834 1 UNITED STATES DISTRICT COURT FOR THE 2 SOUTHERN DISTRICT OF FLORIDA 3 **************************** 4 UNITED STATES OF AMERICA, * Plaintiff * 5 * Case Number VS. * 88-1886-CIV 6 * Hoeveler SOUTH FLORIDA WATER * 7 MANAGEMENT DISTRICT, ET AL., * Defendants * 8 ***************************** 9 10 Deposition of WILLIAM W. WALKER, JR., 11 taken on behalf of the defendants South Florida 12 Water Management District and John R. Wodraska 13 pursuant to the applicable rules of the Federal 14 Rules of Civil Procedure, before Linda Marie 15 MacDonald, Registered Professional Reporter and 16 Notary Public within and for the Commonwealth 17 of Massachusetts, at the offices of Skadden, 18 Arps, Slate, Meagher & Flom, One Beacon Street, 19 Boston, Massachusetts, on Tuesday, February 12, 20 1991, commencing at 9:08 a.m. 21 22 23 LINDA MARIE MacDONALD, RPR-CM REGISTERED PROFESSIONAL REPORTER 24 60 LAWRENCE ROAD, PLYMOUTH, MA 02360 (508) 747-6615 835 1 A P P E A R A N C E S: 2 UNITED STATES ATTORNEY'S OFFICE By A.U.S.A Richard Harrison 3 155 South Miami Avenue, Suite 600 Miami, FL 33130 4 for the United States of America. 5 SKADDEN, ARPS, SLATE, MEAGHER & FLOM By Attorney Laura B. Ahearn 6 1440 New York Ave., N.W. Washington, D.C. 20005 7 for South Florida Water Management District and John R. Wodraska. 8 PEEPLES, EARL & BLANK 9 By Attorney Rick J. Burgess One Biscayne Tower, Suite 3636 10 Miami, FL 33131 for the cities of Belle Glade and 11 Clewiston, defendant intervenors. 12 STATE OF FLORIDA OFFICE OF GENERAL COUNSEL By Asst. Gen. Counsel David A. Crowley 13 Department of Environmental Regulation Twin Towers Office Building 14 2600 Blair Stone Road Tallahassee, FL 332301 15 for the Florida Department of Environmental Regulation. 16 17 A L S O P R E S E N T: 18 Douglas Robson, Consultant, SFWMD John Davis, Consultant, Belle Glade and 19 Clewiston Peter Ghavami, Legal Assistant, Skadden 20 Arps 21 22 23 24 DEPOSITION OF WILLIAM W. WALKER, JR. 836 1 I N D E X Witnesses Examination 2 WILLIAM W. WALKER, JR., resumed 3 (By Ms. Ahearn) 838 4 E X H I B I T S 5 Number For ID DX 38 Total Phosphorus Trend Analysis, 841 6 Shark Slough 7 DX 39 S12 Composite, Shark River Slough, 909 Taylor Slough, Coastal Basin 8 DX 40 Yearly Total P Concs & Loads, 923 9 ENP Inflows, with attachments 10 DX 41 Total P Times Series - ENP Inflows 923 Excluding Outliers, Flow > 0, 11 with attachments 12 DX 42 WQ Summary - ENP Inflows 923 Not Flow-Weighted 13 DX 43 ENP Flow-Weighted Mean Concs 923 14 DX 44 WQ Summary - ENP Marsh Stations 923 15 Not Flow-Weighted 16 DX 45 ENP Marsh Data - Trend Analysis, 923 All Results by Station 17 DX 46 ENP Marsh Data - Trend Analysis, 923 18 All Results for Variable = DO, TNTP and TP 19 DX 47 Station P35 Total P/Stage Graph 923 20 DX 48 Station P36 Total P/Stage Graph 923 21 DX 49 Memo to Garver from Walker 923 22 11/14/90; Re: Data Needs to Support Research 23 DX 50 Document dated 1/7/91 923 24 Data Needs: Supplement to 11/9/91 Memo to G. Garver DEPOSITION OF WILLIAM W. WALKER, JR. 837 1 E X H I B I T S 2 Number For ID 3 DX 51 Letter to Scheidt from Higer 923 dated 6/29/89, with attachments 4 DX 52 Memo to Clint Leaks from Walker 923 5 WATSTORE Retrieval Request 6 DX 53 Document entitled "Meeting Agenda" 923 Subject: Access to Technical Data 7 Maintained on District Computers 8 DX 54 Letter to Scheidt from SFWMD 923 (Mary Lou Daniel), 12/13/89, 9 with attachments 10 DX 55 Document entitled "Trends at 923 Other WCA Stations" 11 DX 56 Simulation of Trend Detection 985 12 Procedures; Tests on Means and Frequency, Clean and Messy Data 13 14 15 16 17 18 19 20 21 22 23 24 DEPOSITION OF WILLIAM W. WALKER, JR. 838 1 P R O C E E D I N G S 2 WILLIAM W. WALKER, JR., 3 having been previously duly sworn, was deposed 4 and testified as follows: 5 CONTINUED DIRECT EXAMINATION 6 BY MS. AHEARN: 7 Q. Good morning, Dr. Walker. 8 A. Good morning. 9 Q. What is the Chi2 test for homogeneity of trend? 10 A. Are you asking that in reference to a 11 particular document? 12 Q. Well, I guess first I'd like a working 13 definition of this test. 14 MR. HARRISON: Object to form. No 15 foundation, no predicate laid to show that it's 16 a term of art. You may answer. 17 A. As I have applied that test in the trend 18 analysis as described in Exhibit 17, it is a 19 test to determine the likelihood that there are 20 significant differences in the trend magnitude 21 from one season to another. 22 Q. Is the Chi2 test for homogeneity of trend a 23 special term in the field of science of 24 statistics? DEPOSITION OF WILLIAM W. WALKER, JR. 839 1 A. I have used the term and the equations as they 2 are defined in a book by Gilbert that is 3 referenced in Exhibit 17. 4 Q. Could you, please, point me to that reference, 5 if you could identify for me where in 6 Exhibit 17 we'll see reflected your Chi2 test 7 for homogeneity of trend? 8 MR. HARRISON: Do you want the second 9 one first, Counsel, or the reference? It's 10 compound. 11 Q. Are those two different things, your reference 12 to Gilbert and where in the -- let's start all 13 over. 14 Direct me to the reference to Gilbert, 15 please. 16 A. The reference to Gilbert is on page 45 of 17 Exhibit 17. It's a book entitled "Statistical 18 Methods for Environmental Pollution 19 Monitoring." 20 MS. AHEARN: And I would like the record 21 to reflect that we have numbered each page on 22 the original Exhibit 17 here to which 23 Dr. Walker is referring to make sure that there 24 is a legible page number on each page in the DEPOSITION OF WILLIAM W. WALKER, JR. 840 1 exhibit. 2 Q. Okay. That was in the list of references, 3 correct? 4 A. Correct. 5 Q. Could you point to me the textual discussion of 6 this Gilbert method? 7 A. I don't recall actually discussing that in the 8 report. This test for homogeneity of trend was 9 something that is included in the computer 10 program that I wrote for the purpose of 11 conducting these tests. 12 But the results -- as I recall, the 13 results of that trend did not indicate that 14 there were significant differences from one 15 season to another with respect to trend 16 magnitude, so there was no reason to discuss 17 those results in the context of the report. 18 Q. Just so it's clear, on reviewing Exhibit 17, I 19 found no mention of the Chi2 test. 20 A. That's right. That's probably correct. I do 21 not recall actually describing it in the text, 22 but it is a test that I applied. 23 Q. Do you recall if you discussed the Chi2 test in 24 any prior drafts of Exhibit 17? DEPOSITION OF WILLIAM W. WALKER, JR. 841 1 A. I do not believe I did. 2 Q. When in the sequential process of your trend 3 analysis did you perform the Chi2 test? 4 A. I don't recall when I added that particular 5 algorithm to the computer program that I was 6 working with. 7 (Exhibit No. 38 marked for 8 identification) 9 Q. Dr. Walker, I'll ask the court reporter to hand 10 you Exhibit 38. Can you identify that? 11 A. This is two pages of graphs and statistics 12 entitled Total Phosphorus Trend Analysis for 13 Shark slough as described on the first page. 14 And I believe the second page describes -- 15 summarizes a similar analysis for Station S332 16 -- that is Taylor slough -- and Station S18C, 17 which is the Coastal station. 18 Q. I see at the bottom of each page here a 19 reference to your Chi2 test. 20 A. That's correct. 21 Q. Let me first ask you, You generated both pages 22 of Exhibit 38? 23 A. Yes, I did. 24 Q. And this was on your personal computer? DEPOSITION OF WILLIAM W. WALKER, JR. 842 1 A. Yes. 2 Q. I asked because it looks to be a somewhat 3 different format than other things I have seen 4 you produce. 5 Does this Exhibit 38 illustrate how you 6 performed the Chi2 test? 7 A. No. This Exhibit 38 merely states the results 8 of the Chi2 test. 9 Q. Do you recall if you produced any other 10 documents or computer files that illustrate how 11 the Chi2 test was performed? 12 A. The methods that were used to calculate the 13 Chi2 test are reflected in the FORTRAN computer 14 software that I turned over with my other 15 computer files. 16 Q. Those are the files reflected in Exhibit 18, 17 the printout of the directories? 18 A. That's correct. 19 Q. Can you, please, identify by page number and 20 name the directory where I'll find the program 21 that incorporates the Chi2 test algorithms? 22 A. Okay. We're referring now to Exhibit No. 18. 23 The program that contains the Chi2 test for 24 homogeneity of trend would be included in the DEPOSITION OF WILLIAM W. WALKER, JR. 843 1 directory listed on -- starting on page 14, the 2 directory G:\LIB\FOR. 3 Q. Can you identify a particular file or files 4 that contains the Chi2 test? 5 A. I believe that a portion of the test is 6 contained in the file on page 18 called 7 SKEND.FOR. That's the sixth file from the top 8 on page 18. Other subroutines may be used in 9 calculating that test, as well. 10 Q. I note that there is one labeled CHISQP.FOR. 11 It sounds like a likely candidate. 12 A. Yes. That routine may be used as well in 13 calculating that test result. That's located 14 on page 14. 15 Q. Are each of the trend programs which we have 16 discussed before on page 13 of Exhibit 18, are 17 each of those trends programs designed to call 18 up the Chi2 subroutine from the FORTRAN 19 directory? 20 A. Yes. 21 Q. While we're here on Exhibit 18, I want to ask 22 you a couple more questions I'm not clear on. 23 You identified your G:\DBASE directory as 24 containing the surface water quality data that DEPOSITION OF WILLIAM W. WALKER, JR. 844 1 you used with the KTEST program for producing 2 Exhibit 17? 3 MR. HARRISON: Counsel, are you on a 4 particular page on Exhibit 18? 5 MS. AHEARN: The DBASE is on page 24. 6 Q. I believe when I had asked you about this 7 before, I only spoke in terms of the surface 8 water quality data. 9 Are all of the files for flow, rainfall 10 and stage data which the KTEST program 11 retrieved for purposes of doing the analysis 12 reflected in Exhibit 17, are all of those data 13 files also included in this G:\DBASE? 14 A. To the best of my recollection, yes. 15 Q. And in G:\DBASE we also see a number of files 16 for various variables that appear to relate to 17 marsh stations; is that correct? For example, 18 entries for P33, those files would denote data 19 concerning a marsh station within Everglades 20 National Park? 21 A. That's correct. 