Construction of hydrological models for natural systems management

Mathematics North-Holland

and Computers

in Simulation

32 (1990)

13

13-37

CONSTRUCTION OF HYDROLOGICAL SYSTEMS MANAGEMENT

MODELS

FOR NATURAL

T.G. CHAPMAN Emeritus

1.

Professor,

University

of New South

Wales, Kensington,

NS W, Australia

scorn

1.1 Deiinition of a natural system

For the purpose environmental man-made

of this paper, the term ‘natural system’ will not be restricted

systems which occur without human intervention,

system which has sources

impoundment

or sinks in the natural

of mine process water falls within this definition,

but will include

to any

Thus an

environment.

because it is subject to

inputs of rainfall from the atmosphere, and it loses water by evaporation to the atmosphere and possibly to the underlying groundwater system. 1.2 Examples of types of models considered The aim of the paper is to try to draw some threads

together

in relation

to the

construction of hydrological models for the widest possible range of situations and purposes related to natural systems management.

Some examples of such models recently reported

in the Australian literature are the forecasting of crop yields in different environments predicting salinity

the effect of changes in land management [2], predicting

impoundments

the fate

of solutes

entering

on groundwater groundwater

[l],

levels and stream from

landfills

or

of polluted water [3], predicting runoff and seepage from waste rock dumps

[4], predicting the quantity and quality of runoff from urban areas [5,6], determining the roof area and size of storage tank required to provide a given quantity of supply to a dwelling [7], predicting the hydrologic effects of forest management [81 and fire in forests [91, modelling saline intrusion into aquifers [lo], relating plant interception losses to canopy architecture and forest management [ll],

modelling the inflow and transport of salinity and pollutants in

rivers

schemes

[12,13,141,

studying

for artificial

recharge

of groundwater

[151, using

modelling to evaluate irrigated agriculture [161, and predicting erosion hazard [17]. 1.3 Coupling with other models

These examples

show that hydrological

models must frequently

coupled with other models. Figure 1 exemplifies 0378~4754/90/$3.50

8 1990,

IMACS/Elsevier

Science

Publishers

be designed

to be

such a coupling, for the case where the B.V. (North-Holland)

14

T. G. Chapman

/ Hydrological models construction

outputs of a plant growth model depend on the state of the soil water in the plant root zone. The plant growth model provides feedback to the hydrological model by varying the depth of plant roots which deplete the soil water, the area of surface available to transpire water back into the atmosphere,

and possibly by

modifying

the evaporation

from the soil between

individual plants, through the effect of shading.

Fixed hydrological

Climatic inputs

HYDROLOGICAL

[Rainfall, evap. etc)

MODEL M c; m ‘Auk 2.5; %E @a &e”

Induced

changes

(Nutrients etc)

Outputs (streamflow etc) &

A

2 3

-S 3% ?a a: *a 8% %2

2 8 2 r;: Z

PLANT GROWTH MODEL

FIGURE 1 Coupling a hydrological process model with a biological process model 1.4 Space and time scales The examples cited above show that the area of interest and application of a hydrological model may range from what is generally referred to as a ‘site’ (a few m2 in extent) to subcontinental areas, such as the Great Artesian Basin. from a few minutes in discriminating

Similarly, the time scale may range

the peak of a flood on a small urban catchment, to

decades in estimating the long-term effects of a change in land management on the level of the water-table. 1.5 Climate and tqmgraphy It will be shown that the active pathways in the hydrological system, and sometimes the directions

of flow in those pathways,

precipitation hydrological

depend

on the relative

(rain plus snow) and the evaporative

demand

magnitude

of average

of the atmosphere.

The

dryness of the climate in a given location can be estimated by the ratio of

T.G. Chapman

precipitation

to potential evaporation,

15

/ Hydrological models consfruction

calculated by an energy balance technique such as

that of Budyko or Penman, and world maps of this index have been published f.18,19]. It will also be apparent that topography is a major determinant

of the nature of the

surface runoff system, which finds expression in areas with an organized drainage network (with a typical organized

tree structure)

pattern

comparative

when surface land slopes are adequate,

(distributaries,

hydrology

braided

channels

etc) in flatlands.

and in a less

In a new text on

[201, the main breakdown in the chapters on regional hydrology is

between ‘areas with catchment response’ and ‘flatlands’. A complicating

factor in classifying hydrological

regimes in different areas is that the

hydrology is not necessarily determined by inputs within the area (endogenous conditions), but may depend depends

on external

inputs

(exogenous

on the size of the area under

conditions

can be seen as occurring

exogenous

inputs

climatic zone.

occurring

conditions).

consideration.

in the repetitive

episodically

from adjacent

This definition

On a small scale, landscapes sloping

of course

endogenous

of arid plains, land within

with

the same

On a larger scale, a typical arid regime may be substantially modified by a

river which has its source in a more humid zone hundreds of kilometers Murray-Darling

basin under pre-irrigation

It is noteworthy

that most textbooks on hydrology are strongly biased towards humid

areas with well-organized area of Australia.

away (e.g. the

conditions).

drainage systems, conditions which occur over a relatively small

While trying to maintain generality, this paper will place some emphasis

on the hydrology of flatlands in low rainfall areas.

