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Rapid forage inventory of Kenyan rangelands by double sampling for regression estimation : a feasibility… Mwanje, Justus Inonda 1981

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RAPID FORAGE INVENTORY OF KENYAN RANGELANDS BY DOUBLE SAMPLING FOR REGRESSION ESTIMATION: A FEASIBILITY STUDY USING AN AIRBORNE DIGITAL RADIOMETER by JUSTUS INONDA MWANJE, B.Sc. (Hons.) , U n i v e r s i t y of N a i r o b i , 1978 A THESIS SUBMITTED IN. PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Department of Fo re s t r y ) UNIVERSITY QF BRITISH COLUMBIA We accept t h i s t h e s i s as conforming to the r equ i r ed standard THE UNIVERSITY OF BRITISH COLUMBIA May, 1981 © Jus tus I. Mwanje, 1981 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an advanced degree a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e head o f my department o r by h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . . Department o f The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 Wesbrook P l a c e V a n c ouver, Canada V6T 1W5 Date i i ABSTRACT There i s a growing need f o r an inventory technique which can be r e a d i l y a pp l i ed to extens i ve and remote rangelands as cu r rent de s t r u c -t i v e and non -de s t ruc t i ve sampling methods are slow and expens ive. An attempt to r e so l ve t h i s problem i s made. The major o b j e c t i v e of t h i s s tudy, t h e r e f o r e , i s to determine the f e a s i b i l i t y of us ing a i rborne d i g i t a l rad iometers (b iometers) to inventory range forage. Remotely sensed i n f o rmat i on of s p e c t r a l rad iance or r e f l e c t a n c e r a t i o (RR) and l o c a l - l e v e l re fe renced b i o p h y s i c a l c h a r a c t e r i s t i c s v a r i a b l e s from the c l i m a t i c a l l y d i v e r s i f i e d Ka j i ado D i s t r i c t , Kenya has been processed. A l i g h t - a i r c r a f t f i t t e d w i t h d i g i t a l radiometer (biometer) was used i n a double-sampl ing s t r a tegy f o r r ap i d a c q u i s i t i o n of s p e c t r a l da ta . Biomass c l i p p i n g of sample m i c r op l o t s on s e l ec ted t r an sec t s prov ided l o c a l - l e v e l re fe rence i n f o rma t i on . These data e l u c i d a t e d f a c t o r s c h a r a c t e r i z i n g vege ta t i on s p e c t r a l response and hence behav ior , l i m i t a t i o n s and a p p l i c a b i l i t y of d i g i t a l radiometers as a t o o l f o r r ap i d i n ven to r y i ng of range forage ( s tand ing c r op ) . Least - squares r eg re s s i on methods have been app l i ed on the c o l l e c t e d da ta . S t a t i s t i c a l l y s i g n i f i c a n t l i n e a r r e l a t i o n s h i p s have been found to e x i s t between s p e c t r a l rad iance or r e f l e c t a n c e r a t i o (RR) and biomass f r e sh weights (FW) ( r = 0.703, P <0.01, df = 17), and l e a f water content (LW) ( r = 0.83, P <0.01, df = 17). Po lynomia l r e l a t i o n -sh ip between s p e c t r a l r e f l e c t a n c e r a t i o (RR) and biomass f r e s h weights i i i (FW) was significant (r = 0.872, P <0.01), and exponential relationship between the same variables was also significant (r = 0.61, P <0.01, d.f. = 17). Comparing the spectral regressions demonstrated that the linear equations are the best, simple and ease to apply* Total ecosystem moisture capacity was found to influence plant canopy reflectivity on a large scale. The soil catena characteristics were identified as an influencing factor on transect spectral reflectance dynamics.' Recommendations for further investigations, have been made and an improvement on the present sensor systems (radiometers) is desirable to optimize acquisition of spectral information. Percent vegetation greenness estimates were found to provide acceptable predic-tions of range forage in place of spectral data. However, such estimates need to be properly defined as they are primarily subjective. The digital radiometers have been shown to be a precise and expedient method for estimating standing crop. However, the present model (Tektronics J-16) should be used only in grasslands because its inability to penetrate the canopy gives inaccurate readings in brush-lands and woodlands. The use and reliance on remote sensing techniques show a great potential for monitoring tropical rangelands, in particular Kenya, for providing the necessary information for their ultimate resource development. TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS iv LIST OF TABLES vi LIST OF FIGURES ix LIST OF PLATES (PHOTOS) xi LIST OF VARIABLES CONSIDERED/MEASURED x i i ACKNOWLEDGEMENT x i i i DEDICATION xv 1.0 INTRODUCTION 1 2.0 LITERATURE REVIEW 6 3.0 THE STUDY AREA 18 3.1 Location 18 3.2 Landforms 18 3.3 Soils 20 3.4 Climate 21 3.5 Vegetation Cover 24 4.0 METHODS 26 4.1 Transect Selection Procedure 26 4.2 The Double-Sampling Technique 26 4.3 Sampling for Spectral Reflectances 30 '4.4 Sampling Biophysical Characteristics of Sample Plots 32 4.5 Data Analyses Procedures 40 V TABLE OF CONTENTS (cont'd) Page 5.0 RESULTS 48 5.1 Summary Statistics 48 5.2 The ANOVA of Spectral Reflectance Ratio (RR) Data .. 50 5.3 The Least Squares Regression Equations 55 5.4 The Double-Sampling Parameters 73 6.0 DISCUSSION, RECOMMENDATIONS AND CONCLUSIONS 79 6.1 Double-Sampling and Land-Use Policy Design 86 6.2 Recommendations 89 6.3 Conclusions 93 LITERATURE CITED 95 APPENDIX I 106 APPENDIX II 108 APPENDIX III 110 APPENDIX IV 115 vi LIST OF TABLES Page Table 5.1a The statistical summary of the biophysical characteristics variables measured in Kajiado study area, for n = 18 transects, surveyed July - August, 1980. 