\n
\n<\/li>\n
\n
\n<\/li>\n
The\u00a0following text presents three case studies that demonstrate different approaches to the\u00a0treatment of\u00a0confluence areas. These involve selected reaches of\u00a0watercourses with significant flood risk, delineated within\u00a0the\u00a03rd\u00a0planning cycle in\u00a0accordance with the\u00a0requirements of\u00a0the\u00a0Floods Directive:<\/p>\n
- \n
- DYJ 09 Svitava, K\u0159et\u00ednka, T\u0159eb\u011bt\u00ednka, Kladorubka,<\/li>\n
- MOV 10 Valov\u00e1, Hlou\u010dela, Rom\u017ee, \u010cesk\u00fd potok,<\/li>\n
- MOV 01 Morava, Ol\u0161ava, Dlouh\u00e1 \u0159eka, Okluky.<\/li>\n<\/ul>\n
The\u00a0hydrodynamic calculation was carried out using a\u00a02D shallow-water flow model\u00a0[13, 14]. The\u00a0simulation results describe steady-state conditions of\u00a0depth-averaged flow velocities and water depths for individual flood scenarios with an average return period of\u00a0N years. For comparison of\u00a0the\u00a0calculation results, historical flood hazard data prepared within\u00a0previous planning cycles\u00a0[5] or as part of\u00a0studies of\u00a0runoff conditions and floodplains\u00a0[8\u201312] were used. The\u00a0case studies focus on issues related to confluence areas from the\u00a0perspective of\u00a0the\u00a0availability of\u00a0hydrological data (DYJ\u00a009, MOV 10) and the\u00a0possibilities for merging flood hazard data\u00a0[5] derived using different computational approaches or prepared by different contractors (MOV 01).<\/p>\n
DYJ 09 Svitava, K\u0159et\u00ednka, T\u0159eb\u011bt\u00ednka, Kladorubka<\/h3>\n
The\u00a0case study of\u00a0reach DYJ 09 focuses on the\u00a0procedure for determining upstream boundary condition (UBC) values in\u00a0the\u00a0given confluence area. The\u00a0conceptual model is shown in\u00a0Fig.\u00a01<\/em>, including the\u00a0locations of\u00a0upstream (UBC) and downstream (DBC) boundary conditions. At the\u00a0UBC, the\u00a0discharge Q(t) and the\u00a0energy line slope\u00a0IE are defined. At the\u00a0DBC boundary, a\u00a0rating curve h(Q, t) is specified. The\u00a0confluence model requires the\u00a0definition of\u00a0UBCs for individual flood scenarios on the\u00a0delineated reaches as the\u00a0corresponding value of\u00a0the\u00a0peak discharge QN on the\u00a0selected watercourse and discharge contributions from related tributaries in\u00a0the\u00a0area\u00a0[4].<\/p>\n
![\"\"](\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\")
<\/a>\nFig.\u00a01. Conceptual model DYJ 09<\/h6>\n
The\u00a0procedure for determining all UBCs is documented for the\u00a0loading scenario from the\u00a0Svitava river at discharge QN. The\u00a0hydrological profile closest to the\u00a0downstream boundary condition (DBC) on the\u00a0Svitava is Svitava\u00a0\u2013 below Sem\u00ed\u010d (A) (Fig.\u00a02<\/em>). Similarly, the\u00a0closest profile upstream of\u00a0the\u00a0confluence is Svitava\u00a0\u2013 above Sem\u00ed\u010d (C). The\u00a0discharge contribution from the\u00a0UBC at Sem\u00ed\u010d can be derived according to\u00a0[4] as follows:<\/p>\n
