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I believe that all events pass through God's permissive will (or else He would not be sovereign). However, in a fallen world, there are also events (as I think that Jesus was indicating in Luke 13:1-5) that occur either due to underlying human causes based on free-will decisions; the activity of Satan and his demons; and even randomness (including "natural" disasters such as earthquakes, hurricanes, and so forth). The outcomes of these events do not always accord with our notion (from our human perspective) of what is good, right, just, rational, or explainable. However, God (for reasons based in His omniscience; His respect for human free will (so that people can be held accountable for their actions and decisions); and/or because the time has not arrived for Him to totally end the "natural" functioning of this world that He created, despite the corruption of both our free will and the world) does not always intervene to stop them. Yet God can still also make even the worst of them to work for the ultimate, eternal good (which may or may not be the same as the temporal good) of those who love and serve Him (Romans 8:28). I also believe that we will never know until we are in God's presence in eternity the number of times that He DID in love and mercy intervene in circumstances or events in this life to protect us or work on our behalf in ways that we never even knew about or were aware of. (Not to even mention the grace of God in providing a means for humans to receive eternal life, after humanity had universally rebelled (and continues to rebel) against Him, justly deserving nothing but separation from Him.)
The first few chapters of Genesis shown that death and suffering came into this world when Adam and Eve disobeyed God and brought sin into this world. Part of this sin effect are natural disasters, diseases, suffering and eventually death (Romans 5). In the sinless new Heaven and earth there will be no suffering (Rev 21), death or natural disasters just joy and peace in the presence of the Lord.
I do believe that God allows certain natural disasters to occur, but we are now able to be warned ahead of time & have the intelligence God gave to us to either stay & hunker down, like with hurricanes or flee for safer shelter like with tornadoes. If we are stubborn with our human nature & decide to stay, we risk consequences of possible serious harm or death & that is on us, not God because we chose not to listen, like Noah will arming if the flood & people laughed at him, not believing until it was too late.
In the body of your question you mentioned 3 possible explanations for why natural disasters occur. Yet in my view, you have not suggested the real culprit behind all these disasters - Humans! In Genesis ch 1 God created the universe and the earth we live in. After each day of his creation he saw that it was good. Then he created human beings in his own image and gave them dominion over the whole earth. He told them to be fruitful, increase in number, fill the earth and subdue it, to rule over all the fish, birds and animals. When God saw all that he had made it was very good. God placed Adam and Eve in the garden of Eden to look after it and to partake from the tree of life and live forever. Their world was a paradise. No natural disasters would ever take place in this perfect world that God created. So what went wrong. Humans rebelled against the only commandment God gave them and ate the forbidden fruit from the tree of the knowledge of good and evil. The world God created was very good but our first humans wanted to know what evil was like and they were captivated by it. Satan and his demonic hordes had been driven out of heaven and given dominion over the space above the earth. But when Satan deceived our first humans into rebelling against God then he usurped dominion over the earth also. This rebellion brought immediate changes to the world God created. Humans died spiritually and were separated from God. Humans began to die physically as they were driven out of the garden of Eden and denied the fruit of eternal life. God cursed the earth and life became a struggle for survival. Evil and wickedness became rampant upon the earth. So much so that God decided to wipe out humans with a worldwide flood and start over with Noah's family (8 people). But the rebellion continued. God is sovereign over all of his creation. Nothing happens in his created world unless he wills it so. Sometimes his will is "active" and sometimes it is "permissive". When God's will is active, he initiates events to accomplish his purposes. When God's will is passive, he permits "Satan" and "Humans" to carry out their will but the result still accomplishes God's purposes. When it comes to natural disasters, I believe God has 2 alternative purposes in mind. First, he causes disasters to punish evil and wickedness in the world. Second, he causes these disasters to get humans to wake up to their desperate spiritual condition and seek God. Why does God punish evil and wickedness in the world? Because most of the world has rejected his plan of salvation through faith in Jesus Christ. These unbelievers are destined for judgement and eternal punishment in hell. But God's will is for everyone to receive his salvation and through the Christian church to transform his world to the goodness he intended at creation. Why does God use natural disasters to wake people up? Humans are so captivated by their sinful nature that they are not even searching for God. Natural disasters cause those who survive to realise how fragile life is and to question what happens when they die. As people search for God with all their heart they will find him and receive his salvation. Is God being cruel by causing death through natural disasters? It is the sin of human beings that brought death into the world. God intended us to live forever in his perfect world. Early humans lived 900 years, Noah lived over 600 years, Abraham lived 130 years and now we live 70 or 80 years. It is the cancer of sin in our own lives and the pollution of sin in this world that brings an early death to all of us. God knows the spiritual condition of every human heart. He knows every person who will reject his salvation no matter how many times he offers it to them. He also knows those people who need a push to get started on their journey to receive his salvation. The good news is that Jesus is coming to create a new heaven and earth free from sin for all believers to live with God forever.
Isaiah 45:7 says I form light, I create darkness, I create evil and good, I the Lord do all these things. 2 chronicles 7:13-14. If I shut up heavens that their be no rain, if I command pestilence upon my people, if I command locust to devour the land, if my people which are called by my name shall repent from their wicked ways and pray, I will hear them and heal their land. Deuteronomy 28:from verse 15 to last told us about diverse curses that will come upon the children of disobedience. Natural disasters are also included. Jeremiah 10:5 says that the devil has no power in him either to do good or evil. God is behind every natural disaster and not the devil. Although sometimes human factors can be involved. Yet God allows humans or use them to achieve His purpose, as the book of Deuteronomy 28 from the 15th verse to the end clearly stated.
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