The inverted nor easter of February 2010-Draft Round 5 By Richard H. Grumm National Weather Service Office, State College, PA 16803

Transcription

1 The inverted nor easter of February 2010-Draft Round 5 By Richard H. Grumm National Weather Service Office, State College, PA INTRODUCTION Strong nor easter impacted the northeastern United States on February This storm produced record snows over portions of northeastern Pennsylvania and eastcentral New York State (Fig. 1a). East of the storm, heavy rains were observed with over 200 mm (8 inches) in southeastern Maine (Fig b). In addition to the heavy snow and rain, the storm produced gale force winds and wind gust reaching hurricane force (Fig. 2). A summary of the larger snowfall amounts and rainfall amounts are summarized in Tables 1 & 2 respectively. This storm is called the upside-down nor easter due to the surge of warm air north and east of the low-level cyclone center. This produced an interesting situation where rain was observed hundreds of kilometer north of areas receiving heavy snow. Through much of the storm evolution, Albany, NY was 37F with rain while heavy snow affected New York City. New York City would receive over 20 inches of snow during the event. In a historical context, inverted storms have been observed in the past to include the 26 November 1950 storm and the Cleveland super-bomb of January This unique aspect of this storm would be an interesting course of study. Another interesting issue with this storm, not explored but worthy of mentioning here, is how to convey a storms potential impact to the public. As this storm approached, the term snowicane was attached to this storm. It garnered considerable attention and clearly piqued the public s interest in both the storm and the term. To paraphrase from Carl von Clausewitz, a newly minted meteorological term emerged from the fog of the forecast. The traditional term, nor easter is used herein. The Glossary of meteorology definition of a nor easter is reiterated here: Nor easters may occur at any time of year but are most frequent and most violent between September and April. Northeast storms usually develop in lower middle latitudes (30 40 N) within 100 miles east or west of the coastline. They progress generally northward to northeastward and typically attain maximum intensity near New England and the Maritime Provinces. They nearly always bring precipitation, winds of gale force, rough seas, and, occasionally, coastal flooding to the affected regions. Other definitions include hurricane force wind gusts and the fact that the high winds, ice, and snow can cause widespread power outages. Some nor easters are stronger and more powerful than others. The anomalies of key meteorological fields used to discriminate strong from weaker East Coast Winter Storms (ECWSs:Hirsh et al. 2000) are presented here. Following the methods of Hart and Grumm (2000) the analysis of ECWS by Stuart and Grumm (2006) it will

2 be shown that numerical guidance predicted are gridded datasets and were displayed Figure 1. Snowfall (in) and rainfall (in) for the 2-day event of February Values taken from National Weather Service public information statements. a major nor easter which was correctly interpreted by human issued forecasts. It would be interesting to know what an extreme forecast index (EFI) would have predicted for this storms snow and winds. using GrADS (Doty and Kinter 1995). Snowfall data was retrieved from the National Snow site and from National Weather Service Public information statements. This paper presents and overview of the inverted nor easter of February It was a powerful and memorable extratropical cyclone, one of many that contributed to the record breaking snowfall observed in many locations in the eastern United States during the highly negative Arctic Oscillation winter of METHODS AND DATA Rainfall data used here were obtained from the unified precipitation dataset (UPD) and the Stage-VI rainfall data (Seo 1998). Both The 500 hpa heights, 850 hpa temperatures, 850 hpa winds, and other standard level fields were derived from the NCEP NAM and GFS data using the NCEP/NCAR (Kalnay et al. 1996) data as the climatological comparison. The means and standard deviations used to compute the standardized anomalies were from the NCEP/NCAR data as described by Hart and Grumm (2001). Anomalies were displayed in standard deviations from normal, as standardized anomalies. All data were displayed using GrADS (Doty and Kinter 1995).

