Characteristics of the water cycle and land–atmosphere interactions from a comprehensive reforecast and reanalysis data set: CFSv2
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The behavior of the water cycle in the Coupled Forecast System version 2 reforecasts and reanalysis is examined. Attention is focused on the evolution of forecast biases as the lead-time changes, and how the lead-time dependent model climatology differs from the reanalysis. Precipitation biases are evident in both reanalysis and reforecasts, while biases in soil moisture grow throughout the duration of the forecasts. Locally, the soil moisture biases may shrink or reverse sign. These biases are reflected in evaporation and runoff. The Noah land surface scheme shows the necessary relationships between evaporation and soil moisture for land-driven climate predictability. There is evidence that the atmospheric model cannot maintain the link between precipitation and antecedent soil moisture as strongly as in the real atmosphere, potentially hampering prediction skill, although there is better precipitation forecast skill over most locations when initial soil moisture anomalies are large. Bias change with lead-time, measured as the variance across ten monthly forecast leads, is often comparable to or larger than the interannual variance. Skill scores when forecast anomalies are calculated relative to reanalysis are seriously reduced over most locations when compared to validation against anomalies based on the forecast model climate at the corresponding lead-time. When all anomalies are calculated relative to the 0-month forecast, some skill is recovered over some regions, but the complex manner in which biases evolve indicates that a complete suite of reforecasts would be necessary whenever a new version of a climate model is implemented. The utility of reforecast programs is evident for operational forecast systems.
KeywordsWater cycle Seasonal forecast GCM Land–atmosphere interactions Precipitation Soil moisture CFSv2
Evidence exists from a large number of modeling studies, as well as a more limited number of observational studies, that the state of the land surface can affect the atmosphere on intra-seasonal and longer time scales (e.g., Namias 1960; Charney et al. 1975; Shukla and Mintz 1982; Delworth and Manabe 1989; Koster and Suarez 1995, 2004; Douville and Chauvin 2000; Dirmeyer 2003). As with the impact of ocean surface temperature states on the overlying atmosphere, land surface influences on the atmosphere can be a source of predictability (Shukla 1985; Koster et al. 2004a; Dirmeyer 2006). Predictability is a necessary condition for prediction skill (Shukla 1998). For the purposes of operational forecasts, realistic initialization of land surface states can enhance the skill of sub-seasonal to seasonal climate forecasts in certain regions (Koster et al. 2004b, 2011; Dirmeyer 2005; Jeong et al. 2008) because anomalies in states like soil moisture possess a persistence or memory in many regions that is much longer than the typical deterministic range of weather forecast skill (Schlosser and Milly 2002; Dirmeyer et al. 2009).
The National Centers for Environmental Prediction (NCEP) Coupled Forecast System, version 2 (CFSv2) reanalysis and reforecast data sets (CFSRR; Saha et al. 2010) have several characteristics that are highly useful for exploration of this pathway from terrestrial boundary conditions to predictability and prediction skill. First, the reanalysis is semi-coupled, with an offline land data assimilation system that keeps soil moisture and other hydrologic states constrained by observations. Second, the reforecasts use these realistic land surface states as part of their initial conditions. Third, there are many reforecasts in the CFSRR data set—four per day over a span of more than three decades with durations ranging from 45 days to about 10 months. This allows for statistically sound and thorough investigations of the water cycle and land–atmosphere coupling in the context of short-term climate forecasts. Finally, the existence in parallel of a reanalysis and forecasts at various lead times, all valid at the same “real time” and generated by exactly the same global models, allows for clean comparisons of model behavior when unconstrained (forecast mode) versus constrained by observations (via data assimilation).
There have been some preliminary investigations of aspects of the water cycle in CFSRR. Yuan et al. (2011) found CFSv2 ensemble mean precipitation skill to be poor after the first month of reforecast, but overall skill appeared to be better than for other global forecast models, particularly the older version of CFS. Mo et al. (2012) have shown that CFSv2 precipitation reforecast errors, after bias correction, slightly improve soil moisture simulations over the United States with hydrologic models at longer lead times compared to statistical forcings that emphasize the role of the initial hydrologic state. These studies focused on a very limited subset of seasons, forecast lead times and variables. Kumar et al. (2011) performed a more detailed analysis of the original version of CFS, examining precipitation skill at lead times finer than monthly steps.
