Frequently Asked Questions (Updated Regularly)

(08 May 2000)

Estimator Software

The 7-Parameter Model

What is the "7 Parameter Model"?

Estimator 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 + b4 T^2 + b5 Sin[2*pT]  + b6 Cos[2*pT] + e


       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.

Where is this model appropriate?
The model has been tested in a number of watersheds. Generally, it should work in large watersheds (greater than 100 square miles).

Why use a 7 Parameter Regression Model?
The 7 parameter model is the simplest model that captures the main sources of variability for most nutrient species.  The first coefficient is a constant;  the next two address variability connected with discharge; the next two deal with time trends; the final two capture annual seasonality.  Simpler models are appropriate in some circumstances; the 7 parameter model seems to work for almost all nutrient species for large (greater than 100 square miles) watersheds.

Estimator Software

An "official USGS" version of Estimator (which will be called Loadest3) is currently (March 2002) being developed by Rob Runkle.  While the new version will retain Estimator's statistical approach, it promises to have a much-improved interface.  Stay tuned!

Estimator's Data Requirements

  • What data does Estimator use?

  • Estimator uses a daily value discharge record (streamflow) and a set of unit value nutrient ("water quality") data.
  • What is the required format for the discharge record?

  • It is the USGS ADAPS "2 and 3" 80-character card format.  This is primitive, but it works.  Conversion software is available that will produce this file format from other formats.
  • The water quality file?

  • This is stored in the USGS QWDATA "PSTAT" format.  Again, conversion software is available.
  • How much data is needed to run Estimator?

  • Estimator requires a continuous record of daily discharges, which must cover the time period of the calibration data set (at least those data that are to be used) and the period for which load esimates are desired.  The more water quality data, the more precise the load estimates will be.  Estimator works well with 25 water quality samples each year, half at high flow and half uniformly distributed over the course of the year (bi-weekly sampling).
  • Can you restrict the data used for calibration to a specific time interval?

  • Yes, Estimator allows the user to specify a time interval for the calibration data set.  This can be useful for many purposes.  Where watersheds are changing rapidly (due to development; phosphate bans; agricultural practices; etc.), it may be desirable to limit the calibration data set to include only those data collected at around the same time that one want estimates.
  • Does it make sense to use a "moving window" of calibration data?

  • Sometimes.  In work done related to Chesapeake Bay, an asymmetrical 10-year moving window was used.  Because of management needs, preliminary load estimates were given for the current year -- year "10" -- based on data collected during years "1" through "10".  These were then made final one year later based on fitting the model to a different 10 year window:  the last 9 years of data plus the year of new data. Final estimates (which are for year "9" of the new 10-year window) are made using data from years 1 through 10.

    In addition to meeting management needs, there was a statistical justification for this:  The quadratic approximation to the time trend in the 7-parameter model is arguably not quite right, and it is desirable to consider the impact of a higher-order series.  However, any omitted third-order term will have roots at {1.13, 5.0, 8.87} (assuming uniform sampling, etc.; this is a consequence of orthogonal polynomials), which means the omitted term will have minimal impact in years "2", "5", "6" and "9".

    Third Order Orthogonal Polynomial on (0,10)
    Note that roots occur at {1.13, 5, 8.87}

    Thus, by estimating in year "9", the model is nearly exact for any third-order time trend.


    Interpreting the Estimator Output File