DS {clim.pact} | R Documentation

## Downscaling of monthly means

### Description

Identifies statistical relationships between large-scale spatial climate patterns and local climate variations for monthly and daily data series. Calibrates a linear regression model using step-wise screening and common EOFs (`EOF`) as basis functions. Evaluates the statistical relationship. Predicts local climate parameter from predictor fields. Works with ordinary EOFs, common EOFs (`catFields`) and mixed-common EOFs (`mixFields`). The rationale for using mixed-common EOFs is that the coupled structures described by the mixed-field EOFs may have a more physical meaning than EOFs of single fields [Benestad et al. (2002), "Empirically downscaled temperature scenarios for Svalbard", Atm. Sci. Lett., doi.10.1006/asle.2002.0051].

The downscaling analysis returns a time series representing the local climate, patterns of large-scale anomalies associated with this, ANOVA, and analysis of residuals. Care must be taken when using this routine to infer local scenarios: check the R2 and p-values to check wether the calibration yielded an appropriate model. It is also important to examine the spatial structures of the large-scale anomalies assocaiated with the variations in the local climate: do these patterns make physical sense? Experiment with both single and mixed fields. It is also a good idea to check whether there are any structure in the residuals: if so, then a linear model for the relationship between the large and small-scale structures may not be appropriate. It is furthermore important to experiment with predictors covering different regions [ref: Benestad (2001), "A comparison between two empirical downscaling strategies", Int. J. Climatology, vol 21, Issue 13, pp.1645-1668. DOI 10.1002/joc.703].

The function `ds()` is a generic routine which in principle works for when there is any real statistical relationship between the predictor and predictand. The predictand is therefore not limited to a climate variable, but may also be any quantity affected by the regional climate. It is important to stress that the downscaling model must reflect a well-understood (physical) relationship.

The trend-estimation uses regression to fit a 5th-order polynomial (in time) to fit the observed time series. The rate-of-change is estimated by taking the time-derivative of this equation. If

y= c0 + c1 x + c2 x^2 + c3 x^3 + c4 x^4 + c5 x^5,

where x is the time, then the rate-of-change is:

y= c1 + 2 c2 x + 3 c3 x^2 + 4 c4 x^3 + 5 c5 x^5.

[ref: Benestad (2002), What can present climate models tell us about climate change?, Climatic Change, accepted.]

The routine uses a step-wise regression (step) using the leading EOFs. The calibration is by default carried out on de-trended data [ref: Benestad (2001), "The cause of warming over Norway in the ECHAM4/OPYC3 GHG integration", Int. J. Clim., 15 March, vol 21, p.371-387.].

The downscaled scenario is saved in a text file in the output directory (default: 'output').

The course notes from Environmental statistics for climate researchers http://www.gfi.uib.no/~nilsg/kurs/notes/course.html is a useful reference to statistical modelling and regression.

### Usage

    DS(dat,preds,mon=NULL,direc="output/",cal.id=NULL,
                  ldetrnd=TRUE,i.eofs=seq(1,8,by=1),ex.tag="",
                  method="lm",plot=TRUE,leps=FALSE,param="t2m",
                  plot.res=FALSE,plot.rate=FALSE,xtr.args="",
                  swsm="step",predm="predict",lsave=TRUE,rmac=TRUE,
                   silent=FALSE)

### Arguments

`dat` | A climate.station object (`station.obj` or `station.obj.dm`). [e.g. from `getnacd`, `getnordklim` or `station.obj`].
`preds` | The predictor `EOF`.
`mon` | month or season to downscale, this is automatically changes if predictor only contains a different month (this is normally a redundant feature).
`direc` | name of directory inwhich the output is dumped (e.g. figures, tables).
`cal.id` | ID tag used for calibration. By default use the first field (`catFields`) for calibration.
`ldetrnd` | F for no detrending; T for removing linear trends before model calibration.
`i.eofs` | select which EOFs to include in the setp-wise screening.
`ex.tag` | Extra labelling tag for file names for experiments.
`method` | Sets the method to use for regression. Method is set to "lm" by default, but "anm" allows the incorporation of an analog model, see `anm`. "anm.weight" weights the principal components according to the eigenvalues, whereas "anm" uses unweighted series.
`plot` | 'TRUE' produces figures.
`leps` | 'TRUE' produces EPS figures (files).
`param` | Name of parameter (for plot labels).
`plot.res` | 'TRUE' shows statistics for residuals.
`plot.rate` | 'TRUE' shows analysis of rate-of-change.
`xtr.args` | Extra/additional arguments in the formula.
`swsm` | Step-wise screening method, default=='step'; 'none' skips stepwise sceeening.
`predm` | Prediction method, default is "predict"
`lsave` | TRUE -> saves the result on disc
`rmac` | TRUE -> subtracts (removes) the annual cycle in station data.
`silent` | TRUE -> no output to screen.

.

### Value

A 'ds' object - a list of following elements:

X.1 .. X.n | 1..nth predictor pattern for n fields (mixFields).
lon.1 .. | Longitude coordinate of spatial fields (a vector).
lat.1 .. | Latitude coordinate of spatial fields (a vector).
n.fld | Number of fields (different types of predictors, mixFields).
unit | Unit of quantity in station series.
pred.name | Name of predictor.
lon.loc | Longitude of predictand location.
lat.loc | Latitude of predictand location
yy.gcm | Years corresponding to scenario (GCM).
mm.gcm | Months corresponding to scenario (GCM).
dd.gcm | Days corresponding to scenario (GCM).
yy.cal | Years corresponding to observation (Calibration).
mm.cal | Months corresponding to observation (Calibration).
dd.cal | Days corresponding to observation (Calibration).
yy.o | Years corresponding to station series (obs.).
mm.o | Months corresponding to station series (obs.).
dd.o | Days corresponding to station series (obs.).
rate.ds | Estimated linear rate of change of downscaled scenario.
rate.err | Error estimate for rate.ds.
gcm.trnd.p | P-value of linear trend in downscaled scenario.
fit.p | ANOVA p-value for fit between large-scale and small-scale
| variability(from regression analysis).
fit.r2 | ANOVA R2 for fit between large-scale and small-scale
| variability (from regression analysis).
pre.gcm | The downscaled scenario (a vector).
pre.y | The downscaled results using the calibration data.
location | Nsme of location of predictor.
gcm.stat | ANOVA of linear trend fit to scrnario.
month | Month of study (0-> all months).
v.name | Name of downscaled element.
region | Region used for downscaling.
pre.fit | Linear fit to prediction (downscaled scenario) (a vector).
pre.p.fit | Polynomial fit to the downscaled scenario.
tr.est.p.fit | Rate of change derived from a fifth-order polynomial
| trend-fit to prediction (downscaled scenario) (a vector).
id.1, id.2 | IDs labelling which data was used for calibration (id.1).

### Author(s)

R.E. Benestad

### Examples

    library(clim.pact)
    data("oslo.t2m")
    data("eof.mc")
    a<-DS(dat=oslo.t2m,preds=eof.mc,plot=FALSE)

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