Influence of Irrigation Drivers Using Boosted Regression Trees: Kansas High Plains

Abstract

Groundwater levels across parts of western Kansas have been declining at unsustainable rates due to pumping for agricultural irrigation despite water‐saving efforts. Accelerating this decline is the complex agricultural landscape, consisting of both categorical (e.g., management boundaries) and numerical (e.g., crop prices) factors that drive irrigation decisions, making integrated water budget management a challenge. Furthermore, these factors frequently change through time, rendering management strategies outdated within relatively short time scales. This study uses boosted regression trees to simultaneously analyze categorical and numerical data against annual irrigation pumping to determine the relative influence of each factor on groundwater pumping across both space and time. In all, 45 key water use variables covering approximately 19,000 groundwater wells were tested against irrigation pumping from 2006 to 2016 across five categories: (1) management/policy, (2) hydrology, (3) weather, (4) land/agriculture, and (5) economics. Study results showed that variables from all five categories were included among the top 10 drivers to irrigation, and the greatest influence came from variables such as irrigated area per well, saturated thickness, soil permeability, summer precipitation, and pumping costs (depth to water table). Variables that had little influence included regional management boundaries and irrigation technology. The results of this study are further used to target the factors that statistically lead to the greatest volumes of groundwater pumping to help develop robust management strategy suggestions and achieve water management goals of the region.

Full text

1. Introduction
Groundwater level decline of the High Plains Aquifer (HPA) underlying western Kansas has been exten-
sively analyzed with most efforts focused on irrigation related to one of four domains: (1) physical (e.g.,
climatic and atmospheric factors and underlying geology; Edwards,2016; MardanDoost etal.,2019; Whit-
temore etal.,2016), (2) agricultural (e.g., crop type, irrigation limits and management, cover crops, and
irrigation efficiency; Butler etal.,2016; Kisekka etal.,2017; Pfeiffer & Lin,2014), (3) socioeconomic (e.g.,
environmental policies, energy costs, irrigation efficiency, global markets, and crop prices; Hrozencik
etal.,2017; Sanderson etal.,2017; Sukcharoen etal.,2020), or (4) an integrated approach among the first
three categories (e.g., Haacker etal.,2019; Majumdar etal.,2020; Smidt etal.,2016). While these studies
provide a comprehensive overview of the complexity of factors that drive irrigation use, little is known
about the relationship between these factors across both space and time relative to irrigation pumping. For
example, studies have shown that irrigation efficiency drives groundwater use (Pfeiffer & Lin,2014), yet it
cannot conclusively be determined that efficiency is more or less influential than annual weather patterns
in driving total withdrawals from the aquifer. The same applies for management strategies versus crop
prices or any other combination of factors compared to others. So, while there is a clear understanding of
Abstract Groundwater levels across parts of western Kansas have been declining at unsustainable
rates due to pumping for agricultural irrigation despite water-saving efforts. Accelerating this decline
is the complex agricultural landscape, consisting of both categorical (e.g., management boundaries)
and numerical (e.g., crop prices) factors that drive irrigation decisions, making integrated water budget
management a challenge. Furthermore, these factors frequently change through time, rendering
management strategies outdated within relatively short time scales. This study uses boosted regression
trees to simultaneously analyze categorical and numerical data against annual irrigation pumping to
determine the relative influence of each factor on groundwater pumping across both space and time.
In all, 45 key water use variables covering approximately 19,000 groundwater wells were tested against
irrigation pumping from 2006 to 2016 across five categories: (1) management/policy, (2) hydrology,
(3) weather, (4) land/agriculture, and (5) economics. Study results showed that variables from all five
categories were included among the top 10 drivers to irrigation, and the greatest influence came from
variables such as irrigated area per well, saturated thickness, soil permeability, summer precipitation, and
pumping costs (depth to water table). Variables that had little influence included regional management
boundaries and irrigation technology. The results of this study are further used to target the factors that
statistically lead to the greatest volumes of groundwater pumping to help develop robust management
strategy suggestions and achieve water management goals of the region.
Plain Language Summary Water use for crops has lowered groundwater levels in western
Kansas. Past studies have shown that this water use is driven by many factors spanning policy, economics,
and the physical environment. Because of this complexity, it has been difficult to fully understand which
factors most drive irrigation use relative to each other. This study uses a machine-learning model to
rank the influence of 45 factors on irrigation pumping. These factors are analyzed over space (∼19,000
wells across western Kansas) and time (2006–2016). Based on this study, drivers to water use include
total irrigated area, summer rainfall, and depth to the water table. Factors that have little influence
include management district boundaries and irrigation system type. These results are used to make water
management suggestions for the region.
LAMB ET AL.
© 2021. The Authors.
This is an open access article under
the terms of the Creative Commons
Attribution License, which permits use,
distribution and reproduction in any
medium, provided the original work is
properly cited.
Influence of Irrigation Drivers Using Boosted Regression
Trees: Kansas High Plains
Susan E. Lamb1 , Erin M. K. Haacker2 , and Samuel J. Smidt1
1Soil and Water Sciences Department, University of Florida, Gainesville, FL, USA, 2Department of Earth &
Atmospheric Sciences, University of Nebraska-Lincoln, Lincoln, NE, USA
Key Points:
• The relative influence of drivers
to irrigation pumping in western
Kansas is modeled from 2006 to 2016
using boosted regression trees
• Site-specific factors are more
influential than regional policies,
and weather-related factors are more
influential at longer time scales
• Irrigation decision making largely
follows resource availability and
operation cost considerations over
localized management schemes
Supporting Information:
Supporting Information may be found
in the online version of this article.
Correspondence to:
S. E. Lamb,
susan.lamb@ufl.edu
Citation:
Lamb, S. E., Haacker, E. M. K., & Smidt,
S. J. (2021). Influence of irrigation
drivers using boosted regression trees:
Kansas High Plains. Water Resources
Research, 57, e2020WR028867. https://
doi.org/10.1029/2020WR028867
Received 18 SEP 2020
Accepted 14 MAR 2021
10.1029/2020WR028867
Special Section:
The Quest for Sustainability
of Heavily Stressed Aquifers at
Regional to Global Scales
RESEARCH ARTICLE
1 of 16

