Jason Ching

Sylvain Dupont

Rob Gilliam

Steven Burian

Ruen Tang

Neighborhood scale air quality modeling in

INTRODUCTION

Advanced capability of air quality simulation models towards accurate performance at finer scales will be needed for such models to serve as tools for performing exposure and risk assessments in urban areas (Ching et al., 2004). It is recognized that the impact of urban features such as street and tree canopies on air quality simulations will become more pronounced as the grid sizes decreases. This paper will focus on (a) methods to introduce urban features into the MM5, the predictive model to provide accurate, temporally and spatially resolve meteorological fields and as a preprocessor for (b) running the Community Multiscale Air Quality (CMAQ) (Byun and Ching, 1999) modeling system run at neighborhood scales (order 1 km grid horizontal resolution) (see also http://www.epa.gov/asmdnerl/models3/doc/science/ science.html)

The difficulty of performing predictions of air quality and pollutant dispersion at high spatial resolution is exacerbated by the need for high quality, high definition of the meteorological fields that govern transport and turbulence in urban areas. Air quality fields are now being modeled at finer spatial resolution to reveal "pollutant hot spots" in urban areas.

These fine resolution mesh simulations will need to be driven by meteorology at commensurate mesh sizes. The presence of urban street and tree canopies can affect the emission dispersion and transport, and play a major role in defining the spatial variability of the air quality fields. Preliminary results (Ching et al., 2003) using a set of urban canopy parameters for Philadelphia based on simple surveys of urban building geometries (Otte et al., 2004) have shown that the resulting MM5 and CMAQ fields are

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The corresponding author is on assignment To the National Exposure Research Laboratory of the United States Environmental Protection Agency. Email address: ching.jason@epa.gov significantly impacted by the introduction of urban canopy parameters (UCPs) of buildings at 1.3 km mesh size. Given the sensitivity of the meteorology prediction to this set of UCPs, it is important to further examine the predictive consequence with data on building and vegetation on high spatial definition and accuracy. The basis for this study is the implementation of the DA-SM2-U/MM5 system (Dupont, et al., 2004). Further, as Houston, Texas will be the area for this study, the mesoscale circulation associated with its lake-land breeze will exerts an important influence and has implications for the fine scale modeling and so this subject will also be part of our study.

STUDY APPROACH

A set of urban canopy parameters (UCP) have been derived for a 1 km grid mesh from high definition building and vegetation database from airborne lidar measurements, ancillary data from satellites, high altitude photography, as well as detailed residential, commercial and industrial maps and for a modeling domain encompassing Harris County and surrounding areas (Burian et al., 2004a,b). A total of 23 UCP (combination of vertical profiles and surface values and shown in Table 1 listed according to the following categories, canopy, building, vegetation and other.

These gridded UCPs were specifically developed for the DA-SM2-U/MM5 system (Dupont et al., 2004), which incorporated a canopy drag approach into an advanced urbanized surface layer model (SM2-U) which was further implemented into the NCAR-Penn State Mesoscale Meteorological Model, Version 5 (MM5). Our effort provides the first implementation of this detailed set of gridded UCPs into the DA-SM2-U/MM5 system. We chose to simulate a case study for August 30, 2000 for a domain encompassing the greater Houston-Galveston area. The period of interest also correspond to the TEXAS 2000 photochemical oxidant and PM study. Simulations were made at grid sizes of 36 km, 12 km, and 4 km using 30 sigma layers in the vertical. For the UCP driven version run at 1 km grid size, six (6) additional sigma layers were introduced near the surface to simulate the flows within the building and vegetative canopy region. Subsequently, the impact of introducing urban canopy features into the MM5 for the simulation of air quality using the CMAQ modeling system is examined. The MM5 and CMAQ were run in standard one-way nesting mode (Byun and Ching, 1999) and the system applied at 36, 12, 4, and 1 km grid mesh sizes. The meteorological output from MM5 was applied to CMAQ by invoking the MCIP, a Meteorology-Chemistry Interface Processor. Emissions for CMAQ were obtained using the Model-3 SMOKE processor, which produces gridded, hourly emissions outputs at the different grid mesh sizes and chemically speciated for the chemical mechanism used in the CMAQ modeling system. For this study, we used CBIV-AT, an advanced research version of the Carbon Bond-IV mechanism (CBIV) modified to predict gaseous air toxics species such as formaldehyde, acetaldehyde, acrolein, and others.

RESULTS

We first present results from the 1 km grid simulations using DA-SM2-U/MM5 with the gridded UCP for Houston area. The figures 1-6 are for August 30, 2000 at 2000GMT (3pm local time). Figure 1 presents planetary boundary layer (PBL) parameters simulated by this model. The patterns show complex but highly resolved spatial patterns. The northern edge of Galveston Bay appears on the far right hand side of each of the figures; the model predicted reduced heat and momentum fluxes and mixing heights as expected.

Figure 2 shows simulations of formaldehyde (HCHO) from the CMAQ-AT modeling system for both 4 km and the 1 km grid sizes. The panel on the top right is the result of the 1 km grid simulations driven by the DA-SM2-U version of MM5. Regions of high concentration are exhibited in the results. These are the so-called "hot spots" that can be associated with increased exposure and an increased probability of health risk. The panel on the top left is a 4 km simulation reconstructed by aggregating 16 of the 1 km outputs per 4 km cell.

