Evaluation of the Effect of Low Soil Temperature Stress on the Land Surface Energy Fluxes Simulation in the Site and Global Offline Experiments

The root water uptake (RWU) rate of plants is influenced by various environmental factors. Low soil temperature stress can reduce RWU rate by inhibiting the growth of plant roots and increasing the hydraulic resistance of water transport among the soil‐plant‐atmosphere continuum. Given that low soil temperature stress is not accounted for in current land surface models (LSMs); in this study, we introduce three functions to represent low soil temperature stress, and modify the RWU scheme of the Common Land Model to quantify the role of low soil temperature stress on water and energy exchange between land and atmosphere. The simulated water and energy fluxes are evaluated using both in situ and global observational data sets. The results from in situ simulations show that ignoring effects of low soil temperature stress, latent, and sensible heat fluxes in spring are overestimated and underestimated, respectively, with the root mean square error up to 40 W/m2. By incorporating the low soil temperature stress functions into the RWU scheme, nearly 40% of the simulated errors are reduced. The global simulated results also highlight the importance of accounting for low soil temperature stress on increasing the accuracy of the modeled latent heat flux over high latitude areas. While uncertainties from related physical processes and parameters warrant further investigations, our results indicate that consideration of low soil temperature stress significantly affects water and energy transport from land to atmosphere by restricting RWU rate, emphasizing the need to integrate it in LSMs to increase the model reliability, especially over cold regions.

is still low (e.g., in spring), the canopy transpiration demand of plants will be considerable. Restricted by low soil temperature, the RWU rate cannot meet the large demand of canopy transpiration due to restriction by low soil temperature, which may cause the detriment of dehydration. When the soil temperature is low, the transport rate of water from the soil to plant roots will decrease and the water viscosity will increase, which leads to less absorption of water through roots (Ameglio et al., 1990;Bloom et al., 2004;Running & Reid, 1980;Wan et al., 2001). Besides, the low soil temperature can also inhibit the growth of plant roots, thus reducing the RWU capacity of plants (Nagasuga et al., 2011;Vapaavuori et al., 1992;Zia et al., 1994).
In order to study the effect of low soil temperature stress on the RWU process, many field studies have been carried out by botanists. For example, a study on the response of the RWU rate of cucumber to soil temperature showed that the RWU efficiency of cucumber roots decreased when the soil temperature was below 12°C. Above this temperature, the RWU rate did not change much (Yoshida & Eguchi, 1989, 1991. A field study about rice revealed that the root hydraulic conductivity descended with decreasing soil temperature, and the change in root hydraulic conductivity was most pronounced below 15°C (Murai-Hatano et al., 2008). Another field study on the RWU of maize also indicated that the root hydraulic conductivity was proportional to temperature change between 10° and 20°C (Ionenko et al., 2010). Reduction of root hydraulic conductivity increases the resistance when soil water entered the root system, which in turn reduced the rate of water uptake by the plant root system. A study on the influence of soil temperature on RWU and transpiration of young Scots pines showed that soil temperature was a main factor behind the decrease of RWU rate of roots under 8°C. This study also found that low soil temperature stress could lead to a decrease in stomatal conductance and root activity, which then reduces the root water uptake rate and transpiration (Mellander et al., 2004). Numerous observational studies have shown that low soil temperature stress is an important factor restricting the soil water supply to plants (Aroca et al., 2003;Kuwagata et al., 2012).
In most of current land surface models, the RWU rate is calculated by distributing transpiration into each soil layer according to soil water content and root density fraction. Then the water change due to RWU is treated as a sink term and adds to the soil vertical water flow equation (Cox et al., 1999;Dai et al., 2003;Dickinson et al., 1993;Jarvis, 1989;Niu et al., 2011;Wang et al., 2011;Yang et al., 2011). This parameterization scheme focuses only on the overall water content in the soil and the proportion of plant root density, without considering the influence of various environmental factors including the low soil temperature on the RWU process. Hence, with a low soil temperature and a large difference between soil temperature and atmospheric temperature, canopy transpiration is always overestimated by the models accordingly (Mellander et al., 2006). Some numerical studies have shown that incorporating the effect of soil temperature into the simulation of RWU scheme can improve the accuracy of the RWU rate and transpiration rate by the models (Lv et al., 2012). Therefore, it is necessary to improve the RWU parameterization scheme current in the existing land surface models by incorporating a function describing the effects of low soil temperature stress and to further evaluate the role of this function. It is expected that accounting for effects of low soil temperature stress can improve the performance of land surface models on the simulation of energy fluxes, which are further beneficial to the prediction of global weather and climate change, carbon and nitrogen cycles and crop yield by earth system models (Zhu et al., 2017).
