General circulation model (GCM) outputs are a primary source of information for
climate change impact assessments. However, raw GCM data rarely are used directly for
regional-scale impact assessments as they frequently contain systematic error or bias. In this
article, we propose a novel extension to standard quantile mapping that allows for a continuous
seasonal change in bias magnitude using localized regression. Our primary goal is to examine the
efficacy of this tool in the context of larger statistical downscaling efforts on the tropical
island of Puerto Rico, where localized downscaling can be particularly challenging. Along the
way, we utilize a multivariate infilling algorithm to estimate missing data within an incomplete
climate data network spanning Puerto Rico. Next, we apply a combination of multivariate
downscaling methods to generate in situ climate projections at 23 locations across Puerto Rico
from three general circulation models in two carbon emission scenarios: RCP4.5 and RCP8.5.
Finally, our bias-correction methods are applied to these downscaled GCM climate projections.
These bias-correction methods allow GCM bias to vary as a function of a user-defined season
(here, Julian day). Bias is estimated using a continuous curve rather than a moving window or
monthly breaks. Results from the selected ensemble agree that Puerto Rico will continue to warm
through the coming century. Under the RCP4.5 forcing scenario, our methods indicate that the dry
season will have increased rainfall, while the early and late rainfall seasons will likely have a
decline in total rainfall. Our methods applied to the RCP8.5 forcing scenario favor a wetter
climate for Puerto Rico, driven by an increase in the frequency of high-magnitude rainfall events
during Puerto Rico's early rainfall season (April to July) as well as its late rainfall season
(August to November).
Introduction
In general, island climates are distinctly difficult to characterize, with Puerto Rico being no
exception. Puerto Rico is situated well within the belt of easterly trade winds. These winds carry
seasonal weather, generally dry from December through March when sea-surface temperatures typically
reach a minimum and
wetter from April through November. The wet season is broken into two distinct periods: the early
rainfall season (ERS; April–July), and the late rainfall season (LRS; August–November)
. While hurricanes are typically the most extreme events arising from
these tropical waves, severe weather commonly occurs seasonally in Puerto Rico from less well
developed systems. As a consequence of this, accurate short-term and long-term forecasting at the
local scale is a particularly desirable objective for this island. The long-term forecasting of a
single extreme event may not be feasible, but what is of particular interest in these long-term
forecasts is the frequency and intensity of these extreme events.
Many studies have utilized dynamic downscaling (DD) and statistical downscaling (SD) techniques in
an effort to accurately model Puerto Rico's future climate. and
employ high-resolution regional climate models (RCMs)
to develop dynamically downscaled climate estimates across a 2 km grid in Puerto Rico.
and examine the utility of neural
networks as a method for downscaling precipitation within Puerto Rico, while other studies
focus on the impacts of climate change on water
availability in Puerto Rico using several downscaled products.
In this study, we will employ SD in Puerto Rico in an effort to generate realistic daily
temperature and precipitation data at 23 locations spanning Puerto Rico
(Fig. ). This work is unique in the fact that many prior Puerto Rico
downscaling efforts do not focus on a suite of climate variables in tandem. A primary disadvantage
of statistical downscaling is that the individually downscaled variables do not always act together
in a physically consistent fashion, although some more recent approaches attempt to address this
issue .
Data sources and cleaningGlobal Historical Climatological Network data
The primary historical climate data are from the publicly available Global Historical
Climatological Network (GHCN). Specifically, we are using the 23 weather stations listed in
Table (labeled west to east); refer to Fig. for
location.
The 23 GHCN weather stations of interest in Puerto Rico along with the proportion of
missing observations (after cleaning – see Sect. and
) from 1 January 1978 through 31 December 2017.
At each of these locations we have daily climate data consisting of maximum temperature (TMAX;
∘C), minimum temperature (TMIN; ∘C), and total precipitation (PRCP; mm). We focus
on a 40-year time period from 1 January 1978 through 31 December 2017. Ideally, at each of our 23
stations we would have 14 610 observations (one for each day), but as is the case with many
climate datasets, this dataset has many missing data points. We use the multivariate vector
autoregressive time series methods of to infill missing values in this
climate network. These methods extend the general multivariate autoregressive methods to allow for
the inclusion of contemporaneous observations (as opposed to just lagged observations).
Temperature data cleaning
According to the National Weather Service (NWS), the hottest temperature ever recorded in San Juan,
Puerto Rico, is 104 ∘F, while the minimum temperature ever recorded is 40 ∘F.
These values have been cross-validated by the NCEI and/or by the State Climate Extremes Committee
and determined to be valid. While these NWS temperature extrema should not be used as strict
temperature cutoffs (any values outside of these bounds are removed), they still represent a
plausible range of observed temperature values in Puerto Rico. By cross-referencing the monthly
temperature boxplots reported in Fig. and this NWS observed temperature
range, it is apparent that there are a considerable number of potentially invalid temperature
readings, thus exhibiting the need for quality control.
TMAX (left) and TMIN (right) seasonal temperature boxplots for all 23 GHCN stations along
with the NWS San Juan maximum and minimum observed temperature extrema (red and blue lines,
respectively). This figure was created using .
Figure provides a representation of the seasonal cycle for temperature data
across all 23 locations of interest; however, this general trend can be expected to vary from
station to station. To identify temperature inaccuracies, all observations are first standardized
across season and station as in and . Suppose {Xt,j,ν}t=1N represents our daily temperature series at time t, for station j, in
month ν, where N indicates the total sample size. Then, borrowing notation and terminology
from , the seasonally standardized anomaly (SSA) time series is constructed
as in Eq. ().
At,j,ν=Xt,j,ν-E[Xt,j,ν]Var(Xt,j,ν)1/2=Xt,j,ν-μ^j,νσ^j,ν,j=1,…,23;ν=1,…,12.
Here, At,j,ν represents the SSA value at time t, station j, and month ν;
E[Xt,j,ν]=μ^j,ν denotes the station j, month ν mean; and
Var(Xt,j,ν)1/2=σ^j,ν denotes the station j, month ν
standard deviation. With the seasonally standardized temperature readings, inaccurate values may be
more easily detected. Figure displays the daily temperature maxima from
1 January to 31 December 1993 (left panel) and the corresponding SSA time series (right panel)
for the Adjuntas Substation weather station (Location 8 in Fig. ).
Daily temperature maxima from 2008 (left) and the
corresponding SSA series (right) at the Adjuntas Substation in
Puerto Rico. This figure was created using .
In Fig. , one clearly incorrect value can be observed on 3 September 1993,
although there are possibly more incorrect values over this calendar year (in particular, 20 June).
Suspected inaccuracies can be more easily observed in the right panel of Fig. as
they have been seasonally standardized. We use an automated temperature verification method which
relies on a preliminary examination of the SSA series to flag anomalous temperatures.
These flagged temperatures are then examined more closely.
Designate any observation with an absolute SSA value that is larger than 4 as a flagged value,
the validity of which must be examined more closely.
Extract an 11 d interval of temperature readings within 5 d on either side of the
flagged observation for all 23 weather stations. For example, 29 August to 8 September is
the 11 d window surrounding the flagged value on 3 September 1993, from
Fig. . These observations are then used to estimate the distribution of SSA
values across this 11 d window.
Finally, if the flagged SSA value is more than 5.5 standard deviations away from the mean
SSA value in this 11 d window, then the flagged temperature is recorded as not available
(NA). The 5.5 standard deviation cutoff, though arbitrary, was chosen after examining the
number of flagged observations from several potential cutoffs between 3 and 6 standard
deviations.
