Ralph T. Cheng

Witness for the People:  Guilt Phase

September 30 & October 4, 2004

Request for Kelly-Frye hearing on Cheng’s Testimony

JUDGE: All right. Let the record show the jury's been excused for the afternoon recess. And I understand the next witness is going to be Dr. Cheng?

HARRIS: Yes.

JUDGE: Is that right? C-H-E-N-G?

HARRIS: Yes.

JUDGE: Okay. And there's some -- something you want me to look at, of some maps?

GERAGOS: Yeah, I'd like you to take -- probably just best if you take a look at it, and then after you looked at it, then I'll make the arguments. Going to take you a little while to look at this stuff.

JUDGE: How much?

HARRIS: It's a PowerPoint presentation. I think there was 23 or 26 lines. I've printed it out in hard copy form so you can look at.

JUDGE: You want to pass it up here? Okay. Very interesting. I've seen that. What's the objection?

GERAGOS: There's no foundation for this as any kind of scientific theory.

JUDGE: Are you saying we need a Kelly-Frye?

GERAGOS: Yes.

JUDGE: Oh, I don't think so.

GERAGOS: It's going to become readily apparent when you hear the testimony.

JUDGE: Well, I don't -- well, I don't think we have to have a Kelly-Frye to have somebody testify as to tides. That's generally accepted in the scientific community. They've been charting tides since Sir Francis Drake went up the coast.

GERAGOS: Sir Francis Drake wasn't asked to predict where bodies were going to float based on certain --

JUDGE: Well, is he going to predict where the bodies ended up?

GERAGOS: Yes.

JUDGE: Or is he just going to say this is where the tide and this is possibly where the bodies could end up?

HARRIS: There was two phases of his work. We aren't really interested in the first phase, but we believe the defense will probably ask about that. The Modesto Police Department contacted him before the bodies were found and said, based on the currents and all the different factors in the Bay, where would a body go based on where an estimate is of where it's placed. So he did some computer simulations for them based on that. After the bodies were recovered, he then went back and plotted, based on where they were recovered, going back, based on wind conditions, tide conditions, currents, trying to predict the most likely location where it's at. With regards to that, counsel's already elicited a lot of that core information through Detective Hendee, asking about the FBI searches and saying Didn't Dr. Cheng predict this particular location.

GERAGOS: Which is that -- which is reasonable, given the fact that they testified and brought up the Bay search and why they were searching in specific areas. The second part of their prong, which is kind of a revisionist history, so to speak, has to be subject to Kelly-Frye. You can't have somebody come up -- I don't believe that there has ever been admitted into evidence the proposition which they are going to do, which is -- in actuality, in some ways, I want it to come in because I believe his ultimate conclusion is that he can't say anything about Laci.

JUDGE: Then why are you objecting?

GERAGOS: Well, because he's got a -- observations about Conner which I think, besides being ludicrous, there is no basis upon which he can come to that conclusion.

JUDGE: Well, I don't think that this is the subject matter of Kelly-Frye. I mean, you know, this is -- this is most -- a lot of this stuff is, you know, the -- the -- why the sea level rises, why the sea level goes down. That's generally accepted in the scientific community, and I don't think you have to have Kelly-Frye to determine that. And with respect to his opinion, I think that goes to the weight rather than the admissibility.

GERAGOS: What? I'm sorry, I didn't hear the last part.

JUDGE: It goes to the weight rather than admissibility.

GERAGOS: Not admissibility.

JUDGE: Pardon me?

GERAGOS: I said it goes to weight, not admissibility.

JUDGE: Yeah. It's going to come in, okay?

GERAGOS: (Nods head)

Direct Examination by David Harris

HARRIS: Doctor, can you tell us, what is your occupation?

CHENG: I'm a Senior Research Hydrologist with the U.S. Geological Survey.

HARRIS: What is a Senior Research Hydrologist?

CHENG: My occupation is to conduct research, to investigate certain water properties and physical movement of water. My particular assignment is study the movement of water in San Francisco Bay.

HARRIS: And the movement of water in the San Francisco Bay, or in bays in particular, does it have a particular label or title?

CHENG: Currents. That is what you are referring to.

HARRIS: Are you also referred to as an Estuary Hydrologist?

CHENG: You can say that. Sometimes call ourself Shallow Water Oceanographer.

HARRIS: Okay. Regardless what the title is for what it is that you do for the U.S. Geological Service, do you have a background or education and training that allows you to do your job?

CHENG: Yes, I do. I'm educated from Berkeley with the higher degree from Berkeley studying aerodynamics actually transferred my field to study fluid movements in water bodies in the natural environment and water bodies. So the basic principles are the same, whether we study the flow around aircraft or flow in the lakes, or estuaries in this case. San Francisco Bay is one of the examples.

HARRIS: You indicated it was an advanced degree. Do you have a Masters and a PhD from Berkeley?

CHENG: That is correct.

HARRIS: And what were the actual fields of study that the degrees are in?

CHENG: Both were involving investigation of applied mathematics and fluid dynamics.

HARRIS: When you -- I don't want to date you. But when was it that you graduated from Berkeley?

CHENG: My higher degree is obtained in 1967.

HARRIS: And have you been working for the USGS since then?

CHENG: No. Actually I taught -- took a teaching job in the State University of New York in Buffalo for several years before I joined the U.S. Geological Survey in 1974.

HARRIS: And have you been working for the Federal Government since 1974?

CHENG: That is correct.

HARRIS: What is -- what is it that you do in terms of the work that you do for the USGS since 1974?

CHENG: Well, primarily I'm studying San Francisco Bay, among others. But my research involved in the team work. We have a team of scientists, researchers, looking at issues of San Francisco Bay, involving the movement of water, the chemistry, water quality, and biological activities in the bay. Of course, the task is huge. So my responsibility is studying the hydraulics, that is now the physical processes, how does the water move within The Bay.

HARRIS: This physical process of how water moves, can you explain that a little bit to us?

CHENG: In bays and estuaries, the movement of water is mostly driven by the tides. Tides are processes, the balancing of forces of the sun, the moon rotating around each other. And, of course, sometimes also affected by the river inflow. In our case, in San Francisco Bay the fresh water coming in from Sacramento River and San Joaquin River.

JUDGE: Before we get to the substance of his testimony, are you offering him as an expert?

HARRIS: I will in a moment. I was going to ask him a few more questions.

JUDGE: Okay.

HARRIS: Now, doctor, to help explain what currents are, tides, and how the moon, all those things relate, did you prepare a Power Point presentation prior to coming to court?

CHENG: Yes, I did.

HARRIS: And would that help us understand what some of your testimony is going to be?

CHENG: I hope so.

HARRIS: Okay. Prior to getting to the Power Point, in this particular field of hydrology, you have been doing this for a long period of time. Have you written anything, or published any works in this particular area?

CHENG: Sure. I have published, I don't know -- I didn't count -- but many papers, scientific papers in the referee reviewed journals, and so forth, yes.

HARRIS: When you say refereed journals, that is a peer-review process?

CHENG: Peer-reviewed, yes. Independently refereed, then passing certain quality control criteria before it's published.

HARRIS: Have you also won any awards, or had any recognition for your work in this particular field?

CHENG: I have.

HARRIS: Could tell us about some of those?

CHENG: Well, I think I was promoted to Senior Research Hydrologist in early nineties. That was a recognition. That's actually a very rare recognition in the organization in the Federal Government in the research position. I have been awarded as the Engineer of the Year. I don't remember the exact year. Maybe in 1995. And been serving as advisor, serving on international conference organizations, boards, and so forth.

HARRIS: Just looking at your CV in front of me. In 1967 there was a Freeman Memorial Prize in Berkeley. Is that an award that you won?

CHENG: That was an award derived from my PhD thesis.

HARRIS: In 1984 was a service award from the USGS?

CHENG: Yes.

HARRIS: 1988 you won a National Science Foundation award?

CHENG: I don't recall any particular one. I believe so. If that's the record, yeah.

HARRIS: And you also, as part of the International Conference on Physics of Shallow Estuaries and Bays, did you do -- in 1989 receive a Special Achievement Award?

CHENG: That is correct.

HARRIS: Another Superior Service Award from the Department of Interior, 1989?

CHENG: That's correct.

HARRIS: And you were not sure of the year, see if this is the same the one. 1994, Federal Engineer of the year award from the National Society of Professional Engineers?

CHENG: That is correct.

HARRIS: And then also 1996 a Meritorious Service Award from the Department of Interior?

CHENG: Correct.

HARRIS: And 1999 a Legacy Award from the California State Lands Commission?

CHENG: Yes.

HARRIS: At this point in time –

Voir dire by Judge Delucchi

JUDGE: One other question. Have you ever qualified as an expert in court in the field hydrology?

CHENG: Never served as an expert witness before.

JUDGE: Qualified before?

CHENG: What do you mean by qualified?

JUDGE: Have you ever qualified as an expert in a court of law and given an opinion about hydrology prior to today?

CHENG: No.

JUDGE: This would be the first time?

CHENG: That's correct.

Voir dire by Mark Geragos

JUDGE: Did you have any questions you want to ask him, Mr. Geragos?

GERAGOS: It goes to just to his qualifications, to voir dire on the qualifications as an expert on hydrology?

JUDGE: Yes. If you want to voir dire him as to his qualifications. Do you have the CV there?

GERAGOS: Yes, I do. Doctor, as to your qualifications as a hydrologist, could I ask you, is that how you are employed by the USGS?

CHENG: Yes.

GERAGOS: And what do they have you do at the USGS?

CHENG: My particular position is to conduct basic research. As I explained, my particular assignment is to study those physical processes in San Francisco Bay in a team that addresses broad questions about San Francisco Bay.

GERAGOS: What kind of broad questions?

CHENG: Water quality, biological processes, and plankton balance. Basic environmental issues that come to pass.

GERAGOS: Okay. So is it fair to say that most of your experience or your work is involved in the environmental issues of The Bay?

CHENG: Well, that is the bigger brush question. My particular responsibility is concerning with the movement ofthe water that supports the research of broader issues.

GERAGOS: And the movement of the water as to how that affects things that are in the water?

CHENG: That is correct.

GERAGOS: And meaning, specifically, environmental factors in the water? When you say plankton, you are talking about biological organisms, correct?

CHENG: I'm providing the physical information, physical science information. The biologists and chemists take over that aspect of the research.

GERAGOS: Right. So you give them the research, if you will, on the --

CHENG: The results of the movement of water, how that -- when it happens, in what fashion, and at what degree and magnitude of the movement, in what direction, and so forth.

GERAGOS: And is it a -- is it a fair statement that nowhere in your work have you been asked, prior to this case, to ever give an opinion as to bodies floating up anywhere in the bay?

CHENG: That is correct.

GERAGOS: And is it a fair statement that you had said that this would not be -- or you made a statement that what they were asking you to do was not science, but just a estimate?

