fdc: Flow Duration Curve
In hydroTSM: Time Series Management, Analysis and Interpolation for Hydrological Modelling
Description
Usage
Arguments
Value
Author(s)
References
See Also
Examples
Description
Computes and plots the Flow Duration Curve (FDC) corresponding to a given time series of streamflow discharges.
Usage
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fdc(x, ...)
## Default S3 method:
fdc(x,lQ.thr=0.7,hQ.thr=0.2, plot=TRUE, log="y",
main="Flow Duration Curve", xlab="% Time flow equalled or exceeded",
ylab="Q, [m3/s]", ylim, yat=c(0.01, 0.1, 1), xat=c(0.01, 0.025, 0.05), col="black",
pch=1, lwd=1, lty=1, cex=0.4, cex.axis=1.2, cex.lab=1.2, leg.txt=NULL, leg.cex=1,
leg.pos="topright", verbose= TRUE, thr.shw=TRUE, new=TRUE, ...)
## S3 method for class 'matrix'
fdc(x, lQ.thr=0.7, hQ.thr=0.2, plot=TRUE, log="y",
main= "Flow Duration Curve", xlab="% Time flow equalled or exceeded",
ylab="Q, [m3/s]", ylim, yat=c(0.01, 0.1, 1), xat=c(0.01, 0.025, 0.05),
col=palette("default")[1:ncol(x)], pch=1:ncol(x), lwd=rep(1, ncol(x)),
lty=1:ncol(x), cex=0.4, cex.axis=1.2, cex.lab=1.2, leg.txt=NULL,
leg.cex=1, leg.pos="topright",verbose=TRUE, thr.shw=TRUE, new=TRUE, ...)
## S3 method for class 'data.frame'
fdc(x, lQ.thr=0.7, hQ.thr=0.2, plot=TRUE, log="y",
main= "Flow Duration Curve", xlab="% Time flow equalled or exceeded",
ylab="Q, [m3/s]", ylim, yat=c(0.01, 0.1, 1), xat=c(0.01, 0.025, 0.05),
col=palette("default")[1:ncol(x)], pch=1:ncol(x), lwd=rep(1, ncol(x)),
lty=1:ncol(x), cex=0.4, cex.axis=1.2, cex.lab=1.2, leg.txt=NULL,
leg.cex=1, leg.pos="topright", verbose=TRUE, thr.shw=TRUE, new=TRUE, ...)
## S3 method for class 'zoo'
fdc(x, lQ.thr=0.7, hQ.thr=0.2, plot=TRUE, log="y",
main= "Flow Duration Curve", xlab="% Time flow equalled or exceeded",
ylab="Q, [m3/s]", ylim, yat=c(0.01, 0.1, 1), xat=c(0.01, 0.025, 0.05),
col=palette("default")[1:NCOL(x)], pch=1:NCOL(x), lwd=rep(1, NCOL(x)),
lty=1:NCOL(x), cex=0.4, cex.axis=1.2, cex.lab=1.2, leg.txt=NULL,
leg.cex=1, leg.pos="topright", verbose=TRUE, thr.shw=TRUE, new=TRUE, ...)
Arguments
x
numeric, zoo, data.frame or matrix object with the observed streamflows for which the flow duration curve have to be computed.
Measurements at several gauging stations can be stored in a data.frame of matrix object, and in that case, each column of x represent the time series measured in each gauging station, and the column names of x have to correspond to the ID of each station (starting by a letter). When x is a matrix or data.frame, the flow duration curve is computed for each column.
lQ.thr
numeric, low-flow separation threshold. If this value is different from NA, a vertical line is drawn in this value, and all the values to the right of it should be deemed as low flows. Default value is 0.7.
hQ.thr
numeric, high-flow separation threshold. If this value is different from NA, a vertical line is drawn in this value, and all the values to the left of it should br deemed as high flows. Default value is 0.2.
plot
logical. Indicates if the flow duration curve should be plotted or not. Default value is TRUE.
log
character, indicates which axis has to be plotted with a logarithmic scale. Default value is y
main
See plot. An overall title for the plot: see title.
xlab
A title for the x axis. See plot.
ylab
A title for the y axis. See plot.
ylim
The y limits of the plot. See plot.default.
yat
Only used when log="y".
numeric, with points at which tick-marks will try to be drawn in the Y axis, in addition to the defaults computed by R. See the at argument in Axis.
xat
Only used when log="x".
numeric, with points at which tick-marks will try to be drawn in the x axis, in addition to the defaults computed by R. See the at argument in Axis.
col
The colors to be used for lines and points. Multiple colors can be specified so that each point can be given its own color. If there are fewer colors than points they are recycled in the standard fashion. Lines will all be plotted in the first colour specified. See plot.default.
pch
A vector of plotting characters or symbols: see points. See plot.default.
lwd
The line width, see par. See plot.default.
lty
The line type, see par. See plot.default.
cex
See plot.default. A numerical vector giving the amount by which plotting characters and symbols should be scaled relative to the default.
This works as a multiple of par("cex"). 'NULL' and 'NA' are equivalent to '1.0'. Note that this does not affect annotation
cex.axis
magnification of axis annotation relative to 'cex'.
cex.lab
Magnification to be used for x and y labels relative to the current setting of 'cex'. See '?par'.
leg.txt
vector with the names that have to be used for each column of x.
leg.cex
numeric, indicating the character expansion factor for the legend, *relative* to current par("cex"). Default value = 1
leg.pos
keyword to be used to position the legend. One of the list ‘"bottomright", "bottom", "bottomleft", "left", "topleft", "top", "topright", "right", "center"’. This places the legend on the inside of the plot frame at the given location. See legend.
verbose
logical; if TRUE, progress messages are printed (when x is a matrix or data.frame).
thr.shw
logical, indicating if the streamflow values corresponding to the user-defined thresholds lQ.thr and hQ.thr have to be shown in the plot.
new
logical, if TRUE (default), a new plotting window is created.
...
further arguments passed to or from other methods (to the plotting functions)
Value
numeric, matrix or data.frame whose columns contains the % of time each one of the streamflow magnitudes given as input was equalled or exceeded. The resulting values have to be multiplied by 100 to get a percentage.
When plot is TRUE (default), the resulting flow duration curve is plotted in a new window.
Author(s)
Mauricio Zambrano-Bigiarini, mzb.devel@gmail
References
Vogel, R., and N. M. Fennessey (1994), Flow duration curves I: A new interpretation and confidence intervals, ASCE, Journal of Water Resources Planning and Management, 120(4).
Vogel, R., and N. Fennessey (1995), Flow duration curves II: A review of applications in water resources planning, Water Resources Bulletin, 31(6), 1029-1039, doi:10.1111/j.1752-1688.1995.tb03419.x.
Yilmaz, K. K., H. V. Gupta, and T. Wagener (2008), A process-based diagnostic approach to model evaluation: Application to the NWS distributed hydrologic model, Water Resour. Res., 44, W09417, doi:10.1029/2007WR006716.
See Also
Examples
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## Loading daily streamflows at the station Oca en Ona (Ebro River basin, Spain) ##
data(OcaEnOnaQts)
## Daily Flow Duration Curve
fdc(OcaEnOnaQts)
###################
# Getting the streamflow values corresponding to 5 and 95% of time equalled or
# exceeded (and also the first streamflow value in 'x' just for verification)
x <- OcaEnOnaQts
# First streamflow value (x1=42.1 m3/s)
x1 <- x[1]
# Daily FDC for 'x'
y <- fdc(x)
# value of the FDC for x1 (y1=0.002739726)
y1 <- y[1]
# Performing cubic (or Hermite) spline interpolation of 'x' and 'y'
f <- splinefun(y,x)
# Getting the (known) streamflow value for 'y1'
f(y1) # 42.1 m3/s, equal to the known 'x1'
# Streamflow values corresponding to 5 and 95% of time equalled or exceeded
f(c(.05, .95))
###################
## Getting
data(OcaEnOnaQts)
## Daily Flow Duration Curve
fdc(OcaEnOnaQts)
Example output
Loading required package: zoo
Attaching package: 'zoo'
The following objects are masked from 'package:base':
as.Date, as.Date.numeric
Loading required package: xts
[1] 0.002739726 0.010045662 0.004566210 0.016438356 0.030136986 0.023744292
[7] 0.040182648 0.028310502 0.055707763 0.067579909 0.055707763 0.033789954
[13] 0.093150685 0.120547945 0.120547945 0.129680365 0.137899543 0.137899543
[19] 0.102283105 0.120547945 0.129680365 0.044748858 0.096803653 0.102283105
[25] 0.113242009 0.113242009 0.113242009 0.137899543 0.113242009 0.113242009
[31] 0.124200913 0.144292237 0.151598174 0.144292237 0.165296804 0.165296804
[37] 0.173515982 0.178082192 0.194520548 0.194520548 0.151598174 0.173515982
[43] 0.216438356 0.229223744 0.236529680 0.250228311 0.263926941 0.278538813
[49] 0.291324201 0.300456621 0.305936073 0.317808219 0.317808219 0.322374429
[55] 0.326027397 0.330593607 0.326027397 0.326027397 0.335159817 0.340639269
[61] 0.340639269 0.347031963 0.355251142 0.355251142 0.355251142 0.355251142
[67] 0.368949772 0.382648402 0.382648402 0.390867580 0.400913242 0.400913242
[73] 0.410958904 0.419178082 0.428310502 0.440182648 0.455707763 0.440182648
[79] 0.355251142 0.390867580 0.410958904 0.440182648 0.455707763 0.455707763
[85] 0.465753425 0.465753425 0.465753425 0.476712329 0.482191781 0.482191781
[91] 0.497716895 0.497716895 0.497716895 0.482191781 0.476712329 0.476712329
[97] 0.482191781 0.482191781 0.465753425 0.465753425 0.410958904 0.428310502
[103] 0.440182648 0.455707763 0.455707763 0.465753425 0.419178082 0.440182648
[109] 0.455707763 0.455707763 0.440182648 0.455707763 0.455707763 0.440182648
