Introduction

Version 2.1 of the Hydrologic Engineering Center Flood Damage Reduced Analysis Software is released. This version supersedes previous versions.

Changes and Resolved Issues

Issue	Description
Graphical Frequency Uncertainty Incorrect	For unique situations, the graphical frequency uncertainty algorithm was ineffective at modeling good sampled frequency curves. Sampled frequency curves are forced to be monotonic with a new a bidirectional monotonicity forcing procedure that forces monotonicity of sampled graphical frequency curves from the bottom (most frequent) coordinate up for sampled curves below the median, and forces monotonicity from the top (least frequent) coordinate down for sampled curves above the median. This approach respects the highest quantile of the uncertainty about the least frequent coordinate as the maximum of the entire function with uncertainty, and respects the lowest quality of uncertainty about the most frequency coordinate as the minimum of the entire function with uncertainty. The order of operations for the computation of uncertainty about a graphical frequency function has changed. Input frequency functions are first interpolated, then extrapolated, and then the standard deviations of uncertainty are calculated. This order of steps better respects the way that local slope behavior influences local uncertainty. Graphical Frequency UI now updated to accurately communicate the processed data used in the compute.
Geospatial	Shapefile reading is now more robust to out-of-spec shapefiles. Previously, out-of-spec shapefiles often showed up as incorrect decimal values for structure values or "EMPTY" occupancy types. Geospatial libraries have been updated to latest published RAS-2025 packages. This is largely invisible to users, but as HEC-FDA continues to mature, this will lead us to greater stability, better error messaging, and sets us up for future feature development.
UI Bug Fixes	Projections are no longer being archived and unset if the user saves properties after the initial specification. Threshold now has a "set" button that ensures user input is saved. Previous behavior utilized an inefficient workflow, only saving threshold input after focus left the textbox. Alternative computes have improved reporting of issues the software finds while computing equivalent annual damage. Previous behavior would throw an exception when doing a batch compute with an invalid alternative definition. The software now displays more information about the error. The capability for copying data out of a FDA for paste into Excel is repaired.
Histograms	The approach for calculating the mean of an aggregate histogram (empirical distribution) is improved. Histograms aggregate results for expected annual damage (EAD), equivalent annual damage (EqAD), expected annual life loss (EALL) across many different possible dimensions. That aggregation now consistently tracks the mean of the sampled data, rather than calculating it from the distribution itself. For many studies the change will be negligible, but can be significant for studies with heavily skewed EAD distributions (such as those with tall, fail proof levees). This behavior is consistent with prior behavior for all metrics except mean EqAD.
Life Safety Risk	HEC-FDA now computes expected annual life loss using aggregated stage-life loss functions in combination with the study hazard and performance data. The capability to import consequence results from LifeSim has been added as an aggregated stage-life loss function. Hydraulic modeling matching that which was used in the LifeSim model is required. Index points are required and are used to identify the stages from the hydraulic model for each frequency in the consequences model.

Differences in Results

Several case studies were evaluated to compare differences in results produced by Versions 1.4.3, 2.0.1, and 2.1. In this section, we look at differences in the uncertainty about graphical frequency functions and then look at the resulting differences in mean expected annual damage.

The purpose of this page is to describe the validation and verification (V&V) testing undertaken by HEC staff to ensure proper functioning of the HEC-FDA Version 2.1 (beta) software and to compare and explain results where they differ from the previous release, HEC-FDA Version 2.0.2.

Case Study Models

For this effort, nine case study models were utilized for V&V testing consistent with previous version releases. A base year, without-project condition was modeled for each case study and results were recorded for Version 2.0.2 and Version 2.1 to compare expected annual damage (EAD) and performance results. These models were also utilized to ensure functional forward migration of studies.

Additional modeling was conducted and recorded for Version 2.1 for future and with-project conditions. These results were utilized to confirm equivalent annual damage (EqAD) results against an independent spreadsheet model, confirm damages reduced calculations, ensure proper functioning of with-project inputs, and to ensure general proper functioning of the standard user interface (UI).

The table below describes the input components of each model.