49 Table 5.1b The statistical summary of the spectral radiance or reflectance ratios (RR) grouped by major vegetation cover types in Kajiado study area, for n = 80 transects, surveyed in July, 1980. 49 Table 5.2 The analysis of variance of the spectral reflectance ratio data for Kajiado study area (n = 80 transects, each with 20 observations). 55 Table 5.3 A summary of the linear regression equations characterizing the relationship between the spectral radiance or reflectance ratios (RR) to biomass fresh weights (FW), vegetation or foliage height (VHT), percent vegetation green-ness (GREN), percent vegetation cover (CEST), leaf water content (LW), estimated annual index of water availability (WA), biomass density (BD), percent crude fibre (CF), herbage density (HD), and percent dry matter digestibility (DGM); biomass dry weights (DW) to spectral radiance or reflectance ratios (RR); and green-ness variation index (GVI) to leaf water content (LW) and estimated annual index of water availa-bility (WA) in Kajiado study area (July-August, 1980). 57 Table 5.4 The linear regression equations showing the relationship between the biophysical character-istics variables: biomass fresh weights (FW), biomass dry weights (DW), percent vegetation cover (CEST), percent vegetation greenness (GREN), herbage density (HD), and estimated annual index of water availability (WA), leaf water content (LW), and biomass density (BD), in Kajiado study area, July-August, 1980. Table 5.5 The multiple linear relationship between the spectral reflectance ratios (RR); the fresh biomass weights (FW) and dry biomass weights (DW), in Kajiado study area, July-August, 1980. 59 61 v i i LIST OF TABLES (cont'd) Page Table 5.6 The multiple linear relationship between the spectral reflectance ratios (RR); the estimated annual index of water availability (WA) and leaf water content (LW), in Kajiado study area, July-August, 1980. 62 Table 5.7 The multiple linear relationship between the spectral reflectance ratios (RR); and the sample plot biophysical characteristics variables: the percent cover estimate (CEST), the percent green (GREN) and the vegetation or foliage height (VHT), in Kajiado study area, July-August, 1980. 63 Table 5.8 The multiple linear relationship between the spectral radiance or reflectance ratios (RR); biomass density (BD), herbage density (HD), dry biomass weights (DW), vegetation or foliage height (VHT), percent vegetation greenness (GREN) and the estimated annual index of water availability (WA%) in Kajiado study area, July-August, 1980. 65 Table 5.9 The multiple linear relationship between the spectral radiance or reflectance ratios (RR); biomass fresh weights (FW), percent dry matter digestibility (DGM), percent crude protein (CP), percent crude fibre (CF), percent vegetation cover (CEST), vegetation or foliage height (VHT), percent vegetation greenness (GREN), and the estimated annual index of water availability (WA%) in Kajiado study area, July-August, 1980. 66 Table 5.10 The multiple linear relationship between the greenness variation index (GVI); biomass fresh weights (FW) and the estimated annual index of water availability (WA%), in Kajiado study area, July-August, 1980. 67 Table 5.11 The polynomial relationship between the spectral radiance or reflectance ratios (RR) and biomass fresh weights (FW) in Kajiado study area, July-August, 1980. 68 Table 5.12 The exponential relationship between the spectral radiance or reflectance ratios (RR) and the biomass fresh weights (FW) in Kajiado study area, July-Aguust, 1980. 69 v i i i LIST OF TABLES (cont'd) Page Table 5.14 Spectral radiance or reflectance ratio (RR), biomass fresh weights (FW) equations and the mean bias. 70 Table 5.13 Correlation matrix for the spectral reflectance and biophysical characteristics variables observed in Kajiado study area (July-August, 1980). 74 ix LIST OF FIGURES Page Figure 2.1 Calculated ratio versus total L.A.I. 10 Figure 2.2 Empirical infrared/red reflectance ratio for oats canopies with light and dard soil versus biomass. 11 Figure 2.3 Spectral acceptance of the radiometer probes. Each probe consists of a silicon photodiode that views the clipped sample through an interference fi l t e r . 13 Figure 2.4 The ratio concept: spectral reflectances at 0.675 m and 0.800 m are inversely and positively related to biomass respectively. Rj...Rn are the sample plot reflectance ratios (0.800 J^ m/0.675j^  m) for equal probes' reception. 15 Figure 3.1 Kajiado Map: location of some transects surveyed. 19 Figure 3.2 Distribution of average annual rainfall in milli-meters in Kajiado District and adjacent areas. 22 Figure 3.3 Distribution of three rainfall pattern types in Kajiado study area. The type numbers are assigned to the locations of raingauges. 23 Figure 4.1a Laboratory set-up of the digital radiometer used as a green/brown estimation device. The instru-ment consists of a digital radiometer which measures radiances from vegetative samples through two filtered probes. 33 Figure 4.1b Radiometer filter probes' projection to the vegetative sample plots. 