Assessing water resources availability - Inductive methods

Estimation of water resources availability is an essential step for devising efficient water resources management strategies. In particular, design and management of water resource systems necessarily needs a preliminary assessment of water demands and water availability. Assessment of water resources is not an easy task, for many reasons including the complexity and the difficult monitoring of groundwater dynamics and the limited availability of observations. Assessment of surface water resources is less complicated with respect to groundwater, for the observability of surface water bodies. Nevertheless, the rigorous quantification of river discharge and storage for natural basins is one of the most relevant challenges for water resources management. The task is more complicated in conditions of water scarcity, as the analysis needs to be more rigorous.

The most relevant challenge when assessing water resources is lack of data. This is a widespread problem in hydrology, as observations of climate and hydrology started relatively recently. Moreover, even when data are available it is not always easy to have access at them, for the institutional fragmentation that usually affects water resources management, especially in Europe.

1. Brief history of water resources systems

Urban hydraulic systems started to develop in the Bronze Age and particularly in the mid-third millennium BC in an area extending from India to Egypt. About the same time advanced urban water technologies were developed in Greece and particularly in the island of Crete where the Minoan civilization was flourishing. These included construction and use of aqueducts, cisterns, wells, fountains, bathrooms and other sanitary facilities, which suggest life style standards close to those of present day. More details are provided by Mays L.W., Koutsoyiannis D. and Angelakis A.N., A brief history of urban water supply in antiquity (2007). The first sources of water were surface bodies like rivers and lakes. These were preferred for the possibility of a direct and inexpensive access to water. When water is taken at a higher altitude with respect to the users, it is possible to deliver it by gravity therefore saving energy and human resources. However, surface water are less protected against human impact and pollution and therefore already in ancient times people used to dig wells in order to exploit groundwater resources. Water use is increased along time. Today, agriculture accounts for about 70 percent of all the fresh water uses globally. Industries around the world use 20 percent of the fresh water, and only 10 percent is used for domestic activities, including drinking. A comprehensive set of statistics for water uses is given by FAO. An interesting picture of the distribution of percentage freshwater uses for agriculture is again given by FAO.

2. Assessment of water resources availability

Assessing the availability of surface water resources needs to be based on the analysis of the features of the related water bodies. If water is taken from a lake with enough recharge, the estimation of water resources availability reduces to estimation of the water volume in the reservoir. If water is taken from a flowing water body, either superficial or sub-superficial, we need to estimate water fluxes. This is usually done by deciphering the dynamics of the water body itself, with a deductive (i.e. with a model) or inductive (i.e., by using observations). The former class of methods is also called "indirect methods" while the latter is called "direct methods", as the direct analysis of data is the core of this category of approaches. With surface water bodies the problem is relatively easy as the dynamical features that we need to investigate are largely observable. Here below we will refer to direct methods, while the ungauged (or poorly gauged) problem will be discussed later.

2.1. Inductive assessment of water resources availability in rivers

When estimating river water resources availability we need to make reference to a location along the river where water is to be withdrawn. Usually such location is placed at a higher altitude with respect to the place of use. In such a location we need to refer to a river cross section, where we need to estimate the regime of the river discharge.

The river cross section is the geometric figure that is obtained by cutting the river with a plane that is perpendicular to the average velocity vector for a given fluid particle within the river flow (within a river flow water particle follow approximately the same direction). Cross sections represent the geometric boundary of the stream. The theory of fluidmechanics provides the tools for estimating the average velocity vector in a river cross section under given assumptions. We will not get into these details here.

Given that the velocity vector crosses the river section, it follows that a certain amount of water flows through it. In a given river cross section, the river discharge (or river flow) is the volume of water that flows through the cross section per unit time. It is usually measured in m3/s. Measuring the river discharge along a sufficiently long observation period allows one to assess water resources availability. This is a direct method to assess water resources, based on the identification of the river regime. There is an underlying implicit assumption that past observations are representative of current and future conditions.

In gauged rivers with a relatively long record of observations, inductive estimation of water resources availability is a classical technical problem, which is usually resolved by estimating the flow duration curve (FDC). The FDC is a graphical representation, for which an analytical approximation can be provided. The use of a graphical representation presents the advantage of providing a more immediate communication to stakeholders, therefore enhancing transparency.

The FDC depicts the percentage of time (duration) over a given observation period during which a given streamflow is equalled or exceeded (see Figure 1).

