ESP Trace Analysis Interface - Making Selections and Interpreting Results
The ESP Trace Analysis interface provides tremendous flexibility in deriving products
and information from the available ensemble streamflow traces. It is very important that the selections
and information be well understood, as potential for misinterpretation can be quite high. A very general
overview of the ESP process is provided in General Ensemble Theory for
Streamflow Forecasts. Please also see ESP - A Few Words of Caution to review
the current limitations of ESP as implemented at the CNRFC.
The user interface allows for custom product and information generation based on the
following selections:
Select an ESP Trace Location
Select an Accumulation Type
Select an Interval
Select a Distribution Type
Select a Starting Date
Select an Ending Date
Select a Plot Option and Generate
Select a Table Option and Generate
Users are encouraged to thoroughly review this document as well as other ESP
documents available on this website. If you would like interpretative assistance, please send an
email to the CNRFC webmaster or call us at the number provided at the bottom of every page.
Select an ESP Trace Location
Ensemble streamflow prediction can only be performed at specific locations. These are
usually streamflow gaging stations were stages and flow observations are available. It should be noted
that unless otherwise indicated, the flows for the location you select will be “full natural
flow”. That is the streamflow that would have occurred without upstream water management (reservoir
regulation, diversions, etc.).
Select an Accumulation Type
and
Select an Interval
These two selections really need to be addressed together because they are related. The accumulation type refers to how the data will be treated during the interval.
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Mean |
Day |
Mean daily flow for each day in the analysis period |
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Week |
Mean weekly flow for each 7-day period, starting with the first day of the analysis period |
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Month |
Mean monthly flow for each calendar month fully contained within the analysis period |
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Entire Period |
Mean flow for the full analysis period |
Minimum |
Day |
Same results as Mean-Day because the data are mean daily flows |
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Week |
Minimum daily flow for each 7-day period, starting with the first day of the analysis period |
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Month |
Minimum daily flow for each calendar month fully contained within the analysis period |
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Entire Period |
Minimum daily flow for the full analysis period |
Maximum |
Day |
Same results as Mean-Day because the data are mean daily flows |
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Week |
Maximum daily flow for each 7-day period, starting with the first day of the analysis period |
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Month |
Maximum daily flow for each calendar month fully contained within the analysis period |
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Entire Period |
Maximum daily flow for the full analysis period |
Summation |
Day |
Same results as Mean-Day because the data are mean daily flows |
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Week |
Weekly volume for each 7-day period, starting with the first day of the analysis period |
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Month |
Monthly flow volume for each calendar month fully contained within the analysis period |
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Entire Period |
Total flow volume for the full analysis period |
Select a Distribution Type
Your choices here are (1) Empirical and (2) Wakeby. The distribution selection is used to fit or describe the relationship between probability and forecast magnitude. Choosing a distribution that fits the data very poorly can lead to inaccurate estimates of probability. Fortunately, the two options provided should fit the data reasonably well, however, they will be different. Which is better? That's up to you and your analysis of the fit and application.
The "Empirical" is a simple recurrence interval distribution = (n+1)/m, where n=number of years and m=rank of the event being considered. This is the easiest distribution to calculate and a good choice if you're not sure what to choose. Probabilities are interpolated between the fixed points of your data.
The "Wakeby" distribution is a theoretical nonlinear function that does a pretty good job of describing probability - magnitude relationships for hydrologic variables. It is particularly good when one is assessing streamflow volumes over periods of weeks to seasons. The CNRFC uses the Wakeby distribution for all of its probablistic volume forecasts. This distribution takes longer to estimate, so you may see a slight delay in the generation of your selected product.
Regardless of your choice, it is always a good idea to assess the fit of your selected distribution. You can do that by clicking on the Exceedance Plot (7a). This plot shows forecast magnitude on the y-axis and probability on the x-axis. Probability products will be generated by the line and not the points. If the line fits the points well, the inferred probabilities should be fine. If they fit poorly, the inferred probabilities may be suspect. With a little experience you should develop a sense of which distribution you prefer for each type of analysis you typically select.
Select a Starting Date
Select the beginning date for your analysis period of interest. The system will not
allow you to select a date in the past. If you select a starting date that is not contained within the
currently available traces, you will be provided with an error message that indicates what dates are
available in the current traces.
Select an Ending Date
Select the ending date for your analysis period of interest. If you select an
ending date that is beyond what is available in the currently available traces, you will be provided
with an error message that indicates what dates are available in the current traces. Selecting the
last day of the currently available traces will result in an error because the traces end at midnight
on that day and no mean daily value is available.
