# Background

SPHY is a spatially distributed leaky bucket type of model, and is applied on a cell-by-cell basis. The main terrestrial hydrological processes are described in a conceptual way so that changes in storages and fluxes can be assessed adequately over time and space. SPHY is written in the Python programming language using the PCRaster (Karssenberg et al. 2001; Karssenberg et al. 2010; Karssenberg 2002; Schmitz et al. 2009; Schmitz et al. 2013) dynamic modeling framework.

SPHY is grid based and cell values represent averages over a cell (Figure 1). For glaciers, sub-grid variability is taken into account: a cell can be glacier free, partially glacierized, or completely covered by glaciers. The cell fraction not covered by glaciers consists of either land covered with snow or land that is free of snow. Land that is free of snow can consist of vegetation, bare soil, or open water. The dynamic vegetation module accounts for a time-varying fractional vegetation coverage, which affects processes such as interception, effective precipitation, and potential evapotranspiration. Figure 2 provides a schematic overview of the SPHY modeling concepts.

![Figure 1: Illustration of SPHY sub-grid variability. A grid cell in SPHY can be (a) partially covered with glaciers, or (b) completely covered with glaciers, or (c1) free of snow, or (c2) completely covered with snow. In the case of (c1), the free land surface can consist of bare soil, vegetation, or open water.](https://1703319430-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FqMZcdbfMcflSgnLW9i26%2Fuploads%2FWLqYdQD8haKwSHrpAJ7h%2F2?alt=media)

![Figure 2: SPHY modelling concepts. The fluxes in grey are only incorporated when the groundwater module is not used. Abbreviations are explained in the text.](https://1703319430-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FqMZcdbfMcflSgnLW9i26%2Fuploads%2F2bDv5pHLHmbdjpMppnrk%2F3?alt=media)

The soil column structure is similar to VIC (Liang et al. 1994, 1996), with two upper soil storages and a third groundwater storage. Their corresponding drainage components are surface runoff, lateral flow and baseflow. SPHY simulates for each cell precipitation in the form of rain or snow, depending on the temperature. Precipitation that falls on land surfaces can be intercepted by vegetation and evaporated in part or whole. The snow storage is updated with snow accumulation and/or snowmelt. A part of the liquid precipitation is transformed in surface runoff, whereas the remainder infiltrates into the soil. The resulting soil moisture is subject to evapotranspiration, depending on the soil properties and fractional vegetation cover, while the remainder contributes to river discharge by means of lateral flow from the first soil layer, and baseflow from the groundwater layer.

Melting of glacier ice contributes to the river discharge by means of a slow and fast component, being (i) percolation to the groundwater layer that eventually becomes baseflow, and (ii) direct runoff. The cell-specific runoff, which becomes available for routing, is the sum of surface runoff, lateral flow, baseflow, snowmelt and glacier melt.

If no lakes are present, then the user can choose a simple flow accumulation routing scheme: for each cell, the accumulated amount of water that flows out of the cell into its neighboring downstream cell is calculated. This accumulated amount is the amount of water in the cell itself plus the amount of water in upstream cells of the cell, and is calculated using the flow direction network. If lakes are present, then the fractional accumulation flux routing scheme is used; depending on the actual lake storage, a fraction of that storage becomes available for routing and is extracted from the lake, while the remaining part becomes the updated actual lake storage. The flux available for routing is routed in the same way as in the simple flow accumulation routing scheme.

As input, SPHY requires static data as well as dynamic data. For the static data, the most relevant are digital elevation model (DEM), land use type, glacier cover (including differentiation in debris-free and debris-covered ice surfaces), lakes/reservoirs and soil characteristics. The main dynamic data consist of climate data, such as precipitation, temperature, and reference evapotranspiration. Since SPHY is grid based, optimal use of remote sensing data and global data sources can be made. For example, the Normalized Difference Vegetation Index (NDVI) (Tucker 1979; Carlson and Ripley 1997; Myneni and Williams 1994) can be used to determine the leaf-area index (LAI) in order to estimate the growth stage of land cover. For setting up the model, streamflow data are not necessary. However, to undertake a proper calibration and validation procedure, flow data are required. The model could also be calibrated using actual evapotranspiration, soil moisture contents, and/or snow-covered area (SCA). Section 3.2 contains an example application in which the SPHY model has been calibrated using MODIS snow cover images. An overview of the adjustable SPHY model parameters is shown in Appendix 1 (Table 6).

The soil erosion model is based on the Modified MMF model (Morgan and Duzant, 2008). Total soil erosion is calculated from detachment by raindrop impact and detachment by runoff, considering within cell deposition. Detachment of soil particles from raindrop impact is determined from the total rainfall energy, which is determined for direct throughfall and leaf drainage, respectively. Detachment of soil particles by runoff is determined from the accumulated runoff from the hydrological model. Both soil erosion equations account for the fraction of the soil covered by stones and vegetation or snow and are determined separately for three texture classes (sand, silt, clay). Within cell deposition is calculated as a function of vegetation and surface roughness. The remainder of the detached sediment is taken into transport.

The SPHY model provides a wealth of output variables that can be selected based on the preference of the user. Spatial output can be presented as maps of all the available hydrological processes, i.e., actual evapotranspiration, runoff generation (separated by its components), and groundwater recharge, and storage components, i.e. root zone water content, snow storage, groundwater storage, and canopy storage. These maps can be generated on a daily basis, but can also be aggregated at monthly or annual time periods and as long-term monthly averages or sums. Time series can be generated for each cell in the study area. Time series often used are streamflow, actual evapotranspiration and recharge to the groundwater.
