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Vegetation on the riverbed, banks and flooding areas of watercourses significantly affects energy losses. Energy dissipation takes on different values depending on whether the vegetation is emergent or submerged, rigid or flexible. Many models have been proposed in the scientific literature for its evaluation.
Vegetation is an important issue on the viewpoint of catchment hydrology ^{[1]}^{[2]}^{[3]}, since rain drops interception, evapotranspiration, infiltration are elements to consider in surface and subsurface water balance. Moreover, riparian vegetation plays a key role both on the ecologic and habitat viewpoints, as well as a source of biodiversity. Indeed, vegetation prevents fertilizers and pollutants from getting to the watercourses^{[4]} and, because of the effect on landscape, has a significant recreational function.
On a more strictly technical viewpoint, riparian vegetation interacts with water flow, with effects both on the bank stability and on the river hydraulics. Vegetation acts on bank stability since it mechanically strengthens the soil because of the presence of roots^{[5]}^{[6]}^{[7]}^{[8]}; moreover, it reduces the soil water content because of evapotranspiration with the consequence of reducing interstitial pressures ^{[9]}.
As to river hydraulics, vegetation clutters up part of the river crosssection^{[7]}^{[10]}^{[11]}, increases the roughness and reduces the velocity; all this results in increased water levels and reduced water conveyance. Moreover, while the smaller average velocity on one hand reduces the erosion of riverbed and banks, on the other one increases the sediment deposition, what makes the water crosssections smaller and raises flooding risk. On the scale of the hydrographic network, the general velocity reduction influences the travel time of water particles, making easier the peak flow control^{[12]}^{[13]}.
Therefore, one cannot know in advance the general effect of vegetation, but every case should be considered singularly, using proper procedures. Indeed, this effect depends on both the hydraulic and mechanical properties of the water crosssection, as to of the present vegetation, that may be different according to species, phenological stage, age and, possibly, maintenance.
Usually, in the literature the vegetation is considered as rigid or flexible, and according to the water level, as emergent or submerged. Flexible vegetation refers to grass, reeds and shrubs, or, when speaking about trees, to the branch and leaf system. Combinations of the above categories, really found in natural streams and channels, are still difficult to treat.
In the following we will present the methods found in the literature, allowing estimation of flow resistance coefficients to input into models for flood simulation, based on different types of vegetation in the river banks and floodplains.
According to Chow^{[14]}, the resistance to flow in artificial channels and watercourses is influenced by several factors, i.e. size and shape of the grains of the material forming the wetted perimeter, vegetation, silting and scouring, , etc.
As it is well known the resistance to flow can be expressed by the DarcyWeisbach f friction factor, the Chézy’s C or the GaucklerStrickler k velocity coefficients and the Manning n roughness coefficient; the relation among these coefficients is the following
(1) 
where V is the mean flow velocity, R the hydraulic radius, J the energy line slope and g the gravity acceleration.
The contribution of vegetation to the roughness coefficient can be evaluated by means of descriptive approaches, photographic comparison approaches or by analytical methods.
In these methods, one roughness coefficient is chosen on the basis of the class to which the river reach belongs. Among the descriptive methods, the best known is the Chow’s one^{[14]}. The author gives, for every class of channels, the minimum, average and maximum values of Manning n coefficient, warning that when the channel is artificial, the average values should be used in case of good maintenance only. The photographic comparison approach consists in evaluating the Manning coefficient of a given river reach on the basis of similarity with the pictures of other similar cases, for which the coefficient was estimated in ordinary or flood conditions.
When the vegetation is made up by trees, in an analogy of the resistance to flow due to immersed bodies, the roughness coefficient is expressed as a function of the drag force exerted by the flow on the body, depending then on the number of trees, their arrangement, the diameters of their trunks and, where appropriate, the branch system. Usually, in the laboratory tests, the rigid vegetation is simulated by cylinders.
