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The default vertical discretization uses 25 soil layers with a depth of 8.5 m in CLM5.0. Recent studies have indicated the need to have a deeper soil column in LSMs to properly capture changes in freeze-thaw cycles and active-layer dynamics in permafrost areas (Alexeev et al., 2007; Lawrence et al., 2012). However, a deeper soil column implies larger soil hydraulic memory and, more importantly, thermal memory that require proper initialization to be able to capture the evolution of past, current, and future changes (Elshamy et al., 2020). The wrong setting may increase the deviation of the simulation, as little is known about the soil hydrothermal state below 2.4 m without observed data. By testing different soil layers in CLM5.0, we found that for the simulation of permafrost on the XDT site, the simulated ST and SM were closer to the observation by selecting 15 soil layers with a depth of 3.5 m in CLM5.0. Meanwhile, this setting can be adapted to simulations of permafrost at this site since the average active layer thickness of the XDT site was about 1.5 m over the most recent 10 years (Liu et al., 2021a). Therefore, in this paper, the vertical discretization used 15 soil layers with a depth of 3.5 m.
We designed six simulation experiments in this study (Table 1). TEST1 was run by the default initial schemes of ST, SLW, and SI, while TEST2 to TEST4 was run by modified initial schemes of ST, SLW, and SI. As shown in Table 1, the initial ST was set as the default value of CLM5.0 (274 K or 0.85°C) in TEST1 and it was set as 272.3 K (–0.85°C) in TEST2. In these two experiments, the volumetric soil water content
$ {\theta }_{{\mathrm{i}}} $ was set as the default value of CLM5.0 (0.15 m3 m−3) and the mass of SLW and SI were initialized by Eqs. (1) and (2). Since the initial ST was higher than the freezing temperature in TEST1, the initial mass of SI was zero and all soil water was SLW; in TEST2, since the initial ST was lower than the freezing temperature, the initial mass of SLW is zero and all soil water was SI. In TEST3, the initial ST was set as 272.3 K (–0.85°C), and the mass of SLW and SI were initialized by the modified soil conditions (see Eqs. (3) and (4). In TEST4, in the active layers (1st–7th layer for XDT), the initial ST was set as 274 K (0.85°C), while in the permafrost layers (8th–10th layer for XDT), the initial ST was set as 272.3 K (–0.85°C). The mass of SLW and SI were also calculated by Eqs. (3) and (4) in TEST4. It can be concluded from the calculation of Eq. (5) that in TEST3 and TEST4, the maximum liquid water content at 272.3 K can reach 0.17 m3 m−3 for the XDT station. Here, we set the initial volumetric soil water content,$ {\theta }_{{\mathrm{i}}}, $ to 0.25 m3 m−3 in TEST3 and TEST4. From TEST1 to TEST4, the model was run with 14 months of forcing data (from 1 July 2015 to 31 August 2016). In practice, we found CLM4.5 reached a state of rough equilibrium in the first two months when it was forced by observational data in the seasonally frozen soil on the TP (Luo et al., 2017). In this paper, the simulations of the last 12 months (1 September 2015 to 31 August 2016) for these four experiments were compared with the observations (equal to a two-month spin-up in the model).Experiment Initial soil temperature (ST) design Initial soil moisture (SM) design TEST1 Default initial ST (274 K) Default initial volumetric soil water content (0.15 m3 m−3), the mass of SLW and SI by Eqs. (1) and (2) TEST2 Modified initial ST (272.3 K) Default initial volumetric soil water content (0.15 m3 m−3), the mass of SLW and SI by Eqs. (1) and (2) TEST3 Modified initial ST (272.3 K) Modified initial volumetric soil water content (0.25 m3 m−3), the mass of SLW and SI by Eqs. (3) and (4) TEST4 Default initial ST (274 K) in the active layers (1st–7th layer), Modified initial ST (272.3 K) in the permafrost layers (8th–10th) Modified initial volumetric soil water content (0.25 m3 m−3), the mass of SLW and SI by Eqs. (3) and (4) TEST1-SP The same as TEST1, but for 100 years of spin-up TEST2-SP The same as TEST2, but for 100 years of spin-up Table 1. Design of the experiments.
