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1 STATE OF FLORIDA
DIVISION OF ADMINISTRATIVE HEARINGS
2 ----------------------------------------------------------
SUGAR CANE GROWERS COOPERATIVE
3 Of FLORIDA, a Florida Agricultural
Cooperative Marketing Association,
4 ROTH FARMS, INC., and WEDGWORTH
FARMS, INC.,
5 and CASE NOS. 92-3038
FLORIDA SUGAR CANE LEAGUE, INC, 92-3039
6 and UNITED STATES SUGAR CORPORATION, 92-3040
and
7 FLORIDA FRUIT AND VEGETABLE
ASSOCIATION, LEWIS POPE FARMS,
8 W.E. SCHLECHTER & SONS, INC,
and HUNDLEY FARMS, INC.,
9 Petitioners,
vs.
10 SOUTH FLORIDA WATER MANAGEMENT
DISTRICT, an Agency of the State.
11 of Florida,
Respondent,
12 and
MICCOSUKEE TRIBE OF INDIANS OF
13 FLORIDA, The United States of
AMERICA and The FLORIDA DEPARTMENT
14 OF ENVIRONMENTAL PROTECTION, The
FLORIDA WILDLIFE FEDERATION,
15 THE FLORIDA AUDUBON SOCIETY, and
THE SIERAA CLUB,
16 Intervenors.
----------------------------------------------------------
17 DEPOSITION OF HARVEY PETER KNUDSEN, JUNIOR
18
Taken at:
19 UNITED STATES ATTORNEY'S OFFICE
400 NORTH MAIN
20 181 FEDERAL BUILDING
BUTTE, MONTANA
21 APRIL 6, 1994
3:12 p.m.
22
23 CHRISTINE D. LIVELY
REGISTERED PROFESSIONAL REPORTER
24 WAYRYNEN & LIVELY REPORTING SERVICE
2900 LEXINGTON STREET
25 BUTTE, MONTANA 59701
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1
2
3 APPEARANCES
4
FOR THE FLORIDA SUGAR CANE LEAGUE, INC., and
5 UNITED STATES SUGAR CORPORATION:
6 MR. SCOTT D. LIEBERMAN
ATTORNEY AT LAW
7 EARL, BLANK, KAVANAUGH & STOTTS
ONE BISCAYNE TOWER; SUITE 3636
8 TWO SOUTH BISCAYNE BOULEVARD
MIAMI, FLORIDA 33131
9
10 FOR THE UNITED STATES OF AMERICA:
11
STEPHEN G. BARTELL
12 TRIAL ATTORNEY
U. S. DEPARTMENT OF JUSTICE
13 ENVIRONMENT & NATURAL RESOURCES DIVISION
601 PENNSYLVANIA AVENUE, N.W.
14 FIFTH FLOOR; ROOM 5613
WASHINGTON, D.C. 20004
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I N D E X
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3 PAGE
4
HARVEY PETER KNUDSEN, JUNIOR,:
5
6 Examination by Mr. Bartell.................... 1
7 CORRECTION PAGE................................... 133
DEPONENT'S CERTIFICATE............................ 134
8 COURT REPORTER'S CERTIFICATE...................... 135
9
INDEX TO EXHIBITS
10
11 EXHIBIT NO. MARKED
12
Deposition Exhibit No. 1.......................... 3
13 Deposition Exhibit No. 2.......................... 8
Deposition Exhibit No. 3.......................... 29
14 Deposition Exhibit No. 4.......................... 33
Deposition Exhibit No. 5.......................... 33
15 Deposition Exhibit No. 6.......................... 73
Deposition Exhibit No. 7.......................... 74
16 Deposition Exhibit No. 8.......................... 75
Deposition Exhibit No. 9.......................... 79
17 Deposition Exhibit No. 10......................... 85
Deposition Exhibit No. 11......................... 100
18 Deposition Exhibit No. 12......................... 104
Deposition Exhibit No. 13......................... 115
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20
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24
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1 BE IT REMEMBERED THAT, pursuant to notice, the
2 deposition of Harvey Peter Knudsen, Junior was taken at
3 the time and place and with the appearances of counsel
4 hereinbefore noted before Christine D. Lively, a Notary
5 Public for the State of Montana.
6 The following proceedings were had:
7 HARVEY PETER KNUDSEN, JUNIOR,
8 a witness, after having been first duly sworn, testified
9 upon his oath as follows:
10 EXAMINATION
11 BY MR. BARTELL:
12 Q. Good afternoon. My name is Steve Bartell. I work
13 with the Department of Justice out of Washington D.C.,
14 and I represent the United States of America in this
15 ongoing litigation concerning the SWIM Plan that has been
16 proposed by the South Florida Water Management District.
17 Would you please state your name for the record.
18 A. My name is Harvey Peter Knudsen, Junior.
19 Q. Dr. Knudsen, I'm going to be asking you a number of
20 questions this afternoon. If there's any questions I ask
21 you and you don't understand them, I would ask you to
22 please let me know that so that I can try to rephrase the
23 question or restate it so that you do understand it.
24 If there is any questions you've answered, I'll assume
25 you've understood my questions. And that will be my
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1 assumption. Is that agreeable?
2 A. Yes.
3 Q. Have you ever been deposed before?
4 A. No.
5 Q. Have you previously testified in any judicial or
6 administrative type hearings?
7 A. No.
8 Excuse me, except in a divorce. Mine.
9 Q. If at any time during this deposition you would like
10 to take a break, or you feel you just need a few minutes,
11 please let me know and we'll do so.
12 I would also like to state for the record, although
13 I'm sure the record will reflect this, that we are
14 starting at about 3:15 this afternoon. And every attempt
15 will be made to try to make this as brief as possible,
16 this deposition, while I try to ensure that I've covered
17 everything adequately, just considering the time of day.
18 Dr. Knudsen, can you tell me what you've done to
19 prepare for today's deposition?
20 A. I guess I really don't know what you mean done to
21 prepare for it. I've reviewed the work that I did for Dr.
22 Allen Lefohn, is the main preparation I've done.
23 Q. Have you met with your counsel?
24 A. Yes, I have. This morning.
25 Q. Have you seen the Notice of Deposition?
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1 A. Yes, I have.
2 (Whereupon, Deposition Exhibit No. 1 was marked for
3 identification.)
4 Q. Dr. Knudsen, I'm handing you what's been marked as
5 Knudsen or Deposition Exhibit No. 1. Is this the notice
6 that you previously saw?
7 A. It appears to be the same one.
8 Q. Do you know approximately when you first saw this
9 document?
10 A. I can't remember what day it was. Last week, last
11 Thursday, Friday.
12 Q. Just approximately.
13 A. I believe it was Wednesday or Thursday of last week.
14 Q. And have you had an opportunity to go through this
15 Notice of Deposition and try to produce all the documents
16 that have been requested?
17 A. Yes.
18 Q. We will be getting into the documents produced later
19 this afternoon, but at this point, is it your opinion that
20 you have produced everything that is responsive to this
21 notice?
22 A. Yes.
23 Q. I would like to refer you to page 7. The second
24 question here or the second request asks for all documents
25 relating to any relationships you have with a number of
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1 parties, which are primarily petitioners in this matter
2 and counsel for the petitioners.
3 Are there any documents which reflect any
4 relationships you may have with any of the parties listed
5 in No. 2 here?
6 A. No documents at all other than the attorneys. And I
7 don't really have any documents with the attorneys, is the
8 only ones.
9 Q. I understand that just this afternoon I was given a
10 copy of a subcontracting agreement which appears to be
11 between yourself and A.S.L. & Associates. Do you have any
12 other contract or agreement in this matter with any of the
13 other petitioners or the attorneys in this case?
14 A. No.
15 Q. If you would look at No. 3 here, if you would just
16 briefly read that to yourself?
