31:T88b,{ var data = [ { x: [2028,2043,2043,2028], y: [300,300,1700,1700], fill: 'toself', mode:'none', hoverinfo:'skip', fillcolor: 'rgba(150,150,150,0.3)', showlegend:false, type: 'scatter' }, { x: [1990,1990], y: [400, 1700], showlegend:false, mode: 'lines', hoverinfo:'skip', type: 'scatter', line: {width:1.5,color: 'rgba(0,0,0,0.6)'}, }, { x: [1970,2055], y: [1100,1100], mode: 'lines', hoverinfo:'skip', name: 'Historic Mean Annual Flow', line: {width:1.5,color: 'rgba(0,0,0,0.7)',dash: 'dot'}, type: 'scatter' }, { x: simul_select.map(ex=>ex.Year), y: simul_select.map(ex=>ex.Climate_Change), mode: 'lines', hoverinfo:'x+y', name: 'Model of Climate Change Impact on Mean Annual Flow', line: {width:2,color: 'rgba(0,100,0,0.7)',dash: 'dot'}, type: 'scatter' }, { y: flow_yearly.map(y=>Math.round(y.Flow_mean)), x: flow_yearly.map(y=>y.WaterYear), marker: {color: colr(1,0.3)}, hoverinfo: 'x+y', showlegend:false, type: 'bar' }, ]; var layout = { width: width, height:230, font: font, margin: { l: 90, r: 140,b: 0, t: 0 }, showlegend: true, legend:{ orientation: "h" }, annotations: [ { x: 2034, y: 500, text: 'Debt Period', showarrow:false,xref: 'x',yref: 'y',xanchor:"center", ayref:'y',ay:0 }], xaxis: { position:0.9, anchor:'free', showgrid: false, zeroline: false, showticks: false, ticks:'', range:[1970,2055] }, yaxis: { title: 'Mean Flow', range:[250,2200], zeroline: false, showline: false, separatethousands:true, visible:false } }; const div=DOM.element('div') plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div}

Fig 1. A simple model for the possible impact of climate change. The average of mean annual flows decreases from 1990 by a fixed percentage each year per year. The 15 years of the power station debt repayment period is highlighted.

` }32:Taa5,{ var data = [ { y: movingAverage(flow_yearly.map(y=>y.Flow_mean),10,true), x: flow_yearly.map(y=>y.WaterYear), mode: 'lines', hoverinfo:'none', name:'10 Year Moving Average', line: {shape: 'spline', color: colr(1), width:1.5}, type: 'scatter' }, { y: flow_yearly.map(y=>y.Flow_mean), x: flow_yearly.map(y=>y.WaterYear), marker: {color: colr(1,0.3)}, showlegend:false, hoverinfo:'skip', type: 'bar' }, { x:[], y:[], mode:'markers', showlegend:false, hoverinfo:'skip', marker:{color: colr(5), size:7}, type:'scatter' }, { x: [1955,2010], y: [1700,1700], mode: 'lines', hoverinfo:'skip', showlegend:false, line: {width:1,color: colr(1),width:2.5}, type: 'scatter' } , { x: [2028,2043,2043,2028], y: [300,300,1700,1700], fill: 'toself', mode:'none', hoverinfo:'skip', fillcolor: 'rgba(150,150,150,0.3)', showlegend:false, type: 'scatter' }, { x: [1924,2050], y: [1100,1100], mode: 'lines', hoverinfo:'skip', name: 'Overall Average', line: {width:1.5,color: 'rgba(0,0,0,0.7)',dash: 'dot'}, type: 'scatter' }]; var layout = { hovermode:'closest', width: width, height:230, font: font, margin: { l: 90, r: 140,b: 0, t: 0 }, showlegend: true, legend:{ orientation: "h" }, annotations: [{ x: 2033, y: 500, text: 'Debt Period', showarrow:false,xref: 'x',yref: 'y',xanchor:"center", ayref:'y',ay:0 }, { x: 1982, y: 1570, text: '55-years', font:{color:'hsv(6,100,100)'}, showarrow:false,xref: 'x',yref: 'y',xanchor:"center", ayref:'y',ay:0 }], xaxis: { position:0.9, anchor:'free', showgrid: false, zeroline: false, showticks: false, ticks:'', range:[1924,2050] }, yaxis: { title: 'Mean Flow', range:[250,2200], zeroline: false, showline: false, separatethousands:true } }; const div=DOM.element('div') plt.newPlot(div, data, layout,{displayModeBar: false}); div.on('plotly_hover', data => { let yr=data.points[0].x plt.restyle(div,{marker:{color: flow_yearly.map( y=>y.WaterYear<=yr+5 && y.WaterYear>yr-5?'rgba(255,50,50,0.7)':colr(1,0.3) )}},1) plt.restyle(div,{x:[[data.points[0].x]],y:[[data.points[0].y]]},2) }) div.on('plotly_unhover', data => { plt.restyle(div,{marker:{color: colr(1,0.3)}},1) }); return html`

${div}

Fig 2. Historic mean annual flow to 2016. The overlaid 10 year moving average shows the climate variability which may be a periodic, cyclic effect with higher and lower average flows.

