**5. Conclusions**

In this study, we applied satellite data products in combination with meteorological reanalysis datasets to evaluate the interannual and seasonal dynamics of terrestrial biophysical variables, including the meteorological variables, vegetation, and evapotranspiration (ET) over the Three-River Headwaters Region (TRHR). We then further investigated the response of vegetation and ET to climate change during the period 1982–2015. Our results showed that the Ta and P increased by 0.597 ◦C and 41.1 mm per decade, while the RH and Rs declined at a rate of 0.9% and 1.8 <sup>W</sup>/m<sup>2</sup> per decade, respectively. The

largest upward movement of Ta associated with the decline in RH occurred in winter (0.901/decade and 0.6%/decade, respectively), and the increment of P and the reduction of Rs were largest in summer (6.66 mm/decade and 4.57 <sup>W</sup>/m2, respectively). A 'dryer warming' tendency and a 'wetter warming' tendency exist in di fferent areas of the TRHR. Generally, most areas of the TRHR became warmer and moister, except for some areas in the southern TRHR, with a trend of being dryer and warmer.

Our findings illustrate that the NDVI of the TRHR fluctuated in the period 1982–2015, with a slight increase (0.0051/decade) particularly in the northern and western meadow areas. The NDVI significantly increased over 56.8% of the TRHR, and the largest increment occurred in spring, followed by summer. In well-watered regions, Ta was the primary driver of vegetation greening, while in the water limiting areas, vegetation growth was mainly governed by the variation of P. Our results sugges<sup>t</sup> that the warming and wetting tendencies of the climate characterized by increasing Ta and P contribute most to the increment of vegetation in the TRHR.

The annual mean terrestrial ET was about 230.23 mm/year and varied 162 mm/year to 362 mm/year from the northwest to southeast over the TRHR in the period from 1982 to 2015. The ET of the TRHR showed a significant increasing trend at a rate of 3.34 mm/decade, particularly in winter (0.154 mm/decade), which corresponded to the expected acceleration associated with climate warming. In the arid region of western TRHR, ET was limited by the terrestrial water supply, which includes soil moisture (SM) and P. By contrast, atmospheric evaporative demand derived from Ta and relative humidity (RH) were the main controlling factors over the relatively humid region of southeastern TRHR. In addition, the intensification of agriculture irrigation is also responsible for the temporal and spatial variation of ET. Moreover, the impacts of carbon flux and anthropogenic disturbance on the biophysical variables need further exploration.

**Author Contributions:** Conceptualization, Y.Y.; Formal analysis, K.J.; Investigation, X.C.; Methodology, K.S.; Software, L.Z.; Supervision, T.X.; Validation, J.X.; Visualization, X.Z.; Writing—original draft, X.B.

**Funding:** This work was also partially supported by the National Key Research and Development Program of China (No. 2016YFB0501404) and the Natural Science Fund of China (41671331).

**Acknowledgments:** The authors thank Xianhong Xie and Bo Jiang from Beijing Normal University for their helpful suggestions. The authors thank Jie He and Kun Yang from the Institute of Tibetan Plateau Research, Chinese Academy of Sciences (http://westdc.westgis.ac.cn/) for providing the China Meteorological Forcing Dataset. The GIMMS NDVI product was obtained from NOAA (http://islscp2.sesda.com/ISLSCP21/data), and the land cover type product of GlobeLand30 was obtained online (http://www.globallandcover.com). The Climate Prediction Center soil moisture dataset was obtained online (http://www.esrl.noaa.gov/psd/).

**Conflicts of Interest:** The authors declare no conflict of interest.

## **Appendix A Algorithms**

The MS-PT algorithm can be described as

$$ET = ET\_{\mathfrak{s}} + ET\_{\mathfrak{c}} + ET\_{\mathrm{ic}} + ET\_{\mathrm{uns}},\tag{A1}$$

$$ET\_s = (1 - f\_{\rm net}) f\_{\rm sm} \alpha \frac{\Delta}{\Delta + \gamma} (R\_{\rm ns} - G)\_{\prime} \tag{A2}$$

$$ET\_c = (1 - f\_{\rm uvt}) f\_c f\_T \alpha \frac{\Delta}{\Delta + \chi} R\_{\rm uv} \tag{A3}$$

$$ET\_{\rm ic} = f\_{\rm uvet} \alpha \frac{\Delta}{\Delta + \gamma} R\_{\rm uv} \tag{A4}$$

$$ET\_{\rm us} = f\_{\rm wet} a \frac{\Delta}{\Delta + \mathcal{V}} (R\_{\rm ns} - G), \tag{A5}$$

where *ETc* is the canopy transpiration, *ETs* is the unsaturated soil evaporation, *ETic* is the canopy interception evaporation, and *ETws* is the saturated wet soil surface evaporation. Moreover, *fwet* is the relative surface wetness ( *f* 4*sm*), in which *fsm* refers to soil moisture constraint and can be derived from *ATI* (*ATI* = ( 1*DT* )*DT*/*DTmax* , *DTmax* = 40 ◦C), *fT* represents plant temperature constraint exp(− (*Tmax* − *Topt*/*Topt*)2), *Topt* is an optimum temperature (25 ◦C), *Rns* is the surface net radiation to the soil (*Rns* = *Rn*(1 − *fc*)), *G* is soil heat flux (μ*Rn*(<sup>1</sup> − *fc*), μ = 0.18), *Rnv* represents the surface net radiation to the vegetation (*Rnv* = *Rn fc*), *fc* is the vegetation cover fraction (*fc* = (*NDVI* − *NDVImin*/(*NDVImax* − *NDVImin*)), and *NDVImin* and *NDVImax* are the minimum and maximum NDVI, respectively. Δ is the slope of the saturate vapor pressure curve, and γ is the psychrometric constant (0.066 kPa/ ◦C).
