Abstract

A pilot coupled climate sensitivity study is presented based on the newly developed adjoint coupled climate model, Centrum für Erdsystemforschung und Nachhaltigkeit (CEN) Earth System Assimilation Model (CESAM). To this end the components of the coupled forward model are summarized, and the generation of the adjoint code out of the model forward code through the application of the Transformation of Algorithms in FORTRAN (TAF) adjoint compiler is discussed. It is shown that simulations of the intermediate-complexity CESAM are comparable in quality to CMIP-type coupled climate models, justifying the usage of the model to compute adjoint sensitivities of the northern Europe near-surface temperature to anomalies in surface temperature, sea surface salinity, and sea ice over the North Atlantic and the Arctic on time scales of up to one month. Results confirm that on a time scale of up to a few days surface temperatures over northern Europe are influenced by Atlantic temperature anomalies just upstream of the target location. With increasingly longer time lapse, however, it is the influence of SSTs over the central and western North Atlantic on the overlying atmosphere and the associated changes in storm-track pattern that dominate the evolution of the surface European temperature. Influences of surface salinity and sea ice on the northern European temperature appear to have similar sensitivity mechanisms, invoked indirectly through their influence on near-surface temperature anomalies. The adjoint study thus confirms that the SST’s impact on the atmospheric dynamics, notably storm tracks, is the primary cause for the influence of northern European temperature changes.

1. Introduction

For several decades data assimilation has played a critical role in numerical weather forecasts by providing initial conditions for numerical forecast models. The same holds for seasonal forecasts (Anderson 2010), which today, like weather forecast, is provided on a routine basis, often even by the same numerical forecast centers. In contrast to weather and seasonal forecasts, however, the subject of initialized climate predictions on interannual–decadal time scales has only recently moved into the focus of climate science. Although first respective attempts go back to the beginning of the twenty-first century (Barnett et al. 2004; Pierce et al. 2004), the systematic groundwork for the new field of decadal prediction was laid only more recently through studies by Smith et al. (2007), Keenlyside et al. (2008), Pohlmann et al. (2009), and most recently by Marotzke et al. (2016).

Over the last decade the field of decadal forecast has made considerable progress to the point that today initialized multimodel ensemble forecasts are being produced on a regular basis (Bellucci et al. 2015). They suggest that aspects of decadal variability are much better represented in initialized hindcasts, compared to noninitialized simulations (Meehl et al. 2014; Marotzke et al. 2016), and that it is especially the oceanographic information that provides the memory for improved forecasts by initializing climate modes superimposed to externally forced climate changes (e.g., Rosati et al. 1997; Alexander and Deser 1995; Polkova et al. 2014). Nevertheless, the notion is evolving that the initialization of sea ice as well as the terrestrial hydrology also improves the skill of the forecasts, besides the impact of atmospheric initial conditions (Bunzel et al. 2016).

Regardless which component of the model is being initialized, for most climate forecast efforts the initialization of the coupled forecast model is done using a hybrid approach, employing an offline ocean-only (or sea ice or hydrology) synthesis together with a simple technique required to incorporate this information into the coupled model, subsequently. Because of the additional surface fluxes or subsurface sources associated with this initialization step (e.g., nudging) the resulting fields are not consistent with the dynamics of a coupled model used during the forecast step. Therefore, an initialization shock in the coupled system is inevitable, which very likely degrades the forecast skill (Mulholland et al. 2015; Liu et al. 2016). Nevertheless, ongoing decadal prediction efforts show promising results, for example, in global-average temperature up to a decade in advance, originating from both initial conditions, but in particular from the climate change signal related to the known emission of greenhouse gases. Moreover, predictive skill is also found in the North Atlantic region associated with Atlantic meridional overturning circulation (AMOC) variability (Meehl et al. 2014).

Despite the existing success stories, one needs to recall that the science of producing optimal initial conditions for the purpose of initializing decadal forecasts from the existing, incomplete, climate observing system is still in its infancy. At the time of writing, various approaches are being explored with differing amounts of success. However, it can be expected from first dynamical principles that the best way to initialize any coupled forecast model is to use the same model for estimating the initial conditions in a dynamically consistent way and for performing the forecast subsequently. Such a dynamically consistent initialization procedure requires a coupled data assimilation (CDA) procedure.

First pilot applications of CDA exist (e.g., Sugiura et al. 2008; Fujii et al. 2009; Laloyaux et al. 2016), and others are spinning up (e.g., Blessing et al. 2014). As an example, Zhang et al. (2007) applied an ensemble Kalman filter (EnKF) approach to an ocean–atmosphere CDA system with a fully coupled general circulation model (GCM). Karspeck et al. (2015) applied such an approach to the problem of decadal predictions. However, their results were of mixed nature, partly because, like any state estimated using a filter approach, their initialization remains dynamically inconsistent with the coupled system, because the additional sources and sinks of heat and freshwater employed to correct the model toward the data are no longer present in prediction mode. In contrast, the value of an adjoint model approach in the context of coupled model initialization lies in the fact that during the assimilation step, coupling parameters or other uncertain model parameters can be changed so as to adjust the model to better match the observations (e.g., Stammer et al. 2016). The benefits of such an approach hold also in a coupled context. Using those adjusted model parameters in conjunction with the estimated initial conditions of a coupled system will remedy the initial model shock allowing for a dynamically adjusted model initialization.

We note that any adjoint model at its core describes the evolution of the sensitivity of a target function (cost function) to perturbations of the model state, including initial condition or other control parameters. Climate adjoint sensitivities thus refer to influences of state variables on specific climate parameters such as air temperature or precipitation, typically defined as averages over some regions. The sensitivities of those parameters show from where (geographically) and how (causal) they get influenced, for example, by sea surface temperature (SST) changes over the Atlantic or changes in sea ice coverage over the Arctic and associated changes in atmospheric wave or advection pattern.

Climate adjoint sensitivities can be used to study the dependence of the climate system on specific climate parameters since the adjoint model provides as its state vector information about the sensitivity of this parameter as a function of prior time. In principle one can study climate sensitivities also through perturbation approaches during which various model runs are being performed with one parameter being perturbed at a time in a specific region. Clearly such an approach will require many model runs in case one wants to map out the full spectrum of possible influences. In contrast, adjoint models obtain the same results with just one single forward and backward run after specifying the target parameter as the cost function of the model.

Previously, various adjoint model sensitivity studies have been performed to study the influence space of ocean parameters. The problem of estimating the sensitivities of atmospheric quantities to various model parameters has been successfully addressed with the aid of the adjoint of atmospheric models (e.g., Hall 1986; Amerault et al. 2008; Ancell and Hakim 2007; Doyle et al. 2012). More recently sensitivity analyses were also carried out for oceanographic problems (e.g., Galanti and Tziperman 2003; Masuda et al. 2010). As detailed by a review of Stammer et al. (2016), respective ocean applications include the initial study of Marotzke et al. (1999) on the sensitivity of the heat transport in the Atlantic across 24°N using the newly developed ECCO adjoint model. Stammer et al. (2008) used the same ECCO adjoint model setup to study causes for variations in freshwater content in the North Pacific north of the Hawaiian Islands as they were observed by the Hawaii Ocean Time Series (HOT). Köhl and Stammer (2004) identified important observations required to better constrain an optimization procedure. Through the recent generation of the Centrum für Erdsystemforschung und Nachhaltigkeit (CEN) Earth System Assimilation Model (CESAM) it becomes possible now to also compute coupled adjoint climate sensitivities in a general sense, thereby opening a new avenue to climate predictability studies and climate predictions.

As a first prerequisite to perform fully coupled assimilation efforts, the purpose of this paper is to take advantage of the adjoint CESAM framework and to provide first climate sensitivity experiments of the Northern Hemisphere climate to ocean surface conditions in the subpolar Atlantic and the Arctic. In detail we study sensitivities of the air temperature over northern Europe to influences emerging from the Atlantic or the Arctic. The goal is to compute the sensitivity of daily mean near-surface air temperature (T2M) in northern Europe to SST, for simplicity referred to here as sensitivity to SST. The study is a first application of its kind to a fully coupled adjoint model and is intended to demonstrate the potential of the CESAM setup for climate sensitivity studies.

In principle climate adjoint sensitivities need to be computed over climate time scale, thereby representing the seasonal to interannual–decadal and longer interactions in the system. In this first paper using the new setup we are more modest by computing the sensitivities first up to one month since such computations can serve as the test of the new system and will establish a reference against which later climate-scale experiments can be compared.

The structure of the remainder of this paper is as follows. Section 2 will present the components of the forward model; its quality will be discussed in section 3. Section 4 will then introduce the CESAM adjoint assimilation system, and section 5 will present results of the adjoint sensitivity computations. Section 6 will conclude with a discussion and concluding remarks.

2. The coupled CEN climate model

In this section we describe the individual components of the CESAM forward and adjoint model. In combination with the commercially available compiler TAF the forward code can be used to generate adjoint model code for sensitivity and assimilation approaches (see section 4 for details).