In another two experiments (TEST1-SP and TEST2-SP), the model was designed for long-term spin-up. A study showed that LSMs need such a long term to achieve strict convergence of ST and SM (Ji et al., 2022). Here, we designed 100-year spin-up experiments. The forcing data of spin-up experiments which usually comes from gridded datasets or observed data has a certain effect on the simulation results. Despite many available reanalyses of gridded datasets that can provide long-term forcing data, most of them are substantially biased on the TP (Zhang et al., 2020; Zhou et al., 2021). Meanwhile, it is very difficult to obtain continuous long-term observational data as the long-term forcing data in the permafrost region on the TP. As a compromise, the long-term spin-up simulation can be driven by spin-up cycling with time and correspond to an average meteorological condition. There are three common spin-up cycling schemes for generating the forcing 1) observations from a single year, 2) observations from multiple years or their averages, and 3) all available observations (Ji et al., 2022; Li et al., 2023). Here, we use a single-year cycling scheme. In TEST1-SP and TEST2-SP, the model was repeatedly run for over 100 years by forcing data from one year (1 July 2015 to 30 June 2016), then the simulation continued for 14 months using 14 months of forcing data (from 1 July 2015 to 31 August 2016). Also, the simulations of the last 12 months (1 September 2015, to 31 August 2016) in TEST1-SP and TEST2-SP were used for comparison with the observations as well as the simulated results of TEST1 to TEST4. In short, the initial ST and SM conditions in TEST1-SP and TEST2-SP were the same as TEST1 and TEST2, but for 100 years of spin-up using one year of forcing data (1 July 2015 to 30 June 2016).
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In this paper, the active layer of permafrost was divided into two periods, the freezing period and the thawing period. To avoid the influence of random fluctuations on ST, the freezing and thawing onsets were determined based on the average of the daily STs taken for five consecutive days; they were below and above 0°C, respectively, and varied depending on the soil layer (Guo and Wang, 2014; Yang et al., 2021).
The simulation results from six tests were compared with the observed data using the root-mean-square error (RMSE), mean bias error (MBE), and the Nash–Sutcliffe efficiency (NSE). The methods used to calculate RMSE, MBE, and NSE are given as follows:
where
$ N $ is the time series length,$ {M}_{i}(i=\mathrm{1,2},3,\cdots ,N) $ is the simulation,$ {O}_{i}(i=\mathrm{1,2},3,\cdots ,N) $ is the observation, and$ \overline{O} $ represents the average of observations. Normally, MBE (smaller values are desireable) has a minimum value of zero under the hypothetical situation that the model is capable of perfect (long-term) simulations of the system. An NSE = 1 indicates a perfect correspondence between simulations and observations; an NSE = 0 indicates that the model simulations have the same explanatory power as the mean of the observations; and an NSE < 0 indicates that the model is a worse predictor than the mean of the observations (Schaefli and Gupta, 2007; Knoben et al., 2019). -
The equilibrium conditions in TEST1-SP and TEST2-SP were defined as follows. If ST (year N+1) minus ST (year N) is within 1°C and SLW (year N+1) minus SLW (year N) is within of 0.1 m3 m−3, the soil is said to reach a rough equilibrium condition. If ST (year N+1) minus ST (year N) is within 0.1°C and SLW (year N+1) minus SLW (year N) is within of 0.01 m3 m−3, the soil is said to reach a strict equilibrium condition. Figure 2 shows the convergence in ST and SLW during the first 10 years of 100-year spin-up time for 10 soil layers for TEST1-SP and TEST2-SP. We found that the equilibrium conditions were established relatively quickly in these two long-term spin-up experiments. As shown in Figs. 2a and b in TEST1-SP, the equilibrium conditions of ST and SLW were established in the second year for all soil layers regardless of whether the constraint of a rough equilibrium condition or a strict equilibrium condition is used. As shown in Figs. 2c and d, given a rough equilibrium condition in TEST2-SP, the equilibrium conditions of ST and SLW for all soil layers were also quickly established in the second year; however, there were slight differences when given a strict equilibrium condition; ST needed 3 years and SLW needed 7 years. From Figs. 2a and c, though ST reached the strict threshold of 0.1°C in the second or third year, it did not change consistently. As shown in Fig. 2a, after 6 years of spin-up, the ST in layers 1 to 6 was not stable, and ST (year N+1) minus ST (year N) was larger than the threshold of 0.1°C in some years. The possible reasons for this instability are that the summer of 2016 was the end of the spin-up cycle, and it was used to reinitialize the model in the summer of 2015. This approach makes the whole study highly dependent on the climate within this year. But ST has a reasonable fluctuation within 1°C until the end of the 100-year spin-up. To summarize, in both experiments, CLM5.0 only took one year to reach a rough equilibrium in ST and SLW at the XDT site.
Figure 2. Convergence in soil temperature (a and c) (ST, units: °C) and soil liquid water (b and d) (SLW, units: m3 m−3) at 10 soil layers in TEST1-SP (a and b) and TEST2-SP (c and d).
