Instructions for Using the Estimator Software


G. Baier, T. Cohn and E. Gilroy, July 25, 1995
(last updated by T. Cohn, January 01, 2000)

Introduction

In 1988 the ESTIMATOR program was developed to assist U. S. Geological Survey personnel in estimating stream nutrient loads entering Chesapeake Bay through its major tributaries. ESTIMATOR has since been used to estimate loads of toxic organics and trace metals.

ESTIMATOR implements the Minimum Variance Unbiased Estimator (MVUE) described in Cohn et al. [1989], Gilroy et al. [1990], and Cohn et al. [1992a]. Cohn et al. [1992a] discusses the MVUE's applicability in estimating fluvial transport of nutrients and sediment. The Minimum Variance Unbiased Estimator makes ESTIMATOR a powerful tool for estimating constituent loads.

ESTIMATOR also implements the Adjusted Maximum Likelihood Estimator (AMLE), discussed in Cohn [1988] and Cohn et al. [1992b]. The AMLE allows ESTIMATOR to use data sets containing censored values. For data sets without censoring the AMLE is equivalent to the MVUE.

The first section of this report describes the input data files required by the ESTIMATOR program. Sections 2 and 3 provide insight into creating these files using the U. S. Geological Survey's (USGS) Automated Data Processing System (ADAPS) and Water Quality Data Base (QWDATA). ESTIMATOR input data files created inside ADAPS and QWDATA require little or no editing. Section 4 provides step by step instructions for using ESTIMATOR for load estimation. The basics behind interpreting ESTIMATOR's output file are explained in Section 5. A brief discussion of potential problems is presented in Section 6. Section 7 explains how to obtain the current version of the ESTIMATOR software.
 
 

1. Required Input Data Files

Three input data files are required for ESTIMATOR to properly execute. These three files are: the daily discharge data file (Q-file), the water quality data file (QW-file), and the .cmnd-file.
 
 

1.1. Daily discharge data file (Q-file)

As its name implies, the daily discharge data file, or Q-file, contains daily discharge data for the load estimation station. ESTIMATOR was designed to read Q-files created by the USGS's Automated Data Processing System (ADAPS). Section 2 of this report explains how to retrieve Q-file daily discharge data from ADAPS.

1.1.1. How much daily discharge data is needed A Q-file must contain discharge data for each day of the load estimation period. If discharge data is missing for a given day, then the load can not be calculated for that day. (Therefore, more data will be required for long estimation periods than for short estimation periods.)
  1.1.2. Format of the daily discharge data file Because ESTIMATOR was designed to read Q-files created inside ADAPS, Q-files created inside ADAPS require no editing or reformatting. For this reason, use of ADAPS generated Q-files is recommended.

The Q-file is read into ESTIMATOR with the following format:

(I2,I8,6X,I4,I2,I2,8F7.0,3(/,24X,8F7.0))

Although "F7.0" is specified, any floating point number occupying no more than seven characters will be read correctly. Q-file data should be in cubic feet per second [cfs].

Figure 1.1 shows the first six lines of a Q-file created inside ADAPS. These lines, which come from the discharge data file q.01578310, contain daily average discharges for the Susquehanna River at Conowingo from October 1, 1967 to November 8, 1967. Discharge units are cubic feet per second.

Figure 1.1: The first six lines of a Q-file created inside ADAPS

2 01578310 0006000003 ENT

3 01578310 19671001 12100. 41900. 21200. 21200. 22900. 20300.9290.002310.00

3 01578310 19671002 14300. 13500. 13700. 10900. 14500.9590.00 480.00 10600.

3 01578310 19671003 10600. 10500. 21700. 31600. 26400. 23900. 40200. 36300.

3 01578310 19671004 29000. 40800. 51900. 69700. 73700. 59100. 50100.

3 01578310 19671101 38800. 43800. 48000. 58900. 83400. 86500. 79300. 70600.

1.2. Water quality data file (QW-file)

As its name implies, the water quality data file, or QW-file, contains water quality data for the load estimation station. ESTIMATOR was designed to read QW-files created by the USGS's Water Quality Data Base (QWDATA). Section 3 of this report explains how to retrieve QW-file water quality data from QWDATA.

1.2.1. How much water quality data is needed The amount of water quality data needed for load estimation varies with the model. As a general rule of thumb a QW-file should contain: 1. at least 25 observations per year for two years,

2. at least 20% of the observations should be above the detection limit, and

3. at least 3 observations should be above the detection limit for each parameter fitted in the model. For a 7-parameter model, this implies 21 observations above the detection limit.
 
 

1.2.2. Format of the water quality data file
Because ESTIMATOR was designed to read QW-files created inside QWDATA, QW-files created in P-STAT (flat-file) format inside QWDATA require no editing or reformatting. For this reason, use of QWDATA generated QW-files (in P-STAT format) is recommended.

Figure 1.2 shows the first few lines of a correctly formatted QW-file. These lines come from the file qw.01578310 and contain water quality data for the Susquehanna River at Conowingo for January 29, 1978, August 3, 1978, and November 9, 1978. Each date in a QW-file will contain at least two lines of data. The first line identifies the station number, date, and sample collection time. Follow-on line(s) contain(s) water quality data. Variables which were not sampled on the recorded date are marked with a dash (-).

Figure 1.2 The first few lines of a correctly formatted QW-file

01578310 19780129 1115 - -

- - - - - - - -

- - - - - -

01578310 19780803 1200 - -

- - 17700. - - - - -

- - - - - -

01578310 19781109 1115 - -

<2.0000 - 61000. <20.000 - 5.0000 - 5.0000

- <0.500 - - - -
 
 

1.3. The .cmnd-file
 

1.3.1. Why the .cmnd-file is needed The .cmnd-file provides ESTIMATOR with important information about the QW-file. As seen in Figure 2.2, QW-files provide no information about constituent identities. Without information about constituent identities ESTIMATOR can not relate a request for constituent loads with the available water quality data. The .cmnd-file contains information which allows ESTIMATOR to relate requests with QW-file data. Figure 2.3 is the .cmnd-file which corresponds to Figure 2.2's QW-file. 1.3.2. Format of the .cmnd-file QWDATA automatically creates a .cmnd-file with every QW-file. Figure 1.3 is a correctly formatted .cmnd-file. This file provides information about the water quality file qw.01578310. The cell labeled "01042" identifies the location for total recoverable copper data in the qw-file. The number and order of variables is determined during the QWDATA retrieval.
 

Figure 1.3 A correctly formatted .cmnd-file

Station # Date(Yr,Mo,Day) Time End Date(Yr,Mo,Day) Time

01027 01113 00061 01034 01118 01042 01119 01051

01114 71900 71901 39630 39632 82612
 

1.4. Suggested Naming Conventions

Creating a standardized naming convention for input data files is recommended. One suggested technique is to select a convention which includes information on both file type and station number. Data files for the USGS station at Conowingo, MD (station 01578310) were used in this report. The daily discharge data file (Q-file) is named q.01578310. The water quality input data file (QW-file) is named qw.01578310. The .cmnd-file containing information about qw.01578310 is named qw.01578310.cmnd.
 

