A STATISTICAL ANALYSIS OF LAKE EFFECT SNOW FORECASTING PARAMETERS OVER SOUTHWEST LOWER MICHIGAN

 

Gary Garnet (1)
National Weather Service Office
Grand Rapids, Michigan

 

 

I. INTRODUCTION

Lake effect snow is a well known mesoscale phenomenon that occurs over the Great Lakes Region during the cold season. The movement of arctic air over the relatively warmer waters of Lake Michigan generates vertical fluxes of moisture and heat to the lower troposphere. The magnitude of these fluxes are often large enough to produce convective clouds or lake effect snow bands. These mesoscale snow bands have a significant impact on the snow climatology of the Great Lakes Region and present a formidable challenge to forecasters.

Several lake effect snow forecast techniques have been documented over the years (Rothrock 1969, Dockus 1985, Niziol 1996). The majority of there techniques have been derived using traditional synoptic scale parameters (850 mb temperature, 700 mb temperature, 700 mb vertical velocity, 500 mb heights and vorticity, wind and lake water temperature ).

Recent advancements in mesoscale modeling have produced operational numerical output that is higher in both temporal and spatial resolution. These models provide a unique insight to forecast parameters not previously available to forecasters. In particular, high resolution hourly forecast soundings are available at several locations in the Great Lakes Region (Mahoney 1997). These model soundings are able to provide a detailed numerical simulation of the lower tropospheric conditions associated with lake effect snow on the lee side of Lake Michigan.

This study used statistical regression techniques to evaluate some of the traditional lake effect snow parameters derived from synoptic scale models along with some non-traditional parameters derived from hourly sounding data.

II. DATA

Three years of lake effect snow data was collected for this study. Lake effect snow observations from cooperative observers and volunteers were collected over Southwest Lower Michigan for the winter periods of 1995-1996, 1996-1997 and 1997-1998. Out of this data set, 65 cases were selected for this study. To qualify as a case, observed lake-induced fluxes of heat and moisture must have been present for a 24 hour period from 1200Z (1200 UTC) to 12Z. The flux was estimated by using the difference between the lake temperature and 850 mb temperature. A difference of 10°C or greater over the 24 hour period was considered as a possible case. A second requirement of a trace or more of lake effect snow must have been measured by an observing site during the 24 hour period. All potential cases were recorded on log sheets by operational forecasters at the National Weather Service.

The data used in this study consisted of observed snowfall data, 12Z Eta hourly BUFR sounding output and 12Z Eta gridded model output. The snowfall data was collected from a network of National Weather Service Cooperative Observers, National Weather Service Observations and trained Weather Spotters. The spotters were educated on snow observing techniques and made one snow observation per day. The snow observation was taken for a 24 hour period ending at 12Z each morning. The significance of the 12Z observation was to synchronize the times of the observational data with the model output. Observers logged snowfall data on observation forms and transmitted the hard copy once a month. Outliers were eliminated from the snowfall data set and the remainder of the quality controlled data was input into a database. Comparisons of the snowfall data to nearby sites was used for quality control and the determination of outliers. Questionable or erroneous data was deleted from the snowfall data set.

This snow data was averaged across each county. Counties were selected as the base geographic unit since the majority of forecasts issued by the National Weather Service are at the county level. Using the Arcview (ESRI 1996) statistical system of natural breaks, counties with similar average lake effect snowfall for the three season period from 1995 to 1998 were combined. The counties were grouped together based on total snowfall only, no other meteorological parameters were considered in the determination of the groupings. Three groups were calculated using the GIS statistics and are labeled as Group A, Group B and Group C. The observed average snowfall used to calculate these groupings can be referenced using (Figure 1).

The model output was a combination of meteorological variables derived from both the 12Z Eta gridded model output and the12Z Eta BUFR output. The Eta-32 was the model version used for the study. Variables were calculated using an 80 km grid and interpolated at a grid point nearest to Grand Rapids. All meteorological forecast output was recorded at one location, Grand Rapids Michigan (Figure 1). This site was chosen for several reasons. First, this data point was within close proximity to Lake Michigan (25-30 nm), it was a central location within the Grand Rapids County Warning Area and it was the only Eta model grid point in the Grand Rapids CWA that BUFR hourly sounding data was available. The meteorological output recorded at Grand Rapids Michigan was assumed to be representative of the lee side lake synoptic atmospheric conditions.