This process not only allows one to identify potential outliers quickly (Item 1), but also provides
a screening method to examine the validity of these potential outliers more closely (Item 2) and a
threshold for acceptance–rejection (Item 3). By selecting an 11 d window around a flagged
observation (Item 2), we allow for the possibility of a brief hot spell or cold spell. For example,
it may be the case that a flagged observation (|SSA|>4, Item 1) may be unexpected when compared
to the entire 40-year time frame but may not be unexpected when compared to its 11 d time window.
After the screening was completed, 128 of the 933 flagged TMAX values were changed to NA, and 235 of
the 855 flagged TMIN values were changed to NA. Finally, if a TMAX value is less than or equal to
the corresponding TMIN value, both of the values are reported as NA. Altogether, these temperature
quality control efforts omitted 252 TMAX and 359 TMIN recorded values. Combined with pre-screening
missing values, this brings our total TMAX and TMIN missing values to 52 064 (15.5 % missing)
and 52 886 (15.7 % missing), respectively.
Precipitation data cleaning
Precipitation quality control is particularly challenging in the tropics where isolated warm-water
processes can drop large amounts of rain very quickly. found that these
isolated convective storms contributed a larger proportion of the total precipitation in the
eastern Caribbean than larger-scale systems did. Furthermore, precipitation data are commonly
zero-inflated and right-skewed, suggesting a need for an alternative cleaning mechanism (i.e., a
seasonal standardization may not be appropriate for zero-inflated precipitation data). As was done
with temperature, we identify and cull precipitation anomalies by examining them both spatially and
seasonally. The quality control process is detailed below.
For each month, identify the largest 0.5 % of precipitation
totals as flagged observations to be examined more
closely.
For each flagged value, extract all 23 PRCP observations,
representing each weather station on the given day.
If the flagged PRCP observation is more than 4 standard deviations away from the mean PRCP
value on this day, then the precipitation value is rejected and recorded as NA.
Of the 1431 flagged precipitation observations (determined by taking the largest 0.5 % of each
month's precipitation totals, Item 1), 158 of these were converted to NA as a result of the method
described above for a total of 45 890 missing observations (13.7 % missing).
General circulation model data
We restrict ourselves to two common radiative forcing scenarios: RCP4.5 and RCP8.5 – that is, 4.5
and 8.5 W m-2 of additional radiative forcing beyond what the
Sun is contributing. We are using data from the most recently completed Coupled Model
Intercomparison Project at the time of this research: CMIP5 (however, now CMIP6 has been
completed). In the CMIP project, ensemble model runs (or realizations) are named using what is
referred to as the RIP nomenclature: R for realization (the starting point), I for initialization
(initial model parameters at the beginning of the “burn-in” period), and P for physics
(quantifiable atmospheric relationships), followed by an integer .
This study uses the first ensemble number (denoted: r1i1p1) for each of the three models
(Table ) to compare general circulation model (GCM) projections from two
forcing scenarios (RCP4.5 and RCP8.5). Within each model, a fixed ensemble member allows for
historical data to join seamlessly with the corresponding future projections .
For each of the three climate models listed within Table below, we have
three separate data sources: simulation data using historical radiative forcing conditions and two
future emission scenarios (RCP4.5 and RCP8.5). The variables of interest include daily average
precipitation flux (kg m-2 s-1), daily minimum near-surface air temperature (K), and
daily maximum near-surface air temperature (K). Although the temporal resolution (daily data) is
consistent, the calendar type, spatial resolution, and temporal extent may differ across climate
centers. The grid structure and temporal extents for each model are reported below.
The grid structure and temporal extents of each of the three GCMs utilized in this study.
Model nameModeling centerCalendar typeHistorical simulation rangeRCP simulation rangeGrid structureCanESM2Canadian Centre for Climate Modelling and Analysis (CCCMA)365 d (no leap day)1 Jan 1850 to31 Dec 20051 Jan 2006 to31 Dec 2100128 longs by 64 latsESM2GNOAA's Geophysical Fluid Dynamics Laboratory (GFDL)365 d (no leap day)1 Jan 1861 to31 Dec 20051 Jan 2006 to31 Dec 2100144 longs by 90 latsHadGEM2-ESUnited Kingdom's Hadley Centre (MOHC)360 d (12 30 dmonths)1 Dec 1859 to30 Nov 20051 Dec 2005 to30 Nov 2099192 longs by 145 lats
Because this work is focused on Puerto Rico, we may greatly reduce the size of our GCM data.
Figure displays the CanESM2 grid structure surrounding Puerto Rico. Only
coordinates which fall inside of the bounding box (highlighted in red) are retained in the
reduction. As these models have their own spatial resolutions, the number of locations retained
will vary (see Fig. (GFDL-ESM2G) and Fig.
(MOHC-HadGEM2-ES) in Appendix ).
Many Caribbean downscaling methods used in climatology are applied to univariate time series and
neglect dependence between variables . Clearly, there is a strong correlation
between daily minimum and maximum temperatures. For this reason, multivariate downscaling methods
should be applied. To this end, we present a combination of ideas from to downscale climate data at K=23 locations simultaneously.
employs a two-part multivariate multisite statistical downscaling model (MMSDM): (1) a multivariate
multiple linear regression (MMLR) model combined with (2) a spatially correlated stochastic
component to downscale maximum and minimum temperatures at K=9 weather stations in southern
Quebec. In the MMSDM model is used to downscale precipitation probability and
precipitation amount.
For each station (k=1,…,K), we consider three predictands: daily temperature maximum
(TMAXk), daily temperature minimum (TMINk), and daily total precipitation (PRCPk). As
accurate forecasting of future precipitation behavior is so critical in this region, we decompose
PRCPk into two separate variables: probability of precipitation occurrence (POCk) and
precipitation amount (PAMk). POCk is coded as 1 for a rainy day (a day having more
than 1 mm of rain) or a 0 for a dry day . In addition to this, many studies have
found precipitation amounts to be gamma-distributed . To combat
this right skew, we log-transform precipitation amount prior to downscaling: LogPAMtk=ln(PAMtk+1), where t=1,…,T designates the time (day). We add a small
positive value to PAMtk in order to log-transform days with no precipitation; the value 1 preserves zeros: (ln(1)=0).
Final precipitation values are generated by drawing a single uniform random number for each day,
ut∼Unif(0,1), and comparing this uniform draw to all of the POCtk values
(there should be 23 of them in our example) on day t. If ut<POCtk, it will be deemed
a rainy day at station k; otherwise, it will be deemed a dry day at station k. For rainy days,
final precipitation amounts will be generated by back-transforming LogPAMtk values. We define
the T×M dimensional (M=4K) response matrix Y grouping all
T×1 predictand vectors (TMAXk, TMINk, POCk, and LogPAMk)
as follows.
Y=[TMAX1,TMIN1,POC1,LogPAM1,…,TMAXK,TMINK,POCK,LogPAMK]
Define XT×l to be the design matrix containing l-1 predictor variables. The
exact dimensions of X will depend on the number of GCM locations retained and are noted
in Sect. . The MMLR model can be expressed via
YT×M=XT×l×βl×M+ET×M,
where E is the residual matrix. The parameter matrix β can be
estimated via the standard ordinary least-squares (OLS) estimator: β^=(XTX)-1XTY. The MMLR predicts only the deterministic
components which are explainable by a linear relationship between the predictands and the GCM data
(the predictor variables). The MMSDM introduced by utilizes the MMLR model
as a means of simulating deterministic climate series from coarse-scale GCM data. The MMLR is
unable to reproduce the spatial correlation observed between each location adequately.
In order to correct for the spatial bias, spatially correlated random noise is added to the
simulated deterministic climate series. This random noise is generated from a multivariate normal
distribution. The multivariate covariance matrix is estimated from the error matrix E.