[115] 0.455707763 0.428310502 0.476712329 0.497716895 0.497716895 0.428310502
[121] 0.520547945 0.540639269 0.551598174 0.560730594 0.560730594 0.560730594
[127] 0.587214612 0.607305936 0.607305936 0.631050228 0.643835616 0.618264840
[133] 0.618264840 0.643835616 0.643835616 0.670319635 0.643835616 0.618264840
[139] 0.670319635 0.670319635 0.670319635 0.686757991 0.670319635 0.578082192
[145] 0.428310502 0.212785388 0.257534247 0.489497717 0.497716895 0.540639269
[151] 0.520547945 0.528767123 0.551598174 0.578082192 0.587214612 0.596347032
[157] 0.607305936 0.607305936 0.631050228 0.631050228 0.643835616 0.670319635
[163] 0.670319635 0.643835616 0.643835616 0.670319635 0.670319635 0.670319635
[169] 0.643835616 0.607305936 0.618264840 0.618264840 0.540639269 0.607305936
[175] 0.670319635 0.596347032 0.368949772 0.440182648 0.250228311 0.607305936
[181] 0.693150685 0.737899543 0.737899543 0.326027397 0.631050228 0.670319635
[187] 0.686757991 0.693150685 0.746118721 0.798173516 0.798173516 0.870319635
[193] 0.870319635 0.921461187 0.958904110 0.958904110 0.958904110 0.958904110
[199] 0.958904110 0.870319635 0.921461187 0.921461187 0.870319635 0.921461187
[205] 0.921461187 0.968036530 0.958904110 0.870319635 0.921461187 0.827397260
[211] 0.921461187 0.194520548 0.643835616 0.774429224 0.827397260 0.870319635
[217] 0.870319635 0.958904110 0.958904110 0.974429224 0.968036530 0.968036530
[223] 0.968036530 0.968036530 0.921461187 0.968036530 0.958904110 0.968036530
[229] 0.974429224 0.978995434 0.984474886 0.984474886 0.991780822 0.984474886
[235] 0.978995434 0.978995434 0.974429224 0.974429224 0.991780822 0.991780822
[241] 0.998173516 0.991780822 0.991780822 0.998173516 0.998173516 0.998173516
[247] 0.587214612 0.798173516 0.827397260 0.870319635 0.984474886 0.991780822
[253] 0.984474886 0.991780822 0.991780822 0.998173516 0.998173516 0.998173516
[259] 1.000000000 1.000000000 0.984474886 0.774429224 0.746118721 0.968036530
[265] 0.968036530 0.974429224 0.974429224 0.978995434 0.978995434 0.921461187
[271] 0.631050228 0.618264840 0.921461187 0.958904110 0.921461187 0.827397260
[277] 0.921461187 0.921461187 0.921461187 0.504109589 0.476712329 0.921461187
[283] 0.958904110 0.968036530 0.974429224 0.958904110 0.958904110 0.551598174
[289] 0.400913242 0.643835616 0.705022831 0.178082192 0.551598174 0.686757991
[295] 0.798173516 0.774429224 0.774429224 0.798173516 0.827397260 0.827397260
[301] 0.827397260 0.870319635 0.737899543 0.774429224 0.746118721 0.798173516
[307] 0.827397260 0.827397260 0.827397260 0.827397260 0.827397260 0.827397260
[313] 0.827397260 0.737899543 0.596347032 0.031963470 0.018264840 0.105936073
[319] 0.124200913 0.120547945 0.168949772 0.207305936 0.222831050 0.236529680
[325] 0.005479452 0.047488584 0.096803653 0.102283105 0.113242009 0.030136986
[331] 0.021004566 0.066666667 0.000913242 0.010045662 0.037442922 0.044748858
[337] 0.031963470 0.058447489 0.090410959 0.055707763 0.089497717 0.096803653
[343] 0.105936073 0.151598174 0.089497717 0.105936073 0.165296804 0.178082192
[349] 0.185388128 0.194520548 0.209132420 0.222831050 0.236529680 0.243835616
[355] 0.243835616 0.257534247 0.278538813 0.236529680 0.199086758 0.072146119
[361] 0.113242009 0.173515982 0.022831050 0.015525114 0.012785388 0.014611872
[367] 0.001826484 0.003652968 0.010958904 0.020091324 0.034703196 0.049315068
[373] 0.058447489 0.066666667 0.058447489 0.072146119 0.078538813 0.093150685
[379] 0.036529680 0.041095890 0.063013699 0.072146119 0.025570776 0.017351598
[385] 0.050228311 0.062100457 0.063926941 0.072146119 0.084018265 0.102283105
[391] 0.144292237 0.137899543 0.151598174 0.157990868 0.165296804 0.185388128
[397] 0.195433790 0.129680365 0.096803653 0.124200913 0.144292237 0.165296804
[403] 0.185388128 0.082191781 0.006392694 0.051141553 0.078538813 0.074885845
[409] 0.068493151 0.044748858 0.047488584 0.062100457 0.074885845 0.085844749
[415] 0.102283105 0.120547945 0.137899543 0.151598174 0.157990868 0.157990868
[421] 0.157990868 0.153424658 0.129680365 0.082191781 0.124200913 0.144292237
[427] 0.024657534 0.008219178 0.013698630 0.047488584 0.062100457 0.033789954
[433] 0.026484018 0.021917808 0.052054795 0.059360731 0.044748858 0.052968037
[439] 0.066666667 0.082191781 0.089497717 0.097716895 0.113242009 0.129680365
[445] 0.137899543 0.144292237 0.153424658 0.165296804 0.146118721 0.178082192
[451] 0.185388128 0.194520548 0.204566210 0.194520548 0.199086758 0.007305936
[457] 0.036529680 0.078538813 0.082191781 0.129680365 0.151598174 0.165296804
[463] 0.173515982 0.185388128 0.194520548 0.199086758 0.212785388 0.216438356
[469] 0.222831050 0.229223744 0.250228311 0.194520548 0.204566210 0.229223744
[475] 0.236529680 0.257534247 0.278538813 0.284018265 0.038356164 0.105936073
[481] 0.144292237 0.165296804 0.199086758 0.137899543 0.207305936 0.204566210
[487] 0.194520548 0.212785388 0.222831050 0.243835616 0.257534247 0.263926941
[493] 0.291324201 0.243835616 0.300456621 0.322374429 0.317808219 0.243835616
[499] 0.263926941 0.278538813 0.291324201 0.322374429 0.335159817 0.317808219
[505] 0.340639269 0.330593607 0.347031963 0.355251142 0.347031963 0.355251142
[511] 0.368949772 0.368949772 0.382648402 0.390867580 0.400913242 0.368949772
[517] 0.382648402 0.390867580 0.390867580 0.410958904 0.410958904 0.419178082
[523] 0.428310502 0.440182648 0.465753425 0.465753425 0.476712329 0.497716895
[529] 0.497716895 0.382648402 0.440182648 0.465753425 0.083105023 0.355251142
[535] 0.419178082 0.465753425 0.482191781 0.497716895 0.540639269 0.551598174
[541] 0.520547945 0.540639269 0.551598174 0.551598174 0.560730594 0.578082192
[547] 0.560730594 0.560730594 0.578082192 0.578082192 0.578082192 0.578082192
[553] 0.587214612 0.587214612 0.578082192 0.560730594 0.578082192 0.578082192
[559] 0.587214612 0.578082192 0.587214612 0.587214612 0.596347032 0.607305936
[565] 0.607305936 0.618264840 0.618264840 0.631050228 0.631050228 0.631050228
[571] 0.631050228 0.643835616 0.670319635 0.686757991 0.686757991 0.705022831
[577] 0.705022831 0.693150685 0.686757991 0.643835616 0.670319635 0.686757991
[583] 0.686757991 0.693150685 0.705022831 0.737899543 0.705022831 0.737899543
[589] 0.737899543 0.746118721 0.746118721 0.746118721 0.746118721 0.746118721
[595] 0.774429224 0.774429224 0.774429224 0.774429224 0.798173516 0.798173516
[601] 0.827397260 0.827397260 0.827397260 0.827397260 0.827397260 0.827397260
[607] 0.798173516 0.798173516 0.827397260 0.827397260 0.870319635 0.827397260
[613] 0.870319635 0.870319635 0.921461187 0.921461187 0.921461187 0.921461187
[619] 0.958904110 0.958904110 0.958904110 0.921461187 0.921461187 0.958904110
[625] 0.958904110 0.958904110 0.958904110 0.774429224 0.774429224 0.798173516
[631] 0.798173516 0.798173516 0.774429224 0.746118721 0.774429224 0.774429224
[637] 0.774429224 0.774429224 0.786301370 0.786301370 0.806392694 0.836529680
[643] 0.836529680 0.836529680 0.836529680 0.859360731 0.859360731 0.896803653
[649] 0.896803653 0.759817352 0.806392694 0.737899543 0.786301370 0.759817352
[655] 0.786301370 0.786301370 0.806392694 0.786301370 0.759817352 0.759817352
[661] 0.737899543 0.737899543 0.786301370 0.786301370 0.806392694 0.806392694
[667] 0.786301370 0.759817352 0.759817352 0.759817352 0.759817352 0.737899543
[673] 0.737899543 0.737899543 0.737899543 0.737899543 0.737899543 0.737899543
[679] 0.737899543 0.737899543 0.737899543 0.737899543 0.737899543 0.737899543
[685] 0.737899543 0.737899543 0.737899543 0.737899543 0.705022831 0.536073059
[691] 0.527853881 0.568036530 0.599086758 0.632876712 0.657534247 0.679452055
[697] 0.657534247 0.657534247 0.657534247 0.657534247 0.679452055 0.657534247
[703] 0.657534247 0.657534247 0.657534247 0.657534247 0.689497717 0.705022831
[709] 0.737899543 0.737899543 0.737899543 0.737899543 0.705022831 0.610958904
[715] 0.476712329 0.174429224 0.201826484 0.364383562 0.488584475 0.554337900
[721] 0.476712329 0.503196347 0.536073059 0.545205479 0.568036530 0.568036530
[727] 0.568036530 0.536073059 0.406392694 0.386301370 0.415525114 0.084931507
[733] 0.048401826 0.186301370 0.201826484 0.226484018 0.214611872 0.247488584
[739] 0.219178082 0.239269406 0.205479452 0.115981735 0.168036530 0.231963470
[745] 0.253881279 0.305022831 0.305022831 0.288584475 0.231963470 0.131506849
[751] 0.208219178 0.253881279 0.298630137 0.298630137 0.328767123 0.333333333
[757] 0.364383562 0.386301370 0.378082192 0.378082192 0.344292237 0.364383562
[763] 0.378082192 0.446575342 0.397260274 0.446575342 0.422831050 0.378082192
[769] 0.314155251 0.364383562 0.180821918 0.226484018 0.239269406 0.274885845
[775] 0.288584475 0.274885845 0.168036530 0.210045662 0.247488584 0.115981735
[781] 0.226484018 0.253881279 0.261187215 0.253881279 0.274885845 0.274885845
[787] 0.288584475 0.274885845 0.274885845 0.298630137 0.298630137 0.305022831
[793] 0.298630137 0.305022831 0.314155251 0.319634703 0.337899543 0.337899543
[799] 0.314155251 0.219178082 0.214611872 0.247488584 0.283105023 0.283105023
[805] 0.274885845 0.298630137 0.274885845 0.298630137 0.298630137 0.168036530
