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**CENTRAL REGION APPLIED RESEARCH PAPER 16-10
**

Analysis of a Heavy Snow Event Using PCGRIDDS

Dean T. Melde

National Weather Service Forecast Office

Bismarck, North Dakota

**1. INTRODUCTION**

On March 22-24, 1994, moderate to heavy snow fell from southern Montana, along the North and South Dakota border, into Minnesota and northern Wisconsin. Six to 14 inches of snow occurred in southern North Dakota on March 23.

The ETA model forecasted Q-vector convergence and dual jet streak circulations in the area of heavy snow. It is suggested that synoptic scale vertical motion, implied from Q-vector convergence, created an environment conducive to snow and the dual jet interaction enhanced and refined the area.

The purpose of this paper is to show that the ETA gridded model output did indicate, through Q-vector convergence and dual jet streak interactions, where conditions were favorable for heavy snow. Only the 0000 UTC 23 March 1994 Eta gridded model forecast fields, utilizing the PCGRIDDS software package was examined. That was the gridded model data available to an operational forecaster at that time. The focus will be in southern North Dakota during the first 24 hours of the event.

The ETA model did a good job predicting the axis of maximum precipitation (Figure 1). However, lighter amounts of precipitation were forecast to far north. Figure 2 shows the actual snowfall in southern North Dakota. Water equivalent amounts averaged 0.35 inches (not shown). The most fell in the southwest where 0.70-0.80 inches were common. In areas where less than six inches of snow was reported, water equivalents ranged from a trace to 0.20 inch. The model forecast precipitation in southern North Dakota had the maximum in the southwest. The following sections breakdown the analysis of this event.

. Eta Model forecast precipitation in tenths of an inch.

. Observed snowfall in inches. Snowfall at each station is noted to the right and the solid lines are contoured at six-inch intervals.

**2. MODEL FORECAST**

Snow was first reported in Dickinson and Bismarck between 0600 UTC and 0700 UTC 23 March (not shown). Bismarck reported periods of moderate snow with accumulations of an inch an hour between 1000 UTC and 1200 UTC. Snow spread east and by 1700 UTC all of southern North Dakota was reporting reduced visibilities.

The model initial conditions at 0000 UTC 23 March had a 500-mb trough in the western US, with a weak ridge over the Dakotas (Figure 3a). By 1200 UTC the trough was forecast to move east and become more negatively tilted (Figure 3b). The western Dakotas were under the influence of cyclonic vorticity advection (CVA) at this time. At 0000 UTC 24 March, the trough was forecast to move into the central plains, placing most of North and South Dakota in weak CVA (Figure 3c).

. Model initialization of 500 mb heights (solid, dm) and vorticity (dash, 10^{-5}a^{-1}) at 0000 UTC 23 March.

. Model forecast 500 mb heights (solid, dm) and vorticity (dash, 10^{-5}a^{-1}) at 1200 UTC 23 March.

. Same as Figure 3b except at 0000 UTC 24 March.

The initialization of the model at 850 mb, 0000 UTC 23 March, had a low located in western Wyoming (Figure 4a). Warm air advection (WAA) was implied to be across occurring most of the Dakotas except in northern North Dakota, where cold air advection was possible. The low and WAA were forecast to intensify by 1200 UTC (Figure 4b). The forecast from 1200 UTC 23 March to 0000 UTC 24 March had the low moving northeast and cold air advection becoming dominant over most of the Northern Plains (Figure 4c). Mixing ratios at 850 mb over the area of interest were forecast to be between 2 and 3 g/kg throughout the event (not shown).

. Model initialization of 850 mb heights (solid, dm) and temperatures (dash, C) at 0000 UTC 23 March.

. Model forecast 850-mb heights (solid, dm) and Temperatures (dash, C) at 1200 UTC 23 March.

. Same as 4b except at 0000 UTC 24 March.

At the surface, a low (as inferred from the mean sea-level isobars) was located in western Wyoming at 0000 UTC 23 March (Figure 5a). From 0000 UTC 23 March to 0000 UTC 24 March the surface low was forecast to move from western Wyoming to southern Nebraska and then into central Iowa (Figure 5b).

. Model initialization of Mean Sea-Level pressure (mb) and subjectively analyzed Fronts (dark solid) and Trough (dashed) at 0000 UTC 23 March.