22 Q. In the preliminary analysis that you have 23 performed of Everglades marsh data, am I 24 correct you used a program called MULTI? DEPOSITION OF WILLIAM W. WALKER, JR. 845 1 A. That's correct. 2 Q. All of the data files set up to be retrieved by 3 the MULTI program, are all of those data files 4 contained in directory G:\DBASE? 5 A. I believe I testified previously regarding the 6 procedures that one would use to execute these 7 programs. Basically the procedure involves 8 editing the file, in this case MULTI.DAT, which 9 contains essentially the instructions of the 10 program to access certain data files, so in 11 that file MULTI.DAT should be the directory and 12 the specific file names that would be used in a 13 particular analysis or run of the program. 14 Q. Would you need to actually look at that entry 15 in the program to ascertain where all of the 16 data files for use in that program are located? 17 A. That's correct. In the listing of that 18 MULTI.DAT input file should be an indication of 19 where the files are located and what their 20 names are. 21 Q. Is the same true for the RMED program? You 22 would need to look at the .DAT file in order to 23 tell us exactly in which directories the 24 appropriate data files were stored? DEPOSITION OF WILLIAM W. WALKER, JR. 846 1 A. Yes. 2 Q. Just trying to see if I can cut some corners. 3 Dr. Walker, when you edited Exhibit 17 4 for submission to the Water Resources Bulletin, 5 did you look for statements that were more 6 likely to draw questions or criticisms from the 7 peer reviewers? Was that a consideration in 8 deciding which statements to take out of the 9 text? 10 MR. HARRISON: I object to the 11 characterization. I think we had a round on 12 that, whether it was editing or what it was. I 13 think there is a separate exhibit in here, 14 Counsel, that went to the Water Resources 15 Bulletin if you want to refer to that. 16 A. I believe I testified previously that my 17 objective in editing Exhibit 17 for submission 18 to Water Resources Bulletin was to shorten it 19 to provide an acceptable length for 20 publication. 21 Q. And you explained to us why you omitted the 22 section on the loading analysis. Did you omit 23 other parts of the text? 24 A. I may have omitted certain sentences or certain DEPOSITION OF WILLIAM W. WALKER, JR. 847 1 paragraphs in the effort of -- in the interest 2 of shortening the overall text. 3 Q. In Exhibit 17, would you turn to page 3, 4 please? The last sentence in the first 5 paragraph, is there any reason why you deleted 6 that sentence from the draft submitted to the 7 Water Resources Bulletin? 8 A. I don't recall whether specifically I did 9 delete that sentence. 10 Q. If you would like to refer to Exhibit 12 to 11 verify that, it would be page 2 of Exhibit 12. 12 MR. BURGESS: Exhibit what? I'm sorry? 13 MS. AHEARN: Exhibit 12. 14 A. Well, as I stated, my primary emphasis in 15 editing this for submission was to shorten the 16 document. That was a sentence that I thought 17 was not essential to the rest of the document, 18 and it was rather long and it was an 19 opportunity to shorten the document. 20 I believe that the concept expressed in 21 that sentence is something that is generally 22 accepted in the water quality management field 23 and is not something that is essential for the 24 purposes of understanding this technical DEPOSITION OF WILLIAM W. WALKER, JR. 848 1 document and understanding the analysis which I 2 performed. 3 Q. Do you feel that you would be able to defend 4 this sentence, the last sentence in the first 5 paragraph of page 3, Exhibit 17, before the 6 peer reviewers of the Water Resources Bulletin? 7 A. Yes. 8 Q. Let me see if I can shorten this up. 9 Recognizing the need to shorten the 10 document, can you tell me what other criteria 11 guided your exercise of judgment in deciding 12 which statements to extract from Exhibit 17? 13 MR. HARRISON: Object. Asked and 14 answered. Also, no foundation for your 15 characterization that there were other 16 criteria. 17 Q. Were there other criteria other than there was 18 a page limitation? 19 MR. HARRISON: Asked and answered. 20 MS. AHEARN: Excuse me. You just told 21 me -- 22 A. No. 23 Q. There were no other criteria that guided your 24 judgment? DEPOSITION OF WILLIAM W. WALKER, JR. 849 1 A. My objective was to shorten the document. And 2 in the process of selecting which particular 3 pieces I would remove for the purpose of 4 shortening the document, I removed those pieces 5 which I felt were not necessary to communicate 6 the essential components of the work and those 7 parts which were separable in a sense as I 8 described earlier. 9 I believe the analysis on the loading is 10 a separate piece that could very well 11 constitute a separate paper, a separate journal 12 article, and I may very well submit that for 13 publication separately. Those are the kinds of 14 considerations that I had, but my overall 15 objective was to shorten the article to make it 16 more acceptable for publication in a journal. 17 Q. Thank you. We had proceeded through page 5 of 18 Exhibit 17 yesterday. Would you turn to 19 page 6? On the first line there you refer to 20 fixed minimum delivery schedules. What do you 21 mean by that phrase? 22 A. I mean that there were certain volumes of water 23 that were scheduled to be released through 24 Structures S332 and S18C. And as distinct from DEPOSITION OF WILLIAM W. WALKER, JR. 850 1 the schedule for Shark slough, where the 2 volumes were based upon rainfall, these 3 deliveries at S332 and S18C were not based upon 4 antecedent rainfall. 5 Q. I just want to make sure that we're clear here. 6 By "schedules," are we talking about hydrologic 7 ranges as opposed to a calendar schedule? 8 A. What do you mean by "hydrologic ranges"? 9 Q. By "delivery schedule," are you referring to a 10 preset time period for water deliveries? Is it 11 a schedule in that sense like scheduled for 12 every Monday or it's already established on a 13 calendar that deliveries occur on X day? 14 MR. HARRISON: Object to form. 15 Q. Is that what we mean here by "schedules"? 16 MR. HARRISON: Object to form. It might 17 be easier just to ask him when he -- what his 18 understanding of the schedules are. 19 A. To my recollection, the flows through S332 and 20 S18C are operated to provide a certain 21 guaranteed minimum amount of flow. I'm 22 uncertain as to whether that is an annual flow 23 or whether that flow is broken out on a 24 seasonal basis. And then on top of that DEPOSITION OF WILLIAM W. WALKER, JR. 851 1 minimum guaranteed amount would be any flows 2 that would occur as a result of excess runoff 3 or drainage from the basin following storm 4 events. 5 Q. Are water deliveries scheduled to be made at 6 any specific time? 7 A. I believe that there is a seasonality to the 8 delivery schedule. 9 Q. Are you knowledgeable of the currently 10 effective operating criteria for water 11 deliveries to Everglades National Park? 12 MR. HARRISON: Object to form. There's 13 different delivery points to the Park. 14 A. Which -- which basin are you referring to? 15 Q. Are you familiar with the operating criteria 16 for all three basins? 17 A. I am generally familiar with the operating 18 criteria as they are discussed in Exhibit 17. 19 Q. Are you aware of any changes in operating 20 criteria since the time period which ends 1989 21 that's discussed in Exhibit 17? 22 A. I'm not aware of any such changes. 23 MR. HARRISON: Was that December '89, 24 Counsel? DEPOSITION OF WILLIAM W. WALKER, JR. 852 1 MS. AHEARN: The text says 1989, 2 Mr. Harrison. 3 MR. HARRISON: But without a month. 4 Q. In the second full paragraph on page 6, the 5 second sentence, you state that: 6 Values reported to be below the 7 detection limit are set equal to the 8 detection limit minus a small 9 concentration increment. 10 At what point in your trend analysis 11 work did you set these below-detection-limit 12 values minus a small concentration increment? 13 A. What do you mean by "point"? 14 Q. Did you do trend analyses with the detection 15 limits without deducting the small 16 concentration increment? 17 A. I believe that the first draft of the work did 18 not perform that task. In other words, the 19 first set of trend analyses that I performed 20 that's described in the July 1990 draft I did 21 not make that adjustment in detection limit. 22 Q. Is there a reason why that wasn't attempted for 23 the first draft? 24 A. To perform that task, it involved a substantial DEPOSITION OF WILLIAM W. WALKER, JR. 853 1 amount of work. I had to go through and 2 essentially edit the data files, the source 3 data files, to make that adjustment. And I 4 felt in the first draft that since the overall 5 percentage of total phosphorus values below 6 detection limits was on the order of 7 percent 7 or less, it was unlikely that that adjustment 8 would make a significant difference in the 9 results of the trend analysis. Therefore, I 10 did not undertake that adjustment in the first 11 draft. 12 Q. Why did you feel it was worthwhile to do that 13 substantial work after the first draft? 14 A. Because I was given more time -- as I testified 15 earlier, I was under some commitment to 16 complete the first draft by July of 1990, and I 17 had additional time between July and September. 18 And it was also -- a comment regarding this 19 topic was made by one of the reviewers. So 20 those were the reasons why this adjustment was 21 made in the second or in the final version of 22 the trend analysis. 23 Q. Did you have this in mind independent of the 24 comment of the reviewer? DEPOSITION OF WILLIAM W. WALKER, JR. 854 1 A. I had it in mind as something that might be 2 done as part of the analysis. 3 Q. Did you perform sensitivity analyses to see the 4 effect of setting below-detection-limit values 5 at other levels? 6 A. As the text on page 6 describes, the trend test 7 is based upon ranks of the data and, as such, 8 the results for the trend analyses would not be 9 sensitive to the particular magnitude selected 10 for this adjustment. 11 Q. Could you set it at zero and not have any 12 impact on the trend analysis? 