17 A. (Witness complies.)
18 Q. Are there any documents that you have relied upon in
19 formulating your opinions in this matter other than what's
20 been produced, for example, previous work you might have
21 done, maybe general types of books you may have studied
22 pertaining to kriging or things of that nature?
23 A. Nothing really on this topic at all. I'll just say
24 I teach courses in geostatistics, and I've published
25 textbooks or short course notes. And I guess my knowledge
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1 I've accumulated over 25 years and this is what I've
2 relied, what I've written.
3 Q. What is geostatistics?
4 A. It's just a branch of statistics relating to
5 geological and spatial variables.
6 Q. Does that involve teaching kriging methodology?
7 A. Yes.
8 Q. I would like to ask you to turn to page 8 of this
9 Exhibit No. 1. And in No. 6 on page 8, there are five
10 categories set forth, a through e. I would like to ask
11 you to read through these five categories to yourself.
12 A. (Witness complies.)
13 Q. Would you say that that is a pretty accurate
14 representation of what you intend to testify to in this
15 litigation?
16 A. I would say some parts of this are not in my area of
17 expertise or what I did on this project.
18 Q. Which parts are those?
19 A. Well, parts of the rainfall chemistry, for instance,
20 I would not be qualified to comment on those, not on
21 rainfall collections. I'm not positive what you mean by
22 (c) on EPA rainfall phosphorus concentrations.
23 Q. When it sets forth EPA, did you understand what EPA
24 meant in this notice?
25 A. I must not have.
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1 Q. Okay. EPA, while I understand that it could
2 certainly mean Environmental Protection Agency--
3 A. Right.
4 Q. --in this case is generally referring to the
5 Everglades Protection Area?
6 A. Oh.
7 Q. With that understanding, is there anything
8 additional that you would have produced in response to
9 this notice?
10 A. No.
11 Q. Other than these few areas you've mentioned that you
12 do not intend to testify to, is there anything you would
13 add as to what you intend to testify to?
14 A. No.
15 Q. If you were to briefly describe what your
16 understanding of your testimony in this case is going to
17 be, could you do so in just, say, a brief statement?
18 MR. LIEBERMAN: Object to form.
19 THE WITNESS: I guess I don't know what you --
20 Can you rephrase it or explain more.
21 Q. Sure.
22 Can you explain your understanding of what you intend
23 to testify to in this litigation?
24 MR. LIEBERMAN: Object to form again.
25 THE WITNESS: It's my understanding that you will
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1 be questioning me on the work I did for A.S.L. &
2 Associates in determining some krig models for rainfall
3 and deposition in the areas that we modeled, which were
4 the WCA areas.
5 Q. Is that basically the extent of what you expect to
6 testify to at this point?
7 A. At this point, yes.
8 Q. Are you currently in the midst of doing any work for
9 this case?
10 A. Currently, no.
11 Q. Have you done all the work that you intend to do at
12 this point?
13 A. I've done all the work that's been requested of me.
14 Q. And you're not aware of anything that is anticipated
15 to be asked of you?
16 A. No, I'm not.
17 Q. I would like to refer you to page 12 of this
18 document, and ask you to read No. 21 to yourself.
19 A. (Witness complies.)
20 Yes.
21 Q. Have all the documents which would reflect
22 correspondence between Dr. Allen Lefohn and yourself been
23 produced?
24 A. Yes.
25 Q. Is that limited to the subcontracting agreement and
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1 the data that has been exchanged?
2 A. Subcontracting agreement, the data that he provided
3 me, and I produced the krig results that were given to Dr.
4 Lefohn and which you have also been provided to you.
5 Q. And there are no other correspondence between--
6 A. No, sir.
7 Monthly billing.
8 (Whereupon, Deposition Exhibit No. 2 was marked for
9 identification.)
10 Q. Dr. Knudsen, I'm handing you what's been marked as
11 Knudsen Exhibit No. 2. for identification, which is your
12 C.V. For the record, this has been just provided just
13 before the beginning of this deposition. Is this your
14 most current or accurate C.V.?
15 A. No. I have -- This is about a year and a half old.
16 There are a couple of corrections to it.
17 Q. Would you please identify for me what those
18 corrections would be.
19 A. No. 1, my age is incorrect. No. 2, I have been
20 promoted to professor and this one lists me as associate
21 professor. I was promoted in 1993 I think, just last
22 year.
23 Q. What is your new position?
24 A. I'm a full professor in mining engineering. All my
25 other titles are the same.
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1 Q. And what year did you say that was?
2 A. I was trying to think. I'm getting academic and
3 fiscal year all screwed up. Okay, '92 I was promoted, in
4 the fall of 1992. So that would be academic year '93.
5 Q. In your role or in your position as professor, this
6 is at Montana Tech university?
7 A. Its present name is Montana College of Mineral
8 Science and Technology. We refer to it as Montana Tech.
9 Q. What courses do you teach as professor there?
10 A. I teach courses in the mining engineering department
11 and in the computer science department. I teach courses
12 ranging from freshman courses all the way up to graduate
13 level courses.
14 This year, I've taught a freshman level course in
15 basic introductory computer science. I've taught a second
16 freshman level course in how to make maps, computerized
17 maps, surveying. That's for our engineering students.
18 I've taught a course in ore reserve estimation and
19 geostatistics. That's a senior level course. I'm
20 teaching two senior mine design courses.
21 I'm trying to think of what else I taught last fall.
22 Oh, and I taught a course in computer methods in mining
23 and geology last fall. And my core subjects I teach
24 changes every year, so there are graduate level courses we
25 teach every other year. But those courses I taught this
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1 year.
2 Q. What other functions do you undertake as professor
3 at the college other than teaching?
4 MR. LIEBERMAN: Object to form.
5 THE WITNESS: Can you explain more what you're
6 interested in.
7 Q. Sure.
8 Do you publish material? Do you serve
9 administratively? I want to know if there's anything else
10 you do at the university.
11 A. Yes. I have a heavy teaching load, which is
12 unusual, but I'm also department head of the mining
13 engineering department. It's an administrative function.
14 I'm also associate dean of the division in mining
15 engineering, minerals engineering division. That includes
16 the department of mining engineer, geological engineering
17 metallurgical engineering. And that is an administrative
18 function.
19 I am probably on five academic committees on campus,
20 and I do limited research depending on availability of
21 contracts, whatever is available. Professors like to do
22 research. I publish whenever possible.
23 In fact, I see one correction on here. There's a
24 paper here, it says, "Blasthole samples - a source of
25 blasting," accepted for publication. That was in fact
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1 published in 1993. There has been a couple comments
2 published about that paper since then. So that is an
3 addition to this research or to this C.V.
4 Advise students. Very much typical professor
5 functions.
6 Q. And other than what you just mentioned as additional
7 comments to this first listed journal, is there any other
8 publications that are not set forth on this C.V.?
9 A. Yes. This C.V. is a curriculum -- or C.V. that is
10 prepared for our accreditation two years ago. We're
11 accredited by a group called ABET. It stands for American
12 Board for Engineering and Technology Accreditation. And
13 they limit publications to usually within the last five or
14 seven years.
15 And I believe that there are probably no publications
16 on here that go further back than 1985. So all my
17 publications from 1975, is when I first published a paper,
18 up until 1985 are not listed on this curriculum vitae.
19 Q. In looking through these journals, I see that there
20 are quite a number which refer to kriging. And what I
21 would like to do is I would just like to ask you a few
22 questions pertaining to some of these publications.
23 Before I do so, could you describe to me -- Let me
24 strike that.
25 Other than understanding kriging and maybe teaching
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1 kriging, do you actually apply kriging to real world
2 situations for clients or in the course of your role at
3 the university?
4 MR. LIEBERMAN: Object to form.
5 THE WITNESS: Can you explain a little further.
6 Q. Sure. Let me maybe rephrase that.
7 Could you explain to me what types of situations you
8 have used kriging for in the past?