Model	Hydraulic Data Type	Terrain Data Type	Ground Elevations Source	Frequency Function
Glendive	Gridded	N/A	Inventory	Stage-Only
Greenbrook	Unsteady	N/A	Inventory	Stage-Only
London Orleans	Gridded	N/A	Inventory	Stage-Only
Muncie	Gridded	HDF	Terrain	Analytical Flow
North DeSoto	Gridded	N/A	Inventory	Stage-Only
River Des Peres	Gridded	TIF	Terrain	Stage-Only
Tafuna	Gridded	TIF	Terrain	Graphical Flow
Watertown	Gridded	TIF	Terrain	Graphical Flow
West Sacramento	Unsteady	N/A	Inventory	Analytical Flow

Case Study Results

Equivalent Annual Damages

Equivalent annual damages (EqAD) results in Version 2.1 were compared to an independent spreadsheet model. Results in Version 2.1 were exactly equal to the results in the spreadsheet model. The spreadsheet model and EqAD results from Version 2.1 are included at the shared drive location listed below.

Performance

Annual exceedance probability (AEP) performance results in Version 2.1 were compared to Version 2.0.2. Results are shown below for the base-year, without-project condition. Note that the case studies that leverage graphical frequency demonstrate some difference in results while the case studies that depend on analytical frequency have nearly identical results between versions. The two largest differences in performance are AEP for Glendive at the 0.04 and mean AEP for Tafuna. Both Glendive and Tafuna case studies have graphical frequency functions that contain frequency shapes that result in moderate changes in results after the update to the graphical frequency algorithm.

More detailed results are available at the shared drive location listed below.

Glendive	Threshold Value	Mean	Median	10	30	50	0.1	0.04	0.02	0.01	0.004	0.002
2.0.2	13.65	0.0349	0.0325	0.2988	0.6552	0.8305	0.9969	0.6293	0.2585	0.1084	0.0298	0.0164
2.1	13.65	0.0351	0.0325	0.3001	0.6572	0.8321	0.9969	0.6495	0.2601	0.1098	0.0299	0.0167
Difference	0	0.0002	0	0.0013	0.002	0.0016	0	0.0202	0.0016	0.0014	1E-04	0.0003

Greenbrook	Threshold Value	Mean	Median	10	30	50	0.1	0.04	0.02	0.01	0.004	0.002
2.0.2	100.11	0.999	0.9991	1	1	1	0	0	0	0	0	0
2.1	100.58	0.999	1	1	1	1	0	0	0	0	0	0
Difference	0.47	0	0.0009	0	0	0	0	0	0	0	0	0

London Orleans	Threshold Value	Mean	Median	10	30	50	0.1	0.04	0.02	0.01	0.004	0.002
2.0.2	5.82	0.1716	0.1728	0.8478	0.9965	0.9999	0.0734	0.02	0.0191	0.0148	0.0027	0.0009
2.1	5.82	0.177178	0.172832	0.8577	0.9971	0.9999	0.075	0.0047	0.0048	0.0047	0.0027	0.0009
Difference	0	0.005578	3.2E-05	0.0099	0.0006	0	0.0016	-0.0153	-0.0143	-0.0101	0	0

Muncie (IA1)	Threshold Value	Mean	Median	10	30	50	0.1	0.04	0.02	0.01	0.004	0.002
2.0.2	945.78	0.0537	0.0496	0.4243	0.8092	0.9367	0.9022	0.3906	0.1663	0.0845	0.0468	0.0338
2.1	945.78	0.0539	0.0497	0.4251	0.81	0.9372	0.9003	0.3879	0.1662	0.0837	0.0443	0.0325
Difference	0	0.0002	0.0001	0.0008	0.0008	0.0005	-0.0019	-0.0027	-0.0001	-0.0008	-0.0025	-0.0013

North DeSoto	Threshold Value	Mean	Median	10	30	50	0.1	0.04	0.02	0.01	0.004	0.002
2.0.2	9.12	0.5418	0.5433	0.9996	1	1	0.0001	0.0001	0.0001	0	0	0
2.1	9.12	0.5447	0.5433	0.9996	1	1	0	0	0	0	0	0
Difference	0	0.0029	0	0	0	0	-0.0001	-0.0001	-0.0001	0	0	0

