GADA - the "Generalized ADA" (Algebraic Difference Approach) - is a methodology designed to move the self-referencing modeling beyond the ADA-like limitations of accepting previously existing single-independent-variable (2-D) base models (such as, Richards 1959, Schumacher 1939, Korf 1939, Hossfeld 1822) as defining self-referencing relationships. The most compelling argument for not using directly these 2-D models for self-referencing modeling is that:
The self-referencing modeling must model infinitely more than the 2-D base models can model.
While a 2-D model defining a two-dimensional relationship (a relationship between two variables) can define only one curve for any given set of parameters, a self-referencing model must define for such a set of parameters an infinite number of curves or rather a continuous relationship between three variables, such as: Site, Size, and Time. Redefining one of the parameters in a 2-D model as a site variable redefines this model's meaning beyond its original structure into a three-dimensional relationship. Hence, a 3-D model. However replacing only one parameter with a site variable is in most cases too simplistic of an approach to model various possible scenarios of site quality influence on the modeled dynamics even if the 2-D model is changed to a 3-D model by replacing one of its original parameters by a new variable. Indeed, the most fundamental property of GADA is that it goes beyond the use of the traditional 2-D base models (i.e., Y=f(ß1,Z)) and their original parameters, and allows the user to work explicitly with the three-dimensional relationships using 3-D base models of the type Y=F(ß2,X,Z), which are subsequently reformulated to the self-referencing forms of the type Y=F(ß3,Z0,Y0,Z).
Letting go of the traditional 2-D models and applying the more advanced dynamic site equations based on the 3-D GADA modeling have yielded superior results in many practical implementations of self-referencing modeling, such as for example in:
Adame, P., I. Canellas, S. Roig, M. Del Río. 2006. Modelling dominant height growth and site index curves for rebollo oak (Quercus pyrenaicaWilld.). Ann. For. Sci. 63 (2006) 929-940.
De los Santos-Posadas, H.M., M. Montero-Mata, M. Kanninen. 2006. Dynamic dominant height growth curves for Terminalia amazonia (gmel.) Excell in Costa Rica. Agrociencia 40: 521-532.
Diéguez-Aranda, U., H.E. Burkhart, R.L. Amateis. 2006a. Dynamic Site Model for Loblolly Pine (Pinus taeda L.) Plantations in the United States. Forest Science, 52(3), pp. 262-272.
Diéguez-Aranda, U., J.A. Grandas-Arias, J.G. Álvarez-González, K.v. Gadow. 2006b. Site quality curves for birch stands in north-western Spain. Silva Fennica 40(4): 631-644.
Elfving, B., A. Kiviste. 1997. Construction of site index equations for Pinus sylvestris L. using permanent plot data in Sweden. For. Ecol. Manag. 98: 125-134.
Eriksson, H., U. Johanssen, and A. Kiviste. 1997. A site-index model for pure and mixed stands of betula pendula and betula pubescens in Sweden. Scand. J. Forest Res. 12:149-156.
Krumland, B., H. Eng. 2005. Site index systems for major young-growth forest and woodland species in northern California. California Forestry Report No. 4. California Department of Forestry and Fire Protection. Sacramento, CA. 219 p., found at: http://www.demoforests.net/Warehouse/Docs/ForestryReports/ForestryReport4.pdf
Nord-Larsen, T. 2006. Developing Dynamic Site Index Curves for European Beech (Fagus sylvatica L.) in Denmark. For. Sci. 52(2): 173–181.
Rivas, J.J.C., J.G.Á. González, A.D.R. González, K.v. Gadow. 2004. Compatible height and site index models for five pine species in El Salto, Durango (Mexico). For. Ecol. Manag. 201: 145–160.
Trincado, G. V., A. Kiviste, K.v. Gadow. 2003: Preliminary site index models for native Roble (Nothofagus obliqua) and Rauli (N. alpina) in Chile. New Zealand J. of Forestry Science 32 (3): 322-333.