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In many environmental applications, recurrent neural networks (RNNs) are often used to model physical variables with long temporal dependencies. However, due to minibatch training, temporal relationships between training segments within the batch (intra-batch) as well as between batches (inter-batch) are not considered, which can lead to limited performance. Stateful RNNs aim to address this issue by passing hidden states between batches. Since Stateful RNNs ignore intra-batch temporal dependency, there exists a trade-off between training stability and capturing temporal dependency. In this paper, we provide a quantitative comparison of different Stateful RNN modeling strategies, and propose two strategies to enforce both intra- and inter-batch temporal dependency. First, we extend Stateful RNNs by defining a batch as a temporally ordered set of training segments, which enables intra-batch sharing of temporal information. While this approach significantly improves the performance, it leads to much larger training times due to highly sequential training. To address this issue, we further propose a new strategy which augments a training segment with an initial value of the target variable from the timestep right before the starting of the training segment. In other words, we provide an initial value of the target variable as additional input so that the network can focus on learning changes relative to that initial value. By using this strategy, samples can be passed in any order (mini-batch training) which significantly reduces the training time while maintaining the performance. In demonstrating the utility of our approach in hydrological modeling, we observe that the most significant gains in predictive accuracy occur when these methods are applied to state variables whose values change more slowly, such as soil water and snowpack, rather than continuously moving flux variables such as streamflow. 

Process‐based land surface models are important tools for estimating global wetland methane (CH₄) emissions and projecting their behavior across space and time. So far there are no performance assessments of model responses to drivers at multiple time scales. In this study, we apply wavelet analysis to identify the dominant time scales contributing to model uncertainty in the frequency domain. We evaluate seven wetland models at 23 eddy covariance tower sites. Our study first characterizes site‐level patterns of freshwater wetland CH₄fluxes (FCH₄) at different time scales. A Monte Carlo approach was developed to incorporate flux observation error to avoid misidentification of the time scales that dominate model error. Our results suggest that (a) significant model‐observation disagreements are mainly at multi‐day time scales (<15 days); (b) most of the models can capture the CH₄variability at monthly and seasonal time scales (>32 days) for the boreal and Arctic tundra wetland sites but have significant bias in variability at seasonal time scales for temperate and tropical/subtropical sites; (c) model errors exhibit increasing power spectrum as time scale increases, indicating that biases at time scales <5 days could contribute to persistent systematic biases on longer time scales; and (d) differences in error pattern are related to model structure (e.g., proxy of CH₄production). Our evaluation suggests the need to accurately replicate FCH₄variability, especially at short time scales, in future wetland CH₄model developments.

 

Abstract Atmospheric concentrations of methane, a powerful greenhouse gas, have strongly increased since 2007. Measurements of stable carbon isotopes of methane can constrain emissions if the isotopic compositions are known; however, isotopic compositions of methane emissions from wetlands are poorly constrained despite their importance. Here, we use a process-based biogeochemistry model to calculate the stable carbon isotopic composition of global wetland methane emissions. We estimate a mean global signature of −61.3 ± 0.7‰ and find that tropical wetland emissions are enriched by ~11‰ relative to boreal wetlands. Our model shows improved resolution of regional, latitudinal and global variations in isotopic composition of wetland emissions. Atmospheric simulation scenarios with the improved wetland isotopic composition suggest that increases in atmospheric methane since 2007 are attributable to rising microbial emissions. Our findings substantially reduce uncertainty in the stable carbon isotopic composition of methane emissions from wetlands and improve understanding of the global methane budget. 

Abstract. Agricultural nitrous oxide (N2O) emission accounts for a non-trivialfraction of global greenhouse gas (GHG) budget. To date, estimatingN2O fluxes from cropland remains a challenging task because the relatedmicrobial processes (e.g., nitrification and denitrification) are controlledby complex interactions among climate, soil, plant and human activities.Existing approaches such as process-based (PB) models have well-knownlimitations due to insufficient representations of the processes oruncertainties of model parameters, and due to leverage recent advances inmachine learning (ML) a new method is needed to unlock the “black box” toovercome its limitations such as low interpretability, out-of-sample failureand massive data demand. In this study, we developed a first-of-its-kindknowledge-guided machine learning model for agroecosystems (KGML-ag) byincorporating biogeophysical and chemical domain knowledge from an advanced PBmodel, ecosys, and tested it by comparing simulating daily N2O fluxes withreal observed data from mesocosm experiments. The gated recurrent unit (GRU)was used as the basis to build the model structure. To optimize the modelperformance, we have investigated a range of ideas, including (1) usinginitial values of intermediate variables (IMVs) instead of time series asmodel input to reduce data demand; (2) building hierarchical structures toexplicitly estimate IMVs for further N2O prediction; (3) using multi-tasklearning to balance the simultaneous training on multiple variables; and (4)pre-training with millions of synthetic data generated from ecosys and fine-tuningwith mesocosm observations. Six other pure ML models were developed usingthe same mesocosm data to serve as the benchmark for the KGML-ag model.Results show that KGML-ag did an excellent job in reproducing the mesocosmN2O fluxes (overall r2=0.81, and RMSE=3.6 mgNm-2d-1from cross validation). Importantly, KGML-ag always outperformsthe PB model and ML models in predicting N2O fluxes, especially forcomplex temporal dynamics and emission peaks. Besides, KGML-ag goes beyondthe pure ML models by providing more interpretable predictions as well aspinpointing desired new knowledge and data to further empower the currentKGML-ag. We believe the KGML-ag development in this study will stimulate anew body of research on interpretable ML for biogeochemistry and otherrelated geoscience processes.