INTRODUCTION
The Amazonian rainforest is connected to the global hydrological cycle (Yoon & Zeng, 2010). Deforestation so as intense fires are factors affecting rainfall distribution and the Amazonian climate in general (Coe et. al., 2013). Bonini et. al. (2014) found negative correlations between deforestation and rainfall in Mato Grosso. Some studies have shown a decrease in regional evapotranspiration and precipitation due to increase in surface temperature associated to large-scale deforestation (Sellers et. al., 1997). This alters the hydrological cycle and influences the regional climate (Bagley et. al., 2014). Debortoli et. al. (2015) found that the rainy season was shorter at 88 % of the 200 observed rain gauges. Rainfall occurrence at the Northeast and the Southern regions of Brazil is influenced by the seasonal displacement of the Intertropical Convergence Zone and the South Atlantic Convergence Zone (Marengo et. al., 2011).
Rainfall variability in the Amazonia is correlated with the sea surface temperature patterns in the Atlantic and Pacific oceans during December, January and February (Martins et. al., 2015). The reality is complex since past investigations have shown a decadal intensification of rainfall over the whole Amazon basin (Chen et. al., 2002). The vulnerability of the region could be clear by the fact that Amazonia experienced its worst drought events in 2005 and 2010 (Davidson et. al., 2012). However, it has been hypothesized that a physical mechanism of forest-induced atmospheric circulation called biotic pump by Makarieva & Gorshkov (2007) was responsible of the Amazonian forests greened-up during that 2005 drought (Saleska et. al., 2007).
Costa et. al. (2008) used geostatistical methods for analyzing precipitation extremes in Southern Portugal while Sarangui et. al. (2015) mapped the rainfall variability over the island of St. Lucia. In general, geostatistical analysis of climatic variables has been very difficult to perform due, in part, to the limited availability of measurement points which affects the estimation at ungauged sites (Sarangi et. al., 2005). Webster & Oliver (1992) demonstrated that at least 150 spatial points (e.g. rain gauges or meteorological stations) are required for a reliable geostatistical analysis. Once this problem has been solved, an appropriate kriging estimator (Burgess & Webster, 1980) could be a valuable tool for predicting rainfall data at ungauged sites. The spatial variability of precipitation also controls the spatial variation of other variables such as evapotranspiration and water storage. Due to the environmental significance of the Amazonian basin, the analysis of the spatial distribution of rainfall patterns is essential for agricultural, engineering and ecological planning. The objectives of the present work are to model the spatial structure of rainfall patterns in the Brazilian rainforest using three timescales and to search for any statistical relationship between deforestation and rainfall occurrence.
MATERIALS AND METHODS
Study area and rainfall data
The present study spanned 64 municipalities corresponding to 9 Amazonian states from Brazil. The geographical zone covered approximately from 5.03 ºN to 16.45 ºS and 42.83 to 70.93 ºW. Rainfall data refer to historical monthly mean and annual records collected from 218 rain gauges (Figure 1).
Figure 1.
Study region and rain gauge locations.
The records ranged from the last 16 years for Rondonopolis (Mato Grosso state) to the last 106 years for Manaus (Amazonas state). The last date for data collection was December 2015. Three timescales were considered: individual months with minimum (September) and maximum (March) rainfall, January-June (rainy season), July-December (dry season) and annual rainfall. Note that January-June and July-December overlap winter and summer periods. However, our main goal was to establish a 6-month timescale separating wet and dry seasons.
Deforestation data
We performed an analysis on the potential relationship between the deforestation index and the annual rainfall including all the Amazon states. Most investigations try to search for relationships between deforested areas (km2) and rainfall. From our point of view that approach could be fictitious in this case as different states have different spatial extensions. We used instead the percentage of forest loss which relates forest loss (ha) to the total forest area (ha) for a particular site or state. The forest loss percentages are available at http://www.mongabay.com for 2001-2012 period (Butler, 2014). With that proposal, we averaged the available historical annual rainfall record for each studied Amazonian state and correlated them with the corresponding forest loss index.
Theoretical background on Geostatistics
Geostatistics incorporates the spatial coordinates of observations in data processing. It is fundamental for the modeling of spatial patterns, prediction at unsampled points and estimation of the uncertainty inherent to those predictions (Goovaerts, 1998). The semivariance function, , is one of the key components of geostatistics as it summarizes the spatial variation of the studied variable.
Where is the value of the experimental semivariance at each separation distance (lag), h, N(h) is the number of data pairs separated by the lag , and are the rainfall values at location and , respectively. A plot of ((h) versus defines the experimental semivariogram. Different models are available for fitting the experimental semivariogram (see for instance McBratney & Webster, 1986). We explored three transitive models (spherical, exponential and Gaussian models).
