Statistical procedure to analyse sparse data on the morphometric parameters of aeolian sand ripples obtained by the shadow cast technique

This paper outlines a statistical procedure to deal with the data on the morphometric parameters of aeolian sand ripples provided by the shadow cast technique (SCT). In order to cope with a small sample problem which we face in the process of applying the SCT, we simulate M merged data sets corresponding to many dissimilar linkages between short time series obtained from single photographs. For each merged data set, the value of the Ljung–Box statistics is computed to seek dependence within a setting of aeolian sand ripples. We derive a formula to evaluate the level of uncertainty, which approximates a probability of misclassification in the process of testing using numerical simulations. We test the procedure by processing the data gained during the fieldwork conducted on the beach along the Baltic coast of Poland. The data on heights and length-to-height ratios of cross-sectional settings of aeolian sand ripples, considered separately, exhibit self-dependencies. We interpret this result as a cumulative effect of various dependent – probably superimposed – processes producing ripples. Hence, our simple and computationally efficient procedure helps to confirm the existence of dependent mechanisms behind ripple formation using the field data.