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  • View in gallery

    Difference in ensemble mean JJA root zone soil wetness and EC minus control (Ctl) averaged over 1992–2001. Units are in fractions of soil saturation.

  • View in gallery

    (left) Observed GPCP precipitation, model precipitation from Ctl, and EC cases. (right) The errors (Ctl minus GPCP and EC minus GPCP) and the difference (Diff; EC minus Ctl) for JJA 1992–2001. Units are in mm day−1 with color bars at the bottom.

  • View in gallery

    As in Fig. 2, but for recycling ratio. Estimates are from Dirmeyer and Brubaker (2007). Units are percentages when scaled to a common reference area of 105 km2.

  • View in gallery

    As in Fig. 2, but for total evaporation. The GSWP-2 multimodel analysis (GSWP). Units are in mm day−1.

  • View in gallery

    As in Fig. 2, but for the evaporative sources for precipitation over the Mississippi River basin (outlined in red) during JJA 1992–2001. The estimates are from Dirmeyer and Brubaker (2007). Units are in kg m−2.

  • View in gallery

    (left) The spatial correlation and (right) RMSE for the model evaporative source calculated for each land grid point, as compared to Dirmeyer and Brubaker (2007). (top) The control (Ctl) case, (middle) the EC case, and (bottom) their differences (EC − Ctl). Units of RMSE are in kg m−2.

  • View in gallery

    (top to bottom) Vertically integrated moisture transport for JJA 1992–1001 from NCEP–NCAR reanalysis, the control case (Ctl), the EC case, and their differences (EC − Ctl). Colors of the streamlines indicate magnitude, the difference plot has its own scale, and units are in kg m−1 s−1.

  • View in gallery

    (left) Temporal RMSE and (right) anomaly correlation coefficient for the control (Ctl) and difference (EC − Ctl) for (top) precipitation and (bottom) total evaporation. Units of RMSE are in kg m−1 s−1. Correlations are shown in terms of two-tailed significance thresholds, which are ±0.305 for the 90% significance level, ±0.360 for 95%, and ±0.461 for 99%.

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Limits to the Impact of Empirical Correction on Simulation of the Water Cycle

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  • 1 Center for Ocean–Land–Atmosphere Studies, Calverton, Maryland
  • 2 George Mason University, Fairfax, Virginia, and Center for Ocean–Land–Atmosphere Studies, Calverton, Maryland
  • 3 Centre for Australian Weather and Climate Research, Melbourne, Victoria, Australia
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Abstract

Empirical correction is applied to wind, temperature, and soil moisture fields in a climate model to assess its impact on simulation of the water cycle during boreal summer. The empirical correction method is based on the biases in model forecasts only as a function of the time of year. Corrections are applied to the prognostic equations as an extra nudging term. Mean fields of evaporation, precipitation, moisture transport, and recycling ratio are all improved, even though humidity fields were not corrected. Simulation of the patterns of surface evaporation supplying rainfall at locations over land is also improved for most locations. There is also improvement in the simulation of evaporation and possibly rainfall, as measured by anomaly correlation coefficients and root-mean-square errors of the time series of monthly anomalies. However, monthly anomalies of other water cycle fields such as moisture transport and recycling ratio were not improved. Like any statistical adjustment, empirical correction does not address the cause of model errors, but it does provide a net improvement to the simulation of the water cycle. It can, however, be used to diagnose the sources of error in the model. Since corrections are only applied to prognostic variables, shortcomings due to physical parameterizations in the model are not remedied.