3 Figure 2. As in Figure 1 except showing wind gusts in MPH. The standardized anomalies computed as: 3. SD = (F M)/σ ( ) Where F is the value from the reanalysis data at each grid point, M is the mean for the specified date and time at each grid point and σ is the value of 1 standard deviation at each grid point. NCEP determinist model and ensemble data shown here were primarily limited to the GFS and NAM and the ensembles systems shown are the NCEP GEFS and SREF. Displays will focus on the forecasts of the pattern conducive for precipitation and snowfall and products showing the amount and gradients of the QPF used to produce snowfall forecasts. For brevity, times will be displayed in day and hour format such at 24/1200 UTC signifies 24 February 2010 at 1200 UTC. 4. RESULTS i. Large scale overview The large scale pattern during the key period of the event over North America is shown in Figure 3. As with the 4 previous significant winter storms of the winter of , a strong 500 hpa blocking ridge was present. As the trough to the south deepened and moved over the East Coast, it was stuck beneath the block and forced to meander over southern New England forming a clearly defined Rex Block (Rex 1950a). Figure 4 shows the precipitable water and anomalies over North America during the event. In the early stages of the evolution of the storm, it was able to tap a deep plume of high PW air. PW values of over 20 mm were ingested by the system with 1 to 3 SD PW anomalies surging into the evolving storm. The storm, in its early stages had a rich supply of deep moisture. ii. Regional view The NCEP NAM is used to show the regional character of the storm. Figure 5 shows the mean sea level pressure (hpa) over the region. These data show the evolution of a deep cyclone over time. Initially, the remnants of early cyclone were present over southern New England (Fig. 5) with second cyclone off the coast of Georgia. The cyclone moved rapidly northward and deepened to at least 978 hpa

4 east of Long Island (Fig. 5e). The storm retrograded over southern New York and then slowly filled. The 850 hpa winds and u-wind anomalies associated with the storm are shown in Figure 6. Similar to Figure 4, these data show the remnants of the previous cyclone to affect the area with -3 to -4 SD u-wind anomalies about the older cyclone center (Fig. 5a-c). These data and values in and of them self suggest a potent storm. The 850 hpa cyclone for the storm of interest here generated -5SD u-wind anomalies by 25/1800 UTC. Typically, u- wind anomalies on the order of -4 to -5 SDs are associated with historically significant storms (Stuart and Grumm) and the historic storms of 5-6 February and February also produced -5 to -6SD u-wind anomalies. This storm was clearly a storm for the record books. Between 26/0000 and 26/1200 UTC this incredible low-level jet moved into southern New England and then northward into southern Quebec. The nose of this impressive jet was aimed into New England and into eastern New York. In the warm air it produced historic rainfall amounts and in the cold air it produced record snowfall. Figure 7 shows the NAM 850 hpa temperatures and temperature anomalies associated with the storm. These data show the surge of warm air on the east side of the storm. Additionally, they show that a broad region of +1SD above normal air was present over northern New England and Quebec in the wake of February storm (Fig. 7a-c). The approaching storm further wrapped this warm air around it and beneath the anchoring block to the north (Fig. 3). Thus the storm was somewhat thermally inverted with 1 to 2SD above normal 850 hpa temperatures to the north and -1 to -2 SD below normal 850 hpa temperatures to the south. This unique configuration produced rain in eastern and northern New England, extreme eastern interior New York and Quebec, while heavy snow fell from Pennsylvania, across New Jersey and into New York City and western Long Island. The NAM PW fields (Fig. 8) shows a similar pattern as that produced by the 850 hpa temperature field. The remnant moisture surge from the first storm with above normal PW air (Fig. 8a-c) was stuck beneath the block over New England and Quebec. The surge of moisture with the second storm merged with it and this plume would slowly wrap around the low and back over the western Great Lake by 27/0000 UTC. The moisture field (Fig. 8) shows how these two storms wrapped the high PW air around the Rex Block iii. Ensemble forecasts-gefs This event was relatively well predicted by the NCEP models and Ensemble forecast systems. This event was good test of the utility of the recently released NCEP GEFS at approximately 70 km. Figures 9-11 show 9 GEFS forecasts of the event initialized from 20/0600 through 23/0000 UTC. All of these forecasts successfully predicted a major cyclone along the East Coast with strong winds and the potential for a significant amount of precipitation. The strong winds actually were predicted to move into New England and affect southern regions before reaching the locations shown I Figure 10. These are ensemble forecasts which serve as a basis for forecasts meteorologists interpret and present to users. A second set of GEFS forecasts is presented in Figures These shorter range forecasts show a consistent trend toward a strong cyclone. Due to the decreased range and the rather long predictability horizon of the storm, the anomalies are considerably a larger. These data showed a deep cyclone with significant pressure anomalies, a strong 850 hpa cyclone with strong winds. Wind anomalies in these course 70-75km data were on the order in some times (not all shown) of 6SD above normal. The QPF field

