基于太白红杉树轮宽度重建近172年太白山自然保护区7月NDVI

利用太白山自然保护区南北坡采集的太白红杉树轮数据、气象数据和区域NDVI数据进行相关分析,重建太白山自然保护区近172年NDVI变化序列.结果表明: 太白山自然保护区的NDVI年内变化规律与植被生长周期具有一致性,生长季的水热条件是控制NDVI值的主要因素;树轮宽度与植物生长季的NDVI呈显著正相关,7月相关性最强.利用长时间序列的树轮宽度指数重建太白山自然保护区历史时期7月的NDVI变化序列,发现重建的历史时期7月NDVI变化序列存在5个低值时段和5个高值时段,这些时段与秦岭地区的气候变化趋势及旱灾发生记录相对应.重建的太白山自然保护区南北坡7月NDVI变化序列存在60年左右的准周期变化.     

厦门典型树种的HJ-1A/B NDVI时序数据滤波算法及物候特性

植被指数具有明显的季节节律,归一化植被指数(Normalized Difference Vegetation Index,NDVI)时间序列可以获取地表植被物候信息,HJ-1 A/B兼具高空间分辨率和高时间分辨率的特点,为中小尺度范围树种物候特性应用与分析提供了丰富的时间序列数据。本文针对厦门市8个典型树种,选择Savizky-Glolay (S-G)滤波法和时间序列谐波分析法(Hants)对58景HJ-1 A/B NDVI曲线进行滤波重构,选用平均值、平均绝对误差和相关系数等指标对滤波结果进行定量评价,结合NDVI比率对8个树种的物候特性进行分析,最后探讨了气温和降水等气象因子对树种NDVI时序波动的影响。结果表明:S-G和Hants滤波方法均能很好地还原物候特征变化明显的植被,Hants谐波的平滑程度最好; 7个树种(尾叶桉除外)的NDVI值均处于较高的水平,NDVI时序年内波动并不剧烈,双峰形态表现明显,NDVI值在5、6月达到顶峰,7、8月下降,10月达到第二个峰值,第二个峰值比第一个峰值低; 8个树种的生长期持续时间较长,持续7～8个月,除尾叶桉的生长起始时间为2月底外,其他树种均在4月底进入生长期,11月生长期结束,在7月达到生长顶峰;生长期内出现生长期减缓的情况,8月出现生长谷值,生长曲线表现为双峰形态;树种的生长对7月降水量骤减有很明显的响应,不同树种的滞后期不同,生长降低的速度存在一定的差异,但大多表现为8月NDVI比率谷值。研究成果为亚热带地区HJ-1 A/B NDVI时间序列数据的滤波方法选择、典型树种物候特性及树种精细分类研究提供了一定的参考。     

基于NDVI假彩色合成法的土地覆被变化监测

土地覆被变化监测对区域生态系统保护、环境变化研究具有重要的作用,研究旨在提供一种基于归一化植被指数(NDVI)的假彩色合成法的土地覆被变化监测方法。该研究以黄河三角洲为研究区,以3期 Landsat TM影像(成像时间分别为1987年5月7日,1998年5月5日,2009年5月3日)为数据源,在进行相对辐射校正的基础上,生成3期NDVI图像,然后分别以三期的NDVI图像作为红、绿和蓝波段生成假彩色合成图像。基于彩色合成原理,对黄河三角洲的1987-2009年间的土地覆被变化进行了分析。结果表明:(1) 假彩色合成图像上的灰白色区域表示其土地覆被状态稳定,三个时期的NDVI值均较大,黑色区域的土地覆被状态也较稳定,但是三个时期的NDVI值均较小,而青色、绿色、红色则反映相应地区的NDVI处在不稳定状态;(2)不同的颜色反映了不同的土地覆被变化方式,较为直观地反映了土地覆被的变化特点,尤其是自然植被与农田之间的转换;(3)限于NDVI的瞬时性,该方法需要与基于遥感影像分类的方法相结合,才能更好地监测土地覆被变化。     