2.

HYDROLOGICAL

SYSTEMS

2.1 Systems of storages and flows The

most

common

conceptual

framework

for hydrological

analysis

and model

construction is a set of water storages linked by pathways of water movement.

The number

and definition of these storages depends on the nature of the problem under study, but the main processes

occurring

at catchment

scale can be described

by the system of twelve

For each of these storages, the water balance (conservation

of mass) equates the net

storages shown in Figure 2. sum of inputs and outputs in a given time to the net gain in stored volume in the same period.

It is usually convenient

to express these volumes as depths of water in mm, as

though the water were spread in a uniform sheet over the whole area.

The water balance

equation may be applied to a group of storages, so eliminating from consideration the fluxes between them, and it may be calculated

for different times (day, month or year).

The

advantage of using a long balance period, such as a year, is that changes in storage are then small, relative to inputs and outputs, and may be neglected as a first approximation.

16

T.G. Chapman

WATER

4

t

f

I-

PLAN- r TR i7

I I

I I

t

I

I I

IN ATMOSPHERE

t

I I

I

I

G1 I

SNOW/K :E

I I

I[

models construction

+ I

CANOPY , I-lINTERCEPTION

/ Hydrological

I I

I

GENERALLY UNSATURATED PLANT ROOT ZONE I

, I 1

I

t

I

I

I I

I I

I I I

I I

I

IA

I II

II

UNSATURATED ZONE BELOW PLANT ROOTS

I

r PERMANENT GROUNDWATER

b

liquid/solid

+--

vapour flow

essentially

flow

essentially

vertical movement within storage horizontal

movement

FIGURE 2 Hydrological

system

for a catchment

(from

[21])

2.2 Turnover times To obtain conceptual defined

a simple

storages

and readily

shown on Figure

as the time required

component.

In the hydrological

estimated

to replace context,

Tr =V/q

measure

of the typical

2, we can adopt a turnover a quantity

of substance

the turnover

time Tr

rates

of change

time as used in ecology equal

to the amount

is defined

by

of the 1221, in the

17

T. G. Chapman / Hydrological models construction

where V is the average volume of water stored and q is the average rate of output. Table 1 shows that there is a characteristic

range of turnover times for each of the

storages shown in Figure 2. These typical times are an indication of the dampening effect of the storage on inputs of water or energy, and show clearly why the effect of a change in input may not be detected for a long time in subsurface storages below the plant root zone. If the precipitation occurs as snow or if the water in the storage is frozen, the turnover times will generally be much longer than those listed in Table 1. TABLE1 Typical

parameters

of hydrological

___---_-------------------------------------------------------_-

DEPTH (mm)

STORAGE

--~--------------------------

ATMOSPHERE INTERCEPTION LITTER PLANTS DEPRESSIONS OVERLAND FLOW STREAMS & RIVERS PLANT ROOT ZONE VADOSE ZONE GROUNDWATER LAKES & RESERVOIRS OCEANS

2.3

25 0.045 2-7 5-50 0.2-40 l-10 5-3500 10-104 104-105 3.7 x 10s

storages

in sloping

TURNOVER TIME

land

(from

[21])

EVENT HORIZONTAL TRAVEL DISTANCE

--_~---_---_~---~---_---

-----------

8-10 days

Episodic processes With the exception

hydrological

of storages with turnover times of the order of months or years,

processes are essentially

episodic, that is, there are periods of activity (flow

between and within storages), usually called a hydrological event, interspersed with usually longer periods of quiescence, inactive.

Most

during which many of the pathways

of the transport

of surface

and near-surface

between water

storages are

occurs

during

hydrological events, and for each event there will be a range of distances moved by the water in the active storages; Table 1 shows some characteristic

values.

Similar considerations

apply to material, dissolved or otherwise, which is transported by the water. 2.4 Vertical and horizontal procAs also illustrated in Figure 2, hydrological processes can be conveniently

categorized

into two groups, depending on whether the direction of water movement is mainly vertical or mainly horizontal [23,24].

18

T. G. Chapman

/ Hydrological

Vertical processes include interception,

models construction

infiltration and water flow in the unsaturated

zone, both within and below the plant root zone. The extent of horizontal water movement in these processes is typically of the order of a meter. While this movement may be critical to the water balance and nutrient growth,

it has no effect

transpiration

status of vegetation,

at catchment

can also be included

scale.

and so determine

The output

in these vertical

fluxes

processes,

its survival and

of evaporation

and

since the predominant

movement of water is vertical until it reaches the interface with the atmosphere. The mainly horizontal

processes

are overland

flow, channel

flow and groundwater

flow, including shallow saturated flow such as may occur above a relatively impermeable soil horizon. The proportion

of vertical and horizontal

climate and the morphology

processes in an area depends on both the

of the land surface.