In this paper the behavior of the water cycle over global land is investigated within the CFSRR framework. Specifically, two aspects of CFSRR are explored. First, the model climatology is examined, with particular interest in how the model climate drifts in forecast mode over the course of months and seasons. Forecast model drift can be seriously detrimental to hydrologic forecasting (Wood and Schaake 2008). Second, the skill of CFSv2 forecasts of water cycle quantities is analyzed with an eye toward to potential impact of the realistic land surface initialization on the forecasts. Finally, possible mechanisms for the realization (or lack of realization) of potential predictability as prediction skill are explored.
Section 2 of this paper gives a brief description of the CFSRR data sets that are used in this study, as well as independent validation data used to assess systematic errors and forecast skill for precipitation. For other water budget quantities, the reanalysis serves as the validation data set for forecasts. The model climate and its drift in forecast mode are explored in Sect. 3. Section 4 analyzes the forecast skill. Mechanisms of the model’s behavior are probed in Sect. 5, and discussion and conclusions are presented in Sect. 6.
2 Models and data
Saha et al. (2010) describe the CFSv2 reanalysis in detail. The reanalysis covers the period from the beginning of December 1978 through the end of 2009. Relevant to this study, there are data assimilation streams for the atmosphere, ocean and land, which are coupled at 6 or 24 h intervals depending on the model component pairing. The land surface data assimilation stream updates the Noah land surface model using observed precipitation in place of the atmospheric model’s guess forecasts, but otherwise uses the near-surface meteorology from the atmospheric stream. At 0000UTC each day the land surface states from the Noah-only assimilation stream are placed back into the fully coupled stream, to prevent terrestrial states from drifting over time due to systematic errors in precipitation or snowpack. This “semi-coupling” of the assimilation stream for land and atmosphere attempts to strike a compromise, achieving high degrees of both agreement with reality and internal model consistency (cf. Koster et al. 2009).
Here we use only the 9-month forecasts, which are distributed as a limited set of variables at monthly means accumulated from 24 ensemble members for each month (there are 28 members in the November set, to account for the extra pentad as 365/5 = 73, which does not divide evenly by 12; we use only the first 24 members of the November forecasts to keep the sample sizes consistent among months). There are actually 10 monthly values given—the first monthly mean is called the “0-month” forecast, which includes ensemble members that started anywhere from 19 to 24 days before the start of “month zero” through 3–7 days after. Thus, the 0-month forecast includes a mix of weather and sub-seasonal climate forecast time scales, and even the initial conditions for a few of the ensemble members, evident from Fig. 1.
Two observational data sets are used to validate precipitation. Over land, the gauge-based Climate Prediction Center (CPC) unified precipitation analysis (Chen et al. 2008) is used. This data set is gridded at 0.5° horizontal resolution, daily temporal resolution which are averaged to monthly, and covers the entire period of the CFSv2 reforecasts. Over ocean, version 2.2 of the Global Precipitation Climatology Project (GPCP) monthly analysis at 2.5° resolution is used (Adler et al. 2003).
For land surface states, validation of the reforecasts is performed against the CFSv2 reanalysis. This likely produces higher skill scores and correlations than validation against an independent product based directly on observations of quantities like soil moisture, but no such global products exist for the reforecast period. However, validation against the reanalysis ensures consistency in the definition of soil moisture in the forecasts (Koster et al. 2009). There exist other global data sets of model-estimated soil moisture for the period (e.g., CPC, Fan and van den Dool 2004; GLDAS-2, Rodell et al. 2004), but they are also the products of models driven by gridded meteorology derived from some combination of observations and analyses, like that in the CFSv2 reanalysis. Using the CFSv2 reanalysis has the added benefit of providing an easy assessment of drift in the terrestrial water cycle terms.
In this paper, most of the focus is on results of forecasts that validate during the boreal summer months of June through August, as this is the season when land–atmosphere interactions have the largest potential impact on climate when considered globally. However, figures for the other seasons are included as supplementary material for many of the calculations. The overlap between CFSv2 reforecasts and reanalyses is 28 years from 1982 through 2009, but many of the monthly and seasonal calculations use only 27 years (reforecasts initialized during 1982–2008) as the longer forecasts in that last year validate during 2009.
