利用浙江省中尺度自动站的温度资料， 引入已广泛应用于测绘、 地球物理、 地图绘制等领域的Multiquadric插值法， 并与目前气象领域内采用较多的Cressman方法进行比较， 分析两者在不同站点分布和数量下对实况场的逼近程度， 并对Multiquadric中的自由设定参数进行讨论。结果表明， 总体而言, Multiquadric方法的均方根误差小于Cressman方法。当站点数为100时， 两者差异达0.3℃； 当站点数>1000时， Multiquadric方法相对Cressman的改进已经<1%， 两者差异非常小。在站点数较少或是站点间隔较大的情况下， Cressman方法较易产生虚假中心, 而Multiquadric方法则更加接近实况。Multiquadric平滑参数λ可以被认为是一种低通滤波器， 它将高频波滤去， 留下较大尺度的系统， 同时冷暖空气温度中心的强度随着平滑强度的增加也逐渐减弱。Multiquadric参数c存在一个上限值， 当c大于或小于该值时， 客观分析结果表现出不同的敏感度。
Objective analysis of mesoscale meteorological data has an important role in real time monitoring and diagnostic analysis. The Cressman method is very popular in meteorology.The Multiquadric method has been widely applied in geodesy, geophysics, geography and surveying and mapping problems. The Multiquadric method is compared to the Cressman method by using conventional observations and variable number of mesoscale automatic observationsto analyze the approximate extent to real data with different datadistribution and quantity.The results indicate that: The root mean squared error of the Multiquadric method is less than that the Cressman method. The difference between these two methods gradually diminishes with the increasing number of observations for objective analysis. When the distancebetween two observations is large or few observations are used, the Cressman method tends to produce untrue centers while the analytical field by using the Multiquadric method is more closer to observations. Multiquadric smoothing parameter λ is regarded as a low-pass filter which screens high frequency waves and preserves large scale systems. The intensity of temperature centers gradually diminishes with increasing λ. The multiquadric parameter c has an upper limit. When c is greater or less than the threshold, the analytical result shows different sensitivities.
[1]王跃山. 客观分析和四维同化(站在新世纪的回望（II）客观分析的主要方法（1）[J]. 气象科技, 2001, 29（1）: 1-9.
[2]王跃山. 客观分析和四维同化(站在新世纪的回望（II）客观分析的主要方法（2）[J]. 气象科技. 2001, 29（3）: 1-11.
[3]Cressman G P. An operational objective analysis system[J]. Mon Wea Rev, 1959, 87: 367-374.
[4]苏志侠, 程麟生. 两种客观分析方法的比较(逐步订正和最优内插[J]. 高原气象, 1994, 13(2): 194-205.
[5]岳文泽, 徐建华, 徐丽华. 基于地统计方法的气候要素空间插值研究[J]. 高原气象, 2005, 24(6): 974-980.
[6]李新, 程国栋, 卢玲. 青藏高原气温分布和空间插值方法比较[J]. 高原气象, 2003, 22(6): 565-573.
[7]Nuss W A, Titley D W. Use of Multiquadric interpolation for meteorological objective analysis[J]. Mon Wea Rev, 1994, 122: 1611-1631.
[8]Franke R. Scattered data interpolation: Tests of some methods[J]. Math Comput, 1982, 38: 181-200.
[9]Rap A, Ghosh S, Smith M H. Shepard and Hardy Multiquadric interpolation methods for multicomponent aerosol-cloud parameterization[J]. J Atmos Sci, 2009, 66: 105-115.
[10]王思维, 刘勇, 朱超洪, 等. 青海省逐日地面气温数据不同插值方法的对比[J]. 高原气象, 2011, 30(6): 1640-1646.
[11]俞善贤, 钟元, 滕卫平. 热带气旋路径人工神经元预报方法对比试验研究[J]. 热带气象学报, 2004, 20(5): 523-529.
[12]王艳姣, 张鹰, 邓自旺, 等. RBF神经网络的汛期旱涝预报方法研究[J]. 热带气象学报, 2005, 21(1): 100-106.
[13]Hardy R L. Multiquadric equations of topography and other irregular surfaces[J]. J Geophys Res, 1971, 76: 1905-1915.
[14]Madych W R, Nelson S A. Multivariate interpolation: A variational theory[J]. J Approx Theory Appl, 1990, 4: 77-89.
[15]陶士伟, 仲跻芹, 徐枝芳, 等. 地面自动站资料质量控制方案及应用[J]. 高原气象, 2009, 28(5): 1202-1209.
