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MODULE 4.2D

SHORT RANGE FORECASTING OF , AND RESTRICTIONS TO VISIBILITY

Convective Cloud and Precipitation

Table of Contents

1. INTRODUCTION ...... 1

2. WARM CONVECTIVE ...... 1

ANALYSIS OF REAL DATA ...... 1 MODIFYING THE TEPHIGRAM...... 1 DIURNAL AND SEASONAL TRENDS ...... 2 SYNOPTIC CORRELATIONS TECHNIQUES...... 3 PHYSICAL PROCESSES APPROACH ...... 4 : WHAT TO DO WITH THEM ONCE YOU KNOW WHERE THEY ARE...... 8 3. WINTERTIME - SNOWSQUALLS ...... 9

AIR MODIFICATION TABLE...... 9 SNOWSQUALL FORECAST PROCEDURE ...... 11 NEW SNOWFALL TO ESTIMATED MELTWATER CONVERSION TABLE ...... 13

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1. INTRODUCTION Convective weather comes in a wide range of forms and sizes. The result of convection can be a variety of and weather ranging anywhere from relatively innocent cumulus to cumulonimbus thunderstorms to mesoscale convective complexes and tornadoes. In , convective activity is considerably subdued over the continental regions. Any that occurs is mostly constrained to areas lying over and to the lee of open water bodies or else is embedded in synoptic cloud associated with developing lows. Wintertime convective activity frequently results in snowsqualls and enhanced snowfalls.

The major portion of the material in the first section will cover warm season convective weather, which is generally applicable for the , summer and when low level heating is of significance. Wintertime convection, in the form of snowsqualls and enhanced snowfalls, will be covered in the second section.

2. WARM SEASON CONVECTIVE WEATHER A number of techniques for forecasting summertime convective weather are described below. These techniques include the careful analysis of real time data, selection and modification of a tephigram, a consideration of diurnal trends, use of synoptic correlations, and the physical processes approach. Following will be a discussion on short range techniques for forecasting thunderstorms once they have formed and once you know where they are.

Analysis of Real Time Data

Convective weather is a mesoscale event which develops and dissipates rapidly. That makes it an ideal problem for short range forecasting techniques. Careful analysis and diagnosis of real time data is crucial in forecasting all short range events including convective events. Of particular value is examining the hourly weather data to determine dynamic and thermodynamic forcings. Examples are dewpoint analysis, which highlights areas of available low level moisture and trough lines, which highlight lines of low level convergence. The forecaster can use both traditional surface analyses and areal displays of weather elements using workstation display tools to analyze the data. Satellite, radar, and are also short range analysis tools which give real time clues to the state of the .

Modifying the Tephigram

The basic tool for stability analysis and consequently, for and forecasting, is the tephigram. Convective weather of all types is associated with an unstable sounding or can be expected to occur after dynamic and thermodynamic processes act to produce an unstable sounding.

One of the most common techniques for first guessing the intensity of convective activity is selection and modification of a representative sounding. When a morning sounding is selected that could represent the airmass over a site of interest at forecast time, the 12Z profile must be

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modified in the low levels for daytime heating. When a 00Z representative sounding is used, on the other hand, the observed profile can be considered roughly representative of daytime heating. In general, the 12Z representative sounding is commonly used as a forecast tool while the 00Z sounding is more useful as a diagnostic tool. To have greatest utility, the representative sounding (whether 12Z or 00Z) should be modified for processes other than daytime heating. When time permits, the most satisfying approach is the production of a prognostic tephigram.

An alternative approach that has some utility is the estimation of stability changes at a site. It is a quick assessment of the thermal advections based on the current hodograph. By examining the hodograph, the forecaster can quickly assess stabilization and destabilization trends at the site and can adjust (qualitatively or quantitatively) the current sounding for these changes as well as for daytime heating effects.

