基于随机森林算法对青藏高原TRMM降水数据进行空间统计降尺度研究
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Spatial statistics of TRMM precipitation in the Tibetan Plateau using random forest algorithm
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通讯作者: 魏瑗瑗(1992-),女,硕士研究生,主要从事大气遥感方面的研究。Email:weiyy@radi.ac.cn。
责任编辑: 李瑜
收稿日期: 2017-03-2 修回日期: 2017-04-12 网络出版日期: 2018-09-15
Received: 2017-03-2 Revised: 2017-04-12 Online: 2018-09-15
作者简介 About authors
徐彬仁(1990-),男,硕士研究生,主要从事大气遥感方面的研究。Email:xubr@radi.ac.cn。 。
提高气象数据空间分辨率对水文、气象和生态等领域的流域尺度研究至关重要。青藏高原气候变化在全球气候研究中占有重要的位置,并且对局域降水分布的研究在大气科学中处于基础地位。为获取青藏高原地区准确、有效、更高空间分辨率的降水数据,基于随机森林算法,引入植被和地形因子,采用热带降水测量计划卫星(Tropical Rainfall Measuring Mission, TRMM)3B43降水数据(0.25°×0.25°)、NOAA-AVHRR归一化植被数(normalized difference vegetation index,NDVI)数据(8 km×8 km)、航天飞机雷达地形测绘任务(Shuttle Radar Topography Mission,SRTM)数字高程模型(digital elevation model,DEM)数据(90 m×90 m)以及经纬度信息,建立了非线性空间统计降尺度模型,最终获得8 km分辨率降水降尺度结果。另外,采用将时间序列分析和非线性回归分析融合的方法,基于2000—2012年TRMM年均降水数据和NDVI数据,建立降水量时间尺度预测模型。分析结果表明,综合考虑植被和地形因子对青藏高原地区降水空间分布的影响,基于随机森林算法建立的降尺度模型,其降尺度结果与地面站点测量值拟合系数为0.89,高于TRMM数据与地面站点测量值的拟合系数0.81,说明降尺度结果提高了卫星遥感降水数据的空间分辨率。另外,降水预测模型能够较好地描述青藏高原地区的年际降水变化趋势和数量级,2006—2012年的预测降水量与TRMM降水数据拟合系数均高于0.80。
关键词:
So far, precipitation products with high spatial resolution have been crucial for the basin scale hydrology, meteorology and ecology. The climate in the Tibetan Plateau is of vital significance to global climate variation. So, the study of the distribution of precipitation with high spatial resolution is in the basic position of environmental science. Based on random-forest algorithm, the authors introduced environmental factors such as topography and vegetation, which was developed for downscaling the remote sensing precipitation products accurately and effectively. The non-linear spatial statistical downscaling model was demonstrated with the Tropical Rainfall Measuring Mission (TRMM) 3B43 dataset with the spatial resolution of 0.25°, the Normalized Difference Vegetation Index (NDVI) from NOAA-AVHRR with the spatial resolution of 8km, the Digital Elevation Model (DEM) from Shuttle Radar Topography Mission (SRTM) with the spatial resolution of 90 m and the information of slope, aspect, longitude and latitude. And the model based on time series and vegetation factor, which was demonstrated with TRMM3B43 annual data in order to forecast the precipitation, was introduced in this paper. The downscaling results were validated by applying the observations from the rain gauges in the Tibetan Plateau and the coefficient of determination R 2 is 0.89. The analytical results showed that the downscaling results improved the spatial resolution and accuracy by applying the random-forest algorithm and introducing environmental factors. And the model, which was developed for forecasting the precipitation, captured the trends in inter-annual variability and the magnitude of annual precipitation with the R 2 ranging from 0.81 to 0.87.
Keywords:
本文引用格式
徐彬仁, 魏瑗瑗.
XU Binren, WEI Yuanyuan.
