“…However, rainfall linkages with the CV and latitude are strongly related only with winter and the pre‐monsoon. Similar findings are reported for Nigeria, where monthly rainfall has a power‐law relationship with the CV (Nnaji et al ., ). Looking at moderate to very strong linkages for geographical and statistical parameters with the mean, this study subsequently used the PCA to identify the influential geographical and statistical parameters dominating each cluster.…”
Section: Resultsmentioning
confidence: 97%
“…In other study, Nnaji et al . () grouped 24 rainfall stations into five clusters in Nigeria based on the co‐efficient of variation (CV) through hierarchical cluster analysis (HCA). Furthermore, linkages between mean annual rainfall and the CV resulted in linear, power law and logarithmic relationships.…”
This study used hierarchical cluster analysis (HCA) to delineate the spatial patterns of monthly, seasonal and annual rainfall by clustering 62 stations in the western arid region of India based on a 55 year data set. The statistical properties of clusters were computed and box-whisker plots plotted. Furthermore, the relative influence of three geographical factors (longitude, latitude and altitude) and five statistical parameters (the mean, standard deviation (SD), co-efficient of variation (CV), and maximum and minimum rainfall) on mean rainfall was investigated using principal component analysis (PCA). The use of HCA resulted in four rainfall clusters geographically located at a distinct position. Cluster I, characterized by the lowest mean rainfall and highest CV, was located in the western portion, whereas mean rainfall was the highest for cluster IV situated in the eastern portion. Box-whisker plots revealed a slight skewness, although the monsoon and annual rainfall followed a normal distribution. The PCA results indicted two to three significant principal components (PCs) with eigenvalues > 1. In four clusters, two PCs explained the major variance, ranging from 69.41% (June) to 91.83% (August) in monthly rainfall, from 63.62% (monsoon) to 93.30% (post-monsoon) in seasonal rainfall, and from 71.48% to 90.73% in annual rainfall. In monthly and seasonal rainfall, first PC 1 is termed the "mean rainfall component", which has strong to moderate associations with longitude, and is equally opposed by the CV. These findings are vital for planners and decision-makers to formulate strategies to manage unusual rainwater quantities.
“…However, rainfall linkages with the CV and latitude are strongly related only with winter and the pre‐monsoon. Similar findings are reported for Nigeria, where monthly rainfall has a power‐law relationship with the CV (Nnaji et al ., ). Looking at moderate to very strong linkages for geographical and statistical parameters with the mean, this study subsequently used the PCA to identify the influential geographical and statistical parameters dominating each cluster.…”
Section: Resultsmentioning
confidence: 97%
“…In other study, Nnaji et al . () grouped 24 rainfall stations into five clusters in Nigeria based on the co‐efficient of variation (CV) through hierarchical cluster analysis (HCA). Furthermore, linkages between mean annual rainfall and the CV resulted in linear, power law and logarithmic relationships.…”
This study used hierarchical cluster analysis (HCA) to delineate the spatial patterns of monthly, seasonal and annual rainfall by clustering 62 stations in the western arid region of India based on a 55 year data set. The statistical properties of clusters were computed and box-whisker plots plotted. Furthermore, the relative influence of three geographical factors (longitude, latitude and altitude) and five statistical parameters (the mean, standard deviation (SD), co-efficient of variation (CV), and maximum and minimum rainfall) on mean rainfall was investigated using principal component analysis (PCA). The use of HCA resulted in four rainfall clusters geographically located at a distinct position. Cluster I, characterized by the lowest mean rainfall and highest CV, was located in the western portion, whereas mean rainfall was the highest for cluster IV situated in the eastern portion. Box-whisker plots revealed a slight skewness, although the monsoon and annual rainfall followed a normal distribution. The PCA results indicted two to three significant principal components (PCs) with eigenvalues > 1. In four clusters, two PCs explained the major variance, ranging from 69.41% (June) to 91.83% (August) in monthly rainfall, from 63.62% (monsoon) to 93.30% (post-monsoon) in seasonal rainfall, and from 71.48% to 90.73% in annual rainfall. In monthly and seasonal rainfall, first PC 1 is termed the "mean rainfall component", which has strong to moderate associations with longitude, and is equally opposed by the CV. These findings are vital for planners and decision-makers to formulate strategies to manage unusual rainwater quantities.
