More storms: Airlines already grounding Tuesday flights

Last update: 8:50 p.m. ET.

Air travelers faced more headaches Monday, the third day in a row that at least 1,000 flights had been grounded across the nation. And in an ominous sign for weather-weary fliers, cancellations had already begun to trickle in for Tuesday.

Combined, nearly 4,800 flights have been canceled just since Saturday morning.

For Monday, more than 1,630 flights had been canceled and another 3,850 delayed as of 8:50 p.m. ET, according to flight-tracking service FlightAware. The worst of those problems were worst in Texas and parts of the mid-South, where a messy ice storm was moving through the region.

For Tuesday, about 425 flights had been preemptively canceled as of 8:50 p.m. ET. Most of those came in Atlanta and Dallas. Ice had been falling much of the day in Dallas and temperatures were forecast to remain below freezing until later on Tuesday.

However, perhaps the most worrisome sign for Tuesday flights was in Atlanta, where the tally of preemptive cancellations jumped sharply by Monday evening. As of 8:50 p.m. Monday, more than 105 departures and 125 arrivals had already been grounded for Tuesday at the world's busiest airport.

More broadly, airlines had waived change fees for customers ticketed to fly into regions experiencing poor weather. The policies varied by airline, though they generally allowed customers to make one change without paying the customary change fee.

Back to Monday, the bulk of the day's disruptions came in the Dallas-area, where about 1,100 flights had been canceled at the busy Dallas/Fort Worth International Airport (DFW). The cancellations -- most of which were preemptively announced on Sunday -- represented more than half of the airport's entire schedule for the day.

DFW is the biggest hub for American Airlines, and most of Monday's cancellations there were either on American or on one of its regional affiliates. FlightAware calculates American and its regional affiliates have canceled about half of their schedule today, not including merger partner US Airways. Such a broad disruption means ripple effects are possible even in other parts of the country.

A flight from Los Angeles to Salt Lake City, for example, could become delayed or canceled if its aircraft or crew gets knocked off schedule in icy Texas.

In a statement, DFW acknowledged Monday's disruptions, noting "arlines serving DFW Airport have proactively cancelled about half of the flights scheduled into and out of DFW. … Customers of most airlines are advised they can make changes to their reservations free of charge as a result of the weather issues."

Also hard-hit was Dallas Love Field, where about 120 flights – about a quarter of the day's schedule – were canceled as of 8:45 p.m. ET.

In Houston, there was no ice, but about 5% of the day's schedule had been grounded at Bush Intercontinental and Hobby airports. Many of those cancellations were likely on flights schedule to fly to or from Dallas or other icy airports in the region.

Elsewhere, cancellations were affecting other airports across Texas and in the region. Airport with cancellation tallies running at above-normal levels included: Amarillo, Texas; Austin; Beaumont, Texas; Fayetteville/Northwest Arkansas Regional; Jackson, Miss.; Little Rock; Houston Hobby; Midland, Texas; New Orleans; San Antonio; Shreveport, La.; Tulsa and Oklahoma City.