The Danube River water discharge according to satellite optical data of the Landsat series

Толық мәтін

Introduction

The Black Sea occupies a unique geographical position due to the system of the Bosphorus, Dardanelles and Gibraltar Straits, making it the most isolated water body in the Atlantic Ocean basin. Under such conditions, the water mass coming from the estuaries has a particularly pronounced effect on the dynamics as well as the optical and biochemical characteristics of waters at the mouths of marine areas. For the Black Sea, the Danube River runoff is a decisive factor in physico-chemical processes both in the north-western shelf area and in the whole sea in general [1, 2]. The contribution of the Danube to long-term and seasonal changes in sea level is also significant [3]. Therefore, quantification of the volume of water flowing from the Danube into the Black Sea is highly demanded in different fields of scientific knowledge.

With the development of the Earth surface remote sensing from artificial satellites, new opportunities arise for monitoring the areas of the river mouth interface with a lake or sea ¹, ².

The problem of studying river discharge from satellite data in the optical spectral range is not new. For example, this problem is addressed in [4–6]. In these works, a two-band approach [5] or an automatic classification system (ISODATA) [4] are used to separate the surface occupied by water and land. Application of the obtained results with synchronous measurements of river discharge at gauging stations made it possible to construct a regression relationship between these parameters, which can be used for monitoring the river discharge based on satellite measurements only.

Altimetric methods [7–9] and estimation with high-resolution data from the Sentinel-2 satellite [10–13] are also known. However, it should be noted that the above methods, despite their advantages, are difficult to use by domestic researchers, as access to satellite products is currently limited. The use of these methods requires consideration of many factors (vegetation cover, water chromaticity, atmosphere aerosol component, spectral indices based on several bands, etc.), which complicates the estimation of river discharge.

The paper aims to find the correlation relationship between the land–water area ratio and the total water discharge of the Danube River from observations of a fixed area of the river delta using medium resolution second level satellite data (i.e. after atmospheric correction) in the near-infrared spectral range, using one band. The article uses materials of the report on the XII All-Russian Conference with international participation “Current Problems in Optics of Natural Waters (ONW’2023)” [14].

Materials and methods

Reanalysis data obtained from the SMHI Hypeweb website ³ were used as input data of the discharge at the Danube River mouth. The source provides information on daily water discharge (sector 9600704) from 1 January 1981 to 31 December 2010 (Fig. 1).

 

Fig. 1. Water discharge at the Danube River mouth (sector 9600704) according to reanalysis data from the SMHI Hypeweb website

 

Landsat series satellite products (a joint project of the US Geological Survey and NASA) were obtained from the Landsat Missions website ⁴. For the study, cloud-free images of the second level, i. e. after atmospheric correction, were selected from the entire available image array in band 5, wavelength range 1.55–1.75 μm with a spatial resolution of 30 m. This satellite product characterises the reflection coefficient of natural sunlight (in r. u.) of the study area of the Earth surface, taking into account atmospheric influence and observation geometry. For the water surface, the reflection coefficient values themselves and its variability associated with the observation geometry are minimal, as when selecting scenes, we excluded data with sea surface glare. The choice of band was stipulated by its lower sensitivity to errors associated with aerosol in the atmosphere and high content of mineral suspension in river waters, which determined a better separation of land and water surface.

 

A total of 132 images were selected for 1984–2010:

January	3	July	22
February	5	August	19
March	8	September	11
April	9	October	11
May	14	November	5
June	18	December	7

 

As would be anticipated, the largest number of suitable scenes is observed in the warm period of the year, a phenomenon primarily attributable to the frequency of cloud coverage throughout the year. The selected images are distributed uniformly over the years in the time interval under consideration, with an average of five months of the year being covered.

The study area (fixed delta area) coordinates are 44.9–45.4°N and 29.55–29.60°E (Fig. 2, a). In addition, a control area of the mouth seashore with coordinates 44.9–45.4°N and 29.80–29.85°E, located close to the study area, was selected (Fig. 2, b).

 

Fig. 2. Study areas: a – the fixed section of the delta; b – the control area of the mouth seashore (adopted from: https://earthexplorer.usgs.gov/)

 

For Band 5, histograms (Fig. 3) were plotted for the two selected areas (Fig. 2). The control area of the mouth seashore (Fig. 3, b) exhibits variability in signal amplitude from the water surface, ranging from 7000 to 8000 r. u. Conversely, the entire range of variability for the fixed delta area (Fig. 3, a) extends from 7000 to 26,000 r. u. Fig. 3 demonstrates the obvious fact that the signal from the water surface (Fig. 2, b) is significantly weaker than that from land (Fig. 2, a) for the near-infrared range.

 

Fig. 3. An example of count in band 5 (1.55–1.75 µm) signal histograms for the fixed delta area (a) and the control area of the mouth seashore (b) for 5 September 2009

 

Thus, the share of water-occupied surface at the fixed delta area in Fig. 2, a (weight water) was found as the ratio of the number of pixels in the histogram from the range of 7000–8000 r. u. to all pixels in the area. The relationship between the discharge of the Danube River and the weight water was determined by the corresponding date of the survey, i. e. the same day. Since the cross-section of the channel (effluents) varies with depth, there must be a relationship between the width of the channel (effluents) and the water discharge. At the same time, the width of the channel (effluents) is obviously related to the area covered by water observed on the satellite scene.