34 Figure 5.1 Histogram for spectral radiance or reflectance ratio (RR) data collected (n=29, transects) in grasslands, Kajiado study area. 51 Figure 5.2 Histogram for spectral radiance or reflectance ratio (RR) data collected (n=25, transects) in bushlands, Kajiado study area. 52 X LIST OF FIGURES Page Figure 5.3 Histogram for spectral radiance or reflectance ratio (RR) data collected (n=26, transects) in wood-grasslands, Kajiado study area. 53 Figure 5.4 Histogram for combined spectral radiance or reflectance data collected (n=80, transects) in all vegetation cover types surveyed, Kajiado study area. 54 Figure 5.5 The relationship between spectral or radiance reflectance ratio (RR) and biomass fresh weights (FW) 75 Figure 5.6 The relationship between second sample (n) and first large sample (n') size for specified population correlation coefficient (p) in a double-sampling scheme. 78 Figure 6.1 General relationship (suggested) between spectral reflectance ratios and biomass over the three stages of growth. 87 xi LIST OF PLATES (PHOTOS) Page Plate 1: Aircraft fitted with digital radiometer (biometer) equipment. 31 Plate 2: Clipping of sample microplots (local-level reference) for biomass sampling. 36 Plate 3: Shompole area - a typical overgrazed grassland range. Characteristic of erratic biometer behaviour. 37 Plate 4: Ngong Hills area - savanna shrubland illustrating the overtopping of grasses by shrubs. Fluctuations in biometer readings reflect different levels of range forage. 38 Plate 5: Ecotone between grassland and woodland where radio-meter (biometer) readings are erratic. 39 x i i LIST OF VARIABLES CONSIDERED/MEASURED FW : Biomass (Standing Crop) Fresh Weights (gm/m^ ) DW : Biomass (Standing Crop) Dry Weights (gm/m^ ) LW : Leaf Water Content (LW = FW - DW) RR : Spectral Radiance or Reflectance Ratio DGM : Dry Matter Digestibility (%) CP : Crude Protein (%) CF : Crude Fibre (%) CEST : Vegetation Cover Estimate (%) GREN : Vegetation Greenness (%) VHT : Vegetation or Foliage Height (m) WA : Estimated Index of Annual Water Availability (%) GVI : Greenness Variation Index BD : Biomass (Standing Crop) Density (= FW/CEST) HD : Herbage Density (= VHT * CEST) x i i i ACKNOWLEDGEMENTS I am deeply indebted to Dr. Roy M. St rang, my major supe rv i s o r , f o r h i s f i r m d i r e c t i o n and encouragement throughout the per iod of my graduate s t u d i e s , and to the members of my committee—Drs . A. Kozak, J . P . Demaerschalk and A.R.E. S i n c l a i r f o r rev iewing the t he s i s d r a f t and f o r t h e i r v a l uab l e comments. I am p a r t i c u l a r l y g r a t e f u l to Dr. A. Kozak f o r gu id ing me through the f i n a l stages of my graduate s t u d i e s . I am most g r a t e f u l to Dr. Donald G. Peden of the Kenya Rangeland E c o l o g i c a l Mon i to r i ng Un i t (K.R.E.M.U.), c u r r e n t l y w i th Canadian W i l d l i f e Se rv i ce (CWS) f o r suggest ing the problem and fo r h i s i n v a l u a b l e comments dur ing the many long d i s cu s s i on s we had throughout the development of t h i s t h e s i s , to Mr. J . M u t i r a , Mr. Y. Kadaya and Mr. Aduvaga f o r the a s s i s t ance i n data c o l l e c t i o n and fo r t h e i r pa t ience w i t h me dur ing the f i e l d work i n Ka j i ado D i s t r i c t , Kenya, to Mr. Fred Hamilton f o r e x c e l l e n t s e r v i ce as my survey p i l o t , and to the s t a f f of the Ant i -Poach ing Un i t (A.P.U.) at Nguruman Out Post f o r t h e i r dependable scout ing through the t h i c k bushes of S.W. Ka j iado and fo r keeping an eye on the v o l a t i l e b u f f a l o s . I should l i k e to extend my thanks to Dr. Dennis J . Her locker and Mr. Helmet Epp f o r t h e i r input i n the p lann ing of the a e r i a l surveys and f o r t h e i r v a l uab l e comments on research content s , to Mr. Sammy Ng ' ang ' a and Miss C h r i s t i n e Mu le i f o r the comp i l a t i on and p r e l i m i n a r y a n a l y s i s of the da ta , and to Mr. Edward Mbiyu of K.A.R. I . , Muguga, fo r the chemical a n a l y s i s of the vege ta t i on samples. xiv I extend my sincere appreciation to the government of Canada through the Canadian International Development Agency (C.I.D.A.) for the fellowship received, to the government of Kenya through K.R.E.M.U. for giving me a paid leave of absence while furthering my studies in Canada, and to the University of British Columbia for providing additional funding in the form of McPhee Fellowship; without these financial resources, this thesis would probably not have been possible. I am most grateful to Dr. Ward Stevens (C.W.S.) and Mr. D.K. Andere (K.R.E.M.U.) for initiating my training program, to Mr. Ross Pritchard and Mr. A.F. Shirran for their help through C.I.D.A., and to my sponsors for funding my trips to conferences at La Paz, Mexico, San Diego and Tulsa, U.S.A. These conferences provided valuable experience and contacts that proved very helpful to the development of this thesis. I should like to extend my special thanks to my colleagues— Stephen A.Y. Omule, Jose C. Zanuncio, Winston J.K. Mathu and Simon S. Chiyenda—for the benefit I derived from many discussions I had with them at the time of writing this thesis, to Drs. C.S. Rolling and A. Chambers for their encouragement, to Dr. and Mrs. Andrew Brockett of Vancouver and the Harold Hark family of Nelson, B.C. for their hospitality and for introducing me to the Canadian culture. Finally, I am very grateful to my parents: Alfred M. Mugalo and Recho Kanguha, my brothers and sisters and to the rest of my family who, despite my long absence from home, continued to provide the very much needed encouragement and moral support that