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As part of a project to model the integrated spectra and colors of elliptical galaxies through evolutionary synthesis, we have refined our synthetic spectrum calculations of M giants. After critically assessing three effective temperature scales for M giants, we adopted the relation of Dyck et al. (1996) for our models. Using empirical spectra of field M giants as a guide, we then calculated MARCS stellar atmosphere models and SSG synthetic spectra of these cool stars, adjusting the band absorption oscillator strengths of the TiO bands to better reproduce the observational data. The resulting synthetic spectra are found to be in very good agreement with the K-band spectra of stars of the appropriate spectral type taken from Kleinmann & Hall (1986) as well. Spectral types estimated from the strengths of the TiO bands and the depth of the bandhead of CO near 2.3 microns quantitatively confirm that the synthetic spectra are good representations of those of field M giants. The broad-band colors of the models match the field relations of K and early-M giants very well; for late-M giants, differences between the field-star and synthetic colors are probably caused by the omission of spectral lines of VO and water in the spectrum synthesis calculations. Here, we present four grids of K-band bolometric corrections and colors -- Johnson U-V and B-V; Cousins V-R and V-I; Johnson-Glass V-K, J-K and H-K; and CIT/CTIO V-K, J-K, H-K and CO -- for models having 3000 K < Teff < 4000 K and -0.5 < log g < 1.5. These grids, which have [Fe/H] = +0.25, 0.0, -0.5 and -1.0, extend and supplement the color-temperature relations of hotter stars presented in a companion paper (astro-ph/9911367).Comment: To appear in the March 2000 issue of the Astronomical Journal. 60 pages including 15 embedded postscript figures (one page each) and 6 embedded postscript tables (10 pages total

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Context. Our ability to extract information from the spectra of stars depends on reliable models of stellar atmospheres and appropriate techniques for spectral synthesis. Various model codes and strategies for the analysis of stellar spectra are available today. Aims. We aim to compare the results of deriving stellar parameters using different atmosphere models and different analysis strategies. The focus is set on high-resolution spectroscopy of cool giant stars. Methods. Spectra representing four cool giant stars were made available to various groups and individuals working in the area of spectral synthesis, asking them to derive stellar parameters from the data provided. The results were discussed at a workshop in Vienna in 2010. Most of the major codes currently used in the astronomical community for analyses of stellar spectra were included in this experiment.Results. We present the results from the different groups, as well as an additional experiment comparing the synthetic spectra produced by various codes for a given set of stellar parameters. Similarities and differences of the results are discussed. Conclusions.Several valid approaches to analyze a given spectrum of a star result in quite a wide range of solutions. The main causes for the differences in parameters derived by different groups seem to lie in the physical input data and in the details of the analysis method. This clearly shows how far from a definitive abundance analysis we still are.Key words. stars: atmospheres -stars: late-type -stars: abundances -stars: fundamental parameters Based on observations obtained at the Bernard Lyot Telescope (TBL, Pic du Midi, France) of the Midi-Pyrénées Observatory, which is operated by the Institut National des Sciences de l'Univers of the Centre National de la Recherche Scientifique of France.Tables 6-11 are only available in electronic form at http://www.aanda.orgThe spectra of stars 1 to 4 used in the experiment presented here are only availalbe at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via