DS: Downscale

In metno/esd: Climate analysis and empirical-statistical downscaling (ESD) package for monthly and daily data

Downscale

Description

Identifies statistical relationships between large-scale spatial climate patterns and local climate variations for monthly and daily data series.

Usage

DS(
  y,
  X,
  verbose = FALSE,
  plot = FALSE,
  it = NULL,
  method = "lm",
  swsm = "step",
  m = 5,
  rmtrend = TRUE,
  ip = 1:7,
  weighted = TRUE,
  ...
)

Arguments

y	The predictand - the station series representing local climate parameter
X	The predictor - an EOF object or a list of EOF objects representing the large-scale situation.
verbose	TRUE: suppress output to the terminal.
plot	TRUE: plot the results
it	a time index e.g., a range of years (c(1979,2010)) or a month or season ("dec" or "djf")
method	Model type, e.g. lm og glm
swsm	Stepwise screening, e.g. step. NULL skips stepwise screening
m	passed on to crossval. A NULL value suppresses the cross-validation, e.g. for short data series.
rmtrend	TRUE for detrending the predicant and predictors (in the PCs) before calibrating the model
ip	Which EOF modes to include in the model training.
weighted	TRUE: use the attribute 'error.estimate' as weight for the regresion analysis.
...	additional arguments

Details

The function calibrates a linear regression model using step-wise screening and common EOFs (EOF) as basis functions. It then valuates the statistical relationship and predicts the local climate parameter from predictor fields.

The function is a S3 method that Works with ordinary EOFs, common EOFs (combine) and mixed-common EOFs. DS can downscale results for a single station record as well as a set of stations. There are two ways to apply the downscaling to several stations; either by looping through each station and caryying out the DS individually or by using PCA to describe the characteristics of the whole set. Using PCA will preserve the spatial covariance seen in the past. It is also possible to compute the PCA prior to carrying out the DS, and use the method DS.pca. DS.pca differs from the more generic DS by (default) invoking different regression modules (link{MVR} or CCA).

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 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 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.].

DS.list can take a list of predictors and perform a DS on each of them, seperately, at once. First, DS is used on the first predictor, then, it is repeated by applying DS on the residuals from the first step. The DS is repeated for all predictors. The final DS output is list containing as many DS object as the number of predictors. To get the final DS object, a summation of the different values in the list data object must be done.

DS.seasonalcycle is an experimental set-up where the calibration is carried out based on the similarity of the seasonal variation to make most use of available information on a 'worst-case' basis, taking the upper limit view that at most, all the seasonal cycle is connected to the corresponding seasonal cycle in the predictor. See Benestad (2009) 'On Tropical Cyclone Frequency and the Warm Pool Area' Nat. Hazards Earth Syst. Sci., 9, 635-645, 2009 http://www.nat-hazards-earth-syst-sci.net/9/635/2009/nhess-9-635-2009.html.

The function biasfix provides a type of 'bias correction' based on the method diagnose which estimates the difference in the mean for the PCs of the calibration data and GCMs over a common period in addition to the ratio of standard deviations and lag-one autocorrelation. This 'bias correction' is described in Imbert and Benestad (2005), Theor. Appl. Clim. http://dx.doi.org/10.1007/s00704-005-0133-4.

Value

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?

It is 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].

There is a cautionary tale for how the results can be misleading if the predictor domain in not appropriate: domain for northern Europe used for sites in Greenland [ref: Benestad (2002), "Empirically downscaled temperature scenarios for northern Europe based on a multi-model ensemble", Climate Research, vol 21 (2), pp.105–125. http://www.int-res.com/abstracts/cr/v21/n2/index.html]

Author(s)

R.E. Benestad

See Also

biasfix sametimescale

Examples

# One exampe doing a simple ESD analysis:
X <- t2m.DNMI(lon=c(-40,50),lat=c(40,75))
data(Oslo)
#X <- OptimalDomain(X,Oslo)
eof <- EOF(X,it='jan')
Y <- DS(Oslo,eof)
plot(Y, new=FALSE)
str(Y)

# Look at the residual of the ESD analysis
y <- as.residual(Y)
plot.zoo(y,new=FALSE)

# Check the residual: dependency to the global mean temperature?
T2m <- t2m.DNMI()
yT2m <- merge.zoo(y,T2m)
plot(coredata(yT2m[,1]),coredata(yT2m[,2]))

# Example: downscale annual wet-day mean precipitation -calibrate over
# part of the record and use the other part for evaluation.
T2M <- as.annual(t2m.DNMI(lon=c(-10,30),lat=c(50,70)))
cal <- subset(T2M,it=c(1948,1980))
pre <- subset(T2M,it=c(1981,2013))
comb <- combine(cal,pre)
X <- EOF(comb)
data(bjornholt)
y <- as.annual(bjornholt,FUN="exceedance")
z <- DS(y,X)
plot(z, new=FALSE)

## Example on using common EOFs as a framework for the downscaling:
lon <- c(-12,37)
lat <- c(52,72)
ylim <- c(-6,6)
t2m <- t2m.DNMI(lon=lon,lat=lat)
T2m <- t2m.NorESM.M(lon=lon,lat=lat)
data(Oslo)
X <- combine(t2m,T2m)
eof <- EOF(X,it='Jul')
ds <- DS(Oslo,eof)
plot(ds)

## Example downscaling statistical parameters: mean and standard deviation
## using different predictors
data(ferder)
t2m <- t2m.DNMI(lon=c(-30,50),lat=c(40,70))
slp <- slp.NCEP(lon=c(-30,50),lat=c(40,70))
T2m <- as.4seasons(t2m)
SLP <- as.4seasons(slp)
X <- EOF(T2m,it='Jan')
Z <- EOF(SLP,it='Jan')
y <- ferder
sametimescale(y,X) -> z
ym <- as.4seasons(y,FUN="mean")
ys <- as.4seasons(y,FUN="sd")
dsm <- DS(ym,X)
plot(dsm)
dss <- DS(ys,Z)
plot(dss)

## Example for downscaling with missing data
data(Oslo)
dnmi <- t2m.DNMI(lon=c(-10,20),lat=c(55,65))
y <- subset(Oslo,it='jan')
X <- EOF(subset(dnmi,it='jan'))
ds <- DS(y,X)
plot(ds) # Looks OK
# Now we replace some values of y with missing data:
y2 <- y
set2na <- order(rnorm(length(y)))[1:50]
y2[set2na] <- NA
ds2 <- DS(y2,X)
plot(ds2) 

## Use downscale results to fill in missing data:
y3 <- predict(ds2,newdata=X)
## Plot a subset of y based on dates in predicted y3
plot(subset(y,it=range(index(y3))),col='grey80',lwd=4,map.show=FALSE)
points(as.station(predict(ds2)))
# The downscaled 
lines(y3,lty=2)

metno/esd documentation built on Sept. 9, 2024, 5:07 a.m.