With increasing

aridity there is less

opportunity for rainfall excess to occur at the ground surface, and less opportunity for water to move past the plant root zone and join the groundwater system. With increasing flatness of land, overland and channel flow will move more slowly, and the distance moved in all but extreme

hydrological

groundwater

events

velocities

will

decrease;

will be very low.

associated

with dry climate

important

as the climate becomes

because

of low

Thus predominance

water-table of vertical

and/or flat land, while horizontal

processes

gradients, processes become

is

more

more humid and/or the land surface has increasing

slope. These generalizations

for the average climate in an area can be extended to extreme For example, a sand plain or a dunefield in an arid zone

hydrologic events or non-events.

may in an extreme flood display humid zone behaviour, by becoming a shallow lake of water which may move considerable distances along the low regional gradients. a sufficiently long interval between hydrological

Again, if there is

events, horizontal .water movement may

peter out even on sloping land in humid zones, and a regime typical of drylands will exist for a while. 2.5 Energy and materials balances Referring again to Figure 2, it will be noted that each of the fluxes shown by broken lines represents a flux of water vapour.

For this flux to occur, sufficient energy must be provided

to the source storage to causes the change in phase from liquid to vapour.

The energy

balance is therefore critical in determining the partition of the water balance, particularly in relation to the transpiration related

to transpiration,

precipitation,

and evaporation fluxes.

it can be argued

that

Since plant productivity

potential

evaporation,

should be used as the first descriptor of a hydrological

cloud cover and other factors

cause variations

in incoming

is closely

rather

than

regime C251. While

solar energy,

there is an

T.G. Chapman

/ Hydrological

19

models construction

underlying diurnal and annual energy pattern which affects the water balance, particularly on a seasonal basis. When relating

the hydrological

system to natural systems management,

the water

balance equation must be supplemented

by one or more materials balance equations, such

as a sediment balance or a salt balance.

However, these balance equations, which must be

applied to the conceptual storages.

storages in the system, do not define the flows between

the

Another equation is required for each such flow; sometimes these equations can

be based on physical principles (conservation of momentum or energy, Darcy’s law etc), but frequently the complexity of the process necessitates a semi or wholly empirical approach. It is of course vital that such empiricisms should be capable of representing

the range of

behaviour of flows in the real catchment. 3.

HYDROLOGICAL PROCESSES This section will cover only those features of processes which are most pertinent to

model construction; for a more complete description and references to key sources, see [21]. The processes involving mainly vertical movement will be treated first. 3.1Precipitation Most hydrological models regard precipitation as an input rather than a process; where there are multiple rain gauges or rainfall recorders, a lumped input may be obtained by weighted averaging or the model may be run for each gauge and the outputs appropriately distributed or routed.

However, in view of the effect of precipitation characteristics (in terms

of intensity, duration and area1 extent, and whether the precipitation falls as rain or snow) on the nature and extent of subsequent hydrological years been expended

on modelling

the space-time

processes, much effort has in recent fields of both convective

and frontal

rainfall [26]. More simple models [e.g. 271, which use available historical data to produce a synthetic time series of annual, monthly or daily point rainfall, are an important tool when long-term effects of management are to be examined. 3.2 Interceptionby vegetation There precipitation

are three

stages

of the interception

process:-

strikes leaves or wood; then it is re-distributed

in the first,

the incoming

by splashing or flowing on to

other leaves or wood; and finally it falls to the ground as throughflow, runs down the main plant stem as stemflow, or evaporates impact of interception

back into the atmosphere.

is that it reduces the precipitation

amount of water which is evaporated during and and after precipitation.

The main hydrological

that reaches the ground, by the

from the wetted parts of the intercepting

The proportion of the precipitation

surfaces

so ‘lost’ depends on

the nature of the vegetation (usually categorized by an ‘interception storage capacity’), the

20

T. G. Chapman

/ Hydrological

models construction

precipitation regime and the potential evaporation, and ranges from negligible figures up to over 40% [28]. As an example of the impact of land management, the initial increase (-10%) in streamflow following deforestation

of a catchment in southwest Western Australia has

been attributed [29] to the decrease in interception loss (-13% of rainfall) from the vegetation. Interception is usually modelled as a simple storage into which the precipitation falls, and which overflows to the land surface; the water in the storage is assumed to evaporate to the atmosphere

at a rate determined

by the potential evaporation.

storage can be determined independently storm throughflow

and stemflow

on experimental

against

storm rainfall

The capacity of the

plots, by regression analysis of [30].

While

this structure

is

appropriate for models operating at short time intervals (I 1 hr), its common use for daily models is questionable,

and leads to artificially high apparent values of the interception

storage capacity. Where plant litter occurs on the soil surface, it also intercepts both precipitation

and

throughfall from the leaf canopy. While turnover times for canopy water are of the order of minutes, turnover times for water in the litter are likely to be of the order of weeks.

There

has been little attempt to include litter in hydrological modelling, except as part of a freedraining soil surface layer. 3.3 infiltration The process of infiltration 1311has probably received more research effort than any other hydrological

process, particularly

changes resulting

since it has been seen as the key to the hydrological

from manipulation

of the soil surface by agricultural

practices.

In

modern infiltration theory [32] the process is seen as one in which the supply of water to the soil surface results in the downward advance of a wetting front, at a rate which depends on the initial soil water content and which falls with time.

