Binary Tree Models Research Articles

Investment decision analysis of shipping desulfurization project based on a fuzzy real option approach

ABSTRACT This study addresses shipping companies’ compliance with the International Maritime Organization’s 2020 sulfur emission limits, providing guidance for investment decisions in desulfurization projects. The paper uses a novel RCFM model, integrating real option theory (R), shipping cycle theory (C), fuzzy set theory (F), and Monte Carlo simulation (M). Key findings are: (1) During high oil price volatility, traditional binary tree models show computational distortions corrected by Monte Carlo simulation, whereas in lower volatility, the fuzzy binary tree model offers reliable investment intervals. (2) Investment in desulfurization depends on remaining vessel life and fuel price differences. For example, during the recovery period, for vessels with a remaining life of less than 5 years, investing in a desulfurizer is profitable if the fuel price difference exceeds $550/t and using low-sulfur fuel is advisable if below $400/t. For vessels of remaining life of 5-9 years, invest in a desulfurizer if the difference exceeds $500/t and use low-sulfur fuel if below $300/t. For over 9 years, invest in a desulfurizer if the difference exceeds $450/t and use low-sulfur fuel if below $200/t.

The development and application of pediatric complicated appendicitis prediction model.

Acute appendicitis in children refers to the acute inflammation of the appendix, which accounts for 20% ∼ 30% of cases of acute abdomen in pediatric surgery. This study aimed to establish a decision tree model of complicated appendicitis in children using appendiceal ultrasound combined with an inflammatory index and evaluated its clinical efficacy in pediatric patients. A total of 395 children admitted to the Emergency Department of the Shanghai Children's Hospital from January 2018 to December 2021 and diagnosed with appendicitis by postoperative pathology were retrospectively analyzed. According to the postoperative pathology, the children were divided into a complicated and non-complicated appendicitis group, respectively. Routine laboratory inflammatory indicators, including white blood cell count, N(%), neutrophil (Neu) count, Neu/lymphocyte ratio (NLR), C-reactive protein (CRP), and procalcitonin were collected from the two groups. Collecting data on ultrasound examination of the appendix includes whether the appendix diameter is thickened, whether the echogenicity of the mesenteric rim surrounding the appendix is enhanced, whether there is rich blood supply in the appendix, and whether there are fecaliths in the appendix lumen. The risk factors for complicated appendicitis were screened out by univariate and multivariate logistic regression analyses, the binary logistic regression prediction and decision tree models were established, respectively, and the receiver operating characteristic (ROC) curve was used to verify the accuracy of the two prediction models. Binary logistic regression analysis showed that CRP, NLR, the presence of an appendicolith, and peripheral retina echo enhancement were independent risk factors for complicated appendicitis in children (P< 0.05). The decision tree model had an overall accuracy of 79%, an area under the ROC curve (AUC) of 0.809 (95% confidence interval [CI] 0.780-0.865), and sensitivity and specificity of 71.3% and 77.7%, respectively. The logistic regression model had an overall accuracy of 74.9%, an AUC value of 0.823 (95% CI, 0.765-0.853), a sensitivity value of 80.3%, and a specificity of 71.8%. This predictive model, based on ultrasound of the appendix combined with inflammatory markers, provides a useful method to assist pediatric emergency physicians in diagnosing childhood appendicitis. The decision tree model reflected the interaction of various indexes, and the model was simple, intuitive, and effective.

