## Pore Volumes Based On Length Units

Jury et al. (1991, pp. 224-225) calculate pore volumes by multiplying the length of a column by the water content. They give the formula dwb= Jwtb= JWL/V = Ld, (12.7)

where dwb is the drainage water (cm) evolved at the breakthrough time dwb = Jw^b, Jw is the soil water flux (cm/sec), tb is the breakthrough time (sec), L is the length of the soil column (cm), and V is the solute velocity (cm/sec) (Figs. 12.12 and 12.13). (We will assume this velocity is the average pore velocity that Kirkham and Powers define; the definition is given in a preceding section.) Jury et al. (1991) say that the value Ld is the volume of water per unit area held in the wetted soil pores of the column during transport. For this reason dwb = Ld is called a pore volume, and it requires approximately one pore volume of water to move a mobile solute through a soil column (Jury et al., 1991, p. 225).

Why do Jury et al. (1991) use a length instead of a volume in getting a pore volume? A pore volume is a calculation of the equivalent amount of transmitted water in depth units (where the area has been taken out, as with evapotranspiration, where we use the units of mm). So in the case of Kirkham and Powers (1972), they deal with soil in which the water is being transmitted through the water-filled porosity. The calculation is turning the water that is being transmitted (i.e., a d) into a volume, by multiplying by the soil's volume. But if one is dealing with areas, one can divide through by an area, as we do when we turn a [volumetric] water content (m3/m3)

FIG. 12.12 Schematic diagram of a soil column outflow experiment, where solute is added at t = 0. (From Jury, W.A., Gardner, W.R., and Gardner, W.H., Soil Physics, 5th ed., p. 224, ©1991, John Wiley & Sons: New York. This material is used by permission of John Wiley & Sons, Inc.)

FIG. 12.13 Outflow concentration versus time for a step change in solute input at t = 0. D = dispersion coefficient and it has units of length2/time. If D = 0, there is no dispersion. Curves correspond to different values of D (V = 2 cm day-1, L = 30 cm). (From Jury, W.A., Gardner, W.R., and Gardner, W.H., Soil Physics, 5th ed., p. 224, ©1991, John Wiley & Sons: New York. This material is used by permission of John Wiley & Sons, Inc.)

FIG. 12.13 Outflow concentration versus time for a step change in solute input at t = 0. D = dispersion coefficient and it has units of length2/time. If D = 0, there is no dispersion. Curves correspond to different values of D (V = 2 cm day-1, L = 30 cm). (From Jury, W.A., Gardner, W.R., and Gardner, W.H., Soil Physics, 5th ed., p. 224, ©1991, John Wiley & Sons: New York. This material is used by permission of John Wiley & Sons, Inc.)

into a depth of storage water (mm) (B.E. Clothier, personal communication, February 25, 1999).

### VI. MISCIBLE DISPLACEMENT

Pore volumes are analyzed in miscible displacement studies. Miscible displacement is the process that occurs when one fluid mixes with and displaces another fluid. Leaching of salts from a soil is an example, because the added water mixes with and displaces the soil solution. A pioneer in the application of miscible displacement techniques to soil science is D.R. Nielsen. (For a biography of Nielsen, see the Appendix, Section VIII.) In a key paper, Nielsen et al. (1965) showed that chloride movement in soil depends upon the method of water application. They found that intermittently ponding the soil with 2-inch (5-cm) increments of water was more efficient in leaching applied chloride from the soil surface than continuous ponding or leaching with 6-inch (15-cm) increments. This finding has important applications in salinity management.

For a mathematical discussion of miscible displacement, the interested reader is referred to Kirkham and Powers (1972; see their Chapter 8).

VII. RELATION BETWEEN MOBILE WATER CONTENT AND PORE VOLUME

As noted in the first paragraph of this chapter, calculation of pore volumes does not tell us about the mobility of a solute, as we determined in Section IX, Chapter 11. The question arises, "How does one relate mobile water content to pore volumes?" Or, in other words, "How does the ratio of c*lcm, needed to determine mobility, relate to C/Co on the ordinate in breakthrough curves?" The answer to this question is tricky. If we know that the soil wets to 6o (the soil water content under a tension infiltrome-ter), then we can calculate the nonpreferential pore volume using this 6o. But if our solute comes through earlier (i.e., a smaller pore volume), then not all the pore volume could have been active. So we could define an active pore volume, which we could directly relate to a mobile (volume) fraction, 6m (B.E. Clothier, personal communication, February 25, 1999).

VIII. APPENDIX: BIOGRAPHY OF DONALD NIELSEN

Donald Rodney Nielsen, soil and water science educator, was born in Phoenix, Arizona, on October 10, 1931. He got his B.S. degree in agricultural chemistry and soils at the University of Arizona in 1953; his M.S. degree in soil microbiology at the University of Arizona in 1954; and his Ph.D. in soil physics at Iowa State University in 1958. His career has been spent at the University of California, Davis, where he started as an assistant professor in 1958, moved to associate professor in 1963, and then to professor in 1968. He was the director of the Kearney Foundation of Soil Science from 1970-1975; associate dean, 1970-1980; director of the Food Protection and Toxicology Center, 1974-1975; chairman of the Department of Land, Air, and Water Resources, 1975-1977; executive associate dean of the College of Agricultural and Environmental Sciences, 1986-1989; and chairman of the Department of Agronomy and Range Science, 1989-1991 (Marquis Who's Who, 1994). In his administrative duties, he emphasized the important links between agriculture and environmental science.

Nielsen has been a pioneer in three areas of soil-science research: linking theory to field measurements of water movement, miscible displacement (Nielsen and Biggar, 1962), and geostatistics. One of his first papers with colleagues on geostatistics (Nielsen et al., 1973) became a citation classic (Institute for Scientific Information, 1983). He is co-author of a book on soil hydrology (Kutilek and Nielsen, 1994) and a book on spatial and temporal statistics (Nielsen and Wendroth, 2003). He has edited several books, including a major compendium on nitrogen (Nielsen and MacDonald, 1978).

Nielsen has had an outstanding career not only in research and administration, but also in teaching and serving as editor on important journals. Nielsen was an associate editor of Water Resources Research from when it was established in 1965 until 1986, and he was its editor-in-chief from 1986-1989. He has taught 15 different courses dealing with soil physics, water science, and irrigation. He has guided 17 students through to the M.S. degree and 20 students through to the Ph.D., and they are leaders in the field now. Seventy-five scientists from around the world have spent leaves with him.

He has taught workshops at numerous locations around the world, including the International Atomic Energy Agency in Vienna, Austria, and the famous International Centre for Theoretical Physics, established by the Nobel Prize-winning Pakistani physicist, Abdus Salam, in Trieste, Italy.

Nielsen has won many awards. He is Fellow of the American Society of Agronomy, the Soil Science Society of America, and the American Geophysical Union. He has been president of the Soil Science Society of America, the American Society of Agronomy, and the Hydrology Section of the American Geophysical Union. He was on the National Research Council's Board on Agriculture. He received an honorary doctor of science degree from Ghent State University in Belgium and received the M. King Hubbert Award of the National Ground Water Association. He was made an honorary member of the European Geophysical Society and in 2001 he received the Horton Medal from the American Geophysical Union for outstanding contributions to the geophysical aspects of hydrology.

Nielsen married Joanne Joyce Locke on September 26, 1953. They have three daughters and two sons.