagin, and others, the analysis of the symmetries of the generalized Rapoport-Leas equations has been carried out; finite-dimensional dynamics and conditions of attractors existence have been found. Since the generalized RapoportLeas equations are nonlinear partial differential equations of the second order with two independent variables; the methods of the geometric theory of differential equations are used to study them in this paper. According to this theory differential equations generate subvarieties in the space of jets. This makes it possible to use the apparatus of modern differential geometry to study differential equations. We introduce the concept of admissible transformations, that is, replacements of variables that do not derive equations outside the class of the Rapoport-Leas equations. Such transformations form a Lie group. For this Lie group there are differential invariants that separate its regular orbits, which allow us to classify the generalized Rapoport-Leas equations.

Classes of 2×2 first order quasilinear partial differential equations involving arbitrary continuously differentiable functions that can be mapped into autonomous and homogeneous form through equivalence transformations are considered. Equivalence transformations are point transformations of independent and dependent variables of differential equations involving arbitrary elements. The transformations act on the arbitrary elements as point transformations of an augmented space of independent, dependent variables and additional variables representing values taken by the arbitrary elements. Projecting the admitted symmetries into the space determined by the independent and dependent variables, we determine some finite transformations mapping the system into autonomous and homogeneous form. Some physical applications are considered and a comparison with reduction of quasilinear first order systems to autonomous and homogeneous form through Lie point symmetries is discussed.

As the finite difference methods or other methods of discreet variables both in time andspace coordinates are used to solve the initial value problems. One of the sufficient conditionsfor computational stability is to maintain the conservation or boundness of the total energy ofthe original physical problems in the computational schemes. Those schemes, which do not exactlyguarantee the conservation or boundness of energy, have always some special computational un-stable solutions. Until recently, all published and the so-called energy-conservative finite dif-ference schemes for integrating the dynamical equations of compressible fluid or the meteoro-logical primitive equations conserve the total energy only instantaneously, i.e. when the differen-tial in time remained, but cannot exactly conserve it as the finiie difference in time is also usedinstead of the differential. In this paper, by using some transformations of independent (co-ordinates) or dependent variables, we have successfully designed some time-space finite differ-ence schemes guaranteeing the energy and mass conservations perfectly. Thus the problem ofcomputational stability is solved completely. In order to solve these finite difference equations, some split methods have been developedalso. They possess the internal consistency and reduce the original problem into successivelysolving several onedimensional initial value problems, to which the economical method of fac-torization can be applied effectively. Thus, both computational stability and economy are guar-anteed. These methods can be used in routine.

Estimating Leaf Area of Big Sagebrush from Measurement of Sapwood

Group analysis of variable coefficients heat and mass transfer equations with power nonlinearity of thermal diffusivity

CHAPTER 3 - Expansion of Nonlinear Terms: The An Polynomials

MRT lattice Boltzmann method for 2D flows in curvilinear coordinates

Groundwater is considered one of the most valuable fresh water resources. The main objective of this study was to produce groundwater spring potential maps in the Koohrang Watershed, Chaharmahal-e-Bakhtiari Province, Iran, using three machine learning models: boosted regression tree (BRT), classification and regression tree (CART), and random forest (RF). Thirteen hydrological-geological-physiographical (HGP) factors that influence locations of springs were considered in this research. These factors include slope degree, slope aspect, altitude, topographic wetness index (TWI), slope length (LS), plan curvature, profile curvature, distance to rivers, distance to faults, lithology, land use, drainage density, and fault density. Subsequently, groundwater spring potential was modeled and mapped using CART, RF, and BRT algorithms. The predicted results from the three models were validated using the receiver operating characteristics curve (ROC). From 864 springs identified, 605 (≈70 %) locations were used for the spring potential mapping, while the remaining 259 (≈30 %) springs were used for the model validation. The area under the curve (AUC) for the BRT model was calculated as 0.8103 and for CART and RF the AUC were 0.7870 and 0.7119, respectively. Therefore, it was concluded that the BRT model produced the best prediction results while predicting locations of springs followed by CART and RF models, respectively. Geospatially integrated BRT, CART, and RF methods proved to be useful in generating the spring potential map (SPM) with reasonable accuracy.

As a key indicator of the urbanization level, impervious surface has widely been used as an environmental indicator linking development to its impact on the environment. Many have for example suggested that there is a direct correlation between the amount of impervious surface and the environmental characteristics of an urban area. In recent years, researches and applications utilizing classification and regression tree (CART) technology have increased and been successfully applied in ecology and image processing or analysis. An approach to quantify urban impervious surfaces as a continuous variable by using QuickBird images as verification data and CBERS images as primary data source was developed. To evaluate model performance, extracted imperviousness from CBERS was compared against that derived from the QuickBird imagery of high resolution. The relative error of this method decreased to 2.9% compared with that of traditional CART method which was 5.8%.

