New approach to detect trends in extreme rain categories by the ITA method in northwest Algeria

ABSTRACT

A new approach for the modified method of innovative trend analysis (ITA) was applied to the categories of maximum daily rains coming from 41 pluviometric stations of Macta (northwest Algeria) for the period 1970–2010. Six categories of maximum daily rainfall were considered: light: 0–4 mm/day (A); mild to moderate: 4–16 mm/day (B); moderate to heavy: 16–32 mm/day (C₁); heavy: 32–64 mm/day (C₂); heavy to torrential: 64–128 mm/day (D₁); and torrential: equal to or greater than 128 mm/day (D₂). The results show that during the second period (1990–2010), increasing trends were detected in the middle categories B (most frequent: 20.78%), C₁ (17.85%), C₂ (20.21%) and D₁ (4.92%). In addition, migratory movements and rainy events towards the higher categories were detected (in particular towards C₁ (8.84%)). These results show an increase in extreme rains in the Macta watershed during the period 1990–2010.

KEYWORDS:

• extreme rain
• migration movements
• trends
• modified ITA
• Macta-Algeria

Editor A. Castellarin Associate Editor K. Kochanek

1 Introduction

Unprecedented changes in the global climate system have occurred since the 1950s, and global warming is now unequivocally accepted as a phenomenon that disrupts the climate (IPCC 2013). These global climate changes are modifying rainfall regimes in different regions of the world, with far-reaching environmental, social and economic impacts for local communities (Elouissi 2016, Dabanlı et al. 2017, Benzater et al. 2018, 2021, Abul Basher et al. 2018).

In recent years, an increase in the frequency and/or intensity of extreme weather events (minimum and/or maximum extremes), such as heat waves and sand winds, droughts, heavy rains and floods, has been observed worldwide (Groisman et al. 2005, Trenberth 2011, IPCC 2013, Kundzewicz et al. 2014, Kreibich et al. 2017, Elouissi et al. 2021) and in Algeria (Nekkache and Megnounif 2016, Benzater et al. 2019, 2021, Bouklikha et al. 2020), Germany (Berg et al. 2013), Saudi Arabia (Subyani 2012, Almazroui 2013, Labban 2016, Abdelkarim and Gaber 2019), Canada (Requena et al. 2019), China (Hu et al. 2012), South Korea (Jung et al. 2017), Spain (Eekhout et al. 2018), the USA (Kunkel et al. 1999, Wilhelmi and Wilhite 2002, Villarini et al. 2011, Mallakpou and Villarini 2017), France (Blanchet et al. 2018), India (Chandrashekar and Shetty 2018, Tirupathi et al. 2018, Chattopadhyay et al. 2019, Saha et al. 2020), Iran (Bhalta et al. 2019, Attar et al. 2020) and Italy (Brugnara et al. 2012, Caloiero et al. 2016, 2017).

In this context, extreme rainfalls cause some of the most frequent and catastrophic economic and social impacts of all meteorological phenomena (Attar et al. 2020). Floods are systematically observed in association with these phenomena, especially in urban areas where drainage may be inadequate to convey a sudden and significant amount of rainfall in a short time (Bui et al. 2019, Abdelkarim and Gaber 2019, Costache and Bui 2020). Similarly, in rural areas, agricultural activity may suffer losses due to excessive rainfall (Carvalho et al. 2002).

Disproportionate changes in the extreme rainfall intensity have been observed around the world. For example, despite the decrease in total rainfall, there has been a paradoxical increase in extreme rainfall in some Mediterranean areas (Alpert et al. 2002, Benzater et al. 2019, 2021) and in West Africa (Zahiri et al. 2016). These extreme events lead to harmful effects on the ecosystem, society and the economy (Mishra and Singh 2010, Trenberth et al. 2015, Dabanlı et al. 2017). Therefore, concerns about variations in extreme weather conditions are increasing considerably (Estrela and Vargas 2010, Kreibich et al. 2017, Wu et al. 2018).

