Signatures

Below we provide a list of signatures with a short description organised according to the signature sets. A more detailed description of each signature can be found in the Matlab functions which can be opened by clicking on the function name. At the end of the page we also provide a list with all remaining signatures contained in TOSSH which are not (yet) part of any set.

Click here to browse through all Matlab functions contained in TOSSH.

List of signature sets

Basic set

The basic set of signatures (calc_BasicSet.m) is designed to cover the five components of a natural streamflow regime as defined by Richter et al. (1996) [1] and Poff et al. (1997) [2]: magnitude, frequency, duration, timing, and rate of change. As Poff et al. (1997) [2] state, these components “can be used to characterize the entire range of flows and specific hydrologic phenomena, such as floods or low flows, that are critical to the integrity of river ecosystems”.

Basic set

Signature	Function (click for code)	Unit	Description
Magnitude
Q_mean	sig_Q_mean.m	mm/timestep	Mean streamflow
Q5	sig_x_percentile.m	mm/timestep	5-th streamflow percentile
Q95	sig_x_percentile.m	mm/timestep	95-th streamflow percentile
Q_mean_monthly a	sig_Q_mean_monthly.m	mm/timestep	Mean monthly streamflow
Q_7_day_min	sig_Q_n_day_min.m	mm/timestep	7-day minimum streamflow
BFI	sig_BFI.m	–	Baseflow index
CoV	sig_Q_CoV.m	–	Coefficient of variation
Frequency
high_Q_frequency	sig_x_Q_frequency.m	–	High flow frequency
low_Q_frequency	sig_x_Q_frequency.m	–	Low flow frequency
zero_Q_frequency	sig_x_Q_frequency.m	–	Zero flow frequency
Duration
high_Q_duration	sig_x_Q_duration.m	timestep	High flow duration
low_Q_duration	sig_x_Q_duration.m	timestep	Low flow duration
zero_Q_duration	sig_x_Q_duration.m	timestep	Zero flow duration
Timing
HFD_mean	sig_HFD_mean.m	day of year	Half flow date
HFI_mean	sig_HFI_mean.m	days	Half flow interval
Rate of change
AC1	sig_Autocorrelation.m	–	Lag-1 autocorrelation
FDC_slope	sig_FDC_slope.m	–	Slope of the flow duration curve
BaseflowRecessionK	sig_BaseflowRecessionK.m	1/d	Exponential recession constant

^a Note that this signature function returns a value for each month.

Benchmark sets

Addor et al. (2018) set

Addor et al. (2018) [3] use 15 signatures (calc_Addor.m) that “characterize different parts of the hydrograph, and […] are sensitive to processes occurring over different time scales”. The signatures are selected from those commonly used in the literature, and are used to explore the strength of relationships between signatures and catchment attributes.

Addor et al. (2018)

Signature	Function (click for code)	Unit	Description
Q_mean	sig_Q_mean.m	mm/timestep	Mean streamflow
TotalRR	sig_TotalRR.m	–	Total runoff ratio
QP_elasticity	sig_QP_elasticity.m	–	Streamflow-precipitation elasticity
FDC_slope	sig_FDC_slope.m	–	Slope of the flow duration curve
BFI	sig_BFI.m	–	Baseflow index
HFD_mean	sig_HFD_mean.m	day of year	Half flow date
Q5	sig_x_percentile.m	mm/timestep	5th streamflow percentile (low flows)
Q95	sig_x_percentile.m	mm/timestep	95th streamflow percentile (high flows)
high_Q_freq	sig_x_Q_frequency.m	–	High flow frequency
high_Q_dur	sig_x_Q_duration.m	timestep	High flow duration
low_Q_freq	sig_x_Q_frequency.m	–	Low flow frequency
low_Q_dur	sig_x_Q_duration.m	timestep	Low flow duration
zero_Q_freq	sig_x_Q_frequency.m	–	Zero flow frequency

Sawicz et al. (2011) set

Sawicz et al. (2011) [4] use 6 signatures (calc_Sawicz.m) drawn largely from Yadav et al. (2007) [5], that are chosen to be uncorrelated and to be linked to catchment function. The signatures are used to analyse hydrological similarity between catchments, and link the resulting clusters to climate and landscape attributes.