If sufficient water is available to

keep the surface saturated, i.e. in a ‘ponded’ condition, the infiltration rate depends almost entirely on the hydraulic characteristics ponding has little influence.

and initial condition of the.soil, and the depth of

If the surface is not saturated,

the rate of infiltration

is

constrained to be equal to the rate of supply. These features are modelled in the infiltration algorithm

of the Australian

Representative

Basins

model

[33], the time-compression

algorithm described in 1341, and in the multi-layer model of Markov and Mein [35]. Particularly

in natural catchments,

complex, due to spatial heterogeneity, swelling

and cracking

soils,

surface

modelling

the infiltration

process is much more

vertical and horizontal variations in soil properties, sealing,

entrapped

air,

and the presence

of

macropores (soil cracks, root channels, earthworm holes etc) in sufficient numbers to have a major influence

on the infiltration

process.

Recent

improvements

in experimental

techniques, such as the disc permeameter [36, 371, make it possible to carry out replicated

T. G. Chapman

measurements infiltration

at a reasonable

/ Hydrological

21

models consiruction

scale, and so estimate appropriate

parameter

values for

modelling.

3.4 Soil water redistribution This term is usually applied to the processes which occur between infiltration and which may affect the whole soil profile down to the water-table.

Redistribution

events in the

lower layers may continue while infiltration occurs near the surface. These processes are profoundly

affected by the presence or otherwise of active plant

roots, to the extent that the unsaturated soil zone must be modelled as two separate storages defined on this basis.

The presence of plant roots provides a sink for removal of water,

which results in a relatively

rapid turnover

time, of the order of a few weeks.

In the

underlying vadose zone, turnover times are more likely to be of the order of years, and values of the order of 50,000 years have been established for a semi-arid environment [38]. It follows

that the vadose

zone can be conceived

as a zone of one-dimensional

unsaturated flow, with episodic inputs at the interface with the plant root zone, and quasisteady flow towards the water-table. process

of groundwater

recharge,

vegetation cover (particularly

Most of the attempts at modelling

which can be profoundly

this important

altered by changes

in the

changes which affect the depth of the plant root zone), have

been in relatively humid regions. 3.5 Evaporation and transpjration Evaporation

has a primary meaning

which requires the input of energy. from living plants and animals. fluxes between different

of the change in phase from liquid to vapour,

Transpiration

implies the emission of water vapour

For most natural surfaces it is difficult to apportion vapour

sources, and the term ‘evapotranspiration’

[39] is used for the aggregate of all vapour sources in an area.

or ‘total evaporation’

Since evapotranspiration

is

usually second only to precipitation in the water balance, and transpiration is closely related to plant productivity, model structures for this process merit careful attention. In an area with uniform vegetation, the use of the energy balance with the equations for transfer of sensible heat and water vapour into the atmosphere results in the ‘combination equation’ [39] for transpiration E = [CR,-G)S/A

+ ypD/r,l/~S~y~l~r~lr~~l

where Rn is the net radiation

(2)

received at the surface, G is the heat flux into the ground, S

is the slope of the psychrometric curve at the prevailing temperature, A is the latent heat of vaporization

of water, y

is the psychrometric

pressure to the latent heat of vaporization),

p

constant ( ratio of specific heat at constant

is the density of moist air, D

is the saturation

T.G. Chapman

22

/ Hydrological

vapour deficit, ra is the wind-dependent

models construction

aerodynamic resistance of the vegetated surface,

and rs is another resistance which accounts for the vapour path through the leaf stomata. This leaf resistance can be a major determinant

of the transpiration

from the vegetation,

and its value at any time is determined by complex feedback mechanisms depending on the water content in the leaf tissue, the saturation deficit in the air at the leaf surface, and the plant demand for carbon dioxide, which in turn depends mainly on light and temperature. As a result of these complexities, the usual approach to modelling evapotranspiration is to define a potential evaporation E0 by setting r, to zero in (21, and to use the estimated soil water content in the plant root zone as a surrogate for rS . The potential evaporation can be calculated

from meteorological

data and an assumed relationship

for the wind velocity

profile near the surface. evapotranspiration

There are two commonly used algorithms to estimate actual E from potential evaporation EO and soil water content 8 . In the

first (e.g. [40] >,the ratio E / E,, is taken to be a simple monotonic function of 8 , E = E, f(e/e,) where E + E,

as 8 +

(3)

$ , the soil water content at saturation, and E +

the soil water content at a high soil water potential (the ‘wilting point’). the evapotranspiration

0 as 0 +

f3, ,

In the second [33],

is taken as the smaller of the atmospheric demand for water and the

ability of the soil-plant complex to supply it:E = min [E,, where Es is the maximum

Esf3/f3s]

rate of evaporation

(4) under conditions

of non-limiting

water

Although the second algorithm appears conceptually more satisfactory, supply. comparison of the effectiveness of the two approaches appears to have been made.

no

We now move to those processes in which horizontal movement predominates. 3.6 Surface runoff generation The classical view of the surface runoff process, developed by Horton [41], is that it results

from

rainfall

excess

which

occurs

when

the rainfall

intensity

exceeds

the

infiltration rate. While this concept is valid and useful at a site, its extension to catchment scale

can

be

microdepressions

quite

misleading.

on the land surface.