Because of the changes in extreme rains, which can alter the strategy and policy regarding water resources as well as the criteria for the design of hydraulic infrastructures, a better understanding and better quantification of these extremes, now and in the future, are essential to prevent floods (Abdelkarim and Gaber 2019, Almazroui and Saeed 2020). Several authors have worked on the extreme rainfall trends in the world, but there are few studies on the categorization of this catastrophic weather event (Alpert et al. 2002, Yosef et al. 2009, Caloiero et al. 2016, 2017, Bhalta et al. 2019, Saha et al. 2020). In India, a statistically significant increase in the trend of very heavy and heavy rain categories, accompanied by a significant decreasing trend in the moderate extreme rain category, has been observed (Chandrashekar and Shetty 2018). In the South of Italy, Caloiero et al. (2016) showed that the lowest rain categories (A and B) show increasing trends, while the highest rain categories (D₁ and D₂) show no trends. Similar results were obtained for the number of rainfall days falling in the different categories. Faced with this increase in extreme rainfall in different regions of the world, it is essential to analyse the changes by category of the different intensities of extreme rain and highlight the evolution of each.

The north of Algeria is subject to floods generated directly by this kind of extreme rainfall. The evolution of these events with climate change is a key issue for this region with strong demographic dynamics. Northern Algeria is known for its frequent catastrophic floods. For most of the year, most rivers remain in their lower states of well-defined alluvial channels. During these periods, the proximity of the wadis provides a water supply and an appropriate means of discharge. At rare intervals, during periods of high water, the alluvial plains serve to absorb, and to a certain extent to drain, flood waters that exceed the capacity of the river bed. Despite their appeal otherwise, the occupation of floodplains carries a risk during extreme floods. This risk can turn into a peril causing serious damage to property and agriculture, and disrupting communications systems, commerce and industry. The maximum floods occur at the beginning of autumn, because of the frequency of thunderstorms accompanied by torrential rains, which leads to devastating floods of the Mekerra (a tributary of the Macta) which was the subject of a regular flood generally in October of each year (Yahiaoui 2012).

The study of extreme rains is of paramount importance. It contributes effectively to several hydrological parameters, such as flood estimation where gauging data are lacking. These flow data are used in the design of hydraulic installations such as dam spillways and to protect cities against flooding.

In this study, the monthly maximum rainfall series recorded at 41 weather stations in the Macta watershed (Northwest Algeria), during the period 1970–2010, were analysed by separating them into different categories of rainfall according to the classification used by many studies (Alpert et al. 2002, Yosef et al. 2009, Caloiero et al. 2016, 2017). Then, the modified innovative trend analysis (ITA) technique was applied to the different categories to distinguish the trend of each one.

The objective of this article is to provide a new approach for the ITA method applied to extreme rains. The new visualization of the modified ITA method will make it possible to illustrate the trend in each category of extreme rains, to transform the graphic interpretation into a digital one. Finally, another original goal that has not been pursued in previous work is the detection of migration movements from one category to another.

2 Study area and data

The study is devoted to the Macta watershed, which is located in the northwest of Algeria (Fig. 1a). Its geographical position is between 1.25°W and 0.6°E longitude, and between 34 and 36°N latitude. Macta is a basin that covers an area of 14 410 km². Average annual rainfall is low. The spatial variation of average rainfall is moderate (25%). The Macta watershed is drained by two main rivers: the El-Hammam Wadi to the east and the Mekkera Wadi (called the Mebtouh Wadi downstream) to the west (Elouissi et al. 2017) (Fig. 1b).