In this study, we modify the RWU scheme of the Common Land Model (CoLM) and incorporated three empirical functions to investigate the effect of low soil temperature stress (Jansson & Karlberg, 2010). The observational data of three FLUXNET forest sites are used to evaluate the influence of the low soil temperature stress functions on simulated energy fluxes. After that, the global offline simulations are carried out to further verify the possible impact of low soil temperature stress functions on the global land surface process simulation. This study is organized as follows. In Section 2, the data sets, model, and experimental design are described. Results are presented in Section 3, which is followed by the discussions and conclusions in Sections 4 and 5.

Model Default
The CoLM is a state-of-the-art land surface model (Dai et al., 2003). It was adopted as the land component for the community atmospheric model (CAM; Zeng et al., 2002) in the version 2 of the community climate system model (CCSM2; Bonan et al., 2002) and named as the community land model (CLM). The CoLM has been developed independently in China, and it possesses many new features such as two big leaf models used for leaf temperature and the photosynthesis-stomata resistance, and the two-stream approximation for the calculation of canopy albedo with the solution for singularity point (Dai & Ji, 2005;Dai et al., 2004Dai et al., , 2014. As a result, the CoLM is now fundamentally different from both its original version (Dai et al., 2003) and the recent versions of CLM (Lawrence et al., 2019;Oleson et al., 2013). The CoLM has been widely applied to land surface process modeling by many weather forecasting models and climate models.
Low temperature stress in the soil environment can reduce the RWU rate (Kramer & Boyer, 1995). In order to account for the effects of low soil temperature stress in the CoLM, a modification of the RWU scheme is conducted in the model. The soil water content changes in the CoLM are calculated by the following equation: where θ is the volumetric soil moisture content, t is time (s), z is soil depth (mm), E R (mm s −1 ) is root water extraction and evaporation (only in the surface layer) from the soil, and q is the vertical water flow (mm s −1 ).
The sink term E R,j in soil layer j is calculated as follows: where E tr is the transpiration in the canopy (mm s −1 ), and f eroot,j refers to the effective root fraction in layer j. The effective root fraction f eroot,j that considers both the root fraction and soil water condition is calculated as follows: where f root,j is the root fraction in soil layer j and W lt,j represents the water stress level in soil layer j. In CoLM, the integrated water stress level in all soil layers is represented by f roota , which is the standardization of the sum of f root, j W lt,j in 10 soil layers and ranges from 0 to 1. In the default CoLM, the soil temperature is not considered when f roota is calculated. To incorporate the environmental temperature stress into CoLM, the modified f roota is introduced into the RWU scheme: where f roota,t is the replacement of f roota used for calculating the max canopy potential transpiration E tr,max in the model. The parameter f t , which represents the effect of low soil temperature stress, varies from 0 to 1. In this study, three different functions originated from the coupled heat and mass transfer model (COUP-MODEL, Jansson & Karlberg, 2010) are used in the CoLM to calculate the value of f t . The first one is a double-exponential function (Ågren & Axelsson, 1980): where T g represents the soil temperature and T trig is the empirical triggering temperature. When soil temperature gets higher than T trig , the influence of low soil temperature stress decreases gradually. t WA and t WB are the empirical parameters.
The second way to calculate f t is a polynomial function: where T ref is the reference temperature and f t equals 1 when the soil temperature is higher than T ref , which represents the relief of low soil temperature stress when soil temperature is above T ref . And t WE is an empirical parameter.
ZHU ET AL. The third function used to solve the value of f t is a single-exponential function: where the definitions of T g , T trig , and T ref are same as those in the first two functions. The parameters in the three functions are set according to the previous work (Jansson & Karlberg, 2010;Mellander et al., 2006). Table 1 lists the value of each parameter used in this study.

