Table of contents
History of Geotop
You can find a complete description of the model's hystory and evolution at the site bedu or: here at the http://www.cuahsi.org/biennial2008/archive.html
Introduction
GEOtop is a distributed model of the mass and energy balance of the hydrological cycle, which is applicable to simulations in continuum in small catchments. GEOtop deals with the effects of topography on the interaction between energy balance and hydrological cycle with peculiar solutions. In this manual is explained the the theoretical backgound, the model's structure, the code organization, the input and output files and some applications examples.
Background
The purpose of the distributed hydrological model GEOtop is to estimate in an integrated way the rainfall-runoff and the energy fluxes, with particular attention to evapotranspiration in small mountain catchments.
Such a model satisfies the requirements of a modern management of the water resources and of the hydrogeological risk and could use the modern tools offered by DEMs (Digital Elevations Models) and data as those produced in specialized measurement campaigns like FIFE (First ISLSCP Field Experiment, Sellers et al., 1992), PILPS (Heanderson-Sellers and Brown, 1992), HAPEX-MOBILHY (Modelisation de Bilan Hydrique, André et al, 1988), SGP97, Tarrawarra (Western et al., 1998), DMIP (Distributed Models Intercomparison Project,http://www.nws.noaa.gov/oh/hrl/dmip/), MARVEX (Woods, 1997), to mention a few experiments only.
In the last thirty years several distributed hydrological models have been developed and, independently, models of soil-atmosphere interaction for the computation of the energy balance at the soil. Actually, the inflow-runoff models based on the paradigms of the unitary instantaneous geomorphological hygrograph (IUH) (Rodriguez-Iturbe e Valdes, 1979; Rodriguez-Iturbe e Rinaldo, 1997), of the TOPMODEL (Beven e Kirkby, 1979), and other distributed and semi-distributed models like the THALES (Grayson et al., 1995) or the TOPKAPI (Ciarapica e Todini, 1998) and many more reported in Beven (2000), are successful in the flood events modelling (assuming opportune conditions of initial moisture and/or calibrating some other parameters, generally two or three), but they are generally unable to follow the runoffs evolution in the time after the floods and, obviously, to estimate evapotranspiration precisely enough.
Viceversa, also numerous models LSMs (Land Surface Models) have been developed: they represent the soil-atmosphere interactions with a different degree of complexity and accuracy, from the simple bucket model (Manabe, 1969), to a complex representation of the multilayer vertical interactions like the models BATS (Dickinson et al., 1986), SiB (Sellers et al., 1986), VIC (Wood ed al., 1992), NOAH-LSM (Mitchell et al, 2000). Nevertheless, having been developed mainly to support the global circulation atmospheric models (GCM), they are not endowed with a detailed representation of the superficial hydrological processes at catchment scale.
GEOtop can be seen both as an inflow-runoff model able to simulate the hydrological cycle with continuity during the time, and as an attempt to incorporate in the LSMs an adequate treatment of the hydrological variability on a small scale, in particular the effects due to an use of the heterogeneous soil, to the spatial distribution of the soil moisture, and to the presence of a complex topography and of a channel network.
Model Description
The model GEOtop simulates the complete hydrological balance in a continuous way, during a whole year, inside a basin and combines the main features of the modern land surfaces models with the distributed rainfall-runoff models.
The new 0.875 version of GEOtop introduces the snow accumulation and melt module and describes sub-surface flows in an unsaturated media more accurately. With respect to the version 0.750 the updates are fundamental: the codex is completely eviewed, the energy and mass parametrizations are rewritten, the input/output file set is redifined.
GEOtop makes it possible to know the outgoing discharge at the basin's closing section, to estimate the local values at the ground of humidity, of soil temperature, of sensible and latent heat fluxes, of heat flux in the soil and of net radiation, together with other hydrometeorlogical distributed variables. Furthermore it describes the distributed snow water equivalent and surface snow temperature.
GEOtop is a model based on the use of Digital Elevation Models (DEMs). It makes also use of meteorological measurements obtained thought traditional instruments on the ground. Yet, it can also assimilate distributed data like those coming from radar measurements, from satellite terrain sensing or from micrometeorological models.