Results and discussion

Fig. 4 shows the result of the relationship between the proportion of pixels (weight water) occupied by water at a fixed delta site and the Danube River discharge for 1984–2010. The correlation coefficient is 0.78 and the total number of points is 132.

The choice of individual effluents in the Danube River delta as a fixed delta area has little effect on the nature of the obtained relationship (Fig. 4). A similar observation can be made regarding the increase in the fixed area within the delta.

 

Fig. 4. Relationship between the proportion of pixels (weight water) occupied by water for the fixed delta area and the Danube River discharge for 1984–2010: the dots denote separate scenes and the line is the general regression relationship: y = 7.78∙10^–4∙x ^0.09 – 5.98∙10^–4

 

The nature of the obtained functional relationship can be qualitatively explained within the framework of a simple hypothesis, for which it is sufficient to consider two trivial cases of river channel cross-sections: rectangular and triangular. In the first case, the channel width is fixed; hence, a change in discharge will not affect the increase in channel width or surface area occupied by water, i.e. it is a period of low discharge. In the second case, the relationship will be a quadratic function of channel width, and all other variants with less steep channel cross-sections will approach the relationship obtained.

The seasonal variability analysis shows that weight water over 0.5 corresponds to the months from March to May, whereas the minimum values of weight water under 0.3 correspond to July–September. All this is consistent with the period of intensity of precipitation and snowmelt in the Danube River water intake area ⁵.

Conclusions

To solve the problem of determining the Danube River discharge using Landsat series satellite products, a simple one-band method was proposed, which is characterised by its accessibility to a wide range of users. The possibility of dividing the river delta area into land- and water-occupied zones based on their signal in the near-infrared spectral range is shown. It was found that the water surface corresponded to the range of 7000–8000 r. u. and the land to 7000–26,000 r. u.

By calculating the ratio of the number of pixels corresponding to water-occupied areas to all pixels of the selected delta area and relating this share to the river discharge from the hydrological model reanalysis data for the same date, we obtained regression relationship y = 7.78∙10⁻⁴∙x^0.09 – 5.98∙10⁻⁴. The above relationship can be applied to calculate the inflow of the Danube river water into the Black Sea. It was found that water–land pixel ratio exceeding 0.5 was typical for spring months and less than 0.3 corresponded to summer – early autumn, which coincides with the period of precipitation intensity and snowmelt in the Danube River basin.

 

¹ Scott, J.W., Moore, L., Harris, W.M. and Reed, M.D., 2003. Using the Landsat Enhanced Thematic Mapper Tasseled Cap Transformation to Extract Shoreline. U.S. Geological Survey Open File Report OF 03-272. 14 p. https://doi.org/10.3133/ofr2003272

² NASA. The Thematic Mapper. 2025. [online] Available at: https://landsat.gsfc.nasa.gov/thematic-mapper/ [Accessed: 11 February 2025].

³ SMHI. Europe Time Series. 2025. [online] Available at: https://hypeweb.smhi.se/explore-water/historical-data/europe-time-series/ [Accessed: 11 February 2025].

⁴ U.S. Geological Survey. Landsat Missions. 2025. [online] Available at: https://www.usgs.gov/landsat-missions [Accessed: 11 February 2025].

⁵ Ivanov, V.A. and Minkovskaya, R.Ya., 2008. [Sea Estuaries of Rivers of Ukraine and Estuarine Processes]. Sevastopol: ECOSI-Gidrofizika, 448 p. (in Russian).

Авторлар туралы

Vyacheslav Suslin

Marine Hydrophysical Institute of RAS

Хат алмасуға жауапты Автор.
Email: slava.suslin@mhi-ras.ru
ORCID iD: 0000-0002-8627-7603
SPIN-код: 1681-7926
Scopus Author ID: 6603566261
ResearcherId: B-4994-2017

Head of Department of the Oceanic Processes Dynamics, Leading Research Associate, PhD (Phys.-Math.)

Ресей, Sevastopol

Stanislav Sholar

Marine Hydrophysical Institute of RAS

Email: sa.sholar@mail.ru
ORCID iD: 0000-0002-7242-3403
SPIN-код: 4220-6994
Scopus Author ID: 57189886286
ResearcherId: GSD-9744-2022

Research Associate, PhD (Tech.)

Ресей, Sevastopol

Evgeny Podgibailov

Marine Hydrophysical Institute of RAS

Email: e.podgibailov@yandex.ru
ORCID iD: 0009-0002-2570-1367
SPIN-код: 4659-9259
Scopus Author ID: 58687010100
ResearcherId: KHZ-5622-2024

Leading Engineer

Ресей, Sevastopol

Oleg Martynov

Marine Hydrophysical Institute of RAS

Email: oleg.martynov.49@mail.ru
Scopus Author ID: 57201603369
ResearcherId: 9669-6935

Senior Research Associate

Ресей, Sevastopol

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