1.5. Required Naming Conventions

The .cmnd-file name must be the water quality file name with the suffix ".cmnd" added. For example, the .cmnd-file containing information about the QW-file qw.01578310 must be named qw.01578310.cmnd. If the water quality file's name is changed, the .cmnd file's name must also be changed.
 

2. Extracting Discharge Data From ADAPS
 

2.1. Purpose and Scope

This section provides a basic guideline for using ADAPS to create Q-files for input into ESTIMATOR. To extract discharge data from ADAPS the eight-digit station code is needed.
 

2.2. What is ADAPS?

The Automated Data Processing System (ADAPS) is part of the National Water Information System. It was developed to process, store, and retrieve water data. ADAPS can be used to create Q-files for input into ESTIMATOR. Detailed information on ADAPS is available in NWIS User's Manual, Volume 2, Chapter 3.

ADAPS contains daily discharge data by station. For some stations daily values are available for water temperature, specific conductance, suspended sediment concentration, suspended sediment loads, and gage height.

ADAPS can be used to determine a station's eight-digit code and station name, as well as other station information.
 
 

2.3. Accessing ADAPS

After getting an account and logging onto the computer, type, "adaps". The ADAPS main menu (Figure 2.1) should appear. RT -- "RETRIEVE/WRITE ADAPS DATA" is the only option needed to retrieve discharge data. The RT option can also be used to determine a station's eight-digit code.

Figure 2.1 ADAPS Main Menu

ADAPS Revision 91.2 25 Jun 92 09:29:36 Thursday

Entering ADAPS . . . .

Opening MIDAS data bases and getting user information.

Please wait . . . .

****************************************************************************

| US. GEOLOGICAL SURVEY AUTOMATED DATA PROCESSING SYSTEM (ADAPS) |

| REVISION 91.2 25 Jun 92 09:30:22 Thursday |

| MAIN MENU - WATER DATA PROCESSING OPTIONS |

****************************************************************************

IN -- DATA INPUT

PR -- PROCESS PRIMARY DATA

DI -- DISPLAY UNIT- AND DAILY-VALUES DATA

RT -- RETRIEVE/WRITE ADAPS DATA

SA -- START/STOP PROCESSING/TRANSFER OF SATELLITE DATA

AP -- ADAPS APPLICATIONS

LA -- LOCAL APPLICATIONS

PD -- PRINT DOCUMENTATION

UT -- MISCELLANEOUS UTILITY FUNCTIONS

HT -- HYDROLOGIC TOOLBOX (MEAS./SHIFTS/DATUMS AND EOY SUMMARY)

DOC menu_opt -- Display documentation PGM -- Display program_names

QU -- Exit to previous menu EX -- Exit to Primos

Select desired menu option or program_name ([CR] for menu):
 
 

2.4. Generating output files in ADAPS

Generating a Q-file from ADAPS requires the station of interest's eight-digit station code. Figure 2.2 is a typical ADAPS user dialogue generated while creating a Q-file for the James River at Cartersville, VA (station 02035000). This dialogue starts at the RT -- "RETRIEVE/WRITE DATA" sub-menu. User responses appear in bold type. Comments appear in italics type.

Figure 2.2 A typical ADAPS user dialogue generated while creating a Q-file for the James River at Cartersville, VA (02035000)

****************************************************************************

| US. GEOLOGICAL SURVEY AUTOMATED DATA PROCESSING SYSTEM (ADAPS) |

| REVISION 91.2 25 Jun 92 09:30:58 Thursday |

| (RT) SUB-MENU : RETRIEVE/WRITE DATA |

****************************************************************************

1 -- Retrieve/Write Daily-Values Data

2 -- OUTWAT - Retrieve DV/UV/Measurement/Shift/Rating/Site Data

FROM THE PREVIOUS MENU -- IN, PR, DI, RT, SA, AP, LA, PD, UT, HT,

DOC menu_opt -- Display documentation PGM -- Display program_names

QU -- Exit to previous menu EX -- Exit to Primos

Select desired option or program_name ( <CR> for menu ): 1
 
 

RETR_DV - RETRIEVE/WRITE DAILY-VALUES DATA

VIRGINIA

DATE: 06-25-1992 TIME: 09:31:18

******************************************************************************

CURRENT USER INFORMATION

PA - FILE PATH - <VAGISA>GUEST>

------------------------------------------------------------------------------

DB - DATA BASE - VIRGINIA

AG - AGENCY - USGS GEOLOGICAL SURVEY

ST - STATION(S) - 02035000 JAMES RIVER AT CARTERSVILLE, VA

DD - DATA DESCR. - DISCHARGE, IN CFS

YR - PERIOD - WATER YEAR - 1977TO END PERIOD

******************************************************************************

Enter: PA,DB,AG,ST,DD,YR to edit field or

[CR] to continue:[cr]

Caution, if the entry under DD-DATA DESCR. is not, "DISCHARGE, IN CFS," it must be changed. To do this enter DD instead of [cr].

RETR_DV - RETRIEVE/WRITE DAILY VALUES

Enter output file name (<CR>=DV.RETR.920625.093451): q.02035000

Available output formats:

D - DV Card output - Type 2 and 3 cards only

N - DV/Header Card output - Type Z, H, N, 2, and 3 cards

M - WATSTORE Monthly Format - 408 byte records

Y - WATSTORE Yearly Format - 1656 byte records

A - ADAPS Yearly Format - 2560 byte records

Enter your choice (D,H,M,Y,or A, [CR]=D: d

Enter up to 10 retrieval statistic codes:,

each separated by a blank, or

"L" for list: L
 
 

CURRENT STATISTIC CODE LIST

CODES NAMES

3 MAXIMUM

4 MINIMUM

5 MEAN

6 AM

7 PM

8 SUM

9 MODE

10 MEDIAN

11 STD

12 VARIANCE

13 INSTANTANEOUS

14 EQUIVALENT MEAN

15 SKEWNESS

16 TIDAL HIGH (DAILY)

17 TIDAL LOW-HIGH DAILY

18 TIDAL HIGH-LOW DAILY

19 TIDAL LOW (DAILY)

20 0.1 PERCENTILE

Enter up to 10 retrieval statistic codes:,

each separated by a blank, or

"L" to continue list: 3

Retrieve FINAL data only? [Y/N DEFAULT=N]: N

RETR_DV - RETRIEVE/WRITE DAILY VALUES

Control file

FILE <VAGISA>GUEST>T$0000.0100 OPENED ON UNIT 29.

Another retrieval? [Y/N DEFAULT=Y]: N

N O R M A L T E R M I N A T I O N

O F P R O G R A M " R E T R _ D V "

****************************************************************************

| US. GEOLOGICAL SURVEY AUTOMATED DATA PROCESSING SYSTEM (ADAPS) |

| REVISION 91.2 25 Jun 92 09:35:49 Thursday |

| (RT) SUB-MENU : RETRIEVE/WRITE DATA |

****************************************************************************

A.4.21. -- Retrieve/Write Daily-Values Data

A.4.22. -- OUTWAT - Retrieve DV/UV/Measurement/Shift/Rating/Site Data

FROM THE PREVIOUS MENU -- IN, PR, DI, RT, SA, AP, LA, PD, UT, HT,

DOC menu_opt -- Display documentation PGM -- Display program_names

QU -- Exit to previous menu EX -- Exit to Primos

Select desired option or program_name ( <CR> for menu ): EX

N O R M A L T E R M I N A T I O N

B Y S U B R O U T I N E "S _ Q R Y C "

I N P R O G R A M " R E T R _ D V "

3. Extracting Water Quality Data From QWDATA

3.1. Purpose and Scope

This section provides a basic guideline for using QWDATA to create "QW" input files for input into ESTIMATOR. To extract data the user will need a five-digit parameter code and an eight-digit station code for each parameter and/or station of interest. Using QWDATA to determine parameter codes is discussed in section 3.4.

