SPATIOTEMPORAL VARIATIONS OF ARIDITY IN THE BRAZILIAN SEMI-ARID AND ITS INFLUENCE ON MAIZE YIELDS
Mateus Pereira Lavorato
Universidade Federal de Viçosa
SPATIOTEMPORAL VARIATIONS OF ARIDITY IN THE BRAZILIAN SEMI-ARID AND ITS INFLUENCE ON MAIZE YIELDS
Resumo: A aridificação é um dos principais desdobramentos do aquecimento global. No Brasil, o semiárido se destaca pela vulnerabilidade aos efeitos das mudanças climáticas. Isso é especialmente verdadeiro para os agricultores familiares, devido à ameaça que isso representa para seu sustento. Com foco no milho, uma das culturas mais cultivadas na região, realizamos uma análise aprofundada das variações espaço-temporais da aridez, investigando se tais mudanças influenciam a produtividade agrícola. Nossa análise identificou uma tendência de aridificação em algumas partes do território, ao mesmo tempo que constatou que aumentos no grau de aridez levam a diminuições na produtividade do milho. Como consequência, a adoção de medidas adaptativas no semiárido brasileiro é imprescindível.
Palavras-chave: aridez, semiárido, Brasil, produtividade agrícola, milho
Abstract: Aridification is one of the main developments of global warming. In Brazil, the semi-arid region stands out in terms of vulnerability to the effects of climate change. This is especially true for family farmers, due to the threat posed on their livelihood. Focusing on maize, one of the most cultivated crops in the region, we conduct an in-depth analysis of spatiotemporal variations of aridity, investigating whether such changes influence agricultural productivity. Our analysis identified a tendency for aridification in some parts of the territory, while finding that increases in the degree of aridity lead to decreases in maize yields. As a consequence, the adoption of adaptive measures in the semi-arid of Brazil is imperative.
Keywords: aridity; semi-arid; Brazil; crop yield; maize
JEL codes: Q13, Q51
1. Introduction
Climate change is expected to lead to decreasing rainfall and rising temperature in several parts of the world, including Brazil. As a consequence, the expansion of areas with arid-like climates is identified as one of the main developments of global warming (Pour et al., 2020). In fact, the number of people living in arid lands worldwide may rise by more than 20% in the near future (Park et al., 2018). Therefore, evaluating and monitoring this phenomenon is of very importance, especially for the regions where agriculture and livestock production corresponds to an expressive share of local economy (Pellicone et al., 2019).
Considering the Brazilian territory, the semi-arid region stands out in terms of the (possible) effects of climate change. Being primarily composed by municipalities from the Northeast region, the semi-arid of Brazil is, among the arid regions of the world, the most densely populated (Marengo, 2008). The region experiences great interannual variability in rainfall, which leads to the periodic occurrence of drought episodes (Marengo and Bernasconi, 2015). These phenomena have severe social, economic and environmental consequences (Silva, 2004), which are possibly driven by declines in the yields of crops—especially those grown by family farmers.
Family farmers, which are extensively present in the semi-arid, have a prominent role in the regional economy as they provide food on local scale (Angelotti and Giongo, 2019). Data from the 2017 Census of Agriculture show that family farmers guide roughly 1.45 million rural establishments in the region, generating a production value of more than R$11.5 billion. Among the crops most cultivated in the semi-arid, maize stands out. In 2017, approximately 45% of family farms in the region grew maize, relying on more than 630,000 hectares to produce roughly 570,000 tons of the crop.
In the Brazilian semi-arid, rainfed cultivation of maize predominates, which surges the risk of crop frustration due to the region’s climatic variability. Despite this, many farmers still grow this crop primarily for human consumption, but, when corncobs fail to grow, stover is used as animal feed (Silva and Regitano-Neto, 2019). Ultimately, the residents of the semi-arid, which often exclusively depend on the outcomes of agricultural production for their livelihood, face the challenge of achieving a sustainable rainfed production with an increasingly-limited water supply (Melo and Voltolini, 2019).
Therefore, climate aridification poses a serious threat on the livelihood of the semi-arid population. Seen this, we conduct an in-depth analysis of spatiotemporal variations of aridity in the Brazilian semi-arid, investigating whether such changes influence maize yields. Gridded data on precipitation and temperature are used in the construction of De Martonne’s aridity index, whose behavior is investigated using the Mann-Kendall trend test and the Theil-Sen’s slope estimator. Lastly, maize yield responses to aridity are estimated via Geographically Weighted Panel Regression in order to account for spatial heterogeneity.