helped me complete this work. 1 1.0 INTRODUCTION The Republic of Kenya covers a total land area of about 596,260 9 km . Some 80% of this is semi-arid or arid. At present much of this land is the home of nomadic cattle-owning people, whose main economic occupation is animal husbandry. It is true, also, that these areas form the home of world-famous wild animals and so forage produced on these lands is competitively utilized by both wildlife and domestic livestock. In recent years, the government of Kenya has set up the Kenya Rangeland Ecological Monitoring Unit (KREMU) using technical aid provided by the government of Canada through a bilateral agreement (Annual Report, KREMU, 1978). The primary objective of KREMU is to establish an efficient resource monitoring programme centred on the vast rangelands. Monthly and seasonal inventories of the wildlife and livestock population densities have been carried out fairly efficiently. However, the problem of collecting sufficient and reliable data on range forage production has posed major challenges. As the area being monitored is extensive, the present procedures for inventorying range forage have proved to be time-consuming and expensive. Ground transport between sampling plots has been practically impossible, and even when possible, i t is expensive to cover the area under the monitoring programme. A more serious problem is associated with the lack of a reliable road network. Also the problem of organizing large personnel groups for tedious exercises of 2 range forage clipping has proved to be a major obstacle against efficiency and acceptable job productivity. Hence, there is an increasing need to develop a rapid method of range forage (standing crop) inventory for rangelands, which are extensive and often inaccessible by road. To be able to study stocking rates of range mammals effectively, such a method would allow better estimates to be made of rangeland forage and hence carrying capacity, or, perhaps, even short-term stocking rates for economic management of the rangeland resources. Recent work, by Lamprey et al. (1980), mentions gaps in our present knowledge on browse productivity and methods for measuring i t . The need for developing reliable and economic techniques for assessing browse production, at various geographic scales, is stressed. They observe that development of such techniques would require the use of destructive sampling to generate predictive probabilistic models for each technique (whatever i t might be). Another dimension to consider in this endeavour is the lack of adequate documentation of the limitations facing the inventory procedures and equipment currently in use. In addition, the importance of elucidating limitations and advantages of new inventory procedures and equipment is to be given priority. It is not uncommon that documentation of any inventory procedure seems to present the procedure per se, unwittingly ignoring problems associated with its application. This is a problem that must be resolved. 3 In particular, equipment used in inventorying resource data is somewhat often, normally employed without understanding its functional components and any such interactions with the target variables being inventoried. It is important to understand the equipment' limitations so as to be able to detect possible anomalies in the data collected.. Factors that characterize the performance and readings by such equipment must be isolated. This problem has been more pronounced, particularly in the use of electronic sampling equipment like digital radiometers (biometers). In regional and national rangeland resource inventories, rapid acquisition of information is essential. Current methods do not allow a high degree of efficiency for inventorying data for regional and national planning activities. Not only is i t difficult to collect reliable data on seasonal variation, but i t is also equally difficult to compare inter- and intraseasonal variations as they are not readily available. Further, i t is also difficult to guarantee synchronization of the acquisition of such data. Hence, regional and national planning based on such information may be erroneous and therefore, may generate serious problems in the long run due to the adoption of unreliable resource development strategies. The use of digital radiometers (biometers) has been so far restricted to inventorying areas that are predominantly ecologically uniform such as forage production in grasslands. However, most of the Kenyan rangelands are covered with savanna, bushlands and wooded-grasslands. Some vegetation communities referred to as wooded and bushed-grasslands, are known to be complex in composition and structure. 4 The need for rapid range forage inventorying in these heterogeneous vegetation communities has provided a major challenge to KREMU. The use of remote sensing procedures would be useful as these areas are difficult i f not impossible to inventory rapidly using conventional methods. It is important to appreciate the fact that, such areas are highly productive as regards range forage, and its utilization by both wildlife and domestic animals that use the resource competitively. Some definitions of commonly used terms are given in Appendix I. This is for the sake of clarity of the subject under study. Some of these definitions are derived from Kotthmann (1974). The major objective of this study was to determine the feasibility of using an airborne digital radiometer (biometer) to inventory range forage (standing crop) of Kenyan rangelands covering a heterogeneous spectrum of biophysical characteristics. To be able to achieve this objective, the threefold sub-objectives to be also considered are: (i) To correlate digital radiometer estimates of spectral radiance or reflectance ratios of vegetation "greenness" with the biophysical characteristics of paired vegetative sample plots. (ii) To generate appropriate probabilistic regression equations based on variables considered in, (i) above. ( i i i ) To examine critically the limitations and applicability of these equations for determining the usefulness of the digital radiometer as a tool, in rapid forage inventory. 