Adjustment of FDCs in Scotland for the influence of natural lakes and lochs

The storage associated with natural lakes within a catchment tends to maintain (increase) base flow and hence low flows and attenuate high flows. Qube incorporates a procedure for estimating the influence of natural lakes and lochs in Scotland on the estimation of flow duration statistics. This procedure was developed in the original LowFlows research in Scotland and revised in collaboration with SEPA. The procedure is based on available data from a relatively small number of larger Scottish lochs, supplemented by data from Cumbrian lakes. It is currently only deployed in Scotland for ‘significant’ lakes identified in consultation with SEPA. It is not currently deployed in the rest of the UK.

It is important to note the distinction between a natural lake and a reservoir or managed lake. The influence of the latter on the downstream flow regime may be complex and will be directly related to how outflows from the reservoir are managed by the operator.

A Lake Adjustment Term ( $LAT$ ) has been calculated for each lake/loch in Qube based on the ratio of the surface area of the lake ( $LA$ ) and the catchment area of the lake ( $LCA$ ) multiplied is the natural Q95 as $\%MF$ at the outlet of the lake ( $Q95\%MF_{Lake}$ ), as follows;

If $LA < 0.1 km^2$ , $LCA < 1.5 km^2$ , or $LA/LCA<2\%$ , then $LAT = 0$

If $2 \% \leq LA/LCA < 10 \%$ , then $LAT = 0.068 \times e^{(0.344{{LA} \over {LCA}})} \times Q95\%MF_{Lake}$

If $LA/LCA \geq 10\%$ , then $LAT = \big({{-31.6} \over ({LA \over LCA})}+5 \big) \times Q95\%MF_{Lake}$

Where $LA$ is the lake surface area ( $km^2$ ) $LCA$ is the catchment area above lake ( $km^2$ ) $LAT$ is the lake Adjustment Term ( $\%MF$ ) $Q95\%MF_{Lake}$ is the natural Q95 as $\%MF$ estimate at the outlet of the lake

The ‘raw’ estimate of Q95 as $\%MF$ for the target catchment obtained from the ROI algorithm, $Q95\%MF_{ROI}$ , is then adjusted as follows:

$Q95\%MF_{LakeAdjusted} = Q95\%MF_{ROI} + \sum_{n}^{i=1} \Big( LAT_i \times {LCA_i \over CA} \Big)$

Where $LAT_i$ is the $LAT$ value for the $i^{th}$ lake $LCA_i$ is the catchment area of the $i^{th}$ lake $CA$ is the catchment area of the target catchment

The adjustment statistic for high flows is defined at Q5 to be:

$Q5\%MF_{LakeAdjusted} = {Q5\%MF_{ROI} \over {\big(-0.82 \times {Q95\%MF_{ROI} \over Q95\%MF_{LakeAdjusted}} + 1.82\big)}}$

The adjustment of other flow percentiles is then made as a non-linear interpolation between the $Q5\%MF_{LakeAdjusted}$ and $Q95\%MF_{LakeAdjusted}$ noting that at Q30 there is no adjustment applied (ie. point of inflexion suggests that lakes have no impact on mean flow).