Managing water resources in a complex adaptive natural–human system is a challenge due to the difficulty of modeling human behavior under uncertain risk perception. The interaction between human-engineered systems and natural processes needs to be modeled explicitly with an approach that can quantify the influence of incomplete/ambiguous information on decision-making processes. In this study, we two-way coupled an agent-based model (ABM) with a river-routing and reservoir management model (RiverWare) to address this challenge. The human decision-making processes is described in the ABM using Bayesian inference (BI) mapping joined with a cost–loss (CL) model (BC-ABM). Incorporating BI mapping into an ABM allows an agent's psychological thinking process to be specified by a cognitive map between decisions and relevant preceding factors that could affect decision-making. A risk perception parameter is used in the BI mapping to represent an agent's belief on the preceding factors. Integration of the CL model addresses an agent's behavior caused by changing socioeconomic conditions. We use the San Juan River basin in New Mexico, USA, to demonstrate the utility of this method. The calibrated BC-ABM–RiverWare model is shown to capture the dynamics of historical irrigated area and streamflow changes. The results suggest that the proposed BC-ABM framework provides an improved representation of human decision-making processes compared to conventional rule-based ABMs that do not take risk perception into account. Future studies will focus on modifying the BI mapping to consider direct agents' interactions, up-front cost of agent's decision, and upscaling the watershed ABM to the regional scale.
Managing water resources for growing demands of energy and food while sustaining the environment is a grand challenge of our time, especially when we are dealing with a complex adaptive natural–human system that is subject to various sources of uncertainty. Nowadays, almost every major basin in the world can be considered as a coupled natural–human system (CNHS) where heterogeneous human activities are affecting the natural hydrologic cycle and vice versa (Liu et al., 2007). The interaction between human activity and the natural environment needs to be explicitly addressed and the uncertainty within this complex system characterized according to a formal approach if benefits toward improved water resource management (Brown et al., 2015) are to be realized.
Recently, agent-based modeling (ABM) has become a commonly used tool in the scientific community to address CNHS issues. An ABM framework identifies individual actors as unique and autonomous “agents” that operate according to a distinct purpose. Agents follow certain behavioral rules and interact with each other in a shared environment. By explicitly representing the interaction between human agents (e.g., farmers) and the environment (e.g., a watershed) where they are located, ABM provides a natural bottom-up setting to study transdisciplinary issues in CNHS. Applying the ABM approach in water resources management began a decade ago and became a popular topic in CNHS analyses (Berglund, 2015; Giuliani et al., 2015; Giuliani and Castelletti, 2013; Hu et al., 2017; Khan et al., 2017; Mulligan et al., 2014; Schlüter et al., 2009; Yang et al., 2009, 2012; Zechman, 2011).
However, one major challenge of applying the ABM approach to water management decisions is the difficulty of characterizing human decision-making processes and meeting the real-world management intuition. The traditional approach through, for example, survey or interview with local decision makers, is extremely limited (e.g., Manson and Evans, 2007) in space and time. This study introduces the theory of planned behavior (TPB), a well-known theory in psychology used to predict human behavioral intention and actual behavior (Ajzen, 1991), into the ABM framework to quantify human decision-making processes. The TPB states that an individual's beliefs and behaviors can be expressed in terms of a combination of attitude toward behavior, subjective norms, and perceived behavioral control. Attitude toward behavior and subjective norms specify an individual's perceptions of performing a behavior affected by their internal thinking processes and social normative pressures, while perceived behavioral control describes the effects from external uncontrollable factors (e.g., socioeconomic conditions). If an individual has high belief about making a specific decision, then it has an increased confidence that she/he can perform the specific behavior successfully. On the other hand, the tendency of a person for making a specific decision increases/decreases if social normative pressures decrease/increase.
Implementing the TPB into ABM requires that all the three components be modeled explicitly. In this study, we adapt the Bayesian inference (BI) mapping (Pope and Gimblett, 2015; Kocabas and Dragicevic, 2012) and the cost–loss model (CL) (Thompson, 1952) for this task. The BI mapping (also called Bayesian networks, belief networks, Bayesian belief networks, causal probabilistic networks, or causal networks), built on the Bayesian probability theory and cognitive mapping, calculates the likelihood that a specific decision will be made (Sedki and de Beaufort, 2012 via Pope and Gimblett, 2015) while sequentially updating beliefs of specific preceding factors (model parameters) as new information is acquired (Dorazio and Johnson, 2003). By applying the BI mapping, an individual's beliefs affected by their internal thinking processes and perceptions of social normative pressures can be described as a cognitive map between decisions and relevant preceding factors. Ng et al. (2011) developed an ABM using BI to model the farmer's adaptation of their expectations (or belief) and uncertainties of future crop yield, cost, and weather. Yet the preceding factors were assumed to be independent of each other, which is not always true, especially if two preceding factors are spatially related (e.g., downstream reservoir elevation, and upstream precipitation). More importantly, the internal thinking processes of all farmers were assumed to be the same (i.e., no spatial heterogeneity is modeled). As a result, a more realistic framework of applying BI to ABM is still needed to improve representation of human decision-making processes.
While BI mapping specifies the human psychological decision-making process, the CL model addresses the effect of external socioeconomic conditions on an individual's decision-making (i.e., perceived behavioral control in the TPB). The CL model is frequently used as a simple decision-making model in economic analysis to quantify human decision-making according to economic theory (Thompson, 1952). CL modeling has been widely used in estimating the economic value of weather forecasts (Keeney, 1982; Lee and Lee, 2007; Murphy, 1976; Murphy et al., 1985). Tena and Gómez (2008) and Matte et al. (2017) incorporated the constant absolute risk aversion theory in CL modeling to evaluate risk perception of decision makers since the original CL model assumes a risk-neutral decision maker. They used a parameter, the Arrow–Pratt coefficient, to represent risk-averse and risk-seeking decision makers but did not specify how this parameter could be determined. They also did not clarify what will happen if different decision makers in the system have different perceptions of risk (again, no spatial heterogeneity).
To address these aforementioned research gaps, we developed an ABM based on the BI mapping and the CL model as an implementation of the TPB (referred to as the “BC-ABM” hereafter). The BC-ABM is two-way coupled with a river-routing and reservoir management model: RiverWare (details in Sect. 2.1). The four objectives of this study are listed as follows: (1) use the BC-ABM to quantify human decisions considering uncertain risk perception, (2) demonstrate the improvement of BC-ABM compared to conventional agent behavior rules, (3) use the coupled BC-ABM–RiverWare model to explicitly model the feedback loop between human and nature systems, and (4) test the BC-ABM–RiverWare for different scenarios. The San Juan River basin in New Mexico, USA, is used as the demonstration basin for this effort. The calibrated BC-ABM–RiverWare model is used to evaluate the impacts of changing risk perception from all agents to the water management in this basin. In this study, multiple comparative experiments of a conventional rule-based ABM (i.e., without using the BI and CL) are conducted to demonstrate the advantages of the proposed BC-ABM framework in modeling human decision-making processes. We also evaluate the effect of changing external economic conditions on an agent's decisions.
The paper is structured as follows. We introduce our methodology in Sect. 2. The background of the case study area, the San Juan River basin, and calibration of the BC-ABM–RiverWare are presented in Sect. 3. We show different scenario results of the model in Sect. 4 (Results). The generalization of the framework and current model limitations are discussed in Sect. 5 (Discussion) followed by the Conclusion section.
River-routing and reservoir management modeling is designed to simulate the deliveries of water within a regulated river system (Johnson, 2014). Many river-reservoir management models have been developed to address different objectives within a geographic region such as MODSIM, RiverWare, CALSIM (Draper et al., 2004), IQQM (Hameed and O'Neill, 2005), and WEAP (Yates et al., 2005). These models use a node–link structure to represent the entire river network where “nodes” are important natural (sources, lakes, and confluences) or human (water infrastructures and water withdrawals) components and “links” represent river channel elements.
RiverWare, developed in 1986 by the University of Colorado Boulder, is a
model of water resource engineering systems for operational scheduling and
forecasting, planning, policy evaluation, and other operational analysis and
decision processes (Zagona et al., 2001). It couples watershed and reach
models that describe the physical hydrologic processes with routing and
reservoir management models that account for water use for water resources
assessment. RiverWare has a graphic user interface and uses an
object-oriented framework to define every node in the model as an “object.”
Each object is assigned a unique set of attributes. These attributes are
captured as “slots” in RiverWare. There are two basic types of slots: time
series and table slots for each object to store either time series or
characteristic data. Details of the RiverWare structure and algorithm can be
found at Zagona et al. (2001) and the following website:
There is an emerging research topic in Earth system modeling (Di Baldassarre et al., 2015; Troy et al., 2015) and water resources system analysis (Denaro et al., 2017; Giuliani et al., 2016; Khan et al., 2017; Li et al., 2017; Mulligan et al., 2014) to couple models together. Coupling an ABM with a process-based model has been done before but mostly focused on groundwater models such as Hu et al. (2017) and Mulligan et al. (2014). One of the few examples that involve coupling with a surface water model, Khan et al. (2017) developed a simple ABM that coupled with a physically based hydrologic model, the Soil and Water Assessment Tool. In this paper, we perform a two-way coupling (or sometimes called “tight” coupling) of models which means data/information will be transferred back and forth between the ABM and RiverWare, where selected objects in RiverWare are defined as agents. To facilitate the two-way coupling, we utilize a convenient built-in tool within RiverWare: the data management interface (DMI) utility which allows automatic data imports and exports from/to any external data source (RiverWare Technical Documentation, 2017; see also Fig. S1 in the Supplement).
The ABM developed in this paper, as an implementation of the TPB, consists of two components: the Bayesian inference mapping and the cost–loss modeling. This unique setup allows us to explicitly describe human decision-making processes and associated uncertainty caused by information ambiguity in water management decisions. We describe the details in this section.
In this study, the Bayesian inference (BI) mapping is applied to specify a decision maker's (or agent's) internal thinking processes by building a cognitive map (also called a causal structure) between decisions (or specific management behaviors) and relevant preceding factors that could affect decision-making (Dorazio and Johnson, 2003; Pope and Gimblett, 2015; Schlüter et al., 2017). In this setting, the goal of an agent is to develop a decision rule (or management strategy) that prescribes management behaviors for each time step that are optimal with respect to its objective function. The uncertainty associated with these management behaviors is specified by a risk perception parameter (Baggett et al., 2006; Pahl-Wostl et al., 2008) representing the extent to which decision makers explicitly consider limited knowledge or belief about (future) information in their decision-making process (Müller et al., 2013; Groeneveld et al., 2017). This is the definition of Knightian uncertainty which comes from the economics literature where risk is immeasurable or the probabilities are not known (Knight, 1921).
In the field of water resource management, a decision is often made based on
whether the preceding factor is larger (or smaller) than a prescribed threshold
(i.e., exceedance). A simple example is that a farmer's belief of changing
the irrigation area will be affected by the forecast of snowpack in the
coming water year or water availability in an upstream reservoir at the
beginning of the growing season. The probability of a preceding factor
The probability of
The overall probability of taking a management behavior
A solution of
In this study, we rename the variables in Eq. (5) as follows (Shafiee-Jood et
al., 2017):
In Eq. (7), the agent's prior belief of
In most water resources management cases, multiple preceding factors affect
the probability of a single management decision. In this paper, we assume
that agents will make a decision based on the most highly recognized
preceding factor following the suggestion from Sharma et al. (2013). The
fundamental assumption is that a decision maker will pay the closest
attention to the most abnormal of any preceding factors, such as the severity
of droughts or floods, historic low or high water levels of an upstream
reservoir, or an extreme upstream water diversion. The way we represent this
tendency is by calculating the “extremity” factors (
The BI mapping method described in Sect. 2.2.1 characterizes an agent's
behavioral intentions related to their internal (psychological)
decision-making processes. According to the TPB, a real-world management
decision or action also depends on external uncontrollable factors such as
socioeconomic conditions. The CL model is applied in this study to address
this concern. The CL model measures the probability of an adverse event
affecting the decision of whether to take costly precautionary action to
protect oneself against losses from that event. Based on the theory of
cost–benefit analysis, the probability of taking an action
To fit the CL model into the proposed ABM framework, we modify the above CL
model following the concept of Tena and Gómez (2008) and Matte et
al. (2017) which added the perception of risk into the decision-making
process. We define “
Figure 1 summarizes the methodology in Sect. 2.2 applied to this study. An
agent's decision-making and action process will start when receiving
information (
The flow chart of agent decision-making process inside the two-way coupled ABM–RiverWare model (ABM.exe in Fig. S1). Agents make their decisions with uncertainty based on the method developed in this paper (joint BI mapping and CL model), and RiverWare runs the simulation based on these decisions.
The San Juan River basin (Fig. 2) is the largest tributary of the Colorado
River basin with a drainage area of 64 570 km
The upper San Juan River basin. Different colors of the basin represent the geographical regions that this paper used to group major irrigation districts (agents, marked as dots). The location of the Navajo Reservoir is marked as a triangle.
The Navajo Indian Irrigation Project (NIIP) is another major water consumer
within the basin beside the 16 major irrigation ditches. The NIIP supplies
water to Native American tribes in the region. San Juan-Chama Project manages
transbasin water transfers into the Rio Grande Basin, augmenting supply for
Albuquerque, NM, irrigation and instream flow needs. Finally, the San Juan
River Basin Recovery Implementation Program (SJRIP) implemented by the Fish
and Wildlife Service manages environmental flows within the basin, dictating
timing and magnitude of releases from the Navajo Reservoir and maintenance of a
daily 500 ft
To improve water planning and management in the basin, several state and federal agencies established a steering committee with the main responsibility of overseeing the institutional complexity for the water plans operated under the 1922 Colorado River Compact and 1948 Upper Colorado River Basin Compact. Although a regional water plan report (RWP) was updated in 2016 (State of New Mexico Interstate Stream Commission, 2016) by interested stakeholders, issues still exist under the terms of the 1948 Upper Colorado River Basin Compact. For example, New Mexico's entitled 642 380 ac-ft (0.793 billion cubic meters) consumptive use is substantially greater than the corresponding consumptive use.
The RWP summarizes the related information of water planning such as water
rights, future water supply and demand projections, and newly available data.
For example, 10 of the largest water users have cooperated to develop a
shortage sharing agreement to keep the Navajo Reservoir from drawing down the
reservoir pool elevation below 5990 ft (2041 m), which is the elevation
required for NIIP diversion. The agreement stipulates that all parties share
equally in shortages caused by drought (2013–2016 shortage agreement is
available at
USBR developed a RiverWare model for the San Juan River basin to support
water management and resource planning efforts. RiverWare includes 19
irrigation ditch objects, 21 domestic and industrial use objects, 2 power
plant objects, and 3 reservoir objects. Input data for the RiverWare model
include historical tributary inflows, evapotranspiration rates for each
irrigation ditch limited by the crop water requirement, historic water
diversion for NIIP and the San Juan-Chama Project, and reservoir operation
rules. Ungauged local inflows were determined by the simple closure of the
local water budget. The model operates on a daily time step from
1 October 1928 to 30 September 2013 (85 years) with four cycles of
simulation. Each cycle is a complete model run for the entire modeling period
to fulfill part of the necessary information (e.g., some downstream water
requirements need to be precalculated for the Navajo Reservoir to set up the
release pattern). In this study, farmers that can make management decisions
are quantified as 16 major irrigation ditch objects in RiverWare. They are
defined as agents in the study and will decide whether to expand or reduce
their irrigated area (e.g., management behavior,
The BI mapping was applied to each group with different causal structures.
The climatic preceding factors considered in this study include the mainstem
(Navajo) upstream winter precipitation, the tributary (Animas River) winter
precipitation, the mainstem downstream winter precipitation, the water level
in the Navajo Reservoir, and the flow violations at the basin outlet (days below
500 ft
Name of agent groups, number of agents in each group, and the proceeding factors considered in decision-making processes. Superscript “c” means climatic factors and superscript “s” means social factors. Numbers in the bracket are mean and standard deviation if applicable.
In this study, the information of winter precipitation was taken from NOAA
ground-based rainfall monitoring gauges where we used the coming year's
winter precipitation as a proxy for the snowpack forecast in the causal
structure. Winter precipitation has a positive effect on snowpack but there
is an uncertainty about how much snow will be accumulated. Therefore, when
agents expect more winter precipitation, if they believe it will lead to a lot
more snowpack, they will be more aggressive in the irrigated area
expansion. Flow violation at the basin outlet and water level of the Navajo
Reservoir are two system-wide preceding factors that are considered by all the
three groups. When flow violation is too frequent or water level is too low,
agents tend to be more conservative in the irrigated area expansion. If a
shortage were declared, the RiverWare model would reduce the targeted
streamflow at the basin outlet to 250 ft
To summarize, the data transfer from RiverWare to ABM at the end of a water year included (1) irrigation areas for the 16 irrigation agents, (2) the basin outflow, (3) water level in the Navajo Reservoir, and (4) the NIIP water diversion. After the completion of the ABM simulation, data transfer from ABM to RiverWare included (1) updated irrigated areas and (2) the corresponding water diversion of each agent. The next section will demonstrate the capability of the proposed model to recreate historical patterns in the San Juan Basin.
One of the major criticisms of ABM development is that ABM results are
difficult to verify or validate (Parker et al., 2003; An et al., 2005, 2014;
National Research Council, 2014). In this study, we address this concern by
calibrating the coupled BC-ABM–RiverWare model to recreate the historical
trend of (1) an individual agent's irrigated area and (2) San Juan River
discharge. USBR provides the observed irrigated acreage for all 16 ditches
and the flow measurements at two different locations along the San Juan River
(at the outlet of the San Juan River basin and directly downstream of the
Navajo Reservoir) for the calibration purpose. The calibrated parameters are
the risk perception parameters (
The calibration results of the ABM–RiverWare model: individual
agents' irrigated area changes from 1928 to 2013 organized by irrigation
ditch and region (see groups in Fig. 3). Each figure includes the
simulated irrigated area change from the best-fit BC-ABM (solid red) and the
corresponding Nash–Sutcliffe efficiency (NSE), multiple runs of BC-ABM
(solid gray) to visualize the stochasticity (30 runs) of agents' random
behavior, non-BC-ABM with extremity (dashed black), and non-BC-ABM using
precipitation only (solid black) against historical record (solid blue). 1 ac
The calibration results of irrigated areas are given in Fig. 3 and arranged by group (region). The blue curves are the historical irrigated area. The red curves are the best-fit result among multiple (30) modeling runs (shown by the gray curves, which represents the stochasticity) of each agent. In general, BC-ABM captures the pattern and trend of irrigated area for all agents, and we particularly focus on agents with the largest irrigated areas since their decision can dominate the basin. A figure showing the time variations of extremity values for each group of agents is given in the Supplement (see Fig. S2) to illustrate the preceding factors adopted by different groups of agents for making decisions at each time step.
The overall (area) weighted Nash–Sutcliffe efficiency (NSE, Nash and Sutcliffe, 1970) of the best-fit result is 0.55, which represents a reasonable calibration result. There are a few cases where structural changes occurred with some of the ditches that the model does not capture. Specifically, construction of the Navajo Reservoir in the 1960s inundated the New Mexico Pine River Ditch, while construction of the dam made it possible to expand the Hammond Irrigation Ditch (located directly downstream of the Navajo Reservoir). Similar structural changes are evident with the Echo, New Mexico, Animas, and Fruitland-Cambridge ditches. The model limitation associated with the use of BI mapping in ABM is discussed in the Discussion section.
To demonstrate the enhanced performance of the proposed BC-ABM framework in
representing human decision-making processes, we conducted comparative
experiments with conventional rule-based, deterministic ABMs (such as our
previous work in Khan et al., 2017), referred to as the non-BC-ABMs. In the
non-BC-ABMs, agents make decisions based on either past experience (e.g., flow
violation or NIIP diversion) or future forecast (winter precipitation) alone,
implying that agents have perfect foresight in terms of received information. Using
precipitation as an example, an agent will expand irrigation area if the
precipitation forecast is greater than the given threshold, and vice versa.
Excluding BI mapping implies that the agents make decisions purely based on
the forecast or new incoming information and fully ignore the information
from past experience, while excluding the CL model means that the agents do not
take socioeconomic factors into account when making decisions. Two
non-BC-ABMs were tested and results are also shown in Fig. 3. The black solid
curve represents the non-BC-ABM simulation still utilizing extremity for
selecting the reference preceding factor, while the black dashed curve is the
non-BC-ABM using only the precipitation in the decision-making processes. The
better performance of the proposed BC-ABM framework, compared to the
non-BC-ABMs, is evidenced by the closer agreements between the simulated and
historical patterns of irrigated area from BC-ABM as well as weighted NSE
(0.55 for BC-ABM vs.
Calibrated probability of expanding area (
The time variations of
The calibration results of the ABM–RiverWare model:
The calibration results in Sect. 3.3 demonstrate the credibility of the coupled BC-ABM–RiverWare model in representing human psychological, uncertain decision-making processes. The encouraging results suggest that we can apply the proposed BC-ABM framework to test some extreme conditions to perform different scenario analyses. Two scenarios are tested in this section: the effect of changing agents' risk perception and the effect of changing socioeconomic condition.
Different risk perception scenarios are tested by making a stepwise change in
all agents'
The cumulative density frequency throughout the entire simulation
period of
There are two interesting observations. First, it is clear that when all agents become risk-seeking, their emerging actions will result in a larger irrigated area in the basin (Fig. 6a). Since all agents want to expand their irrigated area, the Navajo Reservoir will reserve more water at the end of each year, resulting in slightly higher water levels (Fig. 6b). Streamflow violations show a somewhat counterintuitive result. The volume of violation under risk-seeking scenarios increases as expected (green curve shifts to right in Fig. 6d), but the frequency of violation decreases (green curve shifts to left in Fig. 6c). This is due to the fact that the Navajo Reservoir holds more water for irrigation season to satisfy downstream increasing water demand, which results in much fewer streamflow violation days during the irrigation season. Although this operation slightly increases streamflow violation days in the following season, the total number of violation days still decreases (Fig. S4). Second, the baseline results (red curves) are closer to the “all agents risk-averse” scenario results (blue curves). This is consistent with the findings from previous studies (e.g., Tena and Gómez, 2008), which suggest that farmers are commonly risk-averse when the stakes are high (Matte et al., 2017).
Individual agents' irrigated area changes under calibrated (green
curves), risk-averse (blue curves), and risk-seeking (red curves) scenarios.
The simulation results with different values of agents' risk perceptions
(
We also look at the time variations of individual irrigated area changes for
characterizing risk perceptions of different agents. Figure 7 shows the
simulated irrigation area changes for four selected large irrigation ditched
since they are the major players in the basin. The results clearly show
that Jicarilla (group 1) and NMAnimas (group 2) are historically risk-averse
agents (red curves overlap with blue curves). In contrast, Hammond and
Hogback (group 3) are relatively risk-neutral, compared to agents in group 1
and 2, as the red curves lie in between the green and blue curves. Group-3 agents
are located downstream of the Navajo Reservoir and most of them consider
the Navajo Reservoir as a steady water source, so they can have relatively more
aggressive attitudes toward risk compared to their upstream counterparts.
Also, note that Jicarilla, Hammond, and Hogback under the risk-seeking
scenario eventually reach their maximum available irrigated area. Therefore,
their irrigated area flattens out at the end of the simulation. The gray
curves in Fig. 7 represent the simulated irrigation area changes for agents
corresponding to different agents' risk perceptions. It shows that the
irrigation area generally increases with an increasing
The proposed BC-ABM framework allows us to quantify the influences of
external socioeconomic factors on human decision-making processes by
adjusting the CL ratio. In this study, we conducted a sensitivity analysis on
the cost–loss ratio to test what happens if economic conditions change and it
becomes more expensive or cheaper to expand the irrigated area by
systematically increasing (
The sensitivity analysis of changing economic conditions on an
agent's decision on irrigated areas. Blue (
According to the San Juan River basin regional water plan, several
strategies and constructions such as on-farm and canal improvements and
the municipal and irrigation pipeline from the Navajo Reservoir will be authorized
for meeting the future water demand (State of New Mexico Interstate Stream
Commission, 2016). These strategies and constructions could lead to a change
in future socioeconomic conditions, in terms of the cost of water usage and
changing irrigated area (e.g., up-front cost) for stakeholders. In this
study, we quantify the effects of up-front cost on the changes of irrigation
area (i.e., irrigation water demand) using the proposed BC-ABM framework. We
can look at the influence of up-front cost on human decision-making
processes from two perspectives. First, it directly changes the
socioeconomic condition of an agent (change of CL ratio). Second, it
influences an agent's decision-making processes by introducing more
information (change of causal network in BI mapping). As a result, the
proposed BC-ABM framework can take up-front costs into account without
theoretical and technical difficulties if related information is available.
Two scenarios assuming a general increasing and decreasing up-front cost for
agents over time are tested in the study. For each agent, a
time varied
Irrigation area changes of each agent under the scenario of
increasing (cyan) and decreasing (green)
The time variation of irrigated area for all 16 agents under different
up-front cost trends is shown in Fig. 9. The cyan and green curves are the
irrigated area change under an increasing and decreasing
The proposed BC-ABM framework in this paper is intended to be a generalizable
approach in water resources management and other fields that need to quantify
human decisions. This framework directly addresses the four
challenges summarized by Scalco et al. (2018) about how to apply the TPB in
an agent-based setting. The model diagnostic process and the use of the historical
irrigated area answer the first challenge: data and preliminary model
assessment. Applying the BI mapping provides a stochastic representation
of the decision-making process which eliminates the concern of working
with a static model. Combing with the CL model, we can mathematically
calculate when does intention become behavior. Finally, coupling the
ABM with RiverWare is our solution to address the feedback
mechanisms challenge in a CNHS. The method can be applied to other basins
given that the required input data for BI mapping are publically available,
such as the precipitation from NOAA and the streamflow from USGS, and risk
perception (
The modeling results can be used to inform water management policy. For
example, the sensitivity analysis (see Fig. 8) suggests that the collective
action of farmers has the potential to influence the irrigation of
Here we discuss two areas of limitation of the current study: data availability
and model structure. The lack of historical data to serve as the calibration
target is mentioned in the above section. Another data limitation is
the CL ratio calculation and the up-front cost. Currently, the CL ratio is
treated as a calibrated parameter in BC-ABM framework. The value of the CL ratio
can be estimated directly by acquiring relevant data, if available. For
example, the farm production expense data provided by the US Department of
Agriculture could be used as an approximation of the expected cost of
changing irrigation area (
Regarding the model structure limitation, the farmer's belief is currently calculated using one single preceding factor in the cognitive map that has the most extremity. The use of extremity from a single preceding factor in the decision-making processes assumes that the joint probability of decision-making from multiple preceding factors is not taken into account (the agent may not respond to the cumulative effects of environmental conditions). Finally, the current method does not explicitly consider direct interaction among agents in the BI mapping. We do model agents as interacting indirectly through irrigated water withdrawal (i.e., upstream agents' water uses will affect downstream agents' water availability). However, effects like peer pressure, word of mouth, and potential water markets are not currently considered in the model.
Making water resources management decisions in a complex adaptive natural–human system subject to uncertain information is a challenging issue. The interaction between human and natural systems needs to be modeled explicitly with associated uncertainties quantified and managed in a formal manner. This study applies a two-way coupled agent-based model (ABM) with a river-reservoir management model (RiverWare) to address the interaction between human and natural systems. The proposed ABM framework characterizes human decision-making processes by adopting a perspective of the theory of planned behavior implemented using Bayesian inference (BI) mapping joined with cost–loss (CL). The advantage of ABM is that, by defining different agents, various human activities can be represented explicitly while the coupled water system provides a solid basis to simulate the feedback between the environment and agents.
Combining BI mapping and CL modeling allows us to (1) explicitly describe human
decision-making processes, (2) quantify the associated decision uncertainty
caused by incomplete/ambiguous information, and (3) examine the adaptive
water management in response to a changing natural environment as well as
socioeconomic conditions. Calibration results for this coupled
BC-ABM–RiverWare model, as demonstrated in the San Juan River basin, show
that this methodology can capture the historical pattern of both human
activities (irrigated area changes) and natural dynamics (streamflow changes)
while quantifying the risk perception of each agent via risk perception
parameters (
Future work can target further methodology development to include direct
agent interaction into the BI mapping. For example, agents' decisions can be
affected by observing their neighbors' actions, and this information will
always be treated with
The input data and modeling results of the ABM-RiverWare
model are available at
The supplement related to this article is available online at:
YCEY led the entire project. JYH, SYH, and YCEY developed the ABM. VT prepared RiverWare. JM reviewed the model coupling. SYH and YCEY prepared the manuscript with contributions from all co-authors.
The authors declare that they have no conflict of interest.
This research was supported by the Office of Science of the US Department of Energy as part of research in the Multi-Sector Dynamics, Earth and Environmental System Modeling Program. We want to thank the editor and anonymous reviewers, who helped us improve the quality of this paper. Special thanks are given to Susan Behery in USBR for providing historical data on the San Juan Basin and Majid Shafiee-Jood in the University of Illinois, who discussed the methods of BI mapping and CL modeling with us in the earlier version of the manuscript. All data used for both the RiverWare model (inflow, crop ET, and water diversion, etc.) and the agent-based model (winter precipitation, historical basin outflow, and historical irrigated area, etc.) are explicitly cited in the reference list.
This paper was edited by Pieter van der Zaag and reviewed by Andres Baeza and one anonymous referee.