` }33:T6e9,{ var data = [ { x:[1827,1907], y:[560,560], mode: 'lines', line: {width:2.5,color: colr(1)}, type: 'scatter',showlegend:false }, { x:[1910,1965], y:[560,560], mode: 'lines', line: {width:2.5,color: colr(1)}, type: 'scatter', showlegend:false }, { x: tring.map(ex=>ex.Year), y: tring.map(ex=>ex.Precip_Recon), mode: 'lines', type: 'scatter', name: 'Tree Ring Reconstructed Rainfall', line: {width:2,color: 'rgba(0,0,0,0.4)'}, }, { x: tring.map(ex=>ex.Year), y: tring.map(ex=>ex.Precip_recon_20yr), mode: 'lines', name: '20y Moving Mean', line: {width:1.5,color: colr(1)}, type: 'scatter' }, ]; var layout = { width: width, height:250, font: font, margin: { l: 140, r: 170,b: 0, t: 0 }, showlegend: true, legend:{ orientation: "h" }, annotations: [ { x: 1870, y: 570, text: '80-years', font:{color:'hsv(6,100,100)'}, showarrow:false,xref: 'x',yref: 'y',xanchor:"center", ayref:'y',ay:0 }, { x: 1940, y: 570, text: '55-years', font:{color:'hsv(6,100,100)'}, showarrow:false,xref: 'x',yref: 'y',xanchor:"center", ayref:'y',ay:0 }], xaxis: { showgrid: false, zeroline: false, showticks: false, ticks:'', }, yaxis: { title: 'Annual Rainfall (mm)', zeroline: false, showline: false, separatethousands:true, range:[410,620] } }; const div=DOM.element('div') plt.newPlot(div, data, layout,{staticPlot: true}); return html`

${div}

Fig 3. Total annual rainfall reconstructed from tree ring measurements in northern Zimbabwe. 20 year moving average overlaid. From: Therrell et. al. (2006).

` }34:T43b,html` Long-period cycles are also be apparent when looking at other data related to continental scale climate. Fig 3. shows 180 years of total annual rainfall data reconstructed from tree-ring measurements collected from trees in northern Zimbabwe.

Whilst this tree-ring data appears to show long-period cycles with relatively wetter and drier periods, again, considerable care needs to be taken in identifying or extrapolating this trend to determine future flow and therefore power station generation:

The cycle periods are very long compared to the dataset length and very long period averaging windows have been used.
The cycle periods are variable and not predictable.
The cyclic trend is very weak compared to the year to year variation and there is a risk the observed cycles are an artefact of random variation.
The underling measurement is tree-ring width in Zimbabwe and correlation of this to rainfall in norther Zambia and Angola and then river flow is not straightforward.

`35:T491,html` When considering Climate Change or Climate Variability or their possible combined impact on the future operation and production of the power station we can either:

estimate the base case of the impacts to ensure that the project design has been optimised to the most probable expected future scenario, or;
model the worst case of these effects and undertake a stress test, to investigate whether the economics of the design are resilient to worst possible future scenario.

The simplest base case for future river flows is that they will be statistically identical to the recorded historic flows.

For Climate Variability, there may not be sufficient historic data or the historic data may show that this characteristic is of such a fundamentally unpredictable nature that the simple base case of the continuation of the long-term average is the most appropriate prediction.

In the case of Climate Change, both the worst case and base case can be estimated by using predictions for the catchment-scale impacts of climate change made using global models. `36:T48d,html` These published research papers operate in broadly similar ways:

Take the predicted changes in temperature due to climate change from global models
Model changes in rainfall over the basin due to changes in temperature
Use rainfall and temperature as inputs to Rainfall-Runoff-Routing models to forecast river flow

The climate stress test completed by MML has shown that under the worst case of climate change impact identified (WC2), annual flow in the river would reduce by 36% by 2070. These gradual flow reductions would lead to a reduction in mean energy production of 11% compared to the baseline during the debt financing period (2025+18 years).

The reduction in energy is not proportional to the reduciton in average flow because:

A characteristic of the project site is that lower flows lead to higher generation head so the impact of reduced flows is minimised.
Energy production is not directly proportional to mean annual flow as it depends on the shape of the hydrograph as well as its scale.

`37:T692,html`

Base Case Modelling

Although the Worst Case Climate change stress test modelling has shown that the project is resilient to the worst case of climate change impact it is likely that a further analysis of the most probable impact, (the Base Case), of Climate Change will be necessary:

Hydropower project financiers are likely to require more detailed forecasts of Climate Change Impact.
The Project is located at the centre of Southern Africa where surrounding regions have been identified as susceptible to different impacts from Climate Change.
Further analysis of Climate Change impact may be required by the Project's environmental regulator.

The next phase of modelling which is now proposed to further investigate the probable Climate Change impact is a Basic Water Balance Regression model.

This catchment-scale model is simpler than a full Rainfall-Runoff-Routing model and works by establishing the historic relationships between rainfall in the catchment and runoff (flow) at the project site. Once these relationships have been identified then future forecast rainfall from global models can be used as an input to forecast future river flow.

Unlike Rainfall-Runoff-Routing models or similar approaches, there is no need to attempt to model complex temperature-rainfall-runoff-evapotranspiration relationships within the basin - which is treated as a 'black-box'.