0 引言
水循环促进了自然界的物质运动和能量交换,对气候的形成与变化产生了深刻影响。流域降水量是影响流域水循环最重要的因素。有“亚洲水塔”之称的青藏高原是亚洲大江大河的发源地,印度河、恒河、雅鲁藏布江、长江和黄河均源自青藏高原[1,2]。因此,青藏高原的流域的降水资料对我国乃至全球的水文、气象、生态和农业等领域的发展具有重要的研究意义。与气象站点降水资料相比,卫星资料空间覆盖连续,有助于解决研究区站点数量不足、分布不均匀的问题。但是,由于探测平台的限制,卫星遥感降水产品的分辨率仍然无法满足流域尺度研究的要求。为进一步了解青藏高原流域尺度上降水的时空分布特征,需要开展青藏高原遥感降水数据的空间降尺度方法的研究。
目前,空间降尺度方法主要有动力降尺度和统计降尺度2种。空间动力降尺度是借助全球环流模式(global climate models, GCMs)和嵌套区域气候模式(regional climate models, RCMs)来提高气象要素的空间分辨率。该方法不受观测资料的影响,但其计算量大、模型不易构造,获得的气象要素的空间分辨率不能满足区域尺度的要求[4]。统计降尺度充分考虑到局地气候不仅以大尺度气候为背景,且顾及下垫面特征的影响,利用下垫面特征信息建立大尺度和小尺度气候变量的联系[5]。与空间动力降尺度方法相比,统计降尺度方法构造的模型更加灵活多样,引入较高空间分辨率的区域下垫面特征变量,能大大提高遥感降水资料的空间分辨率[6]。2009年Immerzeel团队以欧洲南部伊比利亚半岛为例,基于降水与植被的关系,采用热带降水测量计划卫星(Tropical Rainfall Measuring Mission, TRMM)降水数据与SPOT -VEGETATION 归一化植被指数(normalized difference vegetation index, NDVI)数据,建立了的指数回归降尺度模型,最终将TRMM降水数据降尺度为1 km分辨率。基于Immerzeel的研究,2011年贾绍凤研究团队开展了柴达木盆地降水降尺度研究,同时引入了植被数据SPOT-VEGETATION NDVI和航天飞机雷达地形测绘任务地形数据(Shuttle Radar Topography Mission,SRTM) 数字高程模型(digital elevation model,DEM)因子作为流域降水的影响因子,建立了多元线性回归模型,也得到了1 km空间分辨率的降水数据 [8]。与Immerzeel团队的研究相比,后者引入DEM变量代表地形因子参与建模,并对降水的降尺度结果进行了误差分析,进一步提高了降水资料的准确性。此外,非线性时间序列可以提高降水的预测精度[16]。在诸多非参数统计回归模型中,随机森林算法在分类和预测方面对自变量的多元共线性不敏感,可以同时输入多个影响因子,在很大程度上解决了过度拟合的问题等。因此,本文基于Immerzeel和贾绍凤研究团队的研究和随机森林算法的优势,选择NDVI,DEM,坡度、坡向和经纬度信息,针对青藏高原流域的长时间序列TRMM遥感降水数据,开展了空间统计降尺度分析研究。
1 研究区概况
受孟加拉湾暖湿空气的影响,雅鲁藏布江大拐弯区域年降水十分充沛; 高原的腹地湖泊数量较多,湖泊集聚区的降水分布普遍高于周围地区; 而受喜马拉雅山体影响,来自印度洋的水汽输送受到阻挡,喜马拉雅山北坡的降水明显少于周围地区。总体而言,青藏高原降水空间分布呈现自东南向西北递减、自南向北逐渐减少的趋势[14]。
2 数据源及其处理
2.1 TRMM卫星降水数据与气象站降水数据
TRMM是世界上第一颗搭载测雨雷达的卫星,携带了微波成像仪、可见光和红外扫描仪[15]。TRMM3B43产品综合了4类相互独立的降水数据,包括微波、近红外等传感器融合估算数据,以及美国国家海洋、大气管理局和全球降水气候中心的降水雨量计分析数据等[14],是卫星降水数据与其他降水数据联合反演的最佳降水产品。本文选用2000—2012年间空间分辨率为0.25°×0.25°的TRMM3B43日降水产品,对青藏高原地区进行降水数据降尺度研究,数据由中国气象科学数据共享服务网站提供。此外,采用研究区内92个站点气象站点在2000—2012年间降水观测数据作为参照。与站点实测降水量相比,TRMM3B43数据产品普遍存在高估的现象(图1)。已有学者研究发现,利用最小二乘方法建立TRMM3B43与站点降水数据的幂函数回归模型,可以取得较好的校准效果[8]。
图1
图1
气象站与TRMM降水数据的回归分析图
Fig.1
Regression analysis of precipitation data from weather station and TRMM
图1中,纵坐标表示气象站点年总降水量,横坐标是TRMM年均降水量,幂函数作为回归方程时,判断系数为0.78,拟合方程为