基于NDVI_Ts特征空间的中国土地覆盖分类研究

 归一化植被指数（NDVI）与地表温度（Ts）是描述地表覆盖特征的两个重要参数, 其构成的NDVI_Ts特征空间具有丰富的地学和生态学内涵。该文在NOAA/AVHRR连续时间序列数据反演Ts的基础上,通过主成分分析、非监督分类和基于DEM的分类后处理等方法,以Ts/NDVI为指标对中国土地覆盖进行分类。结果表明,Ts/NDVI对中国较大尺度上不同土地覆盖类型的差异具有较强的敏感性,其对中国土地覆盖分类结果的野外抽样检验精度比传统的单独利用NDVI时间序列进行非监督分类提高了3.3%,Kappa系数提高了0.020 2;在综合其它反映植被特征及其环境的指标（如气候、地形等）的基础上,利用Ts/NDVI将有可能较为准确 地提取中国植被或土地覆盖的信息,有利于对其进行分类和变化监测,具有深远的研究潜力 和应用价值。     

油松树轮指示的秦岭中部过去194年5—7月NDVI变化

由于归一化差异植被指数(NDVI)观测记录较短,对长时间尺度的NDVI变化研究较少,限制了我们对于全球变暖背景下气候驱动的植被生产力变化及其影响的理解。本研究利用陕西秦岭中部油松树轮样本建立区域树轮宽度指数年表,基于秦岭中部区域年表与5—7月NDVI的较高相关(r=0.624,P<0.01,n=34),利用线性回归模型重建秦岭中部1825—2018年5—7月NDVI变化,方差解释量为38.9%。空间分析表明,重建序列能够较好代表研究区范围内NDVI变化。重建序列表明,秦岭中部过去近194年经历了6个高值期和5个低值期,其中2006—2018年植被生长最好,即在最近的升温停滞期,秦岭中部植被生长呈显著恢复性生长。NDVI低值期与研究区区域干旱事件有着良好的对应关系。小波分析表明,重建序列存在2～4、12～16年准周期。SEA分析表明,重建序列在厄尔尼诺年出现显著下降,而在拉尼娜年事件发生后第1年至第3年出现显著上升。预测油松生长在SSP2-4.5、SSP3-7.0和SSP5-8.5情景下会略微上升。     

近20年来中国植被活动在增强

为阐明近20年来中国植被覆盖变化的整体状况, 利用归一化植被指数(NDVI)作为植被活动的指标, 使用第3代NOAA-AVHRR/NDVI时间序列数据, 研究了1982~1999年间中国地区NDVI的变化. 为消除地表非植被因素的影响, 参考国际惯例, 定义年NDVI≥0.1的地区为有植被覆盖地区(简称植被地区), NDVI < 0.1的地区为植被稀少地区. 结果表明, 18年来, 我国大多数地区的NDVI都呈现不同程度的增加趋势, 表明我国的植被活动在增强. 与80年代初相比, 90年代末植被地区的面积增加3.5%, 植被稀少地区的面积下降了18.1%. 全国平均年NDVI增加了7.4%. 生长季节的延长和生长加速是我国NDVI增加的主要原因, 而温度上升和夏季降水量的增加以及农业活动的加强可能是其主要的驱动因子. 我国NDVI变化趋势显示了较大的空间异质性: 东部沿海地区呈下降趋势或变化不明显; 农业产区和西部地区增加显著. 这种空间异质性是由于城市化过程、农业生产活动、区域气候特征以及植被对气候变化的区域响应等综合因素作用的结果.     

基于雪岭云杉树轮宽度重建过去339年天山中部巴音布鲁克地区夏季NDVI

归一化差异植被指数(NDVI)被广泛应用于植被研究的各个领域,但由于观测时长较短,难以满足长时间尺度的研究需要。基于巴音布鲁克地区雪岭云杉建立了树轮宽度年表(STD),计算年表和NDVI同气象观测数据的相关系数。结果表明:树轮宽度指数和NDVI均与同时段的气象数据具有显著相关。结合宽度年表与6—8月NDVI间的显著正相关(r=0.7,P＜0.01,n=38),使用回归模型重建了研究区过去339年的夏季(6—8月)NDVI变化序列,在1680—2018年,重建序列有4个高植被覆盖时段(1738—1765、1786—1798、1964—1973和2000—2018年)和5个低植被覆盖时段(1690—1714、1825—1834、1850—1880、1895—1920和1945—1955年)。重建结果也反映了天山中部水文气候。与周边重建的对比显示,当开都河径流量增加,且研究区处于较为潮湿的环境时,植被覆盖相对较高,反之植被覆盖偏低。重建序列的极值也捕捉了历史文献中一系列自然灾害。混合单粒子拉格朗日综合轨迹模型(HYSPLT)后向轨迹模型和风场分析表明,NDVI异常受到西风带来的降水影响。     

