A regional hourly maximum rainfall extraction method for part of Upper Blue Nile Basin, Ethiopia

Chapter 9

A regional hourly maximum rainfall extraction method for part of Upper Blue Nile Basin, Ethiopia Animut M. Alem*, Seifu A. Tilahun†, Mamaru A. Moges†,‡ and Assefa M. Melesse§ *Hydrology and Hydroinformatics Department, Ethiopian Construction Works Corporation, Addis Ababa, Ethiopia, † Faculty of Civil and water resources Engineering, Bahir Dar Institute of Technology, Bahir Dar University, Bahir Dar, Ethiopia, ‡ Blue Nile Water Institute, Bahir Dar University, Bahir Dar, Ethiopia, § Department of Earth and Environment, Florida International University, Miami, FL, United States

9.1

Introduction

Hydrologists involved in the design of hydraulic structures such as dams, bridges, and culverts, need to accurately assess the frequency and magnitude of extreme hydrological events (Knoesen and Smithers, 2009). Heavy rainfall over a short period of time often causes damage to infrastructure and thus represents an economic challenge as well as a threat to human safety (Dyrrdal et al., 2014). Common problem in hydrological studies is the limited availability of data at appropriately fine temporal and/or spatial resolution (Knoesen and Smithers, 2009). Note that in many countries the number of rain gages providing hourly or sub-hourly resolution data is smaller than the number of daily gages. The challenges are worse in developing countries such as Ethiopia where the gauge networks are sparse and instruments are non-recording. The majority of the gages are nonrecording and the records from gages are aggregated form of rainfall data, such as daily rainfall depth, where these values do not provide the degree of resolution needed to estimate design flood. This is due to the high cost of collecting and processing high resolution rainfall data (Econopouly, 1987). As a result, other options to extract finer resolution of rainfall data are needed. However, there are no such approaches available in the country to extract this valuable data. A conventional approach is to ascertain the design rainfall intensity (or design storm hyetograph) from available intensity duration frequency (IDF) curves developed for the region, and convert into a corresponding flood hydrograph using a rainfall runoff model. Such procedure is followed in Ethiopian Road Authority (ERA) manual. Another approach stated in the irrigation and drainage design (IDD) manual for the design of small irrigation structures in Ethiopia estimates the maximum hourly rainfall to be 50% of the daily rainfall for areas <5 km2. Extreme Hydrology and Climate Variability. https://doi.org/10.1016/B978-0-12-815998-9.00009-9 © 2019 Elsevier Inc. All rights reserved.

Different methods have been proposed in the literature to obtain fine temporal scale rainfall data from a coarser scale as a daily to sub-daily level, through rainfall disaggregation. The first and the easiest way of disaggregation is uniform distribution technique. The uniform distribution method disaggregates daily rainfall by assuming that the hourly rainfall intensity distribution is constant throughout the day. A second way of disaggregation method is robust and parsimonious regional disaggregation method (Mar
echal and Holman, 2004). This is a regional rainfall disaggregation method from daily to hourly intensities which is presented for the entire United Kingdom, and was developed for use with regionalized hydrological and water quality models. The approach is based on the inter-dependence of the hourly rainfall intensities during a rainfall event. Another approach of daily rainfall disaggregation method is developed by Connolly et al. (1998). The model simulates the number of events on a rainy day, such as starting time, duration, rainfall amount, and time to peak intensity and peak intensity of each event. In addition, many stochastic models have been developed such as Random Cascade Models based on scale invariance theory (G€untner et al., 2001), the Bartlett Lewis or Neyman Scott rectangular pulse models based on point process theory (Uggioni et al., 2011), method of fragments (MOF) (Wey, 2006), HYTOS rainfall disaggregation method (Hanaish et al., 2011), and multivariate rainfall disaggregation model (Koutsoyiannis et al., 2003). However in Ethiopia there are no such methods applied to disaggregate the daily time scale rainfall in to sub-hourly finer resolutions while this finer resolution records are vital for water resource facilities design and development. Hence, this chapter is based on a study designed to develop regional maximum hourly rainfall extraction method to fill

93

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Extreme hydrology and climate variability

the gap in this area. The study carried out the extraction of hourly maximum rainfall from daily maximum rainfall. The method was developed in such a way that the ratio of hourly maximum rainfall to daily maximum rainfall follows a specific probabilistic distribution and was modeled with site-specific parameters. The modeled ratio is then reprocessed further for hourly maximum rainfall extraction.