Looking back in the rearview: Insights into Queensland’s rear-end crashes

Objective Rear-end crashes cost the most out of any crash type to the Compulsory Third Party insurance scheme of Queensland. Rear-end crashes are also one of the most common types of crashes, peaking as the most common type of crash in Queensland in 2019. This study investigated the environmental, driver, and vehicle characteristics associated with rear-end collisions in Queensland, Australia. Methods A totle of 367,230 crashes in the Queensland crash database between 2001 and 2021 were used to identify crash trends in Queensland, particularly related to rear-end crashes. For crashes between 2015 and 2021, additional information was gathered and allowed further analysis of factors contributing to rear-end crashes using the quasi-induced exposure method. Two binary classification tree models were used. Model 1 investigated the environmental characteristics that predicted a crash being a rear-end or not. Model 2 investigated the controller and vehicle characteristics that predict a rear-end crash-involved vehicle to be either the striking (at-fault) or struck (not-at-fault) vehicle. Results Model 1 indicated that rear-end crashes were overrepresented in urban areas and major cities and where speed limits exceeded 50 km/h. Model 2 indicated that occupants of struck vehicles (not at-fault) were more likely to be severely injured than the striking (at-fault) vehicles in rear-end crashes. License type and vehicle type also influenced the frequency and severity of rear-end crashes. Conclusion Rear-end crashes can be unjust in that the not-at-fault party is typically more severely injured. Results from the current study suggest that keeping speed limits no higher than 50 km/h could help reduce the severity of rear-end crashes. Increased enforcement of safe following distances could also assist in preventing road trauma as a result of rear-end crashes.

Explainable Boosting Machine for Predicting Wind Shear-Induced Aircraft Go-around based on Pilot Reports

The go-around is a safety-critical procedure in civil aviation that is rarely executed but is essential to avoid risky landings. Analyzing the factors that trigger go-around events can aid in identifying measures that could lower their frequency. This involves circumstances that could be deemed abnormal and intrinsically harmful. The study employed the Explainable Boosting Machine (EBM), a contemporary transparent model, to predict aircraft go-arounds and interpret different influential factors. The model proposed exhibits comparable accuracy to black-box models. The study utilized pilot reports and applied SMOTE-ENN to address the imbalance problem. The EBM model was trained with treated data in conjunction with Bayesian optimization. The EBM model's performance was evaluated using holdout data and compared to binary logistic regression and decision tree models, as well as black-box models such as adaptive boosting, random forest, and extreme gradient boosting. The EBM model exhibited superior performance compared to other models in terms of precision (83.15%), recall (79.77%), geometric mean (77.29%), and Matthews's correlation coefficient (0.453). The EBM algorithm enables the comprehensive interpretation of individual and pairwise factor interactions in predicting aircraft go-around outcomes from both global and local perspectives. This facilitates the assessment of the impact of different factors on go-around outcomes.

An Integrated GIS and Machine-Learning Technique for Groundwater Quality Assessment and Prediction in Southern Saudi Arabia

One of the most critical stages for developing groundwater resources for drinking water use is assessing the water quality. The use of a Water Quality Index (WQI) is considered an effective method of evaluating water quality. The objective of this research was to evaluate the performance of six multiple artificial intelligence techniques, i.e., linear regression (stepwise), support vector regression SVM (linear and polynomial kernels), Gaussian process regression (GPR), Fit binary tree, and artificial neural network ANN (Bayesian) to predict the WQI in Jizan, Southern Saudi Arabia. A total of 145 groundwater samples were collected from shallow dug wells and boreholes tapping the phreatic aquifer. The WQI was calculated from 11 physicochemical parameters (pH, TDS, Ca2+, Mg2+, Na+, K+, Cl−, SO42−, HCO3−, NO3−, and TH). The spatial distribution results showed that higher values of Cl− and SO42− were recorded in the places close to the coastline, indicating the occurrence of seawater intrusion and salinisation. Seven wells had a WQI of greater than 300, indicating that the water was unfit for consumption. The results showed that the GPR, linear regression (stepwise), and ANN models performed best during the training and testing stages, with a high correlation of 1.00 and low errors. The stepwise fitting model indicated that pH, K+, and NO3− were the most significant variables, while HCO3− was a non-significant variable for the WQI. The GPR, stepwise regression, and ANN models performed best during the training and testing stages, with a high correlation and low errors. In contrast, the SVM and Fit binary tree models performed the worst in the training and testing phases. Based on subset regression analysis, the optimum input combination for WQI model prediction was determined as these eight input combinations with high R2 (0.975–1.00) and high Adj-R2 (0.974–1.00). The resultant WQI model significantly contributes to sustainable groundwater resource management in arid areas and generates improved prediction precision with fewer input parameters.