中国北方草地与农牧交错带植被的NDVI-Ts空间的年内变化特征

利用多时相或时序植被指数(normalize difference vegetation index,NDVI)数据进行地表覆盖研究已取得了大量成果.随着陆地表面温度(1and surface temperature,Ts)遥感反演精度的不断提高,将Ts与NDVI结合起来进行地表植被动态变化的监测已成为可能.本文主要包括以下三部分内容:1)介绍了基于卫星遥感数据的NDVI、Ts和Ts/NDVI计算方法.2)讨论NDVI、Ts和Ts/NDVI数据对植被覆盖信息表达的差异,并分析了中国北方草地与农牧交错带植被在NDVI-Ts空间的年内变化特征.3)利用信息熵和平均梯度,定量分析了NDVI、Ts和 Ts/NDVI数据在信息表达丰富度方面的差异,并对在不同地表植被覆盖下,Ts/NDVI数据对信息提高程度的敏感性进行了讨论.     

黄土高原不同植被覆被类型NDVI对气候变化的响应

植被与气候是目前研究生态与环境的重要内容。为探究黄土高原地区植被与气候因子之间的响应机制,利用线性趋势分析、Pearson相关分析、多元线性回归模型以及通径分析的方法,对黄土高原2000—2015年全区和不同植被覆被类型区内NDVI与气候因子的变化趋势以及相互作用关系进行分析。植被覆被分类数据和植被指数数据分别来源于ESA CCI-LC(The European Space Agency Climate Change Initiative Land Cover)以及MODND1T/NDVI(Normalized Difference Vegetation Index)。结果表明:(1) 2000—2015年黄土高原全区植被年NDVI_(max)显著增加的区域占总面积的74.25%,不同植被覆被类型年NDVI_(max)分别为常绿阔叶林常绿针叶林落叶阔叶林落叶针叶林镶嵌草地农田镶嵌林地草地灌木,并且都呈显著增加趋势,其中常绿阔叶林和农田增加幅度最大,为0.012/a。(2)黄土高原全区NDVI与气温、日照、降水和相对湿度等气候因子之间没有显著相关性,但在不同植被覆被类型区,气候因子对NDVI存在显著作用,且不同植被覆被类型差异明显。(3)在全区和不同植被覆被类型区NDVI仅对降水的响应比较一致,气温无论在整个区域尺度还是不同植被覆被类型区对植被的影响均不显著。(4)常绿阔叶林、落叶阔叶林、常绿针叶林及镶嵌林地等以乔木为主的植被覆被类型受年均相对湿度和年总日照时数的显著负效应驱动,草地、镶嵌草地等以草本为主的植被覆被类型则受到年总降水量的显著正效应影响。这说明对植被类型进行区分,更有利于揭示气候对植被的作用机制。     

基于时间序列分割算法的雅鲁藏布江流域NDVI(1985-2018)变化模式研究

归一化植被指数NDVI可有效表征植被生长信息,其中,长时间序列NDVI在分析全球和局部植被变化扮演重要角色。利用Google Earth Engine提供的全系列Landsat卫星数据,应用LandTrendr时间序列分割算法,讨论了雅鲁藏布江区域植被覆盖变化特征,并对植被变化模式进行判别。研究结果表明：1985-2018年间雅鲁藏布江流域,（1）NDVI总体呈现上升趋势,仅在局部区域出现下降,自上游至下游NDVI变化强度逐渐增加,1986-1990年NDVI变化最为剧烈,1991-2000年次之,2001-2017年NDVI变化强度逐渐减弱;（2）NDVI干扰变化95%集中在0-0.42之间,平均干扰时间4.96年;NDVI恢复变化95%集中在0-0.4之间,平均恢复时间12.55年;（3）NDVI干扰模式主要以持续下降为主,但2000年前的下降速率小于2000年后的下降速率;NDVI恢复模式以持续上升为主,但2000年前的上升速率大于2000年后的上升速率。     