Should it become necessary to undertake further, more complex, modelling for Climate Change impact then the work undertaken for the Basic Water Balance Regression will be reused. `38:Taa9,{ function getCol(year){ if(year<=2016-next_period.next_period) {return colr(1,0.4)} if(year>2016-next_period.next_period && year<=2016-next_period.next_period+8) {return colr(1,0.3)} if(year>2016-next_period.next_period+8 && year<=2016-next_period.next_period+8+18) {return 'rgba(250,100,100,0.6)'} if(year<=2016) {return colr(1,0.3)} if(year<2025) {return 'rgba(70,150,70,0.4)'} if(year<2043) {return 'rgba(70,150,70,0.8)'} return 'rgba(70,150,70,0.4)' } let combined_y=flow_yearly.map(y=>Math.round(y.Flow_mean)).concat(flow_yearly.map(y=>Math.round(y.Flow_mean)).slice(-next_period.next_period)) let combined_x=flow_yearly.map(y=>y.WaterYear).concat(flow_yearly.map(y=>next_period.next_period+y.WaterYear).slice(-next_period.next_period)) let ppa_period=[] combined_x.map((x,i)=>{if (x>=2025 && x<=2050) {ppa_period.push(combined_y[i])}}) let ppa_mean=d3.mean(ppa_period) let debt_period=[] combined_x.map((x,i)=>{if (x>=2025 && x<=2042) {debt_period.push(combined_y[i])}}) let debt_mean=d3.mean(debt_period) var data = [ { y: movingAverage(combined_y,10,true), x: combined_x, mode: 'lines', hoverinfo:'none', name:'10 Year Moving Average', line: {shape: 'spline', color: colr(5), width:1.5}, type: 'scatter' }, { x:[2025,2042], y:[debt_mean,debt_mean], mode:'lines', hoverinfo:'none', text:['',d3.format(',.0f')(debt_mean)+' m\u00b3/s'], textposition:'top-left', textfont:{color:'black'}, line:{color:'rgba(0,0,0,0.9)', width:4} }, { y: combined_y, x: combined_x, marker: {color: combined_x.map(x=>getCol(x))}, showlegend:false, hoverinfo:'x+y', type: 'bar' }, { x: [1924,2055], y: [1100,1100], mode: 'lines', hoverinfo:'none', name: 'Overall Average', line: {width:1.5,color: 'rgba(0,0,0,0.7)',dash: 'dot'}, type: 'scatter' }]; var layout = { width: width, height:200, font: font, margin: { l: 90, r: 140,b: 5, t: 0 }, showlegend: false, annotations: [{ x: 2043, y: debt_mean, text: 'Debt Period
Average ' + d3.format(",.0f")(debt_mean) + ' m\u00b3/s', showarrow: true,xref: 'x',yref: 'y',xanchor:"center", ayref:'y',axref:'x',ay:1500, ax:2055 }], xaxis: { visible:false, range:[1924,2055] }, yaxis: { title: 'Mean Flow', range:[200,2200], zeroline: false, showline: false, separatethousands:true } }; const div=DOM.element('div') plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div}

` }39:Tdba,{ function getCol(year){ if(year<=2016-next_period.next_period) {return colr(1,0.4)} if(year>2016-next_period.next_period && year<=2016-next_period.next_period+8) {return colr(1,0.3)} if(year>2016-next_period.next_period+8 && year<=2016-next_period.next_period+8+18) {return 'rgba(250,100,100,0.6)'} if(year<=2016) {return colr(1,0.3)} if(year<2025) {return 'rgba(70,150,70,0.4)'} if(year<2043) {return 'rgba(70,150,70,0.8)'} return 'rgba(70,150,70,0.4)' } let combined_y= yearly.map(y=>Math.round(y.Energy/1000)) .concat(yearly.map(y=>Math.round(y.Energy/1000)).slice(-next_period.next_period)) let combined_x= yearly.map(y=>y.WaterYear).concat(yearly.map(y=>next_period.next_period+y.WaterYear).slice(-next_period.next_period)) let ppa_period=[] combined_x.map((x,i)=>{if (x>=2025 && x<=2050) {ppa_period.push(combined_y[i])}}) let ppa_mean=d3.mean(ppa_period) let debt_period=[] combined_x.map((x,i)=>{if (x>=2025 && x<=2042) {debt_period.push(combined_y[i])}}) let debt_mean=d3.mean(debt_period) var data = [ { y: movingAverage(combined_y,10,true), x: combined_x, mode: 'lines', hoverinfo:'none', name:'10 Year Moving Average', line: {shape: 'spline', color: colr(5), width:1.5}, type: 'scatter' }, { x:[2025,2042], y:[debt_mean,debt_mean], mode:'lines', hoverinfo:'none', line:{color:'rgba(0,0,0,1)', width:4} }, { y: combined_y, x: combined_x, marker: {color: combined_x.map(x=>getCol(x))}, showlegend:false, hoverinfo:'x+y', type: 'bar' }, { x: [1924,2055], y: [d3.mean(yearly.map(y=>y.Energy/1000)),d3.mean(yearly.map(y=>y.Energy/1000))], mode: 'lines', hoverinfo:'none', name: 'Overall Average', line: {width:1.5,color: 'rgba(0,0,0,0.7)',dash: 'dot'}, type: 'scatter' }]; var layout = { width: width, height:200, font: font, margin: { l: 90, r: 140,b: 30, t: 0 }, showlegend: false, annotations: [{ x: 2043, y: debt_mean, text: 'Debt Period
Average ' + d3.format(",.0f")(debt_mean) + ' GWh', showarrow: true,xref: 'x',yref: 'y',xanchor:"center", ayref:'y',axref:'x',ay:1050, ax:2055 }], xaxis: { showgrid: false, zeroline: false, showticks: false,ticks:'',range:[1924,2055] }, yaxis: { title: 'Annual Energy', range:[450,1120],zeroline: false,showline: false, separatethousands:true } }; const div=DOM.element('div') plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div}

Fig 5. Mean flow (top) and total energy production (bottom) by year between 1924 and 2016 simulating power station operation over the complete historic flow record with a 10 year moving average. The result of the Sampling method with a 'cycle period' chosen by the slider above the figure (default 55 years) is shown in green from 2017 to 2055. The 18 year period of the debt financing is highlighted in dark green and the mean over this period by a black line. The historic period 'sampled' for the debt period is highlighted in red. The mean for the whole of the historic period is shown as a dashed line. Note that on the default 55 year 'cycle period' the average mean annual flow is below the long term average but the average annual energy is above the long term average showing the difficulty in using mean annual flow as a predictor for energy.

` }3a:T68b,html ` A drawback of the Sampling method is that it does not take account of the current position in the cycle. For example the 20 yr moving average of mean annual flow appears to be currently (2017) close to or at a maximum. However, a sample with a start date which is more or less than 55 years ago (the apparent period of the last cycle), will begin at a different point in the cycle - e.g. on a down-leg, at the trough etc. This problem is compounded by the difficulty in knowing whether the current cycle has already reached a maximum or is already on the downward leg.

A further problem with the Sampling method is that it assumes that not only will the Climate Variability cycle repeat but that the pattern of high and low flow within that cycle will also repeat. This means that the resulting average flow and energy production over the forecast period will be influenced by annual variation and any unusual years as much as by the cycle trend.

