The sensitivity of the precipitation over Puerto Rico that is simulated by the Weather Research and Forecasting (WRF) Model is evaluated using multiple combinations of cumulus parameterization (CP) schemes and interior grid nudging. The NCEP–DOE AMIP-II reanalysis (R-2) is downscaled to 2-km horizontal grid spacing both with convective-permitting simulations (CP active only in the middle and outer domains) and with CP schemes active in all domains. The results generally show lower simulated precipitation amounts than are observed, regardless of WRF configuration, but activating the CP schemes in the inner domain improves the annual cycle, intensity, and placement of rainfall relative to the convective-permitting simulations. Furthermore, the use of interior-grid-nudging techniques in the outer domains improves the placement and intensity of rainfall in the inner domain. Incorporating a CP scheme at convective-permitting scales (<4 km) and grid nudging at non-convective-permitting scales (>4 km) improves the island average correlation of precipitation by 0.05–0.2 and reduces the island average RMSE by up to 40 mm on average over relying on the explicit microphysics at convective-permitting scales with grid nudging. Projected changes in summer precipitation between 2040–42 and 1985–87 using WRF to downscale CCSM4 range from a 2.6-mm average increase to an 81.9-mm average decrease, depending on the choice of CP scheme. The differences are only associated with differences between WRF configurations, which indicates the importance of CP scheme for projected precipitation change as well as historical accuracy.
A significant reduction in precipitation from anthropogenic climate change is predicted in subtropical regions (Chou et al. 2009), which makes these areas vulnerable to significant impacts to multiple sectors, including agriculture, infrastructure, and wildlife. This drying is suggested both by the “rich get richer” mechanism (the tendency of rainfall to increase in convergence zones with large climatological precipitation and decrease in subsidence regions) and by the global climate models (GCMs) used in phase 5 of the Coupled Model Intercomparison Project (CMIP5; Scheff and Frierson 2012). The rich-get-richer mechanism is, however, considered in the absence of additional local topographic factors and forcing, which could mitigate the predicted drying. Efforts are under way to dynamically downscale selected CMIP5 GCMs under different greenhouse gas emission scenarios to aid in the development of adaptation strategies that respond to anthropogenic climate change for the island of Puerto Rico, located on the boundary between the Caribbean Sea and Atlantic Ocean (Fig. 1). Credible simulation of rainfall is critical in this effort, including consideration of how climate change could affect rainfall intensity, distribution, frequency, and totals. Puerto Rico has complex topography that forces spatial variability in precipitation patterns across the island (Jury 2009). The current generation of GCMs is unable to resolve this complexity and other precipitation-generating processes.
Dynamical downscaling using regional climate models (RCM), such as the Weather Research and Forecasting (WRF) Model (Skamarock et al. 2008), has the potential to resolve the convective-scale processes that are required to simulate the precipitation across the island. While the potential exists for WRF to capture the processes in this region, it remains unclear which configuration of WRF is the most appropriate to dynamically downscale to a high horizontal grid spacing over the island. Here we test eight WRF configurations in a hindcast mode to select a WRF configuration that provides the most accurate simulation of precipitation from 1-yr WRF simulations down to a 2-km horizontal grid spacing. The configurations reflect combinations of two cumulus parameterization (CP) schemes and three interior-grid-nudging approaches along with activation of the CP schemes at convective-permitting scales (grid spacing of a few kilometers). Interior grid nudging is an approach used to constrain the RCM simulation to the driving fields (Bowden et al. 2012). Select WRF configurations are also tested in a climate change context by downscaling the CCSM4 climate model for two 3-yr time slices (1985–87 and 2040–42). The goal is to aid climate change adaptation planning by systematically evaluating the internal structural uncertainty associated with the WRF configuration differences between CP scheme and interior-grid-nudging approach. It is essential to characterizing the uncertainty for dynamically downscaled precipitation over the island.
Studies have shown that in areas with deep convection, such as Puerto Rico, precipitation is a large source of uncertainty for climate modeling, even at grid spacings of a few kilometers (Sherwood et al. 2014; Brisson et al. 2016; Prein et al. 2015). The use of CP schemes at grid spacings between 1 and 5 km is sometimes referred to as a “gray zone” because not all convective processes are resolved at these scales (Niemelä and Fortelius 2005; Craig and Dörnbrack 2008; Hong and Dudhia 2012). Therefore, the gray zone is convective permitting (and not necessarily convective resolving), and some locations may still warrant the use of a CP scheme to represent the subgrid-scale convective processes in a high-resolution simulation (Deng and Stauffer 2006). Lee et al. (2011) and Sun and Barros (2014) demonstrated that activating the CP scheme in the high-resolution inner domain improves the representation of precipitation beyond the ability of explicit microphysics alone. To be specific, Lee et al. (2011) demonstrated that activating the CP scheme at high resolutions improved the representation of heavy-rain events. CP schemes applied in the gray zone also have important implications for the thermodynamic and dynamic environments of tropical cyclones by influencing both model convergence and the strength of convection in the eyewall (Sun et al. 2013). Also, CP schemes have an impact on the marine boundary layer structure (by influencing boundary layer depth, temperature, moisture, and winds) and on the geographic placement of clouds (Zhang et al. 2011), which is important for simulating impacts in areas where clouds are an important source of moisture in addition to rainfall (e.g., Comarazamy and Gonzalez 2011).