5 It is desirable to present results in this thesis in the most simplified fashion. This will enable some of the resource managers, unfamiliar with advanced statistics, to comprehend and appreciate this documentation. Sophisticated regression models are therefore to be excluded in this work. The Kajiado study area (Fig. 3.1) has been chosen for this investigation. The area is appropriate in the sense that it covers a wide range of biophysical and ecological characteristics, and hence provides representative findings applicable to other rangelands with only minor modifications. In this thesis, a brief review of some of the most relevant literature related to conventional and current developments of rapid inventorying of range forage (standing crop), is given in Chapter 2. Next, a brief presentation of an introduction to the Kajiado study area, is given in Chapter 3. In Chapter 4, a detailed treatise of the research methodology is given. In Chapter 5, the results of the study are presented, and finally in Chapter 6, these results are discussed. Also included are conclusions and some important recommendations based on the findings. 6 2.0 LITERATURE REVIEW Measurements of standing crop have traditionally been made by hand clipping plots (Tucker, 1975). The clipped material is weighed to determine biomass fresh weights (FW) and later oven-dried and re-weighed to determine biomass dry weights (DW) per unit area. This method has proved to be tedious, inefficient, and time-consuming and above a l l , expensive. This is specially so, if collecting data for national inventories. Furthermore, plot remeasurements, after a time interval to estimate vegetation productivity, may not guarantee acceptable confidence in comparable results, especially so in shrub-dominated rangelands. A number of non-destructive techniques for estimating standing crop are also in use, Mannetje (1978). Teare (1963), as reported in Alcock and Lovett (1967), gave an early review of methods for rapid non-destructive estimates of the yield of growing pastures. These include capacitance measurements, ocular estimation, and beta-attenuation techniques. The electronic capacitance meter has received extensive attention from a number of researchers. Some of these workers include Alcockand Lovett (1967), Jones and Heydock (1970), Kreil and Matschke (1968), Currie et al. (1973), and Neal et al. (1976). The development and use of ground sampling methods for inven-torying range forage (standing crop) has been in effect for a long time. Some of the workers who have been involved in this exercise 7 include Pechanec and Pickford (1937), Canfield (1941), Brown (1954), Evans and Jones (1958), Pasto et a l . (1959), Campbell and Arnold (1973) , Hutchings and Schmautz (1969), Haydock and Shaw (1975), Payne (1974) , Harris and Fowler (1970), Mannetje (1978) and Bonham (1980). Few workers have faced the challenge of evaluating the usefulness of some of these ground sampling techniques. The notable ones include Black et. al. (1969), Bryant et al. (1971), Currie jit al. (1973), Jones et al. (1977), and Michalk and Herbert (1977). Double sampling methods (ratio or regression estimators) are used to inventory information on an auxilliary variate x^, which is then utilized to make, estimates of the variable of interest y^ (Cochran 1963; 1977). Some workers have employed this procedure in inventorying range forage. Examples include Morley et. aT. (1964), Black et al. (1969), Kuchar (1980, personal communications), and Reese et al. (1980). These few examples demonstrate the importance of regression estimates of range forage (standing crop) and other variables and the need to develop and refine efficient and economically-viable inventory techniques. The methods considered in the literature cited in the foregoing paragraphs may be suitable for inventorying forage data on fairly small areas. However, when inventorying large areas which require time and an extensive network of ground transport, their suitability is extremely limited. Hence the need for aerially-based methods is evident. The development and use of aircraft and satellite inventory procedures have been on the increase. For instance, Western (1977), 8 and Gwynne and Croze (1977) have demonstrated that subjective estimates of greenness, which is an integral of factors that influence primary production, are good estimators of the biomass distribution of large mammals in tropical rangelands. This suggests that standing crop itself can be predicted from such subjective estimates, collected during low level, systematic reconnaisance flights. In the case of satellite techniques, Gwynne (1978) used LANDSAT DATA of Kajiado District of Kenya (40,000 km2) to derive the Composite Greenness Index (CGI) by photometric methods