What factors influence global temperature anomalies?

A simple climate/temperature parameterization model that can be used to reproduce temperature anomalies from 1980 is available here. This approach considers variations in four main components that can influence global temperatures:

• ks: variations in the total solar irradiance (TSI)
• ke: the El Niño-Southern Oscillation (ENSO). The SOI index is taken as a proxy for ENSO using data from NOAA
• kv: stratospheric aersol optical depth from volcanic eruptions
• ka: anthropogenic forcing, including well-mixed greenhouse gases (WMGHG) and land-use changes

Disclaimer: this simple hindcast model was developed primarily as an undergraduate teaching tool, in order to demonstrate the major processes that influence global temperature - and in particular, to demonstrate that the temperature changes observed over the past 40 years cannot be re-created without considering anthropogenic effects. This approach is not intended to serve as a detailed or accurate analysis of climate forcing effects, and the k values discussed below serve as rough proportionality constants. For further reading I recommend the following (not exhaustive):

• Marvel, K., G.A. Schmidt, R.L. Miller, and L. Nazarenko (2016) Implications for climate sensitivity from the response to individual forcings. Nature Climate Change, 6, no. 4, 386-389.
• Canty, T. Mascioloi, N.R., Smarte, M.D., and Salawitch, R.J. (2013). An empirical model of global climate – Part 1: A critical evaluation of volcanic cooling. Atmospheric Chemistry and Physics, 13, 3997-4031.
• Kopp, G. and Lean, J.L. (2011) A new, lower value of total solar irradiance: Evidence and climate significance. Geophysical Research Letters, 38, L01706.
• Lean, J.L. and Rind, D.H. (2009) How will Earth’s surface temperature change in future decades? Geophysical Research Letters, 36, L15708.
• Lean, J.L. and Rind, D.H. (2008) How natural and anthropogenic influences alter global and regional surface temperatures: 1889 to 2006. Geophysical Research Letters, 35, L18701.
• Hansen, J. et al. (2005) Efficacy of climate forcings. Journal of Geophysical Research, 110, D18104.
• Douglass, D.H. and Clader, B.D. (2002) Climate sensitivity of the Earth to solar irradiance. Geophysical Research Letters, Vol. 29, No. 16.

## Method

### Temperature Records

The baseline used for the hindcast model is 1980; the temperature records must therefore be normalized (i.e., such that the temperature anomaly in 1980 = 0 C by definition) to show the temperature increase from 1980 forward. For example,

• NASA GISTemp; 1980 temperature anomaly = 0.2745 C, so that $t_{model} = t_{{record}} - 0.2745$
• Hadley-CRU; HadCRUT4 1980 temperature anomaly = 0.092 C, so that $t_{model} = t_{{record}} - 0.092$
• Berkely Earth Land+Ocean time series; 1980 temperature anomaly = 0.20 C, so that $t_{model} = t_{{record}} - 0.20$

Note that these normalization values may be adjusted for comparison over other time intervals.

### Climate Model Components

The “hindcast” or 4-component model temperature is determined using the following expression:

$\delta t_{model}=k_{s}(y_{s}+c_{s})+k_{e}(y_{e})+k_{v}(y_{v})+k_a(y_a+c_a)$

where the k values are treated as free parameters in the model. The k value relates the observed temperature anomaly to some observed change in the data set, e.g.

• solar component: $\delta t_{s}=k_{s}(y_{s}+c_s)$ gives the temperature anomaly (δt) from variations in the total solar irradiance (TSI in W/m2, given by ys). The cs term normalizes the solar data to ~1980 baseline. The (model_k_solar) data uses a 1-month lag and 1-month smoothing of daily data. Corrected TSI data from Dudok de Wit et al. 2017.
• El-Nino-Southern-Oscillation (ENSO) component: $\delta t_{e}=k_{e}(y_{e})$ gives the temperature anomaly (δt) from variations in Souther Oscillation Index (SOI), given by ye. This term is already a normalized index, so no ce term is included. The (model_k_enso) data uses a 0-, 2-, and 10-month lag and 3-month smoothing of monthly data following the approach of Kopp & Lean (2011). SOI data adopted from NOAA.
• stratospheric aerosol (volcanic) component: $\delta t_{v}=k_{v}(y_{v})$ gives the temperature anomaly (δt) caused by strasopheric aerosols following volcanic eruptions, characterized by an optical depth term yv. No contribution from strasospheric aerosols provides an optical depth of zero, so no cv is included. The (model_k_volcano) data uses a 0- and 10-month lag following the approach of Kopp & Lean (2011). Stratospheric optical thickness data taken from NASA GISTEMP.
• anthropogenic component: $\delta t_{a}=k_{a}(y_{a}+c_a)$ gives the temperature anomaly (δt) from anthropogenic forcings (ya), including land-use changes and greenhouse gases (GHG). The (model_k_anthro) data considers 10-year lag of annual data; the ca term allows for normalization to 1980. Anthropogenic forcing values adopted from NASA GISS Model E forcings.

This project is released under CC BY-SA 4.0