式中: v为气象站年均实测降雨量; u为校准后的TRMM3B43年均降雨量。图中虚线为y=x线,由此可见经校准模型修正后的数据较好地克服了TRMM原始数据在研究区内对降雨量高估的问题。图2为青藏高原地区TRMM校准后的多年平均降水分布情况。
图2
图2
2001年青藏高原TRMM降水量空间分布图
Fig.2
Spatial distribution of TRMM precipitation in the Tibet Plateau in 2001
式中: ll(i,j)表示第i列第j行像元的经纬度比; lon(i,j)和lat (i,j)分别表示第i列第j行像元的经度和纬度。
2.2 归一化差值植被指数数据
本文采用最大合成算法(maximum value composite,MVC)计算每个像元的月最大值,并计算每一年12个月最大NDVI数据的年平均值,应用最邻近像元法将8 km分辨率数据重采样为0.25°分辨率。图3以2001年为例,青藏高原地区年平均NDVI空间分布,可知植被分布的总体趋势,与降水量分布的总体趋势大致相同。
图3
图3
2001年青藏高原NOAA-AVHRR NDVI空间分布图
Fig.3
Spatial distribution of NDVI from NOAA-AVHRR in the Tibet Plateau in 2001
2.3 SRTM DEM数据
梭雷达地形测量任务是由美国国家地理空间情报局(NGA)和NASA共同推行的国际研究项目。其雷达系统可获得56°S~60°N近全球覆盖范围的数字高程模型,空间分辨率有30 m和90 m两种。本次研究采用青藏高原地区90 m分辨率的DEM数据,并变换为0.25°尺度。数据由http: //gdem.ersdac.jspacesystem.org提供。在模型建立的过程中,除DEM外,并根据青藏高原DEM数据提取坡向和坡度数据[21]。
3 方法
3.1 降尺度方法
3.1.1 随机森林算法
随机森林算法(random forest,RF)在分类和预测方面具有优势,目前已被广泛地应用于降水和生态等诸多领域。20世纪80年代Breiman等人将分类树方法发展成为随机森林算法。与神经网络算法相比,其计算量小且精度较高。该算法的优点在于: ①对多种资料,可以产生高准确度的分类器; ②可处理大量的输入变量; ③在决定类别时,能够评估变量的重要性。鉴于降水与多个变量存在相关关系,模型不仅需要多个输入变量,而且有大量数据作为训练样本。因此,本次研究采用随机森林算法建立降尺度模型是可行的。
本文应用R软件中随机森林程序包作为建模工具,针对本文的研究问题进行建模,表1简单地罗列了该程序包中包含的主要函数。
表1 随机森林包主要函数名与功能
Tab.1
函数名 | 函数功能 |
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Random Forest | 建立随机森林模型 |
Plot | 绘制误差曲线 |
Predict | 模型预测 |
3.1.2 模型的假设
已有研究表明,NDVI是降水量降尺度模型的重要输入因子。由于本文研究区内存在水体,它们对分析植被与降水的统计关系有很大的影响。因此,在建立模型的过程中不考虑NDVI小于等于零的样本,将其视为异常值从数据中剔除。
3.1.3 模型的准备与建立
本次研究基于随机森林算法,以2001年为例对校准后的TRMM降水数据进行降尺度方法的研究,步骤如下: ①分别将8个变量:降雨量(precipitation),降水与归一化差值植被指数(NDVI)、数字高程(DEM)、经纬度比值(ll)、坡向(aspect),坡度(slope),经度(lontitude)及纬度(lattitude)读入数组中,使每个数组对应位置的元素值代表图像中同一个像元的特征,并写入同一个矩阵中; ②剔除异常值; ③将数据随机分成大小相同的两组,组1数据作为建模样本,组2数据用来检验; ④利用R软件的建模工具,建立Random Forest模型; ⑤输入组2模型进行检验。
3.1.4 模型的应用
对上节中建立的模型进行有效性检验后,本节将对降水数据进行降尺度计算,具体步骤为: ①采用最邻近像元法将NDVI,DEM,ll,slope及aspect原始数据重采样为8 km×8 km分辨率数据; ②按照模型输入变量的数据格式,创建经纬度和经纬度比值数据; ③剔除异常值; ④输入已建立随机森林,计算8 km分辨率的降水量; ⑤采用最邻近像元法,对未进行降雨量预测的异常值像元进行降雨量插值; ⑥将上文获得的订正误差与预测值求和,计算得到降尺度结果; ⑦采用最邻近像元法获得与气象站位置对应像元降尺度结果,与气象站数据进行回归分析。
3.2 降水量的预测
降水量变化是典型的非线性时间序列,其中包含了大量的时序动态变化特征。由表2 可知,降水量与环境具有强相关性。目前常见的预测方法是将相关因子作为输入向量,建立多元回归预测模型,这种方法考虑了环境因子对降水时序变化的影响,但是缺乏时序动态分析,不能反映内部变化规律; 另一种常见的方法是时间序列分析,该方法充分考虑了降水变化的内部因子,却忽略了降水与外在因子之间的关联,进而影响预测精度。
