**5. Effect of the CDH on SH Diurnal Variation**

Previous studies [38] have pointed out that the uncertainty in the estimate of SH over the TP can be strongly attributed to the heat transfer coefficient CDH. CDH is affected by ground roughness and atmospheric stratification stability and has obvious seasonal and diurnal variations [39]. In order to address whether CDH is the dominant factor giving rise to the bias between calculated SH and observed SH, here the diurnal variation characteristics of the heat transfer coefficient (CDH-O hereafter) derived with the observed SH according to Equation (1) is examined (Figure 8). Due to the limitation of observational data, only the CDH-O at NAMORS can be obtained.

**Figure 8.** Seasonal mean of the diurnal variation in the derived heat transfer coefficient (CDH-O), observed SH (Obs\_SH, unit: W m−2) and calculated SH (Cal\_SH, unit: W m−2) at NAMORS in (**a**) spring, (**b**) summer, (**c**) autumn, and (**d**) winter. The two horizontal dashed lines indicate zero SH and 0.004 CDH-O, respectively.

As shown in Figure 8, the value of CDH-O in summer is the largest, followed by spring and autumn, and the smallest is in winter. This may be due to the unstable atmospheric stratification in summer over the TP and the greater roughness of the underlying surface vegetation, resulting in a larger CDH-O in summer. In general, the CDH-O values in all seasons are basically larger and stable in the day but fluctuate significantly at night, especially during the time from 00:00 to 10:00. Because the surface roughness at the fixed station has almost no diurnal variation, the CDH-O should be mainly considered to be affected by the stability of atmospheric stratification.

For the calculated SH, the CDH is set as 4 × <sup>10</sup>−3, which is the average value often used in previous studies. However, the derived transfer coefficient CDH-O is much lower than 4 × <sup>10</sup>−<sup>3</sup> throughout the day (Figure 8), which suggests that the calculation of SH by choosing a fixed value of 4 × <sup>10</sup>−<sup>3</sup> will be overestimated, and also be biased in the diurnal variation. Clearly, the difference in diurnal variation between the calculated SH and the observed SH is the largest in spring, followed by summer, winter, and autumn, and the deviation can be up to 69.53 W m−<sup>2</sup> and 194.46 W m−<sup>2</sup> in autumn and spring, respectively. Therefore, the value of CDH is very important, which will bring a certain uncertainty to the SH calculation and its diurnal variation.

A more reasonable value of the heat transfer coefficient is urgently needed to reduce the uncertainty and obtain a more accurately calculated SH. Usually, the TP is a strong heat source in spring and summer, and most studies on SH also focused on these two seasons. Therefore, by further calculations, the seasonal mean CDH-O values in spring and summer at NAMORS are about 2.24 × <sup>10</sup>−<sup>3</sup> and 2.78 × <sup>10</sup>−3, respectively, and the new SH in these two seasons is obtained by using these new CDH. Here, Figure 9 shows the relationships between the originally calculated SH, the new SH, and the observed SH. Obviously, the new SH is much closer to the observations on a diurnal scale, especially in spring, with a maximum deviation of 27.89 W m−2, only being 12.7% of the maximum deviation between the originally calculated SH and the observed SH. Moreover, the new SH shows interannual variations comparable with the observed SH (Figure 10). Of note is that, during the spring of 2006–2012, the change of the new SH is completely consistent with the observed SH, and the relative deviation of the new SH is only 13.1%, while that of the calculated SH is 101.9%. Considering the scarcity of directly observed flux data over the TP region, it is inevitable to calculate SH for the research involving TP SH. Therefore, the new and better heat transfer coefficient (2.24 × <sup>10</sup>−<sup>3</sup> in spring and 2.78 × <sup>10</sup>−<sup>3</sup> in summer) presented here is conducive to calculating SH more accurately in the future.

**Figure 9.** The relationship between the originally calculated SH and observed SH (blue lines, unit: W m<sup>−</sup>2), and between the new SH and observed SH (red lines, unit: W m−2) in the seasonal mean of the diurnal variation in (**a**) spring and (**b**) summer at NAMORS. RMSE1 and RMSE2 denote the root mean squared error of the originally calculated SH and the new SH, respectively.

**Figure 10.** Time series of the annual mean in observed SH (Obs\_SH, units: W m−2), originally calculated SH (Cal\_SH, units: W m−2), and new SH (New SH, units: W m−2) in (**a**) spring and (**b**) summer at NAMORS during the period 2006–2016.

#### **6. Conclusions and Discussion**

Obvious diurnal variation exists in SH over the TP. Here we adopted the hourly observational SH from the Tibetan Plateau Scientific Data Center to deeply understand the characteristics of the SH diurnal variation over the TP. In addition, the differences between the observed and calculated SH are also examined. The main conclusions are as follows:


Research related to turbulent flux has always been the core issue of land–atmosphere interaction [40], and an in-depth understanding of diurnal variation characteristics in SH over the TP can help us to understand the key land surface processes. Due to the uneven distribution of observations in high mountain regions [28], especially over the TP, the model performance is still poor [41], so various parameterization schemes and numerical models for SH are usually developed. An in-depth understanding of the diurnal variation characteristics of SH over the TP can help to improve and calibrate the numerical modes. Moreover, the new CDH obtained by comparing the calculated SH and observed SH on a diurnal scale can boost the accuracy of SH calculations. However, the impact of the diurnal variation in TP SH on the weather has not been mentioned in this study, and it therefore needs further exploration in the future. It is also worth noting that the suggested new CDH is obtained only from NAMORS due to data limitations, so there is still a certain one-sidedness.

**Author Contributions:** Conceptualization, M.W.; formal analysis, Z.Z.; writing—original draft, Z.Z.; writing—review and editing, M.W., J.W., X.M., J.L. and X.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was sponsored by the National Natural Science Foundation of China (42030605), the Second Tibetan Plateau Scientific Expedition and Research (STEP) program (2019QZKK0105), the National Natural Science Foundation of China (41605039, 41807434, 42030611), the Natural Science Foundation of Jiangsu Province, China (grant no. BK20221449), Meteorological soft science of China Meteorological Administration (2022ZDIANXM28), and the open project of Key Laboratory of Meteorological Disaster (KLME), Ministry of Education & Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters (CIC-FEMD), Nanjing University of Information Science & Technology (grant no. KLME202203).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are openly available in [National Tibetan Plateau Data Center] at [https://doi.org/10.11888/Meteoro.tpdc.270910], reference number [27].

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