# Derived Stability Indices - Total Operational Weather Readiness - Satellites (TOWR-S)

### GOES-R Derived Stability Indices

**Frequently Asked Questions about the GOES-R Derived Stability Indices Product**

**1) What is this product?**

The GOES-R Derived Stability Indices product produces five different stability fields: Convective Available Potential Energy (CAPE), Lifted Index (LI), K-Index, Total Totals Index (TT), and Showalter Index. All five of these fields are contained in one product file that is ingested and decoded by AWIPS. The horizontal resolution of this product is 10km. The range of values for CAPE are from 0 to 5,000 J/kg, with a product accuracy of 1,000 J/kg. The range of values for LI are from -10 to 40 Kelvin, with a product accuracy of 2.0 Kelvin. The range of values for K-Index are from 0 to 40, with a product accuracy of 2. The range of values for TT is -43 to >56, with a product accuracy of 1. The range of values for Showalter Index is >4 to -10 Kelvin, with a product accuracy of 2 Kelvin.

The Derived Stability Indices product is produced both day and night. It is not produced beyond 67 degrees local zenith angle of the satellite.

**2) How often do I receive this data?**

The cadence of the GOES-R Derived Stability Indices product is dependent upon which image from the satellite one is looking at. For Full Disk imagery, an image is produced every 60 minutes. For CONUS imagery, an image is produced every 30 minutes. For a Mesoscale scan, an image is produced every 5 minutes.

**3) How do I display this product in AWIPS-II?**

To display this product in AWIPS-II, go to the "GOES-R" tab of the CAVE menu, then select "Derived Products." From there, select the region of interest (GOES-E, GOES-W, or GOES Test and Full Disk, CONUS, and Mesoscale). Then, select the "Derived Stability Indices." From there, select either "CAPE," "Lifted Index", "Total Totals", "Showalter Index", or "K-Index."

Alternately, use the AWIPS Product Browser. Select "Sat", then either "GOES-16" or "GOES-17". From there, choose "Full Disk", "CONUS", or "Meso", then select "CAPE", "LI", "SI", "KI", or "TT".

**4) How do I interpret the color maps associated with this product?**

Color maps have not yet been established for these products. There is a baseline ability for AWIPS to display them, however the colormaps have not been vetted with any forecasters and therefore may not be yet be ideal.

**5) What other imagery/products might I use in conjunction with this product?**

The derived stability indices can give an indication of areas of the atmosphere that are becoming unstable. Overlaying the visible satellite imagery and toggling back and forth with the derived stability indices can lend credence to the product that there is indeed cloud-free areas that are being destabilized by daytime heating. Displaying model-derived stability indices (such as CAPE) and overlaying them with the satellite-derived stability indices can identify which model is best grasping the state of the atmosphere. This can help in deciding which model to trust in the next few hours in terms of locations of developing convection and also timing of that convection. Radar data plotted in conjunction with the derived products might also lead to a focus on certain areas where convection is likely to occur, as the radar data will indicate as soon as that potential convection develops.

**6) How is this product created?**

The GOES-R Derived Stability Indices products are only calculated on pixels that are determined to be either "clear" or "probably clear" by the GOES-R Cloud Mask algorithm. It utilizes GOES-R bands 6.2 um, 7.0 um, 7.4 um, 8.5 um, 9.6 um, 10.33 um, 11.2 um, 12.3 um, and 13.3 um channels. The product relies on the infrared observations to avoid discontinuities associated with the transition from day to night. The algorithm performance is sensitive to imagery artifacts or instrument noise.1

The ancillary data used to calculate the derived stability indices include1:

- Surface pressure from 6–18 hour forecast from NWP model.

- Surface pressure level index from 6–18 hour forecast from NWP model.

- Near surface wind speed vectors (zonal and meridional) from 6–18 hour

forecast from NWP model.

- Surface skin temperature from 6–18 hour forecast from NWP model.

- Temperature profile from 6–18 hour forecast from NWP model.

- Moisture profile from 6–18 hour forecast from NWP model.

- Forecast error covariance matrix from comparisons between forecast and radiosondes. Assume there is no correlation between temperature and moisture in the error covariance matrix.