Figure 1. Construction of flow duration curve from an observed hydrograph (courtesy by Attilio Castellarin)

The FDC is a key signature of the hydrologic behaviour of a given basin, as it results from the interplay of climatic regime, size, morphology, and permeability of the basin. From a statistical viewpoint, the FDC is the cumulative probability distribution of the random variable streamflow. In fact, being the FDC an indication of the frequency with which a given flow is equalled or exceeded, if the observation period is sufficiently long the FDC itself is an approximation of the probability of equalling or exceeding a given river flow. Note that for a real random variable the probability of "equalling or exceeding" is technically coincident with the probability of "exceeding". Remember that the frequency of an event is an approximation of its probability. We will discuss about probability theory and its implications later on.

2.2. Estimation of the FDC for a gauged site
The construction of FDC from a time series of river flows observed at a given and fixed time step is straightforward. One should:
  • Pool all observed streamflows in one sample.
  • Rank the observed streamflows in descending order.
  • Identify the position of the ith observation in the ordered sample.
  • Plot each ordered observation versus its position duration, in relative or absolute terms (i.e., in percentage terms with respect to the sample size or actual position; for instance, from 1 to 365 for daily values over an observation period of one year in absolute terms).
If Fi is estimated using a Weibull plotting position, the duration Di is Di = Pr{Q > q(i)} = i/(n + 1) where n is the length of the daily streamflow series and q(i), i=1, 2, ..., n, are the observed discharges arranged in descending order. The above computed FDC is called the "period-of-record" FDC.


An alternative method to compute the FDC from an observed time series is to build one FDC for each year of the observation period and then compute, for any within-year duration, the average of the corresponding river flow across all annual curves. Therefore, if the record counts y years:

  • y annual FDC's (AFDC) are constructed from the y-year long record of streamflows (for leap years, the streamflow measured on February 29 is discarded).
  • From the group of y empirical AFDC’s one may infer the mean or median AFDC (an hypothetical AFDC that provides a measure of central tendency, describing the annual streamflow regime for a typical hydrological year).
  • By using the same methodology adopted for inferring the median AFDC one may also construct the AFDC associated with a given non-exceedance frequency p/100 (which is indicated as "Percentile AFDC" in Figure 2).
An example of the results from the computation of AFDC is provided in Figure 2.

Figure 2. Construction of annual flow duration curve from an observed hydrograph (courtesy by Attilio Castellarin)

FDCs can be displayed according to different graphical representations (Figure 3).

Figure 3. Graphical representations of flow duration curve from an observed hydrograph (courtesy by Attilio Castellarin)

Hitherto is was mentioned that FDCs provide a very comprehensive picture of the river regime. Figure 4 shows an example of how the different ranges of river flow can be identified.

Figure 4. River flow regimes identified by the FDC (courtesy by Attilio Castellarin)

2.3. Estimation of design water withdrawal

Once water resources availability is defined through the FDC, the next step is to estimate the design water withdrawal, depending on the specific water use. Water is usually withdrawn by rivers for civil, agricultural or industrial use, or hydropower production. Design water withdrawal is defined basing on water availability and water needs. In most of the cases water withdrawal is conditioned by water availability and therefore the FDC is an essential information for completing the related design project. In this case, the best solution is the optimal compromise between the cost of the infrastructure (river barrage to allow the withdrawal, hydropower plant, water supply system) and the attainable benefit. An infrastructure that is designed for a river flow that is rarely available is unjustifiably oversized, while an undersized infrastructure would offer a limited benefit with respect to what is potentially attainable. The cost benefit analysis should include environmental and societal values in the widest sense (recreation, societal well being and any other relevant issue).

When designing run-of-the-river hydropower plants, it is usual practice to adopt as design flow the river discharge with a duration of 60 days over an observation period of one year, namely, 15-20% of the year. Once the design water withdrawal Qp is fixed, the FDC allows one to estimate the volume of withdrawn water, by also taking into account the release of the environmental flow. The procedure is presented by the graph in Figure 5.

Figura 5. Estimation of the volume of water withdrawal. The lower yellow region indicates a withdrawn volume, being it equivalent to the upper yellow region, which represents a portion of integrated river discharge exceeding the planned volume of water withdrawal, which then contributes to the DMV.

Once Qp is defined, it is possible to compute the average withdrawn river flow Qmp. Then, one can compute the following indexes which quantify the impact of the withdrawal:

  • Water withdrawal index Ic=Qp/Qm, where Qm is the average river flow in pristine conditions.
  • Water use index Iu=Qmp/Qm.
3. Examples of river barrages for river management and water withdrawal
A relevant example of a river infrastructure designed to allow river navigation and hydropower production is given by the Ybbs-Persenbeug on the Danube River. An aerial image of the barrage is presented in Figure 6. One can see from the satellite image the navigation locks on both sides of the river.


Figura 6. Aerial view of the Ybbs-Persenbeug barrage on the Danube River. The river flows from left to right.

