Rainfall-runoff modelling of the Ouse basin, North Yorkshire: an application of a physically based distributed model

Journal

Journal of Hydrology 181 (1996) 323-342

Rainfall-runoff modelling of the Ouse basin, North Yorkshire: an application of a physically based distributed model L.S. Kuchmenta,*, V.N. Demidova, P.S. Nadenb, D.M. Cooperb, P. Broadhurstb aWater Problems Institute, Russian Academy of Sciences, Moscow, Russia bInstitute of Hydrology,

Wallingford OX10 8BB, UK

Received 14 July 1995; accepted 25 July 1995

Abstract

A physically based distributed rainfall-runoff model is applied to the basin of the River Ouse, North Yorkshire, with a catchment area of 3315 km’. The model includes a description of overland flow, subsurface flow, vertical water transfer in the soil, evapotranspiration, and channel flow in the river network. The finite-element schematization of the catchment provides a representation of the drainage network and the spatial pattern of topography, soils, and meteorological inputs. Most of the parameters of the model are determined on the basis of the topography and measured soil characteristics. Other parameters are calibrated using 15 min rainfall and flow data for six flood events and daily rainfall and runoff data for 1986. Temporal disaggregation based on the average variability method of Pilgrim et al. (Civ. Eng. Trans. Inst. Eng. Aust., CEll: 9-14, 1969) is used to generate hourly estimates of rainfall from daily measurements. Model simulations are compared with daily flow measurements for the years 1987-1990. Results show that the model can simulate catchment outflows satisfactorily while giving hydrologically meaningful estimates of internal variables.

1. Introduction The impetus for the further development and application of physically based distributed models of runoff generation has come from two directions: first, the wish to improve the process representation and predictive capability of runoff modelling through the effective use of available experimental and observational data; second, * Corresponding author. 0022-1694/96/$15.000 1996 - Elsevier Science B.V. All rights reserved SSDI

0022-1694(95)02916-8

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the need to help solve urgent environmental problems associated with man’s impact on the hydrological cycle, erosion and water quality. Examples of physically based models of runoff generation and their applications have been given by Kuchment (1980), Abbott et al. (1986a,b), Bathurst (1986a,b), Kuchment et al. (1986), Beven et al. (1987) and many others. Perspectives on the development and application of physically based models have been reviewed by Abbott et al. (1986a), Beven (1989), and Bowles and O’Connell (1991). Lumped conceptual models, which are commonly used in hydrological practice, contain aggregated empirical parameters which have a complicated physical interpretation and a large range of variation. In contrast, physically based distributed models of runoff generation include parameters with clear physical meanings. The values of these parameters can, therefore, in principle, be evaluated from direct measurements in a given river basin or from a priori information gained from laboratory or field investigations of hydrological processes and of runoff formation in similar physiographic conditions. However, physically based models of runoff generation, although attempting to depict processes accurately, are still only models and their ability to simulate and predict the behaviour of any given river basin depends on the adequacy of their representation of the basin, available information, and the computational procedures used. Furthermore, because of small-scale spatial variability in river basin characteristics and inadequacies in representing the hydrological system, physically based models of runoff generation can, in practice, give satisfactory results only if, instead of measured or a priori values, effective values are used for some parameters. These are assumed to take into account additional processes not described by the model, subgrid effects, and any systematic errors. They are commonly estimated by calibration with observed runoff and, therefore, physically based models may, in practice, differ little from conceptual models and include the same basic assumptions and relationships. They do, however, offer scope for preserving observed internal structure and known variation. It is also anticipated that the agreement between effective and measured parameters will be continuously improved with refinement of the models and better treatment of available information. Another important advantage of physically based models of runoff generation is the opportunity to use simulation to explore different assumptions and physical hypotheses about the particular basin and its mechanisms of runoff generation. Such sensitivity analyses, coupled with observed data, allow the ‘deciphering’ of dominant processes and the choice of model structure. A good correspondence between the model structure and the prototype may be supposed to facilitate fitting the model parameters and increase the predictive capability of the model. Although it is clear that success in model fitting depends to a great extent on available data, in many cases a priori information even on the possible range of parameter values can significantly decrease uncertainty in their estimation. The clear physical meaning of the parameters in a physically based runoff model also simplifies the prediction of anthropogenic changes and the coupling of runoff production with models of other hydrological and geophysical phenomena. In this study, a physically based model of runoff generation for the basin of the