Figure 1. (a) Selected stations in the Macta watershed; (b) hydrographic network

The raw maximum daily rainfall data (P_dmax) (in mm/day) were collected from the National Agency for Water Resources (ANRH). The 41 stations selected for the study are spread over all the regions of the Macta watershed (Fig. 1a). The rainfall stations used in this work are represented numerically (for example, Sidi Bel Abbes: 110305; Mascara: 111429). The monthly maximum values were considered for the ITA method. For a given month, the value adopted stands for the maximum daily rainfall.

The reliability of an assessment of hydrometeorological extreme events risks strongly depends on the quality of the rain time series data (Chuan et al. 2019). Indeed, a graphical adjustment of the monthly maximum rains to a generalized extreme value distribution (GEV) allows us to visually prejudge the reliability of these data (Berolo and Laborde 2003). Thus, a homogeneous database of monthly maximum rainfall, with statistical parameters, for 41 Macta stations over a period of 41 years (1970–2010) was formed (Table 1)

Table 1. Statistical parameters of the extreme rainfall (1970–2010)

Number	Station name	Station code	Longitude (°)	Latitude (°)	Z (m)	Max (mm)	Average (mm)	Standard deviation	CV (%)
1	RAS EL MA	110102	−0.809 334	34.494 740	1097	118.3	57.8	26.7	46
2	SID ALI BEN YOUB	110201	−0.734 043	34.978 248	635	210.7	99.1	43.1	44
3	EL HACAIBA	110203	−0.755 568	34.702 013	950	168.0	80.8	29.7	37
4	SARNO Bge	110304	−0.574 060	35.180 350	425	209.7	101.2	41.2	41
5	SIDI BEL ABBES	110305	−0.658 583	35.191 520	485	186.4	88.6	32.1	36
6	HASSI DAHO	110309	−0.538 585	35.091110	650	181.6	95.3	35.2	37
7	MOSTEFA BEN BRAHIM	110312	−0.356 967	35.192 004	590	195.3	99.9	37.1	37
8	AIN TRID	110314	−0.675 747	35.285 762	530	226.8	115.0	43.8	38
9	CHEURFAS BGE	110402	−0.251 628	35.404 398	230	218.9	90.3	41.1	46
10	MERINE	110501	−0.451 765	34.781 331	970	153.8	81.3	28.5	35
11	DAOUD YOUB	110802	−0.214 122	34.920 480	660	178.7	64.7	28.9	45
12	MEFTAH SIDI BOUBEKEUR	111102	0.055986	35.031000	530	205.2	81.5	37.0	45
13	AIN EL HADJAR	111103	0.149 130	34.757 058	1025	168.8	88.7	31.9	36
14	HAMMAM RABI	111112	0.186 280	34.931 920	710	138.8	74.7	28.4	38
15	OUED TARIA	111201	0.091058	35.115 659	501	180.1	79.3	32.4	41
16	AIN TIFRIT	111204	0.401 859	34.917 816	970	185.7	93.5	35.3	38
17	TAMESNA	111210	0.464 584	34.847 322	1105	239.9	84.9	37.2	44
18	BENIANE	111217	0.231 450	35.101 077	630	218.3	86.2	38.4	45
19	MAOUSSA	111401	0.248 202	35.378 314	494	153.5	85.6	26.3	31
20	MATEMORE	111405	0.215 025	35.329 824	482	142.0	79.1	21.5	27
21	TIZI	111413	0.076127	35.320 075	453	166.4	96.6	27.7	29
22	SIDI KADA	111414	0.344 322	35.330 201	549	167.3	93.5	29.7	32
23	AIN FARES	111417	0.247 782	35.481 576	806	247.0	110.9	40.8	37
24	NESMOTH MF	111418	0.381 819	35.251 571	930	263.7	133.5	50.8	38
25	GHRISS	111424	0.166 501	35.246 272	498	213.6	90.2	41.1	46
26	MASCARA	111429	0.146 428	35.392 860	550	164.1	96.5	32.6	34
27	SAHOUET OUIZERT	111502	−0.079531	35.207 846	361	161.0	66.7	24.3	36
28	BOU HANIFIA BGE	111503	−0.069807	35.291 959	306	174.9	75.5	29.8	39
29	SFISSEF	111508	−0.226 020	35.231 837	545	199.1	96.4	36.1	37
30	HACINE	111509	−0.004537	35.459 880	145	206.0	95.4	37.5	39
31	MOHAMMADIA GRHA	111511	0.104 206	35.590 378	50	183.1	93.6	34.5	37
32	TROIS RIVIERES	111516	−0.085948	35.218 519	315	159.8	65.5	31.2	48
33	OGGAZ	111604	−0.255 370	35.564 871	73	148.0	78.0	27.9	36
34	BOU HENNI	111605	−0.086492	35.565 329	26	132.5	72.8	24.5	34
35	FORNEKA	111606	−0.056751	35.774 381	78	178.2	79.4	35.6	45
36	SAMOURIA	111607	0.115 319	35.622 188	48	189.6	82.2	28.2	34
37	MOCTA DOUZ	111610	−0.046623	35.609 550	18	180.6	83.4	38.8	47
38	FERME BLANCHE	111611	0.013060	35.657 361	20	165.6	83.4	31.0	37
39	BLED TAOURIA	111612	0.230 748	35.835 681	118	234.9	96.9	40.3	42
40	MARAIS DE SIRAT	111616	0.176 414	35.750 668	30	223.0	87.0	36.6	42
41	FERME ASSORAIN	111617	0.277 981	35.902 936	222	189.0	95.5	34.5	36