The CESAM forward model

The CESAM forward model consists of 1) the ocean MITgcm (Adcroft et al. 2004) and 2) the PlaSim atmosphere (Fraedrich et al. 2005a,b), 3) with both being coupled together through exchange of surface flux fields.

  1. The CESAM ocean component consists of the MITgcm (Adcroft et al. 2004), which is a state-of-the-art oceanic circulation model based on a finite-volume approximation of the primitive equations on an Arakawa C grid. Its nonhydrostatic capability (Marshall et al. 1997a,b) enables the simulation of processes from convection scales to large-scale circulations. In the vertical, a height (z level) coordinate is being used with partially filled cells at the bottom. Several formulations for the sea level are implemented in the MITgcm, and users can choose between rigid lid and nonlinear free surface formulations. Physical parameterization packages are included for unresolved processes. Among those, the surface mixed layer is represented by the nonlocal K-profile parameterization (KPP) scheme of Large et al. (1994) or the second-order closure model for the turbulent kinetic energy by Gaspar et al. (1990). The effect of mesoscale eddies is simulated by the Gent–McWilliams/Redi eddy parameterization (Gent and McWilliams 1990). The model can be forced at the surface with fluxes or via bulk formulas by variables of the atmospheric state. The model of sea ice dynamics and rheology is based on the formulation by Zhang et al. (1998) and adopted for the C grid. In principle biogeochemistry packages allow the simulation of various tracers but are not used in the present implementation of the coupled adjoint setting. The model is parallelized based on domain decomposition.

  2. The Planet Simulator (PlaSim) is a spectral model of intermediate complexity (Fraedrich et al. 2005a,b). Its atmospheric dynamical core is provided through the spectral Portable University Model of the Atmosphere (PUMA; Fraedrich et al. 1998, 2005c), which is combined with schemes for atmospheric radiation, cloud cover, precipitation, runoff, soil temperature and wetness, surface fluxes, and a terrestrial biosphere component (SIMBA). Atmospheric dynamics are modeled using the primitive equations formulated for vorticity, divergence, temperature, and the logarithm of surface pressure. The equations are solved by the spectral transform method (Eliasen et al. 1970; Orszag 1970). Moisture is included by transport of water vapor (specific humidity). Stratiform precipitation is generated in supersaturated states, and the Kuo scheme (Kuo 1965, 1974) is used for deep moist convection. Parameterized unresolved processes include longwave (Sasamori 1968) and shortwave (Lacis and Hansen 1974) radiation with interactive clouds (Stephens 1978; Stephens et al. 1984; Slingo and Slingo 1991). Horizontal diffusion is applied according to Laursen and Eliasen (1989). Formulations for boundary layer fluxes of latent and sensible heat and for vertical diffusion follow Louis (1979), Louis et al. (1982), and Roeckner et al. (1992). The land surface scheme uses five different diffusive layers for the temperature and a bucket model for the soil hydrology together with a simple scheme for continental runoff. Continental ice sheets are prescribed.

  3. The coupling of the two model components is realized via the exchange of surface fluxes of heat, freshwater, and momentum without applying flux corrections or flux adjustments. The land–sea mask of PlaSim was adapted to obtain the best possible fit with the mask used by MITgcm. During the coupled integration, atmospheric wind stresses, freshwater flux (precipitation, evaporation, and continental runoff), and heat flux (latent and sensible heat flux and shortwave and longwave radiation) are averaged over the coupling interval (one oceanic time step) and given to the ocean. River discharge is computed in the land module included in the atmosphere model by a river transport scheme with linear advection. The resulting freshwater input into the ocean is redistributed geographically before it is interpolated onto the ocean grid and passed on to the ocean by the coupler. The ocean model provides the SST field seen by the atmosphere. The interpolation between the atmospheric and the oceanic grid ensures global conservation of momentum, heat, and freshwater. To ensure energy conservation, sea ice is computed from a thermodynamic sea ice (Semtner 1976) within PlaSim if SST is below freezing level, replacing the original MITgcm sea ice module.

3. The CESAM climatology

Before applying any coupled model to climate problems, a demonstration of its skill in simulating the Earth climate is mandatory. In the following we will describe the resulting CESAM climate and compare it against known information. This will be done first in a control run with a resolution comparable to CMIP5 models (Collins et al. 2013) to allow direct comparability with the existing literature. We will subsequently repeat a similar experiment but with a lower resolution to demonstrate the quality of the model version that is actually used in the adjoint sensitivity computations.

a. Model control configuration

All forward runs were performed on a global domain with an asymmetric resolution in the ocean. To this end we have set up a version of the model with a spectral T42 horizontal resolution in the atmosphere equivalent to a 2.8125° resolution on a Gaussian grid, with 10 vertical, nonequidistant levels in sigma coordinates are used (σ = p/ps, where p and ps are pressure and surface pressure, respectively). The ocean resolution in meridional direction is 3° at the poles and 1° otherwise. The longitudinal resolution is uniformly 1°. The vertical resolution of the ocean consists of 23 unevenly spaced levels, ranging from 10 m near the surface to several hundred meters in the deep ocean (the top eight layers are located within the first 200 m of the ocean). Laplacian viscosity and diffusivities are used in the horizontal and vertical, with υh=104 m2 s−1, kh =102 m2 s−1, υυ = 10−3 m2 s−1, and kυ = 6 × 10−5 m2 s−1. A land surface component is also used as described above. For this configuration a time-step of 3 h is used in the ocean using an implicit scheme for the vertical mixing and 30 min in the atmosphere. The ocean and atmosphere components are coupled every 3 h (at each ocean time step) without invoking any flux adjustments.

b. Control run experiment

To simulate the model climate a 500-yr simulation was performed, starting from the World Ocean Atlas 2013 (WOA13; see Locarnini et al. 2013 and Zweng et al. 2013) climatology of temperature and salinity in the ocean, and initial fields for the atmosphere from an uncoupled run driven by AMIP-II SST and sea ice. Time series of the maximum AMOC amplitude in the Atlantic Ocean and of the global mean surface temperature are used to illustrate the performance of the model during the 500-yr run (Fig. 1). The AMOC maximum represents the maximum amplitude found in every monthly mean field, which typically was found near the depth of 1000 m and in the latitude range of 40°–50°N. As can be seen from Fig. 1a the AMOC strength is close to 20 Sv (1 Sv ≡ 106 m3 s−1) after the model initialization and oscillates around this amplitude for the first 50 years of the coupled run. The amplitude slowly declines subsequently and after an additional 150 years reaches a new, quasi-stable level of 15 Sv, common to many other coupled climate models (Collins et al. 2013). Superimposed to secular AMOC changes are variations that are especially pronounced on a seasonal cycle. This can be seen in detail in Fig. 1b showing the AMOC time series of the last 50 years of the 500-yr-long model run. Seasonal AMOC changes are on the order of 5 Sv, while interannual changes are on a 1–2-Sv level, again in agreement with state-of-the art coupled climate models (Flato et al. 2013).

Fig. 1.

Full time series of (a) the maximum AMOC amplitude (Sv) identified in the latitude range of 40°–48°N in the Atlantic Ocean and (c) the global mean surface temperature (°C). The last 50 years used during the analysis to describe the model climatology are expanded for (b) the maximum AMOC amplitude and (d) the global mean surface temperature (thick red line represents climatological HadCRU absolute surface temperature for the period 1961–90 that is 13.97°C).

Fig. 1.

Full time series of (a) the maximum AMOC amplitude (Sv) identified in the latitude range of 40°–48°N in the Atlantic Ocean and (c) the global mean surface temperature (°C). The last 50 years used during the analysis to describe the model climatology are expanded for (b) the maximum AMOC amplitude and (d) the global mean surface temperature (thick red line represents climatological HadCRU absolute surface temperature for the period 1961–90 that is 13.97°C).

Figures 1c,d show similar plots but for the global mean temperature, which can be compared to climatological Hadley Centre/Climatic Research Unit (HadCRU) absolute surface temperature for the period 1961–90; relative to the HadCRU SST dataset the model shows only an insignificant negative bias close to 0.1°C. The amplitude of the seasonal cycle is close to 3°C while interannual changes are on the order of a few tenths of a degree. Clearly visible are also variations occurring on time scale of 50–100 yr, especially during the first part of the run.

In the following we will use the model output from the last 50-yr period to describe the model climatology. To be compatible with other similar model descriptions in the literature (e.g., Holden et al. 2015) we will stick to a few characteristic parameters separated into the domains ocean, atmosphere, and sea ice.

1) Ocean

Biases in surface properties are summarized in Figs. 2a,b in terms of 50-yr time-mean differences of sea surface temperature and sea surface salinity between CESAM and the WOA13 climatology, respectively. Resulting temperature biases (Fig. 2a) are on the order of 3°–4°C with patterns that are not unlike large-scale circulation and upwelling structures. Those differences are typical for coupled climate models and are comparable to what was found for the MPI-ESM [e.g., see Fig. 2 of Jungclaus et al. (2013)]. In some regions differences reach 6°C, notably in the Kuroshio Extension, suggesting that either a shift in the spatial frontal position or the lack of eddy effects can contribute to the observed differences.