Corresponding author address: Paul Dirmeyer, Center for Ocean–Land–Atmosphere Studies, 4041 Powder Mill Rd., Suite 302, Calverton, MD 20705-3106. E-mail: dirmeyer@cola.iges.org

Abstract

Empirical correction is applied to wind, temperature, and soil moisture fields in a climate model to assess its impact on simulation of the water cycle during boreal summer. The empirical correction method is based on the biases in model forecasts only as a function of the time of year. Corrections are applied to the prognostic equations as an extra nudging term. Mean fields of evaporation, precipitation, moisture transport, and recycling ratio are all improved, even though humidity fields were not corrected. Simulation of the patterns of surface evaporation supplying rainfall at locations over land is also improved for most locations. There is also improvement in the simulation of evaporation and possibly rainfall, as measured by anomaly correlation coefficients and root-mean-square errors of the time series of monthly anomalies. However, monthly anomalies of other water cycle fields such as moisture transport and recycling ratio were not improved. Like any statistical adjustment, empirical correction does not address the cause of model errors, but it does provide a net improvement to the simulation of the water cycle. It can, however, be used to diagnose the sources of error in the model. Since corrections are only applied to prognostic variables, shortcomings due to physical parameterizations in the model are not remedied.

Corresponding author address: Paul Dirmeyer, Center for Ocean–Land–Atmosphere Studies, 4041 Powder Mill Rd., Suite 302, Calverton, MD 20705-3106. E-mail: dirmeyer@cola.iges.org

1. Introduction

Studies of the water cycle, particularly on large scales, have always been plagued by the problem of insufficient good-quality data. Observational studies of the water cycle began on a regional scale with in situ observations (e.g., Rasmusson 1968; Ropelewski and Yarosh 1998) and progressed to use operational analyses (e.g., Roads et al. 1994), numerical model forecast products (e.g., Berbery et al. 1996), and reanalyses (e.g., Higgins et al. 1996). The advent of reanalyses allowed for long time period, self-consistent global studies of the water cycle (e.g., Trenberth and Guillemot 1998; Ruane and Roads 2008).

A problem with observational and reanalysis-based studies of the water cycle is that the local water budget is not closed by the data at hand. Observational studies often close the water budget by tallying all but one of the budget terms and attributing the residual to the remaining term. In reanalyses, the assimilation of observations introduces analysis increments to the prognostic equations for state variables. Thus, if atmospheric humidity or soil moisture is assimilated, the water budgets in the reanalyses will not close either.

Free-running general circulation models (GCMs) do close the water budget within the atmosphere and at the land–atmosphere interface. They can also include tracers for water, allowing for precise tracking of the atmospheric branch of the water cycle (e.g., Druyan and Koster 1989; Numaguti 1999; Bosilovich and Chern 2006). However, because they are unconstrained by data within the atmosphere or land surface, estimates of the water cycle in free-running GCMs contain substantial systematic errors.

There exist methods to correct or constrain GCMs that are not as restrictive (or unsuitable for forecasting) as data assimilation. Statistical corrections may be applied a posteriori to elements of the water budget in GCM simulations (Piani et al. 2009). Selective adjustment of individual water cycle components can cause significant improvements in other aspects of the hydrologic cycle (Dirmeyer and Zhao 2004; Nunes and Roads 2007). In the climate sense, one can ameliorate model skill by reducing systematic errors, thus improving model climate. A posteriori corrections applied separately to various prognostic variables would introduce dynamical and thermodynamic inconsistencies between these variables. Correction applied within the GCM during the course of the simulation would propagate consistently through the state variables and fluxes. DelSole and Hou (1999) describe the method of empirical correction (EC), which accomplishes this by determining the short-term tendency errors in the model’s prognostic equations and constructing a forcing term to oppose these tendencies. DelSole et al. (2008, 2009) applied this method to the prognostic equations in a coupled land–atmosphere system. This study examines how land–atmosphere EC affects the simulation of the water cycle in a GCM.

Section 2 describes the GCM, the data used as the basis for EC, and the datasets used to validate the water cycle variables responding to the correction. Results are presented in section 3 and conclusions are given in section 4.

