Atmospheric Rivers Details
Tuesday, March 07, 2023
7:05 AM
Fig. 1. Schematic summary of the structure and strength of an atmospheric river based on dropsonde measurements deployed from research aircraft across many atmospheric rivers and on corresponding reanalyses that provide the plan-view context. Magnitudes of variables represent an average midlatitude atmospheric river. Average width is based on atmospheric river boundaries defined by vertically integrated water vapor transport (IVT; from surface to 300 hPa) lateral boundary threshold of 250 kg m−1 s−1. Depth corresponds to the altitude below which 75% of IVT occurs. The total water vapor transport (a.k.a. flux) corresponds to the transport along an atmospheric river, bounded laterally by the positions of IVT = 250 kg m−1 s−1 and vertically by the surface and 300 hPa. (a) Plan view including parent low pressure system and associated cold, warm, and warm-occluded surface fronts. IVT is shown by color fill (magnitude; kg m−1 s−1) and direction in the core (white arrow). Vertically integrated water vapor (IWV; cm) is contoured. A representative length scale is shown. The position of the cross section shown in (b) is denoted by the dashed line A–A′. (b) Vertical cross-section perspective, including the core of the water vapor transport in the atmospheric river (orange contours and color fill) and the pre-cold-frontal low-level jet (LLJ), in the context of the jet-front system and tropopause. Water vapor mixing ratio (green dotted lines; g kg−1) and cross-section-normal isotachs (blue contours; m s−1) are shown. [Schematic is from Ralph et al. (2017). It was prepared by F. M. Ralph, J. M. Cordeira, and P. J. Neiman based on the composite of research-aircraft-based observations of 21 atmospheric rivers presented in Ralph et al. (2017), including adaptations of earlier results from Ralph et al. (2004), Cordeira et al. (2013), and others. The 21 observed cases were compared with thousands of ARs found in ERA and MERRA-2 over 37–38 years in the same region and season (Guan et al. 2018). The composite of the 21 aircraft-observed cases was shown to be representative of the broad spectrum of ARs in the reanalyses.] 
From [link]
See [link]. That's the source of the two images below.
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Reno during the 1997 flood:
Atmospheric river rain on snow event in the Sierras.
Atmospheric River Rating System.
W = Typical Width: 400-600 km, nominally 500 km.
Typical Length: 1600 km
t = Long Duration: 72 hours = 2.6 x 105 seconds

Extreme Case Total water vapor mass transported by river = IWVT * W * t = 1.3x103 * 5x105 * 2.6x105 kg = 1.7x1014 kg * 0.26  gal/kg = 4.4x1013 gallons of water = 66 million Olympic-size swimming pools. 

With US water use per person per year = 29900 gallons/person/year, that's enough water (if all water vapor were converted to precip) for 147 million people in the US for a year for 82 gallons/day average use.
Typical Values from Observations and Modeling
Integrated over the full AR event and landfall region, studies (e.g., Ralph et al., Guan et al., CW3E/Scripps) find precipitation efficiencies on the order of 20–50 %.
Lower efficiencies (~20–30 %) are common when:
The AR is fast‑moving.
Much of the vapor is advected inland without precipitating near the coast.
There is limited orographic lift.
Higher efficiencies (~40–50 % or more) occur when:
The AR stalls or slows against coastal mountains.
Strong orographic forcing wrings out moisture quickly.
The air mass is already near saturation and uplift is deep.
In extreme, localized orographic zones (e.g., windward slopes of the Coast Ranges or Sierra Nevada), instantaneous efficiencies can approach near‑complete condensation of incoming vapor, but this is over a narrow cross‑section and short time.
Why it’s not 100 %
Not all water vapor condenses — some passes over or around terrain and continues inland.
Entrainment of drier air dilutes the plume.
Re‑evaporation of falling precipitation can return water to vapor form before it reaches the ground.
Moisture recycling inland means some vapor precipitates later, far from the initial landfall zone.