Statistical Methods for the Qualitative Assessment of Dynamic Models with Time Delay (RPackagequalV)

Abstract

Results of ecological models differ, to some extent, more from measured data than from empirical knowledge. Existing techniques for validation based on quantitative assessments sometimes cause an underestimation of the performance of models due to time shifts, accelerations and delays or systematic differences between measurement and simulation. However, for the application of such models it is often more important to reproduce essential patterns instead of seemingly exact numerical values. This paper presents techniques to identify patterns and numerical methods to measure the consistency of patterns between observations and model results. An orthogonal set of deviance measures for absolute, relative and ordinal scale was compiled to provide informations about the type of difference. Furthermore, two different approaches accounting for time shifts were presented. The first one transforms the time to take time delays and speed differences into account. The second one describes known qualitative criteria dividing time series into interval units in accordance to their main features. The methods differ in their basic concepts and in the form of the resulting criteria. Both approaches and the deviance measures discussed are implemented in an R package. All methods are demonstrated by means of water quality measurements and simulation data. The proposed quality criteria allow to recognize systematic differences and time shifts between time series and to conclude about the quantitative and qualitative similarity of patterns.

Evaluation of Urban Local-Scale Aerodynamic Parameters: Implications for the Vertical Profile of Wind Speed and for Source Areas

“…Eq. 1) is accounted for by using the root-mean-squared geometric error (RMSGE z 0 ) (Jachner et al 2007)…”

INDISIM-Paracoccus, an individual-based and thermodynamic model for a denitrifying bacterium

“…Additionally, in order to compare the simulation results with the experimental data we also used the geometric reliability index (GRI) values, a statistical method to determine the reliability of a model (Jachner et al, 2007). This coefficient can deal with precise notions of model accuracy.…”

Potential effects of climate change on inundation patterns in the Amazon Basin

“…3 (details in Table 5). We evaluate the quality of our model simulations with the Willmott's index of agreement, which ranges from 0 to 1, with 1 indicating complete agreement (Willmott, 1982) and the error of the qualitative validation (QualV), which ranges from 0 to infinite, with low values indicating high agreement (Jachner et al, 2007). We also calculate the normalised RMSE, Nash-Sutcliffe coefficient and Pearson correlation coefficient (Mayer and Butler, 1993;Nash and Sutcliffe, 1970).…”

“…During the flooding season between January and March (Foley et al, 2002) the water rises with an amplitude of 5 to 15 m (Junk, 1985) and an average speed of 0.05 m d −1 (Junk and Piedade, 1997). The extent of flooded area in central Amazonia increases from about 4 % during low water to 16 % during high water stage (Richey et al, 2002).…”

“…These floodplains are alternately suitable for aquatic and terrestrial organisms. The distribution of these species is especially influenced by the duration of the aquatic and terrestrial phase (Junk and Piedade, 1997). Floodplain forests cover approximately 97 000 km 2 (Parolin et al, 2004) and contain about 20 % of the Amazonian tree species (Naiman et al, 2005).…”