Z (m): Altitude (m), Max (mm): Maximum rains (mm), CV(%): Variation Coefficient (%).

.

3 Methodology

As suggested by Alpert et al. (2002), Yosef et al. (2009) and Caloiero et al. (2016, 2017), six categories of daily rainfall were taken into account: light: 0–4 mm/day (A); mild to moderate: 4–16 mm/day (B); moderate to heavy: 16–32 mm/day (C₁); heavy: 32–64 mm/day (C₂); heavy to torrential: 64–128 mm/day (D₁) and torrential: equal to or greater than 128 mm/day (D₂).

The ITA technique was developed by Şen (2012) to analyse trends in time series. This method has been widely used by several researchers because of its simplicity and efficiency. It consists in dividing the series into two equal parts. Each one is arranged in ascending order, forming a scatter plot with the first part on the x-axis. A 1:1 line, indicating neutrality, is drawn to represent the boundary between the classes with decreasing and increasing trends.

In the new modified ITA approach (Fig. 2), five modifications have been made:

1. the two axes (x and y) of the graph have been sub-divided according to the six categories considered (A, B, C₁, C₂, D₁ and D₂);

2. the graph axes of the graph have been transformed into a bi-logarithmic scale, for better visibility of the values in the lower categories;

3. symbols $\mathrm{\Delta },\mathrm{\nabla }$and —, representing increasing trend, decreasing trend and no trend, respectively, are displayed along with their percentages for each category at the top of the figure (Fig. 2);

4. a minimum distance from the non-trend line which shows whether a positive or negative trend is fixed. Each value of the 2^nd half is considered increasing (decreasing) if it is greater (less) than that of the 1^st half plus (minus) 10% (Wu and Qian 2016);

5. finally, this new configuration of the ITA allows the detection of migration movements from one category to another. If a scatter point of a given category on the x-axis is in a higher (lower) cell on the y-axis, this signifies a migration to the upper (lower) category.

Figure 2. Template for the modified innovative trend analysis (ITA) method

4 Results and discussion

All the calculations for this work were carried out using the R written software. In order to analyse the spatiotemporal evolution of the categories of extreme rainfall, the observation period was divided into two sub-periods, P₁ (January 1970–June 1990) and P₂ (July 1990–December 2010) (Benzater et al. 2019, 2021), using 1990 as the baseline year (Hegerl et al. 2007, Prudhomme and Davies 2009, IPCC 2013, Buric et al. 2015, Mathbout et al. 2018, Zhang et al. 2021).

