Hydrologic Prediction over the Conterminous United States Using the National Multi-Model Ensemble

Kingtse C. Mo Climate Prediction Center, NOAA/NWS/NCEP, College Park, Maryland

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Dennis P. Lettenmaier Department of Civil and Environmental Engineering, University of Washington, Seattle, Washington

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Abstract

The authors analyzed the skill of monthly and seasonal soil moisture (SM) and runoff (RO) forecasts over the United States performed by driving the Variable Infiltration Capacity (VIC) hydrologic model with forcings derived from the National Multi-Model Ensemble hindcasts (NMME_VIC). The grand ensemble mean NMME_VIC forecasts were compared to ensemble streamflow prediction (ESP) forecasts derived from the VIC model forced by resampling of historical observations during the forecast period (ESP_VIC), using the same initial conditions as NMME_VIC. The forecast period is from 1982 to 2010, with the forecast initialized on 1 January, 1 April, 5 July, and 3 October. Overall, forecast skill is seasonally and regionally dependent. The authors found that 1) the skill of the grand ensemble mean NMME_VIC forecasts is comparable with that of the individual model that has the highest skill; 2) for all forecast initiation dates, the initial conditions play a dominant role in forecast skill at 1-month lead, and at longer lead times, forcings derived from NMME forecasts start to contribute to forecast skill; and 3) the initial conditions dominate contributions to skill for a dry climate regime that covers the western interior states for all seasons and the north-central part of the country for January. In this regime, the forecast skill for both methods is high even at 3-month lead. This regime has low mean precipitation and precipitation variations, and the influence of precipitation on SM and RO is weak. In contrast, a wet regime covers the region from the Gulf states to the Tennessee and Ohio Valleys for forecasts initialized in January and April, the Southwest monsoon region, the Southeast, and the East Coast in summer. In these dynamically active regions, where rainfall depends on the path of the moisture transport and atmospheric forcing, forecast skill is low. For this regime, the climate forecasts contribute to skill. Skillful precipitation forecasts after lead 1 have the potential to improve SM and RO forecast skill, but it was found that this mostly was not the case for the NMME models.

Corresponding author address: Kingtse Mo, Climate Prediction Center, NOAA/NWS/NCEP, 5830 University Research Ct., College Park, MD 20740. E-mail: kingtse.mo@noaa.gov

Abstract

The authors analyzed the skill of monthly and seasonal soil moisture (SM) and runoff (RO) forecasts over the United States performed by driving the Variable Infiltration Capacity (VIC) hydrologic model with forcings derived from the National Multi-Model Ensemble hindcasts (NMME_VIC). The grand ensemble mean NMME_VIC forecasts were compared to ensemble streamflow prediction (ESP) forecasts derived from the VIC model forced by resampling of historical observations during the forecast period (ESP_VIC), using the same initial conditions as NMME_VIC. The forecast period is from 1982 to 2010, with the forecast initialized on 1 January, 1 April, 5 July, and 3 October. Overall, forecast skill is seasonally and regionally dependent. The authors found that 1) the skill of the grand ensemble mean NMME_VIC forecasts is comparable with that of the individual model that has the highest skill; 2) for all forecast initiation dates, the initial conditions play a dominant role in forecast skill at 1-month lead, and at longer lead times, forcings derived from NMME forecasts start to contribute to forecast skill; and 3) the initial conditions dominate contributions to skill for a dry climate regime that covers the western interior states for all seasons and the north-central part of the country for January. In this regime, the forecast skill for both methods is high even at 3-month lead. This regime has low mean precipitation and precipitation variations, and the influence of precipitation on SM and RO is weak. In contrast, a wet regime covers the region from the Gulf states to the Tennessee and Ohio Valleys for forecasts initialized in January and April, the Southwest monsoon region, the Southeast, and the East Coast in summer. In these dynamically active regions, where rainfall depends on the path of the moisture transport and atmospheric forcing, forecast skill is low. For this regime, the climate forecasts contribute to skill. Skillful precipitation forecasts after lead 1 have the potential to improve SM and RO forecast skill, but it was found that this mostly was not the case for the NMME models.

Corresponding author address: Kingtse Mo, Climate Prediction Center, NOAA/NWS/NCEP, 5830 University Research Ct., College Park, MD 20740. E-mail: kingtse.mo@noaa.gov

1. Introduction

Atmospheric predictability on seasonal time scales results from slowly varying boundary forcings such as sea surface temperature (SST), snow cover, and soil moisture. As indicated by the early study of Charney and Shukla (1981), such slowly varying forcings strongly impact interannual variability in the tropics. One example is El Niño–Southern Oscillation (ENSO). Most coupled general circulation models (CGCMs) have some success in predicting the SST anomalies (SSTAs) associated with ENSO and its impact in the tropics (Brankovic et al. 1994). In the extratropics, the predictability is lower because of the chaotic nature of the atmosphere. The models may be able to predict some aspects of tropical SSTAs, but many models are unable to capture the downstream impact on precipitation P or surface temperatures T surf over the conterminous United States (CONUS; Shukla 1984; Wang et al. 2011). Furthermore, to the extent that there is predictability, it is seasonally dependent. For the CONUS, the predictability is higher during winter and lower in summer because the teleconnections that link the tropics to the CONUS as well as Rossby wave dynamics are stronger in winter. In contrast, these linkages are weaker during summer, and it is difficult to forecast dominantly convective dynamics, and thus land–atmosphere interactions, during this period.

Yuan et al. (2013) evaluated precipitation and runoff forecasts from the National Centers for Environmental Prediction (NCEP) Climate Forecast System, version 2 (CFSv2). They found that P forecast skill is higher for forecasts initialized in winter and lower in transition seasons. Skill is also higher over the southern states where ENSO has a relatively strong impact. For CFSv2, P forecasts are more skillful than the ensemble streamflow prediction (ESP) P forecasts. However, the skill drops quickly after lead 1 month.

CGCMs have coarse spatial resolutions relative to the heterogeneities of the land surface (e.g., topography, river channel networks, and land cover variations). In part for this reason, unless forecasts are initialized properly, hydroclimate forecasts of soil moisture (SM) and runoff (RO) taken directly from CGCMs are not skillful. Therefore, SM and RO forecasts are commonly performed by using a land surface model such as the Variable Infiltration Capacity (VIC) hydrology model driven by climate forcing (CF) derived from CGCM outputs (e.g., Wood et al. 2002; Wood and Lettenmaier 2006). To minimize the systematic errors of the CGCM outputs, the forcing terms are usually error corrected and downscaled to high spatial resolutions (Luo et al. 2007; Wood et al. 2002; Wood and Schaake 2008) to force a land surface model, which predicts land surface variables such as snowpack, soil moisture, runoff, and evapotranspiration. The error correction removes systematic biases, but it does not correct errors in the CGCM’s representation of interannual variability.