Figure 6 shows the average energy production over the 18 year debt payback period for samples (cycle periods) back 80 years in the historic flow data. It is only the samples taken from recent periods (debt period starting after 1977) which produce on average less than the long term average energy of 832 GWh. Using Figure 5 it can be seem that this is because it is only years which sample both 1994 and 1995 - which model extreamly low energy output - which produce less than the long term average energy.

Because the long term average modelled energy of 832 GWh includes the very low production years of 1994 and 1995 it can be considered a conservative estimate for future production. `3b:T7f2,{ var data = [ { x: sims_summary.map(sim=>sim.EquivalentPeriod), y: sims_summary.map(sim=>Math.round(sim.DebtAvEnergy)), text: sims_summary.map(sim=>sim.StartYear-8), hovrinfo:'x+y+text', mode: 'lines', name:'Debt Period Mean', line: {shape: 'spline', color: colr(1), width:1.5}, type: 'scatter' }, { y:[d3.mean(yearly.map(yr=>yr.Energy/1000)),d3.mean(yearly.map(yr=>yr.Energy/1000))], x:[80,30], mode:'lines+text', text:[d3.format('.0f')(d3.mean(yearly.map(yr=>yr.Energy/1000))) + ' GWh',''], textposition:'top-right', line:{color:'rgba(0,0,0,0.7)', dash:'dashdot', width:1.5} } ]; var layout = { width:width, height: 290, font: font, showlegend: false, title:plotTitle('Average Energy Production over Debt Period'), margin: { l: 90, r: 120,b: 70, t: 30 }, legend: {x: 1,xanchor: 'right',y: 1}, annotations: [ { x: 55, y: 900, text: '55yr Cycle.', showarrow: true,arrowhead: 2,ax: 0,ay: 940,ax: 55,xref: 'x',yref: 'y',axref:'x',ayref:'y' }, { x: 40, y: 770, text: '40yr Cycle.', showarrow: true,arrowhead: 2,ax: 0,ay: 850,ax: 40,xref: 'x',yref: 'y',axref:'x',ayref:'y' } ], xaxis: { showgrid: false, zeroline: false, ticks:'outside', range:[80,30], title:'Next Cycle Period (years)' }, yaxis: { title: 'Energy (GWh)', zeroline: false, showline: false, separatethousands:true, range:[700,1000] } }; const div=DOM.element('div') plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div}

Fig 6. The resulting mean of energy production over the 18 year debt period for the Sampling method for all 'cycle periods'. The 55 year period is highlighted as this was the period of the last cycle. The 40 year period is highlighted as the worst case.

` }3c:T893,{ var data = [ { x: simul_select.map(c=>c.Year), y: simul_select.map(c=>c.Cyclic), mode: 'lines', hoverinfo:'skip', name: 'Cyclic Component', line: {width:1.5,color: 'rgba(250,0,0,0.7)',dash: 'dot'}, type: 'scatter' }, { x: [2025,2042,2042,2025], y: [300,300,1700,1700], fill: 'toself', mode:'none', hoverinfo:'skip', fillcolor: 'rgba(150,150,150,0.3)', showlegend:false, type: 'scatter' }, { y: movingAverage(flow_yearly.map(y=>y.Flow_mean),20,true), x: flow_yearly.map(y=>y.WaterYear), mode: 'lines', hoverinfo:'skip', name: '20 year Moving Average', line: {width:1.5,color: 'rgba(0,0,0,0.7)'}, type: 'scatter' }, { x: [1924,2050], y: [1100,1100], mode: 'lines', hoverinfo:'skip', name: 'Overall Mean', line: {width:1.5,color: 'rgba(0,0,0,0.7)',dash: 'dot'}, type: 'scatter' }, { y: flow_yearly.map(y=>Math.round(y.Flow_mean)), x: flow_yearly.map(y=>y.WaterYear), marker: {color: colr(1,0.3)}, showlegend:false, hoverinfo:'x+y', type: 'bar' }]; var layout = { width: width, height:230, font: font, margin: { l: 90, r: 140,b: 0, t: 0 }, showlegend: true, legend:{ orientation: "h" }, annotations: [{ x: 2033, y: 500, text: 'Debt Period', showarrow:false,xref: 'x',yref: 'y',xanchor:"center", ayref:'y',ay:0 }], xaxis: { position:0.9, anchor:'free', showgrid: false, zeroline: false, showticks: false, ticks:'', range:[1930,2055] }, yaxis: { title: 'Mean Flow', range:[250,2200], zeroline: false, showline: false, separatethousands:true, } }; const div=DOM.element('div') plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div}

Fig 7. A Cycle Parameters simulation with a sinusoidal mean with a period of ${cyclic_params.period} years and amplitude ${cyclic_params.amplitude} m\u00b3/s forecast for future periods. The phase is set by observation of the crossing point of the 20 year moving average in 2003.

