Multivariate framework for the assessment of key forcing to Lake Malawi level variations in non-stationary frequency ana
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Multivariate framework for the assessment of key forcing to Lake Malawi level variations in non-stationary frequency analysis Cosmo Ngongondo
&
Yanlai Zhou & Chong-Yu Xu
Received: 4 December 2019 / Accepted: 23 July 2020 # The Author(s) 2020
Abstract Lake Malawi in south eastern Africa is a very important freshwater system for the socio-economic development of the riparian countries and communities. The lake has however experienced considerable recession in the levels in recent years. Consequently, frequency analyses of the lake levels premised on timeinvariance (or stationarity) in the parameters of the underlying probability distribution functions (pdfs) can no longer be assumed. In this study, the role of hydroclimate forcing factors (rainfall, lake evaporation, and inflowing discharge) and low frequency climate variability indicators (e.g., El Nino Southern Oscillation-ENSO and the Indian Ocean Dipole ModeIODM) on lake level variations is investigated using a monthly mean lake level dataset from 1899 to 2017. Non-stationarity in the lake levels was tested and confirmed using the Mann-Kendall trend test (α = 0.05 level) for the first moment and the F test for the second moment (α = 0.05 level). Change points in the series were identified using the Mann-Whitney-Pettit test. The study also compared stationary and non-stationary lake level frequency during 1961 to 2004, the common periC. Ngongondo Department of Geography and Earth Sciences, University of Malawi, Chancellor College, P.O. Box 280, Zomba, Malawi C. Ngongondo (*) : Y. Zhou : C. u1 − α/2, corresponding to a 1-α/2 quantile of the standard normal distribution (Hisdal et al. 2001; Karlsson et al. 2014). The MK is the most widely used rank-based non-parametric test (Kundzewicz and Robson, 2004, Bayazit 2015). The MK test is considered robust as compared with other tests and is recommended by the World
Environ Monit Assess
(2020) 192:593
Page 7 of 23 593
Meteorological Organisation (WMO) for application in the detection of monotonic trends in hydrometeorological variables (WMO 1988). In addition, the F test was used to determine any differences in the second moment (variance) of the lake level time series. The test was undertaken under the null hypothesis (H0) of equal variance (H0 : σ21 ¼ σ22 Þ and an alternate hypothesis (H 1 ) of unequal variances (H1 : σ21 ≠σ22 Þ as follows: F c ¼ s21 =s22 , s21 > s22 , and H0 are rejected if F c ≥ F 1−α;n1 −1;n2 −2 where F 1−α;n1 −1;n2 −2 is the critical value from the F-distribution table (Li et al. 2013). Stationery and non-stationary frequency analysis Extraction of extreme lake levels Extreme lake levels were determined using two approaches from the lake levels (Rosbjerg and Madsen 2004, Ngongondo et al. 2015 and references within): through analysis of the annual maximum series (AMS) and partial duration series (PDS), also called peak over threshold (POT). AMS involves a series composed of one maximum mean lake level in each hydrological year (November to October), resulting in a total of 119 values for the
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