The UK regional models within Qube do not explicitly take into account local hydrometric data in the context of the estimation of long term mean flow and only partially within the estimation of the flow duration curve. The estimation of flow duration curves in catchments with local gauged data can be improved through the explicit incorporation of the gauged flows data within a catchment.

Any gauging station loaded within Qube with natural or naturalised annual flow duration curve data can be nominated as a local data gauge. The User can select whether local data are to be incorporated within the estimation procedure (see guidance on Gauge Suitability for Local Data). The algorithms for explicit use of local data within Qube also offer the potential for over-riding the natural estimates by alternative sources of data (e.g. groundwater models). This is not explored further within this method statement but is achieved by setting up a dummy gauging station and loading up with FDC data.

Potential Configurations of Local Gauging Stations

An outflow site of an ungauged catchment may be positioned upstream or downstream of sites on the same river system, at which flow data have been recorded. Where a gauging station is positioned downstream of the ungauged site there may be additional gauges on tributaries which also contribute to flows at the downstream gauging station which may be considered to be adjacent to the ungauged site. The upstream gauges are nested within the ungauged catchment and the ungauged catchment is nested within the catchment of the downstream gauge. The adjacent catchments are nested within the downstream gauge but not the ungauged catchment. Within the local data algorithm is assumed that a water balance is closed by a gauging station (with no significant gauge bypass) and that travel times are insignificant over the scales considered.

An ungauged site may have an arbitrary number of upstream or downstream gauges positioned in direct sequence and which are hence nested with one another. However, in the current algorithm, only flow data from the first upstream gauge(s) and/or downstream gauge are used to constrain estimates of flow statistics for the ungauged catchment.

The algorithm is based on the following assumptions:

data from all gauges defined as local data gauges is of equal quality and of zero hydrometric error.
the gauged flows are natural (i.e. the gauged catchment has few influences or the flows have been derived/modelled, for example by flow naturalisation, to produce a record that can be considered natural).
an ungauged catchment may have multiple non-overlapping proximal upstream gauges, which are entirely contained within the boundary of the ungauged catchment.
an ungauged catchment may have a single proximal downstream gauge within the boundary of which the ungauged catchment is entirely contained.
all of the flows recorded at an upstream gauge, pass directly through all points further downstream, including the ungauged catchment outflow.
all of the outflow from an ungauged catchment flows through a downstream gauge.
the catchment of a downstream gauging station may contain multiple adjacent upstream gauges, which do not overlap either with themselves or the ungauged catchment.

Figure 1 shows examples of the configurations in which local data may be used to constrain estimates of flow statistics at ungauged sites. In each example, the shaded areas denote the catchments for which local gauged data are available. It is noted that currently Qube does not make use of adjacent gauges.

Figure 1 - Definition of a) upstream local gauges b) downstream and adjacent local gauges

Use of Upstream Gauged Data

Where gauged data are available from one or more upstream gauges (Figure 1.a), the flow at the ungauged catchment may be considered to be the total of all the flows recorded at the upstream gauges, with additional runoff from the incremental area, which is the area within the ungauged catchment which is not included in any of the gauged sub-catchments.

The mean flow for the incremental area is determined by subtracting the total Qube runoff-derived mean flow for all of the gauged catchments, from the Qube runoff-derived mean flow for the ungauged catchment:

$ROMF_{inc} = ROMF_{ug} - \sum_{n=1}^i ROMF_{gi}$

where; $ROMF_{inc}$ , $ROMF_{ug}$ and $ROMF_{gi}$ are the runoff-derived mean flow for the selected period of record from the incremental area, the ungauged area, and the $i$ th gauged area respectively.

The estimated mean flow for the ungauged catchment, $MF_{ug}$ , is obtained by adding the runoff-derived mean flow for the incremental area, $ROMF_{inc}$ , to the total recorded mean flows for the selected period of record at all of the upstream gauges $\sum_{n=1}^i MF_{gi}$ .

$MF_{ug} = \sum_{n=1}^i MF_{gi} + ROMF_{inc}$

Where the total area of the gauged catchments is small in comparison to the area of the ungauged catchment estimates of mean flow using this method are unlikely to be strongly influenced by the upstream gauged data and will be similar to the mean flow estimated by the runoff method within Qube.

The $Q(x) \% MF_{inc}$ value for each of the 101 plotting positions for the incremental area is estimated using the Qube ROI algorithm.

The $Q(x)$ statistic for the ungauged catchment is determined by summing the $Q(x)$ values for all gauged catchments, and adding the $Q(x)$ value for the incremental area:

$Q(x)_{ug} = \sum_{n-1}^i Q(x)_{gi} + Q(x) \% MF_{inc} \bigg({ ROMF_{inc} \over 100 } \bigg)$

where $Q(x)_{ug}$ and $Q(x)_{gi}$ are the $p(x)\%$ exceedence flows, in m³/s, for the ungauged and $i$ th gauged catchments respectively.

