Assessment of missing data infilling method effect on flood quantile estimates

Benue rivers, Nigeria

The results of the Permutation and Kolmogorov - Simonov tests presented in Table 9 assesses statistical significance of the difference between flood quantiles estimated using multiple imputation and radar altimetry infilling approaches. Radar altimetry data was not available for all the missing data years, hence the Missing /infilled-RA column of Table 9 shows the number of missing data points and available altimetry data points. Umaisha gauging station had the most missing data (19), of which (14) radar altimetry data points where available to fill the gaps, and the remaining (5) filled with multiple imputation. At Lokoja, the 6 missing data points where equality filled with multiple imputation and radar altimetry approach, thus providing a reference station for equal comparison of both approaches.

Permutation test results (Pperm = 0.02) at Umaisha station with inconsecutively gapped

data suggests that flood frequency estimates derived from MI and RA imputation approaches differed significantly, and the Dks statistic = 0.571 and Pks = 0.017 for the

Kolmogorov - Simonov test further reveals the difference in the quantile distribution for both estimates. This deviation is attributed to the high number of missing data filled by the contrasting techniques i.e. 14 out of 19 missing data, and MI inability to accurately fill inconsecutively gapped datasets (Graham et al., 2007, Rochtus, 2014, Tyler et al., 2011). At Lokoja station where an equal number of missing data were filled by both techniques, the difference between derived flood frequency estimates and distributions was not statistically significant (Pperm = 0.713, Dks = 0.143, and Pks = 0.98). Similarly, at

Onitsha and Baro, the estimated quantiles and probability distribution were not statistically different (P> 0.05), implying that the application of altimetry in filling missing data did not result in any viable change in the quantile estimates and distributions when compared to MI. Therefore, both approaches can be applied interchangeably depending on the number of gaps and spread within the historical time series.

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Table 9: Kolmogorov-Simonov and Permutation test results Stations Missing/infil

led-RA

Permutation test Pperm-Value

Kolmogorov - Simonov test K-S Statistic (Dks) Pks-Value

Umaisha 19 (14) 0.020 0.57143 0.0017

Onitsha 16 (9) 0.407 0.19048 0.8531

Lokoja 6 (6) 0.713 0.14286 0.9870

Baro 12 (1) 0.063 0.38095 0.0948

4.6.2. Assessment of Radar Altimetry and Multiple Imputation infilling at Taoussa, Mali

Flood frequency estimates and the upper and lower uncertainty bounds for a 1-in-2 to 1- in-100year flood events are presented in Table 10 to capture varying scenarios of gaps (consecutive and inconsecutive) and infilling approaches (Radar Altimetry and Multiple Imputation). The results show that flood estimates for both infilling approaches are within the uncertainty bounds of the complete data flood events for all return periods, except the 1-in-2year flood derived from inconsistently gapped data filled with radar altimetry. Permutation and Kolmogorov - Simonov test results (Table 11) further revealed that though flood estimates did not significantly differ (Pperm> 0.05), the Dks

and Pks-Values for the radar altimetry estimates for both consecutive and

inconsecutively gapped time series showed significant differences in distribution when compared to complete data. The observed difference in distribution suggests that the two complete and RA imputed flood estimates are not drawn from the same distribution despite not being significantly different (Ewemoje and Ewemooje, 2011). Therefore, an assessment of the optimal probability distribution for fitting the historical time series derived infilling the varying infilling approaches is suggested, rather than using a

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predefined distribution such as GEV as was the case in this study, given that varying probability distribution can result in very different flood estimates even for the same dataset (Laio et al., 2009).

Table 10: Taoussa flood quantile estimates and uncertainty boundaries for complete historical data and consecutively and Inconsecutively gaped missing data filled with MI and RA approaches Return Period Discharge Complete Lower Limit (Complete) Upper Limit (Complete) Discharge (Consecutive) MI Discharge (Consecutive) RA Discharge (Inconsecutive) MI Discharge (Inconsecutive) RA 2 1787.79 1734.88 1842.2 1760.15 1709.32 1779.18 1669.77 5 1898.39 1850.91 1954.0 1874.26 1861.13 1887.62 1835.12 20 1983.25 1938.07 2087.7 1978.07 1984.19 1976.08 1986.4 50 2015.89 1967.17 2170.6 2025.17 2034.14 2012.2 2055.43 100 2033.39 1978.96 2229.2 2053.36 2061.89 2032.35 2096.89

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Table 11 Kolmogorov-Simonov and Permutation test results, Taoussa gauging station

Data gap infilling comparison Permutation (Pperm-Value)

Kolmogorov - Simonov test K- S Statistic (Dks) Pks - Value

Complete Vs Consecutive (MI) 0.731 0.381 0.095

Complete Vs Consecutive (RA) 0.870 0.429 0.041

Complete Vs Inconsecutive (MI) 0.997 0.238 0.603

Complete Vs Inconsecutive (RA) 0.873 0.476 0.016

5. Conclusion

Missing data in hydrological time series is an unavoidable part of ground monitoring and emanates due to varying factors that include natural, technical, physical, procedural and financial constraints. These challenges consequently result in uncertain design flood estimates (Tyler et al., 2011, Starrett et al., 2010), thus increasing flood exposure and/or cost of flood control and management measures implementation based on such results. Advancement in open-access radar altimetry provides reasonably accurate continuous water level measurements not hampered by gaps as evident in in situ measurements (Escloupier et al., 2012), especially during extreme flood events. Also, advances in computational hardware and software have reduced the challenges associated with undertaking complex statistical imputations to estimate missing data (Little, 2002). This study applies Radar Altimetry and Multiple Imputation to fill gaps in hydrological historical time-series and flood frequency estimations, thereby capturing scenarios of supplementary data availability as unavailability respectively, as usually, the case along several rivers in developing regions. Furthermore, the effect of both approaches on

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flood frequency estimates was evaluated for gauging stations along the Nigeria and Benue rivers, accounting for the variation in missing data apparent in the study area, i.e. consecutive (1-3 years) and inconsecutive (> 3 years). To further evaluate the most suitable infilling approach, data was deliberately removed from complete dataset to depict these missing data variations.

Results from this study revealed (i) improved correlation between in situ water level measurements and radar altimetry as the distance between them reduce and vice versa, (ii) the size of the gaps in the hydrological time series (consecutive and inconsecutive) determines to a large extent the missing data imputation approach applied; (iii) Radar Altimetry missing data infilling approach outperformed Multiple Imputation, especially for widely gapped time series (> 3 years), but did not differ much for data sets with gaps of 1-3 years, hence can be applied interchangeably for datasets with consecutive gaps; and (iv) the previously unquantified 2012 and 2015 flood events in Nigeria were quantified as 1-in-100 and 1-in-50year floods respectively, and can be applied to inform flood management decisions having filled the historic data gaps. Despite the progress and potential portrayed in this study, the outcome could contain residual uncertainties that have propagated from in situ and altimetry hydrological data collection process, rating curve extrapolation, probability distribution and methodology selection. The quantification of these uncertainties is however beyond the scope of this study. Furthermore, hydrodynamic flood modelling and mapping of flood depth and extent based on the outcome of this section will be undertaken in Chapter 6.

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