: .5/7 ; .-OO A* NOAA Technical Report ERL 382-OD 13 *< 0F f% % t* -> <^ ^ss S ?ATES O* an Advection-Diffusion Model of the DOMES Turbidity Plumes Wilmot N. Hess Walter C. Hess November 1976 U.S. DEPARTMENT OF COMMERCE National Oceanic and Atmospheric Administration Environmental Research Laboratories •& GPO 777-045 „dP ATMOSP^ Nonn =% ^i^ cCf 3 NOAA Technical Report ERL 382-OD 13 an Advection-Diffusion Model f the DOMES Turbidity Plumes Wilmot N. Hess Walter C. Hess Office of the Director Boulder, Colorado November 1976 a ft. o '3! q U.S. DEPARTMENT OF COMMERCE Juanita M. Kreps, Secretary National Oceanic and Atmospheric Administration Robert M. White, Administrator Environmental Research Laboratories Wilmot Hess, Director Digitized by the Internet Archive in 2013 http://archive.org/details/advectiondiffusiOOhess Contents Abstract 1 1. Introduction 1 2. Ocean Currents 2 3. Vertical Motion 3 3.1 Initial Nature of the Discharge 3 3.2 Expected Settling 3 3.3 Vertical Mixing in the Wind-Mixed Layer 3 3.4 Vertical Mixing Below the Wind-Mixed Layer 4 4. Horizontal Diffusion 4 5. Calculation of the Surface Plume 5 5.1 Case A. Using Uniform Velocity 5 5.2 Case B. Using Halpern's Measured Currents 6 5.3 Case C. Using Halpern's Currents With Settling Out 7 6. The Benthic Plume 14 7. Bottom Water Plume 16 8. Material Released From the Sediments 19 9. References 22 Figures Figure 1. DOMES sites in the central Pacific. Figure 2. Daily average currents at Site C 2 Figure 3. Settling velocities for small particles calcu- lated using Stokes Law 3 Figure 4. The puff model of advection-diffusion 5 Figure 5. Case A sediment plume densities calculated using S=1000 tons/day and X=20 km/day for a time of 2 weeks 6 Figure 6. Case A sediment plume densities calculated using S=1000 tons/day and V=20 km/day for a time of 2 months 6 Figure 7. Case A sediment plume densities calculated using S= 100 tons/day and V = 20 km/day for a time of 2 weeks 7 Figure 8. Case A sediment plume densities calculated using S= 100 tons/day and V = 20 km/day for a time of 2 months 7 Figure 10. Case A sediment plume densities calculated using S= 100 tons/day and V=10 km/day for a time of 2 months 8 Figure 11. Case A sediment plume densities calculated using S=1000 tonslday and V=40 km/day for a time of 2 months 8 Figure 12. Case A sediment plume density along the center line of the turbidity plume 9 Figure 13. Advection and diffusion of sediments 9 Figure 14. Sediment plume calculated using Halpern cur- rents (Case B) and S=W00 tons/day for days 1-10 9 Figure 15. Sediment plume calculated using Halpern cur- rents (Case B) and S=1000 tons/day for days 1-20 9 Figure 16. Sediment plume calculated using Halpern cur- rents (Case B) and S=1000 tons/day for days 1-30 9 Figure 9. Figure 17. Case A sediment plume densities calculated Sediment plume calculated using Halpern cur- using S= 2000 tons/day and V=10 km/day for rents (Case B) and S=1000 tons/day for days a time of 2 months 8 24-34 9 Figure 18. Sediment plume calculated using Halpern cur- rents (Case B) and S= 1000 tons/day for days 24-44 10 Figure 19. Sediment plume calculated using Halpern cur- rents (Case B) and S=1000 tons/day for days 24-54 10 Figure 20. A comparison of sediment plumes for D=10 5 cm 2 /sec and D=20 6 cm 2 /sec 10 Figure 21. Assumed particle size distribution (A) having 50% of particles with d > 4/x io Figure 22. Assumed particle size distribution (B) having 90% of particles with d > 4/u. 11 Figure 23. Case C. Diminished surface sediment plume allowing the heavy particles to settle out. Halpiern currents for days 1—10 are used. 11 Figure 24. Case C. Diminished surface sediment plume allowing the heavy particles to settle out. Halpern currents for days 1—20 are used. 11 Figure 25. Case C. Diminished surface sediment plume allowing the heavy particles to settle out. Halpern currents for days 1—30 are used. 11 Figure 26. Change, with time, of PSD-A due to settling out of heavy particles 12 Figure 27. Change, with time, of PSD in the mixed layer due to settling out of heavier particles. . . 12 Figure 28. Case C. Sediment plume below the mixed layer due to settling out of heavier particles for days 1-10 12 Figure 29. Case C. Sediment plume below the mixed layer due to settling out of heavier particles for days 1-20 13 Figure 30. Case C. Sediment plume below the mixed layer due to settling out of heavier particles for days 1-30 13 Figure 31. Typical PSD for the below-thermocline plume at locations indicated in Figure 25 13 Figure 32. Particle size cumulative curves at station B for depths m, 56 m, 1 73 m, 298 m, and 800 m 13 Figure 33. Diminished surface sediment plume (Case C) including settling of heavy particles for days 1-30 14 Figure 34. Benthic blanket thickness for ship moving 1 m/sec and bottom current flowing 1 cm/sec and 