Climate and terrestrial biosphere models consider nitrogen an important factor in limiting plant carbon uptake, while operational environmental models view nitrogen as the leading pollutant causing eutrophication in water bodies. The community Noah land surface model with multi-parameterization options (Noah-MP) is unique in that it is the next-generation land surface model for the Weather Research and Forecasting meteorological model and for the operational weather/climate models in the National Centers for Environmental Prediction. In this study, we add a capability to Noah-MP to simulate nitrogen dynamics by coupling the Fixation and Uptake of Nitrogen (FUN) plant model and the Soil and Water Assessment Tool (SWAT) soil nitrogen dynamics. This model development incorporates FUN's state-of-the-art concept of carbon cost theory and SWAT's strength in representing the impacts of agricultural management on the nitrogen cycle. Parameterizations for direct root and mycorrhizal-associated nitrogen uptake, leaf retranslocation, and symbiotic biological nitrogen fixation are employed from FUN, while parameterizations for nitrogen mineralization, nitrification, immobilization, volatilization, atmospheric deposition, and leaching are based on SWAT. The coupled model is then evaluated at the Kellogg Biological Station – a Long Term Ecological Research site within the US Corn Belt. Results show that the model performs well in capturing the major nitrogen state/flux variables (e.g., soil nitrate and nitrate leaching). Furthermore, the addition of nitrogen dynamics improves the modeling of net primary productivity and evapotranspiration. The model improvement is expected to advance the capability of Noah-MP to simultaneously predict weather and water quality in fully coupled Earth system models.
Over the past several decades, eutrophication – high concentrations of nutrients in freshwater bodies leading to severe oxygen depletion from the resultant algal blooms – has become a worldwide problem facing river, lake, and coastal waters (Conley et al., 2009; Howarth et al., 2006). As one of the greatest threats to freshwater and coastal ecosystems, eutrophic conditions lower biotic diversity, lead to hypoxia and anoxia, increase the incidence and duration of harmful algal blooms, and change ecological food webs that reduce fish production (Diaz and Rosenberg, 2008; National Research Council, 2000). These eutrophic conditions are attributed to excessive fertilizer leaching in river basins (Boesch et al., 2009; Boyer et al., 2006). To complicate this further, climate variation and climate change also determine the variation of hypoxia extent (Donner and Scavia, 2007): higher temperatures may extend the thermal stratification period and deepen the thermocline, thereby resulting in the upwelling of nutrients from sediment and increasing the concentration of nutrients in the bottom layer of water in lakes (Komatsu et al., 2007). Further, higher precipitation produces more runoff, and very likely more nutrients are delivered to the ocean as well (Donner and Scavia, 2007).
Nitrogen (N) is recognized as the leading nutrient causing eutrophication.
Without human interference, N cycling is relatively slow, as most ecosystems
are efficient at retaining this in-demand nutrient. N enters soil regularly
either through atmospheric wet and dry deposition or through atmospheric
N
Many of these N processes have been included in land surface, hydrologic, and water quality models developed particularly for environmental, climate, and agricultural applications (Bonan and Levis, 2010; Dickinson et al., 2002; Fisher et al., 2010; Kronvang et al., 2009; Schoumans et al., 2009; Thornton et al., 2007; Wang et al., 2007; Yang et al., 2009). These developments are still in their infancy, and large-scale climate models lack N leaching parameterizations that are comparable to those used in water quality models. Thus, large-scale models are not feasible for inherently fine-scale applications such as agricultural fertilization management and water quality prediction. Therefore, the present study improves these weaknesses by incorporating the strength of agriculture-based models into large-scale land surface models (LSMs).
The community Noah LSM with multi-parameterization options (Noah-MP) (Niu et al., 2011; Yang et al., 2011) is used as an exemplar of LSMs because it is the next-generation LSM for the Weather Research and Forecasting (WRF) meteorological model (Rasmussen et al., 2014) and for the operational weather and climate models in the NOAA/National Centers for Environmental Prediction. Because Noah-MP has an interactive vegetation canopy option – which predicts the leaf area index (LAI) as a function of light, temperature, and soil moisture – it is logical to augment this scheme with N limitation and realistic plant N uptake and fixation. The state-of-the-art vegetation N model is the Fixation and Uptake of Nitrogen (FUN) model of Fisher et al. (2010), which is embedded into the Joint UK Land Environment Simulator (JULES) (D. B. Clark et al., 2011) and the Community Land Model (CLM) (Shi et al., 2016). Modeling the impacts of agricultural management (e.g., fertilizer use) on N leaching is the strength of the Soil and Water Assessment Tool (SWAT) (Neitsch et al., 2011). Therefore, this study incorporates into Noah-MP both FUN's strength in plant N uptake and SWAT's strength in soil N cycling and agricultural management.
