The Hydrologkal Basis for Water Resources Management (Proceedings of the Beijing Symposium, October 1990). IAHS Publ. no. 197,1990.

Water resources planning of the River Po basin: a surface and groundwater hydrology study

S. ARTTNA, M. FERRARESL E. TODINI & F. ZOCCOLI* Institute of Hydraulic Construction, Engineering Department, University of Bologna, Viale Risorgimento 2,1-40136 Bologna, Italy

Abstract The paper summarizes a hydrologkal study of the Po River catchment area within the framework of a water resources planning study for the next two decades. The analysis of hydrologkal data and their treatment, together with the establishment of an efficient data bank is presented as a prerequisite for the regionaliza-tion of the hydrologkal information. The calibration of surface and subsurface water flow models is then introduced in order to allow for the verification of congruence of historical data and for the analysis of compatibility and risk of future development plans.

Planification des ressources en eau du bassin du Pô: étude d'hydrologie de surface et d'hydrologie souterraine

Résumé L'article résume une étude hydrologique du bassin du Pô, dans le cadre de la programmation des ressources en eau des deux prochaines décennies. On présente ici l'analyse des données hydrologiques et leur traitement, avec la mise en oeuvre d'une banque de données, étape préliminaire pour la régionalisation de l'information hydrologique. En outre, on a procédé à la calibration des modèles de simulation du mouvement des eaux de surface et souterraines pour vérifier la congruence des données historiques, la compatibilité et les risques liés aux plans futurs de développement.

INTRODUCTION

In this paper the hydrologkal aspects of a water resources planning study for the Po River are described, in order to emphasize the problems arising in a large scale project, together with the aims and perspective which can reasonably be expected. The optimal allocation of water resources in the River Po basin represents a management problem of great concern, owing to the size of its catchment area and the importance of the related economical and social interests.

The Po basin, approximately 70 000 km2, covers most of northern Italy, a little less than one fourth of the entire national territory (Fig. 1). Over 18

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S. Artina et al. 428

Fig. 1 The River Po basin and its plain area (within the dotted line).

million inhabitants live in this area, producing more than 40% of the total national gross product. The Po valley, about 28 000 km2, has an extensive agricultural development, well supported by the water availability.

The size of the problem at hand can better be appreciated by considering Table 1, which shows the main contributions, expressed in km3, to the overall water balance of the plain for the year 1981. The plain is the area on which the interest for water resources planning is focussed, and represents one of the two regions into which the whole River Po catchment has been subdivided, the second being the mountain areas.

The latter cover the external part of the Po basin and are drained by rivers coming from the Alps and the Appennines, which are mostly impervious and where aquifers usable for exploitation are virtually absent.

The plain covers the remaining central portion of the Po catchment, ranging from 150 m of altitude to the Adriatic Sea (Fig. 1).

In order to determine optimal management policies, a preliminary identification of the River Po hydrological system is required, together with an analysis of the interconnected agricultural, industrial, municipal and social systems.

For this purpose, the Canale Emiliano Romagnolo, a land reclamation agency of the Po valley, was commissioned by the Italian Ministry of Agriculture and Forestry to lead a multidisciplinary water planning study, which is outlined in Ministry of Agriculture (1984). The present paper deals only with the hydrological system and closely related aspects of the study.

429 Water resources planning of the River Po basin

Table 1 Main contributions to the 1981 water balance in the Po valley (area = 28 000 km2)

INFLOWS km*

Surface discharges from mountain basins 34.7 Precipitation 21.7 Groundwater supply from mountain basins 2.4 Total inflow 58.8

OUTFLOWS km3

Po discharge to the sea 42.6 Evapotranspiration 15.6 Artificial drainage 0.6 Total outflow 58.8

INTERNAL EXCHANGES

Abstractions for agriculture 19.0 Abstractions for domestic use 3.9 Abstractions for industry 3.4

HISTORICAL DATA ANALYSIS AND MANAGEMENT

The historical data used in this study relate to the years 1951-1981 and were mainly provided by the Italian Hydrographie Service. Additional information was given by the Ministry of Aeronautics and by agricultural and hydropower agencies.

The number of measurement stations over the entire catchment area is:

Rainfall stations Temperature stations Water levels or discharge stations Wind stations Humidity stations Solar radiation stations Water table wells

1123 217 131 45 18 6

1080

The first problem to be solved was obviously the storage of this huge amount of information, sampled at monthly intervals, in the most effective and efficient way. A hydrologie data bank was set up, following the guidelines of Component. GO6.3.01 of HOMS (Hydrological Operational Multipurpose Subprogrammes) (WMO, 1974) where the data were introduced in a direct access mode, on a relational basis, by station and year, together with "catchment files" describing the relevant stations for each basin and providing the correct addresses for the retrieval of the corresponding necessary information.

