Frequency of occurrence of flow regime components: a hydrology-based approach for environmental flow assessments and water allocation for the environment

Figures & data

Figure 1. Conceptual procedure for setting the inter-annual and seasonal variability limits of the hydrological conditions of low flows based on frequencies of occurrence

Figure 2. Conceptual procedure for setting the peak-flow events based on frequencies of occurrence. (a) First, the daily maximum annual flow per year of the complete set of records is identified. (b) Second, the characteristic magnitude of the peak flows is set based on the average magnitude associated with a return period of 1, 1.5 and 5 years derived from historical, log-normal, Gumbel and log-Pearson Type-III logarithmic regression models. (c) Third, the events from characteristic magnitudes are identified in the full set of records and filtered from the low-flow component. Fourth, from this filtered set of records the characteristic duration (d) and timing (e) of the peak-flow events are identified and their cumulative frequency is calculated. Fifth, the degree of daily changes (f) is calculated for rise and fall rates

Table 1. Frequency factors of occurrence for the integration of low-flow regimes into annual volumes for environmental water allocation, according to a desired ecohydrological state and environmental objective class

Desired ecohydrological status	Environmental objective	Frequency of occurrence of low-flow regimes
		Wet	Average	Dry	Very dry
Very good	A	0.1	0.4	0.3	0.2
Good	B	0.0	0.2	0.4	0.4
Moderate	C	0.0	0.0	0.4	0.6
Deficient	D	0.0	0.0	0.0	1.0

Table 2. Frequency factors of occurrence for the integration of the peak-flow events (categories I, II and III) into annual volumes for environmental water allocation, according to the desired ecohydrological state and environmental objective class

Desired ecohydrological status	Environmental objective	Frequency of occurrence of number of peak-flow events
		Category I	Category II	Category III
Very good	A	10	6	2
Good	B	5	3	2
Moderate	C	3	2	1
Deficient	D	2	1	1

Figure 3. Overall schematic procedure to determine environmental volumes for annual-based water allocation according to the hydrology-based frequency-of-occurrence approach

Table 3. Flow variability indices for both the reference (earlier) and the assessment (later) periods from the case studies. MAR: mean annual runoff, CV: coefficient of variation, MABF: mean annual baseflow, BFI: baseflow index and CVB: overall index of flow variability (CV/BFI)

River basin	Gauging station (code)	Period of record	MAR (m^3/s)	CV (%)	MABF (m^3/s)	BFI (%)	CVB
San Pedro Mezquital	11012 and 11039	1944–1973	86.7	195.7	3.0	3.5	55.7
		1974–2003	86.8	275.3	1.9	2.2	123.2
Baluarte	11016	1948–1969	49.8	176.4	0.7	1.5	117.5
		1970–1992	60.3	185.4	0.8	1.3	146.5
Acaponeta	11014	1945–1976	41.6	115.8	1.6	3.9	29.9
		1977–2008	40.6	197.4	1.5	3.8	52.4

Figure 4. Reference and assessment low-flow discharge residuals (a–c), scatter plots of the low-flow hydrological conditions (d–f) and scatter plots of the integrated low flows based on the frequency factors of occurrence according to each environmental objective class (g–i)

Figure 5. Scatter plots from characteristic magnitudes for 16 peak-flow events (floods) associated to different return periods between the reference and assessment periods (a–c), and their logarithmic distribution individual models (d–f)

Figure 6. Daily maximum annual flow per year of the complete set of records and magnitudes of the peak-flow events of the case studies. The event magnitudes correspond to 1-, 1.5- and 5-year return periods (Categories I, II and III, respectively) for both the reference and assessment periods (left and right in each graph)

Figure 7. Number, duration (days) and cumulative frequency (percentage) of the peak-flow events of the case studies. The event magnitudes correspond to 1-, 1.5- and 5-year return periods (Categories I, II and III, respectively) from the reference (a, c and e) and assessment (b, d and f) periods

Table 4. Coefficient of determination (R²) and slope between the periods of reference and assessment for the performance validation indicators of the case study rivers

