Diagnosing nonlinearities in the local and remote responses to partial Amazon deforestation
Abstract
Using a set of fully coupled climate model simulations, the response to partial deforestation over the Amazon due to agricultural expansion has been analyzed. Three variations of 50% deforestation (all of western half, all of eastern half, and half of each grid box) were compared with total deforestation to determine the degree and character of nonlinearity of the climate response to partial deforestation. A metric is developed to quantify the degree and distribution of nonlinearity in the response, applicable to any variable. The metric also quantifies whether the response is saturating or accelerating, meaning significantly either more or less than 50% of the simulated response to total deforestation is attained at 50% deforestation. The spatial structure of the atmospheric response to Amazon deforestation reveals large areas across the tropics that exhibit a significant nonlinear component, particularly for temperature and geopotential height. Over the domain between 45°S and 45°N across all longitudes, 50% deforestation generally provides less than half of the total response to deforestation over oceans, indicating the marine portion of climate system is somewhat resilient to progressive deforestation. However, over continents there are both accelerating and saturating responses to 50% Amazon deforestation, and the response is different depending on whether the eastern or western half of Amazonia is deforested or half of the forest is removed uniformly across the region.
Key Points
- By analyzing three 50% deforestation scenarios, nonlinearities appear
- Certain regions appear to be sensitive to deforestation, regardless of deforestation pattern
- A new metric to determine linearity of a system is proposed
1 Introduction
Land use change has largely been regarded as a local environmental issue. However, large-scale land use change, such as Amazon deforestation, may potentially have remote impacts [Henderson-Sellers et al., 1993; McGuffie et al., 1995; Zhang et al., 1996; Foley et al., 2005; Hasler et al., 2009; Nobre et al., 2009; Jonko et al., 2010; Snyder, 2010; Badger and Dirmeyer, 2015a].
Although conversion of rainforest for agricultural applications is the driving trend in Amazon deforestation [Davidson et al., 2012], few studies have used crops as replacement vegetation. Amazon deforestation simulations have historically focused on covering the entire Amazon region with a single vegetation type, typically grass or shrubland [e.g., Dickinson and Henderson-Sellers, 1988; Shukla et al., 1990; Nobre et al., 1991; Henderson-Sellers et al., 1993; McGuffie et al., 1995; Costa and Foley, 2000; Costa et al., 2007; Hasler et al., 2009; Nobre et al., 2009; Davin and de Noblet-Ducoudré, 2010]; while some experiments have used bare soil [e.g., Snyder et al., 2004; Snyder, 2010]. As discussed in Lawrence and Vandecar [2015] and Walker et al. [2009], observationally, the local response is a warming and drying with unclear, scale-dependent local circulation responses that are very sensitive to the pattern of deforestation. Partial deforestation simulations with realistic land cover are the necessary next step.
Costa et al. [2007] is one example that used soybean as replacement vegetation, investigating the local response to deforestation by replacing 25%, 50%, and 75% of the Amazon with soybeans and pastureland in separate model simulations. The responses for varying the degree of deforestation with crops produced a 6.2%, 11.6% and 15.7% decrease in precipitation, respectively. Meanwhile, pastureland as a replacement vegetation produced a +1.4%, −0.8%, and −3.9% change in precipitation. While precipitation response to increasing levels of soybean coverage [Costa et al., 2007] was relatively linear, the response to varying levels of pastureland was not; these results suggest nonlinear responses are possible.
Lejeune et al. [2014] simulated 33%, 66%, and 100% deforestation using predicted deforestation distributions. They found through the analysis of areal averages of temperature and precipitation that partial deforestation behaves relatively linearly. However, it is suggested that this behavior may be model dependent and that feedback may be suppressed due to the model setup.
The results of Costa et al. [2007] and Lejeune et al. [2014] prompt several questions that are addressed in this study: (1) How linear is the local response to deforestation in climate quantities besides precipitation? (2) Are the remote responses linear or nonlinear? (3) Can we quantify the degree of nonlinear response in a useful manner? Building on previous work using a realistic heterogeneous crop distribution of corn, soybean, sugarcane, irrigated rice, and cotton as replacement vegetation [Badger and Dirmeyer, 2015a, 2015b], we approach the question of the linearity of the response to Amazon deforestation by comparing several experiments with 50% deforestation to a case with total deforestation. If 50% deforestation were to produce significantly more or less than 50% of the total deforestation signal, a nonlinear response would be indicated, suggesting feedback processes in the climate system were amplifying or dampening the response.
