Introduction

Global warming has a profound impact on ecological processes and biodiversity1,2, driving many species and ecosystems to alter their geographical distribution in order to track their thermal comfort requirements3. Forest ecosystems, occupying approximately 30% of the terrestrial surface and constituting 60% of terrestrial biodiversity4, have a three-dimensional canopy structure and can create shading, affect air mixing, exert evapotranspirative cooling and thus form a phenomenon known as “forest microclimate”. This microclimate in forests is different from the open-ground environment and often shows a stable low temperature, thus creating microrefugia with a comfortable habitat for species to mitigate extreme heat under global warming5,6,7,8,9,10.

Such forest microclimate effects have been quantified at site-level by comparing field-observed air temperature (ΔTa) or land surface temperature (ΔTs) between paired forest and nonforest lands, known as the space-for-time analogy method11,12. They often observe the temperature difference at 1–2 m above the ground13,14,15. Based on meta-analysis, a number of studies have further indicated that the directions and magnitudes of ΔTa reported in these previous literatures differ greatly, ranging from −5.6 °C to 3.3 °C16; Therefore, the conclusions from site-level observations are likely to be regional, and may not be applicable elsewhere17. However, a long-term and global-scale assessment of the biophysical effects of forests on the sub-canopy microclimates (e.g., ΔTa and ΔTs) are still lacking15,18,19. This is mainly because forest microclimate cannot be measured directly by satellite sensors, which are a feasible way of mapping global surface temperatures, but not possible for capturing thermal signals from sub-canopy atmosphere and surface soil8,17,18,19,20. In addition, global forests have been undergone dramatic changes in the twenty-first century21, inevitably leading to much greater spatial and temporal heterogeneity in microclimate. Therefore, there is an urgent need to develop ways to investigate the variations in understory microclimate and its underlying drivers at both moderate resolution and across broad spatial scales8,20.

Forest microclimate models provide an alternative way to estimate the biophysical effects of forests on understory Ta and Ts14,16,22. Previous studies have compared the energy balance between forest and nonforest lands23,24,25 and derived, for example, the Intrinsic Biophysical Mechanism (IBM)22 model to simulate the biophysical effects of forest on local temperatures (TLee), which differ from understory Ta and Ts. This is because previous studies mostly simplified forest land surface as one single layer and thus the temperature variable17, such as ΔTLee in the IBM model, was more like a mixed proxy for surface temperatures effect composed of not only understory Ta and Ts effect but also overstory air temperature effect15,22. Su et al.14,16 divided the forest land surface into three vertical layers: canopy, understory air space, and understory soil surface (CAS), developed a three-layer CAS radiation transfer model (Supplementary Fig. 1), and decomposed the biophysical effects of forests on understory Ta and Ts, hereafter denoted as ΔTa and ΔTs, respectively. Nevertheless, how ΔTa and ΔTs respond to seasonal and long-term forest dynamics remains issues that have not yet been explored.

To fill this research gap, we combine the CAS microclimate models of Su et al.14 and IBM model22 to evaluate seasonal and long-term variations of ΔTa and ΔTs and to reveal the mechanism of these variations. Seasonal variations of temperature (ΔΔTS) are approximated by ΔT of the warm season minus ΔT of the cold season, while the long-term variations of temperature (ΔΔTC) are estimated by the multi-year average ΔT from 2008 to 2011 minus the multi-year average ΔT from 2003 to 200 6. Additionally, we propose an indicator (ΔTSu) for evaluating the mixed temperature effects composed of both ΔTa and ΔTs, that is, \(\Delta {T}_{{\rm{Su}}}=\Delta {T}_{{\rm{s}}}+(\frac{1}{{f}_{{\rm{r}}}^{1}}-1)\Delta {T}_{a}\) and \({f}_{{\rm{r}}}^{1}\) is the vertical ratio of aerodynamic resistance between the forest air and canopy layer compared with that between soil and forest air layers, to explain the mechanism discrepancies between ground-observed and IBM-simulated biophysical effects of forests. It is worth noting that in this study, and the warm and cold seasons refer to local seasonal conditions (details are provided in Methods).

Results

Validation of simulated ΔT s and ΔT a

The 1833 samples of in-situ observations collected from 32 global forest flux sites (Supplementary Fig. 2), which included 7 deciduous broadleaf forests (DBF), 4 evergreen broadleaf forests (EBF), 19 evergreen needle-leaf forests (ENF) and 2 mixed forests (MF), were used for model validation. Results showed that both modeled ΔTs and ΔTa are well correlated with observed ΔTs (R = 0.776, P < 0.001, RMSE = 1.236 °C) and ΔTa (R = 0.870, P < 0.001, RMSE = 0.905 °C), respectively (Supplementary Fig. 3). In particular, seasonal dynamics of ΔTs and ΔTa modeled by CAS performed better at high latitudes (P < 0.001, Fig. 1i–l) and low latitudes (P < 0.001, Fig. 1a-d) than at moderate latitudes (P < 0.001, Fig. 1e–h).

Fig. 1: Seasonality validations of modeled ΔTs and ΔTa.
figure 1

a, c, e, g, i, k The corresponding degree of monthly change trend between the modeled-ΔT and the observed-ΔT at three latitudes. b, d, f, h, j, l The scatter plots of monthly and long-term values of the modeled-ΔT and observed-ΔT at three latitudes from 2003 to 2011. The gray shading of seasonal curves and regression lines represent the standard error of the mean (SE) and 95% confidence interval, respectively. P-values were determined by a two-sided Student’s t-test.

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Seasonal and long-term variation patterns of ΔT s, ΔT a, and ΔT Su

Seasonal variations (ΔΔTS, i.e., the ΔT in the warm season minus the ΔT in the cool season) of the temperature effects induced by forest seasonal dynamics at three latitudes are shown in Fig. 2a. High latitudes showed the strongest negative seasonal variations in the biophysical effects on forest microclimate (i.e., \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{S}}}\) = −2.528 ± 0.028 °C, \(\Delta \Delta {T}_{{\rm{s}}}^{{\rm{S}}}\) = −3.311 ± 0.015 °C and \(\Delta \Delta {T}_{{\rm{a}}}^{{\rm{S}}}\) = −1.345 ± 0.027 °C), followed by moderate latitude forests (\(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{S}}}\) = −2.469 ± 0.037 °C, \(\Delta \Delta {T}_{{\rm{s}}}^{{\rm{S}}}\) = −2.069 ± 0.021 °C, and \(\Delta \Delta {T}_{{\rm{a}}}^{{\rm{S}}}\) = −1.280 ± 0.032 °C). In contrast, low-latitude forests exerted positive seasonal variations in the air temperature effects (\(\Delta \Delta {T}_{{\rm{a}}}^{{\rm{S}}}\) = 0.146 ± 0.013 °C), weak negative seasonal variations in the soil temperature effects (\(\Delta \Delta {T}_{{\rm{s}}}^{{\rm{S}}}\) = −0.039 ± 0.007 °C) and, in turn, positive seasonal variations in \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{S}}}\) (\(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{S}}}\) = 0.090 ± 0.014 °C).

Fig. 2: Seasonal variations and long-term changes of ΔTsu, ΔTs and ΔTa.
figure 2

a the seasonal variations (ΔΔTS). b the long-term changes (ΔΔTc) of ΔTsu, ΔTs and ΔTa. The error bars represent the standard error of the mean (SE).

