Unpublished Results Related to BROOK90

By C.A. Federer

[Last revised - May 2, 2002]
To the BROOK90 Model page

All scientists produce information that for one reason or another can't or won't make it into publication. The web provides a good way to at least inform a few people. So here is my contribution to web publishing.

Field Capacity - May 2, 2002
Comparison of BROOK90 with UNSAT-H - May 2, 2002
DURATN Parameter - February 8, 1999
Clear-sky Longwave Radiation - March 24, 1998

Field Capacity - May 2, 2002

The term "field capacity" has been defined in various ways:
A) the maximum water holding capacity of the soil, above which all excess water drains or overflows;
B) an upper limit of water available for transpiration;
C) a water potential of -33 kPa (-1/3 bar);
D) a water potential generally between -10 and -33 kPa depending on soil texture and other properties;
E) when drainage becomes negligible after thorough wetting ;
F) 2 or 3 days after a thorough wetting;
G) at specified depth at a specified time with drainage from saturation;
H) a specific value of drainage rate, such as 2 mm/d;
J) a specific value of hydraulic conductivity;
K) none, because the term is vague and useless.

Because the K-psi-theta relationships for all soils are continuous functions through the whole range from oven-dry to saturation, field capacity can only be some arbitrarily defined point on the curves. Although some scientists therefore support definition K, "field capacity" has proven so useful in practice that it refuses to go away.

The concepts in A and B are used in "bucket" models of soil water in which excess water "overflows" the soil water bucket. Soil hydraulic conductivity is thus assumed to undergo a step change between zero and infinity at field capacity. Although obviously incorrect, such models can still be very useful. Unfortunately, in the literature, the maximum water holding capacity in A is sometimes called "saturation", which it definitely is not. The B concept combined with a lower limit of available water defines the amount of water available for transpiration, a value commonly used in transpiration methods involving the concept of potential evapotranspiration. All these models must rely on using one of the other definitions for determining an actual value for field capacity.

Definition E is the classic or original definition, based on the obsolete concept of a sharp break between rapidly draining "gravitational" water and non-draining water. Because "negligible" turned out to be hard to define, F has been generally used. Early studies attempting to link field data from definition F with laboratory data on the psi-theta relation produced definition C, and the -1/3 bar water content still may be the only known point on the psi-theta curve for a given soil. These studies may mostly have been done on agricultural silt loam soils, because in coarser and finer-textured soils the field definition F corresponds better to the lab definition D.

Baver, Gardner, and Gardner (1972, 4th ed.) introduced definition H. They state "some indication must be given as to precisely what constitutes negligible drainage. Perhaps the terminology should include designation of the drainage rate, say, 'field capacity for 2 mm/day drainage.'" They then put in an unsuccessful plea for definition K!

For BROOK90, prior to now, I had equated definition J with definiton H and recommended using a hydraulic conductivity of 2 mm/d as a definition. The two definitions are the same only when there is no matric potential gradient, but when this is specified at the bottom of the soil column, e.g. at 2 m depth, then there is considerable upward matric potential gradient at a reasonable field capacity depth of say 30 cm, so the two definitions are not the same.

Without going into detailed justification, definition G seems to be the best, particularly in the form I propose: "the water volume fraction at 30 cm depth after 48 hours of drainage from an initially saturated homogeneous profile with a fixed gravity potential gradient at 2 m depth". I call this the "30-48" definition of field capacity.

I have used BROOK90 to examine drainage curves for various soils. Clapp and Hornberger (1978) give mean K-psi-theta parameters for each of eleven texture classes. The values are given in BROOK90-Help-Contents-Soil Parameters. Another set of parameters can be obtained for 10 Saxton et al. (1986) texture classes. Each parameter set represents a "mean" soil for that texture class. In BROOK90 I used a profile of 20 identical 10 cm thick layers all with the same soil parameters, and shut off all processes except downward matrix flow with gravity drainage at the bottom. Initial matric potential was set to zero for all layers (saturation) . To ensure a good solution for water movement I set the Fixed parameter DTIMAX to 0.001 d.

Drainage flux at 30 cm depth initially drops very rapidly for all 21 soils, but by 2 days the rapid flux period is over and the soil begins to drain much more slowly. Note the log scale; the transition is even sharper than it appears here. Drainage flux at 30-48 ranges from 1.3 to 4.2 mm/d while the hydraulic conductivity ranges from 2.9 to 13.1 mm/d.

Note that the 2 mm/d drainage flux suggested by Baver, Gardner, and Gardner (1972, 4th ed.) is reached at 30 cm in from 1.5 to 4 days.

