Creation of digital elevation models for river floodplains

Creation of digital elev ation mo dels for riv er flo o dplains Anna Klikuno v a 1 ∗ , Alexander Khop ersk o v 1 1 V olgograd State Univ ersit y , V olgograd, 400062 , Russia E-mail: ∗ Correspond ing author e-mail: klikunova@ volsu.ru Abstract. A proced ure for constructing a digital elev ation mo del (DEM) of the northern part of the V olga-Akhtuba i nterfluve is described. The basis of our DEM is the elev ation matrix of Sh uttle Radar T op ograph y Missio n ( SR TM) for which w e carried out t h e refinement and up dating of spatial data using satellite imagery , GPS data, depth measurements o f the Riv er V olga and River Akhtuba stream b eds. The most imp ortant source of high-altitude data for the V olga-Akhtuba floo dplain (V AF) can be the results of observ ations of th e coastlines d ynamics of small rese rvoirs (lak es, eriks, small c han n els) arising in the pro cess of spring flo o ding and disapp earing during lo w-flow p eriods. A set of d igitized coastlines at different times of floo ding can significantly improv e the qualit y of t h e DEM. The metho d of constructing a digital elev ation mod el includes an iterative pro cedure that uses the results of morphostructu ral analysis of the DEM and the numerical hydrodyn amic simulatio ns of the V AF flo odin g based on the shallo w w ater model. 1. In tro duction A high-resolution 3D top ographic mo del for th e large areas is essent ial to solving a v ariet y of applied p roblems in the geosciences that are asso ciated with modeling and m onitoring the en vironment . The progress of computer tec h nology and n umerical metho ds giv es us new opp ortunities for mo deling fluid dynamics in certain territories. Such problems include storm surges, spring flo o ds in riv er v alleys, floo ding d u e to hea vy rainfall [1 , 2]. Hydro dynamic mo dels allo w tec hnical and environmen tal exp ertise in the design of h ydrological structures [3, 4]. The imp ortan t tasks are the determin ation of the w atersheds’ b oundaries [5], the creating tools to help authorities respond to emergency sit uations [6]. One imp ortan t researc h area is the creation of decision supp ort systems (DSS) for s olving v arious hydrological problems, and the effec tiv eness of these DSS is determined by the qualit y of the applied digital el ev ation mo dels (DEM) [7, 8, 9]. Such DSS belong t o the class o f Spatial Decision-Supp ort S y s tem, whic h com b in e standard decision-making to ols with geographic information systems, pro v id ing new o pp ortu nities for w ater r esources m an agement [4, 10], cit y and reg ional planning, r eal-t ime decision-making f or land managemen t [11], t ransp ortat ion engineering [12], protec ting the n atural resources in conditions of increasing h uman pressu res on the ecosystem. 0 Cite as : Klikuno v a A.Y u., Kh opersko v A.V. Creation of digital elev ation mo dels for river floo dplains // CEUR W orkshop Proceedings, 2019, vol. 2391, 275-284 Figure 1. T h e n orthern part of the V olga-Ah tuba fl oo d plain. A qu alit y DEM is a critical comp onent for all these tasks [13]. The terrain is a ma j or physical factor that influ ences the dynamics of w ater. Un fortunately , th e accuracy of b est top ographic maps i s not h igh e nough for n um erical simulat ions. In addition, n ew problems app ear o n small spatial scales, and they are asso ciated with changes in the s urface of the relief caused by n atural and man-made factors [14, 15]. Ch anges in the profile of the b ottom and adj acen t areas are a con tinuous process due to activ e sediment transfer and erosion pro cesses, w hic h require the use of the self-co nsistent model of w ater and sedimen t dynamics and