implemented within each case study. In particular, a semi-distributed version of a
continuous Kalinin-Milyukov-Nash (KMN) cascade hydrological model is applied
on the Brue catchment, while a semi-distributed hydrological and hydraulic model
developed by the Alto Adriatico Water Authority is implemented in the
Bacchiglione catchment. In this study, synthetic flow observations derived from
observed and simulated quantitative streamflow are used. Synthetic data are used to
evaluate the potential of the proposed approaches as real qualitative observations
may be affected by different unpredictable errors.
3.1 Brue Catchment (UK)
The Brue catchment is located in Somerset, South West England, with a drainage
area of about 135 km
2 and a time of concentration of 10 h at the catchment outlet,
Lovington. Hourly precipitation data are supplied by the British Atmospheric Data
Centre from the NERC Hydrological Radar Experiment Dataset (HYREX) project
[67, 68] and available at 49 automatic rain stations; average annual rainfall of
867 mm is measured in the period between 1961 and 1990. Discharge is measured
at the catchment outlet by one station at a 15 min time step resolution, having an
average value of 1.92 m
3 /s. For both precipitation and discharge data, a 3-year
complete data set, between 1994 and 1996, is available.
A semi-distributed hydrological model is used to assess the flood hydrograph at
the outlet section of the Brue catchment and to represent the spatial variability of the
CS flow observations. The Brue catchment is divided into 68 sub-catchments having
a small drainage area (on average around 2 km
2 ) so that any observation at a random
location in a given sub-catchment would provide the same information content that
an observation at the outlet of same sub-catchment [60]. For each sub-catchment, a
conceptual lumped hydrological model, continuous Kalinin-Milyukov-Nash (KMN)
cascade, is implemented to estimate the outflow discharge [69]. The KMN model
considers a cascade of storage elements (or reservoirs), assuming that the relation
between stage, discharge and stored water volume is linear and that the water storage
x t is only a function of the outflow of the reach Q t [60]. Subsequently, the KMN is
represented as a dynamic state-space system to apply data assimilation techniques as
explained in the previous section. In the case of the linear systems, the discrete statespace system can be represented as follows [69]:
x t ¼ Φx tÀ1 þ ΓI t þ w t
ð1Þ
z t ¼ Hx t þ v t
ð2Þ
where t is the time step, x is vector of the model states (stored water volume in m
3 ),
Φ is the state-transition matrix (function of the model parameters n and k), Γ is the
input-transition matrix, H is the output matrix and I and z are the input (forcing) and
model output, while w and v are the system and measurements errors.
214
M. Mazzoleni et al.
continuous Kalinin-Milyukov-Nash (KMN) cascade hydrological model is applied
on the Brue catchment, while a semi-distributed hydrological and hydraulic model
developed by the Alto Adriatico Water Authority is implemented in the
Bacchiglione catchment. In this study, synthetic flow observations derived from
observed and simulated quantitative streamflow are used. Synthetic data are used to
evaluate the potential of the proposed approaches as real qualitative observations
may be affected by different unpredictable errors.
3.1 Brue Catchment (UK)
The Brue catchment is located in Somerset, South West England, with a drainage
area of about 135 km
2 and a time of concentration of 10 h at the catchment outlet,
Lovington. Hourly precipitation data are supplied by the British Atmospheric Data
Centre from the NERC Hydrological Radar Experiment Dataset (HYREX) project
[67, 68] and available at 49 automatic rain stations; average annual rainfall of
867 mm is measured in the period between 1961 and 1990. Discharge is measured
at the catchment outlet by one station at a 15 min time step resolution, having an
average value of 1.92 m
3 /s. For both precipitation and discharge data, a 3-year
complete data set, between 1994 and 1996, is available.
A semi-distributed hydrological model is used to assess the flood hydrograph at
the outlet section of the Brue catchment and to represent the spatial variability of the
CS flow observations. The Brue catchment is divided into 68 sub-catchments having
a small drainage area (on average around 2 km
2 ) so that any observation at a random
location in a given sub-catchment would provide the same information content that
an observation at the outlet of same sub-catchment [60]. For each sub-catchment, a
conceptual lumped hydrological model, continuous Kalinin-Milyukov-Nash (KMN)
cascade, is implemented to estimate the outflow discharge [69]. The KMN model
considers a cascade of storage elements (or reservoirs), assuming that the relation
between stage, discharge and stored water volume is linear and that the water storage
x t is only a function of the outflow of the reach Q t [60]. Subsequently, the KMN is
represented as a dynamic state-space system to apply data assimilation techniques as
explained in the previous section. In the case of the linear systems, the discrete statespace system can be represented as follows [69]:
x t ¼ Φx tÀ1 þ ΓI t þ w t
ð1Þ
z t ¼ Hx t þ v t
ð2Þ
where t is the time step, x is vector of the model states (stored water volume in m
3 ),
Φ is the state-transition matrix (function of the model parameters n and k), Γ is the
input-transition matrix, H is the output matrix and I and z are the input (forcing) and
model output, while w and v are the system and measurements errors.
214
M. Mazzoleni et al.