Diurnal and Seasonal Trends

Diurnal trends must be considered when forecasting convective clouds and precipitation. As already mentioned, the most obvious diurnal trend is a maximum in convective activity near the time of greatest daytime heating and, in some locales, a secondary maximum near sunrise after greatest nocturnal cooling. In general, airmass thunderstorms tend to occur in the period from early afternoon to early evening with thunderstorms developing a bit later from about mid afternoon onwards. Frontal showers or thundershowers, on the other hand, may occur at any time although they may be more violent and widespread in the late afternoon to early evening due to the added contribution of daytime heating.

Given an airmass situation, Figure 1 is a fairly common summertime sequence of convection on a day when the air is rather convectively unstable and diurnal heating is of significance.

Figure 1.

The intensity of the convection, the rate at which it develops, and the areal coverage or frequency (i.e. scattered or broken, isolated, widespread) all depend upon the degree of instability and the amount of moisture available. When the airmass is relatively dry, the timing of the convection will be delayed considerably and the convection will be much decreased in intensity and frequency. When daytime heating wanes, as in the autumn months, airmass convective activity tends to be less intense and less widespread as well as delayed to the point of perhaps not reaching the shower or thundershower stages shown in the above sequence. In late spring, however, airmass convection can sometimes develop surprisingly rapidly and become intense and widespread. Forecasters sometimes forget the potential for airmass convection in

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spring; at this time, solar insulation increases rapidly and low level moisture often is abundant while the airmass aloft may be quite cool and convectively unstable.

In many sections of the country, a significant secondary maximum in airmass convective activity occurs near sunrise. This secondary maximum reflects radiative cooling at cloud top levels (usually mid levels). The ACC and TCU associated usually develop a couple of hours before or near sunrise and dissipate by midmorning. In climatologically susceptible regions, early morning ACC can be suspected if scattered to broken AC was present overnight or if significant convection the previous day dissipated during the evening or overnight. Sometimes, AC and ACC can appear to suddenly form near sunrise, even though little cloud was observed previously (a phenomenon which also could be related to the observation).

Synoptic Correlations Techniques

Synoptic correlation techniques have limited value in forecasting the development of convection. However, once the convection has formed and can be tied to a synoptic feature, the activity often can be forecast in the short term through association with the correlated features. When the convective activity has not yet formed, synoptic correlation techniques cannot really be applied unless, of course, it is assumed that yesterday's correlated convective patterns will also apply later today.

Considering the limitations inherent in synoptic correlation techniques (i.e. that the correlators are significant and that the correlations will persist), and considering the complexity of the thermal and dynamic influences that produce convective activity, much caution is advised if synoptic correlation is used to forecast development.

A few situations, however, can lend themselves to prediction by synoptic correlation techniques with reasonable success. Most of these situations involve dynamically strong synoptic features. An active , for example, that generated convective activity on one day often can be expected to persist this activity next day. Cold lows also can be very persistent in supporting convective activity - often diurnally. As the moisture associated with a cold low gradually decreases, the convection may change from embedded to that diurnally developed. A sample cloud pattern associated with a deep cold low is given in Figure 2. Note that much of the cloud can be convective. Sometimes, the convective weather associated with a summer cold low can become severe - a situation not unusual over the Prairies.

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Figure 2. Clouds Associated With An Upper Cold Low

Physical Processes Approach

The most successful of all procedures for forecasting convective activity might be described as the physical processes approach. Formal procedures have been developed by forecasters to achieve this objective. The procedures are a way for forecasters to summarize relevant factors to determine potential areas for convection. Once potential areas are established the forecaster establishes the threat, i.e. whether the convection will be ordinary or severe. An example of this is demonstrated in Module 6.4D Ingredients for Convective Weather using the Miller Technique and available on the CMC web site at:

http://iweb.cmc.ec.gc.ca/cmc/CMOP/tve/tve_e.html

A scaled down version is recommended for all forecasters to ensure a thorough Convective assessment. Table 1 is an example of a short Convective work up which the forecaster can use for both analysis and prognosis of convective parameters. The current discussion will not cover these procedures in detail but will attempt to present an overview of the factors that the forecaster should assess qualitatively in discerning the potential for convection.