Thus, from the global initial matrix of (41 years, 12 months, 41 stations; i.e. 20 172 rainy events), two matrices (20 years and 6 months; 41 stations) were created to form 246 monthly maximum rainy events for each station.

The contributions (as a percentage of rainy events) for the six categories of daily rainfall were calculated for the two periods (Table 2). During the first period (1970–1990), it is clear that the contribution coincides with the order of categories. The light category A (30.20%) is the first contributor (Table 1), followed immediately by the light to moderate category B (20.70%), then the moderate to heavy C₁ (18%). The lowest contribution is that of the torrential category (D₂), at only 1.60%.

Table 2. Average values (%) of annual contributions (as a percentage of rainy events) for each category of daily rain for the Macta

Period	Rainfall category
	A	B	C1	C2	D1	D2
1970–1990	30.20	20.70	19.00	18.30	10.20	1.60
1990–2010	26.40	21.30	20.70	21.70	8.80	1.00

For the second period (1990–2010), there is a change in the contributors’ order. In fact, the heavy rainfall category (C₂) becomes second (21.70%), before the light to moderate category B (21.30%) and moderate to heavy C₁ (20.70%), and after the light class A (26.40%), whose contribution decreased compared to the first period. The heavy (D₁) and torrential (D₂) categories have low contributions of 8.80% and 1%, respectively.

4.1 New modified ITA approach

The new approach applying the modified ITA method to the monthly maximum rainfall on 41 weather stations in the Macta watershed makes it possible to visualize the spatial behaviour of the 41 graphs during the two periods P₁ (1970–1990) and P₂ (1990–2010) (Figs 3 and 4).

Figure 3. Trends in extreme rainfall identified by the modified innovative trend analysis (ITA), 1970–1990

Figure 3. (Continued)

Figure 4. Trends in extreme rainfall identified by the modified innovative trend analysis (ITA), 1990–2010

Figure 4. (Continued)

The first reading from the modified ITA method for the 41 stations during the first period (1970–1990) (Fig. 3) shows that, over time, 3356 out of 5043 rainy events (66.55%) show a decreasing trend (Benzater et al. 2019, 2021), while 1341 rainy events (26.59%) show no trend and only 346 rainy events (6.86%) show an increasing trend. This decline in extreme rainfall trends prior to 1990 has been observed in several regions of the world (Venkata Rao et al. 2020).

To identify the trend for each category of extreme rain, and from Fig 3, 41 matrices were established. Examination of these matrices makes it possible to visualize one decision matrix (Table 3). On a spatial scale (Table 3), categories B, C₁, C₂, D₁ and D₂ show a decreasing trend (of 82.93%, 87.80%, 97.56%, 90.24% and 53.66%, respectively), while 40 stations (97.56%) in the light A and D₂ categories showed no trend.

Table 3. Trends of extreme rainfall categories (1970–1990)

