From a mechanistic perspective, tillage directly changes the mixing of soil and crop residue as well as soil structure, which then affect soil biogeochemistry and crop performance through various mechanistic pathways . As such, all other impacts on water, energy, carbon and nutrient cycles from tillage are then simulated as an emergent outcome in a coherent way. In contrast, some models represent the effect of tillage as direct modification of evaporation flux and decomposition rates based on multiplication factors derived from empirical data , which introduces excessive parametric uncertainty and strong context dependence on the empirical data used for model parameterization. Simulate as many measurable variables as we can, such that the model simulation can be thoroughly validated, and measurable constraints can be easily incorporated to further improve the model simulation. For example, as discussed in Section 2.3, GPP largely determines the carbon input to the soil , and crop yield are major carbon outputs from cropland, thus models with observational constraints from ground or satellite measured GPP and/or crop yield will unsurprisingly outperform models without such constraints. From a mass-balance perspective.GPP could serve as a particularly strong constraint for quantifying litter and root exudates, two critical carbon cycle components that have significant spatial heterogeneity but are hard to measure . Another example is the recent paradigm shift from using conceptual and non-measurable SOC pools to using measurable SOC fractions for SOC simulation in process-based models . SOM is a complex mixture of materials with heterogeneous origins, chemical compounds, microbial accessibility, and turnover rates . Physical fractionation of SOM differentiate particulate organic matter and mineral-associated organic matter ,danish trolley which all are measurable in the laboratory and have different characteristic residence times .
Beyond the change in total SOC, quantifying the changes and distributions of POM and MAOM may help address the permanence issue of soil carbon credit. However, most previous soil carbon models simulate SOM dynamics as non-measurable fluxes between conceptually defined and non-measurable soil carbon pools . Only if POM and MAOM are properly conceptualized and represented in the models can they be used to simulate the changes of those SOM fractions and can measured SOM fractionation data be used as direct constraints for models . Model-data fusion here refers to a set of techniques that reduce the uncertainty of states and parameters of process-based models or data-driven models using local information to obtain improved estimation of carbon outcomes . MDF also has the ability to evolve by incorporating new sensors/sensing data or new model developments to this framework. MDF is the core part of the “System-of-Systems” solution, with the basic rationale that available observations can only see part of a system, but a model that has the necessary processes can leverage available observations to help constrain the overall system and thus improve prediction accuracy for the processes that observations do not see. The most successful example of MDF is weather forecast – the integration of weather models with satellite observation – leading to its everyday use by different industries . MDF is not a new concept in earth science and ecological studies , as methods such as Bayesian Inference, Data Assimilation, and Emergent Constraint have been extensively used to improve various predictions at some sites, watersheds, or relatively coarse spatial grids ; however, the use of MDF for field-level carbon outcome quantification has many new requirements. We propose a new MDF approach to enable MDF being conducted at every individual field level, while also quantifying critical components of the carbon cycle to inform both science and management practices.
Essentially, for every field in a targeted region, cross-scale sensing provides high-resolution and spatially-explicit E, M, C observations, which are then used as either inputs or constraints for a model with necessary processes represented , and a set of location-specific parameters will be constrained for every field. By doing so, carbon outcome quantification allows the uncertainty quantification at every field, and model verification at every field is also made possible when extra carbon-related observations can be used as independent validation data. This MDF approach to enable high resolution and spatially-explicit model constraining represents a major advance over any of the existing quantification protocols that only require validation at the regional scale. This new MDF approach fulfills the model validation needed to test whether a model or a solution has true scalability, which was defined earlier as the ability of a model to perform robustly with accepted accuracy on all targeted fields. Only models that can reproduce the accepted ‘accuracy’ at any random fields can be used as an accepted MRV tool for agricultural carbon outcome quantification. Meanwhile, such a new MDF calls for new computational techniques, as the conventional implementation of MDF techniques would be too computationally expensive to handle the field-level MDF. Take Champaign county in Illinois alone as an example, it has ~12,000 fields in active cultivation; and the state of Illinois has ~1,000,000 fields in active cultivation; conducting intensive MDF using traditional implementation for each of these fields is infeasible. Moving to AI-based solutions and fully leveraging GPU computing to facilitate efficient and effective scale-up of the field-scale MDF over a broad region is the only path forward, which will be discussed further in Section 3.4. Scaling a System-of-Systems solution to all the individual fields with similar accuracy and at a low cost is a twofold problem: cross-scale sensing to generate rich E, M, C information for constraining various aspects of agricultural carbon cycles ; and scalable application of MDF over millions of individual fields .