2. Model and data

All experiments are conducted using the Center for Ocean–Land–Atmosphere Studies atmospheric general circulation model, version 3.2 (COLA AGCM), coupled to the Simplified Simple Biosphere land surface scheme (SSiB). The details of the GCM are reviewed in Misra et al. (2007). Observed sea surface temperatures are specified as a boundary condition. This is the same model configuration used by DelSole et al. (2008, 2009). The horizontal resolution, vertical discretization, and surface topography are identical to the model used for the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis (Kalnay et al. 1996). This reanalysis data, along with an updated version of the SSiB-based Global Offline Land Surface Dataset (GOLD; Dirmeyer and Tan 2001), provide the ground truth for the empirical correction methodology.

Six-member ensembles of 3-month boreal summer [June–August (JJA)] integrations are performed for 10 yr (1992–2001). In the control case, the simulations are initialized from NCEP–NCAR reanalysis and GOLD and allowed to evolve freely (the “a” run from DelSole et al. 2008). The EC case nudges atmospheric temperature, zonal and meridional winds, as well as soil moisture and temperature in an attempt to compensate for systematic errors in the GCM (the “p” run of DelSole et al. 2008). The EC procedure is described in detail in DelSole et al. (2008). Briefly, the GCM is initialized on every day of JJA for the period 1982–91 from NCEP–NCAR reanalysis and GOLD land surface state variables and integrated for 24 h. Output at 6-h intervals is analyzed to determine the systematic short-term tendency errors in the model at each grid point and each model (tropospheric and soil) level. The forecast errors at 6, 12, 18, and 24 h is fitted to a linear function of lead time, and the resulting slope is adopted as an estimate of the instantaneous tendency error. These are applied as an additional term in the prognostic equations of the nudged variables, much as an analysis increment is used in data assimilation. The nudging term varies from month to month, but not from year to year (i.e., a mean annual cycle empirical correction is applied). Validation was performed for an independent time period during 1992–2001 in DelSole et al. (2008, 2009).

Attempts to fit the tendency errors to a diurnal cycle proved unsuccessful, presumably because the 6-h sampling frequency is too coarse to properly resolve the diurnal cycle. Since initial conditions are taken from an independent assimilation, they probably are not balanced with respect to the dynamical model and therefore spurious adjustments are likely to occur during the 24-h integration. However, these imbalances are expected to be random and hence average out when 30 months of daily data are pooled to estimate the tendency error. DelSole et al. (2008) showed that the average 1-day forecast errors have nearly the same structure as the tendency errors estimated by fitting a line through the 6-, 12-, 18-, and 24-h forecast errors, suggesting that the structure of the tendency errors is, on average, roughly the same on time scales up to 1 day. Finally, we note that the tendency error correction method has been applied to both the COLA model and to the operational Global Forecast System (Yang et al. 2008) and found to significantly reduce forecast bias, suggesting that the methodology is robust and effective despite potential problems.

As shown in DelSole et al. (2009), the spatial distribution of the nudging parameters does not correspond exactly to the resulting changes in the nudged variables. Nonlinear processes in the model and the impact of physical parameterizations (commonly called “model physics”) ensure the correspondence is not perfect. Nevertheless, there is often great similarity. Figure 1 shows the impact of EC on the model’s root zone soil wetness. The EC increases soil wetness in most locations. This is a compensation for extreme drying in the control case, driven mainly by excessive net radiation at the surface (cf. Dirmeyer and Zhao 2004). However, the small-scale dipoles seen over land in several monsoon regions and areas of steep topography are mainly due to errors in the magnitude and position of climatological precipitation features in the GCM.

Fig. 1.
Fig. 1.

Difference in ensemble mean JJA root zone soil wetness and EC minus control (Ctl) averaged over 1992–2001. Units are in fractions of soil saturation.

