A model-based site selection approach associated with regional frequency analysis for modeling extreme rainfall depths in Minas Gerais state, Southeast Brazil

Abstract

Extreme rainfall data are usually scarce due to the low frequency of these events. However, prior knowledge of the precipitation depth and return period of a design event is crucial to water resource management and engineering. This study presents a model-based selection approach associated with regional frequency analysis to examine the lack of maximum daily rainfall data in Brazil. A generalized extreme values (GEV) distribution was hierarchically fitted using a Bayesian approach and data that were collected from rainfall gauge stations. The GEV model parameters were submitted to a model-based cluster analysis, resulting in regions of homogeneous rainfall regimes. Time-series data of the individual rainfall gauges belonging to each identified region were joined into a new dataset, which was divided into calibration and validation sets to estimate new GEV parameters and to evaluate model performance, respectively. The results identified two distinct rainfall regimes in the region: more and less intense rainfall extremes in the southeast and northwest regions, respectively. According to the goodness of fit measures that were used to evaluate the models, the aggregation level of the parameters in clustering influenced their performance.

Appendices

Appendix A

See Tables 4, 5.

Table 4 Rainfall stations identification

Table 5 Return periods estimation with respective uncertainties for each model of the point frequency analysis and the model-based associated to RFA method

Appendix B

See Figs. 6, 7.

Fig. 6

Time series of annual maximum daily rainfall depths for each candidate rainfall station

Fig. 7

Return periods estimation with respective uncertainties for each model of the point frequency analysis and the model-based associated to RFA method, NWM (North-West Model) in a and SEM (South-East Model) in c. The size of the circles are defined by the respective standard deviation values adjusted to ×0.2 scale factor used to aesthetic purposes. The 95% HPD interval for the SEM and NWM models are showed as lower bound 0.025 and upper bound 0.975; The standard deviation inflation (SDI, in %) values represent the standard deviations (sd) of a given Return Period (RP) in comparison to the respective regional model, the NWM in B and the SEM in d. SDI = (sd_j/(sd_j + sd_j’)) × 100, where sd _j and sd _j ’ are the standard deviation values of the jth RP of a given station (e _i) and the respective regional model

Appendix C

Algorithm C2. The algorithm of clustering from Müllner (2013)

• 1. Let S be the current set of nodes with implicit or explicit dissimilarity information. Determine a pair of mutually closest points (a; b).

• 2. Join a and b into a new node n. Delete a and b from the set of nodes and add n to the set.

• 3. Output the node labels a and b and their dissimilarity d(a; b).

• 4. Update the dissimilarity information by specifying the distance from n to all other nodes. This update can be performed explicitly by specifying the distances or by denying a cluster representative in the stored data approach.

• 5. Repeat steps 1–4 until there is a single node left that contains all of the original nodes.

Distance formula for the complete agglomerative clustering procedure:

$$MAX\left[ {d\left( {I,K} \right), \, d\left( {J,K} \right)} \right],$$

where I and J are clusters that are joined into a new cluster, and K is any other cluster.