The magnitude of the concentration for the hot spots from the 1 km results are reduced in this display. The CMAQ run performed at a native 4 km (Parent) resolution is shown in the bottom left panel. While the general pattern is similar to that from the aggregated results, the hot spot features are considerably diminished. This is not an unexpected result; the modeled concentration as impacted by atmospheric chemistry, transport, deposition processes that operate at a 1 km resolution yield results that are not expected to be reproducible with coarser resolution modeling and its inherent artificial dilution effects associated with representing emission at coarse resolution. Finally, the bottom right hand panel displays resulting differences between the reconstructed 4 km set from aggregation of the 1 km results minus the native 4 km simulation and normalized using the aggregated mean results. The figure displays both positive and negative differences of several tens of percentage magnitude. We will see other pollutants exhibiting similar behavior but somewhat different degrees of differences in magnitude and pattern (cf Figure 4 and 6 below). Another example showing differences as well as value using higher resolution modeling is illustrated in Figure 3. This example reflects two (of many other) ways to depict the degree of sub grid variability associated with the 4 km resolution concentration variations that are possible using the finer 1 km predictions. The results are obtained by sampling the 16 1 km grid values for the maximum (peak) and the range (maximum -minimum) values in each 4 km cell, and for all cells in the modeling domain. On the left hand side, we see normalized peak-to-mean values exceeding 50% throughout the model domain and several areas which exceed factor-of-two values. The normalized range-ofvalues also exceeding 50% applies throughout the entire modeling domain. Several grid cells have sub grid variabilities exceeding factor of two or more. Such results are not possible with purely interpolation-based methodologies. Figures 45and 6-7 present results for ozone and NOx, respectively. They are set up in identical manner to figures 2 and 3. The notable feature for the ozone results is the ability of the 1 km grid mesh simulations to resolve the titrating effect of high NOx along highway corridors and industrial areas especially along the ship channel region (Top right hand panel of Figure 4). The results of aggregating the 1 km results to 4 km grid size shown in the top left hand panel also show evidence of the titration effect, but greatly filtered. The native 4 km simulation mutes this effect even further. Even with such filtering, differences shown in the bottom right hand panel shows differences exceed 50% and are mostly negative near highways and industrial areas. In Figure 5, results for ozone are similar to that for formaldehyde in that the range-to-mean values exceed 50% throughout the modeling domain. Also, the peak values are comparable or greatly exceed their respective cell mean values throughout the modeling domain. The results for NOx are shown in Figures 6 and7. While these results are qualitatively similar to that of ozone, some additional features are noteworthy. First, the 1 km grid size simulation shows the areal coverage of high NOx to be considerably larger than that simulated at 4 km grid sizes. The normalized difference in the bottom right panel shows a much larger areal extent of positive differences, exceeding 50% throughout most of the modeling domain and not limited to the highways and industrial areas. Likewise, the sub-grid variability indicators in Figure 7 show peak-to-mean values exceeding 50% throughout the modeling domain, but with ratios higher and more extensive than for ozone. This is to be expected because NOx gradients are sharper and more localized. The same conclusion is reached for the range-to-mean display. It appears that photochemical modeling at 1 km produces results that yield both a high degree of spatial variability as well as predicting important differences as compared to coarser grid simulations.

PBL Parameters (2000 GMT)

DISCUSSION

The results described in this paper should be considered a work-in-progress. The presentation at the Symposium will provide additional details regarding: (a) sensitivity studies with comparisons between results of the "urbanized" MM5 system and the standard version of MM5 run at 1 km resolution and its impact on the prediction with the CMAQ system; (b) a sensitivity study to examine the degree of accuracy of the input boundary condition of the flow field from the coarser 4 km grid nest. In this regard, it is important to recognize that pollutant transport in the Houston area is strongly affected by breezes induced by the Gulf of Mexico, and the close proximity of Galveston Bay.

In an effort to resolve the bay/sea breeze evolution, high resolution (~1 km) sea surface temperature observations taken from the Polar-orbiting Operational Environmental Satellites (POES) Advanced Very-High Resolution Radiometer (AVHRR/2) sensor are used in a sensitivity run. A comparison of Bay temperatures shows a difference as large as 4 o C warmer in the sensitivity as compared to the base or control simulation) (Figure 7a). The results show the Bay water temperature warms up to 4 degrees while remaining constant in the control simulation. Figure 7b shows the resulting difference in the near surface wind direction at Site C608 (of the Texas 2000 study) which is ~6 km west of the northwestern part of Galveston Bay. As a result, the accuracy of the near surface land-bay breeze circulation simulations at 4 km grid resolution in the MM5 predictions was greatly improved. The sensitivity run clearly reproduces the observed wind directions and the wind shift at the time of the Bay breeze passage; the control run does not capture the details of the Breeze passage. Consequently, this provides a much more reasonable set of IC/BC for the nested, 1 km grid predictions. The presentation at the Symposium will further allow us to demonstrate the degree to which the flow and air quality prediction will depend on the introduction of more accurate temporally resolved sea surface temperatures (of the proximate Galveston Bay) and the subsequent improvement in representation of the modeled landsea (lake) breeze features.

SUMMARY

We have successfully implemented the DA-SM2-U/MM5 system using a sophisticated set of gridded UCPs based on high resolution building and vegetation data. We have now achieved the development of modeling tools that can resolve physically, flows in urban areas that are impacted by the presence of canopy features at 1 km grid sizes. This method reduces the problems or uncertainties associated with simple interpolation schemes that cannot be expected to accurately represent the flow in urban areas. Also, we have demonstrated that the CMAQ system can be successfully driven using these meteorology fields as inputs for simulating air quality (and air toxics species) at relatively high spatial resolution. We have further shown that by employing a finer grid resolution mesh, that areas of enhanced pollutant concentration become evident, a situation that will permit the resolution of pollution "hot spots" for more accurate human exposure and risk assessments. Clearly, efforts to evaluate all these findings will be necessary.

Thus, the combination of UCP-driven meteorology for fine scale modeling and more accurately modeled lake-land breeze circulations will, in our opinion, provide a strong scientific basis for advancing the simulations of the flow and air quality for Houston and other urban areas with similar climatic features.

Disclaimer: This paper has been reviewed in accordance with United States Environmental Protection Agency's peer and administrative review policies and approved for presentation and publication.

Burian

Figure 1 .

 1 Figure 1. PBL parameters from 1 km grid simulations of DA-SM2U/MM5 (with high resolution UCPs) at 2000 GMT as follows: Top left, Sensible heat Flux (w/m 2 ) ; Top right, Latent Heat Flux (w/m 2 ); Bottom left, Mixing height (m); Bottom right, ustar (m/s).