Fig. 2.

Biases in CESAM surface properties: (a) sea surface temperature (°C) and (b) salinity (psu) differences between the mean over the last 50 years and WOA13 climatology. Global time-mean (c) potential temperature (°C) and (d) salinity (psu) profiles (depth on the y axis in meters) relative to WOA13 climatology. Atlantic Ocean zonal averages for (e) potential temperature (°C) and (f) salinity (psu) differences between the mean over the last 50 years and WOA13 climatology.

Fig. 2.

Biases in CESAM surface properties: (a) sea surface temperature (°C) and (b) salinity (psu) differences between the mean over the last 50 years and WOA13 climatology. Global time-mean (c) potential temperature (°C) and (d) salinity (psu) profiles (depth on the y axis in meters) relative to WOA13 climatology. Atlantic Ocean zonal averages for (e) potential temperature (°C) and (f) salinity (psu) differences between the mean over the last 50 years and WOA13 climatology.

With respect to salinity biases (Fig. 2b) the situation appears different in that differences reflect large-scale pattern, as they would result from biases in the exchanges of freshwater between the terrestrial hydrology and the ocean, superimposed to evaporation minus precipitation (EP) biases in the model. Salinity biases are maximum over the Arctic as it would result from a lack of runoff from the subpolar continents. In contrast, the Atlantic and Indian Oceans and the European northern seas all suggest too much net freshwater flux into the model oceans resulting in too-fresh surface layers.

The vertical structure of the temperature and salinity biases are illustrated in Figs. 2c,d in terms of globally averaged vertical profiles of the model–observation data biases. Both parameters show fairly similar vertical structures indicating too-warm and too-salty thermoclines and too-cold and too-fresh deep-water masses. Biases also show a clear geographic pattern as illustrated by zonal averages of the temperature and salinity model–observation data differences in the Atlantic (Figs. 2e,f). Obviously the North Atlantic Deep Water is too warm, while the subpolar region is too cold near the surface. Likewise, the subtropical near-surface gyre is too cold, while the tropical Atlantic is biased warm over the top 3000-m depth. For salinity a somewhat different picture emerges in that the upper 500 m seem too fresh throughout the Atlantic south of 40°N. In contrast, the model is too salty at the depth roughly coinciding with the AMOC maximum, as it is in the subpolar Atlantic. Both effects together have a partly compensating effect on the stratification of the model ocean relative to the observed climatology.

The time-mean barotropic streamfunction of the model reveals gyre volume transports on the order of 52.16 Sv in the North Pacific (maximum values of the subtropical gyre associated with the Kuroshio, to the south of Japan) and 20.76 Sv in the North Atlantic (subpolar gyre maximum values of BSF to the south of Greenland) (Fig. 3a). In the Southern Ocean the ACC transport is on the order of 86.3 Sv through the Drake Passage, which is clearly too low compared to observations (137 ± 8 Sv; see Cunningham et al. 2003). Figure 3b reveals a meridionally coherent Atlantic overturning streamfunction with a maximum located between 40° and 50°N at a depth of around 1000 m. Figure 3 reveals also a fairly pronounced inflow of Antarctic Bottom Water into the Northern Hemisphere Atlantic deep basin.

Fig. 3.

(a) Barotropic streamfunction (Sv; contour interval is 20 Sv) and (b) Atlantic meridional overturning streamfunction (Sv; contour interval is 2 Sv).

Fig. 3.

(a) Barotropic streamfunction (Sv; contour interval is 20 Sv) and (b) Atlantic meridional overturning streamfunction (Sv; contour interval is 2 Sv).

The time-mean meridional transports of heat and freshwater are shown in Figs. 4a,b for the global ocean computed from the net ocean–atmosphere fluxes. Simulated transports are generally consistent with independent estimates obtained from data analyses and ocean state estimates (Wunsch and Heimbach 2013; Stammer et al. 2003; Macdonald and Baringer 2013; Wijffels 2001; Talley 2008).

Fig. 4.

Meridional (a) heat (PW) and (b) freshwater (Sv) transport for the global ocean computed from the net ocean–atmosphere fluxes. For (a), symbols depict global estimates from Wunsch and Heimbach (2013) (blue), Stammer et al. (2003) (cyan), and mean value of different estimates by Macdonald and Baringer (2013) (green); the uncertainties are a measure of the seasonal signal. For (b), blue symbols indicate observational estimates from various sources compiled in Wijffels (2001) and Talley (2008).

Fig. 4.

Meridional (a) heat (PW) and (b) freshwater (Sv) transport for the global ocean computed from the net ocean–atmosphere fluxes. For (a), symbols depict global estimates from Wunsch and Heimbach (2013) (blue), Stammer et al. (2003) (cyan), and mean value of different estimates by Macdonald and Baringer (2013) (green); the uncertainties are a measure of the seasonal signal. For (b), blue symbols indicate observational estimates from various sources compiled in Wijffels (2001) and Talley (2008).

Mean sea surface height pattern show gyre type structures as they are common to non-eddy-resolving models (Fig. 5). The simulated range from +1.0 to −1.5 m is in agreement with other models, but underestimates the observed range from 1.0 to −1.9 m, derived from a combination of satellite altimetry with geodetic models. Gradients across the Gulf Stream and the Kuroshio are on the order of 1 m; across the ACC the sea level drop is −1.4 m. Altogether these parameters are comparable to other climate models of similar resolution.

Fig. 5.

(a) Model mean dynamic topography (m). (b) Differences between last-50-yr model climatology and mean dynamic topography derived from the difference of the CNES CLS11 mean sea surface observed by satellite altimetry and the GOCO02 geoid (Pail et al. 2010). The contour intervals are 0.25 m.

Fig. 5.

(a) Model mean dynamic topography (m). (b) Differences between last-50-yr model climatology and mean dynamic topography derived from the difference of the CNES CLS11 mean sea surface observed by satellite altimetry and the GOCO02 geoid (Pail et al. 2010). The contour intervals are 0.25 m.

2) Atmosphere

As a form of integral atmospheric statement, we show in Fig. 6 the globally averaged energy balance of the CESAM together with numbers available from IPCC Fifth Assessment Report (AR5) models (Wild et al. 2015) and with numbers derived from the ERA-Interim atmospheric reanalysis (Berrisford et al. 2011). For the surface, a too-low upward longwave radiation reflects a cold bias in the surface temperature while all other components of the energy budget fall within the range spanned by the IPCC AR5 models. For the top of the atmosphere too-large reflected solar radiation indicates a possibly too-high cloud albedo. In addition an underestimation of the atmospheric window may contribute to a lower outgoing longwave radiation. We intend to correct these deficits in a following study through data-assimilation-related parameter optimization using the CESAM adjoint model.

Fig. 6.

Global energy flows (W m−2) of CESAM (top numbers; mean of the last 50 years). Values in parentheses denote the mean and ensemble spread of 43 CMIP5 models from IPCC AR5 (Wild et al. 2015); numbers in square brackets denote values from ERA-Interim. The values represent data from 1989 to 2008 (after Berrisford et al. 2011).

Fig. 6.

Global energy flows (W m−2) of CESAM (top numbers; mean of the last 50 years). Values in parentheses denote the mean and ensemble spread of 43 CMIP5 models from IPCC AR5 (Wild et al. 2015); numbers in square brackets denote values from ERA-Interim. The values represent data from 1989 to 2008 (after Berrisford et al. 2011).

Time-mean fields of the near-surface (2 m) air temperature, of mean sea level pressure, and of the height of the 500-hPa layer are shown in Figs. 7a,d,g as they result from the CESAM run. Difference fields of the CESAM results relative to ERA-Interim are shown in Figs. 7b,e,h. The global mean near-surface air temperature exhibits a cold bias of about 2°C (Figs. 7b,c). However, while over the ocean a general cooling is found, warmer temperatures are present over the center of the continents. The largest negative anomalies are located at the sea ice margins related to an enhanced winter sea ice extent in CESAM. In addition, the cold bias is related to a reduction of SST zonal contrasts in the tropical Pacific, in particular to a weakening of the western Pacific warm pool.

Fig. 7.

T2M (°C): (a) the time mean over the last 50 years of CESAM, (b) the difference between CESAM and ERA-Interim (1979–2014), and (c) the zonal average of the respective field for CESAM (black) and ERA-Interim (blue). (d)–(f) As in (a)–(c), but for the sea level pressure (hPa). (g)–(i) As in (a)–(c), but for the geopotential height anomaly of the 500-hPa layer (m). For (g), the zonal mean is subtracted from the global field.

Fig. 7.

T2M (°C): (a) the time mean over the last 50 years of CESAM, (b) the difference between CESAM and ERA-Interim (1979–2014), and (c) the zonal average of the respective field for CESAM (black) and ERA-Interim (blue). (d)–(f) As in (a)–(c), but for the sea level pressure (hPa). (g)–(i) As in (a)–(c), but for the geopotential height anomaly of the 500-hPa layer (m). For (g), the zonal mean is subtracted from the global field.