Rainfall

excess

tends

to

accumulate

first

in

When these are surrounded by areas of non-ponding

infiltration, runoff occurs from the ponded areas across the non-ponded

areas, so that the

catchment consists of a patchwork of runoff and runon areas. As surface slope is critical in determining both depression storage capacity and the rate at which surface water will move downslope, runoff into the streams may occur from only favourable parts of the catchment,

23

T.G. Chapman / Hydrological models construction

called source areas.

These source areas will vary in extent during the progress of a rainfall

event. An alternative

mechanism

of surface runoff generation is that infiltration

raises the

level of the saturated zone to the point where it reaches the surface in lower parts of the land profile, and overland shallow groundwater relatvely impermeable

flow occurs in these areas.

developed over

If the topography is sufficiently steep and the surface soil

subsoils.

to stream channel flow. mentioned

zone may be the local

system, or it may be a transient perched water-table

sufficiently permeable, groundwater Australia

The saturated

flow in this zone may add significantly

(as ‘interflow’)

In the example of the deforested catchment in southwest Western

earlier 1291, a gradual

five-year

increase

in streamflow,

after the

initial increase due to decreased interception, was attributed to a slowly rising water-table which increased the area of groundwater There are major differences mechanisms

discharge.

between

the flow velocities

Flow velocities

of runoff production.

associated

due to the Hortonian

with these two process range

between 10 and 500 m h-l, while saturated overland flows range from 0.3 to 100 m h-l; in contrast, subsurface storm flow velocities are typically of the order of 10e4 m h-l [71]. 3.7 Surface flow routing In contrast with the difficulties in predicting the space-time characteristics runoff generation,

there has been considerable

as it moves down the catchment.

of surface

success in modelling the runoff hydrograph

The problem is one of open channel hydraulics with given

inputs (and outputs, in the case of a stream undergoing transmission loss to groundwater), but the complexity of the channel pattern in upland catchments prevents the use of the full hydraulic equations except for routing flows on main rivers.

Techniques with smaller data

requirements are systems methods, storage routing, and the kinematic wave assumption. The best known system technique is the unit hydrograph, flow system is linear.

For a gauged catchment, the unit hydrograph can be determined [42]

from analysis of distinct flood hydrographs by assumptions

which assumes the surface

and the associated rainfall excesses, estimated

about the time distribution

of infiltration

and other

‘losses’.

These

assumptions can be eliminated by recently developed techniques which use streamflow data only [43], but there remains a subjective element in separating the surface runoff from the base flow. The

parameters

characteristics

of such

(area, length

unit

hydrographs

may

then

and slope of main channel

be related

to catchment

etc) by statistical

techniques

[42,44,451. The errors of prediction of such methods are relatively high, due to the arbitrary choice of catchment hydrograph

parameters

parameters.

Recent

and the unknown developments

nature of their interactions

146,471 attempt

with the

to make better use of

established morphometric properties [481 of the stream channel network.

24

T. G. Chapman / Hydrological models construction

The systems approach has also been extended to nonlinear Volterra

series

method

of Amorocho

and Orlob

techniques,

[491, recently

further

such as the developed

by

Napierkowski and O’Kane 1501. The storage routing approach attempts to integrate simple mathematical

relation between

channel flow parameters

the water stored in a channel

overland flow paths and network of channels in a subcatchment) channel or subcatchment. K

subcatchment.

reach (or in the

and the output from the

Sometimes, as in the well-known Muskingum technique [51], the

input is also included in the equation. parameter

into a

If linearity is assumed, there is one catchment

(the ratio of storage to output, i.e. the turnover time) for each reach or Frequently

the relative K - values for subcatchments

are estimated from

measurements of channel morphometry [42], and the single value required to establish their magnitude is obtained by fitting predicted output to observed flood hydrographs. The extension of the storage routing approach to nonlinearity is relatively simple, and usually involves a power relationship [52] between storage S and discharge Q of the form (5)

S=KQm

where m is an exponent which is usually less than 1 for catchments and more than 1 for river

reaches,

subcatchments.

and is usually

taken

As the parameters

catchment characteristics is difficult.

to have

K

and M

the

same

value

for all reaches

are not independent,

relating

and

them to

Recent work on the behaviour of river channels [53]

questions the ability of power functions to describe catchment response over a wide range of discharge. 3.8 Groundwater recharge and discharge There are two main mechanisms

of groundwater

recharge, general percolation

of soil

water which moves past the plant root zone, and percolation from the beds of streams, rivers and alluvial fans. With some qualification, the first is typical of humid areas and the second of arid areas. In the first

mechanism,

there

is likely

to be considerable

spatial

groundwater recharge, with much of it having its source in local runon areas.

variation

in

There have

been few attempts to quantify such variations and relate them to the characteristics

of the

land surface and subsurface. Although water balance considerations

suggest that rainfall in arid zones will seldom

move beyond the depth (typically two meters) above which it may be transpired or evaporated back into the atmosphere, general percolation to groundwater may occur in extreme events in which the land surface is generally flooded.

These very rare recharge pulses, which may

25

T. G. Chapman / Hydrological models construction

then take decades or centuries to reach the water-table, may be the only source of recharge in areas with no stream channels, and in dunefields. The second recharge

mechanism,

percolation

to the water-table

from stream beds,

takes two forms, depending on whether there is a saturated connection between the stream and the water-table

[54].

