# An Interpretable Deep Learning Approach for Detecting Marine Heatwaves Patterns
## 2 Methods
### Marine Heat Waves (MHWs) Definition and Indices  
Marine heatwaves are mutually discrete and persistent anomalous warming events that occur in the ocean. In general, the determination of whether an extremely high SST event is a marine heatwave is based primarily on whether SST exceeds the marine heatwave threshold for multiple consecutive days [32]. Currently, there are two main types of marine heatwave thresholds that are commonly used. One is a fixed SST threshold, called the Absolute Threshold, and the other is a selected threshold that varies over time, named Relative Threshold (or Comparative Threshold). The function in previous studies to find MHW events includes absolute temperature threshold, cumulative threshold, temporally fixed threshold, and high percentile threshold [32; 33; 34]. The absolute temperature threshold is determined with reference to factors such as environmental elements and the upper absolute temperature to which marine organisms can adapt, while the threshold determined by accumulating the temperature difference above the absolute temperature threshold is called the accumulation threshold [32; 33]. For quantitative analysis of marine heatwaves, [PERSON] et al. [12] provided a stricter definition considering the duration, intensity, rate of evolution, and spatial extent of MHW events. Figure 4 illustrates several MHW events that occurred at the ZLG station (115.625\({}^{\circ}\) N, 22.625\({}^{\circ}\) E) from March to September 2021, with a zoomed-in area showcasing an MHW event in March-April 2021. From Figure 4, it can be observed that the MHW event began when the sea surface temperature (SST) first exceeded the MHW threshold after 24 March 2021. The SST reached its peak during the middle phase of the event. Subsequently, it fell below the MHW threshold in early April and remained below the threshold, indicating the end of the MHW event. The duration of this event corresponds to the time span it covered, and the difference between the peak SST and the climatological mean SST represents the intensity of the MHW event during that period. The calculation formula for the climatological mean can be expressed as shown in Table 3. Here, temperature \(T\) is expressed as a function \(T(t)\) of time \(t\), as well as a function \(T(y,d)\) of year \(y\) and day of the year \(d\). \(T_{m}\) represents the climatological average temperature calculated over a reference period. \(T_{\%}\) defines the seasonal threshold temperature value for marine heatwaves (MHWs), and \(D\) signifies the duration over which the temperature exceeds this threshold. Within the context of a MHW event, \(i_{max}\) indicates the maximum temperature anomaly, \(i_{mean}\) represents the mean temperature anomaly during the MHW, and \(i_{max}\) signifies the variation in MHW intensity over the duration of the event. Figure 4: Several marine heatwave events occurred between March and August 2021 at coordinates (115.625\({}^{\circ}\) N, 22.625\({}^{\circ}\) E). The marine heatwave events from March to April are used to define marine heatwaves, and the specific definition and formula can be found in Table 4.  
[PERSON] et al. [12] classified MHWs based on the intensity of MHWs, using the following definition:  
\[N=\frac{I_{MHW}-\Delta T}{\Delta T} \tag{2}\]  
MHWs can be categorized into several classes based on the magnitude of \(N\). The term \(\Delta T=T_{threshold}-T_{clim}\) represents the temperature anomaly with \(T_{threshold}\) as the temperature threshold and \(T_{clim}\) as the climatological mean temperature. The intensity of an MHW is denoted by \(I_{MHW}\). When \(N\leq 2\), the event is classified as a moderate-intensity event (Category I); when \(2<N\leq 3\), it is classified as a strong MHW event (Category II); when \(3<N\leq 4\), the event is considered severe (Category III); and when \(N>4\), the event is classified as extreme (Category IV).