## 1 Introduction  
The processing capabilities of modern supercomputers are improving at a tremendous pace. However, input/output (I/O) bandwidth has advanced at a much slower rate, leading to bottlenecks in many applications [1, 2]. This is one of the most pressing matters for large-scale scientific simulations. Simulations can result in multiple tera- or petabytes of generated data, making it challenging to save all necessary data to permanent storage due to limited storage capacity or time-consuming I/O operations [3, 4, 5, 6]. In-situ or in-transit visualization and analysis are often used for each time step while the data is generated. In-situ co-processing is typically performed on the same compute nodes as the simulation and can achieve high performance, partly because of the locality of the data. However, in-situ co-processing takes up valuable simulation time. Many researchers are reluctant to dedicate computing resources used by the simulation to other compute-intensive tasks [2, 4], meaning that the time available for in-situ co-processing often is short compared to that of the simulation. One option to reduce the co-processing time is to lower the frequency at which time steps are analyzed. Another is to limit the available time to perform co-processing for each analyzed time step. Both these options are undesirable because they limit the amount of data available to the researcher after the simulation has been completed. Furthermore, a significant amount of the available memory is used by the simulation in an in-situ scenario, meaning that only a tiny amount can be allocated for visualization or analysis purposes [7]. In contrast, in-transit co-processing [8; 9], illustrated in Figure 1, is generally performed on a separate group of compute nodes, which we refer to as transit nodes. Utilizing a different group of nodes means that co-processing can be performed asynchronously during the simulation stage, resulting in a less strict time limitation than an in-situ approach. Furthermore, the transit nodes can be equipped with different hardware to accelerate the co-processing tasks. The main drawback of in-transit co-processing is that the relevant simulation data needs to be transferred to the transit nodes. Moreover, it is not guaranteed that the simulation nodes can hold an extra copy of the data in memory. It is often impossible to transfer the data asynchronously while simulating the next time step. The data transfer required to perform in-transit co-processing can be accelerated by reducing or compressing the simulation data. However, using a reduction or a lossy compression method could lower the detail and accuracy of the whole data set, including regions of interest. It could instead be beneficial to selectively compress areas of data based on their contribution to the simulated phenomenon. Reducing or compressing areas that are not of interest would result in less time-consuming data transfers without any significant loss in the data quality. To determine the frequency at which data is analyzed, the time available for co-processing and what compression method(s) to use to accelerate the data transfers, there is a need to identify the importance of the underlying simulation data. Such information can be used for a wide variety of cases, including guiding the simulation, determining which time steps of the simulation to analyze or save to permanent storage, removing or reducing unimportant data, and finding interesting camera locations for co-processing purposes. Some of these cases have been explored in related work [10; 11; 12; 13; 14; 15; 16; 17]. However, these methods have either been limited in the amount of used importance metrics [10; 12; 13; 14; 15; 16; 17] or been unable to combine multiple metrics to create advanced importance metrics and to make more advanced decisions [11]. We propose a method that efficiently can identify the importance of subsets of simulation data, which consists of multivariate and temporal data sets in the form of structured rectilinear grids.