Trivial improvements of predictive skill due to direct reconstruction
of global carbon cycle

Abstract. State-of-the-art carbon cycle prediction systems are initialized from reconstruction simulations in which state variables of the climate system are assimilated. While currently only the physical state variables are assimilated, biogeochemical state variables adjust to the state acquired through this assimilation indirectly instead of being assimilated themselves. In the absence of comprehensive biogeochemical reanalysis products, such approach is pragmatic. Here we evaluate a potential advantage of having perfect carbon cycle observational products to be used for direct carbon cycle reconstruction. Within an idealized perfect-model framework, we define 50 years of a control simulation under pre-industrial CO2 levels as our target representing observations. We nudge variables from this target onto arbitrary initial conditions 150 years later mimicking an assimilation simulation generating initial conditions for hindcast experiments of prediction systems. We investigate the tracking performance, i.e. bias, correlation and root-mean-square-error between the reconstruction and the target, when nudging an increasing set of atmospheric, oceanic and terrestrial variables with a focus on the global carbon cycle explaining variations in atmospheric CO2. We compare indirect versus direct carbon cycle reconstruction against a resampled threshold representing internal variability. Afterwards, we use these reconstructions to initialize ensembles to assess how well the target can be predicted after reconstruction. Interested in the ability to reconstruct global atmospheric CO2, we focus on the global carbon cycle reconstruction and predictive skill. We find that indirect carbon cycle reconstruction through physical fields reproduces the target variations on a global and regional scale much better than the resampled threshold. While reproducing the large scale variations, nudging introduces systematic regional biases in the physical state variables, on which biogeochemical cycles react very sensitively. Global annual surface oceanic pCO2 initial conditions are indirectly reconstructed with an anomaly correlation coefficient (ACC) of 0.8 and debiased root mean square error (RMSE) of 0.3 ppm. Direct reconstruction slightly improves initial conditions in ACC by +0.1 and debiased RMSE by −0.1 ppm. Indirect reconstruction of global terrestrial carbon cycle initial conditions for vegetation carbon pools track the target by ACC of 0.5 and debiased RMSE of 0.5 PgC. Direct reconstruction brings negligible improvements for air-land CO2 flux. Global atmospheric CO2 is indirectly tracked by ACC of 0.8 and debiased RMSE of 0.4 ppm. Direct reconstruction of the marine and terrestrial carbon cycles improves ACC by 0.1 and debiased RMSE by −0.1 ppm. We find improvements in global carbon cycle predictive skill from direct reconstruction compared to indirect reconstruction. After correcting for mean bias, indirect and direct reconstruction both predict the target similarly well and only moderately worse than perfect initialization after the first lead year. Our perfect-model study shows that indirect carbon cycle reconstruction yields satisfying initial conditions for global CO2 flux and atmospheric CO2. Direct carbon cycle reconstruction adds little improvements in the global carbon cycle, because imperfect reconstruction of the physical climate state impedes better biogeochemical reconstruction. These minor improvements in initial conditions yield little improvement in initialized perfect-model predictive skill. We label these minor improvements due to direct carbon cycle reconstruction trivial, as mean bias reduction yields similar improvements. As reconstruction biases in real-world prediction systems are even stronger, our results add confidence to the current practice of indirect reconstruction in carbon cycle prediction systems.