Env Parameters and Indices

Convective Season Environmental Parameters and Indices

Evaluation of Stability

Lapse rate: Refers to the rate of temperature change with height in the atmosphere. A steep lapse rate is one in which the environmental temperature decreases rapidly with height. The steeper the environmental lapse rate, the more potentially unstable is the atmosphere.

• Absolute stability:
  LR(e) < LR(p)   (Parcel lapse rate has a steeper slope than the environment, i.e., parcel is cooler than the surrounding environment).
• Neutral stability:
  LR(e) = LR(p)   (Parcel lapse rate has the same slope as the environment).
• Absolute instability:
  LR(e) > LR(p)   (Parcel lapse rate has less slope than the environment, i.e., parcel is warmer than the surrounding environment).
• Conditional instability:
  Exists when the environmental lapse rate curve LR(e) is between the dry [LR(da)] and moist [LR(ma)] adiabatic lapse rate curves on a SkewT-LogP diagram. In these cases, the atmosphere is unstable with respect to saturated (the "condition") parcel ascent [i.e., LR(p) = LR(ma)] since the rising parcel will be warmer than the environment.
• Potential (convective) instability:
  Exists when Qe or Qw (equivalent and wet bulb potential temperature, respectively) decreases with height (dQe/dz < 0). When this occurs, an initially stable layer will destabilize as it is lifted, since the top of the layer will cool faster than the bottom, thereby steepening the lapse rate. In reality, whole layers may not be lifted at once; instead, parcels often lift from the boundary layer to their level of free convection (LFC) to form thunderstorms. Thus, the physical process that potential instability represents may or may not occur often during convection. However, Qe (which is more sensitive to moisture than temperature) decreasing with height IS important, since it represents the presence of dry air above moist air which enhances downburst and possibly hail potential if thunderstorms develop.

Evaluation of Moisture

An evaluation of moisture is critical for determining the potential for convection, severe weather, and heavy rainfall. Thunderstorms can develop in an area of significant ambient or inflow moisture. In evaluating moisture, consider the surface to 700 mb dewpoints, 1000-500 mb precipitable water (PW), the K index, and moisture convergence. During the warm season, rough threshold values (and higher values representing better potential) for heavy rain include:

• Surface dewpoint:  60 F (70 F)
• 850 mb dewpoint:  10-12 C (14 C)
• 700 mb moisture:  Can be moist or relatively dry for heavy rain and severe weather. However, moisture increases precipitation efficiency, while dry air (dewpoint depression roughly 10 C or more) increases convective instability and downburst/hail potential.
• 1000-500 mb PW:  1.0 inch (1.5 inches)
• K index:  30 (35).  K values will be lower if dry air is present at 700 mb, but severe weather or even heavy rain still can occur (see K index section).

These are rough numbers and heavy rain or severe weather may still occur at values below these, especially if significant forcing is present, or during the cool season.

Total Totals Index (TT)

The Total Totals Index consists of two components, the Vertical Totals (VT) and the Cross Totals (CT). The VT represents static stability or the lapse rate between 850 and 500 mb. The CT includes the 850 mb dewpoint. As a result, TT accounts for both static stability and 850 mb moisture, but would be unrepresentative in situations where the low-level moisture resides below the 850 mb level. In addition, convection may be inhibited despite a high TT value if a significant capping inversion is present.

    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.

Delta-T Index (DTI)/700-500 mb Lapse Rate

These parameters assess the contribution of middle-level lapse rate to convective instability. A steep 700-500 mb lapse rate overtop low-level moisture is quite favorable for strong/severe convection including microbursts and hail. The DTI measures the temperature difference between two mandatory pressure levels (often 700-500 mb). The DTI is similar to the Vertical Totals.

K Index

The K index is a measure of thunderstorm potential based on the vertical temperature lapse rate, and the amount and vertical extent of low-level moisture in the atmosphere.

     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.
 

Lifted Index (LI)

The LI is a commonly utilized measure of stability which measures the difference between a lifted parcel's temperature at 500 mb and the environmental temperature at 500 mb. It incorporates moisture and lapse rate (static stability) into one number, which is less vulnerable to observations at individual pressure levels. However, LI values do depend on the level from which a parcel is lifted, and rally cannot account for details in th environmental temperature curve above the LCL and below 500 mb. LI was originally intended to utilize average moisture and temperature properties within the planetary boundary layer.

     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).

Showalter Index (SI)

The SI is based on the properties of the 850 and 500 mb levels. The SI is calculated by lifting a parcel dry adiabatically from 850 mb to its LCL, then moist adiabatically to 500 mb, and comparing the parcel versus environmental 500 mb temperatures similar to the LI. The SI may be better than the LI in showing instability aloft given a shallow low-level cool airmass north of a frontal boundary. However, the SI is an unrepresentative index and inferior to the LI in showing instability if the low-level moisture does not extend up to the 850 mb level.

     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).

Deep Convective Index (DCI)

The DCI attempts to combine the properties of equivalent potential temperature (Qe) at 850 mb with instability.

     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.

Severe Weather Threat Index (SWEAT)

The SWEAT Index evaluates the potential for severe weather by combining several parameters into one index. These parameters include low-level moisture (850 mb dewpoint), instability (Total Totals Index), lower and middle-level (850 and 500 mb) wind speeds, and warm air advection (veering between 850 and 500 mb). Therefore, an attempt is made to incorporate kinematic and thermodynamic information into one index. As such, the SWEAT index should be utilized to assess severe weather potential, not ordinary thunderstorm potential.

    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.

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.