Where no connection

stream bed to the water-table, laterally

exists, water moves downward from the

forming a linear groundwater mound which then dissipates

away from the stream.

This is typical in arid zones, where water-tables

generally deep (some tens of meters).

are

In less arid areas, water-table levels tend to rise closer

to the stream bed, and a hydraulic connection may be developed between the stream flow and the groundwater;

the recharge

rate will then decrease

recharge process will be dominated by horizontal

as the water-table

rises.

The

rather than vertical flow 1611, and will

have a much shorter turnover time than the disconnected flow process. There are also two main mechanisms for groundwater discharge, largely depending on whether the climate is humid or arid. The first consists of approximately horizontal flow to springs, streams, lakes [61] or the sea, while the second consists of vertical movement by transpiration from phreatophytes

or evaporation from shallow water-tables.

In more humid areas, transpiration groundwater

discharge,

from wetlands

with much of the groundwater

not far from where it reached the water-table.

can be a major mechanism

for

being returned to the atmosphere

This contrasts with evaporation from playas

and salt lakes in the arid zone [551, which often are the terminal points of an extensive groundwater system, with a travel time typically of hundreds or thousands of years between points of recharge and discharge. 3.9

Transport

and reaction processes

The relation of hydrology to natural systems necessitates

consideration

of the role of

water as a solvent, and as a means of transport of sediment, nutrients and pollutants.

In its

role as a solvent, it is often possible to study a particular chemical or biological reaction from the viewpoint of either equilibrium or kinetics, depending on the rate of reaction relative to the turnover equilibria hydrological

time of the system [56].

are reached

in periods

turnover

times which

For example,

many chemical

of less than a second generally

and ion exchange

to minutes

compared

range from hours to years,

with

while other

reactions are so slow as to warrant neglect except over periods of geological time. However, there is a wide range of reactions (including most biological processes) where the reaction rates are comparable with hydrological turnover times, and these must be considered on the basis of reaction kinetics 1571. Space does not permit the description here of the changes in water quality associated with the individual processes in the hydrological system; an account is given in [58].

T.G. Chapman

26

4

/ Hydrological

models construction

MODEL CONSI’RUCTION The foregoing description of the main hydrological

processes has been slanted in the

direction of emphasizing the relation of the mix and nature of processes to the environment, which may be broadly categorized in terms of climate, topography,

so& and

vegetation.

The

greatest care must therefore be taken in constructing a model which is appropriate to the environment

under study, and which has the capacity to meet an objective

in natural

systems management. Most hydrological catchment,

models have been constructed

to meet objectives

of extending

in the context of a time-invariant

streamflow

sequences in gauged catchments,

estimating streamflow in ungauged catchments, or modelling groundwater

systems.

Their

use for natural systems management immediately implies a changing catchment, and the need for the model to be able to predict the short and long term effects of catchment changes on surface and subsurface water flows and quality.

This requires much greater emphasis

on modelling the interaction between vegetation and hydrology, and on modelling what are often small residuals in the overall water balance, such as groundwater hydrological

models used for non-changing

determined

from

a calibration

process,

catchments models

recharge.

Where

can be effective with parameters

for changing

catchments

must

use

parameters which can be identified with the changes taking place. 4.1 Model classi6cation While a complete classification useful for present purposes.

scheme is not proposed here, some definitions may be

The first is a distinction between complete and partial models.

A complete model can be considered as one which models all the hydrological processes in the land phase of the hydrological

cycle, that is, all the relevant storages in Figure 2,

except the atmosphere and the oceans. the sink for evapotranspiration,

The atmosphere is the source for precipitation and

while the catchment outlet is the sink for streamflow.

Partial models focus on selected storages in the hydrological system, and either omit or use very simplistic algorithms surface hydrology accounted

for the other storages.

which regard

groundwater

for, and models of groundwater

recharge

Common examples are models of as a ‘loss’ which

systems which make arbitrary

need not be assumptions

about the amount and distribution of recharge. The distinction between deterministic and stochastic models is well known and need not be elaborated here.

In the context of natural systems management,

have at least a major deterministic

it seems essential to

component, but stochastic techniques

have utility in

handling uncertainty due to errors in data and model structure [591, and in providing longterm synthetic input sequences [27] from which the full range of model responses may be determined.

T.G. Chapman

/ Hydrological

27

models construction

A less sharp distinction is between simulation or process models on the one hand and black box or empirical models on the other.

In fact, most process models employ empirical

algorithms to describe processes which are not well understood or too complex for analytical treatment at the space and time scales under consideration,

while the more modern black

box models [e.g. SO] deliberately employ a structure intended to distinguish between different flow components in the hydrological system. Models can also be categorized as ‘lumped’ or ‘distributed’, spatial

distribution

‘stationary’

of inputs

is ignored

or ‘non-stationary’,

depending

depending on whether the

or included

in the model

structure,

on whether

the parameters

and as

are constant

or

change with time, due to biological processes or changes in land management. 4.2 Time SC&S Hydrological

models for natural systems management

are generally

concerned

with

determining the changes in average water balance, or flows in particular components, over relatively long periods of time (months or years).