CHENG: Well, that -- it's based on science. But as you know being a lawyer, that you know that that's a disclaimer that all science has a little room of tolerance.

GERAGOS: Did you say that -- you called this just bold assumptions?

CHENG: Well, all science starts with bold assumptions, yes.

GERAGOS: Okay.

CHENG: But the important thing, the end result of validation. You can prove the assumption, then the result is valid.

GERAGOS: Right. But all what I'm asking you specifically, is, did you tell these people when they came to talk to you that the -- what they were asking you --

JUDGE: This goes to his opinion not to his qualifications.

GERAGOS: Well, I believe the qualifications -- I mean he is qualified as a hydrologist. What he's - - what they are asking him to do is a completely different matter.

JUDGE: Well, that may go to the weight the jury wants to assign his opinion, and that's a subject of cross examination. Any other questions as to his qualifications?

GERAGOS: No.

Judge Deluchi: Okay. Based upon his answers and his background, the Court will accept Doctor Cheng as an expert hydrologist and qualified to give an opinion about the movement of water in San Francisco Bay, among other things. Go ahead.

Direct Examination, resumed

HARRIS: If can he could have marked at this time a Power Point presentation.

JUDGE: That would be 283.

HARRIS: Doctor, if I can show you, 283 is a hard cop, a printout of the Power Point presentation that you prepared before coming to court?

CHENG: Yes, it is.

HARRIS: And is this Power Point presentation, as you indicated, something that you believe will help the jury understand your testimony?

CHENG: I believe so.

HARRIS: If I could go ahead and show you the Power Point presentation.

JUDGE: Are you going to have him use the laser?

HARRIS: We'll try it with the laser and, if not, we have the pointer available for him.

CHENG: Maybe the lady should move, otherwise I'll laser her hair.

HARRIS: Doctor, just starting right at the very beginning. This is kind of a title page of this particular Power Point. This is -- it says A Brief Overview of Tides, Tidal Currents, Winds, and Waves?

GERAGOS: No pun intended.

HARRIS: That's what we were about to talk about with this presentation?

CHENG: Yes.

HARRIS: Can you go through the next -- this particular slide and describe for us -- start to talk about what it is that happens with the movement of water in the San Francisco Bay?

CHENG: Really just an introductory slide to show what's to come. Preview the contents of this presentation. I'm going to address somewhat the property of the astronomical tides, that is referring to the movement of celestial bodies and tides in San Francisco Bay, and moving on to what tidal currents, typically referring to the rise and fall of water level alone, tidal currents, meaning the movement, the water velocity in particular in Central Bay using Central Bay tidal current movement in Central Bay as an example. Following that, I show -- I will discuss the wind pattern over San Francisco Bay region. And wind, of course, generates the waves. Then I will go into the wave movement and what waves will do to the water body. Generally generates what we call the wind-driven drift, how the body floating in the wavy water condition that will be drifting along with the waves and current, and so forth.

HARRIS: Let me go to the next slide. This one we see is a tide definition. Could you take us through this?

CHENG: This is the typical illustration -- not to scale mind you, that it shows the pulling forces and the centrifugal forces that I mentioned. Now, these -- one of these, the moon, the sun, the earth. And for that matter, here they are in sort of rotational balance here. Therefore, we have two typical forces here. One is centrifugal force. Put this another way of seeing it, it's just like you have you and your friend holding your hands together. You are spinning together. You feel like you are being pulled away. That's called centrifugal force. And, again, there is certain force you need to hold your hands together. That's the attractive force, based on Newton's First Law which says big masses have a tendency to attract each other. They actually are in balance. However, there is a layer of water schematically on the surface of earth, and on the face of the side of the earth facing the moon is subject to stronger attractive force. Therefore, the water surface bulges up. That's how the water level rises. That's the high tide. The opposite side of the water of the earth here, because centrifugal force, it's in balance, because distance is large, have also a bulging up there. The tides caused by the moon actually there is two highs and two lows each day. The earth is spinning around itself here. Most observers standing on the surface of the earth, you experience basically, like you quickly walk around the earth here, one high, one low, and another high and another low. And sun will work in the same way. The combination of these heavenly bodies here causing the water to rise and fall. That's the basic definition of tide.

HARRIS: Let me go to the next slide. This one is titled "Spring Tide". And if you can tell us what a Spring Tide is?

CHENG: Typically tides in the system here is not equal in magnitude throughout the months here. So, therefore, we qualify that. Called first tide. Basically you have a higher magnitude than later. The next slide you will see the Neap tide is higher. Not when the sun and noon line up. They joint forces, the pulling forces on centrifugal forces are lined up. Basically have the additive effect therefore causing higher rise, higher fall of the water. So we are now in the full moon for example in the last few days here, we have Spring Tide right at the moment here. This is the so-called Spring Tide.

HARRIS: Going to the next slide.

CHENG: When they are not aligned up, some of the forces tend to cancel each other. We still will see the high and lows two times, except now the magnitude will not be as large, and some effect from the sun will cancel some effect from the moon, and so forth. Here that particular period of time is called a Neap Tide. Relatively speaking it's a weaker tide.

HARRIS: Going to the next slide. Looks like an math equation. If you can explain this to us.

CHENG: These not math equation this is summarizing. Maybe I can use the words here that now tides typically have two kinds. One we call Semi-diurnal tides. And the basic process happens twice a day. Two highs and two lows. There are certain other effects here, because the earth and moon are not really in a perfect plane. There are some other effects here which we really don't need to get into detail. There are certain tidal components we call -- happen once a day. The combination of these tides is the final result that we will see.

HARRIS: Now, how that relates here in The Bay is when we see the water come in, we see the water go out. And so you are saying that there is like two high tides a day, two low tides a day?

CHENG: That is correct. They are not equal. The point -- I used the slide here. All of the tidal motion, tides are generated by various different components, all add up together. So that they are not equal, just like a perfect science function here. They are unequal. And throughout the month you will see the Spring Tidal Period, Neap Tidal Period. I think I have a slide illustrating that particular part.

HARRIS: Look at the next slide, use that example?

CHENG: This is precisely what I am referring to. Now try to use plottings. This is the observation of water level at the Golden Gate, San Francisco Bay. And here you can see the whole month here. There is a whole cycle, about 28 days. Roughly ten days from the New Moon to Full Moon to New Moon again. So we are at the Full Moon stage here. This is what I referred to as the Spring Tide, that the sun and moon are lining up. They join forces to pull centrifugal forces. And during other periods of time -- for example, during these seven days here tidal amplitudes are relatively week. We call Neap Tides. We are going from Spring Tides to Neap Tides to Spring Tide to Neap Tide, and so forth, here. And enlarging, giving you some definition of terminology here. Enlarging a period of 24 hours -- 25 hours here. That here we see a higher -- we call higher high water. Then you go into a low water. But this time it's lower low water. Then you come to high tide again. However, this high tide is not as high as the higher high tide. So it's given the name called Lower High Water. Then this is a Higher Low Water. So we are going through these four cycles here. In the definition, when you pick up a NOAA Bathymetric chart, how deep the water is, they refer to how deep water. You will see the water depth is referred to Mean Lower Low Water. These are all the Lower Low Water. The average of the Lower Low Water is termed the Mean Lower Low Water. That's how the water depth is referenced.

HARRIS: Let me just stop you there for a second. If you look behind you at what's previously been marked as this

JUDGE: Doctor, you can use the pointer. Why don't you get it for him?

HARRIS: I'm just going to ask him a couple of questions.  In particular chart, this is a nautical chart of the San Francisco Bay. You are referring to that Mean Lower Low Water. Which we see numbers on these type of nautical charts. Is it typically the Mean Lower Low Water mark that's being marked with those numbers?

CHENG: I think somewhere on the chart it should label the -- these numbers are water depths and reference to Mean Lower Low Water, that is correct.

HARRIS: In the area of navigation and hydrology, these tides and currents, is that Mean Lower Low Water, that kind of the mark that's used as a general rule?

CHENG: Well, you need to know what these numbers referred to, so you know what the actual water depth is. If you also know at what phase of the tide you are in when you sail into The Bay -- if you are at the phase of the tide, you can have an exact knowledge in that location what the water depth is there. It is important for navigation.

HARRIS: Looking at this particular slide, you were saying 24 hours 50 minutes, or 25 hours I think is what your testimony was. This cycle of going from the Higher High and to the Lower Low, is that a 24 -- is it a day cycle?

CHENG: It's -- well, we -- roughly at the -- actually the high water shifts by, roughly speaking, you see 50 minutes, roughly speaking. Just for estimate, the high water shifts one hour each day, because there is roughly 25 hours.

HARRIS: Looking at those particular things, I mean there is terminology that we may not be used to. So, again, you have got the tides just coming in higher at different parts of the day than other parts of the day?

CHENG: Sure. The tides vary throughout The Bay. The tide generated basically becomes a much larger body of water. Generally in the ocean, as the water rises and falls then pushes into The Bay, because of the bathymetry in The Bay I modified the tide here. We'll see it isn't similar on a Lower Low water and so -- but the magnitude and the phases -- so-called phases of the time of arrival will vary from different points in The Bay.

HARRIS: Okay. Let's go to the next slide.

CHENG: This might be a little bit too busy, but just to illustrate a point. This particular plot I have shows one month worth of tides. We can separate these are contributions from the two types of information. The 1- 0-1,and so forth, and so on. They are basically -- the point I'm seeing is now -- the end result of these tides is the combination of effect of these tidal components.

HARRIS: Okay. Going on to the next slide. Relating this to the San Francisco Bay.

CHENG: Yes. Now, as I have already mentioned, the tides are generated in the ocean. So as the high water rises in the ocean on this side here, the -- let me orient you a little bit. This is taken from navigation chart. Here is Marin County over here. Richardson Bay refers to -- Sausalito over here. Here is Raccoon Strait, Angel Island. There is the famous Alcatraz. And the City of San Francisco over here. That's the orientation of the map. And here it Golden Gate Bridge right on this. And the sailor, and the ocean -- the captain of the ocean liner, ship captain uses these charts which they have for navigation. Here they are marked sort of channel you should sail into, and so forth, on this side. I'll now show, outside of this slide is the Pacific Ocean. As the water rises -- as I say, the water sea level rises, the ocean -- I was referring to the Pacific Ocean -- pushes the water into The Bay generating the movement of water here. These arrows indicating the movement of water now. Not only indicating -- the arrow indicating -- the arrows indicate the direction and also the magnitude by its size. In other words, now, the larger arrow I employed on the slide meaning the water is moving faster. And the arrow orients according to the bathymetry that modified the slide.

HARRIS: Going to the next slide.

