LOAD ESTIMATOR (LOADEST): A FORTRAN PROGRAM FOR ESTIMATING CONSTITUENT LOADS IN STREAMS AND RIVERS Techniques and Methods Book 4, Chapter A5 U.S. Department of the Interior U.S. Geological Survey 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 U.S. Department of the Interior! U.S. Geological Survey U.S. Department of the Interior Gale A. Norton, Secretary U.S. Geological Survey Charles G. Groat, Director U.S. Geological Survey, Reston, Virginia: 2004 For more information about the USGS and its products:! Telephone: 1-888-ASK-USGS! World Wide Web: http://www.usgs.gov/ Any use of trade, product, or firm names in this publication is for descriptive purposes only and does not imply ! endorsement by the U.S. Government. Although this report is in the public domain, it contains copyrighted materials that are noted in the text. ! Permission to reproduce those items must be secured from the individual copyright owners. iii Contents Abstract . .. 1 1 Introduction . 2 1.1 Background . 2 1.2 Related Reading . 2 1.3 Report Organization . 2 1.4 Acknowledgments . .. 2 2 Theory . 3 2.1 Background – Linear Regression Approach to Load Estimation . 3 2.2 Load Estimation Methods used within LOADEST . 4 2.2.1 Maximum Likelihood Estimation (MLE) . 5 2.2.2 Adjusted Maximum Likelihood Estimation (AMLE) . 5 2.2.3 Least Absolute Deviation (LAD) . 6 2.2.4 Summary of MLE, AMLE, and LAD for Load Estimation . 6 2.3 Multicollinearity and Centering . 7 2.4 Model Selection . 7 3 User’s Guide . 8 3.1 Input/Output Structure . 8 3.2 Input Files . .. 9 3.2.1 The Control File . 9 3.2.2 The Header File . .. 9 3.2.3 The Calibration File . 15 3.2.4 The Estimation File . 17 3.3 LOADEST Execution . 18 3.3.1 Execution under Unix . 18 3.3.2 Execution under Windows . 18 3.4 Output Files . 18 3.4.1 The echo.out file . 19 3.4.2 Constituent Output Files . .. 19 3.4.3 Residual Output Files . 19 3.4.4 Individual Load Files . .. 20 4 LOADEST Applications . 21 4.1 Application 1: Analysis of an Uncensored Constituent using a Predefined Model . 21 4.2 Application 2: Analysis of an Uncensored Constituent using a Seasonal Model . 29 4.3 Application 3: Analysis of a Censored Constituent using a Seasonal Model . 32 4.4 Application 4: Multiple Constituents with Automated Model Selection . 35 4.5 Application 5: User–defined Model with an Additional Data Variable . 40 4.6 Application 6: Regression Model for Concentration . 45 iv 5 Software Guide . .49 5.1 Supported Platforms . .49 5.2 Software Distribution . .49 5.3 Installation . .50 5.4 Compilation . .52 5.5 Software Overview . .52 5.5.1 Software Development . .52 5.5.2 Include Files . .53 5.5.3 Fatal Errors and Warnings . .54 References . ..