Development & Application of Computer Techniques to Environmental Studies VII, C.A. Brebbia, P. Zannetti & G.Ibarra-Berastegi (Editors) 2000 WIT Press, www.witpress.com, ISBN 1-85312-819-8 Modelling solar radiation, evapotranspiration and soil water dynamics in tropical rainforest logging gaps in Guyana O. van Dam Dept. of Physical Geography, Utrecht University, the Netherlands Tropenbos-Guyana Programme, Georgetown, Guyana Abstract Selective logging in the tropical rain forest of Guyana creates gaps in the canopy. The PCRaster model FORGAP was made to calculate the radiation energy, evapotranspiration and soil water dynamics of logging gaps. Model input data was gathered in experimental gaps that differ in size. Calibration was done with measured soil moisture in the experimental gaps. The model proves a good tool in identifying areas within a gap that receive more light, show larger evapotranspiration rates or experience more moisture stress. The model can be used in scenario studies of the effects of gap size, shape and orientation to the sun on the microclimatic conditions and water availability that regulates forest regeneration. 1 Introduction One of the main natural resources of Guyana is timber. Selective logging of the commercial tree species creates openings or gaps in the canopy. Gaps are a natural feature of the forest caused by the falling of dead trees. Logging gaps are usually larger, because more than one tree is felled within a certain area and healthy trees with mature crowns are felled. Furthermore, there are a larger number of gaps per area in a logged forest than in an undisturbed forest. These logging activities change the microclimatic conditions and the water balance of the soil within the forest and within gaps . Radiation, evapotranspiration and water availability in tropical forest gaps are some of the discriminating factors that regulate the regeneration of the forest and the competition between tree species . There is a lack of knowledge on the effects of different sized gaps or multiple gaps on the microclimate and soil water dynamics of a tropical rain
Development & Application of Computer Techniques to Environmental Studies VII, C.A. Brebbia, P. Zannetti & G.Ibarra-Berastegi (Editors) 2000 WIT Press, www.witpress.com, ISBN 1-85312-819-8 290 Computer Techniques in Environmental Studies forest. The large variation between gaps of different size, shape and orientation to the sun and the within gap spatial variability can only be studied with a model. The objective of this study is to identify the effect of gap size on the microclimate and water availability. In 1996 the Tropenbos-Guyana Programme started the Pibiri Gap Experiment . The experiment consists of the creation of 25 experimental gaps in a range of 50 to 3200 nf. Measurements were made of microclimatic conditions, soil moisture levels and nutrient availability. The FORest GAP model FORGAP was made to study the effects of different gaps on the radiation, evapotranspiration and soil water dynamics. This paper describes the FORGAP model and the model performance. 2 The FORGAP model FORGAP is written in the dynamic script modelling language of the PCRaster software . PCRaster is a Geographical Information System that consists of a set of tools for storing, manipulating, analysing and retrieving geographic data. It is raster-based and the software includes cartographic, dynamic and geostatistical modelling using a user-friendly modelling language. PCRaster is DOS based, using a simple ASCII editor. FORGAP consists of three modules: a radiation, an evapotranspiration and a soil water module. These are discussed separately. 2.1 The radiation module The radiation module calculates the potential radiation on the vegetation, the potential radiation on the saplings in the gap and in the area surrounding the gap and the potential radiation on the soil. The gap and the forest are modelled as a digital elevation model of the average height of the vegetation surrounding the gap and the height of the saplings in the gap. The radiation module calculates for each hour the exact position of the sun in relation to the position of the study area with standard solar geometry [overview in 5]. This position determines the total radiation flux through a hypothetical plane perpendicular to the incoming solar beams. The maximum solar radiation is corrected for the angle of incident of the solar beams on the surface. In this study it represents the potential radiation on the vegetation R g. For every hour of the day the model calculates which part of the gap is in the shade of the surrounding vegetation. The shaded part of the gap only receives diffuse sky radiation and radiation that falls through the surrounding vegetation. A vegetated surface is unlike other surfaces translucent. Solar beams penetrate through the openings between the leaves of the vegetation. A radiation extinction function is used to calculate the amount of radiation that can penetrate through the vegetation. This extinction function depends on the leaf area index LAI (cm leaf area per cnf ground area) of the vegetation. Figure 1 shows a cross section of a hypothetical gap with radiation on the vegetation and inside the vegetation. The gap area is normally defined by the perpendicular projection on the forest floor of the perimeter of the crowns that surround the gap. However, the area on the forest floor that is influenced by
