HRRR, RRFS and RDPS, every run from 1 November to 15 April
Snow-band diagnostics
Where each model’s atmosphere is set up for a mesoscale snow band: frontogenesis and deformation in the middle troposphere, weak or negative saturated equivalent potential vorticity above it, and strong lift through the dendritic growth zone. Beside them, what the model actually does with it, and where the ingredients overlap.
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A mesoscale snow band is a stripe of heavy snow, typically 20–100 km wide and hundreds of kilometres long, that can drop 2–4 inches an hour for several hours while places 50 km away get a fraction of that. Most bands in the cold season form on the poleward side of a cyclone, where the middle troposphere is frontogenetic (the flow is packing the temperature gradient together), the air above is weakly stable to slantwise motion, and the column is saturated through the dendritic growth zone (Nicosia and Grumm 1999; Novak et al. 2004). The overview puts the four views side by side; each has its own figure in the rail with the details.
What the panels are. Top left: 700 hPa frontogenesis with potential temperature, height and the axes of dilatation. Top right: saturated equivalent potential vorticity (EPV*) in the 750–500 hPa layer where it is saturated, with 800–600 hPa frontogenesis over it. Bottom left: the strongest lift in the saturated −12 to −18 °C layer. Bottom right: the model’s own precipitation and type.
How it is computed. Every field is smoothed with a Gaussian filter (σ = 18 km) on the model’s own grid before any derivative, and the diagnostics are evaluated on a 12 km grid (10 km for RDPS, 13 km for the RRFS’s North American run). Frontogenesis and EPV are second-order in the wind and temperature; on a raw 3 km grid they are dominated by convective-scale noise, and the band-forcing circulation lives at the scale the smoothing keeps. Derivatives are taken on the native grid with grid-relative winds and the true grid spacing. Levels within 25 hPa of the ground are masked (700 hPa is underground over the Rockies).
Known limits. These diagnostics are only as good as the model’s placement of the system, and band placement errors of 50–100 km are normal: in the Binghamton case study the HRRR’s own f01 frontogenesis and lift axis sat 35–75 km south of the observed band, and the 12Z run’s reflectivity band was 80–150 km south 14–16 hours out. RDPS publishes vertical velocity at only four levels (850, 700, 500 and 250 hPa), so its dendritic-zone lift is interpolated from three; it publishes no reflectivity, so its own bands are shown as 1-hour precipitation. The HRRR’s analysis hour carries no usable vertical motion, so its loops start at f01.
When it runs, and where. 1 November to 15 April, every model to the end of its forecast, every 3 hours: the HRRR’s 00, 06, 12 and 18Z runs to 48 hours, the RRFS to 84 hours and the RDPS to 84 hours, each time the newest full-length run. A cheap check over the whole forecast comes first: a region is drawn only if the model has snow at 20 dBZ or more (RDPS: 1 mm/h) over at least 2 % of it at some hour. Five regions: Northeast and Mid-Atlantic (Virginia to Maine), Atlantic Canada, Ontario and Quebec, the Midwest (the Great Lakes to the central Plains) and the Rockies (the Wasatch to the High Plains). A model is offered for a region only where its grid covers at least 80 % of it: the HRRR covers every region but Atlantic Canada (it reaches under a third of it); the RRFS is drawn everywhere, its diagnostics from NCEP’s 13 km North American output of its 3 km run (the fields are smoothed to 18 km in any case) and its own bands from the 3 km grid wherever that reaches, which is every region but Atlantic Canada; the RDPS covers all five. If a run cannot be fetched, the page keeps the last one that could and says so.