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For the long-term variations (ΔΔTC, i.e., the average ΔT from 2008 to 2011 minus the average ΔT from 2003 to 2006, Fig. 2b), ΔTa increased systematically at all three latitudes (low latitudes: \(\Delta \Delta {T}_{{\rm{a}}}^{{\rm{C}}}\) = 0.060 ± 0.002 °C; moderate latitudes: \(\Delta \Delta {T}_{{\rm{a}}}^{{\rm{C}}}\) = 0.045 ± 0.005 °C; high latitudes: \(\Delta \Delta {T}_{{\rm{a}}}^{{\rm{C}}}\) = 0.056 ± 0.002 °C). However, ΔTs increased weakly at low latitudes (\(\Delta \Delta {T}_{{\rm{s}}}^{{\rm{C}}}\) = 0.029 ± 0.004 °C) and moderate latitudes (\(\Delta \Delta {T}_{{\rm{s}}}^{{\rm{C}}}\) = 0.001 ± 0.005 °C), but decreased slightly at high latitudes (\(\Delta \Delta {T}_{{\rm{s}}}^{{\rm{C}}}\) = −0.007 ± 0.003 °C). Combined with the regulation of term \((\frac{1}{{f}_{{\rm{r}}}^{1}}-1)\), the strongest \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{C}}}\) (\(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{C}}}\) = 0.182 ± 0.008 °C) emerged at high latitudes, followed by low latitudes (\(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{C}}}\) = 0.096 ± 0.013 °C) and moderate latitudes (\(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{C}}}\) = 0.049 ± 0.017 °C). Overall, the magnitude of long-term variations of forest temperature effects consistently showed the following order: \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{C}}}\) > \(\Delta \Delta {T}_{{\rm{a}}}^{{\rm{C}}}\) > \(\Delta \Delta {T}_{{\rm{s}}}^{{\rm{C}}}\).

Energy balance mechanisms for seasonal and long-term changes in forest microclimate effects

Seasonal and long-term changes in ΔTSu (\(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{S}}}\), \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{C}}}\)) can be explained by corresponding changes in surface energy balance, which were diagnosed from satellite observations of albedo, downwelling short-wave radiation (ϕn) and latent heat (LE). Therefore, we calculated the contributions of short-wave radiation (\(\Delta \Delta {T}_{{\rm{Su}},{{{\phi}}}_{{\rm{n}}}}\)), long-wave radiation (ΔΔTSu,R), latent heat flux (ΔΔTSu,LE) and corrected total sensible heat flux (\(\Delta \Delta {T}_{{\rm{Su}},{{\rm{H}}}^{* }}\)) to the \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{S}}}\) and \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{C}}}\) based on Eqs. (9–16). The results of the analysis are shown in Fig. 3.

Fig. 3: The respective contribution of energy components to seasonal and long-term changes in ΔTSu.
figure 3

a and d illustrate the contributions of short-wave radiation (ϕn), long-wave radiation (R), latent heat flux (LE) and corrected total sensible heat flux (\({H}^{* }\)) to the biophysical effects of seasonal and long-term changes in ΔTSu, respectively. The contributions of LE and \({H}^{* }\) to \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{S}}}\) and \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{C}}}\) were decomposed into canopy parts and understory parts in b, c, e, and f, respectively. The error bars represent the standard error of the mean (SE).

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For seasonal variations (Fig. 3a), ϕn and R were two positive drivers to \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{S}}}\) at all latitudes (low latitudes: \(\Delta \Delta {T}_{{\rm{Su}},{{{\phi}}}_{{\rm{n}}}}^{{\rm{S}}}\) = 0.025 ± 0.00 6°C, \(\Delta \Delta {T}_{{\rm{Su}},{\rm{R}}}^{{\rm{S}}}\) = 0.115 ± 0.008 °C; moderate latitudes: \(\Delta \Delta {T}_{{\rm{Su}},{{{\phi}}}_{{\rm{n}}}}^{{\rm{S}}}\) = 0.833 ± 0.058 °C, \(\Delta \Delta {T}_{{\rm{Su}},{\rm{R}}}^{{\rm{S}}}\) = 0.440 ± 0.039 °C; high latitudes: \(\Delta \Delta {T}_{{\rm{Su}},{{{\phi}}}_{{\rm{n}}}}^{{\rm{S}}}\) = 0.432 ± 0.038 °C, \(\Delta \Delta {T}_{{\rm{Su}},{\rm{R}}}^{{\rm{S}}}\) = 0.237 ± 0.019 °C). The stronger contribution of radiation changes in boreal forests was mainly attributed to the lower forest albedo during snow-covered periods26,27,28,29, typically 20% to 50% less than in snow-covered open areas. In addition, the dominant coniferous forests in the boreal region30 were typically darker (lower albedo)6 than the broadleaved forests prevailing elsewhere31,32.

LE and \({H}^{* }\) served as the two dominant negative drivers to \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{S}}}\) at the moderate (\(\Delta \Delta {T}_{{\rm{Su}},{\rm{LE}}}^{{\rm{S}}}\) = −0.909 ± 0.109 °C, \(\Delta \Delta {T}_{{\rm{Su}}{,{\rm{H}}}^{* }}^{{\rm{S}}}\) = −2.833 ± 0.142 °C) and high latitudes (\(\Delta \Delta {T}_{{\rm{Su}},{\rm{LE}}}^{{\rm{S}}}\) = −0.495 ± 0.064 °C, \(\Delta \Delta {T}_{{\rm{Su}}{,{\rm{H}}}^{* }}^{{\rm{S}}}\) = −2.703 ± 0.081 °C), while they played opposite roles to \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{S}}}\) at the low latitudes (\(\Delta \Delta {T}_{{\rm{Su}},{\rm{LE}}}^{{\rm{S}}}\) = 0.125 ± 0.013 °C, \(\Delta \Delta {T}_{{\rm{Su}}{,{\rm{H}}}^{* }}^{{\rm{S}}}\) = −0.175 ± 0.016 °C). The higher seasonal variations in the contribution of LE and \({H}^{* }\) at moderate and high latitudes were induced by the significant seasonal phenology of deciduous forests33,34 compared to evergreen forests, which are mainly located at low latitudes35,36. Overall, the temperature effects of seasonal changes in LE and \({H}^{* }\) overwhelmed the effects of ϕn and R (Fig. 3a), leading to a positive \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{S}}}\) at the low latitudes but negative \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{S}}}\) at the moderate and high latitudes. These findings suggest that for seasonal variations of forests, seasonal changes in LE and \({H}^{\begin{array}{c}\\ * \end{array}}\) are the most plausible causations for the \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{S}}}\), with \({H}^{* }\) contributing more than LE at all latitudes.

For the long-term variations (Fig. 3), ϕn and R were positive contributors to \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{C}}}\) at the low latitudes (\(\Delta \Delta {T}_{{\rm{Su}},{{{\phi}}}_{{\rm{n}}}}^{{\rm{C}}}\) = 0.029 ± 0.001 °C, \(\Delta \Delta {T}_{{\rm{Su}},{\rm{R}}}^{{\rm{C}}}\) = 0.089 ± 0.011 °C), but were negative contributors at the moderate (\(\Delta \Delta {T}_{{\rm{Su}},{{{\phi}}}_{{\rm{n}}}}^{{\rm{C}}}\) = −0.029 ± 0.002 °C, \(\Delta \Delta {T}_{{\rm{Su}},{\rm{R}}}^{{\rm{C}}}\) = −0.023 ± 0.003 °C) and high latitudes (\(\Delta \Delta {T}_{{\rm{Su}},{{{\phi}}}_{{\rm{n}}}}^{{\rm{C}}}\) = −0.014 ± 0.001 °C, \(\Delta \Delta {T}_{{\rm{Su}},{\rm{R}}}^{{\rm{C}}}\) = −0.022 ± 0.004 °C). The inter-annual changes in LE and \({H}^{* }\) caused by long-term variations in the low-latitude forests played an opposite role in \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{C}}}\), increasing \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{C}}}\) by 0.056 ± 0.003 °C and decreasing \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{C}}}\) by 0.079 ± 0.005 °C, respectively. Conversely, LE and \({H}^{* }\) were two positive drivers to \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{C}}}\) at the moderate (\(\Delta \Delta {T}_{{\rm{Su}},{\rm{LE}}}^{{\rm{C}}}\) = 0.046 ± 0.003 °C, \(\Delta \Delta {T}_{{\rm{Su}}{,{\rm{H}}}^{* }}^{{\rm{C}}}\) = 0.055 ± 0.002 °C) and high (\(\Delta \Delta {T}_{{\rm{Su}},{\rm{LE}}}^{{\rm{C}}}\) = 0.090 ± 0.009 °C, \(\Delta \Delta {T}_{{\rm{Su}}{,{\rm{H}}}^{* }}^{{\rm{C}}}\) = 0.129 ± 0.013 °C) latitudes. It is worth noting that the differences in energy fluxes (i.e., ϕn, R, \({H}^{* }\) and LE) between forest and nonforest lands were much stronger at the high latitudes compared to the other two latitudes. Similar to seasonal variations, non-radiative processes dominated the long-term variations in the biophysical effects on forest microclimate.

