Precipitation as a proxy for climate variables: application for hydrological modelling

Figures & data

Figure 1. (a) Paraná River Basin, climate gauges and seasonality index along the basin. The two black squares indicate the Itaipu Dam (in the south) and the city of Brasília (in the north, above gauge no. 7), used in the analysis of Sections 4.2 and 4.3; (b) detail of the Corumbá River Basin (dark blue drainage), used for the analysis in Section 4.5, showing Roncador gauge (red dot), used because of the full availability of daily relative air humidity and hours of sunlight data; (c) the 1424 unit-catchments used for model calculation; and (d) lithological regions used for model calibration

Table 1. Daily data availability (percentage of total period) of sunlight hours (SH), relative humidity (RH), atmospheric pressure (AP), wind speed (WS) and average surface air temperature (ST) for each of the 54 INMET gauges. The starting date (dd/mm/yyyy) of data availability for each gauge is also given; the ending date of 31/12/2011 is the same for all gauges

ID	Gauge name	Starting date	SH	RH	AP	WS	ST	Daily precipitation
1	Aragarças	01/05/1970	80	92	92	92	84	91
2	Araxá	01/04/1963	77	80	82	82	76	81
3	Arinos	01/06/1976	71	88	89	89	79	87
4	Avelar	01/01/1985	88	71	95	95	94	71
5	Bambuí	01/01/1961	70	70	77	77	69	75
6	Barbacena	01/01/1961	88	89	90	90	87	89
7	Brasília	21/08/1961	98	99	99	99	98	98
8	Campo Mourão	02/01/1961	86	92	93	93	87	92
9	Campos Do Jordão	01/01/1961	64	90	93	93	66	91
10	Campos Novos	01/01/1961	67	69	71	71	69	69
11	Capinópolis	01/05/1970	83	83	86	86	78	83
12	Castro	01/01/1961	57	86	90	90	84	88
13	Catalão	01/01/1961	91	99	99	99	94	95
14	Catanduva	01/01/1961	65	91	93	93	92	93
15	Chapecó	01/071973	79	79	82	82	79	80
16	Coronel Pacheco	01/10/1966	84	85	86	86	84	85
17	Curitiba	01/01/1961	89	95	97	97	95	95
18	Divinópolis	11/10/1995	93	96	96	96	96	96
19	Franca	01/01/1961	74	96	96	96	88	96
20	Goiás	01/01/1961	58	97	97	97	91	97
21	Guarulhos	01/071983	94	96	96	96	95	96
22	Indaial	14/12/1970	76	78	81	81	66	79
23	Ipameri	11/2/1977	84	97	97	97	75	94
24	Irati	24/09/1966	93	94	96	96	66	94
25	Iraí	01/01/1961	84	84	88	88	74	85
26	Ituiutaba	01/03/1980	57	77	79	79	77	78
27	Itumbiara	01/09/1993	96	98	98	98	76	97
28	Ivinhema	01/09/1966	73	67	75	75	65	73
29	Jataí	24/11/1978	93	98	99	99	95	98
30	João Pinheiro	01/01/1961	48	80	81	81	77	80
31	Juiz De Fora	01/01/1961	88	89	91	91	87	89
32	Lavras	01/01/1961	86	86	87	87	86	86
33	Londrina	01/01/1961	70	89	90	90	86	88
34	Machado	01/09/1961	86	86	88	88	86	87
35	Maringá	01/01/1961	59	75	77	77	74	75
36	Mirante Santana	01/01/1961	70	98	98	98	97	98
37	Nhum	01/01/1993	94	95	95	95	87	95
38	Paracatu	03/07/1973	76	83	84	84	70	83
39	Paranaguá	01/01/1961	75	91	92	92	81	91
40	Paranaíba	08/07/1971	81	81	81	81	72	81
41	Patos De Minas	01/01/1961	84	86	88	88	87	87
42	Pirenópolis	17/02/1977	96	96	97	97	91	96
43	Poços De Caldas	01/01/1961	57	84	84	84	82	74
44	Presidente Prudente	01/01/1961	92	94	95	95	91	94
45	Resende	01/01/1961	87	78	96	96	93	79
46	Rio Verde	01/11/1971	70	78	79	79	66	71
47	Roncador	01/04/1994	99	100	100	100	98	99
48	Sorocaba	01/01/1961	45	54	55	55	55	55
49	São Carlos	01/01/1961	59	94	95	95	92	94
50	São Lourenço	01/01/1961	87	91	92	92	88	91
51	São Simão	01/01/1961	90	91	92	92	91	91
52	Taubaté	01/01/1961	64	69	69	69	69	69
53	Uberaba	01/01/1961	83	83	86	86	83	84
54	Unaí	01/05/1978	76	90	92	92	88	90