This figure shows that theta at 30 cm depth also has changed from rapid decline to slow decline by 48 hours for all "soils". The 30-48 definition of field capacity (solid circles), of course, varies widely among soil textures. The matric potential at 30-48 ranges from -3.1 to -51.2 kPa. Field capacity at 30 cm by three other definitions occurs after widely varying times of drainage. The K = 2 mm/d definition (X) suggested earlier in BROOK90 occurs from 2 to 17 days after drainage starts. The "classic" -33 kPa definition (diamonds) is reached in less than one day for some of these "soils", but not until long after 30 days for many others. On the other hand, -10 kPa (open circles) is reached while some soils are still draining rapidly, though times of 5 to 27 days also occur. Clearly the 30-48 definition provides a consistent separation between rapid or "gravitational" drainage and slow drainage.

The major drawback of the 30-48 definition of field capacity is that it requires simulation after the Clapp-Hornberger or Brooks-Corey parameters are specified. See the next section "Comparison of BROOK90 with UNSAT-H".

To estimate parameter values when no other information is available, use the B value based on texture class from either Clapp and Hornberger (1978) or Saxton et al. (1986), measure PSIF and THETAF in the field 2 days after a thorough wetting, and assume a KF of 5 mm/d.

Note that BROOK90 does not use the field capacity concept to control either vertical flow in the soil matrix or evapotranspiration. However BROOK90 does use a point on the K-psi-theta curves, which it calls "field capacity" for convenience, in calculations of bypass flow (BYFL) and source area flow (SRFL).

Comparison of BROOK90 with UNSAT-H - May 2, 2002

DURATN Parameter - February 8, 1999

DURATN in BROOK90 defines the average length or duration of a "storm" in hours as a function of month. Originally I used 12 hours for October through March and 4 hours for April through September. I have recently looked at hourly precipitation data for 4 years at various stations from the SAMSON data set, including those of the downloadable .DAT files. Averaging the number of hours per day of precipitation of 0.02 inch (0.5 mm) or greater over days with such precipitation by month gives the following results after a little smoothing

                    J   F   M   A   M   J   J   A   S   O   N   D
San Juan PR         3   2   2   2   2   2   2   3   3   3   3   3 
Atlanta GA          5   5   5   5   4   4   3   3   4   4   5   6
Caribou ME          4   4   5   5   4   4   4   4   4   6   6   5
Madison WI          4   4   5   3   3   2   3   3   4   4   5   5
Lake Charles LA     5   4   3   3   3   3   2   2   3   3   4   5
Phoenix AZ          4   4   4   4   4   2   2   2   2   2   4   4
Rapid City SD       3   3   3   4   4   3   2   2   2   2   4   4
Tacoma WA           6   6   5   4   4   4   4   4   4   4   6   6
Fairbanks AK        3   3   4   4   4   4   3   3   4   4   4   3
Hubbard Brook NH    5   5   5   4   4   4   4   4   4   5   5   5 smoothed from one year

So a default value of 4 for DURATN is a good default for anywhere anytime. A value of 12 for "winter" months gives too high an interception, by about 60 mm for Atlanta with CONIFER2.PAR; the effect on total evaporation is somewhat less.

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Clear-sky Longwave Radiation - March 24, 1998

The Y axis should read "Net Longwave Radiation from Clear Sky".

The methods differ only in how they express the effective emissivity (e) of a clear sky:

where e_a is the vapor pressure in kPa, T is the temperature in degC, and K is the temperature in degK. The (mostly)upper Brunt curve has c_a = 0.65, c_b = 0.134 (kPa^-0.5) (Fitzpatrick and Stern 1966), the middle curve has c_a = 0.52, c_b = 0.206 (Brunt 1932), and the lower curve has c_a = 0.44, c_b = 0.253 (Penman 1948). Note that the Swinbank and Idso-Jackson curves have no humidity dependence. Brutsaert (1982) admits that Satterlund's equation matches the data better below freezing, but Satterlund has a very flat temperature response and is the highest method of all for temperatures of 0 to 20C and humidities above 60%. The Brutsaert method tends to be the most central over the whole range of possible conditions.

At most temperatures, the range of net longwave radiation is about 50 W/m², which is equivalent to an evaporation of 1.8 mm/d! The choice of method for clear-sky emissivity thus plays a major role in the value of PE estimates when net radiation is estimated. A major effort using worldwide longwave data (not estimates from models!) will be needed to improve this situation. Fortunately, the cloud cover correction, approximate as it is, brings the net longwave closer to zero and helps wash out the emissivity error.

COMPASS BROOK