Deat CXTFIT,

I have measurements of bromide at depths from a field solute transport experiment at various times. I would like to use CXTFIT and choose the inverse approach to estimate v and D.

I wonder if you can recommend how to best make initial estimates for parameters of v, D, etc..? Do I need to estimate for mu and omega as well? and which ones should they be fitted?

I have to run it in the deterministic mode and cannot get a solution if I use the stochastic CDE option.

Maybe I have selected the wrong boundary value condition or the wrong nonequilibrium code. What do suggest that I check?

Regards,

J

## Initial estimates for v and D

Thank-you for your reply.[:)]

However, I still do not feel certain how to estimate initial values. In Fig 79b there were initial estimates made, but then there are no final values given for v or D. In this example, it was only beta and omega that were fitted. Consequently, the Table 7.2 on page 100 has the same values for v, D, ? and R, there are only different initial values for â for the two parameter estimation in part (a) and in Part (b). Is it necessary to choose a model (like Fig 79) that requires v, D, R, â and ??

Indeed for Fig 74 the parameters initially estimated are v, D, R and mu.

For my own data (Bromide conc. (ppm) vs. depth) I am not sure that my initial estimate for R and Mu (or v or D for that matter) are correct (or good estimates). Having guessed at some initial values, I am uncertain about the following:

Parameter estimate constraints

[?]

1. Is it better to select no constraints for parameter estimation OR is it better to set a min and max value?

Type of model

The use of a stochastic (e.g. stream tube ) mode of the CDE. I would have assumed that theoretically field observations of bromide would be better modelled using stochastic CDE. However, I’m not sure whether to accept the estimates from the stochastic CDE model or from the deterministic CDE. In the case of the stochastic CDE it is necessary to make initial estimates for quite a number of parameters: Kd, Mu, sigma v, sigma Kd, sigmas D, ?vKd, ?? and I am not sure that I have selected the right values.

For the deterministic CDE I have the following output:

RSquare for regression of observed vs predicted =-.48429771

Mean square for error (MSE) = .1956E+06

V = 2.13E+01, D = 1.00E-02

For the stochastic CDE I have the following output:

RSquare for regression of observed vs predicted =-.48538460

Mean square for error (MSE) = .1958E+06

V= 7.89E+00, D = 1.00E-03

For both cases I had used a Dirac delta input , mass = 29.7500

[?]

2.Can you please suggest to me how to decide whether I use the estimates for v and D from the deterministic CDE or the stochastic CDE? or is it possible to consider both models?

Regards,

Jack

N.B.

If you are interested the data I used are given below:

Depth Bromide concentration

(cm) (ppm)

5 829.6

10 672.8

15 175.4

25 62.6

35 11.9

50 2.0

70 0.5

90 0.0

I guess you are confused regarding transport models (CDE and MIM). Please carefully read soil physics textbooks such as Jury and Hillel. Do not use the stochastic CDE until you understand the deterministic models.

Regarding Fig. 7.9, as stated in p.98, v and D were determined from the nonreactive 3H2O (Fig 7.9(a)). D and theta/theta_m are assumed to be identical for boron and 3H2O. I think Kd was independently determined from the adsorption experiment (see, van Genuchten, 1974)

In Fig.7.4 , v and D are estimated (R and mu are fixed).

If any further questions regarding CXTFIT after studying these transport models, please let me know.

Nobuo

I am doing study on the effect of olive mill waste water on soil transport properties under un saturated condtions. I did a leaching experiment using inert tracer (Br) for 10 days and I took samples to measure Br. I want to draw BTCs and calculate D and V using STANMOD. I tried many times but no good fitting to the original data.