Equation (2) represents the spherical isotropic model. In this case C0 is the nugget variance or nugget effect ( ), is the structural variance ( ), is the upper limit of the semivariogram (sill) and A0 is the distance at which semivariogram reaches a constant semivariance value (correlation range parameter). The Spatial Dependence Degree Index ( ) can be computed as the ratio between the structural variance, , which characterizes the variance accounted for by the spatial dependence and the sill, . For example, suggests weak spatial dependence, corresponds to moderate spatial dependence while indicates strong spatial dependence. This is a modification to the ratio nugget/sill variance proposed by Cambardella et. al. (1994). The range is the limit of spatial dependence. The spherical model characterizes a moving average of a randomized process (Kuzyakova et. al. 2001).
Equation (3) is the isotropic exponential model. It differs from the spherical model in the rate at which the sill is reached. It represents autoregressive processes of first order (e.g. Markov or Poisson processes) as the autocorrelation function decays exponentially (Wang et. al. 2010).
Equation (4) corresponds to the Gaussian or hyperbolic isotropic model. It is almost similar to the exponential model but the departure from the nugget variance is smoother.
Block Kriging
Block kriging is a robust interpolation method for estimating values of the variable (e.g. rainfall values in this case) at ungauged zones (Burguess & Webster, 1980). The block kriging estimator ( ) of the average rainfall on a given zone ( ) is built as a linear combination of the available rainfall data:
Where is the estimated kriged value of in the area and are weighing factors such that:
In this case is the number of rainfall values in the vicinity of . The block kriging estimation is unbiased under the condition:
That is, the mathematical expectation of is the same as that of the real value.
The accuracy of rainfall maps was assessed through a cross-validation process (Davis, 1987). The agreement between estimated and measured values was quantified using mean absolute error ( hereafter) (Voltz & Webster, 1990) and goodness-of-prediction statistics ( statistics hereafter) (Agterberg, 1984). The MAE statistics is in fact a residual sum:
Where is the predicted rainfall value at location .
The statistics is a sort of balance between kriging and sample mean as potential rainfall predictors:
Where is the mean value of all the observations.
Equation (9) defines three possibilities:
indicates that kriged values or sample mean could be used as rainfall predictors,
suggests that sample mean is a better predictor than kriging,
indicates that kriging is more appropriate than sample mean for making reliable predictions at ungauged sites.
It is useful to recall that due to earth curvature the use of geographical coordinates for large scale spatial analysis is inappropriate. Thus, in order to perform the spatial analysis, geographical coordinates were transformed into rectangular coordinates.
Standard statistics and Geostatistical computation
Classical statistics (e.g. first and second order statistics and test of normality) and linear regression analysis were conducted using the StatisticaTM Software Package (StatSoft. Inc., 2011). All the geostatistical analyses were performed using the GS+ Geostatistical Software Package (Gamma Design Software, 2001). In particular, we set the minimum lag class distance to 247.25 km. Block kriging estimation was carried out using local grids and 16 neighbors within a radius equal to the range of the semivariogram. We selected a total of six map contour levels.
RESULTS AND DISCUSSION
March and September were the months with maximal and minimum rainfall values, respectively. Those months also showed the maximum and minimum standard deviation values (117 mm and 60 mm, respectively) (Table 1).
Table 1.
Descriptive statistics of monthly, six month and annual rainfall. KSL is Kolmogorov-Smirnov and Lilliefors test for normality. NS means that Rainfall distribution does not differ statistically from normality at .
The spatial distribution of rainfall based on upper thresholds is highly variable in the whole region (Figure 2A-E). The maximal historical annual rainfall (4253 mm) as represented by the upper threshold was located in Fonte Boa (Amazonian state, 2.35 ºS, 65.12 ºW) while the minimum upper threshold of annual rainfall (1980 mm) was recorded at Caceres (Mato Grosso state, 16.05 ºS, 57.68 ºW) (Figure 2E).
Figure 2.
Rainfall distribution in the study region based on geographical coordinates: A) March, B) September, C) January-June, D) July-December and E) Annual.
Some selected areas from different states like Manaus (3.1 ºS, 60.01 ºW, Amazonas state), Caceres (16.05 ºS, 57.68 ºW, Mato Grosso state), Boa Vista (2.82 ºN, 60.66 ºW, Roraima state), Macapá (0.1 ºS, 51.1 ºW, Amapá state) and Rio Branco (9.96 ºS, 67.8 ºW, Acre state) showed different behavior of rainfall occurrence along the year (Figure 3).
Figure 3.
Monthly rainfall at five selected sites: Manaus (Amazonas state), Caceres (Mato Grosso state), Boa Vista (Roraima state), Macapá (Amapá state) and Rio Branco (Acre state).