River Des Peres	Threshold Value	Mean	Median	10	30	50	0.1	0.04	0.02	0.01	0.004	0.002
2.0.2	543.71	0.3191	0.332	0.9786	1	1	0.0077	0	0	0	0	0
2.1	543.71	0.3302	0.332	0.9818	1	1	0.0059	0	0	0	0	0
Difference	0	0.0111	0	0.0032	0	0	-0.0018	0	0	0	0	0

Tafuna	Threshold Value	Mean	Median	10	30	50	0.1	0.04	0.02	0.01	0.004	0.002
2.0.2	42.33	0.4627	0.5119	0.998	1	1	0.0001	0	0	0	0	0
2.1	42.33	0.5338	0.5117	0.9995	1	1	0.0001	0	0	0	0	0
Difference	0	0.0711	-0.0002	0.0015	0	0	0	0	0	0	0	0

Watertown	Threshold Value	Mean	Median	10	30	50	0.1	0.04	0.02	0.01	0.004	0.002
2.0.2	1704.73	0.0378	0.0345	0.3199	0.6855	0.8545	0.9877	0.5846	0.2574	0.0748	0.0304	0.0108
2.1	1704.73	0.0376	0.0345	0.3181	0.6829	0.8526	0.9877	0.5845	0.2577	0.0746	0.0301	0.0107
Difference	0	-0.0002	0	-0.0018	-0.0026	-0.0019	0	-1E-04	0.0003	-0.0002	-0.0003	-0.0001

West Sacramento	Threshold Value	Mean	Median	10	30	50	0.1	0.04	0.02	0.01	0.004	0.002
2.0.2	21.51	0.7174	0.7237	1	1	1	0	0	0	0	0	0
2.1	21.51	0.7174	0.7237	1	1	1	0	0	0	0	0	0
Difference	0	0	0	0	0	0	0	0	0	0	0	0

Expected Annual Damages

Most of the results show negligible change in EAD. Tafuna demonstrates relatively larger change in EAD due to changes in how uncertainty is estimated for graphical flow frequency functions, as with the performance results above.

The table below shows results by case study broken down by damage category and software version. More detailed results are available at the shared drive location listed below.

Study Name	Damage Category	Version 2.0.2 Mean EAD	Version 2.1 Mean EAD	Percent Change
Glendive	RES	$231.28	$225.6	-2.46%
	COM	$1,084.65	$1,067.6	-1.57%
	Total	$1,315.92	$1,293.27	-1.72%
Greenbrook	RES	$50,336.46	$50,135.10	-0.40%
	IND	$12,267.77	$12,199.33	-0.56%
	COM	$14,836.33	$14,747.31	-0.60%
	UTL	$13.59	$13.05	-3.97%
	APT	$16,301.84	$16,340.11	0.23%
	MUN	$3,830.87	$3,867.56	0.96%
	Total	$97,586.86	$97,302.46	-0.29%
London Orleans	COM	$9,659.69	$9,651.11	-0.09%
	IND	$2,378.43	$2,368.5	-0.42%
	PUBL	$1,292.98	$1,292.26	-0.06%
	RES	$34,832.81	$34,734.13	-0.28%
	Total	$48,163.91	$48,046.00	-0.24%
Muncie (IA1)	RES	$391,451.82	$392,574.71	0.29%
	IND	$46,956.59	$47,135.29	0.38%
	COM	$83,706.71	$84,054.13	0.42%
	PUB	$397,351.69	$398,732.80	0.35%
	Total	$919,466.80	$922,496.9	0.33%
North DeSoto	Residential	$704.80	$704.08	-0.10%
	Commercial	$2,598.89	$2,599.34	0.02%
	Industrial	$138.50	$137.55	-0.69%
	Public	$35.16	$34.77	-1.11%
	Agricultural	$1.27	$1.19	-6.30%
	Total	$3,478.63	$3,476.93	-0.05%
River Des Peres	COM	$2,593.88	$2,574.41	-0.75%
	PUB	$438.97	$439.55	0.13%
	RES	$4,013.10	$4,008.18	-0.12%
	IND	$181.51	$179.53	-1.09%
	Total	$7,227.46	$7,201.67	-0.36%
Tafuna (Impact Area 11)	IND	$112.02	$93.38	-16.64%
	RES	$21.95	$6.58	-70.02%
	Total	$133.97	$99.95	-25.39%
Watertown	RES	$2,479.82	$2,518.59	1.56%
	COM	$2,263.48	$2,305.26	1.85%
	IND	$874.71	$890.45	1.80%
	PUB	$108.61	$111.45	2.61%
	Total	$5,726.62	$5,825.74	1.73%
West Sacramento	RES	$189,002.06	$189,002.06	0.00%
	COM	$1,001,089.69	$1,001,089.69	0.00%
	IND	$430,818.36	$430,818.42	0.00%
	PUB	$22,620.99	$22,621.00	0.00%
	Total	$1,643,531.10	$1,643,531.10	0.00%