Our objective is to develop and utilize a land surface modeling framework for simultaneous climate (carbon) and environmental (water quality) predictions. We first describe the nitrogen dynamic model which combines equations used in FUN and SWAT. We then focus on evaluating the new integrated model at a cropland site, because fertilizer application on croplands globally contributes approximately half of the total N input to soil, with the other half coming from natural processes (i.e., atmospheric deposition and biological N fixation) (Fowler et al., 2013; Gruber and Galloway, 2008). Furthermore, cropland is a major source of N loading in water bodies. We evaluate the new model against observed soil moisture content, concentration of soil nitrate, concentration of nitrate leaching from soil bottom, and annual net primary productivity (NPP). We then analyze the impacts of the addition of N dynamics on the carbon and water cycles. To guide the use of this model on regional scales, we also analyze the impacts from different fertilizer application scenarios. Finally, we discuss other model behaviors, i.e., N uptake from different pathways and the major soil nitrate fluxes.
The Noah-MP model was augmented from the original Noah LSM with improved
physics and multi-parameterization options (Niu et al., 2011; Yang et al.,
2011), based on a state-of-the-art multiple-hypothesis framework (M. P. Clark
et al., 2011). Noah-MP provides users with multiple options for
parameterization in leaf dynamics, canopy stomatal resistance, soil moisture
factor for stomatal resistance, and runoff and groundwater. Until this work,
Noah-MP did not include any N dynamics. The only N-related parameterization
is in the calculation of the maximum rate of carboxylation (
Our modifications to the original Noah-MP mainly concern the sub-models dealing with dynamic leaf and subsurface runoff. The dynamic leaf option is turned on to provide NPP and biomass to the newly coupled N dynamic sub-model. In the original Noah-MP model, subsurface runoff from each soil layer was not an explicit output, but it is now a new output in the updated model. However, N concentrations are different among soil layers, which affects the amount of N removed from each soil layer by subsurface runoff. Therefore, in conjunction with the runoff scheme options 1 (TOPMODEL with groundwater) and 2 (TOPMODEL with an equilibrium water table), the lumped subsurface runoff for all four layers is first calculated, and then the water is removed from each soil layer weighted by hydraulic conductivity and soil layer thickness.
Model input variables and parameters.
Note: some parameters are not described in the paper. The values for
In Noah-MP, the soil N model structure is the same as in SWAT, which includes
five N pools consisting of two inorganic forms (NH
Flow chart of the nitrogen dynamic model. org.N: organic nitrogen.
Plant N uptake and fixation follow the framework of Fisher et al. (2010), which determines N acquired by plants through Eq. (3), advection (passive uptake); Eq. (4), symbiotic biological N fixation; Eq. (5) active uptake; and Eq. (6), retranslocation (resorption).
Noah-MP calculates the NPP or its available carbon,
Because no extra energetic cost is needed, passive uptake,
If
Similar to parallel circuits, each carbon cost is treated as a resistor, and
the integrated cost (Cost
Using Ohm's law, N acquired from C expenditure (
Fresh organic residue is broken down into simpler organic components via decomposition. The plant-unavailable organic N is then converted into plant-available inorganic N via mineralization by microbes. Plant-available inorganic N can also be converted into plant-unavailable organic N via immobilization by microbes.
Immobilization is incorporated into mineralization calculation (net
mineralization). Mineralization and decomposition, which are only allowed to
occur when soil temperature is above 0
The nutrient-cycling water factor for soil layer ly,
The mineralized N from the humus active organic N pool,
The mineralized N from the residue fresh organic N pool,
The decomposed N from the residue fresh organic N pool,
Using a first-order kinetic rate equation, the total amount of ammonium lost
to nitrification and volatilization in layer ly,
Denitrification is the process of bacteria removing N from soil (converting
NO
While the mechanism of atmospheric deposition is not fully understood, the uncertainty is parameterized into the concentration of nitrate/ammonium in the rain for wet deposition, and the nitrate/ammonium deposition rate for dry deposition.
