Hydrological drought vulnerability assessment in Ethiopia using multi-criteria decision-making

Drought events are known to start slowly without being noticed and may cover vast areas through some drought years. The drought that occurred in 2008/2009 covered more than five countries (Eritrea, Djibouti, Ethiopia, Kenya, Somalia, and Burundi) in Eastern Africa; furthermore, the drought event extended to the southeastern of the continent (Masih et al. 2014). Similarly, severe drought in South Asia covered the entire region (Afghanistan, Pakistan, Nepal, India, and Sri Lanka) during the extreme drought between 2000 and 2002 (Mishra & Lilhare 2016; Chandrasekara et al. 2021). Since the occurrence of drought in a particular region is not limited to local factors, the relationship between sea surface temperature gradient and drought plays a significant role in most regions (Tierney et al. 2013). Such broader spatial coverage of drought events has been seen in other continents, affecting millions of people due to drought impact compared to other localized climate disasters. The Horn of Africa region is frequently affected by drought. The estimated number of people affected during different years was 13, 16, 12, and 10 million during the drought years 2002/2003, 2008/2009, 2010/2011, and 2015/2016, respectively (Tierney et al. 2013; Venton 2016). In Ethiopia, more than 85% of electric production relies on hydropower, so frequent power disruption due to hydrological drought has been seen recently and caused a significant impact on the country's GDP.

Investigating natural disasters such as drought requires extensive hydrological and meteorological data. In many regions, particularly in East Africa, constraints of observed data became an obstacle to understanding the spatial extent of drought events. Satellite and remote sensing data could form an alternative solution to fill the data gap. Using geographical information systems (GIS) and remote sensing techniques has transformed how research is conducted in various fields, including hydrology and climatology, and has become increasingly important for society. These techniques are versatile, allowing for detection, monitoring, collecting, and planning for natural disasters, and are frequently used in research (Daruati et al. 2013; Kerebih & Keshari 2017; Sun et al. 2017; Mazzoleni et al. 2018). Remote sensing provides a significant advantage in collecting continuous time and spatially distributed data about physiography, climate, and other factors. At the same time, GIS application tools play substantial roles in data collection, storage, manipulation, processing, and visualizing georeferenced information. Normalized different vegetation index (NDVI), Global Land Data Assimilation System (GLDAS), and Moderate Resolution Imaging Spectroradiometer (MODIS) are used to solve climate data constraints in many studies (Daruati et al. 2013; Awange et al. 2016; Choubin et al. 2019; Liou & Mulualem 2019). Terrestrial water storage (TWS) data from GRACE gained more attention among researchers for detecting hydrological drought and played a significant role in understanding groundwater depletion during prolonged drought events (Long et al. 2014; Sun et al. 2017; Hasan et al. 2019; Khorrami & Gunduz 2021).

In hydrological drought assessment, climatological factors and catchment characteristics play a significant role. Many influencing factors determine the hydrological drought propagation time, duration, and severity, so considering those influencing factors will provide detailed information about particular drought events. However, the most successful and commonly known drought analysis methods (standardized precipitation index (SPI), standardized precipitation evapotranspiration index (SPEI), palmer drought severity index (PDSI), and standardized runoff index (SRI)) consider only limited drought-influencing factors to identify drought events. Multiple hydrology research disciplines use multi-criteria decision-making techniques to investigate vulnerability assessment using several influencing factors (Hurgesa et al. 2016; Alamne et al. 2022; Melese & Belay 2022). Analytical hierarchy process (AHP) is a commonly used technique in most drought vulnerability studies, utilizing catchment, meteorological, and hydrological variables (Pandey et al. 2012; Jain et al. 2015; Palchaudhuri & Biswas 2016; Saini et al. 2022). AHP can be modified to suit the researcher's objectives and is applicable in various hydrological and other studies such as agricultural drought-vulnerable area mapping, flood risk area mapping, groundwater potential zoning, and pollution zone mapping (Winkler et al. 2017 ). This study uses AHP to locate hydrological drought-vulnerable regions, which requires incorporating multiple influencing factors, such as physiographic and hydrological factors.

This study uses a multi-criteria decision-making technique incorporating multiple influencing factors, such as physiographic and hydrological factors developed using remote sensing data, to locate hydrological drought-vulnerable regions. The study overcomes the main limitation of adequate data for drought analysis in the country, especially in southeast Ethiopia basins, which are frequently affected by drought, for future drought mitigation and adaptation measures.