Most severe weather occurs as a result of favourable thermal and dynamic fields interacting or meshing together. The amount and intensity of the convective weather that results is a function of the degree of “favourability” and the degree of interaction of the two. Favourable thermodynamic fields include those that support an unstable sounding while favourable dynamic fields are those that act to trigger or release instability. Generally, this “coming together” of the

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two fields must be phased properly with the diurnal heating (or cooling) cycle in order to support organized convection approaching significant proportions. Only a few cases normally occur where everything fits so well together that the added impetus of insolation is unnecessary. More commonly, ‘ordinary’ convective weather develops under situations where the favourable thermodynamics and favourable dynamics do not phase.

Figure 3. Terrain Induced Convective Clouds

What are the dynamic and thermodynamic processes that are favourable for convective activity? The discussion from Module 6.4D Ingredients for Convective Weather indicates that the presence of latent or potential instability in a sounding does not guarantee the occurrence of convection. The extra ingredient required is a trigger mechanism to initiate the parcel ascent and to release the instability. These trigger mechanisms can take the form of adiabatic or diabatic processes and both can act together or against each other, depending on the situation. Given that a representative sounding shows instability, the forecaster can expect any of the following triggers to play a role in releasing the instability and supporting the convection: • Large scale lift - PVA, thermal advection, boundary layer convergence (troughs), divergence aloft (). • Insolation - effective convective is reached. • Nocturnal cooling - see earlier discussion • Topographic (upslope) lift - CBs often form over higher ground, as shown in Figure 3.

Sometimes, the stability of the air column over a site can change in a very short period of time. An originally stable sounding can quickly become unstable due to several processes. One of the most common mechanisms for this change, which is conducive to convective activity, is cooling aloft. In summer, after sufficient heating in the low levels, the presence of a cold trough aloft can quickly trigger significant convection. As a result, some forecast centres have a practice of carefully analyzing the 500 mb isotherms at 2°C intervals during the warm season; some centres even use the thermal to modify their analysis and to obtain as much detail as possible on the strength and positions of cold troughs. The speeds of cold troughs can be obtained and

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positions forecast in the short term using chart history, satellite information, and hodograph information.

Another mechanism that can significantly increase the instability over an area is a combination of drying in the mid and upper levels and moisture advection in the lower levels. Often, the forecaster can be alerted to this process by quickly glancing at the 850 and 700 mb analyses. In summer, an increased 850 mb flow (low level jet) with warm moist air associated can bring considerable potential for significant convective activity, especially when coupled with a trigger such as daytime heating.

The greater the meshing of instability factors (thermodynamic) with the trigger factors (dynamic), the more intense, organized , and widespread the activity. The job of forecasting or timing these factors is not trivial.

Table 1 Convective Diagnosis/Prognosis Composite Chart - Short Version Feature/Comments Standard Symbol/colour Winds ) 250 mb (high-level) Jet. from isotach J130 analysis indicate max speed. (T+12 bold purple, T+0 dashed purple) 500 mb maximum-wind bands. - particular note is taken of splits in the 65 flow as well as any short wave amplification pattern. (bold blue) 700 mb maximum-wind band 50 (brown) ) 850 or 925 mb (low-level) Jet 35

(bold red) Convergence Zones 850 or 925 mb convergence zones. Use contours and wind patterns to find axis. (red) ) Boundary layer convergence as shown by the surface pressure and surface wind field. Indicate the flow (black) to highlight the maximum convergence areas. Thermal Ridge 850 mb and/or surface axis of maximum temperature. - the thermal ridge of greatest interest will lie just ahead of the strongest convergence zone (major trough). (red)

