Spatial heterogeneity in climate change effects across Brazilian biomes

We present a methodology designed to study the spatial heterogeneity of climate change. Our approach involves decomposing the observed changes in temperature patterns into multiple trend, cycle, and seasonal components within a spatio-temporal model. We apply this method to test the hypothesis of a global long-term temperature trend against multiple trends in distinct biomes. Applying this methodology, we delve into the examination of heterogeneity of climate change in Brazil—a country characterized by a spectrum of climate zones. The findings challenge the notion of a global trend, revealing the presence of distinct trends in warming effects, and more accelerated trends for the Amazon and Cerrado biomes, indicating a composition between global warming and deforestation in determining changes in permanent temperature patterns.

www.nature.com/scientificreports/can reduce the rainfall needed to sustain remaining forests, leading to further deforestation and CO 2 emissions.Deforestation can also alter local and regional climates by disrupting the water cycle 50,51 .Trees play a crucial role in maintaining the hydrological cycle by absorbing water from the soil and releasing it into the atmosphere through transpiration.This process contributes to cloud formation and precipitation.Without forests, regions can experience reduced rainfall, leading to drier climates and more frequent droughts, which further exacerbate climatic changes.Evidence of changes in the water cycle in the Amazon are studied in [52][53][54] and for the Cerrado biome in 46,[55][56][57] .
A further channel through which deforestation affects climatic conditions is by disturbing rainfall patterns.Mu and Jones 58 showed that rainfall trends in Brazilian Legal Amazon are heterogeneous, lacking a consistent pattern across the entire region.Nevertheless, they found coherent connections between declining dry-season rainfall and old-age deforestation areas.This means that, in these areas, dry-season are getting drier.Their results also indicate that deforestation effects have also temporal variability, with deforested areas up to a decade increasing dry-season rainfall and older deforested regions experiencing reduced rainfall during the dry season.Leite-Filho 52 pointed that deforestation impact on rainfall also depends on its extension, showing that rainfall diminishes after deforestation surpasses certain threshold, but this boundary is lower at larger scales.The results are also consistent with 59 .Werth and Avissar 60 simulated deforestation scenarios and pointed that deforestation effect in the Amazon is quite relevant, potentially leading to decreases in rainfall, evapotranspiration, and cloudiness.They also observed impact in various other regions worldwide, many of which exhibit a reduction in rainy season precipitation.
Based on simulations from the Brazilian Earth System Model version 2.5 (BESM 2.5) under the RCP8.5 scenario, Gomes 61 finds that escalating global greenhouse gases and land cover change due to deforestation have significant impacts on the water budget in the Amazon basin.These factors lead to a substantial increase in temperature across the basin, up to 5 °C, driven by changes in energy and water budgets.Under high greenhouse gas emissions scenarios, there are reductions in moisture convergence, precipitation, and evapotranspiration, primarily due to a positive feedback loop.Conversely, in scenarios of future deforestation, precipitation reductions are even more pronounced, driven by a negative feedback mechanism.Hofmann et al. 62 revealed a significant reduction in both rainfall and the frequency of rainy days in the northern and central regions of the Cerrado for all periods, except at the beginning of the dry season.The most pronounced negative trends were observed during the dry season and the early wet season, with reductions of up to 50% in total rainfall and the number of rainy days.Hofmann et al. 62 attributed to the intensification of the South Atlantic Subtropical Anticyclone, which has altered atmospheric circulation and increased regional subsidence.Additionally, reduced regional evapotranspiration during the dry season and early wet season likely contributed to the observed rainfall reduction.
The study by 63 indicates that the process of savannization and the phenomenon of global warming independently extend the duration of the dry season and decrease annual rainfall across extensive areas of South America.When considering the combined impacts of land use changes and global warming, 63 found a significant reduction in mean annual rainfall by 44% and an increase in dry season length by 69%, on average across the Amazon basin, compared to the control scenario.The alteration of inland moisture transport patterns due to savannization emerges as the primary factor driving the observed reduction in rainfall and the lengthening of the dry season over the Amazon and Central-West regions.A related result is presented in 64 , that shows that forests exhibit greater susceptibility to climate change compared to savannas or grasslands.Forested areas demonstrated lower resilience to climatic stress and a heightened likelihood of encountering non-analogous climatic conditions.In such a scenario, forest ecosystems would face greater challenges in adapting compared to savannas or grasslands, primarily due to their narrower climate niche.