Using a more realistic heterogeneous crop distribution of corn, soybean, sugarcane, irrigated rice, and cotton as replacement vegetation [Badger and Dirmeyer, 2015b], this study aims to better quantify the degree of nonlinearity in the climate system. This study investigates the linearity of response to Amazon deforestation using two approaches to representing 50% deforestation; replacing half of the forest cover in each gridbox with tropical crops, and completely deforesting half of the total area of the Amazon leaving the other half untouched.
In reality, most deforestation has been occurring around the edges of the Amazon forest, to the east and southwest, and then moving inward. An eastern deforestation simulation would emulate the progression of deforestation occurring in the Brazilian states of Pará, Maranaho, Tocantins, and Matto Grosso. The western deforestation simulation progresses deforestation occurring in the Brazilian states of Acre, Rondônia, and Amazonas, as well as in Colombia and Peru. These partial deforestation simulations can provide some insight to the real world based on leading deforestation patterns.
It is also of note that differing responses to deforestation have been found in previous studies over the eastern and western portions of the Amazon. Dirmeyer and Shukla [1994] found that after deforestation, precipitation increases in the eastern Amazon and decreases in the western Amazon. McGuffie et al. [1995] notes that changes in surface temperature over after Amazon deforestation are dipolar: a significant increase over the central and eastern Amazon and a significant decrease to the southwest of the deforestation. Medvigy et al. [2011] describes an east-west dipole pattern for changes in temperature. Badger and Dirmeyer [2015b] also find an east-west contrast of significant changes when fully deforesting the Amazon.
Using a state-of-the-art global Earth system model, this study analyzes the climate response to differing spatial patterns of deforestation. This study also includes a full ocean general circulation model, so ocean temperatures are not prescribed. Model description and simulation setup is described in section 2. Regions demonstrating a nonlinear response are discussed to the extent that spatial distributions of deforestation impact remote regions in sections 3.1 and 3.2. This study also proposes a metric that quantifies the temporal nonlinearity of the responses to deforestation over a spatial domain to determine the character of the climate sensitivity to spatial patterns of deforestation in section 3.3.
2 Methods
2.1 Model Simulations
The Community Earth System Model (CESM) with active components of Community Atmosphere Model version 4 (CAM4), the Community Land Model version 4.5 (CLM4.5), the Parallel Ocean Program version 2 (POP2), the Community Ice CodE version 4 (CICE4), and the River Transport Model (RTM) have been used for the model simulations in this study [Vertenstein et al., 2013]. Global simulations have been run at an atmospheric model resolution of 0.9° × 1.25° and a nominal 1° ocean resolution grid with a displaced pole over Greenland for present day, year 2000, initial conditions. Each simulation has a 650 year spin-up simulation for the land surface by running CLM4.5 offline and cycling through the Qian et al. [2006] atmospheric forcing data set to achieve a relatively steady state for the carbon and nitrogen processes of the interactive phenology; the first 600 years are forced with years 1950 to 1990, and the last 50 years are forced with 1950 to 2000 data. The last land state from the offline simulations was then used at the land initial condition in the coupled simulations. Each coupled simulation is 250 years long with the last 125 years used for analysis. The first 125 years are discarded as the coupled ocean and sea ice are stabilizing during this period.
Five fully coupled CESM simulations have been completed for this study: a control run (CON), complete deforestation of the Amazon region (DEF), eastern deforestation (E.DEF), western deforestation (W.DEF), and 50% deforestation (DEF.50). In the DEF, E.DEF, W.DEF, and DEF.50 simulations, a distribution of tropical crops [Badger and Dirmeyer, 2015b] is used to replace Amazon vegetation (Figure 1). Using the data of Portmann et al. [2010] and regridding for use in CLM4.5, each gridbox in the specified domain (85°W–35°W, 30°S–13°N) containing any tree plant functional types (PFT) (tropical broadleaf evergreen and tropical broadleaf deciduous) is deforested; all existing PFTs in that gridbox are removed and replaced with tropical crops. The methodology to determine the spatial distribution of each crop is described by Badger and Dirmeyer [2015b].