We further decomposed the contribution of the LE anomaly (Fig. 3b, e) and \({H}^{* }\) anomaly (Fig. 3c, f) into canopy parts (\(\Delta \Delta {T}_{{\rm{Su}},{{\rm{LE}}}_{{\rm{canopy}}}}\), \(\Delta \Delta {T}_{{\rm{Su}},{{\rm{H}}}_{{\rm{canopy}}}^{* }}\)) and understory parts (\(\Delta \Delta {T}_{{\rm{Su}},{{\rm{LE}}}_{{\rm{understory}}}}\), \(\Delta \Delta {T}_{{\rm{Su}},{{\rm{H}}}_{{\rm{understory}}}^{* }}\)). We found that the canopy parts (\(\Delta \Delta {T}_{{\rm{Su}},{{\rm{LE}}}_{{\rm{canopy}}}}\) and \(\Delta \Delta {T}_{{\rm{Su}},{{\rm{H}}}_{{\rm{canopy}}}^{* }})\) contributed more to \(\Delta \Delta {T}_{{\rm{Su}},{\rm{LE}}}\) and \(\Delta \Delta {T}_{{\rm{Su}},{\rm{H}}}\) than the understory parts (\(\Delta \Delta {T}_{{\rm{Su}},{{\rm{LE}}}_{{\rm{understory}}}}\) and \(\Delta \Delta {T}_{{\rm{Su}},{{\rm{H}}}_{{\rm{understory}}}^{* }})\) in both seasonal and long-term variations. In addition, \(\Delta \Delta {T}_{{\rm{Su}},{{\rm{LE}}}_{{\rm{canopy}}}}\) and \(\Delta \Delta {T}_{{\rm{Su}},{{\rm{LE}}}_{{\rm{understory}}}}\) performed correspondingly at low and moderate latitudes but contrarily at high latitudes, whereas \(\Delta \Delta {T}_{{\rm{Su}},{{\rm{H}}}_{{\rm{canopy}}}^{* }}\) and \(\Delta \Delta {T}_{{\rm{Su}},{{\rm{H}}}_{{\rm{understory}}}^{* }}\) contributed differently at all latitudes except low latitudes.

Impact of vertical aerodynamic resistance on the latent and sensible heat fluxes

Su et al.14 found that the differences in aerodynamic resistances among vertical layers of forest ecosystems (i.e., \({f}_{{\rm{r}}}^{1}\) and \({f}_{{\rm{r}}}^{2}\)) are important indicators regulating the magnitudes of ΔTs and ΔTa, and thus ΔTSu. The \({f}_{{\rm{r}}}^{1}\) is the ratio of the aerodynamic resistance between open air and canopy layers to the aerodynamic resistance between forest air and soil layers (\({f}_{{\rm{r}}}^{1}=\frac{{r}_{{\rm{a}},{\rm{c}}}}{{r}_{{\rm{s}}}}\)). The \({f}_{{\rm{r}}}^{2}\) is the ratio of the aerodynamic resistance between open air and canopy layers to the aerodynamic resistance between forest air and soil layers (\({f}_{{\rm{r}}}^{2}=\frac{{r}_{{\rm{c}},{\rm{a}}}}{{r}_{{\rm{a}},{\rm{c}}}}\)). However, previous studies had not revealed the impact of vertical aerodynamic resistance on the energy transfer process, especially for latent and sensible heat fluxes.

Here, Fig. 4 showed the correlations of \({\Delta f}_{{\rm{r}}}^{1}\) and \({\Delta f}_{{\rm{r}}}^{2}\) with the components of ΔLE (i.e., ΔLEcanopy, ΔLEunderstory) in seasonal variations (Fig. 4a–l) and long-term variations (insets in Fig. 4a–l), while Fig. 5 presented the correlations of \({\Delta f}_{{\rm{r}}}^{1}\) and \({\Delta f}_{{\rm{r}}}^{2}\) with the components of \(\Delta {H}^{* }\) (i.e., \({\Delta H}_{{\rm{canopy}}}^{* }\), \({\Delta H}_{{\rm{understory}}}^{* }\)). Both ΔLEcanopy and ΔLEunderstory linearly decreased with \({\Delta f}_{{\rm{r}}}^{1}\), \({\Delta f}_{{\rm{r}}}^{2},\) respectively, at the low latitudes (P < 0.001) and moderate latitudes (P < 0.001) (Fig. 4a–h), whereas \({\Delta f}_{{\rm{r}}}^{1}\) and \({\Delta f}_{{\rm{r}}}^{2}\) negatively correlated with ΔLEcanopy (P < 0.001) but positively correlated with ΔLEunderstory (P < 0.001) at the high latitudes (Fig. 4i–l). In addition, ΔLEcanopy and ΔLEunderstory were always more sensitive to \({\Delta f}_{{\rm{r}}}^{1}\) than to \({\Delta f}_{{\rm{r}}}^{2}\) at all three latitudes; while \({\Delta f}_{{\rm{r}}}^{1}\) and \({\Delta f}_{{\rm{r}}}^{2}\) made more significant impacts on ΔLEcanopy than on ΔLEunderstory. Specifically, at low latitudes both \({\Delta f}_{{\rm{r}}}^{1}\) and \({\Delta f}_{{\rm{r}}}^{2}\) were positively correlated with \({\Delta H}_{{\rm{canopy}}}^{* }\) and \({\Delta H}_{{\rm{understory}}}^{* }\) (P < 0.001) (Fig. 5a–d). By contrast, at moderate and high latitudes \({\Delta f}_{{\rm{r}}}^{1}\) and \({\Delta f}_{{\rm{r}}}^{2}\) were negatively correlated with \({\Delta H}_{{\rm{canopy}}}^{* }\) (P < 0.001) but positively correlated with \({\Delta H}_{{\rm{understory}}}^{* }\) (P < 0.001) (Fig. 5e–l). Similarly, to the effects of \({\Delta f}_{{\rm{r}}}^{1}\) and \({\Delta f}_{{\rm{r}}}^{2}\) on ΔLEcanopy and ΔLEunderstory, \({\Delta f}_{{\rm{r}}}^{1}\) systematically exerted a greater effect on \({\Delta H}_{{\rm{canopy}}}^{* }\) and \({\Delta H}_{{\rm{understory}}}^{* }\) than did \({\Delta f}_{{\rm{r}}}^{2}\) at low, moderate or high latitudes.

Fig. 4: Correlations of \({\Delta f}_{{\rm{r}}}^{1}\) and \({\Delta f}_{{\rm{r}}}^{2}\) with the components of ΔLE (ΔLEcanopy, ΔLEunderstory).
figure 4

The graphs a–l show the correlations of seasonal variations, while the inserts in a–l represent the correlations in the long-term variations. P-values were determined by a two-sided Student’s t-test.

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Fig. 5: Correlations of \({\Delta f}_{{\rm{r}}}^{1}\) and \({\Delta f}_{{\rm{r}}}^{2}\) with the components of ΔH* (\({\Delta H}_{{\rm{canopy}}}^{* }\), \({\Delta H}_{{\rm{understory}}}^{* }\)).
figure 5

The graphs a–l show the correlations of seasonal variations, while the inserts in a–l represent the correlations in the long-term variations. P-values were determined by a two-sided Student’s t-test.