9.2 9.2.1

Methodology Study area

The Upper Blue Nile River (named Abbay in Ethiopia) starts at Lake Tana and crosses the Ethiopia-Sudan border. The site for this specific study is part of the Upper Blue Nile basin bounded by Amhara region where the Blue Nile River starts. The study area contains most of the highland part of the Upper Blue Nile basin and it covers an area of 93,105.5 km2 with in the Blue Nile basin (Fig. 9.1).

N

15°0′0″N

15°0′0″N 5°0′0″N 10°0′0″N 12°0′0″N 13°0′0″N

E

S 37°0′0″E

38°0′0″E

39°0′0″E

40°0′0″E

36°0′0″E

37°0′0″E

38°0′0″E

39°0′0″E

40°0′0″E

13°0′0″N

36°0′0″E

45°0′0″E

11°0′0″N

40°0′0″E

W

8°0′0″N

9°0′0″N

9°0′0″N

9°0′0″N

10°0′0″N

10°0′0″N

11°0′0″N

10°0′0″N

11°0′0″N

35°0′0″E

12°0′0″N

13°0′0″N

5°0′0″N

10°0′0″N

45°0′0″E

12°0′0″N

40°0′0″E

35°0′0″E

The topographic feature of the Blue Nile is highlands, hills, valleys, and occasional rock peaks. Most of the tributary of the Blue Nile are perennial. The average annual rainfall varies between 1200 and 1800 mm yr
1 ranging from an average of about 1000 mm yr
1 near the Ethiopia-Sudan border to 1400 mm yr
1 in the upper part of the basin, and in excess of 1800 mm yr
1 in the south within Edessa subbasin (Sutcliffe and Parks, 1999). Locally, the climatic seasons are defined as dry season “Bega,” from October to the end of February; short rain period “Belg,” from March to May; and long rainy period “Kiremt,” from June to September, with the highest rainfall occurring in July and August. The year-to-year variation in monthly rainfall is most pronounced in the dry season with the lowest annual variation occurring in the rainy season (Tesemma et al., 2010). Abtew et al. (2009) reported an annual mean rainfall of 1423 mm and standard deviation of 125 mm for the Upper Blue Nile basin. Fig. 9.2 shows monthly mean rainfall and coefficient of variation for the Upper Blue Nile basin.

0 35°0′0″E

36°0′0″E

37°0′0″E

38°0′0″E

FIG. 9.1 Location map of the study area.

39°0′0″E

40°0′0″E

70

140

280

420 Kilometers

350

1

300 250

0.8

200 0.6

150 0.4

100

0.2 Dec

Nov

Oct

Sep

Jul

Aug

Jun

May

Apr

Feb

Mar

0

50 0

Mean monthly rainfall (mm)

1.2

Jan

Coefficient of variation

A regional hourly maximum rainfall extraction method for part of Upper Blue Nile Basin, Ethiopia Chapter 9

Month FIG. 9.2 Mean monthly rainfall and coefficient of variation for the Upper Blue Nile basin (Data source: Abtew, W., Melesse A.M., Dessalegne, T., 2009. Spatial, inter and intra-annual variability of the Upper Blue Nile Basin rainfall. Hydrol. Process. 23, 3075–3082.)