Cumulus parameterization schemes are known to contribute to rainfall errors, however, including the diurnal cycle, frequency, and intensity (Prein et al. 2015), and not all CP schemes are scale aware (assumptions in the parameterization scheme change as one increases the model’s horizontal resolution) and suitable for grid spacing of a few kilometers. At “gray scales,” many of the assumptions that are made in the CP schemes are no longer valid, such as convection being self-contained within one grid column (Arakawa et al. 2011; Grell and Freitas 2014). An alternative approach to using a CP scheme is to increase the horizontal grid spacing to begin explicitly resolving the convection (Grell et al. 2000; Chan et al. 2013). A convective-permitting simulation (turning off the CP scheme) can be particularly advantageous for Puerto Rico, which has a heterogeneous land surface and mountainous terrain in the tropics. Explicitly resolving the convection has been shown to improve (reduce) precipitation errors in terms of diurnal cycle, extreme precipitation on hourly time scales, wet-day frequency, and small-scale processes in tropical cyclones and other convective systems (e.g., Done et al. 2004; Prein et al. 2015). Grell et al. (2000) show that convective-permitting simulations produce precipitation away from the top of mountains as the convection moves with the upper-level flow. Convective-permitting simulations may also provide a different sample of projected change for precipitation, especially for high-precipitation events (Kendon et al. 2012). An additional consideration for convective-permitting simulations is that the choice of the CP scheme used in the outermost domains can affect the convective-permitting simulations in the innermost domain. For example, Perez et al. (2014) simulated precipitation over the Canary Islands with WRF and found that the largest model errors in precipitation for the innermost domain with explicitly resolved convection occurred when changing the CP scheme in the outer domains. They attributed the precipitation changes to the amount of water available in the innermost domain with different choices of CP scheme. In this study, we apply two different CP schemes and assess the effect on simulated precipitation over Puerto Rico. This includes an assessment of differences that result from activating different CP schemes at convective-resolving scales.
Studies have also discussed the importance of interior grid nudging, such as spectral and analysis nudging, for simulating regional climate (von Storch et al. 2000; Bowden et al. 2012, 2013; Otte et al. 2012; Feser and Barcikowska 2012; Cha et al. 2016). In the WRF Model used in this study, analysis nudging adds an artificial tendency term to the prognostic equations that is proportional to the difference between the model state and a value that is interpolated in time and space to a grid point from the reference analysis (Stauffer and Seaman 1994; Otte et al. 2012). Spectral nudging is similar, but the nonphysical term is based on the difference between the spectral decompositions of the driving fields and the model state (Otte et al. 2012). Otte et al. (2012) and Bowden et al. (2012, 2013) demonstrated that using analysis nudging in WRF improved the overall accuracy of the simulated climate over the contiguous United States at 36 km and did not squelch extremes in temperature and precipitation. Bullock et al. (2014) showed additional accuracy in precipitation and temperature when applying analysis and spectral grid nudging in WRF at a 12-km horizontal grid spacing. Using nudging in the interior of the domain has also been shown to improve formation of typhoons and their tracks (Feser and Barcikowska 2012) and synoptic flow and precipitation associated with the East Asian summer monsoon (Cha et al. 2016). All of these improvements, ranging from extreme near-surface meteorological fields to the representation of weather regimes and large-scale atmospheric processes, point toward the need for interior grid nudging. Few studies, however, have analyzed the importance of interior grid nudging for small tropical islands at high horizontal gray-zone resolutions. In this study, we apply three different nudging strategies (from no nudging to applying nudging on the middle and outer domains) to determine the impact on the accuracy of simulated precipitation across the island. Given that high-resolution projections will ultimately be provided to decision-makers in Puerto Rico, it is likely that this high-resolution information will be used for adaptation decision-making and vulnerability assessments, and so such evaluation is critical to drive future projections being produced for this region.
The rest of the paper is organized as follows. In sections 2 and 3, we describe the study region of Puerto Rico and the model setup and sensitivity simulations. Section 4 describes the validation data and verification of the sensitivity simulations. We conclude with a summary and discussion of the results and future directions for research.
2. Study area
The island of Puerto Rico, located in the northern Caribbean Sea, sits in a region dominated by easterly trade winds with available moisture from both the Caribbean Sea and Atlantic Ocean. The island has an area of 9041 km2 but also ranges in elevation from sea level to 4390 ft (1338 m). The dramatic changes in elevation coupled with the easterly flow across Puerto Rico lead to the development of anticyclonic (cyclonic) local circulation on the southwestern (northwestern) sides of the island (Jury 2009; Jury and Chiao 2013). These circulations together with the orographic lifting on the east side of the island result in a sharp contrast in precipitation over short distances. Figure 1 shows the 1981–2010 annual average total precipitation patterns across Puerto Rico and the U.S. Virgin Islands. El Yunque, a mountain on the northeastern corner of the island (circled in red), receives much of its rainfall from orographic precipitation. The interior mountain ridge leads to higher rainfall amounts on the northwestern side (~1270–1905 mm) and less rainfall on the southwestern side (~762–1143 mm). The sharp precipitation gradients result in rapid vegetation shifts from rain forest on the northeastern side to dry forest on the southwestern side.