Similar results were found for the Cerrado biome.Hofmann et al. 62 indicates the impact of changes in evapotranspiration patterns on the Cerrado rainfall regime, and 65 provides evidence that the expansion of cropland in the Cerrado has led to deforestation, which increasingly affects rainfall patterns.Changes in land use and impacts of climate change have significantly impacted river flows in the Cerrado, with large-scale deforestation aimed at the production of irrigated agricultural commodities having a more significant impact on river flows than climate changes, as shown by 57 .Similar results for the biome were found in 66,67 .
The effects of land use change and deforestation on the rainfall pattern in the Caatinga are analyzed in 68 , and the anthropogenic effects on vegetation patterns in this biome are examined by 69 .The negative impact of deforestation on rainfall is also documented for the Atlantic Forest biome 70 , and for the Pantanal 71,72 .
An additional important consideration lies in understanding the connection between tree cover and climate patterns, as examined in 73 .This study investigates how three primary forms of vegetation cover-forests, savannas, and treeless landscapes-influence rainfall patterns and their respective resilience to climate change.Notably, the findings in 73 highlight the anticipated diminished resilience of forested areas in the central eastern and southeastern Amazon basin, which aligns with the increased human activity observed within the deforestation arc.These specific regions are identified as particularly vulnerable to heightened drought risks in future climate projections.
The Albedo effect is another local factor linking deforestation and climate change 74 .Forests typically have a lower albedo compared to other land covers, meaning they absorb more sunlight.However, when forests are cleared and replaced with agricultural land or urban areas, the albedo of the land increases, causing it to reflect more sunlight back into space 75 .While this may initially appear to have a cooling effect on the Earth's surface, it is outweighed by the loss of forests' ability to sequester carbon dioxide, resulting in an overall warming effect on global temperatures.
The results presented by 76 suggest varying vulnerabilities among South American biomes, with those located in the tropical belt likely facing higher temperatures compared to temperate biomes.Additionally, forested biomes are projected to experience greater moisture loss than those with open or desert vegetation.Furthermore, higher vegetation density correlates with a more substantial reduction in humidity, indicating that forest biomes may encounter the most significant decrease in precipitation relative to open vegetation biomes.These predictions align with previous studies by 77 and 78 , which suggest that warmer and drier conditions could facilitate the expansion of open area biomes at the expense of forested biomes.Moreover, these effects may be exacerbated when coupled with significant land-use changes, as highlighted by 79 .
The work of 80 employ the theory of critical transitions to analyze and project significant changes in Brazilian biomes.In the Amazon, climate change is leading to increased tree mortality, reduced forest biomass, and more frequent fire episodes, resulting in biodiversity loss and diminished ecosystem services.Projections for the Caatinga suggest a transition to a more desert-like state, characterized by high temperatures and critical rainfall levels, indicating a tendency towards aridization and expansion of desert areas due to environmental degradation.In the Cerrado, projections indicate expansion into areas previously occupied by the Amazon biome and the Atlantic Forest, particularly under warming scenarios of 1.5 °C and 2 °C.The Atlantic Forest experiences a decline in biome occupation and significant resilience loss, with low resilience dominating most areas, while intermediate and high resilience are concentrated along the coast.The Pampa biome loses its high resilience at all warming levels and contracts to a small fraction in the far south, expanding into former Cerrado areas with low resilience.Modeling indicates an increasing vulnerability to climate change in the Pampa biome due to projected temperature increases and extreme rainfall events, impacting resilience and adaptive capacity.
The findings from our analyses align with previous studies investigating the effects of climate change on Brazilian biomes.Specifically, our results substantiate the combined influence of global warming and local deforestation on the observed temperature rises within the Amazon biome [81][82][83][84] , along with their consequential impacts on rainfall variability and wildfires in this region 34,85 .Moreover, our results also underscore the significance of deforestation and land use patterns in shaping temperature trends across various other biomes including the Cerrado 86 , Atlantic Forest 87 , Caatinga 88 , Pampa 89 , and Pantanal 72,90 .
Our methodology permits us to gather evidence and rigorously test hypotheses concerning climate change patterns in climate series.This statistical rigor is vital for both quantifying and qualifying various facets of climate change.The outcomes derived from our approach can help to monitor and discern between permanent and transient effects within climate series.This delineation is crucial for informing the development of policies aimed at both mitigating and reversing the impacts of climate change, grounded firmly in robust statistical evidence.This monitoring of permanent and transitory patterns is essential to analyze the impacts of climate change on biodiversity and ecosystems 91,92 , food security 93 , health 94 and economics 95 .

