iStock/Thinkstock(NEW BERN, N.C.) — Florence weakened to a tropical depression early Sunday, but that was little consolation to residents in North Carolina who have seen over 2 feet of rain and are now fearing major river flooding to start the week.Sustained winds were down to 35 mph, with the storm starting to speed up a little and move to the west at 8 mph. The center was located approximately 20 miles southwest of Columbia, South Carolina, as of 5 a.m.The storm came ashore as Hurricane Florence on Friday morning at about 7 a.m. with wind speeds of 90 mph.Florence has been blamed for 13 deaths in the Carolinas. Hundreds of water rescues have been carried out by local authorities, the Cajun Navy volunteers and the U.S. Coast Guard since Friday morning.More than 770,000 customers were still without power as of Saturday night.Despite the decrease in wind speeds, heavy rains still a pose a major flooding threat to both North and South Carolina.Florence “will produce catastrophic flooding over parts of North and South Carolina for some time,” Steve Goldstein, the National Oceanic and Atmospheric Administration’s liaison to FEMA, said Saturday.Florence has dropped a tremendous amount of rain in eastern North Carolina, with a widespread 20 to 30 inches reported already. Radar is estimating that some areas between Wilmington and New Bern, North Carolina, have received over 30 inches of rain.These are some of the latest rainfall totals as of 11 p.m. Saturday:Swansboro, N.C. — 30.59 inchesNewport/Morehead City, N.C. — 25.20 inchesElizabethtown, N.C. — 20.17 inchesJacksonville, N.C. — 16.13 inchesConway, S.C. — 9.90 inchesMyrtle Beach Airport, S.C. — 6.74 inchesFlorence is now the third storm to set a tropical cyclone state rainfall record in just the last 12 months. Harvey dropped 60.58 inches of rain last year in Texas, setting the state’s new record. Just last month, Lane dropped a maximum of 52.02 inches of rain in Hawaii, breaking the state record. The 30.59 inches that have fallen in Swansboro sets a new record for North Carolina.Florence also currently stands as the sixth-highest tropical cyclone rainfall total across the U.S. for records dating back to 1950.Heavy rain spreads inlandHeavy rains bands are still coming onshore in eastern South Carolina and North Carolina on Sunday morning. Some of the heavier bands have shifted toward Fayetteville, Charlotte and Raleigh.Torrential rain is causing inland flooding with major roadways closed, including large portions of I-95.An additional 6 to 10 inches of rain is still possible along the southeast border of North Carolina and South Carolina.Life-threatening, catastrophic flash flooding is likely over the southern to central Appalachians from western North Carolina into western Virginia and eastern West Virginia. Torrential rain will cause flash flooding and increase the risk for landslides in the higher terrains.The next issue: flooding riversTorrential rain from Florence is currently causing rapid rises in area rivers. Major river flooding is expected on some rivers from southern Virginia to northern South Carolina, including most of North Carolina.The Lumber River, near Lumberton, North Carolina, will rise into major flood stage Sunday morning. It is expected to reach a level very near the record Hurricane Matthew set in 2016. Mandatory evacuations were issued for South Lumberton on Saturday.The Northeast Cape Fear River, near Chinquapin, North Carolina, will rise above record flood levels set by Hurricane Floyd in 1999. This will cause devastating flooding across much of Onslow County with travel made impossible and many homes completely flooded.The Neuse River — both near Goldsboro and Kinston, North Carolina — will reach major flood stage late Sunday and into Monday. The Waccamaw River, near Conway, South Carolina, will rise near record levels by the end of the week.Florence is still moving very slowly inland. The track shows Florence moving west through Sunday, and then gradually turning north by Monday. Florence will likely become a remnant low within 36 hours.Even though Florence is weakening, it will still bring significant rainfall inland to the Appalachians before moving toward the Northeast on Tuesday. Totals could exceed 4 inches locally for inland New York and Massachusetts.Copyright © 2018, ABC Radio. All rights reserved.