Fuzzy Option Pricing Based on Fuzzy Number Binary Tree Model

In this article, a new method of option pricing in the form of fuzzy number is established based on fuzzy number binary tree model. Firstly,by using the operation rules of fuzzy number addition and number multiplication in cut set form, the fuzzy number binary tree model is equivalently transformed into two families of classical binary tree models which change with the level value, and some properties of the two binary tree model families are obtained, which are related to solve the problem of fuzzy option pricing. Then, based on the results obtained by us, the concepts of fuzzy set option price and fuzzy number option price are defined, and a sufficient condition is obtained for fuzzy set option price to be fuzzy number option price in the fuzzy number binary tree model. And then, for the convenience of practical application, the concepts of fold line fuzzy set and fuzzy number option price are introduced, a sufficient condition for fold line fuzzy set option price to be fold line fuzzy number option price is obtained, and a specific solution method of the fold line set and the fold line fuzzy number option pricing are set up. At last, two specific examples are given to show how to solve the fold line set and the fold line fuzzy number option price.

A multivariate binary decision tree classifier based on shallow neural network

In this paper, a novel decision tree classifier based on shallow neural networks with piecewise and nonlinear transformation activation functions are presented. A shallow neural network is recursively employed into linear and non-linear multivariate binary decision tree methods which generates splitting nodes and classifier nodes. Firstly, a linear multivariate binary decision tree with a shallow neural network is proposed which employs a rectified linear unit function. Secondly, there is presented a new activation function with non-linear property which has good generalization ability in learning process of neural networks. The presented method shows high generalization ability for linear and non-linear multivariate binary decision tree models which are called a Neural Network Decision Tree (NNDT). The proposed models with high generalization ability ensure the classification accuracy and performance. A novel split criterion of generating the nodes which focuses more on majority objects of classes on the current node is presented and employed in the new NNDT models. Furthermore, a shallow neural network based NNDT models are converted into a hyperplane based linear and non-linear multivariate decision trees which has high speed in the processing classification decisions. Numerical experiments on publicly available datasets have showed that the presented NNDT methods outperform the existing decision tree algorithms and other classifier methods.

Characteristics analysis and modeling of occupants' window operation behavior in hot summer and cold winter region, China

Opening windows is an important factor when creating a comfortable indoor environment. However, research on window opening behavior in the Chinese region of hot summers and cold winters is limited. In addition, almost all previous research in this area has focused on the average characteristics of the sample mostly by building models of averageness, which largely erases individual behavioral attributes. To fill the gap, an empirical measurement and modeling study of window opening behavior was conducted in seven households in Zigong, Sichuan Province. The following was found: (1) The window opening behavior of residents in different cities in hot summer and cold winter regions significantly differed. The average daily duration of window opening by the test subjects in this paper is 1122 min/day, which is 2–5.5 times higher than previously published literature on this climate zone suggests. (2) Among the test subjects, three typical window opening behaviors were noticed based on the average daily window-opening probability (R), i.e., positive (R>95%), negative (R ≤ 5%), and high-intensity window opening (65% < R ≤ 95%). The first two categories refer to personal habits of residents independent of environmental and temporal factors. (3) High-intensity window opening behavior provided imbalanced data which is more accurately modeled by the random forest model (98.9% prediction accuracy) than the binary logistic regression and decision tree models, i.e., 14.5% more accurate than the former and 12.5% more accurate than the latter. Moreover, it was found that the relative humidity indoors is the factor that contributed the most to the accuracy of the model.

Influence of Biopsy Gleason Score on the Risk of Lymph Node Invasion in Patients With Intermediate-Risk Prostate Cancer Undergoing Radical Prostatectomy.