Methodology
To analyze the spatial heterogeneity in warming we generalize the model proposed by 24 , using a structure of multiple trend, seasonality and cycle components combined with the continuous spatial random effects introduced by 30 .We allow each biome to have specific latent components, enabling spatial heterogeneity in climate change patterns.To estimate the latent components and the related parameters we apply a Bayesian inference procedure using integrated nested Laplace approximations (INLA).For a detailed exploration of the computational properties of INLA see 24,96,97 .
Within this continuous spatial random effects structure, estimates for missing data can be derived by combining the components of trend, seasonality, and cycle with the prediction obtained for the spatial effect at the station's coordinates through continuous spatial projection.Consequently, the model does not necessitate additional procedures for handling missing data or alternative spatial interpolation structures 24 .
The model can be summarized by the structure: where y(s, t) represents the value of observation y at location s and in period t, µ (t,b) , s (t,b) and c (t,b) are the components of trend, seasonality and cycle for each biome b, with independent Gaussian innovation components η µb , η sb and η cb ; z(s, t) is a set of covariates observed in the location s and period t, ǫ(s, t) is a spatial white noise representing the non-structured spatial errors, and ξ (s, t) represents the spatial random effects following a spatially continuous Matérn covariance function C(h) and h a Euclidian distance.Details on the covariance function are showed in Appendix 1.
The structural decomposition specification for the time series common components is analogous to the basic structural model of 29 .The trend series µ (t,b) is modeled as a first-order random-walk process, a common specifica- tion in the literature to represent permanent trends.The random-walk process can be seen as the accumulation of all shocks that occurred in the past with non-transitory effects.See also 26 for other properties of this process on the modelling of trends for temperature series.The seasonality s (t,b) is based on mean effects by period, with the constraint that these effects must sum to zero on the frequency of the series.To capture a persistent but meanreverting dynamics with a potential periodic pattern, we adopt a formulation akin to unobserved component models 27 for c (t,b) .The cyclic component is depicted by a latent factor exhibiting a second-order autoregressive (AR) structure.The AR(2) can capture cyclic patterns in the presence of complex roots for the associated lag operator's polynomial.In the estimation we use a formulation using partial autocorrelations (PACF) to represent the cycle parameters.
The decomposition structure used in this work is based on some important assumptions.We assume that the spatial variability of temperature is partially explained by latitude effects, and that the remaining spatial effects (1) www.nature.com/scientificreports/are captured by the spatial random effect.In this aspect we assume that the spatial random effects are constant over time, and thus the patterns of spatial variability do not change, and all the dynamics of change are given by the dynamics of the latent components of trend, seasonality and cycle.We tested this assumption by estimating a version of the model with time-varying spatial random effects, using the proposed structure in 33 and 34 , but the results obtained indicate evidence in favor of the formulation with time-constant spatial effects.
To estimate the model, we use a Bayesian estimation using the integrated nested Laplace Approximation (INLA) proposed by 96 , using the prior structure proposed by 24 .Details about the estimation method can be seen in 24,96,97 .
To test the null hypothesis of a homogeneous single trend in warming for all Brazilian Biomes against the alternative hypothesis of multiple trends we formulate a Bayesian test using the Bayes factor, and compare unrestricted (multiple trends) and restrict (single Trend) models using the DIC 98 and WAIC 99 Bayesian information criteria.The Bayes Factor ( BF ) is a measure used in Bayesian statistics to compare the likelihood of two competing hypotheses.It is the ratio of the marginal likelihoods of the data under each hypothesis 100 .We apply the test by calculating the log Bayes Factor by subtracting the logarithm of the likelihood of Hypothesis 2 from the logarithm of the likelihood of Hypothesis 1, with Hypothesis 1 corresponding to multiple trends (spatial heterogeneity in the trend warming) and Hypothesis 2 is the assumption of a unique global trend (spatial homogeneity in trend warming).