9 A. Okay. I do -- In the summer, I do a significant
10 amount of consulting usually to the mining industry. And
11 I'm typically called upon to go to a mine and help them
12 build what they call an ore reserve model, which consists
13 of doing estimations using kriging.
14 And I do that frequently, usually in the summer,
15 because I don't like to accept consulting during the
16 academic year. If you look at some of the recent
17 consulting, there's a variety of different mines
18 throughout the world that I do that for.
19 Q. And in doing this kriging that you do in your
20 consulting work, do you actually collect data or take
21 samples?
22 A. No. The data is -- In the case of a mine, the data
23 is collected by the mining company, usually from what they
24 call drilling. And sometimes it will be 5 to 10 year's
25 time it takes to collect all the data they need to do an
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1 ore reserve model upon which would plan a mine. And I
2 don't get involved in the collection of the data.
3 Q. Have you done kriging for any other purposes other
4 than to determine ore reserve models?
5 A. Yes. Working in conjunction with Al Lefohn, we
6 developed kriging models for surface ozone throughout the
7 United States. I have to go back quite aways further to
8 come up with other variables that I've kriged with. I'll
9 have to think about that for a while.
10 Q. If anything else comes to mind, if you would let me
11 know, I would appreciate that.
12 In doing your kriging for -- Well, let me come back to
13 kriging.
14 Is there anything else in this C.V. that you noticed
15 has changed or that you would update if this was to be
16 current through today's date?
17 A. A recent copy of my C.V. has a couple more recent
18 consulting clients. I believe that would be Freeport
19 MacMorRan copper has been a recent consulting client.
20 Let's see. Mine Development Associates is already there.
21 I believe that would be the only one that's been added
22 since that time.
23 Q. Have you consulted for any types of industry or
24 companies other than mining companies?
25 A. I don't believe so recently other than Allen Lefohn.
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1 He isn't a mining company.
2 Q. Have you done any other consulting for Dr. Lefohn
3 other than the work you're doing for this case?
4 A. Yes.
5 Q. Can you describe for me what that other consulting
6 is.
7 A. The other work with Dr. Lefohn has been in modeling
8 the ozone, ground level ozone. And that's been for the
9 U.S. Forest Service and for the EPA over the years, quite
10 a number of contracts since 1985 we've done, mainly for
11 those two clients.
12 Q. That was in conjunction with Dr. Lefohn?
13 A. Yes.
14 Q. So other than consulting work you've done for mining
15 industry type clients and work for Dr. Lefohn or with Dr.
16 Lefohn, is there any other consulting work that you've
17 done that would be -- would include other types of
18 industries or clients?
19 A. I'm trying to think of what types of industries.
20 I've done some consulting work on lead contamination in
21 soils, but in actuality that was for the mining industry
22 also.
23 Q. Did that involve kriging?
24 A. Yes.
25 Q. Have you ever done any work pertaining to kriging
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1 and rainfall or -- Let me rephrase the question.
2 Have you ever done any kriging work to determine
3 parameters of rainfall or ingredients of rainfall?
4 A. None other than what I did for Dr. Lefohn.
5 Q. And did that work for Dr. Lefohn, does it include
6 both this case and the ozone case or just this case? When
7 I say ozone case, the previous work you did in ozone
8 modeling.
9 A. Well, there wasn't any rainfall information, I mean,
10 as part of the ozone model. That was just gaseous ozone.
11 Q. Are there any differences in the way you krig gases
12 as opposed to kriging rainfall?
13 A. Explain -- Can you clarify that at all?
14 Q. Sure.
15 When you do kriging analysis, is that a proper thing
16 to say or kriging work?
17 A. Okay.
18 Q. When you do kriging work for gases, do you take a
19 different approach than kriging work for rainfall?
20 A. I think I'll answer that no, under the assumptions
21 that -- There are a couple of assumptions I would like to
22 make. The work we did with ozone, it's a gas. And we
23 worked with ozone measurements that were taken over a
24 period of months.
25 We had had a continued reading for a month or, in one
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1 case, over a year. And so we were working with a variable
2 that -- I want to say the correct word. I don't want to
3 say static, but we worked with a variable that was set in
4 time, and time was not a function or a variable that we
5 were interested in. We weren't trying to model ozone as a
6 function of time, how it changes throughout the day.
7 We were interested in a monthly average of ozone
8 content. And that's similar to what we did in the
9 rainfall, except the rainfall, we were interested in
10 rainfall over a year, cumulative rainfall over a year. We
11 weren't interested in kriging daily rainfall events or the
12 dynamics of it.
13 Q. Prior to doing your kriging work for the rainfall
14 with Dr. Lefohn, have you ever done any kriging work to
15 determine kriging results pertaining to time?
16 A. No.
17 Q. Is the kriging work you've done for the mining
18 industry -- I guess I'll try to -- Well, better than
19 myself trying to explain what I understand it to be, could
20 you just briefly describe to me what it is that you're
21 trying to determine. I understand you said ore reserve
22 models. What does that mean?
23 A. Okay. In the mining industry, what a miner does is
24 go out and excavate, mine, dig a volume of rock. And he
25 would hope that when he does that, that he can extract
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1 valuable metals or minerals and pay all the costs
2 associated with that and make a small profit. Okay.
3 Well, before he digs out this volume of rock, he wants
4 to know whether the valuable contents is contained inside
5 the rock. And so what ore reserve estimation is is trying
6 to estimate the quantity of valuable material that's
7 contained inside a rock -- or it could be soil, it could
8 be gravel, whatever, any type of naturally occurring
9 material -- trying to estimate a content.
10 Q. Is that done by taking a number of samples?
11 A. Yes. From that, you will not have samples
12 everywhere, because like a lot of samples are very
13 expensive, so they will be taken throughout the deposit,
14 usually by drill holes drilled from the surface. So that
15 limits the availability of what you can sample.
16 But from that restricted sample set, you will try to
17 determine the content of the rock.
18 Q. I understand that you've done quite a bit of
19 consulting and figuring out or reaching conclusions with
20 these ore reserve models, but is there an average number
21 of samples that you usually use?
22 A. No.
23 Q. Could you maybe give me some typical, if there are
24 typical examples of the number of samples used when you're
25 determining these ore reserve models.
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1 MR. LIEBERMAN: Object to form.
2 THE WITNESS: Could you explain a little bit more
3 what you mean by average number of samples.
4 Q. Let's maybe -- Let me rephrase that.
5 What is the minimum number of samples you've used in
6 putting together an ore reserve model approximately?
7 A. Probably a hundred for an ore reserve model. Now,
8 let me clarify one thing. In ore reserve estimation at a
9 mine, when I say we estimate the content of a block, we
10 take the earth and we divide it up into small volumes
11 maybe 30 meters by 30 meters by 10 meters in size.
12 Now, a mine -- a mine may have a million of those
13 small volumes comprising what could be the mine. Each one
14 of those volumes we will estimate or try to estimate its
15 value based upon surrounding samples. Okay. In the
16 mining industry, we would like to have at least two
17 samples nearby that little volume. Okay. I would be much
18 more happy if I had 10 or 15 samples nearby that volume to
19 make the estimate, one of those little blocks throughout
20 the deposit.
21 You may have thousands of samples, but for any one
22 individual block you may only have from 2 to 15 samples
23 that are close to that block.
24 Q. Can you give me an idea of when you say close, are
25 you talking about meters away or--
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1 A. Close is a relative term. It's relative to -- In
2 ore reserves, it's relative to what type of deposit, what
3 type of mineral you're talking about. In a coal mine,
4 close is 500 feet, 1,000 feet. Even USGS defines close as
5 being a quarter mile, so 1200 feet.
6 In a gold mine, close might be a matter of 50 feet.
7 It all depends upon the spatial variable you're talking
8 about. It's a very relative term.