Objective: To analyze the influence of biopsy Gleason score on the risk for lymph node invasion (LNI) during pelvic lymph node dissection (PLND) in patients undergoing radical prostatectomy (RP) for intermediate-risk prostate cancer (PCa).Materials and Methods: We retrospectively analyzed 684 patients, who underwent RP between 2014 and June 2020 due to PCa. Univariable and multivariable logistic regression, as well as binary regression tree models were used to assess the risk of positive LNI and evaluate the need of PLND in men with intermediate-risk PCa.Results: Of the 672 eligible patients with RP, 80 (11.9%) men harbored low-risk, 32 (4.8%) intermediate-risk with international society of urologic pathologists grade (ISUP) 1 (IR-ISUP1), 215 (32.0%) intermediate-risk with ISUP 2 (IR-ISUP2), 99 (14.7%) intermediate-risk with ISUP 3 (IR-ISUP3), and 246 (36.6%) high-risk PCa. Proportions of LNI were 0, 3.1, 3.7, 5.1, and 24.0% for low-risk, IR-ISUP1, IR-ISUP 2, IR-ISUP-3, and high-risk PCa, respectively (p < 0.001). In multivariable analyses, after adjustment for patient and surgical characteristics, IR-ISUP1 [hazard ratio (HR) 0.10, p = 0.03], IR-ISUP2 (HR 0.09, p < 0.001), and IR-ISUP3 (HR 0.18, p < 0.001) were independent predictors for lower risk of LNI, compared with men with high-risk PCa disease.Conclusions: The international society of urologic pathologists grade significantly influence the risk of LNI in patients with intermediate- risk PCa. The risk of LNI only exceeds 5% in men with IR-ISUP3 PCa. In consequence, the need for PLND in selected patients with IR-ISUP 1 or IR-ISUP2 PCa should be critically discussed.

Assessing the Role of Snow Cover for Post‐Wildfire Revegetation Across the Pacific Northwest

AbstractForested, mountain landscapes in the Pacific Northwest (PNW) are changing at an unprecedented rate, largely due to shifts in the regional climate regime. Documented climate warming trends across the PNW include increasing wildfire frequency and severity and an increasingly ephemeral snowpack, especially at moderate elevations. We analyzed 24 high severity wildfires across four distinct PNW mountainous subregions, examining snow‐vegetation relationships for two years pre‐fire and four years post‐fire. To assess the importance of snow cover for revegetation compared to other climatic, topographic, and burn severity‐related variables, binary regression tree models were constructed for the dominant pre‐fire conifer species within each of the four PNW subregions. Summer precipitation consistently appeared as the most important variable driving post‐fire revegetation across all four subregions. Snow cover variables (snow cover frequency and snow disappearance date), along with elevation, were shown to be secondary but significantly influential explanatory variables for revegetation in the Oregon and Washington Cascades. Revegetation was also analyzed using a time series of linear regressions across 200‐m elevation bands by measuring correlations between winter snow cover and summer vegetation greenness. Results showed strong positive post‐fire correlations at moderate elevations in the western Montana Rockies and at the lowest elevation band in the Idaho Rockies. Considering trends of increasing wildfire activity, lower snowpacks, and earlier snow disappearance dates across the PNW, forests will likely experience more frequent drought conditions that will impact post‐wildfire vegetation regrowth.

Multiparametric MRI may Help to Identify Patients With Prostate Cancer in a Contemporary Cohort of Patients With Clinical Bladder Outlet Obstruction Scheduled for Holmium Laser Enucleation of the Prostate (HoLEP).

Objective: To investigate the value of standard [digital rectal examination (DRE), PSA] and advanced (mpMRI, prostate biopsy) clinical evaluation for prostate cancer (PCa) detection in contemporary patients with clinical bladder outlet obstruction (BOO) scheduled for Holmium laser enucleation of the prostate (HoLEP).Material and Methods: We retrospectively analyzed 397 patients, who were referred to our tertiary care laser center for HoLEP due to BOO between 11/2017 and 07/2020. Of those, 83 (20.7%) underwent further advanced clinical PCa evaluation with mpMRI and/or prostate biopsy due to elevated PSA and/or lowered PSA ratio and/or suspicious DRE. Logistic regression and binary regression tree models were applied to identify PCa in BOO patients.Results: An mpMRI was conducted in 56 (66%) of 83 patients and revealed PIRADS 4/5 lesions in 14 (25%) patients. Subsequently, a combined systematic randomized and MRI-fusion biopsy was performed in 19 (23%) patients and revealed in PCa detection in four patients (5%). A randomized prostate biopsy was performed in 31 (37%) patients and revealed in PCa detection in three patients (4%). All seven patients (9%) with PCa detection underwent radical prostatectomy with 29% exhibiting non-organ confined disease. Incidental PCa after HoLEP (n = 76) was found in nine patients (12%) with advanced clinical PCa evaluation preoperatively. In univariable logistic regression analyses, PSA, fPSA ratio, and PSA density failed to identify patients with PCa detection. Conversely, patients with a lower International Prostate Symptom Score (IPSS) and PIRADs 4/5 lesion in mpMRI were at higher risk for PCa detection. In multivariable adjusted analyses, PIRADS 4/5 lesions were confirmed as an independent risk factor (OR 9.91, p = 0.04), while IPSS did not reach significance (p = 0.052).Conclusion: In advanced clinical PCa evaluation mpMRI should be considered in patients with elevated total PSA or low fPSA ratio scheduled for BOO treatment with HoLEP. Patients with low IPSS or PIRADS 4/5 lesions in mpMRI are at highest risk for PCa detection. In patients with a history of two or more sets of negative prostate biopsies, advanced clinical PCa evaluation might be omitted.

