National parks have tremendous cultural, ecological, and economic value to societies. In order to manage and maintain these public spaces, decision-makers rely on detailed information about park use and park condition. Many parks, however, lack precise visitor counts because of challenges associated with monitoring large and inaccessible areas with porous boundaries. To facilitate better management, we propose a method to estimate percentage changes in park visitation without using any on-site visitor counts. Specifically, using 20 national parks in the United States, we develop a time series model for forecasting future monthly changes in visitation based on the volume of social media images shared by visitors to parks. Forecasts are generated from historic park-level and national-level photo-user-days (PUD) of images posted to Flickr, using singular spectrum analysis (SSA). We further propose an approach for augmenting existing on-site visitation data collected by the US National Park Service. Our model evaluations indicate that the proposed model that only uses social media data achieves competitive performance to the models which partially or fully utilizes on-site visitor counts.