1. Introduction
Florida has unique and highly variable precipitation patterns because of its extensive coastline and mid- to low-latitude peninsular location (Sun and Furbish 1997). In turn, precipitation variability has a major influence on demand and availability of water. Thus, skilled weekly, seasonal, annual, and multidecadal precipitation forecasts and/or predictions would be useful to help water resource managers provide a more reliable, environmentally sound supply of water.
In the Tampa Bay region of Florida, understanding and responding to precipitation variability is particularly important to developing a reliable water supply (Schmidt et al. 2004). Tampa Bay Water (TBW) provides water for more than 2 million residents in the area through a diverse regional water supply system that includes a surface water treatment plant and three surface sources, six groundwater treatment plants, 13 regional well fields, a seawater desalination plant, and almost 200 miles of pipeline. Groundwater provides the least expensive source of water for the region, but pumping is managed so that the 12-month running average does not exceed a permitted value intended to protect wetlands and lakes from environmental harm. Surface water sources are more expensive, and withdrawals are limited by permit to times when the rivers are flowing above flow thresholds in order to protect the ecological integrity of the river systems. Desalinated water, the most expensive source to treat, is also constrained by regulatory, water-quality operational and economic considerations. Tampa Bay Water uses a suite of statistical and physically based hydrologic models to analyze hydrologic conditions and estimate water supply availability to ensure that water demand for the region can be met at the least cost and with minimal adverse environmental impacts.
There are three planning time scales important to Tampa Bay Water: 1) a short-term (weekly to monthly) operational time scale over which Tampa Bay Water must allocate supply among the various water sources to meet immediate demands, 2) a medium-term (1–24 months) planning period over which Tampa Bay Water must allocate supply distributions and maintain reservoir storage to meet expected seasonal demands and to estimate annual costs in order to set water rates for the coming year, and 3) a long-term (decades) planning period over which Tampa Bay Water must determine when new major water supplies must be brought on line to meet future demands. In these planning analyses, recently observed weather patterns or historical climatology are currently used rather than quantitative climate forecast–predictions. The overarching hypothesis underlying this research is that reliability can be improved and risk can be reduced by incorporating climate model predictions into water resources planning process in the Tampa Bay region.
Recent climate modeling improvements have resulted in an enhanced ability to simulate many aspects of climate variability and extremes. However, general circulation models (GCMs) have been found to have too-coarse resolution to resolve small-scale atmospheric circulation (McGregor 1997) and they are characterized by systematic errors and limitations in accurately simulating regional climate conditions (Easterling et al. 2000). Hydrologic applications of climate model predictions often require data (precipitation, temperature, and relative humidity) at a high spatial and temporal resolution (Hewitson and Crane 1996; Enke and Spekat 1997; Yu et al. 1999; Wilby et al. 2000; Leander et al. 2008). This need has resulted in recent attention to improving downscaling techniques for regional applications and evaluations.
Dynamical downscaling uses physically based regional climate models (RegCMs) to translate the large-scale predictions from a GCM into physically consistent, higher resolution predictions (Murphy 1999; Schmidli et al. 2006). Recently it has been shown that, because it represents physical processes at a higher resolution, dynamical downscaling may have advantages over statistical downscaling in the simulation of extremes (Christensen and Christensen 2003, 2004; Pal et al. 2004; Frei et al. 2006; Fowler et al. 2007b). Furthermore, several studies have suggested that downscaling with physically based high-resolution mesoscale RegCMs more realistically predicts precipitation structures over regions with complex terrain and land use [Washington Olympic Mountains (Colle and Mass 1996), Colorado mountain region (Gaudet and Cotton 1998), Pacific Northwest coastal region (Colle et al. 1999), Phoenix metropolitan area (Zehnder 2002), and Great Lakes region (Zhong et al. 2005)].
Fowler et al. (2007a) pointed out that the methodologies by which downscaling skill is evaluated must be tuned to the particular catchment and application being considered rather than using standard assessment criteria. Physically based dynamical downscaling methods must be examined for diverse regions with high climate variability (Hong 2003) so that the strengths and weaknesses of dynamical downscaling can be better understood (Wang et al. 2004).