9.2.2

Data

The main data inputs for this research were hourly and daily rainfall data. Hourly rainfall data were obtained from the record of research sites of Bahir Dar University Integrated Water Management PhD program. Four hourly recording stations in the study area were used, Anjeni (37.53 N, 10.68E), Anditid (39.71 N, 9.78E), Mayber (39.64 N, 10.99E), and Debremawi (37.42 N, 11.33E). The remaining 162 daily rainfall recording data were accessed from the Ethiopian National Meteorological Agency (EMA) website (http:// www.ethiomet.gov.et/) and the long period mean annual rainfall was downloaded from http://data.biogeo.ucdavis. edu/. The hourly recording stations are between 5 and 21 years of record whereas the daily recording stations have 10–61 years of record. Three basic data screening tests were carried out. Outlier test using Grubbs and Beck test (G-B), test for independence and stationarity, using Wald–Wolfowitz (W–W), and Homogeneity and stationarity, using Mann–Whitney (M–W) test (Rao and Hamed, 2000).

9.2.3

Regionalization

9.2.3.1 Cluster analysis in regionalization Cluster analysis is the generic name of a variety of multivariate statistical procedures that are used to investigate, interpret, and classify given data into similar groups or clusters, which may or may not be overlapping (Rao and Srinivas, 2008). Cluster analysis groups objects (observations) based on information found in the data describing the objects or their relationships. There are several clustering algorithms which may be chosen for regionalization. For this specific study, hybrid clustering was applied. It uses K-means algorithm (a partitioned clustering algorithm) to identify groups of homogeneous regions by adjusting the clusters derived from

95

agglomerative hierarchical clustering. The attributes used for clustering are a combination of at-site statistics, mean annual rainfall and site characteristics, latitude, longitude, and elevation. The analysis was done with the XLSTAT application software. A discordancy measure was used to identify sites with gross errors in their data or those that were grossly discordant with the region as a whole. To estimate discordancy values for sites in a region, Hosking and Wallis (2005) consider the sites as points in three-dimensional space of sample L-moment ratios (L-CV, L-Skewness, and L-Kurtosis). Centroid of the region is regarded as a point depicting average of sample L-moment ratios of the sites in the region. Any point that is far from the centroid of the region is flagged as discordant. Mathematically for a region containing N number of sites, the discordancy statistic for site i is defined by Eqs. (9.1)–(9.4). 1 Di ¼ N ðui
uÞT A
1 ðui
uÞ 3

(9.1)

where ui is a vector containing the t, t3, and t4 values of site i in the region expressed as. h iT (9.2) ui ¼ tðiÞ t3 ðiÞ t4 ðiÞ u is the unweighted group average of the L-moment ratios computed using. u ¼ N
1

N X

ui

(9.3)

i¼1

and the covariance matrix A is computed using. A¼

N X

ð ui
uÞ ð ui
uÞ T

(9.4)

i¼1

9.2.3.2 Test for homogeneous regions After cluster analysis the regional homogeneity of stations was tested using daily maximum rainfall data. Out of 166 stations used in regionalization, only 62 stations have daily maximum rainfall data and were used for regional homogeneity test. Among the different goodness-of-fit tests, tests based on L-Moment were selected for the selection of parental distribution in this study. According to Hosking and Wallis (2005), the goodness of fit have to be judged by how well the L-skewness and L-kurtosis of the fitted distribution match the regional average L-skewness and L-kurtosis of the observed data. L-moment approach to test the homogeneity of the delineated regions relies on heterogeneity measure. The heterogeneity measure compares between-site variations in sample L-moments for a group of sites. The aim was to estimate the degree of heterogeneity in a group of sites

96

Extreme hydrology and climate variability

and to assess whether the sites might reasonably be treated as a homogeneous region. Heterogeneity (H1) of a given region was computed based on the magnitude of the site-to-site variability in the L-moment ratios relative to the level of variability expected in a homogeneous regions. To calculate the value of H, a weighted-average regional value of L-Cv (L-CvR) is computed from the sample values of L-Cv for the proposed sites in the region, where the weights are based on record length (Eq. 9.5). tR ¼