表2 降水与其他变量的线性相关性
Tab.2
变量 | TRMM | NDVI | DEM | ll | aspect | slope | lon | lat |
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TRMM | 1.000 | 0.570 | -0.277 | 0.788 | 0.001 | 0.432 | 0.398 | -0.703 |
NDVI | 0.570 | 1.000 | -0.277 | 0.702 | -0.022 | 0.280 | 0.682 | -0.391 |
DEM | -0.277 | -0.277 | 1.000 | -0.204 | 0.076 | -0.086 | -0.476 | -0.171 |
ll | 0.788 | 0.701 | -0.203 | 1.000 | -0.004 | 0.345 | 0.675 | -0.780 |
aspect | 0.001 | -0.021 | 0.076 | -0.004 | 1.000 | 0.009 | -0.009 | 0.001 |
slope | 0.432 | 0.280 | -0.086 | 0.345 | 0.009 | 1.000 | 0.137 | -0.318 |
lon | 0.398 | 0.682 | -0.476 | 0.675 | -0.009 | 0.137 | 1.000 | -0.074 |
lat | -0.703 | -0.391 | -0.171 | -0.780 | 0.001 | -0.318 | -0.074 | 1.000 |
为了提高降水量预测精度,本次研究在考虑降水变化时序动态变化特征的同时,引入了环境因子,基于随机森林算法建立降水量的预测模型。步骤如下: 首先,需要为模型定阶,即判断降水受自身发生量影响的时效长短,采用F测验进行逐步比较确定,本次研究采用2000—2012年均降水数据作为研究对象,预测时效期为预测时间点的前5 a; 然后,将时效时间段内的发生量作为降水内部变化的描述因子,并选择NDVI作为外在影响因子,基于随机森林算法建立非线性预测模型; 将2000—2004年和2005年降水数据和2005年NDVI数据作为输入向量,建立预测模型,随后将2001—2005年降水数据和2006年NDVI数据作为输入向量,预测2006年降水量。4 结果分析与检验
4.1 降尺度模型的检验
图4
图4
随机森林模型预测值与校准的TRMM3B43检验值拟合图
Fig.4
Random forest model predictions and calibrated TRMM3B43 values
图4中,纵坐标代表对模型输入检验数据集的自变量后,输出的降水量的预测值,横坐标代表检验数据集中的TRMM校正值,两者的判断系数R2为 0.87。
4.2 模型的比较
鉴于贾绍凤团队采用线性回归模型,对柴达木盆地的TRMM降水产品进行降尺度研究,其模型取得了较好的检验精度。本文建立降水量与其他自然地理变量之间的线性回归模型,与随机森林模型比较。如表2列出了降水与归一化差值植被指数(NDVI)、数字高程(DEM)、经纬度比值(ll)、坡向(aspect)、坡度(slope)和经纬度(lon和lat)的线性相关性。
根据变量之间的线性相关系数明显可知,降雨量与另外7个变量之间的相关性差别较大。因此,本文采用向后逐步回归的方法,在0.25°分辨率下从模型包含所有预测变量开始,一次删除一个变量直到会影响模型变量(Akaike information criterion, AIC)为止,即
式中: k为参数的数量; L为对数似然值; n为样本数目; sse为残差平方和。AIC的大小取决于L和k。k取值越小,AIC越小; L取值越大,AIC值越小。k小表明模型简洁,L大表明模型精确。因此AIC和修正的决定系数类似,在评价模型是兼顾了简洁性和精确性。
经后向逐步回归分析后本文建立了降水与NDVI,DEM,slope,lon,lat和ll,6个变量(X1,X2,X3,X4,X5和X6)间多元线性回归模型(图5)。模型预测值与检验值的判断系数为0.77。鉴于模型拟合效果不如基于随机森林的降尺度模型效果好,本文选择后者对青藏高原地区降水数据进行降尺度研究。
图5
图5
多元线性模型预测值与校准的TRMM3B43检验值拟合图
Fig.5
Multivariate linear model predictions and calibrated TRMM3B43 values
4.3 降尺度结果与精度检验
图6
图6
2001年青藏高原TRMM降水校准值空间分布图
Fig.6
Spatial distribution of TRMM precipitation calibration value of Tibet Plateau in 2001
图7
图7
2001年青藏高原随机森林输出结果空间分布图
Fig.7
Spatial distribution of random forest output in the Tibet Plateau in 2001
图8
图8
8 km×8 km空间分辨率误差分布图
Fig.8
8 km × 8 km spatial resolution error distribution
图9
图10
图10
TRMM校准值和降尺度结果与站点降水量回归分析图
Fig.10
TRMM calibration and downscaling results with site precipitation analysis
4.4 降水量预测方法结果与检验
图11分别为研究区内5个观测站点降水量测量值和预测结果随时间变化的曲线。5个站点依次为昌都站(31.15°N,97.17°E)、那曲站(31.48°N,92.07°E)、林芝站(29.67°N,94.33°E)、拉萨站(29.7°N,91.13°E)和日喀则站(29.25°N,88.88°E)。分析表明,在5个观测站点处的降水量预测值有效地描述了降水的年际变化趋势和降水量的数量级。
图11
图11
5个站点观测值与预测值的年际变化曲线
Fig.11
Interannual variation of observed and predicted values for five sites
采用上述预测方法,预测结果与原始TRMM降水数据的拟合系数见表3。
表3 2006—2012年预测结果与校准后的TRMM降水量拟合系数
Tab.3
年份 | 2006 年 | 2007 年 | 2008 年 | 2009 年 | 2000 年 | 2010 年 | 2011 年 | 2012 年 |
---|---|---|---|---|---|---|---|---|
R2 | 0.87 | 0.87 | 0.85 | 0.81 | 0.85 | 0.87 | 0.85 | 0.87 |
4.5 降水数据精度对结果精度的影响
本文采用TRMM3B43产品进行降尺度研究。该产品综合了4类相互独立的降水数据,包括微波、近红外等传感器融合估算数据,以及美国国家海洋、大气管理局和全球降水气候中心的降水雨量计分析数据等[14],是卫星降水数据与其他降水数据联合反演的最佳降水产品。首先,数据产品本身存在误差,该误差可能由2方面引起: ①在观测4类相互独立降水数据的过程中引入了误差; ②使用联合反演算法进行数据融合的过程中引入了误差。其次,本次研究采用站点观测数据虽对TRMM3B43原始数据进行了校准,但所用的站点数据较少且分布不匀,导致校准模型在校准过程中引入了误差。以上各种误差均可影响降水数据的真实性,进而降低了降尺度结果的精度。
4.6 输入变量对结果精度的影响
降水是受多种因素影响的气象要素。本次研究仅仅考虑了植被和地形因素对其产生的作用,忽略了气候带、海陆位置、季风和人类活动等因素对降水的影响。另外,本次研究模型的输入变量并不具有相互独立性,在一定程度上降低了模型的有效性,因而影响了降尺度结果的准确性。
影响预测结果精度的因素主要有2个方面: ①统计模型缺乏物理机制,无法充分描述内部和外部因子对降水变化的影响。②本次研究所采用的降水数据为TRMM3B43的2000—2012年间的年均降水数据,时间尺度较短,因而影响了时间序列分析的有效性和准确性,使预测结果无法达到理想的精度。
5 结论
基于已有青藏高原的遥感降水等资料,本文根据降水与植被和地形因子的相关关系,使用TRMM3B43降水、NOAA-AVHRR NDVI和SRTM DEM等数据,采用随机森林算法建立了0.25°尺度下的降尺度模型,并求出了该尺度下的误差分布,采用最邻近像元方法插值为8 km分辨率,结合8 km模型预测值计算得出了青藏高原降水分布的降尺度结果。经分析验证,降尺度结果与地面站点降水量观测数据的R2为0.89,高于TRMM3B43校准值与地面站点降水量观测数据的R2(0.81)。此外,综合考虑内部因子和外部因子对降水变化的影响,基于随机森林算法,融合时间序列分析和多元回归分析,建立降水量预测模型,有效地描述了降水的年际变化趋势和降水量的数量级,并且2000—2012年均降水量预测结果与TRMM3B43降水数据拟合系数均达到0.8以上。因此本研究得出了下述认识:
1)基于下垫面因子和随机森林算法的降尺度方法,能够较准确地估计实际降水情况,不仅可提高卫星遥感降水产品的空间分辨率,同时可提高原始数据的反演精度。
2)融合时间序列分析的降水预测模型,可以有效地描述降水的年际变化趋势和降水量的数量级。
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