Data, Sites Description, and Experimental Design
FLUXNET is a global network of micrometeorological flux measurement sites that provide long-term ground-based ecosystem observations (Baldocchi et al., 2001). It's very useful for land surface model development (Friend et al., 2007;Stöckli et al., 2008). In this study, we use the observational data from three sites in the FLUXNET 2015 data set for the investigation (Pastorello et al., 2020). The three sites all have four distinct seasons and plants will encounter low soil temperature stress at the turn of spring and summer. They are suitable to be used for the investigation of the effect of low soil temperature stress.
The first site is the US-Ha1 site (Munger, 1991). This site is located in the forest near Harvard University in Massachusetts, which is in the northeastern US ( ure 1). It provides measured sensible heat and latent heat fluxes and the related meteorological variables from 1989 (Urbanski et al., 2007). The annual mean temperature and precipitation at the location of this site are 6.6°C and 1,070 mm, respectively. The distribution of precipitation is relatively uniform throughout the year ( Figure 2). Vegetation around this site is dominated by Quercus rubra and Acer rubrum, and sporadic distribution of eastern Tsuga canadensis, Pinus strobus, and Pinus resinosa can also be found. The observation height of this site is 30 m. The simulation period over this site is from 1994 to 2001. The International Geosphere-Biosphere Programme (IGBP) type is Deciduous Broadleaf Forests (DBF).
The second site is the FI-Let site (Koskinen et al., 2014), which is located at Lettosuo in southern Finland (60.64°N, 23.96°E, 111 m above sea level, Figure 1). The annual mean temperature at this site is about 4.5°C, and the annual mean precipitation is about 548 mm ( Figure 2 The third site is the FI-Hyy site (Suni et al., 2003), a forest site locate at Hyytiälä in central Finland next to Lake Kuivajärvi (61.85°N, 24.29°E, 181 meters above sea level, as shown in Figure 1). This site experiences short summers, cold winters, and relatively low annual precipitation (the annual mean temperature is about 4.3°C, and the annual mean precipitation is about 604 mm, see Figure 2). The dominant species at this site is Scots pine (Pinus sylvestris). The observation height is 23.3 m. The simulation period over this site is from 2009 to 2013. The IGBP type for this site is also ENF.
The temperature differences between the soil and air are quite large at these three sites in their local spring and early summer, creating an ideal condition for studying the impact of low soil temperature stress on the RWU process ( Figure 3). With the observational data from these three sites, four sets of different numerical experiments are designed to study the effects of the three low soil temperature stress functions on model results. The experimental design is shown in Table 2. The atmospheric forcing data required for the experiments are all from the observation data sets at the three sites, which included air temperature, specific humidity, wind speed, surface pressure, precipitation, surface downward solar radiation, and downward longwave radiation. The time resolution is half an hour. Each set of simulations was run for 30 years by looping the forcing data, with spin-up employed to balance the initial model variables. Four global offline simulations designed similar as the single point experiments (S01, S02, S03, and S04) are also conducted to evaluate the global performance of CoLM with the three low soil temperature stress functions. These global simulations are run from 1985 to 2004, driven by the forcing data from the National Center for Atmospheric Research (Qian et al., 2006). The first 10 years are used as spinup and the last 10 years are used for analysis. The spatial resolution is T62 (192 longitude grid points and 94 latitude grid points). We use the FLUXNET-MTE (multitree ensemble) global land latent heat flux product (Jung et al., 2009)

Statistical Analysis
To evaluate the performance of the default and modified RWU schemes in CoLM, the root mean square error (RMSE) and the agreement index d (Willmott, 1981) between the observed data and simulated results are employed. They are calculated as follows, respectively: In these two functions, P i and O i are the simulated and observed fluxes at time step i in the CoLM. O refers to the average of the observed fluxes and n is the total number of observed data. The observed fluxes at the three FLUXNET sites used in this study are half-hourly, and they are used in the native time sampling. The value of RMSE is always greater than 0, and the closer it is to 0, the closer the simulation result is to the observation. The index d varies from 0 to 1, and a value of 1 indicates a perfect match between the simulation and observation, while 0 implies no agreement at all.