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River Ouse above York, UK, has been constructed on the basis of hydrological models and numerical procedures developed by Kuchment et al. (1983). The finite-element schematization of the river basin provides a representation of the river network and spatial pattern of topography and soil type within the catchment. The structure of the model was chosen as a result of an analysis of available observations and sensitivity to model parameter values. One of the specific objectives of this model is to provide long time-series of daily fluxes of water from the basin and predict such time-series for a range of scenarios relating to future basin and climate change. This paper focuses on a description of the model, the schematization of the catchment, the available a priori information and how it was used, and the calibration procedure. Simulation of both flood events and the annual flow regime are illustrated.

2. Study area The Ouse basin, North Yorkshire, comprises the three main rivers of the Swale, Ure and Nidd. At Skelton, just above York, the catchment is 33 15 km2 in area. It has a mixed geology of Carboniferous Limestone and Millstone Grit in the Pennine headwaters to the west and Permo-Triassic rocks to the east. Elevation varies from 710 m above sea-level to 10 m at the basin outlet in the Vale of York. The main rivers rise on upland plateau areas, where peat deposits overlie Millstone Grit, and flow through glaciated valleys with steep side slopes and relatively wide, flat valley floors. Much of the area is covered with boulder clay, whereas the Vale of York has a range of drift deposits varying from glacial sands and gravels to lacustrine sands, silts and clays. Following the relief is a steep rainfall gradient from west to east, with average annual rainfall ranging from over 2000 mm to 650 mm. The distribution of land use (Fuller, 1993) in the catchment reflects both the topography and the rainfall distribution, with moorland (24% of the basin) and grassland (33%) dominating in the west and tilled land (3 1%) to the east. Only about 4% of the catchment is woodland and 5% may be classed as urban or suburban. The average annual catchment rainfall is 906 mm and average annual runoff is 464 mm, estimated. over the period 1969-1990. The catchment is responsive to rainfall, having a mean flow of 49 m3 s-i, a mean annual flood of 302 m3 s-i and a maximum flood, in January 1982, of 622 m3 s-l. The flow regime is affected by reservoired headwaters in the Nidd and, to a lesser extent, in the Ure, but these represent only a small proportion of the total catchment area. Analysis of hydrographs for specific events shows a small baseflow component, suggesting that temporal changes in groundwater flow over events can be neglected. However, the catchment has a baseflow index, a measure of the proportion of runoff which comes from stored sources (Gustard et al., 1992), of 0.43. For a catchment the size of the Ouse, this implies that, for the annual water balance, the groundwater contribution does need to be taken into account but is not a dominant component of the flow. Hydrograph analysis further suggests that the direct runoff is made up of two clear components and

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may be separated into quick and slower flow. There is some justification for assuming that a significant part of the horizontal subsurface flow occurs in a saturated or unsaturated form along the upper boundary of the parent material at a depth of 0.8-1.5 m in parts of the catchment where the bedrock is relatively impermeable. Birtles and Reeves (1977) also pointed to shallow aquifers, fed from below, within the drift deposits of the Vale of York, and some subsurface flow may also occur as flow through macropores or along the boundaries of soil horizons where significant changes in hydraulic conductivity occur. The depth of this subsurface flow is commonly small (several centimetres) and it may, therefore, have a weak effect on the vertical transfer of moisture within the soil.

