1.0 Introduction

Hydrologic events, such as floods and droughts, are among the highest impact phenomena in the United States and around the world. Reducing their impact is an important goal of NOAA’s National Weather Service. A necessary step in supporting weather readiness and decision making is to provide forecasts that include explicit estimates of the forecast uncertainties. This information enables users to perform risk assessments and take actions appropriate for their vulnerability.

In this lesson, we will introduce the Hydrologic Ensemble Forecast Service (HEFS). Before we get to the specifics of the HEFS, we will examine some basics of hydrologic ensemble forecasting that underlie it.

After completing this lesson, you should be able to:

1. Describe the need for ensemble forecast information in hydrology
2. Compare and contrast the ensemble forecasts to single-valued forecasts
3. Illustrate how an ensemble forecast is used to build probabilistic guidance
4. Describe the major sources of uncertainty in HEFS (forcing vs hydro model)
5. Identify the main functions for different components of the HEFS
6. Describe the advantages of the HEFS over ESP
7. Interpret HEFS products

2.0 Ensemble Forecasts in Hydrology

2.0 Ensemble Forecasts in Hydrology » 2.1 Single-valued vs. Ensemble Forecasts

An ensemble forecast is, effectively, a collection of single-valued forecasts of the same variable at the same locations and times. For example, a single-valued forecast from a particular model may show the expected evolution of river stage at a specified point. If we run the model multiple times, each with slightly different inputs (such as precipitation or soil moisture states), we will have an ensemble forecast of river stage for that location and time period. An ensemble can also be created using the same inputs from multiple models. Each single-valued forecast is an ensemble member.

2.0 Ensemble Forecasts in Hydrology » 2.2 Flood Risk Example

Probabilistic guidance can be generated from an ensemble forecast to assist forecasters and end users with visualizing the range of possible outcomes and their associated probabilities.

This HEFS graphic provides probability guidance for the same time period and initialization time as the single-valued forecast above.

2.0 Ensemble Forecasts in Hydrology » 2.3 Need for Uncertainty Information

Forecasters know that there is uncertainty in single-valued forecasts. But since a single-valued forecast cannot quantify the uncertainty, forecasters are not able to communicate it to decision makers in a way that lets them mitigate against risk.

In contrast, an ensemble forecast provides multiple, equally likely predictions that can be used to explicitly quantify the probability of a future event, such as flooding, for which some mitigating action is needed. Probability guidance derived from ensemble forecasts can provide more actionable information to users with decision-making responsibility.

Note that the single-valued operational forecast uses only short-term quantitative precipitation forecasts (QPF), perhaps only 24 hours, while the HEFS does not curtail the forecast precipitation. Click the tabs to see the impact on the hydrologic forecasts.

Ensemble forecasts have become a valuable tool in weather and hydrologic forecasting due to the recognition that single-valued or “deterministic” forecasts do not provide essential decision-making guidance about forecast uncertainty. As stated in a 2006 report from the National Research Council, “uncertainty is thus a fundamental characteristic of weather, seasonal climate, and hydrological prediction, and no forecast is complete without a description of its uncertainty.”

As of this writing (early 2017), the HEFS only has a limited number of displays in operation.The number of HEFS guidance products is expected to increase as implementation continues and more user feedback is collected. This lesson provides a good foundation from which forecasters can make the best use of ensemble forecast information.

3.0 Developing Products from Hydrologic Ensembles

3.0 Developing Products from Hydrologic Ensembles » 3.1 Multiple Single-valued Forecasts

Consider this single-valued forecast hydrograph for a 10-day period. The peak stage reaches well above moderate flood stage during the first 48 hours of the forecast period. Making the most effective use of this forecast requires some ability to quantify that uncertainty.

Here are the 48 single-valued forecasts that make up the ensemble for that location and 10-day period. They are displayed in an “ensemble traces” plot, sometimes called a “spaghetti plot.” Note the differences in timing and magnitude associated with the peak stage and rate of change. In addition, some members show high stage occurring after the first 48 hours.

3.0 Developing Products from Hydrologic Ensembles » 3.2 Box Plots

A box and whiskers plot, sometimes called simply “box plots,” helps us visualize how we get probability guidance from an ensemble of single-valued forecasts. Consider this simplified example of an ensemble with seven members, each shown with a different color and line style.

We will develop a box plot for a specific time that shows the following: 1) median member, 2) middle three members, 3) middle five members, and 4) two outliers.

Click on the rectangle for Time 1. In the pop-up window, move the lines for the ensemble members on the left so their positions match their order in the line graph on the right. For example, the median ensemble member should be in the middle of the box. Note that the box part of the box plot represents the middle three ensemble members, including the median. The whiskers capture the middle five members, and the high and low outliers account for all seven members.

Now do the same thing for Time 2. Click the rectangle, then arrange the lines for the ensemble members (right) so they match their order in the line graph in the box plot (left). You'll be matching the median and middle three members, the second highest and lowest members, and the high and low outliers.

