Quoted from: Pellarin, Thierry, Guy Delrieu, Georges-Marie Saulnier, Hervé Andrieu, Bertrand Vignal, and Jean-Dominique Creutin. "Hydrologic visibility of weather radar systems operating in mountainous regions: Case study for the Ardèche catchment (France)." Journal of Hydrometeorology 3, no. 5 (2002): 539-555. https://doi.org/10.1175/1525-7541(2002)003%3C0539:HVOWRS%3E2.0.CO;2

The hydrologic model used herein is based on the well-known topography-based TOPMODEL (Beven and Kirkby 1979; Beven et al. 1995; Beven 1997), which is one of the first attempts to model a distributed hydrologic response with the concept of variable contributing areas, introduced by Cappus (1960) and Dunne and Black (1970). This model was developed with the aim of providing a physically realistic set of modeling concepts, needing only a small number of parameters. Basically, TOPMODEL predicts, at each time step, the spatial distribution of the water content of each digital terrain model (DTM) pixel of the catchment. The water content is calculated as a function of the spatial distribution of an index of hydrologic similarity and of the mean overall water storage. Initially (Beven and Kirkby 1979), the index of hydrologic similarity was a pure topographic index *κ*expressed as *κ* = ln(*a*/tan*β*) with *a* the drainage area per unit length (m) of hillslope and tan*β* (−) the topographic local slope used as an approximation of the hydraulic gradient of the perched hillslope water table. The overall water storage, or storage deficit, is derived from a water balance assessment at each time step [see Beven et al. (1995) for full details]. Because the concept of contributing areas was recognized to be the preponderant runoff generation process over the Ardèche catchments (Datin 1998), the TOPMODEL approach was chosen in this study to investigate the effect of radar rain-rate errors on flood prediction.

However, TOPMODEL assumes that rainfall is uniform in space, which is a reasonable assumption for the small catchments (<100 km

2) for which it was first developed. In the present region, rainfall may have a strong spatial variability (

Bois et al. 1997). A specific version of TOPMODEL, called TOPODYN, was therefore developed (

Datin 1998) with two main new features. First, it offers an improvement in the water balance assessment, ensuring a more accurate mass balance conservation (

Saulnier and Datin 2002;

Habets and Saulnier 2001). Second, the spatial variability of the rainfall is taken into account explicitly by means of a dynamic index of hydrologic similarity defined as

with

*a**i,t* (m) =the drainage area per unit length of hillslope,
- tan
*β**i* (−) =the topographic local slope, and
*R**i,t* (m h–1) =the hillslope recharge of the perched water table.

As opposed to TOPMODEL, which considers a uniform hillslope recharge *R**t*, the hillslope recharge *R**i,t* of the water table can now change in space as the spatial variability of rainfall is taken into account. For a given time step, some parts of the catchment may receive no rain. The lateral subsurface downslope flow on these “dry” parts of the catchment may then decrease and eventually disappear. This means that the surface of the catchment where subsurface flow actually takes place may change in time and space. It is no longer considered to be equal to the overall catchment area, as it is in TOPMODEL. This leads us to consider dynamic drainage areas *a**i,t* in (20) for each pixel, which now may vary between zero (if no subsurface downslope flow takes place on the hillslope) and the total topographic upslope area (if subsurface flow takes place over the entire hillslope). The water content of the dry part of the catchment where there is no lateral subsurface downslope flow is set to a maximal value *do*[expressed as a deficit as in TOPMODEL formalism (see Beven et al. 1995)], as in Habets and Saulnier (2001). Here, the rest of the TOPODYN model is kept the same as the TOPMODEL version used in Saulnier et al. (1998). TOPODYN is used as an event-based model, assuming homogenous soils over the catchment, because no spatial information was available. Four parameters need to be calibrated:

*K*0 (m h–1) the saturated conductivity (an isotropic soil is assumed with identical downslope and vertical conductivity);
*m* (m), the shape of the exponential decrease of the transmissivity with water content deficit respectively;
- SRMax (m), the maximum level of interception and root zone storage (initially empty for each event); and
- INTER (m h–1), the maximum rate of water layer loss by interception and evapotranspiration, determined at each time step from the content available in the interception/root zone storage.

At each time step, the subsurface/return flow drainage from the subsurface store is transferred to the outlet by a routing algorithm based on isochrones. The direct runoff from the contributing areas is converted to an effective rainfall and is transferred to the outlet by a unit hydrograph function, identified by the first differenced transfer function (FDTF)–Eruhdit method (Duband et al., 1993).