3. Structure of the model The model includes a description of overland flow, vertical water transfer in the soil, evapotranspiration, subsurface flow, and channel flow in the river network. Groundwater flow is considered to be equal to the filtration of water through the lower boundary of the soil. The catchment is divided into strips along which the onedimensional overland and subsurface flow to the main river channel network is assumed to occur. The strips consist of irregular quadrilaterals, each of which represents a portion of drainage area with uniform relief, soil, vegetation type and rainfall. The river network is schematized as reaches following the edges of the appropriate quadrilaterals. To model overland flow, the kinematic wave equations are applied in the following form:

(1) qs

=

L ii12$13bs ns

where h,, qs, b,, is and n, are respectively the depth, discharge, width, slope and Manning roughness coefficient for overland flow, R, is the rainfall excess, t is time, and x is the space coordinate. To describe the channel flow, the equations are as follows: b

ah,+aQ,=R

“dt

dx

=

(3)

i~12h~/3b,

Q, = i c

where h,, Q,, b,, i, and n, are respectively the depth, discharge, width, slope and Manning roughness coefficient for river channel flow and R, is the lateral inflow of overland and subsurface flow per unit length of the river channel.

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The equations for lateral subsurface flow are written as

qg =

(6)

K,i,h,b,

where h,, qg are the depth and discharge of subsurface flow, Rg is the recharge of subsurface water, 0, is the soil capillary porosity, OmPis the maximum porosity including macropores and Kg is the coefficient characterizing the horizontal hydraulic conductivity of the soil. It is assumed that subsurface flow follows the same slope and has the same width of flow strip as the overland flow. It is also assumed that the saturated layer hg is formed above the base of the simulated vertical flow layer and that the capillary water (i.e. water at a moisture content less than 0,) does not take part in the horizontal movement. The numerical procedures applied to solve Eqs: (l)-(6) are based on finite element methods and have been described by Kuchment et al. (1983). The quadrilaterals into which the basin is divided, based on similar slope, vegetation and soil type, serve as the finite element areas for numerical integration of the overland and subsurface flow equations. The choice of finite elements for the river channel system is determined by the schematization of the drainage area and the structure of the river network. The diffusion form of Richards equation is used to describe the vertical movement of capillary water in the unsaturated zone:

[D(B) g- K(e)]

g = g

o(e) = K(e)

$j$

where 0 is the volumetric soil moisture content, D(O) is the diffusivity of soil moisture, K(0) is the vertical hydraulic conductivity, $Jis the soil moisture potential and z is the vertical coordinate, which is defined as being positive downward from the surface of soil. The numerical solution of this equation is carried out using the four-point implicit finite difference scheme described by Kuchment et al. (1983). The relationships between soil moisture characteristics and the soil moisture content are used in the forms suggested by Campbell (1974):

(9)

D(e)

=

-KS&

(;)*+y&J

(10)

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328

where K, is the saturated hydraulic conductivity, I/J~is the air entry water potential and X is the pore size index. It is assumed that the vertical flux at upper boundary z = 0 is given by Zo=I,=-Dg+K(B) ZO=P-E

if Z,
(11)

ifZ,,,>.P-E

where P is the precipitation rate and E is the evapotranspiration rate. The vertical moisture flux at the lower boundary of the soil layer JH is assumed to be constant (JH = 5). It is also assumed that recharge of the horizontal subsurface macropore flow system Rg may occur as a result of vertical flow in macropores (bypass flow) or when, owing to the small vertical hydraulic conductivity in the lower boundary of the soil layer, the soil moisture content exceeds the capillary porosity (0 > 0,). In the latter case, input to the subsurface flow is given by

(12) where z, is the thickness of the lower layer for which, from Eq. (7), 8 > 0,. It is assumed that vertical bypass flow occurs when the capillary soil moisture capacity over the entire soil column becomes full (i.e. 8 > 0,,) and that this reaches the subsurface macropore flow system during a single model time step. The evapotranspiration rate is calculated by E =

K,s(el - e,)

(13)

where 6 is the air humidity deficit, 8i is the soil moisture in the top 10 cm layer, Bris the residual water content and K, is an empirical coefficient. To take into account subgrid effects caused by the small-scale variation of soil properties, it is assumed that the saturated hydraulic conductivity inside each finite element is a gamma-distributed variable with a mean equal to the corresponding constant value for a given element. The coefficient of variation is assumed to be a function of the mean value following Gusev’s (1993) analysis of field measurements from the literature and is given by c,

22 zp

(14)

where KS is the saturated hydraulic conductivity in millimetres per minute. This is a unique feature of the model and is used in preference to other probability distributed formulations.