` }3d:T5ab,viewof controls = { const form = html``; form.oninput = () => { form.querySelector("[id=cv_period_disp]").textContent = form.cv_period.valueAsNumber; form.querySelector("[id=cc_rate_disp]").textContent = form.cc_rate.valueAsNumber; form.value = { cv_period: form.cv_period.valueAsNumber, cc_rate: form.cc_rate.valueAsNumber, cc_switch: form.cc_switch.checked, cv_switch: form.cv_switch.checked }; }; form.oninput(); return form; }3e:Tbde,{ var data = [ { x:[2028,2043], y:[debt_av,debt_av], mode:'lines', hoverinfo:'skip', line: {width:4.5,color: 'rgba(150,150,150,1)'}, showlegend:false, type: 'scatter' }, { x:[2028,2053], y:[ppa_av,ppa_av], mode:'lines', hoverinfo:'skip', line: {width:4.5,color: 'rgba(150,150,150,1)'}, showlegend:false, type: 'scatter' }, { x: [1924,2060], y: [1100,1100], hoverinfo:'skip', mode: 'lines', name: 'Overall Historic Average', line: {width:1.5,color: 'rgba(0,0,0,0.7)',dash: 'dot'}, type: 'scatter' }, { x: simul_select.map(ex=>ex.Year), y: simul_select.map(ex=>Math.round(ex.Climate_Change)), mode: 'lines', name: 'Climate Change Impact', line: {width:2,color: 'rgba(0,100,0,0.7)',dash: 'dot'}, type: 'scatter' }, { x: simul_select.map(c=>c.Year), y: simul_select.map(c=>Math.round(c.Cyclic)), mode: 'lines', name: 'Cyclic Component', line: {width:1.5,color: 'rgba(250,0,0,0.7)',dash: 'dot'}, type: 'scatter' }, { x: flow_yearly.map(y=>y.WaterYear), y: movingAverage(flow_yearly.map(y=>y.Flow_mean),20,true), mode: 'lines', hoverinfo:'skip', name: '20y Moving Average', line: {width:3,color: 'rgba(0,0,0,0.8)'}, type: 'scatter' }, { x: simul_select.map(ex=>ex.Year), y: simul_select.map(ex=>Math.round(ex.Mean_Resulting)), mode: 'lines', name: 'Simulated Forward Mean', line: {width:3,color: 'rgba(0,0,0,0.8)', dash: 'dashdot'}, type: 'scatter' }, { y: flow_yearly.map(y=>Math.round(y.Flow_mean)), x: flow_yearly.map(y=>y.WaterYear), marker: {size:10,color: colr(1,0.3)}, name: 'Historic Actual', type: 'bar' }, ]; var layout = { width: width, height:400, font: font, margin: { l: 90, r: 90,b: 50, t: 30 }, showlegend: true, legend:{ orientation: "h" }, annotations: [{ x: 2028, y: debt_av, text: 'Debt Period Average ' + d3.format(",.0f")(debt_av) + 'm\u00b3/s P' + d3.format('.0f')(debt_exceed), showarrow: true,xref: 'x',yref: 'y',xanchor:"center", ayref:'y',ay:1600 }, { x: 2028, y: ppa_av, text: 'PPA Period Average ' + d3.format(",.0f")(ppa_av) + 'm\u00b3/s P' + d3.format('.0f')(ppa_exceed), showarrow: true,xref: 'x',yref: 'y',xanchor:"center", ayref:'y',ay:500 }], xaxis: { showgrid: false, zeroline: false, ticks:'outside', range:[1930,2055] }, yaxis: { title: 'Mean Annual Flow', range:[250,2200], zeroline: false, showline: false, separatethousands:true, } }; const div=DOM.element('div') plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div}

Fig 8. Simple combined model for Climate Change and Climate Variabilty.

` }3f:Tce0,function compare_years(year1, year2) { var data = [ { y: monthly .filter(mn => mn.WaterYear == year1) .map(mn => mn.Energy / 1000), x: monthly .filter(mn => mn.WaterYear == year1) .map(mn => mn.WaterMonth * 30), marker: { color: colr(1,0.5) }, yaxis: 'y2', showlegend: false, name: '', type: 'bar' }, { y: monthly .filter(mn => mn.WaterYear == year2) .map(mn => mn.Energy / 1000), x: monthly .filter(mn => mn.WaterYear == year2) .map(mn => mn.WaterMonth * 30), marker: { color: colr(5,0.5) }, yaxis: 'y2', showlegend: false, name: '', type: 'bar' }, { x: weekly.filter(yr => yr.WaterYear == year1).map(mn => mn.WaterWeek * 7), y: weekly.filter(yr => yr.WaterYear == year1).map(mn => mn.Flow), mode: 'lines', name: year1, type: 'scatter', line: { shape: 'spline', color: colr(1), width: 2 } }, { x: weekly.filter(yr => yr.WaterYear == year2).map(mn => mn.WaterWeek * 7), y: weekly.filter(yr => yr.WaterYear == year2).map(mn => mn.Flow), mode: 'lines', name: year2, type: 'scatter', line: { shape: 'spline', color: colr(5), width: 2 } } ]; var layout = { height: 300, margin: { l: 70, r: 70, b: 50, t: 50 }, legend: { x: 0, xanchor: 'left', y: 1 }, title: { text: year1 + ' and ' + year2 + ' Flow and Energy',font: { size: 18 }}, font: font, xaxis: { showgrid: false, zeroline: false, ticks: 'outside', tickvals: [30.00,60.00,91.00,122.00,150.00,181.00,211.00,242.00,272.00,303.00,334.00,364.00], ticktext: ['Oct','Nov','Dec','Jan','Feb','Mar','Apr','May','Jun','Jul','Aug','Sep'] }, yaxis: { title: 'Flow (m\u00B3/s)', zeroline: false,showline: false, tickformat: ',.2r' }, yaxis2: { showgrid: false,zeroline: false,showline: false, title: 'Energy GWh',separatethousands: true, tickformat: ',.0f',overlaying: 'y',side: 'right', range: [0, 300] } }; const div = DOM.element('div'); plt.newPlot(div, data, layout, { staticPlot: true }); return html`

${div}

	${year1}	${year2}
Mean Flow	${format_flow( flow_yearly.filter(y => y.WaterYear == year1)[0].Flow_mean )}	${format_flow( flow_yearly.filter(y => y.WaterYear == year2)[0].Flow_mean )}
Energy	${format_energy( yearly.filter(y => y.WaterYear == year1)[0].Energy / 1000 )}	${format_energy( yearly.filter(y => y.WaterYear == year2)[0].Energy / 1000 )}