By definition,
E=Y-Y^,
where Y^=Xβ^. Define H∼MVN(0,Σ) to be the cross-correlated error matrix used as a
means of more adequately capturing the spatial correlation among weather stations. Finally, define
Σ=SCS, where S is a diagonal matrix
containing the estimated standard deviations of each column of the residual matrix, E,
and C represents the correlation matrix of the residual matrix, E. Now, this
stochastic component is added directly to the deterministic component to obtain spatially
correlated estimates of the predictands:
Ỹ=Xβ^+H.
Bias-correction methods
Raw GCM output frequently contain systematic error or bias . In many cases,
the errors in GCM simulations relative to historical observations can be quite large
. Downscaling exists not only to refine GCM output both spatially and
temporally, but also to quantify and correct these systematic errors. There are numerous
bias-correcting methods , and no one method is universally accepted
as optimal in all situations. GCM bias may vary spatially, temporally, and across model, variable,
and season. In addition to this, GCMs are known to have a “drizzle problem” where too many
low-magnitude rain events are projected to occur as compared with historical GHCN observations
.
Many downscaling methods are able to capture and correct at least some of a GCM's bias through the
use of transfer functions . However, different transfer functions do not
uniformly capture GCM bias. Furthermore, bias-correction techniques may be applied to the raw GCM
data prior to downscaling or applied to the generated climate data after downscaling. When
applying a post hoc bias correction, one must assume that the spatial and temporal correlations of
the raw downscaled data are preserved after any adjustments to one or more variables in the
network. In this research, we introduce post hoc bias-correction methods where bias is estimated
via a combination of locally estimated scatterplot smoothing (LOESS) methods
and quantile mapping.
Quantile mapping (QM) is a commonly used technique to remove or diminish systematic GCM error
. There are several criticisms of quantile
mapping. Perhaps most notably, standard QM methods adjust a climate variable's distribution as a
whole and do not explicitly account for spatial, temporal, nor multivariate aspects of the
predictands . Put differently, standard quantile mapping inherently assumes that
the bias magnitude is constant across space and time (or season) and, in a multivariate setting, does
not significantly impact the correlation between downscaled climate variables. For this reason,
much of the current literature extends standard quantile mapping to allow bias to vary seasonally.
For instance, utilize a 31 d window (center day ±15 d) to construct the cumulative distribution functions (CDFs). utilize a monthly bias correction so that each month is assumed to have
its own bias magnitude. Despite its criticisms, QM remains a highly regarded and widely used GCM
bias-correction method. We propose a similar extension to standard quantile mapping techniques that
allows for a continuous seasonal change in bias magnitude to be estimated using LOESS smoothing
splines.
LOESS quantile mapping
Through motivating examples using one generation of downscaled CanESM2 precipitation data (as
precipitation is often most difficult to characterize), we introduce and discuss our novel
bias-correction technique we call LOESS quantile mapping or LQM. LQM accounts for a bias
which may vary seasonally by combining elements of LOESS regression and quantile mapping. LOESS
methods approximate a “best-fitting” smoothed scatterplot curve through a
series of weighted regressions. The curve is estimated using a local neighborhood of points
surrounding a location x, weighted by their distance from x: wi=(1-(diD)3)3. The
local neighborhood is chosen using a smoothing parameter, α, where 0<α≤1: α
indicates the proportion of data considered to be neighboring x. In this section, we apply these
methods to the raw LogPAMk (log precipitation amount) values, but these methods will also be
used to correct temperature bias. Figure displays the estimated CDFs of the
observed (red), fitted (green), downscaled RCP4.5 (blue), and downscaled RCP8.5 (purple) log
precipitation distributions.
Log precipitation cumulative distribution function estimates of the observed (red curve),
fitted (green curve), downscaled RCP4.5 (blue curve), and downscaled RCP8.5 (purple curve).
Downscaled projections are derived from Canada's CanESM2. This figure was created using
.
A standard QM procedure maps the fitted CDF (green curve in Fig. ) onto the
observed CDF (red curve in Fig. ). By comparing these two curves, we can see
that the MMSDM downscaling also falls victim to the “drizzle problem” mentioned earlier:
low-magnitude rain events are overpredicted, and high-magnitude rain events are underpredicted. In
the top panels of Fig. , we plot the quartiles of the observed (red) and
fitted (cyan) log precipitation as a function of Julian day. Recall that raw fitted log
precipitation values may be negative. In the bottom panels, we plot the differences between the two
curves (observed-fitted) along with a LOESS smoothing spline.
Quartiles of fitted (cyan) and observed (red) log precipitation (mm) as a function of
Julian day (top panel) using Canada's CanESM2. The differences between the observed and fitted
precipitation along with a LOESS smoothing spline with smoothing parameter λ=0.50 (bottom
panel). This figure was created using .
Perhaps bias is negligible across season for lower-magnitude rain events because a negative
bias-correction factor in LogPAMk may not heavily affect back-transformed PRCPk (first two
columns of Fig. ). However, the bias associated with larger
precipitation events (daily third-quartile rain events, for example) is clearly dependent on season
(third column of Fig. ). Fitted precipitation values in the third
quartile of daily precipitation totals that fall around day 50 (mid-February) are overpredicted,
whereas similar third-quartile rainfall events that occur around day 140 (mid-May) or day 275 (the
beginning of October) are underpredicted. These under-fitted high-magnitude rain events in May and
October are consistent with the Caribbean's distinct bimodal rainy season
. The
LQM methodology is laid out below.
Estimate the percentiles of the observed values, FX,Obs-1(p,ν), and
fitted values, FX,Fit-1(p,ν), of a downscaled random variable, X (log
precipitation, LogPAMk), at specified steps in probability, p (0.01), as a function of
season, ν (day).
Estimate the bias magnitude as a function of probability and season:
B(p,ν)=FX,Obs-1(p,ν)-FX,Fit-1(p,ν), where
ν=1,…,N, and N is the number of unique seasons (365).
Using a localized regression (LOESS) or some other smoothing mechanism, fit a smooth curve
through the estimated bias scatter: l(B(p,ν)). This smoothed-bias estimate will be the
bias-correction factor for a given percentile, p, and a given day, ν.
If the estimated percentile of a value of the random variable X, say xp,ν, falls
exactly at a step increment of the percentile (p=0.00,0.01,0.02,…,0.99,1.00), then
simply correct this value using the estimated bias for that percentile and day:
xp,ν*=xp,ν+l(B(p,ν)), where xp,ν* indicates the corrected value.
More often than not, the estimated percentile of a single value of the random variable X
will not fall exactly at a step increment of p. In this case, round the estimated
percentile to a user-specified resolution (three decimals) and linearly interpolate between
its two nearest step increments – see graphical example in Figs. and
.
Take, for example, a fitted log precipitation value on day ν. Suppose its rounded percentile is
p=0.804 when compared to all other fitted log precipitation values on day ν.
Figure displays the bias magnitudes of the 80th (red) and 81st (cyan) daily
percentiles of log precipitation.
Bias magnitudes of the 80th
(red) and 81st (cyan) daily percentiles of log precipitation (mm). This figure was created using
.
In Fig. , we expand the 100 d period from day ν=101 (11 April) to day
ν=200 (19 July). On day ν=139 (19 May), we graphically display the bias magnitude
interpolation process. Dashed lines indicate bias corrections for fitted values located between
80th (red) and 81st (cyan) percentiles of log precipitation on day ν=139. The solid purple line
indicates the bias-correction factor for a fitted log precipitation on 19 May (Julian day
ν=139) whose percentile (rounded to three decimals) is p=0.804. The intersection of the solid
purple line and the solid black line represents the estimated bias-correction factor for 19 May.