Sawicz et al. (2011)

Signature	Function (click for code)	Unit	Description
TotalRR	sig_TotalRR.m	–	Total runoff ratio
FDC_slope	sig_FDC_slope.m	–	Slope of the flow duration curve
BFI	sig_BFI.m	–	Baseflow index
QP_elasticity	sig_QP_elasticity.m	–	Streamflow-precipitation elasticity
SnowDayRatio	sig_SnowDayRatio.m	–	Snow day ratio
RLD	sig_RisingLimbDensity.m	1/timestep	Rising limb density

Euser et al. (2013) set

Euser et al. (2013) [6] use 8 signatures (calc_Euser.m) that represent different aspects of hydrological behaviour. The signatures are used to test the consistency of model performance, within the FARM model evaluation framework. Some signatures are the same but applied to different parts of the time series, e.g. the low flow period (May to September) or the high flow period (November to April).

Euser et al. (2011)

Signature	Function (click for code)	Unit	Description
AC1	sig_Autocorrelation.m	–	Lag-1 autocorrelation
AC1_low	sig_Autocorrelation.m	–	Lag-1 autocorrelation for low flow period
RLD	sig_RisingLimbDensity.m	1/timestep	Rising limb density
PeakDistribution	sig_PeakDistribution.m	–	Slope of distribution of peaks
PeakDistribution_low	sig_PeakDistribution.m	–	Slope of distribution of peaks for low flow period
FDC a	sig_FDC.m	–	Flow duration curve
FDC_low<sup>a</sup>	sig_FDC.m	–	Flow duration curve for low flow period
FDC_high<sup>a</sup>	sig_FDC.m	–	Flow duration curve for high flow period

^a Note that this signature function returns the whole flow duration curve.

Process-based signature sets

McMillan (2020) groundwater set

Calculates 15 signatures (calc_McMillan_Groundwater.m) from McMillan (2020) [7], related to groundwater storage, groundwater dynamics and baseflow. These signatures come from previous experimental studies that link catchment or hillslope processes to streamflow response dynamics. Some signatures are implemented direct from the original papers, others are interpreted from a qualitative description in the paper.

McMillan (2020) groundwater set

Signature	Function (click for code)	Unit	Description
TotalRR	sig_TotalRR.m	–	Total runoff ratio
RR_Seasonality	sig_RR_Seasonality.m	–	Runoff ratio seasonality
EventRR	sig_EventRR.m	–	Event runoff ratio
StorageFraction a	sig_StorageFraction.m	–	Ratio between active and total storage
Recession_a_Seasonality	sig_SeasonalVarRecessions.m	–	Seasonal variations in recession parameters
AverageStorage	sig_StorageFromBaseflow.m	–	Average storage from average baseflow and storage-discharge relationship
RecessionParameters a	sig_RecessionAnalysis.m	–	Recession analysis parameters approximate storage-discharge relationship
MRC_num_segments	sig_MRC_SlopeChanges.m	–	Number of different segments in master recession curve (MRC)
First_Recession_Slope	sig_MRC_SlopeChanges.m	mm/timestep 2	Steep section of MRC = storage that is quickly depleted
Mid_Recession_Slope	sig_MRC_SlopeChanges.m	mm/timestep 2	Mid section of MRC = water retention capacity of the catchment
Spearmans_rho	sig_RecessionUniqueness.m	–	Non-uniqueness in the storage-discharge relationship
EventRR_TotalRR_ratio b	sig_EventRR.m / sig_TotalRR.m	–	Ratio between event and total runoff ratio
VariabilityIndex	sig_VariabilityIndex.m	–	Variability index of flow
BFI	sig_BFI.m	–	Baseflow index
BaseflowRecessionK	sig_BaseflowRecessionK.m	1/d	Exponential recession constant

^a Note that these signature functions return multiple signatures.

^b Note that this signature is a combination of two other signatures.

McMillan (2020) overland flow set

Calculates 10 overland flow (infiltration excess and saturation excess) signatures (calc_McMillan_OverlandFlow.m) from McMillan (2020) [7]. These signatures come from previous experimental studies that link catchment or hillslope processes to streamflow response dynamics. Some signatures are implemented direct from the original papers, others are interpreted from a qualitative description in the paper. Note that these signatures are all calculated with the same function.