Figure 2. Overview of the methodology used, comparing the simulation scenarios with and without precipitation as proxy. RH: relative humidity; SH: sunlight hours; ST: surface average air temperature; WS: wind speed; AP: atmospheric pressure

Figure 3. Correlation between climatological variables and monthly precipitation for gauges Aragarças and Indaial. The straight (blue) line refers to the linear regression. See Figure 1 for gauge locations

Figure 4. Box plots of p values for each month for the correlations between monthly precipitation and sunlight hours and relative humidity, based on a set of 54 p values (one for each climate gauge). Median values are displayed at the figure bottom

Table B1. Main statistics for the correlations between monthly sunlight hours and precipitation for the months January and July. Pearson correlation (r) and p value are presented for each gauge

ID	Gauge name	Relative humidity regression with precipitation				Sunlight hours regression with precipitation
		r (Jan)	p (Jan)	r (Jul)	p (Jul)	r (Jan)	p (Jan)	r (Jul)	p (Jul)
1	Aragarças	0.7859	0.0000	0.3613	0.1408	−0.6099	0.0001	0.2486	0.3359
2	Araxá	0.7149	0.0000	0.1320	0.5032	−0.7699	0.0000	−0.1453	0.4695
3	Arinos	0.8897	0.0000	0.3589	0.3429	−0.8920	0.0000	−0.5380	0.1351
4	Avelar	0.4858	0.0350	0.5097	0.0307	−0.5093	0.0309	−0.3703	0.1303
5	Bambuí	0.2186	0.1874	0.2177	0.2754	−0.5178	0.0010	−0.2670	0.1782
6	Barbacena	0.5222	0.0002	0.3673	0.0197	−0.6140	0.0000	−0.1028	0.5335
7	Brasília	0.7276	0.0000	0.2706	0.2625	−0.7426	0.0000	−0.4131	0.0787
8	Campo Mourão	0.7370	0.0000	0.3608	0.0109	−0.8046	0.0000	−0.5206	0.0002
9	Campos Do Jordão	0.5687	0.0000	0.2272	0.1380	−0.1895	0.2683	−0.1509	0.4020
10	Campos Novos	0.5692	0.0002	0.5473	0.0006	−0.4132	0.0122	−0.7660	0.0000
11	Capinópolis	0.4109	0.0115	−0.1896	0.4105	−0.5980	0.0001	0.0120	0.9589
12	Castro	0.6700	0.0000	0.3598	0.0141	−0.4146	0.0164	−0.4321	0.0171
13	Catalão	0.7312	0.0000	0.2365	0.2772	−0.6418	0.0000	−0.0030	0.9894
14	Catanduva	0.5942	0.0000	0.5942	0.0001	−0.5895	0.0002	−0.5301	0.0053
15	Chapecó	0.6183	0.0002	0.6114	0.0003	−0.4731	0.0062	−0.7697	0.0000
16	Coronel Pacheco	0.4456	0.0040	0.0248	0.8910	−0.6240	0.0000	−0.2149	0.2298
17	Curitiba	0.4830	0.0004	0.5419	0.0000	−0.4992	0.0004	−0.5867	0.0000
18	Divinópolis	0.9166	0.0000	0.1978	0.5171	−0.2275	0.4148	−0.6882	0.0093
19	Franca	0.6464	0.0000	0.7144	0.0000	−0.4865	0.0017	−0.1912	0.3029
20	Goiás	0.5749	0.0000	0.3055	0.2035	−0.7355	0.0000	−0.3812	0.1452
21	Guarulhos	0.5059	0.0071	0.3980	0.0440	−0.5216	0.0053	−0.3263	0.1114
22	Indaial	0.4966	0.0033	0.4060	0.0172	−0.3631	0.0378	−0.5659	0.0006
23	Ipameri	0.5714	0.0005	0.2383	0.3740	−0.6070	0.0006	0.2588	0.3717
24	Irati	0.5113	0.0004	0.5778	0.0000	−0.4538	0.0020	−0.5760	0.0001
25	Iraí	0.4553	0.0019	0.4304	0.0028	−0.4333	0.0029	−0.5943	0.0000
26	Ituiutaba	0.5508	0.0029	−0.1013	0.8113	−0.6143	0.0051	−0.1416	0.7620
27	Itumbiara	0.7475	0.0004	−0.0871	0.8109	−0.5030	0.0334	0.1337	0.7128
28	Ivinhema	0.2397	0.1790	0.1122	0.5550	−0.7446	0.0000	−0.4036	0.0179
29	Jataí	0.5354	0.0016	0.2848	0.2372	−0.5520	0.0013	−0.3029	0.2372
30	João Pinheiro	0.6759	0.0000	0.3399	0.1217	−0.4992	0.0250	0.0966	0.7537
31	Juiz De Fora	0.4286	0.0024	0.4464	0.0027	−0.5785	0.0000	−0.3628	0.0155
32	Lavras	0.6030	0.0000	0.5140	0.0037	−0.6620	0.0000	−0.1968	0.2973
33	Londrina	0.5867	0.0000	0.3310	0.0246	−0.6822	0.0000	−0.5252	0.0008
34	Machado	0.4325	0.0038	0.4346	0.0064	−0.5298	0.0003	−0.3872	0.0163
35	Maringá	0.5793	0.0001	0.4961	0.0018	−0.7732	0.0000	−0.5020	0.0055
36	Mirante Santana	0.0489	0.7362	0.4956	0.0003	−0.2363	0.1653	−0.3103	0.0696
37	Nhum	0.6499	0.0026	−0.0967	0.7424	−0.7264	0.0004	−0.1979	0.5170
38	Paracatu	0.6247	0.0001	0.5079	0.0637	−0.8192	0.0000	−0.5897	0.0265
39	Paranaguá	0.3500	0.0148	0.3879	0.0064	−0.0881	0.5886	−0.5911	0.0000
40	Paranaíba	0.5594	0.0007	0.4657	0.0144	−0.6120	0.0002	−0.2817	0.1545
41	Patos De Minas	0.6368	0.0000	0.1624	0.4279	−0.6839	0.0000	0.0081	0.9688
42	Pirenópolis	0.7999	0.0000	0.4626	0.0825	−0.7517	0.0000	0.2347	0.3997
43	Poços De Caldas	0.3765	0.0166	0.2683	0.1377	−0.7600	0.0000	−0.3873	0.0615
44	Presidente Prudente	0.7316	0.0000	0.2791	0.0634	−0.7396	0.0000	−0.3137	0.0358
45	Resende	0.4921	0.0017	0.4908	0.0013	−0.2954	0.0642	−0.3869	0.0136
46	Rio Verde	0.5842	0.0011	0.2432	0.2881	−0.3491	0.0686	0.0011	0.9963
47	Roncador	0.6776	0.0028	−0.8481	0.3556	−0.7689	0.0003	−0.9653	0.1681
48	Sorocaba	0.7389	0.0000	0.4987	0.0081	−0.6906	0.0004	−0.4593	0.0275
49	São Carlos	0.5299	0.0001	0.2659	0.0929	−0.6130	0.0002	−0.2364	0.2449
50	São Lourenço	0.2691	0.0739	0.3498	0.0215	−0.3017	0.0493	−0.4496	0.0028
51	São Simão	0.5544	0.0001	0.4711	0.0037	−0.5645	0.0001	−0.2587	0.1276
52	Taubaté	0.5365	0.0019	0.4730	0.0047	−0.4610	0.0091	−0.0366	0.8451
53	Uberaba	0.2788	0.0669	−0.0821	0.7028	−0.7425	0.0000	0.0506	0.8102
54	Unaí	0.7272	0.0000	0.0013	0.9969	−0.8379	0.0000	−0.3199	0.3376