Automated Volume Status Assessment Using Inferior Vena Cava Pulsatility

Assessment of volume status is important to correctly plan the treatment of patients admitted and managed by cardiology, emergency and internal medicine departments. Non-invasive assessment of volume status by echography of the inferior vena cava (IVC) is a promising possibility, but its clinical use is limited by poor reproducibility of current standard procedures. We have developed new algorithms to extract reliable information from non-invasive IVC monitoring by ultrasound (US) imaging. Both long and short axis US B-mode video-clips were taken from 50 patients, in either hypo-, eu-, or hyper-volemic conditions. The video-clips were processed to extract static and dynamic indexes characterizing the IVC behaviour. Different binary tree models (BTM) were developed to identify patient conditions on the basis of those indexes. The best classifier was a BTM using IVC pulsatility indexes as input features. Its accuracy (78.0% when tested with a leave-one-out approach) is superior to that achieved using indexes measured by the standard clinical method from M-mode US recordings. These results were obtained with patients in conditions of normal respiratory function and cardiac rhythm. Further studies are necessary to extend this approach to patients with more complex cardio-respiratory conditions.

Quantitative Structure-Property Relationship (QSPR) models for Minimum Ignition Energy (MIE) prediction of combustible dusts using machine learning

Quantitative Structure-Property Relationship (QSPR) classification models for Minimum Ignition Energy (MIE) classification of 65 combustible dusts have been developed using machine learning algorithms Random Forests (RF) and Decision Trees (DT). Combustible dusts were categorized based on their MIE values: dusts having MIE > 10 mJ and dusts having MIE < 10 mJ. In this work, an important macroscopic property, dust median diameter (d50) was also used as one of the parameters along with the molecular descriptors for model development. The machine learning Random Forest (RF) algorithm was used for identification of the 13 molecular descriptors having maximum effect on MIE prediction accuracy. Thereafter, these descriptors were used as input parameters to develop binary classification Random Forest (RF) and Decision Tree (DT) models. The RF and DT algorithms displayed good MIE category predictability validated through the test set Receiver Operating Characteristic- Area Under Curve (ROC-AUC) of 0.95 for both the models. Thus, this work has displayed that Random Forests can be used as an important tool for descriptor reduction in QSPR studies and can prove to be a valuable resource for MIE category prediction.

Cost-sensitive and hybrid-attribute measure multi-decision tree over imbalanced data sets

One of the most popular algorithms for classification is the decision tree. However, existing binary decision tree models do not handle well the minority class over imbalanced data sets. To address this difficulty, a Cost-sensitive and Hybrid attribute measure Multi-Decision Tree (CHMDT) approach is presented in this paper. It penalizes misclassification through a hybrid attribute measure, which is defined from the combination of the Gini index and information gain measure. It further builds a multi-decision tree consisting of multiple decision trees each with different root node information. The overall objective of the approach is to maximize the classification performance with the hybrid attribute measure while minimizing the total misclassification cost. Experiments are conducted over twelve KEEL imbalanced data sets to demonstrate the CHMDT approach. They show that the classification performance of the minority class is improved significantly without sacrifice of the overall classification accuracy of the majority class.