The input file is

0,000267164 20 0,01875

0,000291045 20 0,09375

0,000377612 20 0,16875

0,000501493 20 0,24375

0,00530149 20 0,328125

0,0153776 20 0,421875

0,0232119 20 0,515625

0,021409 20 0,609375

0,0163731 20 0,703125

0,0128821 20 0,796875

0,00954179 20 0,890625

0,00718955 20 0,984375

0,00502537 20 1,07813

0,00322388 20 1,17188

0,00230746 20 1,26563

0,00152537 20 1,35938

0,00119851 20 1,45313

0,000964179 20 1,54688

0,000764179 20 1,64063

0,000628358 20 1,73438

0,000537313 20 1,82813

0,000292537 20 1,92188

0,00135373 20 2,01563

0,000271642 20 2,10938

0,000535821 20 2,20313

the output file is

Model description

=================

Deterministic equilibrium CDE (Mode=1)

Resident concentration (third-type input)

Real time (t), Position(x)

(D,V,mu, and gamma are also dimensional)

Initial values of coefficients

==============================

Name Initial value Fitting Min value Max value

V........ .4500E+01 Y .1000E-01 .1000E+03

D........ .1000E+01 Y .1000E-01 .1000E+03

R........ .1000E+01 N

mu....... .0000E+00 N

Cin...... .1000E+01 N

T2....... .2200E+01 Y .1000E+00 .2500E+01

Boundary, initial, and production conditions

===========================================

<Initial estimate of b.c.>

Single pulse of conc. = 1.0000 & duration = 2.2000

Solute free initial condition

No production term

Parameter estimation mode

=========================

Maximum number of iterations = 20

Duration time, T2, is fitted to the data

.1000 < T2 < 2.5000

Iter SSQ V.... D.... T2...

0 .1888E-02 .450E+01 .100E+01 .220E+01

1 .1874E-02 .100E-01 .100E+03 .220E+01

2 .1874E-02 .100E-01 .100E+03 .220E+01

Covariance matrix for fitted parameters

=======================================

V.... D.... T2...

V.... 1.000

D.... -.948 1.000

T2... .000 .000 .000

RSquare for regression of observed vs predicted =-.56389164

(Coefficeint of determination)

Mean square for error (MSE) = .8517E-04

Non-linear least squares analysis, final results

================================================

95% Confidence limits

Name Value S.E.Coeff. T-Value Lower Upper

V.... .1000E-01 .3044E+00 .3285E-01 -.6213E+00 .6413E+00

D.... .1000E+03 .5388E+04 .1856E-01 -.1107E+05 .1127E+05

T2... .2200E+01 .9229E-32 .2384E+33 .2200E+01 .2200E+01

------------------Ordered by computer input-------------------

Concentration Resi-

No Distance Time Obs Fitted Dual

1 20.0000 .0187 .0003 .0000 .0003

2 20.0000 .0938 .0003 .0000 .0003

3 20.0000 .1688 .0004 .0000 .0004

4 20.0000 .2437 .0005 .0000 .0005

5 20.0000 .3281 .0053 .0000 .0053

6 20.0000 .4219 .0154 .0000 .0154

7 20.0000 .5156 .0232 .0000 .0232

8 20.0000 .6094 .0214 .0000 .0214

9 20.0000 .7031 .0164 .0000 .0163

10 20.0000 .7969 .0129 .0001 .0128

11 20.0000 .8906 .0095 .0001 .0095

12 20.0000 .9844 .0072 .0001 .0071

13 20.0000 1.0781 .0050 .0001 .0049

14 20.0000 1.1719 .0032 .0001 .0031

15 20.0000 1.2656 .0023 .0002 .0021

16 20.0000 1.3594 .0015 .0002 .0013

17 20.0000 1.4531 .0012 .0002 .0010

18 20.0000 1.5469 .0010 .0002 .0007

19 20.0000 1.6406 .0008 .0002 .0005

20 20.0000 1.7344 .0006 .0003 .0004

21 20.0000 1.8281 .0005 .0003 .0002

22 20.0000 1.9219 .0003 .0003 .0000

23 20.0000 2.0156 .0014 .0003 .0010

24 20.0000 2.1094 .0003 .0004 -.0001

25 20.0000 2.2031 .0005 .0004 .0002

Z= 1.0000 (Resident conc. vs. time)