The annual rainfall ranges from less than 500 mm in arid regions to more than 2,500 mm in the southwest humid region. The country has three seasons: (a) Kiremt season from June to September is the primary rainy season in most parts of the country associated with the movement of intertropical convergence zone (ITCZ) (Zewdu et al. 2008), (b) Bega season from October to January is the dry season; however, some southern Ethiopia areas might record slight rainfall, and (c) Belg season from February to May is the second rainy season, but this period is the primary rainfall season for the southern part of the country (Gissila et al. 2004). Furthermore, the country has a homogenous rainfall season classified into five regions (Beyene et al. 2022). The temperature ranges from ∼50 °C at the Dallol depression to freezing in the Mount Ras-Dashen Plateau (MoWE 2012). The country's physiography influences the 12 drainage systems, 8 of which are River basins, 1 is a Lake basin, and the remaining 3 are dry basins with no or insignificant outflow (Awulachew et al. 2007). All rivers originate in the central highlands except Aysha and Ogaden, which are located in the lowlands. Ethiopia contributes to three major drainage systems: the Mediterranean Sea drainage system (Abbay, Baro-Akobo, Mereb, and Tekeze), the Great East African Rift Valley drainage system (Omo-Ghibe, Awash, Rift Valley lakes, Denakil, and Aysha), and the Indian Ocean drainage system (Genale-Dawa, Wabi-Shebelle, and Ogaden) (Figure 1). The country's annual runoff is estimated at 122 BCM (MoWR 1999). Ethiopia's groundwater resources and distribution vary depending on the geologic, structural, and climatic setups. The potential groundwater of the country has not been fully assessed, so there is no agreed figure yet; the values vary from 2.6 to hundreds of BCM (Kebede et al. 2005). The near-surface geological pattern that mainly governs the hydrogeological characteristics of the country constitutes the oldest basement rocks (18%), Paleozoic and Mesozoic sedimentary rocks (25%), tertiary volcanic (40%), and quaternary sediments and volcanic (17%) (Alemayehu et al. 2016).

The methodology for hydrological drought vulnerability assessment in Ethiopia using multi-criteria decision-making involves several key steps. Initially, data collection is crucial, including time series rainfall data to understand precipitation patterns, TWS data to evaluate changes in water availability, and thematic maps providing spatial information on land use and land cover (LULC), population density, climate zones, elevation, soil texture, slope, and drainage density. These factors are critical in influencing hydrological drought. The rainfall anomaly index (RAI) is calculated to assess rainfall variability and identify deviations from normal patterns, which is essential for understanding drought onset and severity. The water storage deficit index (WSDI) is used to evaluate deficits in TWS, a key indicator of hydrological drought. The analytical hierarchical process (AHP) is employed to prioritize the factors influencing hydrological drought through pairwise comparisons, assigning weightage values that reflect their relative importance. The impact of various physiographic and hydrological factors on drought vulnerability is then analyzed, examining how changes in LULC, population density, climate zones, elevation, soil texture, slope, and drainage density affect susceptibility to hydrological drought. Finally, the assessment involves using the RAI and WSDI to identify drought events and assess their severity, integrating these indices with the weighted factors to comprehensively analyze hydrological drought vulnerability in Ethiopia. This helps identify areas at higher risk and informs drought management and mitigation strategies.

This study used the Climate Hazards Group Infrared Precipitation Stations (CHIRPS) dataset developed using quasi-global geostationary thermal infrared satellite data and ground meteorological station precipitation data. USGS developed the dataset in collaboration with the Climate Hazard Group at 5 km spatial resolution from 1981 to the present at a daily and monthly timescale. CHIRPS dataset performed excellently in the investigation of climate hazards, such as precipitation extremes and drought in Ethiopia (Bitew & Gebremichael 2011; Gebrechorkos et al. 2018; Bayissa et al. 2019); so we used monthly timescale CHIRPS data to estimate rainfall departure in this study.

The digital elevation model (DEM) represents topographic features of the earth's surface without considering other features, such as trees and buildings. This study uses the Shuttle Radar Topography Mission (SRTM) DEM obtained from the USGS Earth Explorer website https://earthexplorer.usgs.gov/ with a 90-m resolution. After processing using the stream order function, the DEM generates a slope map and drainage density data.