Rainfall Category	A	B	C1	C2	D1	D2
Station
110102	0	↑	0	0	↓	↑
110201	0	↑	0	↓	↓	↑
110203	0	↓	↓	↓	↓	0
110304	0	↓	↓	↓	↓	0
110305	0	↓	↓	↓	↓	↑
110309	↓	↓	↓	↓	↓	0
110312	0	↓	↓	↓	↓	↑
110314	0	↓	↓	↓	↓	↓
110402	0	↓	↓	↓	↓	↓
110501	0	0	↓	↓	↓	↓
110802	0	0	0	↓	0	0
111102	0	↓	↓	↓	↓	↑
111103	0	↓	↓	↓	↓	↓
111112	0	↓	↓	↓	↓	0
111201	0	↓	↓	↓	↓	↑
111204	0	↑	0	↓	↓	↑
111210	0	↓	↓	↓	↑	0
111217	0	↓	↓	↓	↓	0
111401	0	↑	0	↓	↓	0
111405	0	↓	↓	↓	↓	0
111413	0	↓	↓	↓	↓	↑
111414	0	↓	↓	↓	↓	↓
111417	0	↓	↓	↓	↓	↓
111418	0	↓	↓	↓	↓	↓
111424	0	↓	↓	↓	↓	↓
111429	0	↓	↓	↓	↓	↑
111502	0	↓	↓	↓	↑	0
111503	0	0	↓	↓	↓	0
111508	0	↓	↓	↓	↓	↑
111509	0	↓	↓	↓	↓	0
111511	0	↓	↓	↓	↓	↓
111516	0	↓	↓	↓	↓	0
111604	0	↓	↓	↓	↓	0
111605	0	↓	↓	↓	↓	↓
111606	0	↓	↓	↓	↓	↓
111607	0	↓	↓	↓	↓	↓
111610	0	↓	↓	↓	↑	↓
111611	0	↓	↓	↓	↓	↓
111612	0	↓	↓	↓	↓	↓
111616	0	↓	↓	↓	↓	↓
111617	0	↓	↓	↓	↓	↓

0: No trend.↑: Increasing trend.↓: Decreasing trend.

For the temporal trend behaviour of the rain events of the 41 stations during period 1 (1970–1990) (Fig. 5), it is clear that the decreasing trend prevails for the five categories: light to moderate (B: 12.69%), moderate to heavy (C₁: 16.89%), heavy (C₂: 19.65%), heavy torrential (D₁: 11.48%) and torrential (D₂: 1.17%). Category A did not show any trend (20.80%).

Figure 5. Trends in extreme rainfall categories during P1 (1970–1990)

On the other hand, during the second period (1990–2010) (Fig. 4), the spatial and temporal behaviour is totally reversed: the trends of the 41 stations are tilting towards an increase (Alpert et al. 2002, Yosef et al. 2009, Benzater et al. 2019, 2021). Temporarily and on average, 3926 rainy events (77.85%) are increasing, 1092 rainy events (21.65%) do not have a trend and only 25 points (0.50%) represent a decreasing trend.

To identify the trend of each extreme rain category for P2 (1990–2010), and from Fig. 4, 41 matrices were established. Examination of these matrices makes it possible to establish one decision matrix (Table 4). In space, the analysis of Table 4 shows a completely opposite situation from the first period. For the 41 stations, it is clear that during this period (1990–2010), the five categories (B, C₁, C₂ and D₁ and D₂) showed an increasing trend (100%, 95.12%, 97.56%, 95.12% 95.12% and 2.40%, respectively). The two ends of the categories, namely light (A) and torrential (D₂) showed no trend (58.53% and 95.12%, respectively).

Table 4. Trends of extreme rainfall categories (1990–2010)

Rainfall category	A	B	C1	C2	D1	D2
Station
110102	0	↑	↑	↑	↑	0
110201	↑	↑	↑	↑	↑	0
110203	0	↑	↑	↑	↑	0
110304	0	↑	↑	↑	↑	0
110305	0	↑	↑	↑	↑	0
110309	↑	↑	↑	↑	↑	0
110312	0	↑	↑	↑	↑	0
110314	0	↑	↑	↑	↑	0
110402	0	↑	↑	↑	↑	0
110501	0	↑	↑	↑	↑	0
110802	↑	↑	↑	↑	↑	0
111102	0	↑	↑	↑	↑	0
111103	↑	↑	↑	0	↑	0
111112	↑	↑	↑	↑	↑	0
111201	↑	↑	0	↑	↑	0
111204	0	↑	↑	↑	↑	0
111210	0	↑	↑	↑	↑	0
111217	↑	↑	↑	↑	↑	0
111401	↑	↑	↑	↑	↑	0
111405	0	↑	↑	↑	↑	0
111413	0	↑	↑	↑	↑	0
111414	↑	↑	↑	↑	↑	0
111417	↑	↑	↑	↑	↑	↑
111418	↑	↑	↑	↑	↑	0
111424	↑	↑	0	↑	0	0
111429	↑	↑	↑	↑	↑	0
111502	↑	↑	↑	↑	↑	0
111503	↑	↑	↑	↑	↑	0
111508	0	↑	↑	↑	↑	0
111509	0	↑	↑	↑	↑	0
111511	↑	↑	↑	↑	↑	0
111516	0	↑	↑	↑	↑	0
111604	0	↑	↑	↑	↑	0
111605	0	↑	↑	↑	↑	0
111606	0	↑	↑	↑	↑	0
111607	0	↑	↑	↑	↓	0
111610	↑	↑	↑	↑	↑	0
111611	0	↑	↑	↑	↑	0
111612	0	↑	↑	↑	↑	0
111616	0	↑	↑	↑	↑	0
111617	0	↑	↑	↑	↑	0