In the E.DEF and W.DEF simulations, the Amazon is divided in half to provide nearly equal deforestation areas. The 62°W is the halfway line based on annual leaf area index (LAI), i.e., the area integral of annual mean LAI in the Amazon region to the east and west of 62°W is nearly identical in the control simulation. The columns of gridboxes east and west of 62°W were immediately used as a transition zone. Depending on the portion being deforested, these gridboxes were deforested 66% and 33% to smooth the transition rather than have a stark boundary along the edge of the grid boxes. In the DEF.50 simulation, 50% of the present PFTs are removed from each gridbox and replaced with the tropical crop distribution.
As previously discussed by Neale et al. [2013], CAM4 in coupled simulations with POP2 does an adequate job of simulating the mean tropical climate, and shows improvement in simulating the tropical circulation and precipitation. CLM4 and CLM4.5 are shown to be improved and have more realistic response to the role of the land surface, as well as being appropriate for studies regarding the role of the land surface in the climate system [Lawrence et al., 2012; Oleson et al., 2012]. Badger and Dirmeyer [2015b] note that tropical crops introduced to CLM4.5 fall within the expected range for leaf area index (LAI), plant heights, seasonal growth cycle, and timing of planting and harvest. Davidson et al. [2012] note that pasturelands are dominant use of cleared land in the Amazon region; representing pasturelands introduces an added level of complexity, as they are periodically burned, adding an additional perturbation to surface LAI and albedo [Fisch et al., 1994]. Using a heterogeneous crop cover makes for a more realistic land cover state than previous simulations that use a homogeneous replacement vegetation.
2.2 A Context for Linearity
(1)
(2)
(3)
(4)
(5)
(6)If equations 5 and 6 are not true, the response to Amazon deforestation is not linear. Realistically, equations 5 and 6 will not be exactly satisfied in a perfectly linear case due to sampling error and natural variability within the Earth system model, a student's t test can be applied to determine whether they are significantly different, which would indicate nonlinearity. When subtracting ΔDEF from the partial anomalies in equations 5 and 6, a positive (negative) significant difference for areas of increase (decrease) in ΔDEF would indicate a saturating response where more than half of the response to complete deforestation is already realized with only half deforestation. A significant negative (positive) difference for areas of increase (decrease) in ΔDEF would indicate an accelerating response where the degree of change starts slowly and accelerates between half and total deforestation. So-called tipping point responses of climate to land use change would manifest as a saturating response if the tipping point is relatively close to the current land cover state and as an accelerating response if the tipping point is closer to complete deforestation. Other statistical measures used will be introduced as they are discussed in context with the results.
3 Results
All nonlocal analysis in this study is within the latitudinal limits of 45°S and 45°N, as these were the limits to which most remote responses were seen [Badger and Dirmeyer, 2015a]. Furthermore, at higher latitudes internal variability in the climate system associated with baroclinic waves produces statistically significant but highly transient responses that are likely meaningless in the context of this study. Four variables are analyzed: temperature, precipitation, midtroposphere geopotential height, and zonal wind at the lowest model level.
3.1 Spatial Distribution of Nonlinearities
To determine the spatial pattern of significant nonlinearities, a student's t test has been used. The first step is to remove the climatological annual cycle of CON from all the deforestation simulations, leaving a time series of anomalies relative to CON. The null hypotheses quantified in equations 5 and 6 are tested; with rejection at the 95% confidence interval indicating that the progressive response to deforestation does not behave linearly. The denominator of the test statistic uses a pooled variance from DEF and the respective partial deforestation case(s) being tested.
Badger and Dirmeyer [2015b] found general warming due to deforestation but cooling in the southeastern region where there are irrigated rice crops. When comparing the spatial patterns of surface temperature change (Figure 2), three areas of change appear prevalent; the local response over the Amazon region and remote responses over the equatorial Atlantic and Africa. The local response in DEF.50 shows more than half of the temperature response from DEF, indicating a saturating response as defined above. In contrast, the summed response ΔW.DEF and ΔE.DEF shows a more linear local response with nonlinearities arising near the transition region (Figure 1). The changes for both scenarios shows a saturating response but as a cooling. The Atlantic region shows a prominent region in both scenarios that is an accelerating response.