The amounts of nitrate and ammonium added to the soil through wet deposition,
NO
The N fertilizer application process is included in the new model as well. If
real fertilizer application data (timing and amount for a specific year) are
available, they can be used as model inputs. Otherwise, a fixed amount of N
fertilizer (e.g., 7.8 g N m
N leaching from land to water bodies is a consequence of soil weathering and erosion processes. In particular, organic N attached to soil particles is transported to surface water through soil erosion. Therefore, the modified universal soil loss equation (USLE) (Williams, 1995) is used to determine soil erosion. The details of the calculation are described in Neitsch et al. (2011).
N in nitrate form can be transported with surface runoff, lateral runoff, or
percolation, which is calculated as follows:
At the regional scale, N-related measurements are very limited. Even at site level, measurements are limited with respect to plant and carbon dynamics. The Kellogg Biological Station (KBS) – a Long Term Ecological Research (LTER) site – is unique in its long-term continuous measurements of N related variables (soil nitrate, N leaching, mineralization, nitrification, and fertilizer application) in an agricultural setting with multiple crop and soil controls. Even within the LTER Network, we cannot find a second site that conducts this integrated suite of measurements. Therefore, the new model is evaluated at this site.
KBS is located in Hickory Corners, Michigan, USA, within the northeastern
portion of the US Corn Belt (42.40
This site features multiple N-related measurements. Soil inorganic N concentration, which is sampled from the surface to 25 cm soil depth, is available from 1989 to 2012. Concentration of inorganic N leaching at bedrock, which is sampled at 1.2 m of soil depth, is available from 1995 to 2013. These two measurements are used to evaluate model-simulated concentrations of soil nitrate for the top 25 cm and nitrate leaching from the soil bottom. Soil N mineralization, which measures the net mineralization potential and is available from 1989 to 2012, is compared with the modeled mineralization rate qualitatively.
In addition, soil moisture content is sampled from the surface to 25 cm soil depth and is calculated on a dry-weight basis. In order to compare with model output, it is converted to volumetric soil moisture by applying the soil bulk density. Annual NPP is converted from annual crop yields (1989–2013) by assuming a harvest index and a root-to-whole-plant ratio for each crop type. The harvest indices for corn, soybean, and winter wheat are 0.53, 0.42, and 0.39, respectively. The root-to-shoot ratios for corn, soybean, and winter wheat are 0.18, 0.15, and 0.20, respectively (Prince et al., 2001; West et al., 2010). Although N uptake cannot be evaluated directly at this site, by evaluating the annual NPP, we can see the model's performance in representing the N limitation effect on plant growth.
Comparison of annual averaged atmospheric forcing data (2008–2014) between site observation and NLDAS.
Noah-MP requires the following atmospheric forcing data at least at a
3-hourly time step: precipitation, air temperature, specific humidity,
surface air pressure, wind speed, incoming solar radiation, and incoming
longwave radiation. The weather station at the site measures all of these
except for incoming longwave radiation, but it does not cover the entire period
from 1989 to 2014 (e.g., hourly precipitation data are only available since
2007), when the N data are available. Therefore, atmospheric forcing data are
extracted from the 0.125
Finally, the site management log records the detailed operational practices such as soil preparation, planting, fertilizer application, pesticide application, and harvest. N fertilizer application data include the date of application, rate, fertilizer type, and equipment used. The fertilizer application date and rate are used as model inputs.
Observed and model-simulated volumetric soil moisture from 1989 to
2012 for
Modeled volumetric soil moisture, which is important for nutrient cycling and plant growth, is compared to measured soil moisture (Fig. 2). The model performs reasonably well on both treatments (i.e., with and without tillage) in terms of capturing the mean and seasonal variation, which is consistent with previous study by Cai et al. (2014b). The model-simulated multiple year averages are both 0.243 for the two treatments. These are very close to observations, which are 0.238 and 0.264 for T1 and T2, respectively. The correlation coefficient is 0.78 for T1 and 0.76 for T2, which are considered high skills, especially on a daily scale.