Select a Plot Option and Generate
These options allow the user to generate a graphical plot. The content of the plot depends on the previous selections made in steps 1-5. The plot options are Trace, Probability, Expected Value, and Exceedence.
Plot Options - Trace
Traces will show the streamflow time series for each calibration year over the selected analysis period. Data will be aggregated for the interval selected. For example, if you selectMean andDay, you will get the mean daily flows each day of the analysis period.
If you selectMean andWeek, then you will get the mean daily flows for 7-day periods beginning on the date selected.
If you selectMinimum andWeek, you’ll get the minimum daily flow within each 7-day period beginning on the day selected. The same thing can be done for Maximum.
If you selectSummation andWeek, you’ll get the volume for the 7-day periods beginning on the day selected. Note that the traces look just like the Mean – Week example, but the scale is ~14 times higher. That makes sense because the former is a mean daily and the later is a summation of 7 mean daily flows multiplied by 1.9835 to convert cfs-days to ac-ft.
Plot Options - Probability
Probability plots allow you to display the statistical probability distribution of
the traces shown above. Instead of showing the individual time series, the time series are collected,
analyzed, and fit with a distribution. From this distribution, ranges of exceedance probabilities are
sampled and displayed. Currently, the CNRFC is fitting a Log-Normal distribution for all analysis on
this website. Further refinement of this may be appropriate in the future.
Users are advised to consider these probabilities as estimates as they do not
represent the uncertainty associated with model errors and current model states. The uncertainty
exhibited by the traces is strictly a function of the uncertainty associated with future weather
and climate. For long-range seasonal volumes, the uncertainty associated with future weather and
climate is so great that the model and model state errors are normally dwarfed. For nearer term
forecast horizons (weeks), the uncertainly associated model and model states may be significant
leading to a higher level of confidence than is appropriate. Work is currently underway to more
appropriately address and include all significant sources of uncertainty.
If you selectMean andDay, you will get the probability distribution for each day in 5 colored regions. The colored regions show the range of exceedance probability which can be resolved by date and flow level. From below, there is a ~90% chance that the flow will exceed ~275cfs on July 1. Note that if you selected Maximum or Minimum, the result would be exactly the same because the fundamental data are mean daily flows. (The mean, maximum and minimum are all the same for an individual day because there's only one value, the mean.)
If you selectMean andWeek, you'll get the probability distribution for each 7-day period, starting on the beginning date in 5 colored regions. The colored regions show the range of exceedance probability which can be resolved by date and flow level. From below, there is a ~90% chance that the average flow during the week starting on 6/29 will exceed ~260cfs.
Now here’s where you can make things interesting.
If you select Maximum andWeek, you’ll get the probability distribution
for maximum mean daily discharge within each 7-day period starting on the beginning date. The colored
regions show the range of exceedance probability which can be resolved by date and flow level. From
below, there is a ~10% chance that the maximum mean daily flow for the week starting on 7/14 will
exceed ~410cfs. You can do the same thing for Minimum and get a similar plot.
If you selectMaximum andEntire Period, you’ll get the probability
distribution for maximum mean daily discharge for the entire period selected. Since the maximum flow is allowed
to take place on any day, it is naturally higher. The colored regions show the range of exceedance probability
by and flow level. Again, there are not dates, because this is for the entire period. From below, there is a
~25% chance that the maximum mean daily flow will exceed ~800 cfs sometime during the selected period. Here
the Mean, Maximum, and Minimum have very different meanings.
Summation products simply add up the mean daily flows for the interval you’ve selected.
If you selectSummation andWeek, you’ll get the
probability distribution of weekly flow volumes for each 7-day period starting with the beginning date. The
colored regions show the range of exceedance probability which can be resolved by date and flow level. From
below, there is a ~50% chance that the flow volume for the week beginning on 6/16 will exceed ~6700 ac-ft.
If you selectSummation andEntire Period, you’ll get
the probability distribution of total volume for the period selected. The colored regions show the
range of exceedance probability by flow level. From below, there is a ~50% chance that the flow volume
for the selected period will exceed ~30,600 ac-ft.
Okay, let's customize this a bit. Let's say you are interested in the probability distribution of low flows during the last half of August.
