Model Results

General Results

GeoSWMM’s Status Report summarizes overall results for the 10-yr simulation. The volume of internal outflow is 2959.07 acre-ft which means flooding occurred within the conveyance network (listed as Flooding Loss in the Flow Routing Continuity section of the report). This is expected because the conveyance system in Tutorial 03 was designed for the 100-yr storm. The Runoff Quantity Continuity section shows the significance of evaporation in the total water budget. Almost 3295 inches of water were evaporated from the depression storage surfaces of the catchment with another 5.4 inches evaporated from the pond; The total depth of evaporation loss was found 3300.4 inches which corresponds to 42.12 % of the total rain over the 10 years (7835.280 inches).Detention Pond

The Status Report section Node Inflow Summary shows that the maximum flow rate into the detention pond (SU1) was 90.44 cfs. The outflow from the pond is 56.25 cfs (as determined by the maximum inflow for outfall O1 in the same table). This control occurs over a period of 1 hour 35 minutes, given that the maximum inflow to the pond was at 12:16 AM of day 1789, while the maximum discharge was at 01:51 AM of the same day. Note that the maximum flow entering the pond is much lower than the initial estimate for the 10-yr storm computed in Tutorial 03, 181.84 cfs. Interestingly, however, the maximum discharge released by the pond in the continuous simulation (56.25 cfs) is larger than 16.62 cfs, the 10-yr peak discharge target used in Tutorial 03. In other words, even though the peak flow entering the pond during the 10-year record is lower than the design value, the peak outflow is actually larger than its original design value.

To explain this result, consider Figure 2.8 which shows the rainfall hyetograph for the storm event (Day 1789) that produced the maximum inflow and outflow from the pond. The intensity of rainfall during the day leading up to the maximum discharge at SU1 is 0.23 in/hr, and on the day itself, it is 0.48 in/hr. It is to be noted that since the rainfall event in Tutorial 10 is a continuous event, the total volume of the rain that falls on the day before and during the approximately 1.5 hour period when the maximum flow event occurs is 6.24 inch (0.23in/hr*24hr + 0.48in/hr*1.5hr). This is larger than the 1.71 inch associated with the 10-yr 2-hr design storm used in Tutorial 01. Yet, the inflow rate into the pond is smaller (90.44 cfs versus 181.84 cfs).  The main reason for this discrepancy is the different rainfall interval used for the two storm events. The 10-yr design storm used a 5 minute interval (see Tutorial 01); in contrast, the rain interval for the storm from the 10 year long continuous record is 24 hr.

This difference explains the considerably smaller peak runoff discharged into the pond for the continuous simulation. The aggregation associated with larger rainfall intervals is a critical issue in continuous simulation that significantly affects model performance. Peak discharges are very sensitive to high rainfall intensities, which typically occur over short periods. These high intensities are lost when data are aggregated into larger time steps, and peak discharges are not well simulated. It is strongly recommended to use rainfall records with fifteen-minute or less finer time resolution, if available.

The difference in maximum intensities does not impact the peak discharges released by the detention pond. As previously mentioned, the highest peak flow discharged by the pond in the continuous simulation was 56.25 cfs, higher than the 16.62 cfs peak produced from the 10-yr design storm. This is consistent with the fact that the storm associated with the continuous simulation peak is larger than the 10-yr design storm. The attenuation effect of the pond over time is such that the rainfall intensity is not as significant as the total volume.

Antecedent Conditions

One of the benefits of continuous simulation is that the model accounts for the initial state of the catchment and its conveyance network at the beginning of each new storm event. For instance, with continuous simulation the model simulates the initial water depth in the detention pond at the beginning of a new rainfall event. A high-water depth will reduce the available volume for managing the next storm, resulting in higher discharges than for if the pond were initially empty.

Figure 2.9 shows the water depth in the pond over a 15-day period (from day 1380 to day 1394, i.e., 10/12/2003 to 10/26/2003). Figure 2.10 presents the corresponding inflow and outflow rates for the pond, along with rainfall data for the same period. Two storm events separated by 1 dry day are shown: Event 1 has a maximum intensity of 2.46 in/h and a total volume of 83.04 inch.; Event 2 has a maximum intensity of 1.4 in/h and a total volume of 71.28 inch. Despite the smaller volume and intensity of the second storm, the water depth in the pond still reaches 7 ft, the same as with the first event. Due to the short dry period (1 day) between the two events, the water level in the storage unit had only receded to 2.20 ft when the second event began. The limited available storage capacity means that although second event generated a smaller peak inflow (59.58 cfs), it is still resulted in a peak outflow of 56.23 cfs-identical to the outflow from first event, which had a peak inflow of 111.71 cfs. This demonstrates how antecedent water levels can significantly impact a pond’s ability to attenuate flow.

In Figure 2.9, we observe that after the peak of the second event, although the rainfall intensity was relatively low (1.4 in/hr), the water depth did not decline significantly, since the pond was already holding water from the first event. From Figure 2.10, it is evident that the inflow and outflow rates are nearly equal, suggesting the storm volume was lower than the volume in the 10yr-2hr design storm. As a result, nearly all the incoming water flowed through the storage unit to outfall (O1) without significant detention.

Evaporation

Finally, another advantage of continuous simulation is the inclusion of evaporation in the overall system water balance. Evaporation from both pervious and impervious depression storage areas occurs between rain events. Thus, the amount of depression storage available to capture the initial portion of the next storm depends on the time interval between storms. As an example, Figure 2.9 shows the rainfall and losses (infiltration plus evaporation) simulated in subcatchment W1 over the period of time from 10/12/2003 to 10/26/2003. It is observed that after large storm events, and once infiltration has stopped, the losses stabilize at 0.31 in/h. These losses are caused by evaporation acting over the water stored on the impervious surfaces. To validate this observation, consider that the average evaporation rate in May is 0.6 in/day or 0.025 in/h; the percent imperviousness of subcatchment W1 is 37.84%, and 25% of that area does not have depression storage. Therefore, evaporation acts over 0.3784 • (1-0.25) =28.4% of the total area. The effective evaporation rate over the entire subcatchment W1 becomes 28.4% • 0.025 in/day = 0.007 in/hr, which is consistent with the loss rate observed in Figure 2.11.

Detention Pond Outflows Statistics

To illustrate the use of GeoSWMM’s Statistics tool, a frequency analysis of the peak outflows from the site’s detention pond is performed. This analysis demonstrates how how frequently the pond discharges occur, their duration, and the statistical distribution of their peak magnitudes. To begin, open the Statistics dialog under the Results section on GeoSWMM’s main toolbar.

Figure 2.14 shows how the dialog should be configured for this analysis. The object to be analyzed is node O1, which receives all outflow from the pond via its outlet devices. The variable selected for this node is Total Inflow, which represents the total discharge from the pond. The event type is set to Event-Dependent, meaning separate events are identified based on consecutive reporting periods where specified threshold criteria are met. Within each event, the statistic analyzed is the Peak value of total inflow-equivalent to the peak pond discharge. And finally, the event threshold criteria are defined such that a new event begins whenever an inflow exceeds 5 cfs, and at least 12 hours have passed since the last inflow of at least 5 cfs. The selection of these threshold values significantly impacts the number of events identified. Higher minimum flow thresholds or longer separation times typically result in fewer total events, while smaller values may increase the count of events and lead to more detailed analysis.

The report generated by running this statistical query contains four sections as shown in Figures 2.13 through 2.16. The first section is the Summary, shown in Figure 2.13. According to this summary, 280 events were identified during the simulation period based on the threshold values for flow and inter-event time defined for the frequency analysis. These events accounted for 11.5% of the total simulation time. Note the high positive skewness coefficient (1.669), which indicates that most of the events involved relatively low discharge rates, with a few events producing significantly higher flows. This is consistent with the relatively low mean peak flow of 17.49 cfs.

Figure 2.13 shows a portion of the second section of the report, the Event tab, for the variable under study. The events are listed in order of decreasing value of the event statistic (the peak value) for the variable being analyzed (total inflow rate at node O1). Five fields are included: Start date of the event, duration, value of the variable under study (in this case peak flow), the exceedance frequency and an estimation of the corresponding return period. A noteworthy observation is the duration of most events, which generally exceeds 24 hours. This aligns with expectations, as the detention pond was designed to release discharges gradually. Moreover, a similar frequency analysis for duration instead of the peak discharge would show that the mean event duration is 36.0 hours.

Where m is the event’s rank, n_R is the total number of events and n is the number of years under analysis. For example, for the 13^th  event occurring on 05/28/2004, the exceedance frequency is equal to F4 = 13 / (280 + 1) = 0.04626= 4.626 %, and the return period is equal to T4 = (10 + 1)/4 = 0.846 years.

The third section of the Statistics report contains a histogram of the event statistic being analyzed, as shown in Figure 2.15. For this particular example it shows what fraction of all the events had a peak flow of a given size. Note how the figure confirms what was said earlier, that the distribution of peak inflows is highly skewed towards the low end of the flow scale. Finally, the fourth section of the report, as shown in Figure 2.16, presents a cumulative frequency plot of the event statistic under study. Here, 30% of the peak discharges over the 10-yr period exceed 16.62 cfs. Note that both the histogram and cumulative frequency plots are just graphical representations of the same information as provided in the event listing.

Detention Pond Water Depth Statistics

A second application of the GeoSWMM Statistics tool to this tutorial will analyze the maximum depth in the detention pond. This will help verify if the Water Quality Capture Volume (WQCV) of the pond was effective in capturing the more frequently occurring storms. Recall from Tutorial 03 that the first 2 feet of storage volume was designated for this purpose. The statistical query used to answer this question is shown in Figure 2.17. Note that this time events are defined to consist of all days where the water depth in the pond was at least 0.05 ft deep. The Daily option is chosen for the Event Period because the drawdown time for the WQCV is 40 hours; thus, a daily analysis of the depth in this portion of the pond is sufficient. Figure 2.18 shows the frequency plot that results from this query. On 48.56% of the days when the pond is wet does its depth exceed the WQCV. Thus, one can conclude that only half of all storms are captured within the WQCV and the pond function as an effective BMP control only half the time.