Water Resources Research
the driving factors that lead to irrigation use, both individually and as a
group (e.g., Haacker etal.,2019; Smidt etal.,2016), uncertainty still exists
in understanding the spatiotemporal influence of how these factors work
together to influence irrigation decision making. Measurement is a hall-
mark of precision agriculture and other targeted management schemes
(e.g., deficit irrigation management; Rudnick etal.,2019), as farmers can
often better manage the resources that they can measure. The uncertain-
ty surrounding the relative influence (RI) of irrigation drivers leads to
mismanagement and continued groundwater level decline for the region
(Smidt etal.,2016).
Past studies analyzing the relationships between irrigation drivers across
space and time have been limited as drivers are both numerical (e.g., av-
erage temperature and crop price) and categorical (e.g., crop type and
Groundwater Management District [GMD]). One approach to overcom-
ing these methodological data challenges has been to analyze numerical
data by category and then compare results (e.g., on a GMD by GMD basis;
Whittemore etal., 2016). This can be useful for resource management,
since the boundaries of the GMDs correspond to some physical features
of the aquifer, and these analyses provide results at the same scale at
which management programs are enacted. However, this limits modeled
relationships by (1) preventing categorical data from interacting directly
with numerical data or (2) minimizing the scale at which drivers can im-
pact aquifer use. Fortunately, advances in machine-learning techniques,
namely boosted regression trees (BRT; Elith etal.,2008), have allowed
for improved analysis when grouping disparate data. BRT is a statisti-
cal ensemble that combines regression trees and data boosting to define
relationships between variables, including the simultaneous analysis of
categorical and numerical variables (Elith etal.,2008). When applied to
irrigation in western Kansas, BRT can accurately characterize the relative influence of sociophysical fac-
tors on annual irrigation pumping and offer strong predictive power for estimating future water use (Elith
etal.,2008; Hu etal.,2017).
Here, we use BRT analysis to quantify the predominant drivers to irrigation use in western Kansas from
2006 to 2016 to (1) improve understanding of how these drivers relate, (2) develop meaningful manage-
ment objectives based on these relationships, and (3) demonstrate BRT as a useful water management tool.
Synchronously, we analyze 45 irrigation drivers spanning five driver groups (management/policy, hydrol-
ogy, weather, land/agriculture, and economy) to quantify the predominant controls of irrigation pumping
across both space and time. We further isolate dominant driver trends to target the most influential social
and physical variables impacting western Kansas. The results of this analysis are then used to prioritize
management efforts across the region to balance agricultural production and groundwater level declines.
2. Methods
2.1. Site Description
Agriculture is the dominant land use across western Kansas. Approximately 94% of land cover was dedi-
cated to agricultural production from 2006 to 2016, and 77% of all cropland was composed of just six com-
modities: winter wheat (38%), corn (19%), sorghum (12%), soybeans (3%), alfalfa hay (3%), cotton (<1%), or
a double crop planting of the six (1%; USDA-CDL,2006–2016). During the same period, HPA groundwater
levels across the region declined by an average of 2.8m (Figure1; derived from Haacker etal.,2016). Despite
this decline, water withdrawals from the underlying HPA remain essential to the agricultural production
and cultural identity of western Kansas, especially due to the region’s low humidity, persistent winds, and
limited precipitation relative to crop water demands (Sanderson & Frey,2014).
LAMB ET AL.
10.1029/2020WR028867
2 of 16
Figure 1. High Plains Aquifer site map (a) and groundwater level
change for western Kansas from 2006 to 2016 (b; derived from Haacker
etal.,2016).

Water Resources Research
Groundwater used for irrigation in western Kansas largely sustains the expansive agricultural production
of the region and can add more than $500 million in annual revenue for the state compared to dryland-on-
ly production (excluding operation costs; Smidt etal.,2019). In 2005, the groundwater was valued at $1.2
billion (as natural capital; Fenichel etal.,2015). However, continued groundwater pumping in Kansas is
estimated to deplete nearly 40% of the underlying HPA in the next half century (Steward etal.,2013). This
depletion will inevitably force some farmers to convert to less productive dryland operations which can pro-
duce 2–4 times lower crop yields per area (Cotterman etal.,2018; Smidt etal.,2016; Steward etal.,2013).
Several strategies have been introduced to slow water loss and stabilize groundwater levels throughout
the region, including efficient technologies (Pfeiffer & Lin,2014), drought-resistant cultivars (Cotterman
etal.,2018), and localized management boundaries (Deines etal.,2019). For example, five GMDs have been
formed since the 1970s to develop and enforce local irrigation policies (Peck,2006). Yet, groundwater lev-
els have continued to decline across the region prompting the development of further management zones
within and across district boundaries (K.S.A. 82a-1036,1978; K.S.A. 82a-1041,2012). While some areas have
found success in these efforts (e.g., Deines etal.,2019), much of the region has yet to stabilize groundwater
levels (e.g., Haacker etal.,2019; Whittemore etal.,2018). A clear gap remains between the intended man-
agement of groundwater, the responding use of irrigation, and the understanding of how these interact
throughout the region.
Compounding this agricultural water management challenge is the socioenvironmental heterogeneities
that further influence water use practices across western Kansas (Figure2; Whittemore etal., 2018). For
example, GMDs 1, 3, and 4 receive less annual precipitation (43–58cm) than GMDs 2 and 5 (58–63 cm;
Whittemore etal.,2018). In regards to management, GMDs 1, 3, and 4 operate under “planned depletion”
strategies while GMDs 2 and 5 have more favorable groundwater recharge and enact a “safe yield” scheme
(Peck,2006; Whittemore etal.,2018). Other differences at the GMD level include a variability in average
monthly temperature, soil permeability, depth to water table, and interstate compacts (IC). Collectively,
through these heterogeneities, western Kansas is a unique case study of mixed physical and social variabil-
ity with high data resolution valuable for informing progressing agricultural water use and management
techniques in this region and elsewhere.
As part of the state’s water management agenda, the Kansas Department of Agriculture and Kansas Ge-
ological Survey have continually managed an open-access Water Information Management and Analysis
System (WIMAS) since 1996 with annual water use records for over 45,000 wells across the state. Of these
wells, 19,000 are located in western Kansas with access to the HPA. Associated data include information
such as well type, installation depth, depth to water, pumping amount, pumping allotment based on gov-
ernment regulation, irrigation system type, and crop type. No other region of the HPA has this type of data
resolution, likely even in private databases. Collectively, this combination of driver complexity and data
LAMB ET AL.
10.1029/2020WR028867
3 of 16
Figure 2. Example data layers for the western Kansas High Plains Aquifer region including dominant groundwater
management boundaries (a; Kansas Department of Agriculture), precipitation (b; PRISM, Oregon State University),
temperature (c; PRISM, Oregon State University), permeability (d; United States Geological Survey), saturated thickness
(e; Haacker etal.,2019), and depth to groundwater (f; derived from Haacker etal.,2016; United States Geological
Survey).

Water Resources Research
resolution make this location an ideal selection for using BRT analysis to better understand influences on
irrigation.
2.2. Data
Data used in this study can be summarized into independent variable (i.e., drivers to irrigation pump-
ing) and dependent variable (i.e., irrigation pumping) categories. Collectively, we analyzed 45 independent
variables and 1 dependent variable. The dependent variable is total annual irrigation pumping amount
reported on the well level. The independent variables were identified as influential to irrigation use based
on published literature and informal conversations with experts, colleagues, and stakeholders and are or-
ganized into five categories: management/policy, hydrology, weather, land/agriculture, and economics. All
data used in the analysis are summarized in Table1.
Well-specific data, such as annual pumping data and crop irrigated, for approximately 19,000 agricultural
irrigation wells in western Kansas for years 2006–2016 were downloaded through the WIMAS maintained
by the Kansas Department of Agriculture, Division of Water Resources and Kansas Geological Survey
(KDA-DWR & KGS, version 5). These data, which included GPS coordinates for each pumping well, were
then read into ArcGIS (version 10.5). Spatial driver data were downloaded as or converted to raster files
in ArcGIS. If downloaded, cell sizes were kept consistent with their original format. If converted from a
shapefile, we assigned a standard 11.1-m × 11.1-m cell size. Well density was produced in with a 1.11km by
1.11km cell size. Annual, statewide market crop value data for alfalfa, corn, sorghum, soybeans, and wheat
grown in Kansas were accessed from the United States Department of Agriculture and integrated into the
well data attribute table (USDA-NASS,2006–2016). Saturated thickness and water table elevation were cre-
ated using the methods described in Haacker etal.(2016). Depth to water table was created in ArcGIS using
the aforementioned water table elevation data and a digital elevation model from the United States Geolog-
ical Survey. The Right variable was generated by concatenating WIMAS data set variables relating to right
type as well as status of the water right file, water right, and point of diversion. The shapefiles for intensive
groundwater use control areas (IGUCAs) are public data and were requested from the Kansas Department
of Agriculture via an Open Records Request. All data were unique annually except for boundary data (e.g.,
GMD, Basin), hydraulic conductivity, and soil permeability as they were effectively static over the temporal
range of the study. No predetermined weights were applied to predictor variables in the analysis due to the
exploratory nature of the research. All data were spatially aligned using the NAD 1927 Geographic Coor-
dinate System and USA Contiguous Albers Equal Area Conic projected coordinate system. All driver data
values were then spatially attributed to each well annually from 2006 to 2016 and exported in spreadsheet
format (i.e., columns are variables and rows are individual wells) for use in the boosted regression tree
modeling.
2.3. Description of Boosted Regression Trees
Boosted regression trees draw on both statistical and machine-learning techniques to determine the rela-
tive influence of each predictor variable (i.e., independent variable) on a response variable (i.e., dependent
variable; Elith etal.,2008). Specifically, BRT relies on two algorithms: (1) regression trees and (2) boosting.
Regression trees are decision trees that have repeating binary splits to identify how a subset of predictor var-
iables relate to the response variable based on a defined predictor value as a split point (e.g., May precipita-
tion>35mm; Elith etal.,2008). Decision tree complexity (i.e., total number of trees and number of nodes in
a tree) is defined by the user. Each regression tree culminates with the calculation of a residual value. Boost-
ing then uses the results of a regression tree (i.e., residual) to improve the fit of the next tree (i.e., improve
the residual). This sequence progresses stage-wise through the model rather than stepwise, thus existing
trees are not changed but instead the model estimates are updated as new trees are added (Elith etal.,2008).
This process continues until the defined number of trees is reached or the residual has reached its optimum
value, at which point improvements in model estimates are negligible. A learning rate further defines the
contribution, or weight, of each tree to the model. Based on the results of the boosted regression trees, the
model can then quantify the relative influence of each predictor variable on the response variable. Refer to
Hastie etal.(2009) for more information and extended derivation of regression trees, Ridgeway(2007) for
boosting, and Elith etal.(2008) and Friedman and Meulman(2003) for an integration of the two.
LAMB ET AL.
10.1029/2020WR028867
4 of 16

Water Resources Research
In addition to its ability to analyze both numerical and categorical data, a BRT model was selected for this
study as it is not sensitive to outliers and missing data in predictor variables (Elith etal.,2008). BRT was
chosen over a random forest model, which tends to perform poorly when there are many low-influencing
variables (Hastie etal.,2009). Furthermore, statistical approaches such as generalized additive models were
not utilized as, unlike BRT, interactions between predictor variables are not automatically modeled (Elith
etal.,2008; Hastie etal.,2009).
LAMB ET AL.
10.1029/2020WR028867
5 of 16
Variable Description Units/scale Mean; standard deviation Source
Dependent variable
Amt_Irr Total annual irrigation pumping m3/year 204,479; 152,316 1
Independent variables
Management/policy
GMD Groundwater Management District Boundary Categorical 1
IGUCA Intensive Groundwater Use Control Area Boundary Categorical 2
RC Rattlesnake Creek Management Plan Boundary Categorical 3
IC Interstate compacts Boundary Categorical 3
Right Water rights Concatenated Categorical 1
Auth_Amt Authorized amount of irrigated water m3/year 326,391; 273,905 1
Auth_Rate Authorized pumping rate m3/min 3; 12 1
Auth_Area Authorized irrigated area ha/year 169; 262 1
Hydrology
Basin River basin Boundary Categorical 1
ST Saturated thickness Meters, 250-m × 250-m 36; 27 6
WT_Elev Interpolated water table elevation Meters, 250-m × 250-m 771; 171 6
K Aquifer hydraulic conductivity Contours, 0–90m/day Categorical 5
Weather
T01, T02, … Mean monthly temperature Celsius, 4-km × 4-km 13; 2 4
T_Annual Mean annual temperature Celsius, 4-km × 4-km 13; 1 4a
P01, P02, … Total monthly precipitation mm, 4-km × 4-km 48; 36 4
P_Annual Mean annual precipitation mm, 4-km × 4-km 48; 15 4a
Land/agriculture
SP Mean soil permeability Very slow to very rapid Categorical 3
System Irrigation technology Type Categorical 1
Area_Irr Reported annual irrigated area ha/year 58; 57 1
WD Well density Wells/km2, 0.01°×0.01° 0.4; 0.2 1
Crop Reported commodity Type Categorical 1
Economics
CV_Area Annual KS crop price per unit area $/ha Crop specific 5
Depth Depth to water table Meters, 250-m × 250-m 41; 28 3, 6a
Note. Mean and standard deviation of collected data from 2006 to 2016. Source key: (1) Water Information Management and Analysis, maintained by the Kansas
Department of Agriculture, Division of Water Resources and Kansas Geological Survey; (2) Kansas Department of Agriculture, Division of Water Resources –
Open Records Request; (3) United States Geological Survey; (4) PRISM Climate Group, Oregon State University; (5) United States Department of Agriculture;
(6) Haacker etal.(2016).
aIndicates that data were derived from these sources rather than utilized directly.
Table 1
Data, Descriptions, and Sources

Water Resources Research
2.4. Construction of BRT Model
We used foundational R code (R Development Core Team,2018) from Elith etal.(2008) to implement the
BRT. While this code utilized the gbm R package, we used its expanded version for this study, the dismo R
package (v. 3.5.2 for Mac and v. 3.5.1 and v.3.6.2 for Windows; Hijmans etal.,2017). This code was then
modified to fit the conditions of our data set.
In BRT analyses, five conditions must be predetermined: (1) the total number of trees to be used in the
analysis, (2) distribution of the loss function, (3) bag fraction (i.e., the amount of data randomly selected at
each step and not replaced), (4) the tree complexity (i.e., number of nodes in each tree), and (5) the learning
rate of the model (i.e., the influence of each tree in the model; a value of 0–1) (Elith etal.,2008). Here, we
did not set a limit to the number of trees and allowed the model run until it optimized the residual loss on
the response variable. We used a Laplace distribution because it is optimal for data sets with a continuous
response variable (Ridgeway,2007) and provides a more robust fit to the data compared to other distribu-
tion options (Lampa etal.,2014; Murphy,2012), which we believe is more suitable for agricultural data that
often have large variability. The bag fraction was set at 0.5. The learning rate was set to 0.05, and the tree
complexity to 24, as determined through a calibration and validation process.
We ran a BRT model using the 2016 data for learning rate (lr) values of 0.1, 0.05, and 0.01 and tree com-
plexity (tc) values of 2–18 in increments of 2. We utilized two values from models run on each combination
of parameters (1) a tenfold cross validation (CV) statistic and (2) r-squared statistic. For each combination
of parameters. We maintain that CV is an appropriate metric for evaluating the best model, as BRT differs
from other statistical methods in that there are no p values and degrees of freedom are difficult to identify
(Elith etal.,2008). Also, CV can be a more robust sensitivity analysis for machine-learning models rather
than Akaike information criterion (Hauenstein etal., 2017). For the r-squared analysis, we conducted a
BRT model on 50% of the data and used the function predict.gbm to predict the remaining 50% of data. This
prediction was plotted against the observed values to determine the r-squared statistic.
BRT is a stochastic technique, thus the CV and r-squared statistics change marginally between iterations
even if conducted on the same parameter combinations. Because of this, we utilized the mean CV statistics
for each learning rate, and the mean r-squared statistics for each tree complexity. Identifying the highest
mean CV and r-squared statistics, we determined that a learning rate of 0.05 and a tree complexity of 24
would produce the best performing model. Please reference the Supplemental Information for more detail
on the calibration and validation steps.
2.5. Application of BRT Models
Once parameters were identified, we conducted four groups of BRT models: (1) annually, (2) annually with
pumping normalized by irrigated area, (3) all years grouped together, and (4) all years grouped together
with pumping normalized by irrigated area. Annual models (Groups 1 and 2) utilized unique data for each
year, whereas aggregated models (Groups 3 and 4) examined all years of data simultaneously and time was
not distinguished as a variable. We normalized pumping by irrigated area in two of the groups to eliminate
an anticipated strong correlation between total pumping and total irrigated area. We also initially ran each
year as an individual BRT model to systematically flag the noninfluential variables using the gbm.simplify
function of the R code. This allowed us to manually reduce noise by eliminating noninformative variables
prior to our analysis. Note that the collective influence of variables will always add up to 100, and even
noninformative variables will be assigned a nonzero value in a BRT analysis, albeit quite small. We used the
simplified sets for Groups 1 and 2. We could not use the simplified sets for Groups 3 and 4 as noninformative
variables were flagged in some years but not others (Table2), leaving incomplete driver data sets for the
groups with years combined together. We also used only a randomly selected 25% of data for each variable
in Groups 3 and 4, as this still included over 2.7 million data points and challenged computing capabilities
(Dell Precision 5820 desktop computer, 2018, Windows 10, Intel(R) Xeon(R) W-2123 CPU @ 3.60 GHz,
32GB RAM). A summary of completed models is outlined in Table2.
LAMB ET AL.
10.1029/2020WR028867
6 of 16

Water Resources Research
3. Results
The relative influences of each irrigation driver on groundwater pumping amount for the Group 1 models
(annual, simplified) and Group 3 model (years combined, unsimplified) are displayed in Figure3; each
variable is further color coded by driver category.
Drivers are arranged by decreasing mean RI for Group 1 over the temporal range of the study, where the
boxes on the Group 1 boxplots are the interquartile range (IQR) and the whiskers extend to the minimum
and maximum values. Hollow points indicate RI outliers from Group 1 results. In Group 1, irrigated area
was the most dominant driver with a mean RI of 18.0%, followed by authorized amount, saturated thick-
ness, and authorized pumping rate (mean RI of 5.3%, 5.3%, and 4.7%, respectively). Localized management
drivers had the least influence on irrigation pumping, with GMDs accounting for 0.1% of influence, IGU-
CAs for 0.1%, and IC for 0.2%. The RI of weather-related drivers ranged from an 0.6% to 5.3%, with annual
precipitation being the greatest influencing weather variable by mean. Weather variables also had the great-
est occurrence of RI outliers across time, likely corresponding to extreme weather events. Regardless of the
month, precipitation had a higher median RI on irrigation pumping than did temperature. For manage-
ment/policy variables, well-scale policies were strong drivers to irrigation pumping whereas regional-scale,
LAMB ET AL.
10.1029/2020WR028867
7 of 16
Year Variables removed Number of trees CV (mean, standard deviation) Deviance (mean, standard deviation)
Group 1: 11 models, annual, simplified (gbm.simplify)
2006 4 (GMD, IC, IGUCA, RC) 2,150 0.834, 0.003 43.257, 0.379
2007 4 (GMD, IC, IGUCA, RC) 1,600 0.836, 0.004 40.124, 0.438
2008 2 (IC, RC) 1,650 0.862, 0.003 41.055, 0.333
2009 4 (GMD, IC, IGUCA, RC) 1,900 0.851, 0.002 38.424, 0.349
2010 4 (GMD, IC, IGUCA, RC) 2,000 0.857, 0.002 38.644, 0.273
2011 2 (GMD, RC) 2,000 0.874, 0.004 44.883, 0.387
2012 2 (IGUCA, RC) 1,800 0.859, 0.004 42.913, 0.420
2013 5 (GMD, IC, IGUCA, RC, Right) 1,450 0.860, 0.003 41.058, 0.404
2014 5 (GMD, IC, IGUCA, RC, Right) 1,800 0.860, 0.002 40.486, 0.371
2015 6 (GMD, IC, IGUCA, K, RC, Right) 1,600 0.833, 0.003 37.077, 0.188
2016 4 (GMD, IC, IGUCA, RC) 1,900 0.845, 0.003 36.923, 0.302
Group 2: 11 models, annual, simplified (gbm.simplify), normalized by area irrigated
2006 4 (GMD, IC, IGUCA, RC) 2,150 0.550, 0.030 0.315, 0.002
2007 4 (GMD, IC, IGUCA, RC) 2,150 0.631, 0.007 0.292, 0.002
2008 2 (IC, RC) 1,900 0.641, 0.014 0.296, 0.002
2009 4 (GMD, IC, IGUCA, RC) 2,350 0.617, 0.016 0.278, 0.003
2010 4 (GMD, IC, IGUCA, RC) 2,150 0.634, 0.005 0.282, 0.001
2011 2 (GMD, RC) 2,700 0.560, 0.007 0.336, 0.003
2012 2 (IGUCA, RC) 2,550 0.566, 0.007 0.327, 0.003
2013 5 (GMD, IC, IGUCA, RC, Right) 1,950 0.653, 0.009 0.301, 0.003
2014 5 (GMD, IC, IGUCA, RC, Right) 2,500 0.619, 0.006 0.294, 0.002
2015 6 (GMD, IC, IGUCA, K, RC, Right) 2,200 0.553, 0.040 0.278, 0.002
2016 4 (GMD, IC, IGUCA, RC) 2,450 0.632, 0.006 0.270, 0.002
Group 3: 1 model, combined years (25% from each year)
Combined years No removed variables 2,650 0.857, 0.002 41.199, 0.230
Group 4: 1 model, combined years (25% from each year), normalized by area irrigated
Combined years No removed variables 2,750 0.597, 0.027 0.310, 0.002
Table 2
BRT Models (Size, Cross Validation, and Deviance)

Water Resources Research
boundary level policies were not strong drivers. The Rattlesnake Creek Management Plan was also a district
boundary examined in this study but was classified as noninfluential by gbm.simplify across all years and
was not considered in the Group 1 model and thus excluded from Figure3. Generally, variables with the
greatest variance in RI across years were among top influencing variables, and those with the smallest
variance in RI across years were among low-influencing variables. With the exception of irrigated area,
all driver variables reported RI values of less than 10% in any given year, with most being less than 5% in
all years. All five variable categories are represented in the top nine influencing drivers, with the top three
drivers accounting for 28.7% of RI by mean across years.
As for Group 3 results (all years combined), the top three drivers included irrigated area with a RI of 21.7%,
saturated thickness with 5.2%, and annual precipitation with 4.8%. Outside the large RI increase for annual
precipitation, trends remained consistent between Groups 1 and 3. In addition to annual precipitation, irri-
gated area also had a notable increase in RI; combined, these increases resulted in the slight RI decrease for
most other variables as all contributing variables sum to 100%. The overall complexity of variables influenc-
ing irrigation pumping is further highlighted through all five categories contributing to the top nine driving
factors and nearly all drivers contributing less than 5% to the total influence on pumping.
The relative influences of each irrigation driver on groundwater pumping amount for the Group 2 models
(annual, simplified, and normalized by irrigated area) and Group 4 model (years combined, unsimplified,
and normalized by irrigated area) are displayed in Figure4; each variable is further color coded by driver
category.
LAMB ET AL.
10.1029/2020WR028867
8 of 16
Figure 3. Boxplots showing RI outputs from BRT runs conducted annually from 2006 to 2016 (Group 1). Black points
show RI from a single BRT run conducted on collective data from 2006 to 2016 (Group 3). Note scale change following
x-axis break. RI, relative influence; BRT, boosted regression trees.

Water Resources Research
Drivers are arranged by decreasing mean RI for Group 2 over the temporal range of the study, where whisk-
ers on the Group 2 boxplots are likewise set at minimum and maximum values and the box is the IQR, and
the hollow dots are outlier RI values. While the collective RI values still summed to 100%, normalizing
pumping by irrigated area allowed for more detailed characterization of other less influential variables.
Here, trends remained similar to those observed in Group 1, with the exception of relative shuffling of the
top five variables. In Group 2, saturated thickness was the top influencing driver (mean RI of 6.3%) and
authorized area was second (mean RI of 5.9%). Depth to water (cost to pump; mean RI of 5.7%) moved
ahead of authorized rate (mean RI of 5.4%) when compared to Group 1. Crop type experienced increased
variability across years, as did crop value per hectare.
Variables with the largest mean RI no longer observed the greatest variance in RI across years, although
generally larger RI values resulted in greater variance. All driver variables still reported RI values of less
than 10% in any given year, with most being less than 5% in all years. All five variable categories are rep-
resented in the top 10 influencing drivers, with the top three drivers accounting for 17.7% of RI by mean
across years.
In Group 4 (all years combined, normalized by irrigated area), the top three influencing drivers were satu-
rated thickness (6.2%), annual precipitation (6.0%), and crop type (4.9%). Similar to Group 3, annual precip-
itation had the greatest increase in RI, resulting in a decrease in RI for other top drivers. Outside the top 10
drivers, Group 4 results matched closely with the results of Group 2. All five categories were present in the
top 10 variables, and all variables had RI values of less than 8% with most contributing to less than 5% of the
total influence on groundwater pumping.
LAMB ET AL.
10.1029/2020WR028867
9 of 16
Figure 4. Boxplots showing RI outputs from BRT runs conducted annually from 2006 to 2016 on data normalized by
irrigated area (Group 2). Black points show RI from a single BRT run conducted on collective data from 2006 to 2016 on
data also normalized by irrigated area (Group 4). RI, relative influence; BRT, boosted regression trees.

Water Resources Research
While RI is a meaningful metric, it fails to characterize whether a given variable contributes to inhibits
pumping. This type of influence is displayed using partial dependence (PD) plots. Figure5 displays PD plots
for 12 example variables from Group 1 in 2012, where positive y-axis values indicate that corresponding
x-axis values are more likely to predict irrigation pumping (stronger prediction). The reverse is also true,
negative y-axis values indicate that corresponding x-axis values are less likely to predict irrigation pumping
(weaker prediction). The magnitude of these values describes the strength of the correlation. These func-
tions reveal the individual impact of the driver on irrigation pumping after the mean impact of the other
drivers in the model is considered (Elith etal., 2008). Because of this, individual variables with strong
interactions may not be well represented in these plots, but it remains a useful tool for understanding the
general relationship between a predictor variable and the response variable (Friedman,2001; Friedman &
Meulman,2003). Reference the Supplemental Information for examples regarding variable interactions.
Drivers are arranged in order of decreasing RI and can be summarized into three general patterns: (1)
increasing PD slopes, (2) decreasing PD slopes, and (3) nonlinear PD slopes. Variables with increasing PD
LAMB ET AL.
10.1029/2020WR028867
10 of 16
Figure 5. Partial dependence plots showing 12 influential variables in 2012 (Group 1), ordered by decreasing relative
influence. Tick marks along the inside of the x-axes represent the distribution of data in deciles.

Water Resources Research
slopes include irrigated area, authorized amount, saturated thickness, depth to water, authorized rate, and
water table elevation. For example, as the number of irrigated areas increased, so did the occurrence of
pumping, creating a positive PD slope. Variables with decreasing PD slopes included July, August, and Oc-
tober precipitation. Here, low precipitation values correlated with pumping activity and high precipitation
values did not correlate with pumping activity, leading to a negative PD slope. Variables with nonlinear
PD slopes included authorized area, well density, and soil permeability. These variables did not have a pre-
dictable PD pattern, showing both correlation with pumping and no pumping at variable points within the
range of their data values. This relationship is also common in categorical data which do not have linear
characteristics or behaviors to generate meaningful slope depictions.
Because outliers can seemingly skew the results of PD plots, decile marks are also included along the x-axis
of each variable to communicate the magnitude of data represented in the plot. To further demonstrate how
these data are interpreted, we plotted empirical cumulative distribution plots of driver data beneath three
example PD plots for three variables in 2012 (Group 1), where shaded values have positive y-axis values,
thus are correlated with pumping (Figure6). These plots also identify the threshold at which pumping is
likely to occur (or no longer occur). For example, pumping was likely to occur when saturated thickness was
more than 41-m, July precipitation less than 77-mm, or water table elevation more than 737-m.
4. Discussion
4.1. Correlative Relationships
In this study, we seek to confirm correlations between predictor variables and irrigation pumping rather
than infer causality. In discussion of results, we offer potential explanations for these correlations as we aim
characterize what drives irrigation use in this region. Beyond identifying strong correlations, the BRT model
also determines noisy variables. These variables have the lowest relative influence, indicating that they not
only are uncorrelated with pumping but also do not drive pumping. Therefore, future water management
efforts can be guided away from these low-influencing variables and redirected toward stronger drivers. This
is a valuable deduction as a wide range of variables impact irrigation decision making and any reduction of
noise helps target effective management.
Furthermore, some predictor variables in this study are endogenous and have potential to cause pumping,
result from pumping, or likely both. For example, water table depth is highly correlated to pumping in this
study which could be a cause of pumping and/or result from pumping. As this work focuses on irrigation
drivers, we propose possible reasons why water table depth could drive pumping without claiming certain
causality. Parsing causality from consequence becomes even more difficult with a variable like depth as it is
temporally nonautonomous. In this way, pumping in a given year can be impacted by the change in water
table depth from the previous year, which can then impact water table depth in the upcoming year. Depth
is unlike autonomous variables such as precipitation, which are not linked to their impact in prior growing
LAMB ET AL.
10.1029/2020WR028867
11 of 16
Figure 6. Partial dependence plots (top) with corresponding empirical cumulative distribution functions (bottom) to
show influence of driver on irrigation pumping along driver data ranges.

Water Resources Research
seasons (i.e., the amount of rain in a given year is not largely impacted by the amount of rain in the previous
year). Rather, depth can both be a driver and consequence of irrigation pumping. Even if this BRT model
was conducted using predevelopment water table depths rather than current measurements, this unique
relationship could not be fully captured.
4.2. Strong Versus Weak Drivers
Strong drivers were primarily those specific to the conditions of an individual well (e.g., total irrigated
area, authorized rate, authorized amount, authorized area, and well density). Weak drivers were primari-
ly those more representative of regional characteristics (e.g., groundwater doctrine, GMD, other localized
management boundaries, river basin, or hydraulic conductivity of the aquifer). This difference between
well-scale and regional influence can likely be attributed to individual farmers making decisions to irrigate
on a case-by-case basis within the regulations of their larger-scale governing frameworks. For example, a
water user more inclined to irrigate compared to a neighbor under the same regional governance will am-
plify well-specific drivers and buffer the influence of regional governance drivers, as regional drivers are
the same between two disparate users. This relationship likely explains why well-specific governance (e.g.,
authorized area) is a strong driver, whereas regional governance (e.g., state groundwater doctrine; Right),
which defines the well-specific governance, is a weak driver.
More directly, this relationship suggests that users are not limited or forced to change behavior by their re-
gional governance and may be self-electing to change behavior despite their legal rights to business-as-usu-
al. For example, GMDs 1, 3, and 4 have less groundwater supply but operate under “planned depletion”
doctrine, and GMDs 2 and 5 have greater groundwater supply under the more conservative “safe yield”
doctrine (Peck,2006; Whittemore et al.,2018). But this does not mean all farmers in planned depletion
zones are seeking to deplete the aquifer. This is especially true as GMD (and thus management scheme) was
a weak driver. Several grassroots movements have been observed throughout the study region to prioritize
water conservation given the limitation that regional governance does not adequately align conservation
goals, and the impacts of these movements on reducing water usage may also be captured here; water man-
agement decisions have been found to correlate with close network members such as families, friends, and
neighbors (Nian etal.,2020). Another contributing explanation as to why well-specific drivers are stronger
than regional drivers may be that Local Enhanced Management Areas (LEMAs) introduced in some por-
tions of the study area have enacted policies shown to reduce irrigation pumping within the frameworks of
larger-scale governing regulations (Deines etal.,2019; Whittemore etal.,2018). However, LEMAs were not
evaluated in this BRT model as the driver did not cover the full temporal range of the study.
Additionally, precipitation drivers were always stronger drivers to pumping than temperature drivers, and
growing season precipitation was more influential than off-season precipitation. This is not only logically
supported as adequate soil moisture is a critical metric to plant production (Basso & Ritchie,2014), but this
is also supported by the greater variability in seasonal values for precipitation compared to temperature.
Irrigation is often used as a tool for overcoming or reducing the negative impacts of seasonal variability
(Whittemore etal.,2016), where water applications can be used to buffer the impacts of drought conditions
or extreme temperatures (Basso & Ritchie,2014; Whittemore etal.,2016). As precipitation was more varia-
ble than temperature during this study, it is reasonable that it would be the stronger driver.
Irrigation technology, such as flood or center pivot, was not an influential variable despite the frequent
discussion that higher-efficient systems lead to water savings (e.g., Schaible & Aillery,2012). This may be
due to nearly 76% of all wells being high-efficiency LEPA systems (KDA-DWR & KGS, 2021), in which
case reduced variability within the driver has less influence on the pumping results. Also possible, this
low influence is because efficient irrigation has been documented not to result in water savings (Pfeiffer &
Lin,2014), as farmers can irrigate more area for a reduced price compared to inefficient technologies. This
behavioral response further supports total irrigated area being the predominant driver to pumping and the
growing understanding that efficient technology does not reduce water use as long as there are incentives
for farmers to irrigate more area (Pfeiffer & Lin,2014; Smidt etal.,2016). Interestingly, few drivers in this
study can be controlled directly by farmers, and those that can were among high-influencing variables (i.e.,
number of acres irrigated, crop type). Irrigation system type is the only farmer-controlled driver among
low-influencing variables.
LAMB ET AL.
10.1029/2020WR028867
12 of 16

Water Resources Research
4.3. Partial Dependence Behaviors
Most of the top influencing drivers followed a positive slope (i.e., as driver values increase, so does the
connection to pumping), with the exception of well density, crop type, and precipitation; well density and
precipitation followed a negative slope, and crop type was categorical. While the partial dependence of these
drivers was mostly as expected (e.g., dry conditions led to pumping), we did observe unexpected results in
moderately influential drivers. For example, the results of depth to water were opposite what seemed intu-
itive. Instead of greater depths leading to a negative pumping slope (i.e., increased pumping costs leading
to decreased pumping), we found greater depths to water led to more pumping. This is perhaps because
pumping is so heavily established in these well locations that increased costs are a necessary, or unavoid-
able, operational factor or because decreased well yields may demand greater time spent for a center pivot
to make its way around a field (Rad etal.,2020), potentially affecting the ratio between evaporation and in-
filtration. It may also be feasible that smaller farm behaviors, acting more in line with expected operational
costs, are buffered in this model by larger farms with larger operational budgets. In addition, as water table
depth changes, aquifer transmissivity can change nonlinearly, causing a ranging impact on wells in a region
(Korus & Hensen,2020). Another possible explanation is that variable is dominated by planned depletion
management schemes (Peck,2006), but this seems unlikely as most of the region is not under planned de-
pletion strategies. Likewise, increased well density did not result in a positive pumping slope. Instead, fewer
wells per area resulted in greater pumping. This may be in part because more wells per area can share the
water demand of a larger area compared to an individual well, so total pumping per well can be reduced.
However, this may be because fewer wells per area may be correlated to more individual landowners and
subsequently different operational decisions. In this case, the connection between pumping and fewer wells
per area may be attributed to smallholder farmers maximizing short-term profits or mitigating seasonal var-
iability risk through increased pumping (Whittemore etal.,2016); these ownership data were not available
specifically for each well and could not be evaluated in this study.
4.4. Irrigation and Climate
For Groups 1 and 2 (annual), the weather category was the last category listed among top variables, while
it ranked as the first category for Groups 3 and 4 (all years combined). Considering that irrigation can be
used as means of climate control (Whittemore etal., 2016), it was intriguing that weather variables were
not more influential in Groups 1 and 2. This could result for two reasons: (1) the total influence is shared
across many weather drivers, so a single driver is ultimately buffered: many weather drivers sum to have
a large influence, but no single driver is largely influential, and (2) weather-related variables in the study
region are sufficient for dryland agricultural production, as irrigation is used to capture incentives other
than baseline production. However, it seems unlikely the weather conditions are sufficient for dryland pro-
duction in western Kansas given regional water demands of the produced commodities and precipitation
patterns (Cotterman etal.,2018). Even with the increase of drought-resistant cultivars (Hu & Xiong,2014),
the shared influence of weather drivers is a likely explanation for the lack of highly influential weather
drivers in Groups 1 and 2. This makes logical sense as seasonal weather extremes are often short lived (U.S.
Drought Monitor,2020), not typically observed in repeated years with the same intensity (U.S. Drought
Monitor,2020), and are not always limiting to crop production as crops can partially rebound within a
season. We also found that the RIs of weather-related variables were not noticeably higher during drought
years within the study range (2011–2014; U.S. Drought Monitor,2020). This may point to the practice of
taking irrigated area out of production during abnormally dry conditions in order to meet higher irrigation
demands of the remaining fields (Deines etal.,2017; Nie etal.,2018).
Furthermore, weather variables in Groups 1 and 2 may be relatively weaker drivers due to the spread of
collective influence across many variables because seasonal extremes are combined into one variable in
Groups 3 and 4. In these groups, annual precipitation became the third most influential driver on irrigation
pumping. So, while annual precipitation may have less influence at the annual scale, its combined influence
at longer time scales (multiyear) on regional pumping is significant. This is further supported in Groups 1
and 2 where annual weather-related variables were more influential than monthly, just as combined years
were more influential than annual. Collectively, these relationships suggest that climate, acting at longer
LAMB ET AL.
10.1029/2020WR028867
13 of 16

Water Resources Research
time scales than weather, is likely to play a significant role on the pumping patterns across the region. Con-
sequently, climate change may reconfigure irrigation drivers in this region.
4.5. Management
This study highlights that irrigation decision making typically follows two questions: (1) how much is avail-
able to irrigate, both in water volume and land area (e.g., irrigated area, saturated thickness, authorized
area, authorized rate, and authorized amount), and (2) how much does it cost (e.g., depth)? Other drivers
or considerations appear to be marginal compared to the answers to these two questions. Observed trends
further indicate irrigation is a default behavior and is intensified by weather conditions and not necessarily
a result of weather conditions. So, while water use is an annual decision, compounding weather-related var-
iables appear to shape behaviors at longer time scales. Collectively, this means water conservation strategies
(even in planned depletion zones) would be better suited to focus on well-specific policies designed within
the framework of these two questions while stabilizing water use incentives over longer time scales.
As each driver category was represented in the top 10 most influential drivers in each model group, policies
must also be well rounded and account for the variations across categories through time, rather than em-
phasizing a suite of specific drivers. Water management is complex in this region and must be approached
as such to avoid unintended water use outcomes. The summed totals of each category for each model group
are reported in Table 3. The Weather category not only contributed the highest collective influence of all
variable categories but also contributed the highest number of variables in the model (26 out of 45). The
Economics category not only contributed the lowest collective influence of all categories but also had the
lowest number of variables in the model (2 out of 45). The contribution of the Land/Agriculture category
was about 2 times higher in Groups 1 and 3 than 2 and 4 due to the inclusion of total irrigated area in Groups
1 and 3.
5. Conclusion
Although many political, economic, and physical factors impact irrigation decision making in western Kan-
sas and elsewhere, characterization of their relative influence on pumping has largely remained unknown.
To quantify the influence of irrigation drivers, we utilized a BRT machine-learning technique on data across
space and time to characterize the impact of 45 drivers relating to five categories (management/policy, hy-
drology, weather, land/agriculture, and economy) on irrigation pumping from approximately 19,000 wells
across western Kansas from 2006 to 2016. BRT is a useful and informative tool for analyzing water use de-
cision making and can effectively capture both numerical and categorical variable relationships across both
space and time. In addition to total driver influence, BRT can also be used to understand the magnitude of
influence as well the conditions in which a user typically decides to stop irrigating. In the future, this tech-
nique can also be used with other models to improve their irrigation prediction (e.g., agent-based irrigation
models; Mewes & Schumann,2019). From this study, we have identified four main conclusions:
(1) Influences on irrigation use in this region are complex, as all five variable categories were represented
in the top 10 most influential variables under all modeling scenarios. In addition, the influence of many
LAMB ET AL.
10.1029/2020WR028867
14 of 16
Relative influence of drivers on irrigation pumping (%)
Management/policy Hydrology Weather Land/agriculture Economics
Group 1 15.0 9.0 42.2 27.7 6.6
Group 2 17.5 11.2 50.5 12.9 8.5
Group 3 11.7 9.2 42.8 30.6 5.7
Group 4 13.3 12.0 54.7 13.1 6.9
Note. Groups 1 and 2 do not sum to 100 as the reported values represent means across 11 models where Groups 3 and
4 are single values reported across one model.
Table 3
Relative Influence of Drivers by Category Across BRT Model Runs

Water Resources Research
drivers, like precipitation and crop value, varied from year to year. As a result of this complexity and
variability, effective policy should focus on comprehensive, multifaceted measures rather than targeting
individual, undesired behaviors.
(2) Well-specific drivers were considerably more influential to irrigation use than regional-specific drivers.
This relationship suggests irrigation applications are a user-by-user decision not largely influenced by
preexisting regulatory frameworks. Instead, water use decisions in this region are more a function of
maximizing crop production across disparate and self-motivated water conservation strategies.
(3) Decisions to irrigate can largely be summarized in response to two questions: (1) how much is available
to irrigate, both in water volume and land area (e.g., irrigated area, saturated thickness, authorized area,
authorized rate, and authorized amount), and (2) how much does it cost (e.g., depth to water, well yield
as a function of saturated thickness)? Other considerations contribute notably less to overall use.
(4) While influential in the short-term, weather-related factors have a greater influence at longer time
scales due to varying impact at shorter time scales (e.g., seasonal compared to annual time scales, an-
nual compared to multiannual time scales). This increased influence at longer time scales suggests
irrigation use in this region may be susceptible to changes in irrigation patterns and behaviors under
changing climate scenarios.
Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
Data Availability Statement
Model data are available at http://www.hydroshare.org/resource/c0b6ebc880f54c92b1c4a633b0b85353
(Smidt,2020).
References
Basso, B., & Ritchie, J. T. (2014). Temperature and drought effects on maize yield. Nature Climate Change, 4(233). 233. https://doi.
org/10.1038/nclimate2139
Butler, J. J., Whittemore, D. O., Wilson, B. B., & Bohling, G. C. (2016). A new approach for assessing the future of aquifers supporting irri-
gated agriculture. Geophysical Research Letters, 43, 2004–2010. https://doi.org/10.1002/2016GL067879
Cotterman, K. A., Kendall, A. D., Basso, B., & Hyndman, D. W. (2018). Groundwater depletion and climate change: Future prospects of
crop production in the Central High Plains Aquifer. Climatic Change, 146, 187–200. https://doi.org/10.1007/s10584-017-1947-7
Deines, J. M., Kendall, A. D., Butler, J. J., & Hyndman, D. W. (2019). Quantifying irrigation adaptation strategies in response to stake-
holder-driven groundwater management in the US High Plains Aquifer. Environmental Research Letters, 14, 044014. https://doi.
org/10.1088/1748-9326/aafe39
Deines, J. M., Kendall, A. D., & Hyndman, D. W. (2017). Annual irrigation dynamics in the U.S. Northern High Plains derived from Landsat
satellite data. Geophysical Research Letters, 44, 9350–9360. https://doi.org/10.1002/2017GL074071
Edwards, E. C. (2016). What lies beneath? Aquifer heterogeneity and the economics of groundwater management. Journal of the Associa-
tion of Environmental and Resource Economists, 3, 453–491. https://doi.org/10.1086/685389
Elith, J., Leathwick, J. R., & Hastie, T. (2008). A working guide to boosted regression trees. Journal of Animal Ecology, 77(4), 802–813.
https://doi.org/10.1111/j.1365-2656.2008.01390.x
Fenichel, E. P., Abbott, J. K., Bayham, J., Boone, W., Haacker, E. M. K., & Pfeiffer, L. (2015). Measuring the value of groundwater and other
forms of natural capital. Proceedings of the National Academy of Sciences, 113(9), 2382–2387. https://doi.org/10.1073/pnas.1513779113
Friedman, J. H. (2001). Greedy function approximation: A gradient boosting machine. Annals of Statistics, 29(5), 1189–1232.
Friedman, J. H., & Meulman, J. J. (2003). Multiple additive regression trees with application in epidemiology. Statistics in Medicine, 22(9),
1365–1381. https://doi.org/10.1002/sim.1501
Haacker, E. M. K., Cotterman, K. A., Smidt, S. J., Kendall, A. D., & Hyndman, D. W. (2019). Effects of management areas, drought, and
commodity prices on groundwater decline patterns across the High Plains Aquifer. Agricultural Water Management, 218, 259–273.
https://doi.org/10.1016/j.agwat.2019.04.002
Haacker, E. M. K., Kendall, A. D., & Hyndman, D. W. (2016). Water level declines in the High Plains Aquifer: Predevelopment to resource
senescence. Groundwater, 54, 231–242. https://doi.org/10.1111/gwat.12350
Hastie, T., Tibshirani, R., & Friedman, J. (2009). The elements of statistical learning: Data mining, inference, and prediction (2nd ed.). New
York, NY: Springer.
Hauenstein, S., Wood, S. N., & Dormann, C. F. (2017). Computing AIC for black-box models using generalized degrees of freedom: A
comparison with cross-validation. Communications in Statistics - Simulation and Computation, 47(5), 1382–1396. https://doi.org/10.10
80/03610918.2017.1315728
Hijmans, R. J., Phillips, S., Leathwick, J., & Elith, J. (2017). Package “dismo”. CRAN. http://cran.nexr.com/web/packages/dismo/dismo.pdf
Hrozencik, R. A., Manning, D. T., Suter, J. F., Goemans, C., & Bailey, R. T. (2017). The heterogeneous impacts of groundwater management
policies in the Republican River Basin of Colorado. Water Resources Research, 53, 10757–10778. https://doi.org/10.1002/2017WR020927
Hu, H., & Xiong, L. (2014). Genetic engineering and breeding of drought-resistant crops. Annual Review of Plant Biology, 65, 715–741.
https://doi.org/10.1146/annurev-arplant-050213-040000
LAMB ET AL.
10.1029/2020WR028867
15 of 16
Acknowledgment
None.