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Results
In this study, we compared the simulation results of the sensible heat flux (Q h ) and latent heat flux (Q le ) in the control run (S01) and three experimental runs (S02, S03, and S04, the definitions are in Table 2). Figure 4 illustrates the comparison between the observed and simulated diurnal mean fluxes of Q h and Q le at the US-Ha1 site. It can be found that in the local spring (March, April, and May (MAM)), compared with the observed data, the model results significantly underestimate the daytime sensible heat flux, especially at noon. After considering the effect of low temperature stress in soil on the RWU process in CoLM, the Q h simulation results from the three sensitivity experiments are improved, and the simulated values of daytime Q h are closer to the observation (Figure 4a). Regarding the simulation of Q le , the daytime Q le is significantly overestimated in the control experiment (S01), which is revised in the three sensitivity simulations (S02, S03, and S04) after introducing low soil temperature stress into the RWU process. Among the three sensitivity experiments, S02 (the double-exponential function) and S03 (the polynomial function) produce almost the same simulation results of Q le , while the Q le results of S04 (the single-exponential function) are relatively closer to the observed values (Figures 4a and 4b). According to a comparison between the observed and simulated annual mean diurnal Q h , the control run (S01) underestimates the daytime Q h (Figures 4c and 4d). However, the differences between the simulated and observed values are smaller than those in spring. Results for Q h from the three sensitivity runs are relatively closer to the observed values. The Q h results of S02 and S03 are almost the same and closer to the observed data at noon. The comparison between the observed and simulated annual mean diurnal Q le suggests that an overestimation of the daytime Q le exists in the control run. After the inclusion of the effect of low soil temperature stress in the three sensitivity experiments, the simulated Q le decreases significantly in the daytime (Figures 4c and 4d). The results of S02 and S03 are almost the same, and S04 yields values that are much closer to the observed Q le than the other sensitivity runs.
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At the FI-Let site and the FI-Hyy site, the differences in Q h and Q le between the observation data and four experimental simulations were relatively smaller than that of the US-Ha1 site (Figures 5 and 6). In the local spring and early summer (May, June, and July [MJJ]), the control run greatly underestimated the daytime Q h and overestimated the daytime Q le at these two sites. After considering low soil temperature stress in the model, the simulation results of Q h and Q le in MJJ are greatly improved, which is quite consistent with the observation data (Figures 5a, 5b, 6a, and 6b). Both the Q h and Q le results of the three experimental runs are relatively close to each other, among which the results of S04 are rather better. In the annual mean results, the deviation of the control run in simulating Q h and Q le is smaller than that in MJJ at these two sites. The model performance for reproducing the variations of half-hour Q h and Q le is also improved after considering the effect of low soil temperature stress at the FI-Let site and the FI-Hyy site (Figures 5c, 5d, 6c, and 6d).
These findings indicate that inclusion of the effect of low soil temperature stress on the RWU process can be beneficial to counteracting the overestimation of Q le by CoLM in regions with large air-soil temperature differences during the local spring and early summer.
When reproducing the seasonal variation of the annual mean energy fluxes at three FLUXNET sites, the modified RWU scheme mainly affects simulation results of the energy fluxes in the local spring and early summer. As can be seen from Figure 7, the control run indicates that the CoLM can well simulate the seasonal variation of Q h and Q le . However, in the results of the control run, the simulated Q h is lower than the observed values in the local spring and early summer at three FLUXNET sites. The simulated Q h in the control run during local spring and early summer at the US-Ha1 site is particularly biased (Figure 7a), while at the FI-Let site and the FI-Hyy site, the bias of Q h in the control run is relatively smaller (Figures 7c and 7e). By taking the effect of low soil temperature stress into consideration, the three experimental simulations correct the underestimation of Q h in the default model, especially at the US-Ha1 site where the simulated value of Q h increases the most after considering the low soil ZHU ET AL.