River basin	San Pedro Mezquital		Baluarte		Acaponeta
	R^2	Slope	R^2	Slope	R^2	Slope
Low flows per hydrological condition
Wet	0.95	0.86	0.96	1.11	0.99	0.80
Average	1.00	1.01	0.97	1.19	1.00	0.98
Dry	0.99	1.16	0.98	1.58	0.96	1.04
Very dry	0.84	0.43	0.96	1.02	0.99	1.23
Low flows per environmental objective
A	0.99	0.95	0.99	1.25	0.99	0.99
B	0.99	0.90	0.98	1.30	0.99	1.09
C	0.98	0.78	0.98	1.29	0.99	1.15
D	0.84	0.43	0.96	1.02	0.99	1.23
Peak flow events
Magnitude	1.00	1.27	0.96	0.64	0.99	0.92
Reference period distribution	0.99	1.08	0.96	1.12	0.99	1.11
Assessment period distribution	0.99	1.09	1.00	1.09	0.98	1.11

Table A1. Low flow volumes for water allocation per hydrological condition and environmental objective class according to Equation (1)(1) $Q_{\mathrm{L}\mathrm{F}}=\left(F_w\times Q_w\right)+\left(F_a\times Q_a\right)+\left(F_d\times Q_d\right)+\left(F_{vd}\times Q_{vd}\right)$(1) . MAR: mean annual runoff

Month	Hydrological condition (hm^3)
	Wet	Average	Dry	Very dry	Volume per environmental objective class (hm^3)
	75^th	25^th	10^th	0^th	A	B	C	D
San Pedro Mezquital
Reference period (1944–1973; MAR = 2735 hm^3/year)
January	106	23	15	9	26	14	11	9
February	53	15	11	8	16	11	9	8
March	25	10	9	7	11	9	8	7
April	12	6	5	5	6	5	5	5
May	9	5	4	3	5	4	3	3
June	106	28	11	7	27	13	9	7
July	541	324	200	183	280	218	190	183
August	831	474	323	217	413	311	259	217
September	1162	515	370	264	486	357	306	264
October	527	184	111	57	171	104	78	57
November	85	33	28	19	34	25	22	19
December	115	24	17	12	29	16	14	12
Discharge	3572	1643	1103	790	1504	1086	915	790
Assessment period (1974–2003; MAR = 2733 hm^3/year)
January	75	17	12	2	18	9	6	2
February	36	11	8	0	10	5	3	0
March	18	8	4	2	6	4	3	2
April	9	3	1	0	2	1	0	0
May	8	1	0	0	1	0	0	0
June	91	21	9	3	21	9	5	3
July	603	320	248	102	283	204	161	102
August	856	497	360	127	418	294	220	127
September	883	500	428	72	431	300	214	72
October	363	144	75	9	118	63	36	9
November	57	27	22	7	24	17	13	7
December	64	19	13	9	20	13	11	9
Discharge	3063	1569	1178	335	1354	919	672	335
Baluarte
Reference period (1948–1969; MAR = 1572 hm^3/year)
January	29	8	5	3	8	5	4	3
February	26	4	3	2	6	3	3	2
March	8	4	2	2	3	2	2	2
April	4	2	1	1	1	1	1	1
May	3	1	0	0	1	0	0	0
June	39	4	2	1	6	2	1	1
July	353	126	112	74	134	99	89	74
August	493	255	187	129	233	177	152	129
September	597	305	172	140	261	186	153	140
October	205	119	48	39	90	58	42	39
November	38	15	9	8	14	10	8	8
December	38	13	8	5	12	8	7	5
Discharge	1833	855	550	404	771	552	462	404
Assessment period (1970–1992; MAR = 1902 hm^3/year)
January	61	9	6	5	12	6	5	5
February	31	5	4	3	7	4	3	3
March	17	3	2	2	4	2	2	2
April	4	1	1	1	1	1	1	1
May	4	1	1	0	1	1	0	0
June	32	6	3	1	7	3	2	1
July	370	199	157	91	182	139	117	91
August	678	292	278	111	290	214	177	111
September	620	370	299	157	331	257	214	157
October	220	85	47	23	75	45	33	23
November	109	19	14	7	24	12	10	7
December	111	11	8	6	19	8	7	6
Discharge	2257	1001	820	406	953	690	571	406
Acaponeta
Reference period (1945–1976; MAR = 1312 hm^3/year)
January	44	8	7	5	11	7	6	5
February	17	6	5	4	6	5	4	4
March	8	5	4	3	4	4	3	3
April	6	4	3	2	4	3	3	2
May	5	4	3	2	3	3	3	2
June	42	8	5	4	10	5	4	4
July	273	134	93	39	117	80	60	39
August	437	242	178	127	220	171	148	127
September	524	250	205	144	243	190	168	144
October	167	73	43	25	64	42	32	25
November	25	13	9	8	12	9	8	8
December	35	10	9	7	11	8	7	7
Discharge	1583	756	563	370	704	524	447	370
Assessment period (1977–2008; MAR = 1281 hm^3/year)
January	34	8	6	6	10	6	6	6
February	19	6	5	4	6	4	4	4
March	10	5	4	4	5	4	4	4
April	7	3	3	2	3	3	3	2
May	5	3	3	2	3	3	2	2
June	25	7	6	3	8	5	4	3
July	242	120	78	68	109	82	72	68
August	375	246	223	150	233	198	179	150
September	402	244	188	177	230	195	181	177
October	149	63	49	20	59	40	31	20
November	56	14	9	3	14	7	5	3
December	23	10	8	6	10	8	7	6
Discharge	1347	729	581	444	690	556	499	444