Graphical display of the interpolation process for fitted log precipitation (mm) values,
with percentiles falling between p=0.80 and p=0.81 on 19 May (day ν=139, vertical black
line). The red and cyan curves represent the 80th and 81st percentiles of log precipitation as a
function of day, respectively. This figure was created using .
Figure displays CanESM2 mean precipitation (mm) across all 23 stations
from 1980 to 2005 as a function of Julian day for the true historical GHCN observation values
(red), raw fitted values (green), LQM bias-corrected values (blue), and QM bias-corrected values
that do not allow bias to vary as a function of season (purple) at three different LOESS bandwidths
and two different step sizes. We can see two distinct peaks in precipitation corresponding to the
ERS and the LRS. As one might expect, and as many other authors have observed
(), we see that the QM method that does not account for
seasonal change is unable to adequately match the ERS and LRS rainfall peaks. Although there is not
much difference between step sizes p=0.01 and p=0.001, we do observe substantial differences
for different smoothing parameters. As intuition would indicate, a smaller smoothing parameter is
more able to capture extreme precipitation.
Average precipitation (mm) across all 23 stations from 1980 to 2005 as a function of
Julian day for observed values (red), raw fitted values (green), LQM bias-corrected values (blue),
and QM bias-corrected values (purple) using Canada's CanESM2 model at three different LOESS
smoothing spans and two different step sizes. This figure was created using .
LQM and QM model fit
In Sect. , we introduced LQM through motivating examples using CanESM2
precipitation data. In this section, we will compare results of LQM and QM on CanESM2 temperature
and precipitation data. In Fig. , we plot the average LQM RMSE (red, smoothing
parameter: 0.05) and QM RMSE (cyan) as a function of Julian day for TMAX (left), TMIN (middle), and
PRCP (bottom right).
LQM RMSE (red) and QM RMSE (cyan) as a function of Julian day for TMAX (left), TMIN
(middle), and
PRCP (right). This figure was created using .
While LQM RMSE does not always outperform QM RMSE by a large margin, it is slightly lower overall.
However, LQM (using smoothing parameter 0.05) does clearly outperform QM when we examine daily mean
fitted values. Figure plots the average TMAX (left), TMIN (middle), and PRCP
(right) across all 23 stations from 1980 to 2005. We observe that the LQM bias-corrected fitted
values (green) tend to match up to the true historical GHCN observations (red) better than the QM
bias-corrected fitted values do (blue). LQM is clearly more able to mimic the observed historical
(GHCN) seasonal cycle for temperature (Fig. ). Furthermore, the LQM
bias-corrected precipitation is more able to capture the ERS and LRS peaks in mean rainfall.
Average TMAX (left), TMIN (middle), and PRCP (right) across all 23 stations from 1980 to
2005. The true historical GHCN observations are plotted in red, while the LQM bias-corrected fitted
values and QM bias-corrected fitted values are plotted in green and blue, respectively. This figure
was created using .
Puerto Rico downscaled climate projections
In this section, we discuss the results of statistical downscaling efforts in Puerto Rico using the
combination of our MMSDM methodology described in Sect. with our LQM
bias-correction methods of Sect. . We focus on results from the Canadian
Centre for Climate Modelling and Analysis' CanESM2. Figures and tables generated for the US GFDL's
ESM2G and the UK Hadley Centre's HadGEM2-ES can be found in Appendices and
, respectively.
CCCMA's CanESM2 downscaled climate
Only one CanESM2 location is used to generate a downscaled climate in Puerto Rico
(Fig. ). The MMSDM downscaled climate estimates are derived from
Eq. (): Ỹ=Xβ^+H, where Ỹ34675×92 contains the downscaled climate
estimates, X34675×4 contains the raw GCM climate projections,
β^4×92 indicates the estimated parameter matrix, and
H34675×92 is a matrix of spatially correlated stochastic noise. The MMSDM
model is trained using 26 years of historical observations (1980–2005) from the GHCN. Leap days,
which are intentionally excluded in these methods, can be reasonably interpolated using a
neighborhood of observations surrounding 29 February; however, we do not dwell on the generation of
leap day climate here.
Temperature
Table reports the extrema and deciles of historical and downscaled daily
temperature maxima (∘C, top panel) and daily temperature minima (∘C, bottom
panel). The extrema and deciles of the downscaled temperature maxima tend to be between
0–2 ∘C warmer than historical GHCN observations, while the extrema and deciles of the
downscaled temperature minima tend to be between 1–3 ∘C warmer than historical
observations. The extrema on the bottom-most ends of these distributions are lower that what might
typically be expected in Puerto Rico, even at its highest elevations. These downscaled values are
likely the result of inaccurate GHCN values that slipped through our culling process. We note
that the occurrence of temperature minima between 1–3 ∘C is extremely rare (literally
on the scale of a handful of times across 23 locations spanning Puerto Rico in the upcoming
century).
Maximum daily temperature extrema and deciles (∘C, top panel) and minimum daily
temperature extrema and deciles (∘C, bottom panel) for the observed historical (GHCN)
climate, the downscaled RCP4.5 climate, and the downscaled RCP8.5.
Figure displays the CanESM2-estimated mean daily maximum
temperature (left panel) and daily minimum temperature (right panel) as a function of year
(1980–2100). We note that the subsequent plots may depict a small gap between the observed GHCN
time series and the downscaled projections. This is merely an artifact of a GCM's “spin-up”
period which represents a random realization of internal variability associated with its forcings
and, therefore, may not perfectly align with GHCN observations. RCP4.5 projections indicate an
increase in mean temperature that tapers off between 2050 and 2075, while RCP8.5 projects
increasing maximum temperatures that continue to grow through 2100. These patterns are likely
directly attributed to the greenhouse gas emissions exhibited by each forcing scenario. By 2100,
maximum temperatures are projected to increase between 1.5–3 ∘C, on average (across all
23 locations), while minimum temperatures are projected to increase between 2–3.5 ∘C, on
average.
CanESM2 mean daily maximum (left panel) and minimum (right panel) temperature (∘C)
as a function of year. Observed historical GHCN data from 1980–2005 are plotted in red, while
downscaled RCP4.5 and RCP8.5 temperatures from 2006–2100 are plotted in green and blue,
respectively. This figure was created using .
These observations are consistent with a large number of other downscaling works focused on the
Caribbean .
Because minimum temperature is expected to increase at a faster rate than maximum temperature, the
average day will not only become warmer, but it will also observe a narrower range of diurnal temperatures.
Both and note a similar decrease in
diurnal temperature variability throughout the Caribbean and Gulf of Mexico.
Precipitation
There is an overwhelming consensus of literature showing agreement that increasing greenhouse gas emissions will directly
contribute to global warming
. In a tropical
climate, it is likely that temperature rise will be accompanied by an increase in specific
humidity. Despite this, precipitation is likely to increase in some regions and decrease in others
making precipitation even more difficult to forecast.
Within the Caribbean, recent literature tends to favor drying conditions, although some literature
does provide conflicting opinions. , , and
all note a general drying pattern for Puerto Rico and its surrounding islands.
note a 30 % decrease specific to spring and summer rainfall.
and project a decrease in Puerto Rico's annual
precipitation, somewhere between 10 % and 30 %. , from the Fourth
Assessment Report of the IPCC, project Latin America's annual precipitation to change anywhere from
-40 % to +10 %. find that the Caribbean will exhibit drying
trends throughout the spring, summer, and fall; however, they project increased precipitation
during the winter months, while project a wetter climate for the
Caribbean through 2050, driven heavily by increased rainfall during the rainy season, most likely a
result of rising sea-surface temperatures which bolster large storm systems, potentially leading to
an increase in the scale of extreme precipitation events.
