Efficient accommodation of local minima in watershed model calibration

The Gauss-Marquardt-Levenberg (GML) method of computer-based parameter estimation, in common with other gradient-based approaches, suffers from the drawback that it may become trapped in local objective function minima, and thus report optimized parameter values that are not, in fact, optimized at all. This can seriously degrade its utility in the calibration of watershed models where local optima abound. Nevertheless, the method also has advantages, chief among these being its model-run efficiency, and its ability to report useful information on parameter sensitivities and covariances as a by-product of its use. It is also easily adapted to maintain this efficiency in the face of potential numerical problems (that adversely affect all parameter estimation methodologies) caused by parameter insensitivity and/or parameter correlation. The present paper presents two algorithmic enhancements to the GML method that retain its strengths, but which overcome its weaknesses in the face of local optima. Using the first of these methods an intelligent search for better parameter sets is conducted in parameter subspaces of decreasing dimensionality when progress of the parameter estimation process is slowed either by numerical instability incurred through problem ill-posedness, or when a local objective function minimum is encountered. The second methodology minimizes the chance of successive GML parameter estimation runs finding the same objective function minimum by starting successive runs at points that are maximally removed from previous parameter trajectories. As well as enhancing the ability of a GML-based method to find the global objective function minimum, the latter technique can also be used to find the locations of many non-global optima (should they exist) in parameter space. This can provide a useful means of inquiring into the well-posedness of a parameter estimation problem, and for detecting the presence of bimodal parameter and predictive probability distributions. The new methodologies are demonstrated by calibrating a Hydrological Simulation Program-FORTRAN (HSPF) model against a time series of daily flows. Comparison with the SCE-UA method in this calibration context demonstrates a high level of comparative model run efficiency for the new method. (c) 2006 Elsevier B.V. All rights reserved.

Management of a previously eroded tropical Alfisol with herbaceous legumes: Soil loss and physical properties under mound tillage

A study was carried out on a previously eroded Oxic Paleustalf in Ibadan, southwestern Nigeria to determine the extent of soil degradation under mound tillage with some herbaceous legumes and residue management methods. A series of factorial experiments was carried out on 12 existing runoff plots. The study commenced in 1996 after a 5-year natural fallow. Mound tillage was introduced in 1997 till 1999. The legumes - Vigna unguiculata (cowpea), Mucuna pruriens and Pueraria phaseoloides - were intercropped with maize in 1996 and 1998 while yam was planted alone in 1997 and 1999. This paper covers 1997-1999. At the end of each year, residues were either burned or mulched on respective plots. Soil loss, runoff, variations in mound height, bulk density, soil water retention and sorptivity were measured. Cumulative runoff was similar among interactions of legume and residue management in 1997 (57-151 mm) and 1999 (206-397 mm). However, in 1998, cumulative runoff of 95 mm observed for Mucuna-burned residue was significantly greater than the 46 mm observed for cowpea-burned residue and the 39-51 mm observed for mulched residues of cowpea, Mucuna and Pueraria. Cumulative soil loss of 7.6 Mg ha(-1) observed for Mucuna-burned residue in 1997 was significantly greater than those for Pueraria-mulched (0.9 Mg ha(-1)) and Mucuna-mulched (1.4 Mg ha(-1)) residues whereas in 1999 it was similar to soil loss from cowpea treatments and Pueraria-burned residue (2.3-5.3 Mg ha(-1)). There were no significant differences in soil loss in 1998 (1-3.2 Mg ha(-1)) whereas Mucuna-burned residue had a greater soil loss (28.6 Mg ha(-1)) than mulched cowpea (6.9 Mg ha(-1)) and Pueraria (5.4 Ms ha(-1)). Mound heights (23 cm average) decreased non-linearly with cumulative rainfall. A cumulative rainfall of 500 mm removed 0.3-2.3 cm of soil from mounds in 1997, 3.5-6.9 cm in 1998 and 2.3-4.6 cm in 1999, indicating that (detached but less transported) soil from mounds was far higher than observed soil loss in each year. Soil water retention was improved at potentials ranging from -1 to -1500 kPa by Mucuna-mulched residue compared to the various burned-residue treatments. Also, mound sorptivity at -1 cm water head (14.3 cm h(-1/2)) was higher than furrow sorptivity (8.5 cm h(-1/2)), indicating differences in hydraulic characteristics between mound and furrow. Pueraria-mulched residues for mounds had the highest sorptivity of 17.24 cm h(-1/2), whereas the least value of 6.96 cm h(-1/2) was observed in furrow of Mucuna-burned residue. Pueraria phas eoloides was considered the best option for soil conservation on the previously eroded soil, cultivated with mound tillage. (c) 2005 Elsevier B.V. All rights reserved.