Load Estimator (LOADEST): A Program for Estimating Constituent Loads in Streams and Rivers

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Welcome to the U.S. Geological Survey (USGS) Web page for the LOADEST software package. This page provides access to the LOADEST software and documentation. These items and additional features may be accessed using the navigational tabs at the top of the page.

LOAD ESTimator (LOADEST) is a FORTRAN program for estimating constituent loads in streams and rivers. Given a time series of streamflow, additional data variables, and constituent concentration, LOADEST assists the user in developing a regression model for the estimation of constituent load (calibration). Explanatory variables within the regression model include various functions of streamflow, decimal time, and additional user-specified data variables. The formulated regression model then is used to estimate loads over a user-specified time interval (estimation). Mean load estimates, standard errors, and 95 percent confidence intervals are developed on a monthly and(or) seasonal basis.

The calibration and estimation procedures within LOADEST are based on three statistical estimation methods. The first two methods, Adjusted Maximum Likelihood Estimation (AMLE) and Maximum Likelihood Estimation (MLE), are appropriate when the calibration model errors (residuals) are normally distributed. Of the two, AMLE is the method of choice when the calibration data set (time series of streamflow, additional data variables, and concentration) contains censored data. The third method, Least Absolute Deviation (LAD), is an alternative to maximum likelihood estimation when the residuals are not normally distributed. LOADEST output includes diagnostic tests and warnings to assist the user in determining the appropriate estimation method and in interpreting the estimated loads.

IMPORTANT NOTE: LOADEST can produce biased load estimates when the selected model is a poor representation of the relationship between load and the explanatory variables. Problems with load bias may be identified through careful analyses of model residuals. LOADEST has therefore been modified since its initial release to include several features that facilitate residual analysis and bias identification. This updated version of the software was placed on the web site on March 27, 2013. LOADEST users who downloaded the software prior to this date are encouraged to download the updated version. A summary of the software update is provided here.

The LOADEST software and related materials (data and documentation) are made available by the U.S. Geological Survey (USGS) to be used in the public interest and the advancement of science. You may, without any fee or cost, use, copy, modify, or distribute this software, and any derivative works thereof, and its supporting documentation, subject to the USGS software User's Rights Notice.

Funding for software development was provided by the USGS Office of Water Quality.