National Weather Service California Nevada River Forecast Center Department of Commerce National Oceanic and Atmospheric Administration National Weather Service

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.

 
Mean Day Mean daily flow for each day in the analysis period
  Week Mean weekly flow for each 7-day period, starting with the first day of the analysis period
  Month Mean monthly flow for each calendar month fully contained within the analysis period
  Entire Period Mean flow for the full analysis period
Minimum Day Same results as Mean-Day because the data are mean daily flows
  Week Minimum daily flow for each 7-day period, starting with the first day of the analysis period
  Month Minimum daily flow for each calendar month fully contained within the analysis period
  Entire Period Minimum daily flow for the full analysis period
Maximum Day Same results as Mean-Day because the data are mean daily flows
  Week Maximum daily flow for each 7-day period, starting with the first day of the analysis period
  Month Maximum daily flow for each calendar month fully contained within the analysis period
  Entire Period Maximum daily flow for the full analysis period
Summation Day Same results as Mean-Day because the data are mean daily flows
  Week Weekly volume for each 7-day period, starting with the first day of the analysis period
  Month Monthly flow volume for each calendar month fully contained within the analysis period
  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 select Mean and Day, you will get the mean daily flows each day of the analysis period.

Mean Daily Flow for West Fork Carson River at Woodfords

If you select Mean and Week, then you will get the mean daily flows for 7-day periods beginning on the date selected.

Mean Weekly Flow for West Fork Carson River at Woodfords

If you select Minimum and Week, 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.

Minimum Weekly Flow for West Fork Carson River at Woodfords

If you select Summation and Week, 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.

Summation of Weekly Flow for West Fork Carson River at Woodfords


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 select Mean and Day, 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.)

Mean Daily Probability Distribution for West Fork Carson River at Woodfords

If you select Mean and Week, 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.

Mean Weekly Probability Distribution for West Fork Carson River at Woodfords

Now here’s where you can make things interesting.

If you select  Maximum and Week, 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.

Maximum Weekly Probability Distribution for West Fork Carson River at Woodfords

If you select Maximum and Entire 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.

Maximum Entire Period Probability Distribution for West Fork Carson River at Woodfords

Summation products simply add up the mean daily flows for the interval you’ve selected.

If you select Summation and Week, 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.

Weekly Summation Probability Distribution for West Fork Carson River at Woodfords

If you select Summation and Entire 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.

Summation Entire Period Probability Distribution for West Fork Carson River at Woodfords

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.

Select Minimum Entire Period Empirical. In and , enter the dates of interest (i.e. 8/15 through 8/31). Then click on Probability and Generate a Plot button sample. 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.

Minimum Entire Period Probability Distribution for West Fork Carson River at Woodfords


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 select Mean and Day, you’ll get something like this:

ESP Mean Daily Expected Value for West Fork Carson River at Woodfords

The daily plot is a bit busy, it's easier to see what's going on if you select Mean and Week.

Mean Weekly Expected Value for West Fork Carson River at Woodfords


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 and Entire Period, you will get something like this:

Mean Exceedence Probability for West Fork Carson River at Woodfords

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.