3.3. Accessing QWDATA

After getting an account and logging onto computer, type "qwdata".The QWDATA main menu (Figure 3.1) should appear. Two systems options may be needed to retrieve water quality data. The first option, QW System Option 4 -- "CHECK SUPPORT FILES", will be needed if the constituent's five-digit parameter codes need to be determined (section 3.4). The second option, QW System Option 3 -- "RETRIEVE SAMPLES", will be used both to identify water quality data for the station of interest(section 3.5) and to write the water quality data to a QW-file (section 3.6).

Figure 3.1 QWDATA Main Menu

QW DATA PROCESSING ROUTINE REV 91.2

YOU ARE USING WATER-QUALITY DATABASE NUMBER 01

QW SYSTEM OPTIONS

1 -- LOGIN SAMPLES 4 -- CHECK SUPPORT FILES INCLUDING

List Sites, Access Parameter,

Code Dictionary, Access Geologic

Unit Code and State/County Files.

2 -- ADD / CHANGE / DELETE 95 -- WATER QUALITY UTILITIES OPTIONS

Enter field or

miscellaneous data

Edit or flag samples,

Count QW records, or

Update Site File.

3 -- RETRIEVE SAMPLES 99 -- EXIT TO PRIMOS

Check entry or make

loglist, Locate samples,

Provide cation/anion

balance, Make tables or

PSTAT data set.

Please enter a number from the above list or a PRIMOS command:
 

3.4. Determining five-digit parameter codes


Five-digit parameter codes are relatively simple to obtain by using constituent names. Choose option 4 'CHECK SUPPORT FILES' from the QWDATA main menu (Figure 3.1). The sub-menu structure shown in Figure 3.2 should appear.

Figure 3.2: QW Sytem Option 4 -- CHECK SUPPORT FILES

QW DATA PROCESSING ROUTINE REV. 91.2

YOU ARE USING WATER-QUALITY DATABASE NUMBER 01

CHECK SUPPORT FILES OPTIONS

1 -- LIST SITE RECORDS

2 -- CHECK PARAMETER CODE DICTIONARY

3 -- LIST PARAMETER CODE DICTIONARY

4 -- CHECK GEOLOGIC UNIT CODE FILE

5 -- CHECK FIPS CODE FILE

6 -- LIST STATE/COUNTY DATA

7 -- DUMP PARAMETER CODE DICTIONARY WITH PRECISION CODES

8 -- EXIT TO MAIN MENU

9 -- EXIT TO PRIMOS

From the CHECK SUPPORT FILES sub-menu option 2 'CHECK PARAMETER CODE DICTIONARY' should be chosen. When the new sub-menu appears option 2 'retrieve records by parameter name' should be chosen. At this point the user will be prompted to enter a parameter name (i.e. ammonia). QWDATA searches the data base for parameter names which approximate the entered parameter name. Selected parameter names and the corresponding five-digit codes will be displayed as in Figure 3.3. The user will have to determine which of the displayed parameters is of interest and record its parameter code. The user may then enter another parameter name or end the search by typing "quit".

Figure 3.3: Example of QWDATA Parameter Code Search Results

Please enter the parameter name (quit, spelled out, to end):

ammonia

Applicable parameter codes for AMMONIA

00604 NITROGEN, AMMONIA, SEDIMENT, SUSPENDED, TOTAL, AS N, MG/L

00608 NITROGEN AMMONIA DISSOLVED (MG/L AS N)

00610 NITROGEN AMMONIA TOTAL (MG/L AS N)

00611 NITROGEN AMMONIA TOTAL IN BOTTOM MATERIAL, DRY WEIGHT(MG/KGAS

00619 AMMONIA UNIONIZED (MG/L AS N)

00623 NITROGEN AMMONIA PLUS ORGANIC DISSOLVED (MG/L AS N)

3.5. Identifying Water Quality Data for a Station of Interest

Figure 3.4: QW System Option 3 -- Retreive Samples Menu

QW DATA PROCESSING ROUTINE REV. 91.2

YOU ARE USING WATER-QUALITY DATABASE NUMBER 01

RETRIEVE SAMPLES OPTIONS

1 -- CHECK QW DATA ENTRY 7 -- RUN QWVALID TO EDIT DATA

2 -- MAKE LOG LIST OF QW 8 -- LOCATE DATA FROM MULTIPLE

RECORD HEADER INFORMATION DATABASES

3 -- LOCATE SITES AND/OR 9 -- MAKE WATER-QUALITY TABLES

SAMPLES FROM MULTIPLE DATABASES

4 -- PROVIDE CATION-ANION 98 -- EXIT TO MAIN MENU

BALANCE

5 -- MAKE A PSTAT (FLAT FILE) 99 -- EXIT TO PRIMOS

DATA SET

6 -- MAKE WATER-QUALITY TABLES

(File of Record NOS. needed,

usually obtained with option 3)

Figure 3.5: Example of QWDATA's Retrieve Samples Option 3--"LOCATE SITES AND/OR SAMPLES"

QW DATA BASE PATHNAME IS: WATSTORE>DATA>QWFILE

THIS PROGRAM RETRIEVES WATER-QUALITY RECORDS

FOR USE BY APPLICATION PROGRAMS

DO YOU WANT TO LOCATE SITES (YES OR NO) ? no

[IF YOU WANT QW DATA FOR SPECIFIC SITES WHOSE STATION NUMBERS

ARE AVAILABLE IN A FILE OR ARE TO BE ENTERED INTERACTIVELY

YOU SHOULD ANSWER THE PROMPT WITH NO]

DO YOU WANT TO RETRIEVE RECORDS FOR SPECIFIC SITES (YES OR NO) ? yes

WILL THE STATION NUMBERS COME FROM THE TERMINAL (YES OR NO) ? yes

DATE: _ ANALYSIS-LEVEL CODES: _ PROJECT ID: _ GEOLOGIC UNIT : _ PROCESSING STATUS: _ PARAMETER VALUES AND CODES: _

CHOOSE THE ITEMS YOU WANT TO RETRIEVE ON FROM THE FORM

ENTER X (OR x) -- TO SELECT AN ITEM

ENTER CR -- TO SKIP AN ITEM

ENTER Q (OR q) -- TO SKIP THE REST

PLEASE ENTER STATION NUMBER (QUIT TO END) 01578310

PLEASE ENTER STATION NUMBER (QUIT TO END) quit

SEARCH COMPLETE -- 724 RECORDS SELECTED

DO YOU WANT THOSE RECORDS SORTED (YES OR NO) ? yes

A -- AGENCY CODE F -- GEOLOGIC UNIT CODE

B -- STATION NUMBER G -- PROCESSING STATUS

C -- DATES AND TIMES H -- COUNTY CODE

D -- MEDIUM CODE I -- STATION NAME

E -- PROJECT ID J -- SITE TYPE

YOU MAY SORT THE RECORDS ON ANY COMBINATION OF THE ABOVE FIELDS

THE FIRST FIELD WILL BE THE PRIMARY SORT,

THE NEXT WILL BE SECONDARY SORT 1, ETC....