Table 2 shows the values of ST, SLW, and SI after 100 years of spin-up in the TEST1-SP and TEST2-SP as the initialization of the simulation. It can be seen that after the CLM5.0 reaches equilibrium, the difference between ST, SLW and SI at each layer in these two experiments was really small. Regardless of whether the simulation started with an above-freezing temperature of 0.85°C or a below-freezing temperature of –0.85°C, after 100 years of spin-up, the ST of 8 layers was higher than the freezing temperature at the initialization of the simulation, and the ST in the deepest two layers was equal to the freezing temperature which was different from the actual situation of permafrost layers. After reaching equilibrium, the difference between the ST at each layer was really small, while the SLW and SI at each layer were almost the same in these two spin-up experiments. Since the initialization ST was higher than the freezing temperature from the surface to 140 cm, the initial SI was zero for these layers. As can be seen from the above, the initial fields of ST, SLW, and SI obtained by the long-term spin-up method was relatively limited at the XDT site, especially in the permafrost layers.
Layer Depth (m) ST (°C) SLW (m3 m−3) SI (m3 m−3) TEST1-SP TEST2-SP TEST1-SP TEST2-SP TEST1-SP TEST2-SP 1 0.0175 7.60 7.64 0.10 0.10 0.00 0.00 2 0.0451 9.11 9.17 0.19 0.19 0.00 0.00 3 0.0906 10.52 10.59 0.21 0.21 0.00 0.00 4 0.1655 11.66 11.75 0.22 0.22 0.00 0.00 5 0.2891 11.17 11.28 0.15 0.15 0.00 0.00 6 0.4929 8.68 8.82 0.14 0.14 0.00 0.00 7 0.8289 6.16 6.34 0.11 0.11 0.00 0.00 8 1.3828 3.42 3.60 0.08 0.07 0.00 0.00 9 2.2961 0.00 0.00 0.07 0.07 0.01 0.01 10 3.8019 0.00 0.00 0.08 0.07 0.03 0.03 Table 2. States of three variables (ST: Soil Temperature; SLW: Soil Liquid Water Content; SI: Soil Ice) for simulated statements for TEST1-SP and TEST2-SP as the initialization of the simulation.
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Figure 3 and Table 3 show a comparison of the observed and six experimental results of ST in different soil layers at the XDT site. It can be seen from the observation (red line in Fig. 3) that in summer and autumn, the STs at 0 to 120 cm were higher than 0°C (the shaded areas in Figs. 3a–d), and the soil at these depths were the active layers of permafrost. The STs at 120 cm to 240 cm (Figs. 3e–h) were below 0°C for the whole year, which represents the permafrost layers. The default CLM5.0 simulation (TEST1, black solid line in Fig. 3) greatly amplified the annual amplitude of ST, especially in the active layers, that is there was a significant underestimation during the freezing period, and conversely a significant overestimation during the thawing period in the active layers. This is also a common problem in the CLM4.5 and CLM5.0 simulations regarding the seasonally frozen ground and permafrost on the TP (Fang et al., 2016; Luo et al., 2017; Deng et al., 2020; Ma et al., 2023). In the deep layers, the STs at 140 to 240 cm were significantly higher than the observation in the whole year. The RMSE of ST in these eight layers was between 2.68°C and 3.99°C. The MBE increased with depth, from 0.85°C at 5 cm to 2.42°C at 240 cm while the NSE decreased with depth, from 0.74 in the topsoil to –12.43 in the deep soil. It can be inferred through the MBE and NSE values, that the simulation effect of ST gradually decreased with increasing depth, in TEST1.
Figure 3. The observed and simulated daily soil temperature (ST, units: °C) at (a) 5 cm, (b) 20 cm, (c) 40 cm, (d) 80 cm, (e) 120 cm, (f) 140 cm, (g) 180 cm, and (h) 240 cm at the XDT site. Shaded areas in the figures denote the thawing period on observed soil temperature.