3 Climate and drift
Climate drift in coupled land–atmosphere models is a significant problem that manifests strongly through the water cycle (Dirmeyer 2001). Even in data assimilation mode, there exist shocks and biases that affect the hydrologic cycle (Betts et al. 2006; Bosilovich et al. 2008). So we first look at errors and drift in the CFSRR products.
The remaining panels show the errors in the CFSv2 reforecasts at leads of 0, 1, 3 and 7 months, as defined in Sect. 2. The errors for the individual months are assessed for the specified reforecast leads, and then averaged together to give seasonal statistics. Over many regions the errors in the 0-month reforecasts are clearly larger than in the reanalysis. Furthermore, the errors usually continue to grow with longer lead times. However, there are exceptions over both ocean (e.g., the equatorial Indian Ocean) and land (e.g., southern United States) where bias may shrink or reverse sign at longer leads. A more striking feature than regional variations in magnitudes is the consistency in the pattern of errors across all lead times. Similar characteristics are present in the other seasons (supplemental material). Such consistency likely reflects robust model biases in atmospheric circulation or thermodynamic quantities.
The root mean square (RMS) error calculated over only land points is larger in the reanalysis than in the CFSv2 reforecasts at all leads by 2–12 % during DJF (maps in the supplemental material) and over 20 % during JJA. Most of the error in the reanalysis occurs as strong positive biases over seasonal monsoon regions, especially southern Africa in DJF and Southeast Asia in JJA. This apparent discrepancy is a well-known aspect of general circulation model behavior in the simulated hours after initialization. Reanalysis precipitation, like all fluxes from reanalyses, is the product of a very short-term forecast (Saha et al. 2010). The model goes through an adjustment period in the first hours, and sometimes days, while the physical parameterizations spin-up and equilibrate to the model’s dynamical state. Thus, the precipitation averaged across the early time steps of a model integration, especially for a model being run in reanalysis mode with frequent application of increments from data assimilation, can be quite different than the climatology of the same model running freely without frequent data assimilation (cf. Betts et al. 2006; Zhang et al. 2012).
Over many regions soil moisture variance across lead times is from 35 % to more than 100 % the interannual variance. Although no longer evident in precipitation during JJA, systematic errors in snowfall are evident in soil moisture, runoff and even in evapotranspiration in roughly zonal bands across northern Eurasia and northern North America; this snow bias is discussed further in the next section. In middle and low latitudes there is evidence of moderate drift in precipitation over many locations, and strong drift relative to interannual variability over the dry season regions around parts of the Mediterranean, Middle East and southwestern Africa. Many areas have inter-lead variance larger than interannual variance for the other water cycle variables—there is more variability in the growing biases than in the climate signal. Some areas such as northern India and the lower La Plata river basin show much stronger drift in evapotranspiration than the other terms.
It should be recalled that many factors affect soil moisture and surface water flux variability, and thus their drift, besides precipitation. Systematic errors and drifts in surface radiation (clouds), temperature and humidity can also contribute to drift, and frozen soil can prevent soil moisture drift from being realized in evapotranspiration or runoff. Nevertheless, it is clear that for many if not most areas, drift in the model climatology with reforecast lead-time must be taken into account when interpreting the anomalies suggested by the reforecasts.
The second panel shows the same evolution of soil moisture over the Great Plains of North America. Here the reforecasts are uniformly biased toward wetter values than reanalysis for all months and lead-times, mirroring biases in precipitation. The biases generally grow with lead-time, and the biggest jump is in the first month of the reforecasts. The bottom panel shows the forecast drift for a region further north and east across much of southern Canada. Here the melting snowpack is a significant source of soil moisture and determines much of the annual cycle. A negative drift is evident during the cold season that reverses to a positive bias in the warm season. There is a heavy snow bias, a cold bias during spring and late snow melt that tend to shift the phase of the annual cycle of soil moisture progressively later with increasing reforecast lead-time.
Other regions of the globe show interesting seasonal cycles of error and drift in the surface water cycle, but the examples in Fig. 6 give some idea of the range of causes and effects. The interannual variability at any month is generally smaller than the annual cycle, and frequently smaller than the spread among the climatologies across different lead-times. The key point is that CFSv2 has a climatological annual cycle that is itself a function of reforecast lead. This extra time dimension should always be considered when interpreting forecasts, as will be illustrated in the following section.
