Semi-distribution based on hydrological response units

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Full list of identified hydrological modelling R packages

A first list of packages with their related documentation was established following the CRAN hydrological Task View (Zipper et al., 2019) and additional searches on GitHub and the R-Forge. This list might not be exhaustive. We report it here along with the short descriptions provided by the authors of each package. The bibliographic references mentioned below correspond to the versions of the packages that were last used. (*: only available on GitHub and not on the CRAN).
– airGR (Coron et al., 2017, 2019): hydrological modelling tool that includes several conceptual rainfall-runoff models (GR4H, GR4J, GR5J, GR6J, GR2M, GR1A), a snow accumulation and melt model (CemaNeige, Valery´ et al., 2014) and the associated functions for their calibration and evaluation.
– airGRteaching (Delaigue et al., 2018, 2019a): add-on package to the airGR package that simplifies its use and was made for hydrology teaching purposes.
– dynatopmodel (Metcalfe et al., 2015, 2018): an R implementation and enhancement of the Dynamic TOPMODEL semi-distributed hydrological model. Includes some preprocessing, utility and routines for displaying outputs.
– Ecohydmod (Souza et al., 2016; Souza, 2017): simulates the soil water balance (soil moisture, evapotranspiration, leakage and runoff), rainfall series by using the marked Poisson process and the vegetation growth through the Normalized Difference Vegetation Index (NDVI).
– EcoHydRology (Fuka et al., 2018): provides a flexible foundation for scientists, engineers, and policy makers to base teaching exercises as well as for more applied use to model complex eco-hydrological interactions.
– fuse (Vitolo et al., 2016): implementation of the Framework for Understanding Structural Errors (FUSE) of hydrological modelling. It is based on the Fortran version described in Clark et al. (2008). The package consists of two modules: a soil moisture accounting module and a Gamma routing module (Press et al., 1992).
– hydromad* (Andrews et al., 2011; Andrews and Guillaume, 2018): a modelling framework for environmental hydrology: water balance accounting and flow routing in spatially aggregated catchments. It supports simulation, estimation, assessment and visualization of flow response to time series of rainfall and other drivers.
– loadflex* (Appling et al., 2015): implements several of the most common methods for modelling and predicting watershed solute fluxes and concentrations.
– RHMS (Arabzadeh and Araghinejad, 2019): an object oriented tool which enables R users to simulate and analyze hydrological events. The package proposes functions and methods for construction, simulation, visualization, and calibration of hydrological systems.
– sacsmaR* (Taner, 2019): R implementation of the Sacramento Soil Moisture Accounting (SAC-SMA) hydrology model (Burnash, 1995). The SAC-SMA is a continuous soil moisture accounting model with spatially lumped parameters that simulates runoff within a basin.
– SWATmodel (Fuka et al., 2014): contains the Soil and Water Assessment Tool (Arnold et al., 1993), which is a river basin or watershed scale model developed by Dr. Jeff Arnold for the USDA-ARS.

