1. Introduction
Over the past several decades, great strides have been made in forecasting streamflow at seasonal leads, largely through the incorporation of climate information into hydrologic forecasts. Improved seasonal streamflow forecasts have many societal and economic benefits. Yao and Georgakakos (2001), for example, demonstrated that improved forecasts can increase hydropower revenues. Hamlet et al. (2002) showed that an alternative operating system that exploited climate forecasts could significantly increase nonfirm energy production from a major Columbia River hydropower dam. Improved forecasts have an obvious impact on the ability of reservoir operators to mitigate the destructive capacity of floods and droughts.
Several potential contributors to skill in streamflow forecasts can be identified. Skill can be derived, for example, from the accurate forecasting of meteorological anomalies (particularly precipitation) during the forecast period. A second contributor is the quantification of snowpack; in the western United States, for example, precipitation is winter dominant, and thus a large fraction [by some accounts more than 70% (Christensen and Lettenmaier 2006)] of streamflow there originates from melting snow. It is no surprise, then, that western water resources managers rely heavily on wintertime snow surveys to project water availability in the subsequent spring (Brumbelow and Georgakakos 2001). A third potential contributor is knowledge of soil moisture. If the soil is dry, incident water at the surface (either snowmelt or precipitation) may infiltrate the soil and later evaporate rather than run off into streams; a wet soil, on the other hand, may encourage greater streamflow and a more efficient filling of reservoirs.
Our ability to take advantage of the first contributor is strongly limited by the minimal skill levels achieved to date in forecasting continental precipitation (and temperature, in snow-dominant areas) at seasonal time scales; indeed, nature, through chaotic atmospheric dynamics, imposes upper limits to the meteorological forecast skill that we can ever hope to achieve. In contrast, we can, at least in principle, estimate water contents in snow and in the soil on the forecast start date with some accuracy, making more tenable the use of the second and third contributors. A number of analyses (e.g., Pagano et al. 2004; Pagano and Garen 2005; Pagano et al. 2009; Wood and Lettenmaier 2008; Li et al. 2009; Bierkens and van Beek 2009) have analyzed the seasonal streamflow forecast skill derived from accurate estimates of snow and other water present in a basin on the forecast issue date. Some recent studies have highlighted in particular the contribution of soil moisture initialization to streamflow forecast skill, both in snow-covered and snow-free areas (Berg and Mulroy 2006; Mahanama et al. 2008). Using a multiple regression approach, Maurer and Lettenmaier (2003) characterized the joint contributions from soil moisture initialization and seasonal climate forecasts in the Mississippi River basin and found that soil moisture dominates runoff predictability for lead times of 1–2 months.
In a recent paper, Koster et al. (2010) used a suite of state-of-the-art land surface models, a multidecadal dataset of meteorological forcing, and time series of streamflow observations in 17 basins (ranging in size from 2000 to 1.4 million km2) to study the sources of streamflow forecast skill—in particular, to isolate and quantify the contributions of realistic 1 January snow and soil moisture initialization to the forecast skill achieved during the snowmelt season (March–July) in the western United States. We expand here on that study, adding to it and to the overall literature in four important ways: (i) we add six verification basins in the eastern Unites States, giving us 23 basins that span much more of the continent; (ii) we add suites of additional forecasts, allowing us to quantify the variations in the skill contributions as a function of both forecast start date and forecast lead; (iii) we show how the skill levels achieved can be related to the statistical character of initial total water storage and forecast period precipitation; and (iv) we extend the analysis in a “synthetic truth” study to the full area covered by the 48 conterminous United States (CONUS). The result is a series of maps showing where and when soil moisture and snow initialization can be expected to contribute to streamflow forecast skill.