4. Data sources 4.1. Model geometry

The basin is schematized for modelling purposes using topographic maps at a scale

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329

Fig. 1. Basin schematization for the Ouse above York, North Yorkshire, showing average slope angles for each element. The thicker lines depict the main river network and catchment boundary.

of 1:250,000 and gridded soils information at scales of 1 km (Boorman et al., 1995) and 5 km (Soil Survey and Land Research Centre (SSLRC), 1994). Slope angles derived from the 1:250,000 maps are approximate; data from a 50 m digital terrain model based on the 10 m contours given on 1:50,000 maps show localized slopes greater than 0.3. However, the general pattern of steep and gentle slopes is preserved in the schematization. Fig. 1 shows the basin divided into 445 finite elements, giving an average area for a single element of about 7.5 km* and providing 99 finite elements along the river network. The values of b, and is have been assigned for each hillslope finite element from the topographic map and the value of bc determined from channel geometry data at gauging stations and interpolated as a function of area drained. Thus, channel widths vary from 3 m in the headtiaters to 113 m at Skelton, the basin outlet. 4.2. Soil parameters Soil types and their estimated parameters were assigned using two data sources. Fig. 2(a) shows the dominant soil, in terms of the Hydrology of Soil Types (HOST; Boorman et al., 1995) on a 1 km grid for the Ouse catchment. This information was coupled with data provided within the SEISMIC package (SSLRC, 1994), which gives details of soil properties and the two most dominant soil series within a 5 km grid. Interpreting these two data sets and grouping like soils, four soil classes for the

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Fig. 2. Assignment of soil types. (a) Dominant soil on a 1 km grid from Hydrology of Soil Types classifi cation (Boorman et al., 1995); white line denotes catchment boundary, tick marks at 10 km intervals. (b) Schematized soils: 0, daily rain gauge; V, flow gauge.

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331

Table 1 A priori soil parameters

Porosity, 0, Field capacity or soil moisture at 5 kPa, f3,, Residual soil moisture at 1500 kPa, 0, Suction at saturation - Eq. (9), Q’s(m) Saturated hydraulic conductivity, KS (m day-‘) Coefficient of variation of KS - Eq. (14), C,

Soil Type !

Soil Type 2

Soil Type 3

Soil Type 4

0.45 0.37 0.20 2.6 0.44 1.5

0.50 0.38 0.18 0.9 0.75 1.2

0.40 0.29 0.10 0.15 2.38 0.8

0.87 0.71 0.17 0.043 1.14 1.0

Ouse catchment were determined and their distribution is shown in schematized form in Fig. 2(b). The picture is consistent with groupings of the soil associations shown on the 1:250,000 map described by Jarvis et al. (1984). Parameters for the four soil types, based on the Wilcocks-Dunkeswick, East Keswick, Wick, and Winter Hill soil series, respectively, are given in Table 1. The model does not differentiate soil layers and so depth-weighted average parameter values have been derived, omitting the C horizon. Parameters for peat were obtained from PBivHnen (1973) and Loxham and Burghardt (1986). Using the fact that the soil moisture potential at residual water content is 1.5 m suction, 9, was calculated for each of the different soil types using Eq. (9) and a value for the pore size index X of 0.20 (Ragab and Cooper, 1993). It was assumed that the maximum porosity including macropores 0,,, M 2f3, - f&. A soil depth of 1 m was assumed for all four soil types. 4.3. Hydrometeorological data Hydrometeorological observations within the Ouse basin for the period 19861990 have been used for model calibration and validation. These data include daily rainfall amounts recorded at eight rain gauges, daily runoff recorded at six reliable flow gauges, the air humidity deficit for MORECS (UK Meteorological Office, 1981) grid squares within which the catchment is located (7 day average), and 15 min records of rainfall and runoff for the six flood events given in Table 2. It is necessary to note that the number of 15 min recording rain gauges varied between five and eight for different flood events and that the locations of the daily and recording rain gauges are different. For the runoff calculations, elements are assigned to the nearest rain gauge to determine their rainfall input. To determine the rainfall rate for each finite-element area a procedure based on Thiessen polygons has been applied.

