祁连山水源林调整林分结构的数学模拟

通过实际调查和分析看出，祁连山林区林分直径结构存在着不合理的分布状态，林木分化比较严重，小径木株数所占比例较大。因此，调整林分直径结构，应将小径木及劣质木做为抚育采伐对象，杜绝以往抚育采伐中的“拔大毛”现象，并且通过Ｗｅｉｂｕｌｌ分布拟合，反映出弱度采伐中，只要尊重现实分布律，制定科学的抚育措施，就能使林分结构向合理方向发展。     

Frequency distributions of sward height under sheep grazing

Cattle and sheep can create and maintain a mixture of relatively tall and short patches in grass swards through selective grazing. In swards that are grazed by cattle this heterogeneous structure can result in the frequencies of height measurements having a skewed distribution that has variously been better described by the double‐normal distribution the gamma distribution and the Weibull distribution than by the more common normal distribution. The fit of these statistical distributions, and the adequacy of the potentially useful log‐normal distribution, to sward height frequencies were tested in sown temperate swards grazed by sheep and compared within a single sward. It was concluded that the single‐normal and Weibull distributions were inadequate and that overall the log‐normal and gamma distributions had the best fit to the measurements.     

江西早稻高温逼熟气象灾害指数保险费率的厘定

以江西早稻“五优157”为试材,于2012年在早稻灌浆期利用人工气候室模拟高温逼熟的气候模式（白天35℃/夜间28℃分别持续2、4、6、8、10、12、14、16d）,建立早稻减产率与高温持续天数间的关系模型.再依据江西省11个市1960-2007年气象数据,采用Weibull分布模型模拟不同地区发生高温逼熟的概率,结合减产率模型确定免赔额为15％、30％、45％的保险纯费率.结果表明：“五优157”的减产率（y,％）与灌浆期高温持续天数（x）呈对数函数关系,即y=32.082lnx-22.681;鹰潭和赣州地区的高温逼熟发生概率较高,达87.5％,抚州、景德镇、宜春和萍乡等地区较低,均在70％以下;江西省高温逼熟气象灾害指数保险纯费率呈北高南低的趋势,鹰潭地区的纯费率最高,达4.707％,宜春地区的纯费率最低,为2.138％.研究认为在免赔额为30％时的纯费率较适宜,研究结果可为江西省早稻开展政策性气象指数保险提供科学依据.     

三参数韦布分布的参数估计

三参数韦布(Weibull)分布对不同形状的频率分布有很强的适应性。讨论了三参数韦布分布的参数估计，分别给出了参数的矩法估计和最大似然法估计。三参数韦布分布在气象上有时能获得更好的效果．最大风速以很高的拟合精度遵循三参数韦布分布。     

长白山阔叶红松林径级模拟研究——林分模拟

该文利用指数分布、Weibull分布和混合分布3种类型7个方程模拟长白山阔叶红松林径级分布.研究结果表明,长白山阔叶红松林的径级分布不是理想的倒“J”型,基本为“S”型;用3个负指数方程和修正指数方程模拟均为倒“J”型,在半对数图上为直线;Weibull方程模拟出了单峰,但是效果一般;用2个和3个组分的Weibull混合模型对长白山阔叶红松林径级分布进行了成功模拟,3个组分的Weibull混合模型的模拟效果有所提高,但是并没有显著改善.      

华北落叶松人工林直径分布规律及其动态的研究

以山西省现场调查的30块华北落叶松（Larix principis—rupprechtii Mayr）人工林临时标准地为材料,利用分布密度函数对林分的直径分布进行模拟和预测。检验结果表明：86．67％的服从分布,拟合效果良好,并据此建立起了a、b、c参数的预测模型。理论参数方程可用于华北落叶松人工林经营管理的实践中,为合理经营华北落叶松人工林提供了科学的理论依据。     

油松、侧柏人工林树冠率的Weibull分布及动态预测

应用Weibull函数来拟合油松(Pinus tabulaeformis)、侧柏(Platycladus orientalis)人工林树冠率的分布,研究发现林分平均树冠率与相对林分密度指数之间呈极显著线性关系,并随林分相对密度指数增加而降低;Weibull函数参数b与油松、侧柏人工林林分平均树冠率呈极显著线性关系,参数c与侧柏林分平均树冠率呈二次方关系,在油松林分中则为一常数值;通过对未参加建模的油松、侧柏样地进行动态预测,发现Weibull函数对林分树冠率分布预测值与实测值之间没有显著性差异。因此,该方法可以应用于预测油松和侧柏人工林树冠率的动态分布。     

黄龙山林区天然油松林直径结构规律

为研究黄龙山林区天然油松林直径结构规律,在陕西省黄龙山林区蔡家川林场的油松天然林示范区设置4块0.2hm2的标准地。实测各项因子后应用Weibull分布函数和迈耶负指数分布函数对其进行直径结构模拟,分析了研究区林分的树种组成和直径结构规律。     

大豆花叶病侵染介体一次传播距离的概率分布

通过田间试验,测定了点源引起的大豆花叶病一次传播的病株分布。按一次传播距离的大小将新生病株分组,并在每一组内进行重叠侵染转换,从而得到侵染次数或由毒源而来的浸染性分体数在不同距离处的频次分布。采用概率模型进行拟合,结果表明,侵染介体的一次传播距离符合Weibull分布:P(χ;α、λ)=1-exp(λx~α)。不同环境条件下的多数,α、λ值可不同,在两年3个区的试验条件下、有公共参数α=0.8890,λ=0.9765。据此模型得到该病浸染性介体在植株间一次传播的平均距离为1m。一个介体一次传毒到5m、10m、15m、20m以外的概率分别为1.6844×10~2,5.1951×10~(-4),1.9508×10~(-6),8.2725×10~(-7)。     

Modelling stand structure in young Scots pine dominated stands

The purpose of this study was to construct models for predicting the structure of young Scots pine (Pinus sylvestris L.) stands. The two-parameter Weibull function characterized the height distribution of the stands. In young stands height was preferred to dbh as a random variable because of its continuous feature. Tree diameters were predicted using a multiplicative model, fitted as a linearized mixed-effect model. The modelling data consisted of repeatedly measured Scots pine dominated juvenile stands, carried out on a sub-sample of the 7th National Forest Inventory. The data covered a dominant height range from 0.2 up to 17 m. Two independent data sets were used to validate the models. The Weibull function was fitted using the maximum likelihood method. Four methods for predicting the distributions were compared: (1) parameter prediction models (PPM) consisting of seemingly unrelated regression equations, (2) a generalized linear model (GLM) which was a one-stage distribution and model fitting procedure, (3) a hybrid method including PPM for the shape parameter together with moment-based parameter recovery for the scale parameter, and (4) inclusion of moment-based parameter recovery for the scale parameter in the estimated GLM. Goodness-of-fit were tested in terms of Kolmogorov–Smirnov and error index statistics. Parameter recovery showed no improvement when used with PPM, but it improved GLM and gave the overall best performance for this new method. The constructed diameter–height model showed quite flexible and unbiased behaviour. Models are recommended as practical tools for Finnish forest management planning purposes.