In case of one isolated vertical cylinder whose axis is orthogonal to the flow direction the resistance to flow is expressed by the drag force F_{D}, computed as
(2) 
where ρ is the water density, h is the depth of the immersed part of the cylinder, V is the approach velocity and C_{D} is a drag coefficient. C_{D} is a function of stem Reynolds number computed by means of the approach velocity V and the cylinder diameter D, , being ν the water kinematic viscosity.
When the cylinder is a part of a group of elements (see Fig. 1), one cannot ignore that the longitudinal and transversal interference make considerably more difficult the study of the resistance to flow^{[15]}^{[16]}^{[17]}. In Fig. 1 x is the streamwise coordinate, z is the vertical coordinate above the river bed, u_{z} is the local timeaveraged velocity, u is the mean velocity along the vertical, h is the water depth and h_{v} the vegetation height.
Figure 1. Side view of emergent vegetation and velocity profile.
To find the values of C_{D} in case of sparse emergent arrays, both experimental tests and numerical simulations have been carried out, with the vegetation arrangements defined before as linear, or staggered, or random. Among the first studies, we will cite only Petryk^{[18]}, Li and Shen^{[15]} and Petryk and Bosmajian^{[19]}.
Petryk and Bosmajian^{[19]}, to determine the Manning coefficient in a vegetated channel, implement the momentum equation for a reach, imposing that be equal to zero the vector sum of the weight of the control volume, projected on the bed direction, plus the contour resistance, plus that opposed by the tree trunk; they conclude with defining the overall Manning coefficient n as a function of the value relative to the soil, n_{b}, and the one relative to vegetation drag coefficient C_{D}, by writing
(3) 
where L is the reach length, A the area of the water crosssection, ΣA_{i} the area opposed by the vegetation to the flow. The authors consider equal to 1 the drag coefficient C_{D}. For the estimation of C_{D} several expression have been proposed^{[20]}^{[21]}^{[22]}^{[23]}^{[24]}^{[25]}.
In the case of submerged vegetation, very often the profile is schematized as only two interacting zones (twolayer approach): the vegetation layer, containing the cylindrical elements representing the vegetation, and the surface layer, above them, up to the flow surface (Fig. 2). In Fig. 2 u_{s} is the mean velocity along the vertical in the surface layer, and u_{v} is the mean velocity along the vertical in the vegetated layer.
Figure 2. Side view of submerged vegetation and velocity profile
Rigid submerged vegetation has been the subject of a large number of investigations^{[7]}^{[26]}^{[27]}^{[28]}^{[29]}^{[30]}^{[31]}^{[32]} and comparisons^{[33]}^{[34]}^{[35]}^{[36]}^{[37]}^{[38]}. Some researchers provided the average velocity values in the two layers while others derived the velocity distribution and the average values^{[7]}^{[28]}^{[29]}^{[31]}. In the vegetation layer the streamwise velocity is usually considered constant with the flow depth^{[27]}^{[31]}, while in the surface layer various expressions were adopted for the velocity distribution^{[36]}: the logarithmic theory^{[26]}^{[28]}^{[31]}, the Kolmogorov theory of turbulence^{[30]}, the genetic programming^{[27]}, the representative roughness height^{[32]}^{[39]}.
Starting from the velocity distribution it is possible to evaluate the Manning coefficient^{[27]}^{[30]}^{[31]}^{[39]}, and some authors^{[11]}^{[40]} have proposed expressions for both submerged and emergent rigid vegetation.
Sometimes during a flood event, as the discharge increases, the vegetation can lay over or be removed^{[41]}^{[42]}^{[43]}^{[44]}, which leads to a reduction in roughness and to an increase in the flow capacity through the section; therefore the peak flow, which could occur later, takes lower watersurface elevations than it would have had in the case of upright vegetation. To determine under what conditions the vegetation flattens, Phillips et al.^{[41]} referred to the stream power, defined as SP=gRJV, and to the resistance of the vegetation characterized by an index defined as the susceptibility index of the vegetation. This index is given by the product of the vegetation flexibility factor, the vegetation blocking coefficient, the vegetation distribution coefficient and, finally, the flow depth coefficient. For each type of vegetation it is possible to determine the minimum value of the stream power beyond which the vegetation is layover.