“…In this study, cross-validation focusing range parameter estimation was used to optimize the semi-variogram models and associated parameters such as nugget, sill, and range 21 . It should be noted that the area interpolation method was excluded from this comparison, as that method requires data assigned to polygons (areas) and our data were collected from individual stations 34 . Figure 1 Schematic representation of different interpolation techniques selected for comparison.…”
Spatial–temporal rainfall assessments are integral to climate/hydrological modeling, agricultural studies, and water resource planning and management. Herein, we evaluate spatial–temporal rainfall trends and patterns in Pakistan for 1961–2020 using nationwide data from 82 rainfall stations. To assess optimal spatial distribution and rainfall characterization, twenty-seven interpolation techniques from geo-statistical and deterministic categories were systematically compared, revealing that the empirical Bayesian kriging regression prediction (EBKRP) technique was best. Hence, EBKRP was used to produce and utilize the first normal annual rainfall map of Pakistan for evaluating spatial rainfall patterns. While the largest under-prediction was estimated for Hunza (− 51%), the highest and lowest rainfalls were estimated for Malam Jaba in Khyber Pakhtunkhwa province (~ 1700 mm), and Nok-kundi in Balochistan province (~ 50 mm), respectively. A gradual south-to-north increase in rainfall was spatially evident with an areal average of 455 mm, while long-term temporal rainfall evaluation showed a statistically significant (p = 0.05) downward trend for Sindh province. Additionally, downward inter-decadal regime shifts were detected for the Punjab and Sindh provinces (90% confidence). These results are expected to help inform environmental planning in Pakistan; moreover, the rainfall data produced using the optimal method has further implications in several aforementioned fields.
“…In previous hydrology studies, descriptive data mining tools including agglomerative hierarchical and non-hierarchical regionalisation algorithms have been widely used in identifying homogeneous rainfall regions (Ahmad et al, 2013;Awan et al, 2014;Burn et al, 1997;Chuan et al, 2018a;Chuan et al, 2018b;Guttman, 1993;Hamdan et al, 2015;Ngongondo et al, 2011;Nnaji et al, 2014;Terassi & Galvani, 2017). The principal objective of using descriptive data mining tools in hydrology studies is to extrapolate insights from the gauge into ungauged rainfall stations based on the limited amount of historical rainfall time series data, which can increase the reliability of the risk assessment of extreme hydro-meteorological events.…”
Section: Introductionmentioning
confidence: 99%
“…Both previous studies used the L-moments based homogeneity measure to validate the regionalised homogeneous regions. Moreover, Nnaji et al (2014) proposed the use of the ALAH regionalisation algorithm to identify the homogeneous regions in the Federal Republic of Nigeria based on the coefficient of variation extracted from the historical monthly rainfall time series data and Euclidean distance dissimilarity measure. However, this article does not describe the homogeneity validation of the identified homogeneous rainfall regions.…”
Descriptive data mining has been widely applied in hydrology as the regionalisation algorithms to identify the statistically homogeneous rainfall regions. However, previous studies employed regionalisation algorithms, namely agglomerative hierarchical and non-hierarchical regionalisation algorithms requiring post-processing techniques to validate and interpret the analysis results. The main objective of this study is to investigate the effectiveness of the automated agglomerative hierarchical and non-hierarchical regionalisation algorithms in identifying the homogeneous rainfall regions based on a new statistically significant difference regionalised feature set. To pursue this objective, this study collected 20 historical monthly rainfall time-series data from the rain gauge stations located in the Kuantan district. In practice, these 20 rain gauge stations can be categorised into two statistically homogeneous rainfall regions, namely distinct spatial and temporal variability in the rainfall amounts. The results of the analysis show that Forgy K-means non-hierarchical (FKNH), Hartigan- Wong K-means non-hierarchical (HKNH), and Lloyd K-means non-hierarchical (LKNH) regionalisation algorithms are superior to other automated agglomerative hierarchical and non-hierarchical regionalisation algorithms. Furthermore, FKNH, HKNH, and LKNH yielded the highest regionalisation accuracy compared to other automated agglomerative hierarchical and non-hierarchical regionalisation algorithms. Based on the regionalisation results yielded in this study, the reliability and accuracy that assessed the risk of extreme hydro-meteorological events for the Kuantan district can be improved. In particular, the regional quantile estimates can provide a more accurate estimation compared to at-site quantile estimates using an appropriate statistical distribution.
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