Development & Application of Computer Techniques to Environmental Studies VII, C.A. Brebbia, P. Zannetti & G.Ibarra-Berastegi (Editors) 2000 WIT Press, www.witpress.com, ISBN 1-85312-819-8 Computer Techniques in Environmental Studies 291 the presence of a gap is larger than this perimeter. Solar beams that fall into the gap can penetrate in the gap edge area, thereby increasing the actual gap area and thus the area where tree saplings can regeneration. Forest Gap Figure 1: Schematic representation of radiation in a forest gap. The abbreviations are explained in the text. Radiation that falls on the forest soil arrives from two sources: RLAI'. radiation penetrating through the small openings of the canopy trees leaves. The radiation is a function of the amount of radiation that falls on top of the canopy R g (W.m ) and the Leaf Area Index LAI (nr.m ). Rejge' radiation in the forest gap and gap edge. These solar beams can penetrate into the forest and are being extinguished by the edge vegetation (stems, small trees and saplings) surrounding the gap. Radiation on the soil R. (W/nT) under the trees is a function of Rgdge, RLAI, an LAI extinction factor k (0.6 ), a gap edge radiation extinction constant c (0.18), the solar altitude a (deg) and the distance from the gap edge D (m). Radiation on the saplings in the gap and in the forest undergrowth is calculated similar as /?,„//, but with the LAI above the saplings instead of the total LAI. Hemispherical photographs were analysed with Winphot  to determine the constant c. These photographs were taken along a transect from the gap edge into the dense forest and the total radiation per hour for 6 days in a year was calculated. Regression analysis was used to determine c. 2.2 The evapotranspiration module Rain enters the forest system at the top of the vegetation. Rain is either intercepted by the vegetation or falls directly on the soil litter. Most of the intercepted water drips through to the soil litter (e.g. throughfall drip direct throughfall). Only a small proportion is left behind on the leaves or is drained to the soil via the stems of the trees (e.g. stem flow). The water that remains behind will evaporate. Water that was left behind on the soil litter will also evaporate. Transpiration by the vegetation and direct soil evaporation are only possible when it is not raining. The evapotranspiration module calculates the net radiation, evapotranspiration fluxes (mm) and the net precipitation. The net radiation is computed by calculating the long wave radiation from microclimatic
Development & Application of Computer Techniques to Environmental Studies VII, C.A. Brebbia, P. Zannetti & G.Ibarra-Berastegi (Editors) 2000 WIT Press, www.witpress.com, ISBN 1-85312-819-8 292 Computer Techniques in Environmental Studies data and correcting the potential radiation of the radiation module (which equals the short wave radiation) for cloud cover and albedo. The net radiation is used to compute the potential transpiration and soil evaporation. The net precipitation plus the stem flow is the amount of water that enters the soil and that forms the input for the soil water module. Temperature, relative humidity, air pressure, wind, cloudiness and rainfall are supplied as input for the model. The pathways of rainfall are given in figure 2. loT Pnet Figure 2: Schematic representation of the evapotranspiration module. The abbreviations are explained in the text. Canopy openness co (-) and litter openness lo (-) determine the amount of rainfall and throughfall that is not intercepted by either the canopy leaves or soil litter. The storage capacity C x (mm) or L ax (mm) determine the total amount of water that can be stored on respectively the canopy leaves or soil litter. Evaporation of intercepted water by the canopy Ei (mm), leaf litter El (mm) or potential soil evaporation Es (mm) are calculated with Penman open water evaporation. Potential transpiration Et (mm.h"') is calculated with PenmanMonteith . Ei and Et are calculated with R and El and Es are calculated with RWJI. Canopy openness and LAI varies with tree height and tree density and was computed from hemispherical photographs. A literature value for Cmax was used [0.89 in 8]. Litter openness varies with distance from the gap edge and was measured in the field. Rainfall simulations were done to establish a relationship between L ax and litter mass. Litter mass (g.m ) was measured in the forest and in the gap. 2.3 The soil water module Water availability and water stress is calculated in the soil water module. The soil in the model consists of three layers up to the rooting depth of the vegetation (120 cm). Water percolating below this rooting zone is assumed lost from the forest ecosystem. The module is based on SWATRE , which calculates onedimensional unsaturated flow. The module computes actual transpiration and soil evaporation related to the soil water suction and it is the minimum of the soil flux and the evaporative demand of the air (calculated in the previous module).
