Let LR(e) = Environmental lapse
rate.
Let LR(p) = Parcel lapse rate.
Let LR(da) = Dry adiabatic lapse rate (dry
ascent).
Let LR(ma) = Moist adiabatic lapse rate
(saturated ascent).
For dry/unsaturated convection, LR(p) = LR(da).
For moist/saturated convection, LR(p) =
LR(ma).
TT = VT +
CT
VT = T(850
mb) - T(500 mb)
CT = Td(850
mb) - T(500 mb)
in degrees C, where T represents temperature at the indicated level and Td represents dewpoint temperature.
VT = 40 is close to dry adiabatic for the 850-500 mb layer. However, VT generally will be much less, with values around 26 or more representing sufficient static instability (without regard to moisture) for thunderstorm occurrence. CT > 18 often is necessary for convection, but it is the combined Total Totals Index that is most important.
TT = T(850 mb) + Td(850 mb) - 2[T(500 mb)] in degrees C.
10.2 deg C/km: | Dry adiabatic lapse rate (700-500 mb) |
DTI = 26 deg C in warm season: | Dry adiabatic lapse rate (700-500 mb) |
6.5 C/km for 700 mb temp = 0 C: | Moist adiabatic lapse rate (700-500 mb) |
6.0 C/km for 700 mb temp = +5 C: | Moist adiabatic lapse rate (700-500 mb) |
5.6 C/km for 700 mb temp = +10 C: | Moist adiabatic lapse rate (700-500 mb) |
DTI = 18 C in warm season: | Moist adiabatic lapse rate (700-500 mb) |
K = T(850 mb) + Td(850 mb) - T(500 mb) - DD(700 mb)
in degrees C, where T represents temperature,
Td represents dewpoint temperature, and DD represents dewpoint depression
at the indicated level.
In general, the higher the ambient or inflow K
index value, the greater the potential for heavy rain. However, beware
of low (less than 30) values of K. Since the K index includes the dewpoint
depression (i.e., difference between the temperature and dewpoint temperature)
at 700 mb, dry air at this level will cause a low K value. However, given
moisture below 700 mb, unstable air, and a lifting mechanism, strong or
severe organized thunderstorms, and even heavy rain, can still occur. Scattered
diurnal convection occurring in an environment containing high K (and PW)
values can cause a quick burst of very heavy rain.
LI = T(500 mb envir) - T(500 mb parcel)
in degrees C, where T (500 mb envir) represents
the 500 mb environmental temperature and T (500 mb parcel) is the rising
air parcel's 500 mb temperature.
These LI values are based on lifted parcels using the average lowest 50 to 100 mb moisture and temperature values (i.e., the boundary layer). Variations exist on how LI values are calculated, as discussed below.
Surfaced-based LI: Surface-based LIs can be calculated hourly, and assume a parcel is lifted from the surface using surface-based moisture and temperature values, as well as assigned environmental temperatures at 500 mb. This method is valid for a well-mixed nearly dry adiabatic afternoon boundary layer where surface characteristics are similar to those in the lowest 50 to 100 mb layer. However, these values would not be representative of the ambient elevated instability if a nocturnal inversion or shallow cool air to the north of a frontal boundary is present. In these cases, more instability resides above the surface, and parcels may be lifted to form thunderstorms from the top of the inversion.
Best LI: The Best LI represents the lowest (most unstable) LI computed from a series of levels from the surface to about 850 mb. This index is most useful during cases when shallow cool air exists north of a frontal boundary resulting in surface conditions and boundary layer-based LI values that are relatively stable. However, the airmass at the top of the inversion, from which lifting may occur, is potentially unstable. An example of this would be elevated ("overrunning") convection (possibly a nocturnal MCS).
SI = T(500 mb envir) - T(500 mb parcel) in degrees C.
Generally, SI values will not be quite as unstable as LI values (except for the case of shallow low-level cool air discussed above).
DCI = T(850 mb) + Td(850 mb) - LI(sfc-500 mb)
in degrees C, where LI represents the lifted index value from the surface to 500 mb.