Badger and Dirmeyer [2015b] showed precipitation decreases were dominant over deforested areas except over the irrigated rice zone. Figure 3 shows precipitation largely has a linear response annually and seasonally for both scenarios. Regions of nonlinearity appear near the rising branch of the Hadley circulation. It appears the DEF.50 response has more nonlinear features but not to the extent that temperature (Figure 2) exhibits.
Geopotential height and winds illustrate the large-scale dynamical response of the atmosphere [Badger and Dirmeyer, 2015a]. In analyzing geopotential height at 200 hPa (Figure 4), it is seen that 50% deforestation provides a large area of nonlinear response, both locally in the Amazon region and remotely over the Atlantic, Indian, and western Pacific oceans. These appear in all seasons. In June–August (JJA) and September–October (SON), a nonlinear response is found over a majority of central Africa. When combining the anomalies for ΔW.DEF and ΔE.DEF, a significant nonlinear response extends around the equatorial region annually and in all seasons. Both scenarios primarily exhibit changes indicative of an accelerating response.
Zonal wind at the surface (Figure 5) has two primary areas where nonlinearities occur; locally and over Africa. Over the Amazon, DEF.50 does not produce half of the wind change seen in DEF, indicating a local accelerating response. The same can be said about the summed response from ΔW.DEF and ΔE.DEF. While DEF produces a significant change in zonal winds over Africa in JJA and SON, a nonlinear response appears in nearly all season for the partial deforestation scenarios. It is of note that the partial deforestation scenarios show a dipole response over Africa, while DEF provides a homogeneous response, indicating partial deforestation may provide either saturating or accelerating responses over the region.
3.2 Spatial Correlations
In order to determine how the pattern of change for each variable and partial deforestation scenario compares to the complete response to deforestation, a spatial correlation was calculated over the domain of interest. In order to determine the significance threshold, the spatial degrees of freedom (DOF) between 45°S and 45°N are estimated using the method proposed by Bretherton et al. [1999]. This method requires summing the inverse squares of the explained variance for each EOF of the time series [Bretherton et al., 1999, equation (4)]. The method is applied to each individual simulation to obtain the DOF for each season and variable. For each variable across all simulations and in each season, the DOF were similar, so a mean seasonal DOF across all experiments was used to calculate significance. In calculating the correlations between ΔDEF and ΔDEF.50, and between ΔDEF and the sum of ΔE.DEF and ΔW.DEF, a significant result indicates that a linear response cannot be rejected as a possibility.
Table 1 shows the spatial correlations for each scenario, variable and season, along with the associated p values. A significant result at the 95% confidence level using single-tailed test (i.e., linear response), was found for all temperature, precipitation, geopotential height, and zonal wind correlations. This indicates that the overall spatial pattern of changes exhibited by the partial deforestation scenarios is not significantly different from a linear interpolation between control and total deforestation simulations.
| Correlation | p Value | Correlation | p Value | Correlation | p Value | Correlation | p Value | |
|---|---|---|---|---|---|---|---|---|
| Temperature | ||||||||
| DJF (13.88) | MAM (18.83) | JJA (18.45) | SON (13.74) | |||||
| East + west | 0.83 | 0.0001 | 0.86 | 0.0000 | 0.94 | 0.0000 | 0.90 | 0.0000 |
| 2 × Half | 0.69 | 0.0024 | 0.72 | 0.0002 | 0.87 | 0.0000 | 0.84 | 0.0001 |
| Precipitation | ||||||||
| DJF (11.16) | MAM (24.49) | JJA (16.61) | SON (14.39) | |||||
| East + west | 0.81 | 0.0006 | 0.85 | 0.0000 | 0.86 | 0.0000 | 0.86 | 0.0000 |
| 2 × Half | 0.73 | 0.0031 | 0.83 | 0.0000 | 0.72 | 0.0005 | 0.74 | 0.0006 |
| Geopotential Height | ||||||||
| DJF (7.70) | MAM (11.44) | JJA (11.52) | SON (14.74) | |||||
| East + west | 0.70 | 0.0192 | 0.75 | 0.0020 | 0.71 | 0.0037 | 0.81 | 0.0001 |
| 2 × Half | 0.61 | 0.0440 | 0.51 | 0.0430 | 0.50 | 0.0450 | 0.55 | 0.0147 |
| Zonal Wind | ||||||||
| DJF (8.15) | MAM (18.87) | JJA (15.89) | SON (14.31) | |||||
| East + west | 0.84 | 0.0022 | 0.84 | 0.0000 | 0.92 | 0.0000 | 0.91 | 0.0000 |
| 2 × Half | 0.74 | 0.0109 | 0.72 | 0.0002 | 0.75 | 0.0003 | 0.77 | 0.0003 |
- a Degrees of freedom for each correlation in parentheses next to respective season.