In this study, the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5; Grell et al. 1994) was set up for the Tampa Bay region to evaluate its ability to reproduce observed spatiotemporal variability in precipitation important for hydrologic modeling applications. The MM5 dynamical model has been widely applied in a variety of fields in historical and future climate studies. Various case studies have been conducted to examine MM5 parameter sensitivity analysis (Colle and Mass 2000; Colle et al. 2000; Chen and Dudhia 2001a; Kotroni and Lagouvardos 2001; Yang and Tung 2003), MM5 performance assessment (Colle et al. 1999, 2003; Chen and Dudhia 2001b; Westrick et al. 2002; Hong 2003; Zhong and Fast 2003; Boo et al. 2004; Zhong et al. 2005), and model modifications for performance improvement (Chen and Dudhia 2001a; Zehnder 2002). For example, Colle and Mass (2000), Colle et al. (1999), and Colle et al. (2000) verified precipitation forecasts from MM5 for cool seasons over the Pacific Northwest region at 36-, 12-, and 4-km horizontal resolution for the February 1996, December 1996–April 1997, and November 1997–March 1999 time periods. They observed that incorporating high horizontal resolution (e.g., 4 km) in MM5 did not guarantee improvement of precipitation prediction skill for the Pacific Northwest, though noticeable improvement in bias occurred as the resolution was increased from 36 to 12 km.
When GCM predictions are used as initial and boundary conditions for RegCMs, biases contained in GCM fields are propagated to the RegCM scale during the downscaling process. Applications of dynamical downscaling in the literature have consistently shown that outputs from RegCMs cannot be used in impact studies without first applying a bias correction to observations (Fowler et al. 2007a; Lim et al. 2007) because they are subject to systematic biases, particularly for precipitation (Varis et al. 2004)—the dominant variable in most hydrological regimes. Therefore, local-to-regional applications of dynamically downscaled climate predictions typically use bias-corrected results (Wood et al. 2004; Fowler and Kilsby 2007; Fowler et al. 2007a).
The purpose of this paper is to quantitatively evaluate the ability of MM5 to reproduce observed spatiotemporal variability of precipitation needed to drive hydrologic models in the Tampa Bay region over a 23-year period (1986–2008). This period was chosen because it encompasses the time period (1989–1998) for which Tampa Bay Water has calibrated its hydrologic models. The long-term goal of this effort is to assess the utility of using MM5 to downscale GCM hindcasts, forecasts, and/or climate change scenarios for improving water management decisions in the Tampa Bay region. However, in this study we use the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis data (Kalnay et al. 1996) as a surrogate for GCM predictions for specifying the initial and boundary conditions for MM5. Use of the NCEP–NCAR reanalysis data is advantageous because of the availability of long-term daily precipitation and temperature data, which is not always archived for GCM predictions. Furthermore, use of the NCEP–NCAR reanalysis data removes the confounding factors of potential biases related to GCM process simulation, and thus provides a more objective measure of the skill of the MM5 downscaling accuracy (Maurer and Hidalgo 2008; Maurer et al. 2010). The next section briefly describes the study area and data used for climate modeling and verification. Model configuration methodologies employed in the study are described in section 3, and results are discussed in section 4. Finally, the main conclusions are summarized and the future implications of this research are discussed in section 5.
2. Study area and data collection
Tampa Bay is the second largest Gulf Coast estuary and the largest estuary in Florida. The bay covers about 1031 km2, receives freshwater from a 6583 km2 watershed, and encompasses most of Pinellas, Hillsborough, and Manatee counties and portions of Pasco, Polk, and Sarasota counties (Xian et al. 2007). Within the Tampa Bay watershed, four major sources of surface water (the Hillsborough, Alafia, Little Manatee, and Manatee rivers) flow into the bay. This study focused on the Hillsborough (1850 km2) and Alafia (1380 km2) watersheds (see Fig. 1).
Map of study area and rainfall stations used for bias correction and cross validation.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
Map of study area and rainfall stations used for bias correction and cross validation.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
Map of study area and rainfall stations used for bias correction and cross validation.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
Daily precipitation data from 53 observations from several different agency precipitation networks [41 Tampa Bay Water, six National Oceanic and Atmospheric Administration (NOAA), four Southwest Florida Water Management District (SWFWMD), and two U.S. Geological Survey (USGS)] were utilized to evaluate the MM5 precipitation simulations (Fig. 1 and Table 1). The observation density over the Hillsborough and Alafia River watersheds is approximately 1 station per 100 km2, though the distribution of stations is irregular. The data were retrieved from the rainfall data manager Web database (http://gis.tampabaywater.org/rainfall/) maintained by Tampa Bay Water.
Summary of Tampa Bay region rain gauge data.