[811] 0.019178082 0.039269406 0.074885845 0.115981735 0.145205479 0.169863014
[817] 0.131506849 0.154337900 0.180821918 0.180821918 0.201826484 0.226484018
[823] 0.239269406 0.261187215 0.283105023 0.261187215 0.283105023 0.274885845
[829] 0.247488584 0.219178082 0.274885845 0.261187215 0.274885845 0.274885845
[835] 0.288584475 0.305022831 0.314155251 0.314155251 0.288584475 0.283105023
[841] 0.314155251 0.319634703 0.328767123 0.333333333 0.344292237 0.347945205
[847] 0.364383562 0.364383562 0.364383562 0.364383562 0.378082192 0.364383562
[853] 0.378082192 0.378082192 0.386301370 0.406392694 0.406392694 0.415525114
[859] 0.397260274 0.415525114 0.422831050 0.431050228 0.431050228 0.446575342
[865] 0.446575342 0.456621005 0.476712329 0.476712329 0.488584475 0.488584475
[871] 0.488584475 0.488584475 0.503196347 0.503196347 0.517808219 0.517808219
[877] 0.527853881 0.536073059 0.545205479 0.545205479 0.545205479 0.545205479
[883] 0.337899543 0.476712329 0.503196347 0.476712329 0.446575342 0.503196347
[889] 0.536073059 0.554337900 0.568036530 0.568036530 0.579908676 0.592694064
[895] 0.592694064 0.599086758 0.592694064 0.610958904 0.622831050 0.622831050
[901] 0.657534247 0.679452055 0.610958904 0.431050228 0.568036530 0.517808219
[907] 0.657534247 0.622831050 0.344292237 0.554337900 0.568036530 0.592694064
[913] 0.592694064 0.610958904 0.657534247 0.679452055 0.679452055 0.679452055
[919] 0.679452055 0.705022831 0.737899543 0.737899543 0.737899543 0.503196347
[925] 0.488584475 0.622831050 0.632876712 0.657534247 0.679452055 0.705022831
[931] 0.759817352 0.759817352 0.806392694 0.859360731 0.806392694 0.836529680
[937] 0.859360731 0.859360731 0.859360731 0.896803653 0.902283105 0.927853881
[943] 0.536073059 0.896803653 0.836529680 0.896803653 0.896803653 0.806392694
[949] 0.859360731 0.896803653 0.896803653 0.896803653 0.902283105 0.927853881
[955] 0.902283105 0.896803653 0.896803653 0.859360731 0.927853881 0.927853881
[961] 0.927853881 0.927853881 0.927853881 0.958904110 0.958904110 0.958904110
[967] 0.958904110 0.958904110 0.958904110 0.958904110 0.958904110 0.958904110
[973] 0.958904110 0.958904110 0.958904110 0.958904110 0.958904110 0.902283105
[979] 0.896803653 0.896803653 0.896803653 0.896803653 0.896803653 0.896803653
[985] 0.836529680 0.786301370 0.657534247 0.679452055 0.689497717 0.622831050
[991] 0.415525114 0.689497717 0.786301370 0.759817352 0.592694064 0.028310502
[997] 0.075799087 0.536073059 0.705022831 0.737899543 0.737899543 0.759817352
[1003] 0.786301370 0.836529680 0.859360731 0.902283105 0.902283105 0.836529680
[1009] 0.836529680 0.859360731 0.896803653 0.896803653 0.896803653 0.896803653
[1015] 0.896803653 0.896803653 0.896803653 0.896803653 0.896803653 0.896803653
[1021] 0.859360731 0.859360731 0.859360731 0.859360731 0.859360731 0.859360731
[1027] 0.859360731 0.859360731 0.859360731 0.859360731 0.859360731 0.859360731
[1033] 0.859360731 0.896803653 0.896803653 0.859360731 0.859360731 0.806392694
[1039] 0.786301370 0.705022831 0.705022831 0.759817352 0.759817352 0.759817352
[1045] 0.679452055 0.328767123 0.599086758 0.579908676 0.011872146 0.091324201
[1051] 0.314155251 0.344292237 0.314155251 0.378082192 0.446575342 0.517808219
[1057] 0.517808219 0.527853881 0.527853881 0.517808219 0.517808219 0.527853881
[1063] 0.527853881 0.527853881 0.536073059 0.517808219 0.086757991 0.333333333
[1069] 0.231963470 0.314155251 0.386301370 0.364383562 0.406392694 0.406392694
[1075] 0.397260274 0.378082192 0.378082192 0.397260274 0.397260274 0.406392694
[1081] 0.422831050 0.422831050 0.415525114 0.397260274 0.397260274 0.446575342
[1087] 0.488584475 0.517808219 0.517808219 0.517808219 0.517808219 0.517808219
[1093] 0.517808219 0.527853881 0.517808219
[1] 42.1
[1] 15.25640 1.27823
[1] 0.002739726 0.010045662 0.004566210 0.016438356 0.030136986 0.023744292
[7] 0.040182648 0.028310502 0.055707763 0.067579909 0.055707763 0.033789954
[13] 0.093150685 0.120547945 0.120547945 0.129680365 0.137899543 0.137899543
[19] 0.102283105 0.120547945 0.129680365 0.044748858 0.096803653 0.102283105
[25] 0.113242009 0.113242009 0.113242009 0.137899543 0.113242009 0.113242009
[31] 0.124200913 0.144292237 0.151598174 0.144292237 0.165296804 0.165296804
[37] 0.173515982 0.178082192 0.194520548 0.194520548 0.151598174 0.173515982
[43] 0.216438356 0.229223744 0.236529680 0.250228311 0.263926941 0.278538813
[49] 0.291324201 0.300456621 0.305936073 0.317808219 0.317808219 0.322374429
[55] 0.326027397 0.330593607 0.326027397 0.326027397 0.335159817 0.340639269
[61] 0.340639269 0.347031963 0.355251142 0.355251142 0.355251142 0.355251142
[67] 0.368949772 0.382648402 0.382648402 0.390867580 0.400913242 0.400913242
[73] 0.410958904 0.419178082 0.428310502 0.440182648 0.455707763 0.440182648
[79] 0.355251142 0.390867580 0.410958904 0.440182648 0.455707763 0.455707763
[85] 0.465753425 0.465753425 0.465753425 0.476712329 0.482191781 0.482191781
[91] 0.497716895 0.497716895 0.497716895 0.482191781 0.476712329 0.476712329
[97] 0.482191781 0.482191781 0.465753425 0.465753425 0.410958904 0.428310502
[103] 0.440182648 0.455707763 0.455707763 0.465753425 0.419178082 0.440182648
[109] 0.455707763 0.455707763 0.440182648 0.455707763 0.455707763 0.440182648
[115] 0.455707763 0.428310502 0.476712329 0.497716895 0.497716895 0.428310502
[121] 0.520547945 0.540639269 0.551598174 0.560730594 0.560730594 0.560730594
[127] 0.587214612 0.607305936 0.607305936 0.631050228 0.643835616 0.618264840
[133] 0.618264840 0.643835616 0.643835616 0.670319635 0.643835616 0.618264840
[139] 0.670319635 0.670319635 0.670319635 0.686757991 0.670319635 0.578082192
[145] 0.428310502 0.212785388 0.257534247 0.489497717 0.497716895 0.540639269
[151] 0.520547945 0.528767123 0.551598174 0.578082192 0.587214612 0.596347032
[157] 0.607305936 0.607305936 0.631050228 0.631050228 0.643835616 0.670319635
[163] 0.670319635 0.643835616 0.643835616 0.670319635 0.670319635 0.670319635
[169] 0.643835616 0.607305936 0.618264840 0.618264840 0.540639269 0.607305936
[175] 0.670319635 0.596347032 0.368949772 0.440182648 0.250228311 0.607305936
[181] 0.693150685 0.737899543 0.737899543 0.326027397 0.631050228 0.670319635
[187] 0.686757991 0.693150685 0.746118721 0.798173516 0.798173516 0.870319635
[193] 0.870319635 0.921461187 0.958904110 0.958904110 0.958904110 0.958904110
[199] 0.958904110 0.870319635 0.921461187 0.921461187 0.870319635 0.921461187
[205] 0.921461187 0.968036530 0.958904110 0.870319635 0.921461187 0.827397260
[211] 0.921461187 0.194520548 0.643835616 0.774429224 0.827397260 0.870319635
[217] 0.870319635 0.958904110 0.958904110 0.974429224 0.968036530 0.968036530
[223] 0.968036530 0.968036530 0.921461187 0.968036530 0.958904110 0.968036530
[229] 0.974429224 0.978995434 0.984474886 0.984474886 0.991780822 0.984474886
[235] 0.978995434 0.978995434 0.974429224 0.974429224 0.991780822 0.991780822
[241] 0.998173516 0.991780822 0.991780822 0.998173516 0.998173516 0.998173516
[247] 0.587214612 0.798173516 0.827397260 0.870319635 0.984474886 0.991780822
[253] 0.984474886 0.991780822 0.991780822 0.998173516 0.998173516 0.998173516
[259] 1.000000000 1.000000000 0.984474886 0.774429224 0.746118721 0.968036530
[265] 0.968036530 0.974429224 0.974429224 0.978995434 0.978995434 0.921461187
[271] 0.631050228 0.618264840 0.921461187 0.958904110 0.921461187 0.827397260
[277] 0.921461187 0.921461187 0.921461187 0.504109589 0.476712329 0.921461187
[283] 0.958904110 0.968036530 0.974429224 0.958904110 0.958904110 0.551598174
[289] 0.400913242 0.643835616 0.705022831 0.178082192 0.551598174 0.686757991
[295] 0.798173516 0.774429224 0.774429224 0.798173516 0.827397260 0.827397260
[301] 0.827397260 0.870319635 0.737899543 0.774429224 0.746118721 0.798173516
[307] 0.827397260 0.827397260 0.827397260 0.827397260 0.827397260 0.827397260
[313] 0.827397260 0.737899543 0.596347032 0.031963470 0.018264840 0.105936073
[319] 0.124200913 0.120547945 0.168949772 0.207305936 0.222831050 0.236529680
[325] 0.005479452 0.047488584 0.096803653 0.102283105 0.113242009 0.030136986
[331] 0.021004566 0.066666667 0.000913242 0.010045662 0.037442922 0.044748858
[337] 0.031963470 0.058447489 0.090410959 0.055707763 0.089497717 0.096803653
[343] 0.105936073 0.151598174 0.089497717 0.105936073 0.165296804 0.178082192
[349] 0.185388128 0.194520548 0.209132420 0.222831050 0.236529680 0.243835616
[355] 0.243835616 0.257534247 0.278538813 0.236529680 0.199086758 0.072146119
[361] 0.113242009 0.173515982 0.022831050 0.015525114 0.012785388 0.014611872
[367] 0.001826484 0.003652968 0.010958904 0.020091324 0.034703196 0.049315068
[373] 0.058447489 0.066666667 0.058447489 0.072146119 0.078538813 0.093150685
[379] 0.036529680 0.041095890 0.063013699 0.072146119 0.025570776 0.017351598
[385] 0.050228311 0.062100457 0.063926941 0.072146119 0.084018265 0.102283105
[391] 0.144292237 0.137899543 0.151598174 0.157990868 0.165296804 0.185388128
[397] 0.195433790 0.129680365 0.096803653 0.124200913 0.144292237 0.165296804
[403] 0.185388128 0.082191781 0.006392694 0.051141553 0.078538813 0.074885845
