MesoHydraulics: Modelling Spatiotemporal Hydraulic Distributions at the Mesoscale

Abstract

The purpose of this study is to enhance the performance of the mesohabitat model MesoHABSIM by lowering the necessary hydraulic modelling effort. This proof-of-concept study tests an application of the MesoHydraulics model to simulate the hydraulic characteristics of hydromorphological units (HMUs) occurring in a regulated river at different low discharges. In this quantitative approach, hydraulic patterns are transferred from a source site, where depth and velocity distributions were derived from field measurements and a 2D hydrodynamic model, to a target site, where only a single field hydrometric survey was conducted. Instead of modelling changes in individual hydraulic measurement values to estimate hydraulic responses to discharge, the model relies on statistical distributions of these values within HMUs. We were testing whether changes in the distribution of HMU’s and their hydraulics can be transferred between morphologically comparable river sections to serve as a sufficient hydraulic input for mesoscale habitat modelling. The hydrodynamic component of the River2D software (V.0.95a), routinely used in MesoHABSIM, served as a baseline for testing the MesoHydraulic model’s performance and for producing source data for deriving distribution functions. The test was conducted using data from two one-kilometre sites on the upper Oder River (Poland). The model transfers the HMU area distributions, along with corresponding depth and velocity frequency distributions, for a number of flows from one site (the source) to another (the target). The hydraulics at both sites were surveyed under single-discharge conditions. For the source site, the hydrodynamic model was applied to classify the HMU mosaic at three additional discharge stages. At the target reach, the HMU mapping was conducted based on survey data, and statistical frequency functions were used to model distributions of hydraulic patterns at discharges modelled for the source. The hydraulic model’s performance was evaluated at the target reach by comparing simulated hydraulics and HMU patterns with those modelled using River2D. Finally, both models were used to calculate habitat availability for the fish communities, and dissimilarities were observed. The resulting hydraulic distributions were similar, with an average affinity index of 90%. Higher affinity indices were reached at flows close to the measured value, with increasing model disagreement toward flow extremes, most notably for Run and Backwater units. Regardless, habitat models for the fish community were also highly correlated with R² = 0.98 for amounts of suitable habitat and almost identical habitat distribution among the species. Yet, the MesoHydraulics-based model slightly, but consistently, overestimated habitat availability. While the model was tested in a large and regulated river system, its accuracy may vary depending on the natural river morphology. Further research should evaluate modelling uncertainties and their applicability in less-modified water bodies.

1. Introduction

Computer models of the physical habitat of fish in rivers have proven to be highly effective tools for river management. They are most commonly used to determine environmental flows and for planning river restoration. Yet, they are frequently dismissed as too labour-intensive to be applied at a broader scale in river management [1]. Different habitat-modelling approaches have historically been developed, such as Bovee’s [2] PHABSIM, which operate at the microscale and focus on individual channel cross-sections. The Mesohabitat Simulation Model (MesoHABSIM) partially addresses the above criticism by modelling instream habitats at the river and site-specific scale [3]. The system is based on the resolution of input data that reflects species responses to changes in the riverine environment and has a framework for effective extrapolation to a scale that allows planning and management. MesoHABSIM therefore enables research and forecasting in relation to river systems at both catchment and regional scales. Since the inception of MesoHABSIM, efforts are underway to increase effectiveness and further reduce the need for frequent, detailed data collection.

The MesoHABSIM method assumes that the river channel can be classified into several hydromorphological units (HMUs), such as pools, riffles, runs, and backwaters. This aligns with the broader scientific understanding that rivers are composed of spatially discrete segments with relatively homogeneous hydrological and morphological characteristics, commonly referred to as “river landforms,” “morphological units,” “mesohabitat types,” “physical/hydraulic biotopes,” “ecotopes,” “channel geomorphic units” or hydromorphological units (HMUs) [4,5,6,7,8,9,10]. These HMUs collectively form a dynamic mosaic of mesohabitats along longitudinal and transversal profiles, playing a crucial role in shaping aquatic ecosystems and influencing habitat availability for different species. Furthermore, the mosaic of hydromorphological unit types and their areas is spatiotemporally variable and dependent on the river’s hydrological conditions. This variability requires delineation of river reaches based on general geological, fluvial-geomorphological, and topographic characteristics. Within each delineated reach, representative sites are then selected based on expert judgement to capture the best spatial relationships and hydromorphological diversity of the entire reach. Although representative sites are not clearly defined as a spatial category in river delineation, they serve as the basis for model inputs. Therefore, the first input to the model is a map of HMUs from multiple representative sites, captured at a range of hydrological flow conditions, reflecting the fact that both the type and area of HMUs are strongly dependent on hydrological variability. This requires repeated surveys of HMU distribution, measurements of their depth and velocity, and estimates of substrate patterns. In small rivers, these surveys are typically conducted through repeated fieldwork, while in large rivers, a combination of hydraulic boat surveys and high-resolution aerial photography is used [11].

In coarse-scale applications (e.g., entire rivers or watershed assessments), where numerous sites need to be sampled, the required fieldwork can be extensive. This has been criticized as a limitation of MesoHABSIM modelling [12]. However, this fieldwork effort could potentially be reduced through computational modelling of hydromorphological patterns. The challenge lies in the fact that flow-related spatio-temporal changes in HMU distribution can be complex to capture, as spatial units may shift in type or undergo changes in size, expanding or contracting in response to varying hydrological conditions [3].

However, according to Milhous [13], the total hydromorphological changes with flow are relatively constant. Consequently, the quantitative shifts in the area proportions of HMU types at a given site should be less dramatic. This is even more true for reaches in regulated rivers, where flow conditions within each HMU are likely to remain relatively constant. Under such circumstances, and provided that no substantial land use changes or human-induced channel modifications occur within the catchment in the meantime, depth and velocity distributions can be regarded as stable hydraulic signature characteristics of individual HMU types. We hypothesize that the hydraulics properties obtained for one river reach designated as the source site, where velocity and depth were measured across multiple hydrological conditions or where a hydrodynamic model was developed, can be transferred to a target site, where hydrometric data was collected only once or not at all and where only one HMU mapping was conducted, without the need for repeated surveys or developing a hydrodynamic model.

