## 1 Introduction  
Estimation of global vegetation Gross Primary Production (GPP) and Net Primary Production (NPP) and their interannual variations are critical for understanding the feedbacks between the biosphere and the atmosphere. Ecosystem carbon models, inversion models, and inventories have been used for assessing global land primary production, generating total annual global estimates of GPP and NPP converging around 120 [1] and 60 [2] Pg\(\cdot\)C\(\cdot\)yr\({}^{-1}\), respectively. Meanwhile, Net Biome Productivity (NBP), the net carbon accumulation by ecosystems [3], was estimated just 2% of GPP for the 1990s [4]. Therefore, estimation of interannual variations of GPP and NPP are also important as well as their total magnitudes for understanding NBP response to CO\({}_{2}\) emissions and changes in climate. To elucidate the mechanisms that cause the interannual variation in GPP, we need to rely on bottom up modeling approaches [5]. However, in contrast to total magnitude of GPP, there is no consensus on interannual variation in global GPP or NPP even for the last few decades with satellite observations (for example, [6,7]).  
One reason for the models failing to reach agreement on the interannual variations of GPP is the oversimplification of the simulated responses of vegetation to climate variability. By tuning the model parameters to match their output to the data from validation sites, even simple models can provide a reasonable estimate of total GPP [8,9]. Indeed, as more validation data are becoming available, the annual magnitudes of global GPP and NPP estimations from different models have been converging [1,2]. However, it is another issue whether those simple models tuned to acceptable annual GPP range can produce realistic interannual variations in estimated carbon fluxes. In addition, not enough long-term data are available to validate the model results globally on inter-annual time scales.  
The recent availability of a 30-year satellite record of Global Inventory Modeling and Mapping Studies (GIMMS) 3g data, focus of this special issue, from NOAA/AVHRR provides an unprecedented opportunity to examine the interpretation of long-term GPP simulations by simple models. In this study, we focus on the effect of drought stress on the interannual variation in GPP, and assess the structural uncertainty in model-simulated trends of global GPP. Reductions in GPP caused by drought stress can be modeled through increases in Vapor Pressure Deficit (VPD) and/or reductions in precipitation via soil moisture. Because time series of VPD and precipitation are generally highly correlated, some models use only VPD sub-models or only soil moisture sub-models to simulate the impact of drought stress on GPP [10]. Short-term comparisons have shown that VPD-only models can produce variations in GPP that are similar to the ones obtained from models with both VPD and soil moisture sub-models [11]. These similarities are not surprising when precipitation and VPD trends are coherent, but this is not necessarily always the case. For example, it has been reported that while global warming-induced increases in VPD were observed [6], global total precipitation did not show a significant trend for the last three decades [12, 13]. In this case, we would expect the VPD-only models to produce incorrect time series of GPP estimates. Furthermore, according to the Coupled Model Intercomparison Project Phase 5 (CMIP5), reduction in relative humidity with global warming was expected to continue over the 21 st century [14], while globally averaged precipitation was projected to increase with high uncertainty around regional estimates [15]. Therefore, it is crucial to clarify how model structure of drought stress affects the interannual variations in GPP. To address this question, we used the Terrestrial Observation and Prediction System model (TOPS) [16] to produce global GPP estimates from 1982 to 2009 using GIMMS 3g data, and analyze how VPD and soil moisture influence the interannual variation in global GPP.