from standard false infra-red composite imagery (MSS Bands 4, 5 and 7). The index was used to estimate standing crop. Thus, i t appears that some kind of inventory method based on remotely sensed information could facilitate the speed and efficiency of the procedures currently in use. Some workers have investigated the usefulness of spectral information to inventorying standing crop. Wagner and Colwell (1969) processed multispectral scanner data in an attempt to assess the feasibility of using remote sensing techniques to monitor important characteristics of rangeland ecosystems. This study left enough important questions unanswered. These included the effect on vegetation canopy bidirectional spectral reflectance caused by varying soil reflectance, biomass, percent vegetation cover, leaf area index (L.A.I.), canopy structure, amount of live and dead vegetation, solar zenith angle, look angle, and azimuth angle. The spectral regions investigated were the green (.55 urn), the red (.65 ym), and the near IR (.75 urn) • 9 In investigating these unanswered questions, Colwell (1969) found that the optimum spectral bands for remote determination of standing biomass of grasslands vary, depending on such things as the type of vegetation, the range of values of percent vegetation cover present, the soil reflectance, and the look angle and solar zenith angle. No single spectral band can be considered, ji priori, to be effective in a l l situations. He further established indications that under certain conditions a reflectance ratio can be used to determine the amount of standing biomass irrespective of soil reflectance or amount of leaf li t t e r . It was demonstrated that when IR/red bidirectional reflectance ratios from the canopies with both light and dark soil are pooled, it can be seen that the ratio does, in fact, tend to normalize the data with respect to soil reflectance (Fig. 2.1); and ratioing improved the predictability greatly (Fig. 2.2). The applications of these spectrometer-based methods were extended by Pearson and Miller (1972), and Miller et. al_. (1976). Further, studies of spectrometer data elucidated the basic relation-ships involved in estimating green biomass (Tucker et_ al., 1975; Tucker and Miller, 1977; Tucker, 1977; Tucker, 1978; and Tucker, 1979). Kanemasu (1974) found a high correlation between the ratio of green (0.527 - 0.563 ym) to red (0.663 - 0.678 ym) and leaf area index in wheat, sorghum and soybean, a l l of which were virtually 100% green biomass. Drake (1976) applied a similar ratio concept to a study of seasonal changes in reflectance and standing crop in salt marsh 30 i i i i i i I I l 1 1 2 3 4 5 6 7 8 9 10 Total Leaf Area Index Figure 2.1 Calculated Ratio Versus Total L.A.I, (from Colwell 1974). 20 Figure 2.2 Empirical infrared/red reflectance ratio for oats canopies with light and dark soil versus Biomass. (from Colwell 1974). 12 communities. In this study, reflectances of red (0.656 - 0.705 ym) and infrared (0.776 - 0.826 ym) solar radiation and standing crop were examined. It was found that red reflectances declined at the on set of greening in each community and were correlated with standing crop of green biomass. Pearson (1973) used the ratio of IR to red (0.826 to 0.776 ym) and found a high correlation with standing crop. This relationship was linear only when standing crop was less than approximately 350 gm dry weight m . i t was also found that there existed a strong negative correlation between dry weights of standing crop and red reflectance (0.656 to 0.705 ym). Pearson et al. (1976b) reported that spectral radiance or reflectance at 0.675 ym and the amount of standing crop present in the grass canopy exhibit a strong, statistically significant, and inverse relationship. The physiological explanation of this phenomenon is based on strong chlorophyll absorption centred at approximately 0.675 ym. Reflectances at 0.800 ym and the amount of biomass present exhibit a strong, statistically significant, and positive relationship. The physiological explanation for this occurrence is based on lack of appreciable absorption at this wavelength and on the leaf or blade scattering mechanism which results in high levels of reflectance (Tucker et al., 1975). Hence the ratio between these two reflectance measurements were more accurate than either one separately in measuring green flux as related to standing crop (Pearson et al., 1976a). Fig. 2.3, shows the relationship between relative spectral response and wavelength at 0.675 ym and 0.800 ym for two radiometer probes. Figure 2.3. Spectral acceptance of the radiometer probes. Each probe consists of a silicon photodiode that views the clipped sample through an interference filter (from Pearson et al 1976). 