Conceptualization of hydrological processes

So as to emphasize the differences between the models depiction of hydrological processes, some simplified schematics were uniformly applied to all the models (Figure 1). These representations are inspired from Figure 3 of de Boer-Euser et al. (2017), which uses the same legend for each diagram in order to highlight the main characteristics (fluxes and storage) of the models. As a consequence, the schemes are not identical to those found in the literature. Explanations of the schematics are given below. Explanations of GR4J-CemaNeige and WALRUS were slightly modified from de Boer-Euser et al. (2017).
TOPMODEL 1995 version of topmodel: precipitations enter the first interception/root zone store where the actual evapotranspiration to be removed is calculated. A portion of the water contained in this store joins an unsaturated zone represented by a second root zone storage on Figure 3a. When the first store is full, an excess flow is transmitted to the overland routine (yellow to orange colour gradient). An infiltration flux from the unsaturated zone to the saturated zone is calculated. When the maximum capacity of the unsaturated store is reached, an excess flux is transmitted to the overland routine. Consequently, the overland routine deals with storage excess coming from the two root zones, routes the runoff on the hillslopes and generates a part of the flow that will then be routed by the channel routing. The saturated zone, which is represented by a groundwater runoff box, generates a part of the subsurface flow that will reach the channel (or baseflow) and will thus be routed along with the surface runoff. The delay function applies on the sum of these two flows. The dynamic version of TOPMODEL (Beven and Freer, 2001a) implemented in the dynatop-model package: on Figure 3b, hydrological processes of the dynamic TOPMODEL are represented without taking the semi-distributed spatialization into account (i.e. on a single hydrological response unit). Spatial characteristics of the package models will be dealt with in section II.2. The difference between the model in the topmodel package and the model in the dynatopmodel package con-cerns the subsurface runoff and the water table. In the 1995 version of TOPMODEL, the water table is considered as being quasi-steady, whereas the dynamic TOPMODEL includes a time-dependant kinematic routing (Metcalfe et al., 2015). The saturated zone is predicted using implicit kinematic routing between (and within) the computational units. When, within a unit, the local storage capacity is reached, any excess water is routed to downslope units (as “run-on”) or connected river reach. The RHMS package offers different hydrological models. Three functions are used in the process of calculating the discharge at the outlet of a catchment: a production routine (soil moisture ac-counting) that has to be selected within the loss() function; a transfer function chosen through the transform() function; a hydraulic routing function applied by the reachRouting() func-tion. If the SCS method is chosen by the user, the effective rainfall calculation depends on the curve number, which determines the conditions for the production store to reach saturation. This store repre-sents the whole watershed storage (Dingman, 2015), including interception, root zone, and subsurface reservoirs (blue to brown colour gradient store; see Figure 3c). The effective rainfall thereafter goes through a unit hydrograph (transform() function) which computes the watershed response to the excess rainfall input. The generated runoff is routed to the catchment outlet afterwards. In the latest version of the package, a canopy abstraction function can be added to the SCS method but it is not represented on Figure 3c.
The ecohydrological model contained in the Ecohymod package is based on a combination of a soil moisture model and a Normalized Difference Vegetation Index (NDVI) model. The aim of this model is to understand changes in rainfall seasonality on arid and semi-arid tropical vegetation. The Figure 3d represents the soil moisture model. Rainfall is first intercepted by the canopy and then infiltrates the soil pictured as a root zone storage on this representation. A part of the infiltrated water is lost by evapotranspiration and leakage. Runoff is generated when the root zone storage is saturated during a rainfall event. Saturation depends on the soil porosity, the relative soil moisture content and the depth of active soil.
The lumped conceptual Wageningen Lowland Runoff Simulator (WALRUS package): the model consists of three reservoirs: a combined root zone and groundwater reservoir, a combined very quick and fast runoff reservoir and a surface water reservoir. The surface water reservoir represents the frac-tion of catchment where there are ditches and channels. Snow accumulation and melt are simulated in a preprocessing step before WALRUS is run. Interception is not taken into account (see Figure 3e).
GR4J-CemaNeige is a combination of the CemaNeige snow module (Valery´ et al., 2014) and the GR4J model (Perrin et al., 2003). CemaNeige separates liquid and solid precipitation from total pre- cipitation and then calculates snow accumulation and snowmelt from solid precipitation. Snowmelt is added to the liquid precipitation input of GR4J. GR4J is a lumped conceptual daily rainfall-runoff model with a soil moisture accounting routine and two routing routines: one for very quick and one for fast runoff (see Figure 3f). The model includes two reservoirs: a production store (root zone storage) and a routing store for the fast runoff. The division of water between the two routines (unit hydrographs) is fixed at a 0.1–0.9 ratio; both fast and very quick runoff processes interact with the groundwater. Interception is taken into account by subtracting potential evaporation from precipita-tion to obtain net precipitation, which is then transmitted to the root zone store.