Sum(C*dT) = .0031, Sum(Ct*dT)= .0031

Time C Ct (=R*C)

.0000 .00000E+00 .00000E+00

.1000 .26569E-03 .26569E-03

.2000 .41086E-03 .41086E-03

.3000 .52309E-03 .52309E-03

.4000 .61797E-03 .61797E-03

.5000 .70169E-03 .70169E-03

.6000 .77746E-03 .77746E-03

.7000 .84718E-03 .84718E-03

.8000 .91210E-03 .91210E-03

.9000 .97310E-03 .97310E-03

1.0000 .10308E-02 .10308E-02

1.1000 .10857E-02 .10857E-02

1.2000 .11382E-02 .11382E-02

1.3000 .11885E-02 .11885E-02

1.4000 .12369E-02 .12369E-02

1.5000 .12837E-02 .12837E-02

1.6000 .13289E-02 .13289E-02

1.7000 .13727E-02 .13727E-02

1.8000 .14152E-02 .14152E-02

1.9000 .14566E-02 .14566E-02

2.0000 .14969E-02 .14969E-02

2.1000 .15362E-02 .15362E-02

2.2000 .15746E-02 .15746E-02

2.3000 .13870E-02 .13870E-02

2.4000 .12662E-02 .12662E-02

2.5000 .11846E-02 .11846E-02

2.6000 .11219E-02 .11219E-02

2.7000 .10706E-02 .10706E-02

2.8000 .10272E-02 .10272E-02

2.9000 .98967E-03 .98967E-03

Z= 2.0000 (Resident conc. vs. time)

Sum(C*dT) = .0029, Sum(Ct*dT)= .0029

Time C Ct (=R*C)

.0000 .00000E+00 .00000E+00

.1000 .19192E-03 .19192E-03

.2000 .32962E-03 .32962E-03

.3000 .43847E-03 .43847E-03

.4000 .53133E-03 .53133E-03

.5000 .61367E-03 .61367E-03

.6000 .68841E-03 .68841E-03

.7000 .75733E-03 .75733E-03

.8000 .82161E-03 .82161E-03

.9000 .88208E-03 .88208E-03

1.0000 .93934E-03 .93934E-03

1.1000 .99385E-03 .99385E-03

1.2000 .10460E-02 .10460E-02

1.3000 .10960E-02 .10960E-02

1.4000 .11442E-02 .11442E-02

1.5000 .11907E-02 .11907E-02

1.6000 .12357E-02 .12357E-02

1.7000 .12793E-02 .12793E-02

1.8000 .13217E-02 .13217E-02

1.9000 .13629E-02 .13629E-02

2.0000 .14030E-02 .14030E-02

2.1000 .14422E-02 .14422E-02

2.2000 .14805E-02 .14805E-02

2.3000 .13632E-02 .13632E-02

2.4000 .12519E-02 .12519E-02

2.5000 .11742E-02 .11742E-02

2.6000 .11135E-02 .11135E-02

2.7000 .10637E-02 .10637E-02

2.8000 .10213E-02 .10213E-02

2.9000 .98448E-03 .98448E-03

Z= 3.0000 (Resident conc. vs. time)

Sum(C*dT) = .0027, Sum(Ct*dT)= .0027

Time C Ct (=R*C)

