rivers flows reconstruction using reservoirs water balance

RIVERS FLOWS RECONSTRUCTION USING RESERVOIRS WATER BALANCE: ANALYSIS AND RESULTS FOR SARDINIA RESERVOIRS

ANDREA ABIS(1), GIOVANNI M. SECHI(1), ROBERTO SILVANO(2)

(1) CRIFOR – Università di Cagliari

(2) EAF – Ente Autonomo del Flumendosa – Regione Sardegna

Abstract:

In many Italian regions, over the last few decades, rivers water levels have not been regularly measured at gauge sites by the Hydrologic Services and the Water Authorities and, moreover, water level-flow rate relations have not been updated. Therefore, in this situation, the only possibility of having flow rate measures for the last period, characterised by particularly critical drought events, has been the estimation of stream flows by the reconstruction of hydrologic inputs in artificial reservoirs using water balance relations. In the paper a general framework will be provided of this approach defining the elements and variables which are necessary in the estimation of water balance in artificial lakes. Therefore we will examine the results of the data findings and inflow reconstructions for reservoirs in the Sardinia region. To conclude, considerations on results will be provided.

Key words: Reservoirs water balance; rivers flows reconstruction; artificial lakes management.

1. Introduction

Over the last few years in Italy the hydrologic Services and water Authorities have developed the rainfall monitoring system much more (who have allowed the analysis of droughts and their rating with the use of specific indexes) while in getting the data related to hydrometry for runoff measurement has not been taken into the right consideration, excluding some rare exceptions. Specifically, regarding the regional hydrologic Services in Sardinia, rivers water levels have not been regularly measured and water level - flow rate relations have not been updated at gauge sites. Consequently, the only possibility of having flow rate measures in the region for the last two decades (characterised by particularly critical drought events) has been the estimation of these stream flows by the reconstruction of hydrologic inputs in artificial reservoirs using water balance relations. Time interval used in flow reconstruction has been monthly: we will later see that uncertainty in the estimation of variables related to reservoirs water balance doesn’t allow acceptable results with shorter time step using this approach for stream flow evaluation.

Rivers flows reconstruction using reservoirs water balance: Analysis and results for Sardinia reservoirs

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Thereafter a general framework of this approach defining the elements and variables which are necessary in the estimation of water balance in reservoirs it will be provided. We consider reservoirs that have been managed for river flow regulation in order to assure the water resources required by users. Subsequently, it will be illustrated in the activities developed for SEDEMED II EU Project and for the drafting of Regional Water Plan (Piano Stralcio di Bacino; RAS, 2005) to reconstruct river flows in Sardinia using reservoir water balance. Therefore we will examine the results of the data findings and reconstructions, mainly obtained by the Water Authorities, and the analysis carried out for the validation of obtained data. A synthetic framework of these analysis and final considerations will be provided.

2. The water balance of the artificial lakes

The water balance of artificial lakes (i.e.: lakes made by dam constructions) will be examined with the aim to evaluate the rivers flows into the lake. This procedure for the reconstruction of the flow-rate is highlighted with larger difficulties and a higher level of uncertainty in respect to the usual methods of estimating the stream flow at gauge stations (Mosley and McKerchar, 1993). While for the direct estimation at gauge sites of the stream flows the errors can be essentially caused by two elements: errors in water level measurement and errors in the flow rate – water level relation, to obtain the estimation of flows using water balance at the lake we need lots of data measurements. Moreover, some of them are difficult to measure directly and their estimation is a complex operation effected by a higher level of uncertainty. Difficulties in elaborating the data are also due to the lack of homogeneity in the procedures used to gain data by the reservoir management Authorities and, in many cases, from lack of information about these procedures.

Generally speaking, we want to draw attention to the necessity to provide standard procedures in data measurement to the reservoir management Authority if reservoir water balance has to be used for flows input reconstruction. The necessity of a quick check of results obtained in stream flow reconstruction is an other important issue in order to proceed quickly, when necessary, to establish management rule modification. Regarding the issues related to the necessity of an effective documentation of storage management we will come back specifically in the following paragraphs when we will apply the water balance approach to the artificial lakes in Sardinia.

