Chapter 5 ....continued
Dynamic Water Balance Modelling

Section 5.2 (5.2.4 to 5.2.6)


5.2.4 The plant growth module

The plant growth module models plant growth (of up to two vegetation layers) as a function of light, nutrient and water availability, grazing pressure (if livestock are present), ambient temperature and soil salinity and pH. This is done using the Integrated Rate Methodology (IRM), described by Hatton et al. (1992), Wu et al. (1994), Hatton et al. (1995), Dawes et al. (1995) and Vertessy et al. (in press). The module assumes that the actual CO2 assimilation rate is dependent on a maximum rate and the relative availability of light, water, and nutrients. It computes the carbon assimilation index (r) of (Wu et al. 1994):

r = 1 + wH + wN
1/xT xL + wH/xW + wN/xN
5.16

where:

Carbon assimilation (A) is calculated as:

A = r. Amax 5.17

where:

Five carbon pools are defined:

Maintenance respiration is calculated as a function of temperature as in Running and Coghlan (1988) and net photosynthesis is calculated as assimilation less total respiration. When daily respiration exceeds assimilation, carbon is taken from the soluble pool (if present), then from the leaf and root pools. Growth respiration is assumed to be a constant fraction of allocated carbon (Rauscher et al. 1990).

On days when assimilation exceeds respiration, a soluble carbohydrate pool is filled. When it reaches its maximum, the excess is assigned dynamically to leaves, roots and stems. Leaf carbon may not exceed a level where 95% of incoming light is intercepted, nor exceed stem carbon. These conditions recognise that once canopies capture all available light, there is little point adding more leaves, and that leaves require some minimum mechanical and hydraulic support. Carbon allocation to leaves, roots and stems is dynamic and follows the approach of Running and Gower (1991) in that the leaf:root ratio is based on the relative availabilities of above- and below-ground resources (sensu Chapin et al. 1987, Wilson 1988), in this case as calculated by the equation for r.

Increments to root carbon are distributed by dynamic allocation of carbon through the root zone. We assume that root carbon is continuous from the surface downwards, that roots are added to the wettest (most favourable) region of soil, and that roots grow downwards in search of water, if necessary. The favourability of a soil region is a function of the moisture there.

Irrespective of daily assimilation, each of the three living carbon pools suffer daily decrements, representing the turnover of leaves, bark and roots. Shedding from the two above-ground carbon pools, as well as any carbon from net negative assimilation, contributes to the litter pool. This litter pool decays as a function of temperature and moisture (Hatton et al. 1992).


5.2.5 The overland flow module

When Topog_Dynamic is run in the 'stormflow' mode with the kinematic wave overland flow option invoked, overland flow within each catchment element is computed for each timestep using the one-dimensional kinematic wave equation. It is assumed that overland flow occurs uniformly across the catchment element as sheet flow. While such flows are characterised by low depths and velocities, we assume that they are fully turbulent, owing to the effects of raindrop impact and surface obstructions such as vegetation and soil particles.

It should be noted here that the transpiration calculations are not implemented during sub-daily timestep calculations.

The Manning equation is used to relate flow velocity (v) to flow depth (h):

v = h2/3 m1/2
n
5.18

where:

For each element, the volume of overland flow (q) at each timestep (DT) is computed as:

q = v. A. DT 5.19

where A is the element area.

Continuity is governed by:

dh
dt		 + dQ
dx		 = no
5.20
where:

A backwards weighting procedure is used to ensure a smooth and stable solution.


5.2.6 The sediment transport module

For each catchment element, the sediment transport module computes :

  1. detachment of soil by rainfall splash
  2. detachment of soil by overland flow
  3. sediment transport capacity of overland flow
  4. net flux of sediment.


5.2.6.1 Splash detachment

For bare soil, the splash detachment DS is computed as:

D
DS = A(e). . . S . (ND . PD2) = A(e).MR
5.21

where:

The sum of squared momenta for raindrops hitting the ground is approximated by:

MR = 2.04 x 10-8 I 1.63 for I <= 75
MR = 4.83 x 10-8 I 1.43 for I >= 75
 5.22

where I = the rainfall intensity in mm/h.