The MesoHydraulic model proposed in this study builds on this conceptual foundation by enabling the transferability of hydraulic distributions between river reaches. We adopted a statistical hydraulic model concept [14,15,16]; however, here the model simulates hydromorphological patterns for multiple discharges by transferring hydraulic and HMU distributions from a source to a target site. As input, the model uses hydraulic patterns observed at three hydrological conditions at the source site and a single HMU survey of the target site. Simulation is achieved by transferring the change functions for HMUs, depth, and velocity histograms.

Unlike traditional two-dimensional hydrodynamic models, which require detailed bathymetry, water-surface elevations, extensive field measurements, and computationally intensive calibration, the proposed MesoHydraulic model offers a simplified, transferable alternative. By relying on the statistical distribution of key hydraulic parameters derived from a limited number of reference flows, this approach substantially reduces the need for intensive fieldwork and computational time while hopefully maintaining sufficient accuracy for mesoscale habitat modelling. This would make the model particularly suitable for larger and relatively homogeneous rivers, where numerous representative sites and reaches must be evaluated, surveyed, or modelled.

To test and prove this concept study, we chose two reaches on the Oder River that are close to each other and have comparable hydromorphological conditions. This is to reduce the influence of hydromorphologic spatio-temporal variability. For each reach, two hydraulic models (2D hydraulic and MesoHydraulic) were developed to produce input data for the MesoHABSIM habitat models. The differences in resulting hydromorphic and habitat patterns are statistically observed. Such a study design enables the first quantitative evaluation of the transferability of hydraulics distribution patterns for distinct HMU types, thereby providing a novel and substantive contribution to understanding the stability and robustness of mesohydraulic relationships.

2. Materials and Methods

The selection of two adjacent locations along the Other River was deliberate and intended to enable an initial assessment of the model’s conceptual performance under controlled conditions. Both analyzed sites exhibit comparable hydraulics and morphological characteristics, as well as regularly spaced groynes that promote a relatively uniform channel geometry and predictable hydraulics responses across a range of hydrological conditions. These conditions ensure that any differences in model outcomes arise predominantly from the transfer algorithm itself rather than from morphological contrasts between the analyzed river sites. Concurrently, the subtle morphological differences between the straightened site of Osiecznica and the meandering site of Szydłów provide a realistic yet controlled degree of variability, which is required to assess the model’s robustness. Figure 1 demonstrates the procedural steps undertaken in this study.

The MesoHABSIM model requires hydraulic data for at least three calibration flows. For each flow (q), it is necessary to enter the following hydraulic inputs of each identified HMU: wetted area (A_i(q)) and histograms of water depth and mean column flow velocity. Histogram bins are established according to the fish’s sensitivity to hydraulic changes. To improve the transferability of results between reaches, the flows were measured in specific flow units (l/s/km²).

The hydraulic properties analyzed in the present study were distributions of depths and mean column velocities for HMU types, i.e., cumulative histograms were developed for these parameters for the identified HMU types (

Table 1. Identified HMU types with hydromorphological description. (Modified from [18,19,20,21,22]).

HMU Type	Definition
Backwater	Low-velocity, often recirculating or weakly connected zones to surrounding flow in the main channel; typically located behind obstructions or shoreline irregularities.
Pool	Deep, low-velocity areas located along the main channel; concave longitudinal and transversal profile
Riffle	Relatively shallow, fast-flowing units with turbulent flow and coarser substrate; convex streambed shape
Ruffle	Dewatered transitional form between a riffle and a run, characterized by moderate depth, uneven bed topography, and broken-surface flow
Run	Uniform, moderate-velocity, and monotone unit with relatively smooth surface flow and uniform lateral depth profile with pronounced thalweg

). For this study, we conducted one detailed ADCP (SonTek M9) hydrometric survey and field HMU mapping using a mobile GIS application (TMap). To identify and map HMUs at three additional flows, we used low-elevation drone (DJI Matrice) aerial photography. We combined aerial photography and identified HMUs with depth and velocity distributions simulated using the hydraulic component of River2D software (V.0.95a) [17]. Hence, measured and modelled values for different flow rates were available for the source reaches, whereas only measured values were used for the target reach. Both sites were used once each as a source and a target.

To delineate HMU types on aerial photogrammetry and to assign the results from the hydrodynamic model (velocity and water depth calculated at the points of the model grid) to the HMUs in the study sites the ArcGIS Pro V.3.4 (ESRI) software was applied. The combination of the HMU layer with raster layers presenting surveyed and modelled hydraulic allowed the hydraulic results to be assigned to a specific HMU type.

From results of the hydraulic component of River2D model HMU_type, histograms of depth and velocity were built for each of the analyzed flows (q_j; j = 1, …, N_flow; N_flow = number of flows). For each interval of velocity or depth (bins of histograms), a set of tabulated functions of the frequency versus flow was developed for the source site (f_velocity,m(q_j) m = 1, …, NVI; NVI = number of velocity intervals; f_depth,n(q_j) n = 1, …, NDI; NDI = number of depth intervals). Finally, the same procedure was applied to determine the areal proportions of HMU types for each flow (f_HMUtype,k(q_j) k = 1, …, NHMU_type = number of HMU types).

At the target site, frequency distribution tables were developed for the measured flow q sub b. To minimize inaccuracies, it is preferred to model the flows at the target that are close to those measured at the source.

Figure 2 presents the applied principle in simplified form using example of one HMU type. This principle is applied to every HMU type and every bin of hydraulic distributions. It is described in more detail below.