regular up dating of the DEM also [16]. In this pap er, we describ e the k ey sta ges of creating a DEM for river systems based on th e syn thesis of v arious sp atial data using the example of the northern p art of the V olga-Akh tuba flo o dplain (V AF). T h e V olga Hydro electric Station con trols the fl o w of wate r downstream of the V olga Riv er and th e moistur e reserve s for the entire flo o dplain. The volume flow of w ater through the dam is called discharge Q ( t ) (m 3 · sec − 1 ) and it v aries b et w een Q ( t ) ≃ 4000 − 30000 m 3 · sec − 1 during the yea r. Imp ortant comp onen ts of ou r metho d olog y are the u s e of obs er v ational data on th e d ynamics of the coa stlines of numerous small reservoirs in the in terfluve during the spring flo o d and the v erification of DTM u s ing hydro dynamic mo deling. Observ ations of the coastlines motions for a large n u m b er of reserv oirs during the spr ing fl oo d ing are a source of v ery accurate lo cal top ograph y data. These w ater reservoirs are the results of the p assage of spr ing wate r and they usually disapp ear in early summer. Thus, th e water surface area in the territory of V AF v aries strongly d uring a few weeks fr om 2-5% b efore flo o ding (lo w w ater) up to a maximum v alue of 20-40%, which dep ends on the sp ecific conditions in eac h year. In late summer, the w ater basin a rea is smaller than in the early spring p eriod b efore the flo o d, that connected with high summer temp erature and lac k of rain. The coastline coincides with the con tour line (isoli ne) of the heigh ts’ d istribution with v ery high accuracy at eac h time p oint . Th u s, the lo cal DEM ma y b e the result of pr ocessing the monitoring data of the coastl ines d ynamics for a large num b er Figure 2. Stage s and sequence of DEM creation. of small reserv oirs during the spring flo o d. T hese lo cal DEMs are high-resolution data for the most critical areas in term s of h ydr olog y as a part of global DEM for the n orthern territory of the V olga-Akh tuba flo o d plain (Fig. 1). 2. Iterative pro cess of creating DEM 2.1. Main stages of cr e ating DE M Figure 2 sho ws the general sc heme for constructing a digital el ev ation mo d el and highligh ts the most significan t steps whic h w e will discuss b elo w. Our DEM is based on the heigh t matrix b ij = b ( x i , y j ) for n o d es of the Pulk o vo 95 co ordinate system w ith step ∆ x = ∆ y : x i = x 0 + i ∆ x , y j = y 0 + j ∆ y ( i = 1 , 2 , ..., N x , j = 1 , 2 , ..., N y ). W e tak e the SR TM3 S R TMGL1 data b [ S RT M ] ij as the initial heigh t matrix. T h e professional GIS “Panorama” to ols allo w us to recalculate the matrix by a smaller step (∆ x = 15 m, 10 m, 5 m) using t he w eigh ted a v erage in terp olation in 16 directions. Suc h matrix b [0] ij will b e c alled the basic digit al elev ation m od el. The main s tages of the transformation m atrix b [0] ij are discussed belo w. 1) T o clarify the mo del of the b ott om of the V olga Riv er and the Akh tuba River, we use Sailing Directions (shipping charts) and w ater dept h maps . T o r efine the b ottom mo del of the V olga River and the Akht uba Rive r, we use Sailing Directions (ship ping c harts) and reservoir depth maps, and then we obtain the matrix b [1] ij after digitizing and em b edding this data into t he basic DEM b [0] ij . 2) A unique feature of the V AF is a co mplex system of small channels in the in terflu v e (the so-calle d eriks), w hic h form a hierarc hical sys tem of c h annels b et ween Riv er Akh tuba and Rive r Figure 3. a — T ypical d ep endence of d isc harge Q ( t ). b, c, d — Th e hierarchica l structure of the h ydr olog ical system in the V AF at d ifferen t stages of floo d ing. V olga (Fig. 3). W e use the satellite images of the “RESURS-P” series and UK-DMC 2, the Digital Glob e’s satellite constellation (Go ogle Earth services) to v ectorize the linear ob jects of this c hannel system for subsequent introd u ction in to the DEM matrix of b [1] ij . UA V images and geod esic data a re an imp ortan t source for cla rifying th e lo cation of small c hann els (Fig . 