Introduction

One of the key steps in the estimation of artificially influenced low flow statistics at the ungauged location is the construction of a monthly artificial influence profile based on water use upstream of the location. This requires:

Identification of all major occurrences of artificial influences upstream of the ungauged site;
Quantification of monthly impacts for each artificial influence (monthly abstraction and discharges, reservoir release duration curves and complex impact duration curves);
Summation of individual impacts to create a nett monthly artificial influence profile at the ungauged location.

A simple monthly influence profile is illustrated in Figure 1.

Figure 1 - The construction of a monthly artificial influence profile

Surface Water Abstractions

The procedures implemented within Qube for estimating monthly profiles for abstraction data at a site are summarised within the following steps:

For each site purpose the minimum data requirements are:
- the definition of the actual monthly profile, which describe how the abstracted volume is distributed between months,
- the licensed annual volume, and
- the percentage return.
These site purpose values are then aggregated to the site level for use within the flow estimation procedures.
The site percentage return value is applied to the site aggregate actual monthly profile, to give a net abstraction profile which is used within the flow estimation procedure.

The uptake factor is calculated for information as the proportion of the total licensed abstraction quantity which is actually abstracted.

Groundwater Abstractions

Summary

The abstraction licences which authorise abstractions from groundwater sources provide the same information relating to the total annual licensed quantities and actual monthly profile as those of surface water abstractions and a monthly profile can be predicted (from annual licensed quantities, uptake factor and monthly distribution profile) following the same methods.

Like surface water abstractions, for each groundwater abstraction site purpose the minimum data requirements are:

the definition of the actual monthly profile, which describe how the abstracted volume is distributed between months,
the licensed annual volume, and
the percentage return.

However, abstractions from groundwater sources do not have an immediate impact on the flows in the rivers as a result of the complex response of stream flow to the pumping of water from an unconfined, or semi confined aquifer. Hence the monthly profile is adjusted by Stream Depletion Factors (SDF’s) which summarise the net impacts of the stream flow response to groundwater pumping for that particular abstraction site. Hence the impact of a groundwater abstraction on nearby streams is quantified within Qube by considering both the site level monthly profile and the SDF applicable to that site. The algorithm used within the software to calculated SDFs is described below.

Development of Stream Depletion Factors

For an individual well, the impact of the abstraction on the river flow is dependent upon the following factors:

the bulk aquifer hydrogeology and geometry;
the distance from the stream;
the seasonality of pumping;
the pumping rate;
the degree of hydraulic connection between the stream and aquifer;
features such as swallow holes and spring lines.

Items 1, 5 and 6 are impossible to characterise on a regional basis due to their localised nature and the lack of regional databases of variability/occurrence.

The solution taken for predicting the impact of groundwater abstractions on the low flow statistics was to adopt a distributed form of the Jenkins solution of the Theis analytical model.

The analytical solution of the differential groundwater flow equations is based on a number of simplifications to linearise the problem and provide solvable boundary conditions. The conceptual representation of the aquifer/stream systems used in the Theis model is shown in Figure 1.

Figure 1 - Conceptual model of the Theis analytical solution

The principal assumptions and simplifications within the Theis model are as follows:

the aquifer is isotropic, homogeneous and infinite in areal extent;
in cases of unconfined aquifers the head gradients are small, so that the vertical flow components may be neglected and only horizontal flow is considered. This is the Dupuit Forchheimer assumption;
the Transmissivity (T) and Storativity (S) remain constant in time;
the borehole is screened over the entire depth of the aquifer;
the rate of pumping is constant with time;
the temperature of the stream is equal to that of the groundwater, and is assumed to be constant over time;
water is released instantaneously from storage in the aquifer;
the variation of water level in the stream caused by changes in discharge is neglected;
the stream represents the sole source of recharge, thus recharge from infiltrated precipitation can be ignored;
the stream is linear and infinite in extent;
the stream fully penetrates the aquifer and is in perfect hydraulic contact (ensuring Dupuit flow and a solvable stream/aquifer boundary condition).

The hydraulic connection between the aquifer and the stream affect the rate at which water is transferred and also the direction of the transfer. Typical aquifer stream connections are illustrated in Figure 2. The bed of the stream has resistance, which is associated with the unconsolidated layers of fluvial deposits. These layers may have much lower hydraulic conductivities than those of the bulk aquifer. This approach of perfect hydraulic contact can give rise to over estimation of stream depletion due to the omission of the streambed resistance and the Dupuit flow assumption.

Figure 2 - Aquifer stream hydraulic connections

The form in which the Theis solution predicts the impact in terms of the stream depletion factor (SDF) which is the ratio of stream depletion volume to pumped volume (q/Q), and is given by:

${q \over Q }= erfc \bigg({ 1 \over 2\Gamma }\bigg)$

where:

$q$ = Steam depletion (m³/s); $Q$ = Pump rate (m³/s); $erfc(x)$ = the complementary error function of x; $\Gamma$ = dimensionless time.

And where $\Gamma$ is defined by:

$$\Gamma = {1 \over a} \sqrt{tT \over S} $$

where: $T$ = Transmissivity (m²/s); $S$ = Storativity; $t$ = time (s); $a$ = distance from well to stream (m).