However, differences between modeled and observed soil moisture are also found. From observation (Fig. 2), we can see that the treatment without tillage (T2) has slightly higher soil moisture than the treatment with tillage (T1). Therefore, tillage practice reduces soil moisture. However, the difference in modeled soil moisture is negligible between the two treatments (both are 0.243). This is because Noah-MP does not consider water redistribution due to tillage, although N redistribution is considered in the soil N dynamic sub-model. N is redistributed by mixing a certain depth (i.e., 100 mm) of soil with a mixing efficiency (i.e., 30 %) (Neitsch et al., 2011). In addition, observed soil moisture has higher variations. As we can see from Fig. 2, observation tends to have either higher peaks or lower valleys than model simulation. We also notice that some values from observation are extremely low, which may not be necessarily true in reality. Considering the wide spread of the observational ranges defined by up to six replicating plots, Noah-MP provides a reasonable water environment for the N cycling.
Observed and model-simulated soil nitrate concentration from 1989
to 2011 for
Soil nitrate concentration is the outcome of all N-related processes that occur in soil such as decomposition, mineralization, nitrification, denitrification, and uptake. It determines the available N that plants can use. The skills in modeling the soil nitrate concentration reflect the overall performance of the model in simulating the N cycle. Figure 3 shows the comparison of the model-simulated soil nitrate concentration with site observations for both T1 and T2. The model captures the major variations of the soil nitrate. N fertilizer application is responsible for the high peaks. These high peaks drop very fast at first and then drop slowly, which can sustain crop growth for a few months.
Annual averages of Noah-MP-simulated major nitrogen fluxes and NPP. The NPP within the parentheses is from observation.
The multi-year average of modeled soil nitrate concentration is
5.77 mg kg
While both treatments show very similar patterns (Fig. 3), T1 with
conventional tillage tends to have higher soil nitrate concentration. This is
understandable because tillage practices redistribute water and nutrients in
soil, which accelerates the N cycling. Table 3 shows annual averages of major
N fluxes for both treatments. T1 has higher rates of humus mineralization and
residue decomposition, but, at the same time, it also has higher rates of
denitrification and leaching. Therefore, it produces more N
Observed and model-simulated nitrate leaching from bottom of soil
profile from 1995 to 2013 for
N leaching can be transported to rivers through surface and subsurface runoff
and to groundwater through percolation from soil bottom. Only the last
pathway is measured at this site. Figure 4 shows the comparison of
concentrations of the leached solution from the soil bottom between model
simulation and observation. The averaged concentration of N leaching from the
soil bottom for T1 (T2) is 12.84 mg kg
The peak in 2003 is extremely high and long lasting. This is probably due to the abnormal pattern of precipitation distribution in 2003. In a normal year, storms higher than 50 mm usually occur in either summer or fall. However, in 2003, there was an early storm on 4 April which reached 61 mm in 1 day. As we can see from Fig. 3, the soil nitrate concentration is also high. The combination of high water infiltration (due to the storm) and high soil nitrate concentration resulted in a large amount of soil nitrate being brought to the bottom soil layer. A few months following that, there was no large storm, which was again different from a normal year. As a result, the high-concentration nitrate solution was drained slowly out of the bottom layer of soil. The modeled nitrate leaching also shows a peak over this period, but the values are only close to the lower bound of the observed range. This suggests that improvement is needed so the model can better capture peaks under this situation.
We also notice that, without tillage, N leaching is about one-third lower than that with tillage. Without tillage, the temporal variation is also smaller.
Observed and modeled annual NPP from 1989 to 2013 for
NPP indicates the amount of C that is assimilated from the atmosphere into
plants and thus is important in studying not only crop and ecosystem
productivity but also climate change feedbacks. NPP is mainly determined by
plant photosynthesis and autotrophic respiration. It is also affected by
water and nutrient stresses. In this study, N stress on plant growth is
calculated by the reduction of NPP due to N acquisition, which can be
considered another form of plant respiration. Figure 5 shows the comparison
of simulated annual NPP against observation. Since the original Noah-MP
without N dynamics also simulates NPP, its results are also shown here as a
reference. The mean annual NPP simulated by the original Noah-MP is
544 gC m
The modeled rate of NPP down-regulation – the fraction of NPP reduction due to N limitation – is 35.4 and 34.7 % for T1 and T2, respectively. These rates are close to the 33 % of down-regulation rate used in the default Noah-MP. By dynamically simulating the demand and supply of N with time, these become even closer to the observations.