NCEP–NCAR global reanalysis data from 1986 to 2008 (Kalnay et al. 1996; Kistler et al. 2001) were utilized as the initial and boundary conditions for the MM5 model. The NCEP–NCAR global reanalysis dataset is a joint product from the National Centers for Environmental Prediction and the National Center for Atmospheric Research that was created by assimilating observations and global climate model predictions to provide a gridded dataset representing the retrospective state of the earth’s atmosphere over time. The resolution of the global reanalysis dataset is a 2.58° × 2.58° grid with 28 vertical sigma levels.
3. Methodology
a. MM5 modeling
MM5 was run to predict precipitation over a 1701 × 1620 km2 domain at 27 × 27 km2 gridcell resolution and a nested 675 × 729 km2 domain at 9 × 9 km2 gridcell resolution (Fig. 2). Predictions were output at a 6-h temporal resolution continuously over the 23-year period from 1986 to 2008, using University of Florida high-performance computers (UFHPC) with massively parallel architecture and distributed-memory codes. NCEP–NCAR reanalysis data were used as initial and boundary conditions for the outer domain, with boundary conditions updated on the outer grid every 6 h. There was no additional nudging or adjustment in these runs.
MM5 domain configuration: domain1 (1701 × 1620 km2 at 27 × 27 km2 resolution) and domain2 (675 × 729 km2 at 9 × 9 km2 resolution).
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
MM5 domain configuration: domain1 (1701 × 1620 km2 at 27 × 27 km2 resolution) and domain2 (675 × 729 km2 at 9 × 9 km2 resolution).
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
MM5 domain configuration: domain1 (1701 × 1620 km2 at 27 × 27 km2 resolution) and domain2 (675 × 729 km2 at 9 × 9 km2 resolution).
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
The physics configuration used in the present work was set based on sensitivity analyses by Hernandez and Jones (2010, manuscript submitted to J. Geophys. Res.) and is defined as follows. The radiation scheme was set to use the NCAR Community Climate Model, version 2 (CCM2) (Kiehl et al. 1996). Here the annual variability of insolation at the top of the atmosphere depends on the solar constant, zenith angle, and eccentricity. The CCM2 option evaluates longwave and shortwave fluxes, as well as heating rate in multispectral bands, where clouds and aerosols absorb and/or scatter radiation. For cumulus parameterization, the Grell scheme (Grell et al. 1994) was employed. In this simple scheme there is no mixing in the clouds except at the top and bottom because of downdraft and updraft atmospheric processes. The explicit moisture was set to the simple ice scheme (Grell et al. 1994), where cloud water below 0°C is treated as cloud ice and rain is treated as snow. Under these moisture physics, rain or snow vertical distribution and speed is controlled by aerosol size, which is a function of accretion (conversion of cloud to rain or ice to snow). The planetary boundary layer (PBL) physics was set to a nonlocal vertical diffusion scheme (Hong and Pan 1996) employed in the NCEP Medium-Range Forecast Model, which realistically represents large eddy fluxes and their evolution in the atmospheric well-mixed layer. The surface five-layer soil temperature model (Dudhia 1996) was used for land surface processes. MM5 was configured to predict atmospheric conditions at 21 pressure levels between 100 000 and 20 000 Pa, and all simulations were performed in a two-way nesting communication. The 25-category USGS 1999 land use dataset with 1-km horizontal spacing was used for the entire 1986–2006 simulation period (Grell et al. 1994).
b. Bias correction
The simulated and observed CDFs for September for station 36 (Plant City rainfall) and a schematic of the bias-correction procedure are shown in Fig. 3. This station was chosen as a representative example because of its comparatively long observation record. The predicted versus observed CDFs for the other 52 stations show similar behavior. The results of the bias-corrected daily MM5 predictions were evaluated separately for each month of each year independently using a cross-validation procedure that sequentially excluded the observed data for that month and year in the computation of the observed CDFs used in the bias correction. Thus, each month of each year was bias corrected using an observed dataset that did not include the data from that month and year.
Example of CDF for simulated results (domain2; September) and observations at station 36 (Plant City rain gauge; September), and CDF mapping methodology. Semi-log plots with respect to precipitation amount are shown for clarity.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
Example of CDF for simulated results (domain2; September) and observations at station 36 (Plant City rain gauge; September), and CDF mapping methodology. Semi-log plots with respect to precipitation amount are shown for clarity.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
Example of CDF for simulated results (domain2; September) and observations at station 36 (Plant City rain gauge; September), and CDF mapping methodology. Semi-log plots with respect to precipitation amount are shown for clarity.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
c. Spatial correlation structure
Geostatistical methods were used to describe and model the spatial correlation structure of both the observed and simulated rainfall fields and to interpolate the bias-corrected precipitation predictions over the Alafia and Hillsborough River watersheds. Details of geostatistical methods used in this research are described in Goovaerts (1997, 125–152) and Isaaks and Srivastava (1989, 278–313).