S. Artina et al. 430

Another problem, a major one, consisted of the homogeneity analysis of the data and reconstruction of the missing observations. As far as the first aspect is concerned, techniques based upon single linkage cluster analysis were used to discard the inconsistent stations, while autocorrelation functions and power spectra were used to ascertain the natural behaviour of recorded complete time series.

According to the nature of each type of the collected data, different approaches were used in order to fill the gaps and compute the areal averages.

Principal component analysis was performed on those rainfall series which were complete (about 30% of the total); the missing observations were then reconstructed by regressing the incomplete series on the first 15 principal components, which explain more than 90% of the total variance of rain.

Owing to the low spatial variability of temperature, these data series were completed by multiple linear regression on surrounding stations, after scaling the data to a common mean elevation, by means of a gradient of 6°C km"1. Thermal gradients ranging from 4.7 to 6.4°C km"1 were suggested by the existing literature for various basins in northern Italy; the value chosen was the most appropriate as an average over the entire region of interest.

By means of the temperature information, the potential évapo­transpiration was computed according to the Thornthwaite equation (Doorenbos & Pruitt, 1974) and stored in the data bank. The évapotranspiration estimates were then rescaled by comparison with the values computed through the Penman energy budget equation for the stations where wind speed, humidity and solar radiation were available.

Finally, the areal averages of rain and temperature were estimated using an original minimum variance method, which compared favourably with the Gandin (Gandin, 1972) and Kriging techniques (Matheron, 1970).

A summary of all the operations performed on the hydrological data is given in Fig. 2.

SURFACE HYDROLOGY

In order to simulate its hydrological phenomena, the River Po catchment was subdivided into two regions: the mountain areas (about 42 000 km2) and the plain (about 28 000 km2).

The mountain areas

The monthly runoff contribution from the mountain catchment had to be reconstructed at all the sections where the rivers enter the plain.

In a first phase, the runoff data from 75 hydrometric stations with more than six years of continuous measurement were utilized to compute the mean annual runoff, Q, which was successively regionalized by means of regression equations of the type:

431 Water resources planning of the River Po basin

ROW RAINFALL

DATA

COMPLETENESS

A N A L Y S I S ON

H I S T O R I C A L DATA

I D E N T I F I C A T I O N

OF CA"<C£D AND

RELEVANT

CATCHMENTS

ROW DI S O U R C E

DATA

COMPLETENESS

ANALYSIS ON

HISTORICAL DATA

FROM D I F F E R E N T

SOURCES

COMPLETENESS

AND S T A T I S T I C A L

A N A L Y S I S ON

H I S T O R I C A L DATA

CALIBRATION OF MEAN

ANNUAL RUNOFF REGRESSION

VS.HVDROLOCICAL FACTORS

RECONSTRUCTION 0 ? YEARLY

MEAN RUNOFF AT RELEVANT

RIVER SECTIONS RECONSTRUCTION OF

HOMTHtY RUNOFF AT

RELEVANT SECTIONS

I D E N T I F I C A T I O N OF

T I P I C A L MEAN MONTHLY

RUNOFF PATTERNS

DISCHARGE RESIDUAL

S E R I E S EVALUATIONi

10c " 5 B E t ) > / 5 M <t t

CALIBRATION OF DISCHARGE

RESIDUALS REGRESSIONS V S .

HYDROLOCICAL FACTORS

PARAMETERS RECIONALISATIOH

FOR HEAN HONTHLY RUNOFF

AND DISCHARCE RESIDUALS

Fig. 2 Flow chart of the hydrological analyses,

Q + ET = a-S +b-S2 + c-P (1)

where Q is the mean annual discharge volume, ET the mean annual évapotranspiration volume, P the mean annual precipitation volume and S the catchment area.

The form of regression expressed by equation (1) proved to be the best among many others tried with different sets of independent variables, including basin mean altitude, gauging station elevation, permeability and steepness coefficients.

The regression performed on the whole set of hydrometric stations gave a determination coefficient of 0.9990 but large percentage errors for small and medium catchment sises. Since most of the Q values to be estimated relate to basins of such size, the overall regression was split into the three following classes of catchment areas: (a) 5 < 40 km2, (b) 40 km2 < S < 4000 km , (c) 4000 km2 S 5.