 

Figure 1
Figure 1. GIS County Groupings of Average Lake Effect Show (inches) for the period November 1995 to March 1998.

 

The meteorological variables used for regression were a combination of standard synoptic scale parameters traditionally used for lake effect snow prediction along with some non-standard parameters derived from 12Z hourly Eta BUFR output. Traditional lake effect snow forecasting parameters were selected from previous works (Rothrock 1969, Dockus 1985, Niziol 1987, Evans 1996). Non-traditional variables were selected based on work done by the Reinking et al. (1993), Burrows (1991), Braham 1983, Hjelmfelt (1990) and local observations. Traditional forecasting parameters were considered to be temperature, wind, and moisture variables, available from standard pressure levels in synoptic scale models. For the purpose of this study, temperatures, winds and moisture variables extracted or derived from the surface, 1000 mb, 850 mb, 700 mb and 500 mb are considered "traditional forecasting parameters."

Non-traditional parameters were forecasting variables that are derived from hourly sounding output and involve the interpretation of the mixing layer height. In this study all variables not extracted or derived from the standard pressure levels are considered "non-traditional."

Traditional meteorological variables used in this study were extracted using the PCGRIDDS program (Petersen 1997). The BUFKITE program (Mahoney 1997) was used to extract the non-traditional variables. Lake Michigan water temperature was provided by a daily graphic generated by the Great Lakes Environmental Lab in Ann Arbor Michigan. The variables are labeled according to the variable type (first letter) and the data source (second letter). The second letter in the variable indicates whether it was derived using PCGRIDDS (P) or BUFKITE (B). Table 1 shows a complete listing of the derived meteorological variables used in this study.

Average snowfall from each of the three geographic groups was combined with meteorological forecast parameters from the 12Z Eta model run and 12Z Eta BUFR hourly sounding output to construct the data set. Thirty-five meteorological variables were extracted or derived from the model output (Table 1).

 

 

TABLE 1
Derived Lake Snow Forecasting Parameters:
PARAMETER DESCRIPTION:

 

VARIABLE
Average Lake Temperature

 

TG1
Average Temp Mixing Layer

 

TB1
Mixing Layer Height

 

TB2
Strength Inversion

 

TB3
Lake Temperature - Average Temperaure of Mixing Layer

 

TB4
Lake Temperature - Average Temperature of Mixing Layer

 

TB5
850 mb Temperature

 

TP1
700 mb Temperature

 

TP2
Average Lake Temperature - 850 mb Temperature

 

TP3
Average Lake Temperature - 700 mb Temperature

 

TP4
   
Average Wind Direction in Mixing Layer

 

WB1
RMS Wind Direction in Mixing Layer

 

WB2
Average Wind Speed in Mixing Layer

 

WB3
RMS Wind Direction (Time 0 to Time 24)

 

WB4
Average Wind Direction 1000 mb to 850 mb

 

WP1
Average Wind Direction 1000 mb to 700 mb

 

WP2
Wind Direction 1000 mb - Wind Direction 850 mb

 

WP3
Wind Direction 1000 mb - Wind Direction 700 mb

 

WP4
Average Wind Speed 1000 mb to 850 mb

 

WP5
850 mb Wind Speed

 

WP6
   
Average Relative Humidity in Mixing Layer

 

RB1
Average Mixing Ratio 1000 mb to 850 mb

 

RP1
Average Mixing Ratio 1000 mb to 700 mb

 

RP2
Average Relative Humidity 1000 mb to 850 mb

 

RP3
Average Relative Humidity 1000 mb to 700 mb

 

RP4
1000 mb to 700 mb Precipitable Water

 

RP5
Traditional QG Omega 1000 mb to 500 mb

 

DP1
Traditional QG Omega 1000 mb to 700 mb

 

DP2
Traditional QG Omega 1000 mb to 850 mb

 

DP3
1000 mb to 850 mb Divergence Wind

 

DP4
1000 mb to 700 mb Divergence Wind

 

DP5
700 mb Vertical Velocity

 