- Land Mask

- Surface Elevation

- Temperature profile

- Water vapor profile

- IR SEs for ABI bands from UW-Madison baseline fit database. A global database of monthly IR land SE derived from the MODIS operational land surface emissivity product (MOD11). Emissivity is available globally at ten wavelengths (3.6, 4.3, 5.0, 5.8, 7.6, 8.3, 9.3, 10.8, 12.1, and 14.3 µm) with 0.05 degree spatial resolution. Monthly SEs have been integrated into the ABI spectral response functions to match the ABI bands.

- LUT for ABI IR SEs over ocean as a function of LZA and wind speed above

ocean surface. (http://ams.confex.com/ams/pdfpapers/104810.pdf).

- Regression coefficient file. This coefficient file contains 81 regression coefficient datasets. Each coefficient dataset corresponds to one LZA ranging from 0 to 80 degrees. The regression coefficient file is an array of 81*110 * (3*L+1+9), where L(=101) is the atmospheric pressure levels used in RTM.

**Lifted Index**

LI (lifted index) in units of degrees Celsius (°C) provides estimations of the atmospheric stability in cloud-free areas. Among all the potential indices, the LI has been implemented and coded. The LI index (Galway, 1956) expresses the temperature difference between a lifted parcel and the surrounding air at 500 hPa. The parcel is lifted dry adiabatically from the mean lowest 100 hPa level to the condensation level, and then wet adiabatically to 500 hPa. In the LAP algorithm the same routine will be implemented for the GOES sounder. Negative values of LI indicate that the parcel is warmer than its environment and unstable.

The equation used to calculate the Lifted Index is:

LI = T_{76} - (WLIFT5(T_{wb})) + 273.16 where

T_{76} = the air temperature at the 76th level (500 mb)

WLIFT5 = a function to calculate temperature at 500 mb for the given wet-bult potential temperature lifted along wet adiabatic processes

T_{wb} = wet-bulb potential temperature

The LI indicates the atmospheric thermodynamic instability, its value indicates that:

0< LI, stable

-3< LI <0, marginally unstable

-6< LI <-3, moderately unstable

-9< LI <-6, very unstable

LI <-9, extreme unstable

The LI value itself cannot predict whether storms will occur. It gives the forecaster a general idea of the convective forcing if thunderstorms do develop. Unstable LI values (negative values) combined with high TPW values indicate that the troposphere is near saturation and has instability. The LI is less useful in winter when the bottom layer of the troposphere tends to be dry (low dew points) and cold (stable). Precipitation can be produced with stable LI due to other ingredients, which are not correlated with the LI like elevated convection, dynamic forcing without thermodynamic forcing and isentropic lifting.

**CAPE**

CAPE (convective available potential energy) in units of Joules per kilogram (J/kg) is a measure of the cumulative buoyancy of a parcel as it rises. Its definition is:

where

Z_{f} = the level of free convection

Z_{g}_{ = }the equilibrium level

T_{va} = the wet-bulb potential temperature for the air parcel

T_{ve} = the wet-bulb potential temperature for the environment

g = gravity acceleration = 9.806 m/s^{2}

In the GOES-R algorithm code, the integration is performed from the surface level to the 57th level corresponding to 100 mb. T_{ve} and T_{va} at difference levels are calculated with these equations respectively:

T_{ve} = (T + 273.16) * (1000/P)^{0.28541} - 273.16

and

T_{va} = (SATLFT + 273.16) * (1000/P)^{0.28541} - 273.16 where

P = the air pressure at a specific level in mb

T = the air temperature in degrees C

SATLFT = the temperature in degrees C where moist adiabatically crosses P

The original algorithm to derive SATLFT in the sounding code was developed by Herman Wobus, a mathematician formerly at the navy weather research facility but now retired.

CAPE values larger than 1000 J/kg represent moderate amounts of atmospheric potential energy. Values exceeding 3000 J/kg are indicative of very large amounts of potential energy, and are often associated with strong/severe weather.

**Total Totals**

TT (Total Totals) Index in units of degrees Celsius (°C) is indicative of severe weather potential. And is computed using discrete pressure level information. It is a sum of two separate indices: vertical totals (VT: measure of static instability) and cross totals (CT: measure of moist instability):

TT = VT + CT = (T850 - T500) + (T_{d}850 - T500) where:

T850 = air temperature at 850 mb in degrees C

T500 = air temperature at 500 mb in degrees C

T_{d}850 = dew point temperature at 850 mb in degrees C

In the GOES-R algorithm code, the values of T and T_{d } at these specific pressure levels are linear interpolated from the original 101-level pressure ordinate.

Generally, TT values below 40 - 45 are indicators of little or no thunderstorm activity, while values exceeding 55 in the Eastern and Central United States or 65 in the Western United States are indicators of considerable severe weather.

**Showalter Index**

SI (Showalter index) in units of degrees Celsius (°C) is a parcel-based index, calculated in the same manner as the LI, using a parcel at 850 mb. That is, the 850-mb parcel is lifted to saturation, then moist adiabatically to 500 mb. The difference between the parcel and environment at 500 mb is the SI. A SI value smaller than -3 indicates the possible condition for a severe weather.

**K-Index**

KI (K-index) in units of degrees Celsius (°C) is a simple index using data from discrete pressure levels instead of a lifted parcel. It is based on vertical temperature changes, moisture content of the lower atmosphere, and the vertical extent of the moist layer. The higher the KI the more conducive the atmosphere is to convection. The formula for KI is:

KI = (T850 + Td850) - (T700 + Td700) - T500 where:

T850 = temperature at 850 mb in degrees C

T_{d}850 = dew-point temperature at 850 mb in degrees C

T700 = temperature at 700 mb in degrees C

T_{d}700 = dew-point temperature at 700 mb in degrees C

T500 = temperature at 500 mb in degrees C

In the GOES-R algorithm code, the values of T and Td at these specific pressure levels (500/700/850 mb) are linear interpolated from the original 101-level pressure ordinate. Severe weathers are very likely to occur if the value of KI exceeds 30.

Only clear ABI IR BTs within each Field-of-Regard (FOR) are processed for derived products. Usually there are multiple clear sky FOVs in each FOR. Two methods are available in the algorithm to select the representing value for the specific FOR: one is the simple average of all clear sky FOVs for each channel; another method is to determine the warmest FOV with largest value of the IR 10.8 channel and use the values of all IR channels at this FOV as representatives of this FOR. A subroutine named Find_Good_BT is presented for the BT manipulation in the main sounding retrieval module and called right after the determination of clear pixels within the FOR. The simple average method is better to reduce the instrumental noise. However, since there are always some cloudy pixels misidentified as clear pixels, which in general have lower value at IR 10.8 channel, the second method is better than the simple average in mitigating cloud impact. According to several cases with SEVIRI as used as proxy, it is found that the cold bias is much stronger than the instrumental noise; therefore the warmest FOV method is set as the default method in the algorithm.^{1}

Both the current GOES Sounder and ABI have three water vapor absorption channels although the spectral coverage is different. Studies have shown that the ABI, with numerical model forecast information used as the background, will be slightly inferior to the GOES-13/O/P sounder performance, yet both are substantially less capable than a high-spectral-resolution sounder with respect to information content and retrieval accuracy. The ABI will provide some continuity of the current sounder products to bridge the gap until the advent of the GOES advanced infrared sounder. Both theoretical analysis and retrieval simulations show that data from the ABI can be combined with temperature and moisture information from forecast models to produce derived products that will be adequate substitutes for the legacy products from the current GOES sounders.

^{1}Li, Jun, Timothy J. Schmit, Xin Jin, and Graeme Martin.** NOAA NESDIS Center for Satellite Applications and Research GOES-R Advanced Baseline Imager (ABI) Algorithm Theoretical Basis Document: Legacy Atmospheric Moisture Profile, Legacy Atmospheric Temperature Profile, Total Precipitable Water, and Derived Atmospheric Stability Indices v.2.0. **September 2010. http://www.goes-r.gov/products/ATBDs/baseline/Sounding_LAP_v2.0_no_color.pdf