We analyse 400 perturbed-parameter simulations for two configurations of an optimality-based plankton–ecosystem model (OPEM), implemented in the University of Victoria Earth System Climate Model (UVic-ESCM), using a Latin hypercube sampling method for setting up the parameter ensemble. A likelihood-based metric is introduced for model assessment and selection of the model solutions closest to observed distributions of

Earth system climate models (ESCMs) are powerful tools for analysing variations in climate, while resolving interdependencies between changes in the atmosphere, on land, and in the ocean

The basic structure of most marine ecosystem models has been designed for resolving mass fluxes between nutrients, phytoplankton, zooplankton, and detritus, typically referred to as NPZD models. Mathematical formulations that describe growth and fate of marine phytoplankton and zooplankton biomass have been successfully applied over a range of scales, from local 0-D ecosystem models

In order to better represent plankton physiology, the new ecosystem model relies on optimality-based considerations for phytoplankton growth, including

Here, we analyse the new model's performance and evaluate model-ensemble results against observations. Since the model is based on plankton–organism physiology, it includes new parameters whose values have not been estimated for global model applications. Also, we set up two configurations, OPEM and OPEM-H, with different temperature dependencies for diazotrophs, to investigate the effects of different empirical temperature functions on distributions of diazotrophs and

OPEM has been implemented into the UVic-ESCM

The OPEM and its implementation into the UVic-ESCM are described in Part 1

Our setup comprises ensembles of 400 simulations for each of two model configurations that differ in how temperature affects diazotrophy. The original temperature dependence of diazotrophs (

For all simulations, we impose pre-industrial (AD 1850) boundary conditions with a

The 400-parameter combinations are obtained via Latin hypercube sampling (LHS)

The sensitivity (

Parameter names, reference and variational ranges, identified “best” values for the trade-off simulations (OPEM and OPEM-H), units, and definitions. Note that the trade-off simulations share the same parameter combination.

We consider four different types of observations for quantitatively assessing the model simulations. The first three are the objectively analysed monthly (upper 550 m) and annual (below 550 m) concentrations of nitrate, phosphate, and oxygen of the World Ocean Atlas 2013

We define our metric in terms of spatial averages of 17 distinct biogeochemical biomes, as derived and described by

The underlying error model of the likelihood-based metric assumes a Gaussian (normal) distribution, which is well represented by using the first two moments of log-transformed tracer concentrations, in particular for the upper ocean layers

Our metric is derived from a likelihood, assuming a Gaussian error distribution for the residuals, which describes the discrepancy between mean values derived from observations (

The residual vector (

With the consideration of standard errors instead of standard deviations, we implicitly impose weights to
differences in the spatial expansion (i.e. number of data points of the gridded product used) of individual biomes. Overall, the final cost function

In order to estimate uncertainty ranges for selected model results (globally averaged

Table

Ranges of global averages of major tracer concentrations or fluxes in the OPEM and OPEM-H configurations. Chl concentration is for the upper 50 m (surface layer of the UVic grid) and NCP is for the upper 100 m. Observations and reference model simulations are listed in the Reference column.

The sensitivities of globally averaged biogeochemical properties to the variations of each of the 13 parameters in Table

Sensitivities of globally averaged

A surprising finding is that oxygen is sensitive to, and positively correlated with, the subsistence nitrogen quota of ordinary phytoplankton (

The sensitivity of DIC is generally low, because of the relatively large DIC pool compared to the variations in fluxes among the different parameter sets. Similar to oxygen, DIC is most sensitive to

Dissolved iron (DFe) is most sensitive to the remineralisation rate (

The simulated global

Of particular interest are the sensitivities of global NPP and NCP.
Particle fluxes in marine biogeochemical models tend to agree most closely with sediment trap data for depths of about 1000 m or below

First, we discuss the proportions of carbon, nitrogen, and phosphorus in ordinary phytoplankton and diazotrophs, since variations in elemental stoichiometry in autotrophs originate in differential uptake of nutrients under different environmental conditions.