To reduce the computation cost to scale up, both problems require the inclusion of AI and a transition from CPU-heavy to GPU-heavy models on super computing or cloud-computing platforms for massive deployment. Below we will specifically discuss three pathways to help realize the upscaling of MDF, spanning across a spectrum of different levels of integrating process based models with AI. Pathway 1: The most straightforward path to reduce model uncertainty is to use MDF to constrain model parameters. However, the high computational cost of parameter optimization limits the scaling of MDF. A feasible bypass without massive re-coding is to leverage deep learning algorithms and develop GPU-based surrogate models. Forward inference of deep neural network-based surrogates can be orders of magnitude faster than CPU-based process-based models, making them particularly suitable for parameter calibration . Successful applications have been reported in hydrologic and Earth system models , this strategy is also practiced in other complex systems such as agroecosystem and climate models . Traditional parameter optimization algorithms work by iteratively searching for the optimal parameter combination to minimize an objective function , but may get stuck at random local optima where multiple parameter combinations correspond to identical model outputs. If parameters are calibrated for individual pixels, this illposed issue may lead to a discrete spatial distribution of the target parameters. Recently, neural network-based parameter learning methods have demonstrated promising possibilities to address this issue without a searching procedure . For example,vertical aeroponic tower garden the differentiable parameter learning framework developed by Tsai et al. enables the inference of model parameters by an unsupervised parameter learning network, which was automatically constrained by the surrogate network to produce reasonable parameter combinations in the training phase. Compared to the traditional SCE-UA method in calibrating the Variable Infiltration Capacity model, the parameter learning network estimates physically more sensible parameter sets with continuous spatial patterns because the inputs of the parameter network are themselves spatially coherent. Although AI-based surrogate models provide a pathway for the MDF upscaling, the objectives of further research should not be limited to speeding up the parameter calibration procedure but to exploring generalized pathways for estimating interpretable and reasonable model parameters. Pathway 2: The second pathway is a hybrid modeling approach to integrate machine learning and mechanistic modeling in one integrated modeling system to achieve computational efficiency, prediction accuracy and model transferability. Knowledge Guided machine learning is one such approach that learns complex patterns from data while incorporating domain-specific knowledge, such as physical rules , causality and nature of variables , informed by process-based models .
Preliminary success has been achieved in many topics including stream flow prediction , lake phosphorus and temperature estimation , and GHG emission modeling . In particular, the KGML-ag model developed by Liu et al. incorporated knowledge from the ecosys model into a GRU model and outperformed both the ecosys model and pure GRU model in predicting the complex temporal dynamics of N2O fluxes . The expanded KGML-ag method for quantifying carbon budgets exhibited strong agreement with the NEE measurements obtained from 11 eddycovariance sites . Combining KGML with Meta-learning may increase model transferability by accelerating hyperparameter learnings that account for spatial heterogeneity . Despite this early success, efforts to develop hybrid models are still in its nascent stage. Scaling field-level KGML for carbon accounting across millions of fields would require innovative approaches to assimilate multimodal remote and insitu sensing data, possibly by assimilating these data via low dimensional embeddings to constrain neural networks. Future research should also address multi-objective learnings, because existing KGML models are mostly mono-objective and lack synergistic considerations for the coupling of soil biogeochemistry. Pathway 3: Fully upgrading existing agroecosystem models to GPUaccelerated systems necessitates intensive code redesign and rewrite, thus requiring longer coordinated efforts with dedicated funding support . Based on previous explorations for Earth System Models and specific challenges in agricultural carbon outcome quantification , the ideal GPU-accelerated agroecosystem models should have the following characteristics: having the same or higher level of performance and interpretability as in the original model; working freely in the GPU environment and be flexible enough to adapt to hardware improvements; and enabling the assimilation of generic data ensemble from multiple sources with different scales for efficient training/validating/fine tuning and on-time correcting. Progress is faster in upgrading modules with relatively known physical rules, such as in the areas of climate and hydrology than in biogeochemistry or human disturbance . For example, previous efforts on rewriting domain-specific language to adapt the GPU-accelerated systems succeeded in weather modeling and climate modeling . An extensive effort is currently underway to adapt DOE ESMD/E3SM with modern machine learning techniques to next-generation architectures that are capable of GPU computing and generic data assimilation . The recently proposed concept of neural earth system modeling , aiming for a deep and interpretable integration of AI into ESMs, might be the closest solution for upgrading agroecosystem models as well. One profound step for such upgrading is to replace every submodule of the process-based model with a ML surrogate, and to train those surrogates jointly with real world observations. However, proceeding in this direction needs to conquer the challenge of mapping highly non-linear processes involving partial differential equations with different coefficients at different spatial and temporal resolutions. One solution that has shown some early success in predicting global atmospheric circulations is Fourier Neural Operator , a neural network specifically designed for solving an entire family of PDEs by learning mappings between functions in infinite-dimensional spaces . However, FNO is only one kind of “black box” neutral solver for PDEs. To be adopted in agroecosystem simulations, FNO needs to combine with other machine learning models to consider the connections and heterogeneity in space and time, and needs knowledge-guided constraints to provide predictions following physical/biogeochemical rules. Model validation, a procedure to benchmark model simulation with independent, high-quality observational data, is the only way to build model fidelity. The new MDF approach of high resolution and spatially-explicit model constraining essentially proposes a more strict way to test model scalability, defined as the ability of a model to perform robustly with accepted accuracy on all targeted fields. “Scalability” of a model or a solution should not only be demonstrated by model performance at a limited number of sites with rich data, where extensive parameter calibration is allowed; a true test of model “scalability” should be also demonstrated at many random sites, where only limited measurements are available. The latter is what a real world application entails – we are required to quantify the carbon outcomes at any given field. To achieve the above goal to fully validate the model scalability, a three-tier validation approach is needed, and results from these three tiers should be reported to the community for fair and transparent comparison.