Figure 2 .

 2 Figure 2. Formaldehyde at 2000GMT (3 pm local time) as simulated using CMAQ as follows: Top left-4 km grid means from aggregate of 1 km grid values; Top right, 1 km gridded field; Bottom left, Parent 4 km grid results; Bottom right, difference of 4 km aggregated mean from 4 km Parent normalized to the 4 km aggregated mean.

FormaldehydeFigure 3 .

 3 Figure 3. Formaldehyde simulations : August 30, 2000GMT: Left side: Gridded values are the peak values 1 km grid cell value within each 4 km grid cells divided by the mean for each such the cell. Right side, range of concentrations from the 16 1 km grid cell within each 4 km grid cell also normalized to the mean value for each such cell.

Figure 4 .

 4 Figure 4. Same as 2 but for ozone

Formaldehyde

  Figure 5. Same as 3 but for ozone

  Figure 7a: Difference between the 4 km grid control using standard MM5 sea surface temperature vs. the Sensitivity simulation which uses POES-AVHRR/2 data

  , S., W. Han, S.Velugubantla, and S. Maddula, 2004a: Development of Gridded Fields of /MM5. Unpublished EPA Internal Report Burian S., S. Stetson, W. Han, J. Ching, and D. Byun, 2004b: High resolution dataset of urban canopy parameters for Houston, Texas, Extended Abstract: Fifth Urban Environment Symposium, Am Meteorol Soc., Vancouver BC, CA, August 23-26, 2004. Byun, D., and J. Ching, 1999: Science algorithms of the EPA Models-3 Community Multiscale Air Quality (CMAQ) Modeling System EPA/600/R-99/030. See also (http://www.epa.gov/asmdnerl/models3/doc/science /science.html) Ching, J. S. Dupont , J. Herwehe, T. Otte, A. Lacser, D.Byun, and R. Tang, 2004: Air Quality modeling at coarse-to-fine scales in urban areas. AMS Urban Environment Extended Abstract, J2.18, Jan 2004 Dupont, S., Otte, T., and J.K.S. Ching, 2004: Simulation of meteorological fields within and above urban and rural canopies with a mesoscale model (MM5). Boundary layer Meteorology, in press Otte, T., A. Lacser, S. Dupont, and J. Ching, 2004: Implementation of an urban canopy parameterization in a mesoscale meteorological model. Journal of Applied Meteorology, accepted.

Table 1 :

 1 Urban Canopy Parameters (UCP) for Houston Texas

	Canopy UCPs:	Building UCPs:	Vegetation, Other UCPs:
	Mean canopy height	Mean building height	Mean vegetation height
	Canopy plan area density	Standard deviation of building	Vegetation plan area density
	Canopy top area density	height	Vegetation top area density
	Canopy frontal area	Building height histograms	Vegetation frontal area density
	density	Building wall-to-plan area ratio
	Roughness length	Building height-to-width ratio
	Displacement height	Building plan area density	Mean orientation of streets
	Sky view factor	Building rooftop area density	Plan area fraction surface covers
		Building frontal area density	Percent directly connected impervious
			area
			Building material fraction


Jean-Marc Boussard
email: boussard@ivry.inra.fr

Marie-Gabrielle Piketty
email: piketty@cirad.fr

Risk in the commodity chain : The sugar example

A sectoral model of the world sugar industry is presented. Results suggest that sugar prices are naturally chaotic. As a consequence, and contrary to the conventional creed, liberalisation, instead of damping fluctuations out, is likely to increase them. But since decision makers are risk averse, and restrain production when faced with uncertain prices, the average price level without is significantly lower than with liberalisation, thus jeopardising the benefits of a more efficient use of resources due to comparative advantage. The policy implication is that care should be taken not to create undesired situations for the right purpose of a better division of labour between nations.

According to common wisdom, sugar is one of these commodity for which the desirability of liberalization is not questionable. There are three good reasons for that : i -In Europe and Japan, as well as in many other countries, sugar producers are relatively wealthy farmers, for whom the classical "poor farmer argument" -it would be necessary to support incomes by providing high price guarantees because farmers are poor, and that something must be done for helping the poor-obviously does not apply 1 /. On the contrary, the many restrictions to sugar production and exchange implemented in these countries are harmful to consumers, who could otherwise enjoy much cheaper sweetened foods.

ii -By constraining the benefits from trade and comparative advantage, these policies introduce inefficiency into the whole world sugar system. In particular because of the low price of manpower and because sugar cane is probably more efficient than the sugar beet as a solar energy converter, production costs are far smaller in developing than in developed countries. The latter should therefore cease to produce inefficiently, and let poor developing countries enjoy the benefit of the few advantages they can claim without discussion, for the ultimate satisfaction of consumers everywhere.

. This volatility is detrimental for the whole

system, as shown as early as 1944 by an author such as WAUGH(1944) 2 /. It should be therefore removed as far as possible. Now, it turns out that this extreme price volatility must be related with another characteristic of the sugar commodity chain. Only a small part of the production and consumption is presently exchanged through markets. The bulk of production is shielded off from price fluctuations. The world sugar market is typically regarded as a residual market where national economies dump their surpluses that arise because production, due to yield variations, exceed even strict quotas. It is tempting to jump from relation to causality, and infer from the above observations that volatility is the consequence of market narrowness. Under this line of reasoning, liberalization would widens the base for price formation, and stabilize market by the virtue of the law of large number, because droughts or floods rarely occur at the same time in different continents. Trade would therefore play the role of a costless insurance, for the greater advantage of both producer and consumer.

In what follows, we shall not discuss the first two reasons for sugar market liberalization. They are fully justified, and no economist can seriously challenge them. In particular, it is not true to say that taking advantage of the low cost of manpower in developing countries would not bring any other benefits than the ruin of the wealthy developed country farmers : the latter have better to do than inefficient sugar production. They should reorient their efforts in these activities where they have a true comparative advantage, thus widening the joint production possibility set, just as would a technical progress do. Yet, there exist serious problems with the third reason, which does not seem to be so strong as it may appear at first glance. It is indeed the theme which will be developed here that, because markets are probably not capable of solving the volatility problem, and because the losses due to this circumstance are enormous, it may very well happen that the losses associated with point i and ii be only a least evil -an evil which would be replaced by something much worse if corrected by standard liberalization, and withdrawal of all state regulation.