Use of Downstream Gauged Data

Where gauged data are available from a single downstream gauge (Figure 1.b) the flow at the ungauged catchment may be considered to be the difference between the flow recorded at the downstream gauge and estimated as runoff from the incremental area for the selected period of record.

The catchment descriptor (RUNOFF) based estimate of mean flow for the incremental area is determined by subtracting the total runoff-derived mean flow for the ungauged catchment from the runoff-derived mean flow for the gauged catchment:

$ROMF_{inc} = ROMF_{g} - ROMF_{ug}$

where; $ROMF_{inc}$ , $ROMF_{g}$ and $ROMF_{ug}$ are the runoff-derived mean flow for the selected period of record from the incremental area, the gauged area and the ungauged area, respectively.

A first estimate of the mean flow for the ungauged catchment, $MF_{ug}^{/}$ , is obtained by subtracting the runoff-derived mean flow in respect of the incremental area, $ROMF_{inc}$ , from the mean flow recorded at the gauged site, $MF_g$ .

$MF_{ug}^{/} = MF_g - ROMF_{inc}$

Since flows from the ungauged catchment may represent only a small proportion of flows recorded at a downstream gauge, a correction weighting factor ( $CWF$ ), as a ratio of runoff-derived mean flows for a standard period of record, $ROMF_{ug}$ , and $ROMF_{g}$ , for the ungauged and gauged sites respectively, is applied to the first estimate of mean flow for the ungauged catchment, to derive a corrected estimate of mean flow, $MF_{ug}$ .

$CWF = {ROMF_{ug} \over ROMF_g}$

$MF_{ug} = ROMF_{ug} + CWF (MF_{ug}^{/} - ROMF_{ug})$

A first estimate of the $P(x)\%$ exceedence flow statistic, $Q(x)_{ug}^{/}$ , for the ungauged catchment is determined by subtracting the initial ROI estimate of the $Q(x)$ value for the incremental area from the $Q(x)$ value for the gauged catchment both for the selected period of record.

$Q(x)_{ug}^{/} = Q(x)_g - Q(x) \%MF_{inc} \bigg( { ROMF_{inc} \over 100 } \bigg)$

where $Q(x)_{ug}^{/}$ and $Q(x)_g$ are the $P(x)\%$ exceedence flows for the selected period of record, in m³/s, for the ungauged, and gauged catchments respectively, and $Q(x) \%MF_{inc}$ is the $P(x)\%$ exceedence flow for the selected period of record, expressed as a percentage of mean flow, for the incremental area.

The correction weighting factor, $CWF$ , as applied to the downstream estimate of mean flow, is also applied to derive a corrected $P(x)$ % exceedence statistics, $Q(x)_{ug}$ :

$Q(x)_{ug} = Q_{ROI} (x)_{ug} + CWF ( Q(x)_{ug}^/ - Q_{ROI} (x)_{ug})$

where $Q_{ROI} (x)_{ug}$ is the value of the $P(x)\%$ exceedence flow, in cumecs, determined by the ROI method within Qube for the selected period of record. That is:

$Q_{ROI} (x)_{ug} = Q(x)\%MF_{ug} \Big( { ROMF_{ug} \over 100 } \Big)$

Use of Upstream and Downstream Gauged Data

Where gauged data is available for one or more upstream gauges and a downstream gauge is also identified the local data routines make use of both sets of data.

An improved estimate of mean flow is calculated using the upstream and downstream gauged data separately. These estimates are then combined using a weighted averaging scheme which effectively reflects the relative position of the ungauged catchment between the upstream and downstream gauges.

Let $Q_{ug\,us}$ equal the final local adjusted flow estimate using upstream gauging stations and let $Q_{ug\,ds}$ equal the equivalent downstream adjusted flow estimate - Note $Q$ may be $MF$ or $Q(x)$ . Finally let $ROMF$ equal the runoff based estimate of mean flow for a standard period of record for upstream gauges $(us)$ , downstream gauge $(ds)$ and the ungauged site $(ug)$ . The final estimate, combining both locally adjusted estimates will be:

$Q_{final} = \bigg({ 1 - \frac{ ROMF_{ug} - \sum_{i=1}^n ROMF(i)_{us} }{ ROMF_{ds} - \sum_{i=1}^n ROMF(i)_{us} } }\bigg) Q_{ug\,us} +...$

$...+ \bigg({ 1 - \frac{ ROMF_{ds} - ROMF_{ug} }{ ROMF_{ds} - \sum_{i=1}^n ROMF(i)_{us} } }\bigg) Q_{ug\,ds}$