Evaluation of an inverse distance weighting method for patching daily and dekadal rainfall over the Free State Province, South Africa

Abstract

Climate data recorded by national meteorological agencies is either incomplete or faulty for some periods due to a number of reasons. Multi-functional utilization of climate data in complete form necessitates the filling of these gaps. In this study an inverse distance weighting (IDW) method was used to estimate rainfall utilizing neighbouring station data in the Free State Province of South Africa. Six weather stations evenly distributed across the province, and with data for 1950 to 2008, were used to evaluate this patching IDW approach at daily and dekadal time steps. Coefficient of determination (r 2 ), mean absolute error (MAE) and mean bias error (MBE) were the statistics used in the assessment. Firstly, the study conducted a sensitivity analysis of the IDW exponent (p) which showed that the best results are obtained when p is either 2 or 2.5. The estimated values at all six stations were highly correlated with the measured rainfall data with an overall r 2 value exceeding 0.70 for both daily and dekadal estimates. MAE showed low miscalculations with values with an average of 1 mm per day and 4.4 mm per dekad. MBE was very low for both daily and dekadal evaluations but the disaggregated data showed underestimation of the IDW mostly for daily rainfall exceeding 10 mm. Thus, IDW methodology proved to be an acceptable approach for estimating both daily and dekadal rainfall in the Free State Province.

Analysis of a new spatial interpolation weighting method to estimate missing data applied to rainfall records

“…Code Reference 1 Classical normal ratio method NR (Paulhus and Kohler, 1952) 2 Normal ratio method weighted with correlations NRWC (Young, 1992) 3 Inverse distance weighting method IDWM (Teegavarapu and Chandramouli, 2005;Chang et al, 2006;Moeletsi et al, 2016) 4 Weighted correlation coefficient method CCW (Suhaila et al, 2008;Ford and Quiring, 2014) 5 Modification to the weighted correlation coefficient method CCWM (Suhaila et al, 2008) 6 Normal ratio modified with inverse distance method NRIDW (Suhaila et al, 2008) 7 Modified correlation coefficient with inverse distance method CIDW (Suhaila et al, 2008) 8 Inverse distance weighting of normal ratio with correlation NRIDC (Azman et al, 2015) 9 Relation of the height with the weighted method of the inverse distance HIDW (Seyyednejad et al, 2012) related to the IDW method (d it ); however, although q=2 is the most commonly used value (Teegavarapu and Chandramouli, 2005;Boke, 2017) there is no theoretical justification for preferring this value over others (Bajjali, 2018). Therefore, other possible values for q should be investigated as well.…”

Assessing the frequency of drought/flood severity in the Luvuvhu River catchment, Limpopo Province, South Africa

“…2). Station data were not used in this study due to inconsistencies in recording rainfall data and gaps in the data (Moeletsi et al, 2016). Statistical analysis of the CRU grid data and weather station data was conducted (see Appendix).…”

Evaluation of Infilling Methods for Time Series of Daily Temperature Data: Case Study of Limpopo Province, South Africa

“…Historical climate data contain gaps, which usually increase with the length of the dataset. The frequency of gaps in the climate data in most cases makes it difficult for the data users to make sound conclusions, since some of the important climatological events were not sufficiently covered by the records [10,11]. In some instances, there might have been faulty recordings, which further increase the uncertainty in the use of archived climate data.…”

“…Climate data patching and infilling are common phrases used to fill and complete missing climate and hydrological data in a dataset [12,[15][16][17][18][19]. There are three common approaches that are often used to manage missing climate data: (a) use of continuous records and ignoring the prior events, (b) ignoring of gaps based on the assumption that the data is one continuous series of records [10] and (c) data infilling [11,20]. The main disadvantage of the first approach is that it wastes valuable and previous information and that true statistical inferences cannot be made, whereas the second approach will reduce the period of recorded events available for the analysis and these can over-or under-estimate the likelihood of occurrence of climatic events [10].…”

“…The main disadvantage of the first approach is that it wastes valuable and previous information and that true statistical inferences cannot be made, whereas the second approach will reduce the period of recorded events available for the analysis and these can over-or under-estimate the likelihood of occurrence of climatic events [10]. Data infilling is considered the viable option, but it has to be approached in a manner that will eliminate biasness and conform to the climatological variation at the target region [11].…”