Citation: Journal of Hydrometeorology 12, 4; 10.1175/2011JHM1348.1

In this paper, we focus on the simulation of the water cycle in the model with and without EC for the same independent period 1992–2001 as examined by DelSole et al. (2009). We use independent datasets to validate the performance of the model. Precipitation data come from the Global Precipitation Climatology Project (GPCP; Adler et al. 2003). Ground truth for global evapotranspiration is taken from the multimodel analysis of the Second Global Soil Wetness Project (GSWP-2; Dirmeyer et al. 2006), which has been extensively compared to a variety of satellite, model, and statistical estimates (Jiménez et al. 2009), although assessment of the simulation of climate anomalies uses GOLD estimates of evaporation because GSWP-2 does not span all the years of this study. Recycling ratios and the surface evaporative sources supplying precipitation over land grid points come from the observationally based estimates of Dirmeyer and Brubaker (2007). Validation of vertically integrated moisture transport is performed against the NCEP–NCAR reanalysis.

3. Results

a. Precipitation

First we compare the simulation of global precipitation with and without EC. Model precipitation results for boreal summer (JJA) are compared to GPCP in Fig. 2. Even though no corrections are applied to atmospheric humidity, we see that the EC simulation is improved significantly over the control case. As shown in Table 1, spatial correlations over land increase from 0.56 to 0.64, and globally (land and ocean) they increase from 0.64 to 0.71. Root-mean-square errors (RMSEs) in precipitation drop from 2.58 to 2.04 mm day−1 globally and from 2.50 to 2.05 mm day−1 over land. We estimate the significance of the changes in spatial correlation and RMSE using the following bootstrap approach. First, 10 yr between 1992 and 2001 are selected randomly with replacement. For each year, six model runs are selected randomly with replacement from the six ensemble members. The resulting six fields for each year are averaged to construct a bootstrap ensemble mean for each selected year, which is then paired with the corresponding observed mean. The spatial correlation and RMSE for the 10 pairs of fields are then calculated. This procedure is repeated 2000 times. The first 1000 values are paired in 1:1 correspondence to the second 1000 and differences computed, resulting in 1000 differences. The rank of the observed difference with respect to the 1000 bootstrap differences is then computed and converted into a percentile. The resulting percentile is interpreted as the p value of obtaining a difference at least as extreme as the difference that actually was observed, under the null hypothesis of no true difference (i.e., that the differences are due to chance). The p values for each variable are given as percentages in Table 1.

Fig. 2.
Fig. 2.

(left) Observed GPCP precipitation, model precipitation from Ctl, and EC cases. (right) The errors (Ctl minus GPCP and EC minus GPCP) and the difference (Diff; EC minus Ctl) for JJA 1992–2001. Units are in mm day−1 with color bars at the bottom.

Citation: Journal of Hydrometeorology 12, 4; 10.1175/2011JHM1348.1

Table 1.

Correlations and RMSEs for key components of the global water cycle for JJA simulations. (left) Values for the control case, (right) the EC case, and the percentage is the likelihood such a change between cases would occur by chance (see text for details). Error units are as follows: precipitation and evaporation (mm day−1), recycling ratio (%), and vertically integrated moisture transport (kg m−1 s−1).

Table 1.

The EC reduces the dry bias over much of North America and Eurasia, and causes improvement over the Maritime Continent and parts of monsoon Asia. These can be seen by the change (EC minus Control) having the opposite color as the biases for the control case. The dry bias over tropical South America is only slightly alleviated in EC, and simulation of rainfall in sub-Saharan Africa is slightly poorer. There are major changes over the ocean, including a better simulation of the ITCZ and northern storm track over the western Pacific, reduction of the wet bias off the west coast of monsoonal North America (at the expense of increased errors over the Caribbean), and reduction of wet biases over parts of the Atlantic.