NOAA/NCEP HRRR (AWS, byte-ranged) · NOAA/NCEP RRFS v1.0 (NOMADS) · ECCC RDPS 10 km (MSC Datamart) · Nicosia, D. J., and R. H. Grumm, 1999, Wea. Forecasting 14, 346–368 · Novak, D. R., L. F. Bosart, D. Keyser and J. S. Waldstreicher, 2004, Wea. Forecasting 19, 993–1010
Frontogenesis is the rate at which the flow tightens the horizontal temperature gradient. The shading is the 2-D kinematic (Petterssen 1936) frontogenesis of potential temperature at 700 hPa, $F = \frac{d}{dt}|\nabla\theta|$, in kelvin per 100 km per 3 hours. Where it is positive the atmosphere responds with a thermally direct circulation across the zone, and its rising branch, on the warm side of the frontogenesis maximum, is where bands form. Values of 2–10 are typical of banded snowstorms; the strongest bands in Novak et al. (2004) sat under maxima well above that.
Most mid-level frontogenesis comes from deformation: a flow that stretches along one axis and squeezes along the other. The short blue segments are the axes of dilatation where the total deformation is in the top 15 %: when isentropes (dashed) lie at a small angle to them, the flow is packing them together. The black contours are 700 hPa height in decametres. Grey is where 700 hPa is within 25 hPa of the ground.
Petterssen, S., 1936, Geofys. Publ. 11(6), 1–27 · Novak, D. R., et al., 2004, Wea. Forecasting 19, 993–1010 · fields smoothed σ = 18 km, 12 km grid (RDPS 10 km)
Frontogenesis forces a circulation; how narrow and intense its rising branch becomes depends on the stability of the air it rises through. Air that is stable when lifted vertically can still be unstable when lifted along a slanted path, up the sloping isentropes of a front. That is conditional symmetric instability (CSI), and its usual measure is the saturated equivalent potential vorticity, EPV*. EPV* below zero in saturated air means a slantwise parcel would keep accelerating, and a frontal circulation over such air collapses into a narrow, strong updraft: a band.
The shading is EPV* averaged over 750–500 hPa, drawn only where that layer’s relative humidity (over ice below 0 °C) is 80 % or more. Magenta contours are the 800–600 hPa frontogenesis. Hatching marks columns where θes falls with height: there the negative EPV* is ordinary upright conditional instability, not CSI, and upright convection will usually win.
The caveat, and it matters. Schultz and Schumacher (1999) showed how easily EPV* over-diagnoses CSI: negative EPV* is necessary but not sufficient, it also flags upright and inertial instability, it means nothing in unsaturated air, and it measures potential that a circulation must release. Read purple as “the atmosphere would not resist a band here”, never as “a band is here”. Weakly positive EPV* (0 to 0.25 PVU) under strong frontogenesis bands just as readily, which is why the ingredients figure uses that threshold.
Schultz, D. M., and P. N. Schumacher, 1999, Mon. Wea. Rev. 127, 2709–2732 · θes from Bolton, D., 1980, Mon. Wea. Rev. 108, 1046–1053 · EPV* in pressure coordinates with the full wind · fields smoothed σ = 18 km
Ice crystals grow fastest, and into the branching dendrites that aggregate into big, slow-falling, low-density snowflakes, between about −12 and −18 °C. When a band’s strongest lift passes through a deep, saturated layer at those temperatures the snow-to-liquid ratio climbs and snowfall rates jump; this alignment is the “crosshair” forecasters look for (Waldstreicher 2001). Lift that peaks below or above the zone makes smaller, denser flakes and less snow for the same water.
The shading is the strongest upward motion (−ω, microbars per second; 10 µb/s is about 10 cm/s) anywhere in the column where the temperature is between −12 and −18 °C and the air is saturated with respect to ice (80 % or more). Dashed contours are the depth of that layer, in hPa. RDPS publishes vertical velocity only at 850, 700 and 500 hPa, so its lift here is interpolated linearly in pressure between them and cannot show a narrow lift maximum between levels.