. Model forecast Mean Sea-Level pressure (mb) and subjectively analyzed fronts (dark solid) and Trough (dashed) at 0000 UTC 24 March.

**3. Q-VECTOR ANALYSIS**

Q-vectors show graphically the synoptic scale quasi-geostrophic vertical motion resulting from both forcing terms of the omega equation: (1) differential vorticity advection and (2) the Laplacian of thickness advection (LTA) (NWS 1994). Where Q-vector convergence is present upward vertical velocity is implied.

Trenberth (1978) suggests, as is common practice, the assumption that the differential operator acting on omega in the omega equation produces a result that is proportional to -omega, and that this assumption works best in the middle troposphere (where fields of temperature and vorticity are sinusoidal). The assumption that the deformation function in the quasi-geostrophic omega equation is small compared to the advection of relative vorticity by the thermal wind is true, in general, in the middle troposphere (Wiin-Nielsen 1959). Trenberth's calculations support this and it was also consistent with Durran and Snellman's (1987) results. Therefore, in this study, Q-vector divergence in the 700 mb to 400 mb layer was examined.

Throughout this event, negative Q-vector divergence, or convergence, was forecast in southern North Dakota and in South Dakota. The Q-vector convergence pattern (Figures 6a-6e) would suggest the heaviest precipitation would begin shortly before 1200 UTC and end a few hours after 0000 UTC 24 March. This verifies well with Bismarck's and Dickinson's observations (not shown).

The dynamical forcing with this event, like many other past heavy snow events for the area of study, was dominated by thermal advection. During this event the forecasts LTA maximum (positive sign meaning upward vertical motion, from the omega equation) and the forecast Q-vector convergence maximum was coinident. This can be seen by comparing Figures 6a-6e with Figures 7a-7e. A Q-vector convergence maximum was forecast in southwest Montana at 0600 UTC 23 March. Six hours later, Q-vector convergence was forecast in western and south central North Dakota as well as across southern Montana. The forecast LTA pattern closely resembled that. By 1800 UTC the Q-vector convergence maximum was forecast to move east along the North and South Dakota border. Bismarck received 5.5 inches of snow between 0600 UTC and 1800 UTC. This was the period when the Q-vector convergence was forecast over the area. By 0000 UTC 24 March, the maximum Q-vector convergence center was forecast to be in southeast North Dakota and in central Minnesota by 0600 UTC 24 March. By comparing Figure 2 with Figures 6a-6e, one can see the most significant snow fell along the same track as the Q-vector convergence. The ETA model did a good job with the timing of the snow. The heaviest snow fell in Bismarck from 1000 UTC to 2010 UTC (not shown).

. Model forecast 700-400 mb layer Q-vectors (arrows) and 700-400 mb layer Q-vector divergence (dashed) at 0600 UTC 23 March.

. Same as Figure 6a except at 1200 UTC 23 March.

. Same as Figure 6a except at 1800 UTC 23 March.

. Same as Figure 6a except at 0000 UTC 24 March.

. Same as Figure 6a except at 0600 UTC 24 March.

. Model forecast Laplacian of thickness advection at 0600 UTC 23 March.

. Same as Figure 7a except at 1200 UTC 23 March.

. Same as Figure 7a except at 1800 UTC 23 March.

. Same ad Figure 7a except at 0000 UTC 24 March.

. Same as Figure 7a except at 0600 UTC 24 March.

**4. JET STREAK ANALYSIS**

Uccellini and Kocin (1987) showed that the interaction of an indirect and direct circulation from two separate jet streaks ". . . contributes to differential moisture and temperature advections and vertical motions necessary to produce heavy snowfall . . .". They also showed ". . . that distinct two-cell transverse circulations associated with upper-level jet streaks can be identified utilizing the operational radiosonde network . . .". The features mentioned above were forecasted by the 0000 UTC 23 March 1994 ETA model and can be viewed using PCGRIDDS. Only the effect that the dual jet-streak interaction had on enhancing the vertical motion field will be studied here.

The 300 mb divergence and 850 mb convergence were examined and suggested that jet streak interactions contributed to the vertical motion that produced the heavy snow. Cross-sections of ageostrophic winds and vertical velocities will show the forecast direct and indirect circulations in pressure versus distance coordinates.

