An efficient optimum interpolation analysis scheme

Abstract

One of the characteristics of the optimum interpolation analysis scheme is that a matrix problem that depends on the number of observations has to be solved for each grid‐point value that is calculated. In data‐rich regions, this matrix can be quite large and in general, a limit on its size has to be imposed in order to avoid an excessive amount of computation.

In the proposed univariate analysis scheme, the autocorrelation function has been approximated by the second‐order and fourth‐order Taylor series expansion of the Gaussian Hill function. It is shown that the weights given to the observations can then be evaluated analytically by resolving associated systems of order 4 and 9, respectively.

When 24 pieces of data are used, the proposed schemes are, respectively, 6 and 3 times faster than an optimum interpolation analysis scheme using the Gaussian autocorrelation function. Furthermore, the analyses produced by those 3 schemes are almost identical. The search radius being limited, the proposed schemes are useful and worth while only over data‐dense areas.     

基于动态时间规整的气温日值数据二次插补

气温作为研究气候演变最基础的物理量,其日值序列的完整性和准确性对于气候分析与评估工作有着重要意义。近些年随着大量无人值守地面加密自动气象站的布设,不断出现随机站点和随机长度这种双随机特点的气象资料序列缺失,给气候分析和业务应用造成了不小的障碍。针对现有气象数据插补方案的不足,提出了一种全新的基于动态时间规整(dynamic time warping,DTW)的气温日值数据二次插补方法。该方法采用了一种实时的插补策略,主要技术内容包括:1)利用一元线性回归方程将原始气温观测时间序列分解出拟合直线和残差曲线,并将二者重构组成新的气温序列;2)给出了气温插补区的定义和插补条件;3)提出了利用动态时间规整方法计算站点间距离的新模式。利用山东省2021年的气温实况数据对该方法进行了双随机检验,检验结果表明:该方法可以满足日平均气温、日最高气温和日最低气温数据的插补需求;在插补流程中采用DTW距离测度和二次插补的组合方法,其插补效果优于目前常见的基于站点地理临近关系的组合方法;该方法对地形有一定的敏感性,平原或丘陵地区的插补效果要优于山地地区。     

几种数值插值方法的试验比较

该文首先引进３种精度较高的边界条件，借助于Ｓｐｌｉｎｅ函数，近似计算离散网格上的一阶空间微商，并通过数值试验进行比较，然后用Ｌａｇｒａｎｇｉａｎ、Ｓｐｌｉｎｅ和Ｈｅｒｍｉｔｅ方法对不同相对位置的插值点作插值计算，并给出一套较为简单适用的Ｈｅｒｍｉｔｅ方案计算公式。结果表明，这３类插值方法都能达到一定的精度，但其中以取周期性边界条件，用Ｈｅｒｍｉｔｅ方法算得的插值函数最为精确，其误差约为采用二阶或三     

气象要素插值的空间化精度提高方法研究

为了提高气象要素空间化的精度,本文提出通过预先对气象数据进行处理,然后再进行空间化,以比较直接插值与原始数据处理之后再插值的精度的变化。文中采用数据为全国743个常规气象站40 a(1961—2000年)整编气象资料及2005年的常规气象资料;插值方法有反距离加权法(IDW)、克立格法(Kriging)和样条函数法(Spline);数据预处理方法采用距平处理。结果发现:使用IDW、Kriging和spline对平均温度距平进行插值精度比较,发现IDW方法最优;温度距平精度的提高比降水和相对湿度要好;降水距平误差呈现由东向西递增的趋势。由此可见,对气象要素做距平处理可以有效提高插值精度。     

太阳辐射经验系数插值方法的比较

利用江苏省南京、吕泗、淮安3个日射站以及周边省市共10个日射站逐月日照百分率资料和太阳总辐射资料,利用最小二乘法拟合经验系数a、b,并利用除南京、吕泗2个日射站以外的8个日射站的经验系数a、b,采用多种插值方法计算江苏省70个站的经验系数a、b,并据此求出70个站点逐月太阳总辐射值并分析其分布特征。结果表明：采用反距离权重插值法得到的经验系数a、b,误差最小。结论可为求解江苏省各地太阳总辐射提供科学参考。     

流域面雨量的一种估算方法—网格插值法

针对近年来渭河防汛的严峻形势,为搞好防汛气象服务,采用面雨量的3种估算方法,对2003年渭河大洪灾中4次洪峰时期渭河流域面雨量的实际估算和对比分析,结果表明网格插值法的估算精度优于等值线法和算术平均法,运用网格插值法估算渭河流域面雨量是可行的。     