2. Experimental design
a. Models
We employ four independent state-of-the-art macroscale land surface models (LSMs) for our numerical experiments: Variable Infiltration Capacity (VIC), Catchment, Noah, and Sacramento (Sac). VIC, Catchment, and Noah were developed specifically for use with atmospheric general circulation models, and their performances have been evaluated in multiple land intercomparison projects (e.g., Bowling et al. 2003; Nijssen et al. 2003; Boone et al. 2004; Dirmeyer et al. 2006). Sac is a lumped, conceptual model generally used for operational hydrology; for this study, it is run in distributed mode (Koren et al. 2003), and to treat cold-season processes, it is coupled to the Snow-17 model (Anderson 1973). The four models differ to varying degrees in their parameterizations schemes, vertical structures, geophysical parameters, and state variables. Details are provided in Table 1, which also includes relevant references. In the present study, we used model-specific default conditions for all parameters. The model versions are essentially the same as those analyzed for other purposes by Wang et al. (2009).
The LSMs used in the study with brief descriptions on model structures, snow–soil hydrology schemes, parameters, and relevant references.
Note that an earlier version of the VIC model was calibrated at a finer spatial resolution (⅛°) to a set of river basins having some overlap with those examined here (Maurer et al. 2002). This should have little impact on its performance in this study; when this model is removed from the analysis and only the remaining three models are used, the results are essentially the same. The other three models were not subject to any direct or indirect calibration. The behaviors of the four models were compared extensively in a recent analysis of drought simulation (Wang et al. 2009).
b. Numerical experiments
A set of four experiments was performed with each LSM. To some extent the design of the experiment mimics that of Bierkens and van Beek (2009), who examined streamflow forecast skill across Europe in the context of land model initialization and seasonal weather forecasts based on the North Atlantic Oscillation. The details and the goal here, however, are different: we aim to quantify, for a different climatic regime (the continental United States), the relative impacts of snow and soil moisture initialization on streamflow forecast skill for a number of different start dates and leads.
All experiments involved the integration of each LSM on a 0.5° × 0.5° array of grid cells encompassing CONUS. The atmospheric forcing data used in the integrations include hourly 2-m air temperature, 2-m specific humidity, precipitation, shortwave and longwave radiation, wind speed, and surface pressure covering the 89 yr from 1915 through 2003. The data were extracted from the National Oceanographic and Atmospheric Administration (NOAA) Cooperative Observer (Co-op) station archive, gridded as described by Andreadis et al. (2005). Surface wind was taken from the National Center for Atmospheric Research–National Centers for Environmental Prediction (NCAR–NCEP) reanalysis (Kalnay et al. 1996). As in Koster et al. (2010), prior to 1950, average surface wind values computed for the post-1950 period were used.
The first of the four experiments, labeled CTRL (for “control”), is essentially the full integration of the LSM with the 89 yr of meteorological forcing data. For spinup, each model was cycled 10 times through the year 1915 and then integrated through 2003. To further minimize spinup effects, we discarded data from 1915 through 1919; thus, we analyzed output for the 84-yr period 1920–2003. The CTRL simulations are identical to those analyzed for other purposes by Wang et al. (2009).
The next three experiments—labeled Exp1, Exp2, and Exp3—are designed to quantify the degree to which streamflow can be forecasted from different sets of initial conditions on a given forecast start date assuming no skill (beyond knowledge of the climatology) in the seasonal forecasting of meteorological forcings. Note that while some skill in forecasting meteorological forcing may be possible with seasonal climate forecast systems, we do not examine this contribution here. Exp1 quantifies the joint contribution of initial snow and soil moisture conditions to streamflow forecast skill, whereas Exp2 and Exp3 quantify, respectively, the isolated contributions of initial snowpack and initial soil moisture to the skill.
Exp1 consists of 12 sets of forecast simulations. The first set consists of 84 separate 1-yr forecast simulations (one for each year of the period 1920–2003), each forecast initialized on 1 January with the 1 January snowpack and soil moisture states (and other, presumably less important states such as soil temperature) produced by CTRL for the year in question. This mirrors the initialization approach used in many seasonal forecasting studies (e.g., Wood et al. 2005). Here, to represent a lack of knowledge of meteorological forcing during the 1-yr forecast period, we drive the land surface models across CONUS with the geographically varying climatological seasonal cycle of diurnal forcings (at 1-h resolution) determined from the CTRL forcing files, using (for proper cross validation) the 83 yr not including the year of forecast to generate the climatology. The forcing climatology for the year 1932, for example, was computed by averaging the forcings over the periods 1920–31 and 1933–2003. As a result, any skill generated in the forecasted streamflows can be attributed to the initialization alone.