It is worth noting that many things affect the distribution of precipitation. The EC can address problems caused by mean errors in the wind fields by changing the general circulation and shifting areas of low-level convergence, as well as by altering vertical stability through adjustments to the temperature profile. These changes have secondary effects on atmospheric humidity, which may impact the triggering of convection or formation of clouds in the model. However, errors in atmospheric parameterizations (i.e., the model physics) are not addressed by nudging state variables. As a result, improvements to the simulation of precipitation, though significant, are yet rather modest.

b. Recycling ratio

The recycling ratio is an indicator of the strength of local feedbacks in the water cycle, and is defined as the fraction of precipitation over a defined area that originated as evaporation from that same area. The magnitude of the ratio depends on the size of the domain under consideration, but can be scaled to a common reference (Dirmeyer and Brubaker 2007). Figure 3 shows estimates of recycling ratio, scaled to a reference area of 105 km2, for the control and EC cases. The same back-trajectory method is used to estimate recycling ratio in all cases (Dirmeyer and Brubaker 1999; Brubaker et al. 2001). Thus, systematic biases caused by the methodology will be similar in all cases, and will not have much effect on the calculation of differences or errors. Also, the observationally based estimates of Dirmeyer and Brubaker (2007) will be affected by the imperfect atmospheric reanalysis and uneven precipitation observations upon which they are based.

Fig. 3.
Fig. 3.

As in Fig. 2, but for recycling ratio. Estimates are from Dirmeyer and Brubaker (2007). Units are percentages when scaled to a common reference area of 105 km2.

Citation: Journal of Hydrometeorology 12, 4; 10.1175/2011JHM1348.1

There is a general increase in the recycling ratio from the control case to the EC case, but the values are still low compared to the top panel. Errors in the simulation of recycling ratio in a climate model may come from errors in precipitation, evaporation, or the simulation of moisture transport in the atmosphere (incorrect winds or humidity). As shown in DelSole et al. (2009), EC leads to an increase in soil wetness and evaporation over much of the globe in this GCM, so the increase seen in recycling ratios over land is consistent with that change. Decreases are seen in Fig. 2 over some high mountain areas, India, the Canadian Shield, and the Arctic coast of Asia.

Referring again to Table 1, we see that EC has reduced RMSE and increased spatial correlations in recycling ratio, compared to the free-running GCM in the control case. However, the improvements are not as strong as for precipitation.

c. Evaporation

The largest improvements are seen for evaporation, which shows drastic changes in the global mean. Spatial distributions of the changes to seasonal mean evaporation and their comparison to the GSWP-2 estimates are shown in Fig. 4. The EC case does have greater evaporation, following closely the adjustments to soil moisture and changes in precipitation introduced by empirical correction. DelSole et al. (2008, 2009) discuss in detail the systematic errors in the GCM and how they are manifest in the adjustment terms derived in the empirical correction algorithm. The impact of soil moisture adjustment seems to be particularly dominant in the low latitudes (cf. Fig. 1). The fact that evaporation remains too low in the EC case shows that the characteristics of the land surface parameterizations come through despite adjustments to the state variables. The SSiB land model used in this GCM consistently produces lower evaporation rates than most other land models, other conditions being equal.

Fig. 4.
Fig. 4.

As in Fig. 2, but for total evaporation. The GSWP-2 multimodel analysis (GSWP). Units are in mm day−1.

Citation: Journal of Hydrometeorology 12, 4; 10.1175/2011JHM1348.1

Table 1 shows that the relative improvements to the simulation of evaporation in the EC case are the largest of all water cycle variables (soil moisture excepted, since that state variable is directly manipulated by the empirical correction method). Spatial correlation increases from 0.59 to 0.84 and RMSE is reduced from 1.17 to 0.69 mm day−1 after implementation of empirical correction.

d. Evaporative sources

Dirmeyer and Brubaker (2007) characterized the atmospheric branch of the hydrologic cycle between precipitation events over land and the surface evaporation that supplied the moisture for those precipitation events by tracking the advection of water vapor. A quasi-isentropic back-trajectory scheme was used, along with information on the time variation of the three-dimensional distribution of moisture in the atmosphere and the two-dimensional distribution of evaporation from land and ocean. By aggregating the evaporative sources for a large number of parcels and trajectories, a time series of the distribution of evaporation supplying rainfall at any location was constructed. Conceptually, picture any location as being the mouth of an atmospheric river, and rainfall is the discharge of that river. The map of “evaporative source” that supplies the moisture for that rainfall is like the catchment for that atmospheric river (i.e., the atmosphere catching moisture evaporating upward into it). However, since winds and evaporation rates vary in time, this airborne catchment constantly fluctuates. We can aggregate larger and larger areas to find the evaporative source on regional scales, similar to identifying the catchments of large river systems instead of individual tributaries. Dirmeyer and Brubaker (2007) give technical details.