Soil texture data is obtained from the Africa Soil Information Service (AfSIS) website https://www.isric.org/projects/soil-property-map. The soil map was generated using sample data collected from ground surveys; additional auxiliary data used remote sensing information, LULC, and other data; details of the process of collection data and methods used to compile the dataset explained by Leenaars et al. (2014).

LULC and population density were downloaded from the FAO-geospatial website. The LULC data were derived from Landsat data using a supervised classification technique with the help of additional data from the Ethiopia map authority for the year 2013. Population density map is a raster layer with less than 5 km resolution developed for 2015 using FAO and Center for International Earth Science Information Network (CIESIN) method using 2005 data as reference https://www.fao.org/3/a0310e/a0310e00.htm.

Global aridity index datasets are a geospatial raster dataset developed by Trabucco & Zomer (2019) with the support of the Consortium for Spatial Information (CGIAR-CSI), freely available at the website https://cgiarcsi.community/. The dataset was estimated at a monthly timescale using mean annual precipitation and annual reference evapotranspiration using the FAO Penman–Monteith equation.

Gravity Recovery and Climate Experiment (GRACE) satellites were launched with the cooperation of NASA and Deutsches Zentrum für Luft- und Raumfahrt (DLR) (German Aerospace Center) in 2002 to measure TWS at 0.5° grid cell resolution. This study uses the improved GRACE product RL05 mascon for the analysis. Two RL05 mascon products developed by Central for Space Research (CSR-M) and Jet Propulsion Laboratory (JPR-M) monthly time series from 2002 to 2017 are downloaded from the GRACE website https://grace.jpl.nasa.gov/mission/grace/; the missing monthly data in time series were filled by linear interpolation.

The AHP uses a systematic multi-criteria decision-making method by limiting a pairwise comparison variable to minimize error. The process compares two criteria using a matrix and assigns a value based on the importance of the objective. The higher the value of the score, the better the performance of the option concerning the considered criterion (Saaty & Vargas 2000). For each criterion, the eigenvector is estimated, and consistency between assigned weight values during evaluations when building each pairwise comparison matrices involved in the process is checked using the consistency index (CI).

The weightage value is assigned to the categories and maps based on Satty's AHP to show the importance of thematic maps on hydrological drought (Table 1). It determines the influence of each factor on the hydrological drought while integrating thematic maps.

The first step is comparing each sub-criteria within a particular thematic map based on their influence on hydrological drought by pairwise comparison to prevent making a mistake while assigning values; e.g., LULC has seven sub-criteria (agricultural land, settlement, water body, bare land, forest, wetland, and grassland); then, to minimize error during directly assigning value, instead, we compare two sub-criteria such as between grassland and agricultural land, grassland, and water body, and similarly, it continues to all. Since the technique allows for comparing only two features at a time, the error will be minimized. The second step follows a similar procedure by pairwise comparison between criteria (thematic map), e.g., between rainfall departure and LULC, rainfall departure, and soil map (Table 2). Errors through evaluation during comparison are continuously checked by using the CI and reevaluated by comparing values until the acceptable CI value is reached, which is between 0 and 0.1 or less than 10%. Based on the assigned criteria, each pixel is represented by categories on the map. The country has over 35,000 pixels (grid cell), which resized all maps to match CHRIPS rainfall data, with 0.05° by 0.05° grid cells. So, all nine maps match grid to grid to perform AHP based on assigned criteria.

The impact of various physiographic and hydrological factors on drought vulnerability is analyzed, examining how changes in LULC, population density, climate zones, elevation, soil texture, slope, and drainage density affect susceptibility to hydrological drought.

In this study, population density is considered one factor contributing to the worsening of hydrological drought. The higher population density increases water demand; during drought events, the measures used to cope with water shortage most of the time aggravate the situation, such as exploiting groundwater and discharging more water from the reservoir (Figure 2(b)). The population density map is classified into five categories; the population density map shows the majority of the population settlement over the country's highlands. The central part, southern and eastern highlands areas, has the highest population density, with a value between 200 and 5,000 persons per km². The majority of the country falls in the category of less populated, with a value of fewer than 200 persons per km², including vast southeast, northeast, and western lowlands.

