Appendix A
Description of the top-down model structure used in the study-
1.
Snow module: The snow module allows for snow storage and melt using a simple degree-day factor method. The precipitation becomes rain or snow depending on the threshold temperature. If average temperature is less than the threshold temperature, precipitation is converted to snow, otherwise it falls as rain and goes directly to the soil moisture accounting module. Based on DeWalle and Rango [2008], the melt equation is given as,
M

Ddf * ( T av

T b
)
2.
Multiple bucket soil moisture accounting module: This is a multiple bucket model with three stores - an unsaturated store, a saturated store and a deep store that is recharged by the deep percolation from the unsaturated and saturated zones. The deep store only loses water through baseflow, no evapotranspiration losses occur in this store.
(i) Threshold storage parameter and threshold storage in the unsaturated zone f c




 f
 c




 w l t w l t
S
 u s f c

S b

S s a t

1
 f c
(ii) Interception and evapotranspiration - Depletion from the unsaturated and saturated zones is allocated proportionally according to water storages contents in these zones.
E i
  ei
P
S u s

S t

S
S
 u s r p


S u s

S us



0
P

E i
S usfc
S us
S us




S usfc
S usfc where r p
, recharge to the saturated zone, occurs when the field capacity in the unsaturated zone is satisfied.
S t

S
 m i n

S b
 b
,
,
S u s

S
 t

1
S s a t t

1
 r p

S us
S usfc
=
S t
 f c
-
S sat

S b

S sat

E v sat

S sat ME p
S t
E bs sat
=
S sat
(
1
-
M
)
E p
S t

E bs us

S us

1

M

S b
S us

S sat
E p
S t
E v
E b s us







S us
S t
S us
S t
M
E b s u s

E b s
ME p
0
S us
S usfc
E p
S us

S usfc
S
S us us


0
S usfc sa t
E v

E v us

E v sat
E

E i

E v

E bs
3.
Base flow from the deep store and deep storage.
Q bf
  bf
S deep r g
 k d
S s a t
S deep

S deep

Q bf
 r g
4.
Saturated excess runoff, subsurface runoff and soil water storage at the current time step.
Here, S t does not contain soil water storage of the deep store.
S t

S t

1

P

E
Q s e

S
0
S b
S

S t t

S
S b b
S

S
 r g
S s s
 
S s s s a t sat

S sat

Q ss
Q

Q se

Q ss

Q bf
S t

S t

Q se

Q ss
 r g
The stores have a multiple bucket configuration with ten buckets combined in parallel.
These are used to represent a variable soil moisture distribution that fits the Xinanjiang model distribution.
S
F max




1
 b

S b
0 .
05 0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95

S b _ f

S max

 1


1

F
 1 b


5.
Representation of phenology– Water extraction efficiency is used to capture the ability of a plan to use water stored within the root zone layer of the soil. Above a mean daily temperature of 10C, there are no effects on water extraction efficiency from temperature.
Between -5C and 10C, there is assumed to be a linear relationship between temperature and

the efficiency in which ET can occur. Below -5C, it is assumed that ET from vegetation has stopped (value of 0).
P P ((1 M ) Mf I eff
  
( ))
LA
E

Eus

Esat

( E bs
E v

P GS
( t
/ S b
)

E )

( E bs

E
If T m in

10
If
then I
GS

1 , if T min
 
5 then I
GS

0
5 T min

10 then I
GS
 


T min


6.
Variable canopy interception: Canopy interception is assumed to change in a periodic fashion through the year. A maximum and minimum Leaf Area Index (LAI) are two additional parameters that are added, and a sine function is used to estimate the LAI throughout the year. The LAI sine function peaks to the maximum LAI during the summer and drops to its minimum LAI during the winter. Water on the canopy evaporates at the potential rate.
LAI


LAI max
Cei
Max
 

LAI min
 sin
LAI
2 x
 
365 2

0.00575* *

* M
Notation
 fc field capacity [-]
 wlt permanent wilting point [-]
 porosity [-] f c threshold storage parameter [-] (0< f c
<1)
S b maximum storage of the bucket model [mm]
S fc threshold storage [mm]
P precipitation [mmd -1 ]
P eff effective precipitation [mmd -1 ]
E potential evapotranspiration [mmd -1 ] p
E actual evapotranspiration [mmd -1 ]
E i interception [mmd -1 ]
E v vegetation transpiration [mmd -1 ]
E bs bare soil evaporation [mmd -1 ]
E v us
transpiration from unsaturated zone [mmd -1 ]
E v sa t
transpiration from saturated zone [mmd -1 ]
E evaporation from unsaturated zone [mmd -1 ] bs us
E b s
evaporation from saturated zone [mmd -1 ]