3.3 Degree of Nonlinearity
We propose a quantitative method to estimate the temporal degree of nonlinearity (DNL) in the response of climate variables to deforestation. This is to help avoid confusion regarding signs of responses versus acceleration/saturation in the previous sections and to provide a means to assess nonlinearity of responses over arbitrary domains. By the definition of collinearity, if the area of a triangle defined by vertices at three points has an area of zero, then the three points lie along the same line and are completely linear (Figure 6). If the triangle has an area greater than zero, then the three points are not on the same line and are therefore nonlinear to a certain degree.
Using this concept, a metric has been developed to quantify a measure of temporal nonlinearity at each point in the domain (45°S–45°N). The degree of deforestation is known for all three simulations and can be used as a sort of time axis on the abscissa to define triangles; CON =0; DEF.50, E.DEF, W.DEF =0.5, and DEF =1. The corresponding ordinate values are the means (annual or seasonal) of the climate variable for the respective simulation. At each gridbox a triangle can be defined by the three vertices: (0,
), (0.5,
), and (1,
) where DEFX corresponds to one of the partial deforestation simulations (Figure 6). △ADC in Figure 6 denotes the saturating response to partial deforestation, while △AEC represents an accelerating response.
), (0.5,
+σ), and (1,
). The partial deforestation is replaced in the reference triangle by the average of CON and DEF (which alone would give an area of zero) with the addition of 1 standard deviation based on the pooled variance of CON and DEF for the respective annual or seasonal means (Figure 6). The reference triangle defines a confidence level for determining linearity. Areas are calculated for each triangle, summed across all n grid points, and the following ratio defines the degree of nonlinearity:
(7)As seen in equation 7, summing the area of all the real triangles (numerator) would quantify the total nonlinear area, and summing the area of all the reference triangles (denominator) would quantify an expected degree of nonlinearity in an imperfectly sampled linear system. By normalizing the real triangle sum by the reference triangle sum, a single number can be given to state the DNL (see equation 7) for the entire domain. The smaller the ratio, the closer the system is to being perfectly linear, providing a relative measure.
This method can be taken one step further to determine whether the dominant source of nonlinearity is from an accelerating response or a saturating response. By binning the real triangles into either accelerating or saturating response category and signing the areas of the former as positive and the latter as negative, the sum of the signed triangle areas quantify the dominant response, called the binned DNL. Let the binned sum that is normalized be the sum of the reference triangle; a positive value would denote more of the nonlinearites arise from an accelerating climate response to deforestation and a negative value would indicate nonlinearities arise more from a saturating response.
To determine significance of the DNL and binned DNL, a bootstrap method has been utilized. Two sets of 125 years have been selected with replacement from each CON and DEF. One sample (Sample 1) of CON and DEF corresponds to the same years used for the end points above (i.e., (0,
) and (1,
); A and C in Figure 6). The remaining CON and DEF random samples (Sample 2) are averaged together to provide a half response. Real and binned triangles are calculated as previously described using the average of averaged CON and DEF from Sample 2 (i.e., D in Figure 6) with the CON and DEF from Sample 1. The reference triangles are calculated as previously described using the CON and DEF from the Sample 1 (i.e., B+σ in Figure 6). A distribution of 1000 values for DNL and binned DNL are collected to determine nonparametrically the percentiles of the half-deforestation cases. A DNL lying above the 95th percentile or a binned DNL either below the 2.5th or above the 97.5th percentile would indicate a significantly nonlinear response at the 95% confidence level.