By studying the spatiotemporal variation of aridity in the Brazilian semi-arid, we contribute to the literature as we provide a piece of evidence on how recent climatic change has influenced the region's climate. Additionally, we also generate an aridity-based classification of the climate of the Brazilian semi-arid, which can later be used in future studies. Finally, by indicating where and by how much aridity influences maize yields, we offer relevant information that could be used by policymakers to conduct initiatives focused on addressing aridity-related problems, either by mitigating, transferring or coping with those risks.
The remainder of this paper is as follows. After this introduction, we describe the materials and methods, highlighting key aspects of the studied area as well as data collection and manipulation. Next, the outputs of the Mann-Kendall trend test, the Theil-Sen’s slope estimator and the Geographically Weighted Panel Regression are presented. Following, these results are discussed, stressing its implication for the livelihood of maize farmers within the Brazilian semi-arid. Lastly, we present the main conclusions of the study.
2. Materials and methods
2.1. Study area
The semi-arid region of Brazil, depicted in Figure 1, is composed by a grand total of 1,262 municipalities distributed among the states of Maranhão, Piauí, Ceará, Rio Grande do Norte, Paraíba, Pernambuco, Alagoas, Sergipe, Bahia and Minas Gerais. In terms of territorial extension, it covers more than 1.1 million square kilometers, corresponding to slightly more than 13% of the Brazilian territory. With respect to population, the semi-arid region housed approximately 27.9 million inhabitants in 2018 (13.2% of Brazil’s total), leading to a population density of 24.5 inhabitants per square kilometer.
Figure 1. The semi-arid region of Brazil.
Source: Elaborated by the authors.
The semi-arid is located in the extreme northeast of South America, running from the 3rd to the 18th parallel south. Kayano and Andreoli (2009) highlight that, despite region’s location, precipitation does not follow an equatorial pattern. Instead, it is marked by a great spatial-temporal variability, enabling the occurrence of drought episodes that are directly associated with crop losses (Correia et al., 2011). Ultimately, the climate is directly related to the prevalence of poverty within the region. In fact, in 2017, the semi-arid region had a GDP per capita of roughly R$ 12,350.00 per year, which corresponds to 39% of the national figure (IBGE, 2020).
2.2. Data
The data used in this study come from two different sources. Information on maize yields were gathered from the Municipal Agricultural Production (PAM, Produção Agrícola Municipal), an annual survey conducted by the Brazilian Institute of Geography and Statistics (IBGE, Instituto Brasileiro de Geografia e Estatística). Annual yield data are presented at the municipality level for the period between 2003 and 2018, being measured in kilograms per hectare. Although maize is grown twice a year in the Brazilian semi-arid, production is highly concentrated in the first harvest, which is the one considered in this study.
Weather information, in turn, come from the Brazilian National Institute of Meteorology (INMET, Instituto Nacional de Meteorologia). Specifically, we collected monthly data on accumulated rainfall (millimeters) and mean temperature (degree Celsius) from 71 automatic weather stations distributed across the semi-arid of Brazil (Figure 1). Based on information from the National Food Supply Company (Conab, 2015), we defined the planting season of maize’s first harvest as going from January to August. Therefore, in order to construct De Martonne’s aridity index, weather data were specifically aggregated to this season.
2.2.1. Spatial interpolation of weather data
Three different methods were used to spatially interpolate the data from weather stations: inverse distance weighting (IDW), ordinary kriging (OK) and thin plate spline (TPS). IDW estimates the value for unsampled points as the weighted average of the actual points in its vicinity, where weights are a decreasing function of distance (Lu and Wong, 2008). OK estimates the value of a variable over a given region for which a variogram is known, assuming stationarity (Wackernagel, 2003). TPS smooths a scatter plot by fitting a nonparametric regression model that uses penalized least squares (Wood, 2003).
The accuracy of interpolation methods is evaluated by -fold cross-validation. First, weather stations are randomly divided into subsets. Second, spatial interpolation models are fitted to data from subsets and tested over the remaining subset. Third, considering as the value recorded at station and as the value predicted via spatial interpolation, we calculate the mean absolute error and the root mean square error . Fourth, the validation procedure is repeated times. The overall accuracy of each interpolation method is obtained by averaging across the months analyzed.