Figure 5. Number of months of the year with p < 0.01 for each gauge for relative air humidity and sunlight hours

Figure 6. Daily relative air humidity and sunlight hours for Brasilia (north of the basin) and Itaipu Dam (southern region), as computed from precipitation as proxy or only from climate averages

Figure 7. Monthly actual evapotranspiration (ET), with the two types of computation of climate variables, Precipitation as Proxy (ETproxy, blue) and Only Climatological Averages (ETnoproxy, red), and the difference between them (ETproxy − ETnoproxy, green), for Brasília city and Itaipu Dam, and monthly precipitation (P) for the same locations

Figure 8. Relationship between monthly precipitation and simulated monthly evapotranspiration for Brasília City (northern region) for the simulation period 1940–2010

Figure 9. Relationship between monthly precipitation and simulated monthly evapotranspiration for Itaipu Dam (southern region) for the simulation period 1940–2010

Figure 10. Long-term variation in calculated annual average discharge with and without precipitation as proxy. Horizontal lines indicate average values pre- and post-1973

Figure 11. Long-term variation in calculated annual evapotranspiration with and without precipitation as proxy. Horizontal lines indicate average values pre- and post-1973

Figure 12. (a) Discharge at the Corumbá River sub-basin outlet for scenarios a–c; and (b) daily and (c) monthly evapotranspiration for the Corumbá River sub-basin. See Figure 1(b) for the sub-basin location