5). As a result, we ha v e the matrix b [2] ij , whic h con tains the system of small c hannels. 3) T o up date the V olga Riv er b ottom mod el, w e use the data of the last depth measuremen ts ranging from the V olga hydroelectric p o w er s tatio n to th e Svet ly Y ar settlemen t. These data are v er y sparse and after approxima tion to all our grid no des w e ha ve the matrix b [3] ij with the h eight d ata o f the riv er b ed . 4) W e use data on dynamic s of coastlines of transien t r eserv oirs, wh ic h are filled with w ater at the stage of in terflu v e flo o ding (April – Ma y) and d ry out in the summer (Figure 4). These measurements pro vide an additional set of lines with a co nstant lev el of relief with v ery high accuracy . The refined matrix b [3] ij is the result of bin ding these isol ines to heigh ts. O ur studies hav e sho wn the effectiv eness of the UA Vs use to obtain data o n the b oundaries of water b o dies (Fig. 5). UA Vs provide a m ore d etaile d sequence of isolines at the initial stage of flo o din g rise, which is almost unattainable for satellite data. Ho wev er, this appr oac h is lo cal and do es not a llo w to co ve r large areas. Figure 4 shows v ertical profiles along the AB and C D segments for the b [2] ij matrix, in dicating the p ositions of the corresp onding in tersections of coastlines with these segmen ts. The points for the same coastline on opp osite slop es of the reserv oir ha v e different elev ation lev els, whic h indicates th e n eed to up date the matrix b [2] ij . F or example, the heigh t difference is ∆ b = 0 . 5 m for a pair of p oin ts (1a, 1b) in th e fi gure 4 b and ∆ b = 1 m for (2 a, 2d) in t he figure 4 c. 5) Th en we calculate the standard set of morphostructural analysis parameters [17 ]: the p rofile curv atur e k t ( x i , y j ), the tangen tial curv atur e k s ( x i , y j ) and the tilt angles s ( x i , y j ) a) b) c) Figure 4. The position of coastl ines at different p oin ts in time for small b odies of w ater near the villa ge Zonal’n yj. (Figure 6): s = 360 o 2 π arctan q b 2 x + b 2 y , (1) k t = b xx b 2 y − 2 b xy b x b y + b y y b 2 x p √ q , (2) k s = b xx b 2 y + 2 b xy b x b y + b y y b 2 x p p q 3 , (3) b x = ∂ b ∂ x , b y = ∂ b ∂ y , b xx = ∂ 2 b ∂ x 2 , b y y = ∂ 2 b ∂ y 2 , b xy = ∂ 2 b ∂ x∂ y , p = b 2 x + b 2 y , q = 1 + p . W e often encoun ter t wo t yp es of artifacts: a) Strong lo cal errors of heigh ts on the b [0] ij matrix are strongly h ighligh ted against the bac kgrou n d of a r ather flat territory . These errors are often caused by data pro cessing problems for small forests and sm all w ater reserv oirs. b) The s econd d ifficult y is related to the detection of small c hannels connectedness. There are problems with the automatic selection of ob jects ev en in images for urbanized areas, the morphology of whic h is simpler compared to the w o o ded marsh landscap e of the flo o dplain [18]. Analysis of the h yp er s p ectral ob s erv ational data for v arious p latforms allo w s us to impro v e the classificatio n o f ob jects [8], bu t this approac h is algorithmically complex [19]. The sp atial distribu tions of the p arameters (1) – (3) help id entify areas with artifacts, fi rst of all, areas with a violation of hydrologica l connectedness of w atercourses on the digita l elev ation Figure 5. The v ectorization of wate r b o dies images w ith UA V. Th e colored lines sho w the b oundaries o f the reserv oirs. mo del. The morphostructural analysis of the DEM allo ws simp le means to detect p ossib le err ors and promptly correct them, refining the h ydrological net w ork [20, 21]. 