Welcome to the Unofficial Estimator2000 Home Page


Estimator2000 calculates loads of nutrients (and other constituents) carried by rivers.  It employs a statistical regression model, where the constituent concentrations are estimated based on streamflow and time/season.  The application requires daily value streamflow records and unit values of constituent concentrations.

Statistical Aspects of Estimator2000

Estimator2000 uses Cohn's (1988) Adjusted Maximum Likelihood Estimator (AMLE), which is a generalization of the Minimum Variance Unbiased Estimator (MVUE) of Finney (1941) and Bradu and Mundlak (1970).  AMLE allows nearly-unbiased estimation with censored data (below a detection limit).

Model Form

Estimator2000 can fit a variety of models. However, for estimating nutrient loads a 7-parameter model seems to work well (see Cohn et al., 1992):

ln[L] = b0 + b1 ln[Q] + b2 ln[Q]^2 + b3 T + b 4 T^2 + b5 Sin[2* pT]  + b6 Cos[2*pT] + e    (1)


Q    is the daily discharge
T    is time, expressed in years
The parameters b1 and b2 in equation (1) correspond to variability related to flow dependence, the next pair correspond to time trends, and the third pair are used to fit a first-order Fourier series to the seasonal component of variability.

Estimator2000 Output

Estimator generates numerous statistics including: Click here for a sample output file.


Note that Estimator2000 is not user-friendly.  The software is vintage FORTRAN, with a file-oriented interface.  The files need to be nearly-perfectly formatted or the program will not run.

Furthermore, proper application of Estimator's statistical methods requires that the user understand:

One should not attempt to use Estimator2000 without a clear understanding of how it works.  This is probably best obtained through communication with someone who has used it and knows it well.  Otherwise, one is likely to become very frustrated.

History of Estimator

Estimator was developed at the U.S. Geological Survey   by Tim Cohn and a number of colleagues (see below).  The statistical methods are likely going to be available as part of a future USGS software package.  In the meantime, for now all we have is this unofficial version of the program.

Available Software:

Frequently Asked Questions (FAQ) (Under Construction):

Draft (very) Estimator User Manual


Site last updated 03 April 2004

If you have comments or suggestions, email me at: tim@timcohn.com

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