WRD Colorado District

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

By Robert L. Runkel, Charles G. Crawford, and Timothy A. Cohn

Techniques and Methods Book 4, Chapter A5 -Online only

Errata Sheet

This document is available in pdf format: Adobe Acrobat Icon TM2004-TM4A5.pdf(776 KB)
(Requires Adobe Acrobat Reader)

The citation for this report, in USGS format, is as follows:
Runkel, R.L., Crawford, C.G., and Cohn, T.A., 2004, Load Estimator (LOADEST):
A FORTRAN Program for Estimating Constituent Loads in Streams and Rivers: U.S. Geological Survey Techniques and Methods Book 4, Chapter A5, 69 p.


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. This report describes the development and application of LOADEST. Sections of the report describe estimation theory, input/output specifications, sample applications, and installation instructions.



1 Introduction

1.1 Background

1.2 Related Reading

1.3 Report Organization

1.4 Acknowledgments

2 Theory

2.1 Background–Linear Regression Approach to Load Estimation

2.2 Load Estimation Methods used within LOADEST

2.2.1 Maximum Likelihood Estimation (MLE)

2.2.2 Adjusted Maximum Likelihood Estimation (AMLE)

2.2.3 Least Absolute Deviation (LAD)

2.2.4 Summary of MLE, AMLE, and LAD for Load Estimation

2.3 Multicollinearity and Centering

2.4 Model Selection

3 User's Guide

3.1 Input/Output Structure

3.2 Input Files

3.2.1 The Control File

3.2.2 The Header File

3.2.3 The Calibration File

3.2.4 The Estimation File

3.3 LOADEST Execution

3.3.1 Execution under Unix

3.3.2 Execution under Windows

3.4 Output Files

3.4.1 The echo.out file

3.4.2 Constituent Output Files

3.4.3 Residual Output Files

3.4.4 Individual Load Files

4 LOADEST Applications

4.1 Application 1: Analysis of an Uncensored Constituent using a Predefined Model

4.2 Application 2: Analysis of an Uncensored Constituent using a Seasonal Model

4.3 Application 3: Analysis of a Censored Constituent using a Seasonal Model

4.4 Application 4: Multiple Constituents with Automated Model Selection

4.5 Application 5: User–defined Model with an Additional Data Variable

4.6 Application 6: Regression Model for Concentration

5 Software Guide

5.1 Supported Platforms

5.2 Software Distribution

5.3 Installation

5.4 Compilation

5.5 Software Overview

5.5.1 Software Development

5.5.2 Include Files

5.5.3 Fatal Errors and Warnings


Appendix 1. Assignment of Detection Limits

Appendix 2. Example echo.out File from Application 4

Appendix 3. Example Constituent Output File from Application 4



Up arrowBack to top

Water Resources of Colorado

U.S. Department of the Interior, U.S. Geological Survey
Persistent URL:
Page Contact Information: Contact USGS
Last modified: Friday, December 02 2016, 03:43:38 PM
FirstGov button  Take Pride in America button