This is a relatively new index. Therefore, no definitive critical values have been determined. However, DCI values of roughly 30 or higher indicate the potential for strong thunderstorms. Ridge axes of DCI may be even more important and a location for thunderstorm development given the presence of upward motion.
SWEAT = 12 [Td(850 mb)] + 20 (TT - 49) + 2 (f8) + f5 + 125 (S + 0.2)
where TT represents the total totals index value, f8 and f5 represent the 850 mb and 500 mb wind speed in knots, respectively, and S = sin (500 mb minus 850 mb wind direction), i.e., the sine of the angle between the 500 and 850 mb wind directions (the shear term).
The last term in the equation (the shear term) is set to zero if any of the following criteria are not met: 1) 850 mb wind direction ranges from 130 to 250 degrees, 2) 500 mb wind direction ranges from 210 to 310 degrees, 3) 500 mb wind direction minus the 850 mb wind direction is a positive number, and 4) both the 850 and 500 mb wind speeds are at least 15 kts. No term in the equation may be negative; if so, that term is set to zero.
SWEAT over 300:
Potential for severe thunderstorms.
SWEAT over 400:
Potential for tornadoes.
These are guidance values developed by the U.S. Air Force. Severe storms may still be possible for SWEAT values of 250-300 if strong lifting is present. In addition, tornadoes may occur with SWEAT values below 400, especially if convective cell and boundary interactions increase the local shear which would not be resolved in this index. The SWEAT value can increase significantly during the day, so low values based on 1200 UTC data may be unrepresentative if substantial changes in moisture, stability, and/or wind shear occur during the day. Finally, as with all indices, the SWEAT only indicates the potential for convection. There must still be sufficient forcing for upward motion to release the instability before thunderstorms can develop.
CAPE represents the amount of buoyant energy available to accelerate a parcel vertically, or the amount of work a parcel does on the environment. CAPE is the positive area on a sounding between the parcel's assumed ascent along a moist adiabat and the environmental temperature curve from the level of free convection (LFC) to the equilibrium level (EL). The greater the temperature difference between the warmer parcel and the cooler environment, the greater the CAPE and updraft acceleration to produce strong convection.
EL
CAPE = g { [(Tparcel
- Tenvir) / Tenvir] dz
LFC
in Joules/kg. The "{" symbol here represents a vertical integration between the LFC (level of free convection, above which the parcel is warmer than the environment, i.e., the parcel is positively buoyant and will rise) and the EL (equilibrium level, below which the parcel is warmer than the environment).
The above values are based on a parcel lifted with the average temperature and moisture of the lowest 50 to 100 mb layer (i.e., the boundary layer). The value of CAPE is dependent on the level from which a parcel is lifted. Parcels lifted from the surface usually exhibit a higher (sometimes significantly higher) CAPE value than for those lifted using mean boundary layer characteristics.
While CAPE is sensitive to the properties utilized to initialize a parcel, CAPE often is a much better indicator of instability than indices which depend on level data (e.g. lifted index, total totals index, etc). CAPE involves an integration over a depth of the atmosphere and is not as sensitive to specific sounding details.
Using CAPE, the maximum updraft speed in a thunderstorm (w-max) at the equilibrium level can be calculated. In general, w-max = square root of [2(CAPE)] . For example, a range of CAPE of 1500-2500 J/kg gives a w-max range of about 50-70 m/s (100-140 kts). However, due to water loading, mixing, entrainment, and evaporative cooling, the actual w-max is approximately one-half that calculated above.
Finally, the profile or shape of the positive area is important, besides the actual CAPE value. Two soundings could have the same CAPE value, but lead to different convective characteristics due to differences in the shape of the area between the LFC and EL. For example, given the same CAPE value in each, a longer, narrower profile represents the potential for a slower updraft acceleration but taller thunderstorms which is best for high precipitation efficiency. However, a shorter, fatter profile would lead to a more rapid vertical acceleration which would be important for potential development of updraft rotation within the storm.