CHENG: Likewise as the sea level falls in the ocean, then actually it draws the water from the inside of The Bay into the ocean. Water moves out in a terminology we call it ebbing. The ebbing tidal cycle, current goes out. The Bay again, because of the geometry -- bathymetry distribution in the bay that varies, causes of the tidal current distribution. The stronger in the deeper channel over here, and weaker in other parts. Again the arrow represents the magnitude and the direction of the tidal current.

HARRIS: Now, looking at this particular slide, it looks like right around the Golden Gate Bridge area, those are pretty big arrows compared to looking at up by Angel Island around to the right side of Angel Island that are pretty small arrows.

CHENG: That is correct.

HARRIS: Can you explain that, why there is that difference?

CHENG: I think from our research, we have -- in our research we typically do some measurement by deploying instruments in The Bay. And so does NOAA, National Ocean and Atmospheric Administration. We collaborate. We put instruments in The Bay, measure, and from analyzing the data, we have come to a general conclusion water moves faster in the system in proportion to the water depths. In that, very clearly, the water depth under the Golden Gate is the deepest in this area. Water moves the fastest in a shallow area. I believe I have another slide that illustrates that point. In the Richardson Bay in relatively short -- water moves -- there are some small arrows. May not be able to see it, just because, as I say this arrow is meant to represent the intensity of the currents here. So currents are very weak in that low water, and very strong right underneath the Golden Gate.

HARRIS: Go to the next slide.

CHENG: So later I might have used terminology called Numerical Model. What Numerical Model is, I thought I would give a few words about the definition. Numerical Model, as I said now, the Numerical Model is based on the first principles, that is very basic assumption that we can base on those equations and compute the movement of water based on the conservation of mass, momentum, and energy. And these equations, by the way, are the same equations that we use to compute the flow around aircraft. I always find that to be amazing that we can turn metal, can fly in the sky a 747, then with the same equation we use -- more important, you can say people can generate and generate a bunch of numbers and the plots here, what make it the creditable or the reliable result is based on so-called validation. That is we now, not only have to just generate computer models, we need to go to the field to make measurements. To actually measure how fast water moves. We know that. Then we use numerical model and compare it with the observations. That particular process is called validation. So if a numerical model is not validated, it's not a valid result. So it's important that we go through these processes to develop credence, to give credence to the numerical model.

HARRIS: Going on to the next slide. This is -- it says an example of an application.

CHENG: Well, since we're talking about San Francisco Bay, I'm referring to one of the papers we published in 1993, talking about tidal and currents in San Francisco Bay using the model. The model has been carefully calibrated based on hundreds of measurements and so forth here. So that now the model results can be considered reliable. As I say, the paper was published in the refereed, reviewed journal. That's now gone through close scrutiny of the quality of the work, and dependable results. And based on that particular paper, we came to the general conclusion that the magnitude of tidal current is generally proportional to the water depth.

HARRIS: So then going on to the next slide. Is this kind of showing us --

CHENG: To further follow up that particular point here, as I say again, a snapshot. Remember now, tides are moving at every instance of time. Water rises and falls. This is just only a snapshot of tidal current distribution in the Central Bay. Here we show that now the current is strongest where the water is deepest right underneath the Golden Gate, this region here. We -- actually, if you look closely, marked shipping channels here, real larger vessels should follow those, travel through that region. Current is also very strong. And as they follow into the shallow area, current is very weak. When going to -- you can see, even to navigate in the chart here so a lighter color is a reflection of water depth. It is shallower in that area here than the water -- current there is very weak.

HARRIS: You have been talking about water current. Is water current different than waves?

CHENG: Very different. Waves, that's referring to the up-and-down motion. So it is similar to the tides, but they are talking -- we are talking about long wave and short wave. Up-and-down motion is called a wave. The current meaning the actual movement of water mass.

HARRIS: Going on to the next slide. This one is about wind pattern.

CHENG: Yeah. In San Francisco Bay region here, we typically see two different wind patterns in the summer. In particular it is almost predictable. We call it the sea-land breeze. It's actually a very simple physics here, because inland is a desert region. Here the sun rises in the summer months here, heats up the land. Therefore now we know that the hotter air will tend to go up like hot air balloon goes up. Then we need some mass to replace the vacuum that the air goes up, so it draws the air from the sea area here. Therefore, now, you call that -- every afternoon you can predict almost that way, going over, it cools from going the other way. Locally it will be modified by the local topography. However, in the winter, since now the heat -- the temperatures in the coastal regions are not that different in the winter, the wind patterns here are not usually predictable. Okay. You are going -- this is a summer pattern. Then these are the patterns. That's good. Might as well jump into this. This is what I referred to as the summer pattern here. Wind typically coming from north and northwest here because, as I say, it's heated up in the inland, then creates a vacuum. Then the air being pulled from the ocean goes over the Bay region. Then the wind distribution will be modified by the locality, topography, mountain ranges in the south. Here it is not easy to see. Berkeley is over here. That's the south based mountain range. However, in the winter - -

HARRIS: If I can just jump in here for a -- looking at this particular slide, it's from a website. Is this the USGS website?

CHENG: That is the results of the collaboration with the USGS and San Jose State and Frank Ludwig, who used to work for us, but he's now retired.

HARRIS: And in this particular overlay that we are looking in this map in the middle, this is the map of The Bay, and has a bunch of arrows up there. That represents the direction of the wind that's going across that geographic region?

CHENG: Yes, the concept. Same answer, I discussed the tidal current. This is talking about movement of air, air mass movement. The arrow points out the wind speed and the direction.

HARRIS: Let's move on to -- you were describing for us the -- there is a difference with --

CHENG: Here in the winter pattern here, winter typically is weak and variable. We cannot predict the direction of the wind. Occasionally there were some storms typically the windstorms came from the south, because the mechanism that generates the wind is the weather front from the south. It's north in the winter. Either we see this type of variable very weak wind, variable directions. Almost like undefined. Or we see a strong wind pattern coming from the south.

HARRIS: Can I click on the next slide, which is has that snapshot of an example of a winter storm front.

CHENG: This, as you see on the upper right-hand-side corner here, has the date April 12th. That was reference to the time of the year, the late spring, early summer, or however you want to define that. That was one of the examples of one of those typical storms here. You know, the one thing different from the summer pattern here is that now the wind was coming from the south rather than coming from the west.

HARRIS: Right. Moving on to the next slide. And when you are talking about this, how the wind affects the water, if you can explain this for us now, and how was produced.

CHENG: Well, as I mentioned, it was not movement of water mass. That is not mass. It creates a motion that generates the level of the water up and down, and this creates motion, that creates energy down to the bottom that can, in the case of The Bay, can cause sediment erosion. One typical example, since most of you live in the Bay Area here in the summer, if you drive through the San Mateo Bridge, in the shallow area you see the water almost turn chocolate color in the afternoon because of heavy strong winds that stir up the bottom sediments. And in the calm winds the water changes color back to a greenish color that is the sediment resettled back to the bottom here. Now, wind not only generates the wave on the surface here, it also has the friction, just like you blow something, that will move forward. That particular friction drags the water mass. This takes time. An actual water mass begins the up-and-down motion. That wave and actual movement of the water mass in the direction of the wind, typically you can estimate the movement. That particular motion is on the order of two or three percent of the wind speed. That's typically the rule of thumb people use. For example, we had oil spilled on the water here. The oil slick on the water surface here can be estimated using the general rule-of-thumb formula

HARRIS: You are speaking of formulation?

CHENG: We'll look at them next. It's actually formulas that allow -- I didn't mean to confuse you. But I just want to make a distinction here. That wind wave, what we call a short wave here, that basically up-and-down motion here will not even hardly hit the bottom here. However, that so-called long shallow wave is just almost like a tide. Here we have a complete theoretical knowledge in the textbook fashion here. We can predict the properties of so-called long wave and short wave.

HARRIS: We'll move to the next slide which is a little bit less math.

CHENG: I think this is maybe more revealing, when we have a condition of the wind that is blowing over the surface of the water, that generates the up-and-down motion that I referred to as wind wave. This upand- down motion, in turn, moves the water mass in a circular pattern here, what we call orbital motion due to the waves here. The larger motion near the surface, the motion decreases as the depth goes down the -- got down here. But, on the other hand, I have already alluded to, there is a friction on the surface here that creates a little drag motion in the direction of the wind speed here. The combination -- again, the combination of the orbital motion and drag motion here give the water mass inside the water column a trajectory like this. In other words, suppose I have something suspended such as sediment, or whatever, in the water column here. You will see the movement of the particular object in the sort of circular motion; but then, at the same time, rolling forward. So that when net results, what we call wind drift, how far this suspended object is moving with the -- caused by the motion of the wind.

HARRIS: Next one.

CHENG: Also -- by the way, I gave you the reference. I mean this is really textbook material. It's on the bottom of the last slide.

HARRIS: Okay. And this one is a summary?

CHENG: Yes. So, in short here, I gave you a general summary. I hope that would help us to understand the general phenomenon that happens around us every day. The tides and tidal currents, the wind, and then waves. And these are important factors that affect movements of things in The Bay. And astronomical tides and the tidal currents are really very predictable properties, because the astronomical motion we know we can go down to very precise prediction. However, that when we come into the water body here, because of the local water depth variation, that is the symmetry that causes some variation. As I say, it's not uniform throughout The Bay. Modified by the local water depths here. And let me see. Yeah. The last one I said, I also show the wind and tides properties near Richmond very close to the area of interest.

HARRIS: Okay. That's what I want to get to know, kind of put this in some other terms. Going to the next slide here.

CHENG: This -- let me first define --

HARRIS: Doctor, if I can just ask you a question real quick. As part of the -- at some point in time were you contacted by the Modesto Police Department and asked if you could assist them in their particular investigation into the disappearance of Laci Peterson?

CHENG: Correct.

<evening recess>

October 4, 2004

Direct Examination, resumed

HARRIS: Doctor, before we go into the last few slides of the Power Point presentation, I'm going to kind of go back and recap what we were discussing on Thursday afternoon. What you were showing, some of the first few slides of your presentation, would it be fair to say that the moon and the sun affect tides and tidal currents?

CHENG: Yes, sir.

HARRIS: Tidal currents?

CHENG: Yes, sir.

HARRIS: You were talking about how the tides rise and fall. The tide comes in and goes out roughly twice a day?

CHENG: Correct.

HARRIS: When the tide comes in, it comes in roughly twice a day. It doesn't come in equally?

CHENG: That's correct.

HARRIS: And same with when it goes out, the tide goes out roughly twice a day and doesn't go out equally?

CHENG: Correct.

HARRIS: When the tide does come in, so we refer to that's at high tide, it doesn't come in equally, so that there is one that's a high tide, and the other -- the other is the higher high tide?

CHENG: That's correct. One is called Higher High Tide, the other one is called the Lower High Tide.