To model a complete and flow-dependent set of velocity (g_velocity,n(q_j)) and depth (g_depth,m(q_j), for each HMU type, the following steps were taken:

(1) Interpolation of source data to the flow measured at target to have $f_{velocity,m}\left(q_b\right)$, $f_{depth,n}\left(q_b\right)$ $f_{HMU,k}\left(q_b\right)$ (m = 1, …, NVI; n = 1, …, NDI, k = 1, …, NHMU_type)

(2) at source site—calculation of flow driven frequency increments for each of the three parameters p (velocity, depth and HMU) and corresponding number of intervals i (m, n, k):

$$∆f_{p,i}=f_{p,i}\left(q_j\right)-f_{p,i}\left(q_b\right)$$

(3) at target site—calculation of the frequency:

$$g_{p,i}^0\left(q_j\right)=g_{p,i}\left(q_b\right)+∆f_{p,i}$$

$g_{p,i}^0\left(q_j\right)=0 \mathrm{if} g_{p,i}^0\left(q_j\right)<0$

$g_{p,i}^0\left(q_j\right)=1 \mathrm{if} g_{p,i}^0\left(q_j\right)>1$

(4) Normalization for each bin in histogram of p

$$g_{p,i}\left(q_j\right)={\displaystyle \frac{g_{p,i}^0\left(q_j\right)}{{\sum }_{1 }^l{g}_{p,i}^0\left(q_j\right)}}$$

Given that hydraulic conditions, modulated by discharge variability, exert a substantial influence on the spatio-temporal dynamics and typological composition of the hydromorphological units, the classification of HMU types was standardized across all modelled flows. Accordingly, HMU types recorded under low-flow conditions at the source reach but not detected during the target reach survey were systematically excluded from analysis.

3. Model Application on the Oder River

Data collected from two one-kilometre-long sections of the Oder River were used as a case study. The Oder River, extending more than 800 km and forming part of the border between Poland and Germany, drains a basin of 118.861 km², of which 6.1% lies in Czechia, 4.7% in Germany, and 89.2% in Poland (Figure 3) [23,24]. Its longitudinal profile (Figure 4) is characterized by a low and gradually decreasing slope (<1 m/km), and its mean annual discharge at the mouth is 575 m³s⁻¹. The river has been regulated for centuries for industrial navigation, resulting in a channel shortened by approximately 10%. It comprises an upper section with numerous weirs, a relatively undisturbed middle section, and a strongly engineered lower section flowing into the Szczecin Lagoon (Figure 4). Both study sites are situated in the middle course shaped by regularly spaced groynes.

The model was applied to two, one-kilometre-long reaches on the upper Oder River, located in Osiecznica and Szydłów (Figure 5). These reaches were selected from a total of nine locations sampled during an earlier study on the unimpounded section of the river. The distance between the two sites is around 10 km.

Both reaches are characterized by a relatively uniform hydromorphology of 100 m-apart spaced groin fields. Built in the early 20th century, these groynes were designed to deflect the thalweg away from eroding banks [25]. A century of uncontrolled biological succession has led to differences in hydrological processes and the spatial and temporal patterns of the river’s natural dynamics.

The Osiecznica site represents a relatively straight segment of the river with minimal natural meandering, while the Szydłów site is characterized by a more pronounced meandering morphology. These sites serve as good examples of morphological differentiation within the Oder River (Figure 6).

Data collection at these sites was carried out in 2022 under reference discharges of 185 m³/s (3.97 l/s/km²) for Osiecznica and 162 m³/s (3.47 l/s/km²) for Szydłów. Flow velocities and depths were precisely recorded using an Acoustic Doppler Current Profiler (ADCP), while additional drone surveys were conducted to produce high-resolution orthophotography maps. The drone flights were conducted with minimal temporal lag following the ADCP measurements, ensuring that the spatial representations closely reflected the actual conditions at the time of hydraulic data collection.

Based on the measured reference velocities and depths, a River2D hydrodynamic model [16] was developed to simulate specific velocity and depth values under different flows (1.07, 2.14, 3.97, and 5.36 l/s/km² at Osiecznica and 1.07, 2.14, 3.47, and 5.36 l/s/km² at Szydłów). To achieve accurate hydraulic representation, the model was implemented using a numerical mesh with a resolution of 5 × 5 m, proportionally adjusted to the size of the investigated river sections.

The hydrodynamic model was calibrated iteratively to reproduce the reference hydraulic conditions during which the initial field survey took place, corresponding to discharges of 162 m³/s for the Szydłów section and 185 m³/s for the Osiecznica section. The upper boundary condition of the model was the flow rate, while the water surface elevation defined the lower boundary condition.

Given that the riverbed of the Oder is predominantly composed of sand and silt, the substrate Manning’s roughness (n) incorporated into the model ranged from 0.01 [sm^−1/3] in the main channel to 0.1 [sm^−1/3] near the groynes structures. The calibration process also involved multiple iterations to assess numerical stability, solution convergence, and model sensitivity to variations in input parameters. Simulation results were used to create a mosaic of hydromorphological units for each modelled flow, allowing for the quantification of changes in the extent and composition of hydromorphological units, as well as the distribution of depths and mean column velocities.

To compare the MesoHydraulic and River2D model-based results, the relative areas of each HMU type and the associated relative frequency distributions of depth and velocity were compared for each flow. The Affinity Index Model [26] was used to assess the similarities between the distributions.

4. Habitat Model Parameterization

HMU mappings from both models were used to calculate habitat models for the fish community expected in the Oder River with Sim-Stream software (V. 8.0). The fish community structure has been transferred from the Vistula River, as established during the Adaptive Management of Barriers in European Rivers (AMBER) project [27]. The community consists of 8 Habitat Use Guilds (HUG) that use specific functional niches expected for a large river in Poland (Figure 7). Conditional Habitat Suitability Criteria for each HUG are presented in

Table 2. Conditional Habitat Use Criteria for the fish guilds occurring in the Vistula River. (Modified from [27]).