The results still showed a significant agreement with the observed values, giving determination coefficients of 0.9861, 0.9949, 0.9999 respectively and residuals much more acceptable for the two lower classes. The scatter diagram of computed versus observed discharge volumes for class (b) is shown in Fig. 3.

In a second phase, the mean monthly contributions to the mean annual runoff were determined for each station considered. The seasonal pattern of these mean monthly discharges showed a marked regional behaviour: a clear

S. Artina et al. 432

°t>.00 80.00 160.00 210.00 320.00 400.00 480.00 SG0.00

OBSERUED - 1 0 '

Fig. 3 Scatter diagram of computed vs. observed mean yearly outflow (volumes in millions of m3) for basin areas greater than 40 km2 and less than 4000 km .

nivo-glacial behaviour for the Alpine rivers, a marked continental behaviour for rivers coming from the Appennines and a smoothed, more or less regular pattern for the Po gauged along its main channel. The regionalization consisted of assigning the typical shape of the relevant pattern to each section of interest and disaggregating the annual mean discharge with it.

The third phase focussed on modelling, regionalizing, and reconstructing the deviations from the mean monthly values Y, defined as:

Yt =«.vJi;A (2)

where:

y.= Qt-Qt ETt-ETt

— + — —— Q, + ETt Qt + ETt

and X, P ~P

t t

Qt + ETt

Pt, Qt and ET( being long- term averages for month t. They were used

433 Water resources planning of the River Po basin

instead of the corresponding standard deviations, whose monthly values showed an irregular spatial pattern, not amenable to regionalization over the whole basin.

For the Alpine rivers a common value of r = 12 was adopted, while r = 2 was taken for the rivers of the Appennine Range, due to the much smaller amount of snow accumulation, with a consequent smaller storage effect. The opportunity of reducing the memory coefficient for some months of the same alpine station was discarded: although conceptually reasonable, such a procedure would result in very little practical advantage compared to the amount of statistical analysis required.

Finally, the parameters obtained for equation (2) at each hydrometric station were regionalized separately for the Alpine and the Appennine rivers, as a function of the basin area and its mean altitude, on the basis of multiple regression performed on these variables.

One of the most noticeable features of the procedure adopted for the mountain basins is that it tends to preserve the water balance at longer time aggregation, in close agreement with the major scope of the management project, consisting in the evaluation of the compatibility of planning scenarios on a long term basis.

The plain

Once the rivers leave the mountain catchments, a hydrological balance model of the surface waters has to route their contributions in the right directions. Therefore the plain was subdivided into 60 cells, 47 representing land units and 13 representing internal and external boundaries: the rivers Po and Adige and the Adriatic sea (Fig. 4). For each land cell the following contributions

Fig. 4 Discretization of the River Po plain.

S. Artina et al. 434

Fig. 5 Contributions to the hydrological water balance of the plain cells.

to the water balance were taken into account (see also Fig. 5): runoff contribution from mountain basins (VBM), exchange flow with the adjacent cells via the natural and artificial channel network (VEC), inflow from springs to the plain (VS), abstractions from the surface network for agricultural purposes (VA1), return flow to the surface network from agricultural practices (VA2), abstractions for industrial purposes (VII), return flow from industrial uses (VI2), abstractions for municipal and drinking water needs (VU1), return flow to the overland channel network from urban areas (sewers) (VU2) and exchange flow between the surface network and the groundwater table (VEG).

Items VA1, VA2, VII, VI2, VU1 and VU2 were estimated by other teams working on the same project (Ministry of Agriculture, 1984), while VS and VEG were derived from simulations performed with a groundwater model, given a properly defined set of boundary conditions. The contribution of VS to the surface water balance can only be non-negative; it is positive as soon as the water table rises higher than the spring level in a given cell. On the contrary, VEG contributions can be either positive or negative, that is water can leave or enter the surface network, depending on the relative height of the groundwater table and the hydrometric level in the river. The mass balance equation was applied successively to all the cells, from the uppermost to the sea.

THE GROUNDWATER MODEL

Owing to the large groundwater storage available in the Po valley, in a subsurface system whose size and shape coincides with the plain, a groundwater flow model had to be set up and calibrated, in order to simulate the overall water budget. The whole complex aquifer was represented as an equivalent layer, whose thickness increases gradually from the mountains

435 Water resources planning of the River Po basin

toward the sea. The external portion of the aquifer, made of coarse material, was assumed to be unconfined, while the central and eastern part, made of thinner materials alternating with aquitards, was taken as confined and vertically connected to a thin phreatic layer.

