hoods2d uses an object of class “SpatialVx” that includes some information utilized by this function, including the thresholds to be used. The neighborhood methods (cf. Ebert 2008, 2009; Gilleland et al., 2009, 2010) apply a (kernel) smoothing filter (cf. Hastie and Tibshirani, 1990) to either the raw forecast (and possibly also the observed) field(s) or to the binary counterpart(s) determined by thresholding.
The specific smoothing filter applied for these methods could be of any type, but those described in Ebert (2008) are generally taken to be “neighborhood” filters. In some circles, this is referred to as a convolution filter with a boxcar kernel. Because the smoothing filter can be represented this way, it is possible to use the convolution theorem with the Fast Fourier Transform (FFT) to perform the neighborhood smoothing operation very quickly. The particular approach used here “zero pads” the field, and replaces all missing values with zero as well, which is also the approach proposed in Roberts and Lean (2008). If any missing values are introduced after the convolution, they are removed.
To simplify the notation for the descriptions of the specific methods employed here, the notation of Ebert (2008) is adopted. That is, if a method uses neighborhood smoothed observations (NO), then the neighborhood smoothed observed field is denoted <X>s, and the associated binary field, by <Ix>s. Otherwise, if the observation field is not smoothed (denoted by SO in Ebert, 2008), then simply X or Ix are used. Similarly, for the forecast field, <Y>s or <Iy>s are used for neighborhood smoothed forecast fields (NF). If it is the binary fields that are smoothed (e.g., the original fields are thresholded before smoothing), then the resulting fields are denoted <Px>s and <Py>s, resp. Below, NO-NF indicates that a neighborhood smoothed observed field (<Yx>s, <Ix>s, or <Px>s) is compared with a neighborhood smoothed forecast field, and SO-NF indicates that the observed field is not smoothed.
Options for which.methods include:
“mincvr”: (NO-NF) The minimum coverage method compares <Ix>s and <Iy>s by thresholding the neighborhood smoothed fields <Px>s and <Py>s (i.e., smoothed versions of Ix and Iy) to obtain <Ix>s and <Iy>s. Indicator fields <Ix>s and <Iy>s are created by thresholding <Px>s and <Py>s by frequency threshold Pe given by the obj argument. Scores calculated between <Ix>s and <Iy>s include: probability of detecting an event (pod, also known as the hit rate), false alarm ratio (far) and ets (cf. Ebert, 2008, 2009).
“multi.event”: (SO-NF) The Multi-event Contingency Table method compares the binary observed field Ix against the smoothed forecast indicator field, <Iy>s, which is determined similarly as for “mincvr” (i.e., using Pe as a threshold on <Py>s). The hit rate and false alarm rate (F) are calculated (cf. Atger, 2001).
“fuzzy”: (NO-NF) The fuzzy logic approach compares <Px>s to <Py>s by creating a new contingency table where hits = sum_i min(<Px>s_i,<Py>s_i), misses = sum_i min(<Px>s_i,1-<Py>s_i), false alarms = sum_i min(1-<Px>s_i,<Py>s_i), and correct negatives = sum_i min(1-<Px>s_i,1-<Py>s_i) (cf. Ebert 2008).
“joint”: (NO-NF) Similar to “fuzzy” above, but hits = sum_i prod(<Px>s_i,<Py>s_i), misses = sum_i prod(<Px>s_i,1-<Py>s_i), false alarms = sum_i prod(1-<Px>s_i,<Py>s_i), and correct negatives = sum_i prod(1-<Px>s_i,1-<Py>s_i) (cf. Ebert, 2008).
“fss”: (NO-NF) Compares <Px>s and <Py>s directly using a Fractions Brier and Fractions Skill Score (FBS and FSS, resp.), where FBS is the mean square difference between <Px>s and <Py>s, and the FSS is one minus the FBS divided by a reference MSE given by the sum of the sum of squares of <Px>s and <Py>s individually, divided by the total (cf. Roberts and Lean, 2008).
“pragmatic”: (SO-NF) Compares Ix with <Py>s, calculating the Brier and Brier Skill Score (BS and BSS, resp.), where the reference forecast used for the BSS is taken to be the mean square error between the base rate and Ix (cf. Theis et al., 2005).