Hello everyone,

I am working with 16-day MODIS EVI (satellite) data and I want to fit a Piece-wise Logistic Function through my 23 EVI data values. The following formula is for the Piece-wise Logistic Function:

Formula:Please Login or Register to view this content.

where:

t is the day of year

a is vegetation growth time

b is rate of leaf development

c is the amplitude

EVIb is the background EVI value [constant]

The literature provides some ambiguous definition as to which component is a constant, but I am assuming that the EVIb value is a constant but am supposing that we need possibly one or 2 others to be constant to for the function to work properly?

I have little experience with this function, but from the literature I have read, is appliedseparately to the left and then subsequently to the right of this bell-shaped curve- split at the maximum y value.I am hoping someone here with a stronger mathematical background would be able to advise me on which component of the equation above should be a constant and which should be a variable. I have attached the original paper source here 2003 Monitoring vegetation phenology using MODIS.pdf, with a description of the function on page 2, section 2. I have included a series of sample data for one year below.

The series of days of the year are as follows:

1

17

33

49

65

81

97

113

129

145

161

177

193

209

225

241

257

273

289

305

321

337

353

Here is an example EVI data-set I currently have for one year of 23 data points:

0.425

0.3899

0.2417

0.4724

0.4648

0.226

0.245

0.2509

0.2741

0.3711

0.3914

0.3985

0.4433

0.397

0.3329

0.3578

0.2741

0.2912

0.3053

0.2995

0.0959

0.3287

−0.3

I have tried quite for quite some time now to properly model my data using the above equation but have so far been unsuccessful and am really hoping someone would be kind enough to shed some light!

Any help at all would be greatly appreciated. Thank you!

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