As any distributed grid based model, it divide the watershed in cells (sometimes called pixels). For every cell, the model solves both the energy and the water balance, divided in lateral and vertical flows.
The precipitation is partitioned in rain and snow (both in terms of water equivalence depth) using the rule based on air temperature, (U.S. Army Corps of Engineers, 1956).
The lateral runoffs are moreover distinguished in a surface component with a faster motion, and a subsurface component with a slower motion, according to the local slope.
The soil is divided in an unsaturated upper zone, where vertical infiltration occurs, and a saturated lower zone, where water flow is parallel to the bedrock, assumed as an impermeable surface. If the rain intensity is higher than the saturation hydraulic conductivity, or if the water table level reaches the surface, surface runoff occurs, according to the mechanism illustrated in Fig. 1
An important variable of the model is the thickness of the hillslope hydrologically active soil which is determined, if field values are not available, on the basis of a linear model of soil production (Hiemsath et al, 1997, Stocker, 1998).
All basin cells are divided in channel and hillsides cells. The surface runoff in the hillsides is described as a succession of uniform motions and the subsurface flow on the basis of Darcy law. In both cases, the connectivity among the cells is defined by the D8 scheme, with eight drainage directions (Fairfield and Leymarie, 1991).
The channel network is build from the DEM using a stress method (Prosser and Abernethy, 1996). The motion inside the channels is described by the parabolic solution of the De Saint Venant equations, by using a constant celerity in the whole network as proposed in (Rinaldo et al., 1991) and globally described by the:
\begin{equation}
\displaystyle Q(t) = \int_0^t{\int_0^L{\frac{xW(\tau ,x)}{\sqrt{4\pi D(t-\tau)^3}}\exp{\left[-\frac{(x-u(t-\tau))^2}{4D(t-\tau)}\right]}d\tau} \cdot dx}
\end{equation}
where Q(t) is the discharge at the basin's closing section , [[latex($W(t,x)$)]] is the inflow of the water coming from the hillsides into the channel network at a distance $x$ from the outlet and at a time [[latex($t$)]], [[latex($u$)]] an opportune mean celerity, [[latex($D$)]] a hydrodynamic dispersion coefficient, [[latex($L$)]] the maximum distance from the outlet measured along the network.
The model calculates in an explicit way the energy balance as a
function of the soil (or snow) layer specific energy. The heat flux in the soil (or snow) is calculated through the integration at the finite differences of the conduction equation, with an
implicit scheme on an arbitrary number of layers (''Garrat'', 1992).
The snowpack (if present) is represented by the first two layers, of which the upper one has infinitesimal thickness and is used only to calculate the snow surface temperature. For the generic i-th layer the energy balance equation is the following:
\begin{equation}\label{Eq:2sup}\frac{\Delta U_i}{\Delta t} = Q_{e,i-1\rightarrow i} - Q_{e,i\rightarrow i+1}\end{equation}
where [[latex($t$)]] is time as independent variable, [[latex($U_i$)]] the internal energy of the [[latex($i-th$)]] layer, [[latex($Q_{e,i-1\rightarrow i}$)]] and [[latex($Q_{e,i\rightarrow i+1}$)]] are respectively the heat fluxes exchanged between the [[latex($i-1th$)]] and the [[latex($ith$)]] layer (positive according to the arrow) and between the $i{th}$ and the [[latex(i+1th)]] layer. The variable [[latex($i$)]] ranges from [[latex($1$)]] (surface layer) to [[latex($n_l$)]] (deepest layer), where [[latex($n_l$)]] is the number of the layers. The fluxes [[latex($Q_e$)]] include the heat flux exchanged by thermal conduction (due to temperature gradients) and the heat flux advected by mass transport (for example by snow melt). If [[latex($i$)]] is equal to [[latex($1$)]], [[latex($Q_{e,0\rightarrow 1}$)]] is the heat flux from the atmosphere to the surface soil (or snow) layer, which is divided in the following components:) \begin{equation}
Q_{e,0\rightarrow 1}=R_n-Q_s-Q_l+Q_p
\end{equation}
where $R_{n}$ is the net radiation, $Q_s$ is the sensible heat flux (towards the atmosphere), $Q_l$ the latent heat flux (towards the atmosphere) and $Q_{p}$ is the heat flux advected by precipitation. On the other hand, if $i$ is equal to $n_l$, $Q_{e,n_l\rightarrow n_l+1}$ is $0$, as we suppose that there are no heat flux between the last soil layer and the deeper soil.