5 cm/sec perpendicular to ship motion. PSD-A is used 15 Figure 35. Benthic blanket thickness for ship moving 1 m/sec and bottom current flowing 1 cm/sec and 5 cm/sec perpendicular to ship motion. PSD-B is used 15 Figure 36. Sediment densities in the benthic plume in- flight 16 Figure 37. Calculated plume of bottom water in the mix- ed layer after 2 weeks of dredging V=20 km/day; S=100,000 mi/day 17 Figure 38. Calculated plume of bottom water in the mix- ed layer after 2 weeks of dredging V=20 km/day; S=10,000 m^/day 17 Figure 39. Calculated plume of bottom water in the mix- ed layer after 2 months of dredging V=10 km/day; S=100,000 m^/day 17 Figure 40. Calculated plume of bottom water in the mix- ed layer after 2 months of dredging V=10 km/day; S = 10,000 m^/day 18 Figure 41. Calculated nutrient plume of nitrates in the mixed layer after 2 weeks of dredging. ... 18 Figure 42. Calculated nutrient plume of silicates in the mixed layer after 2 weeks of dredging. ... 18 Figure 43. Calculated plume of heavy metals Mn, Fe, Cu, and Ni introduced into surface waters after 2 weeks of dredging 19 Figure 44. Calculated plume of Ca and K introduced into surface waters after 2 weeks of dredging. 20 Figure 45. Calculated plume of nitrates introduced into surface waters after 2 weeks of dredging. . 20 Figure 46. Calculated plume of silicates introduced into surface waters after 2 weeks of dredging. 20 an AD VECTION- DIFFUSION MODEL of the DOMES 1 TURBIDITY PLUMES Wilmot N. Hess and Walter C. Hess 2 The sediment dumped overboard from a manganese nodule mining ship in the Central Pacific Ocean will contain many small particles of diameter — 3 microns. These will not settle rapidly and will form a near- surface plume extending a long distance from the mining ship. A second plume will be formed near the bot- tom due to the disturbance by the mining device. This paper discusses the nature, extent and density of these two plumes. A physical model using advection of the sediment plus horizontal diffusion plus settling of the fines by Stokes Law is used to calculate several cases of plume behavior. Typical surface plume densities are less than 1 milligram/liter except quite near the mining ship. The benthic blanket produced by the bottom plume will typically have thicknesses of less than 100 micrograms/cm 2 . 1. INTRODUCTION In a year or two when mining of deep sea manganese nodules starts in the Pacific Ocean, hy- draulic lift systems will carry not only nodules but also bottom water and resuspended fines to the surface of the ocean. The ship collecting the nodules will sort the material, hold the nodules, and dump overboard the bottom water and fines. Surface currents will carry this stream of fines away from the ship, producing a surface plume of resuspended sediments. A second plume of fines will be formed near the dredge head of the mining ship on the bottom of the ocean. Much of the sediment collected with the nodules from the bottom by the dredge head will be separated out and rejected back into the near bottom water before moving the nodules up the pipe. This plume will slowly settle out and blanket the benthos near the track of the dredge head. The question to be addressed here is what will be the ap- pearance of these plumes of fines from such a one-ship mining operation? In order to describe these plumes we must separate the particle motion into three components: (a) advection, which describes the mean motion of the plumes by some average horizontal current velocity; (b) settling, which describes the fall- ing of the particles back to the bot- tom; and (c) diffusion, which describes the dispersal of material off the track of the mean motion. 1 Deep Ocean Mining Experimental Study 2 Student, California Institute of Technology, Pasadena, California. 60 50 40 120° 135° 150° 165° 180° 165° 150° 135° 120° 105° 90° 30° 20° 10 A 8°27N, 150°47'W B 11°42'N, 138°24'W C 15°00'N, 126°00'W Area of max. commercial interest 60° 50° 40' 30° 20° 10° 120° 135° 150° 165° 180° 165° 150° 135° 120° 105° 90° Figure 1. DOMES sites in the central Pacific. 2. OCEAN CURRENTS First, in the case of advection, let us consider what is known about ocean currents in the DOMES area. The DOMES Project selected three sites for study as shown in Figure 1. Until very re- cently there were no direct cur- rent measurements in these areas. Geostrophic currents had been calculated based on STD measure- ments, but there are uncertainties in this procedure. When carrying out the geostrophic approxima- tion one has to assume a level of no motion somewhere in the water column. For the tropical waters of the eastern Pacific, this is typically taken at 500 m and this may or not be a valid assump- tion. Using the geostrophic ap- proximation, surface currents at Site C, which is about 15° N, are roughly 25 cm/sec to the west. At Site A, which is about 8°N, the currents are about 40 cm/sec to the east (Halpern, private commun- ication). Site A is in the North Equatorial Countercurrent. Recently, the first direct cur- rent measurements in this area were carried out by Dr. David Halpern (1976). Table 1 gives his Table 1. Average Current at Site C Observed During September and October 1975. Total Component Component Depth Velocity E-W N-S 20m 25cm /sec 17 (to W) 10 (to N) 50 20 11 6 100 15 6 2 200 12 +3 2 300 12 +5 preliminary values at Site C. We will make calculations of the tur- bidity plume using constant horizontal advection velocities of V = 10 km/day = 11. 