WikiPrint - from Polar Technologies

# Analysing model drift in South-western Iberia

In this practice, we will analyse the model drift by using the forecast of daily mean surface temperature for July 2001 considering 6 different forecast (lead) months, rfom January to June. The lead month 0 (i.e., the initialization of July itself) will be the reference from which we will compute the anomalies. In this example, we will consider the first member of the CFSv2 hindcast.

```ref <- loadECOMS(dataset = "CFSv2_seasonal_16", var = "tas", members = 1, lonLim = c(-10,-1), latLim = c(36,40), season = 7, years = 2006, leadMonth = 0, time = "DD")
```

```[2014-09-03 17:50:20] Defining homogeneization parameters for variable "tas"
NOTE: daily mean will be calculated from the 6-h model output
[2014-09-03 17:50:20] Defining geo-location parameters
[2014-09-03 17:50:20] Defining initialization time parameters
[2014-09-03 17:50:26] Retrieving data subset ...
[2014-09-03 17:50:31] Done
```
```plotMeanField(ref)
title(main = "Lead month 0 forecast of July 2001")
# This is the spatial mean of the reference field
ref.field <- apply(ref\$Data, MARGIN = c(3,2), FUN = mean, na.rm = TRUE)
```

Next, we will load the forecast of the target variable recursively for lead month values from 1 to 6 (i.e., the initializations from January to June). The different objects are arranged in a list:

```cfs.list <- lapply(1:6, function(lead.month) {
loadECOMS(dataset = "CFSv2_seasonal_16", var = "tas", members = 1, lonLim = c(-10,-1), latLim = c(36,40), season = 7, years = 2006, leadMonth = lead.month, time = "DD")
})
```

In order to visualize the departures of each lead month from the reference in the same range of values, we will use the spplot method for plotting spatial objects of the library sp. To this aim, we will first compute the multi-member spatial mean for each lead month forecast, and then we will arrange the data in a matrix of 6 columns (one for each month), and x * y rows, as follows:

```# The library sp needs to be installed to do this example:
require(sp)
# Matrix of anomalies between lead month and reference
aux.mat <- sapply(1:length(cfs.list), function(i) {apply(cfs.list[[i]]\$Data, MARGIN = c(3,2), FUN = mean, na.rm = TRUE) - ref.field})
# 2D coordinates
xy <- expand.grid(ref\$xyCoords\$x, ref\$xyCoords\$y)
# This step ensures regularity of the CFS grid, which is not perfectly regular:
xy.coords <- coordinates(points2grid(points = SpatialPoints(xy), tolerance = .003))
# Now we create a data.frame with the coordinates X-Y in the first two columns and the mean anomalies in the next 6 columns:
df <- cbind.data.frame(xy.coords, aux.mat)
names(df) <- c("x","y",paste("LeadMonth_",1:6, sep = ""))
str(df)
'data.frame':   55 obs. of  8 variables:
\$ x          : num  -10.31 -9.38 -8.44 -7.5 -6.56 ...
\$ y          : num  40.2 40.2 40.2 40.2 40.2 ...
\$ LeadMonth_1: num  0.0596 0.1601 0.5955 0.9068 1.2601 ...
\$ LeadMonth_2: num  -0.1215 0.0509 0.3622 0.5444 0.6977 ...
\$ LeadMonth_3: num  -0.48 -0.359 -0.402 -0.693 -0.967 ...
\$ LeadMonth_4: num  0.22303 0.27295 0.23869 0.04764 -0.00855 ...
\$ LeadMonth_5: num  -1.212 -0.986 -0.682 -0.587 -0.584 ...
\$ LeadMonth_6: num  -1.314 -0.732 -0.32 -0.5 -0.98 ...
coordinates(df) <- c(1,2)
gridded(df) <- TRUE
class(df)
```

Which returns the new spatial object class:

``` "SpatialPixelsDataFrame"
attr(,"package")
 "sp"
```

In the next lines we use apply the spplot method of package sp, generating a lattice-type map. In first place, we will also load a SpatialLines dataset remotely stored at Santander Met Group server, in order to represent the coastline in the lattice map generated as a geographical reference:

```load(url("http://meteo.unican.es/work/downscaler/aux/wlines.rda"), verbose = TRUE)
l1 <- list("sp.lines", wlines)
spplot(df, as.table = TRUE, col.regions = colorRampPalette(c("blue","white","red")), at = seq(-5.25,5.25,.25), scales = list(draw = TRUE), sp.layout = list(l1))
```

The results show how a increasing lead month leads to a negative bias of the forecast, demonstrating that the mean state of a variable of a forecast is not stationary along the runtime dimension.

Finally, we display the spatial mean of the anomalies w.r.t. the reference for each lead month considered using a barplot:

```barplot(colMeans(df@data), names.arg = abbreviate(names(df)), xlab = "lead month", ylab = "anomaly (ºC)")
title(main = "Mean forecast bias w.r.t. the lead-month 0 initialization")
mtext("Member 1")
```