LA INVERSIÓN DEL ‘DIVIDENDO DE LA PAZ’ (1993-1997)

The physical processes modelled by TopNet in each subcatchment pertain to the storage of water before it reaches the stream network. The five primary storage components are: canopy storage Sc, soil storage in the root zone Sr, aquifer storage Sa, overland or surface storage So, and snowpack storage Ss. They are modelled by a system of five differential equations. However, TopNet does not solve the equations simultaneously, rather in the order Sc, Ss, Sr,

Sa, So, for each timestep. This reduces computational expense, as does employing analytical solutions where applicable.

3.3.2.1 Canopy Storage (Sc)

The canopy storage model was based on the work of Ibbitt (1971), such that

3.1

where p is the rate of precipitation, pt is the rate of throughfall of the canopy, and ec is the rate of evaporation from the canopy.

pt and ec are functions of Sc, such that

( ) _3.2

and

( ) 3.3

where cr denotes a parameter used to quantify evaporation losses from interception relative to the potential evapotranspiration rate epot, determined using the Priestly-Taylor method, and where

( ) ( ) _3.4

and Cc is the water holding capacity of the canopy.

The physical implication of these equations is that as the canopy nears its water-holding capacity, the rate of increase of canopy storage decreases, resulting in increased throughfall.

41 3.3.2.2 Soil Storage (Sr)

Soil and subsurface storage is arguably the most complex physical process modelled by TopNet. The adoption of the topographic index ⁄ , developed by Beven and Kirkby (1979) for Topmodel, allows subcatchment variability to be quantified. a denotes the upslope area per unit contour width draining through a point, and tanβ is the slope at that point. Points with a similar topographic index, resulting from the relationship between upslope area and local slope, are considered to have a similar hydrologic state and consequently display a similar response to change. An area containing points with a higher topographic index is more likely to become saturated more rapidly and may contribute more significantly to surface or subsurface storage.

The depth to the water table at a point z can be computed from the topographic index

̅ [ ( ⁄ )] _3.5

or

( ̅)( ⁄ ) ⁄

3.6

where ̅ is the spatial average of the depth to the groundwater table, m is a depth scaling parameter, n is a dimensionless parameter, and λ and λn are the spatial averages of the transformed topographic indices ( ⁄ ) and ( ⁄ ) ⁄ _{, respectively such that}

∫ ( ⁄ ) 3.7

and

∫ ( ⁄ ) ⁄

3.8

and A is the basin area.

The local depth to the water table in relation to the depth of the soil layer and the ground surface is used to determine whether the catchment soil layer is saturated, influenced, or

uninfluenced by the local groundwater. If the depth to the water table z lies below the soil

layer, the soil layer is uninfluenced, if z lies within the soil layer, the soil layer is influenced by groundwater, and if z is located above the soil layer, denoted by a negative value of z, the soil layer is saturated by the water table.

42 Once the fractional areas of each zone ϕunf, ϕinf, and ϕsat have been determined, along with a cumulative distribution function of the transformed topographic index κ, the storage and the rate of change of storage for each zone can be computed, allowing the change in storage to be determined 3.9

where unf, inf, and sat denote uninfluenced, influenced, and saturated zone, respectively. It should be noted that the restriction is imposed that the relative change in soil moisture is constant across the zones

3.10

This condition may pose some restrictions on processes such as infiltration, soil evaporation, and drainage but results in a more efficient model.

3.3.2.3 Aquifer Storage (Sa)

Under ideal conditions, the groundwater state equation to describe aquifer storage Sa is

3.11

where d is the drainage rate and qb is the rate of baseflow, or aquifer discharge rate.

Change in aquifer storage can be defined as a function of the change in the average water table depth ̅ and the drainable water content across the basin . Hence, the groundwater state equation can be rewritten as

̅

3.12

The overall drainage rate d is the summation of the drainage from each soil zone, such that

_3.13

And baseflow rate qb is a function of hydraulic conductivity, topographic index, and average water table depth.

43 3.3.2.4 Surface Storage (So)

Surface runoff can be generated as infiltration-excess runoff qix, as saturation-excess runoff

qsx, and as baseflow discharge qb. Hence the state equation for surface storage So is a simple mass-balance equation

3.14

where qo is the runoff flow from the surface storage component to the river network, where it is no longer considered surface storage but rather part of the streamflow.

Because the movement of runoff from the land surface to the river network is not instantaneous, at any point in time there will be water storage on the surface before it enters the river network. TopNet assumes that the three forms of runoff do not enter the river network immediately, and instead must spend time as surface storage. When considering baseflow discharge, this implies that groundwater is discharged into small streams that are not considered by the modelled river network.

Infiltration-excess runoff is generated when the rate of precipitation exceeds the rate of infiltration. It occurs in both the influenced soil zone and the uninfluenced soil zone, but to differing degrees, hence the fractional area of each zone ϕunf and ϕinf must be considered. Saturation-excess runoff is generated only in the saturated zone of a catchment and when runoff forcing is positive. Infiltration is taken to be zero and saturation-excess runoff is determined by considering the rate of precipitation and fractional area of the saturated zone. Basin outflow or discharge from surface storage qo requires the consideration of a time delay to account for the transportation of overland flow. The delay is determined using the frequency distribution of overland flow residence time τ, derived from the empirical frequency distribution of overland path length x and overland flow velocity v.

3.3.2.5 Snowpack Storage (Ss)

Put simply, the rate of change of snow water equivalent storage is

3.15

where ps is the rate of throughfall of snow through the canopy and ms is the rate of snowmelt. The rate of snowmelt can be determined through ambient temperature and, if available, solar radiation, wind, precipitation, and other climate inputs.

44