Assessment of hydrological hazards: how to manage missing data on south-west Madagascar

Abstract The south-west of Madagascar faces various climate hazards, especially rising water levels. Each year, the city of Toliara is subjected to quick and devastating floods, which appear to have increased in intensity and frequency. In addition, this region is one that represents completely the “north/south fracture”, that is to say a “...technologic fracture between northern countries and southern countries concerning the availability of data and the model deployment constraints” (Payet, 2015). Thus, all the hydrometric data available for this region are incomplete. Based on this issue of missing data, this study is divided into two parts: the first is the reconstruction of the data and the second is the modeling of these data to obtain a rigorous representation of the chronicles. First, the reconstruction part must fulfill the following two conditions: (i) represent the overall dynamics of the series and (ii) be simple enough to easily take them into account in the analysis and interpretation at the end of the modeling. We offer a way to reconstruct these missing data by combining seasonal decomposition methods and simple linear regression. After that, we use classic statistical methods to adjust the model to our chronicles. We obtain two types of model: a SARIMA model, which is a Seasonally Auto-Regressive Integrated Moving Average model, and an ARIMAX model (Auto-Regressive Integrated Moving Average with eXogeneous inputs), which is a combination of a linear model and our SARIMA model. The two models are quite functional as we tested their quality and the statistical significance of their coefficients. This method can help scientists working in southern countries not to discard incomplete data but to exploit them as much as possible because they convey important and usable information, as long as we consider the uncertainty of their conditions of creation.