Despite the fact that some rainfall records did not fit the normality condition (January, February, April, July, August, October and November), the data sets of our interest (March, September, January-June, July-December and annual rainfall) did not differ statistically from normality according to the Kolmogorov-Smirnov and Lilliefors test for normality at (Table 1). This is a basic condition for geostatistical analysis as one could assume stationarity of the second order. That is, the expectation value and the spatial covariation can be considered as constant.
The selected Geostatistical models described reasonably well the experimental semivariograms. The Gaussian model fitted quite well September ( ) and July-December ( ) rainfall data (Figure 4B and D) while the spherical model was the best choice for describing the spatial structure of rainfall for March, January-June and annual periods (Figure 4A, C and E) with correlation ranges of 1521 km, 1110 km and 1020 km, respectively (Table 2).
Figure 4.
Univariate semivariogram for each selected rainfall period: A) March, B) September, C) January-June, D) July-December and E) annual.
Table 2.
Parameters of the fitted geostatistical models (R is the correlation coefficient).
The interpolation (kriging) maps corresponding to March and September agreed approximately well with the results shown in Figure 3 in terms of maximal monthly rainfall values (Figure 5A and B). In all cases, central Amazonia was the region with less rainfall occurrence. The January-June (wet season) kriging map identified reasonably well the region with rainfall values over 1569 mm (mean value of the 6-month period) at the Northern to Northeast Amazonia (Figure 5C). The interpolation map for the July-December time period (dry season) located the maximum rainfall values at the West Amazonia, approximately (Figure 5D). However, maximal rainfall values at the Western Amazonia in July-December were smaller than those corresponding to Northern-Northeast Amazonia. The kriging map corresponding to annual rainfall combined the spatial distribution of rainfall patterns in the whole studied region for the selected time scales (Figure 5E).
Figure 5.
Kriging maps corresponding to each rainfall period: A) March, B) September, C) January-June, D) July-December and E) Annual.
The as a goodness-of-prediction statistics ranged from 27 mm for September to 346 mm for annual rainfall as expected. The positive value of statistics indicates that kriging could be a better predictor of rainfall at ungauged sites than mean rainfall values. In particular, September and July-December (dry season) were the timescales where kriging interpolation performed better ( and , respectively). At the same time, the cross-validation process indicated that those timescales also rendered the best correlation coefficient between observed and predicted rainfall values ( and , respectively) (Table 3).
Table 3.
Goodness-of-prediction statistics through cross-validation (R is the correlation coefficient between actual and estimated rainfall).
| Period | (mm) | (-) | |
|---|---|---|---|
| Mar | 69 | 0.358 | 0.615 |
| Sep | 27 | 0.627 | 0.792 |
| Jan-Jun | 273 | 0.260 | 0.557 |
| Jul-Dec | 138 | 0.700 | 0.846 |
| Annual | 346 | 0.336 | 0.584 |
It is noted that rainfall records larger than mean values shifted from Northeast to Northwest Amazonia while rainfall values smaller than mean showed the reverse trend. This bias of rainfall has been well documented in the literature. For example, Martins et. al. (2015) have found that Atlantic and Pacific sea surface temperature (SST) modulate the Northern area of Amazonia during June-August period (winter season) while Pacific SST acts on the Eastern region during December-February period (summer season). It is very difficult to define wet and dry seasons within the Amazonian region. In winter (June-August period) an isobar of normal atmospheric pressure ( ) crosses over the Amazon rainforest from Northeast (Amapá state) to approximately Southwest (Acre state). This can produce a rainfall shortage in Macapá, Manaus and Rio Branco. That situation is reversed in summer (December-February period) due, in part, to the presence of a moderate low pressure zone ( ) in Northeast to central Amazonia approximately. That consideration agrees well with a previous investigation by Chaves & Cavalcanti (2001).
The quasi-parabolic shape of the Gaussian model for lag distances near to the origin is indicative of a smooth spatial variability of rainfall in September and July-December. Such spatial organization held for a correlation length of about 1793 km (September) and 2044 km (July-December) with stronger spatial dependence in terms of ( and , respectively). Those larger correlation ranges suggest that rainfall events could be mainly of stratiform nature in September and July-December. It is known that stratiform precipitation is a large-scale process. That sort of seasonal range was previously discussed by van de Beek et. al. (2011) for the case of daily rainfall in The Netherlands.