锡林郭勒草原1983～1999年NDVI逐旬变化量与气象因子的相关分析

 陆地生态系统对气候变化的响应关系一直是全球变化研究的热点。大量研究表明表征植被生长状况的遥感植被指数——NDVI与温度、降水的相关性非常高。但这些研究都忽略了NDVI 数据本身的累积性,而这一点对研究较短时间尺度上植被生长与气候因子间的关系尤为重要。因此,本文提出应以NDVI的变化量序列取代一般研究中使用的NDVI时间序列数据。基于该论点,该文采用1983～1999年NOAA/AVHRR的NDVI逐旬变化量数据序列对锡林郭勒盟草原的草原植被生长与气象因子的相互关系进行了研究。研究结果表明：1）NDVI变化量与气象因子之间的相关性最高的时间段为植被生长过程中NDVI增长阶段部分,这一时期草原植被的生长对气候反映最为敏感,在衰败阶段,其相关性比较弱;2）在典型草原,温度和降水与NDVI变化量的相关性随其主要植被类型的不同而不同,在以羊草（Leymus chinensis ）为主的典型草原,温度比降水的影响作用高;而在以克氏针茅（Stipa krylovii）为主的典型草原,降水的影响高于温度;在大针茅（Stipa grandis）为主的草原,两者与NDVI变化量的相关性相差不大。而在荒漠草原,降水是最主要的影响因子,同期的温度作用并不显著; 3）无论是典型草原还是荒漠草原,该地区草原植被的生长对同期的降水反应最为敏感,而非前期。而在荒漠草原以及以旱生性较强的克氏针茅为主的典型草原,温度对NDVI变化量会有较明显的时滞效应;4）在温度升高、降水基本不变的情况下,典型草原和荒漠草原 N DVI变化量对温度的响应能力都有所提高,降水的响应能力则变化不大。     

Correlation analysis of Normalized Different Vegetation Index (NDVI)difference series and climate variables in the Xilingole steppe,China from 1983 to 1999

There is a crucial need in the study of global change to understand how terrestrial ecosystems respond to the climate system.It has been demonstrated by many researches that Normalized Different Vegetation Index (NDVI)time series from remotely sensed data,which provide effective information of vegetation conditions on a large scale with highly temporal resolution,have a good relation with meteorological factors.However,few of these studies have taken the cumulative property of NDVI time series into account.In this study,NDVI difference series were proposed to replace the original NDVI time series with NDVI difference series to reappraise the relationship between NDVI and meteorological factors.As a proxy of the vegetation growing process,NDVI difference represents net primary productivity of vegetation at a certain time interval under an environment controlled by certain climatic conditions and other factors.This data replacement is helpful to eliminate the cumulative effect that exist in original NDVI time series,and thus is more appropriate to understand how climate system affects vegetation growth in a short time scale.By using the correlation analysis method,we studied the relationship between NOAA/AVHRR ten-day NDVI difference series and corresponding meteorological data from 1983 to 1999 from 11 meteorological stations located in the Xilingole steppe in Inner Mongolia.The results show that:(1)meteorological factors are found to be more significantly correlation with NDVI difference at the biomass-rising phase than that at the falling phase;(2)the relationship between NDVI difference and climate variables varies with vegetation types and vegetation communities.In a typical steppe dominated by Leymus chinensis,temperature has higher correlation with NDVI difference than precipitation does,and in a typical steppe dominated by Stipa krylovii,the correlation between temperature and NDVI difference is lower than that between precipitation and NDVI difference.In a typical steppe dominated by Stipa grandis,there is no significant difference between the two correlations.Precipitation is the key factor influencing vegetation growth in a desert steppe,and temperature has poor correlation with NDVI difference;(3)the response of NDVI difference to precipitation is fast and almost simultaneous both in a typical steppe and desert steppe,however,mean temperature exhibits a time-lag effect especially in the desert steppe and some typical steppe dominated by Stipa krylovii;(4)the relationship between NDVI difference and temperature is becoming stronger with global warming.     

Correlation analysis of Normalized Different Vegetation Index (NDVI) difference series and climate variables in the Xilingole steppe, China from 1983 to 1999

