Chapter 4 DOC dynamics in the peat-fed potable water supply
4.2 Materials and methods
4.2.3 PERSiST and INCA-C modelling
4.2.3.3 Model calibration, evaluation and sensitivity
The baseline period of available datasets was divided into two parts: the first part (2005-2010) was used for calibration and the second part (2011-2016) was used for evaluation. During calibration, slightly shorter periods were available for the Tyne (2006-2010), Tees (2006-2010) and Wye catchments (2005-2009). During evaluation, slightly shorter periods were available for the Tyne (2011-2015) and Wye (2010-2013) catchments. The calibration strategy for PERSiST and INCA-C followed the steps described by Futter et al. (2014) and Ledesma et al. (2012).
PERSiST was calibrated and then used to generate time series of soil moisture deficit (SMD; the difference between the current depth of water and the waterholding capacity) and hydrologically effective rainfall (HER; the fraction of precipitation which contributes to runoff) for running INCA-C. At first, a preliminary manual calibration was performed to maximize the R2 and
N-S (Nash and Sutcliffe, 1970) statistics comparing observed to modelled stream flows. This parameter set was then used as the basis for a Monte Carlo exploration of the parameter space. During each iteration of the Monte Carlo analysis, 100 loops of 600 runs were used for the identification of each parameter set candidate. In all cases, parameters values were sampled from a rectangular prior distribution. The initial boundaries of the rectangle were defined as ±25 % of the parameter value for the best performing initial manual calibration. After each iteration of the Monte Carlo analysis, parameter sensitivity was assessed using the 100 best performing parameter sets, which were defined by ranking the R2 and N-S statistics comparing modelled and
observed DOC. The cumulative parameter distributions derived from the best performing parameter sets were compared to rectangular distributions, and if non-rectangular, the parameter range was adjusted prior to the next iteration of the Monte Carlo analysis. This process was terminated when the Monte Carlo analysis failed to provide any improvement in R2 and N-S values over
the preceding set of model runs. Finally, a single best-performing parameter set from the 100 loops was selected for final best parameter, which was then used to generate time series of SMD and HER. Parameters of PERSiST model used in MC analysis are listed in Table 4.2.
Table 4.2 Parameters of PERSiST model used in MC analysis.
Parameter Units Description
Snow threshold °C Temperature threshold for liquid or solid water
Snow multiplier / Adjustment factor relating measured precipitation to estimated
snowfall
Rain multiplier / Adjustment factor relating measured precipitationto estimated
rainfall
Degree day melt factor mm °C -1 Temperature-dependent rate at which snow melts
Degree day ET mm °C -1 Maximum possible temperature-dependent rate atwhich
evapotranspiration occurs
Growing degree threshold °C Temperature threshold above whichevapotranspiration can occur
Snow interception mm Depth of precipitation intercepted by canopy whenair temperature
is less than or equal to the snow threshold
Rain interception mm Depth of precipitation intercepted by canopy whenair temperature
is greater than the snow threshold
Snow multiplier / Adjustment factor relating measured precipitationto estimated
snowfall
Rain multiplier / Adjustment factor relating measured precipitationto estimated
rainfall
a / Flow velocity multiplier
b / Flow velocity exponent
Infiltration offset mm Offset for different water level baselines between reach and
buckets receiving infiltration
Parameter Units Description
Retained water depth mm Depth below which water no longer freely drains
Runoff time constant d Characteristic time constant for water drainage
Relative ET / The fraction of total evapotranspiration in a landscape unit
occurring in a given bucket
ET adjustment / Exponent for limiting evapotranspiration
Infiltration mm The maximum depth of water that may infiltrate into a bucket from
any source
Drought runoff fraction / The fraction of incoming precipitation contributing to runoff when
the soil water will not freely drain
Relative area index / Fraction of surface area covered by bucket
Inundation threshold mm The depth at which water from the reach can inundate a hydrologic
response unit type
Porosity / The void fraction of a bucket (used for calculating height of the
water column)
The calibration strategy for INCA-C followed a slight adaptation to the approach described for PERSiST and by Ledesma et al. (2012). It should be noted that the initial manual calibration was not only need to be done in hydrological sub-model but also in the biogeochemical sub-model. The parameters controlling the hydrological sub-model were fixed once the performance from manual calibration was similar to the best parameter set performance for PERSiST. Parameters for the biogeochemical sub-model were first calibrated manually, after which ranges for the Monte Carlo analysis were defined as ±25 % of the parameter value for the best performing manual calibration. The Monte Carlo tool was then run to find the best-performing dataset (from 100 loops of 300 runs). Parameter sensitivity was assessed using the 100 best performing parameter sets in an analogous manner as in PERSiST. Finally, the best-performing parameter sets for PERSiST and INCA-C were examined through being employed for modelling the flow and DOC in the catchment with the evaluation periods. Parameters of INCA-C model used in MC analysis are listed in Table 4.3.
Table 4.3 Parameters of INCA-C model used in MC analysis.