5 also showed a significant precipitation event. Again, the GEFS showed a high probability of a significant nor easter to impact the East Coast with strong winds, heavy precipitation, and snow. Human s merely need to interpret these data. iv. Ensemble forecasts-sref The previous section showed the GEFS performance with regards to this relatively predictable storm. With 32km resolution the SREF captured some of the mesoscale details the GEFS could not. Figures show the SREF forecasts from 23/0300 through 25/0300 UTC. The MSLP field shows that the SREF had a deeper cyclone with a few runs showing a - 5SD pressure anomaly with the surface cyclone. These anomalies implied and showed very deep cyclone. The 850 hpa winds and total wind anomalies (Fig. 17) forecast 4-5SD anomalies north of the cyclone in the main precipitation shield and forecast strong northwest winds in the mountains of southwestern Pennsylvania were upslope effects created heavy snow in both States and a 10 hour period of near blizzard conditions at Johnstown, Pennsylvania 1. But the u-wind anomalies were the tip-off as to the severity of this storm (Fig. 18). This storm was predicted and shown (Fig. 7) to have -5 to -6 SD u- wind anomalies. Strong u-winds are a critical tell-tale signal in strong to record nor easters. The SREF predicted this would be one such event. The SREF probability of inch or more QPF in 24 hours ending at 26/1200 UTC from forecasts initialized at 24/0300 and 25/0300 UTC are shown in Figure 19. These data showed a high probability of over 1 inch in 24 hours over southern New York State and 1 not shown observations of strong winds and ¼ mile visibility persisted most of 26 February. The region had over 12 inches of snowfall. eastern New England. The probabilities were higher with the shorter range forecasts. The rain/snow line was another issue. But clearly the SREF got the areas of heavier QPF well. But what about the edges? Figure 19 shows a zoomed in view. The SREF showed a dramatic western edge to the probability of high QPF. The chances of heavy snow in this and other (not shown) time periods dropped off dramatically from east to west. In addition to the location of the higher QPF amounts, this storm, which wrapped warm air well to its north and east, had complex precipitation type issues associated with it (Fig. 21). v. Precipitation The total accumulated precipitation from the UPD is shown in Figure 22. These data show a large are of over 64 mm of precipitation, mainly rain, over southeastern Maine and eastern New Hampshire. As shown in Figure 1b, locally amounts were over 8 inches (200 mm). Other areas of heavy precipitation included southeastern Connecticut and Long Island. Most of this fell as rain but heavy snow was reported in this region toward the end of the storm. Another region of heavy precipitation was in the eastern Catskill Region of New York State. This is the general region of extremely heavy snowfall. The higher resolution Stage- IV data may reveal some of the locations where heavier snow was observed. The higher resolution Stage-IV data showed locally higher amounts and seemed to show the hard hit areas of southern New York (Fig.22 lower panel). 5. CONCLUSIONS A strong nor easter brought strong winds, heavy rains, and heavy snow to the eastern United States on February This storm was relatively well predicted by the

