Description Usage Arguments Details Value Author(s) References See Also Examples

Functions for calculating the Forecast Quality Index (FQI) and its components.

1 2 3 4 5 6 7 8 9 10 11 |

`object` |
list object of class “SpatialVx”. In the case of the |

`X,Xhat` |
numeric matrices giving the fields for the verification set. |

`x` |
list object of class “fqi” as returned by |

`surr` |
three-dimesnional array containing surrogate fields for |

`only.nonzero` |
logical, should the means and variances of only the non-zero values of the fields be calculated (if so, the covariance is returned as NA)? |

`k` |
numeric vector for use with the partial Hausdorff distance. For k that are whole numerics or integers >= 1, then the k-th highest value is returned by |

`time.point` |
numeric or character indicating which time point from the “SpatialVx” verification set to select for analysis. |

`obs, model` |
numeric indicating which forecast model to select for the analysis. |

`...` |
In the case of |

The FQI was proposed as a spatial verification metric (a true metric in the mathematical sense) by Venugopal et al. (2005) to combine amplitude and displacement error information in a single summary statistic. It is given by

FQI = (PHD_k(X, Xhat)/mean( PHD_k(X, surr_i); i in 1 to number of surrogates)) / (brightness * distortion)

where the numerator is a normalized partial Hausdorff distance (see help file for locperf), brightness (also called bias) is given by 2*(mu1*mu2)/(mu1^2+mu2^2), where mu1 (mu2) is the mean value of X (Xhat), and the distortion term is given by 2*(sig1*sig2)/(sig1^2+sig2^2), where sig1^2 (sig2^2) is the variance of X (Xhat) values. The denominator is a modified UIQI (Universal Image Quality Index; Wang and Bovik, 2002), which itself is given by

UIQI = cor(X,Xhat)*brightness*distortion.

Note that if `only.nonzero`

is `TRUE`

in the call to `UIQI`

, then the modified UIQI used in the FQI formulation is returned (i.e., without multiplying by the correlation term).

The `print`

method so far just calls the `summary`

method.

FQI returns a list with with the following components:

`phd.norm ` |
matrix of normalized partial Hausdorff distances for each value of k (rows) and each threshold (columns). |

`uiqi.norm ` |
numeric vector of modified UIQI values for each threshold. |

`fqi` |
matrix of FQI values for each value of k (rows) and each threshold (columns). |

It will also have the same attributes as the “SpatialVx” object with additional attributes defining the arguments specific to parameters used by the function.

UIQI returns a list with components:

`data.name` |
character vector giving the names of the two fields. |

`cor` |
single numeric giving the correlation between the two fields. |

`brightness.bias` |
single numeric giving the brightness (bias) value. |

`distortion.variability` |
single numeric giving the distortion (variability) value. |

`UIQI` |
single numeric giving the UIQI (or modified UIQI if only.nonzero is set to TRUE) value. |

ampstats returns a list object with components:

`mean.fcst,mean.vx` |
single numerics giving the mean of Xhat and X, resp. |

`var.fcst,var.vx` |
single numerics giving the variance of Xhat and X, resp. |

`cov` |
single numeric giving the covariance between Xhat and X (if only.nonzero is TRUE, this will be NA). |

Eric Gilleland

Venugopal, V., Basu, S. and Foufoula-Georgiou, E. (2005) A new metric for comparing precipitation patterns with an application to ensemble forecasts. *J. Geophys. Res.*, **110**, D08111, 11 pp., doi:10.1029/2004JD005395.

Wang, Z. and Bovik, A. C. (2002) A universal image quality index. *IEEE Signal Process. Lett.*, **9**, 81–84.

`locperf`

, `surrogater2d`

, `locmeasures2d`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
data( "ExampleSpatialVxSet" )
x <- ExampleSpatialVxSet$vx
xhat <- ExampleSpatialVxSet$fcst
# Now, find surrogates of the simulated field.
z <- surrogater2d(x, zero.down=TRUE, n=10)
u <- list( X = cbind( quantile( c(x), c(0.75, 0.9)) ),
Xhat = cbind( quantile( c(xhat), c(0.75, 0.9) ) ) )
hold <- make.SpatialVx(x, xhat, thresholds = u,
field.type = "Example", units = "none",
data.name = "ExampleSpatialVxSet",
obs.name = "X", model.name = "Xhat" )
FQI(hold, surr = z, k = c(4, 0.75) )
``` |

```
Loading required package: spatstat
Loading required package: nlme
Loading required package: rpart
spatstat 1.52-1 (nickname: 'Apophenia')
For an introduction to spatstat, type 'beginner'
Note: R version 3.4.1 (2017-06-30) is more than 9 months old; we strongly recommend upgrading to the latest version
Loading required package: fields
Loading required package: spam
Loading required package: dotCall64
Loading required package: grid
Spam version 2.1-1 (2017-07-02) is loaded.
Type 'help( Spam)' or 'demo( spam)' for a short introduction
and overview of this package.
Help for individual functions is also obtained by adding the
suffix '.spam' to the function name, e.g. 'help( chol.spam)'.
Attaching package: 'spam'
The following objects are masked from 'package:base':
backsolve, forwardsolve
Loading required package: maps
Loading required package: smoothie
Loading required package: smatr
Loading required package: plyr
Attaching package: 'plyr'
The following object is masked from 'package:maps':
ozone
Loading required package: turboEM
Loading required package: doParallel
Loading required package: foreach
Loading required package: iterators
Loading required package: parallel
Loading required package: numDeriv
Loading required package: quantreg
Loading required package: SparseM
Attaching package: 'SparseM'
The following object is masked from 'package:spam':
backsolve
The following object is masked from 'package:base':
backsolve
Attaching package: 'turboEM'
The following objects are masked from 'package:numDeriv':
grad, hessian
Comparison for:
ExampleSpatialVxSet X Xhat
Thresholds are: threshold 1 threshold 2
normalized Partial Hausdorff distance
threshold 1 threshold 2
k = 4; 0.8865963 0.9929434
k = 0.75; 1.0353367 1.0732379
modified universal image quality index
threshold 1 threshold 2
[1,] 0.9204923 0.9352584
Forecast Quality Index (FQI)
threshold 1 threshold 2
k = 4; 0.9631763 1.061678
k = 0.75; 1.1247641 1.147531
NULL
```

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.