## 3 Study Area and Data  
The study area is located in the Zhangye area of Gansu Province, China. The Zhangye area is in the midstream zone of the Heihe River Basin (Figure 2). The study area includes various land-cover types, such as desert, cropland, oases, urban areas and mountainous regions. In 2007, an automatic weather station was established by the Institute of Remote Sensing Applications and the Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, in the Yingke district of Zhangye City to perform observations of micrometeorology and evapotranspiration [31, 32, 33]. Through numerous simultaneous airborne, satellite-borne and ground-based remote-sensing experiments carried out in 2008, a large amount of experimental data of the topography, land cover and other attributes of this area was retrieved. This experiment was repeated in 2012, at which time the authors carried out ground observations of FPAR on maize canopy, alfalfa and grassland. Many PAR quantum sensors were also installed to observe PAR automatically. Use of remote sensing data is the best way for FPAR inversion for the whole Heihe River Basin. Based on the input parameters required by the DnD model, the combined \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Vegetation Type** & **Clumping Index** & **Vegetation Type** & **Clumping Index** \\ \hline Broadleaf, evergreen & 0.63 & Shrubs & 0.71 \\ Broadleaf, deciduous & 0.69 & Herbaceous & 0.74 \\ Needleleaf, evergreen & 0.62 & Sparse shrubs & 0.75 \\ Needleleaf, deciduous & 0.68 & Cultivated and managed area & 0.73 \\ Mixed leaf types & 0.69 & Other & 0.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Clumping indices for different vegetation types. Figure 2: Location of the study area. The black-bordered area is Gansu Province; the red-bordered area is the Heihe River Basin; and the blue-bordered area is the region covered by the remote sensing images used for FPAR inversion in this paper. product (MCD15), surface albedo product (MCD43) and land cover product (MCD12) were used. The diffuse PAR proportion is a by-product of PAR estimation. The authors have developed a method for estimating hourly PAR based on a combination of geostationary and polar-orbiting satellite data [34, 35, 36]. The Multifunctional Transport Satellite (MTSAT) was selected to retrieve cloud optical depth (COD) at high temporal resolution, and the polar orbit satellite data of the MODIS products were used to derive surface parameters based on multispectral characteristics. Instantaneous direct and total PAR were estimated by the Second Simulation of a Satellite Signal in the Solar Spectrum-Vector (6 SV) and the Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART) model [37, 38]. Then, instantaneous \(k\) could be calculated using direct and total PAR. The information of the input data is showed in Table 2.  
The SunScan canopy analysis system can obtain vegetation canopy FPAR. It offers convenient and flexible tools for measuring and analyzing incident and transmitted PAR in crop canopies. It provides vital information about the penetration of PAR into crops and is essential in work, such as comparative crop studies, for separating out the effects of cultivar and treatment. It is particularly well suited to low regular canopies (as found in many agricultural crops). The principle of SunScan measurement of canopy FPAR is shown in Figure 3.  
In Figure 3, \(L_{can}\)\(\uparrow\) is the PAR that reaches the top of the vegetation canopy, \(L_{can}\)\(\downarrow\) is the reflective PAR of the vegetation canopy, \(L_{soil}\)\(\uparrow\) is the reflective PAR of the soil and \(L_{soil}\)\(\downarrow\) is the PAR that reaches the soil. These four parameters can be obtained from SunScan measurements. \(L_{s}\) is the absorptive PAR of soil, and \(L_{v}\) is the absorptive PAR of the vegetation canopy. \(L_{s}\) and \(L_{v}\) can be calculated using Equations (22) and (23):