[409] 0.068493151 0.044748858 0.047488584 0.062100457 0.074885845 0.085844749
[415] 0.102283105 0.120547945 0.137899543 0.151598174 0.157990868 0.157990868
[421] 0.157990868 0.153424658 0.129680365 0.082191781 0.124200913 0.144292237
[427] 0.024657534 0.008219178 0.013698630 0.047488584 0.062100457 0.033789954
[433] 0.026484018 0.021917808 0.052054795 0.059360731 0.044748858 0.052968037
[439] 0.066666667 0.082191781 0.089497717 0.097716895 0.113242009 0.129680365
[445] 0.137899543 0.144292237 0.153424658 0.165296804 0.146118721 0.178082192
[451] 0.185388128 0.194520548 0.204566210 0.194520548 0.199086758 0.007305936
[457] 0.036529680 0.078538813 0.082191781 0.129680365 0.151598174 0.165296804
[463] 0.173515982 0.185388128 0.194520548 0.199086758 0.212785388 0.216438356
[469] 0.222831050 0.229223744 0.250228311 0.194520548 0.204566210 0.229223744
[475] 0.236529680 0.257534247 0.278538813 0.284018265 0.038356164 0.105936073
[481] 0.144292237 0.165296804 0.199086758 0.137899543 0.207305936 0.204566210
[487] 0.194520548 0.212785388 0.222831050 0.243835616 0.257534247 0.263926941
[493] 0.291324201 0.243835616 0.300456621 0.322374429 0.317808219 0.243835616
[499] 0.263926941 0.278538813 0.291324201 0.322374429 0.335159817 0.317808219
[505] 0.340639269 0.330593607 0.347031963 0.355251142 0.347031963 0.355251142
[511] 0.368949772 0.368949772 0.382648402 0.390867580 0.400913242 0.368949772
[517] 0.382648402 0.390867580 0.390867580 0.410958904 0.410958904 0.419178082
[523] 0.428310502 0.440182648 0.465753425 0.465753425 0.476712329 0.497716895
[529] 0.497716895 0.382648402 0.440182648 0.465753425 0.083105023 0.355251142
[535] 0.419178082 0.465753425 0.482191781 0.497716895 0.540639269 0.551598174
[541] 0.520547945 0.540639269 0.551598174 0.551598174 0.560730594 0.578082192
[547] 0.560730594 0.560730594 0.578082192 0.578082192 0.578082192 0.578082192
[553] 0.587214612 0.587214612 0.578082192 0.560730594 0.578082192 0.578082192
[559] 0.587214612 0.578082192 0.587214612 0.587214612 0.596347032 0.607305936
[565] 0.607305936 0.618264840 0.618264840 0.631050228 0.631050228 0.631050228
[571] 0.631050228 0.643835616 0.670319635 0.686757991 0.686757991 0.705022831
[577] 0.705022831 0.693150685 0.686757991 0.643835616 0.670319635 0.686757991
[583] 0.686757991 0.693150685 0.705022831 0.737899543 0.705022831 0.737899543
[589] 0.737899543 0.746118721 0.746118721 0.746118721 0.746118721 0.746118721
[595] 0.774429224 0.774429224 0.774429224 0.774429224 0.798173516 0.798173516
[601] 0.827397260 0.827397260 0.827397260 0.827397260 0.827397260 0.827397260
[607] 0.798173516 0.798173516 0.827397260 0.827397260 0.870319635 0.827397260
[613] 0.870319635 0.870319635 0.921461187 0.921461187 0.921461187 0.921461187
[619] 0.958904110 0.958904110 0.958904110 0.921461187 0.921461187 0.958904110
[625] 0.958904110 0.958904110 0.958904110 0.774429224 0.774429224 0.798173516
[631] 0.798173516 0.798173516 0.774429224 0.746118721 0.774429224 0.774429224
[637] 0.774429224 0.774429224 0.786301370 0.786301370 0.806392694 0.836529680
[643] 0.836529680 0.836529680 0.836529680 0.859360731 0.859360731 0.896803653
[649] 0.896803653 0.759817352 0.806392694 0.737899543 0.786301370 0.759817352
[655] 0.786301370 0.786301370 0.806392694 0.786301370 0.759817352 0.759817352
[661] 0.737899543 0.737899543 0.786301370 0.786301370 0.806392694 0.806392694
[667] 0.786301370 0.759817352 0.759817352 0.759817352 0.759817352 0.737899543
[673] 0.737899543 0.737899543 0.737899543 0.737899543 0.737899543 0.737899543
[679] 0.737899543 0.737899543 0.737899543 0.737899543 0.737899543 0.737899543
[685] 0.737899543 0.737899543 0.737899543 0.737899543 0.705022831 0.536073059
[691] 0.527853881 0.568036530 0.599086758 0.632876712 0.657534247 0.679452055
[697] 0.657534247 0.657534247 0.657534247 0.657534247 0.679452055 0.657534247
[703] 0.657534247 0.657534247 0.657534247 0.657534247 0.689497717 0.705022831
[709] 0.737899543 0.737899543 0.737899543 0.737899543 0.705022831 0.610958904
[715] 0.476712329 0.174429224 0.201826484 0.364383562 0.488584475 0.554337900
[721] 0.476712329 0.503196347 0.536073059 0.545205479 0.568036530 0.568036530
[727] 0.568036530 0.536073059 0.406392694 0.386301370 0.415525114 0.084931507
[733] 0.048401826 0.186301370 0.201826484 0.226484018 0.214611872 0.247488584
[739] 0.219178082 0.239269406 0.205479452 0.115981735 0.168036530 0.231963470
[745] 0.253881279 0.305022831 0.305022831 0.288584475 0.231963470 0.131506849
[751] 0.208219178 0.253881279 0.298630137 0.298630137 0.328767123 0.333333333
[757] 0.364383562 0.386301370 0.378082192 0.378082192 0.344292237 0.364383562
[763] 0.378082192 0.446575342 0.397260274 0.446575342 0.422831050 0.378082192
[769] 0.314155251 0.364383562 0.180821918 0.226484018 0.239269406 0.274885845
[775] 0.288584475 0.274885845 0.168036530 0.210045662 0.247488584 0.115981735
[781] 0.226484018 0.253881279 0.261187215 0.253881279 0.274885845 0.274885845
[787] 0.288584475 0.274885845 0.274885845 0.298630137 0.298630137 0.305022831
[793] 0.298630137 0.305022831 0.314155251 0.319634703 0.337899543 0.337899543
[799] 0.314155251 0.219178082 0.214611872 0.247488584 0.283105023 0.283105023
[805] 0.274885845 0.298630137 0.274885845 0.298630137 0.298630137 0.168036530
[811] 0.019178082 0.039269406 0.074885845 0.115981735 0.145205479 0.169863014
[817] 0.131506849 0.154337900 0.180821918 0.180821918 0.201826484 0.226484018
[823] 0.239269406 0.261187215 0.283105023 0.261187215 0.283105023 0.274885845
[829] 0.247488584 0.219178082 0.274885845 0.261187215 0.274885845 0.274885845
[835] 0.288584475 0.305022831 0.314155251 0.314155251 0.288584475 0.283105023
[841] 0.314155251 0.319634703 0.328767123 0.333333333 0.344292237 0.347945205
[847] 0.364383562 0.364383562 0.364383562 0.364383562 0.378082192 0.364383562
[853] 0.378082192 0.378082192 0.386301370 0.406392694 0.406392694 0.415525114
[859] 0.397260274 0.415525114 0.422831050 0.431050228 0.431050228 0.446575342
[865] 0.446575342 0.456621005 0.476712329 0.476712329 0.488584475 0.488584475
[871] 0.488584475 0.488584475 0.503196347 0.503196347 0.517808219 0.517808219
[877] 0.527853881 0.536073059 0.545205479 0.545205479 0.545205479 0.545205479
[883] 0.337899543 0.476712329 0.503196347 0.476712329 0.446575342 0.503196347
[889] 0.536073059 0.554337900 0.568036530 0.568036530 0.579908676 0.592694064
[895] 0.592694064 0.599086758 0.592694064 0.610958904 0.622831050 0.622831050
[901] 0.657534247 0.679452055 0.610958904 0.431050228 0.568036530 0.517808219
[907] 0.657534247 0.622831050 0.344292237 0.554337900 0.568036530 0.592694064
[913] 0.592694064 0.610958904 0.657534247 0.679452055 0.679452055 0.679452055
[919] 0.679452055 0.705022831 0.737899543 0.737899543 0.737899543 0.503196347
[925] 0.488584475 0.622831050 0.632876712 0.657534247 0.679452055 0.705022831
[931] 0.759817352 0.759817352 0.806392694 0.859360731 0.806392694 0.836529680
[937] 0.859360731 0.859360731 0.859360731 0.896803653 0.902283105 0.927853881
[943] 0.536073059 0.896803653 0.836529680 0.896803653 0.896803653 0.806392694
[949] 0.859360731 0.896803653 0.896803653 0.896803653 0.902283105 0.927853881
[955] 0.902283105 0.896803653 0.896803653 0.859360731 0.927853881 0.927853881
[961] 0.927853881 0.927853881 0.927853881 0.958904110 0.958904110 0.958904110
[967] 0.958904110 0.958904110 0.958904110 0.958904110 0.958904110 0.958904110
[973] 0.958904110 0.958904110 0.958904110 0.958904110 0.958904110 0.902283105
[979] 0.896803653 0.896803653 0.896803653 0.896803653 0.896803653 0.896803653
[985] 0.836529680 0.786301370 0.657534247 0.679452055 0.689497717 0.622831050
[991] 0.415525114 0.689497717 0.786301370 0.759817352 0.592694064 0.028310502
[997] 0.075799087 0.536073059 0.705022831 0.737899543 0.737899543 0.759817352
[1003] 0.786301370 0.836529680 0.859360731 0.902283105 0.902283105 0.836529680
[1009] 0.836529680 0.859360731 0.896803653 0.896803653 0.896803653 0.896803653
[1015] 0.896803653 0.896803653 0.896803653 0.896803653 0.896803653 0.896803653
[1021] 0.859360731 0.859360731 0.859360731 0.859360731 0.859360731 0.859360731
[1027] 0.859360731 0.859360731 0.859360731 0.859360731 0.859360731 0.859360731
[1033] 0.859360731 0.896803653 0.896803653 0.859360731 0.859360731 0.806392694
[1039] 0.786301370 0.705022831 0.705022831 0.759817352 0.759817352 0.759817352
[1045] 0.679452055 0.328767123 0.599086758 0.579908676 0.011872146 0.091324201
[1051] 0.314155251 0.344292237 0.314155251 0.378082192 0.446575342 0.517808219
[1057] 0.517808219 0.527853881 0.527853881 0.517808219 0.517808219 0.527853881
[1063] 0.527853881 0.527853881 0.536073059 0.517808219 0.086757991 0.333333333
[1069] 0.231963470 0.314155251 0.386301370 0.364383562 0.406392694 0.406392694
[1075] 0.397260274 0.378082192 0.378082192 0.397260274 0.397260274 0.406392694
[1081] 0.422831050 0.422831050 0.415525114 0.397260274 0.397260274 0.446575342
[1087] 0.488584475 0.517808219 0.517808219 0.517808219 0.517808219 0.517808219
[1093] 0.517808219 0.527853881 0.517808219
hydroTSM documentation built on March 13, 2020, 2:23 a.m.
