Documentation of Supply-Demand Cycle & Reservoir Effect

View the 42 variables sorted by type, module, group, module/group/name, view, Level Structure, or in a view summary.

Model Assessment Results
Model Information Number
Total Number of Variables
42
Total Number of State Variables (Level+Smooth+Delay Variables)
6 (14.3%)
Total Number of Stocks (Stocks in Level+Smooth+Delay Variables) †
8 (19%)
0
0
13 (31%)
40 (95.2%)
0
0
Time Unit
Year
Initial Time
0
Final Time
80
Reported Time Interval
1
Time Step
0.0625
Model Is Fully Formulated
Yes
Modeler-Defined Groups
- No -
VPM File Available
- No -


Warnings Number
0
0
Unavailable
0
0
0
0
0
1 (2.4%)
5 (11.9%)
0

Potential Omissions Number
0
0
0
4
0

Types:
L : Level (4 / 4) * SM : Smooth (1 / 1) * DE : Delay (1 / 3) * † LI : Level Initial (3) I : Initial (0)
C : Constant (24) F : Flow (5) A : Auxiliary (12) Sub: Subscripts (0) D : Data (0)
G : Game (0) T : Lookup (0 / 0) ††      
* (state variables / total stocks)
† Total stocks do not include fixed delay variables.
†† (lookup variables / lookup tables).
 
Groups:
Control (4)
Simulation Control Parameters 		Supply-Demand Cycle & Reservoir Effect (38)
(Default)
Modules:
Default (42)
Views:
View 1 (38)View 2 (0) 
Search: •••    a-b    c-d    e-f    g-h    i-j    k-l    m-n    o-p    q-r    s-t    u-v    w-x    y-z    •••   

