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Key Points A new semi‐analytical spin‐up (SASU) framework combines the default accelerated spin‐up method and matrix analytical algorithm SASU accelerates CLIM5 spin‐up by tens of times, becoming the fastest method to our knowledge SASU is applicable to most biogeochemical models and enables computationally costly study, for example, sensitivity analysis 

Abstract Large across‐model spread in simulating land carbon (C) dynamics has been ubiquitously demonstrated in model intercomparison projects (MIPs), and became a major impediment in advancing climate change prediction. Thus, it is imperative to identify underlying sources of the spread. Here, we used a novel matrix approach to analytically pin down the sources of across‐model spread in transient peatland C dynamics in response to a factorial combination of two atmospheric CO 2 levels and five temperature levels. We developed a matrix‐based MIP by converting the C cycle module of eight land models (i.e., TEM, CENTURY4, DALEC2, TECO, FBDC, CASA, CLM4.5 and ORCHIDEE) into eight matrix models. While the model average of ecosystem C storage was comparable to the measurement, the simulation differed largely among models, mainly due to inter‐model difference in baseline C residence time. Models generally overestimated net ecosystem production (NEP), with a large spread that was mainly attributed to inter‐model difference in environmental scalar. Based on the sources of spreads identified, we sequentially standardized model parameters to shrink simulated ecosystem C storage and NEP to almost none. Models generally captured the observed negative response of NEP to warming, but differed largely in the magnitude of response, due to differences in baseline C residence time and temperature sensitivity of decomposition. While there was a lack of response of NEP to elevated CO 2 (eCO 2 ) concentrations in the measurements, simulated NEP responded positively to eCO 2 concentrations in most models, due to the positive responses of simulated net primary production. Our study used one case study in Minnesota peatland to demonstrate that the sources of across‐model spreads in simulating transient C dynamics can be precisely traced to model structures and parameters, regardless of their complexity, given the protocol that all the matrix models were driven by the same gross primary production and environmental variables. 

Abstract Soils store more carbon than other terrestrial ecosystems 1,2 . How soil organic carbon (SOC) forms and persists remains uncertain 1,3 , which makes it challenging to understand how it will respond to climatic change 3,4 . It has been suggested that soil microorganisms play an important role in SOC formation, preservation and loss 5–7 . Although microorganisms affect the accumulation and loss of soil organic matter through many pathways 4,6,8–11 , microbial carbon use efficiency (CUE) is an integrative metric that can capture the balance of these processes 12,13 . Although CUE has the potential to act as a predictor of variation in SOC storage, the role of CUE in SOC persistence remains unresolved 7,14,15 . Here we examine the relationship between CUE and the preservation of SOC, and interactions with climate, vegetation and edaphic properties, using a combination of global-scale datasets, a microbial-process explicit model, data assimilation, deep learning and meta-analysis. We find that CUE is at least four times as important as other evaluated factors, such as carbon input, decomposition or vertical transport, in determining SOC storage and its spatial variation across the globe. In addition, CUE shows a positive correlation with SOC content. Our findings point to microbial CUE as a major determinant of global SOC storage. Understanding the microbial processes underlying CUE and their environmental dependence may help the prediction of SOC feedback to a changing climate. 

Abstract. Soil represents the largest phosphorus (P) stock in terrestrialecosystems. Determining the amount of soil P is a critical first step inidentifying sites where ecosystem functioning is potentially limited by soilP availability. However, global patterns and predictors of soil total Pconcentration remain poorly understood. To address this knowledge gap, weconstructed a database of total P concentration of 5275 globallydistributed (semi-)natural soils from 761 published studies. We quantifiedthe relative importance of 13 soil-forming variables in predicting soiltotal P concentration and then made further predictions at the global scaleusing a random forest approach. Soil total P concentration variedsignificantly among parent material types, soil orders, biomes, andcontinents and ranged widely from 1.4 to 9630.0 (median 430.0 and mean570.0) mg kg−1 across the globe. About two-thirds (65 %) of theglobal variation was accounted for by the 13 variables that we selected,among which soil organic carbon concentration, parent material, mean annualtemperature, and soil sand content were the most important ones. Whilepredicted soil total P concentrations increased significantly with latitude,they varied largely among regions with similar latitudes due to regionaldifferences in parent material, topography, and/or climate conditions. SoilP stocks (excluding Antarctica) were estimated to be 26.8 ± 3.1 (mean ± standard deviation) Pg and 62.2 ± 8.9 Pg (1 Pg = 1 × 1015 g) in the topsoil (0–30 cm) and subsoil (30–100 cm), respectively.Our global map of soil total P concentration as well as the underlyingdrivers of soil total P concentration can be used to constraint Earth systemmodels that represent the P cycle and to inform quantification of globalsoil P availability. Raw datasets and global maps generated in this studyare available at https://doi.org/10.6084/m9.figshare.14583375(He et al., 2021). 

Earth system models (ESMs) have been rapidly developed in recent decades to advance our understanding of climate change‐carbon cycle feedback. However, those models are massive in coding, require expensive computational resources, and have difficulty in diagnosing their performance. It is highly desirable to develop ESMs with modularity and effective diagnostics. Toward these goals, we implemented a matrix approach to the Community Land Model version 5 (CLM5) to represent carbon and nitrogen cycles. Specifically, we reorganized 18 balance equations each for carbon and nitrogen cycles among the 18 vegetation pools in the original CLM5 into two matrix equations. Similarly, 140 balance equations each for carbon and nitrogen cycles among the 140 soil pools were reorganized into two additional matrix equations. The vegetation carbon and nitrogen matrix equations are connected to soil matrix equations via litterfall. The matrix equations fully reproduce simulations of carbon and nitrogen dynamics by the original model. The computational cost for forwarding simulation of the CLM5 matrix model was 26% more expensive than the original model, largely due to calculation of additional diagnostic variables, but the spin‐up computational cost was significantly saved. We showed a case study on modeled soil carbon storage under two forcing data sets to illustrate the diagnostic capability that the matrix approach uniquely offers to understand simulation results of global carbon and nitrogen dynamics. The successful implementation of the matrix approach to CLM5, one of the most complex land models, demonstrates that most, if not all, the biogeochemical models can be reorganized into the matrix form to gain high modularity, effective diagnostics, and accelerated spin‐up.