6 NCEP models and ensemble forecast systems. These good forecasts were well interpreted by humans who issue forecasts to the public. There are many aspects of this storm worth of study. This was the 5 th major storm of with winter. It occurred as the Arctic Oscillation was rebounding toward zero. The storm was caught under the Rex Block (Fig. 3) and thus the surface system meandered over southern New England and New York. It spun down slowly over the northeastern United States. The -5 to -6SD wind anomalies, key features associated with historic winter storms (Stuart and Grumm 2006) were present with this event and generally well predicted in advance of the event. This was the 3 rd such event to produce such anomalous u-wind anomalies and it was the fifth high impact winter storm to affect the eastern United States. The winds and wind anomalies in Figure 6 clearly show the utility and value of u-winds in discriminating the ordinary from the potentially extraordinary storm. The combination of the block, the remnant early cyclone, and the strong easterly winds ahead of the developing storm produced an inverted thermal structure in the storm (Fig. 7). This unique thermal configuration produced rain in eastern and northern New England, extreme eastern interior New York and Quebec, while heavy snow fell from Pennsylvania, across New Jersey and into New York City and western Long Island. The plume of high PW was over the western Great Lakes by 27/0000 UTC (Fig. 8i). Quite an impressive storm system stuck under an equally impressive Rex Block. Both the NCEP SREF and GEFS predicted a strong if not major nor easter to impact the East Coast of the United States on February The signals for significant snow, heavy rain, and strong winds were well predicted by the models Forecasters clearly interpreted these data well. Some leveraged the information in other ways. The first key point here however is that models and ensembles predicted the event and humans interpreted these forecasts. Another critical issue in the GEFS and SREF products was the locations of the high and the low probability outcomes. Clearly, strong winds and significant QPF areas were outlined well by these systems. But as shown in Figure 19 there were sharp edges to the precipitation shields. On the edges of this storm and its potential impact were not so certain. In fact these locations were difficult to forecast and the uncertainty produced considerable forecast problems for those with a scientific bent and those trying to leverage uncertainty information. These issues were compounded significantly by assertive and definitive terms applied to this storm. Assertive terms often obfuscate problems along the edges of potential powerful storms. This causes a wide range of problems and issues that will not be resolved here. Suffice to say, forecasting along the edge of a significant storm is difficult. Forecasting along the edge of a storm that has been provided unique names presents an entirely new set of challenges. This storm garnered a lot of attention in the news media due to both its potential impact and the unique name assigned to the storm. For the most part, the storm lived up to many of the sensational reports and forecasts. It is left to others to comment on and sort out the impact, sensationalization, and value of the nomenclature associated with this and future storms. An important point to consider may not be the best way to convey information to the public, but rather the ethical implications of, and the wisdom in the sensationalization of science 2. However, the goal here is strictly one of scientific curiosity. Closing thoughts to ponder 2 Concept conveyed to me by Kito Holliday.

7 This storm was well predicted with a long lead time, in the high threat areas. This storm showed many signals that indicated a major nor easter and high impact events. M- TOTAL (Hart and Grumm 2000) and M-Clime (ECMF) products could be produced to highlight these areas. Most forecasters saw and recognized the pattern and its potential quite well. No human predicted this pattern. Forecasting along the edges was difficult where the large snow amounts and high winds were not so certain. Forecasting on the edges is made more difficult when the storm has been assigned unique and assertive names. Meteorology has 3 components, including science, information for decision making, and entertainment. 6. Acknowledgements Snowfall records were summarized by multiple National Weather Service Offices. The HPC summarized the heavy snow and rainfall data place into to the excel tables used here. The snowfall, rainfall, and wind gust maps were produced by an old friend, John LaCorte. Neil Stuart, Dave Schultz, Fred Carr, Kerry Emanuel, and others provided insights into issues of the media and weather. Kito Holliday provided the basis of the concept of science and scientific ethics. 7. REFERENCES Brown, R.F. and R.J. Younkin, 1970: Some Relationships between 850-mb Lows and Heavy Snow Occurrence over the Central and Eastern United States. Monthly Weather Review, 98, 5, Doty, B. E., and J. L. Kinter III, 1995: Geophysical data and visualization using GrADS. Visualization Techniques Space and Atmospheric Sciences, E. P. Szuszczewicz and Bredekamp, Eds., NASA, Goree, P.A., and R.J. Younkin, 1966: Synoptic Climatology of Heavy Snowfall over the Central and Eastern United States. Monthly Weather Review, 94, 11, Grumm, R.H. and R. Hart. 2001: Standardized Anomalies Applied to Significant Cold Season Weather Events: Preliminary Findings. Wea. and Fore., 16, Hart, R. E., and R. H. Grumm, 2001: Using normalized climatological anomalies to rank synoptic scale events objectively. Mon. Wea. Rev., 129, Higgins, R.W., Y. Zhou and H.-K. Kim, 2001: Relationships between El Niño-Southern Oscillation and the Arctic Oscillation: A Climate- Weather Link. NCEP/Climate Prediction Center ATLAS 8. ( Link to Atlas ) Hirsh, M.E, A.T.DeGaetano, S.J. Colucci,2000: An East Coast Winter Storm

