imbrie {astrochron} R Documentation

## Imbrie and Imbrie (1980) ice sheet model

### Description

An implementation of the Imbrie and Imbrie (1980) ice sheet model

### Usage

```imbrie(insolation=NULL,Tm=17,b=0.6,times=NULL,initial=0,burnin=100,standardize=T,
output=T,genplot=1,verbose=T)
```

### Arguments

 `insolation` Insolation, in ka (negative for future, positive for past). Default is insolation over the past 1000 ka from 65 deg. North, 21 June. `Tm` Vector of mean time constants in ka. Default is 17 ka. The order of the Tm values should match vectors b and times. `b` Vector of nonlinearity coefficient (a value ranging from 0 to 1). Default is 0.6. The order of the b values should match vectors Tm and times. `times` Vector of start times for each Tm and b listed above. Leave as NULL if you only need to model one Tm and b value. `initial` Initial value for ice volume, relative to centered record. Default is 0. `burnin` Number of points for model burn-in. This is required to achieve stable model results. Default is 100 points. `standardize` Standardize model output to maximum value of one and minimum value of zero? (T or F) `output` Output model results? (T or F) `genplot` Generate summary plots? (1) plot insolation and ice volume series, (2) plot animated insolation, ice volume and phase portrait.) `verbose` Verbose output? (T or F)

### Details

This function will implement the ice volume model of Imbrie and Imbrie (1980), following the conventions of Paillard et al. (1996).

When using the 'times' vector, consider the following example:

times= c(500,1000)

Tm=c(15,5)

b=c(0.6,0.3)

In this case, a Tm of 15 (b of 0.6) will be applied to model from 0-500 ka, and a Tm of 5 (b of 0.3) will be applied to model 500-1000 ka.

### References

Imbrie, J., and Imbrie, J.Z., (1980), Modeling the Climatic Response to Orbital Variations: Science, v. 207, p. 943-953.

Lisiecki, L. E., and M. E. Raymo, 2005, A Pliocene-Pleistocene stack of 57 globally distributed benthic d18O records, Paleoceanography, 20, PA1003, doi:10.1029/2004PA001071.

Paillard, D., L. Labeyrie and P. Yiou, (1996), Macintosh program performs time-series analysis: Eos Trans. AGU, v. 77, p. 379.

### Examples

```## Not run:
# make a very simple forcing (on/off)
forcing=cycles(0,end=300)
forcing[50:150,2]=1
plot(forcing,type="l")

# use this forcing to drive the imbrie ice model
# set b=0, Tm = 1
imbrie(forcing,b=0,Tm=1,output=F)

# let's view the evolution of the ice sheet
imbrie(forcing,b=0,Tm=1,output=F,genplot=2)

# now increase the response time
imbrie(forcing,b=0,Tm=10,output=F,genplot=2)

# now model slow growth, fast decay
imbrie(forcing,b=0.5,Tm=10,output=F,genplot=2)

# now make a 100 ka cyclic forcing
forcing=cycles(1/100,end=300)
imbrie(forcing,b=0,Tm=1,output=F,genplot=2)
imbrie(forcing,b=0,Tm=10,output=F,genplot=2)
imbrie(forcing,b=0.5,Tm=10,output=F,genplot=2)
# show burn-in
imbrie(forcing,b=0.5,Tm=10,output=F,genplot=2,burnin=0)

# now examine Malutin Milankovitch's hypothesis: 65 deg N, summer solstice
imbrie(b=0.5,Tm=10,output=F,genplot=2,burnin=900)

# use the ice model output to make a synthetic stratigraphic section
res=imbrie(b=0.5,T=10,output=T,genplot=1,burnin=100)
synthStrat(res,clip=F)

# generate ice model for last 5300 ka, using 65 deg. N insolation, 21 June
# allow b and Tm values to change as in Lisiecki and Raymo (2005):
insolation=iso(insolation,xmin=0,xmax=5300)
#  b is 0.3 from 5300 to 3000 ka, then linearly increases to 0.6 between 3000 and 1500 ka.
#  b is 0.6 from 1500 ka to present.
set_b=linterp(cb(c(1500,3000),c(0.6,0.3)),dt=1)
set_b=rbind(set_b,c(5400,0.3))
#  Tm is 5 ka from 5300 to 3000 ka, then linearly increases to 15 ka between 3000 and 1500 ka.
#  Tm is 15 ka from 1500 ka to present.
set_Tm=linterp(cb(c(1500,3000),c(15,5)),dt=1)
set_Tm=rbind(set_Tm,c(5400,5))
# now run model
ex=imbrie(insolation=insolation,Tm=set_Tm[,2],b=set_b[,2],times=set_b[,1])
# time-frequency analysis of model result