In general, SM and RO are expected to have higher forecast skill than the atmospheric variables because, in addition to the CF, the initial conditions (ICs) also contribute to skill at short leads (Wood and Lettenmaier 2008; Li et al. 2009), much more so than for atmospheric variables. Shukla and Lettenmaier (2011) and Wood and Lettenmaier (2008) quantified the contributions of CF and ICs to seasonal SM and RO forecast skill by comparing two sets of experiments: ESP forecasts, which assume perfect initial conditions but random CF (represented by resampling historic observations in the forecast period), and reverse ESP (rESP), which uses observations for CF (hence, perfect CF forecast skill) but random initial conditions resampled from the model simulation driven by observations. They found that the initial conditions have strong influence at 1-month lead (lead 1 month), whereas as the lead increases, the CF starts to contribute and eventually dominates. For most of the western United States, the initial conditions have a strong influence on forecast skill even after lead 1 month. In contrast, for the wetter climates of the Southeast and Northeast, the influence of ICs decays more rapidly, and improvements in CF can increase the skill of SM and RO forecasts at relatively short leads.

The ESP–rESP comparison is an ideal case designed to provide insights into the relative effects of ICs versus CF skill. Mo et al. (2012b) performed more realistic comparisons of SM forecasts from VIC driven by the CFSv2 daily forecasts (CFSv2_VIC) and ESP (ESP_VIC) forecasts for January and July. Their results were mostly similar to those of Shukla and Lettenmaier (2011). In particular, they found that ESP_VIC forecasts are about as skillful over the western United States as forecasts driven by CFSv2 because of the persistence of SM. For the eastern United States, CFSv2_VIC has higher skill where the P forecasts are skillful. Yuan et al. (2013) showed that climate models (CFSv1 and CFSv2) provide better drought forecasts in comparison to ESP over the central and eastern United States, as well as for arid basins and for forecasts initialized during dry seasons. While error-corrected streamflow directly from CFSv2 provides useful information, Yuan and Wood (2012) found that the error-corrected streamflow forecasts from CFSv2_VIC perform better.

The monthly mean archive of National Multi-Model Ensemble (NMME) forecasts has recently been made available (Kirtman et al. 2014). NMME consists of six models, each with 6–24 ensemble members. For P and T surf, the grand ensemble mean of the NMME members usually has equal or higher skill in comparison to the ensemble mean of individual models (Kirtman et al. 2014). For hydroclimate NMME forecasts of SM and RO, this effect may not so clear because of the strong influence of ICs at shorter lead times. Thus, there are two motivating questions for this paper: 1) If all hydroclimate forecasts based on the NMME members are initialized with the same ICs, does the grand ensemble mean still have higher skill than that of the individual models? and 2) Under what conditions do SM and RO have high (low) skill? Overall, the skill of SM and RO is higher than that of the atmospheric variables. If we are able to understand the predictability of hydroclimate over the CONUS, then we should be able to improve forecast skill by identifying the physical mechanisms that lead to high (low) skill.

2. Data and procedures

In this section, we introduce the following elements: the VIC simulation, driven by forcings derived from observations (section 2a), the NMME archived outputs used to derive forcings for the NMME_VIC experiment (section 2b), the NMME_VIC and ESP_VIC experiments (section 2c), and verification methods (section 2d). We discuss each of these briefly below.

a. VIC simulation

The land surface model used is VIC, version 4.0.6 (Liang et al. 1994). We ran the model in water balance mode (meaning that effective surface temperature is taken to be equal to surface air temperature, rather than iterating for energy balance closure) with a spatial resolution of 0.5° over the CONUS. We ran the model with gridded forcings derived from observations following the procedures outlined in Wood and Lettenmaier (2006) from 1 January 1979 to 31 December 2011, with the initial conditions on 31 December 1978 taken from the University of Washington’s operational Surface Water Monitor (SWM) (www.hydro.washington.edu/forecast/monitor). This run is labeled as VIC(SIM). Monthly mean SM and RO taken from VIC(SIM) were used for verification. The initial conditions for forecast experiments were also taken from this run. A longer simulation from 1920 to 2010 taken from SWM was used for diagnostic purposes.

b. NMME

The climate forcings for NMME_VIC were derived from monthly mean T surf and P forecasts from the NMME hindcasts from 1982 to 2010 for January, April, July, and October. There are a total of 6 models in the NMME, of which Canadian Meteorological Centre Third Generation Coupled Global Climate Model (CanCM3) (CMC1), and Fourth Generation Coupled Global Climate Model (CanCM4) (CMC2), Geophysical Fluid Dynamics Laboratory (GFDL), and National Aeronautics and Space Administration [NASA; Global Modeling and Assimilation Office (GMAO) model] have 10 ensemble members each. The National Center for Atmospheric Research (NCAR) model has 6 ensemble members, while CFSv2 has a total of 24 members, of which 16 ensemble members were used. Archived CFSv2 seasonal hindcasts were performed every 5 days from 1 January 1982 to 27 December 2010. On each day, four forecast runs were initialized at 0000, 0600, 1200, and 1800 UTC of that day. Including more members is not likely to increase forecast skill (Kumar et al. 2001). We will use forecasts issued on 1 January as an example. The initial forecast date for ensemble number 17 is 12 December from the previous year, which is 20 days away from the NMME_VIC initial forecast date 1 January. The initial forecast dates 1 January, 1 April, 5 July, and 3 October were chosen according to the configuration of the CFSv2 forecasts. For each model and each ensemble member, monthly mean P and T surf forecasts out to a season were used to derive forcing.

c. ESP_VIC and the NMME_VIC experiments

Both experiments started at the same initial date with the same initial conditions taken from VIC(SIM). The forecasts were run for 3 months.

1) ESP_VIC experiments

For each target year, we randomly selected N years from the historical period from 1950 to 2010. Forcings were taken from VIC(SIM) daily forcing. The experiments followed the same protocols as in Shukla and Lettenmaier (2011). Monthly mean SM and RO were obtained for each of the N ensemble members. The ensemble mean SM and RO forecasts were the equally weighted mean of the N members. In this experiment, N = 20.