2.2.2. De Martonne’s aridity index
The aridity index proposed by De Martonne (1926) is one of the most used indicators of the degree of water deficiency in a region. In fact, despite being one of the oldest indexes developed to assess aridity levels, De Martonne’s aridity index is still applied worldwide due to its efficiency and relevance in classifying regions in arid/humid climates (Pellicone et al., 2019). One of the main advantages of such aridity index regards data requirement, since it only demands information on precipitation and temperature. Specifically, growing season values for the De Martonne’s aridity index are given by
(1)
where is the aridity index; is the growing season accumulated rainfall; and is the growing season average temperature. Precipitation is multiplied by 1.5 in order to annualize the values and 10 is added to the temperature in order to avoid a negative denominator—this goes back to the European origin of the index.
Following Araghi et al. (2018), one can use the De Martonne’s aridity index to classify local climates according to the values presented in Table 1. It is observed that the lower the value of the aridity index, the more arid is the region under investigation. Considering annual values for maize’s crop calendar, temperature seems to not vary significantly in the Brazilian semi-arid, while rainfall presents certain variability across the analyzed years (Annex). Therefore, one could say that the climate classification of the Brazilian semi-arid is mainly guided by the precipitation pattern of the region.
Table 1. Climate classification based on De Martonne’s aridity index
Climate type
2.3. Trend analysis
Trend analysis is conducted in order to identify whether data series present downward or upward trends. To this end, we apply the Mann-Kendall test (Mann, 1945; Kendall, 1946). This is one of the most used non-parametric tests of trend investigation, being widely used in meteorological and hydrological analyses (e.g., Huang et al., 2016; Ahmed et al., 2019; Houmsi et al., 2019; Paniagua et al., 2019; Mutti et al., 2020; Pour et al., 2020). Major advantages of non-parametric tests like Mann-Kendall’s include the non-requirement of normality and the strength against outliers (Ti et al., 2018).
Specifically, the S statistic of the Mann-Kendall test is calculated as follows
(2)
.
(3)
When , the S statistic is normally distributed with variance given by
(4)
where is the number of tied groups and is the number of ties of extent .
Finally, the standard normal test statistic is calculated as
(5)
Positive (negative) values of indicate a trend with increasing (decreasing) behavior. Trends are statistically significant when . Thus, if we consider the 5% significance level, the null hypothesis of no trend is rejected when .
In addition to the recognition of trends, we also calculate their magnitudes. For this purpose, the Theil-Sen estimator (Theil, 1950; Sen, 1968) is used. It is a nonparametric method whose major advantage over linear regression regards its ability in limiting the influence of outliers (Ti et al., 2018). Specifically, the Theil-Sen estimator is calculated as follows. Initially, the slope of data pairs are computed by
(6)
where and denote data values at times and , respectively, with .
Later, the estimator is in fact given by the median of the values previously calculated:
(7)
where a positive (negative) value of indicates an increasing (decreasing) trend.
2.4. Geographically Weighted Panel Regression
Crop yield responses to aridity are empirically modeled by means of a Geographically Weighted Panel Regression (GWPR). Conceptually, this model can be taken as a natural extension of the Geographically Weighted Regression (GWR) model as the only practical difference between them regards the explicit consideration of the time dimension by the former. In order to derive the GWR model and, ultimately, the GWPR model, one must first consider a global regression model (Fotheringham, Brunsdon and Charlton, 2002):
(8)
.
The GWR model is obtained when local parameters are allowed:
(10)
The vector of estimated regression coefficients, which now vary across observations, is
(11)
where denotes a -by- spatial weighting matrix whose diagonal elements indicate the weight assigned to each of the observations for the regression point .
The regression model presented in the Eq. 10 is calibrated via Weighted Least Squares (WLS), assuming that the closer an observation is to the regression point , the greater its influence on the estimation of . Spatial weighting matrices, in turn, are calculated by a kernel function and its respective bandwidth, which provides weights that are inversely related to distance. Therefore, the weighting process takes the assumption that spatial autocorrelation exists, possibly resulting in non-stationary patterns in estimated coefficients (Wheeler and Páez, 2010).
Finally, when the temporal component is considered, the GWPR model is obtained:
(12)
where estimates of vary across space but not across time. This occurs because the spatial relationship between locations does not change over time and thus both the bandwidth and the kernel function are time-invariant (Yu, 2010).