While there may not be a clear consensus about projected annual Caribbean rainfall at the end of
the century, there seems to be majority agreement within the literature that the Caribbean will
exhibit increased variability in precipitation in the future. Many studies project an increased
number of consecutive dry days, consistent with a lengthening of the dry season
. An increased number of consecutive dry days may
have dire effects, not only on Puerto Rico's tropical ecosystem, but also on the water needs of the general public, who, being an island nation, rely heavily on consistent rainfall. Many other studies
project an increase in the frequency and magnitude of extreme rainfall events
,
which have been shown in the recent past to have catastrophic and lasting effects on the island.
Table displays the extrema and deciles of historical daily precipitation
(mm) and projected daily precipitation (mm). The 60th percentiles (and the 70th percentile for
RCP4.5) are smaller than those of the historical precipitation data. This suggests a diminishing
number of small rainfall events in a future Puerto Rican climate. Furthermore, the 80th percentile,
90th percentile, and maximum projected rainfall events are all larger than those of the
corresponding historical rainfall data, suggesting that Puerto Rico will begin to experience an
increased number of large precipitation events.
CanESM2 daily total precipitation (mm) quantiles for the observed historical (GHCN)
climate (1980–2005), the downscaled RCP4.5 climate (2006–2100), and the downscaled RCP8.5 climate
(2006–2100) across all 23 locations.
Despite an apparent reduction in low-magnitude precipitation events, the CanESM2 clearly favors a
wetter future climate across Puerto Rico (Fig. ), on average, across all
stations. The RCP4.5 forcing scenario predicts an increase in average daily rainfall of around
1.5 mm, whereas the RCP8.5 projects an increase of nearly 3.5 mm by 2100.
Observed historical (GHCN) daily mean precipitation (mm) data from 1980–2005 are plotted in
red, while CanESM2 RCP4.5 and RCP8.5 downscaled mean precipitation data from 2006–2100 are plotted in
green and blue, respectively. This figure was created using .
CanESM2 average total precipitation (mm) per weather station by rainfall season for the
RCP4.5 forcing scenario (left) and the RCP8.5 forcing scenario (right). The years 1980–2005
represent historical GHCN observations and are also included on these plots. The years 2006–2100
represent downscaled CanESM2 output. This figure was created using .
Total number of extreme rainfall (ER) events (island daily average rainfall >29.90 mm) by season for the
CanESM2's RCP4.5 forcing scenario (left) and the RCP8.5 forcing scenario (right). The years
1980–2005 represent historical GHCN observations and are also included on these plots. This figure
was created using .
CanESM2 ratio of yearly high-magnitude rainfall (HMR) event total rainfall (island daily average >14.81 mm) to
common rainfall as a function of year. This figure was created using .
In Fig. , we plot average total precipitation (in mm) across the 23
weather stations as a function of year and rainfall season. The RCP4.5 forcing scenario is plotted
in the left panel, while the RCP8.5 forcing scenario is plotted in the right panel. Clearly,
precipitation varies seasonally in Puerto Rico, where the dry season (December through March) tends
to see the least rainfall, and the late rainfall season (August through November) tends to observe
the most rainfall. The CanESM2 projections indicate that Puerto Rico's total precipitation will
increase across each season for both the RCP4.5 and RCP8.5 forcing scenarios. However, the
precipitation increases are much more dramatic under the latter. It is important to keep in mind
that increased water demand from higher temperatures may more than offset any increased
precipitation. In other words, it can still be “drier”, even with more rainfall.
Now, we explore the frequency of large-scale rainfall events. First, we define two types of
high-magnitude rainfall events:
extreme rainfall (ER) events, any day such that the
island daily average precipitation
is larger than the
99th percentile
of observed average daily
precipitation totals from 1980
to 2005: 29.90 mm, and
high-magnitude rainfall (HMR)
events, any day such that the
island daily average precipitation
is larger than the
95th percentile
of observed average daily
precipitation totals from 1980
to 2005: 14.81 mm.
Figure displays the number of ER events as a function of rainfall
season and year. The RCP4.5 emission scenario is displayed on the left, while the RCP8.5 emission
scenario is displayed on the right. The RCP4.5 emission scenario indicates slight increases in ER
events during the LRS and ERS. The RCP8.5 emission scenario indicates a substantial increase in the
number of extreme rainfall events during the LRS and ERS. Under the RCP8.5 emission scenario, the
LRS, or hurricane season, is projected to observe more than seven ER events each year, and the ERS is
expected to see between four and five ER events each year, while the dry season (DS) is expected to continue to
observe very few ER events by 2100.
Figure displays the ratio of yearly HMR event (island daily average
>14.81 mm) total rainfall to the annual total of smaller rainfall events (island daily average
≤14.81 mm). Historically, the total rainfall from HMR events represented around 40 % of the
total rainfall from more common precipitation events. The RCP4.5 emission scenario does not exhibit
a clear shift in this relationship. However, in the RCP8.5 emission scenario, the proportion of
yearly rainfall due to HMR events is projected to increase dramatically. By 2100, the ratio of
yearly HMR to yearly rainfall more common events is nearly 1 : 1.
Summary of downscaled climate data
In Table , we display the approximate changes of several climatological
characteristics from 2005 to 2100. Bolded and italicized cells are used to indicate increases and
decreases of the specified feature. Approximate changes are calculated by first fitting separate
LOESS smoothing splines to the historical and future data. We then take the difference between the
LOESS estimates in 2100 and 2005. For the climate models and methods examined in this study, the
RCP8.5 forcing scenario favors a dramatic increase in rainfall for Puerto Rico. The RCP4.5 forcing
scenario favors much smaller increases in rainfall and even a noticeable decreases across the ERS.
NOAA's GFDL under the RCP4.5 forcing scenario more closely matches projected rainfall patterns
across the Caribbean from other studies
.
Approximate changes of several climatological characteristics from 2005 to 2100. Bolded
cells and italicized cells indicate increases and decreases of the specified feature.
Emission scenarioClimatological characteristicCCCMA-CanESM2GFDL-ESM2GHadGEM2-ESRCP4.5Daily maximum temperature (∘C)+1.7+0.7+1.3Daily minimum temperature (∘C)+1.7+0.4+1.1Daily precipitation (mm)+0.4–0.9+0.1DS total precipitation (mm)+133.6+45.3+165.5ERS total precipitation (mm)–76.6–275.8–138.6LRS total precipitation (mm)+93.1–98.1–26.7DS extreme rainfall events–0.6–0.5–0.5ERS extreme rainfall events–0.1–1.7–1.1LRS extreme rainfall events+0.9–1.50.0RCP8.5Daily maximum temperature (∘C)+2.9+1.5+2.2Daily minimum temperature (∘C)+3.5+1.4+2.6Daily precipitation (mm)+2.9+0.9+2.7DS total precipitation (mm)+320.8+132.1+332.6ERS total precipitation (mm)+297.4–33.3+180.6LRS total precipitation (mm)+460.2+235.9+439.2DS extreme rainfall events–0.40.0+0.3ERS extreme rainfall events+2.4–0.8+2.2LRS extreme rainfall events+5.1+2.0+4.1Summary
In this work, we utilize a novel combination of downscaling methods of . We employ a two-part multivariate multisite statistical downscaling model (MMSDM) to
downscale maximum and minimum temperatures and precipitation at K=23 weather stations in Puerto Rico. To downscale precipitation, we first decompose it into two components: precipitation
probability and log-transformed precipitation amount.