Development & Application of Computer Techniques to Environmental Studies VII, C.A. Brebbia, P. Zannetti & G.Ibarra-Berastegi (Editors) 2000 WIT Press, www.witpress.com, ISBN 1-85312-819-8 Computer Techniques in Environmental Studies 293 The model uses Darcy's law of one-dimensional stationary flow Q -k(h) [8/z / 5z - 1] (cm.h *) in which &(h) is the hydraulic conductivity (cm.h"'), h pressure head (cm) and z the gravitational head (cm). The pressure head h is a function of the soil moisture 0 and A: is a function of h according to the non-linear equations of Van Genuchten and Mualem . A flow chart of the WATBAL module is shown in figure 3. iEpon 1 i ; !Es Et,, Et,: Et,, Temporarily surface sto V ! i Q DL," kk.hu; Q: DL-, k,,, h D k , KL, Q, Q, Figure 3: Flow chart of the soil water balance module. See text for explanation of the abbreviations. The amount of net precipitation P , (mm) that enters the topsoil depends on the maximum amount that can be stored in the top layer. The maximum storage is determined by the saturated soil moisture content 65 (-) and the amount that is already present in the layer. If P t (mm) is in excess of what can be stored in the top layer, the excess water is stored temporarily on the surface and drains into the soil in the next time step or evaporates E n (cm). The amount of rain water that enters the soil Qi (cm.h" ) is calculated with the hydraulic head and conductivity of the atmosphere (/z , rm) and hydraulic head and conductivity of the first node (hi, kj) with a z of V2 Dj (cm). The flux to the second layer gj is calculated with hydraulic potentials A/(6,) and 62(82) and subsequent hydraulic conductivities &/(/%/) and #2( 2) and az of (D; D?)/2. The flux to the third layer gj is likewise computed. The flux below the rooting zone Qj is computed with the h and k of the third layer of the previous time step. After the calculations of all fluxes the water extraction of each layer by evapotranspiration is determined. Actual soil evaporation Es (mm) is only present in the top layer. The actual transpiration of each layer Eta (mm) depends on the evaporative demand of the air, given by the potential evapotranspiration Etp (mm), and the pressure head of that soil layer. The pressure head is needed in a transpiration reduction function that limits transpiration at dry or wet soil moisture conditions . Finally, the new soil moisture conditions for the following time step are calculated. 3 Calibration Field measurements were made between 1996 and 1999 in the experimental gaps. Microclimate data that is used as input for the model was monitored in a
Development & Application of Computer Techniques to Environmental Studies VII, C.A. Brebbia, P. Zannetti & G.Ibarra-Berastegi (Editors) 2000 WIT Press, www.witpress.com, ISBN 1-85312-819-8 294 Computer Techniques in Environmental Studies large gap (3200 nf). Vegetation and soil parameters were measured at study sites along gap-centre to forest transects. Volumetric soil moisture was measured weekly with a Trime FM-2 TDR tube sensor in PVC tubes of one meter length. Soil moisture measurements were used to calibrate the soil water module. Calibration of the model was facilitated with the computer program PEST. Model parameter optimalisation was performed with the computer program PEST . PEST is a model-independent computer program for Parameter ESTimation. For linear models (i.e. models for which observations are calculated from parameters through a matrix equation with constant parameter coefficients), optimisation can be achieved in one step. However for non-linear problems (most models fall into this category), parameter estimation is an iterative process. PEST uses the Gauss-Marquardt-Levenberg algorithm  to solve the nonlinear weighted least squares parameter estimation. A large number of FORGAP parameters could be optimised with PEST. A sensitivity analysis of FORGAP was done for several vegetation and soil parameters. Parameters were selected that showed the largest influence in soil moisture and that were backed with only limited field data. Vegetation height was the only above ground parameter that had any significant influence on soil moisture conditions. Soil parameters that were selected are: saturated hydraulic conductivity, saturated volumetric soil moisture, Mualem's n and a. The user of PEST provides information on the upper and lower boundaries of the parameters that are being optimised. The boundaries that were supplied originate from values measured in the field by the author and by Jetten . 4 Output examples 4.1 Radiation The year sum of potential radiation on the vegetation, saplings and soil in a large gap (3200 m ) is shown in figure 4. Total radiation on the vegetation is uppermost on the trees surrounding the gap. Total radiation increases from the gap edge to the gap centre. 8295 6418 4524 i2638 752 Figure 4: Year sum of potential radiation (MJ.m ) on A) the vegetation, B) the saplings and C) the soil.
Development & Application of Computer Techniques to Environmental Studies VII, C.A. Brebbia, P. Zannetti & G.Ibarra-Berastegi (Editors) 2000 WIT Press, www.witpress.com, ISBN 1-85312-819-8 Computer Techniques in Environmental Studies 295 Total radiation on the vegetation in the gap centre is 85% of total maximum radiation. Total soil radiation in the gap centre is 80% of total radiation on the saplings. Total radiation on the saplings and on the soil in the forest undergrowth is about 10% of the total radiation above the forest. Total sapling and soil radiation decreases with increasing distance from the gap edge. Saplings in a part of a large gap that is extending into the forest, like at the top of the gap in figure 4, only receive 45% of the amount of radiation of the saplings in the centre of that gap. 4.2 Evapotranspiration Figure 5 shows the evapotranspiration fluxes as percentage of annual rainfall of undisturbed forest and in a large 3200 nf gap. Interception, throughfall and stem flow of the undisturbed forest has comparable values as reported by Jetten . The El Nino event in the latter half of 1997 contributes to the high potential evapotranspiration, which normally is about 50-60 % of total rainfall. Interception and transpiration is less in the gap than in the forest. Throughfall, soil evaporation and percolation are larger in the gap than in the forest. 100 80 60 40 20 0 agap Ei Th St El Eta n Esa Loss Ep Figure 5: Interception evaporation (Ei), throughfall (Th), stem flow (St), litter evaporation (El), actual transpiration (Eta) and soil evaporation (Esa), percolation below the rooting zone (Loss) and potential evapotranspiration (Ep) in a forest and a gap centre site expressed as % of annual precipitation. 4.3 Soil water dynamics The effect of gap size on the number of time steps (hours) that the soil moisture suction in the topsoil is lower than -1000 cm is shown in figure 6. Tropical rain forest gaps are usually wetter than the surrounding forest due to a reduced transpiration in the gap . However, very large gaps have a larger soil evaporation that is causing dryer conditions in the topsoil. As can be seen in figure 6, the small gaps experience wetter conditions than the surrounding forest. However, in the large gaps dryer conditions occur more often in the gap than the forest. Dryer conditions also prevail in the gap edge compared to the forest. The actual area that is under influence of the gap is larger than the perpendicular projection of the hole in the canopy.
