The detrended temperature temporal series provides information about the variability associated with short-term events and avoids the long-term variations due to continuous climate change. Due to the climate warming effect on the temperature of the Mediterranean Sea, the differences with respect to the non-detrended case can not be neglected. In the following figures, we show the median daily SST evolution and anomaly from raw data (left) and from detrended data (right), the last available Sea Surface Temperature map, and the last available temperature anomaly from raw data (left) and from detrended data (right).

Latest sea surface temperature of the Mediterranean

We generally define an MHW as a prolonged discrete anomalously warm water event that can be described by its duration, intensity, rate of evolution, and spatial extent. [Hobday et al 2016].

• Prolonged: The warm state should persist at least 5 days
• Anomaously warm state: As compared with the historical registers in the same location, the temperature is larger than the 90% of them. Here, 38 years have been used.
• Discrete: An MHW is considered temporarilyy isolated if in the same place have been registered more than 2 days with temperatures below the 90 percentile after and before of the MHW.

The daily heat spike is defined, in the places affected by a MHW, as the difference between the temperature and the climatologic value corresponding to this day of the year.

The computations of MHW has been performed following the method described by [Martínez et. al 2023]:

Martínez J, Leonelli FE, García-Ladona E, Garrabou J, Kersting DK, Bensoussan N and Pisano A (2023)
Evolution of marine heatwaves in warming seas: the Mediterranean Sea case study.
Front. Mar. Sci. 10:1193164.
doi: 10.3389/fmars.2023.1193164

The temporal series can be separated into components representing trend, seasonality, slow and fast variation, and cyclical irregularity. If the temporal series have a non-negligible trend, then it is necessary to substract it to the original data to obtain the extreme events. In other words, the extreme is detected concerning the instantaneous baseline. This concept is clear by imaging an ideal system in which only few extreme events take place during a given period. The next figure shows, at the left, a original time series in purple. This raw data has a positive trending and blue and green lines stand for the 90^th percentile and the mean respectively. In this case the MHW analysis will classify as a heat wave all the values above the blue line providing false positives (at the end of the time series) and false negatives (at the first part of the time series). If we pretend to detect the extreme events (i.e. the peaks of the plot) it is necessary to perform a detrend of the temporal series before computing the climatology and the 90^th percentile (right plot). In this example, the peaks are located in the upper 3% of the function distribution and will be identified as extreme events without false positives or false negatives.