The key point in estimating the GWPR model regards the calculation of the matrix of local weights. As previously mentioned, is calculated by a spatial kernel, a function that uses the distance between locations and a parameter of the bandwidth to determine weights (Almeida, 2012). We use an adaptive spatial kernel since data density varies considerably across space. In such kernel function, is adjusted to data density so a fixed number of observations is considered in each subsample (Fotheringham, Brunsdon and Charlton, 2002).
The bi-square nearest neighbor kernel, specified below, is used in the weighting process:
(13)
where denotes the weight assigned to when calibrating the model for ; and denotes the set of th nearest neighbors of .
The reliability of GWPR estimates is directly influenced by the selection of and the cross-validation (CV) criterion is considered in the optimization of the bandwidth. Specifically, the following ‘drop-1’ score is minimized:
(14)
where is the estimated value of when the location is dropped.
As some time-invariant aspects specific to each unity of analysis can interfere in the relationship between crop yields and aridity, the use of a fixed effects specification is readily justified. Among such aspects, one could highlight both altitude and soil quality. The spatial rigidity of altitude is straightforward. For soil quality, in turn, this consideration is not so simple. However, for not-so-long time spans one could expect soil quality to remain relatively constant as both the degradation or correction of soil take some time to occur.
Evidence shows that crop yields respond nonlinearly to weather. However, only the linear term of explanatory variables is considered in our models. For instance, nonlinearity is expected to occur when temperature varies more than 10ºC across observations (Schlenker and Roberts, 2009). As the GWPR model estimates local coefficients based on geographically close subsets of data, an expressive variation in aridity is highly unlikely. Additionally, as described by Kayano and Andreoli (2009), average temperature presents little spatial variation in the Northeast. Ultimately, the following model is estimated:
(15)
where , and respectively denote maize yield and the aridity index of location in year ; denotes location-specific, time-invariant fixed effects; denotes a linear time trend; and denotes the error term.
3. Results
3.1. Spatial interpolation
The accuracy of the spatial interpolation methods evaluated—inverse distance weighting, ordinary kriging and thin plate spline—is depicted in Table 2. Overall, IDW generated more accurate data than OK and TPS for both precipitation and temperature. Although the international literature has been showing that geostatistical techniques are better interpolators of meteorological variables than deterministic techniques (Pellicone et al., 2019), our interpolation is still consistent as IDW also produced the best results for Xavier et al. (2016), who investigated Brazil as well.
Table 2. Accuracy of spatial interpolation methods
Evaluation metrics
Interpolation method
3.2. De Martonne’s aridity index
Based on the results of the accuracy evaluation, we used IDW estimates of local precipitation and temperature for the construction of the De Martonne’s aridity index and the assessment of the aridity level of the Brazilian semi-arid. Figure 2 displays the aridity index calculated for the Brazilian semi-arid region for the period between 2003 and 2018. Considering that temperature is relatively stable through the years, the aridity pattern is heavily influenced by changes in precipitation (see Annex 1). In fact, arid-like climates prevail in the region from 2012 onwards, when a severe drought plagued the semi-arid of Brazil.
The climate classification of maize’s growing season obtained via De Martonne’s aridity index expressively varies both in space and time. During the 2000s, a significant portion of the semi-arid region experienced humid-like climates , especially the northern part of the territory. The situation changes dramatically in the 2010s, when arid-like climates predominate across the analyzed area, with emphasis on the center-south zone. The wettest (driest) season was recorded in 2004 (2012), when 95% (87%) of the region presented humid-like (arid-like) climates.
2003
2004
2005
2006
2007
2008
Figure 2. De Martonne’s aridity index, maize’s growing season, Brazilian semi-arid.
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
Figure 2. De Martonne’s aridity index, maize’s growing season, Brazilian semi-arid (cont.)
3.3. Trend analysis
Visual inspection indicates that the degree of aridity has decreased in various parts of the territory during the analyzed period. In order to identify the presence of positive or negative trends, we applied the Mann-Kendall test, whose results are depicted in Figure 3 (a). Black pixels indicate that a statistically significant negative trend exists, i.e., these areas are turning into arid environments. Yellow pixels, in turn, denote exactly the opposite, i.e., locations are becoming more humid. As expected, statistically significant positive trends have not been observed anywhere in the territory.