9 Q. Have you done kriging for gold reserves?
10 A. Yes.
11 Q. Have you done it for coal reserves?
12 A. Yes.
13 Q. I understand that there's probably quite a bit of
14 differences in What I'm seeking to understand here, but
15 what are the general areas or the size of the areas used
16 to determine mining reserves or mineral reserves?
17 MR. LIEBERMAN: Object to form, to the point it
18 calls for speculation.
19 Q. Do you understand my question?
20 A. Well, not exactly. I'm not positive where you're
21 heading.
22 Q. What I'm trying to understand is in some of your
23 previous work as consulting, you would put together or
24 create a reserve model. I'm trying to understand if
25 there's an average size of these models, you know, the
19
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1 land area, if it's a 10 mile by 10 mile size area or a
2 quarter mile by quarter mile, if it encompasses a size the
3 state of Montana.
4 A. There's no average size of a mining area. It's also
5 sort of relative. Coal mines tend to be large in aerial
6 extent. Gold mines tend to be very small.
7 Q. Have you ever put together mineral reserve models
8 that had less than a hundred number of samples that you
9 can recall?
10 A. Not to my knowledge.
11 Q. What is the maximum number of samples used in
12 putting together one of these models to the best you can
13 recall?
14 A. I don't know that I can remember a maximum but
15 certainly, it's in multiple of thousands.
16 Q. When you do your kriging to put together these
17 reserve models, do you use all of the samples, all of the
18 data from the samples?
19 A. When you make an ore reserve model, the way the ore
20 deposit is formed, there's usually quite a number of
21 discrete areas. And these discrete areas are sort of
22 unique in when you're modeling one discrete area, you use
23 only the samples from that area.
24 Also, in a mine, most of the data is of no interest to
25 you, because the miner wants to know just where the
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1 highest grade portions are of the mine. In the process,
2 he has taken a lot of samples over usually a large area
3 that just confirmed there's no valuable mineral.
4 So when you make your ore reserve model, there may be
5 thousands of samples, but there may be a small, relatively
6 small number, maybe only a few hundred, if you're lucky,
7 that are in the area of interest. Mostly ore reserve
8 models in the data bases have a lot of negative -- or the
9 information doesn't tell you anything. It tells you where
10 something isn't.
11 Q. You mentioned earlier that ideally, you want to get
12 samples that are nearby the area of interest. You said
13 sometimes that can be as few as 2 or up to 15. Have you
14 done kriging work--
15 (Brief interruption.)
16 Have you done kriging -- I'm not sure exactly where I
17 left off with my question, but have you done kriging work
18 that has used as few as 2 to 15 sets of data from samples?
19 A. For an individual area or block, yes, that's very
20 routine.
21 Q. Do you ever limit your work to an individual block,
22 though?
23 A. No, not usually. Usually the models consist of lots
24 of blocks.
25 Q. So have you ever done kriging work that has used
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1 collectively, for your final results, less than a hundred
2 data points or data--
3 A. Not in work for ore reserve estimation. In some of
4 the work with Allen Lefohn, even on some of the surface
5 ozone measurements, there is probably in the neighborhood
6 of a hundred or perhaps fewer than that.
7 Q. Okay. Let's talk a little bit about the ozone
8 modeling you've done with Dr. Lefohn. Could you describe
9 to me in a general sense what that modeling was all about,
10 other than figuring out ozone. I understand that.
11 A. Yes. In a general sense, that ozone work started
12 with simply trying to estimate ground level ozone in the
13 crop growing regions of the United States, mainly in the
14 Central United States, an area that has very few ozone
15 monitors.
16 Ozone monitors tend to be in industrial areas around
17 cities. They're not located in agricultural areas. So we
18 use kriging to estimate the content in the agricultural
19 areas using surrounding data that was probably from around
20 a city or an urban area.
21 Q. What's the -- I'm hesitant to use the word average,
22 but how far away are some of these ozone monitors from the
23 areas where you come up with the results of ozone, ground
24 level ozone data?
25 MR. LIEBERMAN: Object to form. Are you talking
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1 any particular ozone monitoring device?
2 MR. BARTELL: My understanding is that -- Maybe I
3 can clarify this through a couple of questions.
4 Q. Dr. Knudsen, have you, other than this one
5 particular piece of work you've done with Dr. Lefohn,
6 figuring out ground level ozone levels in the central part
7 of the United States, the agricultural areas, have you
8 done any other ozone monitoring or measuring?
9 A. Well, the work with Allen Lefohn, actually, like I
10 said, there were quite a number of contracts beginning in
11 1985 starting with models for the NCLAN program. And we
12 modeled about 10 years' worth of data and that covered the
13 entire continental United States ground level.
14 We've also modeled the southwest -- Southeast Forest
15 for the Forest Service. We did that two or three
16 contracts. And I believe the period years was about 1980
17 to 1989, in there. So I don't know how many models were
18 made of that, but certainly the years 1979 to 1990, we've
19 modeled for the entire United States and for the southeast
20 portion.
21 Q. Pertaining to the entire USA, what did you call it,
22 the NCLAN?
23 A. The initial work I did with Allen was for the
24 program that the EPA had at that time or was running, the
25 National Crop Loss Assessment Network.
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1 Q. And is that what you refer to as figuring out the
2 ground level ozone?
3 A. Yes.
4 Q. Measurements for the agricultural area?
5 A. Yes.
6 Q. Other than -- And I understand there may be a number
7 of contracts within each of these two areas.
8 A. Yes.
9 Q. Are those the only two areas for which you've done
10 kriging work other than to determine ore reserves except
11 for the work you're doing in this case?
12 MR. LIEBERMAN: Object to form.
13 THE WITNESS: I believe, to my knowledge, that's
14 certainly all in the last 10 years. Pretty well covers
15 it.
16 Q. Prior to the last 10 years, can you recall any
17 kriging work you've done other than for ozone measurements
18 or for ore reserves?
19 A. When I was down in Arizona, as part of teaching some
20 graduate level classes, we certainly looked at other
21 variables. And I couldn't probably give you a list of all
22 of them right now, but several geophysical parameters,
23 magnetometer readings.
24 Magnetometer readings was as an example. We looked at
25 a variety of -- in classroom work, looked at a variety of
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1 spatial variables to gain experience.
2 Q. That was all limited to the classroom?
3 A. Yes.
4 Q. Did any of that involve determining precipitation--
5 A. No.
6 Q. --amounts?
7 A. (Witness indicates no.)
8 Q. So let's return back to these two ozone areas that
9 you've worked with. In the one dealing with the NCLAN
10 program, how far away was, that you can recall and I'm
11 looking for just approximately, the ozone monitors from
12 the areas where you would come up with a krig value of the
13 ozone level?
14 MR. LIEBERMAN: Again, objection to the point it
15 calls for speculation.
16 MR. BARTELL: How does that look for speculation?
17 MR. LIEBERMAN: If you're asking him if he just
18 recalls specifically his recollection, or if you're just
19 asking him if he recalls about how far they were away,
20 you're asking him to speculate beyond what is his personal
21 knowledge.
22 Q. What is your personal knowledge of how far away
23 these monitoring -- these ozone monitors were from the
24 areas that you would come up with krig values?
25 A. The answer, I can't remember exact distances but it
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1 varied tremendously depending what part of the United
2 States you were talking about. In Montana, for instance,
3 most years there was no ozone monitored.
4 Q. But you would still come up with a krig value for
5 Montana?
6 A. No.
7 Q. Let's say for the areas--
8 A. It wasn't because we weren't up to trying, it was
9 the fact that they didn't request it, because there wasn't
10 a crop that they were interested in Montana was the real
11 reason. That's why there were no monitors run.
12 Q. About how many monitors were set forth around the
13 country?
14 A. If I recall, it varied from year to year, but
15 usually over 200.
16 Q. And from these 200 or so monitors -- and I
17 understand that may have changed -- you were able to come
18 up with krig's values for the agricultural area for the
19 continental United States?