Rainfall Statistics

Another variable typically analyzed using statistics is rainfall. Several quantities that characterize storm events for the rainfall record used in this example will be examined and compared. These are the event duration, mean intensity, total volume, and peak intensity. As before, the record will be separated into a sequence of independent storm events of varying magnitude and duration using GeoSWMM’s Statistics tool.

In rainfall analysis, the separation time used to decide when one event ends and another begins is referred to as the Inter-Event Time. This is the smallest number of consecutive dry periods that must occur before the next wet period is considered as a separate event. There is no established “correct” value for the Inter-Event Time, although 3 to 30 hours are often used for rainfall data (Hydroscience, 1979). See Adams and Papa (2000) for a detailed discussion on this subject. When storm events are characterized as a Poisson process, the time between events follows an exponential distribution for which the mean equals the standard deviation (i.e., the coefficient of variation (CV) is 1). Thus, one suggested approach to choosing an Inter-Event Time is to find a value that produces a CV of 1 for the resulting collection of inter-event times.

Figure 2.19 shows the statistical query used to test how well an Inter-Event Time (separation time) of 24 hours produces a sequence of events whose inter-event times have a CV of near to 1 for the rainfall record used in this chapter. The resulting CV (standard deviation divided by the mean) is 99.218 / 143.666 = 0.7. Since the value of CV is close to 1, it indicates that 24 hours is a reasonable Inter-Event Time to use for this rainfall record.

Rainfall Frequency Analysis

Next a frequency analysis is made for each of the following rainfall quantities: duration, mean intensity, total volume, and peak intensity. Each analysis uses a Statistics dialog that looks the same as that in Figure 2.19, except that a different choice of event statistic is used for each. Table 2.8 lists the summary statistics found for each frequency analysis. The first two properties (number of events and event frequency, or percentage of total time in which rainfall is registered) are the same for each rainfall property since all of the frequency analyses used the same thresholds to define an event.

Table 2.8 : Summary statistics for various rainfall event properties

Figure 2.20 shows the frequency plot produced by this analysis for event duration and total rainfall. (This figure was generated by using GeoSWMM’s Statistics menu option’s Events page from where the data associated with each frequency plot was exported into a spreadsheet program and combined together on a single graph.) This plot can also be used as a less direct indicator than the pond depth frequency analysis performed earlier to see if the Water Quality Capture Volume (WQCV) of 0.1718 inches is sufficient to capture the majority of runoff events.

It is seen (blue line) that about no rainfall events has a total volume smaller than 0.1718 inches (corresponding WQCV in watershed inches in Tutorial 03). Even if the watershed were totally impervious with no surface retention capacity, the pond would control around 100% of the events according to the model. In reality there are infiltration and storage losses so that a larger percentage of the rainfall events are controlled by the pond’s volume.

Another use of this type of multi-variable statistical analysis is to study in more detail the correspondence between the frequencies of the events based on different rainfall characteristics. The largest event is not necessarily the longest one or the most intense. It is useful to determine the degree of dependence among storm event characteristics in order to see if these characteristics are correlated or not, and to identify a subset of the most critical events that could be used for design purposes, depending on the objective of the analysis. The intensity of the events is significant in determining peak discharge, but the magnitude may be more important when storage control structures are designed or evaluated.

Table 2.9 shows the ten most extreme events according to the four characteristics under analysis: duration, mean intensity, volume and peak intensity. The table reveals that the peak and mean intensities are closely correlated; five of the ten events with the largest peak intensity are also in the groups of events with a large mean intensity (dates of these common events are highlighted as green). There is also a correspondence between duration and total volume; four of the longest events are also in the group that contains the largest ones (the dates of these common events are in blue). A weaker correlation is observed between the mean intensity and volume (one common event shown by underscore), between duration and peak intensity (one common event shown in italic font) and between volume and peak intensity (three common events shown by asterisk {*}).

Table 2.9 : Ten most severe events based on duration, depth and intensity

Table 2.10 shows the ranks of the common events identified in Table 2.9. Numbers before and after the “&” symbol indicate the rank according to the variables defined in the first row of the table. For example, from the second column, the second longest event (480 hrs) is also the largest event (168.24 inches). The fifth longest event (384hrs) is the eighth largest event (89.76 inches), and so on. Finally, there are no common events among the ten most severe in terms of both duration and mean intensity. This analysis corresponds to a preliminary step in evaluating the correlation between storm event characteristics. Other methodologies including the use of scatter plots between variables and correlation coefficients can be used. These methods are applied to all the events and not only the most severe ones.

Table 2.10 : Correspondence among the most severe events

Major Outcomes

The major outcomes of the analyses made are listed below:

• Continuous simulation allows modelers to more faithfully represent the behavior of drainage systems because it subjects them to a long sequence of actual rainfall events of varying magnitudes and durations and also accounts for the variability of antecedent conditions that exist from one event to the next.
• GeoSWMM’s Statistics tool is a valuable aid in interpreting the large amount of output data that can be generated from a long-term continuous simulation.