(a)
(b)
Figure 3. (a) Mann-Kendall trend test and (b) Theil-Sen’s trend slope, maize’s growing season, Brazilian semi-arid.
The tendency towards greater aridity, however, is effectively present in the region. In fact, 19% of the Brazilian semi-arid showed statistically significant negative trends for the De Martonne’s aridity index. There, as previously stressed, arid-like climates usually predominate during maize’s planting season. Considering only these areas, Figure 3 (b) displays the slopes calculated using the Theil-Sen’s estimator, which are presented in index-points per year. It is observed that index variations were not that high as the aridity rate decreased by no more than two points per year between 2003 and 2018.
3.4. Geographically Weighted Panel Regression
Table 3 presents the results for the modelling of maize yield responses to aridity in the semi-arid region of Brazil. Considering that coefficients are estimated for several municipalities, results are presented by quantiles. The median of aridity coefficients from the GWPR model is pretty similar to the estimate obtained through a global model[footnoteRef:1], evidencing the robustness of results. As initially expected, estimates vary considerably across the region as confirmed by magnitude of the interquartile range. This indicates that responses are characteristically non-stationarity in space, endorsing the validity of estimating local coefficients. [1: The global model refers to a non-spatial, fixed-effects model for which one and only global estimate of the influence aridity on maize yields is obtained.]
Table 3. Estimation results for the Geographically Weighted Panel Regression model, semi-arid region of Brazil, 2003-2018.
Dep. var.:
Source: Research results.
As earlier discussed, adaptive bandwidths were optimized by cross-validation. For this kind of bandwidth, window size varies according to data density so the number of observations in each local regression is kept constant. Specifically, the number of data points used for the calibration of our model was 347 over the 16 years of analysis—roughly 22 municipalities per year. Among the 951 municipalities analyzed, approximately 74% had pseudo-significant estimates at the five percent level. Pseudo-significance, in this case, refers to the t-statistic for the coefficient of each regression point (Kusuma, Jackson and Noy, 2018).
Figure 4 depicts the spatial distribution of aridity coefficients for the municipalities whose estimates were pseudo-significant at the five percent level. Of the municipalities for which the estimated relationship was not statistically significant, most are located in the southern part of the semi-arid region. Similarly, the few locations for which index values negatively influence maize yields are primarily concentrated in this same part of the territory. Interestingly, this is the area of the Brazilian semi-arid in which arid-like climates were more present during maize’s growing season for the period between 2003 and 2018.
As expected, in most municipalities with pseudo-significant estimates an increase in De Martonne’s aridity index is accompanied by an expansion in maize yields, which means that, in general, maize positively respond to decreases in the degree of aridity. As previously observed, in the median, the increase of one index-point leads to a yield growth of 11 kg per hectare. In some parts of the region, the influence of the aridity index is expressively higher, exceeding gains of 45 kg per hectare. This is especially true for municipalities in the neighborhood of the so-called MATOPIBA region[footnoteRef:2], which is one of the main producing areas of Brazil. [2: The MATOPIBA region comprises the Cerrado biome of the states of Maranhão (MA), Tocantins (TO), Piauí (PI) and Bahia (BA), being currently considered as the major agricultural frontier in Brazil.]
Figure 4. GWPR estimates for aridity, Brazilian semi-arid.
Source: Research results.
4. Discussion
Spatiotemporal variations of aridity have some important implications for the Brazilian semi-arid. As we have identified, certain parts of the analyzed region have shown a decreasing trend in De Martonne’s aridity index, which translates into a tendency towards the aridification of these locations. Such phenomenon can severely impact the livelihood of local population, especially in terms of water availability for human consumption as well as livestock and crop production. In fact, aridity negatively impacts ecosystems’ biological and economic productivity, threatening hydrological and ecological processes (Marengo and Bernasconi, 2015).
Our results showed that from 2003 to 2018, most of the Brazilian semi-arid region exhibited a tendency to increase aridification during maize’s growing season, which ranges from January to August. The highest trend slopes were observed in locations with a higher level of aridity, i.e., the areas in which the De Martonne’s aridity index is usually smaller. Therefore, our findings corroborate the results of other studies, which indicate that the driest parts in a certain region are those that tend to become even drier over time (Feng and Zhang, 2015; Lickley and Solomon, 2018; Pour et al., 2020).