The soil capacity and thermal conductivity are made dependent on the soil water content, which is variable during the time.
If snow is present, the $1-st$ layer has infinitesimal thickness, so that $\Delta U_1=0$ and its temperature $T_1$ is the snow surface temperature. The [[latex(2-nd)]] layer is then the whole snowpack and its temperature $T_2$ is the snowpack mean temperature. The radiation is distinguished in its long- and short-wave components, diffused, directed and reflected, both emitted by the land and shielded by the cloud cover. The effects due to the mountain relief are taken into account: the shadowing, the net radiation variation as a function of exposition and slope, and the reduction of the sky view factor. The air temperature, the atmospheric pressure and the solar radiation absorption are connected to the elevation according to relations valid in a standard atmosphere (Brutsaert, 1982). The latent heat flux is given by: \begin{equation}
Q_h=\lambda ET \;\;\;\;\;\;\; ET=r EP
\end{equation}
where $\lambda$ is either the water evaporation latent heat ($h_e$) or the water sublimation latent heat ($h_s$), according whether water is present in liquid or in solid form, and $ET$ is evapo-transpiration mass, expressed as a portion of potential evapo-transpiration through a coefficient $r$ ranging from $0$ to $1$, as shown in the next chapter.
The sensible heat flux and the potential evapo-transpiration are determined through flux-gradient relations between two reference quotes.
\begin{equation}
\label{eq1} Q_h = \rho c_{p} C_{H} u (T_{s} - T_{a} )
\end{equation}
\begin{equation}
\label{eq2} EP = \rho C_H u (q^{*} (T_{s} ) - q(T_{a} ))
\end{equation}
The sensible heat flux [[latex($Q_s$)]] is expressed as a function of the atmospheric turbulence through the bulk coefficient [[latex($C_{H}$)]], of the wind velocity [[latex($u$)]], of the gradient between soil/snow temperature [[latex($T_s$)]] and air temperature [[latex($T_a$)]], while potential evapotranspiration is expressed as a function of the gradient between saturation specific moisture at the soil [[latex($q^{*}(T_{s})$)]] and specific air moisture [[latex($q(T_{a})$)]]
The bulk coefficient [[latex($C_{H}$)]], which encloses the turbulent transfer processes, takes into account the different roughness features of the various surfaces, through a mapping of the soil use and of the stability or instability atmospheric conditions, which inhibit or force the turbulent motions. [[latex($C_{H}$)]] is expressed according to Louis' theory (1979), which uses as stability parameter the Richardson number, expressed as a function of the potential temperature gradient between soil and atmosphere.
The latent heat fluxes are distinguished in evaporation or sublimation from the soil or snow surface, transpiration on behalf of the vegetation, evaporation of the precipitation intercepted by the vegetation.
To every cell is attributed a fraction covered by vegetation and a fraction covered by bare soil, where the evaporation is calculated with the (\ref{Eq:4}).
A one-level model of vegetation is employed, as in Garrat (1992) and in Mengelkamp et al.(1999). Only one temperature is assumed to be representative of both soil and vegetation. The energy balance of the hydrological bodies is calculated with a specific scheme, in order to take into account the different absorption of the solar radiation and the turbulent heat transport inside them. The model has been successfully applied and tested in some mountain watershed of Trento Province in Italy and is some well monitored basins in the USA of different sizes 10 - 1000 $km^2$. 
fig.1: The fluxes partition scheme used in the GEOtop model. In every cell, the precipitation (P) is partitioned into rain and snow withe air temperature. The snow precipitation becomes to the snowpack, and from this derives meltwater outflow (M$_r$) and sublimation (M$_e$), whereas the rain precipitation is divided in evaporation (ET), subsurface runoff ($