The underlying climate characteristics of an area play a significant role in identifying drought-vulnerable areas. A region with arid climate conditions is already under water stress under normal conditions, so falling a single rainfall season will devastate the region. In East Africa, mainly Ethiopia and Somalia, the most frequently drought-affected regions are semi-arid and arid climate conditions (Masih et al. 2014). In terms of hydrological drought, the arid climate region experiences high evaporation, which makes the region vulnerable to drought. The aridity index (climate zone) is classified into five categories (Figure 2(c)). The lowest annual rainfall region of the northeast and southeast parts of the country is categorized as an arid and semi-arid climate zone. The southwest region has the highest rainfall in the country and is classified as a humid and semi-humid climate region. The dry, semi-humid climate region is located in the country's west, northwest, central, and southern parts.

The variability of topography is one of the factors considered to contribute to hydrological drought. The high and mountainous areas are considered high slopes, which are considered highly vulnerable to hydrological drought compared to low and plane elevation areas (Kalura et al. 2021). The topographic feature of the country (Figure 2(d)), most of the highlands with more than 2,300 m elevations are located at the edge of the Great Rift Valley that extends from central to northern Ethiopia (Abay and Tekeze basins) and in the southeast (Genale-Dawa and Wabi-Shebele basins). The mid-altitude areas with 1,252–2,391 m extended in most of the country. The low elevation areas with less than 1,252 m are located in vast southeast and northeast parts of the country; the northwest and southwest parts are categorized as too low elevation areas.

Soil texture is one factor contributing to hydrological drought since soil plays a significant role in a hydrologic cycle by reducing or increasing infiltration. However, hydrological drought occurs slowly and persists for longer; soil water-holding capacity is more influential than infiltration rate. Clay soil type has less infiltration rate but has the highest water-holding capacity compared to sandy soil texture. The soil texture with the highest water-holding capacity, such as clay, silty clay, and clay loam, will retain water for longer than others during prolonged drought. Ethiopia's main soil texture is classified into six groups (Figure 2(e)). The country's western, northwest, southwest, and southeast highlands have clay and clay loam texture. Sandy–clay–loam soil type is dominated over the northeast, east, and vast areas of the southeast part of the country.

The slope of the area contributes significantly to vulnerability areas to hydrological drought by increasing quick runoff in the basin, causing decreasing soil water-holding capacity. Mountainous regions that have high slopes become more vulnerable than plane areas. The map in this study is classified into seven categories (Figure 2(f)); most of the country experiences the highest slope percentage with a value of more than 10%, dominantly over Tekeze and the upper Abay basins in the northern part of the country. The lowest slope is located in the broad areas of the northeast (Awash and Danakil basins), southeast (Wabi-Shebele and Ogaden basins), and southwest (Baro-Akobo basin).

The drainage density of an area is essential for identifying hydrological drought-vulnerable areas. The high drainage density shows that the number of river networks is greater over the region, which could interpret the community traveling less distance to get water points. The sparse river network will have less drainage density and is considered vulnerable to hydrological drought. The drainage density has seven categories (Figure 2(g)); the highest drainage density area is located in the southwest basin (Baro-Akobo), the upper Abay basin, and the Tekeze basin in the northern part of the country. The low drainage density area is the dry basin with a value of less than 5 km/km², Danakil basin (northeast), Ayesha (east), Ogaden basin (southeast), and limited parts of the lower Genale-Dawa basin.

Rainfall departure and WSDI are used to analyze drought events in the study area. Rainfall departure assesses the deficit in rainfall during drought years, while WSDI evaluates the TWS deficit. These indices help identify areas and periods of significant water stress.

For the 2015 drought year, the standardized rainfall anomalies are shown in Figure 3(a). The central, eastern, and southern parts of the country experienced a rainfall deficit during Jan–Feb–Mar (JFM), FMA, and MAM, with a value range of −1.12 to −1.81. Similarly, a similar rainfall deficit was observed over the northern part of the country during MJJ, during JAS, and ASO over the central part of the countries, showing the highest rainfall with a value of −2.31. The wettest months during the 2015 drought year over broad areas of southern basins were JJA, and at the end of the drought year, DJF, most parts of the countries show drought recovery as shown in Figure 3(a).

