# Welcome to the Unofficial Estimator2000 Home Page

## Introduction

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] = b_{0} +
b_{1} ln[Q] + b_{2} ln[Q]^2
+ b_{3} T + b_{
4} T^2 + b_{5} Sin[2*
pT] + b_{6}
Cos[2*pT] + e
(1)

Where

Q is the daily discharge

T is time, expressed in years

The parameters b_{1} and
b_{2} 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:
- Parameter estimates for the fitted regression model
- Unbiased (nearly for censored data) estimates of the load by month,
season, calendar year (CY) and water year (WY)
- Estimated standard errors
- Estimated standard errors of prediction
- Approximate 95% confidence intervals for the "true" load
- Residuals plots and other regression diagnostics

Click here for a sample
output file.

## Caveats

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:

- Linear modelling
- Retransformation bias
- Regression diagnostics

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:

## References:

- Cohn, T., L. L. DeLong, E. J. Gilroy, R. M.. Hirsch, and D. K.
Wells, "Estimating Constituent Loads," Water Resources Research , 25(5),
pp. 937-942, 1989.
- Cohn, T., D. L. Caulder, E. J. Gilroy, L. D. Zynjuk, and R.
M. Summers, "The Validity of a Simple Statistical Model for Estimating Fluvial
Constituent Loads: An Empirical Study Involving Nutrient Loads Entering Chesapeake
Bay, "Water Resources Research , 28(9), pp. 2353-2364, 1992.
- Cohn, T., E. J. Gilroy and W. G. Baier, "Estimating Fluvial
Transport of Trace Constituents Using a Regression Model with Data Subject
to Censoring," pp. 142-151, Proceedings of the Joint Statistical Meeting,
Boston, August 9-13, 1992.
- Gilroy, E. J., R. M. Hirsch, and T. Cohn, "Mean Square Error
of Regression-Based Constituent Transport Estimates," Water Resources Research,
26(9), pp. 2069-2077, 1990.
- Gilroy, E. J., W. H. Kirby, T. Cohn and G. Douglas Glysson,
"Discussion of 'Uncertainty in Suspended Sediment Transport Curves' by McBean
and Al-Nassri," Journal of Hydraulic Engineering, 116(1), pp. 143-145, January,
1990.
- Cohn, T., "Recent Advances in Statistical Methods for the Estimation
of Sediment and Nutrient Transport in Rivers," chapter 21 in Contributions
in Hydrology, US National Report to the IUGG, pp. 1117-1124, 1995.
- Cohn, T. "Adjusted Maximum Likelihood Estimation of the Moments
of Lognormal Populations from Type I Censored Samples," U.S. Geological Survey
Open File Report No. 88-350, 34 pp., 1988.
- Helsel, D. H. and T. Cohn, "Estimation of Descriptive Statistics
for Multiply-Censored Water-Quality Data," Water Resources Research , 24(12),
pp. 1997-2004, 1988.

*Site last updated 03 April 2004*
If you have comments or suggestions, email me at:
tim@timcohn.com

####

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