Table A2. Peak flow event attributes and flood regime annual volumes for water allocation per environmental objective class according to Equation (2)(2) $Q_{\mathrm{F}\mathrm{R}}=\hspace{0.17em}\frac{\left(F_{fI}\times D_{fI}\times Q_{fI}\right)+\left(F_{fII}\times D_{fII}\times Q_{fII}\right)+\left(F_{fIII}\times D_{fIII}\times Q_{fIII}\right)}{10}$(2)

River basin	Peak event category	Reference			Assessment
		I	II	III	I	II	III
	Return period (years)	1	1.5	5	1	1.5	5
San Pedro Mezquital	Period of records	1944–1973			1974–2003
	Magnitude (m^3/s)	350	785	1780	245	845	2180
	Volume (hm^3/d)	30	68	154	21	73	188
	Duration (days)	7	3	2	11	3	1
	Timing (months)	Jul–Oct			Jun–Oct
	Rate of change (% rise and fall)	68			76
		−39			−38
	Volume per environmental objective class (hm^3/year)
	A	395			402
	B	228			220
	C	135			132
	D	93			87
Baluarte	Period of records	1948–1969			1970–1992
	Magnitude (m^3/s)	305	800	2920	380	995	2695
	Volume (hm^3/d)	26	69	252	33	86	233
	Duration (days)	3	2	1	3	2	1
	Timing (months)	Jul–Oct			Jan, Jul–Oct
	Rate of change (% rise and fall)	181			179
		−68			−55
	Volume per environmental objective class (hm^3/year)
	A	212			248
	B	131			147
	C	77			87
	D	55			60
Acaponeta	Period of records	1945–1976			1977–2008
	Magnitude (m^3/s)	215	505	1705	210	520	1500
	Volume (hm^3/d)	19	44	147	18	45	130
	Duration (days)	3	2	2	3	3	2
	Timing (months)	Jul–Oct			Jan, Jul–Oct
	Rate of change (% rise and fall)	101			156
		−62			−60
	Volume per environmental objective class (hm^3/year)
	A	167			187
	B	113			119
	C	64			69
	D	49			50

Table A3. Magnitude of the peak-flow extreme events associated with each recurrence interval (return period in years) from both the reference and assessment periods of the case study rivers

Return period	San Pedro Mezquital		Baluarte		Acaponeta
	Reference (m^3/s)	Assessment (m^3/s)	Reference (m^3/s)	Assessment (m^3/s)	Reference (m^3/s)	Assessment (m^3/s)
1.0	350	245	305	380	215	210
1.5	785	845	800	995	505	520
2.0	1050	1180	1265	1400	845	790
2.5	1270	1365	1585	1715	1045	960
3.0	1410	1535	2055	1915	1205	1090
3.5	1510	1680	2365	2150	1365	1225
4.0	1610	1890	2605	2305	1480	1350
4.5	1710	2015	2830	2510	1620	1430
5.0	1780	2180	2920	2695	1705	1500
5.5	1870	2200	3120	2775	1865	1615
6.0	1920	2340	3390	3050	1955	1770
6.5	2000	2365	3555	3130	2025	1950
7.0	2180	2615	3890	3295	2225	2015
10.0	2485	2895	4715	3830	2660	2385
15.0	2730	3250	5440	4175	3150	3035
20.0	2905	3500	7285	4705	3590	3285

Figure A1. Location of the San Pedro Mezquital, Baluarte and Acaponeta rivers

Figure A2. Flow–ecology relationships of the San Pedro River in Marismas Nacionales (basin lowlands). The conceptual hydrograph is shown at two time scales: daily, for differentiating the peak-flow events of the flood regime (dark blue; categories in dashed lines) from low flows (light blue); and monthly, for the low-flow regime thresholds (light green and solid lines)