20 A. Yes.
21 Q. Moving to the work you did for the Southeast Forest
22 Region, did that encompass a number of states or was it
23 the whole southeastern part of the continental United
24 States?
25 A. The Forest Service defines that as 13 states in the
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1 southeast. I can't tell you exactly which ones they are.
2 It doesn't include Florida, but the rest of the southeast.
3 Q. About how many monitoring sites were there?
4 A. I can't remember. It's the same data base that we
5 used to get the ozone data. It's the same data base, but
6 I can't remember how many sites were in that area.
7 Q. Do you think it's possible to krig a value based on
8 four sets of data?
9 A. Yes.
10 Q. Without going through each of the examples or each
11 of the journals and publications set forth in your C.V.
12 that list kriging, can you -- Maybe a quicker way to do
13 that in the interest of time is to ask you if any of these
14 publications or reports or presentations have involved
15 doing kriging work for atmospheric deposition?
16 A. No.
17 Q. And just to clarify, have you ever done any kriging
18 work for atmospheric deposition prior to this case?
19 A. No.
20 Q. Did anybody assist you in your kriging work for this
21 case?
22 A. No.
23 Q. Did you obtain data or documents from anybody other
24 than Dr. Lefohn?
25 A. No.
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1 Q. When did Dr. Lefohn first contact you to assist you
2 in working with him on this case approximately?
3 A. Oh, I would say November of '92, he inquired whether
4 I was available time-wise, whether I could work with him
5 on some work he was doing on it.
6 Q. And what did he specifically ask you to do to assist
7 him?
8 A. At that time, he asked whether I would be available
9 to review work specifically on some kriging that was done
10 for the SWIM Plan. I don't know who did it but--
11 Q. And did you subsequently do that?
12 A. Yes, I did.
13 Q. Is that what is set forth in this draft review of
14 the kriging approach used in the SWIM Plan?
15 A. Yes.
16 Q. This draft report is dated January 4th, 1993?
17 A. That's correct.
18 Q. Did Dr. Lefohn ever receive a copy of this?
19 A. Yes.
20 Q. Do you know approximately when he received a copy of
21 this?
22 A. January 4th or 5th, 1993. It would be in that time
23 range.
24 MR. BARTELL: Because I would like the record to
25 reflect that this was not previously produced in Dr.
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1 Lefohn's deposition and which was in February, and that
2 this document was not produced to respondents in this case
3 until today just before this deposition.
4 MR. LIEBERMAN: For the record, I would like to
5 point out that we contacted respondents two days ago about
6 this document, haven't been able to get in touch with
7 respondents, so that's why it was produced today. And due
8 to late notice of deposition, we did not have -- the files
9 were not reviewed, and this document was not put in our
10 possession until, that would be the 4th, april 4th. And
11 we called Mr. Bartell immediately upon receiving it.
12 Q. Have you ever done any research in South Florida?
13 A. No. Other than the work on this stuff, no.
14 Q. Would you summarize your role in this case as being
15 a subcontractor for Dr. Lefohn?
16 A. Yes.
17 (Whereupon, Deposition Exhibit No. 3 was marked for
18 identification.)
19 Q. Dr. Knudsen, I'm handing you what's been marked as
20 Knudsen Exhibit No. 3 for identification. It is a
21 Subcontracting Agreement. Is this a series of three
22 agreements or is this all one agreement?
23 A. I guess I don't know your definition or what the
24 difference would be.
25 Q. Well, I guess I'm looking at three signature blocks,
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1 all with different dates. I guess, let me get more
2 specific.
3 A. Okay. Well, maybe I can answer your question. The
4 last two, January 1, 94 to February 15th, 94 covered the
5 work to krig the WCA areas. And then the March 21 to
6 April 15th covered the work to krig the EAA areas that I
7 just completed, was asked to do.
8 The prior agreement, since he had been working on this
9 project, he did this one in case there was anything that
10 comes up that he wants to ask me questions about or
11 provide further work, that he has this agreement in place.
12 Since 1985 in one form or another, I've usually had a
13 contracting agreement with Allen Lefohn.
14 Q. Pertaining to this case?
15 A. No. Oh, gosh, no. Pertaining to some case.
16 Q. Sure.
17 A. But we've had to do that to make my relationship
18 very clear, since I'm an employee of the State of Montana
19 and I do consulting work, the state, of course, likes to
20 know about the consulting work and likes that done, in
21 fact, through an agreement contract so they know what I'm
22 doing and that I'm doing within the limits that they
23 specify.
24 Q. Does anybody at the university or the state ever
25 review the conclusions you reach in your consulting work?
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1 A. No.
2 Q. Are there any other agreements other than what's
3 been provided in this four-page agreement or series of
4 agreements?
5 A. No.
6 Q. And has all work been concluded--
7 A. Yes.
8 Q. --that is set forth in this?
9 A. Yes.
10 (Whereupon, a brief recess was taken.)
11 Q. Dr. Knudsen, returning briefly to the agreements
12 between yourself and A.S.L. & Associates, were you given
13 deadlines for completing your work? Let's start with the
14 first agreement.
15 A. Well, the first one didn't have a specific deadline,
16 no.
17 Q. And your conclusion that you reached for this first
18 agreement, was this January of '93?
19 A. Yes.
20 Q. Is that January of '93 or supposed to be January of
21 94?
22 A. January of '93.
23 Q. Okay. And for your second task order, kriging the
24 three WCA areas, was there a deadline for completing the
25 work there?
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1 A. I can't remember a deadline.
2 Q. Do you recall when you completed that work?
3 A. To tell you the truth, I can't.
4 Q. Would it have been sometime between January of this
5 year and March of this year?
6 A. Yes.
7 Q. And when did you complete your work for the second
8 task order, which is kriging the areas within the EAA?
9 A. Just about two weeks ago.
10 Q. So then, would it be fair to summarize the
11 conclusions that you've reached in this area as, one,
12 analyzing the work done in the SWIM Plan, the kriging done
13 in the SWIM Plan, two, of kriging the Water Conservation
14 Areas, and three, kriging the Everglades Agricultural
15 Areas?
16 MR. LIEBERMAN: Objection. Just for
17 clarification, the way you're stating it, you're not
18 stating those are his conclusions, what he's drawing
19 conclusions--
20 MR. BARTELL: I don't think those could be
21 conclusions.
22 Q. Are those the three areas?
23 A. Those are the three areas that I did work on, yes.
24 Q. Just to confirm, there are no other areas?
25 A. No.
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1 (Whereupon, Deposition Exhibit No. 4 was marked for
2 identification.)
3 Q. Dr. Knudsen, I'm handing you what's been marked as
4 Knudsen Exhibit No. 4 for identification. This is a
5 photocopy of a computer disk and eight -- a printout of
6 eight directories within that disk. Are you familiar with
7 this disk or the copy of which this represents?
8 A. Yes.
9 Q. Are there any other directories that were set forth
10 on this disk other than these eight that are set forth?
11 A. I don't believe so.
12 (Whereupon, Deposition Exhibit No. 5 was marked for
13 identification.)
14 Q. Dr. Knudsen, I'm handing you what's been marked as
15 Exhibit No. 5 for identification. Could you describe to
16 me what this document is.
17 A. Yes. This document, the first page is data received
18 from Allen Lefohn on volume weighted concentrations for
19 the years 1988 to 1991.
20 Page 2 is the latitude and longitude of the stations
21 that reported that data. Page 3 is a map that shows the
22 locations of those stations.
23 Q. Are there two stations at each of these locations?
24 A. I don't know.
25 Q. Returning to the first page, did you do any work in
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1 coming up with these volume weighted concentrations?
2 A. No.
3 Q. So you just accepted them as they were provided to
4 you from Dr. Lefohn?
5 A. Yes.
6 Q. Is this all of the data that you used for inputting
7 into your kriging model to determine the phosphorus?