PLEASE ENTER THE DESIRED SORT CODES ON ONE LINE,

WITH NO INTERVENING BLANKS

> c

BEGINNING SORT...

SORT COMPLETE

PLEASE ENTER NAME OF FILE TO HOLD THE RECORD NUMBERS : recnos.01578310

DO YOU WANT TO SAVE A LIST OF SITES THAT HAVE QW DATA (YES OR NO) ? yes

PLEASE ENTER NAME OF FILE TO HOLD THE LIST: sites.01578310

**** STOP QWSITEREC PROGRAM END

3.6. Writing Water Quality Data to a QW-file in PSTAT Format

Figure 3.6: Example of QWDATA's Retrieve Samples Option 5--"MAKE A PSTAT (FLAT FILE) DATA SET"

ENTER PATHNAME (MAX 50 CHARS) OF RECORD NUMBER FILE (99 T0 END):

PROGRAM QWPSTAT HAS OPENED FILE

PLEASE ENTER NAME OF FILE TO HOLD THE OUTPUT :

PROGRAM QWPSTAT HAS OPENED FILE

QWPSTAT REMARK HANDLING OPTIONS :

1 -- REMARK CODES (SUCH AS < OR ND) INCLUDED WITH THE DATA,

2 -- REMARK CODES DELETED BUT VALUES ASSOCIATED WITH REMARK

CODES RETAINED (A REMARK CODE OF "ND" WILL HAVE A VALUE

OF "-" (MISSING VALUE OF THE FIRST KIND),

3 -- VALUES WITH REMARK CODES SET TO "--" (MISSING VALUE

OF THE SECOND KIND).

WITH EACH CHOICE, YOU WILL RECEIVE A SEPARATE FILE

CONTAINING COUNTS OF THE REMARKED VALUES

PLEASE ENTER 1, 2, OR 3.

Note: Because much of the data stored in QWDATA is recorded as less than the detection limit (i.e. <dl) 1 -- "REMARK CODES (SUCH AS < OR ND) INCLUDED WITH THE DATA," should be chosen.

DO YOU WANT TO ENTER PARAMETER CODES FROM THE TERMINAL (YES OR NO) ?

PARAMETER ENTRY PROCESSING :

PLEASE ENTER A 5 CHARACTER PARAMETER CODE AT EACH PROMPT.

(PLEASE ENTER A BLANK TO END THE PARAMETER ENTRY).

(ALPHA PARAMETERS ALLOWED: ADDPC, CALCV, SAMPL).

PARAMETER # 1

QWDATA automatically stores the requested data in the user designated output file. In addition to the designated file, QWDATA creates a ".CMND" file and a ".STATS" file. The .STATS file contains a summary of parameters with remarks and is not needed by ESTIMATOR. Remember, both the QW-file and the .cmnd-file are needed for proper execution of ESTIMATOR.

3.7. Potential problems

Care must be taken when selecting the five-digit parameter codes for a given parameter name. The ammonia example in Figure 3.3 demonstrates how several different measurements can have similar parameter names and codes.

Including remark codes (< and ND) with the data is important. With out these remark codes ESTIMATOR will analyze all censored values as the detection limit, not as censored data

4. Running ESTIMATOR

4.1. Purpose and Scope

This section demonstrates and explains how to run ESTIMATOR. Although one will usually employ batch processing through a command file when running ESTIMATOR, one can also use it interactively as demonstrated here.  In general, system prompts to the user appear in upper-case letters, user commands/responses appear in bold lower-case letters, and clarifying remarks/explanations appear in italics.

4.2. Accessing ESTIMATOR

To initiate the ESTIMATOR program double click on the application

Estimator2000

This assumes the file containing the ESTIMATOR program is named "Estimator2000. If the file name contains the version number then that must also be entered. For example, if the file name is "estimator93.06.exe" then "estimator93.06.exe" must be entered.

The following message should be displayed:

 ENTER COMMAND INPUT FILENAME (BLANK TO ENTER COMMANDS) At this point you must enter the name of the input command file that will control the actions of Estimator2000, or a carriage return which will initiate the interactive mode (although this feature may be disabled in some versions). Figure 4.1 shows a typical set of input commands.

Figure 4.1 A typical ESTIMATOR user dialogue

ENTER THE OUTPUT FILE NAME

test01.output

This name will be used for the main output file created by the program. The conventional output file naming scheme is to use a constituent identifier as the prefix and an eight digit station code as the suffix. Take, for example, the file test01.output. The prefix, cu-tr, identifies this file as an output file for total recoverable copper. The suffix, 01578310, identifies the Susquehanna River at Conowingo as the site for which loads were estimated. ENTER 0 FOR EXACT VARIANCES, 1 FOR SPEED (0/1)

1
 
 

This option is not offered in later versions of ESTIMATOR. Entering 0 will yield exact AMLE variance estimates. Exact calculations are time intensive and often unnecessary (see section 6.2.1). Entering 1 will yield linearized estimates, which are usually sufficient. ENTER THE ESTIMATION (Q) FILE NAME

q.01578310

The name of the daily discharge input file. Q-files are discussed in sections 1.1 and 2. ENTER THE PSTAT FILE NAME

qw.01578310

The name of the water quality input file. QWDATA sometimes lists values as either "ND" or "E". If present, these values will not cause a problem. However the following message will appear: " unrecognized remark code found in line .... ND recoded as missing value," to notify the user of their presence. QW-files are discussed in sections 1.2 and 3. PARAMETER CODES CONTAINED IN FILE:

P01027 P01113 P00061 P01034 P01118 P01042 P01119 P01051 P01114 P71900

P71901 P39630 P39632 P82612

This list of parameter numbers comes from the .cmnd-file discussed in sections 1.3 and 3.6. The parameter codes actually listed here will be determined during QWDATA retrieval. These parameter numbers identify constituents for which loads may be estimated. ENTER PARAMETER TO USE (I5):

01042

This number must come from the list of available parameter codes. In this case P01042 (total recoverable copper) was chosen. Note that the "P" is not entered. ENTER BEGIN YEAR FOR CAL. DATA (E.G. 1983.22)

1980.25

The BEGIN YEAR and ENDING YEAR prompts allow the user to restrict the calibration data to a specific time period. To use all available data enter 0 and 2000 respectively. Input Format is f7.2, where 1980.25 corresponds to April 1, 1980. All dates are based on Calendar years. ENTER ENDING YEAR FOR CALIBRATION DATA

1990.00

** DEFINE THE MODEL **

ENTER NAMES OF REGRESSORS TO INCLUDE

CONSTANT LOG-FLOW LOG-FLOW SQUARED SQRT FLOW

DEC_TIME DEC_TIME SQUARED SIN(2*PI*T) COS(2*PI*T)

SIN(4*PI*T) COS(4*PI*T) SIN(6*PI*T) COS(6*PI*T)