There is a crucial need in the study of global change to understand how terrestrial ecosystems respond to the climate system. It has been demonstrated by many researches that Normalized Different Vegetation Index (NDVI) time series from remotely sensed data, which provide effective information of vegetation conditions on a large scale with highly temporal resolution, have a good relation with meteorological factors. However, few of these studies have taken the cumulative property of NDVI time series into account. In this study, NDVI difference series were proposed to replace the original NDVI time series with NDVI difference series to reappraise the relationship between NDVI and meteorological factors. As a proxy of the vegetation growing process, NDVI difference represents net primary productivity of vegetation at a certain time interval under an environment controlled by certain climatic conditions and other factors. This data replacement is helpful to eliminate the cumulative effect that exist in original NDVI time series, and thus is more appropriate to understand how climate system affects vegetation growth in a short time scale. By using the correlation analysis method, we studied the relationship between NOAA/AVHRR ten-day NDVI difference series and corresponding meteorological data from 1983 to 1999 from 11 meteorological stations located in the Xilingole steppe in Inner Mongolia. The results show that: (1) meteorological factors are found to be more significantly correlation with NDVI difference at the biomass-rising phase than that at the falling phase; (2) the relationship between NDVI difference and climate variables varies with vegetation types and vegetation communities. In a typical steppe dominated by Leymus chinensis, temperature has higher correlation with NDVI difference than precipitation does, and in a typical steppe dominated by Stipa krylovii, the correlation between temperature and NDVI difference is lower than that between precipitation and NDVI difference. In a typical steppe dominated by Stipa grandis, there is no significant difference between the two correlations. Precipitation is the key factor influencing vegetation growth in a desert steppe, and temperature has poor correlation with NDVI difference; (3) the response of NDVI difference to precipitation is fast and almost simultaneous both in a typical steppe and desert steppe, however, mean temperature exhibits a time-lag effect especially in the desert steppe and some typical steppe dominated by Stipa krylovii; (4) the relationship between NDVI difference and temperature is becoming stronger with global warming. __________ Translated from Acta Phytoecologica Sinica, 2005, 29(5): 753–765 [译自: 植物生态学报]     

Analysis on Jinghe watershed vegetation dynamics and evaluation on its relation with precipitation

Vegetation degradation is one of the key subjects in the study of global environmental changes, and the Normalized Difference Vegetation Index (NDVI) is generally recognized as a good indicator of terrestrial vegetation productivity and growth status. To evaluate the vegetation dynamic changes in the Jinghe watershed on Loess plateau from 1982 to 2003, major methods of change slope, principal component analysis and correlation analysis were employed with 8 km resolution NOAA-NDVI time series data. Based on these analyses, the relationship between precipitation and NDVI was discussed. Results show that there has been little change in both amplitude and variety of NDVI during the past 22 years. Vegetation in the upper stream areas, typically the watershed marginal mountain areas, changes significantly. A trend analysis shows that the similar finding on vegetation dynamics in different areas tends to be induced by climate changes and human land use transformation. A standardized principal component analysis indicates that the first two components, PC1 and PC2, are closely related to vegetation and climate changes, while PC3 and PC4 are connected with floodwater in flooding seasons, and PC5 and PC6 reflect the effects of human activities. Finally, the correlation analysis shows that there is a close positive relationship in this region between NDVI and precipitation. The rainfall sensitivity threshold reaches 550 mm or even higher.     

Analysis on Jinghe watershed vegetation dynamics and evaluation on its relation with precipitation

Vegetation degradation is one of the key subjects in the study of global environmental changes, and the Normalized Difference Vegetation Index (NDVI) is generally recognized as a good indicator of terrestrial vegetation productivity and growth status. To evaluate the vegetation dynamic changes in the Jinghe watershed on Loess plateau from 1982 to 2003, major methods of change slope, principal component analysis and correlation analysis were employed with 8 km resolution NOAA-NDVI time series data. Based on these analyses, the relationship between precipitation and NDVI was discussed. Results show that there has been little change in both amplitude and variety of NDVI during the past 22 years. Vegetation in the upper stream areas, typically the watershed marginal mountain areas, changes significantly. A trend analysis shows that the similar finding on vegetation dynamics in different areas tends to be induced by climate changes and human land use transformation. A standardized principal component analysis indicates that the first two components, PC1 and PC2, are closely related to vegetation and climate changes, while PC3 and PC4 are connected with floodwater in flooding seasons, and PC5 and PC6 reflect the effects of human activities. Finally, the correlation analysis shows that there is a close positive relationship in this region between NDVI and precipitation. The rainfall sensitivity threshold reaches 550 mm or even higher.     

泾河流域植被覆盖动态变化特征及其与降雨的关系

植被退化是全球环境变化研究的一个重点问题,植被状况是环境评估的重要指标.利用8km分辨率的NOAA-AVHRR/NDVI时间序列数据,对位于黄土高原的泾河流域1982～2003年植被特征及变化状况进行系统分析,并在此基础上评估降雨与流域植被的相互关系.研究主要利用了变化斜率法、主成分分析法和相关分析法,得到如下结论:过去22a来流域植被NDVI均值波幅和变化都很小,变化较显著的区域集中在流域上游和流域边缘的山区.变化斜率分析得出了类似的结论,气候变化以及人类活动导致的土地利用改变可能是影响在流域不同地区植被状态变化的主要原因.对NDVI时间序列的主成分分析发现PC1和PC2与植被覆盖和气候密切联系,PC3和PC4与流域汛期洪水有关,PC5和PC6体现了人类活动的影响.流域的NDVI与降雨显示了良好的相关性,降雨与NDVI相关性的阈值可能在550mm或更高.     

