The amount of plant organic matter produced on annual basis, so called net primary production or NPP, is the basic characteristic of the biosphere. It shows biosphere potential to supply primary food energy source for non-autotrophic species including humans. Human appropriation of terrestrial net primary production stems not only from the demand for food but also for fuel, construction materials, and paper. It is estimated to be from 8 to 15 PgC y^-1 in total (including 3–6 PgC y^-1 associated with food supply) 1.

NPP also shows biosphere potential to steer the Earth system by absorbing CO₂, a gas whose atmospheric concentration affects global climate. NPP characterizes the "gross" terrestrial carbon sink – the amount of CO₂ annually sequestered by vegetation. The net land-to-atmosphere flux is much smaller because the "gross" sink is compensated for by various carbon sources. Its magnitude is estimated to be from 0.3 to 1.5 PgC y^-1 2. The coupled carbon-cycle-climate models show the wide range of projections for the magnitude of the terrestrial uptake in the middle of this century: from 0 to 8 PgC y^-1 3.

Appropriation (or re-direction) of NPP is also one method of climate change mitigation. Protecting non-living organic matter from decomposition and burning 4, reducing deforestation rates 567, and increasing the forest harvest age 8 will "re-direct" NPP to carbon pools with longer turnover times. Implementation of these measures may partly compensate for emissions from fossil fuel burning.

The total terrestrial NPP is generally assumed to be about 60 PgC y^-1 9. Biosphere models differ on this value. Comparison of global NPP models carried out more than a decade ago revealed that estimates ranged from 44.4 to 66.3 PgC y^-1 10. One of the major results of that comparative study was releasing average estimates of NPP over a geographic grid with a half-degree resolution 11. These were the first normative data on global NPP created by summarizing modelling efforts. ("Normative data" means the data that result from a model ensemble, not from a single model, and therefore may be accepted as norms.)

The data have not been updated since then, although a number of new models and new versions of old models were developed during the last decade. Here we present the series of updates reflecting the evolution of biosphere models.

In modelling terrestrial productivity we are facing the problem of structural uncertainty. Field observations hardly allow us to make a reasonable choice between competing conceptual frameworks, to form an agreement on the best model structure, or even to discriminate between adequate descriptions of significant processes from inadequate ones 18. Therefore, we approach this problem through retrospection of modelling efforts.

Terrestrial productivity has been a focus of biosphere studies over the last three decades. First, the global pattern of NPP was characterized by data collected during the International Biological Program (1964–1974). Then, the data was turned into empirical models that relate gradations in NPP to environmental factors of known geographic distribution. Later, a number of process-based models were developed in connection to the IGBP activities. This is definitely a field of science that hardly may be referred to as immature.

Nevertheless, the range of estimates remains roughly constant over this period. Early estimates of terrestrial NPP range from 10 to 100 PgC y^-1 19. Starting in the 1970s, they fall between 40 and 80 PgC y^-1. The estimates of empirical models 20 vary from 50 to 65 PgC y^-1, and the estimates of process-based models are expected to vary in the same range 10. Re-analysis of the NPP measurements stored in the Osnabrück NPP database show that a 90% confidence interval for the expected value is 50–70 PgC y^-1 21. It seems that it may be difficult to reduce this 20% level of uncertainty in the commonly accepted estimate of terrestrial NPP while leaving research methods unchanged.

Therefore, we are focusing here on the stability of normative estimates – that is, estimates acceptable for use in policy relevant assessments. The diversity of research results does not matter until a viable alternative to the commonly accepted norms emerges. This study confirms that 60 PgC y^-1 remains to be the best candidate for further use in policy relevant assessments.

The major output of this study, gridded normative data on terrestrial productivity, may find use in benchmarking NPP models employed in coupled carbon-cycle-climate models. Could the wide range of projections for the future magnitude of the terrestrial uptake be attributed to the diversity of NPP models employed? Which projections correspond to well-established beliefs, and which do not?

Recent IPCC guidelines focus on objective reporting of uncertainty stemming from climate model pluralism 22. However, epistemological pluralism 2324 is no more a topical issue in "a world that is aware of its responsibility for planetary change and will demand globally concerted actions" 2526. One of the things that the world community is likely to expect from scientists is evaluating effectiveness of these actions in an objective and unambiguous manner 27. Hence, it seems a time for moving the focus of attention to objective reporting of well-established beliefs.

Objective reporting of well-established beliefs suggests drawing distinctions between normative knowledge (or text-book knowledge) and alternative knowledge (or frontier knowledge). The former is the solid knowledge that has stood the test of time and is well confirmed by a number of independent research studies. Frontier knowledge is something new, and something really new cannot be turned into solid knowledge immediately. Since each model may be considered as normative for some regions and as alternative for other regions, we are not drawing distinctions between models. Instead, we are sorting model outputs and doing what is called "knowledge engineering" 28.