Figures 8a-8d show the forecast 300 mb winds greater than 25 m/s and the divergence of the wind at 300 mb for this event. At 0000 UTC there was a jet streak with a maximum core of 56 m/s located across North Dakota, Minnesota, and southeast to Virginia. Southern North Dakota was in the right rear quadrant of this jet. There were two other jet streaks at this time, one in northern Arizona and Utah and the other coming on the northern California coast. An area of divergence centered in southeast Idaho was a possible result from this combination. Twelve hours later, at 1200 UTC, the model has the jet streaks previously in northern California and in Arizona and Utah merging and taking on a west-east orientation. The northern jet streak remained unchanged. The forecast divergence was located over North Dakota with the maximum in the south central. At 1800 UTC the forecast jet structure changed little but the forecast area of divergence increased in magnitude with the maximum in extreme south central North Dakota. Bismarck's observations from 1000 UTC to 2010 UTC reflected this. There were periods of moderate snow with several observations showing snow increases of an inch an hour. By 0000 UTC 24 March 1994 the northern jet streak was forecast to move east and the southern jet to remain in place in northeast Utah, southern Wyoming, and northwest Colorado. The area of divergence was forecast to move into north central Minnesota. The precipitation across southern North Dakota decreased after this time (not shown).

. Model initialization of 300 mb wind greater than 25 (m/s) and divergence of the wind at 300 mb at 0000 UTC 23 March.

. Model forecast of 300 mb wind greater that 25 (m/s) and divergence of the wind at 1200 UTC 23 March.

. Same as Figure 8b except at 1800 UTC 23 March.

. Same as Figure 8b except at 0000 UTC 24 March.

At 850-mb an area of maximum convergence existed in southeast Wyoming. During the next 30 hours it was forecast to move to the north then east northeast into north central Minnesota (not shown). As with the divergence maximum the low-level convergence maximum moved across southern North Dakota from 1800 UTC 23 March to 0000 UTC 24 March.

The area of forecast upper-tropospheric divergence coincided better with the observed conditions than the low-level convergence. The maximum precipitation fell in southern North Dakota and northern South Dakota. Bismarck reported 6 inches between 1200 UTC 23 March and 0000 UTC 24 March, coincident with the time of greatest forecast upper-level divergence. As the forecast divergence and convergence area moved east, the snow diminished in intensity, which suggests this dual jet-streak interaction played a major role in producing heavy snow and was well predicted by the model. Figure 9a indicates the area of the cross-section used to produce Figure 9b. Figure 9b depicts the direct and indirect circulations that interacted to contribute to the vertical motion.

. Model forecast 300 mb wind greater that 25 (m/s) at 1800 UTC 23 March. Solid line indicates the area of the cross-section.

. Cross-section in the area shown in Figure 9a at the same time at Figure 9a. Arrows indicate a true secondary circulation. Solid lines display vertical velocity (ub/s). The direct (indirect) circulation is indicated by D (I).

**5. CONCLUSIONS**

Q-vector convergence over southern North Dakota implied there was synoptic scale upward vertical motion present to produce snow and the dual jet-streak interaction contributed to produce heavy snow. The Q-vector pattern implied the precipitation would occur in southern North Dakota and the areas of maximum divergence, due possibly to the jet interaction, refined the area.

The timing and location of the precipitation were forecast well by the ETA model and the ability to diagnose the Q-vectors and dual jet-streak circulations were straightforward using the ETA gridded model output and the PCGRIDDS software package.

**6. REFERENCES**

DOC, NOAA, NWS, 1994: Omega Diagnostics, Including Q-Vectors. Graphical Guidance., 1-44.

Durran, D.R., and Snellman, L.W., 1987: The Diagnosis of Synoptic-Scale Vertical Motion in an Operational Environment. *Wea. and Forecasting,* **02**, 17-31.

Trenberth, K.E., 1978: On the Interpretation of the Diagnostic Quasi-Geostrophic Omega Equation. *Mon. Wea. Rev., ***106**, 131-137.

Uccellini, L.W., 1987: The Interaction of Jet Streak Circulations during Heavy Snow Events along the East Coast of the United States. *Wea. and Forecasting*, **02**, 289-308.

Wiin-Nielsen, A., 1959: On a graphical method for an approximate determination of the vertical velocity in the mid-troposphere. *Tellus,* **11**, 432-440.

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