2) NMME_VIC experiments

We use the January hindcasts as an example to illustrate the approach. For a given target year and a given model, a hydroclimate forecast was derived from each member separately. For each member, the monthly mean P and T surf were taken from the NMME hindcasts for that member. The NMME outputs have a spatial resolution of 1° latitude by longitude. We bilinearly interpolated the NMME outputs to a 0.5° grid. There are large systematic errors in P and T surf forecasts. The biases of P and T surf are corrected independently. There are many error correction and downscaling schemes available. Luo et al. (2007) used the Bayesian method (Kavetski et al. 2006), while we corrected systematic errors by applying the bias correlation and spatial downscaling (BCSD) method of Wood et al. (2002), which corrects the entire probability distribution of each variable for bias relative to P or T surf analysis derived from observations. Yoon et al. (2012) used both methods to correct P errors in the CFSv1 forecasts and found that their performance was comparable.

The corrected monthly mean P and T surf sequences were disaggregated to daily sequences. We took daily P and T surf time series from 1 January to 31 March from a randomly selected year (from a pool that excluded the target year) from the historical period. Then we adjusted the monthly means of the daily sequences of P and T surf to be the same as the monthly mean error-corrected P and T surf as described in Wood et al. (2002). The low-level winds were also taken from the same year to assure consistency. The daily forcings were used to drive VIC with the initial conditions taken from VIC(SIM) to obtain the daily SM, RO, and SWE forecasts.

The monthly mean SM and RO were obtained from daily outputs of the VIC forecasts for each lead, each target year, and each ensemble member for a given model. We then corrected the model mean computed from all hindcast years except the target year at a given lead. Even though the forcing terms are BCSD corrected, SM and RO forecasts still contain systematic errors because the relationships between SM or RO and forcings is nonlinear. Yuan and Wood (2012) showed, apparently for this reason, that the error-corrected hydrologic outputs gained skill relative to those that were not postprocessed. Therefore, we performed a second-stage error correction.

We formed the ensemble mean for a given model at a given lead for the target year as the equally weighted mean of all ensemble members. Only the ensemble means were verified for each model. The VIC forecasts were performed for all six NMME models. The grand ensemble mean P, SM, SWE, and RO anomaly forecasts at a given lead for the target year were the equally weighted ensemble mean anomalies of the corresponding variable averaged over the six models. This set is labeled as NMME_VIC.

d. Verification

We verified the ensemble mean for each model and the grand ensemble mean for each lead and each year. We used the Pearson correlation to assess the forecast skill. If one year is considered as having 1 degree of freedom (N), then N = 29. For the correlation between the forecasts and the verifying VIC(SIM) sequence at a given grid point to be statistically significant at the 5% (10%) level, the correlation needs to be greater than 0.37 (0.31). If the forecast date was not the first day of the month, then the monthly mean for the first month was the average from the forecast date to the end of that month for both forecasts and the verifying VIC(SIM). For variable A, we denote the forecast skill as skill(A).

To assess the statistical significance of the difference between two correlations r 1 and r 2, we used Fisher’s Z transformation. The quantity z is defined as
e1
for i = 1 and 2. The quantity z is normally distributed with variance (N − 3)−1.
We transformed correlations r 1 and r 2 to z 1 and z 2, and then the statistical significance for the difference in correlation was assessed for
e2
where N1 and N2 are the degrees of freedom for r 1 and r 2, respectively. Here, N1 = N2 = 29. If Z is greater than 1.96, then the difference between two correlations is statistically significant at the 5% level.

In addition to the local statistical significance of correlations at each grid point, field significance was assessed according to Livezey and Chen (1983). There are a total of 4300 grid points over the CONUS. We assume the spatial degrees of freedom to be 20. We have 29 years of hindcasts. We have a total of 580 degrees of freedom; therefore, the area covered by statistically significant correlations must exceed 6.2% of the total area in order to be field significant at the 5% level.

To evaluate model performance for a given year, we used the anomaly correlation defined as the spatial pattern correlation (Miyakoda et al. 1972) between the anomaly forecast and the verifying anomaly from VIC(SIM) for all grid points over the CONUS. The forecast anomaly is defined as the departure from the model climatology at each grid point.

SM and SWE forecasts were evaluated at each grid point. The RO hindcasts are noisier than SM and SWE; therefore, we spatially aggregated RO as the sum of the base flow and surface runoff into the 48 hydrological subregions in Shukla et al. (2012), which were created by merging the 221 U.S. Geological Survey (USGS) hydrological subregions.

3. Precipitation and SWE forecast skill

Precipitation forcing is the primary source of SM and runoff variability. For winter and spring, snow accumulation and snowmelt forecasts (which are performed by VIC given the forcings from ESP or NMME) can also influence RO forecast skill. Therefore, we evaluated the P and snow water equivalent (SWE) forecasts first. Figure 1 shows the grand ensemble mean NMME forecast skill(P) measured by the Pearson correlation between the monthly mean P forecasts and the corresponding P analysis at each lead for forecasts initialized on 1 January, 1 April, 5 July, and 3 October. This is the same P analysis used to derive forcings to drive VIC(SIM). Before computing the correlation, we corrected the model mean computed from all hindcast years except the target year at a given lead. Figure 1 shows that forecast skill(P) is seasonally and regionally dependent. Skill(P) is generally higher in winter than in summer, consistent with Yuan et al. (2013). All maps at lead 1 are field significant at the 5% level. The model is able to capture rainfall over the Southwest up to lead 3 for forecasts initialized in January. January lead-1 forecasts also have high skill over the north-central region. April lead-1 forecasts show skill(P) over the East Coast, the Southeast, and the West Coast. July forecasts are skillful over the Pacific Northwest, the Midwest, eastern Texas, and Arizona. October forecasts are skillful at lead 1 over the southern Great Plains, the central United States, and the Southeast. After lead 1, skill(P) drops sharply. The only maps that are field significant at the 5% level are January lead-2 and October lead-3 forecasts. Large forecast errors indicated by negative correlations are not systematic and are not amenable to correction by postprocessing. These unskillful P forecasts negatively impact the skill of both SM and RO forecasts.

Fig. 1.
Fig. 1.

Forecast skill measured by the Pearson correlation between the NMME P forecasts and the corresponding P analysis for forecasts initialized in (a) January, (b) April, (c) July, and (d) October at lead 1 month. Contours are indicated by the color bar. (e)–(h) As in (a)–(d), but for forecasts at lead 2 months; (i)–(l) as in (a)–(d), but for lead 3 months.

Citation: Journal of Hydrometeorology 15, 4; 10.1175/JHM-D-13-0197.1

Figure 2 shows the skill(SWE) from NMME_VIC. Overall, the forecasts are skillful over the Pacific Northwest, the north-central region including the Great Lakes, and the Northeast for both January and April at lead 1. Both maps are field significant at the 5% level. The forecasts are unskillful over eastern Montana and Wyoming at lead 1 for both forecasts initialized in January and April. The unskillful forecasts have negative impact on the RO forecast skill. Again, the skill(SWE) drops sharply after lead 1. After lead 1, the only map that passes field significance is January forecast at lead 2.

Fig. 2.
Fig. 2.

Correlation between the SWE NMME_VIC forecasts and the verifying SWE from VIC(SIM) for forecasts initialized in January at lead (a) 1, (b) 2, and (c) 3 months; (d)–(f) as in (a)–(c), but for forecasts initialized in April. White indicates areas without snow and gray indicates areas where the skill is not statistically significant at the 5% level.

Citation: Journal of Hydrometeorology 15, 4; 10.1175/JHM-D-13-0197.1

4. Soil moisture and runoff forecasts

a. Forecast skill

Figure 3 shows the Pearson correlation between the grand ensemble mean NMME_VIC SM forecasts and the corresponding SM from VIC(SIM). Correlations for grand ensemble mean RO forecasts are given in Fig. 4. All maps are field significant at the 5% level and forecast skill(SM) and skill(RO) are considerably higher than for the ensemble mean P forecasts (Fig. 1). Overall, the skill(RO) is lower than the skill(SM) at the same lead. After lead 1, forecast skill for both SM and RO shows an east–west contrast. Overall, skill is higher over the western United States than the eastern United States. The areas that forecasts are skillful after lead 1 are the western interior region for all seasons. In January, forecasts over the north-central region, the Southwest, and the areas along the East Coast are also skillful at lead 2 and lead 3. Forecasts initialized in October are skillful over the Southeast and the Gulf states even at lead 3 because of skillful P forecasts (Fig. 1).

Fig. 3.
Fig. 3.

As in Fig. 1, but for SM.

Citation: Journal of Hydrometeorology 15, 4; 10.1175/JHM-D-13-0197.1

Fig. 4.
Fig. 4.

As in Fig. 1, but for runoff over the 48 subregions over the conterminous United States.

Citation: Journal of Hydrometeorology 15, 4; 10.1175/JHM-D-13-0197.1

There are areas with consistently low forecast skill. For January and April forecasts, the skill(SM) is lower along the path from the Gulf of Mexico to the Tennessee and Ohio Valleys, even at lead 1. For July forecasts, the skill(SM) is low for the Southwest after lead 1, probably because most models are not able to capture the North American monsoon rainfall variability. Skill is also low over the Southeast and the East Coast in summer, where rainfall is often caused by tropical storms. Forecast skill for California is high at lead 1 with forecasts initialized in January, but skill drops thereafter.

For RO, the skill(RO) has larger regional and seasonal variations than SM. Overall, forecasts have high skill at the low-flow areas where RO also has low variability. For example, forecasts initialized in January are skillful with correlation above 0.8 over the upper Missouri basin and the north-central region at lead 1, where the climatological runoff is only 0.2 mm day−1. When the RO variability increases from winter to spring, forecast skill deceases. The forecast skill(RO) for the western region has higher skill for forecasts initialized in July than January because RO over the western region is generally low in July (Figs. 4a,c). In January and April, SWE has a large influence on RO over the Pacific Northwest (PNW), the upper Missouri basin, and the Great Lakes (Maurer et al. 2004). In addition to low P forecast skill, the unskillful SWE forecasts initialized in April over Montana at lead 1 may contribute to the low RO forecast skill there. Similarly, the low skill P and SWE forecasts lead to a drop of RO forecast skill over the PNW after lead 1 for January forecasts. At lead 3, July forecasts are skillful over the Missouri basin and California where RO has low values. There is a return of skill in October at lead 3 due to skillful P forecasts.

Comparing with Shukla and Lettenmaier (2011), the areas where NMME_VIC has high skill are also mostly areas where ESP_VIC is skillful, except October, where NMME_VIC is superior because of skillful P forecasts. To quantify the extent to which NMME_VIC skill exceeds that of ESP_VIC, we computed the differences in correlation between NMME_VIC and ESP_VIC SM and runoff forecasts at each lead and each initial forecast time. We assessed statistical significance by using the Fisher’s transformation. Differences in correlation between NMME_VIC and ESP_VIC at lead 1 are generally not statistically significant at the 5% level. At lead 2, some difference maps show areas where the correlation differences are locally statistically significant at the 5%, but the map is not field significant at the 5% level. An example is given in Fig. 5a. The correlation difference map for RO in January at lead 2 shows that NMME_VIC is more skillful than ESP_VIC in Florida, but the map is not field significant at the 5% level. At lead 3, the forecast skill differences for RO forecasts are all field significant at the 5% level. For SM, forecasts initialized in January and October are field significant at the 5% level. For forecasts initialized in October, skill differences are locally significant over the southern United States and Southeast for both SM and RO. For SM, differences over California are also statistically significant. It is interesting that the improvements of skill by knowing CF are overall located in areas where the forecasts have low skill.

Fig. 5.
Fig. 5.

The difference in forecast skill measured as correlation between the runoff forecasts from NMME_VIC and ESP_VIC for forecasts initialized in (a) January, (b) April, (c) July, and (d) September at lead 2 months. Only regions where the differences are statistically significant at the 5% level are shown. Contours are given by the color bar. (e)–(h) As in (a)–(d), but for lead 3 months; (i)–(l) as in (e)–(h), but for SM forecasts.

Citation: Journal of Hydrometeorology 15, 4; 10.1175/JHM-D-13-0197.1

b. Two hydroclimate regimes over the CONUS

At lead 1, the ICs have the largest influence over SM and RO forecasts. After lead 1, we can separate the United States into two regimes based on the relative influence of ICs and CF on forecast skill.

The IC regime includes the western interior region for all seasons, the north-central region, and the Southwest for the cold season. Both ESP_VIC and NMME_VIC are skillful because they have the same ICs. The CF regime includes dynamically active areas and NMME_VIC is overall superior to ESP_VIC after lead 1 if P forecasts are skillful. For January and April, forecast skill is low over the path from the Gulf of Mexico to the Tennessee and Ohio Valleys, the monsoon area, the Southeast, and the East Coast in summer. For October, California has low skill. Rainfall over these areas depends on the atmospheric forcing. If we improve the P forecasts in these regions, SM and RO forecast skill will also improve. Our results are consistent with those of Shukla and Lettenmaier (2011).

c. Physical mechanisms responsible for hydrologic forecast skill

Mahanama et al. (2012) introduced the factor Kappa κ, which is the ratio of the total SM variability at the initial time to the P variability over the forecast period to estimate the relative effect of ICs and CF controls on SM and RO forecast skill. Later, Shukla and Lettenmaier (2011) showed that κ is higher in the IC regime and lower in the CF regime. Figures 6i–l show κ for our experiments. The P and SM anomalies were taken from the P analysis and the SM from VIC(SIM) from 1920 to 2010. The ratio κ is dimensionless and is divided by a constant factor before plotting (Figs. 6i–l). There is a good agreement between κ and the forecast skill (Figs. 3, 4) consistent with Shukla and Lettenmaier (2011). For the IC (CF) regime, κ is large (small) and forecast skill is high (low). Large κ implies that the region is dry and the P variability is low. Small κ is located in the CF regime where rain occurs often and has large P variability.

Fig. 6.
Fig. 6.

Correlation between runoff and precipitation anomalies for (a) January, (b) April, (c) July, and (d) October. Contours are given in color bar. (e)–(h) As in (a)–(d), but for correlation between δSM and P anomalies; (i)–(l) Plots of factor κ.

Citation: Journal of Hydrometeorology 15, 4; 10.1175/JHM-D-13-0197.1

Another framework that determines the forecast skill is the control of P on SM and RO. To estimate the first-order influence of P on RO and SM, we correlated the monthly mean P anomalies and the RO or SM anomalies for each month for the period 1920–2010 (Fig. 6). The correlation needs to be above 0.2 to be statistically significant at the 5% level if one year is considered as having 1 degree of freedom. Precipitation is the major CF source that drives SM and RO variability. If the correlations with P are low (high), then the influence of CF on SM and RO is weak (strong).

For areas with weak correlation, we expect that ICs will persistent longer. These are dry areas where κ is large and has low precipitation variability. These areas are not strongly influenced by unskillful P forecasts after lead 1. We expect SM and RO forecasts be skillful in these areas. For runoff, weak correlations are located over the western region from January to July, the north-central region for January, and Montana for October (Figs. 6a–d). These are areas in the IC regime and forecasts that have high skill. The correlations are high over the dynamically active areas such as the Tennessee and Ohio Valleys in the cold season, the Southwest and the East Coast in July, and the Dakotas in July and October, where correlations are above 0.6. These areas belong to the CF regime. These are also areas with small κ, indicating strong P variability. If P forecasts are skillful enough to capture P variations, the skill for hydrologic forecasts should also be high. Unfortunately, that is not the case for the NMME forecasts.

The forecast skill for SM is higher than RO because the influence of P is stronger on the SM increment δSM than SM. The quantity δSM(t) is defined as the SM anomaly difference between the current month t and the previous month t − 1. For a given month, the correlations (Figs. 6e–h) are overall lower than the correlations between P and RO (Figs. 6a–d). The SM anomaly at the present time depends on SM one month before and weaker influence of P. These are the reasons that the ICs have stronger influence on SM forecasts than RO forecasts and SM forecasts have higher skill than RO in the IC regime. Overall, there is a good correspondence between low (high) correlations between δSM and P and forecast skill. Low (high) correlations are located in areas that belong to the IC (CF) regime with high (low) forecast skill.

5. Ensemble mean and individual model forecasts

We now address the question of whether the ensemble mean has higher skill than individual models. To answer this question, we show the anomaly correlation between the ensemble mean anomaly and anomalies from VIC(SIM) over the CONUS for individual models (thin black lines) and grand NMME ensemble mean (red crosses) for each year and each lead for SM in Fig. 7. The anomaly correlation averaged over all years is given in Table 1. At lead 1, all forecasts have high skill and there is very little spread between the grand NMME ensemble mean and the individual model means. This occurs because the initial conditions dominate the skill of SM forecasts at lead 1, as discussed in the above section, and all ensemble members for all forecast models have the same initial conditions. As the lead increases, CF starts to contribute to forecast skill and the spread (both among models and ensemble members) increases. At lead 3, forecast skill becomes more seasonally dependent than at shorter leads. At lead 3, January forecasts have the highest skill and smallest spread. The mean anomaly correlation averaged over 29 yr for January lead-3 forecasts is quite high (0.74). July lead-3 forecasts have the lowest skill and largest spread, with a mean anomaly correlation of only 0.42.

Fig. 7.
Fig. 7.

Anomaly correlation for grand ensemble NMME_VIC mean (red line) and ensemble mean for each model (thin lines) forecasts initialized in (a) January, (b) April, (c) July, and (d) for October at lead 1. (e)–(h) As in (a)–(d), but for lead 2; (i)–(l) as in (a)–(d), but for lead 3.

Citation: Journal of Hydrometeorology 15, 4; 10.1175/JHM-D-13-0197.1

Table 1.

Mean anomaly correlation averaged over 29 yr for monthly mean SM forecasts.

Table 1.

The model that has highest (lowest) mean anomaly correlation (AC) averaged from lead 1 to 3 months and averaged over four seasons is referred as the best (worst) model. Table 1 also indicates that the grand ensemble NMME mean SM forecasts have skill slightly higher or equal to that of the best model. There is no model that consistently has the highest skill, but the model that has highest skill at lead 1 in general also has highest skill at longer leads. The best model varies from season to season, but the NCAR model generally has the lowest skill. Does the NMME_VIC grand ensemble mean have significantly higher skill in comparison to the ensemble mean of the worst model? Figure 8 shows skill differences between the grand ensemble mean and the ensemble mean of the model that has the lowest skill for SM and RO at lead 3. All maps are field significant at the 5% level except SM in January and RO in July. In the real-time forecast situation, advanced knowledge as to which model will have the highest skill is not available. This argues for using the NMME ensemble mean. The interesting point is that areas where differences are locally significant are located in the CF regime where forecast skill itself is not statistically significant at the 5% level. These areas are dynamically active and precipitation forecasts have low skill. For example, the areas with local significance for January forecasts are in the Tennessee and Ohio Valleys. For July, the largest differences are in the north-central region. If the model is able to improve P forecast in these dynamically active areas, SM and RO forecasts will also improve.

Fig. 8.
Fig. 8.

The difference in forecast skill measured as correlation between the SM forecasts from NMME_VIC and that of the worst model for forecasts initialized in (a) January, (b) April, (c) July, and (d) October at lead 3 months. Only regions where the differences are statistically significant at the 5% level are shown. Contours are given by the color bar. (e)–(h) As in (a)–(d), but for correlation difference between the RO forecasts from NMME_VIC and the worst model.

