Narrative:

The anti-ice duct warning message illuminated during descent. This changed to an amber anti-ice duct message by the time I was able to run the QRH. We picking up ice at the time; and expected to remain in poh-defined icing conditions for the balance of the flight. We had already briefed the CAT ii ILS into dayton.once the wing anti ice was selected off per the QRH my priority became step 2; 'leave icing conditions.' it was not possible to do this via exiting the cold cloud; either up or down. We were at 280 kts. And descending. I could not remember the sat to tat equation off the top of my head (a check of google says tat = sat + (TAS/100)^2); but I did recall the main point; that it was in proportion to the square of the speed. Therefore; a small change in TAS would result in a large swing in tat; allowing us to directly control the tat as limited by the sat and the speed envelope of the airplane. (Per the equation; 300 kts. = A nine-degree increase; 400 = 16; 450 = 20.25; etc. There is little change at speeds below M 0.2).I immediately called for the first officer (first officer) to increase speed to 320 kts. In order to increase the tat. (I had no time to explain why until later. He complied immediately; though. Nice work). We were out of icing conditions forthwith. And so we remained; but had to exceed 250 kts. Below 10000 ft. In order to do so. This required [us to advise ATC]. As we got lower we were able to maintain adequate tat at normal speeds; and so cancelled the [event] before landing.I wanted to have a viable plan in case I was unable to stay out of ice on the approach. We got weather for the alternate from ATC. It was no good for our purpose. I asked dispatch for the best/closest ice-free airport in my fuel range; and concurred with his recommendation of ZZZ. We informed ATC of that contingency. I was prepared to continue with my desired speed and altitude per emergency authority if necessary. ATC was very helpful; and I'm sure we could have worked it out quickly.we did not run test items with the flight attendants. I was pretty sure the issue would be gone before landing; it did not involve the cabin; and I was way more interested in their normal procedures for the CAT ii at that point. I did make the regular CAT ii announcement on schedule.ATC reported negative ice from aircraft in front of us on the approach. We flew cowls/no wings with a tat of seven to nine-ish on final. It was above 10 below about 500 ft. I flew the CAT ii; of course. We broke out just below CAT I mins and landed normally.[maintenance] showed that both loops detected a leak along the right side of the fuselage.

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Original NASA ASRS Text

Title: Captain reported while in icing conditions; the ice system malfunctioned and the Captain's need to use emergency authority.

Narrative: The ANTI-ICE DUCT warning message illuminated during descent. This changed to an amber ANTI-ICE DUCT message by the time I was able to run the QRH. We picking up ice at the time; and expected to remain in POH-defined icing conditions for the balance of the flight. We had already briefed the CAT II ILS into Dayton.Once the WING ANTI ICE was selected off per the QRH my priority became step 2; 'Leave icing conditions.' It was not possible to do this via exiting the cold cloud; either up or down. We were at 280 kts. and descending. I could not remember the SAT to TAT equation off the top of my head (a check of Google says TAT = SAT + (TAS/100)^2); but I did recall the main point; that it was in proportion to the square of the speed. Therefore; a small change in TAS would result in a large swing in TAT; allowing us to directly control the TAT as limited by the SAT and the speed envelope of the airplane. (Per the equation; 300 kts. = a nine-degree increase; 400 = 16; 450 = 20.25; etc. There is little change at speeds below M 0.2).I immediately called for the FO (First Officer) to increase speed to 320 kts. in order to increase the TAT. (I had no time to explain why until later. He complied immediately; though. Nice work). We were out of icing conditions forthwith. And so we remained; but had to exceed 250 kts. below 10000 ft. in order to do so. This required [us to advise ATC]. As we got lower we were able to maintain adequate TAT at normal speeds; and so cancelled the [event] before landing.I wanted to have a viable plan in case I was unable to stay out of ice on the approach. We got weather for the alternate from ATC. It was no good for our purpose. I asked Dispatch for the best/closest ice-free airport in my fuel range; and concurred with his recommendation of ZZZ. We informed ATC of that contingency. I was prepared to continue with my desired speed and altitude per emergency authority if necessary. ATC was very helpful; and I'm sure we could have worked it out quickly.We did not run TEST items with the flight attendants. I was pretty sure the issue would be gone before landing; it did not involve the cabin; and I was way more interested in their normal procedures for the CAT II at that point. I did make the regular CAT II announcement on schedule.ATC reported negative ice from aircraft in front of us on the approach. We flew cowls/no wings with a TAT of seven to nine-ish on final. It was above 10 below about 500 ft. I flew the CAT II; of course. We broke out just below CAT I mins and landed normally.[Maintenance] showed that both loops detected a leak along the right side of the fuselage.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.