The simulated sea level pressure reproduces observed patterns (Figs. 7d,e). But, while the locations of the stationary waves are in relatively good agreement, CESAM in general overestimates their magnitudes. A good agreement of the stationary wave pattern can also be found for the 500-hPa geopotential height (Figs. 7g,h). Here, however, CESAM underestimates the magnitude of the stationary wave pattern in the North Atlantic region, while the Aleutian low is overestimated.

Zonal averages of full fields from CESAM and ERA-Interim are shown in Figs. 7c,f,i. Essentially the CESAM does reproduce the meridional structure of all variables. Differences seem to be relatively small compared to the actual amplitudes and in some cases might result from a meridional shift of pattern.

In the following we compare climatological (50 yr) annual averages of selected atmospheric variables with ERA-Interim (1979–2014). As a first step, Fig. 8 (left) shows full time-mean CESAM fields of the net surface heat flux [the surface solar radiation plus surface turbulent fluxes (longwave plus latent plus sensible); Fig. 8a], the net surface freshwater flux (surface precipitation minus evaporation plus runoff; Fig. 8d), and the time-mean magnitude of the surface wind stress (Fig. 8g). In Figs. 8b,e,h we show differences of all those fields relative to ERA-Interim. All respective panels reveal that on large space scales differences are small. However, in some locations increased differences can be found, for example, in high latitudes for net surface heat fluxes; and enhanced differences are located in the subtropics and tropics for net precipitation, partially coinciding with the ITCZ.

Fig. 8.

Net surface heat flux (W m−2) [surface solar radiation plus surface turbulent fluxes (longwave plus latent plus sensible)]: (a) the time mean over the last 50 years of CESAM, (b) the difference between CESAM and ERA-Interim (1979–2014), and (c) the zonal average of the respective field for CESAM (black) and ERA-Interim (blue). (d)–(f) As in (a)–(c), but for the net surface freshwater flux (mm day−1) (surface precipitation minus evaporation plus runoff). (g)–(i) As in (a)–(c), but for the magnitude of the surface wind stress (10−3 Pa).

Fig. 8.

Net surface heat flux (W m−2) [surface solar radiation plus surface turbulent fluxes (longwave plus latent plus sensible)]: (a) the time mean over the last 50 years of CESAM, (b) the difference between CESAM and ERA-Interim (1979–2014), and (c) the zonal average of the respective field for CESAM (black) and ERA-Interim (blue). (d)–(f) As in (a)–(c), but for the net surface freshwater flux (mm day−1) (surface precipitation minus evaporation plus runoff). (g)–(i) As in (a)–(c), but for the magnitude of the surface wind stress (10−3 Pa).

Zonal averages of CESAM and ERA-Interim are shown in Figs. 8c,e,f. Similar to Fig. 7, the CESAM does also reproduce the meridional structure of the surface fluxes. Differences seem again to be relatively small compared to the actually amplitudes. Only in a few instances amplitudes are clearly different.

With respect to the coupling parameters, the following can be noted: 1) overall, the simulated total heat flux is in general in good agreement with ERA-Interim (Figs. 8a–c). Larger differences can be found in the Northern Hemisphere over strong western boundary current systems such as the Gulf Stream and Kuroshio Extension and in the Southern Hemisphere over the subtropical frontal region particularly over retroflection areas. A closer inspection reveals that biases in surface solar radiation and surface thermal radiation tend to compensate each other while the remaining differences are mainly due to the latent heat flux. 2) For the net freshwater flux, the model shows a large bias in the tropics mostly related to differences in precipitation (Figs. 8d–f). Here, CESAM failed to reproduce the typical shape of the intertropical convergence zone. To some extent this may be related to the relatively coarse resolution of the atmospheric component. In addition, the reduction of the SST contrasts in the tropical Pacific and the weakening of the western Pacific warm pool diminish the shape and the strength of convective precipitation patterns. 3) Consistent with the sea level pressure, the simulated surface wind stress pattern is in good agreement with ERA-Interim. Also, the magnitudes of the wind stress are in good correspondence except for large regions over the continents where the signal is overestimated potentially due to low orographic drag.

Meridional sections of zonally averaged climatological annual mean zonal winds and temperatures are shown in Fig. 9 for CESAM and as differences between CESAM and ERA-Interim. Clearly the cold bias of CESAM can be detected in the whole troposphere. In addition, a strong stratospheric cold bias is present in polar regions, most pronounced in the Northern Hemisphere. In contrast, the tropical stratosphere shows warmer temperatures than ERA-Interim. While the model captures the tropical easterlies, the jet maxima are shifted toward the poles. Both jets are not closed mainly due to the coarse vertical resolution (10 vertical levels only).

Fig. 9.

Zonal averages of (a) the time mean over the last 50 years of CESAM zonal wind (contours; m s−1) and the air temperature (color shaded; °C) and (b) the time mean difference between CESAM and ERA-Interim (1979–2014). (Height shown on the y axis is in hectopascals.)

Fig. 9.

Zonal averages of (a) the time mean over the last 50 years of CESAM zonal wind (contours; m s−1) and the air temperature (color shaded; °C) and (b) the time mean difference between CESAM and ERA-Interim (1979–2014). (Height shown on the y axis is in hectopascals.)

3) Sea ice

Figure 10 illustrates the sea ice concentration for the Northern Hemisphere (Figs. 10a,c) and Southern Hemisphere (Figs. 10b,d) from March (Figs. 10a,b) and September (Figs. 10c,d). Compared to the observed sea ice extent (red line) the March sea ice coverage is overestimated in both hemispheres. In contrast, September conditions show substantial negative biases in sea ice coverage, especially over the Arctic.

Fig. 10.

Sea ice concentration for (a),(c) Northern Hemisphere and (b),(d) Southern Hemisphere from (a),(b) March and (c),(d) September. The red contours indicate the observed ice extent, defined by 15% ice concentration, derived from observed ERA-Interim sea ice extent covering the period 1979–2010 (after Berrisford et al. 2011).

Fig. 10.

Sea ice concentration for (a),(c) Northern Hemisphere and (b),(d) Southern Hemisphere from (a),(b) March and (c),(d) September. The red contours indicate the observed ice extent, defined by 15% ice concentration, derived from observed ERA-Interim sea ice extent covering the period 1979–2010 (after Berrisford et al. 2011).

Above results illustrate that, given the intermediate complexity of the atmospheric component (PlaSim) and taking into account that no flux adjustment (or flux correction) was used as part of the coupling procedure, CESAM simulates a reasonable climate. However, the model also reveals weaknesses, which need to be improved in the future. Nevertheless, biases appear to be on the same order as those found in CMIP models, suggesting that the model in its present condition can be used for first model sensitivity experiments making use of its adjoint.

c. Forward model sensitivity experiments

Adjoint sensitivities discussed in the next chapter are computed using a model version that for reasons detailed in section 4b is coarser in resolution than the one used above for the control run. To demonstrate that even with this coarser resolution the overall model climate remains reasonable, computations performed with the control setup were repeated but with a 90 × 44 longitude–latitude grid equivalent to a 4° horizontal resolution, with 15 vertical layers. The atmosphere was resolved on a spectral T21 horizontal resolution and split into 10 equidistant vertical sigma levels. The land surface was represented by the original Earth orography discretized on the T21 Gaussian grid. The ocean time step was set to 8 h and the time step in atmosphere was equal to 48 min. The model was initiated from “cold start” conditions (atmospheric/ocean currents at rest, and only a zonal atmospheric temperature distribution is prescribed; climatology of temperature and salinity in the ocean) and spun up until 1) the meridional overturning circulation in the Atlantic became stable and 2) a seasonal model cycle in sea level pressure, wind pattern, and temperature and radiative fields was found comparable to observations.

As a representative result we show in Fig. 11 the time-mean fields of the near-surface (2 m) air temperature, of mean sea level pressure and of the height of the 500-hPa layer from the low-resolution model. A visual comparison with Fig. 7 confirms that to a large extent the results from the two model runs are similar and that the model fields are comparable to ERA-Interim in their meridional structure.

Fig. 11.

Low-resolution forward simulation. T2M (°C): (a) the time mean over the last 50 years of CESAM T21 simulation, (b) the difference between CESAM T21 and ERA-Interim (1979–2014), and (c) the zonal average of the respective field for CESAM T21 (black) and ERA-Interim (blue). (d)–(f) As in (a)–(c), but for the sea level pressure (hPa). (g)–(i) As in (a)–(c), but for the geopotential height anomaly of the 500-hPa layer (m). For (g), the zonal mean is subtracted from the global field.

Fig. 11.

Low-resolution forward simulation. T2M (°C): (a) the time mean over the last 50 years of CESAM T21 simulation, (b) the difference between CESAM T21 and ERA-Interim (1979–2014), and (c) the zonal average of the respective field for CESAM T21 (black) and ERA-Interim (blue). (d)–(f) As in (a)–(c), but for the sea level pressure (hPa). (g)–(i) As in (a)–(c), but for the geopotential height anomaly of the 500-hPa layer (m). For (g), the zonal mean is subtracted from the global field.