8 Climatology.J.Climate,14, Junker, N.W, M.J.Brennan, F. Pereira, M.J.Bodner,and R.H. Grumm, 2009:Assessing the Potential for Rare Precipitation Events with Standardized Anomalies and Ensemble Guidance at the Hydrometeorological Prediction Center. Bulletin of the American Meteorological Society, 4 Article: pp Junker, N. W., R. H. Grumm, R. Hart, L. F. Bosart, K. M. Bell, and F. J. Pereira, 2008: Use of standardized anomaly fields to anticipate extreme rainfall in the mountains of northern California. Wea. Forecasting,23, Neiman, P.J., F.M. Ralph, G.A. Wick, J. D. Lundquist, and M. D. Dettinger, 2008: Meteorological characteristics and overland precipitation impacts of atmospheric rivers affecting the west coast of North America based on eight years of SSMI/satellite observations. J. Hydrometeor., 9, Mon. Wea. Rev., 132, Rex, D. F., 1950a: Blocking action in the middle troposphere and its effect upon regional climate. I. An aerological study of blocking action. Tellus, 2, , 1950b: Blocking action in the middle troposphere and its effect upon regional climate. II. The climatology of blocking action. Tellus, 2, Ryan, T and S Hanes, 2009 A Synoptic Climatology of Texas Winter Storms. NWA Digest,33, Younkin, R.J., 1968: Circulation Patterns Associated with Heavy Snowfall over the Western United States. Monthly Weather Review, 96, 12, Pelly,J.L, and B.J. Hoskins, 2003: A new perspective on blocking. JAS,60, Ralph, F. M., P. J. Neiman, and G. A. Wick, 2004: Satellite and CALJET aircraft observations of atmospheric rivers over the eastern North Pacific Ocean during the winter of 1997/98.

9 Location State Amount SCARBOROUGH 1 ME 8.38 STANDISH 2 W ME 7.48 DURHAM NH 6.73 GORHAM ME 6.68 SOUTH BERWICK ME 6.53 PORTLAND-DEERI ME 6.22 CONWAY NH 5.87 EAST ROCHESTER NH 5.85 LISBON FALLS ME 5.80 GRAY ME 5.63 EXETER 2 E NH 5.48 WESTPORT ISLAN ME 5.45 AUBURN ME 5.03 TANNERSVILLE NY 5.00 GROVELAND 1 WS MA 4.84 WINCHESTER 1 S MA 4.82 HOPE VALLEY 4 RI 4.76 MOUNT WASHINGT NH 4.73 STRAFFORD 1 SS NH 4.72 STERLING MA 4.71 LACONIA NH 4.63 CRANSTON 2 E RI 4.33 PORTSMOUTH/PEA NH 4.26 JAMAICA PLAIN MA 4.23 OAKDALE 3 WNW CT 4.04 AUGUSTA ME 3.99 PORTLAND 1 S CT 3.90 PLATTE COVE NY 3.66 GREENVILLE NH 3.40 BOSTON 1 WSW MA 3.23 Table 2. Summary of rainfall by location and State sorted by amount (inches). Only sites with over 3 inches of total rainfall are incluced. Full summary was provided by NOAA/NWS s Heavy Precipitation Unit.

10 Locations State Snow POTTER HOLLOW NY WOODFORD VT SLIDE MTN NY WOODRIDGE 6 S NY ALTAMONT 3 SSW NY RANDOLPH 4 WSW NH WEST HALIFAX VT BAYARD WE OAKLAND MD SPARTA TWP 4 E NJ LUDLOW VT HARRIMAN NY MONROE NY WARREN VT HAWLEY 2 NNW PA WAITSVILLE 2 W VT ROCKAWAY TWP 1 NJ GOSHEN NY LANDGROVE VT POMFRET 3 N VT WEST MILFORD NJ BEAR CREEK PA VERNON TWP 2 W NJ MONTAGUE NJ HIGHLAND LAKES NJ KANCAMAGUS NH RANDOLPH CENTE VT BROOKFIELD 2 W VT ROWE MA FARMINGTON PA TOBYHANNA PA HINES WV FOREST CITY PA CHESTERFIELD MA EAST LEMPSTER NH NYC/CENTRAL PA NY TEMPLE 1 WNW ME WINSTED 1 SE CT PIERPONT 2 SE OH MASON 6 NW MI 8.10 LYNCH 3 SE KY 7.80 ASHLAND NC 7.00 BURRILLVILLE RI 6.50 HOCKESSIN DE 5.60 Table 1. Summary of snowfall by location and State sorted by amount (inches). Only sites with over 24 inches of total snowfall are included for States where there were many reports. For States with far less snowfall the larges report was used. Full summary was provided by NOAA/NWS s Heavy Precipitation Unit.