8 A. That is all the data.
9 Q. Set forth in these three pages?
10 A. Yes.
11 Q. Is it correct that for kriging, the only data that
12 you would need would be, in this particular situation, the
13 volume weighted concentration and the latitude and
14 longitudes of the stations?
15 A. Yes.
16 Q. I hope you'll bear with me. I'm going to do my best
17 to try to ask questions that make sense. I have found
18 this to be somewhat complicated material, so -- In the
19 kriging that you did for this case, did you do kriging
20 which determined the phosphorus deposition, the average
21 phosphorus deposition as well as the average rainfall for
22 both the EAA and the Water Conservation Areas?
23 A. Yes.
24 Q. So then there would be four situations which you've
25 kriged, for lack of a better term?
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1 A. What do you mean four situations?
2 Q. Okay, four -- You've utilized kriging to come up
3 with four different results. Now, those specific results
4 may breakdown into specific years. What I'm trying to get
5 to is how many different sets of data were used to
6 determine results through kriging?
7 A. Okay. For the rainfall data, there's four sets of
8 rainfall data for years 1988 to 1991 that was used to make
9 the krig estimates of rainfall. The deposition data is
10 also one set of data per year. And that was used to
11 estimate the deposition per year in each WCA.
12 Q. What about for the EAA?
13 A. Also in the EAA.
14 Q. The same data?
15 A. Same data, yes. This is the only data that was
16 used.
17 MR. LIEBERMAN: Let the record reflect that when
18 he states this the only data used, he's talking about the
19 data that is on the computer disk that has been identified
20 as Exhibit 4.
21 Q. Could you describe what kriging is.
22 A. Yes. Kriging is a spatial interpolator.
23 Q. Can you further define that.
24 A. Spatial interpolation method. Probably the easiest
25 way to explain it further than that, it is a stochastic
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1 spatial interpolation method rather than a deterministic
2 interpolation method.
3 Q. What were the--
4 MR. BARTELL: Well, maybe, would you read back
5 the answer, if you can, of what those two words are.
6 MR. LIEBERMAN: Stochastic and deterministic. Is
7 that you're referring to?
8 MR. BARTELL: Yes.
9 Q. Can you describe to me what stochastic means.
10 A. Yes. Basically, it's a term used to describe random
11 variables that we're dealing with, variables that have
12 some randomness in them. And we're utilizing the results
13 from the theory of stochastic variables to do our
14 interpolation.
15 Q. And what about the deterministic?
16 A. Deterministic is -- If we want to do a deterministic
17 interpolation, there might be something like a straight
18 line interpolation. We just arbitrarily say we want to
19 interpolate using a straight line.
20 There's no probabilities or statistics involved. It's
21 just an assumption and then you make it.
22 Q. And which of these two methods was used in this
23 case?
24 A. The stochastic interpolation.
25 Q. Could you have used a moving average procedure to
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1 the extent you know what that means? And if not, let me
2 know and and I'll--
3 A. I know what moving average procedures are, yes.
4 Q. Could that have been utilized to come up with, let's
5 start with the average phosphorus concentration over both
6 the EAA and the WCA's?
7 A. Moving averages do not give -- how do I want to say
8 it -- estimates. Maybe that's the best way to say it.
9 Moving averages do not give spatial estimates.
10 Q. So then, in your opinion, that would not have been
11 appropriate?
12 A. No.
13 Q. Do you understand what piecewise linear least
14 squares is?
15 A. Yes. I've heard the term. That's maybe the best
16 way to explain it, I've heard the term.
17 Q. Are you familiar with whether that would be an
18 appropriate means of determining the average phosphorus
19 deposition rates?
20 A. No, I'm not.
21 Q. Are you familiar with linear projection?
22 A. Yes, I am.
23 Q. And to the extent you're familiar with it, do you
24 think that would be an appropriate means of determining
25 phosphorus deposition rates?
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1 A. To the extent that kriging is a linear projection,
2 yes.
3 Q. Can linear projection be a separate means other than
4 through kriging?
5 A. I don't know.
6 Q. When we talk about kriging, is another word for it
7 punctual kriging? Is that one and the same?
8 A. No. Kriging is a term that often has adjectives
9 describe what particular constraints your kriging is
10 doing. Punctual kriging is kriging to a point.
11 Q. To one specific point?
12 A. To a point, yes.
13 Q. Is the kriging you did in this case punctual
14 kriging?
15 A. No.
16 Q. Could that have been used to find, for instance, a
17 point in one of the Water Conservation Areas?
18 A. Yes, it could have. You could have kriged an
19 individual point using punctual kriging, yes.
20 Q. Then within kriging, I understand that there are a
21 number of different means of kriging. Are you familiar
22 with the term simple kriging?
23 A. Yes.
24 Q. Is what you did in this case simple kriging?
25 A. No.
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1 (Whereupon, a brief recess was taken.)
2 (Whereupon, the previous question and answer were read
3 back as follows: "Q. Is what you did in this case simple
4 kriging? A. No.")
5 Q. Would simple kriging have been appropriate to use in
6 this case?
7 A. No.
8 Q. Can you explain to me why?
9 A. Simple kriging requires the assumption that you know
10 the mean value of the variable. We say the mean value in
11 the domain. In this case, we're trying to estimate the
12 mean value. We don't know it.
13 Q. Are you familiar with a term or procedure called
14 lognormal kriging?
15 A. Yes, I am.
16 Q. Would that have been an appropriate means of kriging
17 to determine phosphorus concentrations?
18 A. I may have to ask one question. When you say
19 appropriate, maybe you should clarify under what
20 situations you want me to answer that question.
21 Q. Are there any situations in which lognormal kriging
22 would be appropriate or effective in determining
23 phosphorus deposition rates?
24 MR. LIEBERMAN: You're talking in the WCA's?
25 MR. BARTELL: Yes.
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1 THE WITNESS: Are these all in reference to the
2 WCA's.
3 Q. Yes. Yeah.
4 A. I guess I don't have enough information to know
5 whether lognormal kriging would be effective.
6 Q. What additional information would you need?
7 A. Okay, lognormal kriging requires the very strong
8 assumption and requirement that the data corresponds or
9 has a lognormal distribution.
10 Q. Why can't you determine that by looking at the data?
11 A. It's not as easy as looking at the data. Most
12 national data does not have lognormal distribution. It
13 looks similar to lognormal distribution, but does not have
14 a lognormal distribution. And lognormal kriging is
15 extremely sensitive to departures from the distribution.
16 It is a distribution dependent method.
17 Q. Through statistical work, could you have determined
18 if the data that you were provided would have been
19 applicable for lognormal kriging?
20 A. I certainly could have rejected it very quickly.
21 With the limited data, it would be very easy to reject a
22 conclusion that the data is lognormal.
23 Q. If additional data were available for the areas in
24 question, and the areas I'm referring to are both the
25 Water Conservation Area and the Everglades Agricultural
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1 Areas, if you had been provided additional data, could you
2 have then made a determination of whether lognormal
3 kriging would have been--
4 A. Yes.
5 Q. And in your opinion, is it possible with this
6 additional data that lognormal kriging may have been
7 appropriate as a possibility?
8 A. A very far-out possibility.
9 Q. Why do you consider it very far-out?
10 A. Lognormal kriging is extremely difficult to apply
11 correctly and get reliable results. We have better
12 methods than lognormal kriging.
13 Q. What are those better methods?
14 A. Ordinary kriging is usually preferred to lognormal
15 kriging.
16 Q. Are there any other methods that are considered
17 better?
18 A. It's not a matter of being considered better. It's
19 a matter of which method is appropriate to use. What I
20 would say about lognormal kriging is it's a very
21 sharp-edgeed tool that has very sensitive departures to
22 lognormal -- to lognormality.
23 Q. Would you expect that if the data were appropriate
24 to use in lognormal kriging in this particular case and
25 you had useed lognormal kriging, would you expect there to
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1 be a different result than had you used ordinary kriging?