$erfc(x)$ is an indefinite integral but can be approximated using the method outlined in relationship:

Figure 3 - Solving the complementary error function of x

The input parameters required are therefore: $a$ , $T$ , $S$ and the mean monthly pump volume, $Q$ and the duration of pumping (months).

The inputs are values for $T$ and $S$ and the monthly abstraction profile. The User can either define values of $T$ and $S$ as attributes for the site or, alternatively, the software will use default values for the aquifer unit assigned to the site. The distance from the stream, $a$ , is calculated by the software, and is taken as the distance between the site and the closest river reach to the site.

The duration of pumping (months) is identified from the abstraction profile. April to Sept would be 6 months with April start, Oct to March would be a 6 month period with a Oct start.

$Q$ is required to rescale the calculated SDF to yield a nett influence volume. For an intermittent pumping regime, the reduction in stream flow will continue after pumping has stopped. By using the method of superposition it is possible to estimate the impact of a sequence of pumping events over irregular periods. The method of superposition assumes that a pumping well continues to pump past the end of the pumping period, but at the end of the pumping period, an imaginary well at the same location starts to recharge the aquifer at the same rate as the pumping well is discharging. The recharge equation can be represented by the stream depletion equation simply by changing the sign. The rate of stream depletion at any time after pumping ends is therefore equal to the difference between the depletion rate that would have occurred if pumping had continued and the augmentation rate of the imaginary recharge well.

When applied at a groundwater site within Qube, the Theis model is run, on a monthly time-step using the duration of pumping and for a period of 50 synthetic years to enable equilibrium to be reached. To undertake this a paired well is set up for the duration of pumping and run for 100 years. This is analogous to a unit hydrograph. This paired well simulation is then convoluted over 50 years at an annual time step.

The 12 monthly SDF values from the last year of simulation are applied to each of the monthly abstraction volumes lagging the 12 month SDF for each month to reflect the position of the month in the year.

The final step is to multiple the SDF profile by the mean monthly abstraction volume to yield a 12 month profile of stream depletion volumes. These are then treated as surface water abstractions would be treated. The predicted or actual monthly abstraction profile is used as the input.

The sensitivity of the stream depletion factor to changes in the ratio of $T/S$ can be summarised as follows:

The magnitude of the SDF response increases with increasing $T/S$ . This is as expected, both intuitively and from analysis of the form of the solution.
The response of the Theis solution to an incremental change in $T/S$ is sensitive to the percentage change in the $T/S$ ratio. This sensitivity is greater for large percentage changes. The sensitivity of the SDF response to changes in $T/S$ is more sensitive the further the distances from the stream and is more important for periodic rather than constant rate abstractions.

Discharges

A monthly profile is required, derived either from actual monthly discharge data or a constant value based on the dry weather flow (DWF). This statistic is a design criteria for sewerage treatment works (STW) and is often recorded for other types of discharge consents. In the case of STWs the dry weather flow is only a crude guide to the actual discharge volumes since it is difficult to accurately quantify the true population served by the works, the per capita water use, industrial effluent flows to sewer, operation of combined sewer overflows and mains leakage.

Impounding Reservoirs

Reservoir impacts are defined as a set of 12 monthly release duration curves each consisting of 101 points corresponding to the FDC plotting positions. The reason for this is that the outflows from a reservoir will be a combination of a compensation (environmental) flow, spills from the reservoir when it is full and, possibly, releases of water for downstream abstraction – regulation releases.

The method for adjusting natural flows for the impact of significant (SIG) impounding reservoirs is equivalent to replacing natural river flows and artificial influences upstream of the dam site by twelve monthly reservoir release duration curves (RDCs) which combine mean monthly compensation flows, reservoir spill and augmentation releases, or freshets if appropriate. Due to the variability in operating policies of reservoirs, illustrated in Figure 1, there has been no attempt to implement methods for predicting monthly reservoir RDCs based on minimal data.

An impoundment is associated with the nearest point on drainage network in Qube, where a catchment is defined and associated with that impoundment. A SIG impoundment must have a RDC sets so that the impact is incorporated into the influenced flow estimation procedure. If no RDC set supplied then the impoundment is flagged as INSIG and does not affect the flow regimes of downstream catchments.

Figure 1 - Examples of reservoir release profiles

Complex Impacts

Based on the Environment Agency CAMS Ledger, complex influences consist of a 26 point annual Impact Duration Curve (IDC). The IDC consists of a positive or negative impact on the flow at the corresponding natural flow percentile (Q1, Q10, Q20, Q30, Q40, Q50, Q55, Q60, Q65, Q70, Q75, Q80, Q82, Q84, Q86, Q88, Q90, Q92, Q94, Q95, Q96, Q97, Q98, Q99, Q99.5 and Q99.9). Complex Impacts can have a negative (abstraction) or positive (discharge) effect or a combination of a positive effect on some parts of the FDC and negative on others.

During flow estimation, the complex impact corresponding to each natural monthly flow, consisting of a 101 point FDC, is calculated. This is based upon the relative natural annual percentile and the impact at that annual percentile, which is linearly interpolated (for consistency within CAMS) from the 26 point IDC. This impact is then applied to the natural flow, along with abstractions and discharges, to calculate the monthly influenced FDC.