Table 2 displays the DNL and binned DNL for each variable, season and partial scenarios as well as their associated percentiles. The DNL for temperature is significant annually and for all seasons across all simulations. The DNL for precipitation is significant annually and during all seasons for E.DEF and W.DEF. For DEF.50, the precipitation response is only significant in JJA and SON. Geopotential height is significant for DEF.50 and E.DEF annually and for all seasons. DEF.W has a significant DNL for annual, March–May (MAM) and SON means. Zonal wind shows a significant DNL annually and seasonally across all simulations.
| Half | West | East | ||||
|---|---|---|---|---|---|---|
| DNL | Binned DNL | DNL | Binned DNL | DNL | Binned DNL | |
| Temperature | ||||||
| Annual | 0.0888 | 0.0349 | 0.0915 | 0.0051 | 0.0911 | 0.0369 |
| DJF | 0.1265 | 0.0331 | 0.1304 | −0.0037 | 0.1210 | 0.0326 |
| MAM | 0.1523 | 0.0395 | 0.1633 | 0.0176 | 0.1478 | 0.0221 |
| JJA | 0.1392 | 0.0428 | 0.1448 | 0.0088 | 0.1612 | 0.0377 |
| SON | 0.1353 | 0.0603 | 0.1375 | 0.0273 | 0.1502 | 0.0441 |
| Precipitation | ||||||
| Annual | 0.0557 | 0.0057 | 0.0620 | 0.0064 | 0.0689 | −0.0049 |
| DJF | 0.0802 | 0.0073 | 0.0918 | 0.0012 | 0.1041 | −0.0124 |
| MAM | 0.0868 | 0.0037 | 0.1060 | 0.0014 | 0.1086 | 0.0013 |
| JJA | 0.0980 | −0.0010 | 0.0952 | −0.0065 | 0.0963 | 0.0027 |
| SON | 0.0949 | 0.0094 | 0.1066 | 0.0112 | 0.1063 | −0.0005 |
| Geopotential Height | ||||||
| Annual | 0.4450 | 0.3438 | 0.3498 | 0.2036 | 0.5269 | 0.4039 |
| DJF | 0.1236 | 0.0747 | 0.1137 | 0.0466 | 0.1506 | 0.0967 |
| MAM | 0.1522 | 0.0937 | 0.1289 | 0.0623 | 0.1622 | 0.0996 |
| JJA | 0.1434 | 0.1029 | 0.1039 | 0.0443 | 0.1914 | 0.1258 |
| SON | 0.1491 | 0.1118 | 0.1253 | 0.0734 | 0.1627 | 0.1034 |
| Zonal Wind | ||||||
| Annual | 0.0614 | 0.0077 | 0.0669 | 0.0088 | 0.0711 | −0.0011 |
| DJF | 0.0856 | 0.0160 | 0.1038 | 0.0133 | 0.1090 | −0.0087 |
| MAM | 0.1039 | −0.0120 | 0.1119 | −0.0067 | 0.1076 | 0.0053 |
| JJA | 0.1119 | −0.0033 | 0.1164 | −0.0101 | 0.1145 | 0.0067 |
| SON | 0.1101 | 0.0502 | 0.1085 | 0.0397 | 0.1014 | 0.0113 |
- a Italics indicate significance at the 95% level using the bootstrap method described in the text.
For binned DNL (Table 2), temperature has a significant response annually and for all seasons in the DEF.50 and E.DEF simulations corresponding to an accelerating response from partial to total deforestation. W.DEF has a significant accelerating response only for SON. Precipitation does not have any significant binned DNL values, suggesting that although there are many areas with nonlinear responses, the accelerating and saturating responses largely balance out geopotential height has a significant binned DNL annually and for all seasons across all simulations indicating an accelerated response. Zonal wind exhibits an accelerating response in SON for DEF.50 and W.DEF due to a significant binned DNL.
4 Discussion
Using three methods to analyze the linearity of the climate system response to progressive deforestation of the Amazon in a state-of-the-art Earth system model has provided some notable results. By testing equations 5 and 6, it is seen that in CESM, regions in the tropics respond differently for each variable and deforestation pattern. Locally, over the Amazon region, deforesting 50% of each grid box provides large areas of with a nonlinear response for temperature, geopotential height, and zonal wind. In contrast, by adding the anomalies of E.DEF and W.DEF, nonlinearity is locally present for temperature and geopotential height.