To gain further confidence in the model, a sensitivity experiment with instantaneously doubled CO2 was performed for both resolutions. Results show that the time scale of the response is nearly the same in both cases and that the global climate sensitivities are in the range of CMIP-type coupled models, with lower sensitivity emerging with higher resolution (Fig. 12a). We note in particular that for northern Europe, which is the target region of this study, the temperature sensitivities to CO2 changes are in good agreement for the two resolutions (Figs. 12b,c).

Fig. 12.

Time evolution of the global averaged annual mean T2M difference (°C) between an instantaneous CO2-doubling run and the respective climatological mean of the control integration: low resolution (T21; blue line) and high resolution (T42; green line). The instantaneous CO2-doubling took place at the beginning of the runs starting from respective control runs after spinup. (b) Surface temperature changes: mean of the last 10 years (141–150) of the CO2-doubling experiment minus the temperature of the control run averaged over the whole time period (years 1–150) using the lower model resolution. (c) As in (b), but for the higher model resolution.

Fig. 12.

Time evolution of the global averaged annual mean T2M difference (°C) between an instantaneous CO2-doubling run and the respective climatological mean of the control integration: low resolution (T21; blue line) and high resolution (T42; green line). The instantaneous CO2-doubling took place at the beginning of the runs starting from respective control runs after spinup. (b) Surface temperature changes: mean of the last 10 years (141–150) of the CO2-doubling experiment minus the temperature of the control run averaged over the whole time period (years 1–150) using the lower model resolution. (c) As in (b), but for the higher model resolution.

4. The CESAM adjoint model

a. Generating the adjoint model

In the context of ocean and climate modeling the adjoint method seeks to find the most likely model solution simulating the observed state by minimizing an objective function J, which measures the weighted quadratic distance between model state variables and observations. The optimization problem is solved with the forward model as constraint. Because typically the problem is weakly nonlinear and large, it is solved by running the forward and the adjoint model in an iterative way. To this end the optimization involves the calculation of the gradients of J with respect to the control parameters using the adjoint to the linearized forward model ∂J/∂ui, where ui are the control parameters. These so-called adjoint sensitivities are being used to adjust control parameters to iteratively reduce the model–observation data difference.

Adjoint equations naturally appear as part of the Euler–Lagrange equations, which are the basis for any variational data assimilation problem (Talagrand and Courtier 1987). In principle one can construct a discrete adjoint model from the respective normal equations (Wunsch 1996). In practice, however, the easiest way to construct an adjoint model is to apply an algorithmic differentiation (AD) tool to automatically obtain the differentiated code of the original numerical forward model as adjoint source code with little effort required from the user (Vlasenko et al. 2016). The first application of the adjoint MITgcm model described by Marotzke et al. (1999) was based on a code constructed from the forward model with the help of the automatic differentiation (AD) tool Tangent–Linear and Adjoint Model Compiler (TAMC) (Giering and Kaminski 1998). Since this pilot construction of the adjoint to the MITgcm, the respective AD tool was further developed and commercialized. It is now available as the Transformation of Algorithms in FORTRAN (TAF; Giering and Kaminski 2003) compiler, which presently serves as the default tool for generating MITgcm adjoint codes from model’s FORTRAN code. Other AD tools are also available for the same purpose, such as OpenAD (Utke et al. 2008).

The TAF tool is based on a source transformation algorithm producing readable code. However, since the typical model configuration contains only the code needed for the specific experiment, the resulting adjoint is not the adjoint of the complete MITgcm but one of specific configurations only. A major step in making efficient use of TAF generated adjoint code is the implementation of TAF directives to help the compiler to efficiently decide which variables have to be either recomputed or stored. The approach involves applying the AD tool every time the forward model configuration is changed; this includes changes in the formulation of the cost function. Marotzke et al. (1999) provide guidelines and a documentation of the generation of the adjoint to the MITgcm and describe a first application of adjoint sensitivities to the Atlantic heat transport.

Building on the previous experience of Marotzke et al. (1999) for the ocean model and Blessing et al. (2004) for the PUMA atmosphere, the same approach of adjoint code generation using TAF is applied here, but now to the fully coupled CESAM climate model. To this end the PlaSim model code was coupled to the MITgcm and adjusted to be compatible with the automatic adjoint code generation using the TAF compiler in a way similar to the MITgcm code. This implies that some individual routines, particularly those related to input/output (I/O) and the communication, were hand-coded with respect to their adjoint formulation. In addition TAF directives were built in that organize the storage, checkpointing, or recomputation of state variables of the forward code required as input during each adjoint backward loop. Checkpointing is an algorithm that allows storing restart files and segments of the trajectory rather than the complete trajectory and is essential to balance storage requirements versus CPU time spent on recomputation. The coupling had no effects on the efficiency of the adjoint of the individual models, and similar to the forward model the adjoints to the atmospheric and ocean components are executed in turn. Further documentation on the generation of the coupled adjoint is provided by Blessing et al. (2014), who also briefly introduce the models functionality for coupled assimilation studies.

b. Computing smoothed ensemble-mean adjoint sensitivities

The goal of the present sensitivity study is to compute the gradients of daily mean northern Europe T2M with respect to the following key ocean surface quantities: SST, sea surface salinity (SSS), and sea ice concentration (SIC). To this end, the cost function represents the daily mean T2M at day 35, that is, the end of the forward run, averaged over the region 55.3°–60.9°N, 8.4°–14.1°E.

The adjoint sensitivities of T2M are computed with the aid of the adjoint CESAM using the coarser-resolution version of the CESAM outlined in section 3c. The coarser resolution was used because adjoint calculations are more demanding, computationally, than forward runs (Vlasenko et al. 2016). More importantly, higher-resolution models are more nonlinear, so adjoint sensitivities are prone to reveal fast-growing unstable modes, which would make it more difficult testing the validity of the adjoint model. For comparison purposes and to highlight the importance of coupled processes, even over these short time scales, the same sensitivities were computed using an uncoupled atmosphere-only setup. In these uncoupled model experiments the SST fields obtained from the coupled forward simulations were used as a boundary forcing. All other settings of the atmospheric model were the same as in the coupled case. However, in future applications the spatial resolution may be increased as will be the duration of the sensitivity runs.

According to Jablonowski and Williamson (2011) high-frequency errors of spectral atmospheric models, often called “ringing,” can result from a band-limited discrete representation in the Fourier space. Since the adjoint of the Fourier transform is just the inverse Fourier transform, this high-frequency error remains also in the adjoint atmospheric models. It can be expected that a fraction of such errors in the adjoint estimates can result from discontinuities in the shape of the cost function as it is the case for the top-hat function used here. As a result, the cost function contains a considerable amount of high-frequency error in the adjoint solution. An example of this error accumulated over three days of model run is shown in Fig. 13a. The associated wavelike pattern has approximately the same amplitude everywhere. However, superimposed at a few, but not connected, grid points are random outliers with larger amplitudes (see below). For display purposes the scale of the color bar is adjusted in such a way that only the ringing error is visible.

Fig. 13.

(a) The ringing adjoint noise and outliers in the T2M–SST sensitivity on day 32 prior to the initialization. (b) As in (a), but after applying all filters. For better visualization the scales of the color bars are truncated. The full scales of the unfiltered and filtered sensitivities are [−0.099 345, 0.099 315] and [−0.014 709, 0.005 949 3], respectively. See text for details.

Fig. 13.

(a) The ringing adjoint noise and outliers in the T2M–SST sensitivity on day 32 prior to the initialization. (b) As in (a), but after applying all filters. For better visualization the scales of the color bars are truncated. The full scales of the unfiltered and filtered sensitivities are [−0.099 345, 0.099 315] and [−0.014 709, 0.005 949 3], respectively. See text for details.

One can argue that the ringing described above results from the fact that the above cost function has a top-hat form and that for a tapered (in space) cost function resulting in a smooth shape a smaller amount of high frequency in the adjoint estimate should be expected. To test whether this is indeed the case, several respective tests were performed with inverse exponent and sinelike cap functions defined on 3 × 3, 5 × 5, and 7 × 7 gridpoint areas. Results did lead to considerably reduced errors (3–5 times smaller); however, the high-frequency noise did not disappear altogether. We therefore decided instead to remove the ringing noise by applying a filter, which is justified by the similarity of the noise pattern in Fig. 13a to truncation structures in a frequency domain. By doing so we followed Jablonowski and Williamson (2011), who were able to show that such a ringing noise can be removed from the results using the Gaussian and Laplacian filters.

Both filters were added manually to the TAF-generated CESAM adjoint code but applied only to the adjoint state variables, not to the forward model state variables. The Gaussian filter is applied to adjoint variables at each time step in the Fourier space only. We note that the Gaussian filter is approximately invariant to the Fourier transform (it remains a Gaussian, albeit different in form), and hence it can be applied in physical and Fourier spaces without producing artifacts associated with space transformation. Since the Gaussian filter suppresses mainly the high wavenumber part of the spectrum, which is representative for the fast-growing modes, such a procedure should be a proper option for damping these modes.