Prediction of deformation twinning statistics in zirconium using the Taylor, ALAMEL and binary tree models and a classical twinning criterion

The classical Chin-Hosford-Mendorf (CHM) criterion for deformation twinning is used widely in polycrystal plasticity computer simulations. It assumes that twin nuclei are abundant, and that twin propagation and growth control the realisation of deformation twins. However, recent experimental studies reported in the literature have found that nominally unfavourable twin systems are activated in grains. This has been attributed to twin nucleation in some of the unfavourable twinning systems with low Schmid factors, and its suppression in some of the nominally more favourable ones. Presently, this explanation is quantitatively examined. Full and relaxed constraint versions of the Taylor, ALAMEL, and binary tree based models, all implementing the CHM criterion are used to simulate uniaxial compression of a zirconium billet. Model predictions are compared with experimentally measured twinning statistics reported in the literature for a Zr polycrystal. The ALAMEL and binary tree models, which explicitly represent intergranular interactions, are found to capture the twinning statistics well. These observations suggest that the CHM criterion is adequate to capture twinning in Zr, provided intergranular interactions are represented in the model used to interpret the experiments.

Quantitative Structure–Property Relationship Models for Recognizing Metal Organic Frameworks (MOFs) with High CO2 Working Capacity and CO2/CH4 Selectivity for Methane Purification

Metal‐organic frameworks (MOFs) can theoretically yield a nearly infinite number of nanoporous materials, which represents a combinatorial design challenge that demands computational tools rather than experimental trial‐and‐error. Here we report Quantitative Structure–Property Relationship (QSPR) models to identify high‐performing MOFs for methane purification solely using geometrical features. The CO2 working capacity and CO2/CH4 selectivity of ca. 320,000 hypothetical MOF structures was computed at conditions relevant to natural gas purification using grand canonical Monte‐Carlo (GCMC) simulations. Using 32,500 MOF structures we calibrated binary decision tree (DT) and support vector machine (SVM) models that can accurately identify high‐performing MOFs based on their pore size, void fraction and surface area. DT models yielded guidelines of pore size, void fraction and surface area for designing high‐performing materials. The SVM machine learning classifiers could be used to quickly pre‐screen MOFs, such that compute intensive GCMC simulations are not performed on all structures. The SVM classifiers were tested on ca. 290,000 MOFs that were not part of the training set and could correctly identify up to 90 % of high‐performing MOFs while only flagging a fraction of the MOFs for more rigorous screening. QSPR models constitute efficient computational tools for the virtual screening of large structural libraries and provide rational design rules for the discovery of sorbents for methane purification.

Classification tree analysis of factors affecting parking choices in Qatar

Qatar has experienced a significant population growth in the past decade. The growth has been accompanied by an increase in automobile ownership rates leading to parking problems especially in the capital city of Doha. The objective of this study was to find the factors affecting people's choice of parking in this rich developing country when different parking options are available. Two commercial centers located in the city of Doha, Qatar were selected for this study; the City Center mall and the Souq Waqif shopping center. Each location has two different parking options available. Parking options vary in many features including distance to destination, paid/free, covered/open, paved/unpaved, and guarded/unguarded. In addition, the parking options also differed in the ITS infrastructure deployed in the form of intelligent parking space detection system to assist visitors to navigate to an available spot. A survey was handed out to randomly selected visitors at the main entrance of each of these shopping areas to obtain a random sample of study participants. Binary classification tree models were developed to understand the factors associated with binary parking choices at both of these commercial centers. In addition to the demographic factors associated with the parking choice; the reasons for choosing a particular parking option were also explored through the survey. The analysis of survey data presented herein provides an interesting insight into parking choices of the visitors that can be used in planning future parking facilities sand managing existing parking locations. Among the reasons cited by respondents for making their parking choices, “Intelligent Parking Space Detection” was chosen as one of the factors affecting people's choice of parking significantly more often than amenities such as “Wider parking spot”. The findings indicate that future parking investments may be better directed towards smart parking solutions.