5 cm/sec, V = 20 km/day = 23 cm/sec, and V = 40 km/day = 46 cm/sec. We will also make calculations of the sur- face plume based on Hal pern's daily average current vectors measured at Site C in September and October 1975 as shown in Figure 2. These currents are at 20- m depth and have been low-pass filtered to remove the high fre- quency components. They show the considerable variability of the currents. There is very little data on near-bottom currents in the DOMES area (Amos et al., 1976). We will assume that the currents are in the range 1 < V < 5 cm/sec (Halpern, private communica- tion). Figure 2. Daily average currents at Site Cat 20 m depth for Sept. 1 to Oct. 26, 1975 (from Halpern) (low pass filtered). 3. VERTICAL MOTION In considering vertical behavior of the plumes we must take into account the initial nature of the discharge, the settling to be ex- pected from Stokes Law, the ver- tical mixing that will occur fairly rapidly in the wind-mixed layer of the ocean, and the considerably slower mixing below the near- surface mixed layer. 3.1 Initial Nature of the Discharge We will assume that the dis- charge of fines takes place at the surface with trivially small initial velocity. The fines and bottom water may not stay at the surface because bottom water is denser than surface water and tends to sink. We will assume it mixes 1 ' / _ "5 F 10 ' m Quartz Sphere t: i (fresh water) _o 9 10- / - 10 ' - / - 10" / i i 1 10 100 1000 Particle Diameter (microns) Figure 3. Settling velocities for small particles calculated using Stokes Law. rapidly and does not sink any ap- preciable distance. We will also assume that the material, when initially pumped overboard from the ship, is so dilute that there is no turbidity current, and that the material is initially deposited in the surface layer of the ocean. This seems reasonable because when dumped overboard the material will be diluted at least ten to one with water and will be at very low velocity. 3.2 Expected Settling A solid object placed in a fluid tends to settle under gravity by Stokes Law which states (*?> where u> is the settling velocity given in cm/day, p is the particle's density, /jl is the coefficient of molecular viscosity of the fluid, g is the acceleration of gravity, and d is the particle diameter in microns. Evaluating with ac- cepted values of the coefficients, we can simplify this to to = 7.85 d 2 . We have assumed that we are dealing here with quartz spheroids in 35 parts per thou- sand salinity sea water at a tem- perature of 20°C. A graph of set- tling velocity is given in Figure 3. A typical particle size in sedi- ments in the nodule zone of the Pacific has been measured to be about 4 microns in diameter (Bishoff, private communication; Cooke, private communication). Using d = 4 microns, we find that a), the settling velocity, is approx- imately 125 cm/sec. There are some oversimplifications made here: for example, we have con- sidered the particles to have a density of 2.2 and it is probably less than this since the particles have odd shapes rather than spherical shapes. This would tend to make the settling velocity less than our estimate. Further, we have ignored flocculation. Parti- cles naturally tend to gravitate together in water and as a result of this probably settle somewhat faster. Also, many particles in the plumes will not be broken down to their fundamental particle size but will be considerably larger and these will, of course, fall faster. Our estimate of the settling velocity is quite small. In fact, it is so small that for part of the work we want to carry out we can com- pletely ignore settling and only treat mixing. We will take a range of values of 100 tons/day to 1000 tons/day (DOMES, 1976) for the daily mass of sediment in- troduced into the plumes. This range of values will allow for some of the particles to settle out rapidly and still permit reasona- ble estimates for the plume den- sity. 3.3 Vertical Mixing in the Wind-Mixed Layer The mixed layer of the ocean in the region of Site C is typically 20 m deep (see data from Dr. Halpern in Table 2) and is an area of rapid mixing. Under condi- tions of fairly