The stability of well-established beliefs stems from the stability of research methods, and therefore it can be temporal. Rapid development of meteorological methods for measuring CO₂ fluxes offers some benefits over traditional methods of measuring productivity. The observation network for measurements of gas, water and energy exchange between terrestrial ecosystems and the atmosphere, so-called FLUXNET 29, produced a large collection of data. This calls for re-calibration of existing models 3031, and, hypothetically, may lead to changes in our judgement on typical values of productivity. Similar effects may have measurements coming from new satellite sensors.

Modern observational tools will eventually improve the consistency of biosphere models through creating multiple constraints for positioning 'true' values for model parameters 32333435 and through filling gaps in knowledge needed for improving descriptions of significant processes. The evolution of normative knowledge on terrestrial productivity is thus limited by the rate at which the research community internalizes new facts and builds consensus on necessary changes in the norms. The scheme of building normative data 36 employed in this study simulates the process of consensus building, but sets transparent criteria for distinguishing between normative and alternative data. It also suggests that an existing consensus should be re-considered when the bulk and consistency of alternative data match the bulk and consistency of normative data (Figure 5). The software tools realizing this scheme are available through web-based services developed for routine checks of model consistency.

The evolution of scientific theories is often considered a Darwinian process of natural selection that determines which theory survives and drifts them toward consensus 37. The scheme of building normative data 36 employed in this study simulates the process of data selection by setting transparent criteria of fitness.

This algorithm works against new estimates that do not fall within the range implied by the initial ensemble: Miami NPP model, Montreal NPP model, TGER-NPP model and the outputs of the Potsdam NPP model intercomparison. Moreover, it works against new estimates that may increase uncertainty in the mean value, which is measured as the width of the confidence interval: δ = 2 c·s·n^-1/2, where n is the number of estimates, s is standard deviation, c is 95th percentile of Student's t distribution with n-1 degree of freedom. All this is filtering out erroneous estimates as well as correct estimates when they are dramatically contradicting normative knowledge formed by the initial ensemble.

Since no well-agreed-upon method exists at the moment for distinguishing between erroneous and correct estimates of NPP, every estimate is included either into the normative ensemble or into the alternative ensemble. The former represents the current state of knowledge, whereas the latter represents emerging alternatives to current knowledge.

Noteworthy also are discrepancies in estimates that may result from different spatial resolution of models and/or input data. They were reduced by filtering out models of low spatial resolution.

The results of this study should be interpreted in the same manner as the results of Potsdam NPP Model Intercomparison 10, and should not be taken out of context. For example, normative productivity of crops under specific crop management system may be either higher or lower than Normative NPP.

The authors declare that they have no competing interests.

The authors contributed equally to the design of the study and to manuscript drafting. Calculations were performed by GAA. Both authors read and approved the final version of the manuscript.

Efforts to model terrestrial productivity may be categorized into three types: (type 1) developing an empirical model interpolating and extrapolating measured NPP values, (type 2) developing an empirical model interpolating and extrapolating parameters of a process-based model of productivity using measured NPP values, (type 3) developing an empirical model interpolating and extrapolating parameters of a process-based model of productivity using measured values of this parameters.

The typical representative of the first type, which is referred to as empirical models, is the Miami NPP model. The observed gradations in the observed data are attributed to factors of known global distribution using mathematical functions that have no biological meaning. Then, these functions are used to produce a global pattern of productivity from given global patterns of mean annual temperature and precipitations.

TsuBiMo represents the second type, which is referred to as semi-empirical process-based models. The measured values of NPP are considered as indirect measurements of light-saturated rates of photosynthesis 18. The values of this parameter are restored from the NPP measurements using technique known as model-data fusion 39. Then, gradations in the light-saturated rate of photosynthesis are attributed to gradations in the temperature and precipitation during the growing season. The temperature dependence is modelled with a generalized Arrhenius function 40, whereas the humidity factor is modelled with a function that has no biophysical meaning.

Biome-BGC represents the third type, which is referred to as process-based models, and GLO-PEM represent a class of so-called production efficiency models (PEMs). A number of such models were developed between 1992 and 1996 (Table 2). The boom has been backed by supportive databasing activities. In 1991, the International Institute for Applied System Analysis (IIASA) released the database for mean monthly values of temperature, precipitation and cloudiness of a global terrestrial grid 41. In 1992, the Environmental Research Laboratory of the US Environmental Protection Agency released a comprehensive geographic database for modelling terrestrial climate-biosphere interactions 42. Data on the global distribution of productivity factors stimulated globalization of process-based models that were originally developed for modelling productivity at an ecosystem scale 4344.

Most process-based models require species-specific parameterization that becomes problematic on a global scale. Since the global distribution of species-specific parameters is not well known, they are normally set at some ad hoc values. The recent development of techniques for model-data fusion 34 opens up possibilities for transforming process-based models into semi-empirical, process-based models.

New techniques for data-fusion (such as neural networks) together with growing databases of NPP measurements offer new opportunities for empirical modelling. The NCEAS model 45 may be a first sign of the new boom in empirical modelling.

The history of modelling efforts is presented in Table 2, where models 44454647484950515253545556575859606162636465666768697071727374757677787980818283848586878889909192939495969798 are listed in chronological order.