10.1029/2020MS002403 9 of 17  Table 2. temperature stress (Figure 7a). At the US-Ha1 site, similar results are gained by experiments S02 and S03, which are closer to the observed Q h in May, while in June and July, the Q h simulated by S02 and S03 is relatively higher than the observed values. The Q h given by S04 is slightly lower than that in S02 and S03 in May, while in June and July, the Q h in S04 is much closer to the observed values. In terms of Q le , the largest differences between the three experimental runs and the control run also appear in the local spring and summer. The control experiment S01 significantly overestimates the Q le values in the local spring and early summer, while the experimental runs S02 and S03 underestimate the Q le in midsummer. The simulation result of Q le by S04 is closest to the observation. At the FI-Let site, the differences of Q h and Q le between the three experimental runs and control run are relatively smaller, mainly in May, June, and July (Figures 7c and 7d). For the simulation of Q le , S04 performs fairly better than the other two experiments. At the FI-Hyy site, in May and June, the Q h results of S04 are relatively closer to the observational data than those of the other two sites. As to reproduce the Q le , S02 and S03 are relatively closer to the observation data than S04 during May and June. However, the S02 and S03 slightly overestimate the Q le and S04 performs slightly better than them in July (Figures 7e and 7f). This further indicates that incorporating the low soil temperature stress might help improve the capability of CoLM to simulate the surface energy fluxes in spring and summer at this site, and yet have limited effect in autumn and winter.  Table 2.
( Figure 8). The results of the three experimental runs indicate that this overestimation (underestimation) of Q le (Q h ) can be corrected by including low soil temperature stress in the parameterization scheme of the RWU process. At the US-Ha1 site, in the experiments S02 and S03, the simulation results underestimate the summer Q le in some years, while in S04, the biases are relatively not significant (Figures 8a and 8b). At the FI-Let site, the three experimental runs performed comparably and get much closer to the observational data than the control run over the whole study period (Figures 8c and 8d). As to the FI-Hyy site, the experiments S02 and S03 produce comparable results. These two runs show a relatively better Q h than S04 in some years, while the S04 run performs better in reproducing Q le during the local spring and early summer (Figures 8e and 8f). The above analysis suggests that among the three low soil temperature stress functions, the single-exponential function (S04) is relatively more suitable for improving the energy flux simulation in CoLM than the other two functions.
From the scatter diagram of the observed and simulated daily mean energy fluxes at the US-Ha1 site, it can be found that the slope of the linear regression trend line between the Q h simulation results of the control experiment (S01) and the observed Q h values is much less than 1 (Figure 9). It indicates that the Q h simulated by the default CoLM is lower than the in situ data. In the three sensitivity runs, the slope of the linear regression trend line is closer to 1, which means the deviation from the observed Q h in S01 is corrected to some extent (Figures 9a-9d). For Q le , the result from S01 is relatively higher than observations, and the slope of the linear regression trend line is greater than 1. However, the Q le simulated by S02 and S03 has lower values than the observed Q le , which corresponds to the linear regression trend lines with slopes below ZHU ET AL.

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11 of 17  Table 2. 1. The Q le simulation result by S04 is closer to the observations, and the slope of its linear regression trend line is the closest to 1 among the three sensitivity runs (Figures 9e-9h).
By comparing the RMSE and the agreement index b between the control run and the three sensitivity runs, we can further quantitatively evaluate how the energy flux simulation is improved by considering the effect of low soil temperature stress. As shown in Table 3, at the US-Ha1 site during MAM, the agreement index of Q h and Q le in the three experimental runs is higher than that of the control experiment, and the RMSE in the sensitivity runs is about 20% lower than that of the control run. The three experimental runs slightly differ in terms of simulation performance, and S03 performs relatively better in spring according to the statistical index. For the annual mean results of Q h and Q le , all three sensitivity runs also generate better performance than the control run. Among the four simulations, S04 yields the highest b values and the lowest RMSE values for both Q h and Q le , indicating that the S04 run has the best performance on reproducing energy fluxes at this site. At the FI-Let site, a similar conclusion can be drawn as at the US-Ha1 site, although the differences in the RMSE and agreement index between the control run and three experimental runs are relatively small. At the FI-Hyy site, in the local spring and early summer (MJJ), the RMSE values for Q h and Q le in the results of S02, S03, and S04 decrease by as much as 30% compared to the control run. The agreement index values increase about 0.1 in the three experiments considering the low soil temperature stress in MJJ. In the annual results, the degree of improvement in the statistical indexes in the three experimental runs is significantly reduced, which is similar to the other two sites. This comparison analysis indicates that by introducing the effect of low soil temperature stress into the RWU process, the modified CoLM can improve its capability for simulating the energy fluxes.