We use the back-trajectory methodology to determine the evaporative source for a number of large river basins in both the control and empirically corrected simulations, and compare them to the observationally based estimates of Dirmeyer and Brubaker (2007). Figure 5 shows an example for the Mississippi River basin. The top panel shows the estimated evaporative moisture source for summertime precipitation over the Mississippi basin, based on data from 1979 to 2004. Average results for 10 yr of JJA simulations are shown below in the left column. In the control simulation, the source of moisture from the Pacific is more intense than the local source over the center of the continent, and in addition to the tongue of high values over the Gulf of Mexico there is an additional oceanic source off the Atlantic coast of Florida that is not present in the observationally based estimate. After EC, the Atlantic feature is gone, and a better distribution of sources between the continent and the eastern Pacific is evident. However, values have become generally too large, as rainfall has increased too much over the Mississippi River basin in the EC case. RMS errors for the evaporative source increase slightly, but the spatial correlation with the observationally based estimate increases from 0.69 to 0.87.

Fig. 5.
Fig. 5.

As in Fig. 2, but for the evaporative sources for precipitation over the Mississippi River basin (outlined in red) during JJA 1992–2001. The estimates are from Dirmeyer and Brubaker (2007). Units are in kg m−2.

Citation: Journal of Hydrometeorology 12, 4; 10.1175/2011JHM1348.1

These results are typical for many basins. Table 2 shows the impacts of EC on RMSE, spatial correlation, and the recycling ratio for selected basins. In almost every case, EC improves the pattern of the evaporative source, measured by an increase in spatial correlation, and reduces errors in the recycling ratio. This is also true when examining individual months (not shown). However, RMSEs often increase. The very high pattern correlations indicate that increases in RMSE are due primarily to errors in simulating the amount of precipitation over the basins. Spatial correlations are highly dependent on the reproduction of moisture advection by the general circulation, and secondarily on the agreement between GCM and reanalysis estimates of total evaporation. Land surface evaporation is a key control on the magnitude and accuracy of the simulation of the recycling ratio.

Table 2.

RMSE and spatial correlation for evaporative sources, and recycling ratio (RR) for Ctl and EC simulations during JJA. Improvements from Ctl to EC are indicated in bold. Units for RMSE are kg m−2, RR values are ×100, and the change in error is the difference between unsigned errors (EC − Ctl).

Table 2.

The data shown in Table 2 for various river basins can be calculated pointwise for each land surface grid box and plotted in the form of a map. Figure 6 plots the spatial correlation and RMSE of the evaporative source for JJA calculated point by point for all land areas except Antarctica. The top row is for the control case, the middle row is for the empirically corrected GCM, and the bottom shows the change from control to EC. The ability of the GCM to simulate the pattern of evaporative source regions for any given location appears to be poorest in arid regions and best in wet regions. Empirical correction improves the correlations nearly everywhere, but particularly over northern India, Sub-Saharan West Africa, eastern Europe, and a large fraction of North America. Tallied over all land grid boxes, the average increase in correlation is 0.07, or averaged in terms of explained variance (r2), +9%.

Fig. 6.
Fig. 6.

(left) The spatial correlation and (right) RMSE for the model evaporative source calculated for each land grid point, as compared to Dirmeyer and Brubaker (2007). (top) The control (Ctl) case, (middle) the EC case, and (bottom) their differences (EC − Ctl). Units of RMSE are in kg m−2.