LSI = Qsw - Qwmax
where Qsw is the maximum saturated Qw (wet bulb potential temperature) between the surface and 500 mb, and Qwmax is the maximum Qw in the lowest 100 mb of the atmosphere.
LSI below 2: | Deep convection generally should not be inhibited. |
LSI above 2: | Deep convection may be suppressed unless sufficient heating, moisture convergence, and/or forced lift overcomes the cap. |
BRN = CAPE / [0.5 (U2)]
where U is a measure of the vertical wind shear in the 0-6 km layer AGL, and U2 simply means U squared, i.e., U taken to the second power. BRN is a dimensionless number.
BRN below 10: | Strong vertical wind shear and weak CAPE. The shear may be too strong given the weak buoyancy to develop sustained convective updrafts. However, given sufficient forcing, thunderstorms may still develop; if so, rotating supercells could evolve given the high shear. |
BRN = 10 to 45: | Associated with supercell development. |
BRN over 50: | Relatively weak vertical wind shear and high CAPE which suggests multicellular thunderstorm development is most likely. |
For BRN values of about 45 or less, the strongly sheared environment is crucial in producing a steady, persistent rotating updraft. This occurs as the ambient vertical wind shear and enhanced horizontal convergence increase the horizontal vorticity, which then is tilted into the vertical updraft. Due to mass continuity considerations, vertical divergence is required resulting in an accelerating updraft with height (i.e., vertical stretching). This, in turn, increases the vorticity about a vertical axis causing the development and strengthening of the mesocyclone. The strong rotation then induces a dynamic lowering of the pressure within the storm which further enhances the steady-state updraft.
Conversely, BRNs around or above 50 often result in multicell development as multiple non-steady updrafts develop due to the high buoyancy but weaker wind shear. However, these cells still could well produce severe weather. In addition, supercells cannot totally be ruled out for two reasons. First, rapidly stretching air in the vertical due to an accelerating updraft (high CAPE) could create enough horizontal convergence to generate vertical vorticity and overcome the limited ambient wind shear, although strong mesocyclones are not likely. Second, thunderstorm and/or boundary interactions can increase the ambient shear and thus produce a local environment that may support supercell development, even within a larger convective regime where no supercells were expected (i.e., a high BRN). However, environments with BRN values much greater than 50 generally will not support supercells.
BRN shear = 0.5 (Uavg)2
in m2/s2, where Uavg, the magnitude difference between the 0-6 km mean wind in the lowest 0.5 km, is squared (i.e., taken to the second power).
BRN shear = 25 to 100 | Associated with tornadic supercells (assuming supercells form on a given day). |
However, values from 25 to 50 can be associated with tornadic and non-tornadic storms, with values near and above 50 more likely to be associated with tornadoes. Nevertheless, BRN shear, which is sensitive to low-level winds and is a function of he degree and depth of the wind shear, tends to be higher for tornadic storms than for non-tornadic storms as lower BRN shear values reflect weaker environmental wind shear. Also, favorable BRN shear values combined with favorable 500 mb storm-relative winds (see section below) are more likely to be associated with tornadic supercells.
500 mb S-R winds = 16 kts (8 m/s) | Lower limit for tornadic supercells. |
500 mb S-R winds = 40 kts (20 m/s) | Approximate upper limit for tornadic supercells |
While tornadic and non-tornadic storms supercells are possible with BRN shear values from 25-50 m2/s2 (see above discussion), tornadic storms in this range are more probable when 500 mb S-R winds are greater than 20 kts (10 m/s). Of course, favorable 500 mb S-R winds does not guarantee tornadogenesis; one must assess radar trends and convective-scale processes. Thus, sufficient S-R winds at 500 mb appears to be a necessary, but not sufficient condition for tornadic supercell storms.
Tornado potential is highest when 500 mb S-R winds are relatively high and low-level storm inflow can be enhanced through boundaries, mesolows, etc. Strong low-level inflow and convergence enhances the generation of baroclinically-induced horizontal vorticity along the forward front downdraft boundary. This vorticity then funnels into the weak echo region where it is tilted vertically and stretched rapidly upward (due to the middle-level mesocyclone). This process can enhance the low-level mesocyclone resulting in tornado development or maintenance.