good winds, a mix- ing time, T, is about half an iner- tial period, Tq, where the inertial Table 2. Depth of Mixed Layer in the Site-C Region. Cast Latitude Longitude Mixed Layer Depth 2 18° N 126° W 40 m 5 17° N 126° W 30 m 9 16° N 126° W 20 m 18 15° N 126° W 25 m 24 14° N 126° W 20 m 28 13° N 126° W 15 m 32 12° N 126° W 10 m Table 3. Values of Inertial Periods (T e ) and Mixing (T). Site Latitude T T=T 0/2 c B A 15° N 12° N 8°N 46 hrs. 58 hrs. 86 hrs. 23 hrs. 29 hrs. 43 hrs. period is given by T g = 12/sin0 and 9 is the latitude. Table 3 below gives inertial periods and mixing times. From this table we see that if the trade winds blow for a day or so we mix the water to a depth of 20 m. There will be periods when the winds are slack and this mixing does not occur; hence the material will tend to re- main near the surface. For the purposes of our present calcula- tions we will assume uniform mixing through the top 20 m of the water and a simple scaling of the numbers to give surface den- sities for the condition of no mix- ing. We will consider that even the first day's fines are mixing to 20 m even though they may tend to stay closer to the surface than this. 3.4 Vertical Mixing Below the Wind- Mixed Layer Mixing through the ther- mocline is very slow. Vertical diffusion coefficients in this region, according to Dr. Claes Rooth of Miami, are in the range 0.1 to 1.0 cm 2 /sec. This mixing is so slow that we will completely ignore it for the time periods in which we are interested, a few weeks or even a few months. However, this clearly should be included in calculating behavior of the plume for years. 4. HORIZONTAL DIFFUSION We will combine all motions into the ocean (other than the average advection velocities) into a simple, uniform horizontal diffusion coefficient. We will con- sider then that the motion is uniform radial diffusion from a point source. The diffusion equa- tion is Bn bt 1 b br [»*] If D can be considered to be a con- stant, this then becomes I) b 2 n br' + D bn bn e7 r br For this situation the solution of the diffusion equation is: " i = settling velocity in cm /day. We can obtain the PSD for each day from n i (t=m+l)=(l-f i )n i (t=m). Now if we take the diminished puffs from each day's plume source and add them together i we have the diminished plumes given in Figures 23-25. Com- parison of these with Figures 14—16 shows the effect of settling out. The contours are considera- bly smaller when we include set- tling out. However, it must be remembered that the contours are in terms of mass per unit volume and using mass emphasizes the large size particles. Particle size distribution A has only 7.66% of particles with d > 12/x,, but this group includes 55% of the mass of all particles. Only 10% of the mass in PSD- A is for particles with d < 6.5yn, but this range includes 73.27% of all particles. ;■><><> 1.25 600 2100 2300 2500 2700 Figure 11. Case A sediment plume densities calculated usingS = 1000 tons \ 'day and V = 40km/dayfora time of 2 months. Contours are micrograms/liter of sediments. 150 Day 1 Figure 12. Case A sediment plume den- sity along the center line of the tur- bidity plume. V = 10 km/day andS — 1000 tons/day. Figure 13. Advection and diffusion of sediments placed in water at DOMES Site C on Aug. 29, 1975, using puff model (Fig. 4). 200 100 Kilometers 200 E 100 — 100 Figure 14. Sediment plume calculated using Halpern currents (Case B) andS = 1000 tons/day for days 1-10. Figure 15. Sediment plume calculated using Halpern currents (Case B) and S = 1000 tons/day for days 1-20. 300 100 300 200 100 100 Kilometers Figure 16. Sediment plume calculated using Halpern currents (Case B) and S = 1000 tons/day for days 1-30. Figure 17. Sediment plume calculated using Halpern currents (Case B) and S = 1000 tons/day for days 24-34. 500 400 300 E 2 200 100 — x - ■ -0.003 0.01^ mg iter — ~o 1 V*. ■ ; %O s \\o3 I 600 400 300 200 Kilometers 100 100 Figure 18. Sediment plume calculated using Halpern currents (Case B) andS = 1000 tons/day for days 24-44. Figure 19. Sediment plume calculated using Halpern currents (Case B) and S = 1000 tons/day for days 24-54. 