1) Variogram modeling
2) Point kriging
The accuracy of the kriged estimates was assessed through cross validation by sequentially comparing the actual observed daily rainfall at each of the 53 rainfall stations to the kriged estimate obtained by ignoring the observation at that station and using only the bias-corrected predicted values from the remaining 52 stations.
d. Error statistics
Where Pi and Oi are the estimate and the observation for day or month i, and N is the total number of estimates.
Note that if the kriging estimator is performing well (i.e., producing unbiased estimates with errors well predicted by the kriging variance), the normalized kriging errors should have a mean error of approximately zero and a root-mean-square error of approximately one.
4. Results and discussion
a. MM5 modeling and bias-correction results
Daily and monthly precipitation totals predicted by the MM5 model at 9-km grid spacing were evaluated at the 53 rain gauge locations in the Tampa Bay region for the 23-year period from 1986 to 2008 using the cross-validation procedure described in section 3. Table 2 presents the ME and RMSE for the daily and monthly raw MM5 results, as well as the bias-corrected MM5 predictions, calculated over the 53 stations separately for each calendar month. The raw daily and monthly MM5 precipitation totals are generally positively biased, particularly during the dry-season months (October–May), and the RMSEs of the raw predictions are larger than the standard deviation of long-term observed daily rainfall for all months. Furthermore, the raw model predictions produced too many wet days with very low rainfall (i.e., below the minimum 0.25 mm recorded by the rain gauges). CDF mapping effectively removes the bias in the daily and monthly predictions for all months (average reduction 95.9% and 95.7%, respectively), reduces the frequency of wet days with very low rainfall, and reduces the RMSEs of the daily and monthly predictions (average reduction 12.7% and 32.6%, respectively).
Daily and monthly mean and standard deviation of long-term observations and error statistics (ME and RMSE) for daily and monthly total precipitation for the MM5 results at 9-km resolution. Statistics are calculated monthly over all 53 stations for the raw and bias-corrected predictions.
In addition to the daily precipitation totals, day-to-day precipitation patterns are important for most hydrologic applications. Hence, daily transitions between wet and dry states were calculated for both the observed data and cross-validated bias-corrected predictions using the first-order transition probability (FTP; Haan 1977). The observed FTPs, raw simulated FTPs, and bias-corrected FTPs for each month are shown in Fig. 4. As discussed previously, the raw MM5 results overestimate the frequency of low-rainfall events. However, the bias-corrected transition probabilities match the observed dry–wet and wet–wet transition probabilities well (R2 of 0.81 and 0.68, respectively) with higher probabilities of transitioning to wet states in the wet season from June to September, as expected.
Observed vs (a) raw simulated and (b) bias-corrected results of first-order transition probabilities for (left) dry to wet day (P_01) and (right) wet to wet day (P_11) for each month. Dashed ellipses enclose the dry-season months from October to May, and solid ellipses enclose the wet-season months from June to September. Here R2 and ME for each case are shown on each figure.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
Observed vs (a) raw simulated and (b) bias-corrected results of first-order transition probabilities for (left) dry to wet day (P_01) and (right) wet to wet day (P_11) for each month. Dashed ellipses enclose the dry-season months from October to May, and solid ellipses enclose the wet-season months from June to September. Here R2 and ME for each case are shown on each figure.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
Observed vs (a) raw simulated and (b) bias-corrected results of first-order transition probabilities for (left) dry to wet day (P_01) and (right) wet to wet day (P_11) for each month. Dashed ellipses enclose the dry-season months from October to May, and solid ellipses enclose the wet-season months from June to September. Here R2 and ME for each case are shown on each figure.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
Figure 5 plots the decomposition of the MSE of the raw and bias-corrected daily precipitation totals for each month. This figure shows that bias correction significantly improves the prediction of the mean and variance of precipitation for each month, but does not significantly improve the correlation of actual daily predicted and observed precipitation. Figure 6 plots average monthly precipitation and the standard deviation of the monthly precipitation over the study period for the raw, bias-corrected, and observed monthly precipitation totals. This figure confirms that CDF mapping effectively eliminates the bias in the average monthly MM5 predictions and, to a lesser extent, improves the standard deviation of the monthly precipitation totals over the study period.