6) Hydrod ynamic mo deling is ca rried out a t the final stage (Fig. 3 a , b ), r ep ro ducing the spring flo o ding of the interfluv e territory in accordance with the pro cedure describ ed in [1, 3, 22]. This allo ws y ou to c hec k the c hannels connectedness of the h ydrological system in addition to the morph ostru ctural analysis. Comparison of sim ulation results with observ ational data is a p o w erful tool for up dating the DEM f or th e most imp ortan t zo nes, whic h primarily pro vide for the form ation of v ast reserv oirs of the lak e type due to the w ater outflo w from small canals (eriks). Suc h verificatio n b ased on hydro dynamic mo deling is the most resource-inte nsive p ro cedure. F or h ydro dyn amic simulatio ns, w e u se the soft ware for the numerical solution of the shallo w wa ter equations describ ed in [1, 22] and taking into accoun t the parallel im p lemen tation for GPUs [23]. 2.2. Assimilation of lo c al sp atial data by the DEM matrix One essen tial feature of building a digital mo del of riv er b ed is the sour ce data sparseness, w hic h include: (i) Th er e are t wo co astlines with w ater lev el mark L coast 1 ( ~ r ), L coast ( ~ r ) 2 . (ii) There are seve ral depth curves on top ographic m aps of L bed i ( ~ r ) ( i = 1 , ..., m B ). W e hav e only m B ∼ 3 − 4 ev en for the large st riv ers. (iii) Seve ral sound ings show, as a rule, only t he deep est points on a top ographic map. (iv) Depth measurements using ec h o sounders require n ew field stud ies. All these data form set of p oin ts P on the h eigh t matrix b ij . Figure 6. a ) The general structure of the V AF flo o ding is based on th e results of our numerical h ydro dyn amic mo deling. b ) The distrib ution of w ater for the sp ecified area of the fr ame. c ) Th e distribution of t he morphometric index k s for the same zone. W e used an ite rativ e p r o cedu re to build a riv er b ottom DEM: b p +1 n,m =    b p n,m + α h b p n +1 ,m − 2 b p n,m + b p n − 1 ,m i + α h b p n,m +1 − 2 b p n,m + b p n,m − 1 i , P n,m / ∈ P b ( exp ) n,m , P n,m ∈ P , (4) where b ( exp ) n,m is the depth at th e p oint s P n,m , α is the parameter th at determines the con vergence of the iterativ e p ro cedure (4). The formula (4) is the finite-difference analog of the diffusion equatio n. W e obtain the s olution to the Poisson’s equatio n in the case of con verging iterations (4). Figure 7 sho w s the results of the constru ction of the DEM of the V olga Riv er area, based on the approac h d escrib ed ab ov e. 2.3. Co astlines dynamics as factor in impr oving DEM Fig. 3 sh o ws a sc hematic diagram of the h yd rologic al regime in the V AF. W ater flo ws from the V olga Riv er to the Akh tuba Riv er in a lo w wate r p erio d in the case Q ≃ 5 − 9 thousands m 3 · sec − 1 , bu t it is not enough to fi ll the c hannels and b esides the moi sture r eserv e is v ery small in the area b et we en the riv ers. All c hannels are quic k ly fi lled with the increase of Q up to 23–30 thousand s m 3 · sec − 1 and the w ater is p our ed on to the flat part of V AF. The water lev el is main tained b y the p o w erful moistening at the third stage w ith Q = 16000 − 200 00 m 3 · sec − 1 . In late spr ing, there is a c h ange to lo w-w ater and the total moisture con ten t decreases in the territory . There is a large num b er of sh allo w lak es on the flat territory b et w een the large and small c h annels in spring and early summer. The coastlines of such reservoirs are m o ve d on consid er ab