DP6
Ageostropic Curvature 1000 mb to 850 mb

 

DP7
Ageostropic Curvature 1000 mb to 700 mb

 

DP8
1000 mb Divergence Wind

 

DP9

 

III. PROCESS

A forward step wise regression technique was used to analyze the data set. Snowfall amounts for each of the geographic groups was used as the dependent variable. The 35 derived meteorological parameters from the Grand Rapids grid point were used as the independent variables. A separate regression was run for each of the GIS groups. The results of the regression were analyzed to determine the significance of the 35 derived meteorological parameters in controlling lake effect snow amounts. Since one the main objectives of this study was to determine parameters that contributed to significant lake effect snow, regression was the logical analytical choice. SigmaStat (SPSS 1997) statistical package was the tool used. Regressions were run for each of the geographic groups using the same independent variables, only the dependant variable (average snowfall) was changed. The dependent variable (average snowfall) was calculated for each county. This was done by taking an average of the 24 hour snowfall amounts observed in each county. The average snowfall amount in inches was changed for each iteration of the regression to represent each county. The independent variables were left unchanged.

The results of the regression were analyzed for each group. The significant variables for each group were compared with the other groups. Patterns and correlations between the different groups were observed to establish relations that may be useful in predicting lake effect snow amounts.

IV. RESULTS

The results of the forward step-wise regression are shown in Tables 2-4. Table 2 shows the results from Group A. The variables are listed along with the coefficients, standard errors, F scores and the P values. The adjusted R square along with the standard error of the total regression are also shown. The variable names can be referenced to the corresponding derived meteorological data using Table 1. The variables beginning with a T indicate temperature lapse rate parameters. The R variables indicate moisture related parameters, variables beginning with D and W are wind derived parameters.

 

TABLE 2
Group A Regression Results

 

 

Group A Regression Results:
R = 0.856 Rsqr = 0.732 Adj Rsqr = 0.704
Standard Error of Estimate = 1.082

 

 

Variable

 

Coef

 

Std. Coeff

 

Std. Error

 

F - to - Remove

 

P

 

TP2

 

0.341

 

0.499

 

0.0925

 

13.589

<0.001

 

TB2

 

0.176

 

0.257

 

0.0807

 

4.7479

0.034

 

RP1

 

0.248

 

0.848

 

0.0907

 

7.452

0.009

 

RP2

 

-0.468

 

-1.313

 

0.112

 

17.378

<0.001

 

RP4

 

0.152

 

0.661

 

0.0285

 

28.276

<0.001

 

DP5

 

-0.199

 

-0.267

 

0.0667

 

8.923

0.004

 

Six variables show up in the Group A regression, the wettest group. Moisture related parameters, "R variables" appeared more frequently than temperature " T variables" or wind derived parameters "D and W variables". TB2 is mixing layer height and TP2 is the temperature lapse rate between the lake and the top of the mixing layer. It is not surprising that these variables appeared in the regression. Traditional lake effect snow forecasting techniques are based on temperature lapse rates within the convective boundary layer. Parameters such as the difference between the 850 mb temperature and the lake water temperature are probably the most common operational proxies for convective boundary layer lapse rates. DP5 which is the divergence of the wind through the 1000 mb to 700 mb layer was also significant. This is consistent with the findings from Burrows (1991) where low level convergence was the key factor in forecasting lake effect snow amounts.

One of the most significant results of the regression are the moisture parameters. The F scores of the RP2, the average mixing ratio in the 1000 mb to 700 mb layer and RP4 the average relative humidity in the 1000 to 700 mb layer were the largest of any parameters. The F score indicates the significance of the variable to the regression. The significance of moisture parameters supports results found by Evans in a forecast study done over Southwest Lower Michigan in 1996.

The regression for group A did produce several significant variables. The results indicated the lapse rate, inversion height, low level convergence and moisture are all important factors in contributing to the intensity of lake effect snow. The lapse rate and inversion height were extracted from the BUFR hourly sounding output. Low level convergence and moisture related parameters were extracted from the Eta model output using PCGRIDDS.

