Search USGS⌕ Search
Home/Archive/USGS

USGS · 70012962

Errors and parameter estimation in precipitation-runoff modeling: 1. Theory

Brent M. Troutman
View original source ↗Export metadata ↓

Abstract

Errors in complex conceptual precipitation-runoff models may be analyzed by placing them into a statistical framework. This amounts to treating the errors as random variables and defining the probabilistic structure of the errors. By using such a framework, a large array of techniques, many of which have been presented in the statistical literature, becomes available to the modeler for quantifying and analyzing the various sources of error. A number of these techniques are reviewed in this paper, with special attention to the peculiarities of hydrologic models. Known methodologies for parameter estimation (calibration) are particularly applicable for obtaining physically meaningful estimates and for explaining how bias in runoff prediction caused by model error and input error may contribute to bias in parameter estimation.

Explore related subjects

Water Resources ResearchArticle

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Brent M. Troutman. 2008-01-08. Errors and parameter estimation in precipitation-runoff modeling: 1. Theory. https://doi.org/10.1029/wr021i008p01195

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related USGS reports

USGS2026

Big data for small streams: Leveraging a coarse national model to enhance fine-resolution stream temperature predictions

Predictive stream temperature models are commonly used to address spatial and temporal gaps in observational data because stream temperature information is essential for environmental management decisions. National models capture broad patterns driven by climate, topography, and seasonality, but often lack the spatial resolution to simulate fine-scale variation in groundwater discharge, riparian shading, or tributary inflows. In contrast, watershed models may simulate finer-resolution patterns but miss regional drivers or be limited by scarcity of observations. To generate watershed-extent, fine-resolution stream temperature predictions, we developed 18 multiscale machine-learning models that leverage (a) a broad-extent, coarse-resolution stream temperature model and (b) finer-resolution observations and predictor data. The coarse-resolution model simulates daily stream temperature across the conterminous United States on the National Hydrologic Geospatial Fabric (13.7 km median reach length; 865,364 km total). The fine-resolution models simulate daily stream temperature on the National Hydrography Dataset Plus version 2 (1.5 km median; 5,192,808 km total). We compared multiscale models to seven purely broad- (national) or watershed-extent models, testing them in eight watersheds (436–985 km 2 ) with differing hydrologic settings and under realistic data availability scenarios. Especially when observations within a watershed were scarce, multiscale models generated more accurate predictions than national or watershed-specific models. A recurrent graph convolution neural network pretrained on coarse predictions and fine-tuned on watershed-specific observations was most accurate across watersheds and data scenarios. These results highlight that leveraging both coarse, national results and watershed-specific data can increase model accuracies, particularly when observations within a watershed are spatially or temporally limited.

Water Resources Research↗
USGS2026

Landscape controls river continuum dissolved organic carbon in northeastern Alaska

Rivers draining continuous permafrost landscapes on the North Slope of Alaska span from the mountains to the coast, integrating gradients in vegetation, soil organic matter, and hydrologic flow. We investigated how these landscape transitions influence dissolved organic carbon (DOC) concentrations, radiocarbon ages, and export along the river continuum over seasonal timeframes in northeastern Alaska. Water samples were collected from the Canning River and its tributaries from the spring freshet through late summer via multiple campaigns during 2011–2024. A simulation from the Permafrost Water Balance Model (PWBM) estimated terrain-specific contributions to freshwater and DOC export. River DOC concentrations peaked during the spring and declined in summer, with episodic increases linked to summer rainfall. Summer river DOC concentrations from the Brooks Range remained low (0.41–0.64 mg C L −1 ) but increased downstream (0.5–3.0 mg C L −1 ), becoming younger from the mountains (805 yBP) to the river delta (525 yBP) as flow from DOC-enriched streams draining the foothills (6–18 mg C L −1 ; Modern yBP) entered the Canning. The PWBM simulation revealed that while the mountains dominate the Canning's annual (90%) and spring-summer (88%–93%) freshwater export, the foothills disproportionately influence its annual (56%) and spring-summer (44%–58%) DOC export. DOC yields from the coastal plain were also high but had little influence due to its small contributing area. Our findings highlight the outsized role of the foothills in modulating river-integrated DOC export to coastal ecosystems. Considering the impact of these landscapes on carbon source and runoff will aid in anticipating future DOC fluxes from Arctic rivers.

Alaska↗
USGS2026

Predicting Minnesota lake ice phenology with deep learning, explainable methods, and a physically based benchmark, 1980-2018

Globally, lakes are losing ice cover, but our understanding of the rates and variability of change are biased toward few lakes with long-term records. Recent works have used remote sensing and predictive modeling to supplement the observational record, but these approaches produce large errors when estimating ice phenology for individual lakes. Accurate, lake-specific estimates of ice formation and breakup through time are important for estimating variability in ice loss across heterogenous lakes and for understanding broader implications. This work explores machine learning (ML) approaches for hindcasting ice phenology using observations from 1980 to 2018 across 625 Minnesota lakes, covering 4359 lake-years of record. We used daily weather and static lake attributes to develop 60 neural networks for hindcasting lake ice time series. We considered LSTMs and attention-based transformers of varying size and initial parameters. We found that the largest LSTM performed most accurately on withheld data, and on a test set of unseen years and lakes, it outperformed a state-of-the-art physically based model in daily accuracy (97% vs. 95%), year-level metrics (RMSE for ice formation = 6.9 vs. 13.2 days; ice breakup = 7.5 vs. 12.2 days; ice duration = 9.6 vs. 13.7 days), and estimating loss of ice cover from 1980 to 2018 (observed = 8.4 days, LSTM = 7.2 days, GLM = 3.4 days). This demonstrates that ML can estimate historical lake ice formation and breakup dates within a week of observed phenology across heterogeneous lakes and recreate broad scale trends in ice cover phenology with limited long-term ice records.

Minnesota↗