The remaining 11 sets of forecast simulations for Exp1 are analogous to the first but with the forecast initialization on 1 February for the second set, on 1 March for the third set, and so on through December. In this way we can examine the impact of the initial conditions on streamflow forecast skill as a function of both lead (up to a year) and forecast start date.
Exp2 is a repeat of Exp1, except that soil moisture values are initialized on the forecast start date with the geographically varying climatological distribution of soil moisture on that start date, as determined from averaging over the 83 yr (outside the year in question) of soil moisture fields from CTRL. Thus, in Exp2, soil moisture initialization cannot contribute to streamflow forecast skill; skill is derived from snow initialization alone. In direct analogy, Exp3 is also the same as Exp1, but with snow amounts initialized to the geographically varying climatological values of snow variables on the forecast start date as derived from CTRL, again using the 83 years outside the year in question. Thus, in Exp3, no skill is derived from snow initialization; skill is derived from soil moisture initialization alone.
Two notes about the experimental design are warranted here. First, our use of climatological seasonal cycles for such forcing fields as precipitation in Exp1, Exp2, and Exp3 has a potential drawback; rainfall in these experiments is effectively characterized as a drizzle without realistic intermittency. Koster et al. (2010) tested the impact of such drizzle in a supplemental repeat of their version of Exp1 using the Catchment LSM. In this supplemental experiment, the climatological precipitation for every 4-day period was forced to fall at night on the first day, with no precipitation falling during the remaining three days. The impact on the results was essentially negligible.
Second, the experiments ignore the possibility, however unlikely, that soil temperature initialization plays a significant role in streamflow forecasting. To examine this possibility, Koster et al. (2010) performed, for the 1 January forecast start date, an experiment in which both soil moisture and snow were initialized to climatology, so that only the initialization of the remaining variables (viz. soil temperatures) could contribute to skill. None of the skill levels produced in this experiment was significantly different from zero at the 95% confidence level, supporting the idea that the impact of soil temperature initialization can indeed be neglected.
c. Observational data
Again, results from running a small subset of the four experiments (the CTRL, Exp1, Exp2, and Exp3 simulations run for 7 months starting on 1 January) have already been documented (Koster et al. 2010) in an analysis of multidecadal March–July forecasts of naturalized streamflow (water management effects removed) in 17 western U.S. basins. The use of these naturalized streamflow observations continues in our analyses below, supplemented by observations in six additional basins covering much of the eastern United States. The locations of the stream gauges and of the upstream basin areas they represent [delineated using HYDRO1k data; Verdin and Verdin (1999)] are shown in Fig. 1. Table 2 provides a description of basin properties and the periods of available data.
Locations of basins examined in this study. The identifier numbers (see Table 2) are positioned at the stream gauge measurement sites.
Citation: Journal of Hydrometeorology 13, 1; 10.1175/JHM-D-11-046.1
Characteristics of the basins examined in this study.
d. Construction of multimodel forecasts; skill metric
We combine the streamflow simulations and forecasts produced independently by the four land surface models via a two-step process. First, for a given experiment (CTRL, Exp1, Exp2, or Exp3), we convert each model’s streamflows into standard normal deviates, or Z scores; this is achieved by subtracting the model’s mean streamflow in that experiment for the time of year in question and then dividing by the corresponding standard deviation. Second, for a given year, we average across the four Z scores (one for each model) to compute that year’s ensemble mean streamflow. For a given forecast evaluation, the time series of multimodel forecasts (one averaged Z score for each year) is regressed against the corresponding time series of naturalized streamflow observations. Because skill is computed from the Z scores for a specific time of year, no artificial skill is derived from capturing the observed seasonal cycle of streamflow.