No	Fish Guilds	Depth [m]	Velocity [m s−1]	Choriotop Type	HMU Type	Covers
1	Highly rheophilic, intolerant species	0.50–1.5	0.3–1.2 (2.0 max)	Gigalithal, megalithal >40 cm, makrolithal 20–40 cm, mesolithal 6–20 cm, microlithal 2–6 cm, psammal, akal	riffle, ruffle, cascade, rapid, fast run, plunge-pool, pool, glide, sidearm	boulders, woody debris
2	Rheophilic benthic species, preferring sandy-gravel bottom substrate	0.3–2.0	0.3–0.15	megalithal >40 cm, makrolithal 20–40 cm, mesolithal 6–20 cm, microlithal 2–6 cm, psammal, akal, xylal, pelal, sapropel	riffle, ruffle, cascade, rapid, fast run, run, glide, plunge-pool, pool,	boulders, undercut banks woody debris, submerged vegetation
3	Rheophilic water column species, preferring sandy-gravel bottom substrate	0.5–4.0	0.15–0.7	mesolithal 6–20 cm, microlithal 2–6 cm, psammal, akal, debris, xylal	run, fast run, pool, plunge-pool	undercut banks woody debris, canopy shading, submerged vegetation
4	Limnophilic benthic species of moderate tolerance	0.25–2.5	0.0–0.5	microlithal 2–6 cm, psammal, pelal, akal, debris, xylal	run, pool, glide, sidearm	undercut banks woody debris, submerged vegetation, canopy shading
5	Intolerant, rheophilic benthic species, preferring detritus or pelal bottom substrate	0.20–0.50	0.15–0.5	detritus, pelal, psammal, sapropel	backwater, glide, pool, run	shallow margins, woody debris
6	Limnophilic lithophilic species of moderate tolerance	0.5–4.0	0.1–0.7	megalithal, macrolithal, mesolithal 6–20 cm, microlithal 2–6 cm, psammal, akal, debris, xylal	riffle, ruffle, run, glide, plunge-pool, pool, backwater, fast run	boulders, woody debris, submerged vegetation
7	Limnophilic phytophilic species of moderate tolerance	0.3–2.0	0.0–0.45	psammal, pelal, akal, debris, xylal	backwater, glide, pool, run, side-arm	submerged vegetation, woody debries, undercut banks, canopy shading
8	Benthic species of moderate tolerance	0.5–2.5	0.15–0.7	mesolithal 6–20 cm, microlithal 2–6 cm, psammal, akal, debris, xylal, pelal, detritus, phytal	run, glide, pool, backwater, side-arm	submerged vegetation, undercut banks, woody debris
9	Generalists—tolerant species	0.25–4.0	0.0–0.45	mesolithal 6–20 cm, microlithal 2–6 cm, psammal, akal, debris, pelal, sapropel, xylal	run, pool, glide, sidearm, backwater	woody debris, undercut banks, canopy shading

. These were applied to the HMU attributes of the Osiecznica and Szydłów reaches over the range of modelled flows to create habitat rating curves for each HUG. Further rating curves for the fish Community, calculated as the sum of effective habitat areas weighted by the proportion of the guild in the community, and for Generic fish, representing the superimposition of all effective habitats, were also calculated for both models.

A linear regression was applied to the incremental values taken from the rating curves of both models. The Community and Generic Fish curves were visually inspected to analyze whether their shapes could influence interpretation. To investigate differences in predicted habitat structure, we plotted cumulative proportions of available habitat for each HUG at modelled flows and used the affinity index to compare the distributions.

5. Results

5.1. Affinity Indices

Table 3. Affinity indices of depth and velocity classes aggregated across HMU, derived from hydrodynamic and statistical models for simulated flows at both sites.

Reaches	Specific Flow (l/s/km2)	HMU Area	Depth (cm)						Velocity (cm/s)								Average Ia
			<25	25–50	50–75	75–100	100–125	>125	<15	15–30	30–45	45–60	60–75	75–90	90–105	>105
Szydłów- Osiecznica	1.07	92%	93%	87%	64%	90%	84%	95%	98%	89%	91%	94%	97%	87%	81%	22%	84%
	2.14	92%	99%	92%	55%	81%	94%	89%	100%	95%	86%	89%	92%	96%	93%	89%	89%
	3.97/3.47	98%	100%	100%	100%	98%	98%	100%	100%	97%	97%	98%	99%	100%	100%	100%	99%
	5.36	95%	100%	100%	50%	93%	97%	92%	97%	94%	86%	82%	95%	69%	89%	99%	89%
Osiecznica -Szydłów	1.07	91%	96%	94%	70%	97%	77%	87%	98%	91%	91%	96%	97%	75%	93%	65%	88%
	2.14	90%	96%	98%	75%	89%	91%	80%	97%	93%	88%	96%	98%	98%	82%	52%	88%
	3.97/3.47	100%	98%	97%	99%	99%	98%	100%	100%	99%	97%	99%	99%	100%	100%	100%	99%
	5.36	96%	0%	50%	95%	74%	36%	97%	96%	95%	92%	95%	94%	96%	98%	99%	81%

presents the affinity indices comparing the distributions of HMUs, depth, and velocity classes obtained with River2D and Mesohydraulic models, for all flows. The average model performance is 90%, with the highest similarity observed for all parameters at the base flow. The lowest affinity occurs at the lowest flows. The only outlier is the high-velocity class (>1 m/s), which has an affinity value of 22%. This discrepancy is due to the MesoHydraulic model significantly overestimating the number of high velocities in Runs only. When broken down by HMUs, predictions for Pools and Riffles generally perform better than those for Runs and Backwaters (Figure 8).