The regression results for Group B (Table 3) produced fairly similar results to Group A. Moisture parameters RP4, RP2 showed up again. Both of these parameters had high F scores indicating the relative importance of these terms to the overall regression. Low level convergence also appeared DP6 (1000 mb-850 mb divergence of the wind), although at different levels than Group A. Noticeably absent from the regression were temperature terms. Both lapse rates and inversion heights were not included in the final regression for Group B.

 

TABLE 3
Group B Regression Results

 

Group B Regression Results:
R = 0.799 Rsqr = 0.639 Adj Rsqr = 0.601
Standard Error of Estimate = 0.821

 

 

Variable

 

Coef

 

Std. Coeff

 

Std. Error
F - to - Remove

 

P

 

WB4

 

-0.0150

 

-0.291

 

0.00484

 

9.653

0.003

 

RB1

 

0.111

 

0.365

 

0.0357

 

9.951

0.003

 

RP2

 

-0.152

 

-0.651

 

0.0301

 

25.446

<0.001

 

RP4

 

0.104

 

0.690

 

0.0173

 

35.992

>0.001

 

DP6

 

-0.108

 

-0.303

 

0.0333

 

10.515

0.002

 

The regression results for Group C (Table 4) deviated from the traditional lake effect snow forecasting model even further. Group C was the inland group. The results from this group were all wind derived parameters. 1000 mb divergence of the wind (DP9) was the most significant variable. Other variables such as the average wind direction in the mixing layer (WB1) also became statistically significant. Both temperature lapse rate terms, inversion heights and moisture parameters did not appear in the results for Group C (Table 4).

 

TABLE 4
Group C Regression Results

 

Group C Regression Results:
R = 0.764 Rsqr = 0.584 Adj Rsqr = 0.549
Standard Error of Estimate = 0.740

 

 

Variable

 

Coef

 

Std. Coeff

 

Std. Error

 

F - to - Remove

 

P

 

WB1

 

-0.0164

 

-0.398

 

0.00442

 

13.782

<0.001

 

WB4

 

-0.00885

 

-0.202

 

0.00440

 

4.035

0.050

 

WP5

 

0.0551

 

0.236

 

0.0225

 

6.013

0.018

 

DP9

 

-0.123

 

-0.674

 

0.0181

 

46.526

<0.001

 

The regression results from the three different geographic groups produced various results. However some commonality can be identified. One must remember that all the cases used for this study had sufficient lake-induced fluxes to produce lake effect snow, partially explaining the lack of temperature lapse rate variables in Groups B and C. The regression focused on the factors controlling the amounts of lake effect snow in conditions favorable for the mesoscale phenomenon. The conditions surrounding the initiation of lake effect snow are well understood.

Group A and Group B consisted of the counties immediately adjacent to Lake Michigan. Both Groups A and B had common moisture variables. Using step-wise regression techniques, RP4 (1000 mb-700 mb average relative humidity) and RP2 (1000 mb-700 mb mixing ratio) appeared statistically significant in both groups. The strength of the 1000 mb-700 mb average relative humidity variable to the regression was at first a bit puzzling. However, after further thought, the relation made sense. The majority of lake effect snow events in the study over Western Michigan had subsidence inversions less than 3000m. The 700 mb level is often higher than this in Michigan during the winter. The majority of the intense lake effect storms over West Michigan had relatively higher subsidence inversions and were characterized by an associated deep moist layer. The subsidence inversion often exceeded both 3000m and the height of the 700 mb level. Therefore, the high moisture values in the 1000 mb-700 mb layer were a good indicator of a higher subsidence inversion and deeper moisture in the ambient air mass. These findings are consistent with those of Evans (1996) who found high values of low to mid level moisture as an important precursor the onset of heavy lake effect snows. The LOWS Project (Reinking et al. 1993) highlighted the possibility of a high inversion height being more important than temperature based instability.

Using hourly model soundings, forecasters in Grand Rapids have noted this trend. Increasing the height of the subsidence inversion and the amount of subsequent low level moisture changed the characteristics of the lake effect snow bands. A deeper boundary layer tended to produce more vigorous convection while increasing low level moisture resulting in greater areal coverage. It is well known that temperature based instability is an important factor in initiating lake-induced fluxes that initiate lake effect snow (Dockus 1985). However, the results of this study show that other factors, such as inversion height and low level moisture, appeared to be significant in controlling snow amounts. Temperature lapse rate terms seemed to play less of a role in the lake effect snow band characteristics once the process had started.

