Saudade: A Feeling Beyond Longing

Saudade. It is what I feel when the plane rises above the clouds and the destination below fades away from view. 
Saudade. It is what I feel at airports, watching people coming and going, into and out of loving embraces that remind me of those special people in my own heart from the past, present, and future to come. 

What, exactly does Saudade mean?