For rigid vegetation, the action of the flow varies with the squared velocity. In case of flexible vegetation, this is not true, since the vegetation reconfigures by reducing the area projected on a plane orthogonal to the flow direction and aligning the leaves with it. The relationship between flow velocity and drag force was expressed as , where the Vogel exponent b^{[17]}, is a measure of the plant reconfiguration. When is b = 1, the drag force varies linearly with the velocity. A linear increase of drag force with the flow velocity was observed for flexible plants by direct measurement in prototype scale by Armanini et al.^{[45]}.
The friction factor due to the vegetation, f_{v}, in a reach of length L is
(4) 
We will first analyze the studies in the case of submerged flexible vegetation and then those related to the nonsubmerged vegetation.
The first studies on submerged flexible vegetation (Fig. 3) are related to the design of irrigation canals^{[46]}. In Fig. 3 h_{vf} is the bent vegetation height. Since the resistance depends on the curvature of the vegetation, the link between the Manning coefficient, n, and the product of velocity, V, and hydraulic radius, R, was identified on an experimental basis. This relationship depends on the type of vegetation and is practically independent on the slope of the canal and its shape. Five experimental curves have been obtained relating the Manning coefficients, also called delay coefficients, with the product VR classified as very high, high, moderate, low or very low and identified with the letters A, B, C, D and E.
Figure 3. Side view of submerged flexible vegetation.
According to Kouwen et al.^{[47]} the friction factor in the case of submerged flexible vegetation can be represented through a semilogarithmic function of the relative roughness, defined as the ratio of the deflected plant height, h_{vf}, to the flow depth
(5) 
where the coefficients C_{0} and C_{1 }depend on u_{*}/u_{*c} with
(6) 
where M is the stem count per unit area, E is the modulus of elasticity and I the second moment of the crosssectional area of the stems. The product MEI is defined as flexural rigidity. The deflected height depends on the drag exerted by the flow and the flexural rigidity of the vegetation.
Studies on nonsubmerged flexible vegetation have been carried out, among others, by Kouwen and Fathi Moghadam^{[48]}, and Västilä et al.^{[49]}.
Kouwen and Fathi Moghadam^{[48]}, performed laboratory experiments on four different types of conifers both in water and in air; the authors, on the basis of dimensional analysis and a series of symplifyng hypotheses proposed to calculate the friction factor as the following equation

(7) 
where ξ takes into account the deformation of the plant, and E is the modulus of elasticity. The term ξE is called vegetation index, it is unique for each species and is obtained from the resonant frequency, mass and length of a tree^{[48]}^{[50]}.
Recently, Västilä et al.^{[49]} proposed to calculate the friction factor, f_{v}, as

(8) 
where A_{c}_{ } represents a characteristic area of plants, A_{b}_{ }is the bed area related to a plant, C_{Dχ} is a speciesspecific drag coefficient, χ depends on the area , and V_{χ }is the lowest velocity used in determining χ. As to the area A_{c}, Västilä et al.^{[49]} compared three areas: the first one, A_{L}, is obtained by means of the leaf area index (LAI), (defined as the ratio between the onesided leaf area and the ground area), the second one as the area projected onto a plan orthogonal to the flow direction when the plant is under the flow action (A_{p}), and the third one as the area projected onto a plan orthogonal to the flow direction when the plant is on free air (A_{0}).
For a detailed analysis of the flow fields and turbulence characteristics one can refer to measurements with particle image velocimetry system (PIV) or acoustic Doppler velocimeter (ADV) probe or, furthermore, on numerical simulations, more or less detailed depending on the flow cases at hand^{[22]}^{[51]}^{[52]}^{[53]}^{[54]} [22,5154]. An excellent review about the numerical models utilized for the analysis of the interaction between flow and vegetation is due to Stoesser et al.^{[55]}.