Surprisingly, even with slower N cycling, T2 produces slightly higher NPP
(Table 3), which is consistent between model and observation. If this is the
case, except for drying up soil, releasing more N
The coupling of the N dynamics into Noah-MP not only adds N-related modeling but also affects other components of the model, i.e., the carbon and water cycles. This is because the change in NPP affects leaf biomass and hence LAI. The change in LAI can affect photosynthesis, which in return affects NPP.
Figure 6 shows the comparison of the simulated C-related state and flux
variables between the default and N dynamics enhanced Noah-MP. We can see
that NPP is decreased from 544 to 432 gC m
Net ecosystem exchange (NEE)
has a similar change. The annual NEE is
(left column) Monthly and (right column) climatologically seasonal
cycle of model-simulated
Same as Fig. 6 except for
(left column) Monthly and (right column) climatologically seasonal
cycle of model-simulated
Through the changes in LAI and soil organic matters (SOMs), the addition of N
dynamics affects not only the carbon cycle but also the water cycle. The
change in SOM is not currently considered, and therefore the impacts on the
water cycle are from the change in LAI only, as shown in Fig. 7. These
impacts are most pronounced on plant transpiration, which is increased by
33 mm yr
Therefore, besides the great implications for C modeling and the potential for being used in environmental predictions, the addition of N dynamics can improve the hydrological simulations as well.
Observed N fertilizer application data are used in this study. However, this
type of data is not always available, especially when models are applied in
large regions. Often we only know the approximate amount of N fertilizer
applied, without information on the exact dates. To guide the future
large-scale application of this model, two additional experiments are run:
(1) N fertilizer is applied on 20 June every year, and (2) N fertilizer is
applied on 15 April every year. The first experiment is designed because in
this site a large amount of N fertilizer is applied mostly during mid-June
and early July. Other dates are also reported in the literature; therefore,
we use 15 April as another example. Both experiments use the same amount of N
fertilizer as in the management log, which on average is
7.8 g N m
Figure 8 shows comparison of some of the most relevant results between the two experiments and the one (real) with recorded dates and amount of N fertilizer application. Despite the different application time, the two experiments produce very consistent NPP with the real case. The 20 June experiment is much closer to the real case; even the seasonal variation is identical. The largest discrepancy is in 1993 and 1996. Based on the management log, in these two years, a large amount of N fertilizer was applied, which resulted in much higher NPP than results from the two experiments. Since 15 April is much earlier than the primary fertilizer application dates, NPP from this experiment is flattened out through the year. This also confirms the statement in Sect. 3.5 that later N fertilizer applications delay plant growth. Simulated N uptake from both experiments shows exactly the same story as NPP.
The simulated N leaching shows the opposite pattern to NPP. The default simulation produces the highest leaching, followed by the 20 June experiment and then the 15 April experiment. This is very likely because the fertilizer application dates are closer to the flood season for the former two cases and the chance of fertilized N being flashed out is higher. The difference in N fertilization dates also clearly affects the simulations of total soil nitrate. In the 20 June experiment, soil nitrate reaches the lowest level in May because no N fertilizer is applied before 20 June. In the default case, N fertilizer can actually be applied as early as April, but with a smaller amount before mid-June, which prevents the soil nitrate concentration from getting too low. Besides a large amount of N fertilizer applied in later months, the other reason that the default simulation reaches the highest concentration of soil nitrate is because it produces higher NPP, which can be returned to soil for decomposition.
Daily climatology (1989–2013) of nitrogen uptake by pathways
expresses as
Overall, the default simulation grows better plants (higher NPP) because N fertilizer is applied based on expert judgment of plants' demand. At the same time, however, it produces more N leaching than the two experiments, which is significant (insignificant) with respect to the 15 April (20 June) experiment at 90 % confidence level. The experiment with closer dates of N fertilizer application to reality can better reproduce the N dynamics in observation. Therefore, although we cannot always know the exact dates of N fertilizer application, a survey on this can help to improve model simulation.