0: No trend.↑: Increasing trend.↓: Decreasing trend.

For the temporal trend behaviour of the rain events of the 41 stations during P2 (1990–2010) (Fig. 6), it is obvious that the situation was completely reversed compared to the first one. Indeed, the extreme rainy events show increasing trends in five categories: light to moderate (B: 20.78%), heavy (C₂: 20.21%), moderate to heavy (C₁: 17.85%) and heavy to torrential (D₁: 4.92%). This ascending behaviour in the middle categories is consistent with the work of Boudiaf et al. (2021) in northeast Algeria, El Alaoui El Fels et al. (2021) in western central Morocco and Caloiero et al. (2016) in southern Italy but does not fully converge with that of Bisht et al. (2018) and Chandrashekar and Shetty (2018) in India.

Figure 6. Trends in extreme rainfall categories during P2 (1990–2010)

This trend increase in the middle categories of extreme rains, during the first period, supports the use of ‘1990’ as baseline year (IPCC 2013). It corresponds to the intensification of the impacts of greenhouse gas emissions following the industrial revolution that began in 1850(Mathbout et al. 2018, Zhang et al. 2021). The two ends of the light (A) and torrential (D₂) categories did not change their trend and retained their monotonic no-trend during the two periods P1 and P2 (Figs 4 and 5).

Finally, this new configuration of the modified ITA method makes it possible to detect migration movements of rainy events from one category to another. Thus, from Figs 3 (1970–1990) and 4 (1990–2010) 41 decision matrices for each period, representing the 41 stations, were constructed to highlight possible displacements from one category to a higher or lower category. Table 5 presents a decision matrix model as an example. Thus, for all 41 stations in the Macta watershed during the period (1970–1990), migration movements from higher categories to lower categories were detected for 1716 rainy events (34.03%). In contrast, migrations to higher categories are negligible (1.39%).

Table 5. Example of categories’ migration movements (station 110102; 1970–1990)

Rainfall category	Trend	A	B	C1	C2	D1	D2
	0	13	0	0	0	0	0
A	↑	0	0	0	0	0	0
	↓	12	0	0	0	0	0
	0	0	0	0	0	0	0
B	↑	0	0	0	0	0	0
	↓	15 (12.19%)↙	12	0	0	0	0
	0	0	0	0	0	0	0
C1	↑	0	0	0	0	0	0
	↓	0	24 (19.51%)↙	1	0	0	0
	0	0	0	0	0	0	0
C2	↑	0	0	0	0	0	0
	↓	0	0	21 (17.07%)↙	8	0	0
	0	0	0	0	0	0	0
D1	↑	0	0	0	0	0	0
	↓	0	0	0	9 (7.32%)↙	6	0
	0	0	0	0	0	1	0
D2	↑	0	0	0	0	0	1
	↓	0	0	0	0	0	0

0: No trend.↑: Increasing trend.↓: Decreasing trend.

