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Symbols and abbreviations

A Soil sorptivity
Ah advected energy into surface layer
a dimensionless number depending on shape of cross-section
B Bowen ratio
B Soil parameter depending on hydraulic conductivity
Cijrs fourth order tensor linking shear and deformation
c state of soil moisture in multilayered soil
c0 initial soil moisture content csat saturated soil moisture content
csat specific heat at constant pressure
Drr local divergence
Drs second order local deformation tensor
E rate of evaporation
EA drying power of air
E0 maximum possible evaporation
ea* saturation vapour pressure ea vapour pressure of the air
F actual rate of infiltration or percolation
Fi i component of body force
Fp specific flux of CO
Ft. rate of potential infiltration
C specific flux of energy into land surface
h(c) specific flux of sensible heat into atmosphere
K(c) unsaturated hydraulic conductivity
Ki intrinsic permiability in i direction
ks species dependent plant coefficient of transpiration (i.e. ratio of transpiration to evaporation from bare damp soil)
kvo equilibrium plant efficiency
L length scale characterizing cross-section of pore space
Le latent heat of vaporization
Lp thermal conversion factor for fixation of CO.
M plant canopy cover
P precipitation
hydrodynamic pressure
p(c) soil water pressure
qe specific humidity
air specific humidity in atmosphere above canopy
qs* air specific humidity in sub-stomata! cavities
RL downward long wave radiation
Rs global short wave downward radiation
Rn net radiative flux density
ra aerodynamic resistance to water vapour movement
rst bulk stomata! resistance to water vapour movement
t elapsed time
Tij i component of surface force on plane normal to j direction
T0 surface absolute temperature
ui i component of velocity
u'i fluctuation of velocity from mean value
mean value of velocity
face velocity
W energy stored in surface layer
Ya direct storm runoff
Yb baseflow
z elevation
b soil parameter depending on pore size distribution
g pyschometric constant
D slope of saturation vapour pressure-temperature curve
d ij Kronecker delta formation
q temperature
l secondary or bulk viscosity
µ dynamic viscosity
P density
s Stefan-Boltzman constant
t ij second order shear tensor


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There is danger of confusion from the use of the relative prefixes micro, meso, and macro unless these are defined. It would seem reasonable in hydrological and climatological contexts to relate them to the thickness of the earth's boundary layer (say ? km).

Whilst it is true that the main aim of GCMs is climatic simulation for periods longer than 15 to 30 days (GARP 1974), it needs to be demonstrated that earth surface pro cesses of much shorter duration do not have significant impacts on regional climates.

Surface information often needs to be collected for time steps as short as 20 minutes (radiation measurements, for example). In fact this interval is comparable to the time steps used in many GCMs. In using average temperatures we ignore the diurnal temperature regime, which is very marked even in the humid tropics. Similarly, within the biosphere we find strong diurnal cycles, transpiration for example, and it is possible that these are coupled with diurnal cycles of convective precipitation. By using such data we may distort the effects of processes that are far from linear. However, at this more detailed scale we find that other parameters, such as soil heat flux, need to be considered.

The current trend of introducing biosphere data among the earth surface processes relevant to global atmospheric circulation results in a need for information about the response times of vegetation. At one extreme the response time of stomata to changing levels of radiation is normally rapid, within tens of minutes. However, it is known that the stomata of drought stressed plants recover their ability to open over a period of several days once water is readily available. High temperatures can also result in longlasting responses. One way of relating plant sensitivities to environmental changes is to determine threshold value of the changes beyond which recovery by the plant is no longer possible (i.e. the plant dies). So far, attempts to introduce relevant vegetation characteristics into macroscale models (e.g. by defining the evapotranspiration as a proportion of the drying potential of the atmosphere) have treated the plant canopy as if in equilibrium with both the climate and the soil and so avoid multiple plant-surface parameters. The development of transient state models, with a time trend towards or away from equilibrium conditions for different vegetation coefficents (leaf area, rooting depth, surface roughness), would be of greater relevance to our present considerations.

There is a danger when working at one scale to become prejudiced against extrapolation of results and even concepts to another scale. Thus descriptions of hydrological processes that form the building blocks of physical hydrology are often abandoned in favour of black box models at the larger scale. However, the approaches to hydrology, in its widest sense, need not be contradictory at different scales. The apparent contradiction arises because when there are enough ordered elements or events combined in a more or less random manner, stochastic methods can be used at the larger scale that would be totally inappropriate at the smaller scale. In fact, Professor Dooge shows that it is possible to combine deterministic approaches (the physics of infiltration) with stochastic methods (the statistical distribution of climatic elements) at the larger scale. This demonstrates that possibly the best approach in the future for transfer between scales in hydrology is to interpolate from both larger and smaller scales to the required intermediate scale. Whilst the procedure must nor violate continuity, it cannot be expected to utilize the laws of conservation of energy which are the basis of macroscale approaches. It is possible that at the mesoscale entropy considerations could be used.

Modern systems hydrology generally adopts an a posterior) approach rather than applying hydrological physics a priori. This former, inductive approach, combining crude approximations of physical processes and considerations of the continuity of the system, generates models that then require empirical adjustment of the many constants to match actual observations of inputs and outputs. By this stage they may often be so remote from the physical processes involved that doubts must arise as to their value in predicting conditions outside the range that was used to construct the model. Whilst we must now try alternative approaches, it must be said that the method has led to useful, if limited, progress over the last 20 years.

The serious limitations of the black box approach were illustrated by a competition initiated by the World Meteorological Organisation. Reliable data from several watersheds were provided for a period of four years to allow calibration of the models in the contest. Water inputs for the following three years were then supplied, from which the models predicted water yield. Most of the models failed to predict the yield any more accurately than a forecasting method that did not attempt to model hydrological processes.

It seems that for some purposes, models of many parts of the hydrological cycle do not warrant great precision because spatial and temporal inhomogeneity mask the effect of this. It appears that conceptual models have many drawbacks, with the results that there is a pressing need to seek radical alternatives that reflect the real world but overcome the inhomogeneities present so that large-scale biosphere hydrological outputs can be used in GCMs.

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