The prediction of streamflows and other environmental variables in unmonitored basins is a grand challenge in hydrology. Recent machine learning (ML) models can harness vast datasets for accurate predictions at large spatial scales. However, there are open questions regarding model design and data needed for inputs and training to improve performance. This study explores these questions while demonstrating the ability of deep learning models to make accurate stream temperature predictions in unmonitored basins across the conterminous United States. First, we compare top-down models that utilize data from a large number of basins with bottom-up methods that transfer ML models built on local sites, reflecting traditional regionalization techniques. We also evaluate an intermediary grouped modeling approach that categorizes sites based on regional co-location or similarity of catchment characteristics. Second, we evaluate trade-offs between model complexity, prediction accuracy, and applicability for more target locations by systematically removing inputs. We then examine model performance when additional training data becomes available due to reductions in input requirements. Our results suggest that top-down models significantly outperform bottom-up and grouped models. Moreover, it is possible to get acceptable accuracy by reducing both dynamic and static inputs enabling predictions for more sites with lower model complexity and computational needs. From detailed error analysis, we determined that the models are more accurate for sites primarily controlled by air temperatures compared to locations impacted by groundwater and dams. By addressing these questions, this research offers a comprehensive perspective on optimizing ML model design for accurate predictions in unmonitored regions.

Streamflow, vital for water resource management, is governed by complex hydrological systems involving intermediate processes driven by meteorological forces. While deep learning models have achieved state-of-the-art results of streamflow prediction, their end-to-end single-task learning approach often fails to capture the causal relationships within these systems. To address this, we propose Hierarchical Conditional Multi-Task Learning (HCMTL), a hierarchical approach that jointly models soil water and snowpack processes based on their causal connections to streamflow. HCMTL utilizes task embeddings to connect network modules, enhancing flexibility and expressiveness while capturing unobserved processes beyond soil water and snowpack. It also incorporates the Conditional Mini-Batch strategy to improve long time series modeling. We compare HCMTL with five baselines on a global dataset. HCMTL's superior performance across hundreds of drainage basins over extended periods shows that integrating domain-specific causal knowledge into deep learning enhances both prediction accuracy and interpretability. This is essential for advancing our understanding of complex hydrological systems and supporting efficient water resource management to mitigate natural disasters like droughts and floods.

Accurate long-term predictions are the foundations for many machine learning applications and decision-making processes. Traditional time series approaches for prediction often focus on either autoregressive modeling, which relies solely on past observations of the target ``endogenous variables'', or forward modeling, which considers only current covariate drivers ``exogenous variables''. However, effectively integrating past endogenous and past exogenous with current exogenous variables remains a significant challenge. In this paper, we propose ExoTST, a novel transformer-based framework that effectively incorporates current exogenous variables alongside past context for improved time series prediction. To integrate exogenous information efficiently, ExoTST leverages the strengths of attention mechanisms and introduces a novel cross-temporal modality fusion module. This module enables the model to jointly learn from both past and current exogenous series, treating them as distinct modalities. By considering these series separately, ExoTST provides robustness and flexibility in handling data uncertainties that arise from the inherent distribution shift between historical and current exogenous variables. Extensive experiments on real-world carbon flux datasets and time series benchmarks demonstrate ExoTST's superior performance compared to state-of-the-art baselines, with improvements of up to 10\% in prediction accuracy. Moreover, ExoTST exhibits strong robustness against missing values and noise in exogenous drivers, maintaining consistent performance in real-world situations where these imperfections are common.

Estimating the landscape and soil freeze-thaw (FT) dynamics in the Northern Hemisphere is crucial for understanding permafrost response to global warming and changes in regional and global carbon budgets. A new framework is presented for surface FT-cycle retrievals using L-band microwave radiometry based on a deep convolutional autoencoder neural network. This framework defines the landscape FT-cycle retrieval as a time series anomaly detection problem considering the frozen states as normal and thawed states as anomalies. The autoencoder retrieves the FT-cycle probabilistically through supervised reconstruction of the brightness temperature (TB) time series using a contrastive loss function that minimizes (maximizes) the reconstruction error for the peak winter (summer). Using the data provided by the Soil Moisture Active Passive (SMAP) satellite, it is demonstrated that the framework learns to isolate the landscape FT states over different land surface types with varying complexities related to the radiometric characteristics of snow cover, lake-ice phenology, and vegetation canopy. The consistency of the retrievals is evaluated over Alaska, against in situ ground-based observations, showing reduced uncertainties compared to the traditional methods that use thresholding of the normalized polarization ratio.

This is especially true in environmental sciences that are rapidly transitioning from being data-poor to data-rich, e.g., with the ever-increasing volumes of environmental data being collected by Earth observing satellites, in-situ sensors, and those generated by model simulations (e.g., climate model runs [113]). Similar to how recent developments in ML has transformed how we interact with the information on the Internet, it is befitting to ask how ML advances can enable Earth system scientists to transform a fundamental goal in science, which is to build better models of physical, biological, and environmental systems. The conventional approach for modeling relationships between input drivers and response variables is to use process-based models rooted in scientific equations. Despite their ability to leverage the mechanistic understanding of scientific phenomena, process-based models suffer from several shortcomings limiting their adoption in complex real-world settings, e.g., due to imperfections in model formulations (or modeling bias), incorrect choices of parameter values in equations, and high computational costs in running high-fidelity simulations. In response to these challenges, ML methods offer a promising alternative to capture statistical relationships between inputs and outputs directly from data. However, "black-box" ML models, that solely rely on the supervision contained in data, show limited generalizability in scientific problems, especially when applied to out-of-distribution data. One of the reasons for this lack of generalizability is the limited scale of data in scientific disciplines in contrast to mainstream applications of AI and ML where large-scale datasets in computer vision and natural language modeling have been instrumental in the success of state-of-the-art AI/ML models. Another fundamental deficiency in black-box ML models is their tendency to produce results that are inconsistent with existing scientific theories and their inability to provide a mechanistic understanding of discovered patterns and relationships from data, limiting their usefulness in science.