<\/a>\u00a0(1)<\/p>\nwhere:<\/p>\n
QN(A)\u00a0\u00a0\u00a0\u00a0\u00a0 is\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 a\u00a0value of\u00a0the\u00a0N<\/em>-year peak discharge at the\u00a0relevant profile A\u00a0(Fig.\u00a02<\/em>).<\/p>\n
<\/a>Fig.\u00a02. Hydrological data at\u00a0the\u00a0confluence of\u00a0Svitava\u00a0\u2013 Sem\u00ed\u010d, K\u0159et\u00ednka, Kladorubka, T\u0159eb\u011bt\u00ednka<\/h6>\nSvitava\u00a0\u2013 Rozhran\u00ed is the\u00a0nearest profile in\u00a0the\u00a0upstream reach of\u00a0the\u00a0model above the\u00a0confluence (Fig.\u00a02<\/em>). According to\u00a0[4], the\u00a0discharge contributions from the\u00a0individual UBCs within\u00a0the\u00a0reach (Fig.\u00a02<\/em>) should satisfy the\u00a0following condition:<\/p>\n
<\/a>(2)<\/p>\nGiven the\u00a0number of\u00a0unknowns in\u00a0the\u00a0equation for this reach, the\u00a0method described in\u00a0[4] cannot be applied, and the\u00a0discharge contributions must be derived using alternative approaches. In\u00a0the\u00a0case study, a\u00a0method based on the\u00a0ratio of\u00a0individual QN values was selected, derived from the\u00a0following equations:<\/p>\n
<\/a>\u00a0(3)<\/p>\n<\/a>(4)<\/p>\nwhich allows the\u00a0determination of\u00a0UBC values using the\u00a0following equations:<\/p>\n
<\/a>(5)<\/p>\n<\/a>(6)<\/p>\nMOV 10 Valov\u00e1, Hlou\u010dela, Rom\u017ee, \u010cesk\u00fd potok<\/h3>\n
The\u00a0case study of\u00a0reach MOV 10 documents, analogously to the\u00a0DYJ 09 reach, the\u00a0procedure for determining UBCs for the\u00a0given confluence area (Fig.\u00a03<\/em>).<\/p>\n
<\/a>\nFig.\u00a03. Conceptual model MOV 10<\/h6>\n
The\u00a0determination of\u00a0all UBCs is carried out for the\u00a0loading scenario QN from \u010cesk\u00fd potok. The\u00a0hydrological profile closest to the\u00a0DBC on the\u00a0Svitava is Valov\u00e1\u00a0\u2013 Polkovice (A) (Fig.\u00a04<\/em>). The\u00a0discharge contribution from the\u00a0UBC on the\u00a0Hlou\u010dela will be:<\/p>\n
<\/a>\u00a0 \u00a0 \u00a0(7)<\/p>\n<\/a><\/h6>\nFig.\u00a04. Hydrological data at the\u00a0confluence of\u00a0Valov\u00e1\u00a0\u2013 Hlou\u010dela, Rom\u017ee, \u010cesk\u00fd potok<\/h6>\n
The\u00a0discharge contribution from the\u00a0UBC on the\u00a0Rom\u017ee can be determined as:<\/p>\n
<\/a>\u00a0 \u00a0 \u00a0 \u00a0 (8)<\/p>\nSimilarly, for the\u00a0loading scenario QN<\/sub> from the\u00a0Rom\u017ee, the\u00a0discharge contribution for the\u00a0Hlou\u010dela UBC can be derived according to equation (7). Given the\u00a0absence of\u00a0hydrological data for the\u00a0Rom\u017ee upstream of\u00a0its confluence with the\u00a0\u010cesk\u00fd potok, the\u00a0discharge contribution from the\u00a0UBC on the\u00a0\u010cesk\u00fd potok can be conservatively assumed to be zero:<\/p>\n
<\/a>\u00a0 \u00a0 \u00a0 (9)<\/p>\nThe\u00a0UBC on the\u00a0Rom\u017ee will then take the\u00a0value of\u00a0the\u00a0corresponding loading scenario QN. When using the\u00a0QN ratio approach, the\u00a0UBCs for the\u00a0\u010cesk\u00fd potok and the\u00a0Rom\u017ee can be determined from the\u00a0following equations:<\/p>\n