Contributions of mean error (dash-dot line), variance error (dash line), and correlation error (solid line) to overall MSE for raw (darker lines) and bias-corrected (lighter lines) daily precipitation by month.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
Contributions of mean error (dash-dot line), variance error (dash line), and correlation error (solid line) to overall MSE for raw (darker lines) and bias-corrected (lighter lines) daily precipitation by month.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
Contributions of mean error (dash-dot line), variance error (dash line), and correlation error (solid line) to overall MSE for raw (darker lines) and bias-corrected (lighter lines) daily precipitation by month.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
Comparison of mean monthly precipitation and standard deviation of monthly precipitation over the study period by month for raw MM5 results, bias-corrected MM5 results, and point observations.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
Comparison of mean monthly precipitation and standard deviation of monthly precipitation over the study period by month for raw MM5 results, bias-corrected MM5 results, and point observations.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
Comparison of mean monthly precipitation and standard deviation of monthly precipitation over the study period by month for raw MM5 results, bias-corrected MM5 results, and point observations.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
As noted above, the CDF mapping bias-correction technique is designed to improve the fit of the MM5 predictions to historic climatology, but does nothing to improve the daily pattern of rainfall, which is still driven by the climate model physics. Therefore, it is possible that in cases where the raw results underpredict mean climatology, bias correction may increase the RMSE of the predictions by increasing rainfall amounts and thus increasing errors on days when precipitation timing is off. In fact, Table 2 shows that this occurs in August when the raw results underpredict mean daily rainfall by 1.50 mm and the RMSE increases slightly from 19.72 to 20.31 mm for the bias-corrected results. Similarly, for August, the raw MM5 results underpredict mean monthly rainfall by 32.56 mm and the RMSE increases from 111.01 to 116.23 mm for the bias-corrected results. Furthermore, Fig. 5 shows that although the mean and variance of August daily precipitation improves substantially, the correlation of August daily rainfall degrades slightly. However, for all other months correlation improves slightly, and to a larger extent in dry months (January through May) when the raw MM5 results significantly overpredict rainfall.
The spatial distribution of the mean daily precipitation for the dry (October–May) and wet (June–September) seasons are mapped in Fig. 7 for the raw MM5 results, the bias-corrected MM5 results, and the point observations. This figure shows that raw MM5 results produce a mean daily precipitation field that is much higher in magnitude than the observations in the dry season (i.e., positively biased) and much smoother in space than the observations for both the dry and wet seasons. Bias correction improves both the magnitude and the spatial distribution of the average daily precipitation for both the wet and dry seasons. It should be noted that the bias-correction technique used here maps the predicted CDF obtained from the 1986–2008 simulation to the observed CDF from the entire time series of record for each station (which is variable; see Table 1). This discrepancy in period of record results in the relatively minor differences between the observed and bias-corrected spatial distribution of mean precipitation fields calculated over the 1986–2008 time period shown in Fig. 7.
The spatial distribution of averaged daily precipitation (mm) for (top) dry (January, February, March, April, May, October, November, and December) and (bottom) wet seasons (June, July, August, and September) for (left) raw MM5 results, (middle) bias-corrected MM5 results, and (right) observations.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
The spatial distribution of averaged daily precipitation (mm) for (top) dry (January, February, March, April, May, October, November, and December) and (bottom) wet seasons (June, July, August, and September) for (left) raw MM5 results, (middle) bias-corrected MM5 results, and (right) observations.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
The spatial distribution of averaged daily precipitation (mm) for (top) dry (January, February, March, April, May, October, November, and December) and (bottom) wet seasons (June, July, August, and September) for (left) raw MM5 results, (middle) bias-corrected MM5 results, and (right) observations.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
Figure 8 plots the raw, bias-corrected, and observed total annual precipitation over the study period. This figure shows that the bias-corrected MM5 results reproduce the long-term mean annual precipitation very well and follow the observed temporal pattern of total annual rainfall over the study period fairly well, but significantly overestimate the interannual variability over the study period. Table 2 and Figs. 4–8 indicate that while the bias-corrected MM5 results successfully reproduce the historical climatology over the study area (i.e., long-term mean and variance of daily and monthly precipitation totals and daily transition probabilities), the prediction of the actual time series of daily, monthly, and annual totals show significant errors, even after the results are bias corrected. Further improvement in day-to-day predictability will require improving the climate model physics, parameterization, and/or boundary condition used in MM5.
