加速广义Laguerre多项式级数的Laplace变换的数值反演方法

本文利用Levin t-变换迭代法，对加速广义Laguerre多项式级数，提出了一种新的Laplace变换的数值反演方法，这种方法在精度上和数值稳定性上的效果都较好。     

二阶线性微分方程的非振动性

本文主要讨论了二阶齐次微分方秘AX″+BX′+CX=0的解的非振动性的充分条件     

近43年黄河上游来水来沙变化特点

选取黄河头道拐站实测水沙序列(1960-2002年)资料,对水沙序列进行了多时间尺度和趋势识别的小波分析。结果表明:①黄河上游来水来沙量汛期所占比例减少,而非汛期所占比例增加;在年际变化上,水沙量逐年减少;同时,水沙相关关系具有一定的变化;②黄河上游水沙序列具有相同的多时间尺度(准周期)变化,但同一尺度下,水沙所处的丰枯变化并不一致;③年水沙序列趋势变化基本一致,20世纪80年代以来,两者存在明显减少趋势;但在非汛期,两者的趋势变化有较大区别。     

北京地区沙尘天气的气候特征分析

本文利用1954-2001年北京地区(20个气象站)逐月沙尘资料,重点对北京地区沙尘天气的空间分布特征、沙尘日数的年代变化规律、沙尘日数的月变化进行分析;分析了近三年北京地区出现沙尘天气特点及成因;同时对近48年的沙尘出现日数变化规律进行了小波分析。     

Periodical characteristics of baseflow in the source region of the Yangtze River

Baseflow,which represents the drainage of groundwater aquifers,is an essential component of runoff in hydrological basins.In the source region of the Yangtze River,the change of baseflow typically reflects the interactions between groundwater system and climatic factors in cold and arid areas.With modified Kalinen separation method,annual baseflow between 1957 and 2009 in this region was estimated and calculated.In comparison with the inner-annual variations of total streamflow,baseflow showed a weaker fluctuation.Before the 1980s,it was in a steady state;and after then,it demonstrated dramatic variations and large amplitudes.Based on the calculation results of baseflow,the real Morlet wavelet method was applied to reveal the periodical characteristics of baseflow as well as the precipitation and air temperature in the study area.It was found that annual baseflow has a 43-year trend as well as a 21-year period and a 7-year period.The 21-year period is most significant,with its wavelet coefficient having the largest fluctuation and amplitude.Summation of wavelet coefficients on these periods exhibits a similar change pattern with respect to that of annual baseflow.The summation curve takes a"W"shape,which means that the baseflow follows a four-stage sequence of descending–ascending–descending–ascending.As analyzed,the relationship among baseflow,precipitation and temperature is implied in the correlation between their normalized wavelet coefficients at different temporal scales.By the significant positive linear correlations both between precipitation and baseflow(correlation coefficient is 0.98)and between temperature and baseflow(correlation coefficient is 0.90)for the 43-year wavelet coefficients,it is suggested that the long-term increasing trends of precipitation and air temperature will lead to an increasing trend of baseflow.For wavelet coefficients of 21-year and 7-year periods,the positive linear correlation between precipitation and baseflow is significant.However,the correlation between air temperature and baseflow is not so evident,especially for the 21-year period.As a conclusion, correlation analysis with normalized wavelet coefficients showed that the change of annual baseflow was contributed mostly by the change of precipitation and secondly by the change of temperature.     

小波变换在土壤有机质含量可见/近红外光谱分析中的应用

使用高光谱仪ASD Field Spec在波长范围400~1 000 nm内采集有机质含量不同的土壤原始光谱;之后,求取土壤原始光谱及其A值的一阶导数(一阶导数光谱);对以上两类一阶导数光谱进行小波去噪处理;并分析这两类一阶光谱在去噪前、后,光谱形态的变化情况,以及它们与有机质含量相关性的改善程度。结果表明:(1)土壤原始光谱及其A值的一阶导数中含有大量噪声,严重影响了对光谱曲线波形轮廓、特征信号点和有机质吸收特征的识别。(2)经小波去噪处理后,土壤原始光谱及其A值的一阶导数中的噪声被有效去除,一阶导数光谱的清晰度明显改善,光谱质量显著提高。(3)去噪后的土壤原始光谱的一阶导数,呈开口向下的"喇叭口"状,波长范围567~598 nm内与有机质含量呈较为稳定、显著的负相关性。(4)去噪后的土壤原始光谱A值的一阶导数,波形呈"凹"状,波长范围524~535 nm内与有机质含量呈比较稳定、显著的正相关性。     

内蒙古中部地区近40年来降水时空变化

内蒙古中部呼和浩特市、包头市、乌兰察布市、鄂尔多斯市、巴彦淖尔市和乌海市是半干旱区向干旱区的生态地理过渡地带。利用该区45个气象站点1961-2003年逐日降水数据,借助小波分析、地统计学分析研究了该区43年来降水量的时空变化特征。结果表明:研究区降水量年际波动大,总体呈现略微增加的趋势;降水量变化的周期性比较明显,存在3～4年、6～7年和14～15年尺度的周期。降水年内分配呈现单峰型模式。在空间上,多年平均降水量呈现由东南向西北逐渐递减的趋势,年降水变化的趋势和波动性区域差异显著。另外发现,作为重要地理分界线的200mm等降水量线空间分布在43年中处于波动之中,对草原和荒漠生态系统产生了直接影响。对该区降水时空变化的探讨,有助于理解水资源的时空分异,同时为全球变化的区域响应提供科学依据。