.0000 .00000E+00 .00000E+00

.1000 .13424E-03 .13424E-03

.2000 .26035E-03 .26035E-03

.3000 .36380E-03 .36380E-03

.4000 .45337E-03 .45337E-03

.5000 .53345E-03 .53345E-03

.6000 .60651E-03 .60651E-03

.7000 .67412E-03 .67412E-03

.8000 .73735E-03 .73735E-03

.9000 .79693E-03 .79693E-03

1.0000 .85345E-03 .85345E-03

1.1000 .90732E-03 .90732E-03

1.2000 .95889E-03 .95889E-03

1.3000 .10084E-02 .10084E-02

1.4000 .10562E-02 .10562E-02

1.5000 .11023E-02 .11023E-02

1.6000 .11469E-02 .11469E-02

1.7000 .11902E-02 .11902E-02

1.8000 .12323E-02 .12323E-02

1.9000 .12732E-02 .12732E-02

2.0000 .13131E-02 .13131E-02

2.1000 .13520E-02 .13520E-02

2.2000 .13901E-02 .13901E-02

2.3000 .13254E-02 .13254E-02

2.4000 .12287E-02 .12287E-02

2.5000 .11569E-02 .11569E-02

2.6000 .10998E-02 .10998E-02

2.7000 .10522E-02 .10522E-02

2.8000 .10114E-02 .10114E-02

2.9000 .97585E-03 .97585E-03

Z= 4.0000 (Resident conc. vs. time)

Sum(C*dT) = .0025, Sum(Ct*dT)= .0025

Time C Ct (=R*C)

.0000 .00000E+00 .00000E+00

.1000 .90758E-04 .90758E-04

.2000 .20233E-03 .20233E-03

.3000 .29866E-03 .29866E-03

.4000 .38383E-03 .38383E-03

.5000 .46084E-03 .46084E-03

.6000 .53161E-03 .53161E-03

.7000 .59743E-03 .59743E-03

.8000 .65920E-03 .65920E-03

.9000 .71757E-03 .71757E-03

1.0000 .77306E-03 .77306E-03

1.1000 .82604E-03 .82604E-03

1.2000 .87684E-03 .87684E-03

1.3000 .92569E-03 .92569E-03

1.4000 .97280E-03 .97280E-03

1.5000 .10184E-02 .10184E-02

1.6000 .10625E-02 .10625E-02

1.7000 .11053E-02 .11053E-02

1.8000 .11470E-02 .11470E-02

1.9000 .11876E-02 .11876E-02

2.0000 .12271E-02 .12271E-02

2.1000 .12657E-02 .12657E-02

2.2000 .13035E-02 .13035E-02

2.3000 .12761E-02 .12761E-02

2.4000 .11973E-02 .11973E-02

2.5000 .11334E-02 .11334E-02

2.6000 .10808E-02 .10808E-02

2.7000 .10363E-02 .10363E-02

2.8000 .99778E-03 .99778E-03

2.9000 .96388E-03 .96388E-03

Z= 5.0000 (Resident conc. vs. time)

Sum(C*dT) = .0023, Sum(Ct*dT)= .0023

Time C Ct (=R*C)

.0000 .00000E+00 .00000E+00

.1000 .59227E-04 .59227E-04

.2000 .15461E-03 .15461E-03

.3000 .24252E-03 .24252E-03

.4000 .32235E-03 .32235E-03

.5000 .39559E-03 .39559E-03

.6000 .46352E-03 .46352E-03

.7000 .52709E-03 .52709E-03

.8000 .58703E-03 .58703E-03

.9000 .64389E-03 .64389E-03

1.0000 .69808E-03 .69808E-03

1.1000 .74994E-03 .74994E-03

1.2000 .79976E-03 .79976E-03

1.3000 .84774E-03 .84774E-03

1.4000 .89408E-03 .89408E-03

1.5000 .93893E-03 .93893E-03

1.6000 .98244E-03 .98244E-03

1.7000 .10247E-02 .10247E-02

1.8000 .10658E-02 .10658E-02

1.9000 .11059E-02 .11059E-02

2.0000 .11450E-02 .11450E-02

2.1000 .11832E-02 .11832E-02

2.2000 .12205E-02 .12205E-02

2.3000 .12184E-02 .12184E-02

2.4000 .11588E-02 .11588E-02

2.5000 .11041E-02 .11041E-02

2.6000 .10571E-02 .10571E-02

2.7000 .10163E-02 .10163E-02

2.8000 .98052E-03 .98052E-03

2.9000 .94872E-03 .94872E-03

Z= 6.0000 (Resident conc. vs. time)

