Recently, many climate indices are known. If one has climate data for a number of years and would like to calculate one of the climate indices, which climate index is achievable with the daily parameters {temperature (Max, Mean, and Min), precipitation, dew point, relative humidity, pressure at sea level, visibility, and wind speed}? and how to calculate that?
There is no general rule of how to find or construct a climate index; it is a field where scientific discoveries are still possible. A climate index typically is a time series derived from observational data which has significance for a larger region or a class of processes. For example, NAO and SOI are composed of air pressure differences over the Atlantic / Pacific and correlate significantly with temperature and humidity anomalies in North America and Europe (NAO) and those between Indonesia/Australia and California/Peru/Chile (SOI). We composed the HIX of temperature, rainfall and air pressure data at St. Helena Island; it represents climate anomalies in the southwest subtropical Atlantic.
https://www.researchgate.net/publication/223276186_The_winter_St._Helena_climate_index_and_extreme_Benguela_upwelling
https://www.researchgate.net/publication/223276186_The_winter_St._Helena_climate_index_and_extreme_Benguela_upwelling
WIBIX was built from ice data, sea level and NAO to represent winter severity over the Baltic Sea region.
https://www.researchgate.net/publication/238732814_Climatic_turning_points_and_regime_shifts_in_the_Baltic_Sea_region_the_Baltic_winter_index_%28WIBIX%29_1659-2002
So, look for long lasting correlations or similarities between different time series you are interested in.
Article The winter St. Helena climate index and extreme Benguela upwelling
Article Climatic turning points and regime shifts in the Baltic Sea ...
There is also a set of indices that was developed for the measurement and characterization of climate variability and change on a global scale with particular focus on extreme events. For more details see the information provided by the Expert Team on Climate Change Detection and Indices (ETCCD): http://etccdi.pacificclimate.org/indices.shtml.
An overview of the indices is given in this paper: http://onlinelibrary.wiley.com/enhanced/doi/10.1002/wcc.147
And this one provides more details on how to calculate the indices and available software as well as on how these indices are represented in climate models:
http://onlinelibrary.wiley.com/doi/10.1002/jgrd.50203/full
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