The MMSDM methodology is unable to correct GCM bias adequately. To quantify and correct for these
biases, we propose LOESS quantile mapping (LQM), which combines elements of localized regression and
quantile mapping. LQM employs standard quantile mapping techniques as a function of season, which
we defined as Julian day. First, percentiles of observed and fitted values of a specified random
variable are estimated as a function of season. Next, bias is estimated as a function of percentile
and season by simply taking the difference between the observed and fitted summaries. Then, LOESS
smoothing techniques are applied to the bias values, and the bias is estimated via LOESS regression
as a function of season. Finally, the estimated bias, which is allowed to vary as a function of
percentile (as in standard quantile mapping) and season (the extension to standard QM), is added
directly to the fitted values (and subsequently added directly to the downscaled climate
projections).
We proceed to combine these new extensions in order to study the future climate of Puerto Rico. The
resulting downscaled temperature projections from the three climate models all agree that Puerto
Rico will experience a warmer future climate. These projections are consistent with the
overwhelming majority of published literature examining future Caribbean climate
. Not only will Puerto Rico experience a warmer
climate, but the average day will also have a narrower temperature range as minimum temperatures
are expected to increase at a faster rate than maximum temperatures. The RCP8.5 forcing scenario
(carbon emissions continue to grow through the year 2100) projects a warmer climate than that of
the RCP4.5 forcing scenario (carbon emissions are curbed and do not grow after a certain date).
The majority of literature agrees that the Caribbean will see reduced rainfall in its future climate
. Within the RCP4.5 forcing scenario, our methods tend to be
consistent with those of the literature. The three models explored here agree that the DS will
observe increased rainfall, while the ERS and LRS will likely observe a decline in total rainfall.
However, GCM output from the RCP8.5 forcing scenario tends to favor the opposite: a wetter climate
for Puerto Rico, driven by an increase in extreme rainfall events.
ESM2G maximum daily temperature quantiles (∘C, top panel) and minimum daily
temperature quantiles (∘C, bottom panel) for the observed historical (from GHCN) climate,
the downscaled RCP4.5 climate, and the downscaled RCP8.5 climate.
ESM2G mean daily maximum (left panel) and minimum (right panel) temperature (∘C)
as a function of year. Observed historical GHCN data from 1980–2005 are plotted in red, while
downscaled RCP4.5 and RCP8.5 temperatures from 2006–2100 are plotted in green and blue,
respectively. This figure was created using .
Precipitation
ESM2G daily total precipitation (mm) quantiles for the observed historical GHCN climate,
the downscaled RCP4.5 climate, and the downscaled RCP8.5 climate.
ESM2G-observed historical (GHCN) daily mean precipitation (mm) is plotted as a function of
year (1980–2005) in red, while ESM2G RCP4.5 and RCP8.5 downscaled mean precipitation from
2006–2100 is plotted in green and blue, respectively. This figure was created using
.
ESM2G average total precipitation (mm) per weather station by rainfall season for the
RCP4.5 forcing scenario (left) and the RCP8.5 forcing scenario (right). Historical GHCN
observations are also indicated on these plots (1980–2005). This figure was created using
.
Total number of ER events (island daily average rainfall >29.90 mm) by season for the
ESM2G's RCP4.5 forcing scenario (left) and the RCP8.5 forcing scenario (right). Historical GHCN
observations are also indicated on these plots (1980–2005). This figure was created using
.
ESM2G ratio of yearly HMR event total rainfall (island daily average >14.81 mm) to
common rainfall as a function of year. This figure was created using .
UK's HadGEM2-ES downscaled climateTemperature
Maximum daily temperature quantiles (∘C, top panel) and minimum daily temperature
quantiles (∘C, bottom panel) for the observed historical GHCN climate, the downscaled
RCP4.5 climate, and the downscaled RCP8.5 climate using the Hadley Centre's HadGEM2-ES.
Mean daily maximum (left panel) and minimum (right panel) temperature (∘C) as a
function of year. Observed historical GHCN data from 1980–2005 are plotted in red, while
downscaled RCP4.5 and RCP8.5 temperatures (from the UK's HadGEM2) from 2006–2100 are plotted in
green and blue, respectively. This figure was created using .
Precipitation
Daily total precipitation (mm) quantiles for the observed historical GHCN climate, the
downscaled RCP4.5 climate, and the downscaled RCP8.5 climate using the UK's HadGEM2-ES.
Observed historical (GHCN) daily mean precipitation (mm) is plotted as a function of year
(1980–2005) in red. RCP4.5 and RCP8.5 downscaled mean precipitation from 2006–2100 is plotted in
green and blue, respectively. This figure was created using .
Average total precipitation (mm) per weather station by rainfall season for the UK's
HadGEM2 RCP4.5 forcing scenario (left) and the RCP8.5 forcing scenario (right). Historical GHCN
observations are also indicated on these plots (1980–2005). This figure was created using
.
Total number of ER events (island daily average rainfall >29.90 mm) by season for the
HadGEM2's RCP4.5 forcing scenario (left) and the RCP8.5 forcing scenario (right). Historical GHCN
observations are also indicated on these plots (1980–2005). This figure was created using
.
The ratio of yearly HMR event total rainfall (island daily average >14.81 mm) to common
rainfall as a function of year. This figure was created using .
Code availability
R codes for performing the statistical analyses described in this paper are
available at https://github.com/captseymour/MMSDM (last access: 31 December 2022). The most
up-to-date published code is available on Zenodo at
https://doi.org/10.5281/zenodo.7497210.
Data availability
All data used in this study are publicly available. The primary historical
climate data are from the publicly available Global Historical Climatological Network (GHCN; ). The
CMIP5 GCM data were downloaded using the Department of Energy Lawrence Livermore National
Laboratory's (DOE/LLNL) data retrieval tool (https://esgf-node.llnl.gov/search/cmip5/, ).
Author contributions
This work, including the code, was originally completed as part of Benjamin Washington's doctoral dissertation in statistics, under the direction of Lynne Seymour. Thomas Mote provided the necessary expertise on the climate modeling, especially as it pertains to Puerto Rico.
Competing interests
The contact author has declared that none of the authors has any competing
interests.
Disclaimer
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional
claims in published maps and institutional affiliations.
Acknowledgements
Support for Thomas Mote was provided
by the National Science Foundation's (NSF's) Long Term Ecological Research (LTER) grant. We are
appreciative of climate data efforts such as the GHCN, which is maintained by the National Oceanic
and Atmospheric Administration's (NOAA's) National Centers for Environmental Information
. Additionally, we are grateful to GCM climate projects such as CMIP. CMIP5 GCM
data are made publicly available via the Department of Energy Lawrence Livermore National
Laboratory's (DOE/LLNL) data retrieval tool. GCM data would not be publicly available without the
support of the Earth System Grid Federation (ESGF), whose aim is to enhance software that powers
most GCMs . Thanks to the ESGF, multiple petabytes of GCM
data are publicly available online on many federal websites, the LLNL being one of them.
Financial support
This research has been supported by National Science Foundation Luquillo Long-Term Ecological Research Program (grant no. DEB1239764).
Review statement
This paper was edited by Michael Wehner and reviewed by Adam Terando and one
anonymous referee.
ReferencesAnanthakrishnan, R., Bell, G., Cinquini, L., Crichton, D., Danvil, S., Drach,
B., Fiore, S., Gonzalez, E., Harney, J. F., and Mattmann, C.: The Earth
System Grid Federation: An Open Infrastructure for Access to
Distributed Geospatial Data, Tech. rep., Oak Ridge National Lab.(ORNL),
Oak Ridge, TN (United States), Center for Computational Sciences, 10.1016/j.future.2013.07.002, 2013.
Angeles, M. E., Gonzalez, J. E., Erickson III, D. J., and Hernández, J. L.:
Predictions of future climate change in the Caribbean region using global
general circulation models, Int. J. Climatol., 27, 555–569, 2007.Angeles, M. E., González, J. E., Ramírez-Beltrán, N. D., Tepley,
C. A., and Comarazamy, D. E.: Origins of the Caribbean rainfall bimodal
behavior, J. Geophys. Res.-Atmos., 115, D11106, 10.1029/2009JD012990, 2010.