Table A1. Model calibrated parameters for rainfall–runoff processes: Wm: maximum water storage in the soil of each HRU; b: parameter from the variable contributing area model for runoff generation; Kbas and Kint: equivalent hydraulic conductivities for baseflow and subsurface flow;; and CS, CI and CB: related to residence time within surface, subsurface and baseflow linear reservoirs, respectively. The HRUs adopted in this study are: Forest_Deep: forest with deep soil; Forest_Shallow: forest with shallow soil; Agric_Shallow: agriculture with shallow soil; Agric_Deep: agriculture with deep soil; Grass_Shallow: grasslands with shallow soil; Grass_Deep: grasslands with deep soil; Floodplain: floodplain areas adjacent to rivers; and Urban: urban areas

Sub-basins	Wm (mm)	b (-)	Kbas (mm d^−1)	Kint (mm d^−1)
Sub-basin 1: Granitoid, volcanic and some metamorphic rock
Forest_Deep	500	0.1	1.5	5
Forest_Shallow	700	0.1	2.5	10
Agric_Shallow	500	0.1	1.5	5
Agric_Deep	700	0.1	2.5	10
Grass_Shallow	500	0.1	1.5	5
Grass_Deep	700	0.1	2.5	10
Floodplain	300	0.1	1	5
Urban	100	0.1	0.1	5
CS	15
CI	150
CB	5000
Sub-basin 2: Basalt and dacite
Forest_Deep	300	0.5	0.3	4
Forest_Shallow	400	0.5	0.8	4
Agric_Shallow	300	0.5	0.3	4
Agric_Deep	400	0.5	0.8	4
Grass_Shallow	300	0.5	0.3	4
Grass_Deep	400	0.5	0.8	4
Floodplain	400	0.5	0.8	4
Urban	100	0.5	0.1	4
CS	10
CI	100
CB	5000
Sub-basin 3: Sandstone and conglomerate
Forest_Deep	1000	0.1	2	20
Forest_Shallow	1200	0.1	3	30
Agric_Shallow	1000	0.1	2	20
Agric_Deep	1200	0.1	3	30
Grass_Shallow	1000	0.1	2	20
Grass_Deep	1200	0.1	3	30
Floodplain	300	0.1	3	30
Urban	100	0.1	0.1	20
CS	10
CI	100
CB	8000
Sub-basin 4: Sandstone, mudstone and conglomerate
Forest_Deep	700	0.1	1.5	35
Forest_Shallow	800	0.1	2	35
Agric_Shallow	700	0.1	1.5	35
Agric_Deep	800	0.1	2	35
Grass_Shallow	700	0.1	1.5	35
Grass_Deep	800	0.1	2	35
Floodplain	200	0.1	1.5	2
Urban	100	0.1	0.1	2
CS	18
CI	180
CB	4000
Sub-basin 5: Sandstone, diamictite, shale, rhythmite, siltstone and conglomerate
Forest_Deep	300	0.5	0.5	12
Forest_Shallow	400	0.5	1	17
Agric_Shallow	300	0.5	0.5	12
Agric_Deep	400	0.5	1	17
Grass_Shallow	300	0.5	0.5	12
Grass_Deep	400	0.5	1	17
Floodplain	100	0.5	0.5	10
Urban	100	0.5	0.1	10
CS	10
CI	100
CB	5000
Sub-basin 6: Basalt and dactite with sandstone outcrops
Forest_Deep	900	0.1	1.5	10
Forest_Shallow	1000	0.1	2.5	10
Agric_Shallow	900	0.1	1.5	10
Agric_Deep	1000	0.1	2.5	10
Grass_Shallow	900	0.1	1.5	10
Grass_Deep	1000	0.1	2.5	10
Floodplain	300	0.1	1	10
Urban	100	0.1	0.1	10
CS	10
CI	100
CB	5000

Table A2. Performance metrics (KGE) after model validation for the 26 gauges presented in Figure A1

Gauge ID	Gauge name	KGE
1	EngenheiroAmorim	0.507
2	Pires do Rio	0.614
3	Ponte Meia Ponte	0.886
4	Fazenda Santa Maria	0.808
5	Maurilândia	0.71
6	Abaixo Barra do Rio Verde	0.833
7	Clube de Regatas	0.719
8	Uhe Marimbondo	0.601
9	Porto Cunha Bueno	0.754
10	Passagem	0.577
11	Uhe Marimbondo Passagem	0.596
12	Ponte Joaquim Justino	0.507
13	Artemis	0.775
14	Fazenda Ipacarai	0.484
15	União da Vitória	0.687
16	Água Vermelha	0.881
17	Ibitinga	0.91
18	Itaipi	0.891
19	Jupia	0.829
20	Marimbondo	0.876
21	N Avanhandava	0.902
22	P Primavera	0.827
23	Porto Ivinhema	0.504
24	Porto Paraiso do Norte	0.562
25	Rosana	0.775
26	Salto Caxias	0.807

Figure A1. Discharge gauges used for model validation. KGE performance metrics are presented in Table A2