**4.1 Time series plots of the data**

**Figure 1** gives the time series plot of the annual daily maximum (AM1) flood heights data at sites, Chokwe, Combomune and Sicacate. The AM1 series for Chokwe is for the period 1951–2010, for Combomune is for the period 1966–2010, and for Sicacate is for the period 1952–2010. Since the original data series for Chokwe and Sicacate are comparable in terms of the starting period, only the two sites were considered for further analysis in this chapter. That is, the series for Combomune site was dropped for further analysis. Therefore, the results for this study are based on the two sites, Chokwe and Sicacate.

Furthermore, since the fundamental approach of this study is on the use of extreme value statistics using the block maxima, only the annual maximum value for each year was recorded and plotted in **Figure 1**. It is assumed that these AM1 data series are independent and identically distributed (iid) since they are blocked by years [9–12]. Similarly, it is also assumed that the annual maxima moving sums are also iid.

Since extreme value analysis is used in this chapter the data used in this chapter was not divided into training period, test period and forecasting period as these are not necessary in extreme value theory (EVT). In EVT special attention is paid to the estimation of the extreme quantiles and their corresponding return periods.

#### **Figure 1.**

*Time series plots of annual daily maximum (AM1) flood heights (in metres) at the three sites: Chokwe (1951–2010), Combomune (1966–2010) and Sicacate (1952–2010) along lower Limpopo River of Mozambique.*

**61**

*Fitting a Generalised Extreme Value Distribution to Four Candidate Annual Maximum Flood…*

The results in **Table 1** show that the shape parameter, ξ, is negative for all the models. This reveals that the distribution of floods in the lower Limpopo River basin at Chokwe site follows a short-tailed Weibull family of distributions. Further analysis on the values of the shape parameter at Chokwe site indicated that the distribution of floods at the site also belong to the Gumbel family of distributions since these values are not significantly different from zero (p-value >0.05) for all

Results in **Table 2** show that model AM5 had the lowest total rank of 3 suggesting that it is the best annual maxima moving sums time series model at the site of Chokwe. Consequently, forecasting at the site in this chapter is based on model

Results in **Table 3** show that the shape parameter, ξ, is negative for all the models at the Sicacate site. This suggests that the distribution of floods in the lower Limpopo River basin at Sicacate site follows a short-tailed Weibull family of

Results in **Table 4** show that model AM10 has the lowest total rank value of 2 which implies that it is the best annual maxima moving sums time series model for Sicacate site. Therefore, forecasting at Sicacate site in this chapter are based on

Flood heights (peaks) corresponding to return periods of 20, 50, 100, 200 and 500 years were estimated for flood disaster risk reduction in the basin (see **Table 5**). The best fitting annual maxima moving sums time series models AM5 and AM10 for Chokwe and Sicacate, respectively, were used to predict return levels for the

**Table 5** presents results for selected return periods and their corresponding return levels for Chokwe and Sicacate sites based on the best fitting models AM5 and AM10, respectively. The predicted return levels were compared with the observed annual maxima moving sums. It was found that only one annual extreme flood peak, the year 2000 flood height of 124.89 m, exceeded the 100-year flood level for Sicacate site. As for Chokwe site, the year 2000 flood height of 50.44 m, exceeded the 500-year flood level which explains why it was very destructive at the site. The 100-year flood level for Chokwe was exceeded by three observed extreme events with two coming in the mid-1970s and the third one being the year 2000 flood peak. These findings suggest that the return periods of extreme flood heights in the lower Limpopo River basin of Mozambique can be used as a proxy for the return periods of the summer flood intensity. Results in **Table 5** can also be used to

The principal aim of this study was to identify suitable annual maxima moving sums time series models for the lower Limpopo River basin and to construct flood frequency tables for the basin at the sites of Chokwe and Sicacate in Mozambique. This study has successfully identified the prevailing models at the two sites Chokwe

*DOI: http://dx.doi.org/10.5772/intechopen.82140*

the models particularly AM2, AM5 and AM10.

**4.2 Chokwe models**

AM5 for Chokwe.

distributions.

model AM10.

**4.4 Return level analysis**

selected return periods.

construct flood frequency curves [14].

**5. Concluding remarks**

**4.3 Sicacate models**

*Fitting a Generalised Extreme Value Distribution to Four Candidate Annual Maximum Flood… DOI: http://dx.doi.org/10.5772/intechopen.82140*

## **4.2 Chokwe models**

*Recent Advances in Flood Risk Management*

study are based on the two sites, Chokwe and Sicacate.