HARRIS: And the same is roughly true when the tide goes out. Doesn't go out equally. So one is referred to as the Lower Tide, or the Lower Low Tide, and the other one is just like a Low Tide?

CHENG: Lower Low Tide and Higher Low Tide.

HARRIS: Kind of distinguishes which one is going out the most and which one is coming in the most.

CHENG: Yes.

HARRIS: When we were talking about the tides -- excuse me, talking about the currents. What you were telling us is that the deeper the water the faster the current?

CHENG: That is correct.

HARRIS: Then we moved into the area of the winds, and you were showing us the different types of wind or the types of waves. So to summarize this, wind produces waves on the water?

CHENG: That is correct.

HARRIS: And the wind producing these waves on the water can transmit the energy through the water down to the bottom on the side, you are talking about that causing erosion?

CHENG: That is correct.

HARRIS: That was the example you were giving us out there by the bridge when it turns looking like chocolate milk?

CHENG: Right.

HARRIS: The last slides we were into, we were talking about the summary of all this, is that the tides and the currents are very predictable?

CHENG: That is correct.

HARRIS: So when you factor in all of that information of the winds, the currents, and the tides, you are able to predict how movement of the water and things in the water occurs in the San Francisco Bay?

CHENG: Within a certain degree of accuracy, yes.

HARRIS: Now, I want to go forward and go back to the Power Point presentation a little bit, and start with this February of 2003. Were you contacted by someone from the Modesto Police Department seeking your expertise in the area of the San Francisco Bay?

CHENG: Yes.

HARRIS: And when the Modesto Police Department -- let me just ask was it Detective Phil Owen that you dealt with?

CHENG: Yes.

HARRIS: And another detective by the name of Dodge Hendee?

CHENG: Correct.

HARRIS: As these detectives would talk to you, did they provide you certain information, and kind of ask you to see if you could help them in terms of how things would move in The Bay?

CHENG: Yes, they did.

HARRIS: As part of the process of going through and helping them with their questions, did you have to go back and look at what the tides were, what the wind conditions were, those factors in different areas of The Bay?

CHENG: Yes, I had to.

HARRIS: Now, I want to go to the Power Point presentation.

CHENG: May I have that pointer back there.

JUDGE: You want the laser?

CHENG: Yeah, laser pointer. And also the lady probably should move her head.

HARRIS: All right, doctor, what we are looking at now is the next slide in the presentation. It says Tides and Wind Near Richmond. And can you describe for us what this particular slide in the presentation is depicting?

CHENG: Like to apologize to the jurors. This particular slide might be a little bit scientific, but I think of great importance. Summarizes the waves and tidal condition near the Richmond area the day the wind was measured by Bay Area Air Quality Management District at Richmond, not far from the area of interest. The plot has three components. Three panels here, the horizontal axis, horizontal section is moving this way, represents the time. And the first panel here shows the wind direction. And, sorry, you cannot read it very much, very clearly. But bottom here is 0 degrees, 90 degrees, 375 -- and 275 and 360. Basically, it shows where the wind is coming from. And you can see now during the period of time, which is indicated on the bottom here, deliberately choose this as an example. We do have this data covering throughout the period of time. In fact, these data collections are ongoing, continuous. Cover the entire period of time. I used this particular slide as an example was now December -- centered on December 24th, one day before this area, called the timeline, the time mark for December 23rd, December 24th, 25th. So you can see the tide come two highs, two lows each day. And so the second panel indicates the wind speed measured in terms of meters per second. One meter per second is roughly two knots in common language. We way 10 knots, 15 knots. One meter is two knots per second -- two knots per hour. And here now we see that now, during period of time, December 24th in particularly around noontime, that the wind was very calm, very weak. Wandering around five or ten knots. Wind direction is not quite defined. You can see the randomness is not well defined, because weakness of the wind. Typically you don't see clear definition of the wind direction. In terms of the tides at that particular time, during December 24th at noontime, it is rising tide from the Higher Low Tide approaching the Higher High Tide, implying it's flooding water coming in from outside the ocean into The Bay.

HARRIS: Let me move toward the next side.

CHENG: This is the graphical summary of what I just described, December 24th, 2002, at noon. We have -- we post a wind distribution web page on the web that the people can obtain. This represent the typical wind direction. As you can see now, the size of the arrows represent the magnitude of the wind here. The color scale represent by color bar from white to green, to light green yellow, brown and red. Red is exceeding 25 knots. Here now you can see the direction is roughly undefined. There is no fixed pattern. Arrows are mostly white. That is around this end, five, or less than five, knots per hour. And here you can see that, in this general -- which are representing the condition of the wind at that time of the day.

HARRIS: Did you also then go and take the same basic information for approximately the time that the bodies were found for Laci and Conner Peterson?

CHENG: I think that shows in the next slide. So this particular graphic -- again, I apologize again that is a little bit scientific; however, carried different meaning. Basic idea is first panel shows the wind direction. Second panel shows the wind speed in terms of meters per second. And third panel again the tide here. We talk about what -- the definition of Mean Low Low Water over here. In this particular graphics, I focused the timeframe. As I say, horizontal axis represents the time. That start from this arrow in noontime of April 11th, April 12th, April 13th. Here there were some exceedingly low tides. That was during the spring period of time. We discussed earlier a lot -- Thursday -- tides is going into Spring Tidal Phases, and Neap Tidal Phases. During the Spring Tide, the water level goes to the extremities. It is very high and very low. In fact now, as I say, the common reference datum reference to Mean Lower Low Water in this time period of time the tides even was so low that was below the Mean Lower Low Water. And the top panel here is really rather interesting during that period of time. The wind -- I also discussed that -- in the Bay Area has two typical patterns. During the winter seasons, there is no well-defined wind direction, unless there was a major storm coming through the area. And usually when the storm comes through the area, the storm front came from the south. So here, as you can see, during this period of time, the wind direction is closely lined up with 180 degrees from north. That is -- now wind is coming from the south 180, degrees, opposite direction from the north. That's now throughout this period of time wind was typically coming from south, which is a usual pattern comparing to the summer prevailing wind direction in which that now wind came from the west. And here now, that's another unusual event. The second panel represents the wind speed. This height of the curve represent magnitude. Again, horizontal axis represents time. During this window of time, here is -- we see that now. In fact, personally I felt that since we ran that web page that day -- not connected to this particular discussion here -- I felt that was, wow, quite a wind event during that day. I really recall in my own mind, you can see now the scientific records showed us now during that particular period of time, in the morning, or starting from the midnight of the midnight April 11th, or early morning of April 12th, you can see wind exceeded 40 knots. 40 knots, wind exceeded. Also a sustained wind for long period of time, subsided slightly, but still continued on for another good twelve, eighteen hours with wind average around twenty knots per hour. So that is quite a magnitude of wind. And during that period of time, there was occurrence of a very low tide right after noon of April 12th.

HARRIS: And did you also do this graphically in the next slide?

CHENG: Yes, I did. So this is the graphic rendition of that particular wind event. You can see now all the arrows pointing, coming from the south. Again, now, I mentioned the color of the rendition of the arrows here represent the magnitude, white arrows I show in the previous slide that meaning wind was very weak from five, to ten, to fifteen. And you can see now areas here with nearly red colors represent the wind exceed 25 knots per hour.

HARRIS: I believe that's the last slide of your presentation. Go ahead and resume the lights. Doctor, as we go through this now, what we'll do, we'll use 215, the map behind you. When we get to that, I'll have you take the pointer and show us the different locations, and we'll go through this. Just to go back to the last part that you were talking about with this wind event that you were discussing, when you have a wind event like this event that was occurring on April 12th of 2003, that amount of wind, is that going to produce a significant amount of energy through the water?

CHENG: It will.

HARRIS: And, again, we talked about how the current, if it's deeper, goes faster. As water starts to move through these wind actions, do the waves go some place? Do they push up against the shore?

CHENG: Wind typically carries -- I believe in the previous slide I have shown last Thursday, wind creates two events. One generates the wave, and the wave produces so-called orbital motion the water mass actually is going to circular motion at the same time that the wind drift -- the wind, because of friction on the surface of the air-water interface, moves the water in the direction where the wind is going. That causes wind drift. Combination of these now produces not only the stirring motion near the bottom, and causes suspension of sediment in The Bay, when we get a color change just to chocolate color in the shallow area, in particular, where energy is easier to transmit to the bottom. In deeper part of the water, even with the same wind, the water depths here, the energy will not go to this depth. Therefore, it is important to recognize during the same wind conditions in the deeper area there is lesser effect than the shallower area, is much greater effect in stirring the bottom.

HARRIS: If we're talking about this, so we make sure I understand this clearly in my mind, you are talking about two distinct things that occur with the water because of the wind. So if he we were to put something on the surface of the water, and wind were to come back -- come across the line, if we were to blow on something on the top of a pond, it's going to move that object in the opposite direction to the wind?

CHENG: Is moving along with the wind.

HARRIS: So as we blow it, or the wind moves, that object would go on the surface?

CHENG: That's how the sailboat works.

HARRIS: And then with the second aspect of that is the movement of the water itself by the wind which is generating these waves, comes up and goes down, and that's that orbital motion that you are talking about?

CHENG: Yes.

HARRIS: And so as it goes down, the shallower the water, the more energy is transmitted to the bottom of the water?

CHENG: That is correct.

HARRIS: And if it's shallower so it can reach the bottom, the sediment, that can produce disturbing the sediment. And I believe in one of your slides you refer to it as erosion?

CHENG: That's correct.

HARRIS: Now, when you were asked to assist with the Modesto Police Department, so you gather this basic information. When they first came to you in February, Laci and Conner's bodies had not been found; is that your understanding?

CHENG: That's correct.

HARRIS: So when they were asking you to assist, when they basically were asking you can you tell us if we put something into the water where it might go?

CHENG: I told them I could try, based on the my best scientific education and best scientific data, yes.

HARRIS: And as the detectives were asking you different hypotheticals, how did you go about doing this? Did you run computer simulations for them?

CHENG: Yes, I did.

HARRIS: Briefly tell us how that works?

CHENG: Well, in order to reproduce -- reconstruct what had happened, the question wasn't how the tide and the currents. I reconstructed the tides and current in The Bay fairly easily within reasonable degree of accuracy. Uncertainty really comes -- we really did not know when and where the body was put in the water. Given that as the initial -- we call the initial condition, then you produce an answer where the body would wind up within a certain time. But it's the initial condition that is where the body started its travel in the bay, and location where it started traveling from The Bay, then you can get -- that particular initial condition is not precise, then we cannot do a precise prediction.

HARRIS: So from the lack of information that the detectives were able to provide you as to where this had occurred, this was somewhat just a scientific exercise at that point in time?

CHENG: That is correct.

HARRIS: Now, after the bodies were found -- moving forward in time after the bodies were found -- did the Modesto Police Department again contact you?

CHENG: They did.