To quantify reforecast skill, a discrete ranked probability skill score (RPSSD Weigel et al. 2007) is used with three categories of equal likelihood based on 27 years of data—above normal, near normal and below normal. Probabilistic forecasts are based on the ensembles of size 24. For this forecast configuration, the ranked probability score of a climatological forecast is exactly 4/9, and bias due to the finite ensemble size is 1/54 (Weigel et al. 2007). The CFS reforecast ranked probability scores are normalized by the expected climatological score, corrected for finite ensemble bias, and the ratio is subtracted from unity so that a positive value indicates skill above and beyond a climatological forecast.
A key determinant of skill scores is how the validation categories are defined. Of course, the proper way to estimate whether a particular model forecast is above, near or below normal, or in other sets of categories if the divisions are not in terciles, is relative to the models’ own climatology. This is in fact the primary motivation for the reforecast project, to provide a forecast model climatology for CFSv2. However, for a variety of reasons, there are situations when a complete set of reforecasts are not generated. A forecast model may undergo small incremental changes and improvements on a relatively frequent basis, where the burden of repeatedly generating new datasets of reforecasts is large. Even when model updates are infrequent, the encumbrance of producing a statistically meaningful set of sample reforecasts can be prohibitive.
The CFSv2 reforecast data set provides an excellent platform to explore the effect of such validation shortcuts to assessing model skill. To do so, we estimate the boundaries between the terciles in several different ways. The most appropriate way is based on the models’ own climatology, which we have seen varies as a function of forecast lead-time as well as time of the year. So if the reforecast precipitation, for instance, would fall in the model’s own upper tercile for that month and lead-time, that would be the forecast, even if the model rain rate would correspond to the middle or lower tercile among observed values. A shortcut often applied is to use instead the climatology of the reanalysis generated by the same model as the forecasts. Lacking any information about model behavior, the validating observations themselves are often used. Naturally, the observations are used for establishing the terciles in the validation data.
The right column of Fig. 7 shows the skill of reforecasts validating during JJA at longer lead times; 1 month (top); 2 months (middle) and 3 months (bottom). Here, RPSSD is calculated in the same way as the top left panel, using the forecast model climatology at the corresponding lead to define the terciles. Except for some tropical regions where precipitation is strongly determined by nearby ocean temperatures, skill drops off quickly after month 0. In fact, month 0 includes the classical weather forecast time scales for many of the ensemble members; the inclusion of these deterministic forecast time scales in these probabilistic forecasts greatly enhances skill scores.
Again, the skill for many areas is appreciably lower when the reanalysis is used as the basis for determining forecast terciles (lower left panels in Figs. 8, 9), except over mostly arid regions for soil moisture. This is because over areas with little to no precipitation, the systematic errors in precipitation are not a factor for biasing soil moisture. Instead, soil moisture biases come from other factors (e.g., errors in evapotranspiration formulations, runoff, or the vertical diffusion of water in the soil) that are the same in the reforecasts and reanalysis, and thus cancel out in terms of formulating terciles and calculating skill scores.
The middle left panels in these figures show the skill scores when the 0-month model forecast climatology is used instead of the 1-month climatology to estimate terciles. This could be thought of as a “shortcut” under the assumption that most of the model drift occurs during the first month. The resulting skill calculated is considerably higher than when reanalysis is used as the basis of estimating terciles, but can still be much worse than using the model climatology from the appropriate forecast lead (e.g., over the northern Amazon Basin).
Overall, reforecast skill for soil moisture is found to be most persistent over semi-arid and arid regions where initial anomalies have the longest autocorrelation time scales. Runoff skill (Fig. 9) is most persistent in many high-latitude and high-altitude regions, where frozen soils and snowpack anomalies can induce persistent anomalies in runoff, as well as over those tropical regions where precipitation forecasts maintain skill well beyond the first month.
