Untitled

Mitigation Scenarios

load('data/windfarms_processed.mat')
load('data/energy_processed.mat');
load('data/birdAtRisk.mat')
%load('../2018/data/Density_estimationMap','g');
%load('../2018/data/Density_estimationMap','gd');

Set to zero if nan

birdAtRisk(isnan(birdAtRisk)) = 0;

Night vs Day

How much energy is produced during the day?

energy_day = nansum(energy(daynight))./nansum(energy(:))
energy_day = 0.4334
nansum(energy(daynight))
ans = 3.1147e+17

Scenario 1 : Ideal world

In addition to the energy produced during the day, more energy is produced without risking the birds:

energy_safe=nansum(energy(birdAtRisk==0))/nansum(energy(:))
energy_safe = 0.5779

We can compare then the reminding power lost by how much bird at risk reduction:

tmp = max(eps, birdAtRisk(:))./energy(:);

[tmp_s,id] = sort(tmp);

id = id(~isnan(tmp_s));

figure('position',[0 0 1200 800]); hold on; box on; grid on

% plot(tmp_s);

tmp_e = cumsum(energy(id),'omitnan')./nansum(energy(:));

plot(tmp_e,'linewidth',2)

tmp_b = cumsum(birdAtRisk(id))./nansum(birdAtRisk(:));

plot(tmp_b,'linewidth',2)

yline(energy_day,'-k','Energy produced during the day')

yline(energy_safe,'-k','Energy produced without any bird at risk')

xline(find(tmp_b>.5,1),'-k','50% of birds at risk reduced')

yline(tmp_e(find(tmp_b>.5,1)))

xline(find(tmp_b>.1,1),'-k','90% of birds at risk reduced')

yline(tmp_e(find(tmp_b>.1,1)))

xline(find(tmp_b>.01,1),'-k','99% of birds at risk reduced')

yline(tmp_e(find(tmp_b>.01,1)))

axis tight;

legend('Energy produced','Number of bird at risk','Location','northwest')

ylabel('Cumulative Sum')

xlabel('Datapoint (grid cells x time) sorted by increasing impact (birds@risk / energey produced)')

figure('position',[0 0 1300 500]); hold on; grid on;

plot((1-tmp_e),tmp_b,'k','linewidth',2);

axis tight; xlim([0 .2])

ylabel('Percentage of bird saved')

xlabel('Percentage of Energy lost')

figure; 
plot(energy(:), birdAtRisk(:),'.r')

Scenario 2: Defined migration period

Daily

[G,t_day] = findgroups(dateshift(time,'start','day','nearest'));

tmp_b = splitapply( @sum, reshape(sum(sum(birdAtRisk),2),1,[]), G);

tmp_e = energy;

tmp_e(daynight)=0;

tmp_e = splitapply( @nansum, reshape(nansum(nansum(tmp_e),2),1,[]), G);

figure;

hold on

plot(t_day,tmp_b./sum(birdAtRisk(:)))

plot(t_day,tmp_e./nansum(energy(:)))

figure; hold on;

y=cumsum(sort(tmp_b))./sum(tmp_b);

plot(y)

yline(.5)

[~,tmp]=min(abs(y-.5));

xline(tmp,'-',['50% of bird at risk in ' num2str(numel(t_day)-tmp) ' days'])

axis tight;

Per block of week

t_week = datetime('1-Jan-2018'):7:datetime('31-Dec-2018');

tmp_col = nan(4,numel(t_week)-1);

for i_t=1:numel(t_week)-1

it = time>t_week(i_t)&time<t_week(i_t+1);

tmp_b = birdAtRisk(:,:,it);

tmp_n = ~daynight(:,:,it);

tmp_e = energy(:,:,it);

tmp_col(:,i_t) = [nansum(tmp_b(:)) nansum(tmp_b(tmp_n)) nansum(tmp_e(:)) nansum(tmp_e(tmp_n))];

end

figure('position',[0 0 1300 1000]);

subplot(2,1,1); hold on;box on

bar(t_week(1:end-1),tmp_col(1,:))