The only possible demonstration of this type of assertion consists in building up a model which could be run "with" and "without" liberalization, in such a way as to compare both situations one with another. Many such models have been built up in the past 3 / -most of them more or less similar in their conclusion, matching the three reasons for liberalization given above. This unanimity in the outcome is not too surprising since these models are also unanimous in the premises. Under classical free trade assumptions, with no expectation errors, producers equating expected and marginal cost, and utility maximizing consumers, it is well known that any restriction to trade implies a loss of welfare. It would be surprising that any model built along this line would yield a different conclusion. But is this framework fully justified ? The contention here is that it is not, mainly because there exist expectation errors, and because risk averse producers will be "variance elastic" as much as "price elastic". This is not new : for instance BOUSSARD (1996) developed a theoretical modified cobweb model, with constant (and constantly false !) mean price expectation, and a producer behavior driven by risk aversion : instead of maximizing expected profit, the producer is assumed to maximize a Markowitz utility function, that is a linear combination of expected mean profit and expected variance of profit. The expected variance of price, itself, is "naïve" -the squared difference between this year and last year price. Under this assumption, the price and quantity series of the cobweb model is shown to be chaotic (in the mathematical sense of the word) over a certain fractal subset of the model parameters subspace. As a consequence, the volatility of the price series is not "random exogenous" but "built-in endogenous", and its general properties are quite different from those of a normal "white noise" series, although it may look similar at first inspection. Especially, while the sum of two white noises is a new white noise, the volatility of which is smaller than the sum of the volatilities of the original series, two chaotic motions forced to "trade" one with each other may just synchronize, yielding a new chaotic series with about the same characteristics as the original ones4 / (ALLIGOOD et al., 1997 p. ).

The BOUSSARD's paper just summarized was only theoretical. Apart for demonstrating the possibility of endogenous fluctuation in a simple dynamic supply and demand system, its main virtue was its ability to be run on a spread sheet. But could such phenomena be reproduced into a larger, "real life" model of a commodity such as sugar, embedded into reality, just as the many models of the sugar market alluded to above demonstrate the possibility of expanding the text book model of supply and demand into computer programs aiming at providing numerical estimates of the benefits of liberalization ? The exercise reported here is an attempt in this direction, with the ambition of providing an estimate of the magnitude of the "loss" associated with "free trade" under these circumstances.

I -Model description

It is extremely similar to most other models of the sugar industry, especially the famous Australian ABARE model [START_REF] Hafi | Market potential for refined sugar exports from Australia[END_REF]SHEAL et al.1999 ), which was widely used by international organization to demonstrate the magnitude of the benefit to be expected from a liberalization of the world sugar market. Especially, it borrows many features and elasticities to the latter. By comparison with the ABARE model, the main originalities are as follows :

1°) No statistical estimation of parameters

There is no attempt for obtaining new statistical estimates of the model parameters. When such estimates may be considered as reliable, as for instance in the case of demand elasticities, we made use of results already published, essentially those provided by ABARE.

When technical data were available, especially in the production modules, we made use of them, for two reasons. First, in general, any well known technical relationship, independent of the model at hand, is always better than any statistical estimate, valid only for the particular statistical framework used to get it. Second, if all observed series are actually chaotic, and cannot be converted into white noise by a suitable transformation, it is well known that standard statistical procedure are of no much use for getting reliable estimates5 . The econometrics of chaotic series, on the other hand, is still in infancy. Thus, it seemed that in such case, guess estimates of unknown parameters were at least not worse than apparently more rigorous statistical analysis -and they were much easier to implement.

2°) Systematic introduction of Markowitz utility functions

The maximization of profit, in all segments of the model where it may take place, is systematically replaced by a Markowitz utility function6 / . The Markowitz utility function of a random income z is given by: (4)

where U is utility, z a random income, with expected mean and expected variance , and

A an absolute risk aversion coefficient.

As a consequence, maximising U subject to :

(5) implies the following first order conditions :

(6) which opens the way to ill-shaped supply curves, as noticed a long time ago by JUST and ZILBERMAN (1986). It has to be noticed from the above equations that the main difference between a production with quota at guaranteed prices and a production at market price lies in the fact that in the second case, production may decrease even when mean expected price are high, and, for instance, higher than guaranteed price, if price volatility is too important. One virtue of market stabilisation policies is to avoid the dampening effect of price volatility on supply.

In effect, in the model reported here, this kind of utility function is assumed to be maximised by : analysts. At best, it stands as a clumsy approximation of the VON NEUMAN / MORGENSTERN expected utility theory, not even satisfying the basic axioms of stochastic dominance. Yet, it is easy to use, and convenient in first approximation. At least, it is certainly better to make use of such an imperfect instrument than to neglect the problem entirely.

ifarmers, when deciding each year how much future contract they will pass with sugar processing factories 7 /.

ii -Sugar processing factories, when they decide how much future contract to buy from farmers and sugar refineries when they decide how much raw sugar will be processed into white sugar.

iii -Sugar processing factories, when, acting as stockholder, they decide how much sugar to sell out of their stocks, on the spot market.

iv -Refineries and sugar processing factories, when they decide to invest in new capacities from their past benefits.

In each case, the A absolute risk aversion coefficient is computed as the inverse of the average wealth of the corresponding decision maker, thus implicitly assuming an approximately constant relative risk aversion coefficient 8 /. In this way, a major characteristic of the heterogeneity of decision makers is taken into account, since the heterogeneity in wealth can be considered as a summary of all kinds of heterogeneity.