As usual, the construction of the water balance, starts from the knowledge of the levels in the reservoir at the beginning of time intervals t = 1,…,T to which it is possible to associate the stored volume V(t) at the beginning of that period. The estimating procedure has to consider the possibility that other than the natural stream flow A(t) could arrive to the reservoir. Water flows withdrawn from other


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artificial lakes or diverted from other rivers are incoming volumes which will be indicated by T(t). In the balance we also have to take into consideration the rainfall falling directly into the lake surface M(t) and the water loss by evaporation from the lake surface, indicated by E(t). Water losses are also due to filtration through the dam and collected by drainage, that are indicated by P(t). Therefore, another element of loss is due to infiltration from the storage site, indicated by F(t).

Required withdraws from reservoir to satisfy different users demands are globally considered and are indicated by U(t). The downstream water releases from the dam are indicated by R(t). The water flowing over the spillways are named S(t).

The continuity equation applied to the storage is used to obtain the water volume flowing from rivers into the reservoir in that period:

The evaluation of the V(t) needs to have the knowledge of the water level in the reservoir and the relation linking levels to storage volumes. The first data, like the flowing water levels at river gauge stations, is normally obtained by direct measures. The conversion from heights to volumes is effected, obviously, by an high possibility of error in the evaluation as it is estimated on the basis of stored volume variation in the time interval. The relation between water levels and reservoir storages normally has been obtained by topographic measures before the construction of the dam. Moreover, possible mistakes raise at higher levels; such as at the same level variation ΔH we obtain greater volume differences ΔV as reaching the upper part of the relation curve.

The estimation of T(t) values is often a difficult task and in some cases it is obtainable only from an indirect way. This happens, for example, when rivers are not flowing naturally into the reservoir and are connected to it by diversion works and when the water transfer has not been properly monitored and measured. When it happens in a multi-reservoirs system and withdraws are monitored in downstream sections and in conveyance works drawing water from the system to demand centres, it is often useful to evaluate the water balance of the entire multi-reservoir system. In this manner it will be possible to evaluate the hydrologic input coming from all the inflowing basins to reservoirs (see in the following the example of reservoirs Flumendosa - Mulargia).

The estimation of M(t) in the period could be fulfilled with the cumulated rainfall and having information of the average surface of the lake in the period using the curve relating water-surface to water-level.

The estimation of E(t) is normally made knowing the average surface of the water and the total evaporation height e(t) in that period. This data could be


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evaluated through direct measures or calculated by usual expressions using meteorological data (temperature, wind velocity, humidity, etc). Even when this data is unavailable we could use the average seasonal values.

The evaluation of P(t) comes from measures in the drainage system of the dam while the estimation of F(t) may be done only indirectly, using water-balance data collected in periods in which all the others can be defined.

The estimation of U(t) is normally possible from measures made by flow-gauges in the diversion system drawing the water to demand centres. More complex is the estimation of the drained water released downstream the dam R(t) and spills S(t); for their estimation it is necessary to know, other than the water load, management factors on flow gates.

The use of the continuity equation to evaluate stream flows into reservoirs has to be done considering time intervals long enough to minimize errors due to variables evaluation. In some cases macroscopic errors can determine unreal estimations (i.e.: negative values). In any case special attention in the evaluation as well in the validation phase is to be made using this method. The different phenomena involved could need different integration times, depending on their kind or in the methodology of measure used. So, the normal procedure in applying the balance equation is to define the river inflow reconstruction time interval equal to at least the longer time interval assumed in the single element reconstruction. This has to be done by minimizing the associated error. Actually, in order to optimise the estimation of every single element, a specific time interval is necessary. Typically, for example, the reservoir volumes are calculated with daily checks; evaporation even using hourly data if available; withdraws and discharge have to be calculated considering even shorter time intervals on the basis of opening modification on flow gates. Although the lack of specific analysis of the problem and the impossibility to give general rules for all situations, it is usual not to consider time intervals shorter than a day and it is more common to consider monthly steps in order to reconstruct the flows.