13 A. Setting it at zero would be problematical for 14 the Series C analyses because the Series C 15 analyses involved taking logarithms -- in fact, 16 all of them involve taking logarithms of the 17 data prior to the trend analysis. So now that 18 I think about it, zero could not have been used 19 in the way I performed this test. 20 Q. Does the selection of the level at which to set 21 below-detection-limit values affect the 22 calculation of the Kendall slope? 23 A. Possibly. 24 Q. Did you do any sensitivity analyses of that? DEPOSITION OF WILLIAM W. WALKER, JR. 855 1 A. Only insofar as the draft -- the July draft did 2 not make any of this sort of adjustment and the 3 final draft did make this adjustment. 4 Q. So you tested between no adjustment and an 5 adjustment of .0001 milligram per liter? 6 A. Correct. 7 Q. What is the difference between those two 8 scenarios? 9 A. Well, it's difficult to generalize about the 10 difference between those scenarios for all 11 variables and all stations. But, for example, 12 if we take what I identified as Series A at 13 Station S12T, the Kendall slope estimated in 14 the July draft when I did not make that 15 adjustment for detection limits was 7.1 percent 16 per year; that is, the median rate of increase 17 in phosphorus concentration at the S12s was 18 7.1 percent per year. 19 Q. Dr. Walker, are you referring to a particular 20 page or table in Exhibit 7? 21 A. Yes. I'm referring to Exhibit 7, Table 5. 22 Q. Thank you. 23 A. And in that Exhibit 7, Table 5, as I just 24 mentioned, the trend for S12T was 7.1 percent DEPOSITION OF WILLIAM W. WALKER, JR. 856 1 per year. And in the final version, Table 5, 2 Exhibit 17, the trend for the same station and 3 variable was 7.0 percent per year. 4 Q. Is the change from 7.1 to 7.0 not significant? 5 MR. HARRISON: Object to form. 6 A. The change from 7.1 to 7.0 is a change from 7.1 7 to 7.0. I don't know what you mean by 8 "significant." 9 Q. Do you have the sense of what the slope would 10 have been if you had set below-detection-limit 11 values at .002? 12 A. I did not test that directly. But as I stated 13 earlier, since on the order of 7 percent of the 14 observations were below detection limits and 15 since the slope is calculated as the median of 16 all the slopes calculated within each season, 17 it is unlikely that a change in this adjustment 18 factor would have influenced the calculated 19 slope. And in no case would an adjustment of 20 this factor for detection limits influence the 21 calculated P level or the significance level 22 upon which we base -- we estimate the 23 likelihood of a trend. 24 Q. Thank you. I understand that distinction DEPOSITION OF WILLIAM W. WALKER, JR. 857 1 there. In the middle of the middle paragraph 2 on page 6, Exhibit 17, you state: 3 The detection limit for total and 4 ortho phosphorus increased from .002 to 5 .004 milligram per liter in 1981. 6 What was the cause of that change? 7 A. I do not know. 8 Q. Do you know if there were any changes in lab 9 technique at this time? 10 A. Not to my knowledge. 11 Q. Are you aware of any changes in the detection 12 limits of other constituents? 13 A. The database that was supplied by the District 14 included measurements of trace metal 15 concentrations, heavy metals. And in reviewing 16 the listing of that data, it was apparent that 17 there were some fluctuations in the detection 18 limit in those cases. I did not conduct a 19 trend analysis on that information. 20 Q. Are you aware of any changes in detection 21 limits among any of the water quality 22 constituents you did analyze? 23 MR. HARRISON: Other than total 24 phosphorus? DEPOSITION OF WILLIAM W. WALKER, JR. 858 1 MS. AHEARN: Yes. 2 Q. Other than the ortho and total phosphorus in 3 '81. 4 A. Of the constituents which I analyzed, the other 5 species for which I recall the presence of 6 values below detection limits would include 7 ammonia nitrogen and nitrate and nitrite 8 nitrogen. The remaining species to my 9 recollection were generally reported at values 10 -- at quantifiable values above the detection 11 limit, so there would be no way of knowing 12 precisely what the detection limit was for 13 those constituents because the concentrations 14 were always above the detection limits. 15 In the case of ammonia nitrogen and 16 nitrite nitrogen, I don't recall a systematic 17 change or a shift in the detection limit in a 18 particular time period. 19 Q. You said that those other constituents were 20 reported at levels. Do you know what the lab 21 detection limit for those constituents were? 22 A. Which constituents? 23 Q. Well, you told us that for ammonia -- I'm 24 afraid I forget the other you pointed out -- DEPOSITION OF WILLIAM W. WALKER, JR. 859 1 you recalled reports below detection limit -- 2 A. Right. 3 Q. -- for those two constituents. And all the 4 others you see as being reported at 5 quantifiable values. 6 A. Correct. 7 Q. Do you know at what level the lab felt they 8 could detect those values for those other 9 constituents? 10 A. I'm still unclear as to what you mean by "other 11 constituents." 12 Q. Among the 20 listed in Table 1 that you 13 analyzed in Exhibit 17. I guess my point is 14 quite simple, Dr. Walker. I asked you if you 15 were aware of changes in detection limits among 16 the constituents other than total and ortho 17 phosphorus, and what you have told me is that 18 you saw these other constituents reported above 19 detection. 20 The fact that they are reported above 21 doesn't tell us what the detection limits were, 22 does it? 23 A. That's correct. 24 Q. Okay. It doesn't tell us whether there were DEPOSITION OF WILLIAM W. WALKER, JR. 860 1 changes of detection limit? 2 A. It tells us if there were detection limits, 3 they were not such that they would be greater 4 than the -- that the new detection limits would 5 not be greater than any value which is reported 6 as quantified in the database. 7 Q. Prior to 1981 were there any values for total 8 or ortho phosphorus reported between .002 and 9 .004? 10 A. There may have been. I don't recall. 11 Q. What was the accurate detection limit for total 12 and ortho phosphorus prior to 1981? 13 MR. HARRISON: Object to form. There's 14 been no predicate laid. 15 A. I don't know what you mean by "accurate." 16 Q. If in 1979 a value for total phosphorus, the 17 .003, was reported, was that value below 18 detection limit? 19 A. If it was reported in the database as a numeric 20 value without a -- an accompanying indicator 21 that would indicate that it was below detection 22 limits such as the less-than sign or K symbol 23 -- I don't recall what the symbol was that the 24 District used in their data sets. But if it DEPOSITION OF WILLIAM W. WALKER, JR. 861 1 was reported as a numeric value, then it was 2 assumed to be above the -- above or equal to 3 the detection limit that was present in the 4 laboratory at that particular time. 5 Q. With the instrumentation available in 1979, 6 what was the lowest detection limit possible 7 for total phosphorus? 8 A. The detection limit reported by the District 9 which reflected the instrumentation that they 10 had at that particular time in their laboratory 11 proceedures was .002 milligrams per liter. 12 Q. Are you familiar with the instrumentation that 13 was generally available for water quality 14 analyses in 1979? 15 MR. HARRISON: Object to form. 16 A. I am aware that there was instrumentation 17 available that was capable of analyzing total 18 phosphorus concentrations to within a detection 19 limit of .002 to .004 milligrams per liter. 20 But in terms of the specific hardware, I 21 couldn't give you any details on that. 22 Q. How about with respect to instrumentation 23 available presently for total phosphorus 24 analysis? DEPOSITION OF WILLIAM W. WALKER, JR. 862 1 A. There may have been some improvements in the 2 instrumentation over time that might have made 3 it possible to detect total phosphorus to lower 4 values, but again I cannot give you the details 5 on the specific hardware involved or the 6 technology. 7 Q. In the other constituents where you said you 8 did see values reported below detection, did 9 you employ the same procedure with regard to 10 those constituents of setting the values equal 11 to detection limit minus a small concentration 12 increment? 13 A. To my recollection, yes, I did. 14 Q. What specific detection limits did you use for 15 these other constituents? 16 A. I don't recall. 17 Q. Do you recall the source of the detection limit 18 which you did use? 19 A. It would have been derived by reviewing the 20 data file and essentially identifying the 21 largest numeric value that was reported as less 22 than the detection limit. 23 Q. You adopted that as the lab detection limit? 24 A. For the purpose of adjusting the data to DEPOSITION OF WILLIAM W. WALKER, JR. 863 1 account for values below detection limit, yes. 2 Q. Just to make sure I'm clear, that's not the 3 source of the .002 and .004 detection limit 4 used for total and ortho phosphorus, correct? 5 A. Yes, it was the same procedure that I used for 6 total and ortho phosphorus. 7 Q. You just derived that by reviewing the data? 8 A. Correct. 9 Q. From that review of the data, you were able to 10 determine that the detection limit changed in 11 1981? 12 A. Yes. 13 Q. Did you have any other source of information on 14 that? 15 A. Well, it may have been discussed in the ONRW 16 meetings. I don't recall for sure. 17 Q. Are there alternative methods for adjusting 18 values reported below detection limits for use 19 in the Seasonal Kendall test other than the 20 method you used here, setting it equal to a 21 detection limit minus a small concentration 22 increment? 23 MR. HARRISON: Did you just say, 24 Counsel, are there other methods or -- DEPOSITION OF WILLIAM W. WALKER, JR. 864 1 MS. AHEARN: Are there alternatives -- 2 A. One could conceive of other procedures. A 3 procedure that I have used is the procedure 4 that was recommended in one or more of the 5 papers by Hirsch and Slack on the Seasonal 6 Kendall test. 7 Q. If I could direct your attention a little 8 farther down in this middle paragraph on 9 page 6, Exhibit 17, there is a sentence that 10 starts "Phosphorus time series have been 11 adjusted..." Could you read that sentence and 12 tell me if it is accurate? 13 A. Phosphorus time series have been 14 adjusted to a uniform detection limit of 15 .004 mg/liter by setting each value 16 equal to the minimum of the reported 17 value and .004 mg/liter. 