Ben Alaya, M. A., Chebana, F., and Ouarda, T.: Probabilistic Gaussian copula
regression model for multisite and multivariable downscaling, J.
Climate, 27, 3331–3347, 2014.
Bhardwaj, A., Misra, V., Mishra, A., Wootten, A., Boyles, R., Bowden, J., and
Terando, A. J.: Downscaling future climate change projections over Puerto
Rico using a non-hydrostatic atmospheric model, Climatic Change, 147,
133–147, 2018.
Biasutti, M., Sobel, A. H., Camargo, S. J., and Creyts, T. T.: Projected
changes in the physical climate of the Gulf Coast and Caribbean,
Climatic Change, 112, 819–845, 2012.
Bowden, J. H., Terando, A. J., Misra, V., Wootten, A., Bhardwaj, A., Boyles,
R., Gould, W., Collazo, J. A., and Spero, T. L.: High-resolution dynamically
downscaled rainfall and temperature projections for ecological life zones
within Puerto Rico and for the US Virgin Islands, Int. J.
Climatol., 41, 1305–1327, 2021.
Campbell, J. D., Taylor, M. A., Stephenson, T. S., Watson, R. A., and Whyte,
F. S.: Future climate of the Caribbean from a regional climate model,
Int. J. Climatol., 31, 1866–1878, 2011.
Cannon, A. J.: Multivariate quantile mapping bias correction: an
N-dimensional probability density function transform for climate model
simulations of multiple variables, Clim. Dynam., 50, 31–49, 2018.
Cashman, A., Nurse, L., and John, C.: Climate change in the Caribbean: The
water management implications, J. Environ. Dev.,
19, 42–67, 2010.Centella, A., Bezanilla, A., and Leslie, K.: Technical report: A study of the
uncertainty in future Caribbean climate using the PRECIS regional climate
model, Institute of Meteorology, Community Caribbean Climate Change Centre,
Cuba, https://www.eldis.org/document/A60777 (last access: 26 January 2023), 2008.
Chen, A. A. and Taylor, M. A.: Investigating the link between early season
Caribbean rainfall and the El Niño+ 1 year, Int. J.
Climatol., 22, 87–106,
2002.Chen, D., Dai, A., and Hall, A.: The Convective-To-Total Precipitation Ratio
and the “Drizzling” Bias in Climate Models, J. Geophys.
Res.-Atmos., 126, e2020JD034198, 10.1029/2020JD034198, 2021.
Cinquini, L., Crichton, D., Mattmann, C., Harney, J., Shipman, G., Wang, F.,
Ananthakrishnan, R., Miller, N., Denvil, S., and Morgan, M.: The Earth
System Grid Federation: An open infrastructure for access to
distributed geospatial data, Future Gener. Comp. Sy., 36,
400–417, 2014.
Cleveland, W. S., Grosse, E., and Shyu, W. M.: Local regression models, in:
Statistical Models in S, Routledge, 309–376, ISBN 9780203738535, 2017.
Comarazamy, D. E. and González, J. E.: On the validation of the simulation
of early season precipitation on the island of Puerto Rico using a mesoscale
atmospheric model, J. Hydrometeorol., 9, 507–520, 2008.Department of Energy Lawrence Livermore National Laboratory (DOE/LLNL): World Climate Research Programme CMIP5, https://esgf-node.llnl.gov/search/cmip5, last access: 26 January 2023.Girvetz, E. H., Zganjar, C., Raber, G. T., Maurer, E. P., Kareiva, P., and
Lawler, J. J.: Applied climate-change analysis: the climate wizard tool, PLoS
One, 4, 10.1371/journal.pone.0008320, 2009.
Guo, Q., Chen, J., Zhang, X., Shen, M., Chen, H., and Guo, S.: A new two-stage
multivariate quantile mapping method for bias correcting climate model
outputs, Clim. Dynam., 53, 3603–3623, 2019.
Gutowski Jr., W. J., Decker, S. G., Donavon, R. A., Pan, Z., Arritt, R. W., and
Takle, E. S.: Temporal-spatial scales of observed and simulated precipitation
in central US climate, J. Climate, 16, 3841–3847, 2003.
Harmsen, E. W., Miller, N. L., Schlegel, N. J., and Gonzalez, J. E.: Seasonal
climate change impacts on evapotranspiration, precipitation deficit and crop
yield in Puerto Rico, Agr. Water Manage., 96, 1085–1095,
2009.
He, J. and Soden, B. J.: A re-examination of the projected subtropical
precipitation decline, Nat. Clim. Change, 7, 53–57, 2017.Jennings, L. N., Douglas, J., Treasure, E., and González, G.: Climate
change effects in El Yunque National Forest, Puerto Rico, and the
Caribbean region, General Technical Report SRS-GTR-193, Asheville, NC,
USDA-Forest Service, Southern Research Station, 193, 1–47, 10.2737/SRS-GTR-193, 2014.
Jeong, D. I., St-Hilaire, A., Ouarda, T., and Gachon, P.: A multivariate
multi-site statistical downscaling model for daily maximum and minimum
temperatures, Clim. Res., 54, 129–148, 2012a.
Jeong, D. I., St-Hilaire, A., Ouarda, T. B., and Gachon, P.: Multisite
statistical downscaling model for daily precipitation combined by
multivariate multiple linear regression and stochastic weather generator,
Climatic Change, 114, 567–591, 2012b.
Kahle, D. and Wickham, H.: ggmap: Spatial Visualization with ggplot2, R
J., 5, 144–161,
2013.
Khalyani, A. H., Gould, W. A., Harmsen, E., Terando, A., Quinones, M., and
Collazo, J. A.: Climate change implications for tropical islands:
Interpolating and interpreting statistically downscaled GCM projections
for management and planning, J. Appl. Meteorol. Clim.,
55, 265–282, 2016.
Lafon, T., Dadson, S., Buys, G., and Prudhomme, C.: Bias correction of daily
precipitation simulated by a regional climate model: a comparison of methods,
Int. J. Climatol., 33, 1367–1381, 2013.
Lashof, D. A. and Ahuja, D. R.: Relative contributions of greenhouse gas
emissions to global warming, Nature, 344, 529–531, 1990.Lintner, B. R., Biasutti, M., Diffenbaugh, N. S., Lee, J.-E., Niznik, M. J.,
and Findell, K. L.: Amplification of wet and dry month occurrence over
tropical land regions in response to global warming, J. Geophys.
Res.-Atmos., 117, D11106, 10.1029/2012JD017499, 2012.
Lund, R., Hurd, H., Bloomfield, P., and Smith, R.: Climatological time series
with periodic correlation, J. Climate, 8, 2787–2809, 1995.Magrin, G., Gay Garcia, C., Cruz Choque, D., Gimenez-Sal, J., Moreno, A., Nagy,
G., Nobre, C., and Villamizar, A.: Climate Change and Climate Variability in
the Latin American Region, in: American Geophysical Union Spring Meeting
Abstracts, https://ui.adsabs.harvard.edu/abs/2007AGUSM.U33B..02M (last access: 23 January 2023), 2007.
Maraun, D.: Bias correction, quantile mapping, and downscaling: Revisiting
the inflation issue, J. Climate, 26, 2137–2143, 2013.
Maraun, D.: Bias correcting climate change simulations – A critical review,
Current Climate Change Reports, 2, 211–220, 2016.
Mattingly, K. S., Seymour, L., and Miller, P. W.: Estimates of Extreme
Precipitation Frequency Derived from Spatially Dense Rain Gauge Observations:
A Case Study of Two Urban Areas in the Colorado Front Range Region, Ann.
