# Replicating Nummelin et al (2017)

## Overview

I’m attempting to replicate Figure 1b of Nummelin et al. (2017) so that I can create a similar plot in my own research, which involves comparing the ocean response to anthropogenic aerosols (i.e. the historicalAA experiment) and greenhouse gases (historicalGHG). I’ve focused on three key curves from Figure 1b: the trend in ocean heat transport convergence ($$\overline{HTC}$$), surface heat flux at ocean surface ($$\overline{SFL}$$) and ocean heat content tendency ($$\overline{OHC^{\prime}}$$).

For my initial attempt (see Figure \ref{fig:noresm_full}; the methodology is described in detail in the appendices below), I regrid from a curvilinear to rectilinear grid at some point to simplify the process. I also present the results in units of $$W\;s^{-1}$$ (as opposed to $$W\;m^{-2}\;s^{-1}$$), as it’s difficult for me to divide the final result by area because once the data is regridded I can’t use the relevant areacello file.

All python scripts referred to below can be found at https://github.com/DamienIrving/ocean-analysis. For reference, the final command in the workflow to produce Figure \ref{fig:noresm_full} is as follows:  \$ python ~/ocean-analysis/visualisation/plot_heat_trends.py hfbasin-convergence_Omon_NorESM1-M_rcp85_r1i1p1_all.nc hfds-by-areacello-zs_Oyr_NorESM1-M_rcp85_r1i1p1_all.nc ohc-zs_Oyr_NorESM1-M_rcp85_r1i1p1_all.nc htc-hfds-ohc_Oyr_NorESM1-M_rcp85_r1i1p1_all_nummelin.png --nummelin 

\label{fig:noresm_full}Linear trend in ocean heat transport convergence (calculated from hfbasin data), surface heat flux and ocean heat content tendency over the period 2006–2100 for the NorESM1-M model, rcp85 experiment and r1i1p1 ensemble.

As shown in Figure \ref{fig:noresm_full}, I’m seeing a bit of a discrepancy between the ocean heat content tendency and that inferred by the sum of surface heat flux and heat transport convergence. This could be due to (a) the regridding, (b) the polynomial fitting approach used to calculate the ocean heat content tendency (i.e. the assumptions underlying that approach), or (c) some other reason. To get a feel for how influential the regridding is, I’ve generated the same plot using CSIRO-Mk3-6-0 and GISS-E2-R data, since the ocean data from those models is on a regular lat/lon grid (bottom panel of Figures \ref{fig:csiro} and \ref{fig:giss}), and have also analysed NorESM1-M on its native grid (Figure \ref{fig:noresm}). I’ve also included a simple analysis of the mean heat budget in the top panel of these plots, just to see how close to balanced the heat budget is in each model.