The Z scores are used here in part because the design of the forecast experiments strongly limits the variance of the simulated streamflows—by design, the forecasted streamflows do not reflect the variability of meteorological forcings during the forecast period. We do not consider this a limitation to our analysis, as we are interested in measuring the ability of the models to reproduce the time variability and relative magnitudes of year-to-year streamflow anomalies rather than the absolute magnitudes of the variations. We quantify this ability with the square of the correlation coefficient (r2) between the 84 synthetic truth streamflows and the corresponding predictions. For the r2 calculation, the use of an averaged Z score, as described above, is fully appropriate. The r2 metric of skill is as informative as a root-mean-square error (RMSE) metric, which is of more direct relevance to operations, given that known biases in the model’s statistical moments allows the conversion of the first metric to the second (Entekhabi et al. 2010). Indeed, through application of the observed moments of streamflow in a considered basin, a time series of Z-score forecasts, as produced through these experiments, can easily be converted to a time series of forecasts with appropriate magnitude for the basin, with the extremes of interest to forecasters easily distinguished from nonextreme conditions. In any case, our aim is to examine the predictability of streamflow and not the performance of operational streamflow forecast systems, for which the treatment of bias is a particular concern (Shi et al. 2008).
Note that our cross-validation procedure produced an occasional negative correlation between observations and model results, particularly in basins with little or no snow. Any negative correlations were zeroed before computing r2.
3. Results
a. Skill as a function of start date and lead
For the 17 westernmost basins in Fig. 1, Koster et al. (2010) demonstrated that the models show significant skill in forecasting observed (naturalized) March–July streamflow based on 1 January initial conditions. Both snow and soil moisture initialization contributed independently to skill to different degrees in different basins; the contribution of snow initialization was generally found to dominate, particularly in the more mountainous basins in the northwestern part of the study area, but the contribution of soil moisture initialization was still significant in many basins, and it even dominated in some of those toward the south-central United States.
In this section, through the experimental approach described above, we extend this analysis to 23 basins and to a more comprehensive collection of forecast start dates and lead times. Some key results are summarized in Fig. 2, which presents, for forecasts of 3-month-average streamflow at 0-month lead, the skill levels achieved by the multimodel system for four different start dates: 1 January, 1 April, 1 July, and 1 October. The salient feature of this plot, relative to that in Koster et al. (2010), is the increased relative importance of soil moisture initialization when other seasons are considered. The strong contribution of snow initialization to springtime forecast skill is consistent with that found in the earlier study, although the six newly considered eastern basins show a relatively significant impact of soil moisture initialization. Figure 2, though, shows that in summer, fall, and winter, initializing soil moisture has a dominant impact on skill across the United States, with contributions sometimes exceeding r2 = 0.6 or 0.7. Overall, the summer, fall, and winter skill scores for Exp1 (both soil moisture and snow initialized) rival or exceed those of spring.
Skill (measured as r2 against naturalized observations) of multimodel ensemble 3-month streamflow forecasts at 0-month lead, for four start dates (columns) and the three experiments (rows)—snow and soil moisture initialization (Exp1), snow initialization alone (Exp2), and soil moisture initialization alone (Exp3). Gray shading indicates that skill levels are not significant at the 95% level.
Citation: Journal of Hydrometeorology 13, 1; 10.1175/JHM-D-11-046.1
Naturally, such a statement must be tempered by knowledge of the seasonal cycle of streamflow—if skill is higher in seasons for which streamflow is relatively low, the usefulness of this skill for at least some applications is accordingly diminished. The top panels of Fig. 3 show the fraction of the observed annual streamflow that occurs in each season. The western basins in particular are dominated by snowmelt runoff, and thus streamflows there are largest during April–June (AMJ). Even so, a large fraction of the streamflow occurs during the other three seasons, suggesting that the dominant impact of soil moisture initialization in these seasons is indeed relevant.