HARRIS: And did they ask you, based on where the bodies were found, if you could go back and do this recreation from what you were talking about, the tides and the currents, and try and plot a path or a course where the bodies had come from?

CHENG: I told them following here I could try. However, it involves similar uncertainty. That is now, when the body was spotted on shore at certain time, it does not imply the body arrived there at that time. Now, we have a little bit better situation that is not -- we know precisely where the body landed. Comparing to the previous scenario, that we were guessing where the body started traveling and at what time. In this case here now, we -- our knowledge has improved. That is now -- the bodies, we know precisely where the body landed. And -- but we didn't know when the body precisely landed at that location. Therefore, in order to reconstruct where the body started moving from, certain position in The Bay, still involves some uncertainty.

HARRIS: That's because there is a -- there is a distinction in terms of what you were looking at when the bodies were found, versus when they actually reached shore?

CHENG: That's correct.

HARRIS: Now, in terms of -- we'll now start looking at 215. The detectives give you --

JUDGE: Doctor Cheng, would you use the pointer when -- not that one. This one. The one --

CHENG: Okay.

HARRIS: Doctor, what we were talking about is when the detectives give you the information of where Laci and Conner's bodies are recovered, that is an area in the Richmond area over there by Brooks Island. Do you -- is that on the map up there?

JUDGE: You can point that out to orient him.

CHENG: Yeah, over here.

HARRIS: That is Brooks Island.

CHENG: Brooks Island. This is Brooks Island over here. I think the -- if I remember, Laci's body was discovered at the Isabel Point. And I don't know the name of the -- Conner's body was found over here, what is the name associated with that?

HARRIS: Looking -- just use this here. It was right by this pipeline symbol?

CHENG: Right.

HARRIS: And so they gave you the locations of those bodies. The area where -- around that where the two bodies were at and in between Brooks Island, what is the generalized depth of that area?

CHENG: It's very, very shallow. I don't remember the exact numbers, but very, very shallow.

HARRIS: If you were to look at this particular map, does this have numbers in that area?

CHENG: Yes, it does. Let me take a look. It shows three or four feet in this -- three or four feet in this general area. Four or five feet, or six feet over in this general are

HARRIS: And if you look at the legend up there, is this -- the feet that we're talking about, this is that Lower Low Mean --

CHENG: Reference to Mean Lower Low Water.

HARRIS: Okay. So that the three or four, the four or five, five or six, in that generalized area, that's that Lower Low Mean?

CHENG: Well, for example, we just saw on the slide here during the very low tide the tide was negative. Let's say -- I don't remember the precise number on the chart. We can go back to that. Let's say chart and the tide was minus one foot. Then you look at the chart here, say three feet. The actual water depth at that particular time should be three minus, actual water two and a half feet. That's how we interpreted the --

GERAGOS: Depth is what?

CHENG: Well, if you look at a location of the three feet on the chart, it references to Mean Lower Low Water. At the Very Low Tide, we saw we have a negative .5 feet. Actual water depth would be 2.5 feet.

GERAGOS: Thank you.

HARRIS: So you go through, and you look at this particular area. You take the information that you have already shown us with the different charts and graphs up there, taking that basic information, were you able to plot a backtracking course as to where you believed that Laci and Conner had started from?

CHENG: Assuming the information is correct, I try my best, yes. We construct it is called a vector -- Progressive Vector Diagram, reconstruct where the body would have started traveling from.

HARRIS: Were you able to make this vector track?

CHENG: Yes, we did.

HARRIS: Can you explain to us how you would have went about doing that? Do you do it by hand? Did you use a computer? Describe the process.

CHENG: It's a combination of the above. Basically we obtain the wind information, time series. We reconstruct, now, based on the U.S. Army Corps of Engineers Coastal Engineering Handbook, they give you certain formulas for certain given wind conditions. So how much actual water movement would be is not a windspeed- water movement here. And then you would reconstruct hour-by-hour here as if -- assuming the bodies started from here, you go backward rather than going forward here until certain -- to a certain time here. We -- of course, we assume that now the body would have started from Mean Lower Low Water. The reason we say that is now when the water depth is shallower, that is when the tidal condition was very low part of the water, that is the higher probability that energy will transmit to the bottom. Therefore, based on that, backtrack to that particular time that -- where the Mean Lower Low Water was negative, I assumed that was the location where the body is dislodged from what might be anchored to The Bay.

HARRIS: I want to go back through there. You -- go ahead, have a seat.

JUDGE: Do you want him to

Mark that on the chart?

HARRIS: Not yet. We have a separate map. Just to go back through this. If -- because you are talking about this storm, that -- was there one a few days before the bodies came ashore? If we're talking about the shallow areas in the map, that we are looking at on 215, what is the usual range of movement in those shallow areas?

CHENG: As I have actually said, the tidal current movement, without considering the wind, is directly proportionate to the water depths. In that particular area, the current seldomly exceeds twenty centimeters per second. Usually it's wandering around five or ten centimeters per second. The tide coming in and out twenty centimeter per second, translating to, as I mentioned, fifty centimeter per second, translates to a common terminology, one knot. Twenty centimeters means that, 0.4 knots of current.

HARRIS: I guess, put it in the further lay person's language, is that a lot of movement, very little movement?

CHENG: Very little movement.

HARRIS: So, generally, in that area is there enough energy for a body that's on the bottom to be moved?

CHENG: I don't think so.

HARRIS: As the storm comes in, you were talking about how it starts to propagate this energy to the bottom. That storm event, is that enough -- does it produce enough energy in the water to move a body?

CHENG: It does. I mean, again, it depends on whether the body is -- well, with it, it doesn't -- in other words, suppose the body is still again anchored here, it may not have enough energy to move it.

HARRIS: And if it's not anchored, if it's broken?

CHENG: Then it would have enough energy to move it, right.

HARRIS: Now, you go through the process of plotting this out, do you take and put this vector -- Reverse Vector that you do, and is it plotted out on a map?

CHENG: I think I did.

HARRIS: And, eventually, do the detectives take that vector and apply it to search grids so they could go out to the bay and conduct searches?

CHENG: That is correct. I think the purpose, when I was receiving -- received the request was that now they wanted to launch additional search for further evidences. They want to have the best chance of finding additional evidences. So my work was based on science and actual physical data observations to make a recommendation where is the best location to start their search.

HARRIS: Do you ultimately come up with that recommendation for them where they should search?

CHENG: Yes, I did.

HARRIS: Like to show you -- could I have something

Marked? Show you a document.

JUDGE: Mark that -- already have marked that already? Do you want to mark that next in order?

HARRIS: Yes.

JUDGE: 284. What does it purport to be?

HARRIS: It would be a grid map.

JUDGE: Drawn by the witness?

HARRIS: Doesn't appear to be drawn. There is drawings on --

JUDGE: Produced by the witness.

HARRIS: Doctor, let me show you 284, have you look at that.

CHENG: Yes.

HARRIS: And do you recognize this?

CHENG: Yes.

HARRIS: Does this appear to have the vector map that you were just describing, the line and the search area?

CHENG: It does.

HARRIS: Put this up on the screen. Looking at this particular document, 284, does this depict on this map -- let me just back up for a second. That is map of the same area that we have been looking at, 215?

CHENG: That is correct.

JUDGE: That's -- wait. Can you point out Brooks Island and Point Isabel on that? Can you do that, Doctor Cheng? Indicate where is Brooks Island.

CHENG: If I can see that chart clear, I think Brooks Island is right here.

JUDGE: Point Isabel?

CHENG: Point Isabel is here, I believe. Is that right? Somewhere here. Close enough.

HARRIS: From -- it's kind of -- let me just point some things out for you. Do you see the words on map -- on the map? There we go. Where it says Point Isabel.

CHENG: Let me see. Do that again, please.

HARRIS: You can barely see it with that laser. Do you see where it says Point Isabel?

CHENG: I think over here.

JUDGE: Do it the old fashioned way.

CHENG: Right there. Right.

HARRIS: All right. Do you also see that there is a -- right next to it, there is an arrow going up from the right, says "Laci Peterson Body"?

CHENG: Yes, I do.

HARRIS: And then we also see that there is a graphic that says "Baby Peterson Body", and it is a little bit more difficult to see. But there is an arrow that comes down, that is the square there?

CHENG: Yes.

HARRIS: That's the area that we were talking about on 215 up there?

CHENG: Yes.

HARRIS: Now, there is this line that comes down from the top, going through the middle of the documents. Do you recognize that particular line?

CHENG: Yes.

HARRIS: And what is that line?

CHENG: That was the -- what I call Progressive Vector Diagram that I constructed based on the wind drift.

HARRIS: Now, next to that particular line, there is little triangles or deltas that are there that have numbers. Could you describe for us what those are?

CHENG: Those were the calculations of the movement between hour-to-hour movement based on the wind drift estimation formula.

HARRIS: Now, you were describing for us before the wind drift. That's where the force of the wind activity moves the water?

CHENG: That is correct.

HARRIS: And you were telling us about that, there is this mathematical formula. I won't put that slide back up there.

CHENG: Yes. As I say, the equation I used was based on the U.S. Army Corps of Engineers Coastal Engineering Handbook.

HARRIS: Now, as you go through this process of doing this vector, that's what we were starting to get into. Does the computer -- or do your calculations include the tidal currents, the wind, all of these different things that you have been talking about?

CHENG: Well, for this particular calculation, I think the tidal currents does not play any significant role, since tidal currents itself, et cetera, is weak. And throughout the period of time, tidal currents reverses to some degree, so tend to cancel out the net movement effect. So this calculation is solely based on the wind drift.

HARRIS: Let's -- what -- the tidal current tends to cancel out the movement effect. What does that mean?

CHENG: Well, just -- let's see, we start from the beginning of a flooding tide, that is no water coming in. If you have life jackets or something floating on the surface here, it will move a certain distance. Let's say, one or two kilometer in that area would -- in that area would probably not move that far. In the second half of the tide going into the ebbing phase, the water is leaving this bay, would go probably drift back to the -- leaving the area, going out of The Bay. Typically we'll find that if you drop something, even if any of you are, say, here, you drop a float in the water. If you sit there long enough, you will find the float drift away from you. However, in the second half of the tide, it typically almost returns to where the point it started.

HARRIS: In this lack of current movement is because the current is so weak in that particular area?

CHENG: It is. And also at the same point is, even in other than parts of The Bay, if you put the body in certain part of The Bay, tidal current is not symmetrical. Slows enough. So now the current might drift away, come back to the close proximity within a tidal cycle.

HARRIS: So as you are describing for us in 284, primarily your calculation is based on this wind drift?

CHENG: Correct. Because I concluded that now the tidal motion would not play a role in this case.

HARRIS: So the wind factor, is that sufficient force that we're talking about that was propagating the energy downward. That would be enough to move something toward the lower line?

