METR 361                                                                                                                                           Spring, 2007   

Stability Indices

 

            Assessing stability of a sounding on a thermodynamic diagram is usually too time-consuming a process considering the daily routine of a weather office.  This is especially true during times when thunderstorms are likely to occur.  For this reason indices have been devised to give a rapid means for making stability assessments.  The various stability indices described below have been statistically linked to shower and thundershower activity.  In the winter, many of these indices are used as indicators of the atmosphere’s tendency to create snow squalls or convective clouds in general.  When using any of these indices for forecasting purposes, one must be careful to anticipate changes that might occur in the environmental lapse rate between the sounding time (usually 12Z) and the expected time of convective activity (usually 5-10 hours after 12Z).

 

            Lifted Index

            This is probably the most well-known index. Lift a parcel from the surface to its LCL.  Then lift it moist- adiabatically to 500 hPa.  Subtract the lifted parcel temperature from the environmental 500 hPa temperature. 

                                    LI = T500 - Temperature of lifted parcel

 

            The LI works well in severe weather situations with a conditionally unstable atmosphere and a low level trigger for lifting, such as a cold front or pressure trough.

 

            K Index

            Subtract the environmental 500 hPa temperature from the 850 hPa temperature.  Add the 850 hPa dew point.  Subtract the 700 hPa dew point depression.

 

                                    K = T850 - T500 + Td 850 - (T700 - Td 700)

 

            The K Index does not work well in severe weather situations because convectively unstable atmospheres usually have mid-tropospheric dry tongues at 700 hPa.  To maximize the K Index, the low level (850 hPa) should be warm and moist, the upper level (500 hPa) cold and the 700 hPa dew point depression should be small, indicating deep low level moisture.

 

            Total-Totals Index

            This index consists of two sub-indices, the Vertical Totals and the Cross Totals.  The Vertical Totals index is the 850 hPa temperature minus the 500 hPa temperature.  The Cross Totals index is the 850 hPa dew point minus the 500 hPa temperature.  The Total-Totals index is the sum of the Vertical and Cross Totals.

 

                                    TT = (T850 - T500) + (Td 850 - T500) = T850 + Td 850 - 2T500

 

            For the TT to work well, the lower level (850 hPa) should be warm and moist and the upper level (500 hPa) cold.  It is a fairly reliable severe thunderstorm predictor.

 

            TQ Index

            From a paper by Henry (2000) in the journal Weather and Forecasting, the TQ index is designed to assess instability for low-topped convective clouds.

 

TQ = T850 + Td850 − 1.7T700

 

 

            Severe Weather Threat Index (SWEAT)

            The SWEAT Index was developed by the Air Force Global Weather Center severe storm group.  It puts more information into an index than any of the others listed.  Wind speeds and shear are included.  To calculate the SWEAT Index, first multiply the 850 hPa dew point by 12.   Then subtract 49 from the Total-Totals Index and multiply the result by 20.  Add twice the 850 hPa speed to the 500 hPa wind speed.  Finally, subtract the 850 hPa wind direction from the 500 hPa wind direction, take the sine, add 0.2 and multiply the result by 125.

 

                        SWEAT = 12Td 850 + 20(TTI - 49) + 2w850 + w500 + 125(S + 0.2)

 

In SWEAT,       Td 850 = 850 hPa dew point in °C

                        w850, w500 = 850hPa and 500 hPa wind speeds in knots

                        S = sin(500 hPa wind direction - 850 hPa wind direction). 

This term is set to zero if either w850 or w500 are less than 15 knots.  S is not computed unless the 500 hPa wind direction is within the range 210° to 310° and 850 hPa wind direction is in the range 130° to 250°.

 

            All negative terms are set to zero. 

 

            CAPE (Convective Available Potential Energy)

 

            This index is calculated from a sounding on the thermodynamic diagram.  Lift a parcel from the surface to the tropopause.  The parcel will saturate at the LCL and rise moist-adiabatically.  Whenever the parcel is warmer than the sounding, add the area between the parcel and the sounding to CAPE.   When the parcel is cooler than the sounding, subtract the area from CAPE. Values around 1500-2000 are high.  CAPE has substantial variability.

 

            CINS (Convective Inhibition)

            The convective inhibition is a measure of the cap or lid.  As in CAPE, lift a parcel.  Before it gets to its level of free convection (LFC), it will have negative buoyant energy, i.e., negative CAPE.  That’s CINS.

 

            LCL (Lifting Condensation Level)

            Not an index but important.  When lifting a parcel from the surface, this is where condensation first occurs.

            CCL (Convective Condensation Level)

            This is the level where condensation occurs if a parcel lifts itself from the surface due to positive buoyancy.  You will need to heat the surface air until it breaks the cap.  The CCL will be higher than the LCL.

 

            LFC (Level of Free Convection)

            This is where negative buoyancy becomes positive.  In practical terms, this is where a lifted surface parcel (not one which was heated as in the CCL) will rise on its own due to buoyancy.

 

           

                        SUGGESTED INDEX THRESHOLD AND CRITICAL VALUES

 

            GENERAL THUNDERSTORMS                   SEVERE THUNDERSTORMS

UNLIKELY     POSSIBLE    VERY LIKELY    UNLIKELY   POSSIBLE    VERY LIKELY

 

LI         > -1                 -1 to -2                        < -2                             > -3                   -3                   < -4

K         > 16                 16 to 36                       > 36                             NA                  NA                  NA

TTI      < 46                 46 to 50                       > 50                             < 50                 50 to 55           > 55

SWEAT < 200             200 to 300                   >300                            < 300              300 to 500        > 500

 

      These are only suggested values that should be applied with caution (or refined) to local areas.