Brazilian biomes and data
The Brazilian biomes The Caatinga biome is characterized by distinct climatic features that shape its ecosystem [101][102][103] .The Caatinga territory comprises three distinct Köppen climatic classifications 104 -BSh: Hot semi-arid climate BWh: Hot desert climate, and Aw: Tropical savanna climate.The Caatinga experiences high temperatures throughout the year, with averages ranging between 23 °C and 27 °C.During the hottest months, temperatures can exceed 40 °C.There is a notable temperature variation between day and night, but seasonal temperature changes are less pronounced.Annual precipitation is low, ranging from 300 mm to 800 mm.This makes the region one of the driest in Brazil.Rainfall is highly variable and unpredictable.It is often concentrated in a short rainy season lasting 3 to 5 months, with the remainder of the year being extremely dry.Prolonged droughts are common and can last for several years, significantly impacting the ecosystem and local agriculture.The dry season is prolonged and severe, typically lasting 7 to 9 months.Due to the high temperatures and low humidity, evaporation rates are high.This contributes to water scarcity even during the rainy season.Relative humidity is generally low, particularly during the dry season, which exacerbates the arid conditions.The soils in the Caatinga are typically shallow, rocky, and nutrient poor.They have low water retention capacity, which further limits the availability of water for plants.The vegetation is adapted to arid conditions, featuring xerophytic (drought-resistant) plants such as cacti, thorny shrubs, and small, hardy trees.Many plants have deep root systems, thick bark, and small leaves to minimize water loss.
The Cerrado biome in Brazil, often referred to as the world's most biodiverse savanna, exhibits distinctive climatic features that significantly influence its unique ecosystem 105,106 .The climatic heterogeneity of this biome can be observed through the different Koppen classifications that encompass this biome.Cfb: Oceanic climate with warm summers, Cfa: Humid subtropical climate with hot summers, Cwb: Subtropical highland climate with dry winters, BSh: Hot semi-arid climate, as described above and Cwa: Humid subtropical climate with dry winters.The average annual temperature in the Cerrado ranges from 20 to 26 °C.The hottest months are typically September and October, just before the onset of the rainy season, while June and July are the coolest months.The Cerrado experiences a pronounced wet-dry seasonal cycle.The rainy season occurs from October to April, accounting for about 90% of the annual precipitation, which ranges between 800 and 2000 mm.The dry season, from May to September, sees very little rainfall, often leading to drought conditions.Due to the proximity to the Amazon rainforest, moisture is often transported by wind to the Cerrado, making it the most humid savanna globally.This humidity is crucial during the wet season as it supports the dense growth of vegetation and the replenishment of water resources.Fire is a natural and essential part of the Cerrado's ecology 107 .The dry season, with its lower humidity and accumulation of dry biomass, creates conditions conducive to wildfires, which help maintain the savanna's structure by clearing old vegetation and promoting new growth.Many plant species in the Cerrado are adapted to withstand and even thrive after fire events.
The Pantanal biome in Brazil, recognized as the world's largest tropical wetland, is characterized by a distinctive climatic pattern that influences its unique ecosystem 71,108 .The Koppen classification for the Pantanal is Aw: Tropical savanna climate, a hot climate with distinct wet and dry seasons.The Pantanal experiences an annual average temperature of about 26.7 °C.The warmest months are from October to March, with average highs around 33-34 °C.Conversely, the coolest months are June and July, where temperatures can drop to an average low of 18-19 °C In the northern parts of the Pantanal, temperatures can soar to 40 °C during the hottest periods.In the southern regions, winter nights can occasionally see temperatures plummeting to near freezing, influenced by cold air masses from Argentina.The Wet Season extends from October to March, and this period is marked by heavy rainfall and flooding.The average annual precipitation ranges from 1,000 to 1,300 millimeters, with peak rainfall occurring between November and March.Floodwaters inundate the landscape, transforming it into a vast aquatic habitat, which supports the area's rich biodiversity.During the dry season, water levels recede, revealing extensive grasslands and savannas.This period experiences minimal rainfall, with June and July being the driest months.The dry season is also marked by cooler temperatures, especially during the nights.
