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USGS-R / rloadest

USGS water science R functions for LOAD ESTimation of constituents in rivers and streams.
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Question about R-LOADEST confidence intervals #20

Open jmusgs opened 7 years ago

jmusgs commented 7 years ago

I have been recently using R-LOADEST to estimate loads at the Connecticut River- in a tidal part of the river where we have an Acoustic Doppler Side Looker that computes our discharge.

Most of the loading work I am doing is based on using measurements of uv-nitrate, and turbidity to predict total nitrogen. We have periods of missing record, and I have been using RLOADEST to backfill the holes in the data, for daily LOADS.

In order to do this, I ran LOADEST for the entire period. I was able to make predictions for daily load, as well as annual load. I am confused however as to how the confidence intervals are calculated for annual load estimates, as they seem to be much smaller than the confidence intervals from the daily load estimates- which makes sense.

I had always assumed that the annual numbers were based on some average of the daily estimates, but I realize I am not correct.

Wondering if you have any thoughts on this? I have used LOADEST for many years, but never worked much with the daily outputs.

See the difference in confidence intervals below. I guess I am interested in how the annual confidence intervals are calculated.

Thanks for any thoughts,

See below

Output from the annual water year LOADEST model

WARNING: The minimum estimation data set steamflow exceeds the minimum calibration data set streamflow. Load estimates require extrapolation.

Constituent Output File Part IIb: Estimation (Load Estimates) Load Estimates for 2008-12-06 to 2014-09-30

Flux Estimates, in metric tons/d, using AMLE

Period Ndays Flux Std.Err SEP L95 U95 1 WY 2009 299 NA NA NA NA NA 2 WY 2010 365 35.79537 0.8031539 0.9129524 34.03918 37.61769 3 WY 2011 365 52.60603 0.9648709 1.1402695 50.40633 54.87595 4 WY 2012 366 37.88657 0.6920841 0.8021472 36.33856 39.48282 5 WY 2013 365 38.72842 0.5725083 0.7078853 37.35939 40.13420 6 WY 2014 365 33.78798 0.7151103 0.8206135 32.20798 35.42458

In this version, I summarized the results from the daily output, taking the mean of the daily loads and the daily confidence intervals by water year.

Statistics on daily output from the same LOADEST model. waterYear mean meanL95 meanU95 sum sumL95 sumU95 NObs 1 2009 38.31362 26.50062 53.64662 11455.77 7923.686 16040.34 299 2 2010 35.79537 24.85938 49.95111 13065.31 9073.675 18232.15 365 3 2011 52.60603 36.56946 73.35049 19201.20 13347.852 26772.93 365 4 2012 37.88657 26.35149 52.80251 13866.48 9644.645 19325.72 366 5 2013 38.72842 26.96705 53.92551 14135.87 9842.974 19682.81 365 6 2014 33.78798 23.48650 47.11421 12332.61 8572.571 17196.69 365

DLLORENZ commented 5 years ago

The standard errors and SEPs for any period longer than a day, which requires summing the estimates, are computed by summing the variances and covariances of each day-to-day estimate. The square root of that sum is taken for the SE and SEP.