Head/Tail Breaks: A New Classification Scheme for Data with a Heavy-Tailed Distribution

This article introduces a new classification scheme—head/tail breaks—to find groupings or hierarchy for data with a heavy-tailed distribution. The heavy-tailed distributions are heavily right skewed, with a minority of large values in the head and a majority of small values in the tail, commonly characterized by a power law, a lognormal, or an exponential function. For example, a country's population is often distributed in such a heavy-tailed manner, with a minority of people (e.g., 20 percent) in the countryside and the vast majority (e.g., 80 percent) in urban areas. This new classification scheme partitions all of the data values around the mean into two parts and continues the process iteratively for the values (above the mean) in the head until the head part values are no longer heavy-tailed distributed. Thus, the number of classes and the class intervals are both naturally determined. I therefore claim that the new classification scheme is more natural than the natural breaks in finding the groupings or hierarchy for data with a heavy-tailed distribution. I demonstrate the advantages of the head/tail breaks method over Jenks's natural breaks in capturing the underlying hierarchy of the data.     

The key indicators of transboundary water apportionment based on international laws and cases

Transboundary water, more competitive utilization and uncertain availability under the globalization trend, the issue of its apportionment which directly impacts national benefits of each riparian state is becoming one of the important topics in the world. Water is scarce in China, the most important upstream state in Asia, and this task has to be thought over in the coming future. Based on ＂International Freshwater Treaties Database＂ （1820-2007） by Oregon State University, and publications and reports on transboundary water utilization and management since 1999, 28 indicators of water apportionment adopted in 49 international treaties and cases in 1864-2002 are divided into 6 types, the spatial and temporal characteristics of the adopted indicators are analyzed in order to find the key indicator（s） of transboundary water apportionment. The major results include： the major adopted indicators, have significant differences among 5 regions/continents, the indicators at rank first and second place in the developed region （North America and Europe） according to the adopted times are ＂keeping minimum water flow＂ and ＂mean annual runoff＂, but in the developing region （Asia, Africa and South America）, the ranking order of the above two indicators is reversed; the major adopted indicators in the watersheds with insufficient water are ＂mean annual runoff＂ and ＂keeping minimum water flow＂, the ones in the watersheds with sufficient water are ＂keeping minimum water flow＂ and ＂maximum water intake＂; the international treaties signed from the first phase to the fourth phase, the developing process shows a progress of ＂fewer-increasing a lot-decreasing rapidly-equation basically＂, the regional distribution of the treaties shifts mainly from the developed region to the developing one, especially to Asia and Africa; the major adopted indicators shifts from ＂keeping minimum water flow＂ and ＂mean annual runoff＂ in 1864-1945, to ＂keeping minimum water flow＂ and ＂maximum water intake＂ in 1946-1971, then to ＂hydraulic facility operation＂ and ＂mean annual runoff＂ in 1972-1991, and finally to ＂keeping minimum water flow＂ and ＂mean annual runoff＂ in 1992-2002, the process shows similar a loop. Finally, the key indicator on transboundary water apportionment can be determined as ＂keeping minimum water flow＂.     

Erosion modelling for land management in the Tahoe basin,USA: scaling from plots to forest catchments

Abstract

Recent developments in hydrological modelling of river basins are focused on prediction in ungauged basins, which implies the need to improve relationships between model parameters and easily-obtainable information, such as satellite images, and to test the transferability of model parameters. A large-scale distributed hydrological model is described, which has been used in several large river basins in Brazil. The model parameters are related to classes of physical characteristics, such as soil type, land use, geology and vegetation. The model uses two basin space units: square grids for flow direction along the basin and GRU—group response units—which are hydrological classes of the basin physical characteristics for water balance. Expected ranges of parameter values are associated with each of these classes during the model calibration. Results are presented of the model fitting in the Taquari-Antas River basin in Brazil (26 000 km² and 11 flow gauges). Based on this fitting, the model was then applied to the Upper Uruguay River basin (52 000 km²), having similar physical conditions, without any further calibration, in order to test the transferability of the model. The results in the Uruguay basin were compared with recorded flow data and showed relatively small errors, although a tendency to underestimate mean flows was found.     