(top) Fraction of total annual runoff flowing past the stream gauges during each of four 3-month periods, from observations. (bottom) The VF diagnostic for each of the four 3-month periods (see text for details).
Citation: Journal of Hydrometeorology 13, 1; 10.1175/JHM-D-11-046.1
The experimental framework allows a look at the skill obtained at longer leads. Figure 4 shows, for Exp1 (both soil moisture and snow initialized), the forecast skill levels obtained in each of the 23 basins for 3-month-average streamflow as a function of lead and start date. A given colored curve corresponds to a 1-yr forecast, with the leftmost point on the curve indicating the skill levels for 0-month lead (i.e., for the first three months of the forecast), the next point on the curve corresponding to the 1-month lead (i.e., for months 2–4 of the forecast), and so on; a point farther to the right on a given curve thus corresponds to a longer forecast lead time, unless of course the curve has wrapped around from the right edge to the left edge of the plot, at the December–February (DJF)–January–March (JFM) boundary.
Skill (r2) of multimodel ensemble 3-month forecast, as a function of start date and lead, for Exp1. Curves of a single color provide results for forecasts of a specific start date. The leftmost point on a curve indicates a 0-month lead for the forecast; points farther to the right on the curve (except for the wrap around at the end of the year) indicate a longer lead time. (See text for details.)
Citation: Journal of Hydrometeorology 13, 1; 10.1175/JHM-D-11-046.1
As should be expected, streamflow forecast skill tends to decrease with increasing lead. (See Pagano et al. (2009) for an operational example of the skill–lead relationship.) The basins clearly show some variability in the lead times allowing skillful forecasts, with some basins having little skill beyond a 0-month lead, regardless of start date (e.g., the Willamette River upstream of Oregon City), and others showing skill for leads exceeding six months for most start dates (e.g., the Green River upstream of Greendale). A number of basins show skillful spring or summer forecasts at multimonth leads, with little or no skill in the fall and winter (e.g., the San Joaquin River upstream of Mokelumne Hill)—a reflection of the dominant contribution of snowmelt to the annual runoff totals in these basins, as indicated by corresponding plots for Exp2 and Exp3 (not shown). Forecasts for start dates early in the year (January–March) in mountainous areas are sometimes characterized by skill that increases with lead and then decreases—a reflection of the fact that skill for these basins does not manifest itself until the snowmelt season begins.
Figure 5 presents this information in a different way; it shows, for each experiment, the number of months into the future for which a forecast of 3-month-average streamflow still has statistically significant skill at the 95% confidence level. (Note that the r2 value corresponding to this confidence level varies with basin according to the length of its observational record. Note also that the skill levels at longer leads, while determined significant, may still be very small, so that the practical value of this particular diagnostic may be limited.) Soil moisture initialization by itself (Exp3) is, for many basins, most effective in the fall (1 October)—a time when snow initialization (Exp2) has no impact at all. In general, snow initialization is most effective during winter and spring. We explore in the next section some important controls on the overall contribution of initialization to skill and the reasons underlying the geographical and temporal variations of skill. For now, though, we note that certain aspects of the soil–snow distinction in Fig. 5 make intuitive sense. Snow is essentially absent on 1 October, necessitating a low impact of snow initialization for 1 October starts. Soil moisture, on the other hand, does exist (and does vary interannually) on 1 October. At least in relatively cold regions, this soil moisture should remain largely unchanged during winter months while evaporation is low and the ground is, in many cases, covered with snow; the impact of the 1 October soil moisture should thus at least partially manifest itself during the snowmelt season, several months into the future.
Number of lead months for which a forecast still has significant skill at the 95% confidence level for (top to bottom) the three experiments and (left to right) Jan, Apr, Jul, and Oct. Gray shading indicates no statistically significant contribution to skill even at a 0-month lead.