However, simulation of surface and near-

surface processes at a site demands much smaller time scales, down at least to the order of an hour, if any degree of similarity with the real world is to be achieved.

When this is not

feasible (as often occurs, since daily rainfall data is much more commonly available than continuously

recorded

data), the model cannot be expected to perform satisfactorily

for

individual events, but may nevertheless give useful predictions of aggregated outputs 1621. Extension of the area of interest from a site to a larger system, such as a catchment or an aquifer, attenuates

short-period

daily or even monthly intervals.

variations and allows the use of a model operating at

However, as noted above in the discussion on interception,

care should be taken in transferring careful

consideration

short-period

of their plausibility

algorithms

and the effect

to longer periods without

on the numerical

values

of

parameters. 4.3 Spacescales The difficulties

in transferring

hydrological

model results

from smaller

to larger

catchments were recognized as long ago as 1963, when Laurenson and Pilgrim showed [63] that

infiltration

considerably

determined

by ring infiltrometers

higher than storm loss rates determined

due to spatial increasing

rates

heterogeneity

importance

in surface

and sprinkled

on catchments.

and subsurface

plots

were

The problems are

catchment

parameters,

the

of storage with increases in catchment size, and the different mix

between surface and subsurface flow components in small and large catchments [64]. It has recently been recognized that difficulties with spatial heterogeneity can be largely attributed to unsuitable scales of measurement of relevant parameters. hypothesized

that many of the complexities

of catchment

processes

It can reasonably be at site scale will be

T.G. Chapman

28

greatly diminished

at catchment

/ Hydrological

models construction

scale, in the same way that the complexities

of porous

media flow at the scale of individual soil or rock particles yield to the simplicity of Darcy’s law at a scale of a few centimetres. infiltration

parameters

Williams

and Bone11 [653 recently

measured at the scale of an infiltration

showed

that

ring (300mm) were much

more variable than parameters measured at the scale of a runoff plot (lOm>, while Sneddon and Chapman

1661, in a photogrammetric

study of surface

depression

on small plots

(2.6x1.2m), found that the predominant storage was in depressions too large to be adequately sampled

at that

scale.

Bear

[671 andYoungs

1681 have put forward

the idea of a

representative elementary volume (REV) large enough to contain an adequate sample of the parameter under study. This gives the impetus to measurements at larger scales than have been usual in the past, but poses the difficulties of considerably increased cost unless new experimental techniques can be devised. ranging from sites through

hillslopes

The idea of measurements

in nested catchments,

to first order and then larger

order streams, as

suggested by Chapman 1691,has not yet been fully exploited, but Wood et al [74] have worked from the subcatchment level upwards, using actual topography and synthetic realizations of rainfall and soils, to demonstrate the existence of a representative for catchment response.

elementary area (REA)

This REA (about 1 km2 in their catchment)

was defined as the

minimum area above which the simulated catchment response stabilized. Similar

difficulties

exist in modelling

groundwater

systems,

where

prohibits more than the most sparse sampling of aquifer properties, significant interchanges mechanisms

and there may be

between aquifers at different levels, with little known about the

of recharge

spatial averaging,

cost usually

and discharge.

field measurable

As stated in [70], ‘....model

values, and spatial variability

parameterization,

are interwoven

in a

complex way’. 4.4 Some aids in model selection It will be clear that careful thought should be given to selecting appropriate

time and

space scales for a hydrological model to meet its objectives as a predictive or monitoring tool in natural systems management.

When these scales have been selected, consideration

can

be given to which hydrological processes must be modelled in some detail and which can be grouped or otherwise receive a broad brush treatment.

The following paragraphs

list a

number of simple tools which can assist the modeller to make these choices. The first step is to consider the climate and land morphology as determining the nature and importance of the hydrological processes in the area under study. An idea of the overall water balance streamflow,

can be obtained taking

evapotranspiration,

the

by looking

difference

at estimates

between

these

as

of mean annual a first

and comparing it with potential evaporation

data to obtain an indication

of the importance

estimate

rainfall

and

of annual

estimated from climate

of plant water stress

as a constraint on

29

T.G. Chapman / Hydrological models construction

evapotranspiration.

Boughton [731 has shown how to use detailed rainfall and streamflow

records to obtain information inconsistencies

about the water balance and, most important, bring out any

in the data.

The effect of land morphology can be studied by using aerial photographs,

which show

the nature and density of the stream drainage system. The depth of the water-table should be considered, in relation to plant root depths and also stream channel

levels.

Model structures

are necessarily

more complex

when the

water-table is sometimes within the plant root zone and sometimes below it, and when the water-table is sometimes above the stream bed and sometimes below it. If both surface and subsurface processes are to be modelled, it will frequently be feasible to have a much longer time scale for the groundwater than for the surface processes, and it may even be possible information

to model the groundwater

is available

on aquifer

geometry

If a little

as a steady flow system.

and hydraulic

characteristics,

it will be

possible to obtain a first estimate of the groundwater turnover time. If this is twenty years or more, a steady flow model will probably be adequate. unsteady flow model of groundwater regional groundwater

It may also be appropriate to couple an

in valley alluvium with a steady flow model of the

system.