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Impact of canopy dynamics on the vertical aerodynamic resistance ratios (\({\Delta f}_{{\rm{r}}}^{1}\), \({\Delta f}_{{\rm{r}}}^{2}\))

In light of the above results, the dynamics of energy redistribution factors (\({\Delta f}_{{\rm{r}}}^{1}\), \({\Delta f}_{{\rm{r}}}^{2}\)) played a major role in regulating the energy distribution of forest non-radiative effects (i.e., \(\Delta {\rm{LE}}\) and \({\Delta H}^{* }\)), which were the two largest contributors controlling temperature effects14. According to the calculation formula for rc,a (the aerodynamic resistances to convection between the canopy and open air), rs (the aerodynamic resistances to convection soil and understory air layer) and ra,c (the aerodynamic resistances to convection between canopy and understory air)14,16, canopy phenology (leaf area index, LAI) and canopy height (hc) were two potential major factors affecting both \({f}_{{\rm{r}}}^{1}\) and \({f}_{{\rm{r}}}^{2}\). Due to data limitations, we analyzed the responses of \({\Delta f}_{{\rm{r}}}^{1}\) and \({\Delta f}_{{\rm{r}}}^{2}\) to ΔLAI using both observational data (Fig. 6) and theoretical derivations (Supplementary Fig. 4), but only obtained theoretical responses for \({\Delta f}_{{\rm{r}}}^{1}\) and \({\Delta f}_{{\rm{r}}}^{2}\) to Δhc (Supplementary Fig. 5). Both \({\Delta f}_{{\rm{r}}}^{1}\) and \({\Delta f}_{{\rm{r}}}^{2}\) showed an obvious decreasing trend as ΔLAI increased in seasonal (Fig. 6a, b) and long-term variations (Fig. 6c, d). \({\Delta f}_{{\rm{r}}}^{2}\) was more sensitive to the variations in ΔLAI than \({\Delta f}_{{\rm{r}}}^{1}\) (Fig. 6, Supplementary Fig. 4 and Supplementary Figs. 6, 7). Both \({f}_{{\rm{r}}}^{1}\) and \({f}_{{\rm{r}}}^{2}\) also exhibited an obvious decreasing trend as hc increased, and \({f}_{{\rm{r}}}^{2}\) was more sensitive to hc than \({f}_{{\rm{r}}}^{1}\) especially when hc < 5 m (Supplementary Fig. 5). Thus, canopy phenology (LAI) and canopy height (hc) strongly influence the biophysical effects of forest cover on temperature by regulating the energy distribution in the forest understory.

Fig. 6: Impacts of ΔLAI on \({\Delta f}_{{\rm{r}}}^{1}\) and \({\Delta f}_{{\rm{r}}}^{2}\) in seasonal and long-term variations.
figure 6

a, b The correlations in seasonal variations. c, d The correlations in long-term variations. P-values were determined by a two-sided Student’s t-test.

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Mechanisms of forest dynamics impact on microclimate effects

Anthropogenic practices21 and various natural causes (e.g., extreme climate-induced tree mortality and forest fires37 have led to an acceleration of forest disturbance rates over the past decades38. Seasonal and long-term dynamics in forest regions can promote or weaken the biophysical effects of forests on climate through biophysical processes, such as surface albedo39, surface roughness40, and evapotranspiration as well as through land cover change (i.e., afforestation or reforestation)23. However, while the local climate effects of changes in land cover had undergone in-depth investigation22,25, to date few studies have delved into the understory microclimate impacts of seasonal and long-term dynamics that occur within the forest region.

Herein, we combined the CAS microclimate models of Su et al.14 and IBM model22 to evaluate seasonal and long-term variations of ΔTa and ΔTs and to reveal the underlying mechanism (Fig. 7). We found that an increase in LAI, either from the cold to warm seasons or after long-term afforestation or reforestation, would result in lower values of \({f}_{{\rm{r}}}^{1}\) and \({f}_{{\rm{r}}}^{2}\). For seasonal variations, at high latitudes (Fig. 7c), such decreases in \({f}_{{\rm{r}}}^{1}\) and \({f}_{{\rm{r}}}^{2}\) produce strong increases in canopy-layer sensible heat fluxes (with their sensitivities (δ) \({f}_{{\rm{r}}}^{1}\) and \({f}_{{\rm{r}}}^{2}\) equal to −500.1 W m−2 and −438.7 W m−2, respectively), strong decreases in understory sensible heat fluxes (\({f}_{{\rm{r}}}^{1}\): δ = 530.2 W m−2; \({f}_{{\rm{r}}}^{2}\): δ = 168.6 W m−2), and moderate increases in canopy latent heat fluxes (\({f}_{{\rm{r}}}^{1}\): δ = 363.4 W m−2; \({f}_{{\rm{r}}}^{2}\): δ = 139.5 W m−2). These changes in sensible and latent heat fluxes jointly lead to an overall negative effect on forest microclimate (Fig. 3a). Our findings are different from most previous studies where latent heat flux was systematically attributed as the main driver17,24. Although some previous studies have mentioned the important role of H30,41,42, our research has shown that \({H}^{* }\) is the main contributor of the forest temperature effects changes instead of LE. This happens because the observed H, mostly representing the canopy-atmosphere layer flux, is underestimated compared to corrected sensible heat flux \({H}^{* }\) that both takes into account the fluxes in the canopy-atmosphere layer and soil-forest air layer30,42,43,44,45,46. At middle latitudes (Fig. 7b), canopy sensible heat flux becomes more negative sensitive to \({f}_{{\rm{r}}}^{1}\) (δ = −2198.8 W m−2) and \({f}_{{\rm{r}}}^{2}\) (δ = −811.0 W m−2) than at high latitudes, while canopy sensible heat flux is more positive sensitive to \({f}_{{\rm{r}}}^{1}\) (δ = −2198.8 W m−2) and \({f}_{{\rm{r}}}^{2}\) (δ = −811.0 W m−2) and there is smaller sensitive of latent heat fluxes to the change of \({f}_{{\rm{r}}}^{1}\) and \({f}_{{\rm{r}}}^{2}\), thus resulting in a slightly weaker negative effect on forest microclimate (Fig. 3a). The situations differ greatly at low latitudes where canopy sensible heat flux is positively sensitive to \({f}_{{\rm{r}}}^{1}\) (δ = 1833.2 W m−2) and \({f}_{{\rm{r}}}^{2}\) (δ = 1669.4 W m−2) (Fig. 7a). The weak negative sensitive of canopy and understory latent heat fluxes but strong positive sensitive of canopy and understory sensible heat fluxes to the change in \({f}_{{\rm{r}}}^{1}\) and \({f}_{{\rm{r}}}^{2}\) finally lead to a positive forest microclimate (Fig. 3a).

Fig. 7: Sensitivity analysis of seasonal changes in ΔTSu to changes in ΔH and ΔLE induced by ΔLAI through changing the vertical aerodynamic resistances.
figure 7

a The low latitudes. b The moderate latitudes. c The high latitudes. P-values sectionwere determined by a two-sided student’s t-test: **P < 0.001.

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The mechanism of long-term changes in ΔTa and ΔTs induced by ΔLAI through changing the vertical aerodynamic resistances is similar to that of seasonal changes (Supplementary Fig. 8). It is worth noting that forest gains had offset more than 60% of the losses at moderate latitudes47 and less than 30% at low latitudes21,48, and therefore, long-term variations in the forest region resulted in smaller positive TSu at moderate latitudes than at low latitudes as a consequence (Fig. 3b). In addition, we conducted an observation of seasonal changes at Haizhu Park in Guangzhou to verify our mechanism based on the CAS model. The results showed a consistent energy change process (Supplementary Table 3).