5.2. Depth Distribution

The comparison of depth distributions between the River2D and MesoHydraulic models for the Szydłów → Osiecznica model application yielded the following percentage correlations for the analyzed discharges:

• For 1.07 l/s/km², the affinity index was 82.58%. The lowest similarity was observed in the Run unit (61.58%), while the highest was recorded in the Pool unit (99.78%).
• At 2.14 l/s/km², the average affinity was 81.85%. The Pool unit again exhibited the highest affinity (99.2%), while the Run unit had the lowest (62.15%).
• For the reference discharge of 3.97 l/s/km², the average affinity reached 99.05%. All hydromorphological units showed a high level of concordance, with the Pool unit achieving the highest affinity (99.99%) and the Backwater unit the lowest (98.3%).
• At the highest discharge of 5.36 l/s/km², the average affinity was 86.34%. All units, except for the Backwater (45.10%), demonstrated affinity above 90%.

When analyzing average percentage deviations in depth distributions across all discharges, the Backwater unit exhibited the greatest dissimilarity (69.93%), followed by the Run unit (79.08%). The Pool unit demonstrated the highest average affinity (99.31%), while the Riffle and Ruffle units showed average correlations of 93.27% and 95.68%, respectively.

The comparison of depth distributions between the River2D and MesoHydraulic models for the Osiecznica → Szydłów model application generally confirms previous findings while further emphasizing discrepancies in depth distributions among individual HMU types compared to the Szydłów → Osiecznica model verification. In the Osiecznica → Szydłów model verification, the following results were obtained:

• At 1.07 l/s/km², the average affinity index was 80.07%. The lowest value was recorded in the Run unit (67.56%), whereas the highest was recorded in the Pool unit (95.96%).
• For 2.14 l/s/km², the average affinity index reached 82.16%. The Pool unit again showed the highest values (99.46%), while the Run unit maintained the lowest (66.91%).
• For reference discharge of 3.47 l/s/km², the average affinity index was 97.79%. The highest concordance was observed again in the Pool unit (99.99%), while the lowest was observed again in the Run unit (95.59%).
• At highest analyzed discharge of 5.36 l/s/km², the average affinity index was 38.1%. The highest similarity was observed for the Ruffle (99.36%) and Pool (98.59%) units, while the Backwater unit exhibited a negative affinity index, which was therefore expressed as 0%. The Run unit also displayed negligible correlation, with an affinity index of only 0.81%.

When analyzing average affinity indices across all discharges cumulatively, in the Osiecznica → Szydłów model application, the Backwater unit once again emerged as the morphological type with the lowest affinity between the hydrodynamic and statistical model, with an average value of 48.2%. The Run unit showed an average affinity index of 57.7%, while the Pool achieved the highest (98.5%), followed by the Ruffle unit (93.7%). These results indicate that, in the reverse application scenario, the patterns of depth distributions among units resemble those in the Szydłów → Osiecznica case. Still, the discrepancies for the Backwater and Run units were further amplified.

5.3. Velocity Distribution

Velocity distributions for the Szydłów → Osiecznica model application also showed variations in affinities between the hydrodynamic and statistical models depending on discharge:

• For 1.07 l/s/km², the average affinity was 71.83%. The lowest affinity was observed in the Run unit (39.58%), while the highest was in the Backwater unit (94.56%).
• At 2.14 l/s/km² s, the average affinity increased to 87.66%. The highest affinity was recorded for the Pool unit (95.82%), while the Riffle and Ruffle units had the lowest values (79.37% and 83.56%, respectively).
• For the reference discharge of 3.97 l/s/km², the average affinity was 97.89%. The highest affinity was found in the Riffle unit (98.91%), while the lowest was in the Run unit (96.39%).
• At 5.36 l/s/km², the average affinity was 82.09%. The Riffle unit demonstrated the highest affinity (94.15%), while the Run unit showed the most significant deviation (62.52%).

Across all discharges, the Run unit exhibited the greatest dissimilarity in velocity distributions (70.96%), while the Backwater unit showed the highest affinity (95.02%). The Pool unit (91.43%), Riffle (87.38%), and Ruffle (79.56%) units followed in decreasing order of affinity.

In the case of the reverse Osiecznica → Szydłów model verification, the following affinity indices for velocity distribution were obtained:

• For 1.07 l/s/km², the average affinity index was 76.49%. The highest values were observed in the Pool unit (98.66%), whereas the lowest values were recorded in the Run unit (53.86%).
• At 2.14 l/s/km², the average affinity index was 75.92%. The Pool unit again showed the highest values (97.49%), while the Run unit once more exhibited the lowest values (54.33%).
• For the reference discharge of 3.47 l/s/km², the average affinity index reached 98.31%. The highest value was recorded for the Backwater unit (99.3%), while the lowest values were once again recorded in the Run unit (96.72%).
• At the highest analyzed discharge of 5.36 l/s/km², the average affinity index was 91.31%. The highest similarity was observed in the Ruffle unit (96.6%), whereas the lowest was in the Pool unit (84.43%).

When analyzing the average affinity index across HMU types over all discharges, the Pool unit emerged as the morphological type with the highest average values (94.88%), followed by the Backwater unit (94.4%). The Ruffle unit reached an average value of 78.14%, while the lowest average was again recorded in the Run unit (74.62%). Thus, the results for the Osiecznica → Szydłów model application are very similar to those obtained for the Szydłów → Osiecznica model application and verification across all HMU types and analyzed discharges.

5.4. Hydraulic Deviation Matrices

To evaluate the model’s application performance under hydraulic conditions between the source and target locations, deviation matrices were constructed to quantify differences between the relative frequency distributions of depth and velocity classes produced by the MesoHydraulics model and the reference values simulated with River2D. Matrices were generated for all combinations of discharges and identified HMU types for both directions of model application (Szydłów to Osiecznica and Osiecznica to Szydłów). In addition, matrices of average deviation across all discharges were computed to identify systematic patterns of divergence. The resulting Δp values (Mesohydraulics-River2D) ranged from −1 to +1, with negative values indicating underestimation and positive values indicating overestimation of the relative frequencies by the MesoHydraulics statistical model relative to the River2D hydrodynamic reference model.