Citation: Journal of Hydrometeorology 13, 1; 10.1175/JHM-D-11-046.1
b. Skill as a function of variability in water storage and precipitation
The spatial and temporal variations in the skill levels illustrated in Fig. 2 can be related, at least conceptually, to two basic water supply quantities: the total water (Winit) stored in surface reservoirs (snow plus soil moisture) on the forecast start date and the total water precipitating during the forecast period (Pfcst). Simply put, under the assumption that Winit and Pfcst are the two primary drivers of streamflow variability during the forecast period, the relative degrees to which the two quantities vary from year to year, along with our ability to estimate each on the forecast start date, determines the degree to which variations in streamflow can be accurately predicted. For example, if the interannual variance of Winit (σw2) is large and that of Pfcst (σP2) is small, then streamflow forecast skill is mostly predicated on our ability to estimate Winit; on the other hand, if σP2 is large and σw2 is small, the skill mostly depends on an accurate prediction of Pfcst.
In Fig. 6, the skill achieved for a forecast of 3-month-average streamflow at 0-month lead is plotted against the corresponding value of κ. Each dot corresponds to a specific basin and start date; given 23 different basins and 12 different start dates, there are 276 dots in the plot. The calculation of the κ values required estimates for both σw and σP. The σP values for a given start date were computed directly from the yearly time series of 3-month precipitation totals following that start date in the meteorological forcing data. The corresponding “multimodel” value of σw was computed from a time series of simulated multimodel total (snow plus soil moisture) water content for the start date in question; this time series was generated by averaging across the models the raw (unstandardized) instantaneous soil moisture and snow water contents generated by each in the CTRL simulation.
Skill (r2) of 3-month streamflow forecast at 0-month lead as a function of κ—the ratio of the standard deviation of initial total water storage (soil water plus snow) to the standard deviation of precipitation during the 3-month forecast period. Each dot represents the skill determined for one of 12 start dates and one of 23 measured basins, for a total of 276 plotted points. The larger dots correspond to locations and start times for which the CTRL simulation (which utilizes observed meteorology during the forecast period) was able to capture the observed streamflow variations with an r2 of at least 0.75.
Citation: Journal of Hydrometeorology 13, 1; 10.1175/JHM-D-11-046.1
The scatterplot shows, to first order, an increase in streamflow forecast skill with κ. This is particularly evident at the extremes; in general, for κ values below about 0.3, the skill achieved is very low (r2 < 0.1), whereas for κ values above about 3, the skill levels are high (r2 > 0.7). The first-order relationship across the full range of κ is made somewhat more evident by considering in isolation the subset of the dots (the larger dots) corresponding to times and locations for which the CTRL streamflows were especially realistic (i.e., r2 > 0.75). A focus on such a subset is sensible because forecast skill for the remaining dots is additionally limited by flaws in the modeling systems, in the forcing data, and/or in the streamflow validation data—for these remaining dots, when the models are run outside of forecast mode, with full knowledge of precipitation during the forecast period, they still have some trouble matching the observed streamflows.
c. Extension of variability analysis to CONUS
The intuitive relationship between κ and streamflow forecast skill levels, demonstrated to first order in Fig. 6, has a broader significance. Given our ability to estimate κ outside of the 23 basins through analysis of observational data and land model integrations, we can estimate for these outside locations the streamflow forecast skill that could potentially be achieved with existing systems, even given the absence of suitable verification data.
Such an estimation is presented in Fig. 7, which shows, for each of the four seasons and at each 0.5° × 0.5° grid cell across CONUS, the values of σW (calculated following the approach in section 3b above), σP (computed from the gridded meteorological forcing data), and the resulting value of κ. The maps show a wide seasonal variation in κ. For much of the United States, κ (and thus expected streamflow forecast skill at 0-month lead) is largest for JFM, with high values across the northern half of the country and south into New Mexico and Texas. For the north-central United States in particular, the high κ values during JFM reflect a seasonal reduction of σP rather than a seasonal increase in σW. For AMJ, κ values are quite high in the western third of the country and very small elsewhere; this season indeed features particularly low σP values and high σW values in the southwest and particularly small σW values in the east. For July–September (JAS), moderately high κ values are seen mostly in the northwestern quadrant of the country and in the far west, reflecting relatively low rainfall variability in these areas. The October–December (OND) κ distribution looks similar to that for JFM but is weaker, with minimal values (and thus no expected skill) in the west, where σW is now small. Notice that most of the southern United States features low values of κ throughout the year, which is a reflection of the consistently high σP values there; the corresponding σW values there, while also high, are presumably limited by the finite capacities of the soil layers, which provide for efficient runoff as the soil gets very wet.
