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Abstract The role of mathematics vocabulary in mathematics has received increasing attention in recent years. Most prior relevant research focused on students in preschool and early elementary grades in the United States and often considered mathematics vocabulary as a single construct in relation to one mathematics outcome. In the current study, we explored how different types of mathematics vocabulary emphasized in curriculum are related to different mathematics outcomes among students in 4th grade in China. Data were collected on mathematics vocabulary, general vocabulary, cognitive skills (IQ, working memory, and processing speed), and mathematics (calculation and word problems) among 237 students. Findings showed that after controlling for general vocabulary, IQ, working memory, and processing speed, mathematics vocabulary still made a unique contribution to mathematics performance, but the effects of mathematics vocabulary varied by different types of mathematics outcomes and mathematics vocabulary. That is, mathematics vocabulary made a unique contribution to word problems but not to calculation. Vocabulary related to measurement and geometry was more important to word problems than vocabulary related to numerical operations. Moreover, measurement and geometry vocabulary partially explained the relation between word problems and general vocabulary and IQ and fully explained the relation between word problems and working memory. These findings, taken together, suggest that mathematics vocabulary may not be a unitary construct, but consists of subtypes that relate to different mathematics outcomes among intermediate graders. Highlights • Mathematics vocabulary was more important to word problems than to calculation. • The effects of mathematics vocabulary differ by mathematics vocabulary subtypes. • Mathematics vocabulary mediated the relation between cognitions and mathematics performance. • Mathematics vocabulary may not be a unitary but a multi-component construct. [ABSTRACT FROM AUTHOR]

A high-resolution surface rainfall product is used to estimate rain characteristics over the continental United States as a function of rain intensity. By defining data at 4-km horizontal resolutions and 1-h temporal resolutions as an individual precipitating or nonprecipitating sample, statistics of rain occurrence and rain volume including their geographical and seasonal variations are documented. Quantitative estimations are also conducted to evaluate the impact of missing light rain events due to satellite sensors' detection capabilities. It is found that statistics of rain characteristics have large seasonal and geographical variations across the continental United States. Although heavy rain events (>10 mm h−1) only occupy 2.6%% of total rain occurrence, they may contribute to 27%% of total rain volume. Light rain events (<1.0 mm h−1), occurring much more frequently (65%%) than heavy rain events, can also make important contributions (15%%) to the total rain volume. For minimum detectable rain rates setting at 0.5 and 0.2 mm h−1, which are close to sensitivities of the current and future spaceborne precipitation radars, there are about 43%% and 11%% of total rain occurrence below these thresholds, and they respectively represent 7%% and 0.8%% of total rain volume. For passive microwave sensors with their rain pixel sizes ranging from 14 to 16 km and the minimum detectable rain rates around 1 mm h−1, the missed light rain events may account for 70%% of rain occurrence and 16%% of rain volume. Statistics of rain characteristics are also examined on domains with different temporal and spatial resolutions. Current issues in estimates of rain characteristics from satellite measurements and model outputs are discussed. [ABSTRACT FROM AUTHOR]

It is of importance to perform hydrological forecast using a finite hydrological time series. Most time series analysis approaches presume a data series to be ergodic without justifying this assumption. To our knowledge, there are no methods available for test of ergodicity to date. This paper presents a practical approach to analyze the mean ergodic property of hydrological processes by means of augmented Dickey Fuller test, Mann-Kendall trend test, a radial basis function neural network, and the assessment methods derived from the definition of ergodicity. The mean ergodicity of precipitation processes at Newberry, MI, USA, is analyzed using the proposed approach. The results indicate that the precipitations of January, May, and July in Newberry are highly likely to have ergodic property, the precipitations of February, and October through December have tendency toward mean ergodicity, and the precipitations of all the other months are non-ergodic. [ABSTRACT FROM AUTHOR]