Investigating climatic variability in northeastern Brazil, where most part of the semi-arid is located, Silva (2004) found that, at that time, significant decreasing trends in relative humidity and precipitation were observed in most of the weather stations analyzed. Therefore, changes in climatic variables associated with the aridification process have been affecting the semi-arid region of Brazil for a long time. Indeed, although drought episodes commonly affect the region, the drought experienced from 2012 to 2017—which, according to Marengo et al. (2017), was the most severe in decades—may be a direct consequence of such climatic changes.
If our study demonstrated that certain parts of the semi-arid region of Brazil showed a tendency to aridification between 2003 and 2018, the literature stress that this inconvenient scenario tends to get even worse. The results obtained by Marengo and Bernasconi (2015), for instance, indicate that the areas with the largest signal of drought increase are usually located where precipitation is projected to decrease. Their projections suggest that drought and arid conditions are expected to prevail by the second half of the 21st century due to temperature increases, rainfall reductions, water deficits and longer dry spells.
In terms of crop yield responses to the degree of aridity, we found robust evidence that maize yields are positively influenced by increases in the De Martonne’s aridity index, i.e., decreases in aridification. Although this holds true for the vast majority of municipalities analyzed, some locations surprisingly presented statistically significant negative estimates for the yield-aridity relationship. These unexpected results may be related to the use, in these places, of maize seeds adapted to local meteorological conditions, so that any climatic variation (e.g., increases in humidity) causes some loss of productivity.
It is also worth noting that the proportion of the analyzed sample for which our GWPR model provided pseudo-significant coefficients are reasonably in line with—or even better than—the (scarce) literature on the same subject that also relied on GWPR estimations. Investigating rice production in Indonesia, Kusuma, Jackson and Noy (2018) found that half of their observations had pseudo-significant estimates. Cai, Yu and Oppenheimer (2014), who analyzed the responses of maize production in the US, found that 65% (53%) of locations were pseudo-significant for temperature (precipitation).
The current scenario is already worrying, but the future tends to be disastrous for family farmers within the Brazilian semi-arid because of climate change and the consequences associated with the aridification of region’s climate. Therefore, applying adaptive measures aimed at guaranteeing the livelihood of vulnerable people is urgent. Traditional rainwater harvesting technologies have long been used in order to store water for human consumption and agriculture (Lindoso et al., 2018). In the last decades, irrigation has also been evolving in the semi-arid region, mainly through the development of public projects (Cunha et al., 2014).
5. Conclusion
This study examined the recent spatiotemporal variations of aridity in the Brazilian semi-arid and its influence on maize yields. Temperature and precipitation data for maize’s growing season were employed in the construction of the De Martonne’s aridity index, which was used in the climate classification of the region. By employing the Mann-Kendall trend test and the Theil-Sen’s slope estimator, we identified statistically significant negative trends for aridity in several parts of the territory, whose magnitude spatially varies within the region, reaching higher paces in the northern part of the territory.
De Martonne’s aridity index was used to assess crop yield responses to changes in aridity using the Geographically Weighted Panel Regression. The model proved to be robust, providing evidence that, for the bulk of municipalities analyzed, maize yields positively respond to increases in the aridity index, i.e., expansion of humid-like climates. Approximately 3/4 of locations presented pseudo-significant estimates at the five percent level and, among the municipalities with positive coefficients, the largest estimates of the yield-aridity relationship were found for the region of MATOPIBA.
From these results we are able to conclude that aridification is indeed a major threat to maize farmers from the Brazilian semi-arid. In fact, the recurrent occurrence of drought episodes in the region jeopardizes the quality of life of the vulnerable population, which is mainly comprised by family farmers. As decreases in aridification positively influences maize yields and the De Martonne’s aridity index has been presenting a negative trend for several areas in the analyzed territory, the diffusion of adaptive measures, such as irrigation, is essential to ensure the livelihood of smallholders.
6. References
AHMED, K.; SHAHID, S.; WANG, X.; NAWAZ, N.; KHAN, N. Spatiotemporal changes in aridity of Pakistan during 1901–2016. Hydrology and Earth System Sciences, v. 23, p. 3081–3096, 2019.
ALMEIDA, E. Econometria Espacial Aplicada. Campinas: Editora Alínea, 2012.