18 I believe there is an error in that 19 equation -- in that sentence. The term 20 "minimum" should be replaced by the term 21 "maximum." That was a grammatical error on my 22 part. 23 Q. If the trend you see in phosphorus 24 concentrations in Park inflows is attributable DEPOSITION OF WILLIAM W. WALKER, JR. 865 1 to the discharge of agricultural waters, what 2 trends would you expect to see in other 3 constituents that you have analyzed in 4 Exhibit 17? 5 MR. HARRISON: I'm going to object to 6 form. Counsel, does your question assume that 7 the trends are solely due to the discharge of 8 agricultural water without any of these other 9 variables? If that is your assumption, I will 10 object to the assumption since the assumption 11 has no basis in evidence in this deposition. 12 But I want the hypothetical cleared up. 13 A. I believe yesterday I testified to my 14 preliminary conclusions regarding possible 15 causes of these apparent trends, and increases 16 in loadings from the watershed -- watersheds of 17 the Water Conservation Areas was indicated as 18 being one of the likely causes, among others. 19 Other -- if one were to take your 20 hypothetical and if it is based on the 21 assumption that it is agriculture runoff that 22 is the causal factor or contributing to these 23 loads, one might be concerned about potential 24 trends in other substances that are also found DEPOSITION OF WILLIAM W. WALKER, JR. 866 1 in agricultural runoff. 2 Q. Which would be those substances? 3 A. Well, agricultural runoff would contain a wide 4 range of substances, including nutrients, 5 inorganic species, pesticides, heavy metals. 6 Q. If a trend in phosphorus was attributable to 7 agricultural runoff, would you expect to see 8 corollary trends in other conservative 9 constituents such as chlorides? 10 A. Not necessarily. 11 Q. Are there any constituents other than ortho 12 phosphorus and the nitrogen species in which 13 you would expect to see corollary trends if the 14 trend in total phosphorus concentrations was 15 caused by agricultural runoff? 16 A. Well, I would be concerned about things such as 17 pesticides. 18 Q. And you have not conducted a trend analysis on 19 pesticides, correct? 20 A. To my knowledge, there's not an adequate 21 database to perform such an analysis. 22 Q. Okay. Any other constituents? 23 (The witness gave no response.) 24 Q. How about ions and cations? DEPOSITION OF WILLIAM W. WALKER, JR. 867 1 A. Well, ions and cations are part of the natural 2 system. They are contained in rainfall, and 3 they are contained in natural drainage. They 4 wouldn't necessarily be exclusively earmarks 5 for agricultural runoff. 6 Q. Could they be earmarks for agricultural runoff? 7 MR. HARRISON: Object to form. 8 A. I said they wouldn't necessarily be earmarks 9 for agricultural runoff. 10 Q. Have you looked for any earmarks for 11 agricultural runoff in the work you have done? 12 A. I have analyzed the data for 12 water quality 13 components for trends at the Park inflow 14 points. 15 Q. Twelve or twenty? 16 A. Excuse me. Twenty. 17 Q. Even apart from this trend analysis, has the 18 work you performed on South Florida water 19 quality issues included any investigation of 20 what constituents might be earmarks for 21 agricultural runoff? 22 A. No. 23 Q. Page 9. We're really moving. 24 For the purposes of the record, DEPOSITION OF WILLIAM W. WALKER, JR. 868 1 Dr. Walker, could you, please, define the term 2 "robust" as you use it, for example, here in 3 the paragraph at the top of page 9, Exhibit 17? 4 A. I used the term "robust" in page 9 in reference 5 to the Seasonal Kendall slope. What I mean 6 when I say that the estimate of the Seasonal 7 Kendall slope is robust is that it is more 8 likely to reflect the underlying distribution 9 of the bulk of the data than to be -- than to 10 reflect a few data points at the extremes of 11 the data and it is less likely to be sensitive 12 to outliers or other unrepresentative samples. 13 Q. I'd like to refer you to page 3 in Exhibit 7, 14 which is your July 3 draft. 15 You can see in the mid paragraph there 16 under the heading "Methods," the last sentence 17 there in Exhibit 7 does not appear in the 18 comparable text in Exhibit 17. Can you explain 19 that difference? 20 A. You're referring essentially to the omission of 21 one sentence, is that -- 22 Q. In Exhibit 17, page 3, middle paragraph, 23 there's a sentence. 24 MR. HARRISON: Exhibit 7, I think, DEPOSITION OF WILLIAM W. WALKER, JR. 869 1 Counsel. 2 MS. AHEARN: Thank you. 3 Q. Exhibit 7, page 3, middle paragraph, the last 4 sentence starts, "Another advantage is that..." 5 That sentence largely does not appear in 6 Exhibit 17 and, if you can, can you explain why 7 this was changed? 8 A. I don't recall specifically. It may have been 9 in response to one of the reviewers' comments. 10 I don't view it as a particularly important 11 statement. 12 Q. The statement as it appears in Exhibit 7? 13 A. Right. 14 Q. Again with reference to Exhibit 7, page 3, the 15 bottom paragraph, midway in the body of that 16 paragraph is a sentence starting, "Loftis et 17 al..." 18 Is there a reason why that does not 19 appear in Exhibit 17? 20 A. Well, the statement that you're referring to, I 21 believe, is: 22 Loftis et al. (1989) cautioned 23 against using the second test because of 24 its relatively low power (ability to DEPOSITION OF WILLIAM W. WALKER, JR. 870 1 detect trends); they felt that 2 "reduction in power was too high a 3 price to pay for insensitivity to serial 4 correlation." 5 That statement was derived from -- I 6 derived that statement from the report by 7 Loftis et al. And I believe one of the other 8 reviewers of my report, I think it was Helsel 9 -- Helsel and Slack who together put together a 10 review of my report, took issue with that 11 statement. They disagreed with that statement 12 and they felt it was Loftis' opinion and they 13 disagreed with it. So I decided that it was 14 not an essential statement as far as I was 15 concerned to the report, so I took it out at 16 the suggestion of the reviewers. 17 Q. Well, you included the statement from Loftis in 18 your draft. Do you agree with Loftis? 19 A. I agree in the sense that if you're using the 20 second version of the Seasonal Kendall test 21 which accounts for serial correlation, you are 22 paying a price in that you are being very 23 conservative; you are trying to account for 24 serial correlation, and you're running the risk DEPOSITION OF WILLIAM W. WALKER, JR. 871 1 of not detecting trends. You are reducing the 2 power of the test. But on the other hand, you 3 are accounting for a real phenomenon -- that 4 is, serial correlation. 5 There are trade-offs involved here. And 6 essentially the decision that I have made in 7 conducting the analysis was in fact to use this 8 more conservative test that accounts for serial 9 correlation even though it may have a chance of 10 failing to detect trends, it may miss trends at 11 some frequency, because I'm trying to account 12 for serial correlation. 13 Q. With a database such that you're using in 14 Exhibit 17, do Helsel and Slack agree that this 15 second version of the Seasonal Kendall test has 16 a reduction in power? 17 (Pause) 18 Q. Do you feel you need to refer to the written 19 comments in order to answer that? 20 A. I'm just looking at one of the previous 21 exhibits for a second. 22 Q. And you're referring to which exhibit number? 23 A. I'm referring to Exhibit No. 37. 24 Q. Thank you. DEPOSITION OF WILLIAM W. WALKER, JR. 872 1 A. Exhibit No. 37 is the paper by Hirsch and Slack 2 entitled "A Nonparametric Trend Test for 3 Seasonal Data With Serial Dependence." 4 Figure 2 of that paper on page 730 shows the 5 results of power tests that were done in order 6 to compare essentially the power of the test 7 when serial correlation was considered as 8 compared with the power of the test when it was 9 ignored. 10 And those results do show that for a 11 series of ten years' worth of data, that the 12 percent of the time that trends -- that a trend 13 was detected was indeed lower when the test 14 accounted for serial correlation. That's for 15 the ten-year time series. 16 Other tests -- other simulations that 17 are described in this same paper show that the 18 power of the test and the Type 1 error is -- 19 other simulations described in this paper show 20 that for time series less than ten years in 21 length, the procedure underestimates the -- the 22 procedure has a Type 1 error rate that is below 23 the nominal Type 1 error rate for time series 24 less than ten years in length. DEPOSITION OF WILLIAM W. WALKER, JR. 873 1 Q. What about time series 12 years in length? 2 A. They consider the case of ten years in their 3 simulations and show that the test closely 4 approximates the nominal Type 1 error rate for 5 that condition. 6 Q. Have Hirsch and Slack or others addressed the 7 power of the test using a 12-year time series? 8 A. They considered five-, ten- and twenty-year 9 time series, and they recommend that the test 10 for periods of ten years or more, that the test 11 involving -- including serial correlation is 12 appropriate. 13 Q. In other words, it has adequate power to -- 14 A. It may -- there may be some loss of power that 15 is associated with using this test which is a 16 more conservative test than the test that is -- 17 that does not account for serial correlation, 18 but it has a more accurate representation of 19 the Type 1 error. 20 Q. When we talk about serial correlation here, 21 what does that mean? 22 A. We are talking about the tendency for the 23 values to be -- to occur not as random values 24 over time but to be correlated from one season DEPOSITION OF WILLIAM W. WALKER, JR. 874 1 to the next. 2 Q. So that the serial correlation accounted for in 3 the modified Kendall test accounts for seasonal 4 serial correlation? 5 A. It accounts for serial correlation in the 6 values after the seasonal effects -- fixed 7 seasonal effects have been removed from the 8 data. 9 Q. Does it account for any serial correlation as 10 between years? 11 A. I believe that we discussed that previously. 12 The test does not account for serial 13 correlation from one year to the next. 14 Q. I apologize, but I'm learning. I want to make 15 sure I keep this straight. 