5. Model calibration and testing

The time step of the input for the flood events was 15 min and space steps for the numerical integration of the vertical soil moisture transfer were chosen to be 10 cm. In

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Table 2 Rainfall in flood events Date of event

1 lo-27 Apr. 1986 2 17-26 May 1986 3 24-31 Aug. 1986 4 29 Dec. 1986-7 Jan. 1987 5 20 Mar.-l5 Apr. 1987 6 l-26 Oct. 1987

Amount of precipitation (mm)

Maximum precipitation rate mm per 60 min

mm per 15 min

107.9 58.4 58.5 44.4 114.4 129.7

19.5 10.0 8.4 3.5 9.8 6.0

13.2 3.2 2.8 1.2 2.4 2.0

the absence of more detailed information, the average weekly air humidity deficit was assumed in each time step. The vertical moisture fluxes have been calculated on each finite element for five different quantiles of the corresponding gamma distribution of K, and then the weighted average values of these fluxes determined. The equations for overland, subsurface and channel flow were solved using a 2 h time step. Applying a physically based distributed model with many parameters, a minimum of calibration and a rational calibration procedure are desirable. The strategy which is adopted here is shown in Fig. 3. It is recognized that the parameters which require calibration are the roughness parameters, the evaporation coefficient K, and some of

r-4

Run model for each complete year to obtain time series of soil moisture

I

Run model for events using initial conditions from above to obtain n,, n, and Ka

I

I

I

I

I

I

Run model for one full year to obtain K, and g0

t Validate model using other years

Fig. 3. Outline procedure for calibrating the model.

I

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333

Table 3 Calibrated parameter values Overland flow roughness coefficient, n, (s m -113) Channel flow roughness coefficient, n, (s m-li3) Coefficient of horizontal hydraulic conductivity, Kg (m s-‘) Coefficient of evaporation, K, (m mbar-’ day-‘) Basal saturation hydraulic conductivity, & (m day-‘)

0.4 0.09 0.1 0.0030 0.00023

the hydraulic conductivity parameters. The model is calibrated on the available flood events to obtain optimal values for n,, n,, and Kg as these are the parameters which control the routing of overland and subsurface flow. However, to calibrate on flood events, initial conditions relating to soil moisture must be specified. Consequently, the model is first run for each year using a priori parameter values to obtain an estimate of the initial distributed soil moisture conditions. The model is then calibrated on the events using the relevant initial conditions. The parameters which control groundwater recharge and evaporative loss, KO and K,, influence the longer-term water balance and have been calibrated over the single year of 1986 assuming the parameters already calibrated. If necessary, the calibration sequence is repeated until consistency is achieved. Finally, the model is validated against the remaining full years of data. The calibration was carried out manually by comparing the calculated hydrographs and volumes of runoff at the outlet of the basin and at intermediate points with observed data. To choose the set of parameters which gives the optimal fit to the observed data, previous experience in the sensitivity of the model has been invaluable in determining the effect of the different parameters on the runoff volume as well as on overland and subsurface flow components. In particular, for the assigned soil constants, vertical bypass flow was found to be very small and can be neglected. The optimal values of the calibrated parameters are given in Table 3.