Mismatch between ground-observed and IBM-simulated temperature effects

Multiple technologies, such as satellite-based observations17,49, land–atmosphere model simulations22,50,51,52 and field investigations53, have been used to investigate biophysical effects of forests on temperatures and have found inconsistent directions (cooling versus warming) and different magnitudes in the biophysical effects of forests at the same location. Satellite signals represent land surface temperatures17, field observations mostly focused on the air temperature54,55,56,57, while models reflect a mixed temperature effects that differ from the field-observed ΔTa and ΔTs22. For examples, ΔTLee estimated from the IBM model is a mixed temperature effect composed of ΔTa, ΔTs, and a residual term resulting from the difference between Tc and Tao22; while ΔTSu estimated from the CAS-IBM model removes such a residual term and is composed of ΔTa and \({\Delta T}_{{\rm{s}}}\)14. Thus, equating the model simulated ΔTLee or ΔTSu to the field-observed ΔTa or ΔTs would lead to bias in quantifying the biophysical effects of forests on understory microclimate.

It is also worth noting that, as shown above, forests could exert biophysical effects on both Ta and Ts. At present, it remains challenge for comprehensively evaluating the biophysical effects of forests on local climate, including both ΔTa and ΔTs. This study used a coefficient (i.e., \(\frac{1}{{f}_{{\rm{r}}}^{1}}-1\)) to convert the air temperature effects (ΔTa) to soil temperature effects (ΔTs) and proposed an indicator – ΔTSu, that is, \(\Delta {T}_{{\rm{Su}}}=\Delta {T}_{{\rm{s}}}+(\frac{1}{{f}_{{\rm{r}}}^{1}}-1)\Delta {T}_{{\rm{a}}}\). This provides a possible benchmark for evaluating the total direct biophysical effects of forests on temperatures.

Discussion

This study conducted a comprehensive evaluation of seasonal and long-term changes in the forest microclimate effects. It demonstrated that high latitudes showed strongest negative seasonal variations in both ΔTa and ΔTs, followed by moderate latitude forests, while low-latitude forests exerted positive seasonal variations in ΔTa and weak negative seasonal variations in ΔTs. However, for the long-term variations, ΔTa systematically increased at all three latitudes, while ΔTs, weakly increased at low and moderate latitudes and slightly decreased at high latitudes. Changes in sensible and latent heat fluxes induced by forest dynamics (like leaf area index), through changing the aerodynamic resistances of canopy and soil surface layers, were the main factors driving the changes in forest microclimate effects. In addition, this study also developed an aerodynamic resistance coefficient \(\left({f}_{{\rm{r}}}^{1}\right)\) to combine the air temperature effects and surface soil temperature effects and proposed an indicator – ΔTSu, that is, \(\Delta {T}_{{\rm{Su}}}\,=\Delta {T}_{{\rm{s}}}+(\frac{1}{{f}_{{\rm{r}}}^{1}}-1)\Delta {T}_{{\rm{a}}}\), as a possible benchmark for evaluating the total biophysical effects of forests on temperatures.

Some limitations or uncertainties still remain in this work. First of all, although the CAS-IBM model has been validated against global eddy-covariance flux tower observations with high accuracy (Supplementary Fig. 1), it is still important to recognize that a comprehensive validation of simulated ΔTa and ΔTs using time-series paired-site field observation data remains challenging. Second, ongoing fine-scale tree cover changes in forest lands can also lead to significant changes in forest microclimate58. This biophysical effect is not analyzed in this study. Last but not least, the mechanism analyses, such as surface energy balance, mostly rely on multi-source remote sensing data where their accuracy may also bring uncertainties.

Methods

The canopy, forest air space, and understory soil (CAS) energy balance model

Conventional energy balance module in most terrestrial atmospheric model treats forests as a single complex layer59,60,61,62,63 (Eq. (1)).

$${{{\phi}}}_{{\rm{n}}}+{R}_{{\rm{sky}}}=H+{\rm{LE}}+{R}_{{\rm{canopy}}}+{G}_{{\rm{tree}}}+{R}_{{\rm{soil}}}+{G}_{{\rm{soil}}}$$
(1)

where ϕn (\({\phi}_{{\rm{n}}}=\left(1-a\right){{\phi}}\)) represents the net short-wave radiation, a represents the surface albedo, ϕ represents the solar radiation flux incident above the canopy; Rsky, Rcanopy and Rsoil represent the long-wave radiation of the sky, canopy and soil, respectively; Gsoil represents the energy flux into soil; Gtree represents the energy flux into tree.

Su et al.16 developed a three-layer radiation transfer module—CAS (canopy, forest air and understory soil) model—as an efficient method to investigate the energy budget under the forest canopy cover to quantify the biophysical effects of air and soil temperature (ΔTa and ΔTs, respectively) under the forest canopy worldwide. The CAS model adds the understory air layer, and the near-surface energy balance is divided into two parts: the energy balance above the understory air layer and the energy balance below the understory air layer (Supplementary Fig. 1). The energy balance for CAS model is expressed as Eq. (2)16.

$$\begin{array}{l}{\phi}_{{\rm{n}}}+{R}_{{\rm{sky}}}-\left\{{R}_{{\rm{soil}}}{\rm{exp }}\left(-\frac{C{\rm{LAI}}}{u}\right)+{R}_{{\rm{canopy}}}[1-{\rm{exp }}\left(-\frac{C{\rm{LAI}}}{u}\right)]\right\}\\\qquad-\,{G}_{{\rm{soil}}}={\rm{LE}}+{H}_{{\rm{soil}}\to {\rm{air}},{\rm{understory}}}+{H}_{{\rm{air}},{\rm{understory}}\to {\rm{canopy}}}+{H}_{{\rm{canopy}}\to {\rm{air}},{\rm{open}}}\end{array}$$
(2)

where LAI is the leaf area index; C is the extinction coefficient; u is the cosine value of the solar zenith angle (θ); \({H}_{{\rm{soil}}\to {\rm{air}},{\rm{understory}}}\) is sensible heat between tree canopy and understory air layer; \({H}_{{\rm{air}},{\rm{understory}}\to {\rm{canopy}}}\) is sensible heat flux between understory air and canopy layers; \({H}_{{\rm{canopy}}\to {\rm{air}},{\rm{open}}}\) is sensible heat flux between canopy and open air layers.

Determining the overall biophysical effects of forest cover on temperature (ΔT Su) and seasonal and long-term variations (ΔΔT Su)

According to Eq. (2), the CAS model can be re-constructed as,

$$\begin{array}{l}H_{{{\mathrm{{soil}}}}\to {{\mathrm{air}}},{\mathrm{understory}}}+H_{{\mathrm{air}},{\mathrm{understory}}\to {\mathrm{canopy}}}+H_{{\mathrm{canopy}}\to {\mathrm{air}},{\mathrm{open}}}{=\phi}_{{\mathrm{n}}}+R_{{\mathrm{sky}}}\\\qquad-\left\{R_{{\mathrm{soil}}}{\rm{exp }}\left(-\frac{C{\mathrm{LAI}}}{u}\right)+{R}_{{\mathrm{canopy}}}\left[1-{\rm{exp }}\left(-\frac{C{\mathrm{LAI}}}{u}\right)\right]\right\}-{{\mathrm{LE}}}-G_{{\mathrm{soil}}}\end{array}$$
(3)

Given \(R={R}_{{\rm{sky}}}-\left\{{R}_{{\rm{soil}}}{\rm{exp }}\left(-\frac{C{\rm{LAI}}}{u}\right)+{R}_{{\rm{canopy}}}\left[1-{\rm{exp }}\left(-\frac{C{\rm{LAI}}}{u}\right)\right]\right\}\), \({H}_{{\rm{canopy}}\to {\rm{air}},{\rm{open}}}=\frac{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}{{r}_{{\rm{c}},{\rm{a}}}}\left({{T}_{{\rm{c}}}-T}_{{\rm{ao}}}\right)\), \({H}_{{\rm{air}},{\rm{understory}}\to {\rm{canopy}}}=\frac{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}{{r}_{{\rm{a}},{\rm{c}}}}\left({T}_{{\rm{af}}}-{T}_{{\rm{c}}}\right)\), and \({H}_{{\rm{soil}}\to {\rm{air}},{\rm{understory}}}=\frac{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}{{r}_{{\rm{s}}}}\left({T}_{{\rm{s}}}-{T}_{{\rm{af}}}\right)\)59,60,64, we come to,

$${\rho }_{{\rm{a}}}{C}_{{\rm{p}}}\left[\frac{1}{{r}_{{\rm{s}}}}\left({T}_{{\rm{s}}}-{T}_{{\rm{af}}}\right)+\frac{1}{{r}_{{\rm{a}},{\rm{c}}}}\left({T}_{{\rm{af}}}-{T}_{{\rm{c}}}\right)+\frac{1}{{r}_{{\rm{c}},{\rm{a}}}}\left({{T}_{{\rm{c}}}-T}_{{\rm{ao}}}\right)\right]+{\rm{LE}}={{{\phi}}}_{{\rm{n}}}+R-{G}_{{\rm{soil}}}$$
(4)

where ρa represents the density of air, with a given value of 1.29 and Cp represents the specific heat capacity of air; Ts, Tc, Taf and Tao are understory soil surface temperature, canopy temperature, understory air temperature and open air temperature (K)65,66,67,68,69, respectively; rc,a, ra,c and rs are the aerodynamic resistances to convection between the canopy and open air, canopy and understory air, soil and understory air layer14, respectively.

Given \({G}_{{\rm{soil}}}=K{R}_{{\rm{n}}}\)70,71,72, \({R}_{{\rm{n}}}={{{\phi}}}_{{\rm{n}}}{\rm{exp }}\left(-\frac{C{\rm{LAI}}}{u}\right)+{R}_{{\rm{sky}}}{\rm{exp }}\left(-\frac{C{\rm{LAI}}}{u}\right)+{R}_{{\rm{canopy}}}\left[1-{\rm{exp }}\left(-\frac{C{\rm{LAI}}}{u}\right)\right]-{R}_{{\rm{soil}}}\), Eq. (4) is changed as,

$$\begin{array}{l}{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}\left[\frac{1}{{r}_{{\rm{s}}}}\left({T}_{{\rm{s}}}-{T}_{{\rm{af}}}\right)+\frac{1}{{r}_{{\rm{a}},{\rm{c}}}}\left({T}_{{\rm{af}}}-{T}_{{\rm{c}}}\right)+\frac{1}{{r}_{{\rm{c}},{\rm{a}}}}\left({{T}_{{\rm{c}}}-T}_{{\rm{ao}}}\right)\right]\\\qquad={\left[1-K{\rm{exp }}\left(-\frac{C{\rm{LAI}}}{u}\right)\right]{{\phi}}}_{{\rm{n}}}+\left[1-K{\rm{exp }}\left(-\frac{C{\rm{LAI}}}{u}\right)\right]R-{\rm{LE}}\end{array}$$
(5)

where K represents coefficient of the energy flux into soil to total radiation70,72.

Given \({T}_{{\rm{af}}}-{T}_{{\rm{ao}}}=\Delta {T}_{{\rm{a}}}\) and \({T}_{{\rm{s}}}-{T}_{{\rm{so}}}=\Delta {T}_{{\rm{s}}}\), Eq. (6) was deduced by Eq. (5).

$$\begin{array}{l}\frac{1}{{r}_{{\rm{s}}}}\Delta {T}_{{\rm{s}}}+\left(\frac{1}{{r}_{{\rm{a}},{\rm{c}}}}-\frac{1}{{r}_{{\rm{s}}}}\right)\Delta {T}_{{\rm{a}}}=\frac{1}{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}\left\{{\left[1-K{\rm{exp }}\left(-\frac{C{\rm{LAI}}}{u}\right)\right]{{\phi}}}_{{\rm{n}}}\right.\\\qquad\qquad+\left[1-K{\rm{exp }}\left(-\frac{C{\rm{LAI}}}{u}\right)\right]R-{\rm{LE}}-\left(\frac{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}{{r}_{{\rm{c}},{\rm{a}}}}-\frac{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}{{r}_{{\rm{a}},{\rm{c}}}}\right)\\\left.\qquad\qquad\left({{T}_{{\rm{c}}}-T}_{{\rm{ao}}}\right)-\frac{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}{{r}_{{\rm{s}}}}\left({T}_{{\rm{s}}{\rm{o}}}-{T}_{{\rm{ao}}}\right)\right\}\end{array}$$
(6)

Here \({H}^{* }=\left(\frac{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}{{r}_{{\rm{c}},{\rm{a}}}}-\frac{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}{{r}_{{\rm{a}},{\rm{c}}}}\right)\left({{T}_{{\rm{c}}}-T}_{{\rm{ao}}}\right)+\frac{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}{{r}_{{\rm{s}}}}\left({T}_{{\rm{so}}}-{T}_{{\rm{ao}}}\right)\), which is seen as the corrected total sensible heat flux. What’s more, setting \({f}_{{\rm{r}}}^{1}=\frac{{r}_{{\rm{c}},{\rm{a}}}}{{r}_{{\rm{s}}}}\), \({f}_{{\rm{r}}}^{2}=\frac{{r}_{{\rm{c}},{\rm{a}}}}{{r}_{{\rm{a}},{\rm{c}}}}\), which are two energy redistribution factors caused by the vertical roughness ratio differences14,16. And then, we defined that the total biophysical effects of forest cover on temperatures (ΔTSu) is the sum of effects on surface soil temperatures (ΔTs) and forest air temperatures (ΔTa)16. Thus, we come to Eq. (7),

$$\begin{array}{l}\Delta {T}_{{\rm{Su}}}=\Delta {T}_{{\rm{s}}}+\left(\frac{1}{{f}_{r}^{1}}-1\right)\Delta {T}_{{\rm{a}}}=\frac{\left[1-K{\rm{exp }}\left(-\frac{C{\rm{LAI}}}{u}\right)\right]}{\frac{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}{{r}_{{\rm{s}}}}}{{{\phi}}}_{{\rm{n}}}\\\qquad\qquad+\,\frac{\left[1-K{\rm{exp }}\left(-\frac{C{\rm{LAI}}}{u}\right)\right]}{\frac{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}{{r}_{{\rm{s}}}}}R+\frac{-1}{\frac{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}{{r}_{{\rm{s}}}}}{\rm{LE}}+\frac{-1}{\frac{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}{{r}_{{\rm{s}}}}}{H}^{* }\end{array}$$
(7)

Furthermore, \({H}^{* }\) can be split into the sensible heat flux from forest canopy to open air (\({H}_{{\rm{canopy}}=}^{* }\left(\frac{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}{{r}_{{\rm{c}},{\rm{a}}}}-\frac{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}{{r}_{{\rm{a}},{\rm{c}}}}\right)\left({{T}_{{\rm{c}}}-T}_{{\rm{ao}}}\right)\)) and the sensible heat flux from soil surface to open air (\({H}_{{\rm{understory}}}^{* }=\frac{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}{{r}_{{\rm{s}}}}\left({T}_{{\rm{s}}}-{T}_{{\rm{ao}}}\right)\)). Simultaneously, LE can also be disassembled into the latent heat flux from forest canopy to open air (LEcanopy) and the latent heat flux from soil surface to open air (LEunderstory). Finally, the forest’s total temperature feedbacks (ΔTSu) is given as,

$$\begin{array}{l}\Delta {T}_{{\rm{Su}}}=\Delta {T}_{{\rm{s}}}+\left(\frac{1}{{f}_{{\rm{r}}}^{1}}-1\right)\Delta {T}_{{\rm{a}}}=\frac{\left[1-K{\rm{exp }}\left(-\frac{C{\rm{LAI}}}{u}\right)\right]}{\frac{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}{{r}_{{\rm{s}}}}}{{{\phi}}}_{{\rm{n}}}\\ \qquad\qquad+\,\frac{\left[1-K{\rm{exp }}\left(-\frac{C{\rm{LAI}}}{u}\right)\right]}{\frac{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}{{r}_{{\rm{s}}}}}R-\frac{1}{\frac{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}{{r}_{{\rm{s}}}}}\left({\rm{L}}{{\rm{E}}}_{{\rm{canopy}}}+{\rm{L}}{{\rm{E}}}_{{\rm{understory}}}\right)\\ \qquad\qquad-\,\frac{1}{\frac{{\rho }_{{\rm{a}}}{C}_{{\rm{p}}}}{{r}_{{\rm{s}}}}}({H}_{{\rm{canopy}}}^{* }+{H}_{{\rm{understory}}}^{* })\end{array}$$
(8)