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Thickness Ridge ) 850-500 mb thickness ridge. - lines tend to develop about 150 km upstream. Take note of diffluent thickness ridges. (black) Theta-E Ridge 850 or 700 mb Theta-E ridge. - under a theta-e ridge if CBs are expected look for pooling of low lvl mstr, (MFC), to find location of first (brown) . CBs will likely merge into MCS. Moisture ) 850 mb axis of maximum moisture - use isodrosotherm analysis; start with 6c and then increase by 2c intervals. (green) 850 mb moist tongue - an area where (green) moisture is abundant, e.g. Td greater10 than 10°C, but note where Td>5°C. (MOIST) Significant moisture - from isodrosotherm analysis, scallop regions of dewpoint spread less than 6c. (MOIST) (brown) Dry Prod 700 mb dry-prod, or dry intrusion or dry line. Watch area where the max-wind band crosses from the dry to (DRY) significantly moist air. (brown) Positive Vorticity Advection 500 mb PVA - note areas coinciding with areas of warm thickness advection. (yellow) Temperature Advection ) 700 mb temperature advection. “CAP” - warm air advection (coloured red) “NO implies region is “CAPPED”, cold air CAP” advection (blue) implies “No CAP” Cold trofs(axis of coldest air) ) 500mb isotherm analysis at 2°C intervals. Outline / label cold pools and areas of cold advection. (blue)

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THUNDERSTORMS: What to do with them once you know where they are.

Depending on the causes, the following guidelines can be considered:

1. For thunderstorms along fronts or associated with synoptic features, the motion will be with the features causing them. When the area of convective precipitation is rather large, then one of the following can give a direction of motion: a) use the direction given in radar reports; b) move the thunderstorm at the direction and speed of the 700 mb flow; c) note the direction and speed of the anvil from the satellite images, but watch for thunderstorms that are merging.

2. Daytime heating, or airmass, thunderstorms tend to move with the upper 700 mb flow, but normally remain over sources of heat. Thus, large cold water bodies or developing sea or lake breezes may protect a site from advancing storms. Here, radar and satellite photos can be a great help in deciding the motion of the thunderstorms.

3. When low level moisture is the main cause, the thunderstorms will dissipate after leaving the area of moisture. For example, when moisture for nearby thunderstorms is provided by a large river in the valley, the result is the dissipation of the storms after leaving the moisture source.

4. Thunderstorms caused by lift over higher ground tend to remain tied to the topographic feature. Occasionally, but not frequently, a dissipating thunderstorm will drift over a station in a large valley.

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3. WINTERTIME CONVECTION - SNOWSQUALLS Each winter, heavy snowfall to the lee of open water on the can cripple transportation and communications in the belt areas of Ontario. These areas hit the news more regularly than other parts of the country that are just as critically affected by such snowfalls. In particular, areas downwind from open water in the Atlantic Provinces, the Manitoba lakes, and areas to the south and east of Hudson Bay can receive significant snowfalls.

The diagnosis of lake and sea induced snowfalls is presented in Document 3.1F and a more detailed discussion can be found in Module 6.4G Lake and Sea Induced Snowfalls. The following discussion is a brief summary of the material presented in that document.

The heaviest accumulations from snowsqualls occur when synoptic factors interact with those on the mesoscale. Typically, snowsqualls can be expected when the temperature difference between the air and the water surface reaches 5-10°C or more and when the difference in temperature between the water and 700 mb reaches at least 25°C. More intense convective cells usually develop over water under the support of a surface trough and a broad trough aloft. Heavy accumulations are also more likely to result when the cold air has a long fetch over water.

The forecaster can gauge the potential for lake or sea induced snow from the tephigram. Information on bases, tops, and thicknesses of the convective clouds and hence, on the intensity of the expected snowsqualls, can be obtained from a tephigram representative of the cold air. A tephigram is needed that could represent the convective conditions possible once cold air crosses open water. The best approach is to pick a tephigram that represents the cold air upstream from the water body. Then the air in the lowest levels can be modified to account for the heat and moisture fluxes added during a fetch over water.