Applying the filters exclusively to the adjoint variables is consistent with Amerault et al. (2008), who suggest removing parameterizations in the adjoint code that are responsible for fast-growing modes in the adjoint variables. While in the forward model nonlinear effects always limit these modes, the adjoint model is linear, and hence these modes will always grow uninterruptedly since corresponding feedbacks do not exist in the adjoint code. However, contrary to Amerault et al. (2008), we do not remove the adjoint processes altogether. Therefore the fast-growing ringing noise appears, which we suppress by filtering. All other estimates resulting from the corresponding adjoint process remain essentially unaffected. Nevertheless, the application of the filter does not affect the correctness of the adjoint sensitivities. Not compromising the forward simulation in any way is beneficial to the realism of the adjoint as the linearization is taken along a more realistic trajectory.

Results confirm that the Gaussian filter removes a significant fraction of the small-scale noise in Fig. 13a. However, some fraction remains and accumulates over time. To further reduce the high-frequency noise we also implemented a biharmonic filter and a high-frequency targeted median filter in the adjoint source code. The high-frequency targeted median filter is designed for damping mainly the Nyquist frequency. Mathematically it can be formulated as follows:

 
formula

where

 
formula

and j is the spatial index. Note that the argument of the sign function is the product of two finite difference derivatives; the sign function equals one only if these derivatives have opposite signs and equals zero otherwise. Note also that spatial derivatives of the ringing noise have always opposite signs in neighboring points; hence, the filter is applied when the ringing noise remains in the state vector. In case xold has no noise and grows or decays monotonically, q = 0 and the filter is not applied.

In additional to spatial component, there is also a temporal component of noise appearing in the adjoint sensitivities. It is removed by using the Robert–Asselin filter [see Jablonowski and Williamson (2011) for details].

As can be seen from Fig. 13b showing the same fields as Fig. 13a but after filtering, the remaining part of the noise in the adjoint atmospheric state vector is represented by outliers that typically appear spontaneously in single grid points. Their absolute value is at least 10 times larger than the absolute values of the corresponding adjoint variable in the neighboring grid points. Adjoint variables represent physical processes, which are smooth in time and space; hence, the adjoint variables also should be smooth functions. Because of this we assume that the outliers represent errors.

Following Amerault et al. (2008), we associate those outliers with unstable modes resulting mostly from parameterization and weather noise. They usually appear as a result of chaotic dynamics of the nonlinear terms and typically are not related to the specific cost function. Tests with different types of cost functions confirmed this fact. Growth appears in cases where the cost function related part of the adjoint is projected onto the growing modes, which is the case of most of the cost function formulations. As before, outliers are removed via filtering. The filter checks each state variable for outliers, and once an outlier is found it is substituted with the mean value of the neighboring points. Although the occurrence of these outliers is negligible in comparison to ringing, they introduce additional errors and may corrupt the model estimates.

Finally, to account for weather-related fast-growing modes in the climate models which would be present also in the adjoint computations, ensemble-mean adjoint sensitivities were generated from an ensemble of adjoint computations as follows: for each parameter, sensitivities were estimated individually for the five Januaries of five consecutive model years. The resulting sensitivity time series were averaged subsequently over a period of 3 days and then the five-member ensemble mean was computed from averaged sensitivities. Such averaging reduces the impact of fast-growing modes due to chaotic dynamics that depend on the background state.

5. Adjoint sensitivities

The CESAM adjoint model automatically computes sensitivities of the T2M with respect to all model state and control variables. For the sake of focus, however, we will limit the following discussion to the three parameters SST, SSS, and sea ice thickness (SIT) distributions over the North Atlantic and the Arctic. These parameters were selected because, in the ongoing climate debate, they are of general interest. This allows us also in the present state of model development to use the analysis as a consistency check of the adjoint model results against already known physical climate insight.

a. SST sensitivities

Ensemble mean T2M sensitivities to SST, averaged over 2-day periods of 3–5, 13–15, and 33–35 days of the backward adjoint integration, respectively, are shown in Fig. 14. The figure reveals that on a short time scale (Fig. 14a) the SST anomalies influencing T2M seem fairly local, and sensitivities can be described as a direct response to higher upstream SST and related higher air temperatures being advected to the target region. However, with increasing backward integration, a more dynamical, wavelike response appears in the sensitivity pattern (Fig. 14c), and an intermediate response stage occurs for time scales of about 2 weeks (Fig. 14b) when the kinematic and dynamical responses are of the same magnitude. The strength and shape of the dynamical response grow fast in the backward integration after the initial 2-week period; in the following two weeks it seems to saturate, reaching a stationary stage after 30 days of backward integration; it remains of the same shape for the remaining period subsequently (Fig. 14c). The correlation coefficient between the sensitivity patterns obtained for 32 and 35 days of backward integration vary from 0.74 to 0.83.

Fig. 14.

The five-member ensemble mean of the averaged sensitivity of day-35 daily mean near-land air temperature over northern Europe to SST between (a) backward days 3–5, (b) backward days 13–15, and (c) backward days 33–35. The air temperature is the mean over the last day. The signal is normalized by the maximum value of the mean of the sensitivity to day 1–3.

Fig. 14.

The five-member ensemble mean of the averaged sensitivity of day-35 daily mean near-land air temperature over northern Europe to SST between (a) backward days 3–5, (b) backward days 13–15, and (c) backward days 33–35. The air temperature is the mean over the last day. The signal is normalized by the maximum value of the mean of the sensitivity to day 1–3.

A response of the surface state to deep ocean processes normally takes at least a couple of months. Because of this the influence of coupling processes on the estimated sensitivities over the considered time scales could be considered negligible. However, a comparison of the model sensitivity obtained from coupled and uncoupled models reveals that the SST patterns for both look similar in all general features; however, they are not identical. Nevertheless, the maximal difference between the two does not exceed 7% on the sensitivity scale in the beginning of the backward integration and increases up to 15% at the end of the integration period, suggesting that because our runs do not exceed 1 month in duration an impact of the deeper ocean remains small and the interaction is confined to the near-surface ocean. We note in this context that the amplitudes of the adjoint variables decay quickly with depth. For instance, the scale of the adjoint potential temperature is 5 times smaller at 300-m depth (which equals three model layers) than the scale of the SST sensitivity. Thus, shallow water mixing and surface cooling/warming seem to be the only ocean processes that contribute to the SST sensitivity.

Since the target region is located in an area with predominant westerly winds, one may expect that the atmospheric state defining the strength and the direction of these winds may have significant impact on the sensitivity pattern. Note that the variability of these winds in the North Atlantic is correlated with the NAO phase. Because of this the NAO phase was chosen as a marker of the atmospheric state. The estimated four members of the sensitivity ensemble correspond to the positive NAO phase; the last member corresponds to the negative NAO phase. A comparison between the positive and neutral sensitivity patterns revealed that they are similar, in general. Thus, one may assume that the NAO has a minor impact on the sensitivity estimates and different mechanisms, which define the maximal T2M variability in the target region. This assumption has been confirmed by forward runs as described below.

The SST sensitivity analysis presented in Fig. 14 has to be considered complementary to the correlation analysis of SST and atmosphere variability discussed by Frankignoul (1985) and more recently by Kushnir et al. (2002). Those authors showed that a tripole, horseshoe-like SST anomaly in North Atlantic strengthens (or weakens, if sign of the anomaly changes) the westerly winds. These findings were supported by Drévillon et al. (2001), who showed from a correlation analysis that on monthly to seasonal periods the Atlantic SST anomaly strengthens cyclonic (anticyclonic) activity over northern Europe and, in turn, results in an enhanced (weakened) atmospheric circulation causing less (or more) severe winters.

Like the correlation analysis, the adjoint sensitivity approach also lends itself to the idea that perturbations in the SST result in changes of the atmospheric state and is aimed to reveal the linear dependence between them, provided that such dependence exists. Assuming that there are no other mechanisms in the ocean that may affect the air temperature during the considered time period in the target region and relying on linearity of that process, it is suggested that sensitivities of T2M to Atlantic SST should have at least some aspects in common with the tripole pattern. However, a comparison of the obtained SST sensitivity pattern (see Fig. 14c) with SST anomaly shown in Kushnir et al. (2002) and Frankignoul (1985) reveals that, despite similarity in shape, there is an apparent lateral shift of the respective pattern by 4°–8° longitude.

We note that Kushnir et al. (2002) and Frankignoul (1985) in their analysis identified SST modes that cause maximal impact on the atmosphere variability on global or basin scales. In our study we focus on the maximal impact on T2M only in the specific part of northern Europe. The mismatch between the areas where the maximum atmospheric response is investigated could result in the northward shift between estimated SST sensitivity and the first mode of the SST variability: the sensitivities are different because the target functions are different.