14 Thus, the concept of taking the ratio between two radiance or reflectance measurements (Fig. 2.4) at two selected wavelength bands to measure above-ground biomass non-destructively has been developed and applied (Tucker et al., 1975; Miller et al., 1976; Pearson et al., 1976a; Pearson et al., 1976b; Tucker, 1977 and Tucker, 1980). Recently, the hand-held radiometer technique for monitoring agri-cultural crop condition has been reported (Tucker el: al., 1979a,b). In yet another report, Tucker et al . (1979c) conducted an experiment in which a ground-based, hand-held radiometer was used to estimate alfalfa forage yield and related agronomic variables such as crop canopy cover, plant height, and drought stress. He also reports that remote sensing techniques have been used to estimate forage production (Pearson and Miller, 1972; Rouse et al., 1973; Deering et al., 1975; Reginato et al., 1978; and others) and estimating yields of nonforage agricultural crops (Thomas et al., 1967; Hammond, 1975; Morain and Williams, 1975; Colwell et al., 1977; Idso et_ al., 1977a,b; and others). Specialized hand-held radiometers have been developed and used by Methy (1977) and Milton (1978) for in situ data collection. Peden (1980) conducted a survey of the Masai Mara Ecosystem. In this investigation, spectral reflectances of vegetation "greenness" were collected from an aircraft fitted with an airborne digital radio-meter (Tektronics Model J-16). Transects were located in fairly homogeneous vegetation cover types. It was learned that the data indicated that relatively small differences in greenness can be detected with the airborne radiometer. However, the effects of the Biomass (gm/m.2) Figure 24 The Ratio Concept: Spectral Reflectances at 0.675fim and 0.800 ym are inversely and positively related to biomass respectively. R1 ..Rj.Rn are the sample plot reflectance ratios (0.800pn/0.675/fln) for equal probes' recep-tion. 16 apparent linear trend that was found to exist on the east-west axis of the Mara ecosystem, and the possible influence of lack of livestock in these surveyed areas which f e l l within the game reserve boundaries, could not be readily explained. Full results of the data analyses of this investigation are given in Appendix 11. McNaughton (1976 and 1979) employed the ratio concept to estimate standing crop by the double-sampling procedure, in the Serengeti grass-lands, Tanzania. Reflectances were received at 0.675 ym and 0.800 ym and the ratio of the two readings was correlated with standing crop measurements. A high degree of accuracy in predictions was found (r = 0.955, P <0.01; d.f. = 18). Such a high correlation could have resulted from the homogeneous character of the grassland type, predominant on the Serengeti plains. Thus, spectral sampling procedures have potential for speeding up range forage (standing crop) inventories of varied vegetation cover types, and possibly even reducing costs. Development of a successful technique will overcome the problems of time and accessibility that limit the efficiency of predominantly ground sampling methods presently in use in East Africa, arid in particular, Kenya. From the literature cited it is observed that (1) ground-based sampling procedures for range forage are site-specific, and may be cost-effective and useful for inventorying small areas; and (2) aircraft or satellite procedures coupled with appropriate sampling techniques (e.g. double-sampling) may permit a 17 rapid inventorying of standing crop for large areas covered with heterogeneous vegetation cover mosaics. Thus, a study combining both approaches for a cost-effective technique for inventorying large heterogeneous areas is desirable, and needs to be examined critically. In the next chapter, the Kajiado study area, which has a complex combination of landforms, soils, climate and vegetation attributes is described. 18 3.0 THE STUDY AREA 3.1 Location The Kajiado study area, which covers approximately 40,000 km2, is located in the southern part of Rift Valley Province of the Republic of Kenya. It lies between 1° 2.5' and 3° 11.4* S and 36° 2.5' and 37° 55' E. To the west lies the Nguruman Escarpment, while to the east are the Nairobi-Mombasa railway, the Chyulu mountain range and the Tsavo National Park boundary. The Central and Nairobi Province boundaries lie to the north while, to the south, is the international border between the Republics of Kenya and Tanzania (Fig. 3.1). Access from Nairobi is from the Nairobi-Namanga or Nairobi-Magadi roads, the only all-weather roads that traverse the study area. All other roads, which are few are in poor condition all year round. 3.2 Landforms Most of the area lies between 3,000 and 4,000 m above sea level. In the southwest lies the low depression that forms the Lake Magadi and Lake Natron drainage systems. The main river in the area is the Ewaso Ng'iro. It drains into the Engare Ng'iro swamp that joins with Lake Natron during the wet season. To the southeast is a series of internal drainage areas; the most notable being the Lake Amboseli basin. Most rivers here are simply "Lagas" filled with water only during the wet season. To the northeast are the vast Athi-Kapiti plains that lie between 1600 and 1800 m above sea level. 20 Some of the notable volcanic h i l l masses in the study area include, the Ngong Hills (2460 m) to the north, Mt. Suswa (1256 m) to the northwest, Mt. Shompole (5132 m) to the southwest and 01 Doiny Orok (8282 m) to the south. The Chyulu Range (7177 m) is located in the south eastern part of the study area, while the Maparasha Hills (6867 m) and Ilaingaruyieni Hills (5082 m) are in the south central portion. The rest of the study area is characterized by undulating plains-and low-lying hills that are covered with various types of vegetation communities. 