Module
Group
Type
 Variable Name and Description
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #1
C
Annual Storage i (Year)
= 1
Description: To calculate water availability, w, water demand should be compared to the annual water stored in the reservoir. Constant i adjusts the unit consistency in calculation of w.
Present in 1 view: Used by:
  • Water Availability A - Water availability is the ratio of available water stored in reservoirs, R, over the total demand, D. When this ratio is below one, water shortage takes place. In that case, there is not enough water in the reservoirs to meet the demand. In this model, water availability is the main input for calculating socioeconomic growth and vulnerability.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #2
C
Carrying Capacity w (MCM)
= 500
Description: The total amount of surface water that can be stored and consumed later. This amount depends on the boundaries of a system. If water transfer from other resources that are miles away becomes an option, this amount increases. However, at the end, there still exists a maximum amount that can be utilized in a system.
Present in 1 view: Used by:
  • Potential Addition to Capacity K - The remaining amount of surface water that has not been stored yet. Potential addition to capacity dictates the maximum capacity of new infrastructures.
  • Recharging Rate F - Recharging rate is the amount of water that annually inflows to reservoir storage infrastructures. Different forces control this inflow, including the amount of free capacity in storages in a year, (C(t)-R(t))/rd, the annual amount of water released as supply in each time step, S, and the maximum available amount of surface water (carrying capacity) that can recharge the storages in each year, w/d.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #3
C
Construction Delay j (Year)
= 4
Description: The average delay in construction of different sorts of water storage facilities, including reservoirs, dams, water tanks and towers, etc.
Present in 1 view: Used by:
  • Construction Rate T - The rate of change in storage capacity or construction rate is formulated as third-order delay of required additional capacity, J.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #4
DE,F
Construction Rate T (MCM/Year)
= DELAY3(Required Additional Capacity J, Construction Delay j)
Description: The rate of change in storage capacity or construction rate is formulated as third-order delay of required additional capacity, J.
Present in 1 view: Used by:
  • Storage Capacity C - The storage capacity, C, includes a range of infrastructure from big reservoirs to small water tanks. Storage capacity imposes the maximum possible water accumulation and therefore the cap for water supply in the system. When the need for supply exceeds the current storage capacity, public pressure requires additional capacity, J. Storage capacity can increase up to the total available surface water or carrying capacity, w, within the boundaries of system.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #5
C
Delay for Population Change c (Year)
= 1
Description: Water availability, w, over time increases the population. The main delay in this process is incorporated in the smooth function of socioeconomic growth, G. It takes time for a society to perceive water availability. After this delay in perception, e, the population changes accordingly within a year.
Present in 1 view: Used by:
  • Population Net Change M - In this generic model, population net changes, M, is only impacted by the socioeconomic growth, G, which in turn is derived from water availability, A. Other forces that govern population in real world are excluded here. M adds to total population when G is positive and decreases population when G is negative.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #6
C
Delay for Vulnerability Decline b (Year)
= 10
Description: When the society wants to adjust itself to drought situation, water dependency declines with a slower rate. This effect is known as stickiness in economics literature. Therefore, the rate of change in vulnerability is different when it is growing or decreasing. When Q>V(t) the delay is a and when Q<V(t) delay becomes b. b is always greater than a.
Present in 1 view: Used by:
  • Vulnerability Change N - The rate of change in vulnerability, N, changes by reservoir effect. When water availability is one or higher, people become more dependent. This extra vulnerability becomes a new norm after few years, a. However, when the society wants to adjust itself to drought situation, water dependency declines with a slower rate. This effect is known as stickiness in economics literature. Therefore, the rate of change in vulnerability is different when it is growing or decreasing. When Q>V(t) the delay is a and when Q<V(t) delay becomes b. b is always greater than a.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #7
C
Delay for Vulnerability Growth a (Year)
= 5
Description: When the society wants to adjust itself to drought situation, water dependency declines with a slower rate. This effect is known as stickiness in economics literature. Therefore, the rate of change in vulnerability is different when it is growing or decreasing. When Q>V(t) the delay is a and when Q<V(t) delay becomes b. b is always greater than a.
Present in 1 view: Used by:
