Maps of rainfall totals in Texas look like maps of snowfall totals after a Nor'easter

Rainfall totals from Friday morning through Tuesday morning. (SERCC)

As we enter Day 5 of heavy rain in Texas, the totals are staggering and still accumulating.  As of late Tuesday morning, several stations are referenced in a NWS list that are now at over three feet of rain:

MARYS CREEK AT WINDING ROAD      49.20
CEDAR BAYOU AT FM 1942           48.64
CLEAR CREEK AT I-45              47.20
DAYTON 0.2 E                     46.08
SANTA FE 0.7 S                   45.02
HORSEPEN CREEK AT BAY AREA BLVD  44.96
FRIENDSWOOD 2.5 NNE              42.76
PASADENA 4.4 WNW                 42.58
HOUSTON WEATHER FORECAST OFFICE  42.11
WEBSTER 0.4 NW                   41.77
LEAGUE CITY 2.7 NE               41.66
BAY AREA BLVD AT HORSEPEN CR     40.64
BERRY BAYOU AT NEVADA            40.32
BERRY B FOREST OAKS              40.28
VINCE BAYOU AT PASADENA          39.29
LITTLE VINCE BAYOU AT JACKSON    39.00
TURKEY CK AT FM 1959             37.96
MIDDLE BAYOU GENOA RED BLUFF     37.76
AMAND BAYOU AT NASA ROAD 1       37.68
JACINTO CITY                     37.60
LITTLE CEDAR BAYOU AT 8TH ST     37.32
TELEPSEN                         36.60
FIRST COLONY 4 WSW               36.34
BEAMER DITCH HUGHES RD           36.32
LA PORTE 1 N                     36.24
TAYLOR LAKE AT NASA ROAD 1       36.23

The report of 49.2" became the all-time record holder for highest rainfall amount associated with a landfalling tropical cyclone in the continental United States. The previous top three in the U.S. were...

Amelia 1978: 48.00" (Medina, TX)
Easy 1950: 45.20" (Yankeetown, FL)
Claudette 1979: 45.00" (Alvin, TX)

Storm-total rainfall maps for Amelia 1978, Easy 1950, and Claudette 1979. (David Roth, NOAA/WPC)

The accumulation map looks more like inches of snow after a strong Nor'easter, not inches of rain in a few days. A huge area is blanketed (or submerged in this case) by totals of 1 foot or greater.  Maxima are now over 4 FEET!!

The primary reason for these incredible amounts is that Harvey has barely moved.  The center is now just 150 miles from where it made landfall on Friday night.  It has also been a tropical storm or hurricane for 84 hours AFTER making landfall. If you add up all of the time it was a named storm prior to landfall (including the eastern Caribbean part) you get 90 hours.  Later today, it will have spent more time as a tropical storm or higher after landfall than it did prior to landfall.

Typically, storms make landfall and keep moving.  People have calculated bulk averages for "typical" rainfall amounts from landfalling storms.
 - In the late 1950s, R. H. Kraft introduced a rough guideline for maximum rainfall totals from a landfalling tropical cyclone: divide 100 by the forward speed of the storm in knots.  So for Harvey which was moving at 6 kts (7 mph) when it made landfall, you would get a maximum of 16.7 inches (if it kept moving at that speed).
 - David Roth (NOAA/WPC) created a chart using storms from 1991-2005 and found that the average landfalling storm produced 13.3 inches of rain.

(David Roth, NOAA/WPC)

But when a storm does not keep moving, these climatology-based estimates break down.  Or do they?  Using the Kraft rule, and Harvey's motion since landfall (150 miles in 84 hours = 1.6 kt), you would get a maximum of 64.4 inches.  We're still 14 inches shy of that extremely crude estimate, but it's also not over yet.
The forecast over the next 3 days still includes impressive totals over eastern Texas.

Today through Thursday, the flooding risk remains high in eastern Texas but also expands eastward to Louisiana, Mississippi, and Alabama.  Strong rainbands will affect these areas in the coming days as Harvey continues to tap into the endless moisture supply in the Gulf of Mexico.

With the center back over water now, it should draw in less dry air than it did on Monday, and a second landfall is forecast to occur on Wednesday afternoon near Lake Charles, LA. Tropical storm warnings and storm surge watches cover much of coastal eastern Texas and Louisiana.  The storm is expected to finally get kicked out of the area on Thursday then accelerate off to the northeast.

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