Other reasons for this shift could be the fact that our model is fairly coarse in resolution or unwanted effects of the applied spatial filters. One should also note that processes in the atmosphere in principle are nonlinear and hence the effect of individual SST anomalies on T2M as suggested by the adjoint sensitivities remains to be demonstrated. This can be done by applying the SST anomalies with patterns of the gradients to the full nonlinear model, which also allows for testing the degree of linearity in the underlying dynamical processes for the chosen time scales. A respective test of the correctness and the physical meaning of the estimated sensitivities has been performed in a series of forward experiments representing two extreme cases in which an SST anomaly field corresponding to the sensitivities shown in Fig. 14c was added to the ocean temperature fields.

In the first experiment the SST anomaly was added at initial time to the first layer of the ocean. This test case is used to validate the adjoint sensitivities. However, since the anomalies are inserted only to the surface layer, the response is likely to underestimate realistic cases with deeper extent of SST perturbations. To explore the upper limit of the response we performed a second experiment, which is an atmosphere-only experiment in which the SST anomaly was persistently added to the SST fields obtained from the reference run. This experiment can be considered a case in which the temperature anomaly spreads over an infinitely deep ocean.

The numerical experiment with the initial SST perturbation was conducted according to the following three-stage scheme: 1) In the beginning of the experiment, CESAM was configured as discussed in the beginning of the section and used for sensitivity estimations. The model was run subsequently for 40 years starting from an established climatology. The corresponding 40 time-varying model state vectors for each 2-month period of January and February were saved over the entire model period. 2) At the next stage, the SST anomaly (which was equal to the scaled SST sensitivity; see Fig. 14c) was added to all 40 initial sea temperature fields of the top 50 m providing the initial states for perturbed forward runs. 3) The experiment was repeated four times for each setting with increasing scaling factors for the SST anomaly leading to anomalies in the range of 2°, 3°, 4°, and 5°C. Then the same experiments were repeated with negative SST perturbation added to the initial sea temperature fields. The effect of the SST anomalies to the unperturbed state is given in Table 1 representing the 40-yr statistically significant averaged daily mean temperature anomaly and corresponding ensemble standard deviation at the end of the target period.

Table 1.

Mean T2M anomaly and standard deviation σ in parentheses in the target region caused by adding and subtracting the SST anomaly according to the sensitivity pattern. The anomaly was set at the initial time in the first ocean layer (coupled case).

Mean T2M anomaly and standard deviation σ in parentheses in the target region caused by adding and subtracting the SST anomaly according to the sensitivity pattern. The anomaly was set at the initial time in the first ocean layer (coupled case).
Mean T2M anomaly and standard deviation σ in parentheses in the target region caused by adding and subtracting the SST anomaly according to the sensitivity pattern. The anomaly was set at the initial time in the first ocean layer (coupled case).

The validation of fidelity of sensitivity estimates can be done by means of the gradient product. The response to the SST can be approximated by the dot product between the gradient of the cost function fc and the SST anomaly: , where ΔT is the T2M response and ΔSST is the imposed SST anomaly. The SST anomaly used in the forward run experiment is just scaled SST sensitivity; that is, , where S and are the scaling and the normalization factors for the SST anomaly, respectively. Thus the T2M response can be estimated as . A comparison of ΔT and with the T2M response obtained in the forward run revealed that the difference between them is not bigger than 8% after 5 days of backward integration. The increase of the period of integrations results in a growing difference, and at the end of the 35-day period it reaches 65% of the expected response.

The results shown in Table 1 reveal that statistically significant positive (negative) T2M responses appear only when the scale of added (subtracted) SST perturbations are on the order of 4°C or larger. Figures 15a,b show the associated wind patterns after averaging over the period of last 3 and 9 days of the 35-day period for the difference between the unperturbed run and the result of adding the negative SST perturbation. Respective results obtained after subtracting the same SST anomaly pattern are shown in Figs. 16a,b. Results from both figures seem consistent with findings from Drévillon et al. (2001), who report that scaled tripole SST anomalies (similar to the presented sensitivity pattern in Fig. 14c) cause a strengthening (weakening) of westerly winds over the target region, and such changes in wind pattern should result in a corresponding increase (decrease) of heat transported from the ocean to the land. As can be seen from Figs. 16a,b, the changes in the atmospheric circulation obtained in our test experiment are consistent with the expectations reported by Drévillon et al. (2001).

Fig. 15.

Ensemble mean of 40 averaged near-surface wind field anomalies obtained after applying a SST anomaly with the pattern shown in Fig. 14c. (a) Mean wind anomalies averaged over the last 3 days of 35-day estimation period. (b) As in (a), but with averaged wind anomalies over the last 9 days. The green square represents the target area; gray area represents the actual land mask in the T21 resolution setup.

Fig. 15.

Ensemble mean of 40 averaged near-surface wind field anomalies obtained after applying a SST anomaly with the pattern shown in Fig. 14c. (a) Mean wind anomalies averaged over the last 3 days of 35-day estimation period. (b) As in (a), but with averaged wind anomalies over the last 9 days. The green square represents the target area; gray area represents the actual land mask in the T21 resolution setup.

Fig. 16.

Mean of 40 averaged near-surface wind field anomalies caused by adding a SST anomaly with the pattern from Fig. 14c. (a) Mean wind anomalies averaged over the last 3 days of 35-day estimation period. (b) As in (a), but with averaged over the last 9 days. The green square represents the target area; gray area represents the actual land mask in the T21 resolution setup.

Fig. 16.

Mean of 40 averaged near-surface wind field anomalies caused by adding a SST anomaly with the pattern from Fig. 14c. (a) Mean wind anomalies averaged over the last 3 days of 35-day estimation period. (b) As in (a), but with averaged over the last 9 days. The green square represents the target area; gray area represents the actual land mask in the T21 resolution setup.

Our experiment confirms that the SST anomaly pattern associated with sensitivity pattern alters the wind direction over the target point and changes the corresponding near-land temperature. In particular, adding the SST sensitivity-like perturbation results in an anticyclonic anomaly over the North and Norwegian Seas, which strengthens the flow of air from the sea over the target area. The differences averaged over nine days confirm the persistence of anticyclonic (cyclonic) anomalies caused by adding (subtracting) the corresponding SST perturbation. In addition, this wind passes over the warm near-shore SST anomaly located at the western coast of Norway. These two factors together provide an increase of heat transport incoming to the target area and corresponding increase of T2M there. Subtraction of SST sensitivity-like perturbations result in a cyclonic wind anomaly over the Bay of Biscay and an anticyclonic wind anomaly over the north of Norway leading to anomalous northeasterly wind pattern over the target area. Passing partially over the negative near-shore SST anomaly located in the northern coastal region of Norway and partially incoming from the continent this wind brings negative heat transport anomalies, which cools the target area.

During the atmosphere-only experiments the same SST sensitivity was persistently added to (or subtracted from) the SST fields obtained from the unperturbed reference run. The resulting fields were saved and used afterward as a forcing for modeling of the atmosphere dynamics. The rest of the experiment agrees with the initial SST perturbation experiment.

The T2M response for the atmosphere-only case is given in Table 2. An obvious difference from the previous experiment is that the atmospheric temperature shows significant responses starting already with 2°C anomaly amplitudes. Note however that the scale of the response and the standard deviation are almost the same for both experiments in case the scale of SST bias is bigger than 3°C. Moreover, the wind anomalies resulting from this experiment (not shown) have patterns similar to those shown in Figs. 15 and 16. From the results, we can conclude that in the forward model a meaningful T2M response appears only if the applied SST anomaly is either large or persistent enough over time; that is, the SST anomaly should not decay fast as a result of cooling or warming caused by ocean–atmosphere feedbacks attributable to near-surface mixing in the ocean. Necessary conditions are therefore that either if the amplitude of the SST anomaly are large enough or if it is deep enough. However, as can be seen from Tables 1 and 2, an increase of the anomaly amplitude does not necessarily result in a proportional increase of the T2M response over the target region.

Table 2.

Mean T2M anomaly and standard deviation σ in parentheses in the target region caused by adding and subtracting the SST anomaly according to the sensitivity pattern. The anomaly was persistently added to (subtracted from) the SST fields obtained in the reference run (the atmosphere-only case).

Mean T2M anomaly and standard deviation σ in parentheses in the target region caused by adding and subtracting the SST anomaly according to the sensitivity pattern. The anomaly was persistently added to (subtracted from) the SST fields obtained in the reference run (the atmosphere-only case).
Mean T2M anomaly and standard deviation σ in parentheses in the target region caused by adding and subtracting the SST anomaly according to the sensitivity pattern. The anomaly was persistently added to (subtracted from) the SST fields obtained in the reference run (the atmosphere-only case).

Moreover, a significant increase of the temperature response over northern Europe occurs only if SST anomalies are in the range between 2° and 3°C. The reason for that can be as follows: The driver of a negative response is the wind anomaly that causes a penetration of cooler air masses located on the continent. The average air temperature at these points is only 2°–3°C lower than the corresponding air temperature in the target region. Thus, a negative T2M response over the target region is bounded by these values. In case of a positive SST fluctuation the wind flux passes over the region with warmer SST anomaly. Thus, scaling the total SST fluctuation should result in corresponding scaling of the positive T2M response. However, warmer SST increases moisture resulting in additional cloud formation over the target region. Note that 2°C anomaly results in the increase of cloud cover over the target region from 39% to 52%, and for 5°C anomaly it becomes 70%. Thus, the lack of solar radiation bounds the scale of positive T2M response over the target region.