Annual total precipitation for raw MM5 results, bias-corrected MM5 results, and observations. Means and standard deviations of annual precipitation over the study period for each case are indicated in mm yr−1.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
Annual total precipitation for raw MM5 results, bias-corrected MM5 results, and observations. Means and standard deviations of annual precipitation over the study period for each case are indicated in mm yr−1.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
Annual total precipitation for raw MM5 results, bias-corrected MM5 results, and observations. Means and standard deviations of annual precipitation over the study period for each case are indicated in mm yr−1.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
The accuracy of the MM5 bias-corrected historical simulation results reported here are similar to other results reported in the literature. Zhong et al. (2005) ran MM5 for the Great Lakes region at 4-km resolution for the 2002/03 winter and 2003 summer season and presented the bias score and threat score, which indicate how well the model predicts the frequency of occurrences of a given precipitation class amount. These statistics, although helpful to assess model skill, offer little information about the actual precipitation prediction errors that are of interest when using the results to make temporally specific hydrologic predictions. However, from Zhong et al.’s (2005) Fig. 6, it appears that the MM5 predictions consistently overestimated rainfall amounts for each month simulated, with errors ranging from approximately 20 mm for December 2002 to 100 mm for June 2003.
Similarly, Schoof et al. (2009) presented results of dynamically downscaled seasonal precipitation hindcasts for the warm months (March–September) for 15 years from 1987 to 2001 over the southeastern United States using the Nested Regional Spectral Model (NRSM) developed by The Florida State University and the Center for Ocean–Atmospheric Prediction Studies. According to their results, the averaged RMSE for bias-corrected monthly total precipitation for the warm season from March to September over Florida was approximately 93.4 mm, similar to the average bias-corrected monthly RMSE of 83.3 mm found in this study for the Tampa Bay region.
b. Precipitation spatial correlation structure
Figure 9 compares the variograms for bias-corrected daily predictions and observed data calculated separately for each month, assuming spatial stationarity and isotropy within each month and temporal stationarity over the study period. These figures show that the bias-corrected MM5 results successfully reproduce the seasonal patterns of spatial rainfall variance in the Tampa Bay region, with higher spatial variances in the wet season (June–October) when convective storms dominate and lower spatial variances in the dry season (November–May) when frontal systems dominate. However, the figure also shows that MM5 consistently overpredicts the spatial correlation of the rainfall fields, with the variograms for the simulated data approaching the variogram sill (or spatial rainfall variance) more slowly than the observed data.
(left) Observed and (right) bias-corrected MM5 variograms of daily precipitation for each month: (a) Jan–Jun and (b) Jul–Dec. The empirical variograms are represented by the symbol × and the dashed lines represent estimated exponential variogram models. Note the change in y axis scale between the June–September (wet) and October–May (dry) periods.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
(left) Observed and (right) bias-corrected MM5 variograms of daily precipitation for each month: (a) Jan–Jun and (b) Jul–Dec. The empirical variograms are represented by the symbol × and the dashed lines represent estimated exponential variogram models. Note the change in y axis scale between the June–September (wet) and October–May (dry) periods.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
(left) Observed and (right) bias-corrected MM5 variograms of daily precipitation for each month: (a) Jan–Jun and (b) Jul–Dec. The empirical variograms are represented by the symbol × and the dashed lines represent estimated exponential variogram models. Note the change in y axis scale between the June–September (wet) and October–May (dry) periods.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
An exponential variogram model was fit to each observed and simulated precipitation variogram using least squares regression. Note that the variability at distances smaller than the typical sample spacing, including measurement error, was observed to be negligible in most cases, so C0 was assumed to be zero. The monthly variogram sills (or spatial rainfall variance) C and the monthly effective ranges (distance over which spatial correlation in precipitation drops by 95%), A, are plotted in Fig. 10 for both the observed and simulated precipitation variogram models. This figure reinforces the conclusion that the bias-corrected MM5 results successfully reproduce the seasonal patterns of spatial precipitation variance (i.e., the C parameters are quite close for the observed and simulated variograms). However, effective ranges (A parameters) for the simulated variograms are consistently higher than the effective ranges for the observed data, indicating that the bias-corrected MM5 daily precipitation fields are spatially correlated over longer distances (i.e., smoother) than the observed data.
Comparison of (a) parameter A and (b) parameter C for observed and simulated variogram models by month. Dashed lines and values in (a) represent the annual averaged parameter A of observed and simulated results.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
Comparison of (a) parameter A and (b) parameter C for observed and simulated variogram models by month. Dashed lines and values in (a) represent the annual averaged parameter A of observed and simulated results.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
Comparison of (a) parameter A and (b) parameter C for observed and simulated variogram models by month. Dashed lines and values in (a) represent the annual averaged parameter A of observed and simulated results.