5.1. Flood event simulation Fig. 4 shows the observed and modelled flow for the flood events. These show a reasonable degree of fit to both simple hydrographs and longer duration complex events. The results are given in Table 4 in terms of both the amounts and percentages of rainfall which go into overland flow, subsurface flow, evaporation, change in transitional storage (including overland, subsurface and channel components), and change in soil moisture. A comparison of using 15 min and hourly time steps is also given. Very little difference is seen in the water balance components as calculated using the different time steps. In the event of May 1986, there is a 17% difference in the overland flow but in all other cases the difference is less than 9%. On the basis of this finding, an hourly time step was later used for the annual calculations. Looking at the water balance components in their percentage terms, overland flow averages about 5% of the runoff in these events with higher values in the events with the

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01

0

50

100

150

200

250

Event 5 400 ;@I 5 g 200 =

0 0

rain

5 10 Event 3 400

:‘\ I

-$J g g 200 =

: I

-b!!J 0

\ \ \

50

-M II

5 \

\

II II

g 200

\

E

\

I\

\

4 0

rrl: II I’\

)I

100 150 time (hours)

200

0

0

200 400 time (hours)

\

.

600

Fig. 4. Model results for the six events given in Table 2: continuous line depicts observed flow; dashed

line

showsmodelledflow. heaviest short-term rainfall (Table 2), and in the summer and early autumn when soil moisture deficits are high. The temporal variation in the water balance components also makes sense in so far as a higher percentage of the rainfall goes into changing the soil moisture status in the August and October events when soil moisture deficits are

Rain mm

107.9

58.4

58.5

44.4

114.4

129.7

1

2

3

4

5

6

15 60 15 60 15 60 15 60 15 60 15 60

Time step min

7.4 7.1 3.5 3.0 3.2 3.0 1.2 1.1 6.0 5.9 6.7 6.3

7 7 6 5 5 5 3 3 5 5 5 5

55.7 55.9 27.4 27.7 15.9 15.9 27.7 27.6 68.5 70.3 66.0 67.6

mm

mm %

Subsurface runoff

Overland runoff

of time steps on flood event simulation

Event

Table 4 Influence

52 52 47 47 27 27 62 62 60 60 51 51

%

4.9 4.8 4.7 4.6 1.5 1.5 3.0 2.9 3.0 3.1 4.1 4.2

mm

Change in transitional storage

5 5 8 8 3 3 7 7 3 3 3 3

% 32.7 32.7 17.3 17.3 12.2 12.2 9.1 9.1 29.1 29.1 27.4 27.5

mm

30 30 30 30 21 21 20 20 25 25 21 21

%

Evapotranspiration

7.2 7.1 5.6 5.8 25.5 25.7 3.8 3.8 5.3 5.5 23.0 23.7

mm

7 7 10 10 28 28 9 9 5 5 18 18

%

Change in soil moisture storage

I

Fig. 5. Rainfall

.z 400

s 20

r

,m

SW

12

W-14.9 mm

6

16

24

profiles

for temporal

I

disaggregation

0 6 12 18 24 hour in day (from 9.00 GMT)

L

I

0

KLJ

a.

based on the method’of

Pilgrim et al. (1969): (a) Towhill

0

8 20 +I

12

210 mm

6

18

24

I

rain gauge; (b) Eccup rain gauge.

0 6 12 18 24 hour in day (from 9.00 GMT)

60 L .: 40 r

3

I

18

0

12

c~

I

24

6

1

b.

hour in day (from 9.00 GMT)

0

:_L

I

L.S. Kuchment et al. / Journal of Hydrology 181 (1996) 323-342

high, and subsurface runoff is high during the December-January events when soil moisture deficits are low.

331

and March-April

5.2. Long-term simulation Long periods of 15 min or hourly data were unavailable for the catchment and so use had to be made of daily rainfall data. However, subdividing daily rainfall into equal hourly values gives very small rainfall rates which are, except in very few cases, much less than the entry hydraulic conductivity of the soil. Although overland flow is not common in the Ouse basin, it does occur on occasions and is important for the generation of large flood peaks and for the entrainment of sediment. Thus, some means of obtaining short-term rainfall rates was desirable. One method would be simply to allocate the day’s rainfall to a single hour. However, there is no basis for such short duration intense storms in the Ouse. Consequently, the average variability method of Pilgrim et al. (1969) was applied to the daily rainfall series. 5.2.1. Rainfall disaggregation The average variability method was developed for the generation of temporal profiles for design storms. It has been applied in the UK by Stewart and Reynard (199 1) to extreme event rainfalls for design purposes. The method has the advantage over other rainfall profile techniques (cf. Natural Environment Research Council (NERC), 1975) in that it provides not only the proportion of rainfall which falls in a given time but also the time intervals in which the rain falls. Thus, there is no need to assume that a storm profile follows a particular distribution. The application of this method here differs in two ways from the original. First, the method is applied to each day’s rainfall independently of adjacent days rather than to defined events. Second, the method is applied to all rainfalls, not just the extremes. Sub-daily data were readily available, on a less than continuous basis, for two rain gauges within the Yorkshire region. The Towhill gauge is located in the headwaters of the Ure and may be thought of as representative of the upland parts of the Ouse Table 5 Results of calculations of annual flow using daily rainfall and disaggregated daily rainfall Years

1986 1987 1988 1989 1990

Rain (mm)

1044 868 1008 747 893

Observed runoff (mm)

538 451 540 324 454

Calculated subsurface runoff (mm)

Calculated overland runoff (mm)

Calculated annual runoff (mm)

1

2

1

2

1

2

416 386 497 272 369

468 319 489 267 362

32 21 30 17 25

44 30 40 23 33

506 407 530 289 390

508 409 532 290 391

1, Daily rainfall used; 2, disaggregated daily rainfall used.

Efficiency 1

2

0.741 0.814 0.844 0.877 0.839

0.134 0.814 0.837 0.872 0.831

L.S. Kuchment et al. 1 Journal of Hydrology 181 (1996) 323-342

338

R.

R

;

O s 10

- - -

observed flow modelled flow

i I’

I

90

160

270

360

time (days since 1 Jan 1999)

AB

’ 20

~ - - -

“0

(b)

90

180

time (days since 1 Jan 1999)

observed flow modelled flow

270

350

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catchment. Data are available for 512 rain days in the period 1985-1992. The number of hours in the day during which rain falls shows no seasonal variation and averages 7.6 h with a coefficient of variation of 0.75. The second gauge is that at Eccup, between Leeds and Harrogate. Although not located within the Ouse basin above York, it can be considered to be representative of the lower parts of the basin which lie in the rainshadow of the Pennines. The total number of rain days available for analysis was 295. The hourly rainfall shows similar characteristics to those of Towhill, although the mean number of wet hours is only 4.9 with a coefficient of variation of 0.80. This, in part, reflects the much lower rainfalls of the eastern half of the basin. In both cases, the number of hours during which rain falls is related to the rainfall depth. Thus, in applying the method, the daily data were grouped into different depth ranges. Five subdivisions (O-4.9 mm, 5-9.9 mm, 10-14.9 mm, 15-24.9 mm and 25 mm or more) were assumed in the case of Towhill; three subdivisions (O-4.9 mm, 59.9 mm and 10 mm or more) were assumed for Eccup. Further subdivision of the data does not improve the results and lumping the data together is inadequate to represent the temporal pattern of the rainfall. The derived rainfall profiles are given in Fig. 5. For the higher rainfall depths, these temporal profiles look realistic, but for the smaller rainfall depths the temporal pattern is skewed towards the beginning and end of the 24 h period. This is partly an artefact of the tipping bucket raingauge technology used in the measurements and partly a result of applying the method to daily values, rather than events, independently of adjacent days. However, the particular hour in which the rain falls is not thought to be vital to the model results. Furthermore, the method, when played back through the daily data, does reproduce the statistical features of the rainfall reasonably well. This is seen in terms of the maximum hourly rainfall in a day, the number of wet hours in a day, the distribution of hourly rainfall depths and the temporal autocorrelation structure of the hourly rainfall series. Defects of the method include the fact that extreme hourly rainfalls are not so well represented and the same profile is applied to each day having the same rainfall amount. The method in general worked less well in the case of Eccup than Towhill. This may be due to the smaller dataset or to the lower rainfalls and more varied methods of rainfall generation. However, for the purpose of the runoff modelling, the results are thought to be a reasonable approximation to an hourly data series. 5.2.2. Results Results of applying the model using both daily rainfall and disaggregated daily rainfall are given in Table 5 for the years 1986-1990. The calculations have been carried out continuously for the 5 years using initial conditions on 1 January 1986. A comparison of the observed and modelled total annual runoff shows that the total runoff is underestimated by between 2% and 14%. There are three possible reasons for this. First, the groundwater may be poorly represented in the model. Much of the area is underlain by Carboniferous Limestone, Tertiary sandstones and Permian limestone and it is not clear that the groundwater catchment is coincident with the