R Package Documentation
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Description Usage Arguments Value Author(s) References See Also Examples
Description
Computes and plots the Flow Duration Curve (FDC) corresponding to a given time series of streamflow discharges.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 | fdc(x, ...)
## Default S3 method:
fdc(x,lQ.thr=0.7,hQ.thr=0.2, plot=TRUE, log="y",
main="Flow Duration Curve", xlab="% Time flow equalled or exceeded",
ylab="Q, [m3/s]", ylim, yat=c(0.01, 0.1, 1), xat=c(0.01, 0.025, 0.05), col="black",
pch=1, lwd=1, lty=1, cex=0.4, cex.axis=1.2, cex.lab=1.2, leg.txt=NULL, leg.cex=1,
leg.pos="topright", verbose= TRUE, thr.shw=TRUE, new=TRUE, ...)
## S3 method for class 'matrix'
fdc(x, lQ.thr=0.7, hQ.thr=0.2, plot=TRUE, log="y",
main= "Flow Duration Curve", xlab="% Time flow equalled or exceeded",
ylab="Q, [m3/s]", ylim, yat=c(0.01, 0.1, 1), xat=c(0.01, 0.025, 0.05),
col=palette("default")[1:ncol(x)], pch=1:ncol(x), lwd=rep(1, ncol(x)),
lty=1:ncol(x), cex=0.4, cex.axis=1.2, cex.lab=1.2, leg.txt=NULL,
leg.cex=1, leg.pos="topright",verbose=TRUE, thr.shw=TRUE, new=TRUE, ...)
## S3 method for class 'data.frame'
fdc(x, lQ.thr=0.7, hQ.thr=0.2, plot=TRUE, log="y",
main= "Flow Duration Curve", xlab="% Time flow equalled or exceeded",
ylab="Q, [m3/s]", ylim, yat=c(0.01, 0.1, 1), xat=c(0.01, 0.025, 0.05),
col=palette("default")[1:ncol(x)], pch=1:ncol(x), lwd=rep(1, ncol(x)),
lty=1:ncol(x), cex=0.4, cex.axis=1.2, cex.lab=1.2, leg.txt=NULL,
leg.cex=1, leg.pos="topright", verbose=TRUE, thr.shw=TRUE, new=TRUE, ...)
## S3 method for class 'zoo'
fdc(x, lQ.thr=0.7, hQ.thr=0.2, plot=TRUE, log="y",
main= "Flow Duration Curve", xlab="% Time flow equalled or exceeded",
ylab="Q, [m3/s]", ylim, yat=c(0.01, 0.1, 1), xat=c(0.01, 0.025, 0.05),
col=palette("default")[1:NCOL(x)], pch=1:NCOL(x), lwd=rep(1, NCOL(x)),
lty=1:NCOL(x), cex=0.4, cex.axis=1.2, cex.lab=1.2, leg.txt=NULL,
leg.cex=1, leg.pos="topright", verbose=TRUE, thr.shw=TRUE, new=TRUE, ...)
|
Arguments
x |
numeric, zoo, data.frame or matrix object with the observed streamflows for which the flow duration curve have to be computed. |
lQ.thr |
numeric, low-flow separation threshold. If this value is different from NA, a vertical line is drawn in this value, and all the values to the right of it should be deemed as low flows. Default value is 0.7. |
hQ.thr |
numeric, high-flow separation threshold. If this value is different from NA, a vertical line is drawn in this value, and all the values to the left of it should br deemed as high flows. Default value is 0.2. |
plot |
logical. Indicates if the flow duration curve should be plotted or not. Default value is TRUE. |
log |
character, indicates which axis has to be plotted with a logarithmic scale. Default value is y |
main |
See |
xlab |
A title for the x axis. See |
ylab |
A title for the y axis. See |
ylim |
The y limits of the plot. See |
yat |
Only used when |
xat |
Only used when |
col |
The colors to be used for lines and points. Multiple colors can be specified so that each point can be given its own color. If there are fewer colors than points they are recycled in the standard fashion. Lines will all be plotted in the first colour specified. See |
pch |
A vector of plotting characters or symbols: see |
lwd |
The line width, see |
lty |
The line type, see |
cex |
See |
cex.axis |
magnification of axis annotation relative to 'cex'. |
cex.lab |
Magnification to be used for x and y labels relative to the current setting of 'cex'. See '?par'. |
leg.txt |
vector with the names that have to be used for each column of |
leg.cex |
numeric, indicating the character expansion factor for the legend, *relative* to current |
leg.pos |
keyword to be used to position the legend. One of the list ‘"bottomright", "bottom", "bottomleft", "left", "topleft", "top", "topright", "right", "center"’. This places the legend on the inside of the plot frame at the given location. See |
verbose |
logical; if TRUE, progress messages are printed (when |
thr.shw |
logical, indicating if the streamflow values corresponding to the user-defined thresholds |
new |
logical, if TRUE (default), a new plotting window is created. |
... |
further arguments passed to or from other methods (to the plotting functions) |
Value
numeric, matrix or data.frame whose columns contains the % of time each one of the streamflow magnitudes given as input was equalled or exceeded. The resulting values have to be multiplied by 100 to get a percentage.
When plot is TRUE (default), the resulting flow duration curve is plotted in a new window.
Author(s)
Mauricio Zambrano-Bigiarini, mzb.devel@gmail
References
Vogel, R., and N. M. Fennessey (1994), Flow duration curves I: A new interpretation and confidence intervals, ASCE, Journal of Water Resources Planning and Management, 120(4).
Vogel, R., and N. Fennessey (1995), Flow duration curves II: A review of applications in water resources planning, Water Resources Bulletin, 31(6), 1029-1039, doi:10.1111/j.1752-1688.1995.tb03419.x.
Yilmaz, K. K., H. V. Gupta, and T. Wagener (2008), A process-based diagnostic approach to model evaluation: Application to the NWS distributed hydrologic model, Water Resour. Res., 44, W09417, doi:10.1029/2007WR006716.
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | ## Loading daily streamflows at the station Oca en Ona (Ebro River basin, Spain) ##
data(OcaEnOnaQts)
## Daily Flow Duration Curve
fdc(OcaEnOnaQts)
###################
# Getting the streamflow values corresponding to 5 and 95% of time equalled or
# exceeded (and also the first streamflow value in 'x' just for verification)
x <- OcaEnOnaQts
# First streamflow value (x1=42.1 m3/s)
x1 <- x[1]
# Daily FDC for 'x'
y <- fdc(x)
# value of the FDC for x1 (y1=0.002739726)
y1 <- y[1]
# Performing cubic (or Hermite) spline interpolation of 'x' and 'y'
f <- splinefun(y,x)
# Getting the (known) streamflow value for 'y1'
f(y1) # 42.1 m3/s, equal to the known 'x1'
# Streamflow values corresponding to 5 and 95% of time equalled or exceeded
f(c(.05, .95))
###################
## Getting
data(OcaEnOnaQts)
## Daily Flow Duration Curve
fdc(OcaEnOnaQts)
|
Example output
Loading required package: zoo
Attaching package: 'zoo'
The following objects are masked from 'package:base':
as.Date, as.Date.numeric
Loading required package: xts
[1] 0.002739726 0.010045662 0.004566210 0.016438356 0.030136986 0.023744292
[7] 0.040182648 0.028310502 0.055707763 0.067579909 0.055707763 0.033789954
[13] 0.093150685 0.120547945 0.120547945 0.129680365 0.137899543 0.137899543
[19] 0.102283105 0.120547945 0.129680365 0.044748858 0.096803653 0.102283105
[25] 0.113242009 0.113242009 0.113242009 0.137899543 0.113242009 0.113242009
[31] 0.124200913 0.144292237 0.151598174 0.144292237 0.165296804 0.165296804
[37] 0.173515982 0.178082192 0.194520548 0.194520548 0.151598174 0.173515982
[43] 0.216438356 0.229223744 0.236529680 0.250228311 0.263926941 0.278538813
[49] 0.291324201 0.300456621 0.305936073 0.317808219 0.317808219 0.322374429
[55] 0.326027397 0.330593607 0.326027397 0.326027397 0.335159817 0.340639269
[61] 0.340639269 0.347031963 0.355251142 0.355251142 0.355251142 0.355251142
[67] 0.368949772 0.382648402 0.382648402 0.390867580 0.400913242 0.400913242
[73] 0.410958904 0.419178082 0.428310502 0.440182648 0.455707763 0.440182648
[79] 0.355251142 0.390867580 0.410958904 0.440182648 0.455707763 0.455707763
[85] 0.465753425 0.465753425 0.465753425 0.476712329 0.482191781 0.482191781
[91] 0.497716895 0.497716895 0.497716895 0.482191781 0.476712329 0.476712329
[97] 0.482191781 0.482191781 0.465753425 0.465753425 0.410958904 0.428310502
[103] 0.440182648 0.455707763 0.455707763 0.465753425 0.419178082 0.440182648
[109] 0.455707763 0.455707763 0.440182648 0.455707763 0.455707763 0.440182648
[115] 0.455707763 0.428310502 0.476712329 0.497716895 0.497716895 0.428310502
[121] 0.520547945 0.540639269 0.551598174 0.560730594 0.560730594 0.560730594
[127] 0.587214612 0.607305936 0.607305936 0.631050228 0.643835616 0.618264840
[133] 0.618264840 0.643835616 0.643835616 0.670319635 0.643835616 0.618264840
[139] 0.670319635 0.670319635 0.670319635 0.686757991 0.670319635 0.578082192
[145] 0.428310502 0.212785388 0.257534247 0.489497717 0.497716895 0.540639269
[151] 0.520547945 0.528767123 0.551598174 0.578082192 0.587214612 0.596347032
[157] 0.607305936 0.607305936 0.631050228 0.631050228 0.643835616 0.670319635
[163] 0.670319635 0.643835616 0.643835616 0.670319635 0.670319635 0.670319635
[169] 0.643835616 0.607305936 0.618264840 0.618264840 0.540639269 0.607305936
[175] 0.670319635 0.596347032 0.368949772 0.440182648 0.250228311 0.607305936
[181] 0.693150685 0.737899543 0.737899543 0.326027397 0.631050228 0.670319635