Hs-r = { (v - c) . W dz
where v = actual ground-relative wind vector,
c = storm motion vector, (v - c) = storm-relative wind vector, W = horizontal
vorticity vector, the dot "." represents a mathematical dot product,
and the "{" represents a vertical integration over a specified depth
(usually the lowest 2 or 3 km of the atmosphere). Units are m2/s2 (i.e.,
meters squared divided by seconds squared).
These values are based on the 0-3 km layer. They assume a storm motion of 1) 20 degrees to the right of the mean wind and at 85 percent of the mean wind speed for 0-6 km mean wind speeds greater than 30 kts, and 2) 30 degrees to the right at 75 percent of the speed for mean speeds less than 30 kts. In other words, these helicity values assume that given thunderstorm development, storms will be right movers with respect to the mean wind with a storm motion "off" the hodograph. In assessing helicity, make sure to consider what the vertical wind shear profile will be at the time of thunderstorm development and what the actual storm motion is. The VAD wind profile (VWP) on the WSR-88D can help greatly in assessing wind speeds and shear in the local environment. Remember that even if the environmental S-R helicity is relatively low, tornadoes are still possible if mesoscale shear regions (not detected synoptically) exist or if interactions between convective cells and boundaries increase the local shear.
S-R helicity is quite sensitive to storm motion and the magnitude of the vertical directional and speed shear. For example, a thunderstorm moving to the right of the mean wind within a vertically-sheared environment will experience higher S-R helicity and S-R flow into the storm than an ordinary cell moving with the mean wind (i.e., "on" the hodograph). In fact, much of the information contained within S-R helicity also can be evaluated from just looking at the shape and length of the hodograph.
EHI = [CAPE (Hs-r)] / 160,000 EHI is a dimensionless number.
The full operational utility of the EHI is not yet completely known. In addition, there is some discrepancy as to what the minimum threshold is for severe thunderstorms and tornadoes. However, general threshold values are given below.
The height of the wet bulb zero is that level on the sounding whereby the lowest temperature attainable (given the ambient temperature and dewpoint at that level) through isobaric evaporation of water is zero degrees C, i.e. Tw = 0 C at this level.
In general, WBZ heights from5,000 to 12,000 ft AGL are associated with hail at the ground. The potential for large hail is highest for WBZ heights of 7,000 to 10,000 ft AGL, with rapidly diminishing hail size below 6,000 and above 11,000 ft AGL. Above 11,000 ft, hail is less common since it has a smaller depth in which to form and may melt before reaching the ground due to a significant warm cloud layer below. However, very heavy rain may occur in these cases. WBZ values too low indicate a shallow warm cloud depth with less warm cloud collision-coalescence occurring to provide the necessary liquid drops and droplets to increase hail size.
Research has suggested that a crucial factor for hail growth is the presence of a broad region of moderate updraft (20-40 m/s), and that hail growth typically occurs on the edges and not within a storm's strongest updraft.
Evaluation of the sounding WBZ height and freezing level are very important in determining whether a given environment has the potential to produce small hail, large hail, or no hail but possibly heavy rain. A very warm airmass/high 1000-500 mb thickness value would contain high WBZ and freezing level heights while a significant trough or cold air aloft would lower these heights significantly. This also relates to the Vertically Integrated Liquid (VIL) product on the WSR-88D. A warm airmass may mean a high "VIL of the day" threshold for hail, while cold air aloft could mean a much lower "VIL of the day." In other words, VIL thresholds for hail can change daily, with a meaningful VIL value one day being less significant another day. Thus, local studies to stratify pertinent VIL values versus various environments are important. For example, the parameter "VIL density" has been established to overcome some of the shortcomings of using VIL by itself. In short, VIL density can be used to identify those storms with high VIL values relative to the storms' echo tops in order to assess large hail potential.