3. Model setup and simulations
Prior studies have used WRF over Puerto Rico at a 1-km horizontal grid spacing (Jury and Chiao 2013; Villamil-Otero et al. 2015) to understand the atmospheric circulation across the island. Villamil-Otero et al. (2015) applied the WRF Model to understand the topographic–thermal circulations in western Puerto Rico, and Jury and Chiao (2013) used WRF to understand the leeside boundary layer confluence and afternoon thunderstorms in western Puerto Rico. Both of these studies illustrated that WRF simulates atmospheric processes that are important for local precipitation across Puerto Rico; therefore, WRF is hypothesized to provide significant value for downscaling climate change projections because GCMs cannot resolve these local-scale processes. WRF is used to downscale the NCEP–DOE AMIP-II reanalysis, version 2 (R-2; Kanamitsu et al. 2002), over Puerto Rico to a 2-km horizontal grid spacing. The R-2 product (which has a horizontal spectral resolution of T62, or 1.875° × 1.875° grid spacing at the equator) is used here to mimic the coarser grid spacing of the GCMs used in CMIP5 to help to establish a dynamic downscaling method for future climate change downscaling efforts. For this study, WRF, version 3.6.1, was used to downscale R-2. The WRF simulation was initialized at 0000 UTC 1 December 2009, run for a 1-month spinup time, and then run continuously through 0000 UTC 1 January 2011. A one-way nested approach is used for three meshes: 30, 10, and 2 km over Puerto Rico (Fig. 2). The lateral boundaries of the outer domain are relaxed toward R-2 using a five-point sponge zone. WRF was run with a 35-sigma-layer configuration that extended up to 50 hPa, with approximately 16 layers in the lowest 1.5 km of the atmosphere. Each simulation shares several physics options: the Rapid Radiative Transfer Model for global climate models (RRTMG; Iacono et al. 2008) is used for longwave and shortwave radiation, the WRF single-moment 6-class microphysics scheme (WSM6; Hong and Lim 2006) is used, the Yonsei University planetary boundary layer scheme (YSU; Hong et al. 2006) is used, and the model is run with the Noah land surface model (Chen and Dudhia 2001).
To provide a WRF configuration for the downscaled climate change projections, precipitation from eight 1-yr WRF simulations (Table 1) is compared with observations for validation. The analysis in this study focuses on rainfall statistics as a result of changes in the application of the CP scheme and interior grid nudging.
The simulations use two different CP schemes: the Tiedtke scheme and the Kain–Fritsch (KF) scheme. The Tiedtke scheme (Tiedtke 1989; Zhang et al. 2011) is used to match similar research efforts that were done for Hawaii (Lauer et al. 2013). The Tiedtke scheme is a mass flux–type scheme and represents various types of convection that occur around the globe, including deep, shallow, and midlevel convection (Tiedtke 1989). In WRF, the Tiedtke scheme has been shown to improve the geographical distribution of marine boundary layer clouds (Zhang et al. 2011). Simulations using KF implement a modified version of the original scheme (Alapaty et al. 2012; Herwehe et al. 2014). The KF scheme is also a mass flux–type scheme that considers shallow and deep convection. This modified CP scheme [as in Alapaty et al. (2012) and Herwehe et al. (2014)], KFMODS, considers cumulus cloud feedbacks to the radiation and has been shown to improve precipitation biases, especially for a humid climate such as is found in the southeastern United States. While the KF and Tiedtke schemes are both mass flux–type schemes that use CAPE closure, they have differences in the trigger mechanism (Suhas and Zhang 2014). The KF scheme uses a temperature perturbation to determine the vertical velocity for potential updraft source layers, whereas the Tiedtke scheme uses both temperature and moisture perturbations. In addition, the KF scheme activates convection if the vertical velocity of the potential updraft source layer has a minimum depth of 3 km, whereas the Tiedtke scheme uses a depth of 200 hPa. Also, the KF scheme searches the lowest 300 hPa for updraft source layers, and the Tiedtke scheme searches the lowest 350 hPa. All simulations use a CP scheme in the two outermost domains (30 and 10 km). The majority of the simulations (six of eight) are convective permitting, with the CP scheme not active in the inner (2 km) domain. For two simulations (KFMODS_INNER and TIEDTKE_INNER) the CP scheme is active in the innermost domain of WRF.