  • Vulnerability Change N - The rate of change in vulnerability, N, changes by reservoir effect. When water availability is one or higher, people become more dependent. This extra vulnerability becomes a new norm after few years, a. However, when the society wants to adjust itself to drought situation, water dependency declines with a slower rate. This effect is known as stickiness in economics literature. Therefore, the rate of change in vulnerability is different when it is growing or decreasing. When Q>V(t) the delay is a and when Q<V(t) delay becomes b. b is always greater than a.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #8
C
Delay in Supply k (Year)
= 1
Description: Time to release supply water from storage facilities. Since we care about annual statistics, this delay is one.
Present in 1 view: Used by:
  • Water Supply S - Water supply, S, in each time step equals to water demand, D. However, it cannot be more than total water stored in supply infrastructures, R, with a certain capacity, C. If demand exceeds the stored water, we can only supply as much as accumulated in the reservoir storage, R. The unfulfilled demand becomes water shortage.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #9
C
Demand per Person per Year z (Liter/Person/Year)
= 1.385e+06
Description: The global annual average of water consumption per capita is 1,385 cubic meters (Scientific American, 2012).
Present in 1 view: Used by:
  • Water Demand D - Water demand is calculated based on the average demand per person per year, z, multiplied by the total population, P. The total demand is the sum of individual demands. Constant u is used to change the units from liter to MCM.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #10
A
Economic Damage E (Dmnl)
= Water Shortage H*(1+Vulnerability V)
Description: In this hypothetical model, the system confronts a certain extent of economic damage, 1+V(t), for each percentage of shortage ratio, H. The total economic damages also depends on the vulnerability of the society in each time step, V(t). When V(t) increases or decreases, the economic damage linearly changes accordingly. Economic damage is normalized here. The absolute amount of damage can be acquired if H multiplied by an average dollar amount of each percentage of shortage ratio.
Present in 1 view: Used by:
  • Public Pressure L - For each percentage of normalized economic damage during shortage period, presumably the society will put an average pressure on government to build more infrastructure for further water supply. Therefore the total pressure is a function of economic damage. This function is assumed to be linear.
Default Control #11
C
FINAL TIME (Year)
= 80
Description: The final time for the simulation.
Not Present In Any View
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #12
LI,C
Initial Population P0 (Person)
= 100000
Description: The initial population, P0, is assumed to be one million people.
Present in 1 view: Used by:
  • Population P - The stock of population, P, accumulates the population net changes, M, over time. The initial population, P0, is assumed to be one million people.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #13
LI,C
Initial Storage Capacity C0 (MCM)
= 150
Description: The initial value for stored water is assumed to be equal to the initial storage capacity, C0. All the storage infrastructures are assumed to be full in t=0.
Present in 1 view: Used by:
  • Reservoir Storage R - Reservoir storage, R, represents the total amount of water stored in reservoirs or other storage infrastructures. This amount increases by recharging rate, F, from precipitation, water transfers, or other means. According to the water demand, D, water will be released as water supply, S. R cannot exceed the storage capacity, C. The initial value for stored water is assumed to be equal to the initial storage capacity, C0. All the storage infrastructures are assumed to be full in t=0.
  • Storage Capacity C - The storage capacity, C, includes a range of infrastructure from big reservoirs to small water tanks. Storage capacity imposes the maximum possible water accumulation and therefore the cap for water supply in the system. When the need for supply exceeds the current storage capacity, public pressure requires additional capacity, J. Storage capacity can increase up to the total available surface water or carrying capacity, w, within the boundaries of system.
Default Control #14
C
INITIAL TIME (Year)
= 0
Description: The initial time for the simulation.
Not Present In Any View
Used by:
  • Time - Internally defined simulation time.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #15
LI,C
Initial Vulnerability V0 (Dmnl)
= 0
Description: Vulnerability in the start time, V0, is assumed to be zero. That means the reservoir effect on the system is zero at t=0.
Present in 1 view: Used by:
  • Vulnerability V - The reservoir effect states that the construction of the reservoirs reduces the incentive for adaptive actions at individual or community levels.The lack of incentive for adaptive actions reduces the resiliency of the system against the negative impacts of water shortages during severe droughts. Excessive water supply increases dependency on water resources and makes the population more vulnerable to extreme water shortages. Vulnerability in the start time, V0, is assumed to be zero. That means the reservoir effect on the system is zero at t=0.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #16
C
Liter to MCM u (MCM/Liter)
= 1e-09
Description: One liter is one billionth of a million cubic meter.
Present in 1 view: Used by:
  • Water Demand D - Water demand is calculated based on the average demand per person per year, z, multiplied by the total population, P. The total demand is the sum of individual demands. Constant u is used to change the units from liter to MCM.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #17
F,A