Fig. 6. Annual hydrographs for the Owe basin: (a) 1988; (b) 1990.

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surface catchment. Second, the representation of the evaporative loss is an empirical relationship which is not calibrated for individual soil and vegetation types owing to lack of data. It also relies on weekly average values of the air humidity deficit which are assumed to apply in each hour of the week. The third reason for the discrepancy in the annual water balance may lie in the rainfall input and its interpolation between sites. The underestimation of the annual runoff is coupled with a systematic overestimation of the flood volumes and flood peaks during events (Table 4 and Fig. 4). This may be due to inconsistency between the 15 min and daily rainfall data owing to the use of different gauge locations or it may be evidence for the need to incorporate interception loss and improve the evapotranspiration and groundwater representation in the model. In the case of large events, the effect of flood plain inundation will also play a role in reducing the observed runoff. In terms of the different components of runoff, as expected, more overland flow is generated by using disaggregated rainfall rather than the single daily values. Overland flow is consistently about 8% of the total modelled runoff in the case of disaggregated rainfall compared with 5-6% for daily rainfalls, representing an overall increase of 30-35%. It is a small component of the annual water budget and is consistent with observations in the UK. Also given in Table 5 are measures of efficiency c where < = 1 - &u$

(15)

gr is the residual variance between observed and calculated values of runoff, and a,, is the variance of the observed runoff values. The values oft indicate the degree of fit between the observed and calculated runoff series in each year. Generally, these lie between 73% and 87%, suggesting that the model is performing satisfactorily in terms of the overall temporal pattern of the basin outflow with the minimum of calibration which has been performed here. This is reflected in Fig. 6, which shows the results for the two years 1988 and 1990. These values of c are as good as or better than those obtained using a lumped conceptual model (L.G. Littlewood, personal communication, 1995) and provide encouragement for the pursuit of distributed modelling at this spatial scale within the model structure reported here. However, for a full validation of the model, an examination of the internal functioning of the components and runoff from dissimilar sub-basins is needed. For this, more detailed soil moisture and flow data are necessary.

6. Conclusion The physically based distributed model presented here includes a description of overland flow, subsurface flow, vertical water transfer in the soil, and the movement of water in the river channel network. The finite-element schematization of the river basin which is used is suitable for representing the main channel network and mosaic of topography, soil, and land use. The validation of the model based on hydrometeorological inputs for the period 1986-1990 has shown that the model successfully simulates the runoff of the Ouse basin and provides meaningful estimates of

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internal variables. The analysis of model simulations confirms the minor role which overland flow plays in runoff production in the Ouse and under similar hydrological conditions. The model allows the generation of long-term hydrological time series and the potential to estimate the hydrological impact of climate and land use change.

Acknowledgements

The research has been carried out as part of the LOIS (Land Ocean Interaction Study) project funded by the Natural Environment Research Council of the UK (LOIS Publication 43). Thanks are due to W.B. Wilkinson and P.G. Whitehead for setting up the research, the National Rivers Authority and Bob Moore for flow and rainfall data during events, SSLRC for the use of the SEISMIC package, Lisa Stewart for her rainfall disaggregation program, and Beate Gannon for manipulation and plotting of spatial data.

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