Water Resources Research
Hu, Y., Quinn, C. J., Cai, X., & Garfinkle, N. W. (2017). Combining human and machine intelligence to derive agents’ behavioral rules for
groundwater irrigation. Advances in Water Resources, 109, 29–40. https://doi.org/10.1016/j.advwatres.2017.08.009
KDA-DWR & KGS, version 5. (2021). WIMAS, Water Information Management and Analysis System, 2006–2016. Kansas Geological Sur-
vey and the Kansas Department of Agriculture, Division of Water Resources. Retrieved from http://hercules.kgs.ku.edu/geohydro/
wimas/index.cfm
Kisekka, I., Oker, T., Nguyen, G., Aguilar, J., & Rogers, D. (2017). Revisiting precision mobile drip irrigation under limited water. Irrigation
Science, 35, 483–500. https://doi.org/10.1007/s00271-017-0555-7
Korus, J. T., & Hensen, H. J. (2020). Depletion percentage and nonlinear transmissivity as design criteria for groundwater-level observation
networks. Environmental Earth Sciences, 79, 382. https://doi.org/10.1007/s12665-020-09123-y
K.S.A. 82a-1036. (1978). Initiation of proceedings for designation of intensive groundwater use control areas; duties of chief engineer;
findings. Retrieved from https://www.ksrevisor.org/statutes/chapters/ch82a/082a_010_0036.html
K.S.A. 82a-1041. (2012). Local enhanced management areas; establishment procedures; duties of chief engineer; hearing; notice; orders;
review. Retrieved from https://www.ksrevisor.org/statutes/chapters/ch82a/082a_010_0041.html
Lampa, E., Lind, L., Lind, M., & Bornefalk-Hermansson, A. (2014). The identification of complex interactions in epidemiology and toxicol-
ogy: A simulation study of boosted regression trees. Environmental Health, 13(57). https://doi.org/10.1186/1476-069X-13-57
Majumdar, S., Smith, R., Butler, J., Jr., & Lakshmi, V. (2020). Groundwater withdrawal prediction using integrated multitemporal remote
sensing data sets and machine learning. Water Resources Research, 56, e2020WR028059. https://doi.org/10.1029/2020WR028059
MardanDoost, B., Brookfield, A. E., Feddema, J., Sturm, B., Kastens, J., Peterson, D., & Bishop, C. (2019). Estimating irrigation demand
with geospatial and in-situ data: Application to the High Plains Aquifer, Kansas, USA. Agricultural Water Management, 223, 105675.
https://doi.org/10.1016/j.agwat.2019.06.010
Mewes, B., & Schumann, A. (2019). The potential of combined machine learning and agent-based models in water resources management.
Hydrologie und Wasserbewirtschaftung, 63, 332–338. https://doi.org/10.5675/hywa_2019.6_2
Murphy, K. (2012). Machine learning: A probabilistic perspective. Cambridge, MA; London, UK: MIT Press.
Nian, Y., Huang, Q., Kovacs, K. F., Henry, C., & Krutz, J. (2020). Water management practices: Use patterns, related factors, and correla-
tions with irrigated acres. Water Resources Research, 56, e2019WR025360. https://doi.org/10.1029/2019WR025360
Nie, W., Zaitchik, B. F., Rodell, M., Kumar, S. V., Anderson, M. C., & Hain, C. (2018). Groundwater withdrawals under drought: Recon-
ciling GRACE and land surface models in the United States High Plains Aquifer. Water Resources Research, 54, 5282–5299. https://doi.
org/10.1029/2017WR022178
Peck, J. C. (2006). Groundwater management in Kansas: Brief history and assessment. The Kansas Journal of Law & Public Policy, 15(3),
441–466
Pfeiffer, L., & Lin, C.-Y. C. (2014). Does efficient irrigation technology lead to reduced groundwater extraction? Empirical evidence. Journal
of Environmental Economics and Management, 67, 189–208. https://doi.org/10.1016/j.jeem.2013.12.002
Rad, M. R., Brozović, N., Foster, T., & Mieno, T. (2020). Effects of instantaneous groundwater availability on irrigated agriculture and impli-
cations for aquifer management. Resource and Energy Economics, 59, 101129. https://doi.org/10.1016/j.reseneeco.2019.101129
R Development Core Team. (2018). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical
Computing. http://www.R-project.org
Ridgeway, G. (2007). Generalized boosted models: A guide to the gbm package. CRAN. https://cran.r-project.org/web/packages/gbm/vi-
gnettes/gbm.pdf
Rudnick, D. R., Irmak, S., West, C., Chávez, J. L., Kisekka, I., Marek, T. H., etal. (2019). Deficit irrigation management of maize in
the High Plains Aquifer region: A review. Journal of the American Water Resources Association, 55(1), 38–55. https://doi.
org/10.1111/1752-1688.12723
Sanderson, M. R., Bergtold, J. S., Heier Stamm, J. L., Caldas, M. M., & Ramsey, S. M. (2017). Bringing the “social” into sociohydrolo-
gy: Conservation policy support in the Central Great Plains of Kansas, USA. Water Resources Research, 53, 6725–6743. https://doi.
org/10.1002/2017WR020659
Sanderson, M. R., & Frey, R. S. (2014). From desert to breadbasket… to desert again? A metabolic rift in the High Plains Aquifer. Journal of
Political Ecology, 21, 516. https://doi.org/10.2458/v21i1.21149
Schaible, G., & Aillery, M. (2012). Water conservation in irrigated agriculture: Trends and challenges in the face of emerging demands.
USDA-ERS Economic Information Bulletin, 99. https://doi.org/10.2139/ssrn.2186555
Smidt, S. J. (2020). Irrigation drivers boosted regression; Kansas HPA. HydroShare. http://www.hydroshare.org/resource/
c0b6ebc880f54c92b1c4a633b0b85353
Smidt, S. J., Haacker, E. M. K., Kendall, A. D., Deines, J. M., Pei, L., Cotterman, K. A., etal. (2016). Complex water management in modern
agriculture: Trends in the water–energy–food nexus over the High Plains Aquifer. The Science of the Total Environment, 566–567(567),
988–1001. https://doi.org/10.1016/j.scitotenv.2016.05.127
Smidt, S., Kendall, A., & Hyndman, D. (2019). Increased dependence on irrigated crop production across the CONUS (1945–2015). Water,
11, 1458. https://doi.org/10.3390/w11071458
Steward, D. R., Bruss, P. J., Yang, X., Staggenborg, S. A., Welch, S. M., & Apley, M. D. (2013). Tapping unsustainable groundwater stores for
agricultural production in the High Plains Aquifer of Kansas, projections to 2110. Proceedings of the National Academy of Sciences, 110,
E3477–E3486. https://doi.org/10.1073/pnas.1220351110
Sukcharoen, K., Golden, B., Vestal, M., & Guerrero, B. (2020). Do crop price expectations matter? An analysis of groundwater pumping
decisions in Western Kansas. Agricultural Water Management, 231, 106021. https://doi.org/10.1016/j.agwat.2020.106021
USDA-CDL. (2006–2016). National Agricultural Statistics Service Cropland Data Layer. Retrieved from https://nassgeodata.gmu.edu/
CropScape
USDA-NASS. (2006–2016). Crop values annual summary. Retrieved from https://usda.library.cornell.edu/concern/publications/k35694332
U.S. Drought Monitor. (2020). National Drought Mitigation Center University of Nebraska-Lincoln, United States Department of Agricul-
ture, National Oceanic and Atmospheric Administration. Retrieved from https://droughtmonitor.unl.edu/About.aspx
Whittemore, D. O., Butler, J. J., & Wilson, B. B. (2016). Assessing the major drivers of water-level declines: New insights into the future of
heavily stressed aquifers. Hydrological Sciences Journal, 61, 134–145. https://doi.org/10.1080/02626667.2014.959958
Whittemore, D. O., Butler, J. J., & Wilson, B. B. (2018). Status of the High Plains Aquifer in Kansas. Kansas Geological Survey Technical
Series, 22, 1–28.
LAMB ET AL.
10.1029/2020WR028867
16 of 16