CHARACTERIZATION OF ALPINE SOILS,EAGLE CAP,WALLOWA MOUNTAINS,OREGON

This study examines alpine soil development along a toposequence on Eagle Cap, Wallowa Mountains, northeast Oregon. Soils studied are from Wind Blown (WB) and Minimal Snow Cover (MSC) sites in the Ridge-Top Tundra geomorphic province. The soils are predominantly loamy sands, and exhibit minimal structural development. Soil pH ranges from 6.5 to 7.3 increasing with depth, and organic carbon ranges from 3.9% in the A horizon to 0.8% in the C horizon. The soils display significant input from Cascade volcanic ash infall and eolian influx from the weathered marble nearby. It is postulated that the ash content in the soils originates from Mazama Ash deposits. Though Eagle Cap soils have developed for the most part on granodiorite, the strong influence of the volcanic ash on pedogenesis leads to a preliminary classification of Andisols, most probably Typic and Lithic Haplocryands. [Key words: Alpine soils, Andisols, Wallowa Mountains.]     

Alpine Plant Communities: A Statistical Assessment of Their Relation to Microclimatological,Pedological, Geomorphological,and Other Factors

Floristic composition and environmental factors vary widely among plant communities in the alpine belt. Thus far no study has attempted to measure all relevant site conditions in a larger number of alpine communities. Here we show (1) which environmental factors were highly correlated with the floristic composition of the 14 plant communities investigated in the Swiss Alps and (2) which plant communities have similar environmental affinities. In every plant community investigated, the main factors potentially having an impact on plant life were measured and the floristic composition was defined. We used nonmetric multidimensional scaling (NMDS) to determine linkage between plant communities and complex environmental gradients. The first axis of the NMDS corresponds to a climate gradient (temperature/wind speed), and the second axis corresponds to a soil gradient (soil suction/pH/Ca content). With the exception of the Nardus grassland and Carex curvula turf, plant communities belonging to the same phytosociological class are exposed to very similar combinations of environmental factors. Our study shows that the variation between phytosociological classes is much larger than within classes. Still, the variation of environmental factors within individual classes leads to a further differentiation of the floristic composition. Thus, our study reinforces the validity of the phytosociological classification.     

Estimating crop net primary production using national inventory data and MODIS-derived parameters

National estimates of spatially-resolved cropland net primary production (NPP) are needed for diagnostic and prognostic modeling of carbon sources, sinks, and net carbon flux between land and atmosphere. Cropland NPP estimates that correspond with existing cropland cover maps are needed to drive biogeochemical models at the local scale as well as national and continental scales. Existing satellite-based NPP products tend to underestimate NPP on croplands. An Agricultural Inventory-based Light Use Efficiency (AgI-LUE) framework was developed to estimate individual crop biophysical parameters for use in estimating crop-specific NPP over large multi-state regions. The method is documented here and evaluated for corn (Zea mays L.) and soybean (Glycine max L. Merr.) in Iowa and Illinois in 2006 and 2007. The method includes a crop-specific Enhanced Vegetation Index (EVI), shortwave radiation data estimated using the Mountain Climate Simulator (MTCLIM) algorithm, and crop-specific LUE per county. The combined aforementioned variables were used to generate spatially-resolved, crop-specific NPP that corresponds to the Cropland Data Layer (CDL) land cover product. Results from the modeling framework captured the spatial NPP gradient across croplands of Iowa and Illinois, and also represented the difference in NPP between years 2006 and 2007. Average corn and soybean NPP from AgI-LUE was 917 g C m⁻² yr⁻¹ and 409 g C m⁻² yr⁻¹, respectively. This was 2.4 and 1.1 times higher, respectively, for corn and soybean compared to the MOD17A3 NPP product. Site comparisons with flux tower data show AgI-LUE NPP in close agreement with tower-derived NPP, lower than inventory-based NPP, and higher than MOD17A3 NPP. The combination of new inputs and improved datasets enabled the development of spatially explicit and reliable NPP estimates for individual crops over large regional extents.     

河北灵寿县变质岩区大理岩系赋水规律分析

河北灵寿县山丘区是太行山前典型的严重缺水地区。在该区广泛分布的片岩、片麻岩等变质岩的富水性一般较差。对变质岩区大理岩系地下水赋存规律的分析可以更好地指导和帮助当地群众解决长期面临的缺水问题。分析结果表明:该区主要存在三种大理岩含水岩组类型和两种蓄水构造类型;地下水水化学类型为Ca-HCO3型水,水质符合国家饮用水标准。     

双介质摄影测量共线理论研究

从摄影光学理论出发,推导摄影物镜成像系统的基点位置公式;利用针孔成像模型,分析得出摄影物镜的投影中心即为成像系统两节点的等效;简要阐述双介质摄影测量的传统观点,利用同一摄影物镜在不同介质中构成的光学系统,说明双介质摄影测量成像系统基点位置相对单介质时发生变化,并在此基础上提出与传统观点不同的看法——双介质摄影测量共线理...