The Pampa biome, also known as the Pampas, is characterized by a temperate climate with well-defined seasons, which significantly influences its unique grassland ecosystem 39  There can be short dry spells, especially in the summer months, but these are not as pronounced as in other Brazilian biomes like the Caatinga or Cerrado.The Pampa biome experiences four well-defined seasons.This seasonal variability contributes to a diverse range of flora and fauna adapted to these changing conditions.The Amazonia biome, encompassing the Amazon rainforest, is characterized by a hot and humid tropical climate with consistent high temperatures and significant rainfall throughout the year 109,110 .The Koppen classifications for the Amazon Biome are Aw: Tropical savanna climate, Am: Monsoon climate, and Af: Tropical rainforest climate.The region's average temperature ranges between 25 °C and 28 °C.Rainfall is abundant, typically ranging from 2000 to 3000 mm annually, with some areas receiving even more.This precipitation is relatively evenly distributed, although there are distinct wet and dry seasons.The wet season usually occurs from December to May, while the dry season spans from June to November, though even during the dry season, rainfall is common.The Amazon basin's humidity levels are high, often reaching 80% to 90%, which supports the dense, diverse vegetation of the rainforest.The biome's climate contributes to its vast biodiversity, making it one of the richest ecosystems on Earth, with thousands of plant species and a multitude of animal species, many of which are endemic to the region.
The Atlantic Forest in Brazil is a diverse and complex biome with distinct climatic features 111,112 .Covering regions of eastern Brazil, it extends into Paraguay and Argentina.The extension of this biome is reflected in the heterogeneity of climate classifications: Cfb, Cfa, Cwb, BSh, Cwa, Aw, Am, and Af.This biome features a warm and humid climate.The average temperatures range between 20 °C and 25 °C, with variations depending on altitude and proximity to the coast.Coastal areas tend to be warmer and more humid, while higher altitudes, such as the Serra do Mar mountain range, experience cooler temperatures.The Atlantic Forest experiences high levels of rainfall, typically ranging from 1200 to 2800 millimeters annually.The precipitation is relatively evenly distributed throughout the year, though certain areas, such as the northern Zona da Mata, receive more rainfall from May to August due to the trade winds.Although the Atlantic Forest does not have extreme seasonal variations, it does exhibit some seasonality with a more pronounced wet season in the southern winter and a slightly drier season in the summer.However, the biome remains relatively humid year-round.The diverse topography of the Atlantic Forest, which includes mountains, valleys, and coastal regions, creates various microclimates.These range from the humid tropical rainforests near the coast to the cooler montane forests at higher elevations.Due to the dense forest cover and high levels of precipitation, the Atlantic Forest maintains high humidity levels throughout the year, contributing to its lush and diverse vegetation.

Data
In this study, we utilize weekly meteorological information sourced from the National Institute of Meteorology (INMET) via the BDMEP system for the period 1961-2023.This system supplies meteorological data from conventional and automatic meteorological stations within the INMET station network.The BDMEP system offers access to daily and monthly data from 1961 onwards.The analyzed data comes from 1069 conventional and automatic stations, and the total sample consists of 999,099 observations.The sample is unbalanced since the operation of the stations can occur at different periods.
We present the estimation results for all six biomes existing in Brazil for the series of weekly average temperature.Figure 1 shows a map of the Brazilian Biomes.Following 24 we define the trend components with a weekly frequency, and the seasonality and cycle components with a monthly frequency.This mixed data sampling structure allows estimating the trend components with the greatest possible precision, and the monthly frequency allows a direct interpretation for the seasonality and cycle components.
The entire territory of Brazil exhibits significant inter annual variability, characterized by extremes of both dry and rainy years, accompanied by pronounced inter seasonal fluctuations.Analyzing historical data for the entire country, the average temperatures typically span from 20 to 28 °C.However, specific regions such as the Chapada Diamantina and Borborema Plateau, situated at higher elevations, experience average temperatures consistently below 20 °C.
Our analysis only uses data from meteorological stations, while it would be possible to use other data sources such as remote sensing images or reanalysis datasets, combining observations from satellites and conventional ground-based stations, as for example in the analysis of climate patterns in the Cerrado used in 113 .Although it is possible to use these data sources in our analysis, these data structures initially present some difficulties for the estimation structure used in our article.
Reanalysis methods use additional data combination structures that can affect the estimation process, in particular spatially smoothing the observed data through the use of the theoretical climate model in spatial interpolation in the construction of the data grid.Our analysis allows us to directly estimate the precision involved in estimating the parameters and latent components of the model, quantifying the limitations placed by the observed data.The use of reanalysis data can lead to a biased estimate of the precision/variability of the estimated components in time and space, and to avoid this limitation we use observed data The use of data obtained by remote sensing is an alternative possibility to the use of station data, and in some aspects, it is better due to possible biases introduced by the location of climate this data in the modeling structure proposed in this article leads to higher computational costs due to the enormous growth in the number of observations, but which may be feasible using a computationally feasible spatial grid.We leave this possibility as a possible extension of our work.However, it is important to note that the results obtained in 113 seem to indicate a consistency in the general climate trends estimated for the Cerrado using data from INMET Network stations, remote sensing data obtained from the MODIS system (MOD11A2) and reanalysis data from the NCEP/DOE Reanalysis II dataset, supporting our results in terms of the use of meteorological station data.