Population Net Change M (Person/Year)
= Population P *Socioeconomic Growth G/Delay for Population Change c
Description: In this generic model, population net changes, M, is only impacted by the socioeconomic growth, G, which in turn is derived from water availability, A. Other forces that govern population in real world are excluded here. M adds to total population when G is positive and decreases population when G is negative.
Present in 1 view: Used by:
  • Population P - The stock of population, P, accumulates the population net changes, M, over time. The initial population, P0, is assumed to be one million people.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #18
L
Population P (Person)
= ∫Population Net Change M dt + [Initial Population P0]
Description: The stock of population, P, accumulates the population net changes, M, over time. The initial population, P0, is assumed to be one million people.
Present in 1 view: Used by:
  • Population Net Change M - In this generic model, population net changes, M, is only impacted by the socioeconomic growth, G, which in turn is derived from water availability, A. Other forces that govern population in real world are excluded here. M adds to total population when G is positive and decreases population when G is negative.
  • Water Demand D - Water demand is calculated based on the average demand per person per year, z, multiplied by the total population, P. The total demand is the sum of individual demands. Constant u is used to change the units from liter to MCM.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #19
A
Potential Addition to Capacity K (MCM)
= MAX(0,Carrying Capacity w-Storage Capacity C)
Description: The remaining amount of surface water that has not been stored yet. Potential addition to capacity dictates the maximum capacity of new infrastructures.
Present in 1 view: Used by:
  • Required Additional Capacity J - We assumed that if public pressure, L, exceeds a normal threshold for a society, t, the government would try to resolve the source of dissatisfaction, water shortage. To do so, the government increases water supply by constructing more capacity for storage. However, there is a natural limit for expansion of infrastructures. This limit is addressed in the potential addition to capacity, K. When K cannot support more water, J will be zero as well.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #20
A
Public Pressure L (Dmnl)
= Economic Damage E*Public Pressure Multiplier p
Description: For each percentage of normalized economic damage during shortage period, presumably the society will put an average pressure on government to build more infrastructure for further water supply. Therefore the total pressure is a function of economic damage. This function is assumed to be linear.
Present in 1 view: Used by:
  • Required Additional Capacity J - We assumed that if public pressure, L, exceeds a normal threshold for a society, t, the government would try to resolve the source of dissatisfaction, water shortage. To do so, the government increases water supply by constructing more capacity for storage. However, there is a natural limit for expansion of infrastructures. This limit is addressed in the potential addition to capacity, K. When K cannot support more water, J will be zero as well.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #21
C
Public Pressure Multiplier p (Dmnl)
= 1
Description: This multiplier shows the sensitivity of a society toward economic damages forced by water shortage. A society with higher p would put more pressure on government to facilitate the supply process.
Present in 1 view: Used by:
  • Public Pressure L - For each percentage of normalized economic damage during shortage period, presumably the society will put an average pressure on government to build more infrastructure for further water supply. Therefore the total pressure is a function of economic damage. This function is assumed to be linear.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #22
C
Public Pressure Threshold t (Dmnl)
= 0.15
Description: Public Pressure forces the government to build more reservoirs, however, it should reach a threshold to become significant in the system.
Present in 1 view: Used by:
  • Required Additional Capacity J - We assumed that if public pressure, L, exceeds a normal threshold for a society, t, the government would try to resolve the source of dissatisfaction, water shortage. To do so, the government increases water supply by constructing more capacity for storage. However, there is a natural limit for expansion of infrastructures. This limit is addressed in the potential addition to capacity, K. When K cannot support more water, J will be zero as well.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #23
C
Recharging Delay d (Year)
= 1
Description: Time that surface water takes to inflow into the storage facilities. Since we care about annual statistics, this delay is one.
Present in 1 view: Used by:
  • Recharging Rate F - Recharging rate is the amount of water that annually inflows to reservoir storage infrastructures. Different forces control this inflow, including the amount of free capacity in storages in a year, (C(t)-R(t))/rd, the annual amount of water released as supply in each time step, S, and the maximum available amount of surface water (carrying capacity) that can recharge the storages in each year, w/d.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #24
F,A

