# An Effective Surrogate Ensemble Modeling Method for Satellite Coverage Traffic Volume Prediction
## 3 Satellite Coverage Traffic Volume Modeling and Prediction Approximation
### Surrogate Ensemble Modeling for SCTV Prediction  
To further improve the SCTV prediction accuracy, an enhanced surrogate ensemble modeling method is investigated by dividing the global earth surface domain into multiple sub-domains and managing multiple surrogates in each sub-domain. The main idea of the proposed surrogate ensemble modeling method is to allow each sub-domain to have independent contributing surrogates and weight factors so that the ensembles are more suitable for the corresponding sub-domains. Compared with direct modeling in the global domain, the proposed method seeks to better capture the local characteristics of the objective function in each sub-domain with different SCTV features. The prior knowledge of the SCTV features in the global domain, namely the geographical knowledge of SCTV distribution, is generally known according to historical experiences, which could be used to guide the sub-domain division effectively [27]. According to aircraft traffic distribution which is dense in population agglomeration while scarce in ocean regions, the global earth surface domain is split into 12 sub-domains: (a) North America; (b) Pacific Ocean; (c) Antarctica; (d) Western Europe; (e) Caribbean Sea; (f) South America; (g) Atlantic and Western Africa; (h) Russia; (i) Middle East; (j) Indian Ocean; (k) East Asia; (l) Oceania, as shown in Figure 3 (the global coastline is drawn in MATLAB (MathWorks, Natick, MA, USA)). Furthermore, (b) the Pacific Ocean, (c) Antarctica, (g) Atlantic and Western Africa and (j) Indian Ocean have scarce traffic distribution due to the large marine area. Hence, the satellite payload could be kept at low power or shut down at these sub-domains, and there is no need to construct the surrogate in these areas. For the other eight regions, the onboard resources need be allocated dynamically, and in this paper surrogates are built for these eight regions. Notice that for different satellite missions, the geographical distribution variances of SCTV present different characteristics. Thus, the division of the global earth surface domain with prior knowledge should be based on the specific mission background. For example, ship traffic distribution is dense in vast ocean regions while aircraft traffic distribution is scarce in those areas, and therefore the focus of the division should be different for these two missions. In this paper, surrogate modeling for air traffic SCTV prediction is studied for illustration. Due to the geographical distribution variances of SCTV, there are distinct SCTV features in each sub-domain. To enhance the surrogate accuracy in each sub-domain, the ensemble modeling method is an effective way [18]. The commonly used approach is the weighted aggregation method described in Section 2.4. However, when forming a weighted ensemble by (13) the weighted sum of all the candidate surrogates, it is possible that the inaccurate surrogate is included which will lead to loss of accuracy. Based on this consideration, instead of employing all the candidate surrogates, in this paper it is proposed to only select a part of them as contributing models with high accuracy to constitute the  
Figure 3: Division of the global earth surface domain for air traffic distribution. (**a**) North America; (**b**) Pacific Ocean; (**c**) Antarctica; (**d**) Western Europe; (**e**) Caribbean Sea; (**f**) South America; (**g**) Atlantic and Western Africa; (**h**) Russia; (**i**) Middle East; (j) Indian Ocean; (**k**) East Asia; (**l**) Oceania. ensemble, which is named partial weighted aggregation method (PWTA). The details of PWTA are as follows. First, for the \(k\)th sub-domain, construct multiple different candidate surrogates, and calculate the corresponding GMSE based on leave-one-out cross-validation by (15) of each surrogate as the criterion to measure its accuracy.