Runoff patterns, hydrograph separation and mixing Models – runoff sources and flow

paths

Key topics –

• Runoff patterns and interpretation• Simple mixing models to determine runoff sources• Rigorous mixing models - End member mixing analysis

(EMMA) • Key Lessons from mixing models

Runoff Patterns and Analysis

Various patterns in solute concentrations –• Dilution trajectory• Concentration trajectory – peak before and after discharge peak

dilution

Concentration, before discharge peak

Concentration, after discharge peak

These temporal patterns can also expressed as CONCENTRATION-DISCHARGE (C-Q) plots

Clockwise hysteresis loop

Anticlockwise hysteresis loop

The shape and hysteresis patterns provide some idea of the runoff flow paths and sources

• Size – small versus large• Shape – linear, tight versus circular, open• Loop – closed versus open

Paper by Evans and Davies, 1998.

Paper by Evans and Davies, 1998.

Be cautious about over-interpretation from CQ loops

Paper by Evans and Davies, 1998.

RUNOFF SOURCES for stream flow –

• Spatial – where does the water come from?

• Temporal – when (age) was the water generated?

HYDROGRAPH SEPARATION – determining runoff sources by decomposing the hydrograph

Various approaches –

• Graphical• Simple mixing models• EMMA – end member mixing analyses – mathematically more rigorous

Graphical Hydrograph Separation

Various models –

http://water.usgs.gov/software/HYSEP/

https://engineering.purdue.edu/~what/

Simple Mixing Models –

Runoff Sources –

Temporal --- “new” versus “old” waters (event versus pre-event)

Geographic - where is the water coming from, what is the flow path?

Tracers used for temporal mixing models –

Isotopes of water and hydrogenIsotopes – 18O and 2H (deuterium) - naturally occurring, stable, not radioactive

Isotopes of Oxygen -Oxygen-18 – heavier isotope, (10 neutrons, 8 protons)Oxygen-16 – lighter isotope (8 neutrons, 8 protons)

Naturally available, behaves exactly like the water molecule in terms of transport

Isotopic composition is expressed in terms of – δ

δHX = [(R sample / R standard) – 1] *1000

X – elementH – heavy isotopeR – is ratio; heavyR / lightRR sample - ratio term for sampleR standard - ratio term for the standard; set by the IAEA

*1000 – per mil or ‰

δ18O = [(R sample / R standard) – 1] *1000

δ18O = [((18O/ 16O) sample / (18O/ 16O) standard) – 1] *1000

Measurement of isotopes - Isotope Ratio Mass Spectrometer (IRMS)

Differences in stable isotopes in nature are generated because of –

• Fractionation - separates out the isotopes

• Mixing – reunites the isotopes

Fractionation – forward moving reactions, where bonds are forged or broken, slight rate or kinetic differences are important.

Kinetic reactions – light isotopes are preferentially moved; require less energy.

Water evaporation – great example of fractionation of Oxygen isotopes.

• Water vapor is depleted in 18O (more 16O)• Water liquid is enriched in 18O

These differences can help separate out – event versus pre-event water or “new” versus “old” water

Where is the most depleted water on earth?

Snow in interior Antarctica – most depleted on earth in 18O = -60 ‰!!!

This separation of isotopes by evaporation nicely used in paleoclimate studies!

Linked to waters locked in glaciers and isotopes remaining in the oceans.

Source: http://www.geol.umd.edu/~jmerck/geol100/lectures/36.html

Main virtues of isotopes in catchment hydrology –

1. Applied naturally across the drainage basin

2. Not subject to chemical reactions during contact with mineral matter

3. Undergo fractionation during evaporation and condensation

4. δ of precipitation decreases with –1. surface air temp2. Increasing latitude3. Increasing altitude4. Distance of vapor pressure transport5. Increasing amounts of precipitation

Precipitation values may change rapidly but groundwater and stream water values are more stable, well mixed.

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Shanley et al 2012.

C1 C2

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Temporal source separation – New versus Old water - two components!

Mixing of the two sources generates the resultant mixture

Two unknowns – so we need 2 equationsWater mass balance -

Qt = Q1 + Q21 = f1 + f2

Solute mass balance -ct Qt = c1Q1 + c2Q2or ct = c1f1 + c2f2

Parameters that are measured or know –Solute concentrations - ct, c1, and c2Unknowns – f1 and f2Solve for f1 and f2

Assumptions –Concentrations are distinct and don’t change during the mixing process (are conservative).

Key Observations –

• Humid temperate forests – more than 50-75% of the runoff is old or pre-event water.

• Event water (new water) contributions increase with size of event

• Event water contributions may be higher for tropical watersheds or urban/agricultural watersheds

• Event water contributions typically show up on the rising limb of the hydrograph

Geographic Source Components

WHERE is the water/ runoff coming from?What are the flow paths taken?Runoff sources could be 2, 3, or more……Spatial watershed sources – groundwater, soil water, rainfall, Etc.