N X i¼1

ni tðiÞ =

N X

ni

(9.5)

i¼1

A weighted-average standard deviation is then computed for the at-site L-Cv values for the collection of sites (VLCv), Eq. (9.6). " #1=2 N N  2 X X ðiÞ R V¼ ni t
t = ni (9.6) i¼1

i¼1

A four-parameter Kappa distribution is fitted using the weighted-average regional values of the L-moment ratios for the sites. The mean (mv) and standard deviation (sv) of a weighted-average standard deviation V for 500 number of simulations are computed. H is then computed as follows (Eqs. 9.7–9.9): H¼

ðV
mv Þ sv

(9.7)

Alternative measures based on L-CV and L-skewness are.  N N 2  2 . X X V2 ¼ ni tðiÞ
tR + t3 ðiÞ
t3 R ni (9.8) i¼1

i¼1

And a measure based on L-skewness and L-kurtosis.  N N 2  2 1=2 . X X ðiÞ R ð iÞ R ni t3
t3 + t4
t4 ni V3 ¼ i¼1

i¼1

(9.9) Hosking and Wallis (2005) suggest that the region be regarded as “acceptably homogeneous” if H < 1, “possibly heterogeneous” if 1 < H < 2, and “definitely heterogeneous” if H > 2.

9.2.4

Regional extraction method

The extraction method was developed based on four hourly recording stations from data in the intense rainfall season, of July, August, and September. A minimum of four maximum hourly (hmax) and daily rainfall (dmax) per year were taken from hourly recording stations to get representative values. These data from several years formed maximum hourly and maximum daily rainfall time series data.

The basic assumptions considered in developing the extraction method was that maximum hourly rainfall for a given time series always corresponds with daily maximum rainfall of that time series. Through extraction, the essential statistics like means, variances, and coefficients of skewness were preserved in the generated maximum hourly series. The method considered that the dimensionless ratio of hourly maximum rainfall to daily maximum rainfall follows a specific probabilistic distribution. This was represented by a statistical distribution of rmax (Eq. 9.10).  (9.10) rmax ¼ hmax dmax To produce specific quantiles in each site of the region, a site-specific scale factor d is introduced which is expressed by the following equation.  (9.11) d ¼ dmax davg where hmax and dmax are the hourly maximum and daily maximum rainfall for a given station at a given time respectively. davg is the average of daily maximum rainfall of a given station for any time series. dis a dimensionless ratio of daily maximum rainfall of a year to the mean of those daily maximum rainfall records of the time series. It is introduced to provide a site-specific value of hmax. In reality for the same value of dmax, two stations, station “X” and station “Y” in the same region, may not have the same hourly maximum rainfall. If site-specific scales were not introduced all stations of a region with the same value of daily maximum rainfall will end up with equal hourly maximum rainfall which may not be true in reality. To account such differences each sites are scaled with a dimensionless ratio d. The developed extraction method follows the following procedure. Daily maximum rainfall series of a given station in the modeled regions was first listed. The mean of those rainfall series and the dimensionless ratio of daily maximum rainfall to mean of daily maximum rainfall d for each record was then computed. For the computed value of d,the cumulative distribution function value of rmax was obtained from the probability table provided in Tables 9.1 and 9.2. Therefore, the value of rmax was estimated with the inverse of the provided distribution and hourly maximum rainfall is computed by the following equation.*** hmax ¼ rmax ∗ dmax

(9.12)

The performance of regional extraction model was tested with standard error of estimate (SSE), percent bias (PBIAS), Nash-Sutcliffe efficiency (NSE) and coefficient of determination (R2) using data from the four stations where hourly data were recorded. Those data were not used in the development of the regional curves.