Sum(C*dT) = .0021, Sum(Ct*dT)= .0021

Time C Ct (=R*C)

.0000 .00000E+00 .00000E+00

.1000 .37254E-04 .37254E-04

.2000 .11611E-03 .11611E-03

.3000 .19473E-03 .19473E-03

.4000 .26848E-03 .26848E-03

.5000 .33736E-03 .33736E-03

.6000 .40197E-03 .40197E-03

.7000 .46291E-03 .46291E-03

.8000 .52069E-03 .52069E-03

.9000 .57574E-03 .57574E-03

1.0000 .62838E-03 .62838E-03

1.1000 .67891E-03 .67891E-03

1.2000 .72755E-03 .72755E-03

1.3000 .77449E-03 .77449E-03

1.4000 .81990E-03 .81990E-03

1.5000 .86392E-03 .86392E-03

1.6000 .90666E-03 .90666E-03

1.7000 .94823E-03 .94823E-03

1.8000 .98872E-03 .98872E-03

1.9000 .10282E-02 .10282E-02

2.0000 .10668E-02 .10668E-02

2.1000 .11044E-02 .11044E-02

2.2000 .11413E-02 .11413E-02

2.3000 .11553E-02 .11553E-02

2.4000 .11144E-02 .11144E-02

2.5000 .10697E-02 .10697E-02

2.6000 .10289E-02 .10289E-02

2.7000 .99250E-03 .99250E-03

2.8000 .95990E-03 .95990E-03

2.9000 .93055E-03 .93055E-03

Z= 7.0000 (Resident conc. vs. time)

Sum(C*dT) = .0020, Sum(Ct*dT)= .0020

Time C Ct (=R*C)

.0000 .00000E+00 .00000E+00

.1000 .22559E-04 .22559E-04

.2000 .85655E-04 .85655E-04

.3000 .15456E-03 .15456E-03

.4000 .22173E-03 .22173E-03

.5000 .28579E-03 .28579E-03

.6000 .34668E-03 .34668E-03

.7000 .40465E-03 .40465E-03

.8000 .45998E-03 .45998E-03

.9000 .51296E-03 .51296E-03

1.0000 .56384E-03 .56384E-03

1.1000 .61283E-03 .61283E-03

1.2000 .66011E-03 .66011E-03

1.3000 .70585E-03 .70585E-03

1.4000 .75019E-03 .75019E-03

1.5000 .79323E-03 .79323E-03

1.6000 .83509E-03 .83509E-03

1.7000 .87585E-03 .87585E-03

1.8000 .91559E-03 .91559E-03

1.9000 .95440E-03 .95440E-03

2.0000 .99232E-03 .99232E-03

2.1000 .10294E-02 .10294E-02

2.2000 .10657E-02 .10657E-02

2.3000 .10892E-02 .10892E-02

2.4000 .10655E-02 .10655E-02

2.5000 .10311E-02 .10311E-02

2.6000 .99696E-03 .99696E-03

2.7000 .96525E-03 .96525E-03

2.8000 .93619E-03 .93619E-03

2.9000 .90960E-03 .90960E-03

Z= 8.0000 (Resident conc. vs. time)

Sum(C*dT) = .0018, Sum(Ct*dT)= .0018

Time C Ct (=R*C)