16 What kind of correlation structure did 17 Hirsch and Slack use in simulating and testing 18 the power of their modified test? 19 MR. HARRISON: You mean in their own 20 report, Counsel, or in their review of 21 Dr. Walker's report? 22 Q. Has Hirsch prepared a review of your report, 23 Dr. Walker? 24 A. Dr. Slack has, yes. DEPOSITION OF WILLIAM W. WALKER, JR. 875 1 Q. Has Dr. Hirsch? 2 A. Not to my knowledge. 3 Q. Okay. You told us about simulations performed 4 of the modified Kendall test for five-, ten- 5 and twenty-year time series -- 6 A. Correct. 7 Q. -- by Hirsch and Slack? 8 A. Correct. 9 Q. What kind of correlation structures were they 10 using for those simulations? 11 A. They used a range of correlation structures 12 that are essentially defined as autoregressive 13 moving average models, ARMA models, and they 14 used a range of coefficients to reflect 15 different levels of autoregressive and moving 16 average dependence in the time series. 17 Q. By "models," does this mean that these are 18 artificially constructed correlation 19 structures? 20 A. These are correlation structures which have 21 been found to be representative of and typical 22 of water quality time series that have been 23 studied and analyzed with -- using these time 24 series techniques. DEPOSITION OF WILLIAM W. WALKER, JR. 876 1 Q. Do you know how representative they are of the 2 correlation structure of the water quality 3 database utilized in Exhibit 17? 4 A. As described in 17, for example, on page 18 I 5 report values for what is called RA, which is 6 the first-order serial correlation coefficient 7 of the values. 8 Also, in Appendix A for each test result 9 I list the serial correlation coefficient for 10 each of the time series or each of the -- for 11 each set of tests that are documented in 12 Appendix A. 13 Q. Is the correlation structure of the water 14 quality data collected from the real world 15 utilized in Exhibit 17 accurately represented 16 by the correlation structures of the models 17 employed by Hirsch and Slack? 18 A. The cases considered by Hirsch and Slack were 19 designed to reflect a wide range of water 20 quality time series that they have examined in 21 their studies. I have not precisely fit these 22 types of time series models to the water 23 quality data that I analyzed for trend, but I 24 have characterized the serial correlation DEPOSITION OF WILLIAM W. WALKER, JR. 877 1 structure as I mentioned with this term RA that 2 is documented in the report. 3 And the other factor that's important is 4 that -- the reason that we are concerned about 5 this serial correlation structure is because we 6 -- one limitation or one assumption of the test 7 is that there's no serial correlation in the 8 data from one year to the next other than 9 whatever serial correlation would be reflected 10 in a trend. And I have characterized that 11 possibility or evaluated that possibility by 12 calculating the serial correlation coefficients 13 from one year to the next within each season, 14 and these are documented on page 18, Table 2, 15 under -- again, under this column RA for each 16 month. 17 The magnitudes of those correlation 18 coefficients are generally low and not in a 19 range where I would be concerned about serial 20 correlation from one year to the next or in a 21 range where I would be concerned about the 22 applicability of the test. 23 Q. Your RA values are calculated based on years, 24 correct? DEPOSITION OF WILLIAM W. WALKER, JR. 878 1 A. The RA value reported for a particular month 2 would be the serial correlation coefficient for 3 the values that are one year apart collected 4 within each month. 5 Q. And that would be a first order of correlation 6 structure? 7 A. That's correct. 8 Q. Did you look at any other correlation 9 structures in this database? 10 A. Since the first-order correlation structure for 11 the values one year apart are generally 12 insignificant, there would be no point in going 13 further in -- the difficulty that we have here 14 is that in order to quantify and define a 15 serial correlation structure from one year to 16 the next, it would be very hard to do with only 17 12 years' worth of data. 18 Q. Is it a limitation of the size of the database 19 that precludes looking at other correlation 20 structures in the database employed? 21 A. In terms of looking at whether higher order 22 terms -- whether there's any high-order serial 23 correlation structure in the values that are 24 spaced one year apart, it would be difficult to DEPOSITION OF WILLIAM W. WALKER, JR. 879 1 identify those -- such terms with -- with only 2 12 years' worth of data. But the data that I 3 do have indicates that the serial correlation 4 coefficients from one year to the next are low 5 and are not in a range where the applicability 6 of the test should be an issue. 7 Q. On Table 2 of Exhibit 17 under your category 8 for RA values, for example, for the first 9 series there, the RA reported for Year* is 10 0.71. Could you, please, explain to me how that 11 was calculated? 12 A. That was calculated by -- starting from the raw 13 data, assigning the value to years and season 14 so that we have one value for each year and 15 season, performing the Seasonal Kendall test, 16 estimating the significance level of the 17 Seasonal Kendall test and estimating the trend 18 slope using the Seasonal Kendall slope 19 estimator, and subtracting from the seasonal 20 values the effect of the long-term trend using 21 that trend slope; so essentially removing the 22 trend from the seasonal values and subsequently 23 calculating the first-order serial correlation 24 coefficient of the remaining values. DEPOSITION OF WILLIAM W. WALKER, JR. 880 1 Q. So you basically took a residual as against the 2 estimated Kendall slope? 3 A. That's correct. 4 Q. Let me ask you one question I missed along the 5 way, then I propose we take a break. 6 We were talking about the method you 7 used for deriving detection limits by reviewing 8 the values recorded from the lab. Would that 9 method allow you to detect a change in 10 detection limit at the time the detection limit 11 is changed by the lab? 12 A. The change in detection limit would be revealed 13 by the first observation in the data set that 14 would have an altered detection limit prior to 15 the -- compared to the prior part of the 16 record. 17 Q. So your answer is yes, it would allow you to 18 detect that change when it's made? 19 A. Only in terms of -- with -- only with respect 20 to the frame of reference of the sampling 21 dates. It can't tell you on what particular 22 date between sampling dates a change might have 23 occurred, and it can't tell you at what 24 particular date between sampling dates that DEPOSITION OF WILLIAM W. WALKER, JR. 881 1 contain values above the detection limit. In 2 other words, the first -- the change in the 3 detection limit would be triggered by the first 4 change in the value reported as below a new 5 detection limit that had not occurred in the 6 previous part of the record. 7 MS. AHEARN: Time for a break. 8 (Short recess) 9 10 BY MS. AHEARN: 11 Q. Referring back to your RA values on Table 2, 12 Exhibit 17, Table 2 is on page 18 of that 13 exhibit. 14 For the RA value under Series A Year*, 15 is this 0.71 a month-to-month serial 16 correlation over the 12-year period? 17 MR. HARRISON: Before we go too far, is 18 Rick Burgess -- 19 MR. DAVIS: You can go ahead. 20 MR. HARRISON: Okay. I didn't know if 21 he was missing. 22 A. Yes, with the trend removed. 23 Q. Is the procedure you used here deriving this 24 first order of serial correlation a procedure DEPOSITION OF WILLIAM W. WALKER, JR. 882 1 commonly used in conjunction with the modified 2 Seasonal Kendall test? 3 MR. HARRISON: Object to form. 4 A. It's a common procedure for calculating a 5 serial correlation coefficient. 6 Q. So this procedure is a common statistical 7 procedure? 8 A. The concept of a serial correlation coefficient 9 and its calculation, yes, is a common 10 statistical procedure. 11 Q. Are you aware of any precedents for using this 12 common statistical procedure as you have 13 employed it here in conjunction with the 14 modified Seasonal Kendall test? 15 A. I'm using it here to quantify serial 16 correlation between years and between adjacent 17 months because that serial correlation bears on 18 the accuracy of the test. 19 Q. In the literature concerning the development 20 and testing of the Seasonal Kendall test, can 21 you point me to any discussions advising on the 22 use of this additional first-order serial 23 correlation? 24 A. I believe there was some discussion of that in DEPOSITION OF WILLIAM W. WALKER, JR. 883 1 the paper by Berryman et al. in the references 2 that I supplied to the District. 3 Q. Are you aware of any applications of the 4 seasonal order of serial correlation method in 5 conjunction with the modified Seasonal Kendall 6 test to databases derived from actual 7 monitoring of other water systems? 8 A. The paper that I mentioned by Berryman may have 9 had some examples in it and some discussion of 10 applications. I don't recall. 11 Q. Table 2 in Exhibit 17 refers to S12T total 12 phosphorus data. Did you perform similar 13 first-order serial correlation calculations 14 with regard to individual S12 structures? 15 A. Yes. 16 Q. And with regard to S333 and S18? 17 A. Yes. 18 Q. Did you perform similar calculations with 19 respect to the other 19 water quality 20 constituents subject to your analysis? 21 A. Yes. 22 Q. Did you perform adjustments of your PROB2 23 values after you calculated the RA values? 24 A. Only as described in the text. DEPOSITION OF WILLIAM W. WALKER, JR. 884 1 Q. And that would be at the top of page 19, the 2 first paragraph there? 3 A. No. 4 Q. I'm sorry. Could you point to me where that's 5 described in the text? 6 A. It would be the second paragraph on page 19. 7 Q. I'm sorry. I misspoke. Thank you. 8 Did you adjust PROB2 values for any 9 constituent other than total phosphorus? 10 A. No. As I stated, the only adjustments that I 11 made are described in that paragraph. 12 Q. I just wanted to make sure I was clear. I 13 don't see where this paragraph specifically is 14 limited to total phosphorus. It is limited 15 specifically to total phosphorus? 16 A. Only in the case of total phosphorus did I go 17 to the trouble of making those adjustments. 