Programa de Evaluación

The distributed hydrological model output, used to determine the raw flow data (Section 1, Hydrology), generates flows into the lakes, but simply routes flow through the ponds (effectively ignoring the potential for a lake to buffer an increase in water volume). In order to better replicate the volumetric dynamics (water level variation) of the lakes to inflow and also the response of the outflow structures, design spillways and functional crest to extreme events, the data generated in the distributed hydrological models was imported into a specifically configured hydraulic model for the lake chains. The models were designed in the isee dynamic simulation modelling package (STELLA®), that has enabled the project to configure the structure specification (pipe diameter, material and gradients) with bathymetric lake volume data to better simulate water level fluctuation and therefore hydraulic head gradients onto the flow structures. There is no industry standard in the modelling of reservoir routing. STELLA® is a flexible and dynamic model which allows the the user to input all ruling equations and to state when conditions require each equation to be used. The main flexibility of the dynamic simulation model is the ability to adjust any parameter, namely pipe diameter or lake volumes in order to explore the options available to route and or store water relative to modelled inflows into the lakes. Dr. Margaretta Ayoung, a principle hydrologist at Atkins has seen the STELLA® model and agrees that this tool is ideal for modelling the reservoir routing at Hampstead Heath. The

conditions and equations used within the build model can be seen in the log files in Appendix A. An example of what the STELLA® interface looks like is shown in Figure 12 below (Golders Chain).

Figur

Model Inflows

The model represents the ponds in order and their various connections and elevation differences. Hydrographs derived from the 1:10,000 year rainfall runoff simulation provide the raw input into the model. The top pond in each chain had the original hydrograph as produced by the rainfall runoff model. Ponds further down the chain had two inputs into their system; the flow derived from upstream ponds and a hydrograph to represent an inflow due to the increased catchment size for each downstream pond. This hydrograph inflow for each pond contained the hydrograph shape as derived for each pond from the 1:10,000 year rainfall runoff simulation. The difference in peaks between each pond and its immediate upstream neighbour was used as the peak for these individual pond inflows. Table 9, below, illustrates original peaks as derived from the rainfall runoff model. Note that in the Highgate chain the flow from the two ponds further up the chain (Thousand Pond and Wood Pond) is represented within the Stock Pond peak flow value (these ponds were not looked at in this analysis as they have recently been upgraded and are not in City of London management). The second column shows the cumulative peaks used in the river cascade model for the 1:10,000, thus the design flood for the spillways. The final column shows the Qpmf values used as the design events for the crest of the ponds. This value is effectively twice that of the 1:10,000 year value. All of these flows will be represented using individual pond hydrographs as derived from the 1:10,000 year rainfall runoff model to correctly show the variance in the time to peak. The options did not need to be designed for these flows as the chain system provides an attenuation function. The STELLA® model was used to assess the design standard of the structures. These can be seen in the model results below.

Table 13 Original peaks as derived from the rainfall runoff model

Chain Pond Name 1:10,000 year

rainfall runoff peak raw data (m-cu/s)

1:10,000 year peak inflow as represented in the model -cumulative (m-cu/s) Qpmf values as represented in the model (2 x 1:10,000 peak flows) - cumulative (m-cu/s) Stock 14.49 14.49 28.98 Ladies Bathing 18.15 3.66 7.32

Highgate Bird Sanctuary 24.14 5.99 11.98

Highgate Model Boating 31.23 7.09 14.18 Men’s Bathing 34.13 2.90 5.80 Highgate No. 1 36.84 2.70 5.40 Viaduct 6.04 6.04 12.08 Vale of Health 4.47 4.47 8.94

Hampstead _{Catchpit N/A N/A N/A}

Mixed Bathing 22.80 12.09 24.18

Hampstead No. 2 25.62 2.82 5.64

Hampstead No. 1 26.30 0.68 1.36

The graph below, Figure 13, shows the inflows in to the Highgate chain. The delay in the peaks at the event moves downstream is shown in this graph. Figures 14 and 15 show the raw 1:10,000 year inflows for the Hampstead and Golders Chain respectively.

Figure 13 Highgate Chain 1:10,000 raw inflow hydrographs  !  !  !  !     " #     " #     " #     " #                         

Figure 15 Golders Hill Chain 1:10,000 raw inflow hydrograph

Model structure input information

The levels and sizes of all structures on and around the ponds were taken from survey data collected by Plowman Craven and Clarke Consultancy. The overflow pipe at the inlet and outlet were lifted from the topographic survey undertaken by Plowman-Craven in March 2010.

The functional crest width was obtained from the topographic survey and is the maximum length of relatively flat crest that has no obstacles such as houses in the way and would be able to pass flow easily into the next downstream pond in the chain (i.e. the most direct path to the next pond). The “crest level” is an average taken over the width of the dam crest. The de-watering pipes have not been modelled in the STELLA® model due to a lack of sufficient information regarding the size and levels of these structures.

For the structures modelled the Colebrook-White and Manning’s n roughness parameters were determined based on the assumption of an unblocked, smooth concrete finish.

Model flow calculations

The STELLA® model was built used three different methods to transport flow from one pond to the next pond. Firstly flow can be transported through an overflow pipe, this used the Mannings equation for unsubmerged flow (equation 1) and the Colebrook White equation for submerged flow (equation 2) to represent the effect of a hydraulic head on the overflow discharge.

Equation 1

Secondly, flow can be transported using the spillway which uses the Broad Crested weir equation (equation 3). Finally, flow can be transported over the crest, again using the Broad Crested weir equation (equation 3). It should be noted that in the current situation only the Model Boating pond has an effective spillway. In this simulation all other spillways have a width of zero to reflect no effective spillway.

Equation 3

In the STELLA® modelling, both option B1 and B2 have been modelled in exactly the same way using the Broad Crested Weir equation. Culverts will be over designed in options B2, so that they do not restrict the flow.

Modelling the wave effect

The upstream water levels of the ponds have been calculated based solely upon the head pressures created by water backing up behind the weirs. Wave effects did not form any part of the these calculations. The numbers were generated in the STELLA® model which dynamically routed the inflow into the lake and tracked the volumetric response of the lake with regards to the inflow and outflow.

The design level of the dam crests for the recommended scheme contain a notional increase in height as a small freeboard allowance due to waves: for the majority of the ponds, this value is 0.1m.

It was agreed that wave effect calculations were not required at this site due to the low fetch and the sheltered conditions; thus no allowance for wind derived wave effect has been incorporated into the recommended designs.

Model assumptions

All simulations assumed a start volume in the ponds as the current invert level volume. Table 14, below, displays the start volumes for the ponds.

Table 14 Inert level volumes of all ponds, used as start volumes in the model

Pond Volume at start of simulation (m-cu)

Stock 3,600 Ladies Bathing 7,400 Bird Sanctuary 7,500 Model Boating 32,800 Men’s Bathing 41,600 Highgate No. 1 24,100 Vale of Health 12,518 Viaduct 3,800 Catchpit 15 Mixed Bathing 9,390 Hampstead No. 2 20,200

Pond Volume at start of simulation (m-cu)

Hampstead No. 1 25,123

Leg of Mutton 2,070

Swan 1,410

The models were simulated over 30 hours to allow the natural water level recovery process to begin after the event.

Note that It is understood that the dewatering pipes need to operate to reduce water levels in the pond by 1m in 24 hours. This is a maintenance issue and for this study they have not been considered. These pipes should not be used in an extreme event.