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Lumped models

Three of the selected packages contain models considered as lumped models (as opposed to dis-tributed models): airGR, Ecohymod and WALRUS. Although they are lumped models (see Figure 5), the spatial distribution is not exactly the same for each of them when using a snow module as ex-plained previously. The fuse package and the hydromad package only contain lumped elements, but we will not detail them here.
GR4J can be considered as a lumped model because it runs on a catchment as a whole. It means that the two reservoirs of GR4J are depicting the total catchment. When GR4J is combined with CemaNeige, the melt outputs of CemaNeige are aggregated on the entire catchment and added to liquid precipitation before entering the GR4J model.
The WALRUS model is a lumped model. The output of its snow function, which is the sum of liquid precipitation and snowmelt, becomes an input of the WALRUS model which then run on the whole catchment.
The soil moisture model of the Ecohymod package does not take snow into account and runs on aggregated data of the whole catchment.

Semi-distribution based on the topographic index

In the TOPMODEL 1995 version contained in topmodel, the rainfall and potential evapotran-spiration inputs are aggregated. A part of the rainfall that does not infiltrate the root zone stores is directly turned into an infiltration overland flow value (fex) for the entire basin (lumped calculation, see Figure 6). The saturated zone is represented as a global saturation value (Smean) or mean water table (lumped calculation). The Digital Elevation Model (DEM) gives elevation values for each cell of a grid with a resolution of less than 30 m for the results to be meaningful (Metcalfe et al., 2018).
The topographic index (Beven and Kirby, 1979) is then calculated for each pixel (distributed calcu-lations). Classes of these index values are created and correspond to areas with similar hydrological behaviors (semi-distributed calculations). The highest topographic indexes are supposed to depict the main stream. Each class has a specific root zone store, an unsaturated zone store and a local depth to the water table (Si). Saturation excess overland flows (exi) and vertical flows (qvi) going to the saturation zone are calculated for each class. A baseflow value (qs, lumped calculation) is derived from the saturation zone (lumped), the sum of vertical flows (semi-distributed calculations) and a global subsurface flow (qss, lumped calculation). Surface flow (q0) is the sum of saturation excess overland flow from each unsaturated zone and the lumped infiltration excess overland flow. The total discharge (Qt, lumped) is the delayed and routed sum of the surface flow and the baseflow. The model parameters are set at the catchment scale.

Semi-distribution based on hydrological response units

The spatial conceptualization of the dynamic TOPMODEL (Beven and Freer, 2001a) is not the same as the one set in the topmodel package. The difference is that the dynamic TOPMODEL is based on landscape Hydrological Response Units (HRUs). These units are generated throughout a preprocessing GIS procedure where the catchment is cut into HRUs that depend on one property or a combination of properties of the basin. The dynatopmodel package offers functions to create these HRUs from a Digital Elevation Model (DEM) and any catchment characteristic entered by the user. These characteristics can be flow distances (Figure 7a), geology, vegetation cover, spatially-heterogeneous properties such as porosity and surface conductivity or combinations of those. Each HRU contains a root zone, an unsaturated zone and a saturated zone. Fluxes between HRUs (Figure 7b) are controlled by a “flux-distribution” matrix based on the connectivity between the grid squares of the base digital elevation map contributing to the HRUs (for more details see Metcalfe et al., 2015). This also allows for connectivity between grids within the same HRU. Inputs can be spatially distributed if need be by associating each HRU with different rainfall and evapotranspiration data. There is one set of parameters for the whole catchment.

Table of contents :

I Overview of packages and models 
I.1 Context
I.1.a Hydrological modelling
I.1.b R packages
I.1.c Hydrological modelling and R packages: state of the art
I.2 Full list of identified hydrological modelling R packages
I.3 Selection of a list of packages of interest
II Structure of the models contained in the selected packages 
II.1 Conceptualization of hydrological processes
II.2 Spatial distribution
II.2.a The case of snow
II.2.b Lumped models
II.2.c Semi-distribution based on the topographic index
II.2.d Semi-distribution based on hydrological response units
II.2.e Other semi-distributions
II.3 Model requirements: inputs, time steps and parameters
II.4 Outputs of the models accessible via the packages
III R implementation 
III.1 Technical features
III.2 Documentation
III.3 Programming languages interfaced by R
III.4 Package dependencies
IV Simulations on two catchments 
IV.1 Methodology
IV.2 Presentation of the catchments
IV.3 Simulation results
References

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