5.4.1. Depth Szydłów → Osiecznica

A comparison of depth-class distributions between MesoHydraulics and River2D in the Szydłów to Osiecznica model application reveals generally minor differences, with most HMU-specific frequency deviations remaining close to zero (±0.05) (Figure 9a,c). The most significant deviations were observed in the Backwater and Run units.

• Backwater—model deviations were particularly noticeable within the 50–75 cm class, where MesoHydraulics consistently underestimated frequencies (average Δp ≈ −0.42)
• Run—model shows deviations in the same depth class as in the Backwater unit, with overestimation of average Δp ≈ +0.2

Across the remaining HMU types (Pools, Riffles, Ruffles), deviations were minimal and mostly below ±0.05, indicating stable predictive performance of the MesoHydraulics model.

5.4.2. Depth Osiecznica → Szydłów

In the reverse model application, somewhat larger deviations in depth distributions were observed within individual depth classes. Yet, the same general pattern persisted, with underestimation in Backwater and overestimation in Run units (Figure 9b,d).

• Backwater—model underestimated frequencies across several depth classes (<25, 25–50, and 100–125 cm), with Δp ranging from −0.22 to −1.00, and a maximum average deviation of Δp ≈ −0.26 in the shallowest class.
• Run—model overestimation occurred at several discharges with Δp reaching +1 in the highest flow simulations (within the same depth range as underestimation of Backwaters). The maximum average deviation of Δp ≈ +0.26 was observed in the shallowest class.

Pools, Riffles, and Ruffles again exhibited minimal differences (typically Δp ≈ ±0.02).

Figure 9. Deviation depth matrices for model application between study sites. (a) Model application across all discharges from Szydłów to Osiecznica. (b) Model application across all discharges from Osiecznica to Szydłów. (c) Average deviation matrix across discharges for the Szydłów to Osiecznica model application. (d) Average deviation matrix across discharges for the Osiecznica to Szydłów model application.

Figure 9. Deviation depth matrices for model application between study sites. (a) Model application across all discharges from Szydłów to Osiecznica. (b) Model application across all discharges from Osiecznica to Szydłów. (c) Average deviation matrix across discharges for the Szydłów to Osiecznica model application. (d) Average deviation matrix across discharges for the Osiecznica to Szydłów model application.

5.4.3. Velocity Szydłów → Osiecznica

Hydraulic deviations between MesoHydraulics and River2D models (Figure 10a,c) across velocity classes were also minor for most matrices, with Δp ≈ ±0.05. The most significant discrepancies, with underestimation in the Ruffle units and overestimation in the Run units, were observed at higher modelled flows.

Ruffle—in class < 105 cm/s, MesoHydraulics on average underestimated frequencies (Δp ≈ −0.11). Moreover, the Ruffle unit exhibited a tendency toward underestimation in the highest velocity classes at higher modelled discharges and slight overestimation in intermediate velocity classes at higher discharges.

Run—model once again showed overestimation (mean Δp ≈ +0.18) in the highest velocity class. This tendency was particularly pronounced for simulated low flows, with overestimation up to +0.78, corresponding to simultaneous underestimation in the Riffle and Ruffle units.

For all other HMU types, deviations were neither considerable nor consistent, without a clear directional trend across all analyzed discharges.

5.4.4. Velocity Osiecznica → Szydłów

In the reverse, Osiecznica → Szydłów model application, deviations across most velocity classes remained very small (most of ≈ ±0.05) (Figure 10b,d).

• Ruffle—the largest underestimations once again occurred in Ruffle units at the highest velocity classes and under low simulated discharges, with Δp values up to −0.48 and maximum mean overestimation of Δp ≈ −0.07 in upper-intermediate classes.
• Run—model overestimates velocity distribution within the same velocity classes as in the case of underestimation in the Ruffle unit, with Δp up to +0.48, and maximum mean overestimation Δp ≈ +0.08 in upper-intermediate velocity classes.

Other units, including Pools and Backwaters, showed minimal deviations across all velocity classes, without a discernible directional pattern across the analyzed discharges.

Figure 10. Deviation velocity matrices for model application between study sites. (a) Model application across all discharges from Szydłów to Osiecznica. (b) Model application across all discharges from Osiecznica to Szydłów. (c) Average deviation matrix across discharges for the Szydłów to Osiecznica model application. (d) Average deviation matrix across discharges for the Osiecznica to Szydłów model application.

Figure 10. Deviation velocity matrices for model application between study sites. (a) Model application across all discharges from Szydłów to Osiecznica. (b) Model application across all discharges from Osiecznica to Szydłów. (c) Average deviation matrix across discharges for the Szydłów to Osiecznica model application. (d) Average deviation matrix across discharges for the Osiecznica to Szydłów model application.

5.5. Habitat Model Performance

Figure 11 and Figure 12 represent habitat rating curves for the fish community and HUGs, respectively, calculated for the entire river section with both models. Community curves follow very similar patterns (R² = 0.98) with an inflexion point around 1 l/s/km². The MesoHydraulic model slightly overestimates habitat area for both community and generic fish.

Only four guilds are showing a substantial amount of suitable habitat. These are the Water column, Generalists, Sandy-muddy bottom, and Rheophylic sandy-gravel bottom. The ratings curves have very similar shapes and highly correlated values with R² = 0.97, 0.98, 0.95, 0.86, respectively. Still, the MesoHydraulics model systematically overestimates available habitat areas. Habitat for the remaining guilds is below one percent of the channel area.

In terms of habitat structure, both models show a very similar distribution of habitat among the HUGs. Figure 13 presents the distribution for four simulated flows. The affinity index is 0.88, 0.93, 0.91, and 0.91, respectively, from the lowest to the highest flow.

