Using the fully coupled climate model MPI-ESM , the temperature response to deforestation at the surface, at 2 m and the lowest layer of the atmosphere are obtained from simulations of large-scale deforestation. Simulations are performed at T63 atmospheric resolution (about 1.9∘) for 550 years, and the last 200 years (which are free of substantial trends in the investigated variables, not shown) are used for the analysis. Two simulations are performed: a first simulation (“forest world”) with forest plant functional types on all areas that can potentially be covered with vegetation (i.e., forests do not exist in deserts, etc., Fig. S1 in the Supplement). These vegetated areas are taken from a previous study , which derived a map of potential vegetation from remote sensing . The non-forest plant functional types were replaced by the forest types occurring in that grid cell (preserving the relative fraction of the different forest types). In a second simulation forests in the forest world are completely replaced by grasslands in three of four grid boxes in a regular spatial pattern (Fig. S1, equivalent to simulation “3/4” in a previous study; ). In both simulations, atmospheric CO2 concentrations are prescribed at preindustrial level in order to obtain only the biogeophysical effects of deforestation. The total, i.e., local plus nonlocal, biogeophysical deforestation effects are then computed as the differences (e.g., in temperature) between these two simulations.

Following the approach in , the total effects can be separated into the local and nonlocal effects of deforestation as follows: 1ΔTtotal=ΔTlocal′+ΔTnonlocal, where ΔTtotal are the temperature changes that are simulated at a deforested grid box and ΔTlocal′=ΔTlocal+ΔTlocal×nonlocal includes both the local effects and possible interactions between local and nonlocal effects. However, such interactions were found to be small across a wide range of deforestation scenarios , and in the following we refer ΔTlocal′ as “local effects”. The nonlocal effects are determined from non-deforested grid boxes, where only the nonlocal effects are present. The nonlocal effects are spatially interpolated to the deforested grid boxes using bilinear interpolation. The local effects at deforested grid boxes can thus be obtained by subtracting the nonlocal effects from the simulated total effects: 2ΔTlocal′=ΔTtotal-ΔTnonlocal. The local effects that are obtained this way are similar to the local effects that were obtained in previous studies by comparing temperatures in sub-grid tiles . In contrast to their methods, the method that is applied in this study includes local feedbacks between the surface and the atmosphere leading, for example, to local changes in clouds or precipitation. In addition, the method used in this study allows us to assess the local effects on the temperature of the lowest layer of the atmosphere (which in most models is not calculated separately for sub-grid tiles) and to assess nonlocal effects on temperature. The choice of deforesting three of four grid boxes is to some extent arbitrary; varying the spatial extent of deforestation influences the magnitude of the nonlocal effects on surface temperature , but the local effects on surface temperature within a grid box are largely insensitive to deforestation elsewhere . A detailed description and discussion of the separation approach can be found in .

This study investigates the response of three types of temperature to deforestation in the MPI-ESM: surface temperature (Tsurf), the temperature of the lowest atmospheric layer (Tatm), and near-surface air temperature (T2m, called “tas” in CMIP5). Although these temperature variables are part of the standard output of climate model simulations, different models may calculate them differently. In the following, details are provided on the calculations of these variables in the MPI-ESM.

The surface temperature Tsurf in the MPI-ESM is determined by solving the surface energy balance equation in a bulk canopy layer. For simplicity this layer has a heat capacity that is independent of the vegetation type. This bulk canopy layer exchanges heat with deeper soil layers via the ground heat flux.

It is not possible to assign one geometrical height to the surface layer in the MPI-ESM because there is an internal inconsistency between the two different aspects that are involved in the process of solving the surface energy balance equation: the calculation of the surface radiative budget (absorption of solar radiation and emission of terrestrial radiation to the atmosphere) and the calculation of the turbulent heat fluxes (latent and sensible heat). From the perspective of the radiative budget, the surface is where this radiative budget is calculated (i.e., where the energy balance is solved). In the presence of vegetation this is somewhere in the canopy, but geometrically its exact height cannot be specified. From the perspective of turbulent fluxes, the geometrical height d+z0 above the surface is where the wind speed would become zero in the wind profile based on Monin–Obukhov theory . Here, z0 denotes the aerodynamic roughness length and d is the zero-plane displacement height. This d takes into account the displacement effect exerted by vegetation . Geometrically the height d+z0 may differ from the height where the radiative budget is calculated.

