Period Comparison

Choose two historical periods to compare. Period 2 will default to the same duration.

Extreme Threshold

Choose a flow threshold and < or > to access Extremes tab.
Download Data

For monthly reconstructions, it is possible to focus on particular months. Selections on the left will populate all other tabs.

On the left, please select time resolution and a site to begin.
Plots are dynamic. Click and drag within the time series to zoom or use the scroll bar at the bottom. Double-click on the graph to zoom out.

Reconstruction Location

Reconstruction Source

Recommended Citation:

Observation Source




Extreme Flows

Extreme Flow Distribution

Extreme Flow Details

Flows are sorted by most extreme. You may re-sort by clicking column headers. You may also change the period of interest using the Date Subset drop-down.

Period Comparison

This tab allows a quick comparison between two user-selected historical periods. Select the period on the left. Extreme threshold can be adjusted.

Extreme Flows

Threshold Exceedances

Flow Distribution Comparison

Flow distributions can be compared between the two periods. Plot will adjust automatically to changes in period.

Goodness of Fit

Reconstructed flows plotted against observed flows for the instrumental (calibration) period. A perfect calibration fit would be along the 1:1 line, shown in red.

Hover over a point to see its date and values. Click and drag to zoom in on an area. Right click to zoom out.


Calibration seeks to find the best predictor variables and calculates the model's ability to reproduce flows within calibration period, often the full observation record.

Calibration statistics indicate the best expected model performance and should be complemented with validation.


Validation simulates the model's ability to predict flows outside the observed record. This is often done by fitting the model using part of the record and predicting the portion that was withheld.

If validation is much worse than calibration, it indicates the model is too sensitive to new data, or 'overfit'

R-squared describes how much of the observed variance in reconstructed flow is accounted for by the predictors (tree-rings).

It represents percent explained (%) and ranges from zero to one, with one being a perfect fit.

Reconstruction-Statistical Background
Reduction of Error (RE) measures a model's predictive skill compared to assuming the long term mean. RE is used for the calibration and is mathematically identical to the Nash-Sutcliffe Efficiency (NSE) commonly used by hydrologists.

RE ranges from 1 (perfect fit) to -∞. Values greater than zero indicate that the model has some skill (performs better than assuming the mean).

Efficiency Criteria
Coefficient of Efficiency (CE) is equivalent to the Reduction of Error (RE), but applied to validation data.

CE therefore ranges from 1 (perfect skill) to -∞. Values greater than zero indicate that the model has some skill (performs better than assuming the mean).

Because CE measures skill for the hold-out set, we expect that CE < RE. However, this drop in skill should not be too large, or it points to over-fitting.

Efficiency Criteria
RMSE provides the 'typical' error and is an absolute measure of fit, meaning it is displayed in flow units.

RMSE is calculated as the square root of mean square of errors (predicted minus observed flow). A perfect model would have no errors, and therefore RMSE = 0.

Reconstruction-Statistical Background
Mean Absolute Error (MAE) calculates the average absolute (no sign) difference between predicted and observed flows. It is displayed in original flow units and a perfect fit have MAE = 0.

MAE is similar in interpretation to RMSE and is the more intuitive of the two. Where RMSE handles negative values by squaring them, MAE simply applies the absolute value ||.
Mean Error (ME) calculates the average error (predicted - observed). It is a measure of bias, if the model consistently over-predicts or under-predicts. Unbiased models have a ME near zero.

Mean Error should always be considered with other metrics because poor predictive models can have ME near zero if large positive and negative errors can cancel each other out.
Validation is typically performed by splitting the observed record into a 'training' set and a 'validation' set. A model fit using the training set is then used to predict values in the witheld valdation set to simulate prediction errors outside the observed record.

'Split Sample' validation defines these training and validation sets explicitly when fitting the model.

'K-fold' cross-validation predicts part of the sample (typically 10%, referred to as 'k') and predicts using the remaining 90%. This is repeated k times until each point is predicted without being used in training.

Leave-One-Out is a commonly used method and is an extreme version of K-fold cross-validation, where each point is predicted using a model fit with all other data.

Comparison of Flow Distributions

Submit a Reconstruction

Thanks, your reconstruction was submitted successfully!

Submit another reconstruction

To submit a new reconstruction, first download the template (Step 1). Then upload the completed template (Step 2). Please include as much metadata in the CSV file as possible, along with entering a name for the reconstruction and a valid email address so that we may contact in case of questions (Step 3). Finally, push Submit (Step 4).

We strongly recommend that the original files submitted to PaleoFlow be housed in a standard repository, such as the International Tree-Ring Data Bank (ITRDB).

Download a blank template and insert data. All submissions must use the template provided. A completed file is provided as an example.
Upload the completed file. Header information is critical and no reconstructions will be posted without proper attribution (creator, citation, etc) or gauge information.



Push submit when finished. You will receive confirmation on the next screen.


The PaleoFlow website was developed and is maintained by James Stagge in conjunction with the Ohio State University , the Utah State University Water Research Lab and the Wasatch Dendroclimatology Research Group . It was funded in part by Utah Mineral Lease funds.


When using the Reconstructed Streamflow Explorer for research or reference, please cite as follows:

Stagge, J.H. (2017) PaleoFlow Reconstructed Streamflow Explorer Version 2.1.0. doi:10.5281/zenodo.583166

All code for this application is available as a GitHub repository , made available under the MIT license. The repository is actively maintained, so we accept feature requests and code contributions submitted as pull requests.

Contact Information

Please direct any questions to James Stagge .