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
c. Kriging results
The bias-corrected point precipitation predictions were kriged over the study area to produce the spatially distributed precipitation fields needed to run the distributed hydrologic model. To preserve the observed spatial correlation, the monthly variograms γ(h) estimated from the observed data were used rather than the variograms estimated from the simulated data. Spatially distributed precipitation totals were created for each day over the 23-year period and then summed to get monthly totals. Daily and monthly kriged values were cross validated at each rain gauge using the procedure described in section 3. Note that the point-kriged estimates of the precipitation distribution did not use the bias-corrected prediction at the cross-validation point, but incorporated bias-corrected predictions for all other rain gauge locations.
Table 3 compares the daily and monthly point-kriging and normalized point-kriging estimates. These data show that point kriging the bias-corrected daily precipitation fields over the watersheds reproduced the observed rainfall with a ME ranging from −0.22 mm in September to 0.65 mm in August and an average RMSE ranging from 9.02 mm in January to 17.72 mm in September over the 53 stations. The ME and RMSE for the monthly total precipitation fields ranged from −5.89 mm in January to 18.46 mm in July and from 43.48 mm in January to 127.52 mm in September, respectively. The average normalized point-kriging ME was 0.01 for daily and 0.06 for monthly results, indicating that the kriging procedure successfully produces unbiased results. The average normalized point-kriging RMSE was 1.04 for daily and 1.27 for monthly results, indicating that the kriging procedure accurately predicted the uncertainty of its estimates.
Kriging error and normalized kriging error statistics (ME and RMSE) for daily and monthly total point-kriged precipitation distributions. Statistics are calculated for over all 53 stations.
Interestingly, the error statistics in Table 3 indicate that the point-kriging results that use bias-corrected data from the other 52 rain stations, but require no data at all at the location being estimated, improve the average RMSE for daily and monthly precipitation predictions over direct bias correction using local gauge data by 38.1% and 8.9%, respectively. The kriging methodology showed most significant reductions over the local bias-correction methodology during the dry season (monthly RMSE reduced by 29.5% in December, 32.4% in January, and 21.4% in February) when the spatial variability of precipitation is comparatively low. This result supports the methodology used by Colle et al. (1999, 2000), who evaluated MM5 predictions in the Pacific Northwest by comparing point observations to corresponding simulations estimated by interpolating the four simulated grid results surrounding the observation.
Additionally, the bias-corrected point precipitation predictions were kriged to produce daily precipitation totals at the centroids of the 172 surface catchments encompassed in the Tampa Bay Water Integrated Hydrologic Model (IHM). Figure 11 shows maps of precipitation volume for observed versus bias-corrected MM5 estimates kriged over the centroids of the 172 surface catchments. Three wet-season precipitation events are presented as representative examples of events in months with the largest daily RMSE (see Table 2) from years that showed relatively good (2000), average (1990), and relatively poor (1995) annual total rainfall predictions (see Fig. 8). Figure 11 shows that while the range of precipitation volumes and degree of spatial variability over the domain is fairly well simulated for all these events, the precise spatial distribution of precipitation is subject to error, as expected by the magnitude of the kriging error statistics shown in Table 3. As mentioned previously, further improvement in day-to-day predictability will require improving the climate model physics, parameterization, and/or boundary condition used in MM5.
The spatial distribution of precipitation volume (in millimeters per event) for (right) observed and (left) bias-corrected MM5 results for three wet-season precipitation events [(top) 2–18 Jul 1990, (middle) 1–7 Aug 1995, and (bottom) 15–21 Sep 2000].
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
The spatial distribution of precipitation volume (in millimeters per event) for (right) observed and (left) bias-corrected MM5 results for three wet-season precipitation events [(top) 2–18 Jul 1990, (middle) 1–7 Aug 1995, and (bottom) 15–21 Sep 2000].
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
The spatial distribution of precipitation volume (in millimeters per event) for (right) observed and (left) bias-corrected MM5 results for three wet-season precipitation events [(top) 2–18 Jul 1990, (middle) 1–7 Aug 1995, and (bottom) 15–21 Sep 2000].