Distributions, as a function of (top to bottom) season, of (left) σW (mm), (middle) σP (mm), and (right) the resulting diagnostic κ (dimensionless).
Citation: Journal of Hydrometeorology 13, 1; 10.1175/JHM-D-11-046.1
Again, according to the relationship illustrated in Fig. 6, these patterns can be interpreted in terms of potential streamflow forecast skill. The relationship in Fig. 6, however, while intuitive, is admittedly noisy. We thus supplement the κ calculations here with skill calculations using a synthetic truth dataset. While the computation of true skill levels outside of the basins in Fig. 1 is precluded by a lack of naturalized streamflow observations of sufficient duration, we can utilize model-generated streamflow data (viz. those produced through the CTRL simulations) as verification data, as long as the basic limitation of such synthetic truth is always kept in mind (i.e., the fact that it is based on imperfect land models integrated with imperfect meteorological forcing).
The left column of Fig. 8 is a repeat of the right column of Fig. 7; it shows the computed distribution of κ for each season. The middle column of Fig. 8 shows the corresponding distributions of 3-month runoff forecast skill at 0-month lead for Exp1, using the CTRL results as the synthetic truth. Notice that the plots in these two columns are very similar, particularly for JFM, AMJ, and JAS. In other words, the κ-based estimates of where and when forecast skill might be achieved through land model initialization appear to be well supported by these alternative calculations.
Comparison between (left) the parameter κ and (middle) the skill (r2) obtained against synthetic truth in Exp1 for 3-month streamflow forecasts at 0-month lead for (top to bottom) seasons. (right) The VF diagnostic: a rough measure, for a given grid cell, of the relative strength of the variance in that season (see text for details).
Citation: Journal of Hydrometeorology 13, 1; 10.1175/JHM-D-11-046.1
For perspective, the rightmost column of Fig. 8 shows VF, as defined in (1), at each grid cell. A comparison of this column with the others quickly shows that the locations for which skill from initialization is especially attainable (i.e., where values of κ are especially high) tend to correspond to a low value of VF—when runoff is very predictable, the variance of the runoff tends to be relatively low. Even so, the fields show substantial overlap between times of significant skill and sizeable runoff variance.
Estimate of annually averaged skill for Exp1 against synthetic truth (CTRL), computed by weighting the seasonal r2 values by seasonal runoff variance [Eq. (3) in text].
Citation: Journal of Hydrometeorology 13, 1; 10.1175/JHM-D-11-046.1
4. Summary and discussion
The multimodel ensemble forecasts of 3-month-average streamflow at 0-month lead are shown to have significant skill across the 23 basins for which we have naturalized streamflow observations (Fig. 2). Snow initialization has a positive impact mainly in spring but also in summer, whereas soil moisture initialization contributes to skill in all seasons, with the largest contributions in summer and fall. In general, outside of spring, the impact of soil moisture initialization dominates over that of snow initialization. 1 October soil moisture initialization contributes, in general, to skill at particularly long leads, presumably because of the reduced activity of soil moisture during the cold season.
As noted in Koster et al. (2010), the skill levels found for Exp1 are similar to those shown in another study for various European stations (Bierkens and van Beek 2009). They are also similar, if sometimes slightly smaller, than those found in two recent studies focusing on the American west (Pagano et al. 2004, 2009). The rough agreement with the latter two studies is interesting because the two Pagano et al. studies examined calibrated forecast systems on (generally) much smaller basins having the benefit, for example, of local snow-course measurements. The models used in our study do not utilize local in situ data or rely on calibration to observed anomalies; they rely instead solely on the integration of antecedent meteorological data at the large scale. This study thus provides evidence that such large-scale, uncalibrated models may prove useful for basin-scale prediction, perhaps in conjunction with existing, proven operational approaches that rely on calibrated, statistics-based models.