Citation: Journal of Hydrometeorology 15, 4; 10.1175/JHM-D-13-0197.1

6. Conclusions and discussion

We analyzed the skill of monthly and seasonal soil moisture (SM) and runoff (RO) forecasts performed by driving the Variable Infiltration Capacity (VIC) hydrologic model with forcings derived from the National Multi-Model Ensemble (NMME_VIC) hindcasts. We compared the skill of NMME_VIC forecasts to ensemble streamflow prediction (ESP) forecasts derived from the VIC model forced by resampling of historical observations during the forecast period (ESP_VIC), using the same initial conditions as NMME_VIC.

Our key findings are as follows.

  1. NMME_VIC SM and RO forecast skill is higher than P forecast skill. The skill of the grand ensemble mean NMME_VIC forecasts is comparable with that of the best model but superior to the skill of the worst model. The improvements of skill are located in the CF regime where forecast skill is low.

  2. ICs have a strong influence on forecast skill at lead 1. There are no statistically significant differences between NMME_VIC and ESP_VIC at lead 1 because of the dominance of ICs, which are the same in the two cases.

  3. After lead 1, CF starts to contribute to forecast skill. Based on hydrologic predictability, we can separate two regimes over the CONUS:

a. IC regime with high forecast skill

The IC regime includes the western interior region for all seasons, the north-central region, and the Southwest for January. Both NMME_VIC and ESP_VIC are skillful even at lead 3. This regime is overall dry and has weak P variability with high κ. The P influence on SM and RO is low, as indicated by the weak correlations between P and RO and between P and δSM. Precipitation is the major forcing to drive SM and runoff variability. For NMME, the P forecast skill after lead 1 is low. Low P influence on SM and RO means that ICs will be more persistent and the unskillful P forecasts will have little influence on SM and RO forecasts. Therefore, hydrologic predictability is high.

b. CF regime with low forecast skill

This regime includes a swath from the Gulf states to the Tennessee Valley in January and April, the Southwest, the Southeast, and the East Coast for July and California during the wet season. These are dynamically active areas. Rainfall depends on the strength and location of low-level jets and moisture convergence that most models are not able to capture. The correlations indicate high influence of P on both RO and SM. If the precipitation forecast improves, then the SM and runoff forecast skill will also increase.

Shukla and Lettenmaier (2011) used ESP and rESP experiments to quantify the contributions of IC and CF to forecast skill. These are ideal cases because there are in practice no “perfect” climate forecasts. Our results confirmed their basic findings by using seasonal forecasts from the current forecast models in 6 institutions. We also show the physical reasons responsible for the differences of the two regimes and discussed the improvement of forecasts due to the ensemble NMME.

From our results, there are few major challenges in the hydrologic forecasts.

  1. The western interior regime belongs to the IC regime where ICs dominate the forecast skill even at lead 3. The ICs usually are taken from the North American Land Data Assimilation System (NLDAS; Wang et al. 2009). However, the NLDAS has the largest uncertainties over the western region because of the uncertainties in the precipitation analysis (Mo et al. 2012a), due largely to delayed station reports. Improved inputs to the NLDAS and better land surface models are likely to improve forecast skill in this region.

  2. For the CF region, the SM and RO forecasts are influenced by P forecasts. The P forecasts at lead 1 have some skill, but the skill decreases quickly. When CF starts to contribute after lead 1, the P forecast skill is too low to make a difference. For winter and spring, the Great Lakes region, and the Missouri basin, the runoff anomalies are modulated by both SM and snow amounts and coverage (Maurer et al. 2004). Skillful SWE forecasts will increase the skill of hydroclimate forecasts. This suggests that a focus of efforts to improve CF skill should focus most on improvements of P and snow properties after lead 1.

This analysis was performed using NMME, so results do not depend on a particular CGCM, but we only used one land surface model (VIC) to run hydroclimate forecasts. We did not take into account errors in the ICs. The extent to which our results are LSM-dependent should be tested. Yuan et al. (2013) noted an asymmetry of forecast skill between dry and wet regions. The relationships among hydroclimate variables during low-flow (dry) and high-flow (wet) cases were different as indicated by Maurer et al. (2004). It is possible that forecast skill may be higher during drought conditions. For drought forecasters, probabilistic forecasts of drought D0–D4 categories may be useful. Extension of our results to probabilistic forecasts will be the focus of our future research.

Because of availability of supercomputers, it is now possible to run CGCMs at 50-km or finer resolution. For example, global seasonal forecasts in the two-tiered Florida Climate Institute–Florida State University Seasonal Hindcasts at 50 km (FISH50) show comparable skill in comparison to individual models in the NMME system (Misra et al. 2013; Li and Misra 2014). The interesting question is whether a high-resolution CGCM will have better hydroclimate forecasts compared to the system used here. This interesting topic will also be a direction of our future research.

Acknowledgments

This project was supported by the NOAA Grant GC11-578 to the Climate Prediction Center and by NOAA Grants NA10OAR4310245 and NA08OAR4320809 to the University of Washington.

REFERENCES

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    • Search Google Scholar
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
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    • Search Google Scholar
    • Export Citation
  • Maurer, E. P., Lettenmaier D. P. , and Mantha N. J. , 2004: Variability and potential sources of predictability of North America runoff. Water Resour. Res., 40, W09306, doi:10.1029/2003WR002789.

    • Search Google Scholar
    • Export Citation
  • Misra, V., Li H. , Wu Z. , and DeNapoli S. , 2013: Global seasonal climate predictability in a two tiered forecast system. Part I: Boreal summer and fall seasons. Climate Dyn.,42, 1425–1448, doi:10.1007/s00382-013-1812-y.

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    • Search Google Scholar
    • Export Citation
  • Mo, K. C., Shukla S. , Lettenmaier D. P. , and Chen L. , 2012b: Do Climate Forecast System (CFSv2) forecasts improve seasonal soil moisture prediction? Geophys. Res. Lett., 39, L23703, doi:10.1029/2012GL053598.

    • Search Google Scholar
    • Export Citation
  • Shukla, J., 1984: Predictability of time averages: Part II: The influence of the boundary forcings. Problems and Prospects in Long and Medium Range Weather Forecasting, D. M. Burridge and E. Kallen, Eds., Springer-Verlag, 155–206.

  • Shukla, S., and Lettenmaier D. P. , 2011: Seasonal hydrologic prediction in the United States: Understanding the role of initial conditions and seasonal climate forecast skill. Hydrol. Earth Syst. Sci.,15, 3529–3538, doi:10.5194/hess-15-3529-2011.