I-JAN I-FEB I-NOV I-DEC

I-1961 I-1962 I-2009 I-2010

These regressors are commonly used in modelling constituent transport. Any combination of the listed regressors may be used. When using Sin and Cos terms (Fourier series) to fit seasonality, one must take them as a pair. If the Sin(2*pi*t) is in the model, Cos(2*pi*t) must be used as well (and vice verse). Also, if you use higher order terms, Sin(k*2*pi*t) and Cos(k*2*pi*t), you must also include the lower-order terms (i.e. Sin(2*pi*t) and Cos(2*pi*t), ..., Sin((k-1)*2*pi*t) and Cos((k-1)*2*pi*t)). Similarly, when using a polynomial model in log-flow or time, if you include a higher-order term you must also include all lower-order terms. Indicator variables may be designated for any month or year with data in the qw-file. For example, I-DEC is the indicator variable for December and I-1990 is the indicator variable for 1990. Note that indicators are not limited to the months or years listed above. When using Indicator variables, be careful about multicollinearity. For example, do not use a Constant if you also specify Indicators for all 12 months, because the predictor variables will no longer be linearly independent. ENTER REGRESSOR NAME; BLANK LINE WHEN DONE

CONSTANT

Upper case letters must be used when entering regressors. ENTER REGRESSOR NAME; BLANK LINE WHEN DONE

LOG-FLOW

ENTER REGRESSOR NAME; BLANK LINE WHEN DONE

LOG-FLOW SQUARED

ENTER REGRESSOR NAME; BLANK LINE WHEN DONE

DEC_TIME

ENTER REGRESSOR NAME; BLANK LINE WHEN DONE

DEC_TIME SQUARED

ENTER REGRESSOR NAME; BLANK LINE WHEN DONE

SIN(2*PI*T)

ENTER REGRESSOR NAME; BLANK LINE WHEN DONE

COS(2*PI*T)

ENTER REGRESSOR NAME; BLANK LINE WHEN DONE
 
 

The model resulting from the sequence of responses shown above is:

ln[CCu] = b0 + b1 ln[Q] + b2 ln[Q]^2 + b3 T + b4 T^2 + b5 Sin[2*pT]  + b6 Cos[2*pT] +    (1)

** SETTING UP MATRICES **

ENTER OUTPUT FILE NAME FOR COMPARISON

(BLANK TO SKIP)

Entering a file name generates an output file which compares predicted concentrations and loads with observed values for each record in the calibration data set. ENTER FIRST YEAR FOR ESTIMATION

1990

The first year for which estimates are desired. ESTIMATOR will automatically compute monthy estimates for the twelve months of the calendar year, and annual estimates for both the water year (WY) and the calendar year (CY). Note, the Q-file must contain daily discharges for the entire period for which estimates are desired. ENTER LAST YEAR FOR ESTIMATION

1991

The last year for which estimates are desired ENTER OUTPUT FILE NAME FOR DAILY LOADS

(BLANK TO SKIP)

Entering a file name results in an output file which contains daily load predictions. Caution should be used when using these values because the MVUE approach can lead to very imprecise daily loads.

5. Interpreting ESTIMATOR Output Files

During program execution, ESTIMATOR prompts the user for an output file name. ESTIMATOR then creates an output file using standard FORTRAN control characters. The results are not printed to the monitor during program execution. Output files are often very long. Therefore, viewing each output file prior to printing is recommended.

5.1. Interpreting Regression Diagnostics

Figure 5.1 is the regression diagnostics section of the output file test01.output. This section of the output contains a large number of regression diagnostics. If the regression diagnostics reveal obvious errors in model specification ESTIMATOR will print comments in the diagnostics section. However, one should not rely on the comments alone to determine model validity. The regression diagnostics are important and anyone analyzing this data who is unfamiliar with ordinary least squares (OLS) regression should refer to Draper and Smith [1982].

Figure 5.1 Regression Diagnostics Section from the Output File test01.output

                     MODEL FOR ESTIMATING CONSTITUENT LOADS
                               TIM COHN VERSION 2000.01


 OUTPUT FILE:test01.result                                     
 *APPROXIMATE VARIANCES*

 CALIBRATION FLOWS FROM DV FLOW FILE

 USER SPECIFIED PERIOD: 1900.00-2100.00

 DATE OF FIRST OBS. USED IN CALIBRATION: 12/19/1978
 DATE OF LAST OBS. USED IN CALIBRATION:  09/05/1990
 STATION NUMBER: 01646500

 REGRESSION OF P00671              
 ON 7 REGRESSORS


                                                    CONCENTRATION MODEL                      LOAD MODEL
 NUMBER   NAME                     CENTER         COEFF.    S.D.      T       P           COEFF.    S.D.      T       P
   1    CONSTANT                     .000         -3.3313    .2376 *****   .000000         6.8562    .2376 28.86   .000000
   2    LOG-FLOW                    9.293           .0802    .0959   .84   .394928         1.0802    .0959 11.26   .000000
   3    LOG-FLOW SQUARED            9.293          -.0539    .0648  -.83   .389298         -.0539    .0648  -.83   .389298
   4    DEC_TIME                 1984.513          -.1191    .0276 -4.32   .000011         -.1191    .0276 -4.32   .000011
   5    DEC_TIME SQUARED         1984.513          -.0188    .0113 -1.67   .084545         -.0188    .0113 -1.67   .084545
   6    SIN(2*PI*T)                  .000          -.8617    .1711 -5.04   .000001         -.8617    .1711 -5.04   .000001
   7    COS(2*PI*T)                  .000          -.0537    .1500  -.36   .715957         -.0537    .1500  -.36   .715957

     S                                                      1.23106                       1.23106

     R**2 (%)                                              26.6                          52.8
     N        198
     M        191
     NCENS     46

     SER. CORR. OF RES.  .51872

           CONSTANT  LOG-FLOW  LOG-FLOW  DEC_TIME  DEC_TIME  SIN(2*PI*
 LOG-FLOW      .0000
 LOG-FLOW      .0000    0.0000
 DEC_TIME      .0000    -.2082    -.0795
 DEC_TIME      .0000     .1071    -.1165    0.0000
 SIN(2*PI*     .0000     .5800    -.3794    -.0167     .0160
 COS(2*PI*     .0000     .2261    -.0214     .1413    -.1341     .1782

 <\pre>

5.2. Interpreting Boxplots of Residuals

Figure 5.2 Boxplot of Residuals from the Output File test01.output

                                                                                                                                     
                                                 BOXPLOTS OF RESIDUALS AGAINST MONTH                                                 
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
                +:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+                
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
     J                                                        |-----|                                                                
     A   N=13                      *                  +-------| |   |----+                                                           
     N                                                        |-----|                                                                
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
     F                                                               |------|                                                        
     E   N=10                           *                         +--|    | |-----+                                                  
     B                                                               |------|                                                        
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
     M                                     |---------------------------|                                                             
     A   N=30              +---------------|      |                    |----------------+                                            
     R                                     |---------------------------|                                                             
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
     A                                                  |--------|                                                                   
     P   N=13              **                           + |      |------------+                                                      
     R                                                  |--------|                                                                   
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
     M                    |-----------------------------------|                                                                      
     A   N=19          +--|            |                      |---------------------------------+                                    
     Y                    |-----------------------------------|                                                                      
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
     J           |-----------------------------------------------------------------|                                                 
     U   N=18    +                      |                                          |--------------+                                  
     N           |-----------------------------------------------------------------|                                                 
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
                +:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+                
             -2.0000   -1.5000   -1.0000   -.5000     .0000     .5000     1.000     1.500     2.000     2.500     3.000              
                                                                                                                                     