Recharging Rate F (MCM/Year)
= MIN(Carrying Capacity w/Recharging Delay d, Water Supply S+(Storage Capacity C-Reservoir Storage R)/Recharging Delay d)
Description: Recharging rate is the amount of water that annually inflows to reservoir storage infrastructures. Different forces control this inflow, including the amount of free capacity in storages in a year, (C(t)-R(t))/rd, the annual amount of water released as supply in each time step, S, and the maximum available amount of surface water (carrying capacity) that can recharge the storages in each year, w/d.
Present in 1 view: Used by:
  • Reservoir Storage R - Reservoir storage, R, represents the total amount of water stored in reservoirs or other storage infrastructures. This amount increases by recharging rate, F, from precipitation, water transfers, or other means. According to the water demand, D, water will be released as water supply, S. R cannot exceed the storage capacity, C. The initial value for stored water is assumed to be equal to the initial storage capacity, C0. All the storage infrastructures are assumed to be full in t=0.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #25
A
Required Additional Capacity J (MCM/Year)
= IF THEN ELSE(Public Pressure L<Public Pressure Threshold t, 0 , Potential Addition to Capacity K/Time to Adjust Capacity h)
Description: We assumed that if public pressure, L, exceeds a normal threshold for a society, t, the government would try to resolve the source of dissatisfaction, water shortage. To do so, the government increases water supply by constructing more capacity for storage. However, there is a natural limit for expansion of infrastructures. This limit is addressed in the potential addition to capacity, K. When K cannot support more water, J will be zero as well.
Present in 1 view: Used by:
  • Construction Rate T - The rate of change in storage capacity or construction rate is formulated as third-order delay of required additional capacity, J.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #26
L
Reservoir Storage R (MCM)
= ∫Recharging Rate F-Water Supply S dt + [Initial Storage Capacity C0]
Description: Reservoir storage, R, represents the total amount of water stored in reservoirs or other storage infrastructures. This amount increases by recharging rate, F, from precipitation, water transfers, or other means. According to the water demand, D, water will be released as water supply, S. R cannot exceed the storage capacity, C. The initial value for stored water is assumed to be equal to the initial storage capacity, C0. All the storage infrastructures are assumed to be full in t=0.
Present in 1 view: Used by:
  • Recharging Rate F - Recharging rate is the amount of water that annually inflows to reservoir storage infrastructures. Different forces control this inflow, including the amount of free capacity in storages in a year, (C(t)-R(t))/rd, the annual amount of water released as supply in each time step, S, and the maximum available amount of surface water (carrying capacity) that can recharge the storages in each year, w/d.
  • Water Availability A - Water availability is the ratio of available water stored in reservoirs, R, over the total demand, D. When this ratio is below one, water shortage takes place. In that case, there is not enough water in the reservoirs to meet the demand. In this model, water availability is the main input for calculating socioeconomic growth and vulnerability.
  • Water Supply S - Water supply, S, in each time step equals to water demand, D. However, it cannot be more than total water stored in supply infrastructures, R, with a certain capacity, C. If demand exceeds the stored water, we can only supply as much as accumulated in the reservoir storage, R. The unfulfilled demand becomes water shortage.
Default Control #27
C
SAVEPER (Year [0,?])
= 1
Description: The frequency with which output is stored.
Not Present In Any View
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #28
C
Socioeconomic Growth Exponent g (Dmnl)
= 0.2
Description: The rate of socioeconomic growth varies in different societies. This rate is addressed by the exponent g. The higher the growth exponent, the faster the society changes.
Present in 1 view: Used by:
  • Socioeconomic Growth G - Socioeconomic growth, G, is a function water availability, A. This function is not linear. This nonlinearity is captured by the log normal function. When water is abundant the G will be positive and during severe water shortages G will be negative. The economy grows even during small tolerable water shortage, f. The rate of socioeconomic growth varies in different societies. This rate is addressed by the exponent g. The higher the growth exponent, the faster the society changes. The smooth function is used because there is an information delay between changes in water availability and changes in socioeconomic growth.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #29
SM
Socioeconomic Growth G (Dmnl)
= SMOOTH( LN((Water Availability A+Tolerable Shortage f)^Socioeconomic Growth Exponent g), Time to Perceive Availability e )
Description: Socioeconomic growth, G, is a function water availability, A. This function is not linear. This nonlinearity is captured by the log normal function. When water is abundant the G will be positive and during severe water shortages G will be negative. The economy grows even during small tolerable water shortage, f. The rate of socioeconomic growth varies in different societies. This rate is addressed by the exponent g. The higher the growth exponent, the faster the society changes. The smooth function is used because there is an information delay between changes in water availability and changes in socioeconomic growth.
Present in 1 view: Used by:
  • Population Net Change M - In this generic model, population net changes, M, is only impacted by the socioeconomic growth, G, which in turn is derived from water availability, A. Other forces that govern population in real world are excluded here. M adds to total population when G is positive and decreases population when G is negative.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #30
L
Storage Capacity C (MCM)
= ∫Construction Rate T dt + [Initial Storage Capacity C0]
Description: The storage capacity, C, includes a range of infrastructure from big reservoirs to small water tanks. Storage capacity imposes the maximum possible water accumulation and therefore the cap for water supply in the system. When the need for supply exceeds the current storage capacity, public pressure requires additional capacity, J. Storage capacity can increase up to the total available surface water or carrying capacity, w, within the boundaries of system.
Present in 1 view: Used by:
  • Potential Addition to Capacity K - The remaining amount of surface water that has not been stored yet. Potential addition to capacity dictates the maximum capacity of new infrastructures.
  • Recharging Rate F - Recharging rate is the amount of water that annually inflows to reservoir storage infrastructures. Different forces control this inflow, including the amount of free capacity in storages in a year, (C(t)-R(t))/rd, the annual amount of water released as supply in each time step, S, and the maximum available amount of surface water (carrying capacity) that can recharge the storages in each year, w/d.
Default Control #31
C
TIME STEP (Year [0,?])
= 0.0625
Description: The time step for the simulation.
Not Present In Any View
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #32
C
Time to Adjust Capacity h (Year)
= 5
Description: Time that a government takes to recognize that more water storage infrastructure is needed.
Present in 1 view: Used by:
  • Required Additional Capacity J - We assumed that if public pressure, L, exceeds a normal threshold for a society, t, the government would try to resolve the source of dissatisfaction, water shortage. To do so, the government increases water supply by constructing more capacity for storage. However, there is a natural limit for expansion of infrastructures. This limit is addressed in the potential addition to capacity, K. When K cannot support more water, J will be zero as well.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #33
C
Time to Perceive Availability e (Year)
= 5
Description: There is an information delay between changes in water availability and changes in socioeconomic growth. It takes time for the societies to change their opinion about the overall availability of water in their region.
Present in 1 view: Used by:
  • Socioeconomic Growth G - Socioeconomic growth, G, is a function water availability, A. This function is not linear. This nonlinearity is captured by the log normal function. When water is abundant the G will be positive and during severe water shortages G will be negative. The economy grows even during small tolerable water shortage, f. The rate of socioeconomic growth varies in different societies. This rate is addressed by the exponent g. The higher the growth exponent, the faster the society changes. The smooth function is used because there is an information delay between changes in water availability and changes in socioeconomic growth.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #34
C
Tolerable Shortage f (Dmnl)
= 0.15
Description: When water is abundant the G will be positive and during severe water shortages G will be negative. The economy grows even during small tolerable water shortage, f.
Present in 1 view: Used by:
  • Socioeconomic Growth G - Socioeconomic growth, G, is a function water availability, A. This function is not linear. This nonlinearity is captured by the log normal function. When water is abundant the G will be positive and during severe water shortages G will be negative. The economy grows even during small tolerable water shortage, f. The rate of socioeconomic growth varies in different societies. This rate is addressed by the exponent g. The higher the growth exponent, the faster the society changes. The smooth function is used because there is an information delay between changes in water availability and changes in socioeconomic growth.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #35
F,A