Physiographic and climatic controls on snow cover persistence in the Sierra Nevada Mountains

AbstractThe persistence of snow cover across mountainous landscapes influences land‐atmosphere energy exchange, water availability, the partitioning of snowmelt into various hydrologic pathways, vegetation productivity, and fluxes of nutrients. Understanding the processes controlling snow cover persistence has been limited as relationships between physiography, climate, and snow persistence are nonlinear and difficult to characterize empirically. The work detailed herein uses 7 years of remotely sensed snow cover persistence observed from the Moderate Resolution Imaging Spectroradiometer over the Sierra Nevada Mountains as a dependent variable in binary regression tree models with a suite of independent variables comprised of both physiographic and climatic metrics. Annual snow cover persistence over 2001–2007 revealed significant inter‐annual variability, with domain‐average snow persistence values exceeding 4.01 (i.e. early April) in the wettest year of 2005 and reaching as low as 2.90 (i.e. late February) in the driest year of 2007. Regression tree models revealed that elevation was the most important explanatory variable regarding snow cover persistence, ranking first in the hierarchical models in 10 out of 13 watersheds. Precipitation (Feather and Owens River basins) and temperature (Kern River basin) were the first‐ranking variables in the remaining three watersheds. Second, the order variables of importance included vegetation, which ranked between 2nd and 5th in 10 of 13 watersheds, and slope, which ranked 4th and 5th in 12 of the 13 watersheds. Interestingly, solar radiation and aspect were of tertiary importance but were more influential in watersheds with north–south orientation (e.g. in the Feather, Mokelumne and Stanislaus watersheds). These results have implications for understanding the sensitivity of snow cover persistence to changes in climate as watersheds where elevation and/or temperature strongly influence snow cover persistence may be more sensitive to future warming. Further work is needed to identify associated ecosystem sensitivities to future changes in snow cover persistence. Copyright © 2014 John Wiley &amp; Sons, Ltd.

Subgrid variability of snow water equivalent at operational snow stations in the western USA

AbstractThe spatial distribution of snow water equivalent (SWE) is a key variable in many regional‐scale land surface models. Currently, the assimilation of point‐scale snow sensor data into these models is commonly performed without consideration of the spatial representativeness of the point data with respect to the model grid‐scale SWE. To improve the understanding of the relationship between point‐scale snow measurements and surrounding areas, we characterized the spatial distribution of snow depth and SWE within 1‐, 4‐ and 16‐km2 grids surrounding 15 snow stations (snowpack telemetry and California snow sensors) in California, Colorado, Wyoming, Idaho and Oregon during the 2008 and 2009 snow seasons. More than 30 000 field observations of snowpack properties were used with binary regression tree models to relate SWE at the sensor site to the surrounding area SWE to evaluate the sensor representativeness of larger‐scale conditions. Unlike previous research, we did not find consistent high biases in snow sensor depth values as biases over all sites ranged from 74% overestimates to 77% underestimates. Of the 53 assessments, 27 surveys indicated snow station biases of less than 10% of the surrounding mean observed snow depth. Depth biases were largely dictated by the physiographic relationship between the snow sensor locations and the mean characteristics of the surrounding grid, in particular, elevation, solar radiation index and vegetation density. These scaling relationships may improve snow sensor data assimilation; an example application is illustrated for the National Operational Hydrologic Remote Sensing Center National Snow Analysis SWE product. The snow sensor bias information indicated that the assimilation of point data into the National Operational Hydrologic Remote Sensing Center model was often unnecessary and reduced model accuracy. Copyright © 2012 John Wiley &amp; Sons, Ltd.

L-cumulants, L-cumulant embeddings and algebraic statis- tics

Focusing on the discrete probabilistic setting we generalize the combinatorial denitionof cumulants to L-cumulants. This generalization keeps all the desired properties of the classicalcumulants like semi-invariance and vanishing for independent blocks of random variables. Theseproperties make L-cumulants useful for the algebraic analysis of statistical models. We illustratethis for general Markov models and hidden Markov processes in the case when the hidden processis binary. The main motivation of this work is to understand cumulant-like coordinates in algebraicstatistics and to give a more insightful explanation why tree cumulants give such an elegantdescription of binary hidden tree models. Moreover, we argue that L-cumulants can be used in theanalysis of certain classical algebraic varieties.