Another relevant example of river infrastructure for water withdrawal is the run-of-the-river hydropower plant located at Isola Serafini over the Po River. The Figures 7, 8, 9 and 10 show the structure of the plant and the related FDC as well as other relevant variables that depend on duration.

Figure 7. The hydropower plant at Isola Serafini on the Po River (courtesy by Attilio Castellarin)

Figure 8. The hydropower plant at Isola Serafini on the Po River (courtesy by Attilio Castellarin)

Figure 9. The hydropower plant at Isola Serafini on the Po River (courtesy by Attilio Castellarin)

Figure 10. The hydropower plant at Isola Serafini on the Po River (courtesy by Attilio Castellarin). FDC and other relevant variables.

2.4. Inductive assessment of groundwater availability
Groundwater availability assessment is much more complicated with respect to surface water, for groundwater fluxes and storage are less observable. Groundwater bodies are stored in aquifers, which are underground layers of water-bearing permeable rock, rock fractures or unconsolidated materials (gravel, sand, or silt) that can store groundwater and allow groundwater fluxes. Water is taken by aquifers typically through wells. Aquifers can be unconfined or confined. The upper boundary of unconfined aquifers is the water table or phreatic surface. Confined aquifers are overlain by a confining layer, often made up of impervious rocks or soil. The confining layer might offer some protection from surface contamination. Figure 11 shows a typical cross section of an aquifer.


Figure 11. Typical cross section of an aquifer. By © Hans Hillewaert /, Public Domain,

The qualitative functioning of aquifers is explained in this video by the Texas Water Development Board. Aquifers are recharged by inflow, which can be given by infiltrated rainfall of water inflows from neighbouring aquifers. Water is released by aquifers in the form of groundwater flow, which may emerge at the surface in the form of springs. Part of groundwater flows directly to receiving water bodies, like lakes, rivers and oceans, without emerging at the surface. Finally, part of groundwater may be withdrawn through wells for human use.

Increasing groundwater withdrawal by humans may become a matter of concern if the withdrawn flow exceeds the recharge flow. In these conditions, the water table may be lowered, therefore possibly originating shortage of water at springs and wells. In fact, much of the groundwater reserves come from “fossil” aquifers. That means that water in the aquifer is very old, in the range of 10,000-20,000 years, when the Earth was in its last glacial period. In many cases, if we use this water today, it will not be recharged during the next thousands of years. Therefore, it is extremely important to determine what is the amount of sustainable groundwater withdrawal from an aquifer.

Aquifer testing and aquifer monitoring are possible means to inductively understand groundwater dynamics. Testing and monitoring is traditionally carried out through wells. An aquifer test (or pumping test) is carried by constantly pumping water from a selected well and observing the aquifer's response, in terms of changes in the water table elevation, in nearby wells. A rapidly lowering groundwater table, in response to a pumping test, indicates that the aquifer has a slow recharge. Conversely, if nearby wells are not impacted by the pumping test then one may conclude that the aquifer is rapidly recharging.

Groundwater monitoring through wells is carried out by regularly observing the groundwater level in selected wells where significant pumping is applied. In this case as well, a groundwater level that is not significantly impacted by pumping indicates that the aquifer is not negatively affected by water withdrawal.

Another possibility to infer aquifer dynamic is to estimate water age. If water withdrawn from a well is very old, it means that the aquifer has a slow recharge. The opposite conclusion is reached when it turn out that water is young, though in this case concerns may arise about aquifer vulnerability to contamination, as fast recharge indicates that groundwater flows close to the topographic surface. The age of groundwater ranges from few hours to million years, or perhaps more. Groundwater age can be determined by referring to tracers, including isotopes. For instance, Carbon 14 is frequently used for dating very old water.

Interesting opportunities have been recently offered by the use of satellites for groundwater monitoring. In particular, NASA’s GRACE mission provides an opportunity to directly measure groundwater changes from space. By observing changes in the Earth’s gravity field, we can estimate changes in the amount of groundwater stored in a region. In fact, the massive presence of groundwater changes the mass of the Earth at the local lever therefore causing a local change in the gravity force. GRACE provides a more than 10 year-long data record for scientific analysis. GRACE has returned data on some of the world’s biggest aquifers and how their water storage is changing. Using estimates of changes in snow and surface soil moisture, scientists can calculate an exact change in groundwater in volume over a given time period.

GRACE and groundwater estimation is the subject of many research papers. The main limitation of GRACE data is that they can provide an estimate of regional groundwater storage, while information is still not reliable at the local level.

Groundwater availability assessment is the subject of several on-going research projects.

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Last modified on March 18, 2018