The results of studies such as the one summarized in the Air Modification Table can be used to account for the heat (and moisture) input. The bases of convective clouds can be estimated from the now representative tephigram while expected tops can be estimated by considering positive and negative energy areas. There are also upper air factors which lead to favourable conditions for developing snow squall activity, and these are discussed in Documents 3.1F and 6.4G.

Once snowsqualls have formed, the forecaster has the benefits of radar and satellite imagery to follow the movement and changes in the snow system.

AIR MODIFICATION TABLE

This table was computed from Phillips’ regression equation (1970). The time over water used was 120 minutes. More than half of the total modification of the air occurs In the first 10 minutes over water. To use the table, input the water temperature and the temperature of the air being advected over the water to obtain the modified air temperature.

Water Temperature (oC)

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Air Temp 0 2 4 6 8 10 12 14 16 18 20 -30 -20 -18 -19 -17 -15 -14 -13 -12 -11 -10 -9 -27 -18 -17 -16 -15 -14 -13 -11 -10 -9 -8 -7 -24 -16 -15 -14 -13 -12 -11 -10 -9 -8 -6 -5 -21 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -18 -13 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -15 -11 -10 -9 -8 -6 -5 -4 -3 -2 -1 0 -12 -9 -8 -7 -6 -5 -4 -2 -1 0 1 2 -9 -6 -6 -5 -4 -3 -2 -1 0 1 3 4 -6 -4 -4 -3 -2 -1 0 1 2 3 4 5 -3 -1 -2 -1 0 1 2 3 4 5 6 7 0 0 1 1 2 3 4 5 6 7 8 9 3 2 3 4 5 5 6 7 8 9 10 11 6 3 5 5 6 7 8 9 9 10 12 13 9 4 6 7 8 9 10 11 11 12 13 14 12 6 6 8 9 10 11 12 13 14 15 16 15 7 8 9 10 11 12 14 15 16 17 18 18 8 9 10 11 12 13 15 16 17 18 19 21 8 10 11 12 13 14 16 17 18 20 21 24 9 10 12 13 14 15 16 18 19 20 22 27 10 11 12 14 15 16 17 18 19 21 22 30 11 12 13 15 16 17 18 19 20 21 23

Regression equations were also developed for dew point modification. Although the results will occasionally be slightly different, the above table may also be used for dew point modification and will give an acceptable approximation. Just input dew points instead of air temperature.

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Snowsquall Forecast Procedure

The following checklist is an adaptation from the technical paper “Forecasting Lake Effect Snow in Ontario” produced by the Ontario Weather Centre. Step 1 of the procedure helps the forecaster determine which type of snowfall may be possible for a given situation based on dynamic and thermodynamic factors. Step 2 determines if the forecaster is dealing with “pure lake (sea) effect snow”, “lake (sea) enhanced snow”, or “combination snow”. Finally, step 3 determines the impact that the strength of the wind has on the forecast; both in terms of blowing and drifting snow, as well as the probable distance inland of the heaviest snowfall accumulation.

Step 1: Basic Assessment

1/ Will TWATER – T850 be at least 13°C? Yes…....go to question 4. No…….go to question 2.

2/ Is there expected to be an 8°C difference between the water and 850 mb?

3/ Is upper level ascent expected to occur (VV700 > 0 from FOCN03)? Yes to both questions…water enhanced snow is possible. Go to step 2 – part B. Otherwise…snowsqualls are unlikely.

4/ Is upper level ascent expected to occur (VV700 > 0 from FOCN03)? Yes…Combination snow is possible. Go to step 2 – part C. No…..Pure snowsqualls are possible. Go to step – part A.

Step 2

Part A - Pure Snowsquall

A1/ Is open water fetch expected to be ≥ 80 nm? Yes...Go to question A2. No...Snowsqualls are unlikely.