Depth/cm Statistical variable TEST1 TEST2 TEST3 TEST4 TEST1-SP TEST2-SP 5 RMSE/ °C 3.20 3.14 2.70 2.73 3.39 3.42 MBE/ °C 0.85 0.64 0.46 0.49 0.79 0.79 NSE 0.74 0.75 0.81 0.81 0.70 0.70 20 RMSE/ °C 3.57 3.42 2.95 2.99 3.91 3.96 MBE/ °C 1.35 0.91 0.59 0.67 1.24 1.24 NSE 0.49 0.53 0.65 0.64 0.38 0.37 40 RMSE/ °C 3.99 3.70 3.35 3.38 4.46 4.51 MBE/ °C 1.75 1.10 0.67 0.79 1.60 1.60 NSE –0.12 0.04 0.21 0.20 –0.40 –0.43 80 RMSE/ °C 3.23 2.36 2.12 2.10 3.58 3.64 MBE/ °C 2.14 0.95 0.40 0.62 1.95 1.95 NSE –0.50 0.20 0.36 0.37 –0.84 –0.91 120 RMSE/ °C 3.55 2.45 2.29 2.10 3.83 3.89 MBE/ °C 2.23 0.82 0.24 0.50 2.02 2.01 NSE –4.24 –1.49 –1.17 –0.84 –5.08 –5.28 140 RMSE/ °C 3.15 1.73 1.68 1.34 3.18 3.22 MBE/ °C 2.30 0.59 0.01 0.31 2.01 2.00 NSE –4.86 –0.76 –0.68 –0.06 –4.98 –5.12 180 RMSE/ °C 2.93 1.13 1.29 0.79 2.70 2.72 MBE/ °C 2.36 0.36 –0.23 0.11 2.01 1.99 NSE –7.23 –0.23 –0.59 0.41 –6.02 –6.10 240 RMSE/ °C 2.68 0.47 0.99 0.61 2.16 2.14 MBE/ °C 2.42 0.19 –0.21 0.10 1.99 1.97 NSE –12.43 0.59 –0.83 0.31 –7.68 –7.55 Active Layer Avg. RMSE/ °C 3.50 3.16 2.78 2.80 3.84 3.88 MBE/ °C 1.52 0.90 0.53 0.64 1.40 1.40 NSE 0.15 0.38 0.51 0.50 –0.04 –0.07 Permafrost Avg. RMSE/ °C 3.08 1.44 1.56 1.21 2.97 2.99 MBE/ °C 2.33 0.49 –0.05 0.25 2.01 1.99 NSE –7.19 –0.47 –0.82 –0.05 –5.94 –6.01 Table 3. Statistical results of simulated and observed soil temperature (ST) in the six experiments.
Compared with TEST1, the annual amplitude of ST in TEST2 (orange solid line in Fig. 3) was smaller and it was closer to the observed values, especially in four permafrost layers. As shown in Table 3, the RMSE (between 0.47°C and 3.70°C) and MBE (between 0.19°C and 1.10°C) of each layer were all smaller than that in TEST1 while the NSE (between 0.75 and –1.49) of each layer were all higher than that in TEST1. In the four permafrost layers, as soil depth increased, the RMSE and MBE decreased while the NSE increased, which was quite different from TEST1. The simulation of ST showed significant improvement, with the average RMSE and MBE reduced to only 1.44°C and 0.49°C, respectively, in these four permafrost layers. In contrast, these values were as high as 3.08°C and 2.33°C in TEST1. The resultant ST in the permafrost layers of TEST2 were significantly better than those in TEST1, evidenced by a reduction of RMSE and MBE by 53% and 79%, respectively, indicating that the simulated ST of permafrost is more accurate when the initial ST is below freezing temperature. This is because when the initial ST is below freezing temperature (–0.85°C), according to the default initial soil conditions (Eqs. (1) and (2)), all soil water becomes ice, which is more consistent with the ice-rich characteristics of permafrost. The results presented in Table 3 demonstrate that improving the simulation of soil hydrothermal processes in permafrost layers also has a significant impact on the accuracy of simulating soil hydrothermal characteristics in active layers. In TEST2, compared to TEST1, there was a reduction in both RMSE and MBE for ST, while NSE increased in the active layers.
The simulated results of ST in TEST3 (purple solid line in Fig. 3) and TEST4 (blue solid line in Fig. 3) were very similar. Compared with TEST1 and TEST2, more substantial improvements occurred in TEST3 and TEST4 both in active layers and permafrost layers. As shown in Table 3, TEST3 and TEST4 exhibited significantly lower RMSE and MBE values, along with higher NSE values in seven soil layers. In the four active layers, TEST3 had the smallest RMSE and MBE with an average of 2.78°C and 0.53°C which is consistent with a reduction of 21% and 61% compared to TEST1 and it had the largest NSE with an average of 0.51. In four permafrost layers, TEST4 had the smallest RMSE with an average of 1.21°C which was consistent with a reduction of 62% compared to TEST1 and it also had the largest NSE which was close to 0. In TEST4, the NSE of ST in six layers was higher than that in TEST3. It can be seen from the above analysis that modification of initial SM schemes (Eqs. (3) and (4)) will greatly impact the ST simulation. Due to the more reasonable distribution of the initial SLW and SI, the soil heat transfer was also closer to the actual state, which greatly improved the simulation of ST.
Since the initialization of ST and SM by long-term spin-up were very close (Table 2), the simulated ST in TEST1-SP (black dotted line in Fig. 3) and TEST2-SP (orange dotted line in Fig. 3) were basically consistent. Compared with TEST2, TEST3, and TEST4, the simulated results in these two long-term spin-up experiments were relatively limited. The MBE of ST was between 0.79°C and 2.02°C, and it was slightly smaller than that in TEST1 but much larger than that in TEST2, TEST3, and TEST4 in all eight layers. The NSE of each soil layer in these two long-term spin-up experiments was also smaller than that in the simulations of the three modified initial schemes.