A regional hourly maximum rainfall extraction method for part of Upper Blue Nile Basin, Ethiopia Chapter 9

97

TABLE 9.1 CDF values of rmax for region 1 Range in d ¼ ddmax avg

F(rmax) for Pearson type III

Range in d ¼ ddmax avg

F(rmax) for Pearson type III

Range in d ¼ ddmax avg

F(rmax) for Pearson type III

0.42

0.9053

0.855

0.6917

1.085

0.7411

0.565

0.0505

0.865

0.8246

1.115

0.9225

0.615

0.2712

0.87

0.3972

1.13

0.1064

0.635

0.1308

0.88

0.5396

1.165

0.8636

0.66

0.6449

0.89

0.4263

1.17

0.2803

0.675

0.5364

0.895

0.8599

1.185

0.5724

0.685

0.5156

0.9

0.5083

1.19

0.1866

0.695

0.1024

0.91

0.8930

1.195

0.0503

0.71

0.3551

0.925

0.5044

1.205

0.4296

0.73

0.3237

0.955

0.1566

1.29

0.4783

0.745

0.0555

0.965

0.8468

1.345

0.7106

0.75

0.7077

0.985

0.9704

1.365

0.0362

0.77

0.0171

0.99

0.2038

1.395

0.8220

0.775

0.0828

1

0.6270

1.405

0.8176

0.78

0.3067

1.005

0.5641

1.42

0.3283

0.785

0.2353

1.015

0.3259

1.455

0.2427

0.795

0.7191

1.025

0.3132

1.7

0.8462

0.805

0.5641

1.04

0.6779

1.715

0.5253

0.815

0.6196

1.055

0.3858

>1.835

0.3839

0.825

0.5904

1.065

0.1803

TABLE 9.2 CDF values of rmax for region 2 Range in d ¼ ddmax avg

F(rmax) for Gen. extreme value (GEV)

Range in d ¼ ddmax avg

F(rmax) for Gen. extreme value (GEV)

d ¼ ddmax avg

F(rmax) for Gen. extreme value (GEV)

0.405

0.5022

0.91

0.937681

1.125

0.17594

0.44

0.6513

0.92

0.637142

1.13

0.65393

0.51

0.9766

0.925

0.398667

1.135

0.45194

0.65

0.1249

0.935

0.818757

1.14

0.04452

0.675

0.7082

0.94

0.269097

1.16

0.02778

0.69

0.9432

0.945

0.702792

1.175

0.68299

0.695

0.5753

0.955

0.974177

1.185

0.11955

0.735

0.6481

0.965

0.80786

1.19

0.26915

0.745

0.9018

0.97

0.12264

1.2

0.41070

0.765

0.1135

0.98

0.079637

1.21

0.83977

0.785

0.9316

0.985

0.607187

1.215

0.33009

Range in

Continued

98

Extreme hydrology and climate variability

TABLE 9.2 CDF values of rmax for region 2—cont’d Range in d ¼ ddmax avg

F(rmax) for Gen. extreme value (GEV)

Range in d ¼ ddmax avg

F(rmax) for Gen. extreme value (GEV)

d ¼ ddmax avg

F(rmax) for Gen. extreme value (GEV)

0.79

0.5426

0.99

0.455006

1.23

0.91415

0.805

0.2121

1.01

0.592264

1.245

0.08397

0.81

0.6075

1.035

0.626345

1.26

0.60572

0.815

0.1246

1.04

0.674999

1.275

0.94194

0.825

0.0612

1.045

0.07875

1.315

0.69730

0.845

0.7853

1.05

0.488003

1.39

0.65824

0.85

0.1000

1.06

0.57496

1.465

0.89047

0.86

0.7651

1.065

0.471127

1.47

0.43727

0.87

0.6596

1.07

0.214302

1.595

0.09925

0.88

0.2019

1.09

0.474035

1.605

0.92746

0.89

0.9554

1.1

0.569534

1.675

0.77830

0.9

0.3273

1.115

0.547408

>1.7

0.49892

9.2.5

Quantile estimation

After the extraction method was developed, hourly maximum rainfall was extracted for each station of the region. The data were fitted with a probabilistic distribution function and parameters were estimated for the selected distributions. According to (Hosking and Wallis, 2005), if there was more than one candidate distribution for quantile estimation, the accuracy of quantile estimated and the selection of best candidate distribution can be evaluated by computing the relative Standard error. The relative error is estimated by Monte Carlo simulation. With this, regional growth curve was developed for each region. Index flood approach was adopted in the quintile estimation.