<\/a>\u00a0(10)<\/p>\n<\/a>\u00a0 \u00a0(11)<\/p>\nFor the\u00a0loading scenario QN from the\u00a0Hlou\u010dela, the\u00a0discharge contributions can be derived as:<\/p>\n
<\/a>\u00a0 (12)<\/p>\nUsing the\u00a0QN ratio, the\u00a0discharge contributions between the\u00a0Rom\u017ee and the\u00a0\u010cesk\u00fd potok can be determined as:<\/p>\n
<\/a>\u00a0 \u00a0(13)<\/p>\n<\/a>\u00a0 (14)<\/p>\nMOV 01 Morava, Ol\u0161ava, Dlouh\u00e1 \u0159eka, Okluky<\/h3>\n
The\u00a0case study of\u00a0reach MOV 01 presents possibilities for merging flood hazard data in\u00a0a\u00a0confluence area derived from inputs prepared by different contractors (see areas A, B, and C in\u00a0Fig.\u00a05<\/em>), in\u00a0all cases using 2D models. The\u00a0analysed reach is significantly influenced by the\u00a0confluence of\u00a0the\u00a0Morava river with the\u00a0Ol\u0161ava, Okluky, and Dlouh\u00e1 \u0159eka. The\u00a0objective of\u00a0the\u00a0work was to create continuous datasets from the\u00a0partial flood hazard maps\u00a0[5] for the\u00a0individual sub-areas A, B, and C.<\/p>\n
<\/a>\nFig.\u00a05. River section MOV 01 with indication of\u00a0sub-areas A, B, C calculated by different authors<\/h6>\n
The\u00a0merging of\u00a0inundation maps was carried out in\u00a0the\u00a0following steps and is demonstrated using the\u00a0Q500 scenario as an example; the\u00a0same procedure can be applied identically to the\u00a0other QN scenarios:<\/p>\n
\n- \n
- The\u00a0updated areas B and C were removed from the\u00a0historical results for area A\u00a0(see Fig.\u00a06<\/em>). The\u00a0boundaries of\u00a0polygons B and C were suitably selected at locations where approximately one-dimensional flow could be assumed (channel flow, embankment overtopping, flow through bridges and culverts).
\n
\n<\/li>\n- The\u00a0updated areas B and C were clipped to the\u00a0extent of\u00a0polygons B and C only. The\u00a0resulting partial map for Q500 corresponds to Fig.\u00a06<\/em>.
\n
\n<\/li>\n- At the\u00a0contact lines between polygon boundaries, the\u00a0datasets were merged and any singularities were removed (Figs. 7<\/em> and 8<\/em>).<\/li>\n<\/ol>\n
<\/a>\nFig.\u00a06. The\u00a0extent of\u00a0data exclusion in\u00a0the\u00a0locations of\u00a0updated areas B and C<\/h6>\n
<\/a>\nFig.\u00a07. Examples of\u00a0polygon boundary merging between areas A\u00a0and B<\/h6>\n
<\/a><\/h6>\nFig.\u00a08. Examples of\u00a0polygon boundary merging between areas A\u00a0and C<\/h6>\n
Based on the\u00a0inundation maps processed in\u00a0this way, the\u00a0raster hazard maps (water depths, flow velocities, and water surface elevations) can subsequently be adjusted. The\u00a0adjustments were carried out in\u00a0the\u00a0following steps:<\/p>\n
\n- \n
- Clipping the\u00a0raster maps to the\u00a0extent of\u00a0the\u00a0polygons of\u00a0areas A, B, and C.
\n
\n<\/li>\n - Merging the\u00a0clipped raster layers.