[187] 0.686757991 0.693150685 0.746118721 0.798173516 0.798173516 0.870319635
[193] 0.870319635 0.921461187 0.958904110 0.958904110 0.958904110 0.958904110
[199] 0.958904110 0.870319635 0.921461187 0.921461187 0.870319635 0.921461187
[205] 0.921461187 0.968036530 0.958904110 0.870319635 0.921461187 0.827397260
[211] 0.921461187 0.194520548 0.643835616 0.774429224 0.827397260 0.870319635
[217] 0.870319635 0.958904110 0.958904110 0.974429224 0.968036530 0.968036530
[223] 0.968036530 0.968036530 0.921461187 0.968036530 0.958904110 0.968036530
[229] 0.974429224 0.978995434 0.984474886 0.984474886 0.991780822 0.984474886
[235] 0.978995434 0.978995434 0.974429224 0.974429224 0.991780822 0.991780822
[241] 0.998173516 0.991780822 0.991780822 0.998173516 0.998173516 0.998173516
[247] 0.587214612 0.798173516 0.827397260 0.870319635 0.984474886 0.991780822
[253] 0.984474886 0.991780822 0.991780822 0.998173516 0.998173516 0.998173516
[259] 1.000000000 1.000000000 0.984474886 0.774429224 0.746118721 0.968036530
[265] 0.968036530 0.974429224 0.974429224 0.978995434 0.978995434 0.921461187
[271] 0.631050228 0.618264840 0.921461187 0.958904110 0.921461187 0.827397260
[277] 0.921461187 0.921461187 0.921461187 0.504109589 0.476712329 0.921461187
[283] 0.958904110 0.968036530 0.974429224 0.958904110 0.958904110 0.551598174
[289] 0.400913242 0.643835616 0.705022831 0.178082192 0.551598174 0.686757991
[295] 0.798173516 0.774429224 0.774429224 0.798173516 0.827397260 0.827397260
[301] 0.827397260 0.870319635 0.737899543 0.774429224 0.746118721 0.798173516
[307] 0.827397260 0.827397260 0.827397260 0.827397260 0.827397260 0.827397260
[313] 0.827397260 0.737899543 0.596347032 0.031963470 0.018264840 0.105936073
[319] 0.124200913 0.120547945 0.168949772 0.207305936 0.222831050 0.236529680
[325] 0.005479452 0.047488584 0.096803653 0.102283105 0.113242009 0.030136986
[331] 0.021004566 0.066666667 0.000913242 0.010045662 0.037442922 0.044748858
[337] 0.031963470 0.058447489 0.090410959 0.055707763 0.089497717 0.096803653
[343] 0.105936073 0.151598174 0.089497717 0.105936073 0.165296804 0.178082192
[349] 0.185388128 0.194520548 0.209132420 0.222831050 0.236529680 0.243835616
[355] 0.243835616 0.257534247 0.278538813 0.236529680 0.199086758 0.072146119
[361] 0.113242009 0.173515982 0.022831050 0.015525114 0.012785388 0.014611872
[367] 0.001826484 0.003652968 0.010958904 0.020091324 0.034703196 0.049315068
[373] 0.058447489 0.066666667 0.058447489 0.072146119 0.078538813 0.093150685
[379] 0.036529680 0.041095890 0.063013699 0.072146119 0.025570776 0.017351598
[385] 0.050228311 0.062100457 0.063926941 0.072146119 0.084018265 0.102283105
[391] 0.144292237 0.137899543 0.151598174 0.157990868 0.165296804 0.185388128
[397] 0.195433790 0.129680365 0.096803653 0.124200913 0.144292237 0.165296804
[403] 0.185388128 0.082191781 0.006392694 0.051141553 0.078538813 0.074885845
[409] 0.068493151 0.044748858 0.047488584 0.062100457 0.074885845 0.085844749
[415] 0.102283105 0.120547945 0.137899543 0.151598174 0.157990868 0.157990868
[421] 0.157990868 0.153424658 0.129680365 0.082191781 0.124200913 0.144292237
[427] 0.024657534 0.008219178 0.013698630 0.047488584 0.062100457 0.033789954
[433] 0.026484018 0.021917808 0.052054795 0.059360731 0.044748858 0.052968037
[439] 0.066666667 0.082191781 0.089497717 0.097716895 0.113242009 0.129680365
[445] 0.137899543 0.144292237 0.153424658 0.165296804 0.146118721 0.178082192
[451] 0.185388128 0.194520548 0.204566210 0.194520548 0.199086758 0.007305936
[457] 0.036529680 0.078538813 0.082191781 0.129680365 0.151598174 0.165296804
[463] 0.173515982 0.185388128 0.194520548 0.199086758 0.212785388 0.216438356
[469] 0.222831050 0.229223744 0.250228311 0.194520548 0.204566210 0.229223744
[475] 0.236529680 0.257534247 0.278538813 0.284018265 0.038356164 0.105936073
[481] 0.144292237 0.165296804 0.199086758 0.137899543 0.207305936 0.204566210
[487] 0.194520548 0.212785388 0.222831050 0.243835616 0.257534247 0.263926941
[493] 0.291324201 0.243835616 0.300456621 0.322374429 0.317808219 0.243835616
[499] 0.263926941 0.278538813 0.291324201 0.322374429 0.335159817 0.317808219
[505] 0.340639269 0.330593607 0.347031963 0.355251142 0.347031963 0.355251142
[511] 0.368949772 0.368949772 0.382648402 0.390867580 0.400913242 0.368949772
[517] 0.382648402 0.390867580 0.390867580 0.410958904 0.410958904 0.419178082
[523] 0.428310502 0.440182648 0.465753425 0.465753425 0.476712329 0.497716895
[529] 0.497716895 0.382648402 0.440182648 0.465753425 0.083105023 0.355251142
[535] 0.419178082 0.465753425 0.482191781 0.497716895 0.540639269 0.551598174
[541] 0.520547945 0.540639269 0.551598174 0.551598174 0.560730594 0.578082192
[547] 0.560730594 0.560730594 0.578082192 0.578082192 0.578082192 0.578082192
[553] 0.587214612 0.587214612 0.578082192 0.560730594 0.578082192 0.578082192
[559] 0.587214612 0.578082192 0.587214612 0.587214612 0.596347032 0.607305936
[565] 0.607305936 0.618264840 0.618264840 0.631050228 0.631050228 0.631050228
[571] 0.631050228 0.643835616 0.670319635 0.686757991 0.686757991 0.705022831
[577] 0.705022831 0.693150685 0.686757991 0.643835616 0.670319635 0.686757991
[583] 0.686757991 0.693150685 0.705022831 0.737899543 0.705022831 0.737899543
[589] 0.737899543 0.746118721 0.746118721 0.746118721 0.746118721 0.746118721
[595] 0.774429224 0.774429224 0.774429224 0.774429224 0.798173516 0.798173516
[601] 0.827397260 0.827397260 0.827397260 0.827397260 0.827397260 0.827397260
[607] 0.798173516 0.798173516 0.827397260 0.827397260 0.870319635 0.827397260
[613] 0.870319635 0.870319635 0.921461187 0.921461187 0.921461187 0.921461187
[619] 0.958904110 0.958904110 0.958904110 0.921461187 0.921461187 0.958904110
[625] 0.958904110 0.958904110 0.958904110 0.774429224 0.774429224 0.798173516
[631] 0.798173516 0.798173516 0.774429224 0.746118721 0.774429224 0.774429224
[637] 0.774429224 0.774429224 0.786301370 0.786301370 0.806392694 0.836529680
[643] 0.836529680 0.836529680 0.836529680 0.859360731 0.859360731 0.896803653
[649] 0.896803653 0.759817352 0.806392694 0.737899543 0.786301370 0.759817352
[655] 0.786301370 0.786301370 0.806392694 0.786301370 0.759817352 0.759817352
[661] 0.737899543 0.737899543 0.786301370 0.786301370 0.806392694 0.806392694
[667] 0.786301370 0.759817352 0.759817352 0.759817352 0.759817352 0.737899543
[673] 0.737899543 0.737899543 0.737899543 0.737899543 0.737899543 0.737899543
[679] 0.737899543 0.737899543 0.737899543 0.737899543 0.737899543 0.737899543
[685] 0.737899543 0.737899543 0.737899543 0.737899543 0.705022831 0.536073059
[691] 0.527853881 0.568036530 0.599086758 0.632876712 0.657534247 0.679452055
[697] 0.657534247 0.657534247 0.657534247 0.657534247 0.679452055 0.657534247
[703] 0.657534247 0.657534247 0.657534247 0.657534247 0.689497717 0.705022831
[709] 0.737899543 0.737899543 0.737899543 0.737899543 0.705022831 0.610958904
[715] 0.476712329 0.174429224 0.201826484 0.364383562 0.488584475 0.554337900
[721] 0.476712329 0.503196347 0.536073059 0.545205479 0.568036530 0.568036530
[727] 0.568036530 0.536073059 0.406392694 0.386301370 0.415525114 0.084931507
[733] 0.048401826 0.186301370 0.201826484 0.226484018 0.214611872 0.247488584
[739] 0.219178082 0.239269406 0.205479452 0.115981735 0.168036530 0.231963470
[745] 0.253881279 0.305022831 0.305022831 0.288584475 0.231963470 0.131506849
[751] 0.208219178 0.253881279 0.298630137 0.298630137 0.328767123 0.333333333
[757] 0.364383562 0.386301370 0.378082192 0.378082192 0.344292237 0.364383562
[763] 0.378082192 0.446575342 0.397260274 0.446575342 0.422831050 0.378082192
[769] 0.314155251 0.364383562 0.180821918 0.226484018 0.239269406 0.274885845
[775] 0.288584475 0.274885845 0.168036530 0.210045662 0.247488584 0.115981735
[781] 0.226484018 0.253881279 0.261187215 0.253881279 0.274885845 0.274885845
[787] 0.288584475 0.274885845 0.274885845 0.298630137 0.298630137 0.305022831
[793] 0.298630137 0.305022831 0.314155251 0.319634703 0.337899543 0.337899543
[799] 0.314155251 0.219178082 0.214611872 0.247488584 0.283105023 0.283105023
[805] 0.274885845 0.298630137 0.274885845 0.298630137 0.298630137 0.168036530
[811] 0.019178082 0.039269406 0.074885845 0.115981735 0.145205479 0.169863014
[817] 0.131506849 0.154337900 0.180821918 0.180821918 0.201826484 0.226484018
[823] 0.239269406 0.261187215 0.283105023 0.261187215 0.283105023 0.274885845
[829] 0.247488584 0.219178082 0.274885845 0.261187215 0.274885845 0.274885845
[835] 0.288584475 0.305022831 0.314155251 0.314155251 0.288584475 0.283105023
[841] 0.314155251 0.319634703 0.328767123 0.333333333 0.344292237 0.347945205
[847] 0.364383562 0.364383562 0.364383562 0.364383562 0.378082192 0.364383562
[853] 0.378082192 0.378082192 0.386301370 0.406392694 0.406392694 0.415525114