300 500 300 200 100 Kilometers Figure 20. A comparison of sediment plumes for D = 10 5 cm 2 /sec and D = 10 6 cm 2 /sec, calculated using Halpern currents for days 1-30, and S = 1000 tons/day. 20 30 Diameter (m) Figure 21. Assumed particle size dis- tribution (A) having 50% of particles with d > 4 fx. Vertical scale is rela- tive number of particles. Figure 26 shows how the PSD- A will change with time in the mixed layer for one puff of parti- cles because of settling out of heavier particles. This is plotted on the basis of number of particles versus particle size. Figure 27 shows the altered values of PSD for the points A, B, and C in Figure 25. Figure 27 has been plot- ted in terms of mass of particles (in each size group of Table 5) ver- sus particle size. We also have calculated the ap- proximate sediment density ex- pected just under the thermocline by taking the settled out particles for one day for each puff, Si = fiPi gm/cm 3 , and summing for all particle groups and for the several over- lapping puffs present at each loca- tion, s(x,y,t) -X 2 puffs 1 Sj(t,x,y) The values for this below-ther- mocline sediment plume density s{x,y) are shown in Figure 28 for the same conditions given in Figure 23. Other below-ther- mocline plumes for later times are shown in Figures 29 and 30. Typi- cal values of PSD in this below- thermocline plume (for the loca- tions shown in Figure 30) are given in Figure 31. Baker and Feely (1976) have measured the PSD of particles in the upper water column in the DOMES area by filtering water samples and then using a scan- ning electron microscope. The PSD-C measured this way is shown in Figure 32 and is also 10 Figure 22. Assumed particle size dis- tribution (B) having 90% of particles with d > 4 fi. Vertical scale is rela- tive number of particles. Figure 23. Case C. Diminished surface sediment plume allowing the heavy particles to settle out. PSD-A and Halpern currents for days 1-10 are used. S = 1000 tons/day. 300 200 ^-"-^ \ I I / S \ \ III \ \ > •ill N 1 0.01 ill ■ \ \ \ \\\ c iW \ \ \ 0.1 -- With Settling Without Settling 01 Kilometers 500 400 300 200 100 Kilometers 100 Figure 24. Case C. Diminished surface sediment plume allowing the heavy particles to settle out. PSD-A and Halpern currents for days 1-20 are used. S = 1000 tons/day. Figure 25. Case C. Diminished surface sediment plume allowing the heavy particles to settle out. Halpern cur- rents for days 1-30 and PSD-A are used. Shown for comparison are the contours for no settling out from Figure 16. given in Table 5. Baker and Feely state, "The size distribution in the water column compares favora- bly with that determined for the bottom sediment by the USGS preliminary report of a box core from Site C. The close agreement suggests that mining debris, when completely disaggregated, will have a PSD very similar to the naturally occurring suspended particle matter." However, recent data from Sallenger (private com- munication) of the USGS would seem to say that PSD-A may be nearer to actuality. Using PSD-C we have recalculated the surface layer sediment plume using Halpern's currents for 1-30 days. Results are shown in Figure 33. In this case, the sediment plume quite closely resembles the plume in Figure 16, which had no set- tling out included. 11 Table 5. Settling Velocities and Times for Different Size Particles, and Particle Size Distributions(PSD) Used in the Calculations. Particle Particle Size Range Av. Diameter (i) T, PSD-A PSD-B PSD-C (**) (/*) (cm/day) (days) (%) (%) (%) 1 0.5 1.96 1020 6.84 0.42 12 2 1.5 17.7 113 15.85 2.08 28 3 2.5 49.0 40.8 15.75 3.32 34 4 3.5 96 20.8 11.60 4.16 16 5 4.5 159 12.6 9.56 5.00 5 6 5.5 238 8.40 7.52 5.48 3 7 6.5 332 6.04 6.15 5.68 2 8 7.5 441 4.54 5.50 5.68 — 9 8.5 566 3.54 4.10 5.51 — 10 9.5 710 2.82 3.56 5.31 — 11 10.5 865 2.32 3.14 5.05 — 12 11.5 1040 1.92 2.60 4.51 — 13 12.5 1230 1.62 1.92 4.37 — 14 13.5 1430 1.40 1.64 4.07 — 15 14.5 1650 1.22 1.37 3.84 — 16 15.5 1880 1.06 1.09 3.52 — 17 16.5 2140 0.94 0.82 3.28 — 18 17.5 2400 0.84 0.55 3.00 — 19 18.5 2680 0.75 0.27 2.80 — 20 19.5 2980 0.67 — 2.60 — 25 22.5 3980 0.50 — 10.00 — 30 27.5 5940 0.338 — 6.02 — 35 32.5 8300 0.241 — 3.12 — 40 37.5 11020 0.181 — 1.25 — 50 Diameter (microns) Figure 26. Change, with time, of PSD- A in the mixed layer due to settling out of heavy particles. 100 t Diameter (microns) Figure 27. Change, with time, of PSD - A in the mixed layer due to settling out of heavier particles. This is calcu- lated for the positions shown on Figure 25. Kilometers Figure 28. Case C. Sediment plume below the mixed layer due to settling out of heavier particles for days 1-10. Halpern currents and PSD-A are used. S = 1000 tons/day. 12 100 100 — 0.0003 mg/l iter -0.003 001 01 mg/liter 100 Kilometers 100 100 Kilometers Figure 29. Case C. Sediment plume below the mixed layer due to settling out of heavier particles for days 1—20. Halpern currents and PSD-A are used. S = 1000 tons/day. Figure 31. Typical PSD for the below- thermocline plume at locations indi- cated in Figure 25. Figure 30. Case C. Sediment plume below the mixed layer due to settling out of heavier particles for days 1-30. Halpern currents and PSD-A are used. S = 1000 tons/day. 5 10 15 Diameter (microns) 20 100 Figure 32. Particle size cumulative curves at station B for depths m, 56 m, 1 73 m, 298 m, and 800 m. The dot- ted line indicates the median diameter. 