\n
\n<\/li>\n - Filling missing data in\u00a0the\u00a0rasters using bilinear interpolation (Fig.\u00a09<\/em>).<\/li>\n<\/ol>\n<\/a>\n
Fig.\u00a09. Example of\u00a0using bilinear interpolation to fill in\u00a0missing values of\u00a0level H during connection of\u00a0sections A\u00a0and B<\/h6>\n
RESULTS AND DISCUSSION<\/h2>\n
DYJ 09 Svitava, K\u0159et\u00ednka, T\u0159eb\u011bt\u00ednka, Kladorubka<\/h3>\n
In\u00a0this case, the\u00a0confluence area is more complex than that considered in\u00a0the\u00a0LABEL pilot project\u00a0[4]. Complete hydrological data were not available for all confluence profiles, in\u00a0particular upstream and downstream of\u00a0the\u00a0analysed confluences. The\u00a0missing hydrological data required for specifying boundary conditions had to be derived using equations (1) to (6).<\/p>\n
The\u00a0selected area cannot be addressed without considering the\u00a0significant tributaries of\u00a0the\u00a0Svitava river. Given the\u00a0relatively complex hydraulic conditions, it was necessary to treat the\u00a0area as a\u00a0whole using a\u00a02D hydrodynamic model. The\u00a02D model of\u00a0the\u00a0confluence area yields markedly different results compared to historical data that did not consider tributaries (Figs. 10\u201312<\/em>).<\/p>\n
<\/a>\nFig.\u00a010. Flood scenario with return period Q20<\/sub> on confluence of\u00a0the\u00a0Svitava and K\u0159et\u00ednka rivers; left\u00a0\u2013 without confluence effect\u00a0[6], right\u00a0\u2013 with confluence<\/h6>\n
<\/a><\/h6>\nFig.\u00a011. Flood scenario with return period Q20<\/sub> on confluence of\u00a0the\u00a0Svitava\u00a0\u2013 Kladorubka and K\u0159et\u00ednka rivers; left\u00a0\u2013 without confluence effect\u00a0[6], right\u00a0\u2013 with confluence<\/h6>\n
<\/a><\/h6>\nFig.\u00a012. Flood scenario with return period Q100<\/sub> on confluence of\u00a0the\u00a0Svitava\u00a0\u2013 Kladorubka and K\u0159et\u00ednka rivers; left\u00a0\u2013 without confluence effect\u00a0[6], right\u00a0\u2013 with\u00a0confluence<\/h6>\n
MOV 10 Valov\u00e1, Hlou\u010dela, Rom\u017ee, \u010cesk\u00fd potok<\/h3>\n
In\u00a0the\u00a0analysed area, it was not possible to apply the\u00a0procedures for determining UBCs according to\u00a0[4], primarily due to the\u00a0unavailability of\u00a0some hydrological data for all confluence profiles. The\u00a0UBCs were therefore derived using equations (7) to (14).<\/p>\n
Given the\u00a0complex hydraulic conditions (for example, water transfers between the\u00a0individual reaches), the\u00a0area had to be treated as a\u00a0whole (Figs.\u00a013<\/em> and 14<\/em>).<\/p>\n
<\/a>\nFig.\u00a013. Flood scenario with return period Q20<\/sub> on confluence of\u00a0the\u00a0Hlou\u010dela\u00a0\u2013 Rom\u017ee rivers; left\u00a0\u2013 without confluence effect\u00a0[6], right\u00a0\u2013 with confluence<\/h6>\n
<\/a><\/h6>\nFig.\u00a014. Flood scenario with return period Q100<\/sub> on confluence of\u00a0the\u00a0Hlou\u010dela\u00a0\u2013 Rom\u017ee rivers; left\u00a0\u2013 without confluence effect\u00a0[6], right\u00a0\u2013 with confluence<\/h6>\n
MOV 01 Morava, Ol\u0161ava, Dlouh\u00e1 \u0159eka, Okluky<\/h3>\n
The pilot area confirmed that merging data produced by different contractors in confluence areas is feasible, but only under relatively strict conditions. Fundamentally important is particularly the existence of suitable profiles for linking the partial reaches. It is also desirable to maintain consistent parameters of the computational models (boundary conditions, surface roughness, and the digital terrain model). When connecting raster layers, it must be taken into account that profiles with completely identical values generally cannot be found, which necessitates creating transition zones and completing missing\u00a0data, for example using simple bilinear interpolation. In\u00a0view of\u00a0the\u00a0above, the\u00a0linking of\u00a0partial reaches in\u00a0confluence areas should be regarded as a\u00a0marginal solution and applied only in\u00a0justified cases.<\/p>\n
CONCLUSION<\/h2>\n
The\u00a0quantification of\u00a0flood hazard in\u00a0confluence areas represents a\u00a0time- and cost-intensive process, not only in\u00a0terms of\u00a0the\u00a0hydraulic calculations themselves but also with regard to securing the\u00a0necessary extent of\u00a0required hydrological data. Hydraulic solutions based on 2D models typically require the\u00a0creation of\u00a0relatively extensive computational domains with a\u00a0large number of\u00a0calculation elements. In\u00a0confluence areas involving multiple watercourses, this is further compounded by the\u00a0need to perform a\u00a0large number of\u00a0simulations for partial scenarios with different combinations of\u00a0boundary conditions.<\/p>\n