[859] 0.397260274 0.415525114 0.422831050 0.431050228 0.431050228 0.446575342
[865] 0.446575342 0.456621005 0.476712329 0.476712329 0.488584475 0.488584475
[871] 0.488584475 0.488584475 0.503196347 0.503196347 0.517808219 0.517808219
[877] 0.527853881 0.536073059 0.545205479 0.545205479 0.545205479 0.545205479
[883] 0.337899543 0.476712329 0.503196347 0.476712329 0.446575342 0.503196347
[889] 0.536073059 0.554337900 0.568036530 0.568036530 0.579908676 0.592694064
[895] 0.592694064 0.599086758 0.592694064 0.610958904 0.622831050 0.622831050
[901] 0.657534247 0.679452055 0.610958904 0.431050228 0.568036530 0.517808219
[907] 0.657534247 0.622831050 0.344292237 0.554337900 0.568036530 0.592694064
[913] 0.592694064 0.610958904 0.657534247 0.679452055 0.679452055 0.679452055
[919] 0.679452055 0.705022831 0.737899543 0.737899543 0.737899543 0.503196347
[925] 0.488584475 0.622831050 0.632876712 0.657534247 0.679452055 0.705022831
[931] 0.759817352 0.759817352 0.806392694 0.859360731 0.806392694 0.836529680
[937] 0.859360731 0.859360731 0.859360731 0.896803653 0.902283105 0.927853881
[943] 0.536073059 0.896803653 0.836529680 0.896803653 0.896803653 0.806392694
[949] 0.859360731 0.896803653 0.896803653 0.896803653 0.902283105 0.927853881
[955] 0.902283105 0.896803653 0.896803653 0.859360731 0.927853881 0.927853881
[961] 0.927853881 0.927853881 0.927853881 0.958904110 0.958904110 0.958904110
[967] 0.958904110 0.958904110 0.958904110 0.958904110 0.958904110 0.958904110
[973] 0.958904110 0.958904110 0.958904110 0.958904110 0.958904110 0.902283105
[979] 0.896803653 0.896803653 0.896803653 0.896803653 0.896803653 0.896803653
[985] 0.836529680 0.786301370 0.657534247 0.679452055 0.689497717 0.622831050
[991] 0.415525114 0.689497717 0.786301370 0.759817352 0.592694064 0.028310502
[997] 0.075799087 0.536073059 0.705022831 0.737899543 0.737899543 0.759817352
[1003] 0.786301370 0.836529680 0.859360731 0.902283105 0.902283105 0.836529680
[1009] 0.836529680 0.859360731 0.896803653 0.896803653 0.896803653 0.896803653
[1015] 0.896803653 0.896803653 0.896803653 0.896803653 0.896803653 0.896803653
[1021] 0.859360731 0.859360731 0.859360731 0.859360731 0.859360731 0.859360731
[1027] 0.859360731 0.859360731 0.859360731 0.859360731 0.859360731 0.859360731
[1033] 0.859360731 0.896803653 0.896803653 0.859360731 0.859360731 0.806392694
[1039] 0.786301370 0.705022831 0.705022831 0.759817352 0.759817352 0.759817352
[1045] 0.679452055 0.328767123 0.599086758 0.579908676 0.011872146 0.091324201
[1051] 0.314155251 0.344292237 0.314155251 0.378082192 0.446575342 0.517808219
[1057] 0.517808219 0.527853881 0.527853881 0.517808219 0.517808219 0.527853881
[1063] 0.527853881 0.527853881 0.536073059 0.517808219 0.086757991 0.333333333
[1069] 0.231963470 0.314155251 0.386301370 0.364383562 0.406392694 0.406392694
[1075] 0.397260274 0.378082192 0.378082192 0.397260274 0.397260274 0.406392694
[1081] 0.422831050 0.422831050 0.415525114 0.397260274 0.397260274 0.446575342
[1087] 0.488584475 0.517808219 0.517808219 0.517808219 0.517808219 0.517808219
[1093] 0.517808219 0.527853881 0.517808219
[1] 42.1
[1] 15.25640 1.27823
[1] 0.002739726 0.010045662 0.004566210 0.016438356 0.030136986 0.023744292
[7] 0.040182648 0.028310502 0.055707763 0.067579909 0.055707763 0.033789954
[13] 0.093150685 0.120547945 0.120547945 0.129680365 0.137899543 0.137899543
[19] 0.102283105 0.120547945 0.129680365 0.044748858 0.096803653 0.102283105
[25] 0.113242009 0.113242009 0.113242009 0.137899543 0.113242009 0.113242009
[31] 0.124200913 0.144292237 0.151598174 0.144292237 0.165296804 0.165296804
[37] 0.173515982 0.178082192 0.194520548 0.194520548 0.151598174 0.173515982
[43] 0.216438356 0.229223744 0.236529680 0.250228311 0.263926941 0.278538813
[49] 0.291324201 0.300456621 0.305936073 0.317808219 0.317808219 0.322374429
[55] 0.326027397 0.330593607 0.326027397 0.326027397 0.335159817 0.340639269
[61] 0.340639269 0.347031963 0.355251142 0.355251142 0.355251142 0.355251142
[67] 0.368949772 0.382648402 0.382648402 0.390867580 0.400913242 0.400913242
[73] 0.410958904 0.419178082 0.428310502 0.440182648 0.455707763 0.440182648
[79] 0.355251142 0.390867580 0.410958904 0.440182648 0.455707763 0.455707763
[85] 0.465753425 0.465753425 0.465753425 0.476712329 0.482191781 0.482191781
[91] 0.497716895 0.497716895 0.497716895 0.482191781 0.476712329 0.476712329
[97] 0.482191781 0.482191781 0.465753425 0.465753425 0.410958904 0.428310502
[103] 0.440182648 0.455707763 0.455707763 0.465753425 0.419178082 0.440182648
[109] 0.455707763 0.455707763 0.440182648 0.455707763 0.455707763 0.440182648
[115] 0.455707763 0.428310502 0.476712329 0.497716895 0.497716895 0.428310502
[121] 0.520547945 0.540639269 0.551598174 0.560730594 0.560730594 0.560730594
[127] 0.587214612 0.607305936 0.607305936 0.631050228 0.643835616 0.618264840
[133] 0.618264840 0.643835616 0.643835616 0.670319635 0.643835616 0.618264840
[139] 0.670319635 0.670319635 0.670319635 0.686757991 0.670319635 0.578082192
[145] 0.428310502 0.212785388 0.257534247 0.489497717 0.497716895 0.540639269
[151] 0.520547945 0.528767123 0.551598174 0.578082192 0.587214612 0.596347032
[157] 0.607305936 0.607305936 0.631050228 0.631050228 0.643835616 0.670319635
[163] 0.670319635 0.643835616 0.643835616 0.670319635 0.670319635 0.670319635
[169] 0.643835616 0.607305936 0.618264840 0.618264840 0.540639269 0.607305936
[175] 0.670319635 0.596347032 0.368949772 0.440182648 0.250228311 0.607305936
[181] 0.693150685 0.737899543 0.737899543 0.326027397 0.631050228 0.670319635
[187] 0.686757991 0.693150685 0.746118721 0.798173516 0.798173516 0.870319635
[193] 0.870319635 0.921461187 0.958904110 0.958904110 0.958904110 0.958904110
[199] 0.958904110 0.870319635 0.921461187 0.921461187 0.870319635 0.921461187
[205] 0.921461187 0.968036530 0.958904110 0.870319635 0.921461187 0.827397260
[211] 0.921461187 0.194520548 0.643835616 0.774429224 0.827397260 0.870319635
[217] 0.870319635 0.958904110 0.958904110 0.974429224 0.968036530 0.968036530
[223] 0.968036530 0.968036530 0.921461187 0.968036530 0.958904110 0.968036530
[229] 0.974429224 0.978995434 0.984474886 0.984474886 0.991780822 0.984474886
[235] 0.978995434 0.978995434 0.974429224 0.974429224 0.991780822 0.991780822
[241] 0.998173516 0.991780822 0.991780822 0.998173516 0.998173516 0.998173516
[247] 0.587214612 0.798173516 0.827397260 0.870319635 0.984474886 0.991780822
[253] 0.984474886 0.991780822 0.991780822 0.998173516 0.998173516 0.998173516
[259] 1.000000000 1.000000000 0.984474886 0.774429224 0.746118721 0.968036530
[265] 0.968036530 0.974429224 0.974429224 0.978995434 0.978995434 0.921461187
[271] 0.631050228 0.618264840 0.921461187 0.958904110 0.921461187 0.827397260
[277] 0.921461187 0.921461187 0.921461187 0.504109589 0.476712329 0.921461187
[283] 0.958904110 0.968036530 0.974429224 0.958904110 0.958904110 0.551598174
[289] 0.400913242 0.643835616 0.705022831 0.178082192 0.551598174 0.686757991
[295] 0.798173516 0.774429224 0.774429224 0.798173516 0.827397260 0.827397260
[301] 0.827397260 0.870319635 0.737899543 0.774429224 0.746118721 0.798173516
[307] 0.827397260 0.827397260 0.827397260 0.827397260 0.827397260 0.827397260
[313] 0.827397260 0.737899543 0.596347032 0.031963470 0.018264840 0.105936073
[319] 0.124200913 0.120547945 0.168949772 0.207305936 0.222831050 0.236529680
[325] 0.005479452 0.047488584 0.096803653 0.102283105 0.113242009 0.030136986
[331] 0.021004566 0.066666667 0.000913242 0.010045662 0.037442922 0.044748858
[337] 0.031963470 0.058447489 0.090410959 0.055707763 0.089497717 0.096803653
[343] 0.105936073 0.151598174 0.089497717 0.105936073 0.165296804 0.178082192
[349] 0.185388128 0.194520548 0.209132420 0.222831050 0.236529680 0.243835616
[355] 0.243835616 0.257534247 0.278538813 0.236529680 0.199086758 0.072146119
[361] 0.113242009 0.173515982 0.022831050 0.015525114 0.012785388 0.014611872
[367] 0.001826484 0.003652968 0.010958904 0.020091324 0.034703196 0.049315068
[373] 0.058447489 0.066666667 0.058447489 0.072146119 0.078538813 0.093150685
[379] 0.036529680 0.041095890 0.063013699 0.072146119 0.025570776 0.017351598
[385] 0.050228311 0.062100457 0.063926941 0.072146119 0.084018265 0.102283105
[391] 0.144292237 0.137899543 0.151598174 0.157990868 0.165296804 0.185388128
[397] 0.195433790 0.129680365 0.096803653 0.124200913 0.144292237 0.165296804
[403] 0.185388128 0.082191781 0.006392694 0.051141553 0.078538813 0.074885845
[409] 0.068493151 0.044748858 0.047488584 0.062100457 0.074885845 0.085844749
[415] 0.102283105 0.120547945 0.137899543 0.151598174 0.157990868 0.157990868
[421] 0.157990868 0.153424658 0.129680365 0.082191781 0.124200913 0.144292237
[427] 0.024657534 0.008219178 0.013698630 0.047488584 0.062100457 0.033789954