Where the water-table is above the stream bed, analysis of streamflow recession curves is a useful tool in determining the magnitude and probable source of low flows.

Recessions

frequently take the form of drainage from a linear storage, and the change of discharge Q with time can then be expressed in terms of the turnover time T,. of the groundwater system by Q = Q.

where t

e4’ Tr

(6)

is the time since the discharge was Q.

. Turnover times of a few days are usually

associated with storage in stream banks or valley alluvium, while values of the order of weeks or months are evidence of a true base flow from a large groundwater water balance groundwater

in the model should have a means of accounting

The

for the source of all

which becomes streamflow.

Groundwater

recharge

from

streams

can seldom

be estimated,

available from more than one stream gauge on a main channel [72]. recharge

system.

from water percolating

unless

data are

A rough value of

beyond the plant root zone may -be obtained from the

annual precipitation and plant root depth. 5.

PBQBLEMSANDPBQSPECI’S This paper has concentrated

on process simulation modelling of hydrological

systems,

because in the context of natural systems management it is necessary to make predictions of

30

T.G. Chapman / Hydrological models construction

changed hydrological behaviour without calibration of parameter values by comparison with observed data. It is therefore important that modellers should be realistic about our current capabilities in this area. In a paper on trends in catchment modelling given in 1975 [69], I pointed out that in an international comparison of lumped catchment models organized by WMO [75], a black box model performed at least as well as any of the process simulation models, and I attributed this at least partly to a lack of use of such catchment data as were available. noteworthy

that all models performed appreciably

It was also

worse on the two catchments

rainfall areas, and these arid zone problems have been subsequently

in lower

highlighted

in later

work [761. Since that time, there has been a strong trend towards the use of distributed models, and much more use has been made of catchment data (particularly topographic data, since this is most readily obtained in computer-compatible topographic

analyses

have been combined

form by automated

with simple hydrological

means).

concepts

These

to define

surface saturation zones in natural catchments I771 and to predict areas subject to erosion [171.

Other models, such as the Institute of Hydrology

Systeme Hydrologique

Europeen

Distributed

(SHE) [791, use a grid concept

Model [78] and the

to define surface and

subsurface properties at a large number of points in the catchment, but suffer from a lack of plausibility

in that the process

descriptions

embodied

in the model

algorithms

are

appropriate to a much smaller scale than the usual grid size (typically 250 x 250 m), while the whole concept of a regular grid appears contra-intuitive surfaces.

in relation to natural land

It has been argued [801 that these current computer- and data-intensive

models

are in fact lumped conceptual models, and offer little advance in physical plausibility over the first generation of lumped models. It has been suggested

earlier that quite different

algorithms

may be required

to

represent at larger space and time scales those processes which may be quite adequately described at smaller scales, but no coherent methodology this task.

Morel-Seytoux

has been formulated to perform

[81] has suggested a reductionist approach to the integration

of

processes of stream-aquifer interaction, while Klemes [821 has shown the utility of relatively simple data analysis

in developing

streamflow and evaporation. climate models,

Eagleson

a structure

for relations

between

monthly

At the even larger scale required for interaction

has developed

concepts

of dynamic

water balances

rainfall,

with world I831 and

ecological optimality [841. However, Kartvelishvili ([851, as quoted in [821) may be realistic in suggesting

that

the development

of an adequate

hydrological

theory

may be more

demanding than was the development of the theory of relativity or the quantum theory. Following such a statement, no breakthrough

could reasonably be expected from any

proposals made in this paper, but I will put forward three low-key suggestions that I hope are constructive.

The first is that I believe that some assistance in spatial integration could

31

T G. Chapman / Hydrological models construction

be provided storages.

by analysis

Particularly

analysis requires parameters

of frequency

distributions

of residence

near the surface, these distributions

further data in the form of time variations

(including

environmental

and applied

isotopes)

times in hydrological

are time-varying, in relevant and/or

and their

water quality

an application

of

queueing or mixing theory, e.g. [861. The next suggestion methods of measuring

is that more effort should be given to developing

the parameters

which determine

transpiration

cost-effective

rates, particularly

the water storage capacity of the active plant root zone, as it varies through the growth, maturity

and senescence

stages of the vegetation.

This appears to be the best single

indicator of the effects of changes in land use and management

on the hydrological

system

Bi'l. Finally, applications of remote sensing to hydrological modelling at the catchment scale should be further pursued, in spite of the disappointing There appear to be real possibilities

of useful area1 estimates

application to modelling requires that measurements intervals,

preferably

sophisticated

level,

progress in the last twenty years.

daily, and this has not been feasible more

use could be made

of soil water [88], but

should be available at relatively short

of aerial

to date.

photograph

attempting to define REA’s from repetitive patterns of vegetation,

At a much less interpretation

in

soils and topography; a

start in this direction was made in the ecological map of the smooth plainlands of Australia [89] developed as a basis for hydrological experiments in the typical repetitive units of these flat landscapes. It will be seen that hydrologists have a long way to go before they can confidently make predictions about the hydrological effects of changes in natural systems management; there is endless scope for the range of disciplines represented at this Simulation Society meeting to make a real contribution in this area. References [l]

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dynamic behaviour

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Water

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