Model description

In developing the model, four hydraulic conditions were considered (based on the biological relevance) Table 1.

Condition	Discharge	Hydraulic characteristics	Biological relevance
No flow	0	Hyporheic moisture seeping out of riffle downface	Moist interstices on downface Pool stagnation and reduction in size Critical (but poorly known) thresholds for the persistence of riffle dependent invertebrate taxa as propagules or as resting stages, or in drought refugia (hyporheic zone, moist microenvironments under rocks)
Trickle flow	very low flow (usually <2ML/day)	Increased downwelling and upwelling. Downface flow is visible on surface but between particles	Emergent rocks required for adult insect oviposition. Habitat for riffle dependent taxa which require flowing water for feeding, predator avoidance or for its higher dissolved oxygen saturation. A diversity of hydraulic conditions supports a diversity of invertebrate species. Nutrient transformation processes within the riffle hyporheic zone generate downstream release of bioavailable nutrients with hyporheic upwelling. These create primary production hot spots.
Low flow	low flow (usually > 2ML/day)	Clear surface flow on downface, but still some substrate emergent from the water (where cobble/boulder). Flow transitions from sub-critical (deep and slow) in the pool to super-critical (shallow and fast) at the riffle crest.	Emergent rocks required for adult insect oviposition. Habitat for riffle dependent taxa which require flowing water for feeding, predator avoidance or for its higher dissolved oxygen saturation. A diversity of hydraulic conditions supports a diversity of invertebrate species. Nutrient transformation processes within the riffle hyporheic zone generate downstream release of bioavailable nutrients with hyporheic upwelling. These create primary production hot spots.
High flow	Less than bankfull	Riffle is drowned out (there is no hydraulic jump at the riffle).	Conditions suitable for fish movement
Very High flow	Close to bankfull	Riffle location is not observable when looking at the water surface.	At very high flow substrate is reworked and periphyton is sloughed off. This prevents riffle interstitial spaces being filled by fine sediment and thus loss of hyporheic flow and habitat. It also maintains epilithic algal diversity and, in particular, prevents dominance of primary producer taxa of less quality as for to macroinvertebrate grazers, promoting for example, a diversity of diatom taxa of high nutritional quality.

Table 1, The key hydraulic conditions present at Riffles

The goal of the model is to allow the prediction when these hydraulic conditions are likely to occur, given the discharge data at a site. This predictions is done via spell analysis methods analysing calculated velocity (at a specified depth), where the threshold is set based on the condition being analysed. There are two alternate methods provided to calculate depth average velocity from a discharge input. Finally, the depth average velocity can be adjusted to provide velocity at a specified depth using the law of the wall.

Width Roughness Method:

Abdulrahman (2017) has devised a numerical solution to allow a direct calculation of depth from discharge without the need for iterative solving (error typically <2%). The Abdulrahman approach is for rectangular channels with a single mannings n and can be applied where width > 5 x depth (although narrower and deeper channels could be considered, these would be rare in nature). This a numerical solution based on a simple rectangular channel and does not include the nuances of cross sectional variability. This is a simplified representation of a natural channel. However, for the purposes of demonstrating relativity between discharge scenarios where cross-sectional survey data is unavailable it may be adequate.

This method requires a bed width (m), manning n and slope (m).

Cross Section Method:

Dingman and Sharma (1997) have used a sample of 520 observations from 78 NZ and 50 US sites to derive an empirical relationship to predict discharge based on channel cross section and slope. They have intentionally excluded channel roughness in their parameters. They have produced a formula to determine discharge (Q) from cross-sectional area (A), hydraulic radius (R) and slope (S):

Q= 1.564A^1.173R^0.400S^{−0.0543logS}

Using a cross section to calculate A and R at a range of depths, a number of discharge (Q) and associated velocity (Q/A) points can be calculated. The Riffle model fits a power curve to generate a relationship between discharge and depth average velocity (usual accuracy of R² > 0.99). The discharge-veleocity power function is used to transform a daily discharge time series to a daily velocity time series at a site.

This method requires a cross section (A number of width, depth points) and slope (m).

Assessment method

Assessment is based on one of the summary statistics (continuous annual value). The summary statistic to be used for assessment is selected via the “Assessment Metric” parameter. These results are then aggregated to a binary yearly result, then to a temporal result based on the defined assessment parameters.

The temporal results are then analysed across locations to report an overall landscape risk by considering the simultaneous occurrence of failures across the system.

Inputs

Data

• Daily flow data

Parameter Sections

• Velocity – define the velocity calculation method (width roughness or cross section) and whether to adjust to a specific depth velocity.
• Season – define the season to identify spells in. Specify the start date and end date. A single continuous spell may span multiple seasons, and will be identified as a single event.
• Event – define the parameters which determine a spell event. Includes the spell type (above threshold, below threshold, range), the threshold (either a set value or the ARI value), the minimum independence between events, the minimum spell length (optional) and the maximum spell length (optional).
• Event Assessment – define the summary statistic to use for assessment.

Outputs

• Daily time series of depth average velocity, adjusted velocity and spell events
• Yearly time series of summary statistics for the given season (As defined in the parameters)
• Event list of all identified events
• Summary results for all events across the analysis period
• Yearly time series of assessment results
• Temporal time series of assessment results
• Spatial time series of assessment results

User interface