18 Q. Our review of the text left off on page 9. I'm 19 really not backing up. We'll go quickly. 20 MR. HARRISON: Two steps forward and 21 four back. Okay. 22 Q. In selecting to transform your Series A and B 23 data to log scale, was that one of the 24 decisions you made during your interactive DEPOSITION OF WILLIAM W. WALKER, JR. 885 1 sessions on the computer? 2 A. The reasons why I used the logtransform are 3 described on page 10. 4 Q. Dr. Walker, this may just be a point of 5 clarification, but we talked about your 6 interactive session on the computer. Was this 7 one of the decisions which you investigated 8 during that session? 9 A. It would be very hard to separate what I 10 learned and the impressions that I got from the 11 interactive sessions with the computer and to 12 identify specifically whether that experience 13 influenced this particular decision. 14 Q. Do you recall if you investigated 15 transformations other than the log10? 16 A. Well, as is stated in the text, the reason for 17 using the log10 was to permit expression of the 18 units of the trend in terms of percent per 19 year, which was a convenient way and less 20 awkward way than expressing it in terms of 21 milligram per liter per year or whatever. 22 Also, the important factor is that the 23 results of the analysis in terms of the 24 significance levels and the probability of a DEPOSITION OF WILLIAM W. WALKER, JR. 886 1 trend or no trend are independent of this log 2 transformation because the procedure -- the 3 Seasonal Kendall test is based upon rankings of 4 the data. 5 Q. Okay. Did you consider any other 6 transformations? 7 A. No, I did not. 8 Q. In Series C why did you limit your samples to 9 samples collected on days with positive flow as 10 opposed to using the Series A basic data? 11 A. The samples collected on days when there was 12 positive flow reflect the concentrations and 13 loadings of materials actually entering the 14 Park on a particular sample day, and they would 15 have, I would think, greater importance in 16 terms of evaluating trends in concentrations 17 and loadings entering the Park as compared with 18 Series A including the data points when there 19 was no flow. The interpretation of those 20 particular data with respect to impact on the 21 Park is difficult because the water was not 22 moving or at least not moving into the Park. 23 Q. But the two hydrologic variables you're looking 24 at here occur outside the Park, correct? DEPOSITION OF WILLIAM W. WALKER, JR. 887 1 A. That's correct. They reflect conditions in 2 Water Conservation Area 3A, which is the 3 immediate source of water entering the Park in 4 Shark slough. 5 Q. Could I have you refer to your Equation 1 as it 6 appears in Exhibit 7, page 4, and compare that 7 with Equation 1 on page 10 of Exhibit 17? 8 Are there any changes in this equation 9 other than those that reflect the change in 10 hydrologic variables that you used? 11 A. Yes. 12 Q. And what are those other changes? 13 A. In Exhibit 7, Equation 1, concentrations or the 14 logarithm of concentration is regressed against 15 the logarithm of flow and upstream water 16 elevation where the -- where both the flow and 17 the upstream water elevation were measured on 18 the same day that the sample for concentration 19 was collected. So there was no lagging of the 20 time factor for the hydrologic variables. 21 And in the case of Exhibit 17, the final 22 report, Equation 1, we are dealing here with -- 23 instead of flow and elevation, we're dealing 24 with rainfall and elevation. That's one DEPOSITION OF WILLIAM W. WALKER, JR. 888 1 difference. And the other difference is that 2 in this final version the antecedent periods or 3 the averaging periods for the hydrologic 4 factors, rainfall and water elevation, are 5 adjusted. They are selected by the computer 6 using stepwise regression to find the time 7 scale of rainfall -- in other words, the number 8 of days of antecedent rain or the average -- 9 the number of days of averaging the antecedent 10 water elevation, which provides the highest 11 degree of correlation with concentration. And 12 those lag periods and factors are subsequently 13 used in the regression equation. 14 Q. With reference to Exhibit 7, I believe you just 15 said that you relate concentration to the 16 elevation measured on the day of the sample; is 17 that correct? 18 A. In Exhibit 7, correct. 19 Q. In the text that starts right under the 20 expression of the equation, the elevation term 21 reflects the average water surface elevation. 22 What is that average? 23 A. That average is a daily average. It's a daily 24 average over the -- over the day at which the DEPOSITION OF WILLIAM W. WALKER, JR. 889 1 sample was collected, not a spatial average. It 2 is actually the -- the water elevation measured 3 upstream of S12C. That sentence is somewhat 4 misleading. 5 Q. So in the analysis performed for the July 3 6 draft, you were using just the one gauge 7 upstream, the 12 -- 8 A. S12C, the only gauge with a consistent record 9 over the entire period, correct. 10 Q. And is this average recording of -- of -- 11 excuse me. Is this average the average of all 12 levels recorded from midnight to midnight on 13 the particular calendar date of a given sample? 14 A. Typically, when one deploys a stage recorder in 15 the field, the stage measurements are recorded 16 at certain time intervals. And there would be 17 some averaging process that would occur to 18 calculate the 24-hour average. 19 In other situations the water elevation 20 may be just recorded at one particular time if 21 it's done manually. I believe that these 22 measurements are made automatically and, 23 therefore, would reflect an average of a number 24 of measurements made over the day. DEPOSITION OF WILLIAM W. WALKER, JR. 890 1 Q. Were these numbers reported to you as averages? 2 A. They were reported -- they were categorized in 3 the District's water quality database as 4 average daily values, to my recollection. 5 Q. So these aren't averages that you computed from 6 raw gauge readings? 7 A. No. 8 Q. Okay. Had you performed the stepwise multiple 9 regression for optimal values by the time you 10 had prepared the July 3 draft, Exhibit 7? 11 (The witness gave no response.) 12 Q. I mean, I recognize you've told us you had a 13 commitment to produce this document. I'm just 14 wondering, had you done the computer work, 15 performed the multiple regression, prior to 16 this time? 17 A. Are you asking me whether I did the multiple 18 regression that is reflected in Equation 1 of 19 Exhibit 17 before I wrote the first draft of 20 the report in July? 21 Q. Okay. That would be a good question. 22 A. No. 23 Q. Why did you subsequently decide to perform the 24 multiple regression? DEPOSITION OF WILLIAM W. WALKER, JR. 891 1 A. Well, both of these equations that I have used 2 are multiple regressions. 3 Q. Let me ask my question more clearly. 4 Why didn't you select optimal values for 5 antecedent periods to employ in Equation 1 in 6 Exhibit 7? 7 MR. HARRISON: Object to form. 8 A. The concept of using variable antecedent 9 periods, which is the distinction we're making 10 here between these two drafts, I felt was 11 especially important when we brought in the 12 concept of using antecedent rainfall because 13 it's not obvious beforehand if one is trying to 14 correlate rainfall with concentration measured 15 at a certain time, there is no basis a priori 16 to specify the averaging period for the 17 rainfall. In other words, should I use the 18 rainfall on the sampling day? Should I use the 19 rainfall over the past week? Should I use the 20 rainfall over the past month? My answer to 21 those questions is I don't know. 22 So the way that I asked -- I get the 23 answer to that question is I do -- I set up the 24 programs so that they select -- they search for DEPOSITION OF WILLIAM W. WALKER, JR. 892 1 the antecedent periods, the lengths of time 2 that provide the highest degree of correlation 3 between concentration and antecedent rainfall 4 and between concentration and antecedent water 5 elevation, and use that to adjust the 6 concentrations for hydrologic variability in my 7 Series C. 8 Q. What do you look at -- what factor or value do 9 you look at to determine which antecedent 10 period provides the highest correlation, the 11 optimal correlation? 12 A. I used a stepwise regression routine. I 13 believe the criterion that was used to select 14 the ideal or the optimal time scale was either 15 based upon something such as R2 or the 16 significance level of the regression term. I 17 don't recall precisely. 18 Q. So you may have used the P values as the 19 criterion for selecting the antecedent period? 20 A. Possibly. 21 Q. But you're not sure? 22 A. The P values in the multiple regression. 23 Q. Would you be able at this point to explain the 24 algorithm that you used? Would you be able to DEPOSITION OF WILLIAM W. WALKER, JR. 893 1 explain that step by step? 2 A. In general terms. 3 Q. Okay. 4 A. The algorithm would involve starting with a 5 complete matrix or a table, if you will, where 6 each row would be a different sample, and for 7 each sample there would be a value for 8 concentration and there would be a value for 9 total antecedent rainfall over one day, seven 10 days, thirty days and so forth as indicated on 11 page 10. And there would also be a value for 12 antecedent water elevation averaged over one 13 day, seven days, thirty days, so forth. So 14 that would comprise a table. 15 I would then compute what is called a 16 correlation matrix or covariance matrix using 17 that table and starting with -- and then 18 address each hydrologic factor. Say if we 19 addressed rainfall, the program would search 20 for the rainfall term or the lag time one day, 21 seven days, thirty days, whatever, that was 22 most highly correlated with concentration and 23 include that in the regression equation. And 24 the next -- if -- it would be included in the DEPOSITION OF WILLIAM W. WALKER, JR. 894 1 regression equation only if the P level for 2 that term was less than .1 -- that is, if in 3 fact there was a significant correlation 4 between rainfall for any of the time scales and 5 concentration. 