Real-time flood forecasting by relating local stage and remote discharge

Figures & data

Table 1 Main geomorphological properties of the selected river reaches. DA_u and DA_d: drainage area subtended by the upstream and downstream section, respectively; DA_int: intermediate drainage area; L: channel length; S₀: mean channel slope.

River reach (river)	DAu (km^2)	DAd (km^2)	DAint (km^2)	L (km)	S0
Pia-PLag (Po)	42 030	70 091	28 061	236.0	0.00014
Pie-MM (Tiber)	1 805	5 279	3 474	71.06	0.0011
PN-MM (Tiber)	4 145		1 134	30.83	0.0009

Pia-PLag: Piacenza-Pontelagoscuro; Pie-MM: Pierantonio-Monte Molino; PN-MM: Ponte Nuovo-Monte Molino.

Fig. 1 Po River: location of the selected hydrometric sections.

Fig. 2 Tiber River: location of the selected hydrometric sections.

Table 2 Po River—Piacenza-Pontelagoscuro reach: main characteristics of the investigated floods (Q_p: peak discharge; T_L: observed wave travel time). The percentage of observed stages within the confidence interval (hCI) is also shown, along with the AW of the 90%CI for all the selected events.

Date	TL (h)	Piacenza	Pontelagoscuro	hCI (%)	AW (m)
		Qp (m^3 s^-1)	Qp (m^3 s^-1)
Calibration
May 2002	35	5937	5403	86	2.5
June 2002	30	4897	4016	89	2.5
July 2002	34	3385	3271	99	2.1
August 2002	35	2523	2552	97	1.9
November 2002	32	5835	6202	100	2.2
December 2002	30	8020	7725	100	2.3
Mean values				95	2.2
Validation
December 2003	38	4955	4293	88	2.3
October 2004	37	4327	5392	100	2.3
February 2006	32	1569	1933	100	1.8
14 September 2006	28	4549	3732	92	2.2
26 September 2006	27	3327	2910	92	2.2
December 2006	30	2808	5900	100	2.0
May 2007	36	1441	1489	100	1.8
June 2007	40	2199	2181	97	2.0
November 2007	34	1493	2663	78	1.9
May 2008	34	2693	4550	96	2.1
September 2008	46	1782	2064	100	2.0
November 2008	36	5410	4808	99	2.3
December 2008	34	5133	5237	90	2.2
February 2009	30	4019	5036	77	2.3
2 April 2009	34	4176	4800	84	2.4
18 April 2009	30	3179	3861	100	2.5
May 2009	24	8745	7331	95	2.2
December 2009	26	2742	3219	91	2.2
April 2010	30	4631	5773	96	2.3
June 2010	36	4955	5188	96	2.2
August 2010	30	2579	3236	94	2.1
October 2010	30	2199	2565	100	2.0
1 November 2010	25	5163	6042	81	2.2
16 November 2010	30	3434	4765	88	2.6
December 2010	29	3681	5313	78	2.4
February 2011	30	1622	2354	100	2.0
March 2011	30	5458	5220	94	2.3
June 2011	38	2636	3234	98	2.2
November 2011	34	5684	5689	98	2.2
Mean values				93	2.2

Table 3 Tiber River reaches: main characteristics of the investigated floods (Q_p: peak discharge; T_L: observed wave travel time). The percentage of observed stages within the confidence interval (hCI) is also shown, along with the AW of the 90%CI for all the selected events.

Date	Pierantonio	Ponte Nuovo	Monte Molino	Pie-MM			PN-MM
	Qp (m^3 s^-1)	Qp (m^3 s^-1)	Qp (m^3 s^-1)	TL (h)	hCI (%)	AW (m)	TL (h)	hCI (%)	AW (m)
Calibration
December 1996	380	728	704	8.0	87	1.90	3.5	82	0.97
April 1997	429	502	525	12.0	95	1.60	5.0	94	0.95
January 1998	223	308	299	9.5	100	1.20	5.5	98	0.88
February 1999	428	764	735	7.5	100	1.80	4.5	89	1.10
December 2000	566	879	808	8.5	92	2.10	6.0	91	0.99
April 2001	240	300	284	11.0	100	1.25	6.0	98	0.84
November 2005	779	1131	1193	8.0	80	2.90	2.5	81	1.30
30 December 2005	417	666	732	8.0	100	1.90	2.0	99	0.95
March 2006	195	278	392	8.5	99	1.30	4.0	100	0.86
13 February 2007	94	173	181	10.5	100	1.09	6.0	99	1.00
March 2008	77	203	259	8.5	99	1.13	5.5	100	0.89
5 December 2008	350	522	540	9.0	90	1.50	3.0	89	0.98
11 December 2008	564	905	1053	9.0	90	2.30	2.5	89	1.10
February 2009	237	319	349	9.5	100	1.40	4.5	100	0.85
Mean values					95	1.67		94	0.98
Validation
November 1997	308	409	431	8.0	80	1.50	4.0	92	1.00
December 1997	123	189	228	9.5	100	1.10	4.5	100	0.89
April 1998	221	441	495	8.0	94	1.40	5.0	99	0.89
December 1998	235	717	751	7.5	83	1.50	2.5	84	0.99
December 1999	135	766	854	7.0	82	1.60	2.0	92	1.00
March 2001	188	367	382	7.5	95	1.26	6.0	100	0.89
2 December 2005	434	631	752	8.0	93	2.10	2.5	96	0.97
5 December 2005	495	871	906	7.5	100	2.50	2.5	88	1.00
February 2006	58	138	146	7.5	99	1.06	3.5	100	1.00
10 February 2007		362	592				5.5	96	0.89
26 February 2007	54	153	149	11.5	97	1.05	6.5	100	1.08
March 2007	49	122	115	12.0	100	1.05	7.0	99	1.04
February 2008	73		338	11.0	100	1.02
January 2009	75	160	152	11.5	100	1.05	7.0	100	0.95
January 2010	756	1021	1105	8.5	91	3.00	3.0	91	1.20
21 November 2010	529	555	658	8.5	85	1.80	3.0	98	0.96
28 November 2010	343	784	995	7.5	76	1.90	3.0	73	1.10
December 2010	437	831	923	6.5	78	2.70	2.5	89	1.06
March 2011	321	402	575	8.0	87	1.50	3.5	90	0.93
Mean values					91	1.62		94	0.99

Table 4 RCM-RT parameters for all the investigated reaches, wherein α_meanT and β_meanT are the RCM characteristic parameters and ∆t* is the forecast lead time. See Table 1 for abbreviations.

River reach (river)	∆t* (h)	αmeanT (-)	βmeanT (m^3 s^-1)
Pia-PLag (Po)	32.0	0.795	500
Pie-MM (Tiber)	9.0	1.003	25
PN-MM (Tiber)	4.0	1.082	–27

Fig. 3 Linear relationship between the downstream discharge, Q_d, and the quantity (A_d(t + T_L)/A_u(t))Q_u(t) for the Piacenza-Pontelagoscuro reach (six calibration events): (a) mean (T_L = 32 h) and (b) observed wave travel time; the Pierantonio-Monte Molino reach (14 calibration events): (c) mean (T_L = 9 h) and (d) observed wave travel time; and the Ponte Nuovo-Monte Molino reach (14 calibration events): (e) mean (T_L = 4 h); and (f) observed wave travel time.

Table 5 Percentage lateral flow for all the investigated case studies. The variation range and mean, m (both in absolute value) of the evaluation measures of the RCM-RT performance are also shown (e_Qp: error in peak discharge; e_hp: error in peak stage; PC_ris: coefficient of persistence for rising limb; NS: Nash-Sutcliffe efficiency coefficient).

	Lateral flow (%)	Discharge			Stage
		eQp (%)	PCris (-)	NS (-)	ehp (m)	PCris (-)	NS (-)
Piacenza-Pontelagoscuro reach (∆t* = 32 h)
Calibration (6)	3–31 (m = 14)	5–23 (m = 14)	0.46–0.83 (m = 0.61)	0.48–0.88 (m = 0.75)	0.12–1.00 (m = 0.55)	0.58–0.94 (m = 0.74)	0.62–0.95 (m = 0.82)
Validation (29)	15–45 (m = 30)	0–31 (m = 12)	0.17–0.92 (m = 0.62)	0.53–0.91 (m = 0.74)	0.02–1.39 (m = 0.46)	0.13–0.93 (m = 0.66)	0.52–0.93 (m = 0.76)
Pierantonio-Monte Molino reach (∆t* = 9 h)
Calibration (14)	25–68 (m = 50)	1–24 (m = 9)	0.46–0.99 (m = 0.84)	0.63–0.97 (m = 0.85)	0.03–1.00 (m = 0.31)	0.30–0.99 (m = 0.85)	0.69–0.97 (m = 0.87)
Validation (18)	43–81 (m = 59)	1–27 (m = 11)	0.23–0.94 (m = 0.67)	0.33–0.90 (m = 0.70)	0.01–1.30 (m = 0.38)	0.14–0.94 (m = 0.67)	0.25–0.89 (m = 0.70)
Ponte Nuovo-Monte Molino reach (∆t* = 4 h)
Calibration (14)	2–28 (m = 12)	0–16 (m = 5)	0.47–0.98 (m = 0.79)	0.86–0.97 (m = 0.91)	0.00–0.70 (m = 0.17)	0.40–0.98 (m = 0.78)	0.84–0.98 (m = 0.91)
Validation (18)	0–35 (m = 18)	0–20 (m = 6)	0.31–0.97 (m = 0.63)	0.55–0.97 (m = 0.88)	0.01–0.80 (m = 0.18)	0.32–0.94 (m = 0.63)	0.55–0.98 (m = 0.88)