bar(t_week(1:end-1),tmp_col(2,:))

ylim([0 18e6]); ylabel('Bird at Risk [nb of bird]')

yyaxis 'right'; ax = gca; ax.YAxis(2).Color = 'k'; box on

ylim([0 18e6]/sum(tmp_col(2,:))); ylabel('Bird ar Risk. ratio of total')

subplot(2,1,2); hold on; box on

bar(t_week(1:end-1),tmp_col(3,:))

bar(t_week(1:end-1),tmp_col(4,:))

ylim([0 3e16]); ylabel('Power potential [-]')

yyaxis 'right'; ax = gca; ax.YAxis(2).Color = 'k'; box on

ylim([0 3e16]/sum(tmp_col(3,:))); ylabel('Power Potential. Normalized with total Produced')

legend('Day+Night','Night');

Off certain Season

thr_date = datetime({...

'1-Mar-2018','1-May-2018','15-Aug-2018','15-Nov-2018';...

'1-Mar-2018','1-Apr-2018','1-Oct-2018','1-Nov-2018';...

});

figure('position',[0 0 1300 500]); hold on

fill([thr_date(1,1) thr_date(1,2) thr_date(1,2) thr_date(1,1)],[0 0 10^6 10^6],'y','EdgeAlpha',0,'FaceAlpha',.5)

fill([thr_date(1,3) thr_date(1,4) thr_date(1,4) thr_date(1,3)],[0 0 10^6 10^6],'y','EdgeAlpha',0,'FaceAlpha',.5)

fill([thr_date(2,1) thr_date(2,2) thr_date(2,2) thr_date(2,1)],[0 0 10^6 10^6],'g','EdgeAlpha',0,'FaceAlpha',.5)

fill([thr_date(2,3) thr_date(2,4) thr_date(2,4) thr_date(2,3)],[0 0 10^6 10^6],'g','EdgeAlpha',0,'FaceAlpha',.5)

plot(time,reshape(sum(sum(birdAtRisk),2),1,[]),'k')

box on

clear tmp_col

tmp_col(1,:) = [nansum(birdAtRisk(:)) nansum(energy(:)) nansum(energy(:).*daynight(:)) nansum(energy(:).*~daynight(:))];

for i_t=1:size(thr_date,1)

it = ~( (time>thr_date(i_t,1)&time<thr_date(i_t,2)) | (time>thr_date(i_t,3)&time<thr_date(i_t,4)) );

tmp_col(i_t+1,:) = [nansum(birdAtRisk(:,:,it),'all') nansum(energy(:,:,it),'all') nansum(energy(:,:,it).*daynight(:,:,it),'all') nansum(energy(:,:,it).*~daynight(:,:,it),'all') ];

end

t=table({'No cut','yellow','green'}',tmp_col(:,1),tmp_col(:,2),tmp_col(:,3),tmp_col(:,4),'VariableNames',{'Mitigation','Bird at risk','Energy','Energy day','Energy night'})

t = 3×5 table 

	Mitigation	Bird at risk	Energy	Energy day	Energy night
1	'No cut'	1.1408e+08	7.1863e+17	3.1147e+17	4.0716e+17
2	'yellow'	5.4235e+06	4.1937e+17	1.7443e+17	2.4495e+17
3	'green'	4.2219e+07	5.7910e+17	2.5086e+17	3.2824e+17

tperc = t;

tperc{:,2:end}=t{:,2:end}./t{1,2:end}*100

tperc = 3×5 table 

	Mitigation	Bird at risk	Energy	Energy day	Energy night
1	'No cut'	100	100	100	100
2	'yellow'	4.7540	58.3573	56.0011	60.1597
3	'green'	37.0071	80.5841	80.5412	80.6169

