2.2.1 Hydro-Meteorological data
The DRB is located in a region where hydro-meteorological data is scarce [20]. The study used climate data from Kasungu, Dwangwa, Kaluluma, and Mwimba climate stations (Fig. 1) for the period 1985–2015 obtained from the Malawi Department of Climate Change and Meteorological Services (DCCMS). The DCCMS data was of relatively high quality and contained no gaps, suggesting some level of inspection before being distributed. However, the selection of the stations was based on the World Meteorological Organisation's (WMO) recommendation that a minimum of 30 years of data is sufficient for analysing trends in hydro-climatic data [20]. In addition, the Malawi Ministry of Water and Sanitation, through the Department of Water Resources (DWR), provided average monthly river discharge data for the upper and lower Dwangwa River Basins from 1985 to 2009. The data were from two gauging stations at Kwengwere upper catchment (6C1) and Dwangwa S53 (6D10) lower catchment (Fig. 1). Unlike the DCCMS data, the discharge data had prolonged periods (2009–2015) of missing data. Average monthly river discharge data for the upper and lower Dwangwa River Basin was collected from the Ministry of Irrigation and Water-Malawi, Department of Water Resources, from 1985 to 2009. Data was not available at Dwangwa Road Bridge S53 station in 1985.
The period from 2009 to 2015 had the longest period of missing data; hence, it was discarded for analysis. Many studies have recommended that for better spatial variability in hydrological analysis, data spanning more than 20 years can be desirable for trend analysis [21]. In a case where missing data exists in the basin, missing flows can be estimated using nearby rivers that have data [22]. Therefore, the study used regression analysis to fill in the missing data. The method has been successfully utilised in hydrological studies [22]. At both discharge gauging stations, data from 1986 to 1989 was complete. Thus, this period was utilised in generating the equation for filling data gaps. There were big gaps between the series on both stations up until 2015. In other situations, data from one gauging station was used due to prolonged missing data at the other stations (alternatively). Therefore, for the hydrological response, the study used 24 years because of the long period of missing data in some years.
Despite the availability of numerous methods for filling in missing hydrological data, there is generally no single method that can be considered universally best [22]. Further, it was mentioned that each method has its own advantages and disadvantages, depending on the characteristics of the data set. However, other factors, for instance, distance between stations, aerial coverage of each gauging stage, length of gap, the season, the climatic region, or the availability and data characteristics of the records, have significant influences on hydrological data estimates [22]. In this regard, the study used simple linear regression (Eq. 1).
$$y={B}_{0}+{B}_{1}X+\in$$
1
\(\varvec{y}\) is the predicted value of the dependent variable \(\left(\varvec{y}\right)\) in the case of the station with missing data.
\({\varvec{B}}_{0}\) is the intercept, the predicted value of y when the X is 0. \({\varvec{B}}_{1}\) is the regression coefficient-how much we expect \(\varvec{y}\) to change as\(\varvec{X}\) increases (Eq. 1). X is the independent variable which is the Station of Dwangwa Road Bridge S53. The R square was chosen as the explanation for the model's best fit when determining the dependent variables [23]. Consider a model where the R2 value is 70%. Here r squared meaning would be that the model explains 70% of the fitted data in the regression model. Generally, when the R square of 2 value is high, it suggests a better fit for the model [24]. Thus, the study found R square of 0.76 data was considered to be the best fit (Fig. 2).
best fit of the model. The r square of 0.75 was assumed the best fit hence it was utilised for
calculating missing values.
2.2.2 Indian Ocean Dipole data
The study used the Dipole Mode Index (DMI) to quantify the Indian Ocean temperature anomalies. The DMI has been used in several studies; e.g., the intensity of the IOD is given by the anomalous SST gradient between the western equatorial Indian Ocean Dipole and the south-eastern equatorial Indian Ocean [8], [25], [26]. When the DMI is positive, the phenomenon is known as a positive IOD event, and when it is negative, it is a negative IOD event (Yamagata et al. 2003). The Dipole Mode Index data was obtained from the Tokyo Climate Centre and the World Meteorological Organisation (WMO) Regional Climate Centre in RA II (ASIA).
Data is available at https://ds.data.jma.go.jp/tcc/tcc/products/elnino/index/iod_index.html. In the period from October to December, a three-month average was determined. The standard deviation of ± 0.5 was the accepted yardstick for declaring ± IOD [8]. Therefore, four years had positive IOD: 1994, 1997, and 2015 (Fig. 2). Negative IOD occurred in 1996, 1998, 2005, and 2010. Ultimately, the neutral IODs occurred in 1986, 2000, 2002, 2004, and 2009 (Fig. 2).