le distances in a short time p eriod (Fig. 8 and S ee Fig. 4). Measuring the p osition of coastline at d ifferen t p oints in time can help us d etermin e an additional set of con tour lines (isolines of a) b) Figure 7. a ) V ector map of the River V olga. b ) Digital elev ation mo del of riverbed of the V olga do wnstream from the hydro electric dam. heigh ts) of the terrain for critical zo nes. Figure 8. S hallo w lak e near the Bulga k o v Channel at v arious stage sof the flo o ding in 2014 is sho wn: a) start the floo d in g (Ma y 6), b) maxim um the flo o ding (Ma y 8), c) the dissip ation of the reserv oir (Ma y 18 ). 2.4. V erific ation b ase d on the r esults of hydr o dynamic simulations Fig. 9 sh o ws the results of h ydro dyn amic simulati ons in the floo dp lain of the small riv er at v arious stag es of the DEM refinemen t: (i) W e u se the DEM after em b edding the riv erb ed in the SR TM matrix and assignment the coastlines, the fairw a y line and the riv er slop e (Fi g. 9 a ). (ii) Pa nel b in the figure demonstrates the wate r distribution in the riv er channel after pro cessing the DEM in the “Construction of horizon tals by ele v ation matrix” service in the GIS P anorama. (iii) The next iteration inv olv es the DEM r ebuilding taking in to accoun t the geo detic transv erse profiles of the river v alley , w hic h are obtained as a result of field me asurements ( Fig. 9 c ). (iv) Th e fi n al step in v olv es up dating the digital model on a sm all sc ale at the h igh water stage (Fig. 9 d ). 3. Conclusions The ob j ect of our study is the v alley b et we en the Riv er V olga and River Akhtuba, the ecosystem of whic h is unique on Earth d u e to the sp ecial h ydrological r egime. W e p rop ose the iterativ e a) b) c) d) Figure 9. Results of lo cal DEM refinement for the small riv er v alley using hydro dynamic sim ulations. By iden tifying the sh ortcomings of the DEM, w e pro vide flo od ing in the mo del for the nearest areas in accordance with th e observ ations. pro cedure for cr eating the DEM for sp ecia l flo o d plain areas with a large n umber of transien t reserv oirs. The initial data are the S R TM matrix, the space images from the “Resource-P ” and UK-DMC-2 satellites, the top ographic m ap s , th e geo detic m easur emen ts of the elev ation profiles, the d epth m easuremen ts. The morph ostructural analysis and the numerical simulati ons of surface wate r dyn amics on r ealistic to p ography can b e p o werful to ols for v erification of the digital el ev ation mo del. The observ ed dynamics of coa stlines allo w s building ele v ation leve ls along the b oundaries o f w ater b o dies, and this appr oac h is activ ely used to construct the DEM. Ho wev er, this method acquires sp ecial v alue in the case of p erio dically fl oo d ed area s, since the mo ving coastlines pro vide d etaile d sets o f con tour lines, b eing the b asis for a v ery high-qualit y and relev an t digital elev ation mo del. Ac knowledgmen ts The work h as b een supp orted by the Ministry of S cience and Higher Education (go ve rnment task no. 2.852.2017 /4.6). T h e researc h is carried out u sing the equ ipmen t of the shared researc h facilities o f HPC co mputing resources at Lomo noso v Mosco w S tate Univ ersit y . The authors are grateful to E. Aga fonniko v a, S. Khr ap o v, A. Pisarev, K. T er tyc hny for their help and assistance in carrying out this pr o ject. A. Klikunov a thanks f or the su pp ort of the RFBR and t he Administration of the V olgog rad r egion ( gran t 18-47-34 0003). References [1] Khrap o v S S , Pisarev A V, Kob elev I A, Zhumal iev A G, Agafo nniko v a E O, Losev, A G and Kh opersko v A V 2013 A dvanc es in M e ch. 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