Abstract

Spatial smoothing of the geo-referenced data could assist in determining the apparent spatial trend or pattern of the variable of interest across a particular geographical area. However, extremely high outliers in the data can distort the smoothed surface, which could lead to misleading interpretations. Murujuga is situated near Karratha, Western Australia. This region contains over one million petroglyphs (rock art engravings) that reflect 65,000 years of Indigenous knowledge and spirituality. A comprehensive study has been conducted to examine the impact of industrial air emissions on rock art. As part of the study, the elemental composition of rocks is evaluated with a portable X-ray fluorescence analyser (pXRF). In this study, four fieldwork campaigns were undertaken between 2022 and 2023. These campaigns involved the measurement of the same 54 rock art panels across Murujuga in each campaign, these measurements included pXRF. Geologists often use ratios of two elements to characterise rock types. Also, the ratio of elements is more consistent than the absolute pXRF measurement. The ratio of silica SiO2 to titanium Ti (from pXRF data) in the granophyre was calculated to determine the spatial trend of this element ratio across Murujuga. However, the ratio had a highly skewed distribution with extreme outliers. The Nadaraya-Watson (N-W) kernel smoother was used, which is a nonparametric method, as well as a computationally efficient method. However, the N-W method is not robust to extreme outliers. N-W kernel smoothing with modifications, such as log transformation, weighted median, probability integral transformation, and winsorization methods, were employed. The performance of the methods was compared using mean absolute error (MAE), root mean square error (RMSE), and bias. The cross-validation results showed that the winsorization method outperformed the other methods. Winsorization is an efficient method to reduce the impact of spurious outliers in N-W spatial kernel smoothing.