9.3 9.3.1

Result and discussion Data screening results

No outlier was observed for hourly maximum rainfall records. For daily maximum rainfall, out of 73 stations 32 had an outlier and the rest 41 had no outlier. The required independence and homogeneity test result was satisfied for hourly maximum rainfall of all four recording stations. For daily maximum rainfall, out of 73 stations 10 stations did not satisfy the independence and stationarity test whereas only three stations failed in homogeneity test. Therefore a total of 11 stations were rejected and 62 stations were used for the required analysis in this study.

9.3.2

Range in

Regionalization result

Considering the availability of hourly recording stations and the result from hybrid clustering, the region was divided into two groups as shown in Fig. 9.3. Discordancy test was conducted for each region and one discordant station, Mekaneyesus, was found. But, the remaining stations in both regions indicated that there were no discordant stations with Di < 3. The result of homogeneity test for the identified regions showed that they were homogeneous. The heterogeneity measure (H1) was computed in R-studio and it showed that both regions were homogeneous with value of H1 < 1 (Table 9.3).

9.3.3

Parental distribution for each region

According to the goodness-of-fit test (test based on Lmoment ZDlST), the best probability distributions that represents the two regions are shown Table 9.4. Region 1 was fitted with Pearson type III distribution and Region 2 was fitted with general extreme value (GEV) distribution.

9.3.4

Model calibration results

The model was calibrated for all hourly recorded stations and thereby distributed to the region as per the regionalization result. The estimated L-moment and distribution parameters are shown in Tables 9.5 and 9.6 for both regions.

A regional hourly maximum rainfall extraction method for part of Upper Blue Nile Basin, Ethiopia Chapter 9

35°0′0″E

36°0′0″E

37°0′0″E

38°0′0″E

39°0′0″E

40°0′0″E

99

41°0′0″E

Homogineous rainfall regions of the basin N

13°0′0″N

13°0′0″N

12°0′0″N

12°0′0″N

11°0′0″N

11°0′0″N

10°0′0″N

10°0′0″N

Legend Region 9°0′0″N

9°0′0″N

Region one 0

Region two

35°0′0″E

36°0′0″E

37°0′0″E

37.5 75

150

38°0′0″E

39°0′0″E

225

40°0′0″E

300 Kilometers 41°0′0″E

FIG. 9.3 Map of homogeneous regions for rainfall analysis.

TABLE 9.3 Regional homogeneity test results

TABLE 9.5 L-moment and distribution parameters of rmax for Pearson type III distribution (region 1)

Mean of

Mean of

Mean of

Max. discordance

Heterogeneity

Region

L-CV

L-CS

L-CK

Di

measure H1

Region 1

0.139

0.124

0.105

2.53

0.88

Region 2

0.137

0.132

0.122

2.51

0.77

TABLE 9.4 Regional goodness-of-fit test results of rmax Distribution

Gen. logistic

GEV

Normal

Region 1

2.97

1.62

1.54

1.20


1.29

Region 2

1.44

0.23

0.12


0.24


2.43

Pearson-III

Gen. Pareto

The selected distributions were fitted and quantiles were estimated. Part of the data was used to evaluate representative values of the CDF and part of it are used for validation. The validation result gave good statistics as

L-moment parameters

Distribution parameters

l1

0.47

m (location)

0.47

l2

0.11

g (shape)

0.20

t(L-CV)

0.23

s (scale)

0.92

t3(L-Cs)

0.15

Α

4.76

t4(L-Ck)

0.09

Β

0.10

x¼k

0.04

Z

0.21

shown in Figs. 9.4–9.7 and Table 9.7. Fig. 9.4 shows correlation between observed and simulated hourly maximum rainfall with an R2 value of 0.73 for Region 1. Fig. 9.5 shows relationship of observed daily maximum and hourly maximum rainfall and simulated hourly maximum rainfall with Pearson Type III probability distribution for Region 1.