Waldstreicher, J. S., 2001, The importance of snow microphysics for large snowfalls, Third Northeast Operational Workshop, Albany NY · column sampled every 5 hPa from the model levels (25 hPa HRRR and RRFS, 50 hPa RDPS)
What the model itself makes of the set-up. For the HRRR and RRFS: composite reflectivity, coloured blue to magenta where the model’s precipitation type is snow and olive where it is anything else. RDPS publishes no reflectivity, so its panel shows 1-hour precipitation in the same colours, snow taken from its instantaneous precipitation type (code 5; the Datamart labels the field with WMO table 4.201 but its codes do not follow it).
A convection-allowing model that draws a band where the diagnostics line up is the strongest signal on this page. The diagnostics without a modelled band are worth watching too: a coarser model (RDPS) can resolve the forcing but not the band itself. Bands the model draws where the diagnostics are weak are often convective or orographic rather than frontal.
NOAA/NCEP HRRR composite reflectivity and categorical snow · RRFS v1.0 composite reflectivity and categorical snow · ECCC RDPS 1-h precipitation and precipitation type
Where the three ingredients overlap: 700 hPa frontogenesis of at least 4 K per 100 km per 3 h, EPV* of 0.25 PVU or less in saturated air (750–500 hPa), and lift of at least 10 µb/s in the saturated dendritic growth zone. Pale orange is two of the three; dark orange is all three. The navy outline is the model’s own snow at 25 dBZ or more (RDPS: 1 mm/h).
This is an overlap of ingredients, not a probability. It says where one model run’s atmosphere is set up for banding; it has not been calibrated against observed bands, and a band can form at the edge of the overlap or not at all. The thresholds are round numbers in the range reported for northeast US banded storms (Novak et al. 2004), chosen to be loose enough to keep the weakly stable cases Schultz and Schumacher (1999) warn a strict EPV* < 0 rule would miss. Placement errors of 50–100 km apply to the overlap as much as to any single field.
thresholds: frontogenesis 4 K/100 km/3 h, EPV* 0.25 PVU, DGZ lift 10 µb/s · Novak, D. R., et al., 2004, Wea. Forecasting 19, 993–1010 · Schultz, D. M., and P. N. Schumacher, 1999, Mon. Wea. Rev. 127, 2709–2732
A case study: every diagnostic from the HRRR’s one-hour forecast of each hourly cycle (f01, the first hour with usable vertical motion), beside the NEXRAD base-reflectivity mosaic at the same hour. With almost no forecast error in the large-scale pattern, it shows whether the diagnosed band axis lines up with the bands the radar actually saw. Rain and snow alike: frontogenesis, deformation and EPV* do not depend on precipitation type, and the dendritic-zone panel shows lift through the −12 to −18 °C layer aloft whatever reaches the ground.
NOAA/NCEP HRRR (AWS) · NEXRAD base-reflectivity mosaic n0q, Iowa Environmental Mesonet
The page between seasons, and a check on the method: every diagnostic on a documented band, with the NEXRAD mosaic at the same hour. The 16–17 December 2020 nor’easter put a nearly stationary band over the Southern Tier of New York for about ten hours; Binghamton recorded 40.2 inches, its biggest snowstorm on record, while places 60 km south got under a foot.
The loop is the HRRR’s one-hour forecast from each hourly cycle (f01, the first hour with usable vertical motion), so it shows the diagnostics against reality with almost no forecast error in the large-scale pattern. Read it as a verification: the frontogenesis maximum, the weakly stable EPV* and the dendritic-zone lift line up along a southwest–northeast axis about 35–75 km south of the observed band, and the HRRR’s own reflectivity band sits with them. The NEXRAD view puts the observed and modelled reflectivity side by side with the full overlap of ingredients outlined in black. In the 12Z run of the same day, the HRRR’s band was 80–150 km south of the observed one 14–16 hours ahead, which is the practical limit on everything in the live loops.
NOAA/NCEP HRRR (AWS archive) · NEXRAD base-reflectivity mosaic n0q, Iowa Environmental Mesonet