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Probability distribution functions (PDFs) provide detailed information on the distribution of rainfall frequency and accumulated volume as a function of rain rate (Chen et al. 2013c). The probability distribution function by occurrence (PDFc) is the ratio of the rain hours within a rain rate interval to the total rain hours. The probability distribution function by volume (PDFv) is the ratio of the rain depth within each rain rate interval to the event-total rain depth. PDFc and PDFv are computed using the ‘Hit’ pairs of gauges and CMPA grids in Table 3.

Table 3

Contingency statistics of the CMPA estimate versus gauge measurements for the seven typhoon rain events

Statistics		N_hit	N_miss	N_false	POD	FAR
Utor	All gauges	25,288	1,671	6,530	0.94	0.21
	Dist: ≤100 km	9,584	484	1,957	0.95	0.17
	Dist: 100–400 km	15,704	1,187	4,573	0.93	0.23
Usagi	All gauges	13,522	999	4,585	0.93	0.25
	Dist: ≤100 km	7,066	411	2,332	0.95	0.25
	Dist: 100–400 km	6,456	588	2,253	0.92	0.26
Linfa	All gauges	8,495	769	2,056	0.92	0.20
	Dist: ≤100 km	4,163	337	959	0.93	0.19
	Dist: 100–400 km	4,332	432	1,097	0.91	0.20
Mujigae	All gauges	12,461	387	2,275	0.97	0.15
	Dist: ≤100 km	1,940	135	833	0.93	0.30
	Dist: 100–400 km	10,521	252	1,442	0.98	0.12
Kalmaegi	All gauges	6,022	542	1,919	0.92	0.24
	Dist: ≤100 km	576	83	260	0.87	0.31
	Dist: 100–400 km	5,446	459	1,659	0.92	0.23
Rammasun	All gauges	3,443	404	1,298	0.90	0.27
	Dist: ≤100 km	793	19	243	0.98	0.23
	Dist: 100–400 km	2,650	385	1,055	0.87	0.28
Rumbia	All gauges	2,825	300	1,004	0.90	0.26
	Dist: ≤100 km	956	50	145	0.95	0.13
	Dist: 100–400 km	1,869	250	859	0.88	0.31

Statistics		N_hit	N_miss	N_false	POD	FAR
Utor	All gauges	25,288	1,671	6,530	0.94	0.21
	Dist: ≤100 km	9,584	484	1,957	0.95	0.17
	Dist: 100–400 km	15,704	1,187	4,573	0.93	0.23
Usagi	All gauges	13,522	999	4,585	0.93	0.25
	Dist: ≤100 km	7,066	411	2,332	0.95	0.25
	Dist: 100–400 km	6,456	588	2,253	0.92	0.26
Linfa	All gauges	8,495	769	2,056	0.92	0.20
	Dist: ≤100 km	4,163	337	959	0.93	0.19
	Dist: 100–400 km	4,332	432	1,097	0.91	0.20
Mujigae	All gauges	12,461	387	2,275	0.97	0.15
	Dist: ≤100 km	1,940	135	833	0.93	0.30
	Dist: 100–400 km	10,521	252	1,442	0.98	0.12
Kalmaegi	All gauges	6,022	542	1,919	0.92	0.24
	Dist: ≤100 km	576	83	260	0.87	0.31
	Dist: 100–400 km	5,446	459	1,659	0.92	0.23
Rammasun	All gauges	3,443	404	1,298	0.90	0.27
	Dist: ≤100 km	793	19	243	0.98	0.23
	Dist: 100–400 km	2,650	385	1,055	0.87	0.28
Rumbia	All gauges	2,825	300	1,004	0.90	0.26
	Dist: ≤100 km	956	50	145	0.95	0.13
	Dist: 100–400 km	1,869	250	859	0.88	0.31

Gauges are separated according to their distance to the typhoon center track: ≤100 km and 100–400 km (POD: probability of detection; FAR: false alarm ratio).

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