In addition, the simulations also reflect three different analysis-nudging approaches. As in prior regional climate-modeling studies, such as Bowden et al. (2012) and Otte et al. (2012), analysis nudging is applied toward horizontal winds, potential temperature, and water vapor mixing ratio above the PBL. Nudging above the PBL is advantageous because it allows WRF freedom to develop and respond to mesoscale forcing while simultaneously being constrained to the large-scale atmospheric circulation in the free atmosphere. The analysis-nudging coefficients are provided in Table 2 and represent the nudging strength, which is the e-folding time that would be required to adjust the model to the observed state in the absence of other (physical) forcing (Bowden et al. 2012). Similar analysis-nudging coefficients have been shown to improve the representation of errors in near-surface fields, including precipitation extremes at similar grid spacing to those used here (Bowden et al. 2012, 2013; Otte et al. 2012; Bullock et al. 2014). The focus of these studies has been on areas outside the tropics, however. As precipitation can have more influence than temperature in tropical regions [e.g., on tropical forests as in Schuur (2003)], exploring the impact of nudging on precipitation simulation is important to improving the simulation of precipitation in tropical regions for use in adaptive management. In this study, we test different CP schemes with different analysis-nudging strategies using annual simulations at a high resolution (2-km grid spacing). The first approach uses analysis nudging on the outer two domains (TIEDTKE, KFMODS, TIEDTKE_INNER, and KFMODS_INNER). The second approach applies analysis nudging only to the outermost domain (TIEDTKE_ON and KFMODS_ON). The final approach does not use analysis nudging (TIEDTKE_NN and KFMODS_NN).
4. Validation procedure
For validating each of the WRF simulations, the Multisensor Precipitation Estimates (MPE) provided by the National Weather Service are used for comparison (Seo and Breidenbach 2002). This dataset used rain gauge–calibrated radar estimates of rainfall to produce a gridded estimate of rainfall at ~4.765-km grid spacing. For this analysis, we use the daily MPE product aggregated to a monthly sum for each month in 2010 for comparison with the WRF simulations. It is important to note that the MPE product is created with modeled processes and has known errors related to these processes. The MPE are created using algorithms that are similar to those used for the Stage IV precipitation estimates produced by the National Centers for Environmental Prediction. The accuracy of the Stage IV estimates is well documented for the continental United States, most recently by Wootten and Boyles (2014). The Stage IV estimates demonstrate a tendency to overestimate light-rain events and underestimate heavy-rain events on a daily time scale. We expect that the MPE in Puerto Rico shares errors that are similar to those of the MPE and Stage IV estimates in the continental United States. This situation should be considered here as a limiting factor for this study.
For this study, the focus is primarily on precipitation since it is one of the primary variables that determine the location of the ecology within Puerto Rico. The specific focus is on the precipitation in the inner (2 km) and middle (10 km) domains of the WRF simulation for the following: 1) seasonal cycle of precipitation totals for 2010, 2) monthly total precipitation, and 3) number of days of rain > 25.4 mm (1 in.) in a month. In addition to the qualitative comparisons of the inner-domain precipitation with MPE, the root-mean-square error (RMSE), correlation, and percent bias are used to provide quantitative comparisons of the accuracy between each simulation. Percent bias is calculated as
where x is the value of MPE and y is the value of the WRF simulation for each time i. Each simulation in the 2-km domain is aggregated via grid averaging to the MPE grid over Puerto Rico, and these metrics are calculated for each grid cell where data are available for both the WRF simulations and MPE grid. The gridcell values are then averaged over the island to provide values of RMSE, correlation, and percent bias and are included in the appropriate figures. In this study, for the statistical metrics described above, much of the focus is on the simulated precipitation within the inner (2-km grid spacing) domain. Given the influence of the outer two domains on the inner-domain precipitation totals, we will also discuss the results in these domains as needed.
For this section, we focus on the differences related to CP scheme and interior grid nudging separately. Section 5a focuses on the differences between WRF simulations with differing CP schemes. Section 5b focuses on the influence of analysis nudging on precipitation in the inner domain of WRF. Section 5c here focuses on the statistical metrics for the inner domain across all the WRF simulations included in this study. Section 5d presents additional analysis that discusses the implications of differences between CP schemes in future projections.
a. CP-scheme sensitivity
The focus in this section is on the differences in precipitation across CP schemes. This includes a comparison of convective- and non-convective-permitting simulations in the 2-km inner domain. For each of the four simulations discussed here, analysis nudging is applied to the winds, moisture, and temperature in the middle and outer domains. January is the middle of the dry season for Puerto Rico, and all simulations have some general agreement on the spatial distribution of the precipitation (Fig. 3). TIEDTKE_INNER is drier than TIEDTKE and does not improve the simulation of drier conditions along much of the southern coast. The differences are small when activating the CP scheme for KFMODS (with KFMODS_INNER slightly wetter than KFMODS), and both have a dry bias relative to MPE. In general during the dry season, we do not see large improvements when activating the CP scheme in the inner domain, which agrees with Sun and Barros (2014). This may be expected because the atmosphere is generally more stable and drier. There are also larger differences between CP schemes relative to the CP scheme being active in the 2-km domain during the dry season.
A similar comparison is made during the middle of the wet season. The magnitude of simulated precipitation is larger during the wet season in all versions (Fig. 4). Each simulation remains drier relative to MPE, but WRF simulates the rainfall patterns with driest conditions in the central part of the island and wettest conditions in the convergence zone on the western side of the island. The TIEDTKE_INNER and TIEDTKE simulations have little difference in terms of precipitation totals, but the TIEDTKE_INNER simulation does provide a better representation of rainfall on the eastern side than does the TIEDTKE simulation. For KFMODS_INNER, activating the CP scheme in the inner domain improves the simulation of precipitation totals by increasing the precipitation amount across the island. In particular, activating the CP scheme restores the precipitation on the northeastern side of the island in the KFMODS_INNER simulation. Activating the KFMODS scheme in the inner domain more accurately represents the precipitation amounts across the island during the wet season. There is little to no improvement gained from activating the TIEDTKE scheme in the inner domain in WRF.