Globally averaged C, N, and P concentrations and ratios of globally averaged N and P of ordinary phytoplankton and diazotrophs are sensitive to

Diazotroph C, N, and P are generally more sensitive to parameter variations than phytoplankton due to the much smaller total biomass of diazotrophs, which is also the reason why diazotrophs are less sensitive in OPEM-H, the model configuration in which their biomass is generally larger because of the growth of diazotrophs at high latitudes

Sensitivities of globally averaged concentrations of ordinary and diazotrophic phytoplankton C, N, and P, and ratios of globally averaged N and P to model parameters. Black and grey shading denotes OPEM and OPEM-H configurations, respectively. Note the different

Particulate

At low latitudes, particulate

The sensitivities of dissolved

Parameter sensitivities of averaged surface (0–130 m) particulate elemental

Costs vs. tracer concentrations and fluxes for annual

Globally averaged oxygen vs. nitrate in OPEM and OPEM-H. Colour represents cost value. Solid red triangle and blue circle annotate the simulations with minimum cost in OPEM and OPEM-H, respectively, and open red triangle and blue circle are the trade-off simulations. The green square, horizontal and vertical lines indicate mean oxygen and nitrate concentrations of
0.176 and 0.031 mol m

The cost function (introduced in Sect.

The cost function penalises solutions that yield

In the following, we will describe the lowest-cost solutions together with the trade-off solutions, as well as respective uncertainty ranges obtained from the bootstrap method described in the materials and methods section. The width of the uncertainty ranges (95 % confidence intervals) in Fig.

While the trade-off solutions exhibit

Figure

Figures

Zonally averaged

Same simulations as in Fig.

Cost is conspicuously correlated only with

Lower parts (

Figure

Remineralisation rate (

These results also put forward a new point of view on the relation between

The strong impact of

While in many global biogeochemical models zooplankton are described by non-mechanistic formulations, such as Holling-type functions

Other parameters in the sensitivity analysis appear less important for the tracer distributions, but this does not necessarily mean that they are negligible. Specific mortality rate (

In general, tracer sensitivities to parameters in OPEM-H configuration are similar to those in OPEM.

Several studies have revealed that

The strong correlation between

To evaluate how water-column denitrification affects our cost function, we arrange our simulations in the order of their cost values and plot the volume of ODZs against cost for both the OPEM and OPEM-H configurations in Fig.

Cost values across all parameter sensitivity simulations ordered from low to high for the two model configurations. Cost values in both misfit and variance

The cost function introduced above is a metric that quantifies the discrepancy between objectively analysed observational data and simulation results. Our cost function proves useful for exploring the 400 ensemble model solutions and identifies model solutions that reproduce deep ocean gradients in the

Even within the 5 % of the simulations with the lowest costs, the estimates of global

Also, the minimum-cost solution yields very low global

A peculiarity of our cost function is that it complements the data–model misfit, i.e. the residuals of spatial mean

The 17 biomes derived by

For low cost-function values, the contribution of the variance term is generally small in most biomes for the deep layers (Fig.

The upper layer's variance term contributes strongly to low costs in North Atlantic biomes. This is particularly striking for the equatorial Atlantic biome (Atl.EQU). The main reason is water-column denitrification that results in a high variance in

We demonstrate sensitivities of various tracers and processes to parameters in two configurations of a new optimality-based plankton–ecosystem model (OPEM) in the UVic-ESCM. While OPEM-H
predicts a wider geographical range for

We introduce a new likelihood-based metric for model calibration. The metric appears capable of constraining globally averaged

The University of Victoria Earth System Climate Model version 2.9 (original model) is available at

The supplement related to this article is available online at:

CTC and MP performed the ensemble solutions and selected the reference simulations. MS set up the likelihood-based metric. All authors contributed to the manuscript text.

The authors declare that they have no conflict of interest.

We would like to thank Sakina-Dorothée Ayata and an anonymous referee for their comments, which greatly improved the manuscript.

Chia-Te Chien, Markus Pahlow, and Markus Schartau were supported by the BMBF-funded project PalMod. Markus Pahlow was supported by the Deutsche Forschungsgemeinschaft (DFG) by SFB754 (Sonderforschungsbereich 754
“Climate-Biogeochemistry Interactions in the Tropical Ocean”,

This paper was edited by Andrew Yool and reviewed by Sakina-Dorothée Ayata and one anonymous referee.