3 4 Particle Diameter (fj.) 13 6. THE BENTHIC PLUME The dredge head on the bottom picks up lots of sediment, separ- ates most of it from the nodules, and drops the sediment about 20 m above the bottom. The dredge puts out sediments of from 14,000 to 120,000 tons/day (DOMES, 1976). The mining ship moves at roughly 1 m/sec so we have a line source of sediment released by the dredge head equivalent to 1.6 x 10 5 to 1.4 x 10 6 gm/m source strengths. We can now use our bottom current estimates of V = 1 to 5 cm/sec to move the sediment horizontally from the dredge track. We assume that V is per- pendicular to the motions of the ship so the material is carried sideways and gradually settles to the bottom with a velocity o> that depends on the particle diameter: dredge track. Diffusion will broaden this group of particles into a Gaussian distribution of half-width given by X 2 4DT 9 = 1 or, in this instance, X = 6.6 km. Now we can treat this problem as two-dimensional motion in the x-z plane. Using a 1-meter length of the source of strength, n^, we follow the particles as they advect and diffuse sideways and slowly settle out to the bottom. We take a source strength of 35,000 tons/day of sediments. Then, if the ship tra- vels at 1 m/sec we will have a linear source strength t% = 0.4 ton/meter. We are dealing here with one-dimensional diffusion from a line in a plane. The diffu- sion equation for constant D is given by dn_ dt D dX 2 and the solution is n{X,t) = *h V47rDf . e - >P/4Df We will allow each particle group to settle for a time,T 20 , calculate the shape of the diffu- sion pattern for each particle group, and then sum them. This gives the thickness of the blanket of fines that is deposited on the bottom near the dredge head. (i) cm/day = 7.85 d 2 with d in microns. We don't really know the particle size distribution but estimates made by the mining companies (DOMES, 1976) say between 50% and 907c of the particles are larger than 4/x in diameter. These parti- cles are mostly clumps, not broken down into the fundamen- tal particles. (Using this range, we constructed the two values of PSD shown in Figures 21 and 22.) We have broken these into \-/jl inter- vals and calculated the settling velocities oj and the times T 20 to settle out to the bottom from 20 m. These are listed in Table 5 with the fractions of the particles in the indicated size intervals. Particles 4-5/u. in diameter will take 12.6 days to settle 20 m to the bottom. In this time, with V = 1 cm/sec, the particle group will move 11 km sideways from the N \ \ "T -((( \ With Settling \ \ \\ Without Settling — V ^0^_ /° 01 m 9/ |iter \ \ \ \T — — ~-^r>^y 003 Nv ' 1 — 0.01 imj'litri .i _^~* — -^*V -»~\NVu3 , 1 I I 300 200 Kilometers Figure 33. Diminished surface sediment plume (Case C) including settling of heavy particles for days J- 30. Halpern currents and PSD-C are used. )4 Figures 34 and 35 show this blanket thickness at different dis- tances from the dredge track for bottom currents of V = 1 cm/sec and 5 cm/sec. We can get estimates of the sediment density in the benthic plume before the sediment settles back onto the bottom. The parti- cles settle toward the bottom from the 20-meter level of the source with the velocity a> shown in Ta- ble 5. Particles of different sizes are sorted vertically by this pro- cess. At a time of 10 5 sec, the parti- cles will have moved 1 km side- ways from the dredge track (using V = 1 cm/sec). The particles also diffuse horizontally to give the horizontal distribution n{x,t) >h y/4-rrDt _exp ( For D = 10 5 cm 2 /sec and n^ = 0.4 ton/meter we obtain n (1 km, 10 5 sec) = 113 gm/m 2 . At t = 10 5 sec, particles of d > 16/x will have settled to the bot- tom. Particles of diameter 8/x < d < 9/u, will have settled a depth of 1 = 6.55 m. We assume they spread out vertically, because of the range of sizes involved, to cover a vertical range of H = 1.56 m around Z. This value of H is half the vertical distance from the center of the next higher group of particles to the next lower group of particles. We can now calculate the sediment density of these par- ticles at z ~ 6.5 m and at x = 1 km to be t sc x in5 ^ (113) (0.0566) n, (z = 6.5 m, t = 10 5 sec) = 1.56 4.08 gm/m 1 where 0.0566 is the mass fraction of particles of 8/x < d < 9/x. Values of the plume density ob- tained this way are shown in Figure 36. 