in this study as a surrogate for the
SWS over the Congo Basin.
In‐situ River Discharge
Observed river discharge data for the Congo Kinshasa station was accessed from the GRDC (www.bafg.de/GRDC) archives and used to assess hydrological response of the Congo River to climatic fluctuations. The Congo River is one of the key rivers in the region, as multiple sources of discharge from other tributaries within the Congo Basin connect with this channel before reaching the Atlantic Ocean. While the Congo River discharge encapsulates most of the flows within the basin (Ndehedehe et al., 2019), this river largely modulates the surface water hydrology of the Congo Basin (e.g., Alsdorf et al., 2016; Ndehedehe et al., 2018b). The monthly river discharge data of the Congo River in Kinshasa station covering the period between 1980 and 2010 was used in combination with sea‐surface temperature to model the impacts of the surrounding oceans on temporal dynamics of Congo River discharge. But in assessing climate influence on surface water hydrology (i.e., TWS) over the Congo Basin, the data covering the period during 2002–2010 was used.
5.2.3. Tropical Rainfall Measuring Mission
The TRMM (Tropical rainfall measuring mission) 3B43 (Huffman et al., 2007; Kummerow et al., 2000) provides monthly precipitation estimates on a 0.25° × 0.25° spatial grid across the globe. The data were used in this study to assess the leading driver of GRACE‐derived TWS and the spatial and temporal distributions of rainfall over the Congo Basin.
5.2.4. Sea‐Surface Temperature Products
This study used the global sea‐surface temperature (SST) data (Reynolds et al., 2002) covering the period between 1982 and 2015 and was accessed from NOAA’s official earth system research laboratory portal (http://www.esrl.noaa.gov/psd/data/gridded/data. noaa.oisst.v2.html). Given that the influence of global SST anomalies on precipitation over tropical central Africa has been reported (see, e.g., Farnsworth et al., 2011; Ndehedehe et al., 2019), SST over the Atlantic, Pacific, and Indian oceans were used in this study to model climate influence on discharge. The global oceans modulate the zonal and local circulation patterns over Equatorial Africa (Nicholson & Dezfuli, 2013; Pokam et al., 2014), thus our motivation to examine the impact of SST on discharge.
5.2.5. Standardized Precipitation Evapotranspiration Index
The SPEI combines precipitation and temperature data in a water balance framework (see Vicente‐Serrano et al., 2010a,b). The SPEI used here was estimated based on a water balance approach as the difference between precipitation (P) and PET (potential evapotranspiration), i.e., δ = P‐PET. As detailed by Vicente‐Serrano et al. (2010b), the computed values of δ are cumulated on different time scales,
(5.1)
where k is the cumulated time scale and n is the calculation number. This cumulated time series are thereafter fitted with a log‐logistic probability distribution function. The SPEI drought characterization here follows the thresholds defined by McKee et al. (1993), in which a drought condition is assumed to occur when the SPEI is consistently negative and reaches a value of –1. On a 12‐month cumulation, this threshold supports hydrological drought characterization in the Congo Basin.
5.2.6. Statistical Analysis and Modeling
The statistical analysis and decomposition of SPEI and TWS into temporal and spatial patterns were based on the principal component analysis (PCA, e.g., Jolliffe, 2002). The need to localize hydro‐climatic signals is increasing due to growing multiple climate signals around the globe (e.g., Ndehedehe et al., 2017b). This has triggered numerous robust applications of multivariate methods in the spatiotemporal analysis of drought patterns and multi‐resolution data (see, e.g., Agutu et al., 2017; Bazrafshan et al., 2014; Ivits et al., 2014; Ndehedehe et al., 2016). To understand the influence of global climate on Congo’s hydrology, the support vector machine regression model (SVMR, Vapnik, 1995) was used to assess the influence of climate on the Congo Basin hydrology. The support vector machine (Cortes & Vapnik, 1995) algorithm was extended by Vapnik (1995) for regression using an ε‐insensitive loss function. The SVMR concept is based on the computation of a linear regression function in a high‐dimensional feature space in which the input data (xi) are mapped through a non‐linear function (e.g., Okwuashi & Ndehedehe, 2017). This mapping is warranted because most of the time, the relationship between a multidimensional input vector x and the output y is unknown and could be non‐linear (e.g., Wauters & Vanhoucke, 2014). After finding a linear hyperplane that fits the multidimensional input vectors to output values, the SVMR predict future output values that are contained in a validation set (e.g., Okwuashi & Ndehedehe, 2017; Smola & Schölkopf, 2004; Vapnik, 1995; Wauters & Vanhoucke, 2014). Assuming the set of data points X = (x i , p i ); i = 1.., n with x i , being the predictand data point i, p i the actual value, and n the number of data points. The linear SVMR function f(x) takes the form (e.g., Vapnik, 1995):
The assumed linear parameterization in equation 5.2 bears similarity to a linear regression model. That is because the predicted value, f(x), depends on a slope w and an intercept b. However, the goal of the SVMR is to identify a function f(x) that has a maximum deviation ε from the target values p i and has a maximum margin for all training patterns xi. In other words, a balance between learning the relation between inputs and outputs while maintaining a good generalization behavior is targeted. As highlighted further in Wauters and Vanhoucke (2014), too much focus on minimizing training errors may lead to overfitting. Hence, a pre‐specified penalty value (C) is introduced as a trade‐off to create the balanced between generalization and good training. That is, C regulates the trade‐off between the regularization term (½ ‖w‖2) and the training accuracy in the formulation below as (e.g., Vapnik, 1995; Wauters & Vanhoucke, 2014),
(5.3)
where the compound risk caused by training errors and model complexity is given as ς. Equation 5.2 provides the estimated values for w and b and comprises the empirical risk measured by the ε‐insensitive loss function, Lε, and the regularization term ½ ‖w‖2, which describes the model complexity (Cortes & Vapnik, 1995; Wauters & Vanhoucke, 2014). Prior to modeling the response of discharge to climate using the SVMR, a regularization approach