6 If that procedure resulted in inclusion 7 of a rainfall term, I would then adjust the 8 concentrations by removing the portion of the 9 variability that is correlated with the 10 rainfall term and then search each of the 11 elevation terms to find the time scale that was 12 most highly correlated with elevation -- with 13 concentration. And from that exercise, I would 14 end up with an equation that had one term for 15 rainfall and one term for water elevation that 16 was correlated with concentration. 17 I tried alternative techniques as part 18 of the sensitivity analysis for fitting these 19 regression equations and found them to lead to 20 similar results in terms of the overall 21 significance level of the trend at S12s. 22 Q. Did you use what Snedecor and Cochran would 23 term a step-up procedure? 24 A. I used a stepwise regression equation. I guess DEPOSITION OF WILLIAM W. WALKER, JR. 895 1 it would be termed a step-up, that's correct, 2 as opposed to a step-down. 3 Q. How many degrees of freedom did you lose when 4 you decided to use the log10 transformation? 5 A. For what purpose? 6 Q. You're asking me for what purpose you decided 7 to use the logarithmic transformation? 8 A. What are you referring to? When I used the 9 log -- you say when I used the log10 10 transformation. I used it in several instances 11 here. 12 Q. When you decided to use the log10 13 transformation for your Series A, B and C data, 14 how many degrees of freedom for application of 15 the Seasonal Kendall test did you lose? 16 MR. HARRISON: Objection, Counsel. For 17 all three combined, all three series? I just 18 want the witness to specify what his answer is 19 relating to, if he is capable of doing that 20 with that question. 21 A. In the case of Series A, B or C, I would not 22 interpret use of log10 transformation as loss 23 of any degrees of freedom. 24 Q. Some of the structures subject to your analysis DEPOSITION OF WILLIAM W. WALKER, JR. 896 1 in Exhibit 17 are pumped structures, aren't 2 they? 3 A. I believe that S332 has a pump. I think 18C 4 may have a pump. I don't recall exactly. 5 Q. Are there any adjustments or special 6 statistical procedures that you should employ 7 to reflect the different nature of pumped 8 structures? 9 A. The flow values -- the daily flow values that I 10 have used for each of the structures would 11 reflect the combined flow through the pump plus 12 whatever might have occurred over a spillway if 13 such a structure existed at the particular 14 monitoring station. Other than reflecting the 15 total flow or the total volume released into 16 the Park on a particular day, there was nothing 17 special that needed to be done to account for 18 pumped flow as compared with released flow or 19 spilled flow. 20 Q. In terms of the factors that may impact a trend 21 in total phosphorus concentrations, are there 22 differences between pumped structures and those 23 structures that are not pumped? 24 MR. HARRISON: Object to form. DEPOSITION OF WILLIAM W. WALKER, JR. 897 1 "Factors" is just too general. Go ahead. 2 A. The problem in your question is that when you 3 say "structures that are not pumped," that 4 could include a wide range of different type of 5 structures that could very well have some 6 distinction with pumped structures. So I can't 7 answer your question. It's way too general. 8 Q. I guess Mr. Harrison's right. 9 Are there any particular factors or 10 features of which you are aware with regard to 11 the impact of a pumped structure on total 12 phosphorus concentrations? 13 MR. HARRISON: Object to form. 14 A. Again, you would have to compare it to some 15 other scenario. 16 Q. Are you aware of any factors with regard to the 17 pumped structures you looked at compared to the 18 other structures that you looked at that didn't 19 have pumps? 20 MR. HARRISON: I object to form. Do you 21 have any of these factors in mind that you 22 might give him some specific guidance as to 23 what you're looking for? 24 MS. AHEARN: I'm wondering if the doctor DEPOSITION OF WILLIAM W. WALKER, JR. 898 1 looked at this issue and if he identified any 2 structures that distinguished the pumped 3 structures from all other structures. 4 A. There is nothing special about the existence of 5 a pump, but there may be some distinguishing 6 characteristics between those structures with 7 pumps and those structures without pumps. 8 Q. Did you identify any such distinguishing 9 features? 10 A. Well, in the case of S332 and S18C the flow 11 releases into the Park are made from 12 essentially canal environments, canal systems, 13 and that is a different situation as compared 14 with releases through the S12s, where flow is 15 essentially released from a reservoir upstream 16 from Water Conservation Area 3A. 17 Q. Have you identified any other distinguishing 18 features? 19 A. Well, there are certainly geographic 20 differences and differences in watersheds. 21 Q. Any other distinguishing features which relate 22 to total phosphorus concentrations? 23 A. The sources of the water at the individual 24 structures would be different. There's lots of DEPOSITION OF WILLIAM W. WALKER, JR. 899 1 distinctions from one structure to another. 2 That's my answer. 3 Q. Dr. Walker, have you performed any tests for 4 trend within the hydrologic variables you have 5 employed in Series C, both your Exhibit 7 and 6 your Exhibit 17 versions? 7 A. You're asking me if I tested for trends in the 8 hydrologic variables themselves? 9 Q. Yes. 10 A. Not to my recollection. 11 Q. If you could, please, turn to page 5 in 12 Exhibit 7. There is an Equation 2 expressed 13 mid page and then a paragraph of text under 14 that. Could you, please, read the last 15 sentence in that paragraph? It starts with 16 "More detailed analyses..." Could you read it 17 aloud, please? 18 A. More detailed analyses would be 19 needed to distinguish among alternative 20 trend shapes and to investigate causal 21 factors for those time series with 22 significant apparent trends. 23 Q. Today do you still agree with that statement? 24 MR. HARRISON: I would caution the DEPOSITION OF WILLIAM W. WALKER, JR. 900 1 witness to ensure that he is comfortable with 2 the context of that statement in Exhibit 7. If 3 he feels the need to read the paragraph, fine. 4 MS. AHEARN: Please, Mr. Harrison. 5 That's a lot of coaching. 6 MR. HARRISON: It's not coaching. I'm 7 not going to let you ask him whether he agrees 8 with a sentence, Counsel, taken out of context 9 if it is out of context. I'm simply cautioning 10 the witness to look at the entire paragraph 11 that it's contained in, which is something that 12 you should have certainly offered in your 13 question. There is no coaching here at all, 14 Counsel. I don't know enough to coach the 15 witness on it. 16 MS. AHEARN: If there's a context, 17 Exhibit 7 clearly provides it. 18 MR. HARRISON: It certainly does. 19 A. Well, as is stated in the sentence above the 20 one that I just read: 21 The basic objective is to determine 22 whether the underlying frequency 23 distribution of concentration (or 24 concentration at a given flow and DEPOSITION OF WILLIAM W. WALKER, JR. 901 1 upstream surface water elevation) is 2 stable over the time period examined. 3 Q. Do you agree with the sentence that follows 4 that? 5 A. I agree that the work that has been completed 6 to date is sufficient for defining the 7 existence of trends in concentration and 8 loading at various -- under various hydrologic 9 conditions at these locations. 10 Q. Is it tough to distinguish among alternative 11 trend shapes? 12 A. The -- as is stated in this sentence and as is 13 also stated in Exhibit 17, the method that I 14 have used does not distinguish among 15 alternative trend shapes. 16 Q. Is it sufficient to investigate causal factors? 17 A. As we discussed yesterday or last week, the 18 analysis provides information on trends. It 19 provides descriptions of correlations that can 20 be used and interpreted that can -- that can be 21 helpful for formulating opinions regarding 22 causation in the system. But the trend 23 analysis itself does not quantify the causal 24 factors. DEPOSITION OF WILLIAM W. WALKER, JR. 902 1 Q. Why was this sentence in Exhibit 7 dropped from 2 Exhibit 17? 3 A. Because I view the investigation of the causes 4 and the delineation of the causes as a separate 5 task, as a more involved task, as compared with 6 the identification of the existence of the 7 trends. 8 Q. If you would turn to page 6 in Exhibit 7, the 9 last line of the first full paragraph on that 10 page, why was that sentence dropped from 11 Exhibit 17? 12 MR. HARRISON: I'm going to object to 13 your characterization. I don't doubt that it 14 was, but I think it's more preferable to ask 15 the witness if it was. And I would just 16 caution the witness to ensure that it was 17 dropped prior to answering that question. We 18 have had no testimony on that yet. 19 MS. AHEARN: But we do have the two 20 versions of the document identified by the 21 witness. 22 MR. HARRISON: Which will speak for 23 themselves, Counsel. I mean, if you don't want 24 the documents to speak for themselves, I'm DEPOSITION OF WILLIAM W. WALKER, JR. 903 1 simply asking you the courtesy of asking him 2 the question to lay a foundation as to whether 3 or not it was dropped. It is certainly 4 conceivable that you could have missed 5 something. 6 A. I can't give a particular reason why that 7 sentence was dropped. It was apparently an 8 editorial decision on my part. 9 Q. Did you employ any analyses using a 10 significance level of .05? 11 A. I -- there was nothing specific to any of this 12 regarding assumptions on significance levels. 13 The results are reported in terms of the P 14 levels, and one can apply whatever -- whatever 15 criterion one wishes in terms of distinguishing 16 between the presence of trend and the absence 17 of trend. 18 As described in both exhibits, a 19 two-tailed hypothesis -- that is, a hypothesis 20 of no trend -- I have used the value of .1 just 21 for convenience purposes just to summarize and 22 tabulate the results. If one is asking the 23 question of whether or not there is an 24 increasing trend in phosphorus, then it is DEPOSITION OF WILLIAM W. WALKER, JR. 904 1 appropriate to divide that significance level 2 in half so that we are actually talking about a 3 significance level of .05 for summarizing the 4 results with respect to a null hypothesis that 5 assumes that there is no increasing trend in 6 phosphorus. 