Analysis on Life Safety Risk

Due to a lack of prior modeling and available case studies, a single case study for life safety risk was utilized to test the UI for functionality and for reasonable results. That case study, Alaiwai, is provided among the supporting data at the shared drive location provided below.

Analysis on Differences in Graphical Frequency Uncertainty

In the below case studies, there is a big improvement the capability of HEC-FDA Version 2 to match the uncertainty produced by HEC-FDA Version 1. HEC-FDA Version 2.1 sampled frequency curves overlap HEC-FDA Version 1.4.3 sampled frequency curves very accurately, while HEC-FDA Version 2.0.1 and HEC-FDA Version 2.0.2 sampled frequency curves have notable departures. The mean functions from all three versions match very accurately. There is however a very small but systematic departure in sampled curves above and below the mean between Versions 2.1 and 1.4.3 beyond the nonexceedance probability of 0.99. There appears to be smoothing taking place in Version 1.4.3 which is not documented and thus not carried forward into Version 2.1. The below analysis compares Versions 1.4.3, 2.0.1, and 2.1. HEC-FDA Versions 2.0.1 and 2.0.2 display the same computational behavior for graphical frequency uncertainty.

Algiers

The Algiers case study involves a unique graphical frequency function with very sharp inflection points. The stage-frequency function has an equivalent record length of 40 years and the following input coordinates. Probability here is represented by nonexceedance probability for ease of visualization, the probabilities entered into the software are provided in terms of exceedance probability.

Nonexceedance Probability	Stage
.5	-2
.8	-1.9
.9	1.93
.96	1.98
.98	2.02
.99	2.04
.995	2.18
.998	2.3

Mean Graphical Frequency Function

Below are the sampled stage-frequency functions for the Algiers case study at the mean. The Version 2.1 function is plotted in solid green, the Version 2.0.1 function is plotted in dashed red, and the Version 1.4.3 function is plotted in dotted green. Nonexceedance probability is on the x-axis and stage in feet is on the y-axis. Observe that the three functions align perfectly.

Algiers Mean Stage-Frequency Curves

Two Standard Deviations Above the Mean

Below are the sampled stage-frequency functions for the Algiers case study at two standard deviations above the mean. The Version 2.1 function is plotted in solid green, the Version 2.0.1 function is plotted in dashed red, and the Version 1.4.3 function is plotted in dotted green. Nonexceedance probability is on the x-axis and stage in feet is on the y-axis. The Version 2.0.1 function demonstrates the impact of both issues with the graphical frequency uncertainty algorithm identified above: the order of steps and the need for bidirectional monotonicity forcing. The Version 2.1 function aligns with the Version 1.4.3 function nicely, except for nonexceedance probabilities beyond 0.99 where Version 1.4.3 appears to use a smoothing procedure.