3. Stream flows reconstruction into the Sardinian reservoirs

As mentioned in the introduction, in the following paragraphs the water balance method will be applied to reconstruct the stream flows in the Sardinian artificial lakes. For each reservoir a short summary of data obtained from the managing Authorities will be provided. Therefore some consideration on the possibility of using the reconstruction approach and analysis on obtained results, also given as time-flows graphs, and some statistical evaluations will also be given. In the reconstruction we will consider the eleven years between 1993 and 2003. The first is that following the year until which the regional hydrological database


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(SISS 1995) has already been provided. For statistical investigation on droughts (as in the aim of SEDEMED II Project) the considered period has been extended for 17 years (1986-2003): this period covers recent drought events.

On the basis of a preliminary investigation, a first screening on reservoirs has been made to verify the possibility and opportunity offered by the managing Authorities to provide the data needed. Dam sites and corresponding code numbers of reservoirs are reported in Figure 1.

In some cases in the documentation provided even the main characterizing data of reservoirs had not been available. On the basis of what was previously illustrated, at least we needed records of reservoir water levels in the examined time intervals; relations between water level, stored volume and surface area; calibration curves for spillways, diversion and discharge data; evaporation and filtration evaluations. Rare are the cases by which all data is available also in the computers. Only main data (i.e.: stored volumes) are on the web site of the Regional Board. More frequently this data, if available, is only posted in the registers of the reservoir managing Authorities.

On the basis of the preliminary investigations the following 14 reservoirs have been examined:

1 - Coghinas a Muzzone 5 - Bidighinzu a Monte Ozzastru 7 - Mannu di Pattada a Monte Lerno 8 - Liscia a Punta Calamaiu 13 - Govossai 14 - Sos Canales 17 - Olai 19 – Torrei 21 - Mannu di Narcao a Bau Pressiu 22 – 25- 26 - Flumendosa Alto e Medio + Mulargia (multi - reservoirs system) 23 - Cixerri a Gennai is Abis 24 - Is Barrocus 28 - Leni a Monte Arbus 31 - Corongiu III

Considering that 37 main reservoirs are the island, reported in Figure 1, the lack of information for many important lakes can be noticed, as the recent one named “Tirso a Cantoniera”, one of the biggest for capacity in Europe. This absence is determined by the lack of adequate documentation managing them. In order to have more information and justification on these aspects we can refer to the regional Water Plan reports (RAS, 2005) where the operations needed to collect data in order to make water-balances are described in detail. The reconstruction of


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the river flows is fulfilled for the total basin upstream the section of interest that generally coincides with the construction site of each dam or, in case of large transfers between reservoirs, with the total basin of the multi-reservoirs system (an example of this is given by the Flumendosa- Mulargia multi - reservoirs system). Table I gives a synthesis of data available for the 14 reservoirs considered for water-balance at the end of the preliminary screening. Reservoir name Height-

storage relation

Height- surface relation

Water levels records

Water storage records

Users demand supplied

Surfaceevapor. losses

Disch. volumes

Spilling volumes

Coghinas a Muzzone

X X X X X

Bidighinzu a Monte Ozzastru

X X X X X

Mannu di Pattada a Monte Lerno

X X X X X

Liscia a Punta Calamaiu

X X X X X

Govossai X X X Sos Canales X X X Olai X X X Torrei X X X Mannu di Narcao a Bau Pressiu

X X X

Flumendosa e Mulargia

X X X X X X X X

Cixerri a Gennai s Abis

X X X X X X X X

Is Barrocus X X X X X X X X Leni a Monte Arbus

X X X X X X

Corongiu III X X

Table I: Synthesis of the available data at the end of the preliminary screening


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Figure 1: Location and codes of reservoirs on the island of Sardinia


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A second screening on reservoirs has then been made on the collected information analyzing significance and consistency of the data in order to proceed with water balance. Finally, the reconstruction of the streamflows has been recognized admissible only for the following 7 reservoirs:

Mannu di Narcao a Bau Pressiu Bidighinzu a Monte Ozzastru Coghinas a Muzzone Flumendosa Alto and Medio + Mulargia Leni a Monte Arbus Liscia a Punta Calamaiu Mannu di Pattada a Monte Lerno

Considering stream flows coming from water balance on these seven reservoirs and from historical data, it has been possibile to fulfil a validation analysis on reconstructed stream flows in the eleven years between 1993 and 2003. As noticed before, there had been significant water crises in this period which had given heavy restrictions to the users. Preliminary, to estimate the behaviour of rainfall-runoff coefficients, reconstructed data has been compared with the regional database 1922-1992 (SISS, 1995) in which the estimation of the flow rates had been made by considering 30 gauge stations on the main rivers in the region.

