Geology Reports⌕ Search
Home/Archive/USGS

USGS · 70011649

Techniques of trend analysis for monthly water quality data

Robert M. Hirsch·James R. Slack·Richard A. Smith
View original source ↗Export metadata ↓

Abstract

Some of the characteristics that complicate the analysis of water quality time series are non-normal distributions, seasonality, flow relatedness, missing values, values below the limit of detection, and serial correlation. Presented here are techniques that are suitable in the face of the complications listed above for the exploratory analysis of monthly water quality data for monotonie trends. The first procedure described is a nonparametric test for trend applicable to data sets with seasonality, missing values, or values reported as ‘less than’: the seasonal Kendall test. Under realistic stochastic processes (exhibiting seasonality, skewness, and serial correlation), it is robust in comparison to parametric alternatives, although neither the seasonal Kendall test nor the alternatives can be considered an exact test in the presence of serial correlation. The second procedure, the seasonal Kendall slope estimator, is an estimator of trend magnitude. It is an unbiased estimator of the slope of a linear trend and has considerably higher precision than a regression estimator where data are highly skewed but somewhat lower precision where the data are normal. The third procedure provides a means for testing for change over time in the relationship between constituent concentration and flow, thus avoiding the problem of identifying trends in water quality that are artifacts of the particular sequence of discharges observed (e.g., drought effects). In this method a flow-adjusted concentration is defined as the residual (actual minus conditional expectation) based on a regression of concentration on some function of discharge. These flow-adjusted concentrations, which may also be seasonal and non-normal, can then be tested for trend by using the seasonal Kendall test.

Explore related subjects

Water Resources ResearchArticle

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Robert M. Hirsch, James R. Slack, Richard A. Smith. 2010-07-09. Techniques of trend analysis for monthly water quality data. https://doi.org/10.1029/wr018i001p00107

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

KEEP EXPLORING

Related USGS reports

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↗
USGS2026

A roadmap for identifying and interpreting physical processes and national water model prediction bias associated with baseflow index regimes across the contiguous United States

Understanding how groundwater–surface water interactions shape streamflow variability is critical for diagnosing low flow behavior and prediction bias in continental scale hydrologic models. We present a process informed framework that links observed baseflow (BF) dynamics, watershed attributes, and National Water Model (NWM) performance across the contiguous United States. Using daily observed streamflow from 797 reference quality streamgages, we developed monthly baseflow index (BFI) signatures using a streamgage specific, calibrated digital filter. Hierarchical clustering of these signatures identified seven distinct BFI regimes capturing regional and seasonal variability. We evaluated NWM v3.0 retrospective streamflow performance within each regime using multiple hydrograph and flow duration curve-based metrics. Model skill varied systematically across regimes: mixed flow systems were simulated most accurately, while predominantly BF dominated and quickflow dominated regimes exhibited substantially poorer performance. Across nearly all regimes, the NWM underestimated observed BFI magnitude and frequently failed to reproduce seasonal BF patterns, indicating systematic biases in simulated low flow contributions. To relate these regimes to potential process controls, we trained a Random Forest classifier using static watershed attributes and applied Shapley Additive Explanations to identify features most strongly associated with each regime. Results highlight regionally varying influences, including the dominant role of snow fraction and seasonal runoff timing in snow dominated basins and the importance of evapotranspiration and aridity in quickflow dominated systems. Collectively, these findings demonstrate how hydrologic signatures combined with interpretable machine learning can diagnose regime specific model biases and generate process-based hypotheses about limitations in large scale hydrologic prediction systems.

contiguous United States↗
USGS2026

Global performance of remote sensing-based and reanalysis-driven models to estimate open water evaporation

Evaporation plays an essential role in the water cycle, influencing local and regional climates while directly impacting water availability in lakes. However, directly measuring evaporation over water bodies remains challenging due to the high costs of installing and maintaining the required in situ instrumentation. Although several remote sensing algorithms have been providing evaporation estimates, the lack of a global validation hinders our understanding of their relative uncertainties and performances across different regions. Here, we analyze the performance of a suite of models that leverage satellite data and meteorological reanalysis to estimate evaporation over lakes worldwide. We compare 3 remote sensing-based models, 1 reanalysis-driven model and 1 ensemble approach, using in situ observations from 27 lakes representing a diverse range of geographic and climatic regions. Our results demonstrate that, overall, the ensemble outperformed any individual model in terms of accuracy, with a RMSE and a bias of 1.3 and 0.3 mm day −1 , respectively. These findings highlight the benefits of using an ensemble approach to estimate open water evaporation with satellite-based models at the global scale, leveraging the unique strengths of each model. For the individual models, differences in the representation of heat storage changes and advection effects led to lower values of RMSE and bias, depending on the location and depth of the lakes. This study sets the path for future improvement of open water evaporation algorithms globally, while remote sensing techniques are proven satisfactory to monitoring of water loss in lakes globally, an essential step toward effective large-scale water resources management.

Water Resources Research↗