 

ASSIGNMENT (due next Wednesday)

   On two thermodynamic diagrams plot the two given soundings for stations AAA and BBB.  Plot temperature, dew point and wind barbs to 100 hPa, using the usual format.  Then:

 

   1. Calculate the LCL and LFC of surface air, the Lifted Index, the K Index, the Total-Totals Index, the TQ Index, and the Severe Weather Threat Index.  Write these indices on the top of each sounding.

 

   2. Assess the potential for severe weather (poor, fair, good, spectacular, etc.)  listing four reasons for your assessment.  Use the indices calculated in part 1 as one of your reasons but be specific about how the individual indices best predicted the severe weather potential.  Examine the sounding itself for the other three reasons.

 

               Station AAA at 12Z                                                                 Station BBB at 12Z

Level                        T     Td                     DDFFF                        Level                      T    Td                     DDFFF

  (hPa)                      (°C)            (°C)     (knots)                        (hPa)                     (°C)            (°C)     (knots)

 

  100                        -64.0            -                                                           100                -72.1      -                       26576

  150                        -59.7            -                       24048                          150                -62.7      -                       26604

  191                        -59.1            -                                                           200                -55.1      -                       26626

  200                        -63.5            -                       24084                          250                -46.3      -                       26621

  250                        -53.0            -                       23597                          300                -39.9    -48.9      27068

  300                        -44.6            -                       23599                          353                -30.9    -40.9   

  317                        -40.0          -44.7                                          400                      -26.3          -56.3      26540

  385                        -32.9          -33.8                                          458                      -17.7          -47.7     

  400                        -30.1          -30.2      23084                          500                      -13.7          -43.7      27029

  444                        -27.5          -36.2                                          579                        -6.5          -36.5

  500                        -16.2          -20.7      23060                          700                         2.2            -2.8      27516

  550                        -10.0          -22.2      22540                          729                         2.6             1.6   

  700                           7.2           -24.8      21542                          766                         5.6             5.1   

  757                        12.0           -18.2                                          850                         8.8             6.8      15521

  769                           7.3              7.2                                          872                      10.8             6.4   

  850                        13.2           12.8      19046                          902                      12.6          11.0   

  900                        16.1           15.3                                        1000                      17.6          16.5      11015

  932                        17.8           16.2                                        1016                      18.8          17.5      10009

  992                        20.2           16.7      17015

 

   Next, here is a sounding from the big severe weather outbreak last year:

 

74560 ILX Lincoln Observations at 00Z 13 Mar 2006

------------------------------------------------------------------------
   PRES   HGHT   TEMP   DWPT   RELH   MIXR   DRCT   SKNT   THTA   THTE   
    hPa     m      C      C      %    g/kg    deg   knot     K      K     
------------------------------------------------------------------------
 1000.0     45                                                               
  985.0    178   18.2   16.5     90  12.13    140     12  292.6  327.2  
  970.4    305   17.5   16.1     91  11.96    150     18  293.2  327.4  
  903.2    914   14.4   14.1     98  11.34    190     30  296.1  329.0  
  850.0   1427   12.2   11.6     96  10.19    210     35  298.9  328.9  
  818.0   1749   10.8   10.0     95   9.51    206     36  300.7  329.0  
  752.6   2438    6.0    4.2     88   6.90    205     35  302.8  323.7  
  706.0   2961    5.0  -15.0     22   1.70    218     35  307.2  312.9  
  700.0   3030    4.6  -17.4     19   1.40    220     36  307.6  312.3  
  646.8   3658   -0.8  -17.4     27   1.51    230     44  308.5  313.6  
  554.0   4877  -10.1  -29.6     19   0.60    245     59  311.4  313.6  
  500.0   5660  -14.9  -31.9     22   0.53    235     62  314.8  316.8  
  434.4   6706  -23.0  -29.2     57   0.79    235     65  317.4  320.2  
  400.0   7310  -27.1  -32.1     62   0.65    240     76  319.7  322.1  
  382.8   7620  -29.6  -33.9     66   0.57    245     80  320.5  322.6  
  300.0   9310  -43.5  -46.1     75   0.20    240    101  323.9  324.8  
  270.0  10009  -49.9  -52.9     70   0.10    243     93  324.5  325.0  
  250.0  10510  -52.5  -55.6     69   0.08    245     88  327.9  328.2  
  200.0  11920  -62.3  -65.3     67   0.03    250    109  333.9  334.1  
  168.0  12994  -61.3  -64.7     64   0.04    250    126  352.7  352.9  
  150.0  13710  -54.5  -60.5     47   0.07    255     71  376.0  376.3 

 

 

3. Plot temperature and dew point from this sounding on a separate skew T-log P chart.  Plot wind flags from mandatory levels only.  Then calculate the LCL and LFC of surface air, the Lifted Index, the K Index, the Total-Totals Index, the TQ Index, and the Severe Weather Threat Index.  Write these indices on the top of this sounding.

 

4. We know there was severe weather associated with this environment.  What indices were the best at predicting that?  Why did those indices succeed when others failed?

 

5. What features of this sounding were favorable for severe weather but not picked up by the indices you calculated?