Simulating heavy-rainfall events is critical for precipitation totals, as having light precipitation occur frequently may lead to the correct rainfall totals but with a skewed distribution. The frequency of heavy-rain events (>25.4 mm, or 1 in.) is also underrepresented in the wet season. Each WRF simulation underestimates the number of heavy rainfall events, with some locations having 7+ fewer heavy-rain days in July than are observed by MPE (Fig. 5). Activating the CP scheme in the 2-km inner domain tends to improve and concentrate the rainfall for the far eastern side of the island for both CP schemes. In particular, places like the northeastern corner show large improvements in the number of heavy-rainfall events when using a CP scheme in the innermost domain. There is more sensitivity between CP schemes in the 2-km innermost domain for the western half of the island, however. Turning on the CP scheme in the TIEDTKE comparison shows a reduction in the number of heavy-rainfall days in general but in particular on the western side. Turning on the CP scheme in the KFMODS comparison shows smaller response to the change in the number of heavy-rainfall days on the western side. This result demonstrates that activating the CP scheme at gray-zone resolutions can provide a different regional response for different CP schemes for extreme rainfall. Overall, the KFMODS_INNER simulation restores heavy-rain events across much of the island, whereas the TIEDTKE_INNER contributes to more heavy-rain events on the eastern side of the island than on the western side.
For each of the above four simulations, we compare the inner-domain monthly precipitation totals (2 km) with those from the middle domain (10 km) averaged over all land points within Puerto Rico (Fig. 6) to assess the consistency between the middle and inner domains. For each CP scheme, the middle-domain precipitation (red dashed line) is closer to the MPE observations (black line) on average for the year with a smaller percent bias (value for KFMOD minus the value for TIEDTKE), unlike the dry bias in the 2-km domain for both CP schemes (blue and green dashed lines). To be specific, for the KFMODS and KFMODS_INNER simulations there is a significant dry bias of 52% and 23%, respectively, in the inner 2-km domain relative to the middle domain. Activating the CP scheme in the inner 2-km domain (KFMODS_INNER; green dashed line in top panel of Fig. 6) increased the simulated monthly precipitation totals relative to the KFMODS simulation (blue dashed line in top panel of Fig. 6). We do not find the same response between TIEDTKE and TIEDTKE_INNER for the inner 2-km domain that was seen in the KFMOD case. The TIEDTKE_INNER simulation (green dashed line in bottom panel of Fig. 6) reduced the total precipitation average, which actually results in a more accurate representation of precipitation totals in December, February–April, and August. During the majority of the rainy season, however, the reduced rainfall total creates a larger dry bias. Overall, the results illustrate the important point that, at gray-zone resolutions, the island average precipitation is underestimated in the innermost 2-km domain with two different CP schemes and was better represented on average at the coarser (10-km grid spacing) resolution with both CP schemes. Note that the CP schemes used here are not scale aware; that is, as the grid spacing decreases they do not relax the typical assumptions (such as the scale-separation assumption, which considers all convection to be contained within one column) that are associated with CP schemes. The scale-aware limitation may help to explain why the simulated rainfall totals on average for the island agree better with observations for the 10-km domain, but the sharp rainfall gradient is not well resolved in the 10-km middle domain whereas it is apparent in the 2-km inner domain with the Kain–Fritsch scheme active (KFMODS_INNER). In our study, it is imperative to model the rainfall gradient for terrestrial ecosystems and thus more emphasis is placed on the rainfall placement. Therefore, efforts were put into improving the rainfall amounts at the gray-zone grid spacing of 2 km. We find that turning on the CP schemes in the inner 2-km domain typically improves the rainfall statistics in the 2-km inner domain for Puerto Rico (see Table 3 for the RMSE, correlation, and percent bias).
b. Nudging sensitivity
This section focuses on the distinct differences in precipitation with regard to how (and whether) analysis nudging is applied. All nudging-sensitivity simulations are convective permitting, that is, the CP scheme is active in the middle and outer domains only. Here we only focus on July during which the precipitation bias is large, as was previously shown. During July 2010, there are distinct differences in total precipitation when comparing model domains (inner 2 km vs middle 10 km) for the KFMODS simulations relative to MPE (Fig. 7). The number of domains to which nudging is applied decreases from the top panel (outer and middle domain) to the middle panel (outer domain only) and then to the bottom panel (no nudging) in Fig. 7 and the following similar figures. A striking contrast is that the inner domain in all three simulations is much dryer (~150–200 mm) overall than the middle domain (which agrees with the time series shown in Fig. 6), especially for the eastern side of the island. The dry bias is independent of the use of analysis nudging for the KFMODS simulations, however. In comparing the July precipitation totals in Fig. 7 with those of KFMODS_INNER in Fig. 4, we see that using the CP scheme in the inner domain had a larger impact on the monthly precipitation totals(increase of 50–75 mm) than did changes to analysis nudging (difference of <50 mm) between them. The changes in island precipitation between the nudging techniques are more noticeable at 10 km, however. For instance, KFMODS in the middle domain is wetter (>200 mm) than KFMODS_ON for the eastern half of the island. Although the dry bias exists in making the transition from the middle to the inner domain, the KFMODS simulation in the middle domain most closely matches the MPE. In contrast, reducing the number of domains to which nudging is applied causes a dry bias to appear in the middle domain on the eastern side of the island. So reducing the number of domains where nudging is applied degraded the representation of precipitation in the middle domain for the KFMODS simulations.