McMillan (2020) overland flow set

Signature	Function (click for code)	Unit	Description
IE_effect	sig_EventGraphThresholds.m	–	Infiltration excess importance
SE_effect	sig_EventGraphThresholds.m	–	Saturation excess importance
IE_thresh_signif	sig_EventGraphThresholds.m	–	Infiltration excess threshold significance (in a plot of quickflow volume vs. maximum intensity)
IE_thresh	sig_EventGraphThresholds.m	mm/timestep	Infiltration excess threshold location (in a plot of quickflow volume vs. maximum intensity)
SE_thresh_signif	sig_EventGraphThresholds.m	–	Saturation excess threshold significance (in a plot of quickflow volume vs. total precipitation)
SE_thresh	sig_EventGraphThresholds.m	mm	Saturation excess threshold location (in a plot of quickflow volume vs. total precipitation)
SE_slope	sig_EventGraphThresholds.m	mm/mm	Saturation excess threshold above-threshold slope (in a plot of quickflow volume vs. total precipitation)
Storage_thresh_signif	sig_EventGraphThresholds.m	–	Storage/saturation excess threshold significance (in a plot of quickflow volume vs. antecedent precipitation index + total precipitation)
Storage_thresh	sig_EventGraphThresholds.m	mm	Storage/saturation excess threshold location (in a plot of quickflow volume vs. antecedent precipitation index + total precipitation)
min_Qf_perc	sig_EventGraphThresholds.m	%	Minimum quickflow as a percentage of precipitation

TOSSH: all remaining signatures

This is a list of all remaining signatures currently contained in TOSSH.

All remaining signatures

Signature	Function (click for code)	Unit	Description
BaseflowMagnitude	sig_BaseflowMagnitude.m	mm	Difference between maximum and minimum of annual baseflow regime
ResponseTime	sig_ResponseTime.m	timestep	Catchment response time
FlashinessIndex	sig_FlashinessIndex.m	–	Richards-Baker flashiness idex
PQ_Curve a	sig_PQ_Curve.m	–	Slopes and breakpoints in cumulative P-Q regime curve
Q_n_day_max	sig_Q_n_day_max.m	mm/timestep	n-day maximum streamflow
Q_skew	sig_Q_skew.m	mm 3/ timestep 3	Skewness of streamflow
Q_var	sig_Q_var.m	mm 2/ timestep 2	Variance of streamflow
RecessionK_part	sig_RecessionParts.m	1/timestep	Recession constant of early/late (exponential) recessions
SeasonalTranslation a	sig_SeasonalTranslation.m	–	Amplitude ratio and phase shift between seasonal forcing and flow cycles
SnowStorage	sig_SnowStorage.m	mm	Snow storage derived from cumulative P-Q regime curve

^a Note that these signature functions return multiple signatures.

References

[1]

Richter, B.D., Baumgartner, J.V., Powell, J. and Braun, D.P., 1996. A method for assessing hydrologic alteration within ecosystems. Conservation biology, 10(4), pp.1163-1174.

[2] (1,2)

Poff, N.L., Allan, J.D., Bain, M.B., Karr, J.R., Prestegaard, K.L., Richter, B.D., Sparks, R.E. and Stromberg, J.C., 1997. The natural flow regime. BioScience, 47(11), pp.769-784.

[3]

Addor, N., Nearing, G., Prieto, C., Newman, A.J., Le Vine, N. and Clark, M.P., 2018. A ranking of hydrological signatures based on their predictability in space. Water Resources Research, 54(11), pp.8792-8812.

[4]

Sawicz, K., Wagener, T., Sivapalan, M., Troch, P.A. and Carrillo, G., 2011. Catchment classification: empirical analysis of hydrologic similarity based on catchment function in the eastern USA. Hydrology and Earth System Sciences, 15(9), pp.2895-2911.

[5]

Yadav, M., Wagener, T. and Gupta, H., 2007. Regionalization of constraints on expected catchment response behavior for improved predictions in ungauged basins. Advances in Water Resources, 30(8), pp.1756-1774.

[6]

Euser, T., Winsemius, H.C., Hrachowitz, M., Fenicia, F., Uhlenbrook, S. and Savenije, H.H.G., 2013. A framework to assess the realism of model structures using hydrological signatures. Hydrology and Earth System Sciences, 17(5), pp.1893-1912.

[7] (1,2)

McMillan, H.K., 2020. Linking hydrologic signatures to hydrologic processes: A review. Hydrological Processes, 34(6), pp.1393-1409.