Between nonexceedance probabilities of 0.5 and 0.8, the Version 2.0.1 function is increasing at a much faster rate than the Version 2.1 and Version 1.4.3 functions due to the order of operations where interpolation of the sampled frequency function was taking place after uncertainty was calculated for the 0.5 and 0.8 nonexceedance stages. This order of operations matters because the uncertainty at the 0.65 nonexceedance stage should only depend on the equivalent record length and the slope of the frequency curve to the immediate left and right of the 0.65 stage. When the order of operations is such that interpolation takes place after calculation of uncertainty and quantile sampling, then the uncertainty at the 0.65 nonexceedance stage depends on the uncertainty at the 0.5 and 0.8 nonexceedance stages, which means that the uncertainty of the 0.65 nonexceedance stage is incorrectly impacted by the slope to the immediate left and right of the 0.5 and 0.8 nonexceedance stages. Version 2.1 corrects this order of operations, and as a result, the Version 2.1 sampled function obtains a the correct quantile by first interpolating the input curve, then computing uncertainty about the interpolated curve, and then sampling within that uncertainty, so that the uncertainty of the 0.65 nonexceedance stage depends only on the equivalent record length and the slope to the immediate left and right of the 0.65 nonexceedance stage.
Between nonexceedance probabilities of 0.8 and 0.9, the Version 2.0.1 function grows much higher than the entire functions computed in Versions 2.1 and 1.4.3. This behavior is the result of forcing monotonicity from the bottom up. There is a lot of uncertainty around the stage with a nonexceedance probability of 0.8 due to the relatively rapid increase in stage over a small range of probability. In Versions 1.4.3 and 2.1, this large uncertainty is truncated by uncertainty of the same quantiles for less frequent coordinates by forcing monotonicity from the top down. Forcing monotonicity from the top down is especially appealing in this case because the curve is very flat for a large range of the infrequent probabilities reflecting little uncertainty in how much higher the river can get, and that little uncertainty needs to be respected for the entire sampled function.

Algiers Frequency Function Two Standard Deviations Above the Mean

Two Standard Deviations Below the Mean

Below are the sampled stage-frequency functions for the Algiers case study at two standard deviations below the mean. The Version 2.1 function is plotted in solid green, the Version 2.0.1 function is plotted in dashed red, and the Version 1.4.3 function is plotted in dotted green. Nonexceedance probability is on the x-axis and stage in feet is on the y-axis. The Version 2.1 function aligns with the Version 1.4.3 function nicely, except for nonexceedance probabilities beyond 0.99 where Version 1.4.3 appears to use a smoothing procedure. This sampled curve in Version 2.0.1 at two standard deviations below the mean only demonstrates the problem of the ineffective order of steps of the frequency algorithm; frequency curves sampled below the input function are forced monotonic from the bottom up in all three versions. Hence, the departure of the sampled frequency function in Version 2.0.1 from Versions 1.4.3 and 2.1 between nonexceedance probabilities of .8 and .96 reflects the ineffective interpolation of uncertainty produced by calculating the magnitude of uncertainty before interpolating and extrapolating the input frequency curve.

Algiers Frequency Function Two Standard Deviations Below the Mean

Tafuna

The Tafuna case study involves a graphical flow-frequency function with an equivalent record length of 20 years with the following input data. Probability here is represented by nonexceedance probability for ease of visualization, the probabilities entered into the software are provided in terms of exceedance probability.

Nonexceedance Probability	Flow
.01	0
.5	1340.37
.8	1899.36
.9	2279.29
.96	2731.60
.98	3000.05
.99	3416.28
.995	3767.17
.998	4207.08

Mean Graphical Frequency Function

Below are the sampled stage-frequency functions for the Tafuna case study at the mean. The Version 2.1 function is plotted in solid green, the Version 2.0.1 function is plotted in dashed red, and the Version 1.4.3 function is plotted in dotted green. Nonexceedance probability is on the x-axis and stage in feet is on the y-axis. Observe that the three functions align perfectly.

Tafuna Sampled Flow-Frequency Curves at the Mean

Two Standard Deviations Above the Mean

Below are the sampled stage-frequency functions for the Tafuna case study at two standard deviations above the mean. The Version 2.1 function is plotted in solid green, the Version 2.0.1 function is plotted in dashed red, and the Version 1.4.3 function is plotted in dotted green. Nonexceedance probability is on the x-axis and stage in feet is on the y-axis. The Version 2.1 function aligns with the Version 1.4.3 function nicely, except for nonexceedance probabilities beyond 0.99 where Version 1.4.3 appears to use a smoothing procedure. The difference between the Version 2.0.1 function and the Versions 2.1 and 1.4.3 functions is largely due to the direction of monotonicity forcing after sharp increase in flow for a small range of probability.