When altering the choice of CP scheme from KFMODS to TIEDTKE, analysis nudging shows larger sensitivity (Fig. 8). In particular, there are larger differences in the middle domain between the analysis nudging approaches for the TIEDTKE simulations in Fig. 8 when compared with the KFMODS simulations in Fig. 7. The large differences in the TIEDTKE simulations for the middle domain clearly have an impact on the inner-domain precipitation. For instance, TIEDTKE_NN in the middle domain is wetter than TIEDTKE_ON (>300 mm on average over the island). The TIEDTKE_NN also has large rainfall totals in the inner domain. In general, the simulation without nudging (TIEDTKE_NN) is an outlier and is much wetter than the analysis-nudging simulations. Even though rainfall is sensitive to choice of CP scheme, the choice to use nudging can also have an important impact on the climatological precipitation over Puerto Rico. The changes and discrepancies between domains are also reflected in the heavy-rain events in WRF (not shown).
c. Overall accuracy for precipitation
The nudging and CP scheme both have an impact on the precipitation produced in the inner domain of WRF for Puerto Rico. Up to this point, however, we have considered this impact qualitatively. This section focuses on quantitative measures of accuracy for the precipitation simulated by WRF relative to the MPE for the inner domain only. Figure 9 shows the RMSE for the monthly total precipitation for each of the eight WRF simulations relative to the MPE. For both CP schemes, applying the grid nudging in the outer domain only (KFMODS_ON and TIEDTKE_ON) increases the RMSE for precipitation in the inner domain. The CP schemes respond very differently when no nudging is applied, however. The RMSE for the inner-domain precipitation is far larger in the TIEDTKE_NN simulation than in the TIEDTKE and TIEDTKE_ON simulations. In contrast, the RMSE for the KFMODS_NN simulation is similar to that for both the KFMODS and KFMODS_ON simulations. Therefore, the nudging does have an influence on the RMSE for precipitation in the inner domain, but each CP scheme reacts differently to the influence of nudging. The TIEDTKE and KFMODS simulations are comparable in RMSE magnitude, and activating the CP scheme in the inner domain of each improves the RMSE. The reduction in the RMSE is largest for the KFMODS_INNER simulation, however. The convective-permitting simulations have an RMSE of approximately 150 mm or more on average for Puerto Rico. The KFMODS_INNER simulation decreased the RMSE to be much less than 150 mm on average. This result suggests that activating the CP scheme in the inner domain improves the magnitude of precipitation in Puerto Rico, but more so for the Kain–Fritsch scheme than for the Tiedtke scheme.
The simulations also have differing representations of the annual cycle of rainfall in the simulation. Each of the eight simulations is correlated well with MPE on the southwestern side of Puerto Rico (Fig. 10), but in six of the simulations there are many locations with a near-zero correlation or with a strongly negative correlation with the MPE. For the TIEDTKE simulations, applying nudging degraded the correlation of simulated rainfall with the MPE in the inner domain on the northwestern side. In contrast, applying nudging to the KFMODS simulations improved the correlation between the simulations and MPE across much of the island as a whole. In both cases, activating the CP scheme in the inner domain also improved the correlation across Puerto Rico (more so for KFMODS_INNER). This result indicates that the annual cycle and magnitude of precipitation are improved with the CP scheme activated in the 2-km inner domain of WRF for this region. So the choice of nudging and CP scheme together can improve the representation of the annual cycle of precipitation.
Each simulation also has a distinct tendency to over- or underestimate precipitation totals in Puerto Rico depending on CP scheme and nudging approach. Figure 11 shows the percent bias for the monthly total precipitation for each of the WRF simulations relative to the MPE. Figures 7 and 8 indicated the tendency for the WRF simulations to underestimate wet-season rainfall in Puerto Rico. Consideration of the entire year shows a slightly different pattern, however. The KFMODS simulations underestimate precipitation along the coasts of Puerto Rico. The KFMODS simulation, which incorporates nudging in the 10- and 30-km domains, underestimates precipitation over a larger area along the coastline than do the other KFMODS simulations. Although the KFMODS simulation underestimates precipitation over a larger area, it improves the correlation of precipitation over the same area. Activating the CP scheme in the inner domain (KFMODS_INNER) reduces this tendency to underestimate precipitation. Using the KFMODS scheme in the inner domain does reduce the underestimation, but it also seems to cause precipitation to remain over the mountains that provide topographic forcing on the island. For the Tiedtke simulations, applying nudging to multiple domains dampens the tendency to overestimate rainfall. In addition, activating the CP scheme in the inner domain further dampened the tendency of the Tiedtke simulations to overestimate rainfall, actually causing a stronger tendency to underestimate rainfall. Of the eight simulations, using the KFMODS CP scheme (active in all three domains: KFMODS_INNER) with nudging applied to the middle and outer domains provides the lowest RMSE, improves the annual cycle while reducing the tendency to underestimate rainfall, and captures many of the gradients of rainfall over the island. In general, activating the CP scheme can improve the representation of precipitation in a high-resolution WRF domain. It is important to note, however, that the interaction between nudging and CP scheme has a significant influence on precipitation. As such, the choice of both should be considered carefully for high-resolution WRF simulations.