What does this inconsistency imply for the comparison between Tsurf in the MPI-ESM and satellite-based products? For comparison with satellite observations only the radiative perspective is relevant – because satellites estimate temperature based on the emissions of terrestrial radiation. That the Monin–Obukhov theory provides a different definition of surface height must be considered as a special approximation to solve the energy balance but has no consequences for comparison with satellite observations of Tsurf.

The “atmospheric temperature” Tatm is defined here as the temperature of the lowest of the 47 atmospheric layers in the MPI-ESM . The thickness of this layer is around 60 m (at 15 ∘C), and the temperature is volume-averaged in this layer. This temperature is used for the calculation of the turbulent heat fluxes and Tsurf.

The near-surface air temperature T2m is estimated in the MPI-ESM as temperature of the air at 2 m above d+z0. Because it is unclear (and irrelevant for the calculations) where within the canopy this d+z0 is, a comparison of T2m between the MPI-ESM and observations is challenging, especially in forests (see Sect. ). The MPI-ESM does not have a representation of within-canopy air temperature or separate temperatures of the surface and the vegetation canopy.

In the MPI-ESM, following , T2m is obtained via a procedure based on Monin–Obukhov similarity theory that uses the values at the surface and the lowest atmospheric layer. This procedure employs dry static energy instead of temperature because dry static energy is a conserved quantity in an adiabatic process. 3szaero=cpTzaero+gzaero, where cp is the heat capacity of moist air, and g is the gravitational acceleration of the Earth, and szaero and Tzaero are the dry static energy and temperature at the aerodynamic height zaero=z-(d+z0) where z is the height above the surface.

At 2 m above d+z0, the dry static energy is then obtained as follows: 4s2m=ssurf+(satm-ssurf)γ2mz0,Ri, where ssurf and satm denote the dry static energy at the surface and the lowest atmospheric layer, and γ is a nonlinear function based on Monin–Obukhov similarity theory with values ranging between 0 and 1 that depends on the roughness length z0 and on the bulk Richardson number Ri, which is closely related to the temperature gradient Tsurf-Tatm. Different functions for γ are used for near-surface neutral (Ri≈0), stable (Ri<0), and unstable conditions (Ri>0) Sect. 3.1.3. Note that both ssurf and satm, but also Ri and z0 are affected by deforestation. After this procedure, T2m is obtained as Taero from Eq. () by setting zaero=2m.

The response of Tsurf and T2m to deforestation in the Northern Hemisphere midlatitudes is compared across a wide range of climate models from CMIP5: CanESM2, CCSM4, CESM1-CAMS, GFDL-CM3, HadGEM2-ES, IPSL-CM5A-LR, MPI-ESM-LR, and NorESM1-M. Given that the these models did not simulate the 3/4 deforestation (see Sect. ), we invoke the difference between “historical” and “piControl” simulations to isolate the local temperature response from the CMIP5 ensemble . The historical simulations are subject to all forcings including changes in greenhouse gases and land use, while the piControl simulations are subject to constant boundary conditions and no forcings. To isolate the local effects of deforestation, we use a method that was already applied and validated on these simulations . This method assumes that temperature in neighboring grid boxes can be affected differently by the local effects of deforestation, depending on the forest cover change in each grid box, whereas other climate forcings (like greenhouse gases, but also the nonlocal effects) influence neighboring grid boxes in a similar way. Linear regressions are fitted between temporal changes in temperature (the so-called predictand) and forest cover change (the so-called predictor) within a spatially moving window encompassing 5×5 model grid boxes. In the center of this moving window, the local effects are then defined as the temperature change for a hypothetical conversion of 100 % forest into 100 % open land (given by the slope of the regression) and is by construction largely independent of the changes due to the nonlocal greenhouse gas forcing and nonlocal deforestation effects (given by the y intercept of the regression).

We consider here the difference between the last 30 years (1971–2000) of historical simulations for which data in all models are available and 30 years of the preindustrial control simulations (piControl), from which the temporal changes in both temperature variables and forest fraction since 1860 are computed. The historical simulations consist of several ensemble members for each model, where each ensemble member experiences the same forcings but starts from different initial conditions. The moving-window method is applied to several combinations of ensemble members from the historical simulations and time slices from the piControl simulations for each model, and the number of analyzed ensemble members is shown in Table S1 in the Supplement.

For this inter-model comparison, we focus on the local effects for two reasons. (1) The nonlocal deforestation effects cannot be isolated from the analyzed set of simulations because the nonlocal deforestation effects cannot be distinguished from nonlocal greenhouse gas forcing in these simulations. (2) The local effects exhibit a better signal / noise ratio compared to the nonlocal effects e.g.,. This is important because the climate variability can be large compared to the nonlocal effects for the short time spans (30 years) that are analyzed here . Furthermore, climate variability is especially large in the midlatitudes that are analyzed in the inter-model comparison.

In the MPI-ESM, deforestation in three of four grid boxes triggers substantial nonlocal cooling in most regions (Fig. ). This happens because deforestation locally reduces the input of latent and sensible heat from the surface to the atmosphere . Thus, the atmosphere becomes cooler and drier (not shown), and this leads to a reduction in Tsurf in many regions, mainly because of reduced longwave incoming radiation . The spatial pattern of these nonlocal effects is very similar for Tsurf, T2m, and Tatm.

In contrast to the nonlocal effects, the local effects differ strongly between Tsurf, T2m, and Tatm. Deforestation strongly influences the local surface energy balance: the imposed changes in surface properties in the model (surface albedo, evapotranspirative efficiency and surface roughness) cause a surface warming for the local effects in most regions, except for the high northern latitudes where the local effects cause a surface cooling (Fig. ). The changes in surface properties influence not only the local Tsurf but also the flux of sensible heat from the surface into the lower boundary layer (not shown). Intuitively one would expect that the change in sensible heat flux alters Tatm; e.g., an increased input of sensible heat into the atmosphere could raise the temperature of the atmospheric air above a deforested location. However, in our model results Tatm is largely unaffected by the local effects of deforestation (Fig. ). We interpret this lack of local effects in Tatm as follows: it takes long enough for the lowest atmospheric layer to warm up (due to the deforestation-induced increase in sensible heat flux) for the heated air to be transported to higher atmospheric layers and the neighboring grid boxes. Due to the advection, the change in Tatm is hence not only seen in a deforested location but also in nearby grid boxes that are not deforested. Thus, this warming or cooling is accounted for in the nonlocal effects. In the nearby grid boxes, the change in Tatm and/or atmospheric moisture can then also influence Tsurf via changes in longwave incoming radiation , which could explain why the nonlocal effects are similar for Tatm and Tsurf. While in Tatm, advection can lead to a direct exchange of heat between neighboring grid cells, the same is not possible for Tsurf; there is no direct horizontal exchange of heat between the surface of neighboring grid cells, and this difference (advection for Tatm but not Tsurf) may explain why local effects can be seen in Tsurf but not in Tatm.

Because T2m is an interpolation between Tsurf and Tatm, we expected that the local response of T2m would also lie in between the response of Tsurf and Tatm. In a lot of regions this is the case, but in other regions, most notably those that show a cooling, the local effects on T2m seem to cool more than Tsurf, and in some regions even the sign differs between Δ Tsurf and Δ T2m (e.g., parts of the US and regions in the southern extratropics; Fig. S3). The different response of Tsurf and T2m in relation to the observation-based findings is discussed in Sect. .

To better understand the apparent discrepancy between Δ Tsurf and Δ T2m, we separately analyze the local temperature response for boreal winter (DJF) and summer (JJA) and the response of mean daily minimum temperature (Tmin, which approximately corresponds to nighttime conditions) and maximum temperature (Tmax, which approximately corresponds to daytime conditions). For Tsurf, the response to deforestation locally differs strongly between DJF, JJA, Tmin, and Tmax values (Fig. ). For Northern Hemisphere DJF and Tmin, deforestation leads to a local Tsurf cooling, while for JJA and Tmax, deforestation leads to a local Tsurf warming. This is qualitatively in good agreement with observation-based studies that show a local cooling in the boreal regions in DJF and in agreement with the local increase in the diurnal amplitude due to deforestation . Similarly as in the case of long-term mean temperature (Fig. ), Tatm locally shows little response to deforestation, neither for DJF, JJA, Tmin, nor Tmax (Fig. ). For both Tsurf and T2m, the annual mean response then depends on the balance between the daytime and nighttime response and on the balance between the responses in different seasons.

For near-surface air temperature, the Tmax response is substantially weaker, and in many areas of opposite sign, than for the surface, similar to the lowest atmospheric layer (land mean absolute changes for Tmax: 1.62 K for Tsurf, 0.19 K for T2m, and 0.10 K for Tatm). On the contrary, most regions exhibit a strong Tmin cooling of T2m, similar to the Tmin response of Tsurf (land mean absolute changes for Tmin: 0.67 K for Tsurf, 0.48 K for T2m, and 0.10 K for Tatm).

Tmax responds differently for Tsurf and T2m not only for annual mean Tmax, but in some tropical or subtropical regions also for Tmax during DJF and JJA (Fig. S9). We interpret this as follows: during the daytime when Tmax occurs, the Tsurf is higher than the temperature of the lowest atmospheric layer (Fig. S4) because the surface is heated by incoming radiation. In accordance with previous studies e.g.,, deforestation further increases Tsurf (Fig. ) and thus also the difference between Tsurf and Tatm (illustrated in Fig. S5b). Intuitively, one would expect that an increase in this difference would result also in an increase in T2m. But by the increased surface temperature, the well-mixed zone in the boundary layer not only extends to larger heights, but also extends further down. Accordingly, the cooler air from above mixes further down, and if this affects heights below 2 m, T2m is lowered. In the model's calculation of T2m, a deforestation-induced increase in Tsurf increases the difference between Tatm and Tsurf and thus leads to an even more negative Richardson number Ri. This Richardson number enters the similarity function for the calculation of s2m (γ in Eq. ; see underlying report; ) such that the vertical profile of s2m becomes more nonlinear and the calculated T2m approaches Tatm. As a result, daily maximum T2m in the model may decrease although Tsurf increases.

During nighttime when Tmin occurs, the surface loses energy via outgoing longwave radiation, and thus the surface is often cooler than the overlying atmosphere (Fig. S4). In accordance with previous studies e.g.,, deforestation further decreases Tsurf and thus Tsurf and Tatm further diverge. For T2m, one expects that less vertical mixing than during the daytime results in T2m tending towards Tsurf. In the model's calculation of T2m, this behavior is a result of the γ in Eq. () being less nonlinear in stable compared to unstable conditions (for the concrete form of the γ function, see ) with the consequence that T2m at deforested locations stays closer to Tsurf compared to daytime conditions (Fig. S5a). As a result, in most regions the calculated T2m follows the deforestation-induced nighttime surface cooling but not necessarily the deforestation-induced daytime surface warming.

The different T2m responses for DJF and JJA in the model may be caused by the same mechanism that may be responsible for the different behaviors for Tmin and Tmax. In JJA, when the surface is often warmer than the overlying atmosphere, deforestation leads to a further local Tsurf warming (Fig. ). Similar to the case of Tmax, T2m barely responds or even responds with a cooling in some regions. In DJF, when the surface is often cooler than the overlying atmosphere, deforestation leads to a local Tsurf cooling. Similar to the case of Tmin, T2m also shows a substantial cooling in most Northern Hemisphere regions. The reason why T2m responds similarly to Tsurf in Northern Hemisphere DJF but not JJA may be similar to the reason why T2m responds similar to Tsurf for Tmin but not for Tmax, as described in the previous two paragraphs. Our findings are in qualitative agreement with the findings of (their Fig. 9), who found a strong deforestation-induced daytime Tsurf warming and a moderate T2m cooling in many regions using the CLM (Community Land Model). Whether or not Tsurf and T2m respond similarly to deforestation may strongly depend on how T2m is calculated in the respective climate model. For the summer and winter response in the northern midlatitudes, the responses of Tsurf and T2m are compared across climate models from CMIP5 in the following.