Tafuna Sampled Flow-Frequency Curves 2 Standard Deviations Above Mean

Two Standard Deviations Below the Mean

Below are the sampled stage-frequency functions for the Tafuna case study at two standard deviations below the mean. The Version 2.1 function is plotted in solid green, the Version 2.0.1 function is plotted in dashed red, and the Version 1.4.3 function is plotted in dotted green. Nonexceedance probability is on the x-axis and stage in feet is on the y-axis. The Version 2.1 function aligns with the Version 1.4.3 function nicely, except for nonexceedance probabilities beyond 0.99 where Version 1.4.3 appears to use a smoothing procedure. The difference between the Version 2.0.1 function and the Versions 2.1 and 1.4.3 functions is due to the order of operations. Sampling uncertainty before interpolating and extrapolating ignored reduction in uncertainty due to flatness of the curve.

Tafuna Sampled Flow-Frequency Curves 2 Standard Deviations Below Mean

Glendive

The Glendive case study involves a graphical stage-frequency function with an equivalent record length of 81 years with the following input data. Probability here is represented by nonexceedance probability for ease of visualization, the probabilities entered into the software are provided in terms of exceedance probability.

Nonexceedance Probability	Stage
.5	1.242
.8	6.646
.9	9.821
.96	12.54
.98	14.803
.99	16.29
.995	17.492
.998	18.196

Mean Graphical Frequency Function

Below are the sampled stage-frequency functions for the Glendive case study at the mean. The Version 2.1 function is plotted in solid green, the Version 2.0.1 function is plotted in dashed red, and the Version 1.4.3 function is plotted in dotted green. Nonexceedance probability is on the x-axis and stage in feet is on the y-axis. Observe that the three functions align very closely.

Glendive Mean Sampled Stage Frequency Functions

Two Standard Deviations Above the Mean

Below are the sampled stage-frequency functions for the Glendive case study at two standard deviations above the mean. The Version 2.1 function is plotted in solid green, the Version 2.0.1 function is plotted in dashed red, and the Version 1.4.3 function is plotted in dotted green. Nonexceedance probability is on the x-axis and stage in feet is on the y-axis. Observe that the three functions align very closely except for some inflection points where the order of operations resulted in loss of important nonlinearity in Version 2.0.1. The Version 2.1 function aligns with the Version 1.4.3 function nicely, except for nonexceedance probabilities beyond 0.99 where Version 1.4.3 appears to use a smoothing procedure.

Glendive Sampled Stage Frequency Functions Two Standard Deviations Above Mean

Two Standard Deviations Below the Mean

Below are the sampled stage-frequency functions for the Glendive case study at two standard deviations below the mean. The Version 2.1 function is plotted in solid green, the Version 2.0.1 function is plotted in dashed red, and the Version 1.4.3 function is plotted in dotted green. Nonexceedance probability is on the x-axis and stage in feet is on the y-axis. The Version 2.1 function aligns with the Version 1.4.3 function nicely, except for nonexceedance probabilities beyond 0.99 where Version 1.4.3 appears to use a smoothing procedure. The difference between the Version 2.0.1 function and the Versions 2.1 and 1.4.3 functions at the lower nonexceedance probabilities is due to the order of operations.

Generated image 1

London-Orleans

The London-Orleans case study involves a graphical stage-frequency function with an equivalent record length of 50 years with the following input data. Probability here is represented by nonexceedance probability for ease of visualization, the probabilities entered into the software are provided in terms of exceedance probability.

Nonexceedance Probability	Flow
.5	3.902
.8	5.677
.9	6.322
.96	6.952
.98	7.56
.99	8.127
.995	8.598
.998	9.14

Mean Graphical Frequency Function

Below are the sampled stage-frequency functions for the London Orleans case study at the mean. The Version 2.1 function is plotted in solid green, the Version 2.0.1 function is plotted in dashed red, and the Version 1.4.3 function is plotted in dotted green. Nonexceedance probability is on the x-axis and stage in feet is on the y-axis. Observe that the three functions align perfectly.

