In part because models with parametrised convection cannot explicitly represent societally-important convection-related hazards, a number of tools to help the forecaster have been developed over the years. These include "Instability Indices". It has historically been ECMWF policy to not generate too many such indices, because we believe needs are nowadays better served by CAPE-related variable that are intrinsic to the convection scheme, and because it is relatively straightforward for users to compute the indices they want locally. Nonetheless a couple of pre-computed indices are made available for the community.

Instability indices are a way of indicating the potential for convection using simple formulae based upon temperature and moisture data observed or forecast at a small number of pressure levels.  Several of these formulae have been derived semi-empirically over the years when less detail, in observed or in model atmospheres, was at one's disposal and when computer processing power was less readily available. 

The indices have the disadvantage of sampling temperature and moisture only at arbitrary pressure levels and thus can easily be unrepresentative in situations where (e.g.) moisture is particularly abundant below the 850hPa level or where convection is inhibited by the presence of a significant lower-level capping inversion.

Typical values of the different indices depend on location and season, and likewise local usage tends to also vary accordingly, via the use of different thresholds. The indices tend to fail in mountainous areas where the surface is above the 850hPa level.  However, instability indices may be used for both air mass and frontal thunderstorm activity.

Although simply constructed, the indices do have a part to play in assessment of any potential convection, particularly when used in conjunction with other meteorological information (e.g. low-altitude convergence, bulk shear, atmospheric cooling at higher altitudes etc.)  Users may have become accustomed to using an appropriate preferred instability index for their region of interest, but for a more detailed and comprehensive assessment users are encouraged to use these alongside forecast values of CAPE (Convective Available Potential Energy) and CAPE-shear, and CIN (Convective Inhibition). All such parameters are available in ecCharts.

Whilst CAPE may be the preferred variable for many, note that using CAPE alone does not always bring the best results.

K-index (K)

The formula is:

K-Index (K) = (T850 - T500) + Td850 - (T700 - Td700)

                                A                B               C

(T is temperature and Td is dewpoint temperature in °C at the indicated pressure level in hPa)

Where:

  • Term A samples the static instability between 850hPa and 500hPa.
  • Term B samples the moisture at 850hPa.
  • Term C samples the dryness of the airmass at 700hPa.


Points to consider:

  • The formula provides no information on the energy required to overcome lower-level stability (CIN).  It may not pick up a capping inversion that prevents storms from developing.
  • The formula provides no information on instability below 850hPa (e.g. where there is strong maritime heating), or on moisture below 850hPa.
  • The values of moisture may or may not be representative of conditions generally, particularly at medium levels.
  • Moist zones near but not at at the 850hPa or 700hPa levels will be missed resulting in an inappropriate value of K-index.
  • The index may have a misleadingly low value if a layer of moisture is just beneath the 850hPa level.
  • The index does not assess wind shear and CAPE.
  • The index works best for flat areas in low to moderate elevations; it does not work well for high elevations.
  • The interpretation of the index value varies with season and location (e.g. tropics or mid-latitude, summer or winter).

At ECMWF, to evaluate the K-index, the standard atmosphere was inspected at the outset to find out which model levels (over the sea) straddle each of the pressure levels required (500, 700, 850hPa) and work out the weights for interpolation.  This is done once, and these particular model levels and their associated weights, are used everywhere, even over mountains, all the time.  The calculation does not actually use the pressure level (500, 700, 850hPa).  This means that the K-Index calculation over a 1500m mountain is based on pressure levels that correspond to a much lower pressure value (i.e. physically much higher above mean sea level) than the standard level.  Equally, when the surface pressure is low, over the sea, say, the pressure levels used will also correspond to a lower value of pressure (though in that case not physically higher up in any large/systematic way). This "standard atmosphere" approach has the benefit of normalising across different regions and different weather types, and it also delivers values over mountains which are much more "usable" than would be values obtained by underground extrapolation. On the other hand there is a disadvantage that user will not generally know which pressure level data is being incorporated on a given day, which in turn means that comparison with observed data, e.g. from radiosondes, becomes difficult.

The K index is quite widely used. Typical values vary with location but can be quite helpful and indicative for the user.

Typical values:

  • Polar lows in Winter Arctic Maritime airmass: max values of 15 to 25K (normally good performance)
  • Mid-latitude continental summer convection: max values of 25 to 35K (weak definition in location, values not unique to areas of deep convection).
  • Tropical pre-monsoon: max values of 40 to 50K (normally good performance)


The K-index can also be related to the probability of occurrence of a thunderstorm.  

K-index            Thunderstorm Probability

<20                        No thunderstorms.

20-25                     Isolated thunderstorms.

26-30                     Widely scattered thunderstorms.

31-35                     Scattered thunderstorms.

 >35                       Numerous thunderstorms.


Charts of K-Index derived from ensemble control forecast values are available on ecCharts. If users have access to ensemble K-Index values (these are not currently available on ecCharts) they should refer to those alongside the ensemble control values.

Total Totals Index (TT)

The formula is:

TT = (T850 – T500) + (Td850 – T500)  =   T850 + Td850 – 2(T500)

                VT                     CT

(T is temperature and Td is dewpoint temperature in °C at the indicated pressure level in hPa)


Where:

  • Term VT  (the Vertical Total) represents static stability or the lapse rate between 850 and 500hPa. 
  • Term CT  (the Cross Total) is a measure of the moisture content.


VT ~ 40 for dry adiabatic conditions in the 850-500hPa layer but generally VT is much less. 

VT> ~26 represents sufficient static instability (without regard to moisture) for thunderstorm occurrence.

CT > 18 is often necessary for convection.


Note: It is the combined Total Totals Index that is most important.


The TT index can also be related to the probability of occurrence of a thunderstorm:
     
TT index            Thunderstorm Probability

 <44                  Thunderstorms not likely.

44-50                Thunderstorms likely.

51-52                Isolated severe thunderstorms.

53-56                Widely scattered severe thunderstorms

56-60                Scattered severe thunderstorms more likely.


Points to consider:

  • The formula provides no information on the energy required to overcome lower-level stability (CIN).  It may not pick up a capping inversion that prevents storms from developing.
  • The formula provides no information on instability below 850hPa (e.g. where there is strong maritime heating), or on moisture below 850hPa.
  • The index does not assess wind shear and CAPE.
  • The index may have a misleadingly high value when the VT component is particularly high and moisture is lacking.
  • The index may have a misleadingly low value if a layer of moisture is just beneath the 850hPa level.
  • The index works best for flat areas in low to moderate elevations; it does not work well for high elevations.
  • The interpretation of the index value varies with season and location (e.g. tropics or mid-latitude, summer or winter).


Charts of Total Totals Index derived from ensemble control forecast values are available on ecCharts.  If users have access to ensemble Total Totals Index values (these are not currently available on ecCharts) they should refer to those alongside the ensemble control values.


Examples

Fig9.6.2-1: Composite diagram showing ecChart presentation of the vertical profile product, and of CIN, CAPE, K-index, and Total totals index from ensemble control/HRES, all valid for T+60hr valid 12UTC 28 July 2018, forecast base time 00UTC 26 July 2018.

  • CIN values >1000J/kg are uncoloured; <10J/kg shown as red.
  • CAPE values <100J/kg are uncoloured; >3000J/kg shown as blue.
  • K-index values <10°C are uncoloured; >35°C shown as magenta.
  • Total totals index values <40°C are uncoloured; >50°C shown as purple.

The values of the parameters and indices at Freiburg (location denoted by the green pin) are shown in the probe box and the vertical profile product for the same location is shown on the left.  Both the K-Index and the Total Totals Index attain high values in Freiburg. Meanwhile the vertical profiles show that ensemble control/HRES Lifting Condensation Level (LCL) and Level of Free Convection (LFC) are at fairly low altitude and close together, potentially facilitating energetic convection to occur (reflected by the low CIN and high CAPE values shown on the charts). However many ensemble members suggest a LCL at a greater altitude with release of less energetic convection. This is highlighted by the CAPE chart on the vertical profile plot (lower right panel), where 8 ensemble members suggest moderate energy is required to overcome CIN but these only have moderate CAPE for subsequent convection. Meanwhile 23 ensemble members (and the Control member) suggest a good deal of energy is needed to overcome CIN, and 18 ensemble members suggest no propensity for convection (CAPE is zero). Only ensemble control/HRES and one ensemble member suggest deep and active convection can be released. Instability indices on ecCharts are derived from ensemble control/HRES forecast values and the user must always bear in mind that ensemble values may be quite different. If possible they should compare with those via local workstation tools.


Fig9.6.2-2: Composite diagram showing ecChart presentations of the vertical profile product, and CIN, CAPE, K-index and Total totals index from ensemble control/HRES, all valid for T+60hr valid 12UTC 28 July 2018, forecast base time 00UTC 26 July 2018. 

  • CIN values >1000J/kg are uncoloured; <10J/kg shown as red.
  • CAPE values <100J/kg are uncoloured; >3000J/kg shown as blue.
  • K-index values <10°C are uncoloured; >35°C shown as magenta.
  • Total totals index values <40°C are uncoloured; >50°C shown as purple.

The values of the parameters and indices at Paris (location shown by the pin) are shown in the probe box and the vertical profile product for the same location is shown on the left. The vertical profile shows very dry air at 700hPa with a low dewpoint (about -35°C) which has a direct influence on evaluation of the K-index (ensemble control/HRES suggests -4.3°C!).  Some ensemble members, however, show air at 700hPa being moister (dewpoint as high as -5°C) and would therefore produce a higher K-index. Therefore the ensemble control/HRES value may well be extreme. A glance at the CAPE diagram suggests about a third of the ensemble members could permit instability release, albeit weak. In contrast to the ensemble control/HRES K-index, the ensemble control/HRES Total totals index (43.3°C, just within the yellow area) suggests that the thunderstorm risk is borderline. Instability indices on ecCharts are derived from ensemble control/HRES forecast values and the user must always bear in mind that ensemble values may be quite different. If possible they should compare with those via local workstation tools.