Development & Application of Computer Techniques to Environmental Studies VII, C.A. Brebbia, P. Zannetti & G.Ibarra-Berastegi (Editors) 2000 WIT Press, www.witpress.com, ISBN 1-85312-819-8 296 Computer Techniques in Environmental Studies Figure 6: Effect of gap size on the occurrence (hours per year) of soil water suctions lower than -1000 cm. 5 Discussion and conclusions 5.1 Calibration The parameter estimation of PEST yielded soil hydrological parameter values against their upper or lower boundary. This implies that most likely a better optimisation can be achieved with hydrological parameter values outside these boundaries. However, the integrity of the model parameters with real field parameter values would be lost. Does this mean that the model does not perform well? There are several possible explanations for the lack of correlation between measured and calculated soil moisture. Jetten  studied the spatial variability of several soil hydrological parameters, including the soil moisture of the topsoil, in comparable soil types as present in the study area. He reported a high short-range (2-20 m) variation for most soil hydrological parameters. Detailed information of soil hydrological parameters would be required for every grid cell. This information is not available and the variation in the output is therefore impossible to model. Another problem is associated with the TDR soil moisture measurements. TDR soil moisture measurements in PVC tubes in wet tropical areas are sensitive for a) the position of the two metal strips inside the tube, b) air pockets between the tube and the soil matrix and c) moist conditions inside the tube or on the metal strips. Calibration of all tubes at all depths (up to 1 m) is necessary, but was not possible due to technical malfunctions. The prolonged wet season in 1999 prohibited the measurement of a wide range of soil moisture conditions needed for a good calibration. The soil moisture measurements with the tube TDR probe have to be treated with caution. 5.2 Model performance The potential radiation on the vegetation is calculated with solar (geometry) equations that are widely accepted. The derivation of the soil radiation is based on own observations and analysis. Radiation on the soil and on the saplings in the gap and in the gap edge gives insight into the spatial variation within and between gaps. Sapling radiation can be a discriminating site characteristic that explains sapling demography differences. The evapotranspiration functions are
Development & Application of Computer Techniques to Environmental Studies VII, C.A. Brebbia, P. Zannetti & G.Ibarra-Berastegi (Editors) 2000 WIT Press, www.witpress.com, ISBN 1-85312-819-8 Computer Techniques in Environmental Studies 297 used in many forest models [9,12]. The magnitude of the evapotranspiration fluxes of FORGAP and for example SOAP [8,12], which was developed for modelling the water balance of a tropical rain forest, are comparable. Unfortunately there were no field measurements available to calibrate the evapotranspiration module. The modelling of unsaturated flow is an iterative process. A change in soil moisture leads to a change in water potential and conductivity that results in changes of the soil moisture. The iteration must continue until a satisfactory balance in a soil layer is established. This iterative process cannot be modelled with PCRaster. The basic unsaturated flow dynamics of the model are sound. It was not possible to match the soil moisture model output with the large spatial variability of the soil moisture measurements. However, FORGAP is a useful tool in providing insight into the cohering processes of microclimate and water cycling in tropical rainforest gaps. The model can be used to explain differences in water availability between and within gaps and provide insight into the processes that gave reason for these differences. 