Abstract Precipitation products with high spatial resolution are important for basin-scale hydrological and meteorological applications. Downscaling techniques commonly used with satellite-derived rainfall data build statistical regression relationships between the precipitation and land surface characteristics to obtain rainfall estimates with improved spatial resolution. However, these relationships tend to be extended mistakenly from the regional scale to the hill slope scale. This paper introduces a quadratic parabolic profile (QPP) model for downscaling precipitation. The proposed technique uses a quadratic parabolic equation to express the rule for changes of precipitation with elevation. It is assumed that precipitation is the primary factor restricting vegetation growth during the growing season. Therefore, an ordinary least square regression method is used to fit an “elevation–normalized difference vegetation index (NDVI)” function to determine the parameters of the QPP model. This method was implemented in the Three-River Headwaters Region (TRHR) during the growing seasons of 2009–2013 for both monthly and total precipitation. The results indicated that the precipitation estimates downscaled using the QPP method had higher accuracies than those of commonly used exponential regression, multiple linear regression, and geographically weighted regression models. The average root mean square errors (RMSEs) and mean absolute percent errors (MAPEs) of total precipitation during the growing season of the commonly used models were 17%–69% and 17%–92% higher, respectively, than those of the QPP model. Meanwhile, the precipitation downscaled using the QPP technique also had lower MAPEs and RMSEs than the PERSIANN-CCS, PERSIANN-CDR, GSMaP-RNL, and GSMaP-RNLG products. Downscaled precipitation estimates from the QPP model exhibited patterns with elevation that were more detailed and more reliable than from the commonly used downscaling methods and another four satellite products. In addition, the QPP model is insensitive to errors in the NDVI or elevation. These findings suggest the proposed approach could be implemented successfully to downscale both monthly and total precipitation of the Tropical Rainfall Measuring Mission (TRMM) 3B43 product throughout the growing season in the TRHR.

中文翻译：

---

考虑宏观地理因素和三河源区局部海拔影响的TRMM降水数据空间降尺度

摘要 空间分辨率高的降水产物对于流域尺度的水文气象应用具有重要意义。通常与卫星衍生的降雨数据一起使用的降尺度技术在降水和地表特征之间建立统计回归关系，以获得具有改进空间分辨率的降雨估计。然而，这些关系往往会错误地从区域尺度扩展到山坡尺度。本文介绍了用于降尺度降水的二次抛物线剖面 (QPP) 模型。所提出的技术使用二次抛物线方程来表达降水随海拔变化的规律。假设降水是生长季节限制植被生长的主要因素。所以，使用普通最小二乘回归方法拟合“高程-归一化植被指数（NDVI）”函数来确定 QPP 模型的参数。该方法在 2009-2013 年生长季节的三河源区 (TRHR) 中实施，用于月降水量和总降水量。结果表明，与常用的指数回归、多元线性回归和地理加权回归模型相比，使用 QPP 方法缩减的降水估计具有更高的准确度。常用模型的生长季总降水的平均均方根误差（RMSEs）和平均绝对百分比误差（MAPEs）分别比QPP高17%~69%和17%~92%模型。同时，与 PERSIANN-CCS、PERSIANN-CDR、GSMaP-RNL 和 GSMaP-RNLG 产品相比，使用 QPP 技术缩减的降水也具有更低的 MAPE 和 RMSE。QPP 模型的降尺度降水估计显示出的高程模式比常用的降尺度方法和另外四个卫星产品更详细、更可靠。此外，QPP 模型对 NDVI 或高程中的误差不敏感。这些发现表明，所提出的方法可以成功实施，以在 TRHR 的整个生长季节降低热带降雨量测量任务 (TRMM) 3B43 产品的月降水量和总降水量。QPP 模型的降尺度降水估计显示出的高程模式比常用的降尺度方法和另外四个卫星产品更详细、更可靠。此外，QPP 模型对 NDVI 或高程中的误差不敏感。这些发现表明，所提出的方法可以成功实施，以在 TRHR 的整个生长季节降低热带降雨量测量任务 (TRMM) 3B43 产品的月降水量和总降水量。QPP 模型的降尺度降水估计显示出的高程模式比常用的降尺度方法和另外四个卫星产品更详细、更可靠。此外，QPP 模型对 NDVI 或高程中的误差不敏感。这些发现表明，所提出的方法可以成功实施，以在 TRHR 的整个生长季节降低热带降雨量测量任务 (TRMM) 3B43 产品的月降水量和总降水量。