The discussion confirms that a full process understanding is required to understand detailed responses in regional temperature, which can sometimes be counterintuitive. The comparison of the results obtained so far for both phases also reveals that the scale of T2M response to positive SST anomaly is 2 times smaller when NAO is in negative phase, but the scales of the response to negative SST anomaly remains the same for both NAO phases.

b. Salinity sensitivity

Contrary to SST, a significant T2M sensitivity to surface salinity appears only along the northern edge of the ocean basins (Fig. 17), suggesting that they are associated with zones of deep convection there. Changes in salinity in these areas caused, for instance, by positive freshwater fluxes from sudden ice formation/melting or abnormal rainfalls, in addition to anomalies being advected by the East Greenland Current, may alter convection, thereby changing the heat exchange with the atmosphere. Although, T2M does not depend on SSS directly, fluctuations in SSS may cause changes in SST by intensification or weakening of vertical mixing. Agarwal et al. (2015) discussed how enhanced surface freshwater release around Greenland can influence the atmospheric circulation and specifically the path of the storm track in the North Atlantic.

Fig. 17.

The five-member ensemble mean of the sensitivity of the daily mean T2M over northern Europe of day 35 to SSS (averaged between days 1–3). The sensitivity is normalized by the maximum value.

Fig. 17.

The five-member ensemble mean of the sensitivity of the daily mean T2M over northern Europe of day 35 to SSS (averaged between days 1–3). The sensitivity is normalized by the maximum value.

To verify the correctness of estimated SSS sensitivity an experiment was carried out similar to the one described above in the context of SST anomalies in which SSS sensitivity was added to and subtracted from the initial SSS field. In the experiments with SSS perturbations, the maximum sizes of the anomalies were set equal to 0.1 and 1 psu. The experiments revealed that adding (freshening) or subtracting (salinification) SSS perturbation with a maximum value of 0.1 psu causes a statistically insignificant response over the period of 1 month. A statistically significant response appears only in the first 10 days when adding (subtracting) sensitivities result in a monotonic decay (increase) of daily mean air temperature, with a scale of 0.1°C at the maximum and the standard deviation for both cases equals 0.03°C. After that period the values of T2M in the target region become random for the remaining estimation time. The results suggest that a 0.1-psu anomaly in a 50-m layer is insufficient for forming persistent SST anomalies and causing a corresponding persistent T2M response for the given time period. This is because the intrinsic variability dominates over the deterministic effects of the perturbations.

In contrast, experiment with a 1-psu anomaly shows a statistically significant result only if salinity anomaly is subtracted. The daily mean temperature response at the end of target period equals −2.4°C with standard deviation equal to 0.87°C. The addition of the anomaly gives almost zero mean with spread equal to 0.98°C. The monthly mean air temperature anomaly, caused by SSS fluctuation, equals 0.47° and −0.19°C, with the corresponding standard deviations for both cases equal to 0.24°C.

c. Sea ice sensitivity

Similar to the SSS sensitivity, the T2M sensitivity to sea ice thickness also indicates a possible connection between sea ice thickness, surface freshening, and mean air temperature anomalies (Fig. 18). From observations, it can be inferred that an increase of ice in the Davis Strait–Labrador Sea region and decay in the Greenland–Barents Seas was associated with positive phase of NAO, and the opposite for negative NAO (García-Serrano and Frankingoul 2016). In particular, it was seen that such ice variations in January cause a statistically significant impact on the atmospheric circulation anomaly patterns over the northern Atlantic.

Fig. 18.

Five-member ensemble mean of sensitivity of the daily mean near-land air temperature over northern Europe of day 35 to SIT (averaged between days 1–3).

Fig. 18.

Five-member ensemble mean of sensitivity of the daily mean near-land air temperature over northern Europe of day 35 to SIT (averaged between days 1–3).

To test the connection between anomalies in SIT according to the estimated SIT sensitivity and T2M in the target region, an experiment similar to the one described in the previous subsection was carried out as follows: An anomaly in SIT of 5 times the normalized sensitivity shown in Fig. 18 was added to the ice thickness. In case of resulting values of ice thickness became negative they were set to zero. Adding the sensitivity leads to the complete ice decay in the Hudson Bay and Davis Strait. This results in an increase of the daily mean air temperature by 0.76°C in the target region. However, the standard deviation of this increase equals 0.67°C, and hence the response to the sensitivities is only weakly significant. The subtraction of sensitivity leads to an increase of sea ice in the Greenland Sea, which causes a decay of daily mean near-surface air temperature over the target region by 0.31°C. However, the standard deviation is equal to 0.78°C, rendering the results insignificant.

6. Discussion and concluding remarks

A central purpose of this paper was to introduce the new adjoint coupled climate model, CESAM, by demonstrating its potential for climate sensitivity studies. The model is a novel tool to provide dynamically consistent initial conditions for coupled climate model predictions by performing parameter optimization through data assimilation in the same model that is being used for the forecast. Beyond this forecast-oriented application, the model can be used in a much more general sense to study adjoint sensitivities of the coupled climate system, thereby revealing interactions and feedbacks within the climate system as well as the impact of regional changes on larger areas. Many respective applications come to mind covering complex feedbacks of the entire climate system. Taking advantage of the reasonable temperature and salinity climatology of the model, we start simply here by demonstrating the use of the coupled adjoint CESAM to identify dependencies of northern Europe surface air temperature on remote temperature, salinity, and sea ice changes in the Atlantic Ocean.

Causes for changes in northern European temperature in response to change of the Atlantic circulation and associated temperature anomalies on time scales beyond weather have been of interest and widely discussed for quite awhile. It is encouraging to find that the adjoint sensitivities lead to conclusions that appear consistent with insights drawn in previous studies how temperature anomaly patterns and resulting mechanisms in the atmospheric circulation may affect northern European temperatures. However, a significant difference from previous studies concerns the time scale considered. To rationalize this difference, the adjoint sensitivities can be interpreted as ocean anomalies that cause a maximum atmospheric response in a particular region for a time scale of one month. The SST anomalies change wind pattern and control through that the amount of heat incoming in those regions from the ocean. The fact that the results obtained here for time scales of up to one month seems to support results inferred for much longer time scales in the literature and might point to the possibility that respective mechanisms establish themselves fairly quickly and then saturate subsequently. In that sense results from Frankignoul (1985) and more recently by Kushnir et al. (2002) might represent a quasi-static reaction of a slowly varying background state.

A second, prominent example addressed is the question to what extent changes in the Arctic sea ice coverage influence weather and thereby the temperature over northern Europe. Presently this question is of central concern to many studies and climate programs. The adjoint sensitivities reveal that the impact of changes to sea ice coverage can influence the air–sea interaction, a process that is very similar to the sensitivities of SST to salinity changes alone. The subsequent influence on the northern European temperature then follows along the same lines as we have seen before from SST anomalies alone. Respective sea ice sensitivities are largest where large changes in sea ice coverage can be observed, notably the Fram Strait and the East Greenland Current.

Dealing with temperature, salinity, and sea ice aspects of adjoint sensitivities in combination appears to be advantageous above interpreting the impact of sea ice changes and freshwater changes in isolation. The anomaly in sea ice thickness, similar to corresponding sensitivity, has also impacted northern coastal regions; however, the scales and the statistical significance are weaker than in the case of the SST anomaly. The SSS sensitivity has the weakest impact and lies below the statistical significance.

Being a pilot application, by its very nature, our study has to be of limited extent and complexity. Nevertheless, the results shown are promising. To what extent interpretations hold also for longer time scales and setups with higher spatial resolution needs to be tested in upcoming longer adjoint sensitivity runs spanning several years. Those studies will go hand in hand with first assimilation studies. First, such studies need to be concerned with the question of how the length of the assimilation window is limited by the predictability time scale of the coupled system and how one can overcome respective limitations for generating coupled climate system reanalyses. A respective first study by Lyu et al. (2018) shows promising results but also suggests that at the end a hybrid assimilation approach is required, taking into account different predictability time scales in the atmosphere and the ocean.

In the future we anticipate that any coupled climate model comes with the possibility of generating its adjoint. At the present time, however, this goal appears far from reachable. How long CESAM as an intermediate-complexity model remains a singularity has to be seen. At the moment it is a unique tool that we invite the community to use. The forward CESAM and its documentation are available online (https://www.cen.uni-hamburg.de/research/cen-models/cesam.html), but generating the adjoint requires access to an automatic differentiation tool.

Acknowledgments

We thank two anonymous referees for their helpful comments. This work was supported in part by the European Community (EU) projects THOR and NaCLIM to Hamburg University. The work was also supported in part through the BMBF MiKLIP project (Modul A). Andrey Vlasenko acknowledges additional support obtained through DFG Grant Vl 82/1-1. Contribution to the DFG funded excellence initiative CliSAP of the Universität Hamburg.

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