                                                                                                                                     
<\pre>                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
                                                                                                                                
                                                                                                                                     
                                                 BOXPLOTS OF RESIDUALS AGAINST MONTH                                                 
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
                +:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+                
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
     J                                                        |---------|                                                            
     U   N=20                      O    O             +-------|   |     |---------+                                                  
     L                                                        |---------|                                                            
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
     A                                       |-------------------------|                                                             
     U   N=17              +-----------------|                    |    |--------------+                                              
     G                                       |-------------------------|                                                             
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
     S                       |-----------------------------------|                                                                   
     E   N=36          +-----|                    |              |----------------------+                                            
     P                       |-----------------------------------|                                                                   
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
     O                           |-----------------------------------|                                                               
     C   N=4                     +               |                   |---+                                                           
     T                           |-----------------------------------|                                                               
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
     N                                 |----------------------------------------------------|                                        
     O   N=13     +--------------------|     |                                              |-----+                                  
     V                                 |----------------------------------------------------|                                        
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
     D           |                                                                                                                   
     E   N=5     +                                                                                                                   
     C           |                                                                                                                   
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
                +:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+                
             -2.0000   -1.5000   -1.0000   -.5000     .0000     .5000     1.000     1.500     2.000     2.500     3.000              
                                                                                                                                     
<\pre>                                                                                                                                     
                                                                                                                                     

5.3. Interpreting Probability Plot for Normal Distribution

Figure 5.3 Probability Plot for Normal Distribution from the Output File test01.output

                                               PLOT OF RESIDUALS AGAINST THEIR Z-SCORES                                              
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
          2.106 +:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::*                
                .                                                 :                                         *  *    .                
                .                                                 :                                       *         .                
                .                                                 :                                   * *           .                
                .                                                 :                                                 .                
          1.648 +                                                 :                                ***              +                
                .                                                 :                            ****                 .                
                .                                                 :                        2*2**                    .                
                .                                                 :                   22222                         .                
                .                                                 :                332*                             .                
          1.191 +                                                 :             333                                 +                
                .                                                 :            2                                    .                
                .                                                 :          34*                                    .                
                .                                                 :         3                                       .                
                .                                                 :        3*                                       .                
          .7335 +                                                 :       2                                         +                
                .                                                 :       2                                         .                
                .                                                 :     44                                          .                
                .                                                 :   44                                            .                
                .                                                 : 44                                              .                
          .2761 +                                                 :2                                                +                
    R           .                                                 *2                                                .                
    E           .                                                *3                                                 .                
    S           ------------------------------------------------33---------------------------------------------------                
    I           .                                              3* :                                                 .                
    D    -.1814 +                                             **  :                                                 +                
    U           .                                             3   :                                                 .                
    A           .                                            2    :                                                 .                
    L           .                                                 :                                                 .                
    S           .                                           42    :                                                 .                
         -.6388 +                                          4      :                                                 +                
                .                                        24       :                                                 .                
                .                                     234*        :                                                 .                
                .                                                 :                                                 .                
                .                                    *2           :                                                 .                
        -1.0962 +                                  332            :                                                 +                
                .                                33               :                                                 .                
                .                              *3                 :                                                 .                
                .                             3*                  :                                                 .                
                .                          222                    :                                                 .                
        -1.5537 +                         2                       :                                                 +                
                .                        2                        :                                                 .                
                .                      2*                         :                                                 .                
                .                     *                           :                                                 .                
                .              ******2                            :                                                 .                
        -2.0111 +                                                 :                                                 +                
                .                                                 :                                                 .                
                .         * * *                                   :                                                 .                
                .                                                 :                                                 .                
                .       *                                         :                                                 .                
        -2.4685 *    *                                            :                                                 .                
                +:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+                
             -2.5741   -2.0593   -1.5445   -1.0296   -.5148     .0000     .5148     1.030     1.544     2.059     2.574              
                                                                                                                                     
                                                                                                                                     
                                                               Z-SCORES                                                              
                                                                                                                                     

   PPCC CORRELATION     =   .98032

<\pre>

5.4. Plot of the Raw Data 5.4.1. Plot of observed concentrations against time Figure 5.4 Plot of observed concentrations against time from output file
                                                                                                                                     
                                                                                                                                     
                                             PLOT OF OBSERVED CONCENTRATIONS AGAINST TIME                                            
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
        -1.3819 +:::::::::+:*6##::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+                
                .                                                                                                   .                
                .                                                                                                   .                
                .                                                                                                   .                
                .                                                                                                   .                
        -1.8397 +                                                                                                   +                
                .                                                                                                   .                
                .                                                                                                   .                
                .                                                                                                   .                
                .                                                                                                   .                
        -2.2976 +                                                                                                   +                
                .                                                        *                                          .                
                .          *       2                    * *       *      *                                          .                
                .                                                                                                   .                
    O           .                                                                        2                          .                
    B   -2.7554 +                                                                                                   +                
    S           .          *     * 3**   *             *                   *                              *2        .                
    E           .                                                                                                   .                
    R           .          *      ****  * *       **        *              *                             **         2                
    V           .                                                                                                   .                
    E   -3.2132 *     3*          *   *                             * *                            *     *          +                
    D           .                                                                                                   .                
                .                                                                                                   .                
    C           . * * 3  * 4        2                **     * *      *      2        *2 * *  *         *     2      .                
    O           .                                                                                                   .                
    N   -3.6711 +                                                                                                   +                
    C           .                                                                                                   .                
    E           .                                                                                                   .                
    N           . *   *    4  ***   2  *                         *         *         *    *           **            .                
    T           .                                                                                                   .                
    R   -4.1289 +                                                                                                   +                
    A           .                                                                                                   .                
    T           .                                                                                                   .                
    I           .                                                                                                   .                
    O           .                                                                                                   .                
    N   -4.5867 + * *     22 2     2                                    *     3 * *2        *       2          *    +                
    S           .                                                                                                   .                
                .                                                                                                   .                
                .                                                                                                   .                
                .                                                                                                   .                
        -5.0446 +                                                                                                   +                
                .     * 2                     * *                                                                   .                
                .    *       7   *                                                *                                 .                
                .   *       *                *                          *                   *      *                .                
                .  *       33                                *                  *                                   .                
        -5.5024 +                                                              2        *         2                 +                
                .                                                                                     *             .                
                .                                                                              22                 2 .                
                .                                                                                                   .                
                .                                                                                                   .                
        -5.9602 .                                                                                               22  .                
                +:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+                
              1979.     1980.     1981.     1982.     1984.     1985.     1986.     1987.     1988.     1990.     1991.              
                                                                                                                                     
                                                                                                                                     
                                                                 TIME                                                                
<\pre>                                                                                                                                     

5.4. Interpreting Plots of Residuals 5.4.1. Plot of residuals against predicted values Figure 5.4 Plot of residuals against predicted values from output file test01.output
                                                                                                                                    
                                                                                                                                     
                                              PLOT OF RESIDUALS AGAINST PREDICTED VALUES                                             
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
          2.106 +:::::::::+:::::::::+:::::::::+:::::::::+::::*::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+                
                .                                        **                                                         .                
                .                                *                                                                  .                
                .                                 *       *                                                         .                
                .                                                                                                   .                
          1.648 +                              2        *                                                           +                
                .                                    *              2         *                                     .                
                .                                *3 3                                                               .                
                .                       *2       4   *                      **                                      .                
                .                           2  4     2*                                                             .                
          1.191 +           2           2      * 2     *                      *                                     +                
                .                                                    *  *                                           .                
                .                      2                        2  *     *   **                                     .                
                .                                *               *      *                                           .                
                .             *              *            *         *                                               .                
          .7335 +                           *         *                                                             +                
                .          *                                                                    *                   .                
                .                          *       *        *       *         *2   *                                .                
                .                          *       * *               **   *   2                                     .                
                .                          2*  2 2                     *                                            .                
          .2761 +                     *     *                                                                       +                
    R           .                                          *          *          *                                  .                
    E           .                                                         *2  *                                     .                
    S           ---------------------------------*-*----*------*-----------*---------------------*-------------------                
    I           .                                       *    **         *                                           .                
    D    -.1814 +                            *                                                   *                  +                
    U           .                                   3                                                               .                
    A           .                           *                 *                                                     .                
    L           .                                                                                                   .                
    S           .         22                    *                          *                                        .                
         -.6388 +                                      *   *      2                                                 +                
                .         2 *                                                                               2       *                
                .    2       2    2                *          *                                   *       *         .                
                .                                                                                                   .                
                .          *       2                                                                                .                
        -1.0962 2                                2                            *                      2      *       +                
                .               2       3             *                                                             .                
                .             *                    *   *             *                                              .                
                .                                    *            *       * *                                       .                
                .           *                        *                           * 2                        *       .                
        -1.5537 +                                   *      *                                                        +                
                .                                       2                                                           .                
                .                  2        *                                                                       .                
                .                     *                                                                             .                
                .             *                    *22 * *                                                          .                
        -2.0111 +                                                                                                   +                
                .                                                                                                   .                
                .                                      *       *  *                                                 .                
                .                                                                                                   .                
                .                                                          *                                        .                
        -2.4685 .                           *                 *                                                     .                
                +:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+                
              3.720     4.378     5.036     5.694     6.352     7.010     7.668     8.325     8.983     9.641     10.30              
                                                                                                                                     
                                                                                                                                     
                                                           PREDICTED VALUES                                                          
                                                                                                                                     
<\pre>

5.4.2. Plot of residuals against flow Figure 5.5 Plot of residuals against flow from output file test01.output
                                                    PLOT OF RESIDUALS AGAINST FLOW                                                   
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
          2.106 +:::::::::+:::::::::+:::::::::+:::::::::+*::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+                
                .                                *                              *                                   .                
                .                     *                                                                             .                
                .                     *                                         *                                   .                
                .                                                                                                   .                
          1.648 +              *          *                          *                                              +                
                .                                      2       *                       *                            .                
                .            *2  4                                                                                  .                
                .*2          4                                 *                **                                  .                
                .    2   4     ** *                                                                                 .                
          1.191 +         2   2  *    2                              *                *                             +                
                .                               *                            *                                      .                
                .                   2                                 *     *  2 *    *                             .                
                .                                         *             *    *                                      .                
                .         *                         *    *            *                                             .                
          .7335 +                               *   *                                                               +                
                .                  *                                                                          *     .                
                .         *                  *             *    *                      3    *                       .                
                .         *       *               *                      *  *    *   2                              .                
                .             *          2    2  *            *       *                                             .                
          .2761 +*                  *                                                                               +                
    R           .                                   *           *                  *                                .                
    E           .                                                                2*    *                            .                
    S           -----------------------------**--*-*-----------------------------*-----*-----------------------------                
    I           .                  *        *           *           *                                               .                
    D    -.1814 +           *                                                          *                            +                
    U           .                                            3                                                      .                
    A           .   *                              *                                                                .                
    L           .                                                                                                   .                
    S           .                                 32                               *                                .                
         -.6388 +                                        *    *        2                                            +                
                .    2  *                                                                    2                      *                
                .                 2       2     2 **                           *          *                         .                
                .                                                                                                   .                
                .          2       *                                                                                .                
        -1.0962 + 2          *                            *                  *      2        *                      +                
                .*  2             *            2                                                                    .                
                *           *    *                                           *                                      .                
                .                                      *               *         *  *                               .                
                .       *               *                                              *  2  *                      .                
        -1.5537 +                                  *       *                                                        +                
                .                         *            *                                                            .                
                .          2        *                                                                               .                
                .           *                                                                                       .                
                *                        *22 *   *                                                                  .                
        -2.0111 +                                                                                                   +                
                .                                                                                                   .                
                .                        *       *   *                                                              .                
                .                                                                                                   .                
                .                                          *                                                        .                
        -2.4685 .    *                    *                                                                         .                
                +:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+                
              7.065     7.617     8.169     8.722     9.274     9.826     10.38     10.93     11.48     12.04     12.59              
                                                                                                                                     
                                                                                                                                     
                                                             LOG OF FLOW                                                             
                                                                                                                                     

 <\pre>                                                                                                                                    

5.4.3. Plot of residuals against time Figure 5.6 Plot of residuals against time from output file test01.output

PLOT OF RESIDUALS AGAINST TIME

                                                                                                                                    
                                                    PLOT OF RESIDUALS AGAINST TIME                                                   
                                                                                                                                     
                                                                                                                                     
                                                                                                                                     
          2.106 +:::::::::+:*:::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+                
                .            *                                                                           *          .                
                .            *                                                                                      .                
                .            *                                                                           *          .                
                .                                                                                                   .                
          1.648 +            **                                                                        *            +                
                .          * 2                                                                            *         .                
                .             7                                                                                     .                
                .             43   2                                                                      *         .                
                .             36                                                                                    .                
          1.191 +          *  *2                                                         2             *            2                
                .             *     *                                                                               .                
                .          *       3                                                  2                    2        .                
                .                   *                                 *                 *                           .                
                .                 **               *                 *                                              .                
          .7335 +                                           *                                *                      +                
                .                                           *                                         *             .                
                . *        3      *  *    *                              *                                          .                
                .          *        2                *        *   * *    *                                          .                
                .                    *                 *                    2        *                       2 *    .                
          .2761 +                                       *                                          *                +                
    R           . *                                   *   *                                                         .                
    E           .          4                                                                                        .                
    S           *----------------*--2--------------------------------------*---------*-------------------------------                
    I           .   *    *               *        *                                                                 .                
    D    -.1814 +                     *                                    *                                        +                
    U           .                                                             3                                     .                
    A           .                       *                                                 *                         .                
    L           .                                                                                                   .                
    S           . *                *                                                                            22  .                
         -.6388 +         *2       *                                                                                +                
                .     2                                                    *    *                   2               .                
                .     **  *                                                               *    22                 2 .                
                .                                                                                                   .                
                .                                                       *                   *         *             .                
        -1.0962 +   * 3       *                                                         *         2                 +                
                .              *                                 *             2   2                                .                
                .               *      *                     *                    *                                 .                
                .  *       3                                                                                        .                
                .     *     3*                                                  *                                   .                
        -1.5537 +           *                *                                                                      +                
                .   *        *                                                                                      .                
                .                                                       *                   *      *                .                
                .                *                                                                                  .                
                .            7                                                    *                                 .                
        -2.0111 +                                                                                                   +                
                .                                                                                                   .                
                .    *  *                     *                                                                     .                
                .                                                                                                   .                
                .       *                                                                                           .                
        -2.4685 .     *                         *                                                                   .                
                +:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+:::::::::+                
              1979.     1980.     1981.     1982.     1984.     1985.     1986.     1987.     1988.     1990.     1991.              
                                                                                                                                     