100 Extreme hydrology and climate variability

35 y = 0.9628x + 0.3429

30 Simulated hmax (mm)

TABLE 9.6 L-moment and distribution parameters of rmax for GEV distribution (region 2)

R2 = 0.85

25

L-moment parameters

Distribution parameters

l1

0.377

x (Location)

0.308

l2

0.084

a (Scale)

0.123

t(L-CV)

0.2217

k (shape)

0.016

t3(L-Cs)

0.1600

5

t4(L-Ck)

0.1376

0 0.00

20 15 10

5.00

10.00 15.00 20.00 25.00 30.00 35.00 Observed hmax (mm) Linear (hmax (mm))

hmax (mm)

Simulated hmax (mm)

40 35

y = 0.9277x + 2.3684

30

R2 = 0.73

25 20 15 10 5 0 0.00

10.00

20.00

30.00

40.00

Observed hmax (mm) hmax (mm)

Linear (hmax (mm))

FIG. 9.4 Scatter plot between observed and predicted hourly maximum rainfall for Region 1.

Hourly maximum Rf hmax (mm)

FIG. 9.6 Scatter plot between observed and predicted hourly maximum rainfall for Region 2.

45

35.00 30.00 25.00 20.00 15.00 10.00 5.00 0.00 20.00

40.00

30.00

50.00

60.00

Hourly maximum Rf hmax( mm)

80.00

Gen. extreme valuve

Observed hmax (mm) 45.00

70.00

Daily maximum Rf dmax (mm)

FIG. 9.7 Observed hourly and daily maximum rainfall and predicted hourly maximum rainfall for Region 2.

40.00 35.00 30.00

TABLE 9.7 Comparison of basic statistics of observed and predicted values of hourly maximum rainfall

25.00 20.00 15.00

Region 1

10.00

Region 2

Statistics

Observed

Predicted

Observed

Predicted

Mean

17.1

18.3

16.2

16.0

Variance

32.9

39.0

27.9

30.4

Skewness

1.0

1.6

0.3

0.5

St. dev.

5.7

6.2

5.3

5.5

5.00 0.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 Daily maximum Rf dmax (mm) Observed hmax (mm)

Pearson type III

FIG. 9.5 Observed hourly and daily maximum rainfall and predicted hourly maximum rainfall for Region 1.

Fig. 9.6 shows correlation between observed and simulated hourly maximum rainfall with an R2 value of 0.85 for Region 2. Fig. 9.7 shows relationship of observed daily maximum and hourly maximum rainfall and simulated hourly maximum rainfall with GEV probability distribution for Region 2.

9.3.5

Model performance test result

The coefficient of determination and the Nash-Sutcliff efficiency (NSE) has acceptable values, and the SSE was relatively small. The extraction method showed good prediction of maximum hourly rainfall from daily maximum rainfall (Table 9.8).

A regional hourly maximum rainfall extraction method for part of Upper Blue Nile Basin, Ethiopia Chapter 9

Region one

TABLE 9.8 Model performance measure result

Region two

3

R

SSE

PBIAS

NSE

Region 1

0.73

3.6



6.6

0.6

Region 2

0.85

2.2

1.6

0.8

2.5 Quantile (q())

Region

1.5 1

0

50 100 150 200 Return period, T (Year) FIG. 9.8 Regional growth curve of hourly maximum rainfall.

