One of the tests of climate models predicting drought in my review of the Drought Exceptional Circumstances Report was the correlation of predicted area under drought with actual observed area under drought. Lazar criticized my inclusion of the R-Squared (r2) coefficient, an issue I didn’t follow up at the time. Read the rest of this entry…
View CommentsHere is a summary of the chapters in my upcoming book Niche Modeling to be published by CRC Press. Many of the topics have been introduced as posts on the blog. My deepest thanks to everyone who has commented and so helped in the refinement of ideas, and particularly in providing motivation and focus.
Writing a book is a huge task, much of it a slog, and its not over yet. But I hope to get it to the publishers so it will be available at the end of this year. Here is the dustjacket blurb:
Through theory, applications, and examples of inferences, this book shows how to conduct and evaluate ecological niche modeling (ENM) projects in any area of application. It features a series of theoretical and practical exercises in developing and evaluating ecological niche models using a range of software supplied on an accompanying CD. These cover geographic information systems, multivariate modeling, artificial intelligence methods, data handling, and information infrastructure. The author then features applications of predictive modeling methods with reference to valid inference from assumptions. This is a seminal reference for ecologists as well as a superb hands-on text for students.
Functions: This chapter summarizes major types, operations and relationships encountered in the book and in niche modeling. This and the following two chapters could be treated as a tutorial in the R. For example, the main functions for representing the inverted ‘U’ shape characteristic of a niche — step, Gaussian, quadratic and ramp functions – are illustrated in both graphical from and R code. The chapeter concludes with the ACF and lag plots, in one or two dimensions.
Data: This chapter demonstrates how to manage simple biodiversity databases using R. By using data frames as tables,
it is possible to replicate the basic spreadsheet and relational database operations with R’s powerful indexing functions.
While a database is necessary for large-scale data management, R can eliminate conversion problems as data is moved between systems.
Spatial:
R and image processing operations can perform many of the
elementary spatial operations necessary for niche modeling.
While these do not replace a GIS, it demonstrates that generalization of arithmetic concepts to images can be implemented simple spatial operations efficiently.
Theory: Set theory helps to identify the basic assumptions
underlying niche modeling, and the relationships and constraints between these
assumptions. The chapter shows the standard definition of the niche as
environmental envelopes is equivalent to a box topology. It is proven that when
extended to infinite dimensions of environmental variables this definition
loses the property of continuity between environmental and geographic spaces.
Using the product topology for niches would retain this property.
Today I am reporting more results of reconstructing past climates with randomly generated sequences (http://www.climateaudit.org/?p=566). Here are a few experiments to identify the critical components of the dendroclimatology methodology. I record the skill of reconstruction with: different types of series (i.i.d., alternating means and fractional differencing), and dropping each component of the methodology in turn (positive slope, positive correlation, calibration with inverse linear model).
Some alternatives for generating random series are: independent and identically distributed errors (called i.i.d), and two ways of generating series with ‘red noise’ or long term persistence (LTP): alternating means and fractional differencing. An example each series with the CRU temperature data overlaid are below.
Figure 1. Three random series generated to simulate CRU temperatures over 2000 years. The i.i.d. series with a standard deviation equal to the CRU temperatures. Parameters for altmeans were arbitrarily chosen, while parameters for fracdiff were calibrated using the R fracdiff package. Note the i.i.d is least realistic, altmeans is similar with some artifactual ‘jumps’, while the fracdiff is very similar to temperatures.
View CommentsTo follow up on the last post, I have calculated the RE as well as the R2 statsitics for the reconstruction from the random series. The same approach was used, i.e. generate 1000 sequences with LTP, select those with positive slope and R2>0.1, calibrate on linear model, and average. Here is the reconstruction again, with the test and training periods marked with a horizontal dashed line (test period to the left, training to right of temperature values):