3°) Introduction of a complex expectation scheme

An implication of the above line of reasoning, however, is the necessity of a complex expectation scheme. For if utility functions depend on prices mean and variance, then, expectations must also pertain on both moments of the probability function. In principle, the two should be completely parallel. If, for instance, the expectation pertaining to mean is a weighed sum of past observations, then the variance should be same weighed sum of square deviations from the mean estimate. But why should weights be the same ?

In addition, any observed regularity is likely to permit high benefits. It is notorious that many traders and market operators are trying to detect cycles in price series. This would imply that any clue of cycle in the data should be interpreted as a periodic mean, and a variance reduced accordingly. But such a reasoning opens way to even more arbitrariness and ad hoc hypothesis generation.

An escape from this dilemma is provided by "rational expectations", after the famous idea by MUTH. Yet, rational expectations are also a minefield 9 /, unless one accept the idea that equilibrium prices, by definition, are the only possible definition of rational expectations. Current casual observation shows that this idea does not reflect reality, while reflection suggests that the word, if it means anything, means that available information is rationally processed by decision makers. Then, the problem is simply displaced, for nobody knows which information is available, and what is a rational way of processing it. Yet, the correct answer to the above question is a matter of facts. One cannot be satisfied with the classical 7 / In effect, farmers pass a sort of future contracts with processing plants, the latter offering to buy the whole production at current price at harvest time. Farmers decision is then which sugar density of production (i.e., tons of sugar per ha of total agricultural area) do they have to promise. Processing plant's decision is which agricultural area to prospect. More details are provided below. 8 / It is well known that A, the absolute risk aversion coefficient, and α, the relative risk aversion coefficient, are related by A = α/w, where w is the wealth of the decision maker. See PRATT (1964). 9 / In this respect, the remark by [START_REF] Lucke | Price stabilization on world agricultural markets[END_REF] that rational expectations, in the case of sugar, are logically impossible, must be taken into consideration. standard hypothesis according to which "rational decision makers expect equilibrium", unless this affirmation is confirmed by empirical data and surveys. Unfortunately, very few references report any valuable information in this respect. It is therefore the probably most important contribution of the present exercise to conclude that expectation formation is a crucial point in any recursive model of this type and that future researches in this field are badly needed.

In the meantime, the results presented below were obtained with what we experienced as the scheme providing the "best" results -"best" being judged in terms of the similarity between "real" and "modelled" time series, as discussed below. In this way, the model presented here relies on some sort of extension of the notion of "maximum likelihood". In effect, these "best" results were obtained with a variance expectation computed from a two years moving average expectation scheme . In the case of stockholders, this "guess" about mean and variance is subject to an important correction. Since the total world existing stock is public and well known guesses are modified by the level of this stock : mean expected price is decreased when stock are too high and conversely.

4°) Processing plants and stockpiling consideration

Just as in the ABARE model, stockpiling plays a major role here. However, we tried to have a better description of this important function through two modelling innovations.

The first is that, instead of a yearly elementary time unit, ours is monthly, thus allowing to picture the seasonal character of the generated price series. Of course, harvesting is yearly, although the year is not the same in the southern hemisphere and in the north. But consumers consume each month, and stockholders have to proceed time arbitrage. Each month processing-stockpiling plants must make a choice between selling, or keeping the current level of stock. The stock is increased regularly at harvested period.

The second is the introduction of risk as it has been mentioned before. Indeed, nobody would keep any stock unless there is some expectation of profit. And given this expected profit (value of sales, minus costs), nobody would sell it unless there is some risk of loss.

Here, the risk is instrumental in regulating the instantaneous supply and demand. The current spot price is the adjustment variable which determines the level of profit necessary to convince stockholders to keep the equilibrium quantity in stock, given their risk aversions10 .

The expected profit from carrying over a stock S t from time t to time t + 1 is given by : (7)

where is the net of cost expected price for t + 1, and P t is the spot equilibrium price of time t. The variance of expected profit is , where is the expected variance associated with the expected mean price . The current spot price p t is then computed in such a way as to clear current month sugar market, assuming each stockholder is maximising , according to risk aversion A.

What is very important in this treatment of stockpiling is that, contrary to some conventional wisdom, this activity may not always reduce price volatility. Indeed, because of imperfect expectations, traders may sell their stocks at period with low price or keep them whereas prices finally decrease in the next period. Moreover, higher price volatility tends to increase large immediate selling which may by itself reinforce price fluctuations.

5°) Other non linearity

Another point which deserves attention in setting up a model of this type is the agricultural production function. As in many such models, we assumed here a very simple reaction from farmers. They just maximise their utilities from a CES function of sugar and "others" productions 11 /. Our results imply therefore that nothing change in the "other" productions conditions while sugar price means and variances are continuously changing. All this is classical, and hardly needs comments.

There is nevertheless in the present model a peculiarity which is tied with a specificity of sugar, may explain some of our results, and deserves explanations. As noticed above, sugar must be processed very quickly after harvest. This means that sugar producers must not be located too far from the processing plant. But how far is too far ?

To provide an endogenous answer to this question, it has been assumed that producers were deciding not simply "a sugar production", but rather a "geographical density of sugar production"a sugar quantity per square kilometre of the total surface of a region. Then, processing plants have to collect this sugar over the area of a disc. It is easy to show (BOUSSARD, 1987, p.215 ) that in this case, the cost of collection per kg of sugar is growing as the square root of the radius of the disc, thus implying a somewhat strange marginal cost. Thus, if the profit of sugar processing is large, it may be profitable to increase the capacity of production, and build a new plan in a virgin area 12 /. These two features (marginal cost of one plant growing as the power ½ of the radius of the contemplated surface and possibility of increasing capacity by reinvesting benefits) are present in our model, and play a role in the generation of irregular price series. Similarly, the capacity of refineries can also be increased, through the reinvesting of profits 13 / However, again, risk plays a role in limiting such investments, since the quantity of money invested in a plant is determined by the relative expected profits and variance of the investment, as compared with profit and variances of alternative uses of money, the latter being exogenous.

11 / An assumption also present in the ABARE model, through the introduction of "price of competing crops".