Results
We first estimated the full model allowing for different trends, seasonal and cycle components for each of the country's biomes, according to Eq. ( 1).As discussed in section "Methodology and data" we use components with mixed sample frequencies.The trend in this specification may vary weekly, whereas the seasonal and the cycle components are specified with a monthly variation due to their low-frequency nature.We also add as a fixed covariate in the model the latitude of each station, for controlling for the effects of angle of sunlight and atmospheric circulation related to latitude effects in the temperature.Latitude is measured in deviations from its average.Note that the model also includes the average temperature of each biome as a fixed effect α b , and thus the components of trend, seasonal, cycle and spatial effects are parameterized as the deviation from this mean.Table 1 shows the estimated parameters for the full model with biome specific trend, seasonal and cycle components, and the DIC, WAIC and the log Marginal Likelihood of the model, and Figs. 2 and 3 show the posterior mean and the 95% credibility interval for the Trend, and Seasonal and Cycles components for each biome.The estimated Trend components in Fig. 2 are summed with the average means α b of each biome.
An important result it's the growth pattern observed in the trend component for all biomes.The model captured an increase of 1.1211 °C in the trend for the Amazon biome between 1961 and 2023, followed by an increase of 0.8501 °C in the Cerrado, 0.6155 °C in Atlantic Forest, 0.5018 °C in Caatinga, 0.3782 °C in Pampa and 0.1743 °C in the Pantanal biome.The results seem to indicate that the estimated heterogeneous trends indicate a composite of global warming effects with the effects of deforestation on temperature, a result consistent with other studies on the impact of deforestation on climate change.
The observed significant temperature increases within various biomes align with previous research suggesting a complex interplay between global warming and local deforestation effects.Studies focusing on the Amazon biome [81][82][83] have underscored the correlation between deforestation activities and temperature rises.Furthermore, these temperature fluctuations have been shown to exacerbate rainfall variability and contribute to heightened fire occurrences 34,85 .Similar findings have been documented for other key Brazilian biomes.For instance, investigations into the Cerrado biome have highlighted analogous trends 86 .Likewise, studies on the Atlantic Forest 87 , Caatinga 88 , and Pampa 89 have reported temperature increases associated with deforestation activities and their ecological repercussions.
Additionally, climate change-induced alterations in extreme drought patterns have been observed in the Pantanal, with evidence suggesting a linkage to climate variations in the Amazon 72,90 .
In the seasonal component there are also great differences between biomes.While the Pampas presents a range close to 10 °C between seasons ( 39 ), the Amazon presents a range of about 1.25 °C ( 40), which is consistent with the relatively constant temperature of the Amazon throughout the year and the greater intra-annual variability of the Pampas, with colder winters compared to the rest of the country.The estimated model cannot identify relevant changes in seasonal patterns in the biomes studied, but this may be linked to the relatively smaller sample available to analyze these patterns.Note that we only have 62 years available to estimate the seasonal pattern, given that this is fact an annual pattern.The seasonal components also show the effect of missing data on the estimation of this component.The seasonal pattern is not accurately estimated for periods with missing data in the Pantanal and Pampa.
To illustrate the problem of missing data in some sample periods, we show in Fig. 4 the number of active days for each station in the Pantanal biome.Stations with numerical codes are manually operated stations, and stations starting with A are automatic stations, which began to be operated from 2002 onwards.The Pantanal was monitored until the 2000s with only six manual stations, and in relevant periods between 1965 and 1974 and between 1991 and 1993, with fewer stations, especially in the period between 1991 and 1993 with even Table 1.Estimated parameters-model with biome specific trend, seasonal and cycle components.The Table summarizes the estimated parameters of the model with specific components of trend, seasonality and cycle for each biome, showing the mean, standard deviation, the quantiles of 0.025, 0.5, 0.975 and the mode of the posterior distribution of each parameter.The parameters were estimated using Bayesian inference through integrated nested Laplace approximations.See Online Methods for details on the interpretation of each parameter.fewer operating stations.This pattern of missing data significantly affects the estimation of the seasonality and cycle components in these periods for the Pantanal biome.A similar problem occurs for the Pampa biome in the period from 1991 to 1993.As we explained in section "Methodology and data", to identify a cyclical component, the estimated AR(2) process must have complex roots.Converting the PACF(2) for AR(2) parameters we found complex roots for the Caatinga, Pantanal and Pampas, with periods of 11.1229, 9.4606 and 12.1924 months, respectively.For the other biomes, the cycle must be interpreted as a second-order autoregressive process without complex roots.