太阳辐射经验系数插值方法的比较

利用江苏省南京、吕泗、淮安3个日射站以及周边省市共10个日射站的逐月日照百分率资料和太阳总辐射资料,利用最小二乘法拟合经验系数a、b,并利用除南京、吕泗2个日射站以外的8个日射站的经验系数a、b,采用多种插值方法计算全省70个站的经验系数a、b,并据此求出70个站点逐月太阳总辐射值并分析其分布特征。结果表明： 采用反距离权重插值法得到的经验系数a、b,误差最小。结论可为求解江苏省各地太阳总辐射提供科学参考。     

基于雷达校正的雨量插值研究

自动站点雨量数据到格点化雨量数据的插值方法一直在气象业务中有着重要应用,但传统插值法一般只考虑距离对估测点的影响,不能够真实地反应降水的落区分布.利用多普勒雷达资料对雨量插值结果进行校正,可使得插值后的结果较好地反映雷达反射率分布特征,也可以较好地克服反距离加权插值法的尖点问题.经过业务测试检验,基于雷达校正的雨量插值方法效果较为稳定,可以在业务中进行应用.     

基于残余插值的卷积神经网络去马赛克算法

在去马赛克问题中,为了精确插值倾斜边缘并提高结果图像的整体质量,提出一种基于残余插值的卷积神经网络去马赛克算法.针对Bayer格式的颜色滤波阵列,插值绿色平面时,对于红蓝通道信息不全的问题,采用同通道邻近像素值近似代替,综合考虑3个通道的梯度,运用倾斜方向的边缘检测算子,将倾斜边缘分为不同方向的边缘分别插值.在插值完成后,利用深度卷积神经网络,进一步训练插值结果.在标准的IMAX数据集上,与目前流行的算法相比,本文算法视觉上更接近原图,具有更高的峰值信噪比和更短的运行时间.     

Spatial interpolation of monthly and annual rainfall in northeast of Iran

Precipitation maps are the key input to many hydrological models. In this paper different univariate (inverse distance weighing and ordinary kriging) and multivariate (linear regression, ordinary cokriging, simple kriging with varying local mean and kriging with an external drift) interpolation methods are used to map monthly and annual rainfall from sparse data measurements. The study area is Golestan Province, located in northeast of Iran. A digital elevation model is used as complementary information for multivariate approaches. The prediction performance of each method is evaluated through cross-validation and visual examination of the precipitation maps produced. Results indicate that geostatistical algorithms clearly outperform inverse distance weighting and linear regression. Among multivariate techniques, ordinary cokriging or kriging with an external drift yields the smallest error of prediction for months April to October (autumn and winter) for which the correlation between rainfall and elevation is greater than 0.54. For all other months and annual rainfall, ordinary kriging provides the most accurate estimates.     

Stochastic interpolation as a means to estimate oceanic fields

Abstract

The method of stochastic interpolation (conditional simulation) is introduced as a means to interpolate / extrapolate a scalar or vector field of an oceanic variable, e.g. currents. Conditional simulation produces the synthesis of a random field that is forced to agree with simultaneous measurements in the same time interval and area where the input data are being synthesized. The conditional simulation is applied to the vector field for two California current measurement programs (Coastal Ocean Dynamics Experiment (CODE) and Central California Coastal Circulation Study fccccsj, north and south of San Francisco, respectively). These field programs covered different areas and were characterized by different instrument spacings. The influence of these spatial factors shows up in the quality of the conditional simulations, i.e. a smaller area and a tighter mooring array led to more physically reasonable flow realizations. The various realizations provided by a series of conditional simulations allow confidence intervals to be defined. Other uses for this technique include optimization of current‐meter (or other sensor) placement and the specification of initial or boundary conditions for numerical models. This latter function could be invoked when real data are sparse or when the data that are available are overly smooth and do not contain enough of the variability of the natural system.     

基于DEM的江苏气温空间插值研究

以江苏省及周边39个常规气象站点1957—2001年的月平均气温数据和90 m空间分辨率的DEM数据为基础,采用基于DEM的多元线性回归插值方法,分析多年平均气温与海拔、坡度和坡向等地形因子的相关关系,建立适合该区域的多元回归空间插值模型.同时与反距离权重法(IDW)和克里格(Kriging)插值法等传统方法的计算结果进行对比,并用交叉验证方法比较5种插值方法的精度.结果表明:该研究区各月气温递减率在 0.5~0.9 ℃/(100 m) 左右;基于DEM的多元线性回归空间插值方法(MLR)无论从插值效果还是误差精度上,均优于其他传统插值方法.插值结果客观地表达了气温与各地形要素的相关性,反映了气温的空间变异性.     