ANGELOTTI, F.; GIONGO, V. Ações de mitigação e adaptação frente às mudanças climáticas. In: MELO, R. F.; VOLTOLINI, T. V. (Ed.). Agricultura familiar dependente de chuva no Semiárido. Brasília: Embrapa, 2019.
ARAGHI, A.; MARTINEZ, C. J.; ADAMOWSKI, J.; OLESEN, J. E. Spatiotemporal variations of aridity in Iran using highresolution gridded data. International Journal of Climatology, v. 38, n. 6, p. 2701-2717, 2018.
CAI, R.; YU, D.; OPPENHEIMER, M. Estimating the Spatially Varying Responses of Corn Yields to Weather Variations using Geographically Weighted Panel Regression. Journal of Agricultural and Resource Economics, v. 39, n. 2, p. 230–252, 2014.
CONAB. Calendário de Plantio e Colheita de Grãos no Brasil 2019. Brasília: Conab, 2015.
CORREIA, R. C.; KIILL, L. H. P.; MOURA, M. S. B.; CUNHA, T. J. F.; JESUS JÚNIOR, L. A.; ARAÚJO, J. L. P. A região semiárida brasileira. In: VOLTOLINI, T. V. (Ed.). Produção de Caprinos e Ovinos no Semiárido. Petrolina: Embrapa Semiárido, 2011.
CUNHA, D. A.; COELHO, A. B.; FÉRES, J. G. Irrigation as an adaptive strategy to climate change: an economic perspective on Brazilian agriculture. Environment and Development Economics, v. 20, n. 1, p. 57-79, 2015.
DE MARTONNE, M. E. Une nouvelle fonction climatologique: l’Indice d’Aridité. La Météorologie, n. 19, p. 449-458, 1926.
FOTHERINGHAM, A. S.; BRUNSDON, C.; CHARLTON, M. Geographically Weighted Regression: the analysis of spatially varying relationships. Chichester: John Wiley & Sons Ltd, 2002.
HOUMSI, M. R.; SHIRU, M. S.; NASHWAN, M. S.; AHMED, K.; ZIARH, G. F.; SHAHID, S.; CHUNG, E.; KIM, S. Spatial Shift of Aridity and Its Impact on Land Use of Syria. Sustainability, v. 11, n. 24, 2019.
HUANG, H.; HAN, Y.; CAO, M.; SONG, J.; XIAO, H. Spatial-Temporal Variation of Aridity Index of China during 1960–2013. Advances in Meteorology, p. 1-10, 2016.
KAYANO, M. T.; ANDREOLI, R. V. Clima da Região Nordeste do Brasil. In: CAVALCANTI, I. F. A.; FERREIRA, N. J.; SILVA, M. G. A. J.; DIAS, M. A. F. S. (Org.). Tempo e clima no Brasil. São Paulo: Oficina de Textos, 2009.
KENDALL, M. G. The Advanced Theory of Statistics, vol. 2. London: Charles Griffin and Co., 1946.
KUSUMA, A.; JACKSON, B.; NOY, I. A viable and costeffective weather index insurance for rice in Indonesia. Geneva Risk and Insurance Review, v. 43, n. 2, p. 186-218, 2018.
LICKLEY, M.; SOLOMON, S. Drivers, timing and some impacts of global aridity change. Environmental Research Letters, v. 13, 2018.
LINDOSO, D. P.; EIRÓ, F.; BURSZTYN, M.; RODRIGUES-FILHO, S.; NASUTI, S. Harvesting Water for Living with Drought: Insights from the Brazilian Human Coexistence with Semi-Aridity Approach towards Achieving the Sustainable Development Goals. Sustainability, v. 10, n. 622, 2018.
LU, G. Y.; WONG, D. W. An adaptive inverse-distance weighting spatial interpolation technique. Computers & Geosciences, v. 34, n. 9, p. 1044-1055, 2008.
MANN, H. B. Nonparametric Tests Against Trend. Econometrica, v. 13, n. 3, p. 245-259, 1945.
MARENGO, J. A. Vulnerabilidade, impactos e adaptação à mudança do clima no semi-árido do Brasil. Parcerias Estratégicas, v. 13, n. 27, 2008.
MARENGO, J. A.; BERNASCONI, M. Regional differences in aridity/drought conditions over Northeast Brazil: present state and future projections. Climatic Change, v. 129, n. 1-2, p. 103-115, 2015.