11 Figure 4. GFS 00-hour analysis of 500 hpa heights (m) and anomalies over North America valid at a) 0000 UTC 25 February, b) 0600 UTC 25 February, c) 1200 UTC 25 February, d) 1800 UTC 25 February, e) 0000 UTC 26 February, f) 0600 UTC 26 February, g) 1200 UTC 26 February, h) 1800 UTC 26 February, and i) 0000 UTC 27 February Figure 3

12 Figure 5. As in Figure 3 except showing precipitable water and precipitable water anomalies.

13 Figure 6. As in Figure 3 except NAM 00-hour forecasts of mean sea level pressure (hpa) and pressure anomalies focused over the eastern United States.

14 Figure 7. As in Figure 5 except 850 hpa wind and u-wind anomalies.

15 Figure 8. As in Figure 6 except NAM 850 hpa temperatures and temperature anomalies.

16 Figure 9. As in Figure 5 except precipitable water and precipitable water anomalies.

17 Figure GEFS forecasts of mean sea-level pressure (hpa) and pressure anomalies the field is the mean of the 21 members pressure field. A forecast are valid at 1200 UTC 26 February 2010 from forecasts initialized at a) 1200 UTC 20 February, b) 0000 UTC 21 February, c) 1200 UTC 21 February, d) 1800 UTC 21 February, e) 0000 UTC 22 February, f) 0600 UTC 22 February, g) 1200 UTC 22 February, h) 1800 UTC 22 Febru and i) 0000 UTC 23 February 2010.

18 Figure 11. As in Figure 10 except GEFS 850 hpa winds (kts) and total wind anomalies valid at 1200 UTC 26 February 2010.

19 Figure 12. As in Figure 10 except ensemble mean liquid equivalent precipitation (mm). Note the QPF encompasses two events.

20 Figure 13 GEFS forecasts of mean sea-level pressure (hpa) and pressure anomalies the field is the mean of the 21 members pressure field. All forecast are valid at 1200 UTC 26 February 2010 from forecasts initialized at a) 0000 UTC 23 February, b) 1200 UTC 23 February, c) 0000 UTC 24 February, d) 0600 UTC 24 February, e) 1200 UTC 24 February, f) 1800 UTC 24 February, g) 0000 UTC 25 February, h) 0600 UTC 25 February, and i) 1200 UTC 25 February 2010.

21 Figure 14. As in Figure 13 except 850 hpa winds and total wind anomalies.

22 Figure 15. As in Figure 13 except GEFS mean QPF valid at 0000 UTC 27 February 2010.

23 Figure 16. GEFS forecasts of mean sea-level pressure (hpa) and pressure anomalies the field is the mean of the 21 members pressure field. All forecast are valid at 1200 UTC 26 February 2010 from forecasts initialized at a) 0300 UTC 23 February, b) 0900 UTC 23 February, c) 1500 UTC 24 February, d) 2100 UTC 23 February, e) 0300 UTC 24 February, f) 0900 UTC 24 February, g) 1500 UTC 24 February, h) 2100 UTC 24 February, and i) 0300 UTC 25 February Return to text.

24 Figure 17. As in Figure 16 except SREF 850 hpa winds and total wind anomalies.. Return to text.

25 Figure 18. As in Figure 17 except SREF 850 hpa winds and u-wind anomalies. Return to text.

26 Figure 19. SREF forecasts of 1 inch of QPF from forecasts initialized at 0300 UTC (left) 24 February and (right) 25 February Upper panels show the probability of 1 inch or more of QPF in 24 hours and the mean 1 inch contour. Lower panels show the ensemble mean QPF and each members 1 inch contour with the thick line showing the ensemble mean 1 inch contour.

27 Figure 20. As in Figure 19 except over the Mid-Atlantic region.

28 Figure 21. SREF initialized at 0300 UTC 25 February 2010 showing the probability of precipitation by type and the 3-hour instantaneous precipitation ending at 1200 UTC 26 February Types clockwise from top are rain, snow, ice pellets, and freezing rain.

29 Figure 22. Total Observed precipitation (mm) from the (top) the UPD and (bottom) the Stage-IV 4km data. Local maximums may not be presented by these data.