Bayesian regional flood frequency analysis with GEV hierarchical models under spatial dependency structures

Figures & data

Figure 1. The Alto do São Francisco River catchment with the drainage system and the stream gauging stations selected for this study (left) and location map (right)

Table 1. Streamflow gauging stations utilized for regional flood frequency analysis. N is the length of the maximum annual daily streamflow series

Code	Area (km^2)	N	Code	Area (km^2)	N	Code	Area (km^2)	N
40830000	84	13	40975000	964	18	40037000	765	25
40577000	244	21	40060001	559	49	40050000	5426	56
40530000	481	22	41340000	4874	42	40300001	1558	25
41050000	1207	31	40930000	876	25	40053000	304	30
40180000	144	11	40170000	1055	28	41300000	626	50
41250000	676	23	41380000	553	21	41780002	3996	23
40818000	273	20	40400000	1802	40	41890000	1435	22
41075001	4143	11	40770000	675	15	40067000	8987	10
40040000	259	31	40579995	579	46	40800001	5680	57
40056002	334	22	40330000	7378	47	40960000	1744	20
40573000	291	15	40710000	2760	25	41818000	16722	46
40790000	188	18	40032000	763	24

Figure 2. Scaling behaviour of the generalized extreme value (GEV) parameters with the catchment drainage areas

Figure 3. Generalized extreme value shape parameter maximum likelihood estimates (MLEs) in the study region

Figure 4. Posterior estimates of regression parameters. $\mu$, $\sigma$ and $\xi$ are, respectively, location, scale and shape parameters

Figure 5. Correlations among the parameters of the spatially dependent model (M1) and the spatially independent model (M2), and the corresponding regression errors

Figure 6. Posterior estimates of the generalized extreme value (GEV) parameters under models M1 and M2. Model M1 point estimates and 95% credible bounds are indicated, respectively, by black circles and vertical black lines; Model M2 point estimates and their 95% credible intervals are indicated by red dashes

Figure 7. Spatial predictive distribution of the regression errors

Figure 8. Quantile curves of the validation sites and their 95% credible intervals estimated by models M1 and M2