Examples are natural disasters, undesirable weather, earthquakes, the corona virus floods, forest fires, economic downturn caused by war or elections elsewhere in the world.
This is a tricky type of suffering. Diavika means appearance. What is meant by this is that the events that would cause this type of suffering are results of īśvara (from the total causative body), presented to us for us to learn from. Everything has a cause and a reason. Disaster and disaster seem to affect us from far outside us, but simply take place within us, as results of previous action (karma) and things to deal with.
What about children who are born into poverty, or in a country that is systematically at war? However painful, this point proves the existence of a law of karma over many lifetimes. The way to bear this type of suffering is with īśvara prasāda buddhi. Being in a spirit of gratitude and devotion with īśvara.
Ādhidaivika is called “-daivika” (of the devas) because the forces of nature are seen as gods in Vedic times. For example, daiva has also come to be called destiny. Karmic twists of fate that I am unexpectedly confronted with. If I have the blessing of recognizing the laws of karma, I can learn to accept this and grow from the peace that arises, using the laws of dharma and karma
Destiny can of course also turn out positively, ādhidaivika sukham. Then daiva means blessing, grace (anugraha). A blessing can mean a favorable development in my life, but also a decisive insight.
A car accident and years of rehabilitative standstill can transform someone into a shining being.
Daiva also means: Unseen (adṛṣṭa), ununderstood causes of bad feeling due to unfavorable karma (pāpa), or an easy, happy flowing life due to favorable karma (puṇya karma). This shows, for example, why one baby or toddler is calm and contented and another, for no apparent reason, is crying, whining and hysterical.
Incidentally, there is a pitfall of being relatively happy. The seeker becomes lazy, and does not yearn for freedom.
By praying “oṃ śāntiḥ śāntiḥ śāntiḥ” (oṃ, peace, peace, peace) one wishes relief for the three kinds of suffering ādhidaivika tāpas, ādhibhautika tāpas, ādhyātmika tāpas.