Despite the\u00a0above-mentioned challenges, it can be unequivocally recommended that confluence areas be modelled as a\u00a0whole, without subdivision into separate individual watercourse reaches. The\u00a0conducted case studies demonstrated that mutual interactions of\u00a0flow between individual watercourses can have a\u00a0fairly substantial influence on flood hazard values.<\/p>\n
The\u00a0conclusions presented will be incorporated into Chapter 4.9, Hydraulic calculations for the\u00a0purposes of\u00a0floodplain\u00a0delineation, of\u00a0the\u00a0Methodology for the\u00a0preparation of\u00a0flood hazard and flood risk maps.<\/p>\n
Acknowledgements<\/h3>\n
The article was prepared within the framework of project No. SS02030027 Water systems and water management in\u00a0the\u00a0Czech Republic under conditions of\u00a0climate change, implemented with financial support from the\u00a0Technology Agency of\u00a0the\u00a0Czech Republic under Subprogramme 3\u00a0\u2013 Long-term environmental and climate perspectives of\u00a0Programme SS\u00a0\u2013 Programme of\u00a0Applied Research, Experimental Development and Innovation in\u00a0the\u00a0Field of\u00a0the\u00a0Environment\u00a0\u2013 Environment for Life.<\/em><\/p>\n
The\u00a0Czech version of\u00a0this article was peer-reviewed, the\u00a0English version was translated from the\u00a0Czech original by Environmental Translation Ltd.<\/p>\n","protected":false},"excerpt":{"rendered":"
The study focuses on assessing changes in runoff conditions and approaches to determining flood hazard in confluence areas of river systems. Based on the analysis of several model catchments, the results of numerical simulations of water flow during floods with different return peri-ods are presented. The analyses revealed that separate modelling of the main river and its tributaries produces distorted results, as the hydraulic conditions in confluence areas are characterized by complex interactions between individual streams. Therefore, the authors recommend a comprehensive approach using 2D numerical models, which allow for more accurate evaluation of inundation extent, water depths, and flow velocities. The study results include proposals for updating the methodological guidelines of the Ministry of the Environment, emphasizing a unified approach to the development of flood hazard and risk maps.<\/p>\n","protected":false},"author":8,"featured_media":37875,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[86,93],"tags":[2455,4028,1333,2454],"coauthors":[3999,2445,488],"class_list":["post-37877","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-hydraulics-hydrology-and-hydrogeology","category-two-articles","tag-2d-numerical-model","tag-confluence","tag-flood-hazard-en","tag-hydraulic-calculation"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/37877","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/comments?post=37877"}],"version-history":[{"count":7,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/37877\/revisions"}],"predecessor-version":[{"id":38003,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/37877\/revisions\/38003"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/media\/37875"}],"wp:attachment":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/media?parent=37877"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/categories?post=37877"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/tags?post=37877"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/coauthors?post=37877"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- The\u00a0updated areas B and C were clipped to the\u00a0extent of\u00a0polygons B and C only. The\u00a0resulting partial map for Q500 corresponds to Fig.\u00a06<\/em>.
- The\u00a0updated areas B and C were removed from the\u00a0historical results for area A\u00a0(see Fig.\u00a06<\/em>). The\u00a0boundaries of\u00a0polygons B and C were suitably selected at locations where approximately one-dimensional flow could be assumed (channel flow, embankment overtopping, flow through bridges and culverts).
![\"\"](\"https:\/\/www.vtei.cz\/wp-content\/uploads\/2026\/02\/Skokan-obr-1.jpg\")
<\/a>\n