The mat is the problem in this shot, otherwise there is no rise in threshold. A zero clearance entryway is so basic that it's somewhat difficult to explain. Your main consideration is the thickness of your floor covering and whether that will require compensation, a lowering of the sub-flooring, which might take some engineering and planning, otherwise no big deal. But let's consider hardwood flooring for instance, that won't cause a massive design headache, really thick ceramic or stone tile might be another matter but that's more complicated regardless.
Sometimes the truly simple seems complex because you cannot at first accept something could be so basic. When describing a no step and zero clearance entry (or step elimination), frequently we're asked, "How do you do that?" Trying not to sound sarcastic or flippant, our answer, "By NOT building steps or stairs." Which often leads to this follow-up as the person tries to come to grips, "Well, why then do most houses have exterior steps?" Honest to goodness because that's the just way it's always been done.
So I'm about to write about a zero clearance (flush) threshold into the house and I don't really know what to write because it's as simple as using an ADA compliant threshold, wider door, thank you and drive home safely. It's not trigonometry. (Water and bug proofing are no different than what's standard.)
However, here are some ideal accoutrements to accompany your zero clearance entrance. As you're planning, imagine rolling in, whether pushing or pulling a baby stroller, luggage, wheelchair, anything with wheels. You want zero curbs or bumps so think SMOOTH cruising through the passageway.
Ideally you'll have a non-slip, 6-by-6 foot entryway for approach and turning radius (absolute minimum of 5 feet square, 5' X 5'). Having a roof overhead, some form of covering to protect from weather is another must. To accentuate ease, include a shelf 12-inches below and to the side of the door knob, a bench or someplace to rest or set down an armful of stuff (e.g. groceries, boxes, etc.). You want to avoid kneeling, stooping, reaching, bending over, any off-balance movement, so handrails might be part of the solution.
Use a 36-inch door (3'0", what's called a "three-oh" door) with a lever handle and kick plate. The minimum width requirement for wheelchair accessibility at knuckle height is 32-inches but make life easier with a 36-inch door. Typically the door will open inward although it can be outward for "pullers" (in-swing versus out-swing). Consider a dead bolt operated by push button or remote control similar to a garage opener. Notice these convenience features would be easy and preferred for anyone of any age or ability, much like automatic doors at a retail store.
Finally, make sure there's good lighting and use a fixture with at least two bulbs to ensure one works. Also, think about motion-activation and other automated features like intercoms and video to make your arrival easier if you'd like assistance, or to confirm visitors. Again, imagine bad weather, low light and an armful of packages as you plan your smooth move through the door.
Next I describe once you arrive on the other side of the door.