` }40:[{"id":"aa1d8fa7dfbe21dff693ea356dfbc71e189af5829f5a145fb6f402a7dc832dfd67ce05fe97def939df011e20381b50667f7047a9cda60563c17785e4ab7d24ee","href":"https://static.observableusercontent.com/files/aa1d8fa7dfbe21dff693ea356dfbc71e189af5829f5a145fb6f402a7dc832dfd67ce05fe97def939df011e20381b50667f7047a9cda60563c17785e4ab7d24ee","name":"africa_rivers.jpg","type":"image/jpeg","lastModified":1582361326282.027,"size":49003},{"id":"11629613e22c76f4d49dfd1aea99dce29e6292a819c4fb2b51343d649a36f358511bd3d9501ae48f2b9b4c1ba73aa160f4aeff37e2a1fddcabb0494bae45372a","href":"https://static.observableusercontent.com/files/11629613e22c76f4d49dfd1aea99dce29e6292a819c4fb2b51343d649a36f358511bd3d9501ae48f2b9b4c1ba73aa160f4aeff37e2a1fddcabb0494bae45372a","name":"resiliance.png","type":"image/png","lastModified":1582364115131.637,"size":19681}] 2f:{"title":"","cells":[{"id":467,"value":"html`\n\nClimate Change and natural long-term Climate Variability are two processes which may impact on river flows and therefore energy generation over the life of the project. \n

\nAn analysis of the possible worst case impact of these effects is needed to ensure the long-term viability of the project. Analysis of the probable base case impact of these effects is necessary to ensure the project is optimised to the most likely future scenarios.\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":424,"value":"html`\n

Climate Change

\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":4,"value":"html`\n\nClimate Change refers to changes in global climate, including changes caused by human processes, which will impact the flow of water in the river over the coming decades. \n

\nClimate Change may cause changes in the average flow in the river, the level of drought and flood flows as well as changes in the timing of flood and drought periods.\n

\nThe effects of Climate Change mean that a basic assumption, that the future pattern of flow in the river will be approximately the same as the past pattern of flow, may not hold true. \n

\nThe effects of Climate Change are generally considered to start from 1990. Figure 1. shows a very simple model of the possible effect of climate change by linearly depressing the mean annual river flow starting from 1990.\n\n\n`\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":440,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":475,"value":"html`\nIn reality, the effects on river flow of Climate Change will be far more complex than simply decreasing the annual mean flow and may change both the shape of the annual hydrograph - the timing of the onset of the flood and drought periods - as well as impacting maximum and minimum flows.\n

\nThe impact on energy generation will be even more complex than the impact on flow as annual energy production is a product of the shape of the hydrograph and is poorly correlated with mean flow or any other simple measure of annual river flow.\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":464,"value":"md`\n## Climate Variability\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":222,"value":"html`\n\nClimate Variability refers to cyclical patterns of change in the global or continental-scale climate causing cyclical changes in the flow of water in the river over multi-decadal periods of time. As with Climate Change, these cycles may impact the average, maximum and minimum annual flow as well as the timing of changes in flow.\n

\n\nClimate Variability may lead to periods lasting tens of years of flows that are higher or lower than the overall average. However, the duration of these periods is not fixed and it is impossible to know how long any particular period will last in advance. \n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":493,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":506,"value":"html`\nA possible cyclic Climate Variability trend can be seen when applying a long period moving average to the historic record of mean annual flows (Fig 2). \n

\nHowever, significant care must be taken in identifying or extrapolating this trend as the apparent period of this cycle (55 years) is very long compared to the length of the historic record and it is possible that a full cycle is not actually captured in the record. The trend is also only apparent when very long moving average windows are used.\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":531,"value":"$33","pinned":false,"hidden":false,"mode":"ojs"},{"id":576,"value":"$34","pinned":false,"hidden":false,"mode":"ojs"},{"id":604,"value":"md`\nFig 4. shows that long period cyclic trends have also been identified in many other rivers across Africa.\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":594,"value":"html`\n

Fig 4. Variation in flow for 9 major African rivers between 1945 and 2000.

\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":502,"value":"html`\nThe fact that these Climate Variability cycles are observed across a range of climate parameters and a large number of African rivers shows that these effects are common to all major African river systems and not unique to the Zambezi or the catchment above the proposed power station. Rather these variations are an entirely usual feature of hydropower stations on rivers of this size.\n

\nBecause of the varying cycle periods and amplitudes and the lack of long series of observation data, there is little value in attempting to forecast future Climate Variability cycles. \n

\nAlthough we do not understand the underlying causes of the observed Climate Variability cycles we must assume that these will be modified by Climate Change and that the two effects are linked. Changes in global and continental climate driven by Climate Change will very likely effect and disrupt the systems which are producing the observed Climate Variability.\n\n\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":431,"value":"md`\n## Base Case & Worst Case\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":188,"value":"$35","pinned":false,"hidden":false,"mode":"ojs"},{"id":623,"value":"md`\n## Modelling Climate Change Impact\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":627,"value":"md`\n

\nAssessment of the possible Climate Change impacts on the project have been informed by the *International Hydropower Association's* **Climate Resilience Guide** which has been produced by the IHA with the *World Bank* and *EBRD*.\n\nThese guidelines recommend a phased approach of increasingly detailed modelling and analysis and ongoing monitoring and evaluation.\n

\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":632,"value":"md`\n

\n `","pinned":false,"hidden":false,"mode":"ojs"},{"id":1505,"value":"html`\n\n

Worst Case Modelling

\n\nTo date, the Project's engineers, Mott MacDonald (MML), have completed a Climate change stress test which has involved determining a set of worst case scenarios for climate change impact on river flow and modelling the resultant changes in the power station energy production over the project life.\n

\nTo select the worst case scenarios, MML conducted a review of recently published research for modelled climate change impacts on the Zambezi basin. Two scenarios were selected (labelled WC1 and WC2) which were based on the latest global projections for climate change impact and which predicted the greatest reductions in river flow due to climate change.\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":643,"value":"$36","pinned":false,"hidden":false,"mode":"ojs"},{"id":668,"value":"$37","pinned":false,"hidden":false,"mode":"ojs"},{"id":713,"value":"html`\n

Modelling Climate Variability

\n\nThe possible impact of Climate Variability, in particular cycles of above and below average flow, can be investigated in two ways:\n

Sampling the historic record of annual flows and using these samples as simulations for possible future flow.
Producing simulations of future patterns of flow using Cycle Parameters including the cycle period and amplitude.

\n\nNeither of these methods are capable of producing a meaningful Base Case forecast for the future impact of Climate Variability cycles because, as described above, there is neither sufficient historic data nor sufficient understanding of the underlying processes at work. These methods can, however, both produce Worst Case forecasts by simply selecting the sample or cycle parameters which produce the worst river flow result - in the context of power station financing and operation.\n\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":757,"value":"html`\n

Sampling

\n\nThe Sampling method works by taking samples of 18 years (for debt period) or 25 years (for PPA period) of consecutive years from the historic flow record and passing these through the power station Power and Energy (P&E) model. \n

\nSelecting a sample which begins 55 years ago (plus an adjustment for construction period) is equivalent to assuming the next Climate Variability cycle will have a period length of 55 years - ie equal to the apparent length of the previous cycle. \n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1515,"value":"html`\nFigure 5 , graphically, the operation of the Sampling method where flow and modelled energy production from an historic period - in red - is assumed to reoccur during the operation of the power station - debt repayment period in dark green. \n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1154,"value":"viewof next_period = {\n const form = html``;\n form.oninput = () => {\n form.querySelector(\"[id=next_period_disp]\").textContent =\n form.next_period.valueAsNumber;\n form.value = {\n next_period: form.next_period.valueAsNumber\n };\n };\n form.oninput();\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1033,"value":"$38","pinned":false,"hidden":false,"mode":"ojs"},{"id":1263,"value":"$39","pinned":false,"hidden":false,"mode":"ojs"},{"id":1525,"value":"$3a","pinned":false,"hidden":false,"mode":"ojs"},{"id":674,"value":"$3b","pinned":false,"hidden":false,"mode":"ojs"},{"id":777,"value":"html`\nThe Sampling method has the benefit of producing absolute figures for energy generation over the forecast period as it is operating on 'real' years which have been passed through the Power & Energy model. The Cycle Parameters method only looks at cycles in mean annual river flow (or some other hydrological variable) and these cannot be converted to energy figures directly. The proxy of 'representative years' can be used to produce energy generation from the Cycle Parameters method but there is poor correlation between mean annual flow and energy generation.\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":785,"value":"html`\n

Cycle Parameters

\n\nModelling possible worst case Climate Variability through Cycle Parameters relies on the observation that the Climate Variability pertubates some climate variable (in this case the mean annual flow) approximately as a sine wave.\n

\nFuture cycle periods can then be simulated by simply generating a sine curve with a fixed period, phase and amplitude. As the 20 year moving average mean annual flow is observed to cross the overall series average in 2003, this is taken as the starting point for the future forecast cycle.\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":808,"value":"$3c","pinned":false,"hidden":false,"mode":"ojs"},{"id":819,"value":"html`\n\nAs with Sampling, this method is only useful in producing a Worst Case forecast as it is impossible to predict with any certainty what the parameters of any future cycle may be or the current cycle position.\n

\nThe Cycle Parameters method has the advantage of looking purely at the impact of Climate Variability cycles of mean river flow. However, this also means that that method fails to capture any other factors that may impact energy generation including changes in the shape of the hydrograph whether these are cyclical or purely random.\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":839,"value":"html `\n

Combined Model

\nA model combining possible Climate Change and Climate Variability can be constructed by producing a forecast mean of mean annual flow which decreases due to Climate Change and also cycles due to Climate Variability. \n

\nThis model can be used to investigate possible Worst Case combinations of Climate Change and Climate Variability. Because this combined model forecasts mean annual flows it cannot take into account the poor correlation between mean annual flow and energy production or possible changes in the shape of the hydrograph. \n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":914,"value":"$3d","pinned":false,"hidden":false,"mode":"ojs"},{"id":42,"value":"$3e","pinned":false,"hidden":false,"mode":"ojs"},{"id":1643,"value":"html`\n

Mean Annual Flow and Annual Energy Correlation

\nOne of the challenges with any kind of forecast based on estimates for Climate Change or Climate Variability is that these methods make estimates for mean annual flow which is a very poor predictor for powerstation energy production. Figure 9 shows an example of two years with very different mean annual flow but almost identical modelled energy production. \n

\nBy contrast, Figure 10 shows two years with very similar mean annual flow but very different total annual energy production because of differences in the shape of their hydrographs.\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1600,"value":"html`\n

\n ${compare_years(1981,1944)}\n

Fig 9. Comparison of flow (lines) and modelled energy (bars) for 1944 and 1981. The mean flow for 1944 is nearly twice the mean flow of 1981 but the modelled energy output for the two years is almost identical. More energy would have been generated from the 'shoulder months' in 1944 particularly February and June but in April more energy would have been generated in 1981 because the very high flows in 1944 flood the gorge around the powerhouse and reduce the generation head.

\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1646,"value":"html`\n

\n ${compare_years(1960,1978)}\n

Fig 10. Comparison of flow (lines) and modelled energy (bars) for 1960 and 1978. The mean flow for the two years is almost identical but the modelled energy production is significantly higher for 1978 than for 1960. The energy production in 1960 is increased by the higher flows in all of the 'shoulder years' in the first half of the season - October to February.

\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1416,"value":"md`\n## References\n\nTherrell, M.D., M. D., Stahle, D. W., Ries, L. P. & Shugart, H. H., 2006. Tree-ring reconstructed rainfall variability in Zimbabwe. Climate Dynamics, Volume 26, pp. 677-685.\n`\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":1680,"value":"html`\n

\n

Next: 8. Upstream Impact

\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":34,"value":"html` \n

\n

Appendix

\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1005,"value":"md`\n## Simulation\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":238,"value":"cc_params = {\n return {\n switch_on: controls.cc_switch,\n pct_reduction_per_year: controls.cc_rate / 100 / 80,\n from_year: 1990\n };\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":272,"value":"cyclic_params = {\n return {\n switch_on: controls.cv_switch,\n period: controls.cv_period,\n amplitude: 700,\n start: 2003\n };\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":243,"value":"simul_select=simul.map(s=>{\n s.Cyclic=cyclic_by_year(s.Year)\n s.Climate_Change=cc_by_year(s.Year)\n s.Mean_Resulting=s.Year>=cyclic_params.start?1100+(s.Climate_Change-1100)+(s.Cyclic==undefined?0:(s.Cyclic-1100)):undefined\n return s\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":300,"value":"cyclic_by_year = function(year) {\n if (year >= cyclic_params.start) {\n if (cyclic_params.switch_on) {\n let a = cyclic_params.amplitude / 2;\n let p = year - cyclic_params.start;\n return 1100 + a * Math.sin((p / cyclic_params.period) * 2 * Math.PI);\n } else {\n return 1100;\n }\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":293,"value":"cc_by_year = function(year) {\n if (year >= cc_params.from_year && cc_params.switch_on) {\n return (\n 1100 -\n cc_params.pct_reduction_per_year * (year - cc_params.from_year) * 1100\n );\n } else {\n return 1100;\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":350,"value":"ppa_exceed=yearly_fdc.filter(f=>f.Meanf.Mean(s.Year>=2028 && s.Year<=2043)).map(s=>s.Mean_Resulting))","pinned":false,"hidden":false,"mode":"ojs"},{"id":139,"value":"ppa_av=d3.mean(simul_select.filter(s=>(s.Year>=2028 && s.Year<=2053)).map(s=>s.Mean_Resulting))","pinned":false,"hidden":false,"mode":"ojs"},{"id":1624,"value":"md`\n## Builders\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1601,"value":"$3f","pinned":false,"hidden":false,"mode":"ojs"},{"id":36,"value":"md`\n## Load Data\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1608,"value":"model_name='Base Case'","pinned":false,"hidden":false,"mode":"ojs"},{"id":1610,"value":"model=models.filter(md=>md.ModelName==model_name)[0]","pinned":false,"hidden":false,"mode":"ojs"},{"id":1606,"value":"models = (await d3.csv(\"https://gis.westernpower.org/data/input_data/2022/models.csv?\" + Math.floor(Math.random() * 1000),d3.autoType))","pinned":false,"hidden":false,"mode":"ojs"},{"id":1612,"value":"monthly = (await d3.csv(\"https://gis.westernpower.org/data/output_data/2022/\" + model.OutputPrefix + \"_pe_monthly.csv?\" + Math.floor(Math.random() * 1000), d3.autoType))","pinned":false,"hidden":false,"mode":"ojs"},{"id":1604,"value":"weekly = await d3.csv(\n \"https://gis.westernpower.org/data/output_data/2022/\" +\n model.OutputPrefix +\n \"_pe_weekly_slim.csv?\" +\n Math.floor(Math.random() * 1000),\n d3.autoType\n)","pinned":false,"hidden":false,"mode":"ojs"},{"id":527,"value":"\ntring = (await d3.csv(\"https://gis.westernpower.org/data/input_data/tree_ring_precip.csv?\" + Math.floor(Math.random() * 1000), d3.autoType))\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":678,"value":"sims_summary = (await d3.csv(\"https://gis.westernpower.org/data/output_data/base_pe_sims_summary.csv?\" + Math.floor(Math.random() * 1000), d3.autoType))","pinned":false,"hidden":false,"mode":"ojs"},{"id":25,"value":"simul = (await d3.csv(\"https://gis.westernpower.org/data/input_data/cc_cv_simulations.csv?\" + Math.floor(Math.random() * 1000), d3.autoType))","pinned":false,"hidden":false,"mode":"ojs"},{"id":344,"value":"yearly_fdc = (await d3.csv(\"https://gis.westernpower.org/data/output_data/2022/ngonye_flow_annual_exceedance.csv?\" + Math.floor(Math.random() * 1000),d3.autoType))","pinned":false,"hidden":false,"mode":"ojs"},{"id":681,"value":"yearly=(await d3.csv(\"https://gis.westernpower.org/data/output_data/2022/base_pe_yearly.csv?\" + Math.floor(Math.random() * 1000), d3.autoType))","pinned":false,"hidden":false,"mode":"ojs"},{"id":1042,"value":"flow_yearly=(await d3.csv(\"https://gis.westernpower.org/data/output_data/2022/ngonye_flow_yearly.csv?\" + Math.floor(Math.random() * 1000), d3.autoType))","pinned":false,"hidden":false,"mode":"ojs"},{"id":45,"value":"md`\n## Styling\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1621,"value":"function format_energy(energy) {\n return d3.format(',.0f')(energy) + 'GWh';\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1619,"value":"function format_flow(flow) {\n return d3.format(',.0f')(flow) + 'm\\u00b3/s';\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1654,"value":"import {book_index} from \"@andyflem/commonlibrary\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":49,"value":"import {font} from \"@andyflem/commonlibrary\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":1069,"value":"import {commonStyle} from \"@andyflem/commonlibrary\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":1067,"value":"import {plotTitle} from \"@andyflem/commonlibrary\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":1065,"value":"import {margin} from \"@andyflem/commonlibrary\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":31,"value":"md`\n## Libraries\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1059,"value":"import {colr} from \"@andyflem/commonlibrary\"","pinned":true,"hidden":false,"mode":"ojs"},{"id":508,"value":"function movingAverage(values, N, center=true) {\n let i = 0;\n let sum = 0;\n const means = new Float64Array(values.length).fill(NaN);\n for (let n = Math.min(N - 1, values.length); i < n; ++i) {\n sum += values[i];\n }\n for (let n = values.length; i < n; ++i) {\n sum += values[i];\n let pos=center?i-Math.floor(N/2):i\n means[pos] = sum / N;\n sum -= values[i - N + 1];\n }\n return means;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":27,"value":"d3 = require(\"d3@5\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":29,"value":"plt = require(\"https://cdn.plot.ly/plotly-latest.min.js\")","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W40","stdlib":"1","titling":"auto"}