Subsequently, seasonal variations of temperature (ΔΔTS) were defined as \(\Delta T\) (i.e., \(\Delta {T}_{{\rm{a}}}\), \(\Delta {T}_{{\rm{s}}}\), \(\Delta {T}_{{\rm{Su}}}\)) of the warm season minus \(\Delta T\) of the cold season, while the long-term variations of temperature (\(\Delta \Delta {T}^{{\rm{C}}}\)) were estimated by the multi-year average \(\Delta T\) from 2008 to 2011 minus the multi-year average \(\Delta T\) from 2003 to 2006. The divide of warm seasons and cool seasons is according the degree of the month average temperature deviating from the local annual average temperature, with daily mean temperatures above the average defined as warm seasons, and below the average defined as cool seasons73.

Calculating the respective contributions of each independent factor to seasonal and long-term variations of ΔT Su

According to Eq. (13), ΔTSu is dependent on ϕn, R, LE, and \({H}^{* }\). Given a seasonal variation period from local warm season (i) to local cold season (j), the ϕn, R, LE and \({H}^{* }\) changes from \({{{\phi}}}_{{\rm{n}},i}\), \({R}_{i}\), \({{\rm{LE}}}_{i}\) and \({H}_{i}^{* }\) to \({{{\phi}}}_{{\rm{n}},j}\), \({R}_{j}\), \({{\rm{LE}}}_{j}\) and \({H}_{j}^{* }\).

The relative contributions (CS) of seasonal changes in ϕn (\({C}_{{{{\phi}}}_{{\rm{n}}}}^{{\rm{s}}}\)), R (\({C}_{{\rm{R}}}^{{\rm{s}}}\)), \({LE}\) (\({C}_{{\rm{LE}}}^{{\rm{s}}}\)), LEunderstory (\({C}_{{\rm{L}}{{\rm{E}}}_{{\rm{understory}}}}^{{\rm{s}}}\)), LEcanopy (\({C}_{{\rm{L}}{{\rm{E}}}_{{\rm{canopy}}}}^{{\rm{s}}}\)), \({H}^{* }\) (\({C}_{{{\rm{H}}}^{* }}^{{\rm{s}}}\)), \({H}_{{\rm{understory}}}^{* }\) (\({C}_{{{\rm{H}}}_{{\rm{understory}}}^{* }}^{{\rm{s}}}\)) and \({H}_{{\rm{canopy}}}^{* }\) (\({C}_{{{\rm{H}}}_{{\rm{canopy}}}^{* }}^{{\rm{s}}}\)) to seasonal variations in \(\Delta \Delta {T}_{{\rm{Su}}}^{{\rm{S}}}\) are given as:

$${C}_{{{{\phi}}}_{{\rm{n}}}}^{{\rm{s}}}=\frac{\left[1-K{\rm{exp }}\left(-\frac{C{\rm{LAI}}}{u}\right)\right]\left(\frac{{\phi}_{{\rm{n}},i}-{\phi}_{{\rm{n}},j}}{\left|\bar{{\phi}_{{\rm{n}}}}\right|}\right)}{{{\rm{SUM}}}^{{\rm{S}}}}* 100 \%$$
(9)
$${C}_{{\rm{R}}}^{{\rm{s}}}=\frac{\left[1-K{\rm{exp }}\left(-\frac{C{\rm{LAI}}}{u}\right)\right]\left(\frac{{R}_{i}-{R}_{j}}{\bar{\left|R\right|}}\right)}{{{\rm{SUM}}}^{{\rm{S}}}}* 100 \%$$
(10)
$${C}_{{\rm{LE}}}^{{\rm{s}}}=\frac{\left(\frac{{{\rm{LE}}}_{i}-{{\rm{LE}}}_{j}}{\bar{\left|{\rm{LE}}\right|}}\right)}{{{\rm{SUM}}}^{{\rm{S}}}}* 100 \%$$
(11)
$${C}_{{\rm{L}}{{\rm{E}}}_{{\rm{understory}}}}^{{\rm{s}}}=\frac{\left(\frac{{{\rm{LE}}}_{{\rm{understory}},{\rm{i}}}-{{\rm{LE}}}_{{\rm{understory}},j}}{\bar{\left|{\rm{L}}{{\rm{E}}}_{{\rm{understory}}}\right|}}\right)}{{{\rm{SUM}}}^{{\rm{S}}}}* 100 \%$$
(12)
$${C}_{{\rm{L}}{{\rm{E}}}_{{\rm{canopy}}}}^{{\rm{s}}}=\frac{\left(\frac{{{\rm{LE}}}_{{\rm{canopy}},i}-{{\rm{LE}}}_{{\rm{canopy}},j}}{\bar{\left|{\rm{L}}{{\rm{E}}}_{{\rm{canopy}}}\right|}}\right)}{{{\rm{SUM}}}^{{\rm{S}}}}* 100 \%$$
(13)
$${C}_{{{\rm{H}}}^{* }}^{{\rm{s}}}=\frac{\left(\frac{{H}_{i}^{* }-{H}_{j}^{* }}{\left|\bar{{H}^{* }}\right|}\right)}{{{\rm{SUM}}}^{{\rm{S}}}}* 100 \%$$
(14)
$${C}_{{{\rm{H}}}_{{\rm{understory}}}^{* }}^{{\rm{s}}}=\frac{\left(\frac{{H}_{{\rm{understory}},{\rm{i}}}^{* }-{H}_{{\rm{understory}},{\rm{j}}}^{* }}{\left|\bar{{H}_{{\rm{understory}}}^{* }}\right|}\right)}{{{\rm{SUM}}}^{{\rm{S}}}}* 100 \%$$
(15)
$${C}_{{{\rm{H}}}_{{\rm{canopy}}}^{* }}^{{\rm{s}}}=\frac{\left(\frac{{H}_{{\rm{canopy}},{\rm{i}}}^{* }-{H}_{{\rm{canopy}},{\rm{j}}}^{* }}{\left|\bar{{H}_{{\rm{canopy}}}^{* }}\right|}\right)}{{{\rm{SUM}}}^{{\rm{S}}}}* 100 \%$$
(16)

where \({\rm{SU}}{{\rm{M}}}^{{\rm{S}}}=\left|\left[1-K{\rm{exp }}\left(-\frac{C{\rm{LAI}}}{u}\right)\right]\frac{{{{\phi}}}_{{\rm{n}},j}-{{{\phi}}}_{{\rm{n}},i}}{\bar{{{{\phi}}}_{{\rm{n}}}}}\right|+\left|\left[1-K{\rm{exp }}\left(-\frac{C{\rm{LAI}}}{u}\right)\right]\frac{{R}_{j}-{R}_{i}}{R}\right|+\left|\frac{{{\rm{LE}}}_{j}-{{\rm{LE}}}_{i}}{\overline{{\rm{LE}}}}\right|+\left|\frac{{H}_{j}^{* }-{H}_{i}^{* }}{\bar{H}}\right|\). \(\left|\bar{{{{\phi}}}_{{\rm{n}}}}\right|\), \(\bar{\left|R\right|}\), \(\bar{\left|{\rm{LE}}\right|}\), and \(\bar{\left|{H}^{* }\right|}\) are the absolute average values of ϕn, R, LE, and \({H}^{* }\).