Here, the price of competing crop is held constant, and only the CES substitutability coefficient matters. These two ways of representing the same phenomenon are substitutable... 12 / As a consequence, any sugar factory enjoys a "monopsony power" over supplier farmers. It is tempting to exaggerate the consequences of this situation. If the benefits from exerting this monopsony power were so large, then why should not competitors try their chance ? A possible explanation could be sought for in the industry Malthusianism. Without neglecting such a possibility, it must be noticed that we provide here a strong technical reason for the perenity of a situation which would certainly not have lasted for so long a time if driven only by "sheer force". 13 / The introduction of a "ratchet effect" in the refinery capacity is the main innovation of the model by WILLIAM AND [START_REF] Williams | Processing Industry Capacity and the Welfare Effect of Sugar Policies[END_REF]. They explain that uncertainty is unimportant in the sugar industry, while the dynamics of investment in production capacity is. This is exactly what we say here, except that expectations are also important, and that "uncertainty" as defined by these authors -that is, the risk deriving from climate and other "external" hazards -can be completely neglected.

Finally, the behaviour of final consumers is represented by a banal constant elasticity demand curve of the individual consumer, calibrated from the condition that present consumption per head conform with present observed behaviours at present prices. In addition, the number of consumers in each country is determined by demographic considerations. In the absence of any other estimates, the elasticity's determined by ABARE were used throughout.

II -A taste of results

The model described above is thus made of a large quantity of submodels, each of which being relatively simple and "classical" in its spirit. Yet, but the main unknown lies in the behaviour of the whole, when constrained by necessity of clearing markets. Two kinds of simulations can be envisaged with such an instrument : 1°) First it is possible to run the model using the present policies constraints (mainly EC, US and ACP production or imports quotas, imports taxes) in order to see if the generated price series would resemble to what can be observed in reality 14 /. Notice that no random exogenous shocks are added in the model, thus making any observed irregularity purely endogenous 15 /. 2°) It is also possible to compare the consequences of alternative policies, in order to see whether one is "better"according to some social judgement criteriathan others.

Both type of experiment have been made with the present model.

Validation

Figure 1 and table 1 show a comparison of "actual" and "modeled" white sugar world price over 240 month. "Actual" stands for the last 240 month available sugar price series, that is the "closing value" of the spot # 11 white sugar the first worked day of each month in the NYSE from February 1981 to January 2001. The "model" series was obtained from a run of the model, with initial conditions corresponding roughly to those prevailing at the beginning of 2000 -and, of courses with the continuation of the present policies, which may change in the near future, but have not been significantly modified during the last 20 years, but for the collapse of the USSR, and the subsequent consequences for the Cuban production. / Note that we do not intend to "predict" anything. If this is any chaotic dimension in our results, as we strongly suspect it is the case, then prediction is futile. What can the subject of a judgment about the model quality is only the probability distribution of simulated and actual prices.

15

/ Of course, such shocks could have been added in the model, and, perhaps, would have increased the similarity between model and reality. Yet, they were not included into the simulations reported here, because we were anxious to bring the demonstration that "exogenous shocks were not necessary to explain fluctuations".

Obviously, large differences do exist between model and reality, in such a way that one may be tempted to reject the idea that this model has something to do with anything actual. Yet, it must be noticed that :

1°)The "actual" and "simulated" situations are not strictly comparable, since the initial conditions are not the same (reproducing the initial conditions prevailing in the early 80's would have been difficult).

2°) In standard econometric, validation relies on some measure of the distance between model and reality, such as the sum of squared "residuals". Here, the problem is complicated from the fact that the model outcome is probably chaotic (as shown by the values of the BDS tests), which means that residuals are not independent of time, and should logically growth to infinity 16 .. In effect, with chaotic series, the predictive capacity of a model is not a good quality criterion. To be precise, the model should still be judged in the basics of its predictive capacity. But what it is supposed to predict is certainly not "natural" endogenous variables such as price levels, or supplied quantities. Rather attention should be focused on the general shape of series. With these provisos in mind, one notice that:

1°)Both series are nearly stationary. (The slope of the regression over time is small, although non negligible, especially in the case of the "simuled" series. It is not significantly different from zero under standard assumptions, see table 1).

2°) there exists a strong suspicion that both of them are chaotic (as shown by the high value of the BDS test, and despite the fact that one must be careful in interpreting such results)

3°) The "model" series is significantly more volatile and "more periodic" than the actual one, as it is clear from the comparison of the autocorrelation functions (figure 2

Policy lessons

Because it is made of 23 "regional" submodels, with, in each region, a representation of the behavior of a variety of agents, the model under examination provides also information on "who gains" and "who looses" from liberalization. The results presented here are illustrative. As shown by figure 4, price increases much after liberalization, and is becoming more volatile. Not surprisingly, governments loose, because imports taxes are suppressed. Farmers loose too (figure 5), except in a few third world countries (but their gains are extremely small by comparison with the losses of EC farmers), because, despite the mean price increase, the necessity of being cautious in presence of more volatile price leads to a reduction of production. Finally, most consumers loose also, (figure 6) because the reduction of production causes consumers prices to rise, even in some countries where high domestic prices were previously linked to protectionist policies. In any case, the overall result is rather negative, and the main reason for that is simply that, in the "liberal" situation, all agents being cautious, the increased volatility induces everybody to be prudent, and to produce only those quantity they are fairly sure to be able to sell. As a consequence, production is restricted (by comparison with the "present policy situation"), and almost everybody is worse off. This is a typical "prisoner's dilemma" 19 / Throughout the rest of this paper, the consumer and producer surpluses are made use of as a proxy for a "true" social utility function. Of course, the authors are aware of the limitations of this indicator, which is "optimal" only under the heroic assumption that the income distribution is optimal, and that changes in prices do not change real incomes. Yet, despite its limitation, it is very commonly used, especially when making recommendation to policy makers. Hence our decision not to take another, more justified indicator. 20 Without a large number of simulations, it is not possible to say whether this result is due to the specific parameters or initial point chosen here, or if it is a permanent feature of the model. 21 / This is a natural consequence of the "ratchet effect" tied with refining capacity limitation. The point is noticed by WILLIAMS and ISHAM (1999). situation, where self interest leads to collective catastrophe, just the contrary of the Adam Smith argument for "laisser faire" .