Three component model was introduced – Bazemore et al. (1994) to address “soil water”

3- COMPONENT MODEL

1 = f1 + f2 + f3c = c1f1 + c2f2 + c3f3d = d1f1 + d2f2 + d3f3Two tracers required. Number of tracers = (n-1)

Or in terms of matrix operationsX = Y Z, where

𝑿𝑿 =𝟏𝟏𝒄𝒄𝒅𝒅

𝒀𝒀 =𝟏𝟏 𝟏𝟏 𝟏𝟏𝒄𝒄𝟏𝟏 𝒄𝒄𝒄𝒄 𝒄𝒄𝒄𝒄𝒅𝒅𝟏𝟏 𝒅𝒅𝒄𝒄 𝒅𝒅𝒄𝒄

𝒁𝒁 =𝒇𝒇𝟏𝟏𝒇𝒇𝒄𝒄𝒇𝒇𝒄𝒄

Or Z = X * Y-1

So, what are the assumptions?

The key assumptions for geochemical mixing models are:

• the tracers behave conservatively, i.e., the tracer concentrations do not change due to biogeochemical processes over the time scale considered by the mixing model;

• the tracer concentrations for the end-members are significantly different• the mixing process is linear• the chemical composition of end-members (tracer concentrations) does

not change over the time scale considered by the mixing model (time invariance)

• the chemical composition of end-members (tracer concentrations) does not change with space (space invariance)

Assumptions – violated more often than notWays to approach the assumptions – discussed later

End member mixing analysis (EMMA) – Hooper Approach

• Hooper proposed an approach that was more rigorous – both in terms of data as well as the mathematics

• Hooper – proposed – we use more tracers – more than the minimum needed for the model – increase the information content

• Dimensionality is reduced using Principal Component Analyses (PCA)

EMMA procedures

• Select tracers – through Bivariate plots • Linear plots suggest conservative mixing

R² = 0.838

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• Stream or runoff concentrations should be normalized by subtracting the mean for each solute and by dividing by its standard deviation. This standardization prevents any particular solute with greater variation from exerting more influence on the model.

• This data is then used to develop a correlation matrix followed by PCA to determine eigenvectors and eigenvalues.

• The standardized stream data can then be projected into PCA space (or U-space) by multiplying it with the eigenvectors. If two eigenvectors are adequate (indicating three potential end-members) the stream chemistry can be plotted in two-dimensional mixing space by using the first two principal components

• To project the potential end-members in this mixing subspace, the tracer concentrations for all potential end-members should be normalized to the stream water by using the mean and standard deviation of the stream solutes.

• The standardized end-member values can then be projected into the stream U-space by multiplying with the two principal components or eigenvectors.

Counter-clockwise mixing loop

Storm event mixing patterns across hydrologic conditions

Critical considerations while using geochemical mixing models

Choice of solute as tracers

• Determining conservative behavior – linear plots• Biologically sensitive tracers like - NO3 and SO4• DOC – a tracer representative of surficial flow paths• Choose tracer that displays largest differences across sources• Test model using solutes which have not been used in model development

Spatial and temporal variability in tracers

• Solute concentrations vary spatially across catchments – geology, soils, topography, etc.

• Spatial variation in solute concentrations is also likely an important reason why mixing proportions of tracers change with catchment scale

• Changes in end-member concentrations have also been observed to occur temporally, both over the short-term and the long-term

• Solute concentrations also vary seasonally – choose concentrations in the immediate vicinity of the storms

Selection of potential end members

• Various approaches have been used in the selection of end-members –all should be used in concert

• Greater attention to shift and hysteresis of the stream chemistry• Precise end-member proportions or contributions may not necessarily

be that important or even reliable, but the overall trends (relative contributions and the temporal sequencing of end-members) may be more helpful in furthering our understanding of catchment response

Uncertainty in EMMA predictions

• Uncertainly analyses should be included• Various approaches have been adopted – first order Taylor Series

expansion and Monte Carlo simulations• Concentrations of end-members are varied – and relative proportions

are evaluated

Validation of EMMA using hydrometric data

Extremely important that totally independent data be used for verification of endmember contributions and timingThis could include –

• Groundwater elevations• 18O data• Trenched hillslope runoff• Soil moisture measurements

Important lessons from applications of mixing models

Runoff end members and the importance of riparian water

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• Large role of the riparian or the alluvial aquifer in catchment response

• During large events or events following wet antecedent moisture conditions, upland contributions have been observed to increase dramatically

• Some researchers have hypothesized that there may be volumetric moisture “thresholds” associated with upland and riparian aquifers which, when exceeded, may result in a sudden shift in relative contributions from these water sources

Temporal patterns of end members and the influence of event size and antecedent conditions

• Not only do the relative amounts of end-member contributions vary with event size and antecedent moisture conditions, but the controlling end-members could also change with events

• Events following wet antecedent moisture conditions have yielded “clean” or “well-defined” mixing diagrams (Inamdar and Mitchell 2007; Rice and Hornberger 1998) whereas those following the dry antecedent moisture conditions have yielded “poor” mixing patterns (Bernal et al. 2006).

• This would suggest that the runoff was “well-mixed” and the watershed compartments “primed” to contribute to runoff for wet event conditions, as opposed to events following dry conditions. It is possible that dry catchment conditions or hydrophobic soil conditions encourage poor runoff mixing and a greater opportunity for preferential, “bypass”, or “fingered” flow mechanisms

End member contributions with catchment scale

• Contributions from the alluvial /riparian zone tended to increase

• In peatland catchments of Scotland (Soulsby et al. 2003), groundwater contributions were reported to increase with increasing catchment size from 100 to 23,300 ha because of the relative importance of freely draining soils and an increase in the size of alluvial aquifers.