To analyze drought sequences in the last few years, it has also been considered the period from 1986 to 2003 obtained combining the reservoirs water-balance data with the flows information drawn from the regional database. Those 17 hydrologic years (each one extends from the September to the subsequent August) period represents the most important for elaborating plans to face droughts in a proactive approach as it was characterised by the heavy water crisis started at the end of the eighties and extended until recent years.

Checks have involved the behaviour of rainfall-runoff coefficient considered as the relation between total precipitation in a hydrologic year and the total stream flow in the same year. Observed values are shown in the diagram in Figure 2 for the main basins on the island. This diagram allowed one to evaluate the effect of the reduction in rainfall Am and to estimate how those reductions affects the surface runoff Dm . They definitely, for reservoirs, represents resources that could be used. This relation could be estimated in the following form:

Dm1/3= c1 + c2 Log(Am) (2)

Parameters of the previous equation for main basins are reported in Table 2.

In Figure 2 the annual values in the period 1922-1992 are reported as dots. In the Figure are also reported the curves obtained by the preceding expression using fitted coefficients for the main basins. Such curves provide the average result in the rainfall-runoff transformation process. In order to compare values from other regions, in the same diagram the curves relative to the water basins of Coghinas,


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Tirso and Flumendosa in Sardinia, have been reported together with those of Bradano (Basilicata) river. From the figure the same behaviour in all basins can be observed.

The trend of curves in Figure 2 emphasises the transformation of rainfall in runoff leads to reduce in a non linear form these last values. This reduction can be synthesized considering the runoff decrease in the two periods expressed as ratio Rm between them. The figure also emphasises the theoretical existence of a minimum value in the annual rainfall below which surface stream flow would not be produced. In the figure it can also be noticed the reduction of 18% between the annual rainfall values between the two periods (1922-1975 and 1986-2003) have determined a reduction of over 50% of the mean annual runoff in main basins in Sardinia.

Figure 2: Relation between rainfall and streamflow in different water basins (source: RAS, 2005)

In the following paragraphs the analysis for the validation of river inflow data in reservoirs obtained by the procedure of storage water balance are reported. We will


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check the congruity of the percentages of stream flow reduction in Figure 2 with our obtained data. Particularly, it has been verified if the rate of reduction between (1922-1975) and (1986-20003) in Rm values is always maintained near to 50% for all basins in Sardinia. The following provides some synthetic results and comments for the seven reservoirs previously identified.

Table II : Parameters of the relation between annual rainfall and runoff

Hydrographic area c1 c2 Sardegna -40.536 16.215 Coghinas -40.536 16.285 Tirso -40.536 16.117 Flumendosa -40.536 16.349 Bradano (Basilicata) -28.200 11.980

In the analysis reported in the following paragraphs for the validation of river inflow data in reservoirs obtained by the procedure of storage water balance, we will check the congruity of the percentages of stream flow reduction in Figure 2 with our obtained data. Particularly, it has been verified if the rate of reduction between (1922-1975) and (1986-20003) in Rm values is always maintained near to the 50% for all basins in Sardinia. The following provides some synthetic results and comments for the seven reservoirs previously defined.


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4. Synthesis of obtained results for reservoir inflow reconstruction

Coghinas a Muzzone From the obtained data the average inflow to the reservoir, which in the period 1922-1975 was of 450.6 106 m3/year, reduces to 235.6 106 m3/year in the period 1986-2003 containing the reconstructed flows using the water balance approach. This determines a reduction Rm equals to 0.52 close to values obtained by expression 2. Between the two periods the coefficient of variations (CV) in the flow rates rises from 0.380 a 0.461. The representation of the total annual inflow to the reservoir in the whole period 1922-2003 is given in the following figure in which it is highlighted the last reconstructed period using the water balance approach.


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Flumendosa Alto and Medio + Mulargia For the system containing the high and medium course reservoirs in the Flumendosa basin and Mulargia reservoir the balance is made at the intake section of the Mulargia into the Flumendosa river. So that we consider the inflow of the entire basin contributing to Flumendosa and Mulargia. The system could be more complex as we do not consider in the balance water transfers coming from the Flumeniddu reservoir by a tunnel connecting it to the Flumendosa lake. The average annual stream flow for the total basins in the period 1922-1975 was equal to 423.8 106 m3/year. In the period between 1986 and 2003 the average stream flow decreased to 209.11 106 m3 /year with a reduction coefficient Rm equal to 0,49. The CV value rises from 0.332 to 0.557. In the figure the total annual inflow to reservoirs in the time horizon 1922-2003 is reported. The last period estimated on the basis of the water balance at reservoirs is highlighted.


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Monte Lerno For this reservoir we moved from an average annual inflow equal to 64.00 106

m3/year in the period 1922-1975 to 28.25 106 m3/year in the recent period 1986-2003 giving Rm = 0.44. The value of CV rises from 0.390 to 0.583.

Leni The values of average annual inflow in this reservoir reduces from 37.10 to 16.54 106 m3/year in the two periods. On the basis of the calculated stream flows therefore results Rm = 0.45. Il CV rises from 0.338 to 0.503 .


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Bau Pressiu

For this reservoir in the directly observed period 1922-1975 an average annual inflow equal to 6.6 106 m3/year was estimated. In the period 1986-2003 the reconstructed data provides an average annual estimation equal to 4.35 106 m3/year and Rm = 0.66. On the basis of the data analysis, it is possible that systematic errors have be made by the reservoir management Authority in the evaluations of variables involved in water balance which tend to over-estimate such streamflows.


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Bidighinzu

Even for this reservoir the results obtained are conditioned by a probable over estimation of the total inflow that depend on the low reliability of the data used in the storage balance. Resulting for the 1922-1975 period an average annual inflow equals to 10.2 106 m3/year, while for the 1986-2003 period equals to 8.23 106

m3/year, so that Rm = 0.81, over the mean values obtained for other reservoirs.


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Liscia a Punta Calamaiu

The average annual inflows in 1922-1975 was equal to 104.3 106 m3/ year and the CV calculated for such period results equal to 0.452. In the 1986-2003 period the average inflow reduces to 52.73 106 m3/ year, so that Rm = 0.52. The CV value for this last period reduces to 0.394. This fact has probably been determined by an over estimation of flows in the more critical summer periods.

5. Conclusions

The procedure for the reconstruction of the flow-rate using reservoir water balance approach is highlighted with larger difficulties and a higher level of uncertainty in respect to the usual methods of estimating the stream flow at gauge stations. On the basis of illustrated applications to reservoirs operating on the Sardinia region only for few of them it is possible to get a correct estimation of inflows into the reservoirs. Most of the difficulties are due the incomplete documentation available by water Authorities on reservoirs management.


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Moreover some of the reservoirs are connected between them and this determines further difficulties in the procedure. Nevertheless, as noticed in the introduction of this paper, we want to draw attention of water Authorities to the necessity to use standard procedures in data measurement in order to apply reservoir water balance for flows input reconstruction. Indeed, in the current situation of lack of direct measures at river gauge stations, the reservoir water balance method give us the possibility of having flow rate estimations for the last period, characterised by particularly critical drought events. The necessity of a quick validation of obtained results is an other important issue in order to proceed, when necessary, to modifications and enhancements in the monitoring system.

Bibliography Mosley M.P. and McKerchar A.I., Streamflow. In D.R. Maidment (ed.) Handbook of Hydrology,

Chapter 8. McGraw-Hill, 1993. RAS (2005) Piano Stralcio di Bacino della Regione Sardegna per l’Utilizzo delle Risorse Idriche.

Autonomous Region of Sardinia, Convention RAS-UNICA-EAF. SISS (1995) Studio dell’Idrologia Superficiale della Sardegna, Cassa per il Mezzogiorno – Regione

Autonoma della Sardegna – Ente Autonomo del Flumendosa, Cagliari.

rivers flows reconstruction using reservoirs water balance

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