3.3 Soils A wide range of soils is found in the area. The Athi-Kapiti plains have grey or black clay soils which vary in degree of cracking, character of surface material and depth of soil according to their position on hilltop (Dunne, 1977). Broad and flat hilltops are characterized by clay loams that cover sub-soils of heavy, angular blocky clays. In the Amboseli area soils are dark red to reddish-brown sandy clays. On gentle slopes the soils are as deep as 1.0 m, while on steeper slopes, soils are shallow and maximum depth may be only 0.5 m. Most areas are covered with shallow volcanic soils which range between brown and dark reddish-brown. Well-drained gentle slopes on hillsides are characterized by sandy clay loams with depths exceeding 1.0 m. Termites mounds are common. On the local scale, these mounds portray a complex dynamic soil structure. Viewed in the context of the ecosystem framework, they represent a major problem as they eliminate 21 vegetation cover. Soils found near these mounds is fairly thick, however, this does not exceed 0.5 m, in depth. Above a l l , such soils are poor in nutrient content. 3.4 Climate The rangeland areas of the Kajiado study area are characterized by low rainfalls (Norton-Griffiths 1977). Figures 3.2 and 3.3 show the distribution of average annual rainfall and the three rainfall pattern types of the study area respectively. Since elevation is a major factor in determining annual rainfall distribution, hilly areas including Ngong, Machackos, and Chyulu are typified by slightly higher rainfalls. Similar areas that have high rainfalls include the slopes of Kilimanjaro (on the Kenyan side) and the western fringing mountain ranges that form the western limit of the ri f t valley. The very low rainfall in the Lake Magadi area and those areas to the north of Kajiado town may be caused by the orographic effect of the eastern r i f t wall and the Machackos Hills in the east. The low rain-falls in the south eastern area may be due to complex dynamics of wind-flows through the depression between the Chyulu Hills and the slopes of Mount Kilimanjaro. Most of the precipitation occurs in two rainy seasons. These are the March to May (long rains) and November to December (short rains) periods. Norton-Griffiths (1977) found that for 80 percent of the rain falling in the region there appears to be no relationship whatsoever between the mean annual rainfall at a site and the distribution of 22 Figure 3.2* Distribution of average annual rainfall in millimeters in Kajiado Study Area and adjacent locations. 'Source: Adapted from Norton-Griffiths (1977) 23 Figure 36* Distribution of three rainfall pattern types in Kajiado Study Area. The type numbers are assigned to corresponding raingauge locations. •Source: Adapted from Norton-Griffiths (1977) 24 rainfall intensities. The remaining 20' percent of the rain does f a l l at very high and potentially damaging intensities. This is an explanation for erosion gullies in the area. The mean monthly air temperatures vary from 12°C to 21°C near Nairobi and from 17°C to 32°C north of the Amboseli Basin (Dunne, 1977). Potential evapotranspiration is high throughout the study area. It varies from 1800 mm/yr, on the Athi-Kapiti plains to 200 mm/yr in the Amboseli Basin. Rangeland plants are, therefore generally facing a marked moisture stress throughout most of the year, especially so during the dry seasons. 3.5 Vegetative Cover The vegetative cover of the study area can be broadly divided into four major groups: pockets of forests; wooded grasslands; shrub-land or bushland; and grasslands. Isolated forests are likely to be found on top of high hills as well as along major drainage systems, like the Ewaso Ng'iro river, fringing the western end of the study area. Wooded grasslands cover the low-lying flat-topped volcanic ridges while shrublands or bushlands occur at lower elevations. Grass-lands cover areas of a wide range of elevation. The vast Athi-Kapiti plains, an area that falls within 1600 and 1800 m above sea level is predominantly grassland, with sparse woody cover of Acacia drapanolobium (Dunne, 1977). Some of the grass species growing in the area include: Themeda  triandra, Cynodon dactylon, Pennisetum mezianum, Eragrostis spp., 25 Digitaria macroblephera, and Sporobolus sp. The shrubland or bushland species include: Duosperma sp., Grewia bicolor, Commiphora africana, and Combreturn collinum. The woodland vegetation species include: Acacia mellifera, Acacia tortilis, Acacia xanthophloea, Acacia Senegal, Commiphora schimperi, Balanites aegyptica, Salvadora persica, and Azima  tetracantha. Some of the swampy vegetation cover consists of species like Cyperus papyrus and Typha angustifolia, found in areas associated with poor drainage (Heady 1960, Karue 1974, Musafiri 1980 (personal communications), and others). The ground cover varies with seasonal rainfall pattern and the grazing intensity of both domestic and wild stock. Ground cover in the grassland areas may vary between 65 and 85 percent during the peak biomass period, with a mean annual rainfall of at least 750 mm. This pattern is typical in the Athi-Kapiti plains. In areas with a mean annual rainfall of less than 500 mm and those under severe grazing pressure, the ground cover may be lower than a mere 1 percent even during the peak biomass period. The study area is generally characterized by fairly complex mosaics of plant communities. These communities could be systematical-ly analysed following a classification of the ecological zones of the area by Pratt, Greenway and Gwynne (1966), and Pratt and Gwynne (1977). This complex structure of plant communities is typical of most range-land areas of Kenya. In the next chapter, the methods employed in this study are explained. 26 4.0 METHODS Field and laboratory procedures followed in this study are presented: first an explanation of the procