Detection of mesoscale thermal fronts from 4km data using smoothing techniques: Gradient-based fronts classification and basin scale application

In order to optimize frontal detection in sea surface temperature fields at 4 km resolution, a combined statistical and expert-based approach is applied to test different spatial smoothing of the data prior to the detection process. Fronts are usually detected at 1 km resolution using the histogram-based, single image edge detection (SIED) algorithm developed by Cayula and Cornillon in 1992, with a standard preliminary smoothing using a median filter and a 3 × 3 pixel kernel. Here, detections are performed in three study regions (off Morocco, the Mozambique Channel, and north-western Australia) and across the Indian Ocean basin using the combination of multiple windows (CMW) method developed by Nieto, Demarcq and McClatchie in 2012 which improves on the original Cayula and Cornillon algorithm. Detections at 4 km and 1 km of resolution are compared. Fronts are divided in two intensity classes (“weak” and “strong”) according to their thermal gradient. A preliminary smoothing is applied prior to the detection using different convolutions: three type of filters (median, average and Gaussian) combined with four kernel sizes (3 × 3, 5 × 5, 7 × 7, and 9 × 9 pixels) and three detection window sizes (16 × 16, 24 × 24 and 32 × 32 pixels) to test the effect of these smoothing combinations on reducing the background noise of the data and therefore on improving the frontal detection. The performance of the combinations on 4 km data are evaluated using two criteria: detection efficiency and front length. We find that the optimal combination of preliminary smoothing parameters in enhancing detection efficiency and preserving front length includes a median filter, a 16 × 16 pixel window size, and a 5 × 5 pixel kernel for strong fronts and a 7 × 7 pixel kernel for weak fronts. Results show an improvement in detection performance (from largest to smallest window size) of 71% for strong fronts and 120% for weak fronts. Despite the small window used (16 × 16 pixels), the length of the fronts has been preserved relative to that found with 1 km data. This optimal preliminary smoothing and the CMW detection algorithm on 4 km sea surface temperature data are then used to describe the spatial distribution of the monthly frequencies of occurrence for both strong and weak fronts across the Indian Ocean basin. In general strong fronts are observed in coastal areas whereas weak fronts, with some seasonal exceptions, are mainly located in the open ocean. This study shows that adequate noise reduction done by a preliminary smoothing of the data considerably improves the frontal detection efficiency as well as the global quality of the results. Consequently, the use of 4 km data enables frontal detections similar to 1 km data (using a standard median 3 × 3 convolution) in terms of detectability, length and location. This method, using 4 km data is easily applicable to large regions or at the global scale with far less constraints of data manipulation and processing time relative to 1 km data.

The transformed-stationary approach: a generic and simplified methodology for non-stationary extreme value analysis

Statistical approaches to study extreme events require, by definition, long time series of data. In many scientific disciplines, these series are often subject to variations at different temporal scales that affect the frequency and intensity of their extremes. Therefore, the assumption of stationarity is violated and alternative methods to conventional stationary extreme value analysis (EVA) must be adopted. Using the example of environmental variables subject to climate change, in this study we introduce the transformed-stationary (TS) methodology for non-stationary EVA. This approach consists of (i) transforming a non-stationary time series into a stationary one, to which the stationary EVA theory can be applied, and (ii) reverse transforming the result into a non-stationary extreme value distribution. As a transformation, we propose and discuss a simple time-varying normalization of the signal and show that it enables a comprehensive formulation of non-stationary generalized extreme value (GEV) and generalized Pareto distribution (GPD) models with a constant shape parameter. A validation of the methodology is carried out on time series of significant wave height, residual water level, and river discharge, which show varying degrees of long-term and seasonal variability. The results from the proposed approach are comparable with the results from (a) a stationary EVA on quasi-stationary slices of non-stationary series and (b) the established method for non-stationary EVA. However, the proposed technique comes with advantages in both cases. For example, in contrast to (a), the proposed technique uses the whole time horizon of the series for the estimation of the extremes, allowing for a more accurate estimation of large return levels. Furthermore, with respect to (b), it decouples the detection of non-stationary patterns from the fitting of the extreme value distribution. As a result, the steps of the analysis are simplified and intermediate diagnostics are possible. In particular, the transformation can be carried out by means of simple statistical techniques such as low-pass filters based on the running mean and the standard deviation, and the fitting procedure is a stationary one with a few degrees of freedom and is easy to implement and control. An open-source MAT-LAB toolbox has been developed to cover this methodology, which is available at https://github.com/menta78/tsEva/(Mentaschi et al., 2016).