Mean
The estimated spatial random effects are shown in Fig. 5.As discussed in 24 , spatial random effects are a way of capturing all systematic patterns not captured by the other components in the model that present spatial dependence, and in this aspect, they serve to incorporate the effects of altitude, local weather patterns and other effects that generate spatial dependence.The high temperature range of spatial effects is also consistent with the climatic variability observed in Brazil and it's large and geographically diverse territory (e.g., 104 ).
The model with individual components for biome presented in Table 1 indicates relevant evidence for the existence of heterogeneity in the permanent effects of climate change on temperature patterns for Brazilian biomes, but to proceed to a statistical test for the validity of this evidence we compare the results of this model with those obtained by a restricted specification, assuming a single global trend for all biomes, using the results of the Bayes Factor, and DIC and WAIC criteria, as explained in section 2. The estimate for the restricted model is shown in Table 2.Note also that in the restricted model we do not assume unique components of seasonality and cycles in the restricted model, as these components must vary in relation to the biome, as is evident from the patterns observed in Fig. 3. Our objective is to verify the hypothesis of heterogeneity in the permanent component of temperature change, measured by the trend.
To obtain the Bayes factor we compute the difference between the estimated log Marginal Likelihood of unrestricted (Table 1) and restricted models (Table 2).The log difference is calculated as 492.2425, indicating a relevant difference according to Jeffreys' criteria 100

Conclusion
We present a methodology to test the spatial heterogeneity of climate change, testing the presence of multiple trends in warming patterns for Brazilian Biomes through a spatio-temporal statistical model, decomposing the The results found are especially relevant as they indicate a trend of more accelerated growth in the increase in temperature for the Amazon and Cerrado biomes and to a lesser extent for the Atlantic Forest.These results are consistent with other work showing the positive relationship between deforestation and increased land temperature 47,82,[114][115][116] .
The largest temperature increases observed for these biomes also support other works indicating the composition of global warming effects with local deforestation effects, as the relationship between deforestation and temperature increases found for the Amazon biome [81][82][83][84] and the related impacts on rainfall variability and fires in this biome 34,85 .Comparable results were also found for the Cerrado 86 , Atlantic Forest 87 , Caatinga 88 , Pampa 89 , and changes in extreme drought patterns in the Pantanal due to climate change in the Amazon 72,90 .
The proposed statistical framework also permits to directly verify the spatial heterogeneity in other climate change effects, as precipitation patterns and changes in the timing of biological events (phenology), and thus is a useful tool for statistical analysis of climate change patterns.
The method used involves some important simplifications.The first relevant simplification is to use the latent component of spatial random effect as a way to capture the effect of all possible covariates that affect the spatial distribution of temperature, and also that this spatial effect is time invariant, as discussed in 24 .In this way, this spatial component captures the composite effect of variables such as altitude, distance to the sea and other climatic effects that are spatially localized.We tested alternative specifications where the spatial effect is made time-varying, but the overall results indicate that for the estimated sample period the assumption of spatial random effects appears valid, which can be explained by the limited sample period used in the analysis.As these effects should not vary significantly over the period of time studied, this assumption seems appropriate in the analysis carried out.
Another limitation is assuming a structure of separability between the trend, seasonality and cycle components and the spatial effects.This structure is imposed on the model and allows the statistical identification of latent parameters and effects.This assumption could be violated if there was a possible interaction between the components and the spatial effect, such as spatial heterogeneity in the trend.Note that by allowing specific trends, seasonality and cycles for each biome we are controlling this possibility, but it is still possible that there are variations in these components within each biome analyzed.One possibility to be explored in future work is to estimate the model using a greater disaggregation in the observed biomes, which would be important for biomes with greater climate variability or spatial extension.Our analyzes suffer from the same problem of the time frame limited by available observations of temperature data affecting estimates of climate change patterns, especially for such a wide spatial region.The precision of the estimates, especially the seasonality and cycle components, is greatly affected by the number of observations over time, since we are estimating periodic patterns of variation, and thus the precision of these components depends on the number of repetitions of the same patterns.This limitation makes it especially difficult to estimate relevant variations in the pattern of seasonal variation, as discussed in 35 .As our main discussion is based on the trend component, we are less exposed to the problem of sample size, since this component is estimated using a weekly frequency, which allows greater precision for this estimation, allowing us to estimate the variations observed in the trend more accurately.