  • Shukla, S., Voisin N. , and Lettenmaier D. P. , 2012: Value of medium range weather forecasts in the improvement of seasonal hydrologic prediction skill. Hydrol. Earth Syst. Sci., 16, 28252838, doi:10.5194/hess-16-2825-2012.

    • Search Google Scholar
    • Export Citation
  • Wang, A., Bohn T. J. , Mahanama S. P. , Koster R. D. , and Lettenmaier D. P. , 2009: Multimodel ensemble reconstruction of drought over the continental United States. J. Climate, 22, 26842712, doi:10.1175/2008JCLI2586.1.

    • Search Google Scholar
    • Export Citation
  • Wang, W., Xie P. , Yo S. H. , Xue Y. , Kumar A. , and Wu X. , 2011: An assessment of the surface climate in the NCEP Climate Forecast System Reanalysis. Climate Dyn., 37, 16011620, doi:10.1007/s00382-010-0935-7.

    • Search Google Scholar
    • Export Citation
  • Wood, A. W., and Lettenmaier D. P. , 2006: A test bed for new seasonal hydrologic forecasting approaches in the western United States. Bull. Amer. Meteor. Soc., 87, 16991712, doi:10.1175/BAMS-87-12-1699.

    • Search Google Scholar
    • Export Citation
  • Wood, A. W., and Lettenmaier D. P. , 2008: An ensemble approach for attribution of hydrologic prediction uncertainty. Geophys. Res. Lett.,35, L14401, doi:10.1029/2008GL034648.

  • Wood, A. W., and Schaake J. , 2008: Correcting errors in streamflow forecast ensemble mean and spread. J. Hydrometeor., 9, 132148, doi:10.1175/2007JHM862.1.

    • Search Google Scholar
    • Export Citation
  • Wood, A. W., Maurer E. P. , Kumar A. , and Lettenmaier D. P. , 2002: Long-range experimental hydrologic forecasting for the eastern United States. J. Geophys. Res., 107, 4429, doi:10.1029/2001JD000659.

    • Search Google Scholar
    • Export Citation
  • Yoon, J.-H., Mo K. , and Wood E. F. , 2012: Dynamic-model-based seasonal prediction of meteorological drought over the United States. J. Hydrometeor.,13, 463–482, doi:10.1175/JHM-D-11-038.1.

  • Yuan, X., and Wood E. F. , 2012: Downscaling precipitation or bias-correcting streamflow? Some implications for coupled general circulation model (CGCM)-based ensemble seasonal hydrologic forecast. Water Resour. Res., 48, W12519, doi:10.1029/2012WR012256.

    • Search Google Scholar
    • Export Citation
  • Yuan, X., Wood E. F. , Roundy J. , and Pan M. , 2013: CFSv2-based seasonal hydroclimate forecasts over the conterminous United States. J. Climate, 26, 4828–4847, doi:10.1175/JCLI-D-12-00683.1.

    • Search Google Scholar
    • Export Citation
Save
  • Brankovic, C., Palmer T. N. , and Ferranti L. , 1994: Predictability of seasonal atmospheric variations. J. Climate, 7, 217237, doi:10.1175/1520-0442(1994)007<0217:POSAV>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Charney, J. G., and Shukla J. , 1981: Predictability of monsoons. Monsoon Dynamics, J. Lighthill and R. Pearce, Eds., Cambridge University Press, 755 pp.

  • Kavetski, D., Kuczera G. , and Franks S. W. , 2006: Bayesian analysis of input uncertainties in hydrological modeling: 1. Theory. Water Resour. Res., 42, W03407, doi:10.1029/2005WR004368.

    • Search Google Scholar
    • Export Citation
  • Kirtman, B., and Coauthors, 2014: The North American Multimodel Ensemble: Phase-1 seasonal-to-interannual prediction; phase-2 toward developing intraseasonal prediction. Bull. Amer. Meteor. Soc. ,95, 585–601, doi: 10.1175/BAMS-D-12-00050.1.

    • Search Google Scholar
    • Export Citation
  • Kumar, A., Barnston A. G. , and Heorling M. P. , 2001: Seasonal predictions, probability verification and ensemble size. J. Climate, 14, 16711676, doi:10.1175/1520-0442(2001)014<1671:SPPVAE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Li, H., and Misra V. , 2014: Global seasonal climate predictability in a two tiered forecast system. Part II: Boreal winter and spring seasons. Climate Dyn.,42, 1449–1468, doi:10.1007/s00382-013-1813-x.

  • Li, H., Luo L. , Wood E. F. , and Schaake J. , 2009: The role of initial conditions and forcing uncertainties in seasonal hydrologic forecasting. J. Geophys. Res., 114, D04114, doi:10.1029/2008JD010969.

    • Search Google Scholar
    • Export Citation
  • Liang, X., Lettenmaier D. P. , Wood E. F. , and Burges S. J. , 1994: A simple hydrologically based model of land surface water and energy fluxes for general circulation models. J. Geophys. Res., 99, 14 41514 428, doi:10.1029/94JD00483.

    • Search Google Scholar
    • Export Citation
  • Livezey, R. E., and Chen W. Y. , 1983: Statistical field significance and its determination by Monte Carlo techniques. Mon. Wea. Rev., 111, 4658, doi:10.1175/1520-0493(1983)111<0046:SFSAID>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Luo, L., Wood E. F. , and Pan M. , 2007: Bayesian merging of multiple climate model forecasts for seasonal hydrological prediction. J. Geophys. Res., 112, D10102, doi:10.1029/2006JD007655.

    • Search Google Scholar
    • Export Citation
  • Mahanama, S. P., Leven B. , Koster R. D. , Lettenmaier D. P. , and Reichle R. H. , 2012: Soil moisture, snow, and seasonal streamflow forecasts in the United States. J. Hydrometeor., 13, 189203, doi:10.1175/JHM-D-11-046.1.

    • Search Google Scholar
    • Export Citation
  • Maurer, E. P., Lettenmaier D. P. , and Mantha N. J. , 2004: Variability and potential sources of predictability of North America runoff. Water Resour. Res., 40, W09306, doi:10.1029/2003WR002789.

    • Search Google Scholar
    • Export Citation
  • Misra, V., Li H. , Wu Z. , and DeNapoli S. , 2013: Global seasonal climate predictability in a two tiered forecast system. Part I: Boreal summer and fall seasons. Climate Dyn.,42, 1425–1448, doi:10.1007/s00382-013-1812-y.

  • Miyakoda, K., Hembree G. D. , Strickler R. F. , and Schulman I. , 1972: Cumulative results of extended forecast experiment: I. Model performance for winter cases. Mon. Wea. Rev., 100, 836855, doi:10.1175/1520-0493(1972)100<0836:CROEFE>2.3.CO;2.