Thereafter, we translated this contribution into a change on temperature of the concerned factors (i.e., \(\Delta \Delta {T}_{{\rm{Su}},{{{\phi}}}_{{\rm{n}}}}\), \(\Delta \Delta {T}_{{\rm{Su}},{\rm{R}}}\), \(\Delta \Delta {T}_{{\rm{Su}},{\rm{LE}}}\), \(\Delta \Delta {T}_{{\rm{Su}},{{\rm{H}}}^{* }}\), Fig. 3). Significantly, the calculation method of contribution of energy component to long-term variations of \(\Delta {T}_{{\rm{Su}}}\) is same as seasonal variations of \(\Delta {T}_{{\rm{Su}}}\).

Intrinsic biophysical mechanism (IBM) and decomposing the understory energy redistribution

The IBM was developed by Lee et al.22 based on the surface energy equilibrium equation, an attribution method consisting of several factors (Eq. (17)).

$$\Delta {T}_{{\rm{Lee}}}\approx {\lambda }_{0}\frac{\Delta S}{1+{f}_{{\rm{\beta }}}}+\left(-{\lambda }_{0}\right){R}_{{\rm{n}}}\frac{\Delta {f}_{{\rm{\beta }}}}{{\left(1+{f}_{{\rm{\beta }}}\right)}^{2}}$$
(17)

where ΔTLee represents the surface temperature difference between forest and nonforest lands estimated by Lee et al.22 \({\lambda }_{0}\) represents expressed as the sensitivity of temperature to changes in net short-wave radiation; \({f}_{{\rm{\beta }}}\) represents considered as an energy redistribution factor caused by the Bowen ratio (\(\beta =H/{\rm{LE}}\)); \({R}_{{\rm{n}}}\) (\({R}_{{\rm{n}}}={\phi}_{{\rm{n}}}+{R}_{{\rm{near}}}={\phi}_{{\rm{n}}}+{R}_{{\rm{sky}}}-{R}_{{\rm{outnear}}}\)) represents net radiation; Rnear represents the differences between incoming and outgoing long-wave radiation for the composite surface; Routnear represents total long-wave radiation of the composite near-surface; ΔS represents the changes of net short-wave radiation.

By partitioning the composite surface layer into canopy, understory air and soil layers, the CAS model decomposed the biophysical mechanism as formulated in Eq. (18)14. In comparison with Lee’s model22, the \(\Delta {T}_{{\rm{Lee}}}\) based on CAS model is a mixed temperature effect composed of understory \({\Delta T}_{{\rm{a}}}\), understory \({\Delta T}_{{\rm{s}}}\), and a residual term resulting from the difference between \({T}_{{\rm{c}}}\) and \({T}_{{\rm{ao}}}\) in overstory14,16 (Eq. 19).

$$\begin{array}{l}\Delta {T}_{{\rm{s}}}+\left(\frac{1}{{f}_{{\rm{r}}}^{1}}-1\right)\Delta {T}_{{\rm{a}}}+\frac{1}{{f}_{{\rm{r}}}^{1}}\left(1-{f}_{{\rm{r}}}^{2}\right)\left({{T}_{{\rm{c}}}-T}_{{\rm{ao}}}\right)\\\qquad\approx {\lambda }^{{\prime} }\frac{\Delta S}{1+{f}_{{{\beta }}}}+\left(-{\lambda }^{{\prime} }\right){R}_{{\rm{n}}}\frac{\Delta {f}_{{{\beta }}}}{{\left(1+{f}_{{{\beta }}}\right)}^{2}}\end{array}$$
(18)
$$\begin{array}{l}\Delta {T}_{{\rm{Lee}}}=\Delta {T}_{{\rm{s}}}+\left(\frac{1}{{f}_{{\rm{r}}}^{1}}-1\right)\Delta {T}_{{\rm{a}}}+\frac{1}{{f}_{{\rm{r}}}^{1}}\left(1-{f}_{{\rm{r}}}^{2}\right)\left({{T}_{{\rm{c}}}-T}_{{\rm{ao}}}\right)\\\qquad\quad=\Delta {T}_{{\rm{Su}}}+\frac{1}{{f}_{{\rm{r}}}^{1}}\left(1-{f}_{{\rm{r}}}^{2}\right)\left({{T}_{{\rm{c}}}-T}_{{\rm{ao}}}\right)\end{array}$$
(19)

Data collection and preprocessing for model field validations

According to Eqs. (1–19), time-series data of global air temperature (Ta), short-wave downward solar radiation (ϕn), vapor pressure deficit (VPD), albedo, latent heat flux (LE), daytime surface temperature (Ts), normalized difference vegetation index (NDVI), leaf area index (LAI), canopy height (hc), cloudiness coverage (Ccover), soil moisture (ms) and wind speed (\(U({V}_{{\rm{z}}})\)) were collected in this study (data sources and resolution see Supplementary Table 1).

First of all, we performed data quality control and filtering. The LE data was subjected to a standardized quality control procedure whereby data were first filtered to remove missing data and LE measurements greater than 1500 W m−2. Meteorological data were also screened for obvious outliers (i.e., air temperature < −30 °C or > 50 °C, net radiation < −500 W m−2 or greater than 1500 W m−2). The pixels with quality assurance (QA) as “Clouds”, “Other errors”, “Cirrus cloud”, “Missing pixel”, “Poor quality”, “Land Surface Temperature (LST) > 3 K”, “Average emissivity error >0.04” of MODIS Ts data were all removed74. Meanwhile, the observations carried out during cloudy days were excluded, which might lead to a degree of uncertainty.

And then, all the data were resampled into 0.05° and averaged to monthly data after quality control and were applied in the CAS model to map global ΔTSu, ΔTs and ΔTa.

It should be noted that the NDVI75 and land use map datasets76 from the Moderate-resolution Imaging Spectroradiometer (MODIS), as well as ice and snow datasets77 from the National Snow and Ice Data Center (NSIDC) were used to identify forest cover in November to January without the impact of ice and snow pixels. As the MODIS LAI78 of high-latitude evergreen forests is relatively biased (i.e., low) during the cold season, it might lead to an overestimation of the vertical aerodynamic resistance ratio parameters (\({f}_{{\rm{r}}}^{1}\) and \({f}_{{\rm{r}}}^{2}\))14,16, which results in a decrease of \(\Delta {T}_{{\rm{s}}}\) (the soil temperature difference between forests and open lands) and \(\Delta {T}_{{\rm{a}}}\) (the air temperature difference between forests and open lands); Therefore, we used the maximum values of LAI during the November to January time period to minimize these impacts. To attenuate the noises, we used adjacent open lands (i.e., grasslands and shrubs) as reference lands for the forests and extracted 10 pixels of soil and air temperature for the open lands, removed the maximum and minimum values and used the average values as soil temperature of open lands and air temperature of open lands.

In order to decompose LE into latent flux of canopy layer (LEcanopy) and latent flux of understory layer (LEunderstory), we used actual evaporation (E) minus interception loss (Ei) and transpiration (Et) from Global Land Evaporation Amsterdam Model (GLEAM) datasets79 as the proportion of canopy (LEcanopy) and understory (LEunderstory), respectively. All acronyms used in this study are listed in Table 1.

Table 1 Definitions of all the acronyms used in this study.
Full size table

We divided the global forests into three regions, high latitudes forests (>50°N), temperate moderate latitudes forests (23.5°N–50°N and 23.5°S–50°S) and low latitudes forests (23.5°S–23.5°N), respectively. Records of eddy-covariance-derived ET and ancillary meteorological data were obtained from global eddy-covariance flux tower sites. Sites were chosen for inclusion in the study if at least ten years of data, including soil moisture data, were available and generally free of large gaps. Finally, global field datasets of 1833 samples from 32 global eddy-covariance flux tower sites (Supplementary Fig. 2 and Supplementary Table 1) were used to validate the modeled \({\Delta T}_{{\rm{a}}}\) and \({\Delta T}_{{\rm{s}}}\) by means of the CAS model at three latitudes. The datasets included 7 deciduous broadleaf forests (DBF), 2 evergreen broadleaf forests (EBF), 19 evergreen needle-leaf forests (ENF), and 2 mixed forests (MF).