Vulnerability Change N (1/Year)
= MAX(0, Vulnerability from Reservoir Effect Q - Vulnerability V)/Delay for Vulnerability Growth a+MIN(0, Vulnerability from Reservoir Effect Q - Vulnerability V)/Delay for Vulnerability Decline b
Description: The rate of change in vulnerability, N, changes by reservoir effect. When water availability is one or higher, people become more dependent. This extra vulnerability becomes a new norm after few years, a. However, when the society wants to adjust itself to drought situation, water dependency declines with a slower rate. This effect is known as stickiness in economics literature. Therefore, the rate of change in vulnerability is different when it is growing or decreasing. When Q>V(t) the delay is a and when Q<V(t) delay becomes b. b is always greater than a.
Present in 1 view: Used by:
  • Vulnerability V - The reservoir effect states that the construction of the reservoirs reduces the incentive for adaptive actions at individual or community levels.The lack of incentive for adaptive actions reduces the resiliency of the system against the negative impacts of water shortages during severe droughts. Excessive water supply increases dependency on water resources and makes the population more vulnerable to extreme water shortages. Vulnerability in the start time, V0, is assumed to be zero. That means the reservoir effect on the system is zero at t=0.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #36
A
Vulnerability from Reservoir Effect Q (Dmnl)
= Vulnerability Multiplier v*LN(Water Availability A)
Description: When water becomes abundant people become more dependent on water. Therefore, Q is a function of water availability. This function is nonlinear. This rate of vulnerability change, v, varies in different societies. The greater the vulnerability multiplier, v, the higher the rate of changes in vulnerability.
Present in 1 view: Used by:
  • Vulnerability Change N - The rate of change in vulnerability, N, changes by reservoir effect. When water availability is one or higher, people become more dependent. This extra vulnerability becomes a new norm after few years, a. However, when the society wants to adjust itself to drought situation, water dependency declines with a slower rate. This effect is known as stickiness in economics literature. Therefore, the rate of change in vulnerability is different when it is growing or decreasing. When Q>V(t) the delay is a and when Q<V(t) delay becomes b. b is always greater than a.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #37
C
Vulnerability Multiplier v (Dmnl)
= 1
Description: When water becomes abundant people become more dependent on water. This rate of vulnerability change, v, varies in different societies. The greater the vulnerability multiplier, v, the higher the rate of changes in vulnerability.
Present in 1 view: Used by:
  • Vulnerability from Reservoir Effect Q - When water becomes abundant people become more dependent on water. Therefore, Q is a function of water availability. This function is nonlinear. This rate of vulnerability change, v, varies in different societies. The greater the vulnerability multiplier, v, the higher the rate of changes in vulnerability.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #38
L
Vulnerability V (Dmnl)
= ∫Vulnerability Change N dt + [Initial Vulnerability V0]
Description: The reservoir effect states that the construction of the reservoirs reduces the incentive for adaptive actions at individual or community levels.The lack of incentive for adaptive actions reduces the resiliency of the system against the negative impacts of water shortages during severe droughts. Excessive water supply increases dependency on water resources and makes the population more vulnerable to extreme water shortages. Vulnerability in the start time, V0, is assumed to be zero. That means the reservoir effect on the system is zero at t=0.
Present in 1 view: Used by:
  • Economic Damage E - In this hypothetical model, the system confronts a certain extent of economic damage, 1+V(t), for each percentage of shortage ratio, H. The total economic damages also depends on the vulnerability of the society in each time step, V(t). When V(t) increases or decreases, the economic damage linearly changes accordingly. Economic damage is normalized here. The absolute amount of damage can be acquired if H multiplied by an average dollar amount of each percentage of shortage ratio.
  • Vulnerability Change N - The rate of change in vulnerability, N, changes by reservoir effect. When water availability is one or higher, people become more dependent. This extra vulnerability becomes a new norm after few years, a. However, when the society wants to adjust itself to drought situation, water dependency declines with a slower rate. This effect is known as stickiness in economics literature. Therefore, the rate of change in vulnerability is different when it is growing or decreasing. When Q>V(t) the delay is a and when Q<V(t) delay becomes b. b is always greater than a.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #39
A
Water Availability A (Dmnl)
= (Reservoir Storage R/Annual Storage i)/Water Demand D
Description: Water availability is the ratio of available water stored in reservoirs, R, over the total demand, D. When this ratio is below one, water shortage takes place. In that case, there is not enough water in the reservoirs to meet the demand. In this model, water availability is the main input for calculating socioeconomic growth and vulnerability.
Present in 1 view: Used by:
  • Socioeconomic Growth G - Socioeconomic growth, G, is a function water availability, A. This function is not linear. This nonlinearity is captured by the log normal function. When water is abundant the G will be positive and during severe water shortages G will be negative. The economy grows even during small tolerable water shortage, f. The rate of socioeconomic growth varies in different societies. This rate is addressed by the exponent g. The higher the growth exponent, the faster the society changes. The smooth function is used because there is an information delay between changes in water availability and changes in socioeconomic growth.
  • Vulnerability from Reservoir Effect Q - When water becomes abundant people become more dependent on water. Therefore, Q is a function of water availability. This function is nonlinear. This rate of vulnerability change, v, varies in different societies. The greater the vulnerability multiplier, v, the higher the rate of changes in vulnerability.
  • Water Shortage H - When water availability, A, is below one, water shortage takes place. In that case, there is not enough water in the reservoirs to meet the demand. Water shortage is one when there is no water in the system (A=0); and it is zero when A equals to or is greater than one.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #40
A
Water Demand D (MCM/Year)
= (Demand per Person per Year z*Population P)*Liter to MCM u
Description: Water demand is calculated based on the average demand per person per year, z, multiplied by the total population, P. The total demand is the sum of individual demands. Constant u is used to change the units from liter to MCM.
Present in 1 view: Used by:
  • Water Availability A - Water availability is the ratio of available water stored in reservoirs, R, over the total demand, D. When this ratio is below one, water shortage takes place. In that case, there is not enough water in the reservoirs to meet the demand. In this model, water availability is the main input for calculating socioeconomic growth and vulnerability.
  • Water Supply S - Water supply, S, in each time step equals to water demand, D. However, it cannot be more than total water stored in supply infrastructures, R, with a certain capacity, C. If demand exceeds the stored water, we can only supply as much as accumulated in the reservoir storage, R. The unfulfilled demand becomes water shortage.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #41
A
Water Shortage H (Dmnl)
= MAX(0,1-Water Availability A)
Description: When water availability, A, is below one, water shortage takes place. In that case, there is not enough water in the reservoirs to meet the demand. Water shortage is one when there is no water in the system (A=0); and it is zero when A equals to or is greater than one.
Present in 1 view: Used by:
  • Economic Damage E - In this hypothetical model, the system confronts a certain extent of economic damage, 1+V(t), for each percentage of shortage ratio, H. The total economic damages also depends on the vulnerability of the society in each time step, V(t). When V(t) increases or decreases, the economic damage linearly changes accordingly. Economic damage is normalized here. The absolute amount of damage can be acquired if H multiplied by an average dollar amount of each percentage of shortage ratio.
Default Supply-Demand Cycle & Reservoir Effect
(Default)		 #42
F,A