Because of the aims of the study, an extremely detailed description of the aquifer did not seem necessary, both for a loss of overall understanding of the exchange dynamics and for the lack of information concerning the disaggregation of inflows and withdrawals on a very fine grid. Therefore the regional aquifer and the phreatic layer were represented by the same coarse grid used for the surface water balance model (Fig. 5).

Aquifer flow is represented by the classical differential equation describing non-steady flow through porous media, integrated using a lumped parameter model similar to the one described by Thomas (1973) based on an integrated finite difference scheme (Narasimhan & Witherspoon, 1976). The model leads to the solution of the following system of linear (for confined conditions) or nonlinear (for unconfined conditions) equations (see also Fig. 6):

h ïfiit iHJ(t) ~ Hi(t))Dt = SA{Hi(t) ~ Hi(t ~ 1)} + Qi{t)Dt (3)

where H ft) is the mean piezometric head in the /th cell for month t (HPt for the unconfined aquifer, HAi for the confined aquifer); Ai is the area of the /th cell; S.(t) is the storativity of the /th cell (SPi for the unconfined aquifer, SAt for the confined aquifer); TM) is the transmissivity between the ;'th and

J-th CELL

PHREATIC AQUIFER

ARTESIAN AQUIFER

IONAL AQUIFER BOTTOM

Fig. 6 Schematic representation of two adjacent cells of the regional aquifer.

S. Artina et al. 436

the z'th cell (time dependent for unconfined conditions); L~ is the width of the boundary between the;'th and the z'th cell; £>~is the distance between the nodal points (centroids) of cells ; and i; and Qft) is the mean inflow or outflow for the z'th cell during month t.

The discharge Qft) is the algebraic sum of several positive and negative contributions, which account for water withdrawals and recharge from urban, industrial and agricultural uses and for all the exchanges between the surface drainage network and the water table. The sum appearing in the discretized equation (3) is over all the cells ; surrounding the z'th cell.

PRESENT AND FUTURE USES OF THE HYDROLOGICAL MODELS

As mentioned above, the water consumption for the various uses in the Po valley was evaluated by different expert teams. Both surface and groundwater models were calibrated by using these estimates, in conjunction with the previously determined flows at the entrance to the plain, rainfall and évapotranspiration volumes over the plain itself, levels of rivers, springs and water table for the years 1981-1982.

Evidence was found for a number of inconsistencies in the estimated values, forcing their amendment by successive approximations.

The final calibration results show an interesting agreement both in the magnitude and in the pattern of seasonal variation of the piezometric levels. Very few cells, where a heavy drawdown is present, still indicate that the water withdrawals estimates have to be reviewed. These conclusions are enhanced by the simulation of the 372 months from 1951 to 1981. As for the future, the extrapolated values of water consumption for the next two decades show a significant increase in the municipal and drinking water uses, a slight decrease in industrial utilization, mainly due to improved technical efficiency, and a more or less stable consumption for agriculture, as can be seen from Table 2.

Table 2 Water consumption (in km3 year'1)

Use 1951 1981 2001 (forecast)

Agricultural 19.0 19.0 18-20 Municipal 1.0 3.9 4-5 Industrial 2.6 3.4 3.2

A number of hypotheses as to the future development of agriculture in the Po valley should provide refined estimates of the water requirements and will constitute the basis for future scenarios to be investigated by the use of hydrological models. Moreover, the generation of rain synthetic sequences based upon the principal components describing rain patterns over the Po catchment area will allow an extensive analysis of compatibility and risk of the selected management policies.

437 Water resources planning of the River Po basin

REFERENCES

Doorenbos, J. & Pruitt, W. (1974) Crop water requirements. FAO Irrigation and Drainage Paper no. 24. FAO, Rome, Italy.

Gandin, L. S. (1972) The planning of meteorological station networks. WMO Tech. Report no. 265. WMO, Geneva, Switzerland.

Matheron, G. (1970) La théorie des variables régionalisées et ses applications. Cahiers du Centre de Morphologie Mathématique, Fasc. 5, Fontainebleau, France.

Ministry of Agriculture (1984) Canale Emiliano Romagnolo: Studies and investigations for a rational application of the Po river basin water resources to agricultural activities. Proc. 5th Int. Conf. Water Resources Planning and Management (Athens, Greece).

Narasimham, T. N. & Witherspoon, P. A. (1976) An integrated flnited difference method for analyzing fluid flow in porous media. Wat. Resour. Res. 12 (1), 57-64.

Thomas, R. G. (1973) Groundwater models, FAO Irrigation Drainage Paper no. 21. FAO, Rome, Italy.

WMO (1974) Hydrological Operational Multipurpose Subprogrammes (HOMS), Reference Manual. WMO, Geneva, Switzerland.