The two drought years, 2009 and 2015, show different rainfall deficit scenarios in the country. The 2009 drought year rainfall deficit was more decentralized across another part of the country; however, during the 2015 drought year, it was more localized dominantly over the central and eastern parts of the country.

During the drought year 2015, the WSDI estimation showed wet conditions in most parts of the country, particularly in the South and Southeastern basins (Wabi-Shebele and Genale-Dawa basins) (Figure 4(b)). Water deficit starts during the primary season, JJA, over the northeastern basins (Tekeze and Denakle basins), and in the following months, water stress expanded to the southwest basins (Baro-Akobo and lower Abay basins) with the highest index value of −1.8 during SON.

The hydrological drought vulnerability result shows that the low and no vulnerable areas over the southwest (Baro-Akobo basin) part of the country shrink and worsen into the medium-level drought vulnerability category during May–Jun–Jul (MJJ), JJA, and JAS (Figure 5(e)–5(g)). This change in drought vulnerability occurred during the primary rainy season (Kiremt season), which points to a cumulative effect of the rainfall deficit in the previous primary season followed by the long dry season. On the contrary, the previous extreme and very high vulnerable category areas of the southeast and southern part of the country improved into high to medium vulnerable categories (Figure 5(a)–5(f)).

The northern (Tekeze and Mereb basins), the lower Abay basin, and central part of the country experienced a hydrological drought of low to no vulnerability categories during MJJ and JAS (Figure 5(e) and 5(g)). However, the extreme and very highly vulnerable areas were reduced due to slight rainfall during the primary rainfall season (June to September) in most parts of the country. Still, most areas were under the highly vulnerable category.

The following months' hydrological drought vulnerability map (Figure 5(i)–5(l)) shows that the north basins (Tekeze and Abay) experienced high vulnerability during SON and OND and northeast (Danakil and lower Awash basins) extreme vulnerability categories during DJF; similarly, the southeast part shows very high vulnerability to hydrological drought (Figure 5(l)).

During the months of SON and OND, the northern part of the country (Tekeze and Abay basins) experienced high vulnerability to hydrological drought. The country's northeast and southeast are among the areas with the lowest annual rainfall and are frequently affected by drought. In this study, Denakil and the lower Awash basins show the extreme exposure to hydrological drought during DJF; similarly, the southeast (Wabi-Shebele and Ogaden basins) shows very high vulnerability to hydrological drought (Figure 5(l)).

The low and not vulnerable areas are limited to the southwest basin dividing the highlands of the Abay, Baro-Akobo, and Omo-Gibe basins during SON and OND. Then, it expanded to the southern highlands (Rift Valley lake and Genale-Dawa basins) in the following months. This indicates that the rainfall during the second rainy season (September to November) over the area helps recover from the hydrological drought. Following the second rainy season during OND and NDJ, the southern highlands (Rift Valley and Genale-Dawa basins) show recovery from the hydrological drought vulnerability into low and no categories.

During the 2015/2016 drought year, the extreme and very high hydrological drought-vulnerable areas concentrated in the northeastern basins, mainly Denakel and the lower Awash basins, with the highest area coverage of 16 × 10⁴ km² during FMA (Table 3). The extreme and very highly vulnerable areas during the 2015/2016 drought year took 1.1 and 7.5% of the country, which is lower than the 2008/2009 drought year.

The high and medium vulnerable categories cover over 70% of the country (Figure 6(b)), particularly during OND and NDJ covers a large part of the country (Figure 6(j)–6(l)). The high vulnerable category was observed at the highest area coverage of 58 × 10⁴ km² during FMA over northeast (Denakel and upper Tekeze basins), central (Awash basin), and vast areas of southeast (Wabi-Shebele, Ogaden, and Genale-Dawa basins). Similarly, vast areas of the country experienced medium hydrological drought vulnerability during most of the months, particularly during MAM and NDJ, observed area coverage of over 56 × 10⁴ and 58 × 10⁴ km², respectively.

The low and not vulnerable categories are limited to western and southwestern basins; this category covers 15 and 1.6% of the country during the 2015/2016 drought year, higher than the 2008/2009 drought year (Figure 7). During AMJ (6 d), vast areas of western (Abay basin), southwest (Baro-Akobo), and south (Omo-Gibe and Rift Valley basins) experience low to no vulnerability to hydrological drought with the highest area coverage of 31 × 10⁴ and 5 × 10⁴ km² (Table 3). Similarly, during the primary rainy season (JJA), the western part of the country experiences low hydrological drought vulnerability with significant area coverage (Figure 6).

