黄土丘陵半干旱区柠条林株高生长过程新模型

黄土丘陵半干旱区柠条林的株高生长不随时间单调增加,在生长末期因生长动力小于生长阻力,株高随时间小幅度减小.采用宁夏固原上黄生态站柠条林的生长观测资料,以经典Logistic方程为基础,添加了生长阻力因素,建立了柠条林生长的改进模型,使得生长速率在生长末期出现负值；并以高密度柠条成林多年生长观测数据为依据,建立了连年生长模型.用数学建模和统计检验的方法对数据进行处理,其结果表明,改进模型较Logistic方程具有更高的拟合度和相关系数.建立的模型与传统生长方程不同,由于微分方程中引入了阻力因子,故生长曲线中存在极值坐标且不具有严格单调性.将多年的株高生长曲线综合到一个坐标系内后,新模型中位置参数a与内禀生长率b的比值随着生长呈现逐渐增大的趋势.改进模型的生长顶点出现在8月,与柠条林株高的实际生长过程吻合；计算了新模型的生长顶点与生长期结束时的株高的差值,并将该值记为生长损失.由于柠条林的灌丛较为矮小,在越冬时干梢现象对株高的影响不可忽略,该过程导致生长方程中第二年初始点小于第一年最末点；在考虑了该现象后所建立的连年生长模型中,2002年和2003年干稍现象的终止点位于2月,与植物生长的节律吻合.本研究为描述半干旱区灌木林生长过程提供了依据.

A new plant height growth process model of Caragana forest in semi-arid loess hilly region

Height growth of Caragana korshinskii in semi-arid loess hilly region was not always monotonous increasing with time. Because growth power was less than growth resistance in late growth stage, plant height weakly reduced with time. In this article, two growth model were established. Adding a growth resistance factor to the classical Logistic model, the first one was improved growth model, which made growth rate negative in late growth stage. The second one was multi-year growth model, which was based on the growth observation data of ripe Caragana korshinskii with a high density of 87 brush per 100 square. The result showed that the improved model had higher goodness of fit and correlation coefficient than that of Logistic model using modeling data to fit and test data to verify. Model established in this article was different with classic plant growth model. Because resistance factor was introduced into differential equation, growth curve, where extreme coordinate exist, was not strict monotonous. Because multi year height growth curves were synthesized into one coordinate system, the ratio of position parameter a and intrinsic growth rate b in new model became more and more large with growth. Growth vertex appeared in middle ten days of August, which was consistent with the actual growth process of height. The difference of growth vertex and plant height in late growth stage, which was called growth loss, was calculated. Because Caragana korshinskii shrub was low, the process that dry topped phenomenon of Caragana korshinskii could influence on plant height in winter could not be ignored. This process caused the height at initial growth point in second year lower than that at last growth point in first year. In consideration of dry topped phenomenon, termination point of the winter drying phenomenon in multi-year growth model from 2002 to 2003 located in February, which was consistent with the rhythm of plant growth. This research provided evidence for describing growth process of shrub in semi-arid region.