S sat soil water storage in saturated zone [mm]
S us soil water storage in unsaturated zone [mm]
S u sfc field capacity of current unsaturated zone [mm]
S de e p soil water storage in deep store [mm]
S t total soil water storage at current time t [mm]
S t

1 total soil water storage at last time step t-1 [mm]
S sat t

1
soil water storage of saturated zone at last time step t-1 [mm] r daily recharge to saturated zone from unsaturated zone in which water storage exceeds field capacity [mm] p r daily recharge from upper saturated zone to deeper store [mm] g
Q total runoff [mmd -1 ]
Q se surface runoff generated by saturation excess [mmd -1 ]
Q ss subsurface flow originating from saturated zone [mmd -1 ]
Q bf base flow originating from deep store [mmd -1 ]
M fraction of catchment area covered by deep rooted vegetation [-]
K v vegetation transpiration efficiency [-]
 ss recession coefficient for subsurface flow from saturated zone store in the linear storage-outflow model [d -1 ]
 recession coefficient for subsurface flow from deep store in the linear storage-outflow model [d -1 ] bf k d deep recharge coefficient from the upper saturated zone to the deep store [d -1 ] b
F shape parameter for spatial soil water storage distribution in the multi-bucket model [-] cumulative probabilities at which soil water storages of 10 buckets fit spatial soil water storage distribution
[-]
S max maximum soil water storage in the watershed [mm]
S b _ f soil water storage capacities in the 10 buckets [mm]
LAI max maximum Leaf Area Index [-]
LAI min
minimum Leaf Area Index [-]
F
DD degree day factor [mm T -1 ]
T
T threshold temperature that classifies snow as rain or snow
Cei
Max
Maximum canopy interception
References
Bai, Y., T. Wagener, and P. Reed (2009), A top-down framework for watershed model evaluation and selection under uncertainty, Environ. Modell. Softw.
, doi:10.1016/j.envsoft.2008.12.012.
DeWalle, D. R., and A. Rango (2008), Modelling snowmelt runoff, In, Principles of Snow Hydrology , 266-305,
Cambridge University Press, New York, USA.
Sawicz, K., 2013. Catchment classification – understanding hydrologic similarity through catchment function. PhD
Thesis , The Pennsylvania State University, University Park, PA.

Appendix B
Table B-1 Estimating the a-priori ranges for field capacity parameter from physical characteristics of the watersheds
Sand
Silt
Average content [%]
30
50
Porosity range*,φ [%]
250
350
Permanent wilting point**,
θ pwp
[%]
4
17
Available water
(θ fc
- θ pwp
)*** [%]
11
11
Porosity –
PWP
Final
Range
(φ- θ pwp)
21-46 0.22-0.61
18-33
Clay 20 50-70 21 11 29-49
*Wicander, R., and J.S. Monroe (2006), Essentials of Geology , Thomson Brooks/Cole, USA.
**http://www.stevenswater.com/articles/irrigationscheduling.aspx
***Estimated from AWCAVE, the average value of the range of available water capacity for the soil layer in the Falcone database [ Falcone et al.
, 2010]
Table B-2 Estimating the a-priori ranges for soil depth (Sb) parameter from physical characteristics of the watersheds in the Falcone database [ Falcone et al.
, 2010]
Average soil thickness [mm] Porosity range*,φ [%]
1156 270
Range for Sb = D*φ [mm]
290-810
Table B-3. Estimating the a-priori ranges for vegetation parameters M, LAI min
, and LAI max
Watershed percent forest [%] Range for vegetation parameter, M
LAI range†
70
†Most of the forests are deciduous
0.6-0.8 0-6

Figure B-1 Example for demonstrating the derivation of recession coefficients 1 and 2 using streamflow data from 1948-1958. The figure shows the recession coefficients derived for an example year in the streamflow record. The segments are arranged in order of decreasing mean flow. For estimating recession coefficient 1, the average slope across all Slope-1 type recessions
(left black box) in the particular year was used. For recession coefficient 2, the Slope-2 type recession segments (right black box) were joined together in a ‘master’ recession curve and the slope of this curve was estimated for each year. The range of recession coefficients 1 and 2 was obtained by carrying out this procedure across all years.
Figure B-2 Ranges of recession coefficients 1 and 2 as derived from analyzing the streamflow hydrographs according to the procedure in Figure E-1. Since the range of recession coefficient 1

is quite large, the 25 th
and 75 th
percentile values (0.07-0.16 mm/day) are used as a-priori ranges.
For recession coefficient 2, the entire range is used (0.012-0.025 mm/day)
Figure B-3 Monthly distribution of streamflow for the Lower Juniata watershed.

Appendix C
Here we include the classification trees for the indicators not included in the main text
(Figures C1-C6) and the data related to the construction of classification trees used in the study in Table C1. Classification trees for the following additional hydrologic indicators are included –
1.
Minimum April flow
2.
Low flow pulse count
3.
Low flow pulse duration
4.
High flow pulse duration
5.
Seasonal predictability of non-flooding
6.
Reversals
Hydrologic indicator
Misclassification error rate [%]
2 S.D.
Cross validation error rate [%]
2 S.D.
Mean annual runoff
Min. April
Max. Aug
Low QP count
Flood Frequency
Low QP duration
High QP duration
Predictability
Reversals
Mean annual runoff
Min. April
Max. Aug
Low QP count
Flood frequency
Low QP duration
High QP duration
Predictability
Reversals
15
41
25
17
39
35
35
21
11
25
52
32
18
50
39
27
NO TREE
15
15
41
25
17
39
35
35
28
11
25
52
32
18
50
39
27
NO TREE
15
Table A1. Misclassification and cross validation error rates for the trees used in the study.
The misclassification and cross validation error rates are estimated from the summary statistics of the statistical package ~ rpart (from R). The misclassification error rates are obtained by multiplying the root node error with the relative misclassification rate and the cross validation error rates are obtained by multiplying the root node error with the relative cross –validation error rate [Therneau and Atkinson, 1997].

Figure C1-6 display the resultant classification trees for these indicators for thresholds fixed at ±2 standard deviations of the historical mean with (a) fixed deep rooted vegetation
(between 60% to 80%) and (b) varying vegetation (between 0 to 100%). The bar plots represent the probability of belonging to a particular class if the path leading to that node is followed. The range of historically observed values and class assignments is also included. For each figure, the color scheme across all subplots is fixed, so the color scheme in the class assignments is the same as the color scheme in the bar plots. The class name associated with each classification is represented by a different color and is provided in the subplot relating probability to classes.
References
Therneau, T.M., and E.J. Atkinson (1997), An introduction to recursive partitioning using the
RPART routines, Technical Report 61, Mayo Clinic, Section of Statistics. Accessed online on 24 th
January 2014 from: http://www.mayo.edu/hsr/techrpt/61.pdf

Figure C-1 Minimum April flow – the color schemes across the plot are fixed. So shades of yellow and red represent increased values as compared to the historically observed range and shades of green represent values of minimum April flow below the historically observed ranges.
Note that the color scheme does not suggest vulnerability but simply the different possibilities.
April is the month of maximum flow, therefore, the impact of an increase or decrease in the minimum flow will be considered vulnerable or not vulnerable depending upon the particular stakeholder.

Figure C-2 Low flow pulse count – the color schemes across the plot are fixed. Only two classes were obtained for this indicator across all the parameter and climate combinations. So gray and black represent historical variability and a decrease from historical variability respectively.

Figure C-3 Low flow pulse duration– the color schemes across the plot are fixed. Five classes were obtained for this indicator across all the parameter and climate combinations. Gray and green represent historical variability and a decrease from historical variability respectively. Since an increase in the duration of low flow pulses can be considered vulnerable, it is shown by shades of yellow and red.

Figure C-4 High flow pulse duration– the color schemes across the plot are fixed. Five classes were obtained for this indicator across all the parameter and climate combinations. Gray and green represent historical variability and a decrease from historical variability respectively. Since an increase in the duration of low flow pulses can be considered vulnerable, it is shown by shades of yellow and red.

Figure C-5 Seasonal predictability of non flooding – the color schemes across the plot are fixed.
Only 2 classes were obtained for this indicator across all the parameter and climate combinations. So gray and black represent historical variability and slight decrease from historical values respectively. The tree with varying vegetation in (b) was trimmed for presentation here and extends another two layers of controls.

Figure C-6 Reversals – the color schemes across the plot are fixed. Only 2 classes were obtained for this indicator across all the parameter and climate combinations. So gray and black represent historical variability and slight decrease from historical values respectively.