Convective Available Potential Energy (CAPE)

CAPE assumes Parcel Theory, in that 1) a rising parcel exhibits no environmental entrainment, 2) the parcel rises (moist) adiabatically, 3) all precipitation falls out of the parcel (no water loading), and 4) the parcel pressure is equal to the environmental pressure at each level. Parcel Theory can have significant errors, especially for large parcel displacements, at cloud edges, and for significant water loading. However, the method often works quite well in the undiluted core of a thunderstorm updraft.

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.

Convective Inhibition (CIN)

CIN represents the amount of negative buoyant energy available to inhibit or suppress upward vertical acceleration, or the amount of work the environment must do on the parcel to raise the parcel to its LFC. CIN basically is the opposite of CAPE, and represents the negative energy area (B-) on the sounding where the parcel temperature is cooler than that of the environment. The smaller (larger) the CIN is, the weaker (stronger) must be the amount of synoptic and especially mesoscale forced lift to bring the parcel to its LFC. High CIN values in the presence of little or no lift can cap or suppress convective development, despite possibly high CAPE values. Remember, CAPE is the "available potential" energy. That energy must be released to become "kinetic" energy to produce thunderstorms.

Cap/Lid Strength Index (LSI)

The LSI measures the ability of a stable layer to inhibit low-level parcel ascent. If the cap is strong enough, then deep moist convection will be suppressed, even if the airmass is very unstable. However, a cap allows the low-level moisture and temperature to increase which ultimately enhances severe weather potential for those stronger convective cells that are able to break the cap. Therefore, thunderstorms which develop rapidly within or near an area of significant capping likely will become severe. Conversely, the lack of a lid allows many storms to develop which then compete for the available moisture and storm-relative inflow.

     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.

Bulk Richardson's Number (BRN)

The BRN usually is a decent indicator of convective storm type within given environments. It incorporates buoyant energy (CAPE) and the vertical shear of the horizontal wind, both of which are critical factors in determining storm development, evolution, and organization.

     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.

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

While BRN can be useful in assessing While BRN can be useful in assessing the potential for supercell and middle-level mesocyclone development, it is less suited to assess low-level mesocyclone and tornado potential. Conversely, BRN shear may be more useful in differentiating between those supercells that will and those that will not produce tornadoes, although BRN shear still cannot be used independently for this purpose as storm-scale interactions are crucial for tornado development.

     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).

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.

Storm-Relative 500 mb Winds

Middle-level (represented well by the 500 mb level) storm-relative (S-R) winds also may be useful to help differentiate between tornadic and non-tornadic supercells within the overall environment, assuming supercells will form on a given day. Middle-level S-R winds are important in order to create a balance between the low-level storm inflow along the forward front flank baroclinic zone and the low-level outflow associated with the rear flank downdraft. If very weak S-R winds are present, a large amount of precipitation tends to wrap around the mesocyclone leading to the generation of excessive rain-cooled outflow along the low-level rear flank of the storm. This cool air then undercuts the middle-level mesocyclone and disrupts the low-level circulation. On the other hand, if middle-level S-R winds are very strong, then the middle-level flow may remove too much precipitation downwind from the mesocyclone, inhibiting the development of enough rain-cooled outflow (i.e., downdraft) along the rear flank to help focus convergence and generate baroclinic vorticity. Between these two extremes exists a balance where the rear flank downdraft is pronounced but balanced by significant low-level S-R flow into the system. S-R winds at 500 mb can be calculated from subtracting the observed or forecasted storm motion from the observed or forecasted 500 mb wind speeds.

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.

Storm-Relative Helicity

Storm-relative (S-R) helicity (Hs-r) is an estimate of a thunderstorm's potential to acquire a rotating updraft given an environmental vertical wind shear profile, assuming thunderstorms are able to develop. It integrates the effects of S-R winds and the horizontal vorticity (generated by vertical shear of the horizontal wind) within the inflow layer of a storm. A S-R wind is the wind that a thunderstorm actually "feels" as the storm moves through the environment. It is different from a true ground-relative (G-R) wind, except for a stationary storm whereby a S-R and G-R wind are equivalent. S-R helicity is proportional to the area "swept out" by the S-R wind vectors between two levels on a hodograph.

     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.

Energy-Helicity Index (EHI)

CAPE and storm-relative (S-R) helicity (Hs-r) are both very important in the formation of a strongly rotating convective updraft. CAPE represents the amount of buoyant energy available, while S-R helicity incorporates the effects of environmental vertical wind shear and storm motion on thunderstorm type and evolution. An intense rotating updraft can form with relatively weak CAPE if the vertical wind shear and storm-relative inflow are strong. On the other hand, relatively low S-R helicity usually can be compensated by high instability to produce a rotating updraft. The EHI attempts to combine CAPE and S-R helicity into one index to assess the potential for supercell and mesocyclone development. High EHI values represent an environment possessing high CAPE and/or high S-R helicity.

     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.

Height of the Wet-Bulb Zero (WBZ)

Wet bulb temperature (Tw) represents the lowest temperature a volume of air at a constant pressure can be cooled to by evaporating water into it. Its value falls between the dry bulb (actual air) temperature and dewpoint. To compute Tw at a particular level (pressure) on a sounding, lift up a dry adiabat and saturation mixing ratio line to the lifting condensation level (LCL; i.e., where parcel saturation is achieved, in other words, cloud base) then come down the moist adiabat to the original pressure and read the Tw value (Note: coming back down to 1000 mb represents the wet bulb potential temperature, Qw).

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 from 5,000 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.

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