CoLM is a land surface model, which is designed for providing the boundary condition to a climate model. Therefore, it is necessary to verify what role these low soil temperature stress functions will have if they are used in global scale simulation and whether they will make the model results more accurate. To this end, we also conducted four groups of global offline experiments as the single point experiments (S01, S02, S03, and S04, see Table 2) to investigate the effect of low temperature soil stress on global latent heat flux simulation in CoLM. The simulation results suggest that the low soil temperature stress functions have little effect over tropical and subtropical regions. The default CoLM overestimates the Q le in many areas over middle and high latitudes in the boreal spring and summer (Figures 10a and 10b). Considering the low soil temperature stress in the model will reduce the bias of Q le in the model results, thus making the results closer to the FLUXNET-MTE data (Figures 10c-10h). However, during autumn and winter in the Northern Hemisphere, three low soil temperature stress functions have little effect on the simulation results of Q le (Figure 11). On the global scale, there is little difference in the simulation performance of the three low temperature stress functions. Concerning the regional results, in North America, the three low soil temperature stress functions help to reduce the overestimation of Q le in spring. In Siberia, from May to September, by introducing the low temperature soil stress, the Q le simulation results are improved and the overestimation of Q le in the simulation by S01 is reduced (Figure 12). The above findings show that the overestimation of Q le in the default CoLM could be reduced by further including the low temperature soil stress effect in many areas over middle and high latitudes such as North America, North Europe, and Siberia. While for other regions, this inclusion won't affect the effect of the original RWU scheme on the simulation. ZHU ET AL.

Discussion
The process of plant water uptake is affected and regulated by various factors, among which the low soil temperature stress is a vital one. Low soil temperature can reduce the activity of root cells, increase the viscosity coefficient of soil water, and reduce the water absorption rate of plant roots. In spring and early summer, there is a large gap between soil and atmospheric temperature, which can reduce the rate of RWU and transpiration of plants, hinder the dehydration, and affect the growth of plants. In most land surface models, the parameterization scheme of the RWU process is relatively simple, and the effect of low soil temperature stress on the RWU process is not taken into account, especially when the difference between the soil and air temperature is large. In this study, we modify the RWU scheme of CoLM by introducing three empirical functions to represent the effect of low soil temperature stress (Jansson & Karlberg, 2010), and evaluate the impact of low soil temperature stress on the energy flux simulation results in three forest sites.
In this study, we selected three FLUXNET sites (US-Ha1, FI-Let, and FI-Hyy) with noticeable seasonal variation as the study sites, and use local observational data to evaluate the effect of low soil temperature stress on the simulation of land surface energy fluxes by CoLM. The results show that the default CoLM has a good capability to simulate the variations of Q h and Q le on different time scales at the three FLUXNET sites. However, the control experiment suggests that, without considering the effect of low soil temperature stress, the RWU parameterization scheme in the default CoLM can lead to an underestimation of the daytime Q h and an overestimation of the daytime Q le . According to the annual mean results, the underestimation of Q h and overestimation of Q le mainly occur in the local spring and early summer. The inclusion of low soil temperature stress can help correct the underestimation of Q h and overestimation of Q le in the local spring and early summer and improve the capability of CoLM to simulate the diurnal and seasonal variations of the land surface energy fluxes at these study sites. The three low soil temperature stress functions adopted in this study can all improve the simulation results of energy fluxes. In the simulation of Q h and Q le , the results of S02 (the double-exponential function) and S03 (the polynomial function) are almost the same, which indicates that despite the different forms of these two functions, their effects on the simulation results are very similar. This is likely due to the empirical choice of parameters in these two functions, as particular combinations of parameters can make different forms of functions have similar effects. On the other side, the Q h and Q le results of S04 (the single-exponential function) are fairly better, and the underestimation of midsummer Q le found in S02 and S03 does not appear in the results of S04. This function and the parameters in it are more suitable for improving the model performance at these three forest sites. In the global offline simulations, the three low soil temperature stress functions are also added to CoLM. Consequently, the model shows more accurate latent heat flux over North America, North Europe, and Siberia, and the overestimation of Q le at these regions is revised.