20 15 E I 10 f\ ^-V=l cm/sec \ ^-V=5 cm/sec 1 J^ Kilometers 5 Kilometers 10 Figure 34. Benthic blanket thickness for ship moving 1 m/sec and bottom current flowing 1 cm/sec and 5 cmjsec perpendicu- lar to ship motion. PSD- A is used. Figure 35. Benthic blanket thickness for ship moving 1 m/sec and bottom current flowing 1 cm/sec and 5 cm/sec perpendicu- lar to ship motion. PSD-B is used. 15 7. BOTTOM WATER PLUME From 10,000 to 40,000 m 3 /day of bottom water will be brought up the pipe from the bottom by the mining ship and released into the surface water (DOMES, 1976). This water will probably be colder and denser than surface water even though it has been fric- tionally heated rising through the pipe. This bottom water might settle out at some intermediate depth where it would be neutrally buoyant but more probably it would mix promptly and become part of the surface waters of the ocean. Assuming it spread uniformly through the 20-m layer, we can calculate directly what the plume of bottom water looks like. Using sources of 10,000 m 3 /day and 100,000 m 3 /day, D = 10 6 cm 2 /sec, and constant ad- vection velocity V, we have found the bottom water plumes shown in Figures 37—40. Typical bottom water concentrations are a few ppm. The bottom water carries nutrients to the surface. If the nutrient concentration in the bot- tom water is n b ar\d in the surface water it is n s then the resultant surface concentration « r will be n r = cn b + (l-c)n s where c is the concentration of bottom water in surface water as shown in Figure 37. Nutrient values measured dur- ing the DOMES project and repre- sentative of all sites are (Ander- son, private communication) Plume Density, mg/hter 20 2 4 6 • • * i • • . 4-5 M • 4— 5 fj. • • • 15 • t "" dJ CD E 10 sz Q. o> Q • < • 4-5/x 3-10/1 t — • • • 5 * • 9-10/i • • 14-15 ft Bottom 1 t .— :•■■"• ■;-•■- ■■■■■: wm Multiplying these bottom water nutrient values n h by the bottom water concentrations given in Figure 37, we obtain the nutrient plumes shown in Figures 41 and 42. Except in regions where the nitrates in the mixed layer are es- sentially zero, the added nutrients Upper mixed layer (n s ) Bottom water (n, ) Nitrate 0-0.5 /Limols/liter 35-36 /xmols/liter Silicate 1-4/nmols/liter 137-138 ^mols/liter Figure 36. Sediment densities in the benthic plume in-flight for V = 1 cm/sec, D = 10 5 cm 2 lsec, n = 0.4 ton/meter. The locations of the various particle groups are shown. Curve (A) is for t = 10 5 sec — 1.15 days and x = 1 km; Curve (B) is for t = 2 x 205 sec ~~ 2.3 days and x= 2 km; Curve (C) is for t = 4 x W 5 sec — 4.6 days and x = 4 km. shown in Figures 41 and 42 repre- sent a small addition to the pre- existing nitrates and silicates in the surface waters given above. 16 0.25 0.125 Figure 37. Calculated plume of bottom water in the mixed layer after 2 weeks of dredging (in ppm). V = 20 km/day; S = 100,000 m>/day. hid Figure 38. Calculated plume of bottom water in the mixed layer after 2 weeks of dredging (in ppm). V = 20 km/day; S = 10,000 mi/day. 0075 0.05 0025 0.0125 200 100 — £ Figure 39. Calculated plume of bottom water in the mixed layer after 2 months of dredging (in ppm). V = 10 km/day; S = 100,000 m^/day. 17 200 Figure 40. Calculated plume of bottom water in the mixed layer after 2 months of dredging (in ppm). V = 10 km/day; S = 10,000 m^/day. e o .'no Figure 41. Calculated plume of nitrates added to the mixed layer after 2 weeks of dredging. Nitrates are introduced by bottom water of 100,000 m^/day. V = 20 km/day. Contours are in micro- micro mol/liter. Figure 42. Calculated plume of sili- cates added to the mixed layer after 2 weeks of dredging. Silicates are in- troduced by bottom water of 100,000 mVday. V = 20 km/day. Contours are in micro-micro mol/liter. 34 17 18 05 0.25 Figure 43. Calculated plume of heavy metals Mn, Fe, Cu, and Ni introduced into surface waters after 2 weeks of dredging. Contours are parts per 10 15 parts of water. V = 20 km I day; S = 1000 tons/day. This plume is an upper limit to the expected heavy metals released from the sediments. 8. MATERIAL RELEASED from the — SEDIMENTS Recently Bishoff (private com- munication) placed sediment samples from the bottom in the DOMES area into clean sea water to find out what proportion of metals, nutrients, and other materials are released from the sediments. He placed 10 grams of sediments in 0.1 liter of sea water and agitated it for 11 days. Table 6 shows the material released from the sediment into the sea water. For most samples the heavy metals Fe, Cu, and Ni levels were obviously below the limit of detectability (about 20 ppb). If we assume that 10 ppb of the heavy metals Fe, Cu, and Ni were actually produced in the resuspension test above, we can produce the heavy metal plume expected from the DOMES min- ing operation. These resuspension tests used 100 grams/liter. If we scale the results down by 10 5 we get the effect expected from 1 mg// of sediment in sea water. We can compare this directly with the appropriate contours of Figure 5 and produce the heavy metal plume shown in Figure 43. Table 7 shows the normal com- position of sea water at sea level (Goldberg, 1963). Comparison shows that at normal sea level it has considerably more heavy metal content than that expected with the sediment from a mining operation. Similarly, we can construct a Ca and K plume (Fig. 44) as well as nutrient