Running windows of 1 and 2 weeks

Per day

time_d = dateshift(time,"start",'day');
birdAtRisk_d = splitapply(@sum, squeeze(sum(birdAtRisk,[1 2])),findgroups(time_d'));
energy_d = splitapply(@sum, squeeze(sum(energy,[1 2],'omitnan')),findgroups(time_d'));

figure; hold on; box on

plot(unique(time_d),birdAtRisk_d)

yyaxis right; plot(unique(time_d),energy_d)

figure;

plot(unique(time_d),movsum(birdAtRisk_d,14)); ylabel('Bird at risk')

yyaxis right; plot(unique(time_d),movsum(energy_d,14)); ylabel('Potential energy')

Scenario 3: Map

Where are the bird at risk during the migration period?

it = ( (time>thr_date(1,1)&time<thr_date(1,2)) | (time>thr_date(1,3)&time<thr_date(1,4)) );
tmp_b = nansum(birdAtRisk(:,:,it),3);
tmp_e = energy(:,:,it);
tmp_n = ~daynight(:,:,it);
tmp_e(~tmp_n) = 0;
tmp_e = nansum(tmp_e,3);

load coastlines
dcoast = pdist2([g.lat2D(:) g.lon2D(:)],[coastlat coastlon], @lldistkm);
dcoast = reshape(min(dcoast,[],2),size(g.lat2D));

figure; hold on; box on;

plot(dcoast(:), tmp_e(:)./tmp_b(:),'.k'); lsline;

[G,dcoast_bin] = findgroups(round(dcoast(:),-1));

plot(dcoast_bin, splitapply(@nanmean,tmp_e(:)./tmp_b(:),G),'-r','linewidth',2)

xlabel('distance to coast [km]');

ylabel('Energy lost per bird saved')

ddd=0:10:500;

tmp_bdd=nan(size(ddd)); tmp_edd=nan(size(ddd));

for i_d=1:numel(ddd)

tmp_bdd(i_d)=nansum(tmp_b(dcoast>ddd(i_d)))/nansum(birdAtRisk(:));

tmp_edd(i_d)=nansum(tmp_e(dcoast>ddd(i_d)))/nansum(energy(:));

end

figure; hold on; box on

plot(ddd,tmp_bdd)

plot(ddd,tmp_edd)

xline(50)

yline(tmp_bdd((ddd==50)))

yline(tmp_edd((ddd==50)))

xlabel('Distance to coast from which WT are turned-off [km]');

ylabel('Percentage of ... ')

legend('Bird saved','Energy lost')

figure('position',[0 0 1400 700]);

ax1=subplot(size(thr_date,1),3,(i_t-1)*3+1); hold on;

h = worldmap([g.lat(1)-2 g.lat(end)+2], [g.lon(1)-2 g.lon(end)+2]);

setm(h,'frame','on','grid','off'); set(findall(h,'Tag','MLabel'),'visible','off'); set(findall(h,'Tag','PLabel'),'visible','off')

bordersm('countries','facecolor',[228 238 243]./255);

tmp = tmp_b;

tmp(tmp==0)=nan;

surfm(g.lat,g.lon,tmp)

c=colorbar('south'); title('Birds saved [birds]');

colormap(ax1,brewermap([],'OrRd'))

ax2=subplot(size(thr_date,1),3,(i_t-1)*3+2); hold on;

h = worldmap([g.lat(1)-2 g.lat(end)+2], [g.lon(1)-2 g.lon(end)+2]);

setm(h,'frame','on','grid','off'); set(findall(h,'Tag','MLabel'),'visible','off'); set(findall(h,'Tag','PLabel'),'visible','off')

bordersm('countries','facecolor',[228 238 243]./255);

tmp2 = tmp_e;

tmp2(tmp2==0)=nan;

surfm(g.lat,g.lon,tmp2/1e12)

%scatterm(tim.Latitude,tim.Longitude,'.k');

c=colorbar('south'); title('Energy lost [TJ]');

colormap(ax2,plasma)

ax3=subplot(size(thr_date,1),3,(i_t-1)*3+3); hold on;

h = worldmap([g.lat(1)-2 g.lat(end)+2], [g.lon(1)-2 g.lon(end)+2]);

setm(h,'frame','on','grid','off'); set(findall(h,'Tag','MLabel'),'visible','off'); set(findall(h,'Tag','PLabel'),'visible','off')

bordersm('countries','facecolor',[228 238 243]./255);

surfm(g.lat,g.lon,tmp2./tmp)