Low soil temperature stress is widespread over midlatitude and high latitudes, and its impact on the RWU process cannot be ignored. Improving the parameterization scheme of the RWU process in land surface models by taking the effect of low soil temperature stress into consideration helps to improve the simulation skill of the RWU, canopy transpiration, and energy fluxes in land surface models. The land surface models are also a part of earth system models, and thus their improvement can contribute to enhance confidence ZHU ET AL. The indexes of experiments (S01, S02, S03, and S04) are defined in Table 2. in the simulation of global climate change. This study demonstrates that the low soil temperature stress can significantly impact the simulation of the surface energy fluxes, which is worthy of more detailed research and evaluation in future work.
The uncertainty caused by various parameterization schemes in land surface models is pervasive. In this study, the parameters of several low soil temperature stress functions are obtained empirically based on some observed data, which brings uncertainties to the evaluation of model results. However, the results of this study also show that these empirical parameters are effective for characterizing the effects of low soil temperature stress in land surface models. When this set of parameters is applied to global simulations, it also shows a good   Table 2. ZHU ET AL.

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15 of 17 applicability among different vegetation types. This may be due to the fact that low soil temperature stress mainly occurs in middle and high latitudes, which limits the areas and vegetation types (mainly ENF and DBF) where low soil temperature stress functions may play a role. In future work, it is necessary to further optimize these empirical parameters, but this requires a large number of field observational data and a large number of model simulation testing work, because the observation of plant physiology and ecology is more difficult, and the representativeness of field observation data is also limited. However, with the increasing amounts of satellite remote sensing data and field observational data, more data can be used for evaluation and optimization of land surface parameterization schemes. Based on further evaluation and optimization, the function of low soil temperature stress can be more accurate, and the parameters used can better reflect the characteristics of local vegetation.
The RWU process is affected by several factors. In addition to the low soil temperature stress mentioned in this study, soil salinity stress, plant root distribution and density, and root age and growth are all important factors. The current RWU scheme in land surface models is still relatively simple, and the comprehensive effects of various factors on RWU process are not considered. If a completer and more accurate parameterization scheme of the RWU process can be proposed in future work, considering the role of multiple influencing factors, it will be bound to contribute greatly to the efficiency enhancement of land surface models. The RWU process of plants is also considered as closely related to the change of soil moisture, and soil moisture has a strong persistence and is a key bridge in the land-atmosphere interaction. Therefore, the improvement of the RWU scheme can be expected to enhance the ability of models to simulate soil moisture and, subsequently, the overall reliability of land surface models.

Conclusions
In this study, three low soil temperature stress functions are incorporated into the CoLM. The results of the modified model were verified by data from three FLUXNET sites and FLUXNET-MTE data, and the following conclusions could be drawn: 1. Considering low soil temperature stress in CoLM effectively reduce the simulation bias of latent and sensible heat fluxes in local spring and early summer at three FLUXNET sites. The three empirical functions introduced in this study to describe low soil temperature stress all play significant roles in reducing the simulation bias, with relatively better performance given by the single-exponential function (eT_SE) 2. In the global offline simulation results, it can be found that low soil temperature stress mainly affects the simulated latent heat flux over the middle and high latitudes such as North America, North Europe, and Siberia during the boreal summer. Considering low soil temperature stress in CoLM will be helpful for restraining the overestimation of latent heat fluxes over these areas

Data Availability Statement
The FLUXNET 2015 data sets are available at https://fluxnet.org/. The authors thank J. W. Munger, the PI of the US-Ha1 site, Barbara Godzik, Timo Vesala, Eero Nikinmaa, and Janne Levula, the PIs of the FI-Hyy site, Annalea Lohila, Mika Korkiakoski, and Tuomas Laurila, the PIs of the FI-Let site for providing the data openly. The code and the data sets of the CoLM can be downloaded from http://globalchange.bnu.edu.cn/ research/. The forcing data for the global offline simulations can be achieved at https://svn-ccsm-inputdata. cgd.ucar.edu/trunk/inputdata. The authors would like to express gratitude to the related researchers and institutes for providing the data.  Table 2.