Forecast low level convergence was also a significant variable. Some form of low level convergence was statistically significant in all of the groups. Low level convergence was most significant over the inland counties (Group C). This result suggests the inland extent of the lake effect snow bands may be highly influenced by the amount of low level convergence. These findings are consistent with those of Burrows (1991) who found 1000 mb convergence to be the key component in controlling lake effect snow amounts over southwest Ontario.

V. DISCUSSION

The results of this statistical study are consistent with the traditional lake effect snow models established by previous works (Rothrock 1969, Dockus 1985, Niziol 1987) . However, this study highlights the importance of variables in the lake effect snow process that may be overlooked. Traditionally, forecasters have focused on temperature based information to forecast lake effect snow amounts (Dockus 1985). The results of this study suggest that a broader scope of meteorological variables should be considered. In particular, deep ambient moisture and low level convergence may play a significant role in controlling snow amounts in lake effect regimes.

A deep moist layer is more conducive to heavy precipitation than a shallow dry layer. The moisture fluxes over the open lake may not be sufficient to moisten the boundary layer to form more efficient precipitation processes.

The open waters of Lake Michigan are a prime example. The majority of the lake effect snow cases in this study occurred with a west to northwest boundary layer wind flow. With this trajectory the open water fetch of Lake Michigan is only in the 70nm to 100nm range. This fetch is considered marginal for true lake effect snow (Rothrock 1969). The existence of a deep moist layer in the ambient regime prior to contact with the open lake seemed imperative for heavy lake effect snow. The moisture fluxes over the short westerly and northwesterly fetches of Lake Michigan may be only sufficient to produce clouds and light snow (Hjelmfelt 1990). Several cases were noted during this study of moderate to extreme to instability (>20°C lake to 850 temperature differences) over Lake Michigan and little lake effect snow. The lack of ambient moisture through a deep subsidence inversion , typically >=7 kft, in the boundary layer appeared to be the contributing factor to the lack of precipitation. These observations are supported by the regression results.

Low level convergence of the wind was also highlighted as an important element controlling lake effect snow amounts. The strength of the convergence in the inland county Group (C) was significantly more important than in the groups near the lake (Groups A and B). Wind variables in general were more statistically significant over the inland groups than the lake shore groups. These results are consistent with the findings from the Burrows (1991) where low level convergence was the dominate forecasting parameter.

While deep moisture in the boundary layer appears to be the significant controlling factor for the lakeshore counties, low level convergence appears to be the primary factor controlling the inland extent of heavy snow. When wind conditions were favorable, the existence of either mesoscale or synoptic scale convergence significantly enhanced the inshore extent of the lake effect snow bands. Local observations have shown significant low level convergence over Southwest Lower Michigan during arctic outbreaks related to lake aggregate-induced forces (Sousounis 1994). The associated low level convergence from the aggregate-induced circulations is often strong enough to maintain lake effect snow bands several hundred miles inland.

VI. CONCLUSIONS

The objectives of this study were to determine the statistical importance of both traditional and non-traditional lake effect snow forecasting parameters over southwest lower Michigan. Statistical step-wise regression techniques and GIS groupings were used to analyze the data.

The results of this study are consistent with many of the traditional views of lake effect snow forecasting. Forecasting parameters such as the difference between lake water temperature and boundary layer temperature differences, open water fetch length and wind direction are well documented. This study emphasizes the importance of the synoptic regime in controlling lake effect snow amounts, in particular, synoptic moisture and low level convergence.

The results of this study suggest a significant contribution of deep ambient moisture to the lake effect snow process. Latent and sensible heat fluxes from the lake into the boundary layer are extremely important in the initiation of lake effect snow convection. However, for marginal fetch lengths (70nm to 100nm), the transport of moisture into the boundary layer by itself may not be sufficient to support significant lake effect snow. The synoptic environment prior to the mesoscale initiation is important. The synoptic scale conditions set the stage for the significance of the mesoscale event. Higher subsidence inversions and subsequent moisture in the boundary layer changed the lake effect snow band characteristics. Convection became more intense and widespread with a deeper, moist boundary layer. Increasing moisture and the height of the inversion proved to be more significant than an increase in the temperature lapse rates in increasing lake effect snow amounts.