                                                                                                                                     
                                                                 TIME                                                                
                                                                                                                                     
<\pre>
5.5. Interpreting Computed Loads

Figure 5.7 is the computed loads section of the output file test01.output. Estimated monthly and annual mean daily loads are given for each calendar year (CY) and water year (WY) in the period of estimation. Accompanying each of the load estimates are standard errors (S.E.) and standard errors of prediction (S.E. PRED.). The units of load are g/day if concentration units in the qw-file are µg/l and kg/day if concentration units in the qw-file are mg/L.

Figure 5.7 Computed loads section from output file test01.output

                             COMPUTED LOADS [KG/DAY] OR [G/DAY]

      YEAR MO.        LOAD:P00671      95% CONFIDENCE INTERVAL           S.E.          S.E. PRED.

  1980 CALENDAR YEAR
            1        2933.4050        1145.7127        6231.6363         708.2666        1328.8673
            2         877.3256         354.1917        1824.4872         213.6195         383.5068
            3        2171.9737         871.6291        4534.3833         408.8300         955.6710
            4        2991.9013        1284.1710        5976.4462         539.8443        1220.2751
            5        3098.1805        1264.9390        6396.0436         562.7873        1337.6232
            6        1349.3394         584.8537        2677.7985         256.8958         544.0450
            7        1074.2609         459.7369        2150.0838         195.1065         439.6528
            8        1214.3991         505.8369        2474.4603         222.8823         512.6934
            9         595.0291         254.3398        1191.8791         127.3456         243.8642
           10         593.5840         239.0117        1236.5202         137.3473         260.2213
           11        1176.4746         387.1881        2776.7908         277.8648         630.6606
           12         836.0575         327.0023        1774.4992         204.4908         378.1788
  Q1  1980           2018.7822        1043.0113        3544.7960         416.2953         645.6858
  Q2  1980           2486.6024        1377.8118        4146.7785         426.9492         712.9702
  Q3  1980            965.2101         540.8950        1596.0268         165.3209         271.5859
  Q4  1980            865.3601         423.2811        1580.2356         195.9708         299.2052
 CY   1980           1580.3346        1061.0595        2267.0815         232.5623         308.9721
 WY   1980           3538.1675        2020.9621        5766.6898         744.3518         963.5743

  1981 CALENDAR YEAR
            1         195.1715          70.4939         435.4811          66.1091          95.7793
            2        1506.6659         526.3076        3431.2692         287.2135         763.8249
            3         706.8887         292.7089        1445.9520         146.1844         300.4285
            4        1272.1084         452.0689        2866.8993         222.8209         634.2994
            5        1239.2878         532.0348        2475.1780         238.9538         505.3296
            6        2311.9715         972.4325        4680.7510         492.1866         965.3124
            7        1128.5285         458.1390        2338.4600         220.4235         490.3194
            8         561.5601         236.0101        1137.5108         108.2825         234.6786
            9        1080.9661         451.4180        2198.8512         210.7075         455.0315
           10         929.8130         203.9135        2734.4925         206.7142         689.8740
           11        1067.3352         394.5638        2347.4855         248.4399         511.8016
           12         879.9335         351.9669        1840.9175         211.4577         388.5562
  Q1  1981            779.4501         367.5412        1460.4124         151.2806         283.0448
  Q2  1981           1603.7398         871.5472        2713.4563         298.2015         474.5609
  Q3  1981            921.9753         509.5761        1540.4327         162.6884         265.4523
  Q4  1981            957.8499         440.9098        1824.8365         214.9129         358.7856
 CY   1981           1065.8486         711.0527        1537.0705         157.4956         211.6473
 WY   1981           1042.5361         704.1388        1488.3090         149.5200         200.8724

<\pre>

Determining a constituent's total load for a given month, or year, requires multiplying the estimated mean daily load by the number of days in that month, or year.

In Figure 5.7 January 1980's estimated mean daily load for total recoverable copper is 2933.4050 kilograms/day. The precision of this estimate can be described in terms of a confidence interval based on the estimated mean daily load and the standard error of prediction. An approximate 95% confidence interval in this case would be:

{1145.7127, 6231.6363}

Because the units of concentration in the qw-file were mg/l, the load units are kg/day. The estimated load of total recoverable copper, transported during January 1980, is

2933.4050 kg/day x 31 days = 90,936 kilograms

The confidence interval for January 1980's load would be

{1145.7127 x (31) , 6231.6363 x (31)} grams or

{35,517 , 193,180} kilograms.

6. Potential Problems

6.1. Situations Which May Cause a Program Crash

ESTIMATOR may crash if something is wrong with any of the input files. A crash may also occur if there are too many parameters (>20) or if there is insufficient data to calibrate the model. Two rules of thumb for ensuring sufficient calibration data are:

1. There must be a minimum of three values above the detection limit for each parameter. For example, a model using five parameters should have at least fifteen values above the detection limit.

2. For predictor variables, X, which are mostly constant (i.e. indicator variables) at least one observation must have a value greater than the detection limit when X = 0.

6.2. Situations Which May Cause "Bad" Estimates

Model validity should be determined by analysis of the residuals and other diagnostics [Draper and Smith, 1982].

6.2.1. Situations Which Cause Long Execution Times During the user interface portion of ESTIMATOR the users is prompted, "ENTER 0 FOR EXACT VARIANCE, 1 FOR SPEED (0/1)," in earlier versions of ESTIMATOR. In most cases 1 should be entered. The calculations for exact variance are time intensive. Therefore, the user needs to understand that if 0 is entered load estimation will take significantly longer than if a 1 is entered. Long execution times are inherent with exact variance calculations and are not caused by error.

7. Obtaining ESTIMATOR

The current version of ESTIMATOR can be obtained from anonymous FTP on srv1rvares.er.usgs.gov or from Tim Cohn of the Office of Surface Water (703/648-5711). The version number (e.g., 95.01) appears after the word estimator in the executable file (ie., estimator_95.01.exe). This number provides the year and month of the latest update. ESTIMATOR is designed to run on any Data General Aviion workstation or file server.

References:

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.

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, 1992a.

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, 1992b.

Draper, N.R. and H. Smith, Applied Regression Analysis, 2nd Edition, John Wiley and Sons, New York, 1981.

Gilroy, E. J., R. M. Hirsch, and T. A. Cohn, "Mean Square Error of Regression-Based Constituent Transport Estimates," Water Resources Research, 26(9), pp. 2069-2077, 1990.