Citation: Journal of Hydrometeorology 12, 6; 10.1175/2011JHM1309.1
These results indicate that the methodology presented here most likely does not have sufficient accuracy to produce spatially distributed predictions of daily rainfall useful for weekly-to-seasonal water resource operations decisions. However, the method should produce spatially distributed rainfall predictions with sufficient realism in the daily, seasonal, and interannual patterns to be useful for distributed hydrologic modeling applications for multidecadal planning decisions in the Tampa Bay region. The daily kriged precipitation fields could be used directly as a best estimate of the actual spatial distribution of the daily precipitation fields needed to drive the hydrologic models in a deterministic manner. Alternatively, the methodology could be used in a conditional simulation algorithm (Deutsch and Journel 1998) to generate an ensemble of possible daily precipitation fields that honor the bias-corrected precipitation fields at observation points but represent equally probable precipitation distributions that honor the spatial structure of the precipitation field (i.e., variogram) at model nodes that do not coincide with bias-correction points.
5. Conclusions
This study quantitatively evaluated the ability of the MM5 model to downscale NCEP–NCAR reanalysis data to reproduce precipitation patterns over the Tampa Bay region for the 23-year period from 1986 to 2008. Data from 53 rainfall stations distributed over the study area were used to evaluate model predictions.
Raw MM5 model results were positively biased, significantly overestimating the mean of daily and monthly precipitation totals. Bias correction using a CDF mapping technique effectively removed the bias in the mean daily, monthly, and annual precipitation, and improved the root-mean-square error in the daily, monthly, and annual rainfall totals over the study area. Decomposition of the mean square error of the raw and bias-corrected daily predictions into bias, variance, and correlation terms showed that bias correction significantly improved the prediction of the temporal mean and variance of precipitation, but the correlation between daily precipitation predictions and daily precipitation observations was not improved after bias correction. These ranges of MM5 daily and monthly precipitation prediction errors are consistent with previous studies; however, they call into question the utility of using MM5 (at least as configured in this study) to downscale GCM climate predictions for weekly-to-seasonal water resource operation and planning decisions.
After bias correction, MM5 successfully reproduced seasonal patterns of spatial variability in precipitation, with higher spatial variance of daily precipitation over the study area in the wet season when convective storms dominate and lower spatial variance of daily precipitation in the dry season when frontal systems dominate. However, the strength of the spatial correlation of the daily rainfall fields was significantly overestimated throughout the year, with the bias-corrected MM5 precipitation fields showing more spatial regularity than the observed fields. Bias-corrected daily precipitation fields were kriged over the study area using observed semivariograms to produce spatiotemporally distributed precipitation fields over the dense grids needed to drive hydrologic models in the Tampa Bay region. Cross validation at the 53 long-term precipitation gauges showed that kriging reproduced the observed rainfall with average RMSEs lower than the RMSEs of the individually bias-corrected point predictions. These results indicate that although significant error remains in actual daily predictions at point locations, kriging the bias-corrected MM5 predictions over a distributed hydrologic model grid produces spatiotemporally distributed precipitation fields with sufficient realism in the daily, seasonal, and interannual patterns to be useful for multidecadal water resource planning applications in the Tampa Bay region. In the next phase of this work, the kriged bias-corrected MM5 precipitation results for the period 1989–98 will be used to drive Tampa Bay Water’s distributed hydrologic model to quantitatively evaluate the ability of the modeled precipitation fields to reproduce historic hydrologic behavior in the region.
It should be noted that using these bias-corrected MM5 predictions downscaled from the NCEP–NCAR reanalysis data in hydrologic models for multidecadal water resource planning applications provides no real advantage over using the long-term historical climate record since the error associated with the bias-corrected MM5 daily rainfall predictions is on the order of the standard deviation of the long-term daily observations. However, the long-term goal of this research is to evaluate the utility of MM5 for downscaling GCM historical simulations, forecasts, and climate change scenarios for driving hydrologic models and improving water management decisions in the Tampa Bay region. Therefore, future work will produce spatially distributed precipitation estimates in the Alafia and Hillsborough River watersheds from downscaled MM5 predictions that use GCM hindcasts, forecasts, and Intergovernmental Panel on Climate Change (IPCC) scenarios as boundary conditions using the methodology developed here. These precipitation fields will subsequently be used in hydrologic models to predict changes in streamflow, permissible reservoir withdrawals from the streams, and subsequent measures of reservoir reliability, for an ensemble of historical hindcasts and future climate change scenarios.
Acknowledgments
This research was supported by Tampa Bay Water and the University of Florida Water Institute. The authors acknowledge computational resources and support provided by the University of Florida High-Performance Computing Center for the MM5 simulations conducted in this study.
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