Parameter Units Description
Base Flow Index / fraction of water that goes to the lower layer from the upper layer
Threshold soil
zone flow m
3 s-1 the threshold flow from the soil at which there is return flow to the
direct runoff layer
Rainfall excess
proportion /
fraction of the hydrologically effective rainfall (HER; precipitation net of evapotranspiration) that goes to the direct runoff layer
Maximum
infiltration rate mm day
-1 the maximum amount of water that can be infiltrated from the direct
runoff layer to the upper layer in a day
Flow a / flow velocity multiplier (dimensionless)
Flow b / flow velocity exponent (dimensionless)
DOC -> DIC self-
shading factor mg L
-1 as DOC increase, factor decreasing the rate in which DOC is
mineralized to DIC as a consequence of photodegradation
DOC -> DIC
radiation multiplier kg m
2 kW-1 multiplier controlling the rate of photodegradation (DOC to DIC) in
the aquatic system
Open water DOC -
> DIC microbial day
-1 velocity in which DOC is transformed into DIC in the stream as a
consequence of microbial degradation
Organic layer SOC
to DOC day
-1 the rate at which SOC is transformed into DOC in the upper layer
Organic layer SOC
to DIC day
-1 the rate at which SOC is transformed into DIC in the upper layer
Mineral layer SOC
to DOC day
-1 the rate at which SOC is transformed into DOC in the lower layer
Mineral layer SOC
to DIC day
-1 the rate at which SOC is transformed into DIC in the lower layer
Organic layer PDC
to SOC day
-1 the rate at which PDC is transformed into SOC in the upper layer
Organic layer PDC
to DIC day
-1 the rate at which PDC is transformed into DIC in the upper layer
Organic layer PDC
to DOC day
Parameter Units Description
Direct runoff PDC
to DOC day
-1 the rate at which PDC is transformed into DOC in the direct runoff
layer
Organic layer
DOC to SOC day
-1 the rate at which DOC is transformed into SOC in the upper layer
Organic layer
DOC to DIC day
-1 the rate at which DOC is transformed into DIC in the upper layer
Mineral layer DOC
to SOC day
-1 the rate at which DOC is transformed into SOC in the lower layer
Mineral layer DOC
to DIC day
-1 the rate at which DOC is transformed into DIC in the lower layer
Organic layer b1 /
parameter b1 to determine the decrease in carbon solubility in the organic layer when there is a strong acidifying anion (i.e. sulphate)
present in the soil solution, i.e. limiting the SOC desorption into DOC, such as dDOC/dt = -(k2 + b1 · [anion]exp b2) · DOC + k1 ·
SOC
Organic layer b2 /
parameter b2 to determine the decrease in carbon solubility in the organic layer when there is a strong acidifying anion (i.e. sulphate)
present in the soil solution, i.e. limiting the SOC desorption into DOC, such as dDOC/dt = -(k2 + b1 · [anion]exp b2) · DOC + k1 ·
SOC
Mineral layer b1 /
parameter b1 to determine the decrease in carbon solubility in the mineral layer when there is a strong acidifying anion (i.e. sulphate)
present in the soil solution, i.e. limiting the SOC desorption into DOC, such as dDOC/dt = -(k2 + b1 · [anion]exp b2) · DOC + k1 ·
SOC
Mineral layer b2 /
Parameter b2 to determine the decrease in carbon solubility in the mineral layer when there is a strong acidifying anion (i.e. sulphate) present in the soil solution, i.e. limiting the SOC desorption into DOC, such as dDOC/dt = -(k2 + b1 · [anion]exp b2) · DOC + k1 ·
SOC Organic layer
retention volume m
3 amount of water per km
2 in the upper layer below which water no
longer freely drains
Mineral layer
retention volume m
3 amount of water per km
2 in the lower layer below which water no
Parameter Units Description
Direct runoff
residence time days characteristic time constant for water drainage
Organic layer
residence time days characteristic time constant for water drainage
Mineral layer
residence time days characteristic time constant for water drainage
Zero rate depth /
parameter used to regulate transformation rates at different moisture conditions. Above a specified SMD (‘Zero rate depth’), processes are
turned off
Max rate depth /
parameter used to regulate transformation rates at different moisture conditions. Above a specified SMD (‘Zero rate depth’), processes are turned off, below they linearly increase until the base level at another
specified SMD value (‘Max rate depth’)
Max rate fraction at box max
capacity
/
parameter used to regulate transformation rates at different moisture conditions. Below the ‘Max rate depth’, another parameter (‘Max rate fraction at box max capacity’) controls the decrease in transformation
rates until SMD=0
Thermal
conductivity of soil W m
-1 K thermal conductivity of the soil
COUP_10Degree
Response /
it multiplies the process rates by the specified value for every 10 degrees increment with respect to the base level soil temperature at
which the processes are multiplied by 1
COUP_BaseT / the base line soil temperature at which the process rates are 1 (°C)
Litterfall kg ha-1 day-1 the amount of literfall per unit of area per day in the catchment
Fast pool fraction / fraction of the total SOC in the upper layer that belongs to the fast
pool
Sensitivity analysis of discharge and DOC-related parameters was assessed by varying best performing parameter sets by ± 25 % in an analogous MC method (de Wit et al., 2016). For each parameter, the Kolmogorov-Smirnov (KS) test was used to compare the ensemble of values from the 100 parameter sets to a rectangular distribution. A significant KS statistic (p<0.05) implied that the posterior distribution was not rectangular and thus that stream
flow or DOC simulations were sensitive to the specific parameter (Futter et al. 2014).