2 MR. LIEBERMAN: Object to form. Are you asking
3 this as a hypothetical?
4 MR. BARTELL: I'm asking if he has an opinion. I
5 would imagine it has to be a hypothetical, because he
6 hasn't run the results of lognormal kriging. He hasn't
7 done it.
8 MR. LIEBERMAN: But your hypothetical had that
9 more data was available. I believe that was the premise
10 in your question.
11 MR. BARTELL: Yes. Yes, okay.
12 Q. Do you understand my question?
13 A. Yeah, I understand the question.
14 Well, maybe rephrase it and make sure I understand it.
15 Q. Okay. In a hypothetical situation where you were
16 given additional data for the areas in question in this
17 case and you found in looking at this additional data that
18 lognormal kriging would have been appropriate, would you
19 then expect to see a different result if you used
20 lognormal kriging and ordinary kriging?
21 A. I would probably not expect any significant
22 difference, if both were correctly applied.
23 Q. Did you use ordinary kriging in this case?
24 A. The work I did used ordinary kriging.
25 Q. Are you familiar with disjunctive kriging?
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1 A. Yes, I am familiar with disjunctive kriging.
2 Q. Would that have been appropriate to use in this
3 case?
4 A. No.
5 Q. Why is that?
6 A. Disjunctive kriging, I believe, with the exception
7 of a few practitioners in France, I believe the
8 geostatistics community has disclaimed it.
9 Q. Are you familiar--
10 A. I am familiar with disjunctive kriging. I did a
11 research project for the U.S. Energy and Research
12 Development Agency published in 1977, wrote the first code
13 for applying disjunctive kriging. Basically proved it
14 didn't work very well.
15 Q. Are you familiar with universal kriging?
16 A. Yes.
17 Q. Could you describe to me under what situations
18 universal kriging would be more appropriate to use than
19 ordinary kriging?
20 A. Yes. Universal kriging, in my opinion, should only
21 be used when there's an extremely strong drift and when
22 you're extrapolating.
23 Q. What do you mean by a drift?
24 A. Drift.
25 Q. Would it be similar to a trend?
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1 A. Drift and tend are similar, yes. The theory of
2 stochastic process, they would refer to drift. Geologists
3 would refer to trend. They are very similar.
4 Q. But they're not the same?
5 A. Not the same exactly.
6 Q. Sticking with the word trend, would you say that
7 there was a trend in the data for South Florida for
8 phosphorus concentrations?
9 A. It didn't appear to me that there was what I would
10 call a trend.
11 Q. Did you have enough data, in your opinion, to
12 determine if there was a trend?
13 A. I would probably say no.
14 Q. In sticking with the word trend and not drift, is it
15 possible to have a trend that doesn't necessarily go north
16 to south, or south to north, or in a direction such as
17 that, but in a situation where you have a point and the
18 trend goes out in all directions from that point going
19 higher or lower in values, could you have a trend in that
20 type of situation?
21 A. You can have a quadratic trend that looks like a
22 mountain.
23 Q. Quadratic trend?
24 A. (Witness indicates yes.)
25 Q. Did you see a drift in the data for the -- the data
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1 that was presented to you from South Florida?
2 A. Which data?
3 Q. Well, did you see a drift in any of the data?
4 A. No.
5 Q. And is that why you felt that universal kriging was
6 not appropriate?
7 A. Yes. Yes.
8 Q. Are there any other reasons that you felt that
9 universal kriging is not appropriate? Again, limited to
10 what we're talking about in this case, the areas in South
11 Florida.
12 A. It's my experience that properly applied, that you
13 get better results for interpolation when you use ordinary
14 kriging rather than universal kriging. And the difference
15 is in my term interpolation.
16 Q. Why is that?
17 A. It really gets down to the purpose of your
18 estimation. In some respects, what is the most important
19 variable to -- that you're trying to estimate. When you
20 use universal kriging, you're more interested in
21 determining -- I'll use the word trend. You're interested
22 in seeing what the trend is and getting a model of the
23 trend rather than necessarily getting an accurate model of
24 the true surface.
25 And sometimes, you want to -- It's sort of whether you
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1 want to see the forest or the trees.
2 Q. When you use the word interpolation in this context,
3 can you define that word for me?
4 A. You have two data points. And you want to know a
5 value that lies in between them. That's an interpolation.
6 Q. Are there any other types of kriging that you're
7 familiar with other than the five that I've mentioned?
8 A. Yes.
9 Q. Are there a lot of other types of kriging?
10 A. Yes.
11 Q. Are there any other types of kriging that may have
12 been appropriate to use to determine phosphorus
13 concentrations over South Florida?
14 A. There's none other that I would feel would be more
15 appropriate than ordinary kriging.
16 Q. Are there any others that may be appropriate?
17 A. The other variations of kriging are variations
18 because they may give a different answer or a different
19 type of estimate. For an estimate of the mean
20 concentration, I think kriging is the most appropriate one
21 here to use.
22 MR. BARTELL: Could you read back that answer for
23 me.
24
25
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1 (Whereupon, the previous answer was read back as
2 follows: "The other variations of kriging are variations
3 because they may give a different answer or a different
4 type of estimate. For an estimate of the mean
5 concentration, I think kriging is the most appropriate one
6 here to use.")
7 Q. Okay, in your last answer, you said kriging is the
8 most appropriate one to use. My question to you is,
9 within the realm of kriging, there are a lot of other
10 types of kriging. I've just listed five. You've
11 indicated that there are a number of others. Are there
12 any other types of kriging that may be appropriate to use
13 to determine phosphorus concentrations in South Florida?
14 MR. LIEBERMAN: Object to form, the word
15 appropriate.
16 MR. BARTELL: Applicable.
17 THE WITNESS: Applicable. Yes. Possibly
18 indicator kriging would be applicable.
19 Q. Any other types of kriging?
20 A. I think we're stretching it far enough.
21 Q. Could you describe to me in what situations
22 indicator kriging would be more appropriate to use than
23 ordinary kriging?
24 A. Indicator kriging is important to use when you want
25 to know the distribution rather than a mean value. In ore
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1 reserve estimation, we may want to know the distribution
2 of grades or of gold in a block rather than just the
3 average value.
4 Q. Other than kriging in general, any types, including
5 ordinary kriging, are there any other methods that may be
6 applicable to determine phosphorus concentrations over
7 South Florida that you're aware of?
8 A. None that I'm well aware of.
9 Q. Okay. Let's talk a little bit about ordinary
10 kriging. My first question to you is what type of
11 software did you use in using this ordinary kriging?
12 A. Okay, the ordinary kriging was using software that I
13 have written.
14 Q. Has anybody ever used the software besides yourself?
15 A. Yes. The software that I used now was developed
16 initially in 1975 for a contract with the United States
17 Energy Research and Development Administration. Since
18 then, it's been incorporated into at least three
19 commercial packages in the mining industry, at least one
20 package in the general area of environmental services.
21 There's a commercial package called ENTEC that
22 incorporates my kriging software. It's had a long life.
23 Q. Is this commercially available?
24 A. My software in the commercial packaging, yes, is
25 commercially available. The software that I use at
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1 Montana Tech is not licensed or sold per se, but it is
2 considered in the public domain, because the work
3 originally done was in the public domain.
4 Q. Is there a difference between the commercial package
5 and the package at the Montana Tech?
6 A. Just in presentation and ease of use. The
7 mathematical algorithms are the same.
8 Q. Have those mathematical algorithms set forth in this
9 software been provided in your production of documents?
10 A. No. They're commonly -- The kriging algorithm is a
11 common algorithm.
12 Q. It's one particular algorithm?
13 A. Ordinary kriging is one particular algorithm. And
14 as a matter of fact, you have slight differences in
15 assumption. In essence, you use the same software for all
16 of the krigings.
17 Q. If somebody else, another scientist, another
18 professor or somebody else who was familiar with kriging
19 were to take your data and perform ordinary kriging, would
20 they come up with the same results that you came up with?