CHENG: This is already the second phase here, that the first part of that is not the wind force. This is somehow breaking up the anchor from the body. Now, then the anchor doesn't -- may not hold, the body becomes a floating object. The wind drift will move the body. That's the calculation I'm doing on this chart.

HARRIS: With this particular time factor that we were talking about, the April 12th, April 13th, 2003 area, the direction of the wind is depicted with that vector chart that it's moving -- the wind is coming from the south and going somewhat to the north, to the northeast a little bit?

CHENG: Correct.

HARRIS: When you provide this information that we see up there to the Modesto Police Department, we see that there is a square -- there is a number of squares up there. It says the large square is one a quarter mile by one and three quarter mile. The small squares are roughly a quarter. Can you predict with any certainty within inches or feet where these bodies would have started from?

CHENG: No, I'm afraid not.

HARRIS: Why is that?

CHENG: Well, for two reasons here. That one of the most important reasons is that now we did not know the precise time, we have already talked about, the body started. In other words now, you told me that body landed at that particular point. But, for example, in this particular case, bodies were found here at -- I don't remember the time. Let's call that 3:00 p.m., but that was the sight time. That wasn't the time the body actually arrived. So without that information, I cannot construct precisely where the body started traveling from.

HARRIS: Now, the fact that there is two bodies, and is that something that you have to look at as well?

CHENG: Yes, I did.

HARRIS: And explain to us that process.

CHENG: Well, obviously people may argue that the two bodies started from the same place, why they wound up in different locations. I need scientific -- I need scientific judgments to make an explanation to this observation.

HARRIS: And do you -- do you go through that process -- since we're talking about the wind, the size of the body or size of the mass that's subject to the wind on the surface make a difference?

CHENG: To some degree, yes, it does. And also the other possibilities here that the -- that you mentioned now, two different bodies here of different -- obviously very different sizes here. When they drift in water, they may behave differently.

HARRIS: Just to back up, kind of put this -- make sure, again, I am putting it in kind of layman's terms. If you use a different size sail, does that make difference of how fast your boat goes?

CHENG: It does.

HARRIS: So, again, whatever force that the wind could put on to an object can effect how it moves through the water?

CHENG: Yes.

HARRIS: You are talking about weight. Is weight another factor that plays into that?

CHENG: To some degree. But, as I say, in the second phase, the body has already started traveling. The wave motion only contributes to the net drift in terms of producing energy and forming the orbital motion. It will not contribute much to the net movement.

HARRIS: Ultimately you gave this to the Modesto Police Department for them to come up with their search plan that you were discussing. Based on what you have been talking about, the energy and the lack of speed, so to speak, of the currents in that particular shallow area, where do you think -- in your expert opinion, where do you think those bodies had to be to reach that particular place that they were at?

CHENG: I think, based on those estimates, and based on the actual observation of the wind and the scientific judgment, that's the location I recommended. As let me address that as the highest probability that might have started from. It's not a deterministic prediction, but it's a highest probability.

HARRIS: So looking --

JUDGE: Can you show us on the map where you think they came from?

CHENG: I mean the little inner square. I recommended that they search for starting from this particular point.

JUDGE: That's where you think maybe the bodies originated from?

CHENG: Yeah.

HARRIS: Now, relating that over to the map, 215, that particular location that's somewhere, if we were to triangulate somewhere between Brooks Island and the Berkeley Marina and where the bodies are indicated?

CHENG: I think put in simple terms, it's lying right in the middle distance between Berkeley Marina and Brooks Island, roughly.

HARRIS: If we were to -- looking again to using 215, we see there is a portion of that particular map where there is, in the middle of the water areas, white and instead of light blue representing the water. Are those the deeper channels that you are referring to?

CHENG: Yes. These maybe give navigation channels in the deeper part here. They color white the shallow area so you have immediate view this. General area is very shallow. They have actual numbers printed on the charts.

HARRIS: The deeper water, as we have discussed, the currents there are faster. So does it have a different energy property of movement than that the shallow areas that we have been talking about?

CHENG: Oh, yeah. Much different. Here in this area here, tidal current typically moves at exceeding two knots, three knots. That is maybe 150 centimeters per second. 20 centimeters per second over here.

HARRIS: If something were to end up in those deep water areas, where ultimately does that go?

CHENG: I think we did some simulations in early phase of the study, that Modesto Police Department recommended that, let's assume the body were lowered into The Bay at this location, that we use the computer simulation. In the end we find either body was washed into the Pacific ocean, or some cases here, the body went behind this Angel Island here, the long island here, had wind up over behind Angel Island again. As the current comes through here behind Angel Island, just like a wake region. When you are on a boat, behind the boat there is an area where water moves slower, so we call a wake. Sort like a wake region behind the island here. The current again slowed down. So, therefore, now the simulation showed that that body started moving here, wind up into the central bay, and somehow wind up at higher probability -- let me stress that body could be landed behind Angel Island if that was the case. And also there were some situations here where the body went over to the Pacific ocean.

HARRIS: Based on the simulations that you were doing for the Modesto Police Department, if the bodies were to go into those deeper parts, they would head toward the Golden Gate Bridge. They don't end up head up to the Berkeley Flat area?

CHENG: No, no way.

HARRIS: If the body started in that Berkeley Flat area, it would take some unusual wind event to produce enough energy to push them on to the shore, as you found?

CHENG: That's what we discussed, yes.

HARRIS: Go ahead and resume your seat. People have no other questions.

Cross Examination by Mark Geragos

GERAGOS: Good morning, doctor. When you were -- first time that they came to you was in February?

CHENG: Yes.

GERAGOS: And when they came in February, they asked you to make some -- to draw some conclusions; is that correct?

CHENG: I don't think so. They didn't ask me to draw any conclusions. They asked me to help to search for Laci's body.

GERAGOS: Right. Well, the one thing that I think I was asking you was, Mr. Harris just finished asking you, you said they gave you some ideas as to where they thought that the body might have been placed in the water; is that correct?

CHENG: That's correct.

GERAGOS: Okay. And was that in February?

CHENG: That was in February, right.

GERAGOS: Okay. And could you point, or could you write on the map with red pen where they suggested that they thought the body may have been placed in the water?

JUDGE: Put an "X", Doctor Cheng. And draw a line to the margin and it put C1. Just put an X. Okay. Do you want to put just draw a line out to the margin?

CHENG: Somewhere over here.

GERAGOS: Okay and was that over off of the tip of Brooks Island?

CHENG: That's correct.

GERAGOS: Okay. Now, when they had you do -- when they suggested that, that's a very shallow area, correct?

CHENG: That's on the edge of a shallow and deep area

GERAGOS: Okay. When you say the shallow area, that's classified there as a shoals, or something like that, is what you used?

CHENG: No. Shoals is sometimes referred to even at low tide, the land at the bottom may be exposed. The shallow is loosely defined. I think it may be one meter, two meters water depth considered shallow.

GERAGOS: Now, specifically when you told -- or when they told you look at this area right here, you have a computer simulation that you do, correct in?

CHENG: Correct.

GERAGOS: Okay. And your computer simulation told you that the bodies would come out into the labeled here

CHENG: Channel.

GERAGOS: The channel, correct?

CHENG: Uh-huh.

GERAGOS: And you told them that -- and I assume that's why they ended up. These are -- if I tell you search areas, this is areas that they went in and searched?

CHENG: I didn't know that, yes.

GERAGOS: Okay. So that didn't work, then they -- how many different computer simulations did you run?

CHENG: Well, that's just basically that's the scenario in that time.

GERAGOS: Okay.

CHENG: But, you know, in the different -- for example, just move the particle tracking, move the particle, make it less personal. Particles a little bit closer to the shore, and a bit out from the shore, so forth, here.

GERAGOS: Okay. Then this was obviously February, the body had not been found. Then they come back to you after the body had been found, correct?

CHENG: Correct.

GERAGOS: And when they come back when the bodies had been found, they asked you to do this analysis that's up here; is that correct?

CHENG: Uh-huh, that is correct.

GERAGOS: Okay. When they asked you -- can I borrow your pointer for a second?

CHENG: The red button here.

GERAGOS: Thank you. And specifically when they asked you to do this, you, at that point, had the locations where the baby is found, and you got the location where Laci is found, and then you do some analysis, and you come up with this section right here with some GPS coordinates, correct?

CHENG: That is correct.

GERAGOS: You do that based upon a couple of -- a lot of assumptions; isn't that correct?

CHENG: Based on assumptions and scientific data.

GERAGOS: Okay. And you -- specifically didn't you tell the officers that there were many variables to took for in some -- you could not factor in, so this would not be a scientific project; is that what you told them?

CHENG: I don't remember the exact words. But, on the other hand, all scientific investigations start with an assumption.

GERAGOS: Okay. I'm going to show you what's been Bates Marked stamped 16836. This is a report by Detective Owen. Could you read that just to yourself, that sentence there that I have got yellow highlighted?

CHENG: Yeah.

GERAGOS: Okay. Does that refresh your recollection as to what you told the officers?

CHENG: Yeah.

GERAGOS: Okay. You told them there were many variables to factor in. Some you could not factor in. So this would not be a scientific project, but a best estimate; is that correct?

CHENG: That is correct. And matter of how you define scientific projects. That's the definition of degree of preciseness.

GERAGOS: Did you also tell them that it was difficult to do what they were asking you to do? I think specifically what you were telling Mr. Harris is because you don't know when the bodies were found, correct?

CHENG: Correct.

GERAGOS: You know when they are found. You don't know when they actually got there, correct?

CHENG: That is correct.

GERAGOS: And you were also told to assume that the bodies had been anchored or weighted -- at least Laci's had, correct?

CHENG: Correct.

GERAGOS: You were told -- you assumed it had been weighted with four or five eight-pound anchors, correct?

CHENG: Correct.

GERAGOS: You were also told to consider the scenario that chicken wire was used; is that correct?

CHENG: I think that once was mentioned, but wasn't emphasized.

GERAGOS: Did they specifically give you any other -- they gave you information did they not, about Laci's size?

CHENG: Yes, they did.

GERAGOS: Okay. And specifically they said they wanted to see if they could determine the area where the bodies had been placed in the water under their theory that there were anchors, correct?

CHENG: Correct.

GERAGOS: And so that they cold go and search for the anchors, right?

CHENG: That was the second phase. The first phase they wanted to search for the body.

GERAGOS: Okay.

CHENG: So I don't know when the -- refer to the February period the first phase.

GERAGOS: I'll call it the May period; is that correct? In the May --

CHENG: May?

GERAGOS: Yes.

CHENG: Yes.

GERAGOS: That's the second period?

CHENG: No. Second phase they did not even -- the body had had already broken away from the anchor.

GERAGOS: If there was anchors?

CHENG: If they were anchors.