Conversely, for the second period (1990–2010), the results show that in total, 1712 rainy events (33.95%) migrated from lower categories to higher categories (Table 6): 393 rainy events (7.79%) migrated from category (A) to category (B), 446 (8.84%) from (B) to (C₁), 426 (8.45%) from (C₁) to (C₂), 379 (7.52%) from (C₂) to (D₁), and 68 (1.35%) from (D₁) to (D₂). No migration to a lower category was detected.

Table 6. Global migration movements (%) of categories (1990–2010)

Rainfall category	B	C1	C2	D1	D2
	7.79
		8.84
			8.45
				7.52
					1.35

The two main results of this study lie in the detection of increasing trends in the middle categories of rains accompanied by migration movements towards the higher categories. These results show the intense nature of the increase in extreme rains in the Macta catchment area during the period 1990–2010.

The new approach of the ITA method, described in this article, made it possible to highlight three points that were not revealed by the initial method:

i)Detection of partial trends in the six categories of extreme rainfall;

ii)Interpretation has become arithmetic instead of visual (for the classic ITA) using a critical difference of 10% (Wu and Qian 2016);

iii)Finally, the most interesting and original point is the detection of migratory movements of rainy events, which previous works did not mention at all.

Several researchers have attempted to study extreme rainfall events (Lu et al. 2021, El Alaoui El Fels et al. 2021) using the ITA method (Alifujiang et al. 2020, Güçlü 2020, Boudiaf et al. 2021) or the Mann-Kendall test (Caloiero et al. 2017, Młyński et al. 2018, Yaduvanshi et al. 2020). The shortcomings noted in the studies cited above are that they cannot identify trends by category, nor the migration of an extreme rainfall event from one category to another (higher or lower). The added value of the present work, compared to the similar work undertaken in Algeria (Boudiaf et al. 2021) and in different regions of the world (Caloiero et al. 2018, Alifujiang et al. 2020), consists in the following: (i) the introduction and identification of the trends in the extreme rainfall categories; (ii) determination of a threshold (10%) to identify a change and therefore avoid the usual visual procedure; and (iii) the most interesting and original point is the detection of migratory movements of rainy events, which was not explored in previous work at all.

5 Conclusion

Several results were produced from this study, by analysing the monthly extreme rains of the Macta watershed, using the new approach of the modified ITA method. The five rainfall categories light to moderate (B), moderate to heavy (C₁), heavy (C₂), heavy to torrential (D₁) and heavy (D₂) shifted from a decreasing trend in extreme rainy events (12.69%, 16.89%, 19.65%, 11.48% and 1.17%, respectively) during the first period (1970–1990) towards an increasing trend (20.78%, 17.85%, 20.21%, 4.92% and 0.10%, respectively) during the second period (1990–2010). The light to moderate rain category (B) is the class that showed the greatest increase (20.78%), followed by the heavy class (C₂: 20.21%) and then the moderate to heavy class (C₁: 17.85%). There was a monotony of trend in the light category (A), which did not show a clear trend during the two periods (20.80% and 16.91%). The two ends of the categories, namely light (A) and torrential (D₂), showed monotony (no trend) during the two periods (1970–1990 and 1990–2010).

Positive trends only appear for the lower and middle classes. All the stations showed this upward trend in these classes. The results obtained show the behaviour of increasing extreme rainy events in the middle categories, as well as the detection of migration movements of rainy events towards higher categories (especially from B to C₁: 8.84%). These two results show the intense nature of the increase in extreme rains in the Macta watershed during the period 1990–2010.

Acknowledgements

The authors thank the National Water Resources Agency (ANRH) for making the data available. The authors thank Prof. Zohair Chentouf (King Saud University, KSA) for his linguistic advice. We extend our gratitude to Prof. Laborde J. for his free Hydrolab software, which was used for data analysis.

Disclosure statement

No potential conflict of interest was reported by the authors.