21 A. Yes.
22 Q. Even if they used other software?
23 A. Yes. There's only one small place that they might
24 have trouble with. If their software doesn't correctly
25 convert from latitude, longitude to -- You have to
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1 calculate distances between sample points using latitude,
2 longitude. That's not commonly done in most kriging
3 programs. The data is usually in a rectangular grid
4 rather than latitude and longitude.
5 Q. How would the data in a rectangular grid be
6 different from latitude and longitude?
7 A. Because most of us work with data on a map
8 projection, projected to a flat plane rather than on a
9 surface of the earth.
10 Q. Is this algorithm that is used in ordinary kriging
11 just a formula, or could you describe to me what the
12 algorithm is?
13 A. Yes. It's just a linear regression. For a
14 statistician, that explains it.
15 Q. Is that something that you could explain on the
16 record or something that you could write as far as what
17 that algorithm is, or is it more complicated than that?
18 A. Well, it's more complicated than that. But I give
19 that lecture many times during a year.
20 Q. How long does that lecture take?
21 A. Well, the preparatory material probably takes four
22 weeks of classes.
23 Q. You mean to be able to understand it?
24 A. Yes.
25 Q. Assuming that--
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1 A. It is a common algorithm. I mean statisticians
2 understand it. There's nothing unique about it.
3 Q. In ordinary kriging then, you take this data and you
4 insert it into the software, which produces results; is
5 that correct?
6 A. Briefly, yes, that's correct.
7 Q. How would you clarify that?
8 A. The ordinary kriging is not totally a black box. It
9 really consists of two steps. One step you have to
10 determine what is referred to as a variogram. The second
11 step is you do the ordinary kriging.
12 Q. How do you come up with -- Is a variogram the same
13 as the semi-variogram?
14 A. Yes.
15 Q. How do you come up with the variogram?
16 A. By analyzing the data in a computer program.
17 Q. Did you come up with a number of variograms before
18 you determined which one was appropriate to use for this
19 case?
20 A. I guess the best way to answer that is yes.
21 Q. And have those different variograms been produced?
22 A. You have somewhere in your exhibits you have the
23 variogram models for the rainfall data. And I think you
24 have them. It was provided to you.
25 Q. The variograms that were not used, were those
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1 provided to us?
2 A. I don't know what you mean by variograms not used.
3 That's a term I'm not familiar with.
4 Q. Maybe the fact -- Bear with me, please. I'm doing
5 the best I can. But my understanding is that you come up
6 with a number of different variograms and then you figure
7 out which one is the best one to use by sort of running
8 it. Is that incorrect? Or is there a better way to sort
9 of describe it?
10 A. I would say that's incorrect.
11 Q. Could you help me understand how you come up with a
12 variogram that you use or how you came up with the
13 variogram you used in this particular case?
14 A. We have a computer program that calculates the
15 variogram. And in that, you specify what direction you
16 want to calculate the variogram. A variogram is a
17 function of direction and distance.
18 And so you usually specify a number of directions to
19 calculate the variogram. And from those, you want to
20 determine what directions the data is most correlated
21 along and which directions the data is least correlated.
22 So it's not a matter of you calculate one and throw it
23 out. From all of them, you have to determine some very
24 specific information.
25 Q. What direction did you seek to determine in this
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1 case?
2 A. Well, I did all directions, basically.
3 Q. And then you insert the distance?
4 A. The distance is a part of the variogram. It's a
5 function of distance and direction.
6 Q. Is there a different means of coming up with the
7 variogram other than what you've just described you did?
8 A. Not really any different means, no.
9 Q. What's your understanding of the way the South
10 Florida Water Management District krigs their numbers?
11 MR. LIEBERMAN: Objection to form.
12 Are you talking about krig their numbers from where?
13 What numbers are you referring to?
14 Q. In the SWIM Plan.
15 A. The ones that were in the appendices we looked at.
16 In reading through their information, that's contained
17 in the appendices, they said they use a technique called
18 universal kriging. They said they used somebody's
19 computer program. I can't remember whose.
20 Q. Do you feel that it is a judgment call on behalf of
21 the person analyzing the data to use ordinary versus
22 universal kriging?
23 A. Yes.
24 Q. Is there a scientifically accepted right way and
25 wrong way to do it?
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1 A. I wouldn't hazard to say that there's a
2 scientifically accepted right way and wrong way to
3 determine which one. There's no hard-and-fast line
4 necessarily.
5 Q. So again, it's a judgment call?
6 MR. LIEBERMAN: Objection. Are you talking
7 judgment call as to the District people who made the call
8 on the SWIM Plan? Are you talking judgment call in a
9 general kriging sense?
10 Q. I'm talking in a general kriging sense.
11 A. In a general sense, yeah. There is a judgment call
12 there, yes.
13 Q. Is it your opinion that the South Florida Water
14 Management District, in kriging the numbers in the SWIM
15 Plan, did it a wrong way?
16 A. I have critiqued their work and I found three, I
17 guess points, that I thought were inappropriate.
18 Q. Are those three points set forth in your January
19 4th, '93--
20 A. Yes, they are.
21 Q. We'll go into that then when we get there.
22 How do you feel or -- Let me rephrase that.
23 How would the numbers have come out had you inserted
24 and used the data that you did use? Had you used
25 universal kriging, for instance, would the phosphorus
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1 concentrations have been higher or lower?
2 A. I have no way of knowing that without doing it.
3 Q. Did you ever run it -- universal kriging?
4 A. On this set of data?
5 Q. On this set of data.
6 A. No.
7 Q. Did you use any other method to determine the final
8 numbers besides ordinary kriging?
9 A. No.
10 Q. And just to clarify for me, do you feel that there
11 is any other means that would have been -- I'm going to
12 use the word appropriate or applicable -- to come up with
13 results other than ordinary kriging?
14 MR. LIEBERMAN: Objection, that that's been asked
15 and answered a few times.
16 THE WITNESS: I don't think there's any other
17 means that are more appropriate maybe is the best way to
18 answer it.
19 Q. You mentioned that kriging is sort of a two-stage
20 process, one of which you come up with the variogram. The
21 second -- Is the second then just applying the data to
22 that variogram to come up with the results?
23 A. Yes. That's the kriging portion.
24 Q. In determining the geographic data points that you
25 use in kriging, how do you know how far to go
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1 geographically? Do you understand my question?
2 A. Well, explain it further to make sure--
3 Q. What I'm trying to understand, is there a point
4 geographically, that is just beyond the scope of being of
5 any benefit in your kriging? For example, in the work you
6 did in South Florida, if you had a point in New Jersey,
7 would you have not used that point because it was simply
8 just too far?
9 A. Yes. There is a point which the data has no
10 relationship, no correlation.
11 Q. Did you make the determination of what data to use
12 in your kriging--
13 A. Yes.
14 Q. --for this case?
15 A. Yes.
16 Q. And how did you make that determination?
17 A. The variogram that you calculate is one way to
18 determine how much data or how far data should be allowed
19 to influence your estimate. One of the parameters is
20 called the range of influence. It's a poor title. It's a
21 poor name, but frequently that is an indicator of how far
22 you can go.
23 Q. Did you choose not to use any data points for your
24 work in this case?
25 A. In the rainfall, there were sufficient points nearby
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1 the areas so that you could not use data that was a long
2 ways away.
3 Q. So did you not use data a long ways away?
4 A. Yes. In each area, there's a maximum limit to the
5 data that you would use.
6 Q. What about in determining the phosphorus
7 concentrations?
8 A. There also was a limit put on there.
9 Q. So there were some points that were not used in
10 determining the phosphorus concentrations?
11 A. Probably not.
12 Q. So to the best of your recollection, you used all of
13 the data that was provided to you for the phosphorus
14 concentrations?
15 A. Yes.
16 Q. Are you familiar -- Just if you