MARENGO, J. A.; TORRES, R. R.; ALVES, L. M. Drought in Northeast Brazil—past, present, and future. Theoretical and Applied Climatology, v. 129, p. 1189-1200, 2017.
MELO, R. F.; VOLTOLINI, T. V. Agricultura familiar dependente de chuva no Semiárido. Brasília: Embrapa, 2019.
MUTTI, P. R.; ABREU, L. P.; ANDRADE, L. M. B.; SPYRIDES, M. H. C.; LIMA, K. C.; OLIVEIRA, C. P.; DUBREUIL, V.; BEZERRA, B. G. A detailed framework for the characterization of rainfall climatology in semiarid watersheds. Theoretical and Applied Climatology, v. 139, p. 109–125, 2020.
PANIAGUA, L. L.; GARCÍA-MARTÍN, A.; MORAL, F. J.; REBOLLO, F. J. Aridity in the Iberian Peninsula (1960–2017): distribution, tendencies, and changes. Theoretical and Applied Climatology, v. 138, n. 1-2, p. 811-830, 2019.
PARK, C.; JEONG, S.; JOSHI, M.; OSBORN, T. J.; HO, C.; PIAO, S.; CHEN, D.; LIU, J.; YANG, H.; PARK, H.; KIM, B.; FENG, S. Keeping global warming within 1.5 °C constrains emergence of aridification. Nature Climate Change, v. 8, n. 1, p. 70-74, 2018.
PELLICONE, G.; CALOIERO, T.; GUAGLIARDI, I. The De Martonne aridity index in Calabria (Southern Italy). Journal of Maps, v. 15, n. 2, 788-796, 2019.
POUR, S. H.; WAHAB, A. K. A.; SHAHID, S. Spatiotemporal changes in aridity and the shift of drylands in Iran. Atmospheric Research, v. 233, 2020.
SCHLENKER, W.; ROBERTS, M. J. Nonlinear temperature effects indicate severe damages to U.S. crop yields under climate change. Proceedings of the National Academy of Sciences of the United States of America, v. 106, n. 37, p. 15954-15598, 2009.
SEN, P. K. Estimates of the regression coefficient based on Kendall's tau. Journal of the American Statistical Association, v. 63, n. 324, p. 1379-1389, 1968.
SILVA, A. F.; REGITANO NETO, A. As principais culturas anuais e bianuais na agricultura familiar. In: MELO, R. F.; VOLTOLINI, T. V. (Ed.). Agricultura familiar dependente de chuva no Semiárido. Brasília: Embrapa, 2019.
SILVA, V. P. R. On climate variability in Northeast of Brazil. Journal of Arid Environments, v. 58, n. 4, p. 575-596, 2004.
THEIL, H. A rank-invariant method of linear and polynomial regression analysis. Proceedings of the Royal Netherlands Academy of Sciences, v. 53, p. 386-392, 1950.
TI, J.; YANG, Y.; YIN, X.; LIANG, J.; PU, L.; JIANG, Y.; WEN, X.; CHEN, F. Spatio-Temporal Analysis of Meteorological Elements in the North China District of China during 1960–2015. Water, v. 10, n. 6, p. 789, 2018.
WACKERNAGEL, H. Multivariate Geostatistics: An Introduction with Applications. Berlin: Springer, 2003.
WHEELER, D. C.; PÁEZ, A. Geographically Weighted Regression. In: FISCHER, M. M.; GETIS, A. (Ed.). Handbook of Applied Spatial Analysis: Software Tools, Methods and Applications. Berlin: Springer-Verlag, 2010.
WOOD, S. N. Thin plate regression splines. Journal of the Royal Statistical Society: Series B (Statistical Methodology), v. 65, n. 1, p. 95-114, 2003.
XAVIER, A. C.; KING, C. W.; SCANLON, B. R. Daily gridded meteorological variables in Brazil (1980–2013). International Journal of Climatology, v. 36, n. 6, p. 2644-2659, 2016.
YU, D. Exploring Spatiotemporally Varying Regressed Relationships: The Geographically Weighted Panel Regression Analysis. In: Joint International Conference on Theory, Data Handling and Modelling in Geospatial Information Science, 2010, Hong Kong. Proceedings… Hong Kong: ISPRS, 2010.
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Figure 2A. Maize’s growing season mean temperature (degree Celsius), 2003-2018, Brazilian semi-arid.
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