Citation: Journal of Hydrometeorology 12, 4; 10.1175/2011JHM1348.1

The impact of empirical correction on RMSE is spotty, much as suggested by Table 2. We see a tendency for zonal bands of increased or decreased error in the Eastern Hemisphere. The Americas are more dominated by decreases in RMSE, but there are large regions where errors increase over the Canadian Shield and much of the tropical rain zone of South America. Even though the areal coverage of red color (increasing error) appears to predominate, the global average of change in RMSE under empirical correction is actually a decrease of 8%.

The fact that the pattern correlations of the evaporative sources show pervasive improvement suggests there may have been significant improvement in the advection of moisture in the empirically corrected case. Figure 7 shows the vertically integrated moisture transport as streamlines, colored by the magnitude of the advection rate. The most outstanding feature affecting the terrestrial water cycle is the error in the mean monsoon transport into South Asia in the control simulation. Empirical correction has a huge effect on this region, greatly reducing the error in the GCM. The difference map (bottom panel) shows strong adjustments across the tropics and in association with the midlatitude storm tracks in both hemispheres. Table 1 shows the correlations and errors for the moisture transport, separated into zonal and meridional components. There are marked improvements in all aspects of the simulation of water vapor advection, except meridional transport over oceans. Recall that atmospheric humidity was not corrected in this experiment. Test cases including the empirical correction of humidity were carried out, but it was found that they did not further improve the simulation (DelSole et al. 2008).

Fig. 7.
Fig. 7.

(top to bottom) Vertically integrated moisture transport for JJA 1992–1001 from NCEP–NCAR reanalysis, the control case (Ctl), the EC case, and their differences (EC − Ctl). Colors of the streamlines indicate magnitude, the difference plot has its own scale, and units are in kg m−1 s−1.

Citation: Journal of Hydrometeorology 12, 4; 10.1175/2011JHM1348.1

e. Interannual variability

Finally we examine the impact of EC on the simulation of interannual variability. It is no surprise that a correction based on mean model drift should have a positive impact on the mean climate of the GCM. Table 3 shows that for evaporation and precipitation, there is also a positive impact on the simulation of monthly anomalies. Values shown are averages over all land points outside Antarctica. Figure 8 shows most of the improvements in the simulation of evaporation anomalies occur across the tropics, monsoonal Asia, and the eastern United States, following the regions of positive soil moisture nudging shown in Fig. 1. In many places local RMSE is cut in half. These are also the regions where anomaly correlation coefficients have the greatest improvement (not shown). The impact on precipitation is subtler—maps show there are regions of strong increase and decrease of RMSE, and impacts on temporal correlations are not as coherent. Improvements in the simulation of precipitation anomalies likely are not significant in this small sample size (30 months of ensemble simulation).

Table 3.

Temporal anomaly correlation coefficient and RMSE for monthly ensemble mean values, compared to observations, for the control case, and empirical correction minus control. Error units are as follows: precipitation and evaporation (mm day−1), recycling ratio (%), and vertically integrated moisture transport (kg m−1 s−1).

Table 3.
Fig. 8.
Fig. 8.

(left) Temporal RMSE and (right) anomaly correlation coefficient for the control (Ctl) and difference (EC − Ctl) for (top) precipitation and (bottom) total evaporation. Units of RMSE are in kg m−1 s−1. Correlations are shown in terms of two-tailed significance thresholds, which are ±0.305 for the 90% significance level, ±0.360 for 95%, and ±0.461 for 99%.

Citation: Journal of Hydrometeorology 12, 4; 10.1175/2011JHM1348.1

Interestingly, the simulation of moisture transport and recycling ratio, which are both strongly a function of the wind fields (fields that were corrected), show increased RMSE and no change in anomaly correlation. Although mean wind fields and these associated water cycle variables are improved under EC, the simulation of interannual variability is less accurate. Most of the degradation in moisture transport is over the monsoon regions of Asia and North America.