Water Supply S (MCM/Year)
= MIN(Water Demand D,Reservoir Storage R/Delay in Supply k)
Description: Water supply, S, in each time step equals to water demand, D. However, it cannot be more than total water stored in supply infrastructures, R, with a certain capacity, C. If demand exceeds the stored water, we can only supply as much as accumulated in the reservoir storage, R. The unfulfilled demand becomes water shortage.
Present in 1 view: Used by:
  • Recharging Rate F - Recharging rate is the amount of water that annually inflows to reservoir storage infrastructures. Different forces control this inflow, including the amount of free capacity in storages in a year, (C(t)-R(t))/rd, the annual amount of water released as supply in each time step, S, and the maximum available amount of surface water (carrying capacity) that can recharge the storages in each year, w/d.
  • Reservoir Storage R - Reservoir storage, R, represents the total amount of water stored in reservoirs or other storage infrastructures. This amount increases by recharging rate, F, from precipitation, water transfers, or other means. According to the water demand, D, water will be released as water supply, S. R cannot exceed the storage capacity, C. The initial value for stored water is assumed to be equal to the initial storage capacity, C0. All the storage infrastructures are assumed to be full in t=0.

List of 1 Variable Using IF...THEN...ELSE Function

Module
Group
Type
 Variable (1)
Default Supply-Demand Cycle & Reservoir Effect A Required Additional Capacity J (MCM/Year)

List of 5 Variables Using MIN or MAX Functions

Module
Group
Type
 Undocumented Variable (5)
Default Supply-Demand Cycle & Reservoir Effect A Potential Addition to Capacity K (MCM)
Default Supply-Demand Cycle & Reservoir Effect F,A Recharging Rate F (MCM/Year)
Default Supply-Demand Cycle & Reservoir Effect F,A Vulnerability Change N (1/Year)
Default Supply-Demand Cycle & Reservoir Effect A Water Shortage H (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect F,A Water Supply S (MCM/Year)

List of 40 Variables Without Predefined Min or Max Values

Module
Group
Type
 Undocumented Variable (40)
Default Supply-Demand Cycle & Reservoir Effect C Annual Storage i (Year)
Default Supply-Demand Cycle & Reservoir Effect C Carrying Capacity w (MCM)
Default Supply-Demand Cycle & Reservoir Effect C Construction Delay j (Year)
Default Supply-Demand Cycle & Reservoir Effect DE,F Construction Rate T (MCM/Year)
Default Supply-Demand Cycle & Reservoir Effect C Delay for Population Change c (Year)
Default Supply-Demand Cycle & Reservoir Effect C Delay for Vulnerability Decline b (Year)
Default Supply-Demand Cycle & Reservoir Effect C Delay for Vulnerability Growth a (Year)
Default Supply-Demand Cycle & Reservoir Effect C Delay in Supply k (Year)
Default Supply-Demand Cycle & Reservoir Effect C Demand per Person per Year z (Liter/Person/Year)
Default Supply-Demand Cycle & Reservoir Effect A Economic Damage E (Dmnl)
Default Control C FINAL TIME (Year)
Default Supply-Demand Cycle & Reservoir Effect LI,C Initial Population P0 (Person)
Default Supply-Demand Cycle & Reservoir Effect LI,C Initial Storage Capacity C0 (MCM)
Default Control C INITIAL TIME (Year)
Default Supply-Demand Cycle & Reservoir Effect LI,C Initial Vulnerability V0 (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect C Liter to MCM u (MCM/Liter)
Default Supply-Demand Cycle & Reservoir Effect F,A Population Net Change M (Person/Year)
Default Supply-Demand Cycle & Reservoir Effect L Population P (Person)
Default Supply-Demand Cycle & Reservoir Effect A Potential Addition to Capacity K (MCM)
Default Supply-Demand Cycle & Reservoir Effect A Public Pressure L (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect C Public Pressure Multiplier p (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect C Public Pressure Threshold t (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect C Recharging Delay d (Year)
Default Supply-Demand Cycle & Reservoir Effect F,A Recharging Rate F (MCM/Year)
Default Supply-Demand Cycle & Reservoir Effect A Required Additional Capacity J (MCM/Year)
Default Supply-Demand Cycle & Reservoir Effect L Reservoir Storage R (MCM)
Default Supply-Demand Cycle & Reservoir Effect C Socioeconomic Growth Exponent g (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect SM Socioeconomic Growth G (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect L Storage Capacity C (MCM)
Default Supply-Demand Cycle & Reservoir Effect C Time to Adjust Capacity h (Year)
Default Supply-Demand Cycle & Reservoir Effect C Time to Perceive Availability e (Year)
Default Supply-Demand Cycle & Reservoir Effect C Tolerable Shortage f (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect F,A Vulnerability Change N (1/Year)
Default Supply-Demand Cycle & Reservoir Effect A Vulnerability from Reservoir Effect Q (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect C Vulnerability Multiplier v (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect L Vulnerability V (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect A Water Availability A (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect A Water Demand D (MCM/Year)
Default Supply-Demand Cycle & Reservoir Effect A Water Shortage H (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect F,A Water Supply S (MCM/Year)

Formulation Complexity Summary (Violations of Richardson's Rule)

Module
Group
Type
 Variable
Complexity Score
Default Supply-Demand Cycle & Reservoir Effect SM Socioeconomic Growth G (Dmnl)
4
Default Supply-Demand Cycle & Reservoir Effect F,A Vulnerability Change N (1/Year)
4
Default Supply-Demand Cycle & Reservoir Effect A Required Additional Capacity J (MCM/Year)
4
Default Supply-Demand Cycle & Reservoir Effect F,A Recharging Rate F (MCM/Year)
5

List of 6 State Variables

Module
Group
Type
 Variable
Default Supply-Demand Cycle & Reservoir Effect DE,F Construction Rate T (MCM/Year)
Default Supply-Demand Cycle & Reservoir Effect L Population P (Person)
Default Supply-Demand Cycle & Reservoir Effect L Reservoir Storage R (MCM)
Default Supply-Demand Cycle & Reservoir Effect SM Socioeconomic Growth G (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect L Storage Capacity C (MCM)
Default Supply-Demand Cycle & Reservoir Effect L Vulnerability V (Dmnl)