A2/ Is low level convergence (cyclonic curvature, thermal troughing) expected to be in evidence?

A3/ Is strong subsidence not expected to occur at mid levels? (i.e. VV700 > -2) Yes to both questions...Go to A4. Otherwise snowsqualls unlikely.

A4/ What is the expected directional shear below 700 mb? ≤ 30°...Heavy snow bands ⇒ 1/8-1/2SM (8-12 cm/6hr). If (TWATER - T850 ≥ 20°) ⇒ 0SM and 12-20cm/6hr. Go to step 3.

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30°-60°...Shifting snow bands ⇒ ¾-11/4SM (3-6 cm/6hr). If (TWATER - T850 ≥ 20°) ⇒ 1/4sm (5-10 cm/6hr). Go to step 3.

Part B - Water Enhanced Snow

B1/ Is open water fetch ≥ 30 nm? Yes...Go to question B2. No...accumulation due to water enhancement unlikely.

B2/ Is strong upper level ascent expected to occur (VV700 ≥ +2)? Yes...Go to question B4. No...Go to question B3.

B3/ What is the expected directional shear below 700 mb? ≤ 30°...A few hours of heavy snow ⇒ ¾-11/4SM (5-10 cm/6hr). Caution must be used if winds are expected to shift during the period. Go to step 3. 30°-60°...Few snowsqualls ⇒ ¾-11/4SM (3-6 cm/6hr). Go to step 3.

B4/ What is the expected directional shear below 700 mb? ≤ 30°...Heavy snowsqualls ⇒ 0-1/4SM (10-20 cm/6hr). Caution must be used if winds are expected to shift during the period. Go to step 3. 30°-60°...Few heavy snowsqualls ⇒ ¾-11/4SM (5-10cm/6hr). Go to step 3.

Part C - Combination Snow

C1/ Is open water fetch expected ≥ 80 nm? Yes...Go to question C2. No...Water enhanced snow may be possible. Go to part B.

C2/ Is strong upper level ascent expected to occur (VV700 ≥ +2)? Yes...Go to question C4. No...Go to question C3.

C3/ ≤ 30°...Heavy snow bands ⇒ 1/8-1/2SM (10-15cm/6hr). If (TWATER - T850 ≥ 20°) ⇒ 0SM and 15-25 cm/6hr. Lesser amounts with shifting winds. Go to step 3. 30°-60°...Moderate multiple banded snowsqualls ⇒ ½-3/4SM (5-8 cm/6hr). If (TWATER - T850 ≥ 20°) localized heavy bands ⇒ 1/8-1/2SM (8-12 cm/6hr). Lesser amounts in shifting winds. Go to step 3.

C4/ What is the expected directional below 700 mb? ≤ 30°...Very heavy snow bands ⇒ 0-1/8SM (12-20 cm/6hr). If (TWATER - T850 ≥ 20°) 0SM and 20-30cm/6hr. Lesser amounts with shifting winds. Go to step 3. 30°-60°...Heavy snowsqualls ⇒ 1/8-1/2SM (8-12cm/6hr). If (TWATER - T850 ≥ 20°) ⇒ 0-1/8SM (12-20 cm/6hr). Lesser amounts in shifting winds. Go to step 3.

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Step 3 - Wind Effects

1/ Is the 950 mb (2000 ft) wind expected to be ≥ 20 kts? Yes...Go to question 2. No...Drifting snow and blowing snow are not expected to be significant. Heaviest snow accumulations close to shore.

2/ What is the expected 950 mb (2000 ft) wind speed? < 30 kts...Frequent drifting snow. Heaviest snow accumulations close to shore. 30-40 kts...Blowing snow and drifting snow significantly reducing visibility. Heaviest snow accumulation somewhat inland. > 40 kts...Heavy blowing snow and drifting snow causing frequent whiteouts and near conditions. Heaviest snow accumulation well inland (up to 70 nm).