[433] 0.026484018 0.021917808 0.052054795 0.059360731 0.044748858 0.052968037
[439] 0.066666667 0.082191781 0.089497717 0.097716895 0.113242009 0.129680365
[445] 0.137899543 0.144292237 0.153424658 0.165296804 0.146118721 0.178082192
[451] 0.185388128 0.194520548 0.204566210 0.194520548 0.199086758 0.007305936
[457] 0.036529680 0.078538813 0.082191781 0.129680365 0.151598174 0.165296804
[463] 0.173515982 0.185388128 0.194520548 0.199086758 0.212785388 0.216438356
[469] 0.222831050 0.229223744 0.250228311 0.194520548 0.204566210 0.229223744
[475] 0.236529680 0.257534247 0.278538813 0.284018265 0.038356164 0.105936073
[481] 0.144292237 0.165296804 0.199086758 0.137899543 0.207305936 0.204566210
[487] 0.194520548 0.212785388 0.222831050 0.243835616 0.257534247 0.263926941
[493] 0.291324201 0.243835616 0.300456621 0.322374429 0.317808219 0.243835616
[499] 0.263926941 0.278538813 0.291324201 0.322374429 0.335159817 0.317808219
[505] 0.340639269 0.330593607 0.347031963 0.355251142 0.347031963 0.355251142
[511] 0.368949772 0.368949772 0.382648402 0.390867580 0.400913242 0.368949772
[517] 0.382648402 0.390867580 0.390867580 0.410958904 0.410958904 0.419178082
[523] 0.428310502 0.440182648 0.465753425 0.465753425 0.476712329 0.497716895
[529] 0.497716895 0.382648402 0.440182648 0.465753425 0.083105023 0.355251142
[535] 0.419178082 0.465753425 0.482191781 0.497716895 0.540639269 0.551598174
[541] 0.520547945 0.540639269 0.551598174 0.551598174 0.560730594 0.578082192
[547] 0.560730594 0.560730594 0.578082192 0.578082192 0.578082192 0.578082192
[553] 0.587214612 0.587214612 0.578082192 0.560730594 0.578082192 0.578082192
[559] 0.587214612 0.578082192 0.587214612 0.587214612 0.596347032 0.607305936
[565] 0.607305936 0.618264840 0.618264840 0.631050228 0.631050228 0.631050228
[571] 0.631050228 0.643835616 0.670319635 0.686757991 0.686757991 0.705022831
[577] 0.705022831 0.693150685 0.686757991 0.643835616 0.670319635 0.686757991
[583] 0.686757991 0.693150685 0.705022831 0.737899543 0.705022831 0.737899543
[589] 0.737899543 0.746118721 0.746118721 0.746118721 0.746118721 0.746118721
[595] 0.774429224 0.774429224 0.774429224 0.774429224 0.798173516 0.798173516
[601] 0.827397260 0.827397260 0.827397260 0.827397260 0.827397260 0.827397260
[607] 0.798173516 0.798173516 0.827397260 0.827397260 0.870319635 0.827397260
[613] 0.870319635 0.870319635 0.921461187 0.921461187 0.921461187 0.921461187
[619] 0.958904110 0.958904110 0.958904110 0.921461187 0.921461187 0.958904110
[625] 0.958904110 0.958904110 0.958904110 0.774429224 0.774429224 0.798173516
[631] 0.798173516 0.798173516 0.774429224 0.746118721 0.774429224 0.774429224
[637] 0.774429224 0.774429224 0.786301370 0.786301370 0.806392694 0.836529680
[643] 0.836529680 0.836529680 0.836529680 0.859360731 0.859360731 0.896803653
[649] 0.896803653 0.759817352 0.806392694 0.737899543 0.786301370 0.759817352
[655] 0.786301370 0.786301370 0.806392694 0.786301370 0.759817352 0.759817352
[661] 0.737899543 0.737899543 0.786301370 0.786301370 0.806392694 0.806392694
[667] 0.786301370 0.759817352 0.759817352 0.759817352 0.759817352 0.737899543
[673] 0.737899543 0.737899543 0.737899543 0.737899543 0.737899543 0.737899543
[679] 0.737899543 0.737899543 0.737899543 0.737899543 0.737899543 0.737899543
[685] 0.737899543 0.737899543 0.737899543 0.737899543 0.705022831 0.536073059
[691] 0.527853881 0.568036530 0.599086758 0.632876712 0.657534247 0.679452055
[697] 0.657534247 0.657534247 0.657534247 0.657534247 0.679452055 0.657534247
[703] 0.657534247 0.657534247 0.657534247 0.657534247 0.689497717 0.705022831
[709] 0.737899543 0.737899543 0.737899543 0.737899543 0.705022831 0.610958904
[715] 0.476712329 0.174429224 0.201826484 0.364383562 0.488584475 0.554337900
[721] 0.476712329 0.503196347 0.536073059 0.545205479 0.568036530 0.568036530
[727] 0.568036530 0.536073059 0.406392694 0.386301370 0.415525114 0.084931507
[733] 0.048401826 0.186301370 0.201826484 0.226484018 0.214611872 0.247488584
[739] 0.219178082 0.239269406 0.205479452 0.115981735 0.168036530 0.231963470
[745] 0.253881279 0.305022831 0.305022831 0.288584475 0.231963470 0.131506849
[751] 0.208219178 0.253881279 0.298630137 0.298630137 0.328767123 0.333333333
[757] 0.364383562 0.386301370 0.378082192 0.378082192 0.344292237 0.364383562
[763] 0.378082192 0.446575342 0.397260274 0.446575342 0.422831050 0.378082192
[769] 0.314155251 0.364383562 0.180821918 0.226484018 0.239269406 0.274885845
[775] 0.288584475 0.274885845 0.168036530 0.210045662 0.247488584 0.115981735
[781] 0.226484018 0.253881279 0.261187215 0.253881279 0.274885845 0.274885845
[787] 0.288584475 0.274885845 0.274885845 0.298630137 0.298630137 0.305022831
[793] 0.298630137 0.305022831 0.314155251 0.319634703 0.337899543 0.337899543
[799] 0.314155251 0.219178082 0.214611872 0.247488584 0.283105023 0.283105023
[805] 0.274885845 0.298630137 0.274885845 0.298630137 0.298630137 0.168036530
[811] 0.019178082 0.039269406 0.074885845 0.115981735 0.145205479 0.169863014
[817] 0.131506849 0.154337900 0.180821918 0.180821918 0.201826484 0.226484018
[823] 0.239269406 0.261187215 0.283105023 0.261187215 0.283105023 0.274885845
[829] 0.247488584 0.219178082 0.274885845 0.261187215 0.274885845 0.274885845
[835] 0.288584475 0.305022831 0.314155251 0.314155251 0.288584475 0.283105023
[841] 0.314155251 0.319634703 0.328767123 0.333333333 0.344292237 0.347945205
[847] 0.364383562 0.364383562 0.364383562 0.364383562 0.378082192 0.364383562
[853] 0.378082192 0.378082192 0.386301370 0.406392694 0.406392694 0.415525114
[859] 0.397260274 0.415525114 0.422831050 0.431050228 0.431050228 0.446575342
[865] 0.446575342 0.456621005 0.476712329 0.476712329 0.488584475 0.488584475
[871] 0.488584475 0.488584475 0.503196347 0.503196347 0.517808219 0.517808219
[877] 0.527853881 0.536073059 0.545205479 0.545205479 0.545205479 0.545205479
[883] 0.337899543 0.476712329 0.503196347 0.476712329 0.446575342 0.503196347
[889] 0.536073059 0.554337900 0.568036530 0.568036530 0.579908676 0.592694064
[895] 0.592694064 0.599086758 0.592694064 0.610958904 0.622831050 0.622831050
[901] 0.657534247 0.679452055 0.610958904 0.431050228 0.568036530 0.517808219
[907] 0.657534247 0.622831050 0.344292237 0.554337900 0.568036530 0.592694064
[913] 0.592694064 0.610958904 0.657534247 0.679452055 0.679452055 0.679452055
[919] 0.679452055 0.705022831 0.737899543 0.737899543 0.737899543 0.503196347
[925] 0.488584475 0.622831050 0.632876712 0.657534247 0.679452055 0.705022831
[931] 0.759817352 0.759817352 0.806392694 0.859360731 0.806392694 0.836529680
[937] 0.859360731 0.859360731 0.859360731 0.896803653 0.902283105 0.927853881
[943] 0.536073059 0.896803653 0.836529680 0.896803653 0.896803653 0.806392694
[949] 0.859360731 0.896803653 0.896803653 0.896803653 0.902283105 0.927853881
[955] 0.902283105 0.896803653 0.896803653 0.859360731 0.927853881 0.927853881
[961] 0.927853881 0.927853881 0.927853881 0.958904110 0.958904110 0.958904110
[967] 0.958904110 0.958904110 0.958904110 0.958904110 0.958904110 0.958904110
[973] 0.958904110 0.958904110 0.958904110 0.958904110 0.958904110 0.902283105
[979] 0.896803653 0.896803653 0.896803653 0.896803653 0.896803653 0.896803653
[985] 0.836529680 0.786301370 0.657534247 0.679452055 0.689497717 0.622831050
[991] 0.415525114 0.689497717 0.786301370 0.759817352 0.592694064 0.028310502
[997] 0.075799087 0.536073059 0.705022831 0.737899543 0.737899543 0.759817352
[1003] 0.786301370 0.836529680 0.859360731 0.902283105 0.902283105 0.836529680
[1009] 0.836529680 0.859360731 0.896803653 0.896803653 0.896803653 0.896803653
[1015] 0.896803653 0.896803653 0.896803653 0.896803653 0.896803653 0.896803653
[1021] 0.859360731 0.859360731 0.859360731 0.859360731 0.859360731 0.859360731
[1027] 0.859360731 0.859360731 0.859360731 0.859360731 0.859360731 0.859360731
[1033] 0.859360731 0.896803653 0.896803653 0.859360731 0.859360731 0.806392694
[1039] 0.786301370 0.705022831 0.705022831 0.759817352 0.759817352 0.759817352
[1045] 0.679452055 0.328767123 0.599086758 0.579908676 0.011872146 0.091324201
[1051] 0.314155251 0.344292237 0.314155251 0.378082192 0.446575342 0.517808219
[1057] 0.517808219 0.527853881 0.527853881 0.517808219 0.517808219 0.527853881
[1063] 0.527853881 0.527853881 0.536073059 0.517808219 0.086757991 0.333333333
[1069] 0.231963470 0.314155251 0.386301370 0.364383562 0.406392694 0.406392694
[1075] 0.397260274 0.378082192 0.378082192 0.397260274 0.397260274 0.406392694
[1081] 0.422831050 0.422831050 0.415525114 0.397260274 0.397260274 0.446575342
[1087] 0.488584475 0.517808219 0.517808219 0.517808219 0.517808219 0.517808219
[1093] 0.517808219 0.527853881 0.517808219
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