RANS models are operated on coarse grids and the drag due to vegetation is accounted for through additional source terms in the governing equations^{[56]}^{[57]}^{[58]}^{[59]}^{[60]} [5660]. The coherent structures that form downstream to the cylinders or over the vegetated layer in the case of submerged vegetation can be obtained by means of LES approach^{[61]}^{[62]}^{[63]}. In the latter simulations, one can explicitly represent the plants by inserting in the mesh some blocked cells representing the vegetation. Stoesser et al.^{[61]} [61] executed a LES with reference to a companion experiment of Liu et al.^{[64]} related to rigid emergent vegetation, obtaining interesting results. It should be noted that numerical simulations have been used not only for comparisons with companion experiments, but also in real situations. As an example^{[55]}^{[65]}, a RANS simulation was carried out to mirror a flood event of the Rhine river with a return period of 100 years.
Riparian vegetation, in particular that located on flood areas, has very heterogeneous characteristics both from a spatial and temporal point of view. These characteristics must be adequately included in the hydraulichydrological models. Conventional groundbased monitoring is often unfeasible as these techniques are timedemanding and expensive^{[66]}, especially for large areas and when they are inaccessible. New opportunities are offered by remote sensing, which has developed considerably in recent decades and has been increasingly used in the environmental field. Some reviews have addressed the use of remote sensing in fluvial studies^{[67]}^{[68]}^{[69]} and, in particular, for mapping riparian vegetation and estimating biomechanical parameters^{[70]}.
Remote sensing is based on satellite images (digital or radar) or aerial platforms (LiDAR (Light Detection and Ranging) and ortophotography). Digital satellite images, in the last decade, have reached a definition similar to those of orthophotos (the pixel sizes in the sensors Quickbird and Ikonos are equal, respectively, to 0.6 m and 1 m) making it possible their application to riparian areas that, very often, are of limited size. Image classification is the process of assigning individual pixel or groups of pixels to thematic classes
The vegetation hydrodynamic maps are also able to well describe the equivalent Manning’s roughness coefficient^{[71]}.
One of the biggest limitations of optical sensors is the inability to penetrate the cloud system. Radar systems are microwavebased and do not depend on the cloud system and are particularly useful during flooding events, that usually occur in the presence of a cloud cover, allowing monitoring of the timing and spatial extent of flooding. Backscatter increases with biomass and this makes it difficult to apply radar sensors in floodplain areas which are usually characterized by very dense vegetation.
Satellite images provide information on the spatial variability of vegetation but do not provide information about its vertical structure. LiDAR technology provides information on the threedimensional structure of vegetation. Laser scanning (LS) is employed in terrestrial (TLS), airborne (ALS) and mobile (MLS) platforms. The airborne laser scanner (ALS) provide accurate information of forest canopy and ground elevations producing a digital terrain model and a digital surface model. The difference between the digital surface model and the digital terrain model gives the tree heights.
Currently research on the interaction between vegetation and flow is focusing on a more correct assessment of the action exerted by the shear stress^{[72]}^{[73]}, on velocity distribution^{[74]}^{[75]}, on sediment transport^{[76]}^{[77]}^{[78]}^{[79]}^{[80]}^{[81]}^{[82]}, on finitesized vegetation patches^{[83]}^{[84]}^{[85]}^{[86]}^{[87]}^{[88]}^{[89]}^{[90]}, on the interaction between jets and vegetation^{[91]}^{[92]}, on processes of transport and dispersion^{[93]}^{[94]}^{[95]}, on evolution of patches of vegetation^{[96]} and on oneline emergent vegetation^{[97]}. New opportunities seem to be offered by the use of remote sensing in fluvial studies^{[67]}^{[68]}^{[69]} and, in particular, for mapping riparian vegetation and estimating biomechanical parameters^{[70]}.