NEW SNOWFALL TO ESTIMATED MELTWATER CONVERSION TABLE

The following table has been adapted from the United States Department of Commerce (1997). This table can be used for determining the amount of newly fallen snow based on captured melt water. Equivalently, this table can be used to determine the amount of melt water based on measured snow depth and the average temperature at which the snow fell. It should be noted that this table should not be used for determining the water equivalency of “old snow”. Packing, melting and re-freezing all have substantial effects on the density of snow.

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MELTWATER NEW SNOWFALL (CENTIMETRES) EQUIVALENT Temperature (°C) (mm) 1.0 to - -2.0 to - -6.7 to - -9.4 to - -12.2 -17.8 - -28.9 - 2.2 6.7 9.4 12.2 -17.8 28.9 40.0 Trace Trace 0.25 0.51 0.76 1.02 1.27 2.54 0.25 0.25 0.51 0.51 0.76 1.02 1.27 2.54 0.51 0.51 0.76 1.02 1.52 2.03 2.54 5.08 0.76 0.76 1.27 1.52 2.29 3.05 3.81 7.62 1.02 1.02 1.52 2.03 3.05 4.06 5.08 10.16 1.27 1.27 2.03 2.54 3.81 5.08 6.35 12.70 1.52 1.52 2.86 3.05 4.57 6.10 7.62 15.24 1.78 1.78 2.79 3.56 5.33 7.11 8.89 17.78 2.03 2.03 3.05 4.06 6.10 8.13 10.16 20.32 2.29 2.29 3.56 4.57 6.86 9.14 11.43 22.86 2.54 2.54 3.81 5.08 7.62 10.16 12.70 25.40 2.79 2.79 4.32 5.59 8.38 11.18 13.97 27.94 3.05 3.05 4.57 6.10 9.14 12.19 15.24 30.48 3.30 3.30 5.08 6.60 9.91 13.21 16.51 33.02 3.56 3.56 5.33 7.11 10.67 14.22 17.78 35.56 3.81 3.81 5.84 7.62 11.43 15.24 19.05 38.10 4.06 4.06 6.10 8.13 12.19 16.26 20.32 40.64 4.32 4.31 6.60 8.64 12.95 17.27 21.59 43.18 4.57 4.57 6.86 9.14 13.72 18.29 22.86 45.72 4.83 4.82 7.37 9.65 14.48 19.30 24.13 48.26 5.08 5.08 7.62 10.16 15.24 20.32 25.40 50.80 5.33 5.33 7.87 10.67 16.00 21.34 26.67 53.34 5.59 5.59 8.38 11.18 16.76 22.35 27.94 55.88 5.84 5.84 8.63 11.68 17.53 23.37 29.21 58.42 6.10 6.10 9.14 12.19 18.29 24.38 30.48 60.96 6.35 6.35 9.65 12.70 19.05 25.40 31.75 63.50 7.62 7.62 11.43 15.24 22.86 30.48 38.10 76.20 8.89 8.89 13.46 17.78 22.67 35.56 44.45 88.90 10.16 10.16 15.24 20.32 30.48 40.64 50.80 101.6 11.43 11.43 17.27 22.86 34.29 45.72 57.15 114.3 12.70 12.70 19.05 25.40 38.10 50.80 63.50 127.0 15.24 15.24 22.86 30.48 45.72 60.96 76.20 152.4 17.78 17.78 26.67 35.56 53.34 71.12 88.90 177.8 20.32 20.32 30.48 40.64 60.96 81.28 101.6 203.2 22.86 22.86 34.29 45.72 68.58 91.44 114.3 228.6 25.40 25.40 38.10 50.80 76.20 101.6 127.0 254.0 50.80 50.80 76.20 101.6 152.4 203.2 254.0 508.0 76.20 76.20 114.3 152.4 228.6 304.8 381.0 762.0

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