Estimating root zone soil moisture at distant sites using MODIS NDVI and EVI in a semi-arid region of southwestern USA

This study investigates the potential of using Normalized Difference Vegetation Index (NDVI) and Enhanced Vegetation Index (EVI) to estimate root zone soil moisture at native in-situ measured sites, and at distant sites under the same climatic setting. We obtained in-situ data from Soil Climate Analysis Network (SCAN) sites near the Texas-New Mexico border area, and NDVI and EVI products from the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor on board the Terra satellite. Results show that soil moisture values of the same depth are highly correlated (r = 0.53 to 0.85) among sites as far as 150 km apart, and that NDVI and EVI are highly correlated at the same site (r = 0.87 to 0.91). Correlation based on raw time series of NDVI and soil moisture is in general higher than that based on deseasonalized time series at every depth. The correlation reaches maximum value when vegetation index (VI) lags soil moisture by 5 to 10 days. NDVI shows a slightly higher correlation with soil moisture than EVI does by using the deseasonalized time series of NDVI and soil moisture. It is found that deseasonalized time series of NDVI and soil moisture are correlated at native sites (r = 0.33 to 0.77), but not at sites where soil moisture is very low. Regression analysis was conducted using deseasonalized time series soil moisture and deseasonalized time series NDVI with a 5-day time lag. Regression models developed at one site and applied to a similar distant site can estimate soil moistures, accounting for 50–88% of the variation in observed soil moistures.     

云南省植被NDVI时间变化特征及其对干旱的响应

基于云南省74个气象站点的1997—2012年逐日降水资料和逐旬SPOT-NDVI值,利用标准化降水蒸散指数(SPEI)多尺度分析了云南省干旱时间和强度演变与NDVI时间动态特征及其相关性分析,进而探讨气候变化对植被的影响。结果表明,1999—2013年云南省年平均NDVI值和年最大NDVI值均呈现波浪式的发展趋势,其趋势线斜率分别为0.0017和0.0011;NDVI年内各月变化情况大体上相同;不同季节NDVI的年际变化特征呈现出显著差异。1997—2012年不同时间尺度SPEI均体现出干旱化加剧的趋势,并随SPEI的时间尺度增大而增大;3个月尺度的SPEI值(SPEI3)结果表明,各月的变化呈现先增大后减小的趋势;SPEI3反映出多年季节水平的干旱强度为:冬季秋季春季夏季。总体上,云南省的年均NDVI与SPEI的相关性极弱,年最大NDVI与SPEI呈正相关;多年月均NDVI与不同尺度SPEI的相关性较强且存在滞后性;不同季节NDVI与SPEI的相关性及滞后性有较大差异,其中冬季NDVI、秋季NDVI与其当年当季SPEI的负相关性较强。     

Statistical model building and model criticism for human circadian data

Mathematical models have played an important role in the analysis of circadian systems. The models include simulation of differential equation systems to assess the dynamic properties of a circadian system and the use of statistical models, primarily harmonic regression methods, to assess the static properties of the system. The dynamical behaviors characterized by the simulation studies are the response of the circadian pacemaker to light, its rate of decay to its limit cycle, and its response to the rest-activity cycle. The static properties are phase, amplitude, and period of the intrinsic oscillator. Formal statistical methods are not routinely employed in simulation studies, and therefore the uncertainty in inferences based on the differential equation models and their sensitivity to model specification and parameter estimation error cannot be evaluated. The harmonic regression models allow formal statistical analysis of static but not dynamical features of the circadian pacemaker. The authors present a paradigm for analyzing circadian data based on the Box iterative scheme for statistical model building. The paradigm unifies the differential equation-based simulations (direct problem) and the model fitting approach using harmonic regression techniques (inverse problem) under a single schema. The framework is illustrated with the analysis of a core-temperature data series collected under a forced desynchrony protocol. The Box iterative paradigm provides a framework for systematically constructing and analyzing models of circadian data.