7 But, as I stated earlier, the report 8 tabulates the actual P levels or the actual 9 significance levels that come out of the 10 Seasonal Kendall test, and they can be 11 interpreted by whoever wants to interpret them. 12 Q. In your interpretations, have you ever employed 13 the .05 significance level? 14 (The witness gave no response.) 15 Q. Well, Dr. Walker, in Exhibit 17 you report the 16 existence of trends, correct? 17 A. I report the likelihood of trends. 18 Q. Okay. In coming to that conclusion from your 19 analysis, what P level did you employ? 20 A. In tabulating the results, as I stated, I used 21 a P level of .1 for a two-tailed hypothesis, 22 which is equivalent to a P level of .05 for a 23 one-tailed hypothesis. 24 Q. A little bit farther down on page 6 of DEPOSITION OF WILLIAM W. WALKER, JR. 905 1 Exhibit 7, the paragraph that starts "The test 2 data set includes 282 observations..." this 3 line in Exhibit 17 has the number 281. 4 MR. HARRISON: What page on 17, Counsel? 5 MS. AHEARN: Page 14. 6 Q. Can you explain the difference? 7 A. To my recollection, there was one sample that 8 was provided to us by the District that was 9 actually collected in October of 1989. We did 10 not have -- or I did not have the flow data or 11 the elevation data or the hydrologic data that 12 would correspond to that sample. And in the 13 draft analysis that is described in the 14 July 30th document, Exhibit No. 7, that sample 15 that was collected in October of 1989 I believe 16 was incorporated in the analysis in the final 17 version. Because I did not have the hydrologic 18 data for the October 1989 period, I excluded 19 that last sample and restricted the period as 20 described to December '77 through September of 21 1989, and that is the reason for the one-sample 22 decrease in the number of observations, which 23 had no significant effect on the results. 24 Q. Did you have to rerun all of the computer DEPOSITION OF WILLIAM W. WALKER, JR. 906 1 programs? 2 A. Yes. 3 Q. What percentage of biweekly sampling values was 4 missing from the data that you obtained from 5 the District? 6 A. I don't recall. 7 Q. Was it as many as 15 percent? 8 A. I don't recall. 9 Q. Is it your understanding that 100 percent minus 10 a significance level is a confidence level? 11 A. I have seen it referred to as that, yes. 12 Q. Is that the definition you employ when you talk 13 about a confidence level? 14 A. Generally, yes. 15 Q. If you turn to page 16 in Exhibit 17, is it 16 accurate to say that the whole of the 17 correlation of hydrologic variables to 18 phosphorus concentration is less than the sum? 19 MR. HARRISON: Object to form. 20 Q. I just want to make sure I conceptualize this 21 properly as a layperson. For example, at the 22 top of page 16 you talk about regression 23 against elevation explaining 40 percent, 24 regression against antecedent rainfall DEPOSITION OF WILLIAM W. WALKER, JR. 907 1 explaining 33.5 percent. 2 If you were to take these and other 3 hydrologic variables and figure out what 4 percentage of the phenomenon they individually 5 explain, you don't get their cumulative effect 6 by adding up those percentages, do you? 7 A. That would depend upon the particular data set 8 that you were analyzing. In some situations, 9 yes, you would get a cumulative -- you would 10 get a sum that would equal the components. 11 Q. Can you give me an example of a data set where 12 you would sum the components? 13 A. Well, you would never perform that sum. You 14 would always perform the regression analyses 15 just as I have done here. 16 Q. Can you give me the example where these 17 hydrologic variables wouldn't have that 18 overlapping effect? 19 A. In situations where the hydrologic factors such 20 as rainfall and water elevation in this example 21 are not correlated with each other. And if 22 their effects on the concentration are not 23 correlated with each other -- that is, 24 correlated between the hydrologic factors -- DEPOSITION OF WILLIAM W. WALKER, JR. 908 1 then you might approach an additive situation 2 such as you described. 3 Q. Do you have a real-world situation in mind 4 where that's the case? 5 A. That's rarely the case. 6 Q. The last sentence of this top paragraph on 7 page 16, you explained a reason for performing 8 your regressions as to generate a time series 9 of residuals which is statistically 10 independent. 11 Wouldn't it be more accurate to say that 12 this time series is uncorrelated? 13 A. Another way of describing it or stating it 14 would be to state that the objective is to 15 generate a time series of residuals which is 16 statistically uncorrelated with antecedent 17 rainfall and elevation for subsequent trend 18 testing. I don't know that stating it that way 19 is any more or less accurate than the way that 20 I have stated it using the word "independent." 21 Q. Are the residual values independent of the 22 hydrologic variables in a literal sense? 23 MR. HARRISON: Object to form. 24 A. In a statistical sense they are uncorrelated DEPOSITION OF WILLIAM W. WALKER, JR. 909 1 and statistically independent of the hydrologic 2 factors because that is what would come out of 3 the regression analysis. 4 (Exhibit No. 39 marked for 5 identification) 6 Q. Dr. Walker, could you, please, identify 7 Exhibit 39? 8 A. These are graphs of total phosphorus 9 concentration, load and flow data from inflow 10 points to the Park. 11 Q. First I'd like to use this for illustrative 12 purposes. If we look at the first graph that 13 appears on page 1 here, you have a number of 14 data points plotted for I guess it's Period 2. 15 Those are the diamonds? 16 A. Correct. 17 Q. And then a regression line for that set of 18 data? 19 A. Correct. 20 Q. If I were to tell you that this diamond that 21 you have in the upper left-hand corner is in 22 error, in fact we have confirmed that there was 23 never any data collected on that day and you 24 should remove that from your analysis, under DEPOSITION OF WILLIAM W. WALKER, JR. 910 1 that hypothesis -- hypothetical, excuse me, if 2 you were to make that change, would the 3 residuals for all other values for Period 2 4 change? 5 A. If you remove one data point from the graph, 6 would the other values change? 7 Q. The residuals. 8 A. Offhand I can't -- I don't understand how 9 removing one data point can change anything -- 10 any of the other data points on the graph. 11 Q. Well, you've plotted concentration against flow 12 here, right? We're talking about actual 13 measurements? 14 A. Correct. 15 Q. And then the distance from each plotted point 16 from the regression line would be the residual? 17 A. Correct. 18 Q. If you remove this data point that I have 19 identified as being spurious, will your 20 regression line change? Will the slope of your 21 regression line change? 22 A. If you repeat the regression? 23 Q. Do whatever recalculations you feel are 24 appropriate. DEPOSITION OF WILLIAM W. WALKER, JR. 911 1 MR. HARRISON: Object to form. 2 A. I don't know what you're asking, so I don't 3 know what's appropriate. I can't see why 4 removing one data point is going to change 5 other data points. 6 Q. Let me try and rephrase it one more time 7 because I think I just had a hard time 8 communicating this thought to you. 9 If we were to remove this spurious data 10 point and you were then to refit the regression 11 line to the corrected data set, would the 12 residuals calculated from that new regression 13 line change, the regression value associated 14 with each particular data point which I'm not 15 changing that are plotted on this graph? 16 A. Well, if you had a hypothetical sample such as 17 that and you hypothetically removed it and you 18 hypothetically fit a new regression line, then 19 there would be -- there may be some effect on 20 the residuals from the other data points, 21 that's correct. 22 Q. So in my hypothetical the residuals of the 23 values in Period 2 are statistically 24 interdependent with the erroneous data value DEPOSITION OF WILLIAM W. WALKER, JR. 912 1 point -- if I change that, I change the rest? 2 A. The regression line would not necessarily 3 change upon removing a particular data point. 4 Q. Well, in my hypothetical here when I'm going to 5 remove this -- 6 A. Well, I don't understand what -- what the point 7 of a hypothetical removal of a hypothetical 8 data point is. 9 Q. Just to try and discuss a concept. That's 10 okay. Let's get back to specifics. 11 Why did you generate Exhibit 39? 12 MR. HARRISON: I don't believe that's 13 been established. Maybe it has. I can't 14 remember hearing him identify it. Maybe that's 15 my problem. 16 Q. You have identified this as being a document 17 you produced, correct? 18 A. I don't think I've identified that for the 19 record. 20 Q. Is this your handwriting on it? 21 A. Yes, it is. 22 Q. Is this a document you produced? 23 A. Yes. 24 Q. Okay. Why? DEPOSITION OF WILLIAM W. WALKER, JR. 913 1 A. This was a sort of an exploratory or 2 supplementary analysis that I did just to 3 examine the relationships between 4 concentration, flow and load, phosphorus load, 5 at each structure for different time periods. 6 Q. At what time did you perform this analysis? 7 A. I don't recall. It would have been probably in 8 1990 sometime. 9 Q. Did you generate Exhibit 39 in conjunction with 10 the analyses which are the basis for 11 Exhibit 17? 12 A. I generated this exhibit using the same data 13 that are used in Exhibit 17, but I wouldn't say 14 that I generated it in conjunction with that 15 exhibit. 16 Q. Did you rely on Exhibit 39 for purposes of 17 performing the analyses reflected in 18 Exhibit 17? 19 A. Well, the results shown in Exhibit 39 are 20 generally consistent with those found and 21 described in Exhibit 17 in that they support or 22 suggest the presence of higher phosphorus 23 concentrations at a given flow and higher 24 phosphorus loadings at a given flow at these DEPOSITION OF WILLIAM W. WALKER, JR. 914 1 structures when one compares the early part of 2 the record which I identify in Exhibit 39 as 3 Period 1, the first five years of data, and the 4 remaining portion of the record identified as 5 Period 2. In other words, the -- excuse me, 6 the phosphorus concentrations were higher in 7 Period 2 as compared with Period