Table 6 Statistical analysis of the RCM parameters α and β. SD: standard deviation.

River reach	Probability distribution		χ^2		Mean		SD
	α	β	α	β			σα	σβ
Pia-PLag	Log-normal	Normal	3.6	5.0	0.868	409	0.152	218
Pie-MM	Log-normal	Normal	6.5	7.4	1.109	9	0.223	17
PN-MM	Log-normal	Normal	2.2	8.8	1.029	–12	0.075	18

Fig. 4 Piacenza-Pontelagoscuro reach (Po River, ∆t* = 32 h): comparison between observed and forecast hydrograph provided by the RCM-RT model for: (a) and (b) the calibration flood event of December 2002; (c) and (d) the validation flood event of 26 September 2006. The assessed CI is also shown along with the alarm threshold.

Fig. 5 Pierantonio-Monte Molino reach (Tiber River, ∆t* = 9 h): comparison between observed and forecast hydrograph provided by the RCM-RT model for: (a) and (b) the calibration flood event of February 2009; (c) and (d) the validation flood event of January 2010. The assessed CI is also shown along with the warning and alarm hydrometric thresholds.

Fig. 6 Ponte Nuovo-Monte Molino reach (Tiber River, ∆t* = 4 h): comparison between observed and forecast hydrograph provided by the RCM-RT model for: (a) and (b) the calibration flood event of 30 December 2005; (c) and (d) the validation flood event of 2 December 2005. The assessed CI is also shown along with the warning and alarm hydrometric thresholds.

Table 7 Contingency table showing the capability of the RCM-RT model to predict exceedence/non-exceedence of hydrometric thresholds. h_alarm: alarm threshold; h_war: warning threshold.

Piacenza-Pontelagoscuro reach (Δt* = 32 h)
halarm = 1.3 m	Observed		Total	Accuracy	BIAS
	Threshold exceedence	Threshold non-exceedence
Forecast Threshold exceedence	7 (Hits)	3 (False alarms)	10	0.91	1.43
Threshold non-exceedence	0 (Misses)	25 (Correct non-events)	25
Total	7	28	35
Pierantonio-Monte Molino reach (Δt* = 9 h)
hwar = 6.0 m	Observed		Total	Accuracy	BIAS
	Threshold exceedence	Threshold non-exceedence
Forecast Threshold exceedence	10 (Hits)	1 (False alarms)	11	0.88	0.85
Threshold non-exceedence	3 (Misses)	18 (Correct non-events)	21
Total	13	19	32
Pierantonio-Monte Molino reach (Δt* = 9 h)
halarm = 6.9 m	Observed		Total	Accuracy	BIAS
	Threshold exceedence	Threshold non-exceedence
Forecast Threshold exceedence	6 (Hits)	1 (False alarms)	7	0.94	1
Threshold non-exceedence	1 (Misses)	24 (Correct non-events)	25
Total	7	25	32
Ponte Nuovo-Monte Molino reach (Δt* = 4 h)
hwar = 6.0 m	Observed		Total	Accuracy	BIAS
	Threshold exceedence	Threshold non-exceedence
Forecast Threshold exceedence	13 (Hits)	0 (False alarms)	13	1	1
Threshold non-exceedence	0 (Misses)	19 (Correct non-events)	19
Total	13	19	32
Ponte Nuovo-Monte Molino reach (Δt* = 4 h)
halarm = 6.9 m	Observed		Total	Accuracy	BIAS
	Threshold exceedence	Threshold non-exceedence
Forecast Threshold exceedence	7 (Hits)	2 (False alarms)	9	0.94	1.29
Threshold non-exceedence	0 (Misses)	23 (Correct non-events)	23
Total	7	25	32