The two major drought years in the country, 2008/2009 and 2015/2016, are recognized as among the severe and broader area coverage. In this study, Figure 7 and Table 3 show the area coverage of different hydrological drought vulnerability categories during those two drought events. The result revealed that during the 2009 drought year, the extreme vulnerable areas coverage reached 5 × 10⁴ km² in total, whereas during 2015, the same category covered 15 × 10⁴ km². Similarly, the same high variation in area coverage was observed in very high vulnerable categories, which had 237 × 10⁴ km² in 2009 and 87 × 10⁴ km² in 2015. The 2015 drought was less severe than the 2009 drought year; it was observed in low vulnerable categories, showing high area coverage during the 2015 drought year with the value of 166 × 10⁴ and 97 × 10⁴ km² during the 2009 drought year.

The area coverage in percentage shown in Figure 7 shows the variation in the spatial extent of the two droughts. During the 2009 drought year, the extreme to high hydrological drought-vulnerable areas covered more than 65% of the country. In contrast, during the 2015 drought year, only 36% of the country was under the same category. The low and no vulnerable area coverage comprised 8.4 and 16.6% of the country during the 2009 and 2015 drought years. In general, our study results coincide with other studies focused on meteorological drought analysis estimates of drought-affected people during those drought years; in their study year, the 2009 drought was the most severe compared to 2015, affecting more than 16 million people in East Africa, including Ethiopia (Vicente-serrano et al. 2012; Awange et al. 2016; Gebremeskel et al. 2019).

Hydrological drought studies in Ethiopia are limited due to the limitation of observed data. However, various types of remote sensing data can play a significant role in data-deficient regions. The present study uses remote sensing data to investigate the hydrological drought vulnerability in Ethiopia during the major drought years 2009 and 2015. The study result shows that the extreme to high hydrological drought-vulnerable areas are extended from the northeast to the southeast part of the country, considerably the lower Awash, Wabi-Shebele, and Genale-Dawa basins and included all three dry basins of the country during the months JFM, FMA, MAM, and AMJ during 2009. The northern part of the country (upper Abay and Tekeze basins) experiences high to very high hydrological drought vulnerability during most of the months; however, during the primary rainfall season (June to September), the category improves to low and medium vulnerability. The persistent region falls in the no to low vulnerable areas category in the southwest part of the country, mainly Baro-Akobo and some parts of the Abay and Omo-Gibe basins in most of the months except during the primary rainy season in JJA and JAS. Most of the country is generally susceptible to hydrological drought during drought events in most months; however, the country's northeast and southeast parts are among the worst regions. The central basin (upper Awash, Omo-Gibe, and Rift Valley lake basins) hydrological drought vulnerability varies between low, medium, and high vulnerability categories. In comparing drought years 2008/2009 and 2015/2016, the study results show similarities in highly vulnerable areas. In terms of area coverage, the country's vast regions experienced the extreme to highly vulnerable areas during the 2008/2009 drought year, more than the 2015/2016 drought year. The hydrological drought vulnerability study shows that the capability of remote sensing data plays a significant role in investigating wider areas with data constraint areas.

A.A. acknowledges the joint funding support from the University Grant Commission (UGC) and DAAD under the Indo-German Partnership in Higher Education (IGP) framework at the IIT Roorkee.

T.K.B.: Data curation, Formal analysis, Investigation, Methodology, Conceptualization Resources, Software, Writing – original draft. A.A.: Conceptualization, Investigation, Methodology, Project administration, Supervision, Writing – original draft, Writing – review & editing. M.K.J.: Conceptualization, Project administration, Supervision, Writing – review & editing. B.K.Y.: Project administration, Supervision.

All relevant data are available from an online repository or repositories: Shuttle Radar Topography Mission (SRTM) digital elevation model: https://earthexplorer.usgs.gov/ Soil texture data is obtained from the Africa Soil Information Service (AfSIS) website at https://www.isric.org/projects/soil-property-map Gravity Recovery and Climate Experiment (GRACE) https://grace.jpl.nasa.gov/mission/grace/ Land use land cover (LULC), and population density https://www.fao.org/3/a0310e/a0310e00.html.

The authors declare there is no conflict.