6. Discussion

This work is a first step towards a much larger goal of building our capability to predict the distribution of HMUs in a river based on singular surveys and knowledge of how their hydraulic patterns evolve with changing flow conditions. The results of this study offer insights into the similarity between the hydrodynamic and statistical models for depths, velocities, and areas of hydromorphological units for application in the MesoHABSIM model. Except for shallow depth at the highest flow, the model results for both sites are quite similar. On average, the base discharge and similar flows exhibited the highest affinity between the models. In contrast, discharges at both ends of the tested spectrum showed greater discrepancies, highlighting the model’s limitations in accurately predicting distributions under low or high flow conditions (

Table 4. Average affinity indices of depth and velocity classes aggregated across HMU derived from both sites.

Specific Flow (l/s/km2)	HMU Area	Depth (cm)						Velocity (cm/s)								Average Ia
		<25	25–50	50–75	75–100	100–125	>125	<15	15–30	30–45	45–60	60–75	75–90	90–105	>105
1.07	92%	94%	90%	67%	94%	81%	91%	98%	90%	91%	95%	97%	81%	87%	44%	86%
2.14	91%	97%	95%	65%	85%	93%	84%	99%	94%	87%	92%	95%	97%	87%	70%	89%
3.97/3.47	99%	99%	99%	99%	98%	98%	100%	100%	98%	97%	99%	99%	100%	100%	100%	99%
5.36	96%	50%	75%	73%	83%	67%	94%	97%	95%	89%	88%	94%	82%	94%	99%	85%

).

Based on the analysis of the deviation matrices, several consistent and systematic patterns were identified in the performance of the MesoHydraulics model across HMU types, hydraulic classes, and model application directions and patterns. The results indicate that the model successfully reproduces the general distributional patterns of depth and velocity for most HMU types and analyzed discharges, while also revealing characteristic systematic shifts that depend on hydraulic classes, HMU types, and model application directions.

The most pronounced deviations occurred in intermediate-depth classes (50–75 cm) and intermediate-to-high velocity classes (75–100 cm/s). In the Szydłów → Osiecznica model application direction, the model consistently underestimated Backwater frequencies in the depth domain and Riffle and Ruffle frequencies in the velocity domain. Conversely, the Run unit exhibited systematic overestimation within the same hydraulic classes, effectively compensating for the reductions observed in other HMU types. This model behaviour suggests that the Run unit functions, in a statistical sense, as a form of hydraulic default, or an inherently broad category that absorbs redistributed areas when the finer morphological and hydraulics characteristics of more complex HMU types are smoothed during the model application process.

In the opposite direction of the model application (Osiecznica → Szydłów), a similar and in some cases more pronounced pattern emerged. The model again systematically overestimated Run frequencies, while lower depths for Backwater and velocity classes for Ruffle tended to be underestimated, particularly at lower simulated discharges.

The mean deviation matrices demonstrate that these error patterns occur consistently across nearly all discharges, showing characteristic positive or negative shifts depending on the HMU type and the direction of the model application. This confirms the stability of the observed model behaviour and the hydraulic and statistical consistency of the MesoHydraulics approach.

The findings underscore the significant role of hydro-morphological unit complexity in determining the correlation between hydrodynamic and statistical models. As noted by Brierley & Fryirs [28] and Dufour & Piégay [29], temporal analysis of varying discharges acknowledges the dynamic nature of river systems, which respond to a range of factors across both spatial and temporal scales. Consequently, the morphological and dynamic complexity of the units is a key factor influencing prediction variability. The Pool unit generally emerged as the least sensitive to model choice across all analyzed conditions, while the Backwater and Run units exhibited greater differences, particularly under extreme discharges.

Given its adaptability to a wide range of depths (including significant proportions of 50–75 cm range), the Backwater unit exhibited pronounced spatial discrepancies in depth distributions. Yet, the morphological complexity of this unit is acknowledged by Wheaton et al. [9], who propose that it may be linked to concavity and the formation of pools in secondary and main channels, or to convexity and the development of backwater bars. As a result, the two distinct morphological configurations of Backwaters and Pools are associated with different depth distribution patterns. Consequently, the Backwater unit can include a range of depth conditions and is further influenced by external factors such as surrounding topography and hydrodynamic conditions, including the presence of groynes.

It is important to note that the default-like behaviour of the Run unit observed in the deviation matrices reflects a statistical effect of the transfer algorithm, primarily due to data distribution rather than its intrinsic geomorphological properties. Conversely, discrepancies in the Run unit’s depth and velocity distributions can also be attributed to temporal variability in hydraulics. The morphology of this unit makes the depth and velocity particularly sensitive to changes in flow. Fryirs & Brierley [30] and Gurnell et al. [31] further substantiate this by differentiating this unit as a transitional form between a riffle and a pool, governed by depth-velocity relationships and the sediment transport capacity of the channel morphology. Given its high dynamism and morphological variability, the differences between the hydrodynamic and statistical models for this unit were predictably more pronounced.

Overall, the study indicates that model accuracy is not solely dependent on hydrodynamic flow conditions, but also on the specific morphological and hydrodynamic characteristics of individual hydromorphological units. Enhancing model precision requires a more detailed consideration of these complexities, particularly in highly variable units such as Run and Backwater.

A statistical hydraulic model that was developed integrates hydrodynamic simulation results to predict changes in velocity, depth, and the spatial distribution of hydromorphological units. This approach enables more rapid and efficient analysis of new flow scenarios while providing detailed insights into system dynamics under varying hydrological conditions. The entire methodology is built on the synergy between precise field measurements and advanced modelling techniques. This combination facilitated the quantification and prediction of changes in the river’s morphological mosaic and flow dynamics, with particular emphasis on predicting changes under different hydrological scenarios.

