How RAPID works© 2015 Cédric H. DavidAll Rights Reserved

By Cédric H. David(cedric.david@jpl.nasa.gov)
12 Dec 2011, updated 21Jan 2015

1

RAPID is based on theMuskingum methodA
k is a time (k ≥ 0) related to the celerity of theflow wave

Direction of flow

x is a non-dimensional parameter (0 ≤ x ≤ 0.5)
related to diffusion of the flow wave

Flow
(m3/s)
AB

x = 0.5

x=0k

kFlow
(m3/s)B

Time (s)ABTime (s)2© 2015 Cédric H. DavidAll Rights Reserved

Two types of RAPID runs• Stream flow computation– Computes flow rate based on Muskingum
parameters and inflow of water from land andaquifers to river network• Optimization of parameters– Automatically calibrates k and x around some
initial values through comparison between
computations and observations of stream flow3
© 2015 Cédric H. DavidAll Rights ReservedTypes of input for stream flow
computations• River network connectivity information• Inflow of surface and subsurface water tothe river network• Model parameters4© 2015 Cédric H. DavidAll Rights Reserved

RAPID solves a vector-matrix
version of the Muskingum method(I − C1 ⋅ N) ⋅ Q (t + Δt ) = C1 ⋅ Qe (t ) + C2 ⋅ ⎡⎣N ⋅ Q (t ) + Qe (t )⎤⎦ + C3 ⋅ Q (t )INIdentity matrix
Network matrix, computed based on network connectivity information

Vector of flow rates from outside the network into upstream ofeach river reach
C1 , C2 , C3 Parameter matrices, computed based on the values of k and xQeQ

Vector of flow rates at the outlet of each river reach (output of RAPID)

5© 2015 Cédric H. DavidAll Rights Reserved

River network connectivity (1/2)
Downstream
River ID
River ID

UpstreamRiver ID 1

Number ofupstream
River IDs

UpstreamRiver ID 3
UpstreamRiver ID 4

UpstreamRiver ID 2

Numberof riverreaches
Max number ofupstream reaches

From David et al. 2011 (JHM)

Time-independent, .csv file6

© 2015 Cédric H. DavidAll Rights Reserved

River network connectivity (2/2)

From David et al. 2011 (JHM)

7© 2015 Cédric H. DavidAll Rights Reserved

Inflow of surface and subsurface
water to the river network

Number of river reaches
Number of
3-hourly
time steps

Time-dependent, .nc file
There are 1460 days between 2004/01/01 and 2007/12/30, i.e.
1460*24/3=11686 3-hourly time steps
Treated as entering upstream of each river reach© 2015 Cédric H. DavidAll Rights Reserved8Model parametersxjkjTime-independent, .csv files© 2015 Cédric H. DavidAll Rights Reserved

9Types of input for optimizationof parameters• River network connectivity information(same as previously)• Inflow of surface and subsurface water tothe river network (same)• Some estimation of model parameters(different)• Observations of stream flow on the river
network (new)10© 2015 Cédric H. DavidAll Rights Reserved

RAPID uses the inverse methodfor optimization⎡⎛ Q (t ) − Qg (t ) ⎞T⎛ Q (t ) − Qg (t ) ⎞ ⎤⎥φ (k , x ) = ∑ ⎢⎜⋅ G ⋅ ⎜⎟⎟⎜⎟
⎜⎟ ⎥ff
t =to ⎢⎝⎠⎝⎠ ⎦⎣t =t f

GGauge matrix

Qg

Observed daily stream flow

Q

Vector of daily flow rates at the outlet of each river reach(output of RAPID)

11© 2015 Cédric H. DavidAll Rights Reserved

First guess of model parametersin optimization modeRAPID looks for λk andλx that minimize the costfunction

k j = λ k ⋅ k jfac
x j = λ x ⋅ 0.1

k jfac estimated based on

length of river reach andon celerity of flow wave

Time-independent, .csv file© 2015 Cédric H. DavidAll Rights Reserved

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Observations of stream flow on
the river network
List of river IDs wheregauges are locatedObservations in m3/s

Number of river gauges

Number of river gauges

Time-independent, .csv file© 2015 Cédric H. DavidAll Rights Reserved

Number ofdaily
observations

Time-dependent, .csv file13

Further information
RAPID website: http://rapid-hub.org/
RAPID source code: https://github.com/c-h-david/rapid/

14© 2015 Cédric H. DavidAll Rights Reserved