plumes. For the ni- trates we get 21 x 10^m//at the location of the 0.1 mg//contour of Figure 5. This produces the con- tours for added nitrates (Fig. 45) and for added silicates (Fig. 46). Comparing these two figures with Figures 39 and 40 we see that bot- tom water puts more nutrients into the surface water than do these sediments. Also, comparison of these four figures with the data on nutrients in the upper mixed layer given in Table 7 indicates that the fraction of nutrients ad- ded to the mixed layer by the ad- dition of the bottom water and sediments is quite small. Table 6. Results of Resuspension Experiments. Depth Mg Ca K Si0 2 Fe Mn Cu Ni N0 3 N0 2 PQ 4 NH 3 Interval (ppm) (ppm) (ppm) (ppm) (ppb) (ppb) (ppb) (ppb) i/xm/f) iju,m//> ifxm/f/ (fxm/f) 2-4 cm 1203 392 404 15 <5 <7 <5 <10 23 0.9 1.7 2.2 10-12cm 1194 399 403 14 <5 <5 <5 <10 15 0.9 1.3 2.8 18-20 cm 1225 395 404 13 <5 <5 <5 <10 18 0.7 1.2 2.2 26-28 cm 1228 391 434 12 <5 <5 <5 <10 26 0.6 2.2 3.5 30-32 cm 1230 397 405 13 400 100 <5 <10 23 0.7 1.4 2.8 Average 1216 395 410 13 80 20 <5 < 10 21 0.7 1.6 2.7 14 Figure 44. Calculated plume of Ca and K introduced into surface waters after 2 weeks of dredging. V = 20 kmlday; S = 1000 tons/day. Contours are in parts per trillion. 20 10 3.1 2.1 1.05 0.52 Figure 45. Calculated plume of nitrates added to surface waters after 2 weeks of dredging. These nitrates are the maximum expected to be released from 1000 tons/day of sediments introduced into the surface waters. V = 20 kmlday; S = 1000 tons/day. Contours are in micro-micro mol/liter. Figure 46. Calculated plume of sili- cates introduced into surface waters after 2 weeks of dredging. These sili- cates are the maximum expected to be released from 1000 tons/day of sedi- ments introduced into the surface waters. V = 20 km/day; S = 2000 tons/day. Contours are in micro-micro mol/liter. 20 . Table 7. Geochemical Parameters of Sea Water. Element Abundance Element Abundance Element Abundance (mg//) (mg//) (mg//) H 108,000 Ti 0.001 Cd 0.00011 He 0.000005 V 0.002 In <0.02 Li 0.17 Cr 0.00005 Sn 0.003 Be 0.0000006 Mn 0.002 Sb 0.0005 B 4.6 Fe 0.01 I 0.06 C 28 Co 0.0005 Xe 0.0001 N 0.5 Ni 0.002 Cs 0.0005 O 857,000 Cu 0.003 Ba 0.03 F 1.3 Zn 0.01 La 0.0003 Ne 0.0001 Ga 0.00003 Ce 0.0004 Na 10,500 Ge 0.00007 W 0.0001 Mg 1,350 As 0.003 Au 0.000004 Al 0.01 Se 0.004 Hg 0.00003 Si 3 Br 65 Tl <0.00001 P 0.07 Kr 0.0003 Pb 0.00003 S 885 Rb 0.12 Bi 0.00002 CI 19,000 Sr 8 Rn 0.6 x 10- 15 A 0.6 Y 0.0003 Ra 1.0 x 10- 10 K 380 Nb 0.00001 Th 0.00005 Ca 400 Mo 0.01 Pa 2.0 x 10- 9 Sc 0.00004 Ag 0.0003 U 0.003 21 9. REFERENCES Amos, A. F., Roels, O. A., and Paul, A. Z. (1976), Environmen- tal baseline conditions in a manganese-nodule province in April-May 1975, Proc. 8th Ann. Offshore Technology Conf., OTC Paper No. 2456 (Houston, Tex.). Anderson, George, University of Washington, Seattle, Wash., private communication. Baker, E. T., and Feely, R. A. (1976), DOMES Preliminary Report, Suspended Matter Program, Pacific Marine En- vironmental Laboratory, Seat- tle, Wash. Bishoff, J., U. S. Geological Survey, Menlo Park, Calif., pri- vate communication. Bowden, K. F. (1962), Turbulence, in The Sea, M. N. Hill, Ed., 1, 820, (Interscience). Conomos, T. J. (1972), Processes affecting suspended particulate matter in the Columbia River effluent system, in Columbia River Estuary and Adjacent Ocean Waters, A. T. Pruter and D. L. Alverson, Eds. (Univ. of Washington Press). Cooke, R. W., International Nickel Corp., Bellevue, Wash., private communication. Csanady, G. T. (1973), Turbulent Diffusion in the Environment, (D. Reidel). DOMES (1976), Mining Industry Meeting, February 24, 1976, Minutes. Office of the Director, NOAA/ERL, Boulder, Colo. Goldberg, E. D. (1963), The oceans as a chemical system, in The Sea, M. N. Hill, Ed., 2, 3-25 (Inter- science). Halpern, David, Pacific Marine Environmental Laboratory, Seattle, Wash., private com- munication. Halpern, David (1976), Upper ocean circulation studies in the eastern tropical Pacific during September and October 1975, Proc. 8th Ann. Offshore Tech- nology Conf., OTC Paper No. 2457 (Houston, Tex.). Munk, W. H., Ewing, G. C, and Revelle, R. R. (1949), Diffusion in Bikini Lagoon, Trans. Am. Geophys. Union. 30, 59. Sallenger, A., U. S. Geological Survey, Menlo Park, Calif., pri- vate communication. 22 LABOR AT DRIES The mission of the Environmental Research Laboratories (ERL) is to conduct an integrated program of fundamental research, related technology development, and services to improve understanding and prediction of the geophysical environment comprising the oceans and inland waters, the lower and upper atmosphere, the space environment, and the Earth. The following participate in the ERL missions: MESA Marine EcoSystems Analysis Program. 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