A Hydrological processes and related mass transport

A Hydrological processes and related mass transport

Mass changes due to changes in terrestrial water storage are conveniently expressed in hydrology in terms of changes in equivalent water thickness Dh, i.e., water mass changes per surface area (with 1mm water column corresponding to ∼1 l/m² or ∼1 kg/m²). The change of mass due to changes in water storage in a thin layer at the Earth’s surface can be written in terms of changes in the geoid shape when expanded as a sum of spherical harmonics according to Equations (A1.4.2) and (A1.4.4):

ϕ and λ are latitude and east longitude, Dσ is the change in surface density (i.e. mass/area), ρ_w is the density of water, R is the radius of the Earth, ρ_ave is the average density of the Earth, P_lm are the normalized associated Legendre functions of degree l and order m, C S˘ , ˘_{lm lm}, C_lm and S_lm are dimensionless coefficients with C_lm and S_lm defining the geoid model derived from GRACE satellite observations, and k_l’ is the load Love number of degree l.

Changes of the water storage Dh per time interval are described for any spatial unit of the land surface, e.g. a river basin, by the water balance equation:

∆h P ET Q= − − (A6.3)

where P is precipitation, ET is evapotranspiration and Q is runoff (all in mm). Spatial units for which Equation3 is valid range from the plot scale of a single soil profile to the catchment area of a river basin being the basic spatial unit of hydrological analysis and water management issues, and up to the continental scale. Precipitation as rain or snow is the main input to the terrestrial water storage. It is measured by point samplers, ground-based radar or remote sensing and subse-quently interpolated to a spatial mean for the area of interest.

Evapotranspiration includes evaporation defined as the transformation of liquid water to vapour from open water surfaces (lakes, rivers), from bare soils and from water stored on plant surfaces (interception). Evapotranspiration also includes the transfer of water from the soil to the atmos-phere by transpiration of plants. On scales with variations in soil and land use it cannot be meas-ured directly like precipitation or discharge. Neither it can be calculated from the water balance equation (Equation A6.3) as the variations in storage cannot be determined with sufficient accura-cy. Thus there is need for a description of evapotranspiration by climatic, soil and land use data . There are a number of physical approaches as the evapotranspiration rate is controlled by the availability of energy and water at the evaporating surface, and by the ease with which water va-pour can diffuse into the atmosphere, i.e., as a function of plant resistances and atmospheric tur-bulence. Basically, evapotranspiration, expressed as latent heat flux lE, is part of to the energy budget of land surfaces:

A R= _n− =G λE H+ (A6.4)

where A is the available energy at the surface, R_n is incoming net radiant energy (i.e., the differ-ence between incoming and reflected solar radiation plus the differdiffer-ence between incoming and

A6Hydrologicalprocessesandrelatedmasstransport

outgoing long-wave radiation), G is the energy transfer into the soil, H is the outgoing sensible heat flux and λ is a proportionality factor (latent heat of vaporization of water) to convert from energy units into equivalent water thickness. Practical models to describe evapotranspiration in hydrology often apply a resistance approach to represent, in addition to the energy balance, the impact of atmospheric turbulence and vegetation characteristics on evapotranspiration. One wide-ly used model of this type is the Penman-Monteith approach. It includes the aerodynamic resist-ance r_a as a function of wind speed and surface roughness due to varying height of the vegetation, and the canopy resistance r_c to represent plant stomata control on the transpiration process as a function of vegetation type, leaf cover, soil water status and micro-meteorological conditions:

E A c D r

D is the water vapour pressure deficit of the air,ρ_a is the density of air, Λ is the gradient of the saturated vapour pressure curve, c_p is the specific heat of moist air and γ is the psychometric con-stant. Being simplifications of Equation A6.5, a number of empirical formulations exist to assess evapotranspiration for large areas where data availability does not allow to account for each in-fluencing factor explicitly.

Total runoff Q as another component of the water balance equation (Equation3) is composed of a surface runoff component, a fast interflow component in the shallow soil zone and a slow groundwater flow component of water percolating to deeper subsurface zones. In a general form, subsurface water flow Q_sub (in mm per time unit) through any cross section in the saturated or un-saturated soil zone can be described by Darcy’s equation for a porous medium:

Q K

sub = −

( )

In Equation (A6.6), written in the one-dimensional form for simplicity, K(θ) is the hydraulic conductivity of the soil which is a highly non-linear function of the actual soil moisture θ, reaching its maximum value for a water-saturated soil. ∂ψ in Equation (A6.6) is the gradient of the hydraulic head (or potential) over a distance ∂x, being the sum of primarily (1) the capillary-pressure head due to capillary forces acting on water in the soil matrix and (2) of the elevation head due to gravitational forces. It should be noted that the capillary-pressure head is again a non-linear function of soil moisture θ, with its form varying considerably with soil characteristics such as porosity and grain size distribution. When written for the vertical direction, Equation (A6.6) is the basis to describe infiltration of rain into the soil. Additional precipitation volumes which exceed the infiltrability of the soil are transformed into surface runoff Q_surf. The applicability of Equation6 for the description of subsurface runoff over large spatial scales such as river basins is limited, however. One reason is the deviation of natural soils from the idealized assumption of being a homogeneous porous medium. Macropores, for instance, may allow a very fast water transport, bypassing the soil matrix. Additionally, in view of the large natural heterogeneity, the available information in particular on soil characteristics is usually not sufficient for large areas to parameterize Equation (A6.6) appropriately. Thus, simplified formulations are often used to describe subsurface storage and water transport by representing the soil zone or the groundwater by one conceptual storage for an entire river basin or a part of it with similar hydrological characteristics. Subsurface runoff per time unit from such a storage, expressed in equivalent water thickness for the catchment area A (m²), is represented as being proportional to the actual storage volume V (m³):

Q V

sub = A

⋅ τ (A6.7)

0

The proportionality constant τ (with units of time) in Equation (A6.7) is a storage coefficient which is related to the average residence time of water in the groundwater or soil storage. τ depends on geological, topographic and soil characteristics and usually is a calibration parameter in hydrological models.

The flow of surface runoff, whether generated directly as infiltration-excess from precipitation or as return flow to the land surface or into river channels after the passage of the soil and ground-water zone, can basically be described by hydrodynamical equations based on mass and energy balancing such as the Saint-Venant equations. In order to describe flow routing in the river net-work of river basins, simplified schemes are often used which essentially introduce a time delay of the downstream movement of water masses as function of flow distance, flow volume and top-ographic gradient. The retention of river runoff in natural and man-made reservoirs or in wetlands causes an additional delay in flow routing. It influences the water balance and related changes in water storage (Equation A6.3) when considered at the basin scale.

A7Satellitemissionfactsheets