**Figure 1** gives the time series plot of the annual daily maximum (AM1) flood heights data at sites, Chokwe, Combomune and Sicacate. The AM1 series for Chokwe is for the period 1951–2010, for Combomune is for the period 1966–2010, and for Sicacate is for the period 1952–2010. Since the original data series for Chokwe and Sicacate are comparable in terms of the starting period, only the two sites were considered for further analysis in this chapter. That is, the series for Combomune site was dropped for further analysis. Therefore, the results for this

Furthermore, since the fundamental approach of this study is on the use of extreme value statistics using the block maxima, only the annual maximum value for each year was recorded and plotted in **Figure 1**. It is assumed that these AM1 data series are independent and identically distributed (iid) since they are blocked by years [9–12]. Similarly, it is also assumed that the annual maxima moving sums

Since extreme value analysis is used in this chapter the data used in this chapter was not divided into training period, test period and forecasting period as these are not necessary in extreme value theory (EVT). In EVT special attention is paid to the

estimation of the extreme quantiles and their corresponding return periods.

*Time series plots of annual daily maximum (AM1) flood heights (in metres) at the three sites: Chokwe (1951–2010), Combomune (1966–2010) and Sicacate (1952–2010) along lower Limpopo River of Mozambique.*

**4.1 Time series plots of the data**

are also iid.

**60**

**Figure 1.**

The results in **Table 1** show that the shape parameter, ξ, is negative for all the models. This reveals that the distribution of floods in the lower Limpopo River basin at Chokwe site follows a short-tailed Weibull family of distributions. Further analysis on the values of the shape parameter at Chokwe site indicated that the distribution of floods at the site also belong to the Gumbel family of distributions since these values are not significantly different from zero (p-value >0.05) for all the models particularly AM2, AM5 and AM10.

Results in **Table 2** show that model AM5 had the lowest total rank of 3 suggesting that it is the best annual maxima moving sums time series model at the site of Chokwe. Consequently, forecasting at the site in this chapter is based on model AM5 for Chokwe.

#### **4.3 Sicacate models**

Results in **Table 3** show that the shape parameter, ξ, is negative for all the models at the Sicacate site. This suggests that the distribution of floods in the lower Limpopo River basin at Sicacate site follows a short-tailed Weibull family of distributions.

Results in **Table 4** show that model AM10 has the lowest total rank value of 2 which implies that it is the best annual maxima moving sums time series model for Sicacate site. Therefore, forecasting at Sicacate site in this chapter are based on model AM10.

#### **4.4 Return level analysis**

Flood heights (peaks) corresponding to return periods of 20, 50, 100, 200 and 500 years were estimated for flood disaster risk reduction in the basin (see **Table 5**). The best fitting annual maxima moving sums time series models AM5 and AM10 for Chokwe and Sicacate, respectively, were used to predict return levels for the selected return periods.

**Table 5** presents results for selected return periods and their corresponding return levels for Chokwe and Sicacate sites based on the best fitting models AM5 and AM10, respectively. The predicted return levels were compared with the observed annual maxima moving sums. It was found that only one annual extreme flood peak, the year 2000 flood height of 124.89 m, exceeded the 100-year flood level for Sicacate site. As for Chokwe site, the year 2000 flood height of 50.44 m, exceeded the 500-year flood level which explains why it was very destructive at the site. The 100-year flood level for Chokwe was exceeded by three observed extreme events with two coming in the mid-1970s and the third one being the year 2000 flood peak. These findings suggest that the return periods of extreme flood heights in the lower Limpopo River basin of Mozambique can be used as a proxy for the return periods of the summer flood intensity. Results in **Table 5** can also be used to construct flood frequency curves [14].

## **5. Concluding remarks**

The principal aim of this study was to identify suitable annual maxima moving sums time series models for the lower Limpopo River basin and to construct flood frequency tables for the basin at the sites of Chokwe and Sicacate in Mozambique. This study has successfully identified the prevailing models at the two sites Chokwe and Sicacate in the lower Limpopo River basin. Annual maxima moving sums of 5 days (AM5) and 10 days (AM10) were identified as suitable time series models for Chokwe and Sicacate, respectively. It was also found in this study that the year 2000 flood height was a very rare extreme event. Flood frequency tables were constructed based on the identified models. It can be concluded that the findings in this study are promising for this vulnerable part of the basin. The findings obtained in this study are aimed to make contributions in the long term forecasts of floods in the basin to complement the much established and sponsored short term forecasts in the region.

Future research studies in the lower Limpopo River basin of Mozambique may advance this study through hierarchical modelling for spatial extremes and Markov chain Monte Carlo methods to the location and scale parameters in a changing climate.
