Input determined to some extent during the run-in phase of the model

A large group of model constants are determined to some extent in the run-in phase. Most often, we begin by estimating or guessing the value of a constant and letting the model carry out a calculation, after which the value is adjusted on the basis of comparison between calculated and measured values.

The many different constituent parts of the model are very closely linked – so closely that very few constants are determined one by one without affecting other model constants. In many cases a certain number of constants are therefore assigned their values in the same

optimisation procedure. A good example is the carbon cycle, the constants of which it is possible to determine before concentrating on the other cycles.

Up till now, it has been our experience that it is crucial to have a very detailed set of measured data available in the run-in phase of the model. Otherwise, the values of some constants will inevitably be assigned on an insufficient basis. It should be noted, however, that many constants are more or less universal and hence transferable from one type of sediment to another.

The many detailed measurements performed in the HAV90 programme cover the dynamics of the seabed during more than a year (January 1990-May 1991) and one of the goals of the model set- up is to be able to reproduce these dynamics by modelling. However, seasonal variations are too difficult to tackle in the run-in phase, and in many instances it is impossible to distinguish natural variations in the seabed from seasonal fluctuations. Therefore, the model constants were determined after the model had calculated data under stationary conditions and compared these data with mean values of data measured in the course of a year. We say that the model is in a stationary state. Here, stationary state refers to the fact that all the boundary conditions laid down in the model, such as bottom-water concentrations and organic matter fluxes, correspond to the mean values of one year’s measurements. Likewise, all temperature- dependent sediment parameters, such as diffusivity, are determined

using the mean sediment temperature, which is 9 o

C. For all substances, dissolved and solid alike, a concentration gradient of 0 was specified as the lower boundary condition. This boundary condition allows concentrations to vary freely between successive calculations at the bottom of the calculation zone. As the upper boundary condition a constant flux is specified for organic material. The boundary condition for all dissolved substances corresponds to the mean value of bottom-water concentrations measured in the course of a year.

C:N and C:P ratios. Initially, we estimated the C:N and C:P ratios of organic matter degradation on the basis of literature values. It is important to keep in mind that these ratios are not the total C:N and C:P ratios normally measured in sediments. After the model is

partially run in, both ratios are adjusted so that the profiles of NH4

+

and PO4

3+

, respectively, coincide with the measured profiles. As shown later, we have achieved a good agreement for both substances without letting the C:N and C:P ratios vary with depth.

The limiting concentrations e.g. O2 lim, NO3

-

lim, MnO2 lim and FeOOHlim

(see section 2.4.1) are initially estimated on the basis of literature values and experience with previous model set-ups. When the model is partially run in, concentrations are adjusted.

Rate constants. The majority of the rate constants are determined in two steps. First, preliminary values are found, after which final adjustment takes place. To that end, numerous comparisons are made between calculated and measured values, which are too extensive to

be presented here. We will therefore confine ourselves to giving a few examples.

The rate constant of the pool of slowly degradable organic matter is a very critical input parameter to the model and is determined on the basis of the average of one year’s sulphate reduction profiles. Obviously, the pool of readily degradable organic matter is used up in the uppermost zone of the sediment, while “the slow pool” penetrates considerably further into the sediment before being degraded. This means that below a certain depth sulphate reduction originates exclusively in the degradation of slowly degradable organic matter. We exploit this fact in order to determine the rate constant of the slowly degradable organic matter pool. Figure 2.8 shows how the model has calculated the degradation rate of the slow

pool as a function of depth at three different rate constants, 10-9

s-1 , 9x10-9 s-1 and 81x10-9 s-1

, respectively. The figure shows that the larger

rate constant leads to too rapid degradation of the CH2Os pool, which

as a result does not penetrate into the sediment far enough to support sulphate reduction. The reverse is the case for the smaller rate

constant, whereas the rate constant of 9x10-9

s-1

gives a good agreement between calculated and measured sulphate reduction rates. Subsequently, the rate constant is adjusted slightly to its final

value of 12x10-9

s-1

.

The rate constant of the pool of readily degradable organic matter is found in the same way, but uppermost in the sediment, where oxygen consumption is the factor determining the degradation rate of “the fast pool”. The ratio between the rate constants of the “slow” and the “fast” pool in Aarhus Bay is approximately 800, which agrees well with ratios found in similar studies.

The remaining rate constants are found through similar reasoning or in the literature. The purpose of the model is to calculate concentration profiles of all dissolved and solid substances entering into the model. On the basis of these the model will be able to finally calculate oxygen and nutrient fluxes between seabed and bottom water and material transport within the seabed. Therefore, one of the most important purposes of running in the model has been to reproduce the measured concentration profiles. Initially, we have “only” calculated the profiles as yearly averages and compared them with averages of the profiles measured in the course of the “model year”. The results of these calculations are shown in Figure 2.9 after determination of all constants and other model input. The figure clearly indicates an excellent agreement between modelled and measured concentration profiles of all substances shown.

The HAV90 programme did not focus only on concentration measurements in the seabed. Several degradation processes were measured as well; e.g. sulphate reduction rates. The model calculates

sulphate reduction rates from concentration profiles of CH2Of and

CH2Os (see Eq.15), temperature and the assigned constants. Figure

2,10 shows how well the model actually calculates sulphate reduction rates compared with annual averages of the measured rates. Here, too, the model reproduces the measured results satisfactorily.

20 16 12 8 4 0 -4 0 0,002 0,004 0,006 KOMS= 9,0 10-9 _s-1 1,0 10-9 _s-1 81,0 10-9 _s-1 Depth (cm) Degradation of OMs (nmol cm-3 s-1)

Figure 2.8. Calculation of the rate constant of the pool of slowly degradable organic matter, which below a certain depth is degraded exclusively by sulphate reduction. Calculated degradation rates of the slowly degradable pool are shown for three different rate constants (solid lines) together with measured sulphate reduction rates (black dots; Aarhus Bay). See text as well.