List of 1 View and Its 42 Variables




 
View 1
  
Total: 38 :Total
Annual Storage i (in 1 view) X Annual Storage i (in 1 view)
Carrying Capacity w (in 1 view) X Carrying Capacity w (in 1 view)
Construction Delay j (in 1 view) X Construction Delay j (in 1 view)
Construction Rate T (in 1 view) X Construction Rate T (in 1 view)
Delay for Population Change c (in 1 view) X Delay for Population Change c (in 1 view)
Delay for Vulnerability Decline b (in 1 view) X Delay for Vulnerability Decline b (in 1 view)
Delay for Vulnerability Growth a (in 1 view) X Delay for Vulnerability Growth a (in 1 view)
Delay in Supply k (in 1 view) X Delay in Supply k (in 1 view)
Demand per Person per Year z (in 1 view) X Demand per Person per Year z (in 1 view)
Economic Damage E (in 1 view) X Economic Damage E (in 1 view)
FINAL TIME (in 0 views)   FINAL TIME (in 0 views)
Initial Population P0 (in 1 view) X Initial Population P0 (in 1 view)
Initial Storage Capacity C0 (in 1 view) X Initial Storage Capacity C0 (in 1 view)
INITIAL TIME (in 0 views)   INITIAL TIME (in 0 views)
Initial Vulnerability V0 (in 1 view) X Initial Vulnerability V0 (in 1 view)
Liter to MCM u (in 1 view) X Liter to MCM u (in 1 view)
Population Net Change M (in 1 view) X Population Net Change M (in 1 view)
Population P (in 1 view) X Population P (in 1 view)
Potential Addition to Capacity K (in 1 view) X Potential Addition to Capacity K (in 1 view)
Public Pressure L (in 1 view) X Public Pressure L (in 1 view)
Public Pressure Multiplier p (in 1 view) X Public Pressure Multiplier p (in 1 view)
Public Pressure Threshold t (in 1 view) X Public Pressure Threshold t (in 1 view)
Recharging Delay d (in 1 view) X Recharging Delay d (in 1 view)
Recharging Rate F (in 1 view) X Recharging Rate F (in 1 view)
Required Additional Capacity J (in 1 view) X Required Additional Capacity J (in 1 view)
Reservoir Storage R (in 1 view) X Reservoir Storage R (in 1 view)
SAVEPER (in 0 views)   SAVEPER (in 0 views)
Socioeconomic Growth Exponent g (in 1 view) X Socioeconomic Growth Exponent g (in 1 view)
Socioeconomic Growth G (in 1 view) X Socioeconomic Growth G (in 1 view)
Storage Capacity C (in 1 view) X Storage Capacity C (in 1 view)
TIME STEP (in 0 views)   TIME STEP (in 0 views)
Time to Adjust Capacity h (in 1 view) X Time to Adjust Capacity h (in 1 view)
Time to Perceive Availability e (in 1 view) X Time to Perceive Availability e (in 1 view)
Tolerable Shortage f (in 1 view) X Tolerable Shortage f (in 1 view)
Vulnerability Change N (in 1 view) X Vulnerability Change N (in 1 view)
Vulnerability from Reservoir Effect Q (in 1 view) X Vulnerability from Reservoir Effect Q (in 1 view)
Vulnerability Multiplier v (in 1 view) X Vulnerability Multiplier v (in 1 view)
Vulnerability V (in 1 view) X Vulnerability V (in 1 view)
Water Availability A (in 1 view) X Water Availability A (in 1 view)
Water Demand D (in 1 view) X Water Demand D (in 1 view)
Water Shortage H (in 1 view) X Water Shortage H (in 1 view)
Water Supply S (in 1 view) X Water Supply S (in 1 view)
Total: 38 :Total
 
View 1
  

* Includes Time, if used in a view. Excludes variables not present in any view.

Level Structure †

Population P = ∫Population Net Change M dt + [Initial Population P0]
Initial Population P0 = 100000
    Population Net Change M = Population P *Socioeconomic Growth G/Delay for Population Change c

Reservoir Storage R = ∫Recharging Rate F-Water Supply S dt + [Initial Storage Capacity C0]
Initial Storage Capacity C0 = 150
    Recharging Rate F = MIN(Carrying Capacity w/Recharging Delay d, Water Supply S+(Storage Capacity C-Reservoir Storage R)/Recharging Delay d)
    Water Supply S = MIN(Water Demand D,Reservoir Storage R/Delay in Supply k)

Storage Capacity C = ∫Construction Rate T dt + [Initial Storage Capacity C0]
    Construction Rate T = DELAY3(Required Additional Capacity J, Construction Delay j)

Vulnerability V = ∫Vulnerability Change N dt + [Initial Vulnerability V0]
Initial Vulnerability V0 = 0
    Vulnerability Change N = MAX(0, Vulnerability from Reservoir Effect Q - Vulnerability V)/Delay for Vulnerability Growth a+MIN(0, Vulnerability from Reservoir Effect Q - Vulnerability V)/Delay for Vulnerability Decline b

†  Level Structure Report still under development.

List of 13 Equations with Dimensionless Units

Module
Group
Type
 Variable
Default Supply-Demand Cycle & Reservoir Effect A Economic Damage E (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect LI,C Initial Vulnerability V0 (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect A Public Pressure L (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect C Public Pressure Multiplier p (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect C Public Pressure Threshold t (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect C Socioeconomic Growth Exponent g (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect SM Socioeconomic Growth G (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect C Tolerable Shortage f (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect A Vulnerability from Reservoir Effect Q (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect C Vulnerability Multiplier v (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect L Vulnerability V (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect A Water Availability A (Dmnl)
Default Supply-Demand Cycle & Reservoir Effect A Water Shortage H (Dmnl)
Source file: Supply-Demand Cycle & Reservoir Effect.mdl (26Mar2019 - 5:06:05 AM)
Report Created on 26/Mar/2019 - 5:06:26 AM
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