.0000 .00000E+00 .00000E+00

.1000 .13135E-04 .13135E-04

.2000 .62037E-04 .62037E-04

.3000 .12124E-03 .12124E-03

.4000 .18153E-03 .18153E-03

.5000 .24045E-03 .24045E-03

.6000 .29732E-03 .29732E-03

.7000 .35203E-03 .35203E-03

.8000 .40467E-03 .40467E-03

.9000 .45536E-03 .45536E-03

1.0000 .50427E-03 .50427E-03

1.1000 .55155E-03 .55155E-03

1.2000 .59732E-03 .59732E-03

1.3000 .64171E-03 .64171E-03

1.4000 .68483E-03 .68483E-03

1.5000 .72678E-03 .72678E-03

1.6000 .76763E-03 .76763E-03

1.7000 .80748E-03 .80748E-03

1.8000 .84639E-03 .84639E-03

1.9000 .88442E-03 .88442E-03

2.0000 .92162E-03 .92162E-03

2.1000 .95805E-03 .95805E-03

2.2000 .99375E-03 .99375E-03

2.3000 .10225E-02 .10225E-02

2.4000 .10133E-02 .10133E-02

2.5000 .98890E-03 .98890E-03

2.6000 .96168E-03 .96168E-03

2.7000 .93497E-03 .93497E-03

2.8000 .90971E-03 .90971E-03

2.9000 .88610E-03 .88610E-03

Z= 9.0000 (Resident conc. vs. time)

Sum(C*dT) = .0017, Sum(Ct*dT)= .0017

Time C Ct (=R*C)

.0000 .00000E+00 .00000E+00

.1000 .73473E-05 .73473E-05

.2000 .44094E-04 .44094E-04

.3000 .93954E-04 .93954E-04

.4000 .14732E-03 .14732E-03

.5000 .20091E-03 .20091E-03

.6000 .25354E-03 .25354E-03

.7000 .30478E-03 .30478E-03

.8000 .35451E-03 .35451E-03

.9000 .40274E-03 .40274E-03

1.0000 .44951E-03 .44951E-03

1.1000 .49491E-03 .49491E-03

1.2000 .53902E-03 .53902E-03

1.3000 .58193E-03 .58193E-03

1.4000 .62372E-03 .62372E-03

1.5000 .66445E-03 .66445E-03

1.6000 .70421E-03 .70421E-03

1.7000 .74305E-03 .74305E-03

1.8000 .78102E-03 .78102E-03

1.9000 .81819E-03 .81819E-03

2.0000 .85459E-03 .85459E-03

2.1000 .89028E-03 .89028E-03

2.2000 .92528E-03 .92528E-03

2.3000 .95656E-03 .95656E-03

2.4000 .95907E-03 .95907E-03

2.5000 .94406E-03 .94406E-03

2.6000 .92368E-03 .92368E-03

2.7000 .90208E-03 .90208E-03

2.8000 .88077E-03 .88077E-03

2.9000 .86031E-03 .86031E-03

Z= 10.0000 (Resident conc. vs. time)

Sum(C*dT) = .0016, Sum(Ct*dT)= .0016

Time C Ct (=R*C)

.0000 .00000E+00 .00000E+00

.1000 .39443E-05 .39443E-05

.2000 .30743E-04 .30743E-04

.3000 .71917E-04 .71917E-04

.4000 .11847E-03 .11847E-03

.5000 .16668E-03 .16668E-03

.6000 .21494E-03 .21494E-03

.7000 .26257E-03 .26257E-03

.8000 .30925E-03 .30925E-03

.9000 .35485E-03 .35485E-03

1.0000 .39934E-03 .39934E-03

1.1000 .44273E-03 .44273E-03

1.2000 .48506E-03 .48506E-03

1.3000 .52638E-03 .52638E-03

1.4000 .56672E-03 .56672E-03

1.5000 .60615E-03 .60615E-03

1.6000 .64471E-03 .64471E-03

1.7000 .68245E-03 .68245E-03

1.8000 .71941E-03 .71941E-03

1.9000 .75563E-03 .75563E-03

2.0000 .79116E-03 .79116E-03

2.1000 .82603E-03 .82603E-03

2.2000 .86027E-03 .86027E-03

2.3000 .89248E-03 .89248E-03

2.4000 .90385E-03 .90385E-03

2.5000 .89733E-03 .89733E-03

2.6000 .88353E-03 .88353E-03

2.7000 .86703E-03 .86703E-03

2.8000 .84975E-03 .84975E-03

2.9000 .83254E-03 .83254E-03

Regards,

osama