5.3 Future developments The effects of tropical rain forest gaps in Guyana will be studied in scenario studies with hypothetical gaps. These scenario studies will focus on the effect of gap size, the effect of gap orientation to the sun, the effect of gap shape and the effect of multiple gaps. A multiple gaps approach is the most realistic view, since a lot of small gaps are usually made in real logging operations. These small gaps together will act as a very large gap. FORGAP can be improved with the inclusion of a plant growth module and a run-off module. Currently the saplings in the gap have a growth relation with net radiation that is only valid for the first 2 years after gap creation. A plant growth model can predict the growth of the saplings in the gaps and thereby make the model useful for long-term predictions. The soil water module only calculates vertical flow. The model can only be used in flat terrain. The expansion to lateral flow and surface run-off could make the model useful for other soil types in more sloping terrain. The radiation module and evapotranspiration module can be used separately to calculate radiation and evapotranspiration of entire regions. The model must be linked to a GIS with information on topography and land use as well as the necessary model parameters per land unit. Detailed calculations related to forest gaps can be left out to improve the velocity of the model calculations. The structure of FORGAP can be adjusted to the environmental settings of any terrain. Acknowledgements The author wishes to thank the people at the Tropenbos-Guyana Programme for their co-operation and support with the fieldwork. Special thanks to dr. V. Jetten
Development & Application of Computer Techniques to Environmental Studies VII, C.A. Brebbia, P. Zannetti & G.Ibarra-Berastegi (Editors) 2000 WIT Press, www.witpress.com, ISBN 1-85312-819-8 298 Computer Techniques in Environmental Studies for assistance with the model and dr. H. ter Steege for the useful comments on an earlier version of the manuscript. References  Ter Steege, H. et al. (19 authors) Ecology and logging in a tropical rain forest in Guyana. With recommendations for forest managers. Tropenbos Series 14. The Tropenbos Foundation, Wageningen, the Netherlands. 1996.  Denslow, J.S. Gap partitioning among tropical rainforest trees. Biotrop. 12: 47-55 (spec, ed.), 1980.  Van Dam, O., Rose, S.A., Houter, N.C., Hammond, D.S., Rons, T.L., & ter Steege, H. The Pibiri Gap Experiment. A study of the effects of gap size on microclimate, edaphic conditions, seedling survival and growth, ecophysiology and insect herb ivory. Site description, methodologies and experimental set-up. Tropenbos-Guyana Interim Reports 99-1, TropenbosGuyana Programme, Georgetown, Guyana, 1999.  PCRaster PCRaster manual Second edition. Utrecht University, dept. of Physical Geography, 1995.  Ter Steege, H. Winphot. A Windows 3.1 programme to analyses vegetation indices, light and light quality from hemispherical photographs. Tropenbos-Guyana Reports 97-3. Tropenbos-Guyana Programme, Georgetown, Guyana. 1997.  Whitmore, T.C., Brown, N.D., Swaine, M.D., Kennedy, D., GoodwinBailey, C.I., & Gong, W.-K. Use of Hemispherical photographs in forest ecology: measurement of gap size and radiation totals in a Bornean tropical rain forest. J. Trop. Ecol 9, pp. 131-151, 1993.  Monteith, J.L. Evaporation and the environment. The state and movement of water in living organisms. Proc. of the XIX symp. of the Soc. For Exp. Biol., Swansea, Cambridge Uni. Press., pp. 205-234, 1965.  Jetten, V.G. Modelling the effects of logging on the water balance of a tropical rain forest. A study in Guyana. Thesis. Dept. Of Physical Geography, Utrecht University, Tropenbos Series 6, The Tropenbos Foundation, Wageningen, the Netherlands. 1994  Feddes, R.A., Kowalik, P.J. & Zaradny, H. Simulation offield water use and crop yield. Simulation Monographs. Centre for Agricultural Publishing and Documentation, Wageningen, 1978.  Mualem, Y. A new model for predicting the hydrological conductivity of unsaturated porous media. Water Res our. Res. 12, pp. 513-522, 1976.  Watermark Computing PEST. Model-independent Parameter Estimation. Manual computer program, Watermark Computing, 1994.  Jetten, V.G. SOAP. SOU Atmosphere Plant model. A one dimensional water balance model for a forest environment (Theoretical framework & Manual) Dept. of Physical Geography, Utrecht University, the Netherlands. The Tropenbos-Guyana Programme, Georgetown, Guyana, 1994.
the presence of a gap is larger than this perimeter. Solar beams that fall into the gap can penetrate in the gap edge area, thereby increasing the actual gap area and thus the area where tree saplings can regeneration. Forest Gap Figure 1: Schematic representation of radiation in a forest gap. The abbreviations are explained in the text.
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