The nugget semivariance (1080 mm2 in September and 27000 mm2 for July-December period) could be related to random spatial variability at distances smaller than or equal to the shortest lag class distance interval (e.g. 247.25 km in this study). At this stage one could assume that local factors such as patches of deforested areas can produce local variations of relative humidity, evaporation, evapotranspiration and/or atmospheric pressure which also contribute to such unexplained rainfall variability. Note that annual precipitation showed the smaller correlation range ( ). One could conjecture that, in average, annual rainfall in the Amazonian rainforest is due mainly to convective mechanisms. We support such an assumption taking into account that January-June period ( ) includes the 68.1 % of the annual precipitation. Adjusting previous interpretations by Jongman et. al. (1995), one could assume that the spherical model describes abrupt rainfall changes at unequal distances. The high value of the nugget effect (7750 mm2 for March, 108200 mm2 for January-June and 163000 mm2 for annual periods) indicates, to some extent, a higher short-range spatial variability for distances smaller than 247.25 km. This also could be due to the local nature of most convective events which depend on the organization of mesoscale (eg. length scale(100 km) processes (Takemi, 2010).
Even though the spherical model fitted reasonably well the annual rainfall data, one can note some sort of alternating rainfall patterns from 824 km to 2060 km along the sill. According to Pendergrass et. al. (2016), General Circulation Models are unable to resolve with precision individual mesoscale rainfall events which produce a lack of knowledge of the effect of climate change on rainfall pattern organization. One of the first steps toward filling that gap was the investigation by Ferreira et. al. (2018) for the case of the Southeast United States. Those authors found that short simulations provided an initial inside but much more simulations are needed for an appropriate understanding of the changes of rainfall organization and intensity under a global warming perspective.
We highlighted two rainfall gradients in the kriging map corresponding to the historical annual rainfall. One rainfall gradient is oriented approximately from the drier central Amazonia (Pará state) to Northern-Northeast Amazonia (e.g. Amapá state) while the other rainfall gradient extent from South Amazonia (Mato Grosso state) to the Western Amazonia (e.g. near the border between Amazonas state and the Eastern region of Peru). That annual spatial variability in the Northern and Western Amazonia has been previously discussed by Ronchail et. al. (2002) in terms of the Intertropical Convergence Zone displacement while Sheil & Murdiyarso (2009) stressed the influence of land surface, atmosphere, soil moisture and evapotranspiration on the hydrological processes in the Amazon basin at inter-annual and annual time scales. Even though any statistical parameter (e.g. and/or parameter) could support the suitability of kriging, one needs additional information on the reality of those interpolated patterns. For example, the kriging map for annual rainfall shows a tendency of rainfall to decrease from Northern-Northeast to approximately Southern Amazonia.
Makarieva et. al. (2009) investigated the relationship between rainfall versus distance from the ocean along a 2800 km transect across the Amazon rainforest. That transect was established from 0 ºS, 50 ºW (Amapá state) to 5 ºS, 75 ºW (western region of Amazonas state and eastern zone of Peru). Those authors did not find a significant statistical relationship between rainfall and distance from the ocean and concluded that rainfall did not decrease along 2800 km inland. In order to gain more understanding on the potential factors affecting the rainfall spatial distribution, we designed an irregular, almost similar, transect of 2708 km but it started at 0.1 ºS, 50 ºW (Amazon estuary, Amapá state) and concluded at 8.95 ºS, 72.8 ºW (Western region of Acre state) (Figure 6A). Similar to Makarieva et. al. (2009), we also did not find a significant statistical relationship between rainfall and distance from the Atlantic Ocean. Nevertheless, one can note a subtle trend to rainfall decline (Figure 6B). It is possible that only 17 sites are not enough and more data points are required for a reliable analysis. However, it is also likely that neither Makarieva et. al. (2009) transect nor our own transect crossed over the most deforested regions. This deserves more investigation in the future.
Figure 6.
A) Irregular transect from the Atlantic coast (the starting point is the Amazon estuary, -0.1 ºS Latitude, -50.0ºW Longitude) and B) annual rainfall versus inland distance.
Deforestation as a man-induced factor can also influence the rainfall pattern organization and to modify the Amazonia hydrometeorology. This has been a controversial issue for many years. We found a significant negative linear relationship between the percentage of forest loss and annual rainfall (Figure 7).
Figure 7.
Deforestation versus historical annual rainfall.
CONCLUSIONS
We have used geostatistical tools for investigating the actual spatial organization of rainfall patterns in the Brazilian Amazonia. Gaussian and spherical models captured approximately well the spatial structure of historical rainfall records.
The parameters of the Geostatistical models could be related to the occurrence of convective or stratiform rainfall in different periods of the year.
The interpolation maps showed a seasonal shift of maximal rainfall from Northern-Northeast to West Amazonia while the South-Central to South region remains drier. This agrees with the assumption of the Amazonian precipitation dipole previously investigated with simulation models.
It was not found any consistent statistical relationship between rainfall and distance from the Atlantic coast. However, it was found a significant negative correlation between average rainfall computed for each state and forest loss as a deforestation index.
Even though many investigations have been conducted, the influence of deforestation and land use change on the actual spatial structure of rainfall patterns deserves much more attention. Future models need to include spatial maps of deforestation and their influence on spatial patterns of rainfall.