For cases where there is a plant canopy, mulch or stones and water ponding on the ground, the net splash detachment rate is computed as:

DR = C1 C2 Kh cos(a) Ds 5.23

where:

The canopy factor is defined as:

C1 = (1-c) MR + c Mc
MR
5.24

where:

The squared momenta of the raindrops from canopy is calculated by:

MC = Inet. p
6		 D3. rw2 . VD2 = Inet. DH
5.25

where:

For a typical drop diameter (D = 5 - 5.5mm), the relationship between the parameter DH and canopy height is approximated by:

DH = 1.29 H for H <= 2
DH = 0.0051H3 - 0.158H2 + 1.6696H - 0.1743 for 2 < H <= 13
DH = 6.2 for H > 13
5.26

where:

A water layer on the ground will influence the ease of detachment in different ways. When the water layer reaches a certain thickness, it starts working as a shield against the forces of the incoming drops, and the viscosity of the water restricts movement of the detached aggregates. We therefore introduce a correction factor in calculating the splash detachment rate, given as:

Kh = 1.0 for h <= Dm
Kh = e(1 - h/Dm) for h > Dm
5.27

where:

and Dm = 1.238 I0.182 (in mm),

where:


5.2.6.2 Transport of particles detached by rainfall splash

The splash detached soil particles are transported by overland flow. Due to gravity, the particles are deposited again a distance downslope according to their fall velocities. Neglecting the wash load, the net transport qr is expressed by:

qR = DR q
2		 S
i		 fi
wi
5.28

where:


5.2.6.3 Entrainment of soil particles by overland flow

The flow entrainment of cohesive soils qE is described by

qE = h qT 5.29

where:

In the sediment transport module h is used as a calibration factor.


5.2.6.4 Transport capacity and total sediment load

Topog_Dynamic uses the Engelund and Hansen (1968) equation to calculate sediment transport capacity of flow for non-cohesive sediments. The formula is used for determining transport capacity of overland flow, because once detached, the soil aggregates are transported as non-cohesive sediments until they settle again. The Engelund-Hansen transport equation is based on a fundamental energy equation for transport and deposition of sediments along a movable bed. It is assumed that the gain in potential energy when a particle is lifted can be equated with the work done by the drag forces of the flow. Thus, the sediment transport capacity of overland flow is calculated by:

qT = 0.04 (Sh)3/2
(s-1)2 d50 g1/2		 v2 = 0.04 ( 2g
f		 )1/6 (Sq)5/3
(s-1)2 d50 g1/2
5.30

where:

The total sediment load qs leaving an element is limited by the transport capacity of overland flow. Thus, if the computed transport is higher than the transport capacity, the flow entrainment and successively the net transport of splashed soil are limited to give a total sediment load equal to the transport capacity.

qs = qR + qE if qR + qE <= qT
qs = qT if qR + qE >= qT
5.31

where:

As an alternative to the Engelund-Hansen (1968) equation, Topog_Dynamic also allows the user to compute total sediment load using Yang's unit stream power theory. With this option, it is assumed that erosion is transportation capacity limited; soil detachment is considered to be non-limiting and surface cover or depression storage effects are not considered. The sediment flux is calculated by:

qs = rg
n0.6b		 q0.4b S1.3b
5.32

where:

g and b constants which are functions of the median sediment size, the kinematic viscosity of the water, and the terminal fall velocity of sediment particles in water.


5.2.6.5 Estimation of net erosion and deposition

The net erosion or deposition for each element and each time step is calculated as the difference between the sediment load entering and leaving an element. The erosion/deposition rate per unit area is estimated by:

Red = qis bi - qos bo
ae
5.33

where:


Take me out of frames Chapter 5 continued .......
last modified on 18 June 1997