Usage of multivariate geostatistics in interpolation processes for meteorological precipitation maps

Long-term meteorological data are very important both for the evaluation of meteorological events and for the analysis of their effects on the environment. Prediction maps which are constructed by different interpolation techniques often provide explanatory information. Conventional techniques, such as surface spline fitting, global and local polynomial models, and inverse distance weighting may not be adequate. Multivariate geostatistical methods can be more significant, especially when studying secondary variables, because secondary variables might directly affect the precision of prediction. In this study, the mean annual and mean monthly precipitations from 1984 to 2014 for 268 meteorological stations in Turkey have been used to construct country-wide maps. Besides linear regression, the inverse square distance and ordinary co-Kriging (OCK) have been used and compared to each other. Also elevation, slope, and aspect data for each station have been taken into account as secondary variables, whose use has reduced errors by up to a factor of three. OCK gave the smallest errors (1.002 cm) when aspect was included.     

复杂山地环境下气候要素空间插值精度比较研究

空间插值可以提供每个计算栅格的气候要素资料,该文运用反距离加权插值法（IDW）、普通克里格插值法、薄盘光滑样条函数拟合法3种空间插值方法,对1971--2000年西南地区复杂山地环境下92个气象站点温度、降水以及相对湿度的各月气候平均值和多年平均值进行了空间插值。并进行了交叉验证和随机站点验证,运用绝对平均误差（MAE）、相对平均误差（MRE）及均方根误差（RMSE）作为插值精度检验的标准。结果表明：插值方法中,薄盘光滑样条函数插值法在山地环境下对3种气象要素的插值精度是最优的,特别是对于温度和降水,而对于相对湿度3种方法差别不大,都可以满足精度要求;在时间尺度上,对于温度相对较低、降水量相对较小的冬季,3种插值方法插值精度都相对于夏季和年平均明显较差,相对湿度插值精度季节差异不明显。     

A simple approach for improving spatial interpolation of rainfall using ANN

The spatiotemporal features of tropical cyclone strikes from 1949 to 2008 at 49 coastal cities of China are investigated in this study. The cities in Hainan, Guangdong, and Taiwan have high strike frequencies, with the severest and most frequent average strikes found in Taiwan. In Hainan, strike clusters appear in the mid-1950s, the early 1960s and 1970s, and the late 1980s, with relative inactive frequencies from the mid-1990s to 2008, and the clusters of strikes in Guangdong are found during the 1970s. In Taiwan, the most active strikes are found during the period 1956–1963. The return periods for all typhoons are either 1 or 2 years at the coastal cities of Taiwan in contrast to 2–5 and 4–8 years at the cities of Guangdong and Fujian, respectively. Super typhoons affect Taiwan with a frequency of once every 12–30 years on average. A tropical cyclone hazard index is also created to investigate the vulnerability at these cities.     

Incorporation of parameter uncertainty into spatial interpolation using Bayesian trans-Gaussian kriging

Quantitative precipitation estimation(QPE) plays an important role in meteorological and hydrological applications.Ground-based telemetered rain gauges are widely used to collect precipitation measurements. Spatial interpolation methods are commonly employed to estimate precipitation fields covering non-observed locations. Kriging is a simple and popular geostatistical interpolation method, but it has two known problems: uncertainty underestimation and violation of assumptions.This paper tackles these problems and seeks an optimal spatial interpolation for QPE in order to enhance spatial interpolation through appropriately assessing prediction uncertainty and fulfilling the required assumptions. To this end, several methods are tested: transformation, detrending, multiple spatial correlation functions, and Bayesian kriging. In particular, we focus on a short-term and time-specific rather than a long-term and event-specific analysis. This paper analyzes a stratiform rain event with an embedded convection linked to the passing monsoon front on the 23 August 2012. Data from a total of 100 automatic weather stations are used, and the rainfall intensities are calculated from the difference of 15 minute accumulated rainfall observed every 1 minute. The one-hour average rainfall intensity is then calculated to minimize the measurement random error. Cross-validation is carried out for evaluating the interpolation methods at regional and local levels. As a result,transformation is found to play an important role in improving spatial interpolation and uncertainty assessment, and Bayesian methods generally outperform traditional ones in terms of the criteria.     

江西省降水空间插值方法适用性分析

文中基于数字高程模型,建立了多元线性回归插值模型(MLR)和PRISM空间插值方法,并与传统的反距离权重法(IDW)和普通克里金插值法(OK)进行比较.结果表明:1)江西省5月、7—10月降水量与海拔高度存在显著的相关性,与坡度、坡向无明显相关.2)从插值精度来看,3—9月PRISM和MLR空间插值精度明显优于IDW和OK,冬半年IDW和OK插值精度略高于MLR和PRISM;4种插值方法的年降水量插值精度排序为PRISM>MLR>OK>IDW;PRISM和MLR在高海拔地区的插值精度远高于IDW和OK.3)从插值效果来看,4种插值方法的降水空间分布具有一致性,MLR和PRISM优于IDW和OK.