d. Climate change context
Distinct differences in the representation of historical precipitation exist with changes to CP schemes and nudging approach. This effect is well documented by many studies (including this one for Puerto Rico), but there is little discussion regarding the implications of changing CP schemes or nudging approach on the spread of projected change from WRF as an RCM. For this supplemental experiment, three of the eight WRF simulations are used with the CCSM4 to downscale historical and future 3-yr time slices for Puerto Rico. The three simulations of WRF used here are the KFMODS, KFMODS_INNER, and TIEDTKE simulations. For this supplemental experiment, the focus is on differences between CP schemes to focus on the possible spread of projections from a common RCM (in this case WRF) and GCM with variations in the CP scheme in the RCM. For this analysis, each WRF simulation is initialized with the CCSM4 simulation data for two 3-yr periods, with a 1-month spinup for each period. The past period that is used is 1985–87 (initialized at 0000 UTC 1 December 1984), and the future period that is used from the CCSM4 RCP8.5 output (here, RCP is the IPCC Representative Concentration Pathway) is 2040–42 (initialized at 0000 UTC 1 December 2039). The three WRF simulations are run using the same domains, nesting, and grid spacing as in the previous sensitivity runs that were initialized with R-2. The two periods are used to determine for each simulation the change in average summer (June–August) total precipitation over Puerto Rico in the high-resolution inner domain of WRF.
Although the only differences between the WRF simulations are the choice of CP scheme and whether the CP scheme is active in the inner domain, there are still obvious differences for the projected change in average summer precipitation over Puerto Rico (Fig. 12). In some locations, the projected change ranges from wetter to drier by midcentury. There is some agreement between the KFMODS_INNER and TIEDTKE simulations for the western half of the island, but the magnitude of the drying is much larger in the KFMODS_INNER for much of the island. In addition, the projected changes are not just different visually but have statistical significance (Fig. 13). Colored areas in Fig. 13 show statistical significance at 90% or greater confidence (p values ≤ 0.1) from an analysis of variance (ANOVA) test run with all three simulations for each grid cell. At the 90% confidence level, 50% of the island shows a statistically significant difference between the WRF simulations for the projected change in summer precipitation. That is, for one-half of Puerto Rico, the projected change in precipitation is significantly different despite the use of the same period, GCM, and RCP for the WRF simulations.
The potential differences between these simulations, although the driving factors (GCM, RCP, domains, grid spacing, and nudging approach) remained constant, highlight an important source of uncertainty in WRF. Not only do changes in CP scheme influence the accuracy of historical precipitation, but there is also an influence on the projected changes for precipitation. Given the prior results for nudging approach and CP scheme, it follows that these results could extend also to projected changes in precipitation and other critical variables of interest for decision-making and impact assessments. Therefore, the choice of CP scheme and its use at gray-zone resolution when using WRF for climate change studies are an important aspect for consideration. The differences between CP schemes represent a source of uncertainty that is not fully represented by the current suite of available RCM output. The computational expense limits most studies that use RCMs to focusing on one set of parameterization schemes or nudging approaches. Note that the periods used for comparison here are short (3 years past and future) and therefore should not be used to study the climate change signal itself for this region. These three years are, however, the start of a longer period that is being downscaled (1985–2005 vs 2040–60). Overall, this is a short time period, but the example analysis highlights that the differences between CP schemes could expand the uncertainty associated with high-resolution projections for a region. Therefore, careful consideration should be given to the choice of parameterization schemes in WRF with regard to both the historical accuracy and potential differences for projected change. In addition, the potential expansion of the envelope of uncertainty is a concern for using projections from WRF in decision-making or impact assessment. This concern therefore should lead to consideration of how this source of uncertainty could influence regional projections of climate change and of whether it is significant in the face of other sources of uncertainty. Such work is far beyond the scope of this study but is suggested as an avenue of future study.
6. Summary and conclusions
In this study we have used several variations of CP scheme and interior grid nudging to assess the uncertainty associated with both of these procedures for precipitation simulated by WRF. This included activating the CP scheme in the 2-km inner domain. With the exception of one simulation (the TIEDTKE_NN), WRF displayed a tendency to underestimate rainfall in Puerto Rico, particularly during the wet season. The lack of nudging in the TIEDTKE_NN simulation in combination with the TIEDTKE CP scheme illustrated the only overestimation of simulated precipitation at the gray-zone 2-km grid spacing. This included all of the simulations for which nudging was applied in either the outer (30 km) domain only or the middle (10 km) and outer domains. This is an interesting result given that all of these simulations downscale R-2, which has been shown to overestimate climatological precipitation in the Caribbean Sea (Wang et al. 2011). The dry tendency, especially for the 2-km domain, is not solely from the lack of days with rain but is also from the lack of days with heavy rain represented in each simulation. Regardless of the CP scheme used, activating the CP scheme in the inner domain improved the representation of precipitation. This result is similar to those of other studies using WRF, including Lee et al. (2011) and Sun and Barros (2014).
