## 1 Introduction
As one of the most widely used and validated ET models, the Surface Energy Balance System (SEBS) developed by [PERSON] [23] estimates turbulent heat fluxes by means of Moni-Obukhov Similarity (MOS) theory [39; 40]. Several important parameters are a part of the MOS and SEBS, including zero-plane displacement (\(d\)), roughness height (\(z_{\rm 0m}\)), and heat roughness height (\(z_{\rm 0h}\)). The scalar \(z_{\rm 0h}\) can be calculated from \(z_{\rm 0m}\) using the \(kB^{-1}\) model that provides excess resistance for heat transportation. For \(d\) and \(z_{\rm 0m}\), experimental methods based on measurements of turbulent fluxes can provide estimates but are only locally valid and cannot be scaled to larger areas. Alternatively, remotely sensed methods have been developed for these parameters using the functions of vegetation structural parameters (_i.e._, LAI, [41], frontal area index (FAI) [42], both LAI and FAI [43], stand density (SD) (trees- ha\({}^{-1}\)), and stem-branch-leaf distributions [44]). For the \(kB^{-1}\) model, some studies have improved parameterization [45; 38; 46]. However, few have focused on forests. Our previous study [47] demonstrated the advantages and disadvantages of four notable models for retrieving \(d\) and \(z_{\rm 0m}\) values in forests located within the Qilian Mountains (QMs), the headwater area of the HRB. A key parameter needed for \(d\) and \(z_{\rm 0m}\) estimates is forest height. Other vegetation structure parameters further affect the ratios of \(d\) or \(z_{\rm 0m}\) over forest height (\(d\)/\(h\) or \(z_{\rm 0m}\)/\(h\)). Incombination with forest measurements, remote sensing is capable of providing reliable instantaneous retrievals of forest height that can be used to parameterize \(d\) and \(z_{\rm 0m}\) models for those time intervals when forest structural parameters (height, LAI, FAI, _etc._) and, thus, \(d\)/\(h\) or \(z_{\rm 0m}\)/\(h\) are assumed to be unchanged. For long-term parameterization, LAI can easily be obtained from moderate resolution remote sensing data (_i.e._, MODIS) over a fine time resolution. However, time-series retrieval for other parameters is a problem, especially for young and immature forests. Normally, the structure (including the height and FAI) of young and immature forests changes markedly over a few years. If constant structural information is used to parameterize \(d\), \(z_{\rm 0m}\), and \(z_{\rm 0h}\), uncertainties will be propagated into ET due to the sensitivity of ET to parameters such as these in models such as the SEBS. Despite having the ability to estimate surface turbulent heat fluxes within various ecosystems, uncertainties in the SEBS arise that result from parameterizations of land surface input data (vegetation height, \(z_{\rm 0m}\), LAI, land surface temperature (LST), _etc._) and from inherent errors in meteorological parameters. A few studies [38; 48; 49; 50] have conducted sensitivity analyses for the SEBS. However, more investigations over heterogeneous forests (for example, forests located in cold and arid areas, as in our study area) are necessary. The objectives of the present study are therefore (1) to investigate the effects of major input variables (including \(d\) and \(z_{\rm 0m}\)) and their changes over a 13 year long period on sensible heat flux as estimated with SEBS, and (2) to obtain a 13 year time series of forest ET in the headwater of the HRB. Below, after discussing our sensitivity data, we propose a time-series parameterization scheme for \(d\), \(z_{\rm 0m}\), and \(z_{\rm 0h}\) using a combination of forest AGB dynamics and remote sensing data. Specifically, the use of regression relationships for forest vertical parameters (the Lorey's height [51] and FAI) _versus_ forest AGB was established based on measurements. Thus, interannual vertical parameters from 2000 to 2012 were connected using the corresponding interannual forest AGB dynamics.