The improvements in RMSE for evaporation and precipitation could be explained by the nonlinear relationship between AGCM physics parameterizations, heat fluxes, and soil moisture. It could be that the RMSE is reduced because the interannual variability in the control case is simply too large. However, the improvement in anomaly correlations suggests there is a genuine improvement in the simulation of climate anomalies, and not just a reduction in their magnitude.

4. Conclusions

We investigate the impact of a form of empirical correction of GCM atmosphere and land state variables on the ability of a global climate model to accurately simulate the water cycle. Empirical correction attempts to minimize the systematic errors in a numerical model by adding nudging parameters to prognostic equations. The nudging parameters are calculated from the errors in a large number of 1-day simulations, and vary in space and time. We correct tropospheric temperature and winds, soil moisture, and temperature at the land surface.

Here, we show how such a correction approach affects the water cycle of a climate model. Empirical correction of soil states, atmospheric kinematic fields, and thermodynamic fields generally leads to reduction in the mean errors and improvement in patterns of evaporation, precipitation, recycling ratio, and the transport of moisture supplying precipitation, as indicated by moisture advection and the patterns of surface evaporative sources. Table 1 shows that over land, empirical correction reduces the RMSE of mean boreal summer evaporation by 41%, moisture transport errors are reduced by 28%, precipitation by 18%, and recycling ratio by 13%. This is accomplished without nudging the humidity fields in the model.

Figure 6 and Table 2 give a clear indication that empirical correction systematically improves the patterns of the atmospheric branch of the hydrologic cycle (i.e., the segment that includes the path from evaporation to moisture advection, condensation, and precipitation). However, there are still significant problems with the simulation of precipitation (Fig. 2) and possibly evaporation (Fig. 4). Empirical correction only addresses errors in the prognostic equations of state variables of the land surface and atmosphere. It does not directly change the “physics” of the models (i.e., the parameterization of subgrid-scale processes that control fluxes of momentum, water and energy, phase changes of water, turbulent transfers, etc.). Systematic errors in the formulation or specification of “tuning” parameters in these components of the model will stubbornly resist reform when presented with felicitous state variables. To a large extent, the errors that empirical correction is methodically removing are likely caused by these imperfect parameterizations. It is well known that reanalysis fields derived via “model physics” are quite dubious despite the use of data assimilation (Kalnay et al. 1996).

This study shows both the promise and limitations of statistical corrections to a model. Removal of systematic errors during the integration of a climate model, using a methodology similar to data assimilation but based on the systematic day-1 drift of prognostic variables in the model, greatly reduces mean errors in the simulation of the water cycle. Additionally, it appears there is some improvement in the simulation of climate anomalies, meaning the method could be useful in forecast mode. Nevertheless, the empirical correction approach predominantly addresses the symptoms of model error, and not their causes. Ultimately, the parameterizations employed in climate models must be improved directly.

The assessment of terms such as recycling ratio and the evaporative sources for precipitation in this study marks a middle ground between the a posteriori tracking of water vapor transport using the unclosed budgets of atmospheric reanalyses, and the implementation of tracers within an unconstrained GCM. The best assessment of the actual water cycle would come from a reanalysis where water vapor tracers are included and the assimilation scheme is designed to conserve water, and ideally mass and energy also. Tracers can be included as long as humidity is not assimilated. Otherwise, there is the quandary of what to do with the “created” and “destroyed” water in the analysis increments. It is possible that mass and energy can be conserved by assimilating fluxes rather than state variables (i.e., by attribution of the analysis increments to the errors in the specific terms on the right-hand side of the predictive equations). These are issues for future research efforts.

Acknowledgments

This work was supported by the National Science Foundation (Grants ATM0332910 and EAR-0233320), the National Aeronautics and Space Administration (Grant NNG04GG46G), and the National Oceanic and Atmospheric Administration (Grant NA04OAR4310034).

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