These views are in fact compatible. God created nature (Genesis 1 verse 1), and can act through nature to His end, through natural means (Moses and Pharaoh: the plagues). Even upon close examination, events can appear to be natural, but it does not preclude that it is or isn't the will of God. Nature and its existence is purely the extension of the will of God.
However when we consider what is and what isn't the will and judgement of God several things are made clear in the bible.
I am saying this because there has been much talk of the judgement of God, and signs from wars and natural disasters. Some are claiming that floods, earthquakes and wars are punishment for all kinds of sins of the nations. God has used disasters to punish the Israelites in the Old Testament countless times when they were living in sin.
So it is tempting in these hedonistic and sinful times to view others as falling under the wrath of God. However the Bible teaches us something very important in this topic, that whatever His judgements are upon the nations (Jonah's message to the city of Nineveh) or on someone (Acts 5 – Ananias and Sapphira), it is not our place to judge.
For us to judge is to fall into the sin of pride, hypocrisy and self-righteousness:
Romans 2: 1-4 1 You, therefore, have no excuse, you who pass judgment on someone else, for at whatever point you judge another, you are condemning yourself, because you who pass judgment do the same things. 2 Now we know that God's judgment against those who do such things is based on truth. 3 So when you, a mere human being, pass judgment on them and yet do the same things, do you think you will escape God's judgment? 4 Or do you show contempt for the riches of his kindness, forbearance and patience, not realizing that God's kindness is intended to lead you to repentance?
Paul tells us that there is no excuse for the judgement of others! Who is perfect in the eyes of God? Who is capable of knowing all truth? Not only is a judgemental attitude hypocritical, but it is rejecting the grace and love of God (v4), and it puts us under the judgement that we impose on others (v3)!
Jesus puts is simply in Matthew 7:1-2, 1 "Do not judge, or you too will be judged. 2 For in the same way you judge others, you will be judged, and with the measure you use, it will be measured to you."
If we are to condemn those around us then we condemn ourselves.
Are therefore, some terrible things the judgement of God? Undoubtedly, on a personal level, living our sinful lives removed from the glory of God, is punishment for our sins.
However the entire Book of Job shows us that what may appear clear-cut judgement may not be so! His friends condemned him claiming his misfortune was the judgement of God. In reality his righteousness and the work of Satan was the source of his troubles.
It is then clear that the judgement of God is an issue for God, only He is perfect in knowledge and truth. It is important to note, that currently (today) any judgement from God is incomplete, and it serves the same purpose as His punishments on Israel, His Judgement is a call to repentance as with Jonah and the people of Nineveh and the followers of the risen Lord when they saw what happened to Ananias and Sapphira.
Let us not be like the friends of Job risking claiming judgement when it is not due. Our role as Christians is not to judge but to bring the nations (our friends and neighbours) to repentance and show them the love of God. Surely even when disaster is the judgement of God, it is a call to bring us all to salvation.
So in these hard times, we should all pray for those not saved, and repent for our own sins, "For God does not show favouritism" (Romans 2:11).