    • Search Google Scholar
    • Export Citation
  • Mo, K. C., Chen L. , Shukla S. , Bohn T. , and Lettenmaier P. D. , 2012a: Uncertainties in North American Land Data Assimilation Systems over the contiguous United States. J. Hydrometeor., 13, 9961009, doi:10.1175/JHM-D-11-0132.1.

    • Search Google Scholar
    • Export Citation
  • Mo, K. C., Shukla S. , Lettenmaier D. P. , and Chen L. , 2012b: Do Climate Forecast System (CFSv2) forecasts improve seasonal soil moisture prediction? Geophys. Res. Lett., 39, L23703, doi:10.1029/2012GL053598.

    • Search Google Scholar
    • Export Citation
  • Shukla, J., 1984: Predictability of time averages: Part II: The influence of the boundary forcings. Problems and Prospects in Long and Medium Range Weather Forecasting, D. M. Burridge and E. Kallen, Eds., Springer-Verlag, 155–206.

  • Shukla, S., and Lettenmaier D. P. , 2011: Seasonal hydrologic prediction in the United States: Understanding the role of initial conditions and seasonal climate forecast skill. Hydrol. Earth Syst. Sci.,15, 3529–3538, doi:10.5194/hess-15-3529-2011.

  • Shukla, S., Voisin N. , and Lettenmaier D. P. , 2012: Value of medium range weather forecasts in the improvement of seasonal hydrologic prediction skill. Hydrol. Earth Syst. Sci., 16, 28252838, doi:10.5194/hess-16-2825-2012.

    • Search Google Scholar
    • Export Citation
  • Wang, A., Bohn T. J. , Mahanama S. P. , Koster R. D. , and Lettenmaier D. P. , 2009: Multimodel ensemble reconstruction of drought over the continental United States. J. Climate, 22, 26842712, doi:10.1175/2008JCLI2586.1.

    • Search Google Scholar
    • Export Citation
  • Wang, W., Xie P. , Yo S. H. , Xue Y. , Kumar A. , and Wu X. , 2011: An assessment of the surface climate in the NCEP Climate Forecast System Reanalysis. Climate Dyn., 37, 16011620, doi:10.1007/s00382-010-0935-7.

    • Search Google Scholar
    • Export Citation
  • Wood, A. W., and Lettenmaier D. P. , 2006: A test bed for new seasonal hydrologic forecasting approaches in the western United States. Bull. Amer. Meteor. Soc., 87, 16991712, doi:10.1175/BAMS-87-12-1699.

    • Search Google Scholar
    • Export Citation
  • Wood, A. W., and Lettenmaier D. P. , 2008: An ensemble approach for attribution of hydrologic prediction uncertainty. Geophys. Res. Lett.,35, L14401, doi:10.1029/2008GL034648.

  • Wood, A. W., and Schaake J. , 2008: Correcting errors in streamflow forecast ensemble mean and spread. J. Hydrometeor., 9, 132148, doi:10.1175/2007JHM862.1.

    • Search Google Scholar
    • Export Citation
  • Wood, A. W., Maurer E. P. , Kumar A. , and Lettenmaier D. P. , 2002: Long-range experimental hydrologic forecasting for the eastern United States. J. Geophys. Res., 107, 4429, doi:10.1029/2001JD000659.

    • Search Google Scholar
    • Export Citation
  • Yoon, J.-H., Mo K. , and Wood E. F. , 2012: Dynamic-model-based seasonal prediction of meteorological drought over the United States. J. Hydrometeor.,13, 463–482, doi:10.1175/JHM-D-11-038.1.

  • Yuan, X., and Wood E. F. , 2012: Downscaling precipitation or bias-correcting streamflow? Some implications for coupled general circulation model (CGCM)-based ensemble seasonal hydrologic forecast. Water Resour. Res., 48, W12519, doi:10.1029/2012WR012256.

    • Search Google Scholar
    • Export Citation
  • Yuan, X., Wood E. F. , Roundy J. , and Pan M. , 2013: CFSv2-based seasonal hydroclimate forecasts over the conterminous United States. J. Climate, 26, 4828–4847, doi:10.1175/JCLI-D-12-00683.1.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Forecast skill measured by the Pearson correlation between the NMME P forecasts and the corresponding P analysis for forecasts initialized in (a) January, (b) April, (c) July, and (d) October at lead 1 month. Contours are indicated by the color bar. (e)–(h) As in (a)–(d), but for forecasts at lead 2 months; (i)–(l) as in (a)–(d), but for lead 3 months.

  • Fig. 2.

    Correlation between the SWE NMME_VIC forecasts and the verifying SWE from VIC(SIM) for forecasts initialized in January at lead (a) 1, (b) 2, and (c) 3 months; (d)–(f) as in (a)–(c), but for forecasts initialized in April. White indicates areas without snow and gray indicates areas where the skill is not statistically significant at the 5% level.

  • Fig. 3.

    As in Fig. 1, but for SM.

  • Fig. 4.

    As in Fig. 1, but for runoff over the 48 subregions over the conterminous United States.

  • Fig. 5.

    The difference in forecast skill measured as correlation between the runoff forecasts from NMME_VIC and ESP_VIC for forecasts initialized in (a) January, (b) April, (c) July, and (d) September at lead 2 months. Only regions where the differences are statistically significant at the 5% level are shown. Contours are given by the color bar. (e)–(h) As in (a)–(d), but for lead 3 months; (i)–(l) as in (e)–(h), but for SM forecasts.

  • Fig. 6.

    Correlation between runoff and precipitation anomalies for (a) January, (b) April, (c) July, and (d) October. Contours are given in color bar. (e)–(h) As in (a)–(d), but for correlation between δSM and P anomalies; (i)–(l) Plots of factor κ.

  • Fig. 7.

    Anomaly correlation for grand ensemble NMME_VIC mean (red line) and ensemble mean for each model (thin lines) forecasts initialized in (a) January, (b) April, (c) July, and (d) for October at lead 1. (e)–(h) As in (a)–(d), but for lead 2; (i)–(l) as in (a)–(d), but for lead 3.

  • Fig. 8.

    The difference in forecast skill measured as correlation between the SM forecasts from NMME_VIC and that of the worst model for forecasts initialized in (a) January, (b) April, (c) July, and (d) October at lead 3 months. Only regions where the differences are statistically significant at the 5% level are shown. Contours are given by the color bar. (e)–(h) As in (a)–(d), but for correlation difference between the RO forecasts from NMME_VIC and the worst model.

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