As described in Sect. 2.2.1, plants can get N for growth from four pathways: passive uptake, active uptake, fixation, and retranslocation, and the last three require C costs. Figure 9 shows the actual N uptake from these pathways and their percentages of contribution to the total N uptake. Passive uptake is the dominant pathway, which contributes 57.7 % of the total N uptake. Fixation, active uptake, and retranslocation contribute 28.6, 8.7, and 5.0 %, respectively. This contrasts the results from the study by Brzostek et al. (2014) for non-fertilized trees, in which passive uptake only accounts for a small contribution. This is understandable because the purpose of fertilization is to minimize active uptake so that more NPP can be retained for crop growth. As demonstrated in Timlin et al. (2009), a higher fertilization rate results in a higher ratio of N uptake in transpiration to total N uptake. On the one hand, fertilization maintains soil nitrate concentration at high level. On the other hand, higher NPP for crop growth in turn results in higher LAI and thus higher transpiration. During peak growing season, therefore, plants receive a large amount of N under the combination of high transpiration and high soil nitrate concentration. During other periods, biological N fixation dominates.
The soil nitrate storage with time is an outcome of the variations in
incoming and outgoing fluxes. Besides N fertilizer and atmospheric
deposition, humus mineralization and residue decomposition are the two major
incoming fluxes. Because N fertilizer is a jumping behavior and atmospheric
deposition is a relatively small fraction in this study
(
Figure 10 shows the seasonal variation of the above major fluxes. During the growing season, N fertilizer provides an important role in meeting the plant N demand; however, residue decomposition still makes the largest contribution and is the dominant factor responsible for the increase in total soil nitrate. During the non-growing season, a large amount of N is lost through denitrification and N leaching. However, when it reaches the peak growing season, plants consume a large fraction of soil nitrate, which leaves very little for denitrification and leaching. N leaching is mostly associated with the timing and intensity of precipitation. Denitrification is also associated with precipitation, but it is directly related to the soil water content. High denitrification rate occurs during high soil water content, especially during water logging.
In this study, a dynamic N model is coupled into Noah-MP by incorporating FUN's strength in plant N uptake and SWAT's strength in soil N cycling and agricultural management.
We evaluated the new model at KBS that provides good-quality, long-term observed N and ecological data. The model-simulated soil moisture is consistent with observation, which shows that Noah-MP provides a good water environment for the N cycling. The simulated concentrations of soil nitrate and N leaching from soil bottom also compare well with observations. Although the model does not simulate some peaks well, especially for N leaching, the averages are very close to the observed values and the correlation coefficients are reasonable. Considering the wide spread of the range error bars defined by the measurements at the six replicates, the model shows high skills in capturing the major N flux/state variables. The significant improvement of annual NPP simulation demonstrates that the N limitation effect on plant growth is well represented in the model.
Daily climatology of the soil nitrate (blue solid line) and some major fluxes (color label bars) going in (humus mineralization and residue decomposition) and out (plant uptake, nitrate leaching, and denitrification) of the soil nitrate pool.
Moreover, the addition of N dynamics in Noah-MP improves the modeling of the carbon and water cycles. Compared to the default Noah-MP, NPP simulations are improved significantly, in terms of consistent averages and much higher correlation coefficients with observation. The temporal pattern of simulated ET is also improved, featuring lower ET during spring and delayed peak.
This enhancement is expected to facilitate the simultaneous predictions of weather and environment by using a fully coupled Earth modeling system.
Noah-MP is an open-source land surface model. The model is being
developed by a community led by The University
of Texas at Austin. The code is archived at both
This work is supported by the NASA grant NNX11AE42G, the National Center for Atmospheric Research Advanced Study Program, and the NASA Jet Propulsion Laboratory Strategic University Research Partnership Program. The first author would like to thank Guo-Yue Niu and Mingjie Shi for their help and the beneficial discussion with them. J. B. Fisher contributed to this research from the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA, and through the University of California, Los Angeles. J. B. Fisher was supported by the US Department of Energy, Office of Science, Terrestrial Ecosystem Science program, and by the NSF Ecosystem Science program. X. Zhang's contribution was supported by NASA (NNH11DA001N and NNH13ZDA001N). We are grateful for the observational data from the Kellogg Biological Station, which is supported by the NSF LTER Program (DEB 1027253), by Michigan State University AgBioResearch, and by the DOE Great Lakes Bioenergy Research Center (DE-FCO2-07ER64494 and DE-ACO5-76RL01830). Edited by: A. B. Guenther