Overall, in the active layers, the default CLM5.0 simulation greatly underestimated ST during the freezing period while overestimating it during the thawing period. In the permafrost layers, the default CLM5.0 overestimated ST for the entire year. When modified, the initial ST and SM schemes can effectively reduce the bias of ST. This improvement has proven to be significantly more profound than long-term spin-up methods. The simulated ST of permafrost was more accurate when the initial ST is sub-freezing. Modified initial SM schemes provide a reasonable distribution of the initial SLW and SI, which greatly improves the simulation of ST, especially in the four permafrost layers. On average, the RMSE was reduced from 3.29°C in TEST1 to 2.30°C in TEST2 to 2.17°C in TEST2 to 2.00°C in TEST4; MBE was reduced from 1.92°C in TEST1 to 0.70°C in TEST2 to 0.24°C in TEST3 to 0.45°C in TEST4. Meanwhile, the average NSEs in TEST2, TEST3, and TEST4 were closer to zero, especially in TEST4, within which it was 0.23, while it was only about –3 in the default and two long-term spin-up experiments. Compared to the default CLM5.0 simulation, the TEST2, TEST3, and TEST4 experiments improved the ST simulation, effectively reducing the average RMSE by 30%, 34%, and 39%. Compared to the results of TEST1, the average MBE was reduced by 64%, 88%, and 77% in the TEST2, TEST3 and TEST4 experiments, respectively, whereas it only experienced an 11% reduction in both the TEST1-SP and TEST2-SP experiments.
Figure 4 shows the spatial and temporal variation in the daily mean ST based on observations and simulations from TEST1 to TEST4. From the observations (Fig. 4a), the active layer at the XDT site began to thaw in early April and thawed completely in December, with a maximum thawing depth of approximately 130 cm. Before the active layer soil thawed completely, the surface soil entered a new freeze-thaw cycle in early November. At the depth of 130 cm to 320 cm in permafrost, the annual variation of ST was small, between –4°C and 0°C. As can be seen from Fig. 4b, TEST1 could not adequately simulate the characteristics of ST in permafrost. The results of TEST1 showed that the characteristics of seasonally frozen ground, and the ST below 300 cm were greater than 0°C for the whole year. The ST profiles in TEST1-SP and TEST2-SP were very similar to the results of TEST1 and also showed the characteristics of seasonally frozen ground (figures not shown). After modifying the initial ST as –0.85°C (TEST2), the model could simulate the characteristics of permafrost, but the simulated active layer thickness (about 280 cm) was obviously larger than the observation in 2016. After further modification of the initial SLW and SI conditions (TEST3), the model could simulate the characteristics of permafrost and also significantly improve the thickness of the active layer (about 170 cm), and the annual variation of the ST further decreases, which was more consistent with the observed value. In the TEST4 experiment, ST in permafrost was further increased compared with the TEST3 experiment and was closer to the observed value.
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Figure 5 shows the simulated and observed daily SLW in different soil layers at the XDT site. It can be seen from the observation (red solid line) that the SLW in the shallowest 20 cm corresponded well with precipitation, while it had a great relationship with the soil freeze-thaw processes in the soil below 40 cm. In the default CLM5.0 simulation (black solid line), the initial SLW between 20 cm and 120 cm was much lower than in the observation, which allowed for a substantial underestimation of SLW during the thawing period in active layers. The SLW between 5 cm and 140 cm decreased earlier than the observed values during the freezing period while increasing earlier than the observed values during the thawing period. The main reason was that the ST in the active layers in TEST1 was lower than the observed value during the freezing period, so the soil froze earlier; while the ST was higher during the thawing period, so it thawed earlier. The RMSE ranged from 0.032 m3 m−3 to 0.162 m3 m−3 while the MBE ranged from –0.098 m3 m−3 to 0.050 m3 m−3. The results of SLW in active layers were generally better than those in permafrost layers, with a smaller RMSE and greater NSE. The simulated results of SLW at 5 cm and 140 cm were better than other layers, with NSEs greater than 0.32. However, the simulated result at 240 cm was poor, with an NSE of up to –46.72. The simulations of the other five soil layers had the same explanatory power as the mean of the observations.
Figure 5. The observed and simulated daily soil liquid water (SLW, units: m3 m−3) at (a) 5 cm, (b) 20 cm, (c) 40 cm, (d) 80 cm, (e) 120 cm, (f) 140 cm, (g) 180 cm, and (h) 240 cm at the XDT site. The blue bar is observed daily precipitation (units: mm).
In the active layer, the results in TEST2 (orange solid line) were generally consistent with those in TEST1, while in the permafrost layers, the results in TEST2 were better than those in TEST1, with a smaller RMSE and MBE, and a larger NSE, especially at 240 cm. Compared with TEST1, the average RMSE and MBE of SLW in four permafrost layers were reduced by 20% and 21%, respectively. The results in TEST2 also indicated that the simulated SLW of permafrost is more accurate when the initial ST is below freezing.
From Table 4, TEST3 and TEST4 provide a better fit for the observed SLW in all eight layers compared to the results of TEST1 and TEST2. The SLW in TEST3 and TEST4 was larger than that in TEST1 and TEST2 during the thawing period in the active layers, effectively reducing the dry biases of SLW. On average, in these two modified experiments, the RMSE of these four active layers was 0.0121 m3 m−3 and 0.0122 m3 m−3 respectively, while the average MBEs were –0.028 m3 m−3 and –0.029 m3 m−3, representing a reduction of nearly 10% compared to the default experiment. Meanwhile, the average NSE in the active layers of these two experiments reached 0.26, which was higher than the results in TEST1 (0.09) and TEST2 (0.06). Moreover, the first date of soil thawing in active layers occurred later than those in TEST1 and TEST2, aligning more closely with the observation. In the four permafrost layers, TEST3 and TEST4 still demonstrated a simulation performance that was better than TEST1, with average RMSEs of 0.052 m3 m−3 and 0.054 m3 m−3, respectively, consistent with a reduction of approximately 15%. Additionally, the average MBE for TEST3 and TEST4 were –0.020 m3 m−3 and –0.011 m3 m−3, indicating a decrease of around 30%.
Depth/cm Statistical variable TEST1 TEST2 TEST3 TEST4 TEST1-SP TEST2-SP 5 RMSE/ m3 m−3 0.097 0.097 0.102 0.102 0.097 0.096 MBE/ m3 m−3 0.050 0.049 0.063 0.062 0.048 0.048 NSE 0.31 0.32 0.25 0.24 0.32 0.32 20 RMSE/ m3 m−3 0.161 0.164 0.139 0.140 0.164 0.164 MBE/ m3 m−3 –0.083 –0.087 –0.056 –0.057 –0.087 –0.087 NSE 0.06 0.03 0.30 0.29 0.03 0.02 40 RMSE/ m3 m−3 0.122 0.127 0.098 0.100 0.128 0.128 MBE/ m3 m−3 –0.061 –0.067 –0.033 –0.034 –0.069 –0.069 NSE 0.09 0.01 0.41 0.39 0.00 -0.01 80 RMSE/ m3 m−3 0.162 0.165 0.143 0.146 0.182 0.183 MBE/ m3 m−3 –0.098 –0.103 –0.086 –0.088 –0.118 –0.119 NSE –0.10 –0.13 0.14 0.10 –0.38 –0.40 120 RMSE/ m3 m−3 0.100 0.100 0.090 0.093 0.116 0.117 MBE/ m3 m−3 –0.052 –0.054 –0.047 –0.049 –0.070 –0.072 NSE 0.10 0.09 0.26 0.22 –0.22 –0.25 140 RMSE/ m3 m−3 0.032 0.037 0.042 0.035 0.043 0.044 MBE/ m3 m−3 –0.013 –0.022 –0.022 –0.012 –0.032 –0.034 NSE 0.42 0.22 –0.02 0.30 -0.06 -0.13 180 RMSE/ m3 m−3 0.048 0.040 0.044 0.057 0.030 0.029 MBE/ m3 m−3 0.037 0.022 0.013 0.036 0.016 0.015 NSE –0.95 –0.35 –0.64 –1.77 0.22 0.26 240 RMSE/ m3 m−3 0.149 0.029 0.032 0.030 0.066 0.062 MBE/ m3 m−3 0.148 -0.019 –0.024 –0.021 0.065 0.060 NSE –46.72 –0.85 –1.23 –1.00 –8.42 –7.19 Active Layer Ave RMSE/ m3 m−3 0.135 0.138 0.121 0.122 0.143 0.143 MBE/ m3 m−3 –0.048 –0.052 –0.028 –0.029 –0.056 –0.057 NSE 0.09 0.06 0.27 0.26 –0.01 –0.01 Permafrost Ave RMSE/ m3 m−3 0.082 0.051 0.052 0.054 0.064 0.063 MBE/ m3 m−3 0.030 –0.018 –0.020 –0.011 –0.005 –0.008 NSE –11.79 –0.22 –0.41 –0.56 –2.12 –1.83 Table 4. Statistical results of simulated and observed soil liquid water (SLW) in six experiments.
The simulated SLW in TEST1-SP (black dotted line) and TEST2-SP (orange dotted line) were also consistent since the initialization of ST and SM using a long-term spin-up are very close (Table 4). Compared with TEST2, TEST3, and TEST4, the simulated results in these two long-term spin-up experiments were relatively limited. During the thawing period, the simulated SLW was found to be even lower than the results from TEST1, resulting in a larger RMSE and a smaller NSE as shown in Table 4.
In general, the default CLM5.0 simulation greatly dried the SLW during the thawing period at the XDT site. The SLW simulation was significantly improved and the average RMSE was effectively reduced by 13%, 21%, and 19% in the TEST2, TEST3, and TEST4 experiments compared to the default CLM5.0 simulation. However, only a 5% reduction was found in the TEST1-SP and TEST2-SP experiments. Meanwhile, the average NSEs in TEST2, TEST3, and TEST4 were also closer to zero, especially in TEST3, which was –0.07. In contrast, the NSE was only about –5.85 in the default experiment and –1 in the two long-term spin-up experiments. Overall, TEST2 significantly improved the SLW in the permafrost, while both TEST3 and TEST4 showed significant improvements in SLW throughout the whole soil column.
From the spatial-temporal variation of observed SLW (Fig. 6a), it can be seen that during summer and autumn, there is an increase in SLW within the active layers due to permafrost thawing, reaching a maximum value of 0.35 m3 m−3. In the vertical direction, two high-value centers were observed at approximately 20 cm and 80 cm, respectively. Below 120 cm, SLW drastically decreased due to the reduced permeability of ice-rich soils near the permafrost table that impeded SLW migration.
Figure 6. The spatial-temporal variation in the daily soil liquid water (SLW, units: m3 m−3) for the (a) observation, (b) TEST1, (c) TEST2, (d) TEST3, and (e) TEST4.
In TEST1, the initial value of SLW throughout the profile was evidently underestimated, resulting in lower simulated SLW levels during the study period compared to observations across the entire profile (Fig. 6b). Upon modifying the initial ST to –0.85 °C (TEST2), a large dry bias also existed throughout the entire profile. After further modification of the initial SLW and SI schemes (TEST3 and TEST4), the simulated SLW in the active layer increased during the thawing period, thereby demonstrating that the model was capable of accurately simulating the spatial distribution characteristics of two prominent high-value centers of SLW in 2016. The long-term memory of SLW significantly impacted the ST simulation. During the thawing period, TEST3 and TEST4 had more SLW in the active layer compared to TEST1 and TEST2, resulting in a lower ST from 5 cm to 180 cm (Fig. 3).
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The simulated spatial-temporal variation of daily SI is presented in Fig. 7. In TEST1 (Fig. 7a), the model exhibited limitations in accurately simulating year-round permafrost with continuous ice, indicating a constraint on its simulation capability. The results of TEST2 (Fig. 7b), TEST3 (Fig. 7c), and TEST4 (Fig. 7d) differed significantly from TEST1. In TEST2, SI was consistently present in the soil below 1.1 m throughout the entire year, while in TEST3 and TEST4, SI was found at depths below 1.3 m and 1.4 m, respectively, for the entire year duration of the study. The high center (SI ≥ 0.10 m3 m−3) in TEST1 was located at a depth of 1.5–2.0 m in the soil from February 2016 to July 2016, while the high center (SI ≥ 0.13 m3 m−3) in TEST2 was situated at a depth of deeper than 1.5 m from February 2016 to June 2016. The SI values in TEST3 and TEST4 were higher compared to those in TEST1 and TEST2. The profiles of TEST3 and TEST4 exhibited two prominent centers of SI. The first center with SI ≥ 0.10 m3 m−3 was located in the active layer, while the second center with SI ≥ 0.24 m3 m−3 was found in the permafrost layer. In TEST2, it is evident that the adjustment of the initial ST to –0.85°C resulted in the detection of multi-year ice within the permafrost soil layers at various depths. In TEST3 and TEST4, subsequent modifications to the initial SLW and SI schemes led to a further increase in SI throughout the entire soil column. SI also has a great influence on the ST simulation due to its long-term memory. Throughout the simulation period, three modified experiments demonstrated higher SI values across the entire soil column, particularly in the permafrost layers, and resulted in a reduced annual amplitude of ST fluctuations in TEST2, TEST3, and TEST4 (Figs. 3, 4). The SI profiles in TEST1-SP and TEST2-SP were similar to the results of TEST1, and they also showed the characteristic features associated with seasonally frozen ground (figures not shown).
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Simulated differences in topsoil ST, SLW, and SI resulted in significant variations in simulated net radiation and surface energy fluxes, as shown in Fig. 8. The average and statistical results of the simulations and observations are presented in Tables 5 and 6. Due to the lack of observations regarding sensible and latent heat fluxes, we only compared the net radiation and ground heat flux in this study. The results of TEST1-SP and TEST2-SP have been omitted in Fig. 8 as they exhibited negligible differences when compared to the results of TEST1 and TEST2.
Figure 8. The observed and simulated daily surface energy flux (units: W m−2), including net radiation (Rn), sensible heat flux (H), latent heat flux (LE), and ground heat flux (G). Shaded areas in the figure denote the thawing period based on observed ST at a depth of 5 cm.
Variable TEST1 TEST2 TEST3 TEST4 TEST1-SP TEST2-SP Obs Rn/ W m–2 74.02 74.57 75.68 75.61 74.03 74.07 81.43 G/ W m–2 1.71 3.36 3.49 3.11 1.77 1.78 2.67 H/ W m–2 48.59 47.94 44.16 44.59 48.85 48.88 − LE/ W m–2 23.74 23.31 28.06 27.95 23.43 23.44 − Table 5. The average values of simulated and observed net radiation (Rn), ground heat flux (G), sensible heat flux (H), and latent heat flux (LE).
Variable Statistical variable TEST1 TEST2 TEST3 TEST4 TEST1-SP TEST2-SP Rn RMSE/ W m–2 22.30 21.90 21.01 21.08 22.45 22.74 MBE/ W m–2 –7.42 –6.86 –5.76 –5.82 –7.41 –7.36 NSE 0.83 0.84 0.85 0.85 0.83 0.83 G RMSE/ W m–2 9.99 10.07 10.30 10.25 10.48 10.36 MBE/ W m–2 –0.96 0.69 0.82 0.44 –0.90 –0.89 NSE –1.78 –1.69 –1.64 –1.66 –1.81 –1.81 Table 6. Statistical results of simulated and observed net radiation (Rn) and ground heat flux (G).
Compared to the observation, six experiments effectively simulated the annual characteristics of net radiation. The observed annual mean net radiation was 81.43 W m–2, while it ranged from 74.02 to 75.68 W m–2 in the six simulated results. The RMSE ranged from 21.01 to 22.74 W m–2, while the MBE ranged from –7.42 to –5.76 W m–2 across these experiments. Moreover, all simulations showed NSE values close to 1, ranging from 0.83 to 0.85. During autumn and winter, a clear underestimation of net radiation was found in six experiments, resulting in significantly higher STs in the active layers (Fig. 3). Among these experiments, TEST3 and TEST4 demonstrated superior simulation results for net radiation with lower RMSE and MBE values and a higher NSE.
The observed ground heat flux at a depth of 5 cm had negative values during the freezing period, with an average of –5.45 W m–2, while it showed positive values during the thawing period, averaging 10.96 W m–2. The offsetting of both positive and negative values throughout the year resulted in an annual mean ground heat flux of only 2.67 W m–2 (Table 5). As shown in Fig. 8, the seasonal variation of ground heat flux was successfully captured in six experiments. However, the simulated ground heat fluxes from TSET1, TSET1-SP, and TSET2-SP were found to be underestimated compared to the observed values, with an MBE ranging from –0.96 to –0.89 W m–2. Conversely, the simulated ground heat fluxes from three modified experiments were slightly overestimated, with an MBE ranging from 0.44 to 0.69 W m–2. Among all experiments, TEST4 demonstrated superior simulation results for ground heat flux with the smallest MBE and largest NSE.
The simulated annual mean value of sensible heat flux ranged from 44.59 to 48.88 W m–2, while the range for latent heat flux was between 23.31 to 28.06 W m–2 (Table 6). TEST3 and TEST4 simulated relatively lower values for sensible heat flux and higher values for latent heat flux, whereas the remaining four experiments demonstrated relatively higher values for sensible heat flux and lower values for latent heat flux.
The modified initial soil schemes as a whole significantly improved the estimations of net radiation and ground heat flux. Comparing the result of TSET1, the average MBE of net radiation was reduced by 7%, 22%, and 21%, respectively, while it was only reduced by less than 1% in the two spin-up experiments. Furthermore, the average MBE of ground heat flux was reduced from –1.78 W m–2 to –1.64 W m–2.
Experiment | Initial soil temperature (ST) design | Initial soil moisture (SM) design |
TEST1 | Default initial ST (274 K) | Default initial volumetric soil water content (0.15 m3 m−3), the mass of SLW and SI by Eqs. (1) and (2) |
TEST2 | Modified initial ST (272.3 K) | Default initial volumetric soil water content (0.15 m3 m−3), the mass of SLW and SI by Eqs. (1) and (2) |
TEST3 | Modified initial ST (272.3 K) | Modified initial volumetric soil water content (0.25 m3 m−3), the mass of SLW and SI by Eqs. (3) and (4) |
TEST4 | Default initial ST (274 K) in the active layers (1st–7th layer), Modified initial ST (272.3 K) in the permafrost layers (8th–10th) | Modified initial volumetric soil water content (0.25 m3 m−3), the mass of SLW and SI by Eqs. (3) and (4) |
TEST1-SP | The same as TEST1, but for 100 years of spin-up | |
TEST2-SP | The same as TEST2, but for 100 years of spin-up |