Generated image 1

Two Standard Deviations Above the Mean

Below are the sampled stage-frequency functions for the London Orleans case study at two standard deviations above the mean. The Version 2.1 function is plotted in solid green, the Version 2.0.1 function is plotted in dashed red, and the Version 1.4.3 function is plotted in dotted green. Nonexceedance probability is on the x-axis and stage in feet is on the y-axis. Observe that the three functions align very closely except for some inflection points at low nonexceedance probabilities where the order of operations resulted in loss of important nonlinearity in Version 2.0.1.

London Orleans Sampled Stage Frequency Curves Two Standard Deviations Above Mean

Two Standard Deviations Below the Mean

Below are the sampled stage-frequency functions for the London Orleans case study at two standard deviations below the mean. The Version 2.1 function is plotted in solid green, the Version 2.0.1 function is plotted in dashed red, and the Version 1.4.3 function is plotted in dotted green. Nonexceedance probability is on the x-axis and stage in feet is on the y-axis. The Version 2.1 function aligns with the Version 1.4.3 function nicely, except for nonexceedance probabilities beyond 0.99 where Version 1.4.3 appears to use a smoothing procedure. The difference between the Version 2.0.1 function and the Versions 2.1 and 1.4.3 functions at the lower nonexceedance probabilities is due to the order of operations.

Generated image 1

Analysis on Histogram Sample Mean

In response to erroneous results from a model run in FDA 2.0.1, The FDA 2.1 update makes a significant change to the way the software reports result statistics. The change itself is minor, but the impact on results can be meaningful for some configurations. The issue was apparent in a dataset where the mean Equivalent Annual Damage (EqAD) fell outside the range of the Base Year to Future Year mean Expected Annual Damage (EAD) which is a mathematic impossibility.

In HEC-FDA, the number of results we'd ideally wish to store for a given scenario quickly exceeds the reasonable expectations for computer memory or disk storage. To manage the many numbers, ex. estimates of EAD, we store our results in histograms. Histograms let us record the shape and scale of the distribution of results, without storing every value at full precision, and if the histogram bins are sized well, this works great for being able to get any desired statistic or quantile from the result.

The following is a histogram of random values sampled with a heavy skew toward 20,000. Notice the mean calculated from the sample is nearly the same as the calculated from the histogram. We didn't lose much precision in our simplification of the data. This histogram is used routinely to query quantiles for EAD, EqAD, etc, while the mean we report is sample mean, as the sample mean (rather than the histogram mean) is the most reliable metric.

However, when calculating EqAD in 2.0.2 and prior, HEC-FDA was making the calculations based on the histogram mean rather than the sample mean. For some datasets that was fine, like the histogram above, where the Sample mean and histogram mean are roughly equal, but for samples that are both skewed and polar, like what you might get from a levee without a system response curve, where most of the results are zero or near zero, but a few which represent overtopping are quite high. For this highly skewed distribution, the histogram mean no longer captures the mean nearly as well. This is demonstrated in the histogram below. The vast majority of the sample has zero damage, but when damage does occur, damage is quite large. The histogram now misses the mean dramatically.

The change in 2.1 to address this propagates the sample mean through the EqAD calculation, and saves sample mean to disk with your results. This way even if the histogram mean fails to capture the central tendency of the aggregate distribution very well, the reported mean is still a reliable metric.

This change in the code will change, to varying degrees, the EqAD result for most studies. The change will be more pronounced in studies with with large lateral structures that have the default, or close to the default, system response curve, where the probability of levee failure is approximately zero up to the top elevation of the levee, immediately after which the probability of failure is 1.

Supporting Documentation and Data

The Github home page can be found here.

Additional technical release notes on Github can be found here.

The certification report can be found here.

HEC-FDA Version 2.1 can be found here. Download the portable package to a location where you have write access, such as C:\Programs and extract the contents of the zip file. Open the HEC-FDA 2.1 folder that contains the extracted contents to find the .exe application HEC.FDA.View with the green house icon. Double-click on HEC.FDA.View to launch the software.

Support Policy

The HEC support policy can be viewed on the HEC website. We encourage users of HEC-FDA to use HEC-FDA Discourse for bug reports and technical questions.