Some clues as to the behavior of CFSv2 skill in predicting components of the water cycle can be found by examining metrics of land–atmosphere interaction. Previous studies have shown that the coupling between land and atmosphere, the ability of land surface states to affect climate on sub-seasonal to seasonal time scales, requires the presence of two feedback “legs”—a connection of surface fluxes to land surface states such as soil moisture (Guo et al. 2006), and a response of the atmosphere to surface fluxes (Guo et al. 2006; Santanello et al. 2009). Zhang et al. (2011) demonstrated that the coupling of the atmosphere and land components of CFSv2 is relatively weak. Wei et al. (2010) showed that the Noah land surface scheme shows weaker coupling than some other land surface schemes when coupled to the same atmospheric model.
The middle column shows the comparable correlation between model forecast monthly precipitation and initial soil moisture. Here, more than half of the area is significant only for the first two leads, and the correlation coefficients are generally much lower. The implication is that there is less persistence, or more noise, in the model precipitation forecasts compared to observations at the monthly time scale. The left column shows the correlation between forecast and observed precipitation, which mirrors the weakness seen between forecast precipitation and initial soil moisture.
6 Summary and discussion
The behavior of water cycle variables in CFSv2 reforecasts and reanalysis is examined. Model forecast biases evolve as lead-time increases, and may differ substantially from the reanalysis. Precipitation biases arise immediately. For other variables, there are no true global observed data sets, so we use the reanalysis as the basis to calculate biases. For soil moisture, snowpack, evaporation and runoff, biases generally grow throughout the reforecasts. However, they can decrease or change sign during the course of the 9-month forecasts in many regions.
Execution of a large suite of reforecasts is expensive, and it has been common to use reanalysis or observations as the climatology against which forecast model anomalies are reckoned. Skill scores are shown here to be highly dependent on the method of calculating anomalies. Skill scores are much higher when CFSv2 reforecast anomalies are calculated relative to the reforecast climatology at the corresponding lead-time than when they are calculated relative to the reanalysis. A short cut could be to assume that the biases in the first month (0-month forecast) contain most of the model drift. This does help in some situations, but because of the convoluted evolution of biases in many locations and seasons, it often falls far short of using the forecast model climatology at the appropriate lead-time.
The Noah land surface scheme shows sensitivity of evaporation to soil moisture in the transition zone between arid and humid regions, a necessary condition for land-driven climate predictability and prediction skill (Koster et al. 2004a, 2011). However, the correlation between initial soil moisture and future precipitation drops much more quickly over the first 7 weeks in CFSv2 than for observations. This suggests that there may be potential prediction skill that the model is not able to realize. The source of impediment is not diagnosed here. It could be the weakness in lagged correlation is a symptom of a problem apart from land–atmosphere coupling, such as the cloud or convection parameterizations. There is demonstrably more precipitation forecast skill over most locations when initial soil moisture anomalies are large than when they are small. This suggests the feedback of the land state on the atmosphere is not completely shut down in the model.
For applications such as hydrologic forecasting, this study touches both issues of initial condition impact and inherent climate model forecast skill (Shukla and Lettenmaier 2011; Mo et al. 2012). The CFSv2 reforecasts are shown to have significant skill in key hydrologic variables such as precipitation in the first month (consistent with Yuan et al. 2011), and in runoff and soil moisture in many locations for several months, but only when the evolving bias climatology is considered and accounted for. A number of studies have considered the effect of model bias on forecast skill and even the interpretation of forecasts (e.g., Wood and Schaake 2008), but this second time dimension of bias has not been directly recognized in most previous studies, even if it is accounted for implicitly in the bias correction. The design of the CFSv2 reforecast suite is ideally suited to expose this issue; knowledge of the time evolving biases can improve the estimation of forecast anomalies and skill scores. The benefits of executing a complete reforecast suite are clear whenever a model version is changed in an operational climate forecast system.
I thank Jin Huang for motivating this study though her leadership coordinating the CFSv2 Evaluation Workshop, along with workshop organizers Annarita Mariotti, Wanqiu Wang, Shrinivas Moorthi and James Kinter, held April 30 and May 1, 2012 in Riverdale, Maryland. Credit for the conceptualization of Fig. 1 goes to Jennifer M. Adams. This work was supported by joint funding of the Center for Ocean Land Atmosphere Studies (COLA) from the National Science Foundation (ATM-0830068), the National Oceanic and Atmospheric Administration (NA09OAR4310058), and the National Aeronautics and Space Administration (NNX09AN50G).
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