Conclusion

We have been able to set up a model of the world sugar commodity chain. It is firmly anchored into elementary economic theory. Yet, contrary to most "classical" models of the same kind, it assumes all agents risk averse, and expectations not always fulfilled, thus opening way to deviation from the otherwise automatically granted conclusion that "liberalization is good". In effect, the main results are that: 1°) Price volatility may be much larger in a " free trade " than in a regulated environment.

2°) This implies a smaller average production, a higher average price, a smaller consumer surplus, and probably a smaller global welfare in most occasions. 3°) Such situations occurs as a consequence not of meteorological or other random events, but of endogenous fluctuations, built up from demand rigidity and traders imperfect knowledge. The remedy to such detrimental fluctuations cannot be found by the market itself. Suitable arrangements, combining as much liberty and as few bureaucracy as possible while correcting market inefficiencies must be sought for in such circumstances. It means obviously that the liberalization of the sugar market, if it were decided, should be conducted with much caution and prudence. Of course, this does not mean that the present situation is as fully satisfactory as it should.

One must be prudent in deriving practical conclusion from a notoriously imperfect model (but notice that most " general equilibrium model " did not even pass the rough test this one has been submitted to). The preceding conclusions should therefore be taken as a set of interesting hypothesis rather than policy recommendations. Yet, they should be taken seriously, and subject to additional investigations, if not for any other reasons, because of the precautionary principle.

More generally, if the tentative results just presented can be more strongly validated, contrary to a pervasive creed, the agricultural price regulation policies which were initiated by President Roosevelt in the aftermath of the great depression were not, or not only, the outcome of rent seeking agricultural lobbyists action 22 /, but rather an efficient mean of protecting consumers -especially, poor consumers. Such findings call for further researches. By comparison with other crops, the originality of sugar lies in fact that production is regulated mainly thought quotas or "PEG" (cf. HARVEY, 1989, among many other), which are costly to consumers, but not to governments. The budgetary cost of sugar policies is therefore small, and the control of supply efficient. Yet, since it creates rents, and does not equate marginal cost to price, such system is not justifiable from a static equilibrium point of view. For that reason, the idea of making use of similar schemes for other commodities, after having been contemplated in the 80's, have been abandoned, and has disappeared from the landscape of agricultural policy discussions. What is shown by the present modeling experiment is that, in a dynamic setting, on the contrary, such a system makes much sense.

Actually, a PEG system can be interpreted as a sort of future market, with the State promising to buy a certain (limited) quantity of commodity, at harvest time, at a prespecified price. The quantity thus bought by the State is then sold back to consumer, either at purchase price (in which case the consumer bear the cost of intervention) or at market price (in which case, the cost is taken by the taxpayer). If the commodity had been sold on a classical futures market, the cost would had been born exclusively by the consumer23 /. Apart for that faculty of having the taxpayer bearing some of the cost instead of the consumer, the essence of both systems is the same. Especially, it may the argued that the allocative consequences are similar : the producer knows the selling price at plantation time, thus being comfortable in making a sound, riskless economic calculus. The distributional consequences, however, are not the same : because the State is risk neutral, it can provide this comfort at a much cheaper price than normal future markets, where risk buyers expect a reward from their contribution to risk reduction.

In the present state of thinking of the agricultural economist profession as a whole, this conclusion is so disturbing that it certainly deserve publication, in order to be discussed. , farmers risk aversion parameter (1/$) 0,001 0,01 0,05 0,05 0,001 0,01 0,05 0 0,01 0 0,05 0,01 0 0 0,001 0 0 0,1 0,1 be White sugar price demand elasticity 0,16 0,02 0,07 0,3 0,29 0,07 0,03 0,1 0,07 0,04 0,13 0,01 0,01 0,2 0,05 0,13 0,04 0,1 0,1 ae Demand function constant -14,7 -3,7 -7 -21 -8,94 -14,7 -3,14 -8 -7,2 -14,6 -6,26 -12,7 -50 -50 -3,07 -15 -15 -6,3 -12,7 ge White sugar income demand elasticity 1,18 0,23 0,55 2,34 0,64 1,48 0,09 0,6 0,55 1,18 0,4 1 5,79 5,8 0,001 1,13 1,18 0,001 0,03 0,01 0,01 0,01 0,01 0,001 0 0,01 0 0,001 0,01 0,02 0,1 0,001 0 0 0 0,001 ASie=: Stockpiler risk aversion (1/$) 0,001 0,03 0,01 0,01 0,01 0,01 0,001 0 0,01 0 0,001 0,01 0,02 0,1 0,001 0 0 0 0,001 wPe factory cost ($/T of month. SEe : normal stock (white) 0,521 0,44 0,44 0,27 0,206 0,44 0,521 0,1 0,44 0,27 0,269 0,269 0,76 0,8 0,76 0,76 0,76 0,8 0,76

3°)

  No other model could sustain comparison over such a long time 17 .

  ), and of the "phase diagram" (that is, xt as a function of xt-1) .

  They are briefly exposed to show unexpected results that may arise from trade liberalization, 01_SugExamp risk commodity chain.doc 01/12/17 13 once innovative features, as exposed above, are introduced in a model of the sugar commodity chain 19 /.