We present a Task-aware modulation using Representation Learning (TAM-RL) framework that enhances personalized predictions in few-shot settings for heterogeneous systems when individual task characteristics are not known. TAM-RL extracts embeddings representing the actual inherent characteristics of these entities and uses these characteristics to personalize the predictions for each entity/task. Using real-world hydrological and flux tower benchmark data sets, we show that TAM-RL can significantly outperform existing baseline approaches such as MAML and multi-modal MAML (MMAML) while being much faster and simpler to train due to less complexity. Specifically, TAM-RL eliminates the need for sensitive hyper-parameters like inner loop steps and inner loop learning rate, which are crucial for model convergence in MAML, MMAML. We further present an empirical evaluation via synthetic data to explore the impact of heterogeneity amongst the entities on the relative performance of MAML, MMAML, and TAM-RL. We show that TAM-RL significantly improves predictive performance for cases where it is possible to learn distinct representations for different tasks.

In hydrology, modeling streamflow remains a challenging task due to the limited availability of basin characteristics information such as soil geology and geomorphology. These characteristics may be noisy due to measurement errors or may be missing altogether. To overcome this challenge, we propose a knowledge-guided, probabilistic inverse modeling method for recovering physical characteristics from streamflow and weather data, which are more readily available. We compare our framework with state-of-the-art inverse models for estimating river basin characteristics. We also show that these estimates offer improvement in streamflow modeling as opposed to using the original basin characteristic values. Our inverse model offers 3\% improvement in R$^2$ for the inverse model (basin characteristic estimation) and 6\% for the forward model (streamflow prediction). Our framework also offers improved explainability since it can quantify uncertainty in both the inverse and the forward model. Uncertainty quantification plays a pivotal role in improving the explainability of machine learning models by providing additional insights into the reliability and limitations of model predictions. In our analysis, we assess the quality of the uncertainty estimates. Compared to baseline uncertainty quantification methods, our framework offers 10\% improvement in the dispersion of epistemic uncertainty and 13\% improvement in coverage rate. This information can help stakeholders understand the level of uncertainty associated with the predictions and provide a more comprehensive view of the potential outcomes.

In recent years, the increasing threat of devastating wildfires has underscored the need for effective prescribed fire management. Process-based computer simulations have traditionally been employed to plan prescribed fires for wildfire prevention. However, even simplified process models like QUIC-Fire are too compute-intensive to be used for real-time decision-making, especially when weather conditions change rapidly. Traditional ML methods used for fire modeling offer computational speedup but struggle with physically inconsistent predictions, biased predictions due to class imbalance, biased estimates for fire spread metrics (e.g., burned area, rate of spread), and generalizability in out-of-distribution wind conditions. This paper introduces a novel machine learning (ML) framework that enables rapid emulation of prescribed fires while addressing these concerns. By incorporating domain knowledge, the proposed method helps reduce physical inconsistencies in fuel density estimates in data-scarce scenarios. To overcome the majority class bias in predictions, we leverage pre-existing source domain data to augment training data and learn the spread of fire more effectively. Finally, we overcome the problem of biased estimation of fire spread metrics by incorporating a hierarchical modeling structure to capture the interdependence in fuel density and burned area. Notably, improvement in fire metric (e.g., burned area) estimates offered by our framework makes it useful for fire managers, who often rely on these fire metric estimates to make decisions about prescribed burn management. Furthermore, our framework exhibits better generalization capabilities than the other ML-based fire modeling methods across diverse wind conditions and ignition patterns.

Time series modeling, a crucial area in science, often encounters challenges when training Machine Learning (ML) models like Recurrent Neural Networks (RNNs) using the conventional mini-batch training strategy that assumes independent and identically distributed (IID) samples and initializes RNNs with zero hidden states. The IID assumption ignores temporal dependencies among samples, resulting in poor performance. This paper proposes the Message Propagation Through Time (MPTT) algorithm to effectively incorporate long temporal dependencies while preserving faster training times relative to the stateful solutions. MPTT utilizes two memory modules to asynchronously manage initial hidden states for RNNs, fostering seamless information exchange between samples and allowing diverse mini-batches throughout epochs. MPTT further implements three policies to filter outdated and preserve essential information in the hidden states to generate informative initial hidden states for RNNs, facilitating robust training. Experimental results demonstrate that MPTT outperforms seven strategies on four climate datasets with varying levels of temporal dependencies.

Causal DAGs(Directed Acyclic Graphs) are usually considered in a 2D plane. Edges indicate causal effects' directions and imply their corresponding time-passings. Due to the natural restriction of statistical models, effect estimation is usually approximated by averaging the individuals' correlations, i.e., observational changes over a specific time. However, in the context of Machine Learning on large-scale questions with complex DAGs, such slight biases can snowball to distort global models - More importantly, it has practically impeded the development of AI, for instance, the weak generalizability of causal models. In this paper, we redefine causal DAG as \emph{do-DAG}, in which variables' values are no longer time-stamp-dependent, and timelines can be seen as axes. By geometric explanation of multi-dimensional do-DAG, we identify the \emph{Causal Representation Bias} and its necessary factors, differentiated from common confounding biases. Accordingly, a DL(Deep Learning)-based framework will be proposed as the general solution, along with a realization method and experiments to verify its feasibility.