Soil organic carbon (SOC) is a key component of the global carbon cycle, yet it is not well-represented in Earth system models to accurately predict global carbon dynamics in response to climate change. This novel study integrated deep learning, data assimilation, 25,444 vertical soil profiles, and the Community Land Model version 5 (CLM5) to optimize the model representation of SOC over the conterminous United States. We firstly constrained parameters in CLM5 using observations of vertical profiles of SOC in both a batch mode (using all individual soil layers in one batch) and at individual sites (site-by-site). The estimated parameter values from the site-by-site data assimilation were then either randomly sampled (random-sampling) to generate continentally homogeneous (constant) parameter values or maximally preserved for their spatially heterogeneous distributions (varying parameter values to match the spatial patterns from the site-by-site data assimilation) so as to optimize spatial representation of SOC in CLM5 through a deep learning technique (neural networking) over the conterminous United States. Comparing modeled spatial distributions of SOC by CLM5 to observations yielded increasing predictive accuracy from default CLM5 settings ( R 2 = 0.32) to randomly sampled (0.36), one-batch estimated (0.43), and deep learning optimized (0.62) parameter values. While CLM5 with parameter values derived from random-sampling and one-batch methods substantially corrected the overestimated SOC storage by that with default model parameters, there were still considerable geographical biases. CLM5 with the spatially heterogeneous parameter values optimized from the neural networking method had the least estimation error and less geographical biases across the conterminous United States. Our study indicated that deep learning in combination with data assimilation can significantly improve the representation of SOC by complex land biogeochemical models.

As an artificial neural network method, self-organizing mapping facilities efficient complete and visualize high-dimensional data topology representation, valid in a number of applications such as network intrusion detection. However, there remains a challenge to accurately depict the topology of network traffic data with unbalanced distribution, which deteriorates the performance of e.g. DoS attack detection. Hence, we propose a new model of the ''statistic-enhanced directed batch growth self-organizing mapping'', renew the definition of the growth threshold used to evaluate/control neuron expansion, and first introduce the inner distribution factor for fine-grained data distinguishing. The numerical experiments based on two datasets, KDD99, and CICIDS2017, demonstrate that the key performance in DoS attack detection including the detection rate, the false positive rate, and the training time are greatly enhanced thanks to the statistic concepts consulted in the proposed model. INDEX TERMS DoS attack detection, statistic-enhanced directed batch growing self-organizing mapping, growth threshold, inner distribution factor.

Land ecosystems contribute to climate change mitigation by taking up approximately 30% of anthropogenically emitted carbon. However, estimates of the amount and distribution of carbon uptake across the world's ecosystems or biomes display great uncertainty. The latter hinders a full understanding of the mechanisms and drivers of land carbon uptake, and predictions of the future fate of the land carbon sink. The latter is needed as evidence to inform climate mitigation strategies such as afforestation schemes. To advance land carbon cycle modeling, we have developed a matrix approach. Land carbon cycle models use carbon balance equations to represent carbon exchanges among pools. Our approach organizes this set of equations into a single matrix equation without altering any processes of the original model. The matrix equation enables the development of a theoretical framework for understanding the general, transient behavior of the land carbon cycle. While carbon input and residence time are used to quantify carbon storage capacity at steady state, a third quantity, carbon storage potential, integrates fluxes with time to define dynamic disequilibrium of the carbon cycle under global change. The matrix approach can help address critical contemporary issues in modeling, including pinpointing sources of model uncertainty and accelerating spin‐up of land carbon cycle models by tens of times. The accelerated spin‐up liberates models from the computational burden that hinders comprehensive parameter sensitivity analysis and assimilation of observational data to improve model accuracy. Such computational efficiency offered by the matrix approach enables substantial improvement of model predictions using ever‐increasing data availability. Overall, the matrix approach offers a step change forward for understanding and modeling the land carbon cycle.

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