When looking remotely, prominent regions of nonlinear responses are seen over the Atlantic Ocean and Africa, implying that these are the most sensitive nonlocal regions to partial deforestation. One notable impact is when comparing partial deforestation changes to total deforestation for temperature over Africa. The Congo Basin is ringed by areas of nonlinear response, while the basin itself is not. This implies that the Congo region is less sensitive to partial deforestation than the surrounding areas. It should be noted that Africa is a region with a significant nonlocal response to total deforestation [Badger and Dirmeyer, 2015a]; southwest North America and extratropical South America feature significant nonlocal responses; however, they are not areas with a significant nonlinear response.
Another inference that can be made by looking at the impacts of partial deforestation is that different elements of the climate system respond differently. Temperature, geopotential height, and zonal wind all have large areas that behave nonlinearly. Temperature response appears nonlinear locally, over the Atlantic and Africa, zonal wind appears nonlinear locally and over Africa, while geopotential height appears nonlinear across a majority of the tropics. Precipitation exhibits a predominantly linear response both locally and remotely.
Analyzing the spatial correlation (Table 1) between partial and total deforestation, it can be seen that all correlations are significant; meaning that the pattern of the climate response to deforestation is robust regardless of the degree of deforestation. This result implies that remote regions that experience changes due to total deforestation are also the regions that experience changes to partial deforestation. Likewise, remote regions that are not sensitive to partial deforestation of the Amazon are also not sensitive to total deforestation.
The deviation from a linear response quantified across 45°S–45°N is significant for nearly all cases and variables, meaning the climate system does not respond linearly as deforestation progresses. Determining whether the nonlinearity is due to an accelerating response as opposed to a saturating response can provide some real world insight about the sensitivity of the climate system.
The only variable to show a significant binned DNL with respect to all partial deforestation scenarios is geopotential height, showing an accelerating response. This should be of particular interest as geopotential height can provide some insight into the large-scale circulation. Having a significant binned DNL means that partial deforestation will not alter the circulation by as much as half of the total response to deforestation. Indicating that there is a threshold of deforestation that the circulation would be sensitive to and cause large changes across the domain.
The fact that temperature has an accelerating response annually and seasonally for DEF.50 and E.DEF highlights an interesting sensitivity to partial deforestation. This indicates that in regard to temperature, the climate system may be sensitive to the spatial pattern of deforestation, as W.DEF does not provide the same binned DNL results. This is unlike the other variables tested that show a similar binned DNL for their respective partial deforestation scenarios.
When comparing W.DEF and E.DEF to DEF, an interesting result arises for temperature (Figure 7). If W.DEF or E.DEF are significantly different from DEF in a region where significant changes are found for equation 1 (shown in Figure 2), then it can be inferred that spatial pattern of deforestation does not cause that change. On the other hand, if there is not a significant change between W.DEF or E.DEF and DEF, then that spatial pattern can explain that change. Along the coast of South America in the eastern Pacific, significant changes in temperature are seen when comparing DEF to CON (Figure 2). In both W.DEF and E.DEF (Figure 7), the temperature change shown by DEF is not significantly different from those partial deforestation scenarios, implying that region is sensitive to Amazon deforestation, regardless of spatial pattern. In contrast, the significant temperature changes near the South American coast over the western Atlantic (Figure 2) cannot be explained by either W.DEF or E.DEF (Figure 7). This result indicates that region is less sensitive to those partial deforestation scenarios, but significant changes occur for total deforestation. Regions that behave like the western Atlantic can be found for other variables (not shown) and further justifies the findings of an accelerating response to deforestation.
Furthermore, when analyzing the percent change of sensible and latent heat flux over the deforested region; DEF.50 provides 82.5% of the sensible heat flux reduction found in DEF, but only 45.5% of the latent heat flux reduction is found in DEF. These differing changes at the surface further indicate that the response locally is not linear and can initiate a nonlinear response to the climate system.
The changes in surface fluxes with deforestation are not linear, and the resulting impacts on the growth of the planetary boundary layer can also be expected to behave nonlinearly, thus impacting the interactions with the free atmosphere and providing a nonlinear change to the atmospheric column over the region. This subsequently could impact diabatic heating and deep convection and alter the rising branch of the Hadley Circulation [Badger and Dirmeyer, 2015a], thus providing a vehicle for the remote nonlinear responses. This type of atmospheric response was noted by Hoerling et al. [1997], who point out how small zonal shifts in diabatic heating associated with another tropical heating anomaly, El Niño, greatly perturb wave trains and remote responses in a nonlinear fashion and generally shows the intrinsic nonlinearity of the climate system where tropical heating anomalies are concerned.