The results of this research indicate that the MesoHydraulic model estimates the spatial distribution of hydromorphological patterns almost as well as the hydrodynamic model. The average affinity index of 90% is quite impressive. The study also demonstrates that the model accuracy varies with channel morphology, a fact that holds for other hydrodynamic models as well [32]. It suggests that the morphological modifications of the Oder River may influence such strong model performance. In more natural environments with higher natural variability, the model may perform less effectively. In the context of habitat modelling, the key question is how much the modelling error impacts the habitat modelling results.

Despite the potential inaccuracies described above, the habitat model based on MesoHydraulics and River2D yielded hydraulics that provided very similar results. Specifically, when analyzed at the community level, there is a minimal difference between the models that cannot lead to different conclusions. The only systematic difference is that the MesoHABSIM model, based on MesoHydraulics, seems to overestimate the amount of effective habitat available for the fish community. From an environmental protection perspective, it is a more conservative result, indicating the need for higher habitat availability. Here, it is worth noting that, for example, in defining environmental flows, the model results are typically interpreted by observing the relative change in habitat area between the flows. Therefore, unless the models are used interchangeably, this difference in modelling results should not affect interpretation. In terms of habitat structure, no significant differences could be discovered between the models. Accordingly, we conclude that MesoHydraulics is well-suited for habitat modelling within the MesoHABSIM framework. Data collection could be reduced to a single hydraulic survey across multiple sites and a repeated survey, or to a hydrodynamic model of only one or two. Considering also that the need for data precision to build a hydrodynamic model is much higher than for the MesoHABSIM survey, application of the model could significantly reduce the effort necessary to gather field data and model hydraulic patterns. One downside, though, is that the statistical modelling results are not spatially specific and therefore cannot be used to draw maps of habitat distributions for simulated flows. For the majority of applications, this is, however, not essential.

It should be noted that the conceptual foundation of the model assumes that hydraulic responses to changes in discharge are sufficiently consistent among hydromorphologically comparable river reaches to allow the transfer of distribution functions from one location to another. For this reason, the present study was deliberately designed to test this assumption under controlled and comparable conditions, using two adjacent regulated reaches of the same river. The high degree of hydraulic similarity resulting from the uniform regulation system provided an ideal setting for isolating the behaviour of the transfer algorithm from broader morphological and hydraulic variability. Although the achieved average affinity index of 90% supports the validity of this assumption within a homogenous and regulated river system, additional investigations across rivers with differing morphological and hydraulic characteristics are necessary to confirm the broader transferability of the approach and the robustness of the model. Future research should therefore examine hydraulic responses within HMU in rivers with various degrees of alteration, gradient, and morphological and hydraulic patterns. Such comparisons may also serve as a basis for integrating machine-learning techniques and remote-sensing data for the prediction of the hydraulic patterns [33,34].

7. Conclusions

The main conclusions from the study are as follows:

• Model Effectiveness: The MesoHydraulic model demonstrated considerable effectiveness in simulating hydromorphological distributions across different flow rates, achieving an average affinity index of 90% when compared to the hydrodynamic model River2D. This highlights the model’s potential as a reliable tool for river management and especially for habitat assessments, for which the obtained accuracy is acceptable.
• A systematic deviation of the model was detected within the depth interval of 50–75 cm, where the model exhibited noticeably higher predictive uncertainty relative to other depth classes. An analogous pattern was identified for velocity distributions, with more pronounced systematic discrepancies occurring in the higher velocity classes under lower simulated discharges. Although the current dataset does not allow for an unambiguous determination of the underlying cause, these deviations likely reflect a combination of the limited empirical value range within these intervals and the discretization scheme applied in constructing the hydraulic frequency histograms. Future model refinements should therefore incorporate adaptive (non-uniform) class binning informed by HMU hydraulic data density, enhanced sampling of mid-range depth classes, and validation across a broader set of river reaches to improve the stability and predictive reliability of depth and velocity distribution estimates, especially in Backwater and Run units.
• Flow Dependency: The model performs most accurately at base flows and flows similar to those measured, showing higher correlations under these scenarios. However, accuracy decreases for low or high flow conditions, indicating limitations in the model’s ability to predict accurately under extreme flow scenarios.
• Variation among HMUs: Different HMUs showed varying levels of predictive accuracy. The Pool unit consistently showed high correlation in both depth and velocity across all discharges, while the Run and Backwater units displayed greater variability, particularly under extreme conditions. This underscores the importance of accounting for the specific morphological and hydrodynamic characteristics of each HMU to enhance model accuracy.
• Morphological Influence: The model’s accuracy is influenced by the river’s morphology. The study suggests that in rivers with fewer artificial modifications to the channel and greater natural variability, the model’s performance might be less reliable. This highlights the need for cautious application of the model in more naturally variable river systems.
• Implication for habitat modelling: Test application of MesoHydraulics in MesoHABSIM model on Oder River documented high correlation of the results with those computed with a model built upon River2D obtained hydraulics. Hence, MesoHydraulics is well-suited for habitat modelling within the MesoHABSIM framework.
• Implications for River Management: The findings suggest that the MesoHydraulic model can be a valuable tool for environmental flow assessments and river restoration planning, particularly in regulated rivers where hydromorphological patterns are relatively consistent. It provides a method for estimating habitat conditions with reduced fieldwork effort, potentially saving both time and resources.
• Future Directions: Further research should investigate how modeling errors affect habitat modelling results and expand the methodology to different rivers or reaches with diverse morphological characteristics. The study also emphasizes the need for model optimization, particularly under extreme flow conditions, and the potential benefits of integrating these models into broader environmental assessments.
• Limitation on Geographic Scope: The study was conducted on relatively close reaches of the same river, indicating that the model’s accuracy might be influenced by similar hydraulic conditions due to similar river regulation practices. Extending the study to different rivers would provide valuable insights into the model’s broader applicability.