100 90 80 70 60 50 40 30 20 10 0

0

Deke Estifanos-50% Lewaye-50% Deke Estifanos-simulated Lewaye-simulated

150 100 200 Return period, T (Year) FIG. 9.9 Comparison between the developed method and 50% assumption.

Quantile

Quantiles for hourly maximum rainfall were estimated by the method of index flood. The distribution of the extracted hourly maximum rainfall was fitted and parameters were estimated using method of L-moment. The result shows that all candidate distributions have approximately the same RMSE. In this study, Pearson type III and Generalized Logistic are selected for Region 1 and Region 2, respectively (Table 9.9). With the selected probability distributions, regional growth curves of hourly maximum rainfall were computed for each region as shown in Fig. 9.8. Comparison was made with the IDD manual, which estimates hourly maximum rainfall as 50% of daily rainfall and the ERA drainage design manual. Comparison of hourly maximum rainfall obtained by the extraction method with estimates in the drainage manuals show large differences as shown in Figs. 9.9 and 9.10. The stations selected for comparison are the ones with highest deviations. Three stations, Deke Estifanos, Lewaye, and Quarit were used to evaluate the deviation between ERA/IDD manuals and the simulated rainfall values. Deke Estifanos represents high rainfall and Lewaye and Quarit represent low rainfall events in the regions ERA drainage manual underestimate hourly maximum rainfall for stations probably receiving high rainfall events and overestimate at stations with low rainfall in the region. The 50% assumption of hourly maximum rainfall (IDD manual) overestimates intense rainfall for return period up to 100 year and underestimates the rest. Estimation of hourly maximum rainfall affects prediction of design floods in hydrologic design. Underestimation or overestimation of design flood causes uneconomic design, failure of hydraulic structures, and flooding.

2

0.5

Quantile estimation results

Hourly maximum Rf hmax (mm)

9.3.6

101

0

90 80 70 60 50 40 30 20 10 0

50

0

20

40 60 Return period

Deke Estifanos

80

Quarit

100

ERA region A2

FIG. 9.10 Comparison between the developed method and ERA design manual.

TABLE 9.9 Distribution parameters of hourly maximum rainfall Region

Selected distribution

Region 1

Pearson type III

Region 2

Generalized logistic

Parameters m (location)

d (scale)

g (shape)

a

b

x

1.00

0.37

0.44

20.55

0.08


0.69

x

a

k

0.96

0.21


0.12

102 Extreme hydrology and climate variability

9.4

Summary

This study presents developed methodology for the extraction of hourly maximum rainfall from daily maximum rainfall data. Basic statistical characteristics of hourly rainfall intensity for part of the Upper Blue Nile basin was obtained from four stations spread across the basin. The region is represented with four stations. Regional partitioning is performed using cluster analysis and grouped stations are screened for discordance. The homogeneity test is evaluated by heterogeneity measure. In all cases, the study result shows acceptable conclusions. The ratio of hourly maximum rainfall to daily maximum rainfall is represented by a specific probabilistic distribution. Five probability distributions, namely, Generalized Logistic distribution, Generalized Extreme-Value distribution, Normal, Pearson type III distribution and Generalized Pareto distribution were tested to model the extraction of hourly maximum rainfall intensity. Regional L-moment goodness-of-fit tests were used to evaluate the best fit distribution for each region. Gamma family and GEV distribution best represents the region. Using the distribution, hourly maximum rainfall data were extracted from the available daily maximum rainfall for each station in the region. The model predicted well as tested by performance test criteria and shows good performance in preserving important statistical properties of the rainfall process. Quantiles were estimated with model output hourly maximum rainfall for each region. Representative distributions were applied. Pearson type III and Generalized Logistic distribution best represent extracted hourly maximum rainfall for Region 1 and Region 2, respectively. Parameters for those distributions were estimated with the L-moment method using RStudio. Using those parameters, regional growth curve was developed and at four sites quantiles were estimated.

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