Precipitable water was considered here but did not explain why the WRF simulations in general are dryer than observations (not shown). While the above was not explicitly discussed by Lee et al. (2011), that study did demonstrate that the explicit microphysics in high-resolution domains can be suppressed as the Kain–Fritsch scheme dries and warms much of the troposphere in the driving domain in convective-permitting simulations. Although the modified Kain–Fritsch scheme was used in this study, the improvement in accuracy by activating this CP scheme in the inner (2 km) domain is similar to the results presented by Lee et al. (2011) for the wet season (which has frequent rain events) and for the frequency of intense events. The improvement with the active cumulus physics is more marginal in the dry season (associated with rain events that are lighter), which is similar to the result shown by Sun and Barros (2014) for light-rain events. We speculate that the mechanism behind this difference in the Kain–Fritsch scheme is similar to those described by Lee et al. (2011). What Lee et al. (2011) describe is that activating the Kain–Fritsch scheme in the inner domain (as in KFMODS_INNER) increases the vertical motion and lower-tropospheric moisture during heavy-rain events when compared with relying on the explicit microphysics (as in KFMODS), improving the representation of rainfall totals for those events. Activating the KFMODS scheme does improve precipitation in the inner (2 km) domain. The middle (10 km) domain provides a better representation of the island average rainfall but does not have the grid spacing needed to resolve the sharp precipitation gradient that is observed over the island. The Tiedtke CP scheme was also used and better represented the gradient of dry-season precipitation in Puerto Rico when activated in the inner domain while making little to no difference during the wet season. Although such case studies of individual events as in Lee et al. (2011) or Sun and Barros (2014) were not the focus of this study, they are recommended for future research because the interaction between microphysics and CP schemes that Lee et al. (2011) demonstrated for the Kain–Fritsch CP scheme is not reflected by the Tiedtke CP scheme in this region. The differing responses may be associated with differences in scale-separation assumptions between the Tiedtke and Kain–Fritsch schemes.
In addition to the CP scheme, the choice of nudging approach also influences the representation of precipitation in the high-resolution domain. In most cases, applying the analysis nudging in both the middle and outer domains improved the representation in the inner domain. This is consistent with Bowden et al. (2012, 2013) and Otte et al. (2012) and is reflected in the quantitative analysis of total monthly precipitation. What has not been highlighted in previous high-resolution climate-modeling studies is the sensitivity of WRF precipitation to the interaction of both nudging and CP scheme for a tropical location at gray-zone resolutions. Since applying nudging at different levels (no nudging, or having nudging active in one or more domains) with different CP schemes does not have the same effect on simulated precipitation, the interaction between the nudging approach and CP scheme can have a strong influence on the simulated precipitation. Care should be taken in future efforts to consider this interaction when using WRF for high-resolution climate modeling.
The distinct differences between CP schemes and the interaction with analysis nudging could have implications for using WRF for very high resolution climate change simulations (<5-km grid spacing). The differences between these simulations imply that the projected change with regard to precipitation can vary widely given choices of parameterization scheme and nudging approach. This was shown in a small experiment here with WRF and different CP schemes. This aspect of uncertainty in regional climate modeling is not well represented in current regional climate-modeling efforts, however, because the focus remains on differences between regional and global climate models rather than on the structural differences that can exist between individual simulations of a single RCM. Therefore, the potential influence on the uncertainty for climate change projections from a regional model is worth exploring given the differences found here in both a historical and climate change context.
As mentioned previously, this study focused solely on the influence of analysis nudging and CP scheme. This study did not change any other parameterization schemes in WRF or use spectral nudging in this region. Given the potential influence on precipitation in this region, it is recommended as an avenue of future work to consider the influence of other parameterization schemes and spectral nudging on the WRF-simulated climate in Puerto Rico. In addition, MPE and R-2 are created using modeling or algorithms that combine radar and station gauge precipitation. They are subject to their own errors that likely had some influence in this study. Given that the focus here was on the eventual application of WRF for use in climate change simulations, the analysis here focused on monthly and annual time scales. We acknowledge that there are challenges in representing the diurnal cycle of convection (e.g., Hohenegger et al. 2015). Therefore, this area is also suggested as an avenue of future research for tropical regions. Last, the focus of this study was on 2010. Therefore, there is no evaluation of the interannual variability of WRF-simulated precipitation. Although this study did evaluate the frequency of heavy-rain events in 2010, an avenue of future study should include an analysis of the frequency of heavy-rain events over multiple years. As mentioned previously, this would be recommended given the discrepancy present between CP schemes shown in this study. Although the results of this study suggest several avenues of future study, for Puerto Rico it is recommended to use the modified Kain–Fritsch CP scheme, active at convective-permitting scales, with analysis nudging applied on the middle and outer domains.
The study presented here was funded by the U.S. Department of the Interior Southeast Climate Science Center (USGS Cooperative Agreement G13AC00408). We thank the Renaissance Computing Institute for providing the supercomputing resources that were required for the WRF simulations. We also thank the anonymous reviewers for their feedback and suggested improvements to this article. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. government.