For the remainder of this lesson, we will use examples from the HEFS with a large number of ensemble members. As shown above, the box in the box plots represents the middle 50%, and the middle 90% falls within the whiskers.

The lowest whisker is at the 95% exceedance probability, meaning that fewer than 5% of the members are at or below this level. The highest whisker is at the 5% exceedance probability, which means that only 5% of members have values above this level. The bottom and top of the box are the 75% and 25% exceedance probabilities. The line near the middle, the median, is the 50% exceedance probability.

3.0 Developing Products from Hydrologic Ensembles » 3.3 Box Plot Example

Here is the box plot representation of the ensemble traces that we studied earlier. Click the tabs to see the actual ensemble traces. Recall that earlier, you outlined the middle 50% of the ensemble members—that’s what the box portion of the box plot represents. Beyond Day 4, when most ensemble members are near 0, only the highest members show up in the whiskers portion of the plot.

3.0 Developing Products from Hydrologic Ensembles » 3.4 Probabilistic Guidance

The information in the box and whiskers plot can be presented in a time series graphic of stage (or discharge), like the one shown in the first tab. We’ll look at how this kind of HEFS probabilistic guidance is constructed and how to interpret it.

The blue shading in the time series shows the middle 50% of possible outcomes according to the ensemble, which is depicted by the box portion of the box plot (tab 2). The dark blue horizontal line is the median. The probability that the outcome will be above the blue shading is <25%. Likewise, the chance of it being below the blue shading is ≤25%. Therefore, the blue shading depicts the probability of exceedance from 75% to 25%.

The medium shade of blue enveloping the darker blue shading represents the middle 80% of possible outcomes according to the ensemble. This interval represents exceedance probabilities ranging from 90% (bottom) to 10% (top).

Finally, the light shade enveloping the medium and dark blue shading represents the middle 90% of possible outcomes according to the ensemble. This interval represents exceedance probabilities ranging from 95% (bottom) to 5% (top), and is consistent with the whiskers on the box plot.

4.0 The Hydrologic Ensemble Forecast Service (HEFS)

4.0 The Hydrologic Ensemble Forecast Service (HEFS) » 4.1 The HEFS Design

The flowchart shows the design of the HEFS. The HEFS utilizes the same hydrologic models that NOAA/NWS River Forecast Centers (RFCs) use to produce their operational single-valued forecasts. These hydrologic models are embedded within the Community Hydrologic Prediction System (CHPS). For a detailed discussion of this design, access the following sites.

The left side of the flowchart shows the time resolution of the input forcing data. The HEFS provides forecasts for a range of forecast time horizons from hours and days to weeks and months. The HEFS is designed to merge the forcings from different time horizons and produce seamless hydrologic forecast products.

The MEFP (meteorological ensemble forecast processor) and EnsPost (Ensemble Post-processor) boxes represent the HEFS functions that quantify uncertainty. In broad terms, hydrologic forecasts deal with two kinds of uncertainty: the uncertainty associated with the meteorological forcing, and the uncertainty associated with the hydrologic response. Both can have biases. The HEFS quantifies the composite uncertainty associated with the meteorological forcing and hydrologic response, while reducing biases.

The Ensemble Verification Service (EVS) is used to verify predictions from the HEFS. The EVS will help with the long term improvement of the HEFS products.

4.0 The Hydrologic Ensemble Forecast Service (HEFS) » 4.2 Meteorological Forcing Uncertainty

The Meteorological Ensemble Forcing Processor (MEFP) is designed to construct calibrated ensemble meteorological forecast forcings. This includes correcting for biases, merging time periods (i.e. forecasts that operate on different time horizons), and downscaling (i.e. to the hydrologic basin scale).

Meteorological inputs can be a major source of error in the hydrologic forecasts as we see in these QPF ensembles from the Global Ensemble Forecast System (GEFS).

Here is the 7-day quantitative precipitation forecast from the Global Ensemble Forecast System (GEFS) for the 21 ensemble members.

We can also view the GEFS QPF data as a cumulative value over the 7-day period. For the 21 ensemble members, the middle 40% are highlighted in orange, and the black line indicates the median for each time step. The spread in the cumulative outcomes, and thus the forecast uncertainty, clearly increases with lead time.

4.0 The Hydrologic Ensemble Forecast Service (HEFS) » 4.3 Hydrologic Modeling Uncertainty

Just as the MEFP helps account for uncertainty with meteorological forcing inputs, the Ensemble Post-processes (EnsPost) quantifies the overall uncertainties in the hydrologic response and corrects for biases in streamflow forecasts.

Use the slider to compare the case without the EnsPost applied (first graphic) with the same data after EnsPost has been applied (second graphic).

We can create plots of the HEFS Probabilistic Guidance from the ensemble traces, like the ones above. Note how the plots change when EnsPost functionality is used, particularly the higher discharge and stages associated with the 5% and 10% exceedance probabilities. By increasing the ensemble spread, the EnsPost is indicating that the hydrologic modeling introduces uncertainty. It is important to capture this uncertainty or a decision maker may incorrectly assume that a particular outcome, such as flooding, is highly unlikely.