Li et al. [2016] attempts to address the nonlinearites that arise from partial global deforestation using an Earth system model with prescribed SSTs. Although Li et al. [2016] considers global deforestation, a mix of accelerating (temperature in the temperate region and precipitation in the tropical region) and saturating (temperature in the tropics and precipitation in the temperate region) responses is found. There is agreement with this study of a local accelerating response. Differences between this study and Li et al. [2016] could be due to differences in the handling of SSTs; Li et al. [2016] uses prescribed climatological SSTs while this study has a fully coupled ocean model. The prescribed SSTs could also constrain the atmosphere toward a climatological state by applying such a strong boundary condition. Additional factors, such as differing model physics and model resolutions, could also contribute to differing results.
Although choosing a fairly simple approach to test the presence of a nonlinear response to partial deforestation, the complexity of the climate model precludes identification of clear mechanisms without further sensitivity tests. For future determination of these mechanisms and with the expense of the fully coupled model simulations, such tests need to be planned carefully. Addressing the mechanisms for the nonlinearities is the clear next step.
5 Conclusions
This study has provided insights into the global response to partial deforestation of the Amazon by examining in CESM a case of total deforestation and three scenarios each representing deforestation of half of the Amazon: 50% deforestation in each gridbox, deforestation of the eastern Amazon, and deforestation of the western Amazon.
Using a student's t test to analyze equations 5 and 6, it was found that there are regions that respond nonlinearly. However, not all variables respond with the same degree of nonlinearity, and both local and certain remote regions in the tropics and subtropics appear to be especially sensitive to the specific form and degree of deforestation. Using a spatial correlation to determine how well the patterns of deforestation are in comparison to total deforestation, it was determined that all correlations were significant, meaning that in terms of spatial patterns, the system behaves linearly.
This study provides a method to determine the degree to which the response of the climate system is nonlinear, which can be applied in other progressive change experiments. Using this method it has been determined that nearly all variables behave nonlinearly in terms of aggregated response over low latitudes between 45°S and 45°N. Taking this method a step further to determine whether the nonlinearity was due to a saturation response or accelerating response, it was found that a majority of the nonlinearity is occurring due to the system being an accelerating response.
This study has highlighted what regions are sensitive to deforestation as well as whether they respond linearly. With a majority of the response in this study showing an accelerating response, this implies that a threshold for sensitivity to deforestation exists. Applied to the real world, this means that the global impacts of Amazon deforestation may not be strongly registered yet, but once the threshold for sensitivity is crossed, global implications could become apparent.
Additionally, an aspect not addressed by this study would be more complex evolutions, such as an “s-shaped” nonlinear response, where 25% and 75% deforestation may exhibit nonlinear tendencies, while 50% deforestation appears linear. Further, modeling simulations would be needed to address this issue. With sensitivity studies targeting specific processes, further analysis could address the cause of nonlinear surface flux responses, as no direct mechanism can be attributed from this study.
An investigation into the degree of nonlinearity in the response of climate to land use change should be expanded to other models as well. Knowing this sensitivity will provide insight into how resilient the climate system is to large-scale land use change and the regions most impacted by such. The Land Use Model Intercomparison Project [Land Use Model Intercomparison Project, 2015] will be investigating the role progressive land use change has in tropical forest areas, as well as other regions, to provide insight for the resulting implications for the global climate system.
Acknowledgments
This research was supported by joint funding from the National Science Foundation (ATM-0830068 and 1338427), the National Oceanic and Atmospheric Administration (NA09OAR4310058 and NA14OAR4310160), and the National Aeronautics and Space Administration (NNX09AN50G and NNX14AM19G) of the Center for Ocean Land Atmosphere Studies (COLA). We would also like to acknowledge high-performance computing support from Yellowstone (ark:/85065/d7wd3xhc) provided by NCAR's Computational and Information Systems Laboratory, sponsored by the National Science Foundation. The authors would also like to thank Tim DelSole and Christiana Stan for discussions about results. Data can be made available upon request to the lead author ([email protected]).
