Fits harmonic models to rainfall probabilities for a Markov model (J.O. Ong’ala & D.B. Baird).
Options
PRINT = string tokens |
Controls printed output for each fitted model (model, deviance, summary, estimates, correlations, fittedvalues, accumulated, monitoring, confidence); default mode, summ, esti, accu |
PLOT = string token |
What plots to display (results); default resu |
NHARMONICS = scalar |
Defines the number of harmonics to fit (1…4); default 2 |
SPREADSHEET = string tokens |
What to save in a spreadsheet (results); default * |
Parameters
COUNTS = table |
Supplies the table of counts by Markov class and day within the year (1…366) |
WINDOW = scalars |
Window to plot the graph; default 3 for a single class and 1 otherwise |
TITLE = texts |
The title for the plot; default forms an automatic description |
RESULTS = pointers |
Saves a pointer to variates of fitted rainfall probabilities by day for each wet state |
OUTFILE = texts |
File (with extension .gwb, or .xlsx) to save the selected spreadsheet components |
Description
RFFPROBABILITY fits harmonic (Fourier) models with a period of 366 days to rainfall counts produced by RFSUMMARY. The Markov model fitted by RFSUMMARY splits the days into different classes based on the history of the preceding days. The daily states, order and type of the Markov model can be formed by RFSUMMARY. The harmonic model is a linear combination of sine and cosine terms with periods of 366/n.. The number of harmonic terms (n) is specified by the NHARMONICS option, and can be 1, 2, 3 or 4.
The COUNTS parameter supplies the table of counts for each Markov class by day within the year (1…366). The RESULTS parameter can save fitted probabilities by wet class for each day.
Printed output of the summaries is controlled by the PRINT option, with the same settings as the FIT directive. The probabilities can be displayed in a spreadsheet by setting option SPREADSHEET=results. This creates a sheet containing variates giving the fitted probabilities for each day in the year by the wet Markov classes. The spreadsheet can be saved to a file by setting the OUTFILE parameter to a Genstat or Excel spreadsheet filename (.gwb or .xlsx).
You can set option PLOT=results to plot the fitted probabilities. The TITLE parameter can supply a title for the graph; if this not set, a descriptive title will be created from the Markov-chain options. The WINDOW parameter specifies the window to use for the graph.
Options: PRINT, PLOT, NHARMONICS, SPREADSHEET.
Parameters: COUNTS, WINDOW, TITLE, RESULTS, OUTFILE.
Method
The procedure calculates sine and cosine terms for the number of harmonics and fits a binomial generalized linear model to the counts of wet days vs dry days for each history from the preceding days.
Reference
Ong’ala, J.O. (2011). Simplifying the Markov chain analysis of rainfall data using Genstat. MSc Thesis, Maseno University.
See also
Directive: FIT.
Procedures: RFFAMOUNT, RFSUMMARY.
Commands for: Basic and nonparametric statistics.
Example
CAPTION 'RFFPROBABILITY example','41 years rainfall for Katumani, Kenya'; \ STYLE=meta,minor IMPORT [PRINT=summary] '%Data%/Rainfall Katumani 1961-2001.gsh' RFSUMMARY [PRINT=*; PLOT=*; DAY=Date; ORDER=1] Rainfall; \ COUNTS=RFCounts; AMOUNTS=RFAmounts RFFPROBAB [PLOT=results] COUNTS=RFCounts; \ TITLE='Katumani rainfall probabilities 1961-2001'