EnsPost may not be included in early implementations of the HEFS. Users of the HEFS should check with their RFC about whether EnsPost is included if it’s not clear from the product label.

4.0 The Hydrologic Ensemble Forecast Service (HEFS) » 4.4 The HEFS Compared to Previous Guidance

Goal: Improve NWS Hydrologic Services
Feature	EPS (Old Service)	HEFS (New Service)
Forecast Time Horizon	Weeks to seasons	Hours to years, depending on the input forecasts
Input Forecasting (“Forcing”)	Historical climate data (i.e. weather observations) with some variations between RFCs	Short-, medium-, and long-range weather forecasts
Uncertainty Modeling	Climate-based; no accounting for hydrologic uncertainty or bias; suitable for long-range forecasting only	Captures uncertainty from multiple sources and corrects for biases in forcing and flow at all forecast lead times
Products	Limited number of graphical products (focused on long-range) and verification	A wide array of data and user-tailored products are planned, including standard verification

Until recently, NWS ensemble streamflow forecasts within NOAA’s Advanced Hydrologic PredictionService (AHPS) were produced exclusively with the Ensemble Streamflow Prediction (ESP) system. The HEFS offers advances in ensemble forecasting that were lacking in ESP, such as:

• Use of short, medium, and long-range NWP model forecasts, such as QPF
• More comprehensive accounting for uncertainty from both the meteorological forcing and the hydrologic modeling
• More products, including verification and user-tailored products

4.0 The Hydrologic Ensemble Forecast Service (HEFS) » 4.5 An Evolving Forecast Service

Currently (as of early 2017), not all HEFS functions have been fully evaluated and implemented in operations. For example, the Climate Forecasts (CFSv2) ingest and the EnsPost step for handling hydrologic model uncertainty will be evaluated at a later stage. The flowchart represents the full functionality that the HEFS will achieve after phased upgrades and enhancements.

For the HEFS Examples section, we will focus mainly on a 10-day HEFS time series forecast like this one. Examples do not have EnsPost processing unless otherwise indicated.

5.0 HEFS Examples

5.0 HEFS Examples » 5.1 HEFS vs. Single-value Operational

Let’s return to the standard 10-day forecast time series from the HEFS for the Little River case in Tecumseh, Oklahoma. The overlays show the single-value (deterministic) operational forecast in black, and the observations in green.

5.0 HEFS Examples » 5.2 Focusing on Specific Thresholds

Probabilistic guidance is often used to asses the risk of certain high or low thresholds. In this graphic, the labels for different flood severity levels have been superimposed on the HEFS probabilistic time series. Although the HEFS does not currently have official tabular products, the HEFS information can be used to generate probabilities of reaching or exceeding important thresholds.

Stage	Action (2.4m, 7.9ft)	Flood (3.4m,11.1ft)	Major Flood (5.1m, 17.0ft)
Probability	40%	25%	3%

The table shows the probabilities of reaching Action, Flood, or Major Flood stage during the 10-day forecast period. Tabular information could also be generated with more time resolution rather than cumulative over the forecast period.

We showed this dataset earlier with the HEFS EnsPost functionality that identifies uncertainty associated with the hydrologic model and adds appropriate spread to the forecast. Here are the values for those cumulative probabilities.

Stage	Action (2.4m, 7.9ft)	Flood (3.4m,11.1ft)	Major Flood (5.1m, 17.0ft)
Probability	55%	38%	16%

Although major flooding was not observed, nearby basins did experience major flooding. Users who are sensitive to such high water can benefit from guidance when small chances of such an event is possible.

5.0 HEFS Examples » 5.3 Time Evolution of the HEFS Guidance

Here’s the HEFS probabilistic guidance compared with the operational single-valued forecast time series for a different basin (Illinois River at Tahlequah, Oklahoma) for the same 26 December 2015 storm event. The overlays show the single-value (deterministic) operational forecast in black, and the observations in green.

6.0 Summary

Displays and guidance from the HEFS offer several advantages to operational forecasters and users of flow and stage forecasts due to the ability to express uncertainty, correct for biases, and provide probabilistic guidance across a range of conditions. In addition, the HEFS can give greater lead times for potential events than previous NWS hydrologic forecast systems because it uses QPF inputs across a range of time steps, while accounting for the uncertainties in those inputs.

Products and forecast displays from the HEFS will continue to evolve after the publication of this lesson. The full set of HEFS products will do the following:

• Provide seamless hydrologic forecast guidance from hours to years
• Use QPF input across multiple time scales
• Provide longer lead-time time evolution of major hydrologic events
• Quantify the combined uncertainty from both meteorological forcing and hydrologic modeling while correcting for biases
• Allow decision making about possible outcomes based on probabilistic guidance
• Evolve to include a wide array of user-tailored products, including standard verification

7.0 Contributors