GERAGOS: Because you -- they told you to assume there were anchors. That's what they wanted to search for.

CHENG: My part here, the anchor doesn't play any role in the second phase because, now, I mean it wasn't for me to determine whether the anchor is attached to the body or not. We have already assumed the body is already floating loose.

GERAGOS: If the body was floating loose, wouldn't the -- and what is the Mean Low Tide on those days?

CHENG: I thought we showed that. We discussed that.

GERAGOS: How many feet? How many feet?

CHENG: Mean Lower Tide.

GERAGOS: Yeah.

CHENG: At that time I mean I think there was one tide was negative.

GERAGOS: Right. So it would have been two to three feet?

CHENG: Total range, you will need to tell me what you like to know, the tidal range.

GERAGOS: I'm asking you specifically --

CHENG: Yeah.

GERAGOS: If your theory is correct, then the bodies were floating in this area, looks to me like it says five and six throughout all of here, three and four in here, correct?

CHENG: Correct.

GERAGOS: So did it's negative one, then you can just take one foot off of the depth there, correct?

CHENG: That is correct.

GERAGOS: Okay. Now, you said the -- specifically that when you came up with this analysis, you then sent an email to the officers; isn't that correct?

CHENG: Correct.

GERAGOS: Okay. And in the e-mail that you sent to the officers, you told them that, therefore, you recommend this location as a starting point for looking for the weight and the anchors; isn't that what you say?

CHENG: Yes, I did.

GERAGOS: Okay.

CHENG: As I say now, that's based on my best judgment, the highest probability.

GERAGOS: Right. So -- but that's what you were trying to determine; isn't that correct?

CHENG: Correct. Okay. I was trying to determine --

GERAGOS: You were trying to construct a diagram that would show you the best estimate of what you said was the separation location, correct?

CHENG: Correct.

GERAGOS: Okay. And you said that the facts were consistent with the baby being found. However, following the same exercise, you cannot reproduce the trajectories of Laci's body?

CHENG: That is correct.

GERAGOS: Okay.

CHENG: However, there are other paragraphs following that too.

GERAGOS: I'm going to get to that. Specifically the other paragraph after that says that there could be several explanations, right?

CHENG: Yeah.

GERAGOS: Well, but what you didn't tell Mr. Harris, they didn't ask you on direct was that when you did this exercise, you couldn't come up with the trajectory of Laci's body, correct?

CHENG: He didn't ask me. I didn't say.

GERAGOS: Right. I know he didn't ask you that. Now, you said there could be several explanations, right?

CHENG: Correct.

GERAGOS: Okay. And you said that since Laci's body was bulkier than the infant, it could I have been stuck on the bay bottom, right?

CHENG: Correct.

GERAGOS: Well, that explanation would mean that the body was not floating around, wouldn't it?

CHENG: Well, I'm not -- I'm not the expert in that area here. I don't know how the body is behaving in water.

GERAGOS: And, specifically, you have never done anything like this before, have you?

CHENG: I have done some similar studies of particle tracking, but not body.

GERAGOS: Not bodies. How big are particles that you track when you have done those similar studies, what are we talking about?

CHENG: I mean just representative scientific particles, for example, you put a float in the water. But something weighted down, drifting like.

GERAGOS: You have never done any study in San Francisco Bay that has anything to do with bodies or things of that size, correct?

CHENG: That is correct.

GERAGOS: Okay. Basically, what the U.S. Geological Service does is -- I went up on the website. You do many great things.

CHENG: Thanks.

GERAGOS: Basically out there to look at contaminants in the bay and tidal studies, and currents, and things like that nature, correct?

CHENG: Well, scientific investigation here. You don't really need to reproduce precisely what you have had done. Actually, the parallels between science, you do one thing, you can extend your knowledge to the other.

GERAGOS: Right. But you said in this, the next paragraph that you wanted me to get to, that you said this brings up an important note, that the procedures used in these estimates invoke large uncertainties, correct?

CHENG: That is correct.

GERAGOS: And the large uncertainties in the wind data and times for that area, correct?

CHENG: Well, all of these things, by using the word uncertainty. The matters are relative. That now since, of course, obviously we cannot measure wind right at the spot, wind was measured some distance away. Therefore, that's what I'm referring to.

GERAGOS: Maybe I could ask that Mr. Harris, if you would, could you give me the slide where you had the wind data? Remember that? Talking about the slide we looked at that had the three pieces of data on it.

CHENG: Right.

GERAGOS: Okay. Okay?

CHENG: Correct.

GERAGOS: Now, when they showed this, when Mr. Harris showed this, at least if I understand your e-mail correct, that the wind data that you are talking about is not for that specific area that's on the map, right?

CHENG: That is correct. However, though, that's just -- as I mentioned, that's just matter of disclaimer. The wind in that location where your finger is would not be that different from the where the wind was measured.

GERAGOS: Well, let's take a look at that for -- Mr. Harris, that other slide with the wind the arrows on it. Now, if I'm not -- if you said it's not that different, where my finger was on the map, this is over here, correct?

CHENG: Not correct.

GERAGOS: Where was it, here?

CHENG: Closer. Go up. This is South Bay. Go up, up, up, up, up. To the left. Okay somewhere over here.

GERAGOS: That's an arrow that looks like what color?

CHENG: I'll call that 10 to 15.

GERAGOS: What's over here red, and the --

CHENG: That's about 25 knots.

GERAGOS: Okay. So really big wind -- big wind over here, and that appeared to me, at least, to -- looks like it's over land; is that correct?

CHENG: That is over Livermore area, yes.

GERAGOS: How far away is that from the Berkeley Marina?

CHENG: About fifteen miles. The wind was measured right at the Richmond station. May I use the pointer to point out where the wind was measured?

GERAGOS: Well, but I'm asking you, in your e-mail you say there are large uncertainties in the wind data for the area and the times, correct?

CHENG: That's what I said in the e-mail, yes.

GERAGOS: And winds were estimated from nearby measurements?

CHENG: Right.

GERAGOS: Then you also put wave conditions were uncertain, right?

CHENG: We never measured the wind. Wind was estimated from the equation based on the wind speed and distance.

GERAGOS: And the wind-generated drifts, things that you are trying to talk about, were all estimated based on theoretical studies at a different site?

CHENG: That's the handbook. That is not derived -- the handbook from Army Corps of Engineers doesn't mean that not every time you go study, you have to repeat the same exercise over and over again. So the theory established at one location can be applied to other places. That's what I'm referring to in trying to be precise.

GERAGOS: And do you study -- you said also that the error bars -- you know what an error bar means? Measure of air, right?

CHENG: Correct.

GERAGOS: Means how far off you could be on all of this?

CHENG: Yes.

GERAGOS: You said in this estimate could be substantial; is that correct?

CHENG: That is correct.

GERAGOS: Error bars.

CHENG: However, it's also -- again, may I remind you that only a relative matter here. I think the error bar is large. As you said, that is not -- I told you that now that area I have pointed out cannot be interpreted as precise since there is an error bar.

Court Reporter: Are you saying arrow bar or error bar?

CHENG: Error bar. E-r-r-o-r.

GERAGOS: Better than you than me, Laron. If I understand correct, the error -- or your final conclusion is that basically all of this is largely uncertain, correct?

CHENG: That is not correct.

GERAGOS: Well, you said it invokes large uncertainties?

CHENG: Well, let me give you have this.

GERAGOS: Let me just ask you the question. What does, "It invokes large uncertainties" mean?

CHENG: Large uncertainty. That is not precise. Not a hundred percent. Nothing is a hundred percent.

GERAGOS: When you say it's a problem, what did you call -- it says probability, but not deterministic?

CHENG: That's correct.

GERAGOS: Okay. What does deterministic --

CHENG: That it's precise.

GERAGOS: That's precise. It's just not precise?

CHENG: That's correct.

GERAGOS: Is that a fair way to characterize it?

CHENG: Uh-huh.

GERAGOS: But it's probable what you are talking about is probable but not precise?

CHENG: That's correct.

GERAGOS: And that there are large uncertainties; is that right?

CHENG: I did. I state it a relative matter. One, it's a large measure, again, what --

GERAGOS: You said specifically that it invokes large uncertainties; isn't that correct?

CHENG: I did say. Did say that.

GERAGOS: That wasn't my words.

CHENG: I did say -- you don't need to show it to me.

GERAGOS: You don't want to see where it invokes large uncertainty?

CHENG: Yes, I did.

GERAGOS: Okay. You wrote that, right?

CHENG: Let me remind you, Mr. Geragos, that, as you know, we are moving into the internet stage here, that when people write e-mails, typically you don't go through the peer review and editing your text, and all these things. You know that.

GERAGOS: That's why we have cross examination.

CHENG: That's why we have typos in the e-mail.

GERAGOS: Got our own peer review here. It's called cross examination.

CHENG: Getting efficiency of communication.

JUDGE: Both talking at the same time.

GERAGOS: Now, specifically, the other thing, I learned a couple of things when I was studying up for yesterday, bathymetric. I learned that term. That means the depth of the water, correct?

CHENG: Correct.

GERAGOS: Then the other one was, it starts with an "E". And it's estuarian?

CHENG: Estuarian.

GERAGOS: What's estuarian mean?

CHENG: That denotes the region where river meets the ocean.

GERAGOS: Estuarian is a region where the river meets the ocean?

CHENG: Again it's a loosely defined. You can say that, yes.

GERAGOS: Okay. And why is that?

CHENG: That's because there is a fresh water coming from the river, and meets the oceanic water coming from the ocean.

GERAGOS: Where does that come into play in this area here?

CHENG: In this area, depend on the month of the year, and --

GERAGOS: How about December?

CHENG: December, no.

GERAGOS: How about April?

CHENG: April, depend on how wet, how dry the previous year -- water year was.

GERAGOS: Okay. What if we had a very large storm in January, extremely large storm in January?

CHENG: Well, the -- as a matter of fact, it's -- I know these days we have developed so reservoirs and dams here, major runoff would not start until March, and is much regulated.

GERAGOS: Now, did you look, for this year, as to what the runoff was for that year, 2003?

JUDGE: 2003? You said this year.

GERAGOS: For 2003.

CHENG: 2003, I think in terms, even the effect from the fresh water runoff would not affect the currents.

GERAGOS: I'm not asking you about the currents. I'm asking you if fresh water runoff goes into this are

CHENG: In the year 2003?

GERAGOS: Yes.

CHENG: I did not look at that.

GERAGOS: You did not look at that. Is it a fair statement that it was your opinion that if the -- one of the factors or variables is that you assume that the body were in the shallow area -- and you call this the shallow area?

CHENG: Yes.

GERAGOS: That you assumed that the body were in the shallow area for months?

CHENG: I did not assume that. I just say I was given the mission to find where the bodies started traveling. Body could have been there for months.