SelectMinimumEntire PeriodEmpirical. Inand , enter the dates of interest (i.e. 8/15 through 8/31). Then click onProbability and. From this you could see that there is a ~50 percent chance that the minimum flow during the last half of August will be greater than ~50 cfs.
Plot Options - Expected Value
The expected value plot simply shows the probability information in a different
way. Inferences related to the selection of Mean, Minimum, Maximum, and Summation can be taken from
the examples related to the plots. Aside, from looking different, the most important distinction is
that there is no assumption or fitting of a theoretical probability distribution. Instead, the
distribution mean, standard deviation, and maximum and minimum values are plotted. This is an
informative plot if you’re interested in quickly seeing the ensemble means. It is also helpful
if you’re interested in the extreme values present in the data set. Extreme values may influence,
but are not explicitly shown on the probability plots.
If you selectMean andDay, you’ll get something like this:
The daily plot is a bit busy, it's easier to see what's going on if you selectMean andWeek.
Plot Options - Exceedence
This display option plots the exceedance probability (%) against the log of flow.
Since the CNRFC is currently using a Log-Normal distribution, this will plot will always show a
straight line. The plotted points, however, may not fall right on the line. The degree to which the
fitted distribution fits the data values affects the degree of confidence one should place on the
probability estimates. When generating probability plots or tables, its always a good idea to check
the exceedance plot to make sure that the assumed distribution is a reasonable fit. Inferences related
to the selection of the Accumulation Type and the Interval can be taken from the section on
Probability.
If you select Mean andEntire Period, you will get something like this:
This is a good fit, but it certainly isn't perfect. Above the 10% exceedence level, one might expect this fitted distribution to slightly underestimate the flows.
Select a Table Option and Generate
This selection option allows the user to generate a table instead of plots. Often, it is difficult to read specific numbers off of a plot. The tables make this easier to read. Inferences related to the selection of the Accumulation Type and Interval can be taken from the section on Probability.
If you select Mean and Week, you'll get a table like this:
# ESP Forecast Information
#
# Analysis Period: 6/16/2005 24 - 9/1/2005 24 (PST)
# Forecast Parameters: River Flow (Mean) - (CFSD)
#
# Forecast Interval: 1 Week
# Forecast Point: W F CARSON-WOODFORDS
#
# W F CARSON-WOODFORDS 0.90 0.75 0.50 0.25 0.10 Units
# --------------------------------------------------------------------------------------------------------
06/16/2005 - 06/23/2005 410.74 443.72 483.43 526.70 569.00 (CFSD)
06/23/2005 - 06/30/2005 324.29 361.84 408.62 461.46 514.90 (CFSD)
06/30/2005 - 07/07/2005 249.89 279.88 317.40 359.94 403.15 (CFSD)
07/07/2005 - 07/14/2005 190.36 217.50 252.17 292.36 334.04 (CFSD)
07/14/2005 - 07/21/2005 133.44 158.23 191.16 230.94 273.84 (CFSD)
07/21/2005 - 07/28/2005 92.73 110.74 134.85 164.21 196.11 (CFSD)
07/28/2005 - 08/04/2005 78.02 87.90 100.34 114.54 129.04 (CFSD)
08/04/2005 - 08/11/2005 59.42 69.98 83.90 100.59 118.46 (CFSD)
08/11/2005 - 08/18/2005 44.21 56.47 74.11 97.26 124.26 (CFSD)
08/18/2005 - 08/25/2005 45.93 52.99 62.10 72.78 83.96 (CFSD)
08/25/2005 - 09/01/2005 45.47 49.18 53.66 58.54 63.32 (CFSD)
From this you can find the flow rates associated with each probability level and each weekly period.
You can do the same sort of table generation for any combination of Accumulation Type and Interval. For example, if you wanted to review the accumulation volume (Summation) for the (Entire Period), with a (Wakeby) distribution,June 16 throughAugust 31, you could get:
# ESP Forecast Information
#
# Analysis Period: 6/16/2005 24 - 8/31/2005 24 (PST)
# Forecast Parameters: River Flow (Sum) - (CFSD)
#
# Forecast Interval: Forecast Window
# Forecast Point: W F CARSON-WOODFORDS
#
# W F CARSON-WOODFORDS 0.90 0.75 0.50 0.25 0.10 Units
# --------------------------------------------------------------------------------------------------------
06/16/2005 - 08/31/2005 13551.85 14419.83 15448.25 16550.03 17610.04 (CFSD)
Note that the units are cfs-days (CFSD). To convert to acre-feet, multiply by 1.9835.
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