Analysis of traffic injury severity: An application of non-parametric classification tree techniques

ABSTRAKKabupaten Tangerang mengalami pertumbuhan penduduk pesat yang mendorong perubahan tutupan lahan. Rencana Tata Ruang Wilayah (RTRW) 2020 digunakan sebagai panduan pemanfaatan lahan, dengan klasifikasi utama: lahan terbangun, badan air, vegetasi, dan lahan terbuka. Penelitian ini menganalisis perubahan tutupan lahan menggunakan algoritma Classification and Regression Trees (CART) pada citra Sentinel-2A tahun 2019 dan 2023 di Google Earth Engine. Hasil menunjukkan peningkatan luas bangunan dan lahan terbuka masing-masing 19,866 km² dan 17,877 km², sementara vegetasi dan badan air menurun 33,446 km² dan 4,297 km². Akurasi klasifikasi mendapatkan 89,36% (2019) dan 90,29% (2023). Selain itu, kesesuaian tutupan lahan dengan RTRW meningkat 36,71 km² atau 4%. Hasil ini menunjukkan efektivitas metode CART dalam memantau perubahan tutupan lahan serta relevansinya dengan kebijakan tata ruang di Kabupaten Tangerang.Kata Kunci : Tutupan lahan; Rencana Tata Ruang Wilayah (RTRW), Google Earth Engine (GEE),Classification and Regression Trees (CART), Penginderaan jauh.ABSTRACTTangerang Regency is experiencing rapid population growth that is driving land cover change. The 2020 Regional Spatial Plan (RTRW) is used as a guide for land use, with the main classifications: built-up land, water bodies, vegetation, and open land. This study analyzed land cover change using the Classification and Regression Trees (CART) algorithm on 2019 and 2023 Sentinel-2A images in Google Earth Engine. The results showed an increase in building area and open land of 19.866 km² and 17.877 km² respectively, while vegetation and water bodies decreased by 33.446 km² and 4.297 km². The classification accuracy was 89.36% (2019) and 90.29% (2023). In addition, land cover conformity with the RTRW increased by 36.71 km² or 4%. These results demonstrate the effectiveness of the CART method in monitoring land cover change and its relevance to spatial policy in Tangerang District.Keywords: Land cover, Regional Spatial Plan (RTRW), Supervised Classification, Google Earth Engine (GEE), Classification and Regression Trees (CART), Remote sensing

A classification tree approach to identify key factors of transit service quality

Traditional radar-based rainfall estimation is typically done by known functional relationships between the rainfall intensity (R) and radar measurables, such as R–Zh, R–(Zh, ZDR), etc. One of the biggest advantages of machine learning algorithms is the applicability to a non-linear relationship between a dependent variable and independent variables without any predefined relationships. We explored the potential use of two supervised machine learning methods (regression tree and random forest) in rainfall estimation using dual-polarization radar variables. The regression tree does not require normalization and scaling of data; however, this method is quite unstable since each split depends on the parent split. Since the random forest is an ensemble method of regression trees, it has less variability in prediction compared with regression trees, but consumes more computer resources. We considered several different configurations for machine learning algorithms with different sets of dependent and independent variables. The random forest model was appropriately tuned. In the test of variable importance, the specific differential phase (differential reflectivity) was the most important variable to predict the rainfall rate (residual that is the difference between the true rainfall rate and the one estimated from the R–Z relationship). The models were evaluated by 10-fold cross-validation. The best model was the random forest model using a residual with the non-classified training set. The results indicated that the machine learning algorithms outperformed the traditional R–Z relationship. Then, we applied the best machine learning model to an S-band dual-polarization radar (Mt. Myeonbong) and validated the result with ground rain gauges. The results of the application to radar data showed that the estimates of the residuals had spatial variability. The stratiform and weak rain areas had positive residuals while convective areas had negative residuals, indicating that the spatial error structure driven by the R–Z relationship was well captured by the model. The rainfall rates of all pixels over the study area were adjusted with the estimated residuals. The rainfall rates adjusted by residual showed excellent agreement with the rain gauge, especially at high rainfall rates.

The first Amden Report defines validation as “The process by which the reliability and relevance of a test are established”. The recommendations of the Amden conference mention the need for biometric methods, but, unfortunately, most publications on alternatives to animal testing procedures do not pay much attention to statistical problems in the validation process. The biometric repertoire consists mainly of scatterplots, correlation coefficients and linear regression. In the evaluation of an interlaboratory study, we applied multivariate statistical methods to analyse the ability of two in vitro tests to identify severely irritating substances. In this study, conducted by the German Bundesgesundheitsamt, two alternatives to the well-known Draize eye irritancy test — the neutral red uptake test and the HET-CAM test — were investigated. The statistical methods applied were discriminant analysis and the Classification and Regression Trees (CART) method. The results presented here show that the combination of the endpoints of the in vitro tests, analysed by using the CART method, can give a sensitivity of about 67% with 76% specificity. Discriminant analysis models only achieve a sensitivity of 55%. The results obtained with the data presented here show that these statistical methods are very suitable and useful for this type of problem. This was confirmed by further analyses with discriminant analysis models, which gave a sensitivity of about 80%.