Am. Assoc. Geogr., 107, 1499–1518, 2017.
Meehl, G. A., Covey, C., Delworth, T., Latif, M., McAvaney, B., Mitchell,
J. F., Stouffer, R. J., and Taylor, K. E.: The WCRP CMIP3 multimodel
dataset: A new era in climate change research, B. Am.
Meteorol. Soc., 88, 1383–1394, 2007.
Meehl, G. A., Goddard, L., Murphy, J., Stouffer, R. J., Boer, G., Danabasoglu,
G., Dixon, K., Giorgetta, M. A., Greene, A. M., and Hawkins, E. D.: Decadal
prediction: can it be skillful?, B. Am. Meteorol.
Soc., 90, 1467–1486, 2009.Meinshausen, M., Meinshausen, N., Hare, W., Raper, S. C., Frieler, K., Knutti,
R., Frame, D. J., and Allen, M. R.: Greenhouse-gas emission targets for
limiting global warming to 2 ∘C, Nature, 458, 1158–1162, 2009.Menne, M. J., Durre, I., Korzeniewski, B., McNeill, S., Thomas, K., Yin, X., Anthony, S., Ray, R., Vose, R. S., Gleason, B. E., and Houston, T. G.: Global Historical Climatology Network – Daily (GHCN-Daily), Version 3. [Puerto Rico], NOAA National Climatic Data Center [data set], 10.7289/V5D21VHZ, 2012a.Menne, M. J., Durre, I., Vose, R. S., Gleason, B. E., and Houston, T. G.: An Overview of the Global Historical Climatology Network-Daily Database, J. Atmos. Ocean. Tech., 29, 897–910, 10.1175/JTECH-D-11-00103.1, 2012b.
Miller, P. W., Mote, T. L., and Ramseyer, C. A.: An Empirical Study of the
Relationship between Seasonal Precipitation and Thermodynamic Environment in
Puerto Rico, Weather Forecast., 34, 277–288, 2019.Müller, C., Cramer, W., Hare, W. L., and Lotze-Campen, H.: Climate change
risks for African agriculture, P. Natl. Acad. Sci. USA, 108, 4313–4315,
10.1073/pnas.1015078108, 2011.NCEI: National Centers for Environmental Information's Daily Observational Data
Map, Version 2.2.0, https://gis.ncdc.noaa.gov/maps/ncei/cdo/daily,
last access: 1 December 2018.
Nesbitt, S. W., Cifelli, R., and Rutledge, S. A.: Storm morphology and rainfall
characteristics of TRMM precipitation features, Mon. Weather Rev.,
134, 2702–2721, 2006.
Park, J., Kang, M. S., and Song, I.: Bias correction of RCP-based future
extreme precipitation using a quantile mapping method; for 20-weather
stations of South Korea, Journal of the Korean Society of Agricultural
Engineers, 54, 133–142, 2012.
Pierce, D. W., Cayan, D. R., and Thrasher, B. L.: Statistical downscaling using
localized constructed analogs (LOCA), J. Hydrometeorol., 15,
2558–2585, 2014.Ramirez-Villegas, J., Challinor, A. J., Thornton, P. K., and Jarvis, A.:
Implications of regional improvement in global climate models for
agricultural impact research, Environ. Res. Lett., 8, 024018, 10.1088/1748-9326/8/2/024018,
2013.Ramseyer, C., Miller, P., and Mote, T. L.: Statistical Downscaling of CMIP5
data to predict future dry day frequency in the El Yunque National
Forest, in: American Geophysical Union Fall Meeting Abstracts, vol.
2018, A21L–2904, https://ui.adsabs.harvard.edu/abs/2018AGUFM.A21L2904R (last access: 23 January 2023), 2018.
Ramseyer, C. A. and Mote, T. L.: Atmospheric controls on Puerto Rico
precipitation using artificial neural networks, Clim. Dynam., 47,
2515–2526, 2016.
Ramseyer, C. A. and Mote, T. L.: Analysing regional climate forcing on
historical precipitation variability in Northeast Puerto Rico, Int.
J. Climatol., 38, e224–e236, 2018.
Ramseyer, C. A., Miller, P. W., and Mote, T. L.: Future precipitation
variability during the early rainfall season in the El Yunque National
Forest, Sci. Total Environ., 661, 326–336, 2019.
Satterthwaite, D.: Cities' contribution to global warming: notes on the
allocation of greenhouse gas emissions, Environ. Urban., 20,
539–549, 2008.
Stennett-Brown, R. K., Jones, J. J., Stephenson, T. S., and Taylor, M. A.:
Future Caribbean temperature and rainfall extremes from statistical
downscaling, Int. J. Climatol., 37, 4828–4845, 2017.Taylor, K. E., Balaji, V., Hankin, S., Juckes, M., Lawrence, B., and Pascoe,
S.: CMIP5 Data Reference Syntax (DRS) and Controlled Vocabularies, in:
Program for Climate Model Diagnosis and Intercomparison, http://pcmdi.github.io/mips/cmip5/docs/cmip5_data_reference_syntax.pdf (last access: 23 January 2023), 2011.
Taylor, K. E., Stouffer, R. J., and Meehl, G. A.: An overview of CMIP5 and
the experiment design, B. Am. Meteorol. Soc., 93,
485–498, 2012.Taylor, M. A., Enfield, D. B., and Chen, A. A.: Influence of the tropical
Atlantic versus the tropical Pacific on Caribbean rainfall, J.
Geophys. Res.-Oceans, 107, 3127, 10.1029/2001JC001097, 2002.
Thrasher, B., Maurer, E. P., McKellar, C., and Duffy, P. B.: Technical Note: Bias correcting
climate model simulated daily temperature extremes with quantile mapping, Hydrol. Earth Syst.
Sci., 16, 3309–3314, 10.5194/hess-16-3309-2012, 2012.
Van Beusekom, A. E., Gould, W. A., Terando, A. J., and Collazo, J. A.: Climate
change and water resources in a tropical island system: propagation of
uncertainty from statistically downscaled climate models to hydrologic
models, Int. J. Climatol., 36, 3370–3383, 2016.Washington, B. and Seymour, L.: An Adapted vector Autoregressive
Expectation-Maximization Imputation Algorithm for Climate Data Networks,
Wires Comput. Stat., 12, e1494, 10.1002/wics.1494,
2019.
Washington, B., Seymour, L., Lund, R., and Willett, K.: Simulation of
temperature series and small networks from data, Int. J.
Climatol., 39, 5104–5123,
2019.Washington, B. J. and Seymour, L.: captseymour/MMSDM: Code for Washington,
Seymour, and Mote (2023), Zenodo [code], 10.5281/zenodo.7497210,
2022.Wickham, H.: ggplot2: Elegant Graphics for Data Analysis, Springer-Verlag New
York, http://ggplot2.org (last access: 22 January 2023), 2016.
Winkler, J. A., Palutikof, J. P., Andresen, J. A., and Goodess, C. M.: The
simulation of daily temperature time series from GCM output. Part II:
Sensitivity analysis of an empirical transfer function methodology, J.
Climate, 10, 2514–2532, 1997.Wood, A. W., Maurer, E. P., Kumar, A., and Lettenmaier, D. P.: Long-range
experimental hydrologic forecasting for the eastern United States, J.
Geophys. Res.-Atmos., 107, 4429, 10.1029/2001JD000659, 2002.Yang, C., Chandler, R. E., Isham, V. S., and Wheater, H. S.: Spatial-temporal
rainfall simulation using generalized linear models, Water Resour.
Res., 41, W11415, 10.1029/2004WR003739, 2005.