We review some of the basic properties of floating point calculations in Chapter 2. We also discuss the fused multiply-add operator, which was added to the IEEE 754 standard in 2008 [2] and is built into the hardware of NVIDIA GPUs. In Chapter 3 we work through an example of computing the dot product of two short vectors to illustrate how different choices of implementation affect the accuracy of the final result. In Chapter 4 we describe NVIDIA hardware versions and NVCC compiler options that affect floating point calculations. In Chapter 5 we consider some issues regarding the comparison of CPU and GPU results. Finally, in Chapter 6 we conclude with concrete recommendations to programmers that deal with numeric issues relating to floating point on the GPU.
The width of the primary crossing structure should not be less than 1.0 times the bankfull width of the channel (USFS 2008). United States Forest Service (USFS) guidelines for stream simulation are based on emulating the geomorphic condition of the bankfull channel (Figure 3).
FULL Point Layout 2008
Data gathered should include at a minimum: channel width at bankfull, bankfull cross-sectional area; the bankfull slope and slope ratio; substrate grain size; key pieces; stream type; bankfull average and maximum depth; low flow channel geometry; flood prone width; stream order; and watershed area (USFS 2008). The reference reach bankfull dimensions should be determined in the field by surveying a detailed cross section at the upper 1/3 of a representative riffle. See Section 2.3.
The channel in the crossing structure should not substantially differ from the reference reach condition in regards to the channel width at bankfull, bankfull and low flow channel cross-sectional area, stream type and bankfull average depth (USFS 2008). Refer to Figure 3.
The crossing slope should be within 25% of the bankfull slope of the selected reference reach. For example, if a reference reach is 1.0% slope, the minimum design slope of the stream simulation culvert would be 0.75% and the maximum design slope would be 1.25% (USFS 2008).
For the Geomorphic analog method, crossing structures should be designed to accommodate at least the 100-year flood flow (USFS 2008). Designing for the 100-year flood is a choice we have made for projects funded by AFPP to maximize success over the long term considering the wide margin of error in hydrologic predictions and expected life of an installation. Although the 100-year flood flow only has a 1% probability of occurring in any given year, for any 50-year period, there is a 40% chance that the 100-year flood will occur and a 64% chance that the 50-year flood will occur. Given the rather high likelihood of exceeding the design flow during the culvert lifetime, the designer should carefully consider the consequences of potential failures during flood events. While keeping in mind that many jurisdictions have minimum hydraulic standards by road type, the road owner and project funders may select a larger design flood that takes into account their tolerance for risk of failure. ADOT&PF design standards require a 50-year flood flow for culvert design at primary and secondary highways, but only a 10-year flood flow for low importance secondary highways (ADOT&PF 2006). During conversations, hydraulic engineers at ADOT&PF have stated they use the 50-year as the design flood as a minimum most of the time, even in low importance areas, as it provides for the more cost effective design in the long run.
2.2.9 Determine new culvert alignment, slope, vertical adjustment potential (VAP) lines, tie in points to the existing stream thalweg and draw this in on the long pro. Reference chapter 6 of the USFS Stream Simulation Publication (USFS 2008) for considerations in choosing tie in points. Make sure new culvert design slope is within 25% of reference reach slope. Expect there may be sediment deposition upstream and/or downstream at the culvert that may need to be removed. Check actual length of culvert in CAD based on tie in points to existing thalweg, embedment depth, minimum cover depth, road width and embankment slope.
Bankfull discharge: A frequently occurring peak flow whose stage represents the incipient point of flooding. The bankfull discharge is expressed as the momentary maximum of instantaneous peak flows rather than the mean daily discharge. It is often associated with a return period of 1-2 years, with an average of 1.5 years (Rosgen, 1996). (Note: return intervals for bankfull of up to 5 years have been found for some streams in the continental United States. Stream gaging is recommended if the designer desires confidence in the bankfull discharge return interval).
Reference Reach: A portion of a stream that represents a stable channel (dimension, pattern, profile) within the geomorphic context that exists in that segment and can represent a natural or a stable, modified condition (USFS 2008). A reference reach should be a minimum 20 times the reference bankfull width and no less than 200 feet in length for creeks less than 10 feet in bankfull width. A reference reach should also include a minimum of 4 stable grade control features. See the definition for Geomorphic Analog Method for further reference reach selection recommendations.
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