It is worth mentioning that our experimental design is limited in some ways and that overcoming or mitigating its limitations could boost the skill levels achieved. For example, we neglect here the time scales associated with river routing. To produce the model-generated basin streamflows, the contemporaneous runoffs generated within the different grid cells of a basin are simply added together; no account is taken of the length of time needed to transport a grid cell’s river water to a stream gauge site. This limitation is addressed only partially here by the consideration of long-term average (3 month) streamflow totals. Another issue is the necessarily approximate definition of the basin boundaries, given that the models are run on a 0.5° grid. Perhaps the two most important limitations to this study, however, involve the uncertainty in the data used to force and validate the models, particularly early in the study period, and the errors associated with the model parameterizations themselves—land models have oversimplified representations of many critical surface processes. Presumably, improved models driven with more accurate forcing data and validated against more accurate streamflow observations would show greater skill.
Land data assimilation (e.g., Reichle et al. 2007) shows particular promise for providing improved estimates of soil moisture states through the mathematically optimal incorporation of satellite retrievals or radiances into the land modeling environment. Streamflow prediction may thus benefit from data assimilation efforts focused on current and upcoming satellite soil moisture missions, particularly Soil Moisture Ocean Salinity (SMOS; launched in November 2009; http://www.esa.int/esaLP/LPsmos.html) and Soil Moisture Active Passive (SMAP; projected launch in 2014; http://smap.jpl.nasa.gov).
The time and space variability of the skill levels achieved in our experiments is addressed in sections 3b and 3c using a simple framework that relates skill to both the variability of water storage on the forecast start date and the variability of precipitation during the forecast period. The parameter κ captures the joint effects of these two controls; a higher κ value implies that the control quantity that is measurable on the forecast start date (water storage) has an increased impact on skill relative to the immeasurable control quantity (forecast period precipitation), so that a higher κ value implies higher skill. Our skill levels in the 23 examined basins are indeed shown to increase, to first order, with an increase in κ (Fig. 6). Furthermore, the spatial distributions of κ across CONUS agree, again to first order, with the spatial distributions of skill obtained with a synthetic truth dataset (Fig. 8), providing support for the idea that the synthetic skill levels are indicative of what could be achieved across CONUS with an extended streamflow forecast system.
The κ framework is necessarily limited. It does not capture, for example, the simple fact that evaporation is higher during summer than winter, which implies a relatively lower soil moisture memory for summer and thus a reduced potential for summer soil moisture to affect streamflow. The standard deviations used in the κ calculation here assume a stationarity that may not exist in nature. The assumption that precipitation during the forecast period cannot be estimated is not precisely true; some predictive skill for rainfall may be attainable with seasonal forecast systems. The κ framework’s neglect of these issues is arguably a weakness; we offer, however, the contrasting view that the framework’s simplicity is in fact a strength. The framework is able to capture, in a single parameter, the joint effects of what are probably the two main controls on streamflow prediction skill, allowing a first-order understanding of where and when this skill may be achieved.
Acknowledgments
We thank James Verdin for discussions at the onset of this study. We also thank the providers of the naturalized western streamflow data: U.S. Army Corps of Engineers, Omaha NB office, for the Missouri River basin; U.S. Army Corps of Engineers, Tulsa OK office, for the Arkansas–Red River basin; Columbia River Basin Climate Change Scenarios Database for the Columbia River basin; California Data Exchange Commission for the California basins; and U.S. Bureau of Reclamation, Lower Colorado Region, for the Colorado River basin. We further thank Professor Edwin Maurer (Santa Clara University) for his assistance in obtaining naturalized streamflow data for the eastern and central U.S. river basins. Funding for much of this study was provided by NASA’s Terrestrial Hydrology Program.
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