Forecast low level convergence was also an important element controlling the lake effect snow process. Statistically, forecast low level convergence was more important over the inland county Group C than the near lake groups (A and B). In general, wind derived variables were more statistically significant over the inland counties than the near lake counties These results suggest the synoptic or mesoscale convergence in the boundary layer may aid in the inshore extent of lake effect snow bands.

Lake effect snow is a mesoscale phenomenon that is initiated by a synoptic scale environment. While mesoscale fluxes of heat over the open lake are imperative to the initiation of the lake effect process, other variables may be as important in controlling amounts. Fluxes of heat generate instability, but moisture and dynamic lift generate precipitation. Concentration on lake generated instability alone will often result in erroneous forecasts. Understanding the lake effect process and the large scale environmental effects on the process will lead to better forecasts.

VII. REFERENCES

 

Braham, B.R., 1983: The Midwest Snow Storm of 8-11 December 1977. Mon. Wea. Rev., 111, 253-272.

Burrows, W.R, 1991: Objective Guidance for 0-24 Hour and 24-48 Hour Meso scale Forecasts of Lake-Effect Snow Using CART. Wea. Forecasting, 6 357-378. <[>Dockus, D.A., 1985: Lake-Effect Snow Forecasting in the Computer Age. Natl. Wea. Dig., 10, 5-19.

Environmental Systems Research Institute, Inc., 1996: ArcView GIS. Environmental Systems Research Institute, Inc., 550pp.

Evans, M.S., 1996: A Method for Forecasting Lake Effect Snow Using Synoptic Scale Model Forecasts of 850 mb Temperature, 850/700 mb Vertical Velocity, and 850/700 mb Relative Humidity. Central Region Technical Attachment 96-09. National Weather Service Central Region Headquarters, Scientific Services Division, Kansas City, MO. 12pp.

Hjelmfelt, M.R., 1990: Numerical Study of the Influence of Environmental Conditions on Lake Effect Snowstorms over Lake Michigan. Mon. Wea. Rev., 118, 138-150.

Mahoney, E.A., and T.A. Niziol, 1997: BUFKit: a Software Application Toolkit for Predicting Lake Effect Snow. Preprints, 13th Conference on IIPS, LongBeach, AMS (Boston), 338-391.

Niziol, T.A., 1987: Operational Forecasting of Lake-Effect Snowfall in Western and Central New York. Wea. Forecasting, 2, 320-321.

____________, W.R. Snyder, and J.S. Waldstreicher, 1995: Winter Weather Forecasting throughout the Eastern United States. Part IV: Lake Effect Snow. Wea. Forecasting, 10, 61-77.

Petersen, R.A., and J.A. Lord, 1987: PCGRIDDS: User Guide. NOAA Technical Publication, Washington, DC., 196pp.

Reinking R.F., R.. Caiazza, R.A. Kropfli, B.W. Orr, B.E. Martner, T.A. Niziol, G.P. Byrd, R.S. Penc, R.J. Zamora, J.B. Snider, R.J. Ballentine, A.J. Stamm, C.D. Bedford, P. Joe, and A.J. Koscielny, 1993: The Lake Ontario Winter Storms (LOWS) Project. Bull. Amer. Meteor. Soc., 75, 1793-1811.

Rothrock, H.J., 1969: An Aid in Forecasting Lake Effect Snows. ESSA Technical Memo WBM CR-30, DOC, Environmental Science Service Administration, Weather Bureau, Central Region, Kansas City, MO, 15pp.

Sousounis, P.J,. and J.M. Fritsch, 1994: Lake-Aggregate Mesoscale Disturbances. Part II: A Case Study of the Effects on Synoptic Scale Weather. Bull. Amer. Meteor. Soc., 75, 1793-1811.

SPSS Inc., 1997: SigmaStat Users's Guide. SPSS Inc. Chicago, IL, 12-1 to 12-190.

 


1. Current Affiliation: National Weather Service Forecast Office Cleveland, Ohio.

 


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