In our analysis we only model climate change patterns in temperatures, but an extension of the work is to model the joint dynamics of temperature with other relevant climate measures, such as rainfall and relative humidity.In this joint modeling it is possible to analyze the joint dynamics and interactions between these measures, allowing us to verify how the relationships between variables are altered due to global and local patterns of climate change.Examples of joint modeling of climate variables can be seen in 117 and 118 .In this aspect, joint modeling can be seen as a spatio-temporal generalization of joint models for climate variation measurements.
A further use of the method is its application to maximum temperature series, particularly in the analysis of temperature records, as examined in. 35.This work analyzes patterns of climate change in annual temperature and daily rainfall records, as well as modeling the probability of occurrence of rain and the duration of droughts for a single meteorological station.Therefore, a possible extension to the present work is to carry out these analyzes of temperature and rainfall records and other climate measures for the set of climate measures for the different biomes analyzed.summarizes the estimated parameters of the model with a global trend, and specific seasonality and cycle for each biome, showing the mean, standard deviation, the quantiles of 0.025, 0.5, 0.975 and the mode of the posterior distribution of each parameter.The parameters were estimated using Bayesian inference through integrated nested Laplace approximations.See Online Methods for details on the interpretation of each parameter.The primary benefit of this format is that, given the value of ν , it reduces the number of parameters needing estimation to just two. https://doi.org/10.1038/s41598-024-67244-xwww.nature.com/scientificreports/

Figure 1 .
Figure 1.Brazil biomes.The figure shows the spatial delimitation of the six Brazilian biomes analyzed.
for the Bayes factor, and thus indicating severe posterior evidence in favor of the unrestricted model, indicating strong statistical evidence in favor of the model with spatial heterogeneity in temperature trends between the biomes of Brazil.The DIC and WAIC information criteria also supports the better support for the unrestricted model, with a DIC of 3760738 for the unrestricted trend model versus a DIC of 3761260.49for the global trend model, and similarly a WAIC of 3760399.15 for the unrestricted model and 3760978.41 for the restricted model, remembering that in comparative analyzes of information criteria, a lower value is indicative of a better fit/complexity relationship between the compared models.

Figure 2 .
Figure 2. Trend components.The figure shows the posterior mean and a 95% credibility interval for the estimated trend components for each biome, for the sample period 1961-2023.Trend components are defined on a weekly frequency.

Figure 3 .
Figure 3. Seasonal and cycle components.The figure shows the posterior mean and a 95% credibility interval for the estimated seasonal and cycle components for each biome, for the sample period 1961-2023.Trend components are defined on a monthly frequency.

Figure 4 .
Figure 4. Active days by station-Pantanal.The figure shows the number of active days for each Station in Pantanal Biome.

Figure 5 .
Figure 5. Spatial random effects.The figure shows the posterior average of the estimated spatial random effects.These effects are obtained as a spatially continuous projection of the Matérn spatial covariance function.
)(4π) d/2 − log σ − ν log ρ log κ = log(8ν) 2 − log ρ . The average annual temperature ranges from 16 to 18 °C.The summers (December to February) are warm with average temperatures around 22 to 24 °C, although maximum temperatures can occasionally exceed 30 °C, and winters (June to August) are mild to cool, with average temperatures ranging from 10 to 12 °C.Minimum temperatures can sometimes drop to near freezing, especially during cold fronts.While there is no extreme wet season, spring (September to November) and autumn (March to May) typically receive slightly higher rainfall, which supports the growth of grasses and other vegetation.Spring and autumn are characterized by moderate temperatures and significant rainfall, fostering lush grasslands.

Table 2 .
Estimated parameters-restricted model with a global trend component.The Table www.nature.com/scientificreports/with K ν being a modified Bessel function of the second type.We use the following representation in terms of log τ and log κ for the covariance function: Vol:.(1234567890) Scientific Reports | (2024) 14:16414 | https://doi.org/10.1038/s41598-024-67244-x