*

  *****************Figure 5 -Effects of liberalization on farmers incomes, by country ************************about this place *****************Figure 6 : Effects of liberalization on consumers, by country ************************about this place Are there any winners ? Some traders really can benefit from the liberalization, but not all of them (For instance, Brazilian traders suffer heavy losses 20 ). The only indisputable beneficiaries from liberalization are the refiners (figure 11), because the increased uncertainty increases the wedge between raw and white sugar, thus allowing them to get substantial profits 21 /. ****************Figure 7 : Effects of liberalization on refiners, by country. ************************about this place

Figure 1 :

 1 Figure 1 : Comparison of actual and simulated white sugar world price over 240 months. ($ / tons)

Figure 4 :

 4 Figure 4 : Comparison between "with" and "without" liberalisation

Table I Comparing actual and simulated series

 I

			m=2, eps=0,0009	13,87	1,94
			m=5, eps= 0,0009	-0,0027	-0,04
			Simuled	Actual
	Case number		240	240
	Mean		16,4029471	9,67296667
	median		15,3482364	9,735
	mode		14,7406392	12,61
	standart deviation	5,03571571	3,42898509
	Kurtosis		0,72003706	1,42596423
	Skewness	0,95528056	0,6124879
	Minimum		5,9562216	2,68
	Maximum	31,7093616	24,3
	Regression over time slope	8,00E-02	5,39E-03
			T statistic	-1,75E-02	1,55E-03
	BDS test	18	m=2,eps=0,03	40,39	159,9
			m=5, eps=0,03	911	2168
	16 As a matter of fact, this specificity of chaotic series is one of the reasons for why so many excellent
	econometric models performed so poorly in the past

17

Actually, to our knowledge, very few recursive model could be run without interruption for so long a time as ours. There is a good reason for that. With rigid demand prameters and elastic supply functions, most of them are simply explosive cobweb device, thus likely to go to infinity after a small number of period. Only a periodic or chaotic dynamic model can stand running such a long time.

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Table A1 : Model regions, and regional parameters

 A1

	Regions Parameters :	Austral-	ia	Brazil	Cuba	India	Thai-	land	Africa,	tropical	Africa,	south	Ameri-	ACP	coun-	USA,	cane	Ma-	grehb,	cane	Asia,	cane	SSSR	(former)	Europe,	eastern	Europe,	EC	Japan	USA,	beets	Magh-	reb, beet	Asia,	Beet
	Nature of production	cane	cane cane cane	cane	cane	beet cane cane cane	cane	cane beet beet beet	beet beet beet beet
	aJe, variable processing cost($/t)		100	30	50	30		40	30	100	50	50	90		30			90	40	50	100	100	90	40		40
	Ck, fixed processing cost		20	5	10	10		5	15		15	5	20	15		5			5	5	5			25	20	15	5		5
	Ct Transportation cost, $/t/km		0,1	0,5	0,3	0,3		0,2	0,6	0,2	0,4	0,4	0,1	0,3		0,4	0,4 0,4	0,1	0,1	0,1	0,3		0,4
	AFe Processing plant risk aversion	0,01	0,01	0,1	0,1	0,01	0,1	0,01 0,1	0,1	0,01	0,01	0,1	0,02 0,1 0,02 0,01 0,01	0		0,1
	Cj, farm gate cost (1000$/T)	51,3	6,3	30	5,4	17,1	0,79		17	2	3,3	32,2 0,771	1,5	4,5 4,5	7,9	7,5 46,9 3,6	0,52
	Sf, average sugar surface per farm (Ha)	16,1	10	320	0		0,4	0,1	0,21	0	0,1	14,1	0,1		0,7	6,6 0,5		1	0,03 2,83 0,4		2,2

Table A2 :Policy variables (removed for "liberal" scenario)

 A2

	Parameters Level of		White sugar	Farm gate		xe: retail tax	ce: "forced"
	quota (million	price under	price under	on sugar (%)	consumption
	T)		quota ($/T)	quota ($ / T)	(e.g. Brazil
							demand for
							alcohol)
							(Million T)
	Australia	0,005	430	40	0	0,02

/ Notice it nevertheless may apply to developing countries : sugar producers in India or Pakistan are not the wealthier farmers… And they are a lot of people !

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/ Eventually, the pertinacity of the WAUGH's conclusion regarding the consequences of volatility for different categories of agents, such as consumers or producers has been questioned. The controversy lasted for years, and produced a large body of literature. Yet, nobody, as far as we know, never argued that volatility could be socially beneficial.

/ For instance, WILLIAM and ISHAM (1999) quote 19 of them recently published -and they are probably not exhaustive.

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/ This phenomenon is very common in electronic, where it is made use of for the automatic turning of radio sets

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See for instanceTONG (1990), and many others.

/ The Markowitz utility function, widely used in finance, has been severely criticized by decision theory

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/ Notice this line of reasoning is borrowed from NEWBERY and STIGLITZ(1981).

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The statistic given columns 3 and 4 is the ratio "BDS/standard deviation of the BDS under null hypothesis of white noise", with embedded dimension m and size of "small quantity" eps. .

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/ As suggested by the famous "farm problem theory"[START_REF] Gardner | Changing economic perspectives in farm problem[END_REF][START_REF] Olson | The logics of collective action public goods and the theory of groups[END_REF].

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/ Of course, in that case, the speculator, the one who sell the contract, loose from time to time. But unless he is crazy, which contradicts the usual assumption of rationality, he cannot loose all the time. In the long run, he must have a profit. Otherwise, he would not speculate…

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01_SugExamp risk commodity chain.doc 01/12/17 21 Figure 3 : Phase diagrams of actual and simulated white sugar price series

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01_SugExamp risk commodity chain.doc 01/12/17 28[Obviously]

Annex : Sugar model equations and parameters I -Market module

[ Equations in this module are solved simultaneously each month (denoted by the subscript t) for bold capital variable. Some equations are generated for some values of the subscripts only: h(e,t) represents the set of region having harvest at time t ] I.1/ Market equilibrium:

(I.1.1 : Supply equates demand):

QQe + Qejt + Lejt = QFet + Cejt + ce.

Qejt: Quantity produced month t in region e, for sugar type j (j="raw", or "white"), in excess of quotas ; Cejt : Quantity consumed, QFet demand from refinery (zero for white) ; Lejt : Net sales (may be negative) from stock; QQe : Quota level for region e. ce : "forced" consumption(e.g. Brazil demand for alcohol);.