While the above results refer only to the MPI-ESM climate model, quantitatively the local effects on Tsurf and T2m also differ in other climate models (Fig. ). We analyze the local effects of historical deforestation and the average over midlatitude areas (40–60∘ N) that have experienced intense deforestation (≥15%) since 1860. We choose the northern midlatitudes for two reasons. (1) This is where most historical deforestation happened, and regions with intense deforestation are required in the moving-window approach for isolating the local effects across models (see Sect. ), and (2) the midlatitudes are a suitable test case because there the local effects on Tsurf have a different sign in the winter (DJF) and summer season (JJA) (Fig. ).

In the areas considered, in most models (with the exception of CanESM2 and GFDL-CM3) Tsurf and T2m respond similarly for changes in annual means (Fig. a). This is also true for the MPI-ESM – Tsurf and T2m respond similarly when averaged over the respective regions (midlatitude areas (40–60∘ N) that have experienced intense deforestation (≥15%) since 1860). A difference in response between Tsurf and T2m becomes apparent also for the midlatitudes when analyzing seasons (DJF and JJA separately) instead of annual means. Almost all of the tested models show substantial differences between Tsurf and T2m at a seasonal scale (Fig. b–c).

In JJA (Fig. c), all but one model show a surface warming locally, with the Tsurf responding more strongly than T2m by a factor of around 2 (Table S1). Only the HadGEM2-ES climate model is an outlier: there, Tsurf responds to deforestation with a local cooling (-0.13 K), which is not in agreement with observation-based studies , and in the HadGEM2-ES T2m cools even more strongly (-0.27 K) than Tsurf. This inter-model comparison confirms that the local deforestation responses of Tsurf and T2m quantitatively differ strongly in JJA, but in contrast with the MPI-ESM results shown above (Fig. ), all models in Fig.  show the same sign of the JJA responses for Tsurf and T2m.

In DJF (Fig. b), all but one model show a surface cooling locally, again with Tsurf responding stronger than T2m in most models. An exception is the CanESM2 model, which locally responds to deforestation with a strong Tsurf warming and T2m cooling. In some of the other climate models (CCSM4, CESM1-CAM5, NorESM1-M, all sharing the same land surface model CLM4), the Tsurf cooling is approximately twice the cooling of T2m, analogous to the JJA response. In other models (GFDL-CM3, HadGEM2-ES, IPSL-CM5A-LR, MPI-ESM-LR), the two variables respond more similarly in DJF compared to JJA.

Overall, the inter-model comparison suggests that the quantitatively different response of Tsurf and T2m is not specific to the MPI-ESM model. In agreement with previous studies , the inter-model spread in the temperature response in Fig.  is large (e.g., in JJA inter-model (excluding the HadGEM2) standard deviation 0.20 K, inter-model mean 0.38 K). However, the investigated models agree better concerning the ratio between the T2m and Tsurf response (JJA inter-model (excluding the HadGEM2) standard deviation 0.11, inter-model mean 0.50). Both for DJF and JJA (Table S1), and for most of the investigated models, the ratio of changes in T2m and Tsurf of 0.5 (range 0.35–0.65, excluding HadGEM2) is largely independent of the magnitude and sign of the Tsurf response. The temperature response of T2m is between zero and the response of Tsurf with a ratio that depends on the exact way in which T2m is calculated in the respective models (but most likely all models use a Monin–Obukhov approach). Further studies may investigate to what extent the calculation of T2m differs across models.