GERAGOS: And just so that I'm clear, it's -- based on your formula and your trajectory, you could not do -- this did not work for Laci Peterson; isn't that correct?

CHENG: That is correct.

GERAGOS: Thank you. I have no further questions.

Redirect Examination

CHENG: Could I add something?

JUDGE: He's going to be asking some questions. That's why we redirect. Mr. Harris, I'm sure, will give you an opportunity to clear up what you wanted.

HARRIS: I'll start with that right away. What was it you wanted to add, doctor?

CHENG: Okay. I just want to clarify typical scientific investigation, even for that, that I -- that you typically would start a hypothesis. Otherwise you don't know where to start. But a boat-laden hypothesis does not mean a jump-on-the boat conclusion. You start with the boat hypothesis here. You need to back it up with some scientific data, scientific theory, to get to the conclusion. And about two or three months ago, I was approached by the DA's office asking me to serve as an expert witness. I agreed to do that. At that time they gave me this piece of document that you also have in your hand here. So at that time, after we did this calculation, backtracking, and all that, I have been questioned by Mr. Geragos that -- about the uncertainty, and all these things here. Typically, in scientific investigation, it is important to have independent cross check -- cross checks. And in this police report -- actually I studied that over the weekend too. And everybody was working on the weekend. Let me flip to the page. I'd like to read to you too, Mr. Geragos.

GERAGOS: I don't believe it's responsive at this point. It's nonresponsive.

JUDGE: It's nonresponsive. It's narrative.

CHENG: Could do more specific things that --

HARRIS: Doctor, that means the Judge wants me to ask you another question. You are talking about peer review. That means that somebody else looks at the same data?

CHENG: Yes.

HARRIS: And from --

CHENG: Did similar analysis.

HARRIS: From your review of this, just going back to what I was looking at up here earlier. Looking at 284, this particular chart, from your information, was this also reviewed by the Coast Guard?

CHENG: I don't know of the fact. But, however, from the police report --

GERAGOS: There is an objection.

CHENG: I had no --

GERAGOS: There is -- he doesn't know about facts, that he can't rely on.

JUDGE: If he relied on it in forming his opinion, he can testify to --

GERAGOS: Right.

JUDGE: You can say -- you have to lay a foundation.

HARRIS: Since you were going through this, you are looking at the police report, does it have an indication in there of whether the Modesto Police Department provided your data or independent data to the Coast Guard for them to conduct the same type of research?

CHENG: By reading from the report --

GERAGOS: There is an objection if he didn't.

JUDGE: I think that's what we are here leading up to.

GERAGOS: Okay.

JUDGE: He is -- I think that's what we are leading up to.

HARRIS: From reading the report, does it appear that the Modesto Police Department provided your information to the Coast Guard as well?

CHENG: Yes, you did.

HARRIS: And does it appear that the Coast Guard came up with results too?

CHENG: That was paragraph --

JUDGE: Okay?

CHENG: I wanted to read --

JUDGE: Doctor Cheng, in forming your opinion that there is the probability, if I can use that word, that's where the body -- the body was located, did you consider the Coast Guard report also in forming that opinion?

CHENG: No. That's not the point. I did not.

GERAGOS: Right. That's why --

JUDGE: Objection is sustained.

HARRIS: Now, to go back through some of these things, counsel was saying that you haven't conducted any tests where you have thrown bodies in the water to see how they drift. And you were talking about how you take scientific principles and you apply them to other tests. I want to go back through though something that you were saying when you first came in here, we were asking about your degrees. What is your degree in?

CHENG: Aeronautical engineering.

HARRIS: Aeronautical engineering has an application to hydrology?

CHENG: They are studying basically the knowledge of fluid mechanics, the basic knowledge shared with hydraulics and aerodynamics. I think the basic understanding of fluid mechanics.

HARRIS: Fluid mechanics are how objects move. That's the same, whether it's an aeronautical engineer, or if it's in -- where things move in The Bay?

CHENG: That is very similar. There is called a law of similitudes.

HARRIS: So in terms of you being asked if you have ever put bodies in The Bay, I think you had said something, you put -- you have put buoys in The Bay?

CHENG: We have put drifters in the oceanographic study. We wanted to track the movement of currents. You put drifters in. That's not a body, but device that follows the movement of the currents.

HARRIS: So this is some type of floating device that would be on the water and you can observe?

CHENG: It can be adjusted to certain weight that could be representing the water movement at certain depths, or near the surface, or at depth.

HARRIS: Is this something that's done on a regular basis in the field of endeavor that you work in?

CHENG: I wouldn't say regular basis. It's commonly used.

HARRIS: So, again, the scientific knowledge of how things move through the water, that is done in your regular scope of employment?

CHENG: That has been used, but not on a regular basis, yes.

HARRIS: You were asked about -- counsel mentioned something about chicken wire. And you said that was not emphasized. I want to go back to that. You were saying that there were different phases -- I think counsel came up with the term of May. If we refer to when the police came to you prior to the bodies, that being phase one, and after the bodies were found being phase two, or the May phase as Mr. Geragos used. So having that reference in mind just to go back through that briefly. When you were doing this track that we is see up there for phase two, or the May phase, you weren't taking this into account, this chicken wire. That was not a factor for study or review at that time, was it?

CHENG: No.

HARRIS: In fact, you were advised by the Police Department that the bodies the body of Laci Peterson had come up and it was not intact at that time.

CHENG: That is correct.

HARRIS: So they were asking you to help find where the missing limbs might have been.

CHENG: Correct.

HARRIS: And what the most probable location was where those limbs and possible weights might be?

CHENG: Correct.

HARRIS: So where you were looking at this particular phase two, or the May phase to try and try to track that, we weren't even dealing with the complete body at that point in time, were we?

CHENG: No.

HARRIS: And counsel also asked you if you had -- you put a box up there where it was in the first phase. We see your box with the "X" up there. Is that by Buoy Number 4?

CHENG: I don't recall. I can't look at the start possibly. I think the location is correct.

HARRIS: If you can, I don't know if you can find it. If you look up there, see if you see Buoy Number 4.

JUDGE: Can you see Buoy Number 4? If it's there, would you point out with a pencil, or pen, or something where the jury can see it?

CHENG: I can use any finger. I don't see Buoy Number 4 and 6. Actually I did not -- I should -- box should switch over slightly. That doesn't make any difference in conclusion between Buoy 4 and Buoy 6, correct.

HARRIS: And so they were asking you, based on whatever information that they had, or for whatever assumptions for you to consider being in that first phase, in that area by Buoy Number 4?

CHENG: Would you do that again, please?

HARRIS: Okay. When the Modesto Police Department in the first phase were asking you to look in that area that you have drawn up there with the X in the box, that's in the area about Buoy Number 4?

CHENG: Yeah.

HARRIS: When you were asked about these things that you had said in the e-mail, when you are talking about -- I think you said it was a definition of the degree of preciseness. In the scientific field, is preciseness something you really strive for?

CHENG: Trying to anyway. But sometimes, because of other limitations, you may not accomplish what the degree accuracy that you would like to accomplish.

HARRIS: And as you conduct scientific experiments in your chosen field all the time, do you try to strive for preciseness?

CHENG: Yes, I do.

HARRIS: Is it always easy to achieve?

CHENG: It's hard work.

HARRIS: When you apply that over into this application of what the Modesto Police Department asked you to do, to try and find the probable location of where Laci and Conner were at, is this what you were talking about precision is not necessarily achievable, but the science doesn't change?

CHENG: I'm trying to, based on my experience, based on the science.

GERAGOS: Objection.

JUDGE: Overruled.

CHENG: I'm trying my best based on my knowledge and experience to achieve the answers that we were looking for.

HARRIS: Now, counsel asked you last whether you were able to reproduce the results for Conner and Laci. So the track that we see up there, your computer -- your simulation, your analysis of this, this particular track is for Conner Peterson?

CHENG: Correct.

HARRIS: Who was the smallest of the two bodies; is that your understanding as well?

CHENG: That is correct.

HARRIS: And then we also have Laci who was in this disarticulated state, that's what were you advised by the Modesto Police Department?

CHENG: Yes.

HARRIS: Again, part of what they had originally told you that she was anchored or weighted down in some fashion when you were doing your initial analysis?

CHENG: Yes.

HARRIS: If she were weighted down, weighted down, or had anchors attached to her, would that make her properties in water behave differently than that of Conner?

CHENG: It would.

HARRIS: People have no other questions.

Recross Examination

GERAGOS: And specifically you were told in your February exercise to assume a number of things, correct?

CHENG: In February, the previous event, right, yes.

GERAGOS: Yes. In February you were specifically told to assume that Laci was 153 pounds, correct?

CHENG: Correct.

GERAGOS: And you were told to assume possibly four anchors at eight pounds apiece, correct?

CHENG: Yes.

GERAGOS: And also the third thing you were told is possibly wrapped in chicken wire and some form of plastic wrap?

CHENG: That is correct.

GERAGOS: And, specifically, you were not able to -- as Mr. Harris just asked you, you were not able to reproduce the trajectory of Laci's body, correct?

CHENG: I did not need that information at the time when we were doing the trajectory, those information.

GERAGOS: I understand that. I'm asking you a separate question.

CHENG: Okay.

GERAGOS: Separately, what Mr. Harris just asked you is, following your same -- the same exercise that you did up here, you were not able to produce the traveling trajectory of Laci's body?

CHENG: Not without further assumptions.

GERAGOS: Okay. And you had already, I believe, specifically said that the two bodies turn up in two different spots, and that you could give some explanations for that. One of the explanations for that is that they were placed in the water separately; isn't that correct? Isn't that a possible explanation?

CHENG: That is a possibility. But even, I think also stated in e-mail, for the two different objects placed in the water at the same location could possibly wind up in the different locations.

GERAGOS: Correct. And you also stated in the e-mail that you couldn't, based on the assumptions that you made and the information you were given, you could not reproduce the trajectory, correct?

CHENG: For Laci, right.

GERAGOS: Right. And you also specifically cannot say, unless you make assumptions when the bodies were placed in the water, correct?

CHENG: That is correct.

GERAGOS: Okay. And, specifically, you can't say -- I guess you did these tests, or you have done tests with things called drifters; is that correct?

CHENG: Uh-huh.

GERAGOS: How much does a drifter weigh?

CHENG: As I mentioned, that a drifter can be adjusted to a neutral density to water. So it weighs in the area -- it's irrelevant how much it weighs in water.

GERAGOS: Right. How much does one of the drifters weigh?

CHENG: Zero.

GERAGOS: Zero.

CHENG: Neutral buoyant.

GERAGOS: So that's what some of these assumptions are based on is your drifter studies, correct?

CHENG: Correct.

GERAGOS: Which has a weight of zero, because you have reduced that, or offset that in the water, correct?

CHENG: Yes.

GERAGOS: Thank you. I have no further questions.