%scatterm(tim.Latitude,tim.Longitude,'.k');

c=colorbar('south'); title('Energy lost per Bird saved [TJ/birds]');

colormap(ax3,viridis)

Scenario 4: Wind direction

Select only during broad migration

i_t = 1;
it1 = time>thr_date(i_t,1)&time<thr_date(i_t,2);
it2 = time>thr_date(i_t,3)&time<thr_date(i_t,4);

Compute average birdflow direction (weighted by the flow)

% tmp = birdFlow(:,:,it1).*exp(1i*birdDir(:,:,it1));
% mid=nanmean(tmp(:));
% wdir_mean(1) = atan2(imag(mid),real(mid));
% tmp = birdFlow(:,:,it2).*exp(1i*birdDir(:,:,it2));
% mid=nanmean(tmp(:));
% wdir_mean(2) = atan2(imag(mid),real(mid));
% rad2deg(wdir_mean)

Instead, we simplify with,

wdir_mean = deg2rad([45 -135]);

Compute the angle difference between direction of wind and the 45/135°

d = abs(mod(wdir(:,:,it1)-wdir_mean(1)+pi, 2*pi) - pi);
diffit1 = abs(mod(wdir(:,:,it1)-wdir_mean(1)+pi, 2*pi) - pi);
diffit2 = abs(mod(wdir(:,:,it2)-wdir_mean(2)+pi, 2*pi) - pi);
diffit=cat(3,diffit1,diffit2);

Compute as a function of the threashold of angle

tmp_b = birdAtRisk(:,:,it1|it2);
tmp_e = energy(:,:,it1|it2);
tmp_n = ~daynight(:,:,it1|it2);
% only consider night time
tmp_e(~tmp_n) = 0;
dd=0:0.1:pi;
tmp_bdd=nan(size(dd)); tmp_edd=nan(size(dd));
for i_d=1:numel(dd)
    tmp_bdd(i_d) = nansum(tmp_b(diffit < dd(i_d)));
    tmp_edd(i_d) = nansum(tmp_e(diffit < dd(i_d)));
end

Illustrations

figure; hold on; box on

plot(rad2deg(dd),tmp_bdd); ylabel('Number of bird saved')

yline(tmp_bdd((dd==.8)))

yyaxis right;

plot(rad2deg(dd),tmp_edd);ylabel('Energy lost')

xline(rad2deg(.8))

yline(tmp_edd((dd==.8)))

xlabel('Wind direction difference below which WT are turned off [°]');

figure; hold on; box on

plot(rad2deg(dd),tmp_bdd./sum(tmp_b(:))); ylabel('Number of bird saved')

%yline(tmp_bdd((dd==.8)))

yyaxis right;

plot(rad2deg(dd),tmp_edd./nansum(tmp_e(:)));ylabel('Energy lost')

xline(rad2deg(.8))

%yline(tmp_edd((dd==.8)))

xlabel('Wind direction difference below which WT are turned off [°]');

Scenario: function of bird flow

Compute bird saved and energy lost for different threashold of bird flow (bird/m^2/hr)

birdf = logspace(-4,-2,100);
birdAtRisk_saved=nan(size(birdf));
energy_lost=nan(size(birdf));
for i_d=1:numel(birdf)
    id = birdFlow > birdf(i_d);
    birdAtRisk_saved(i_d) = sum(birdAtRisk(id));
    energy_lost(i_d) = sum(energy(id));
end

figure('position',[0 0 800 400]); box on; grid on

plot(birdf, birdAtRisk_saved,'linewidth',2); ylabel('bird at risk saved');

yyaxis right;

plot(birdf, energy_lost,'linewidth',2); ylabel('energy lost')

set(gca,'xscale','log')

xlabel('Threashold of bird flow [bird/m^2/hr]')