Estimating ocean biogeochemistry (BGC) parameters in Earth System Models is challenging due to multiple error sources and interlinked parameter sensitivities. Reducing the temperature and salinity bias in the ocean physical component of the Norwegian Earth System Model (NorESM) diminishes the BGC state bias at intermediate depth but leads to a greater bias increase near the surface. This suggests that BGC parameters are tuned to compensate for the physical ocean model biases. We successfully apply the iterative ensemble smoother data assimilation technique to estimate BGC parameters in NorESM with reduced bias in its physical ocean component.  We estimate BGC parameters based on the monthly climatological error of nitrate, phosphate, and oxygen in a coupled reanalysis of NorESM that assimilates observed monthly climatology of temperature and salinity.  First, we compare the performance of globally uniform and spatially varying parameter estimations. Both approaches reduce BGC bias obtained with default parameters, even for variables not assimilated in the parameter estimation (e.g., CO2 fluxes and primary production). While spatial parameter estimation performs locally best, it also increases biases in areas with few observations, and overall performs poorer than global parameter estimation. A second iteration further reduces the bias in the near-surface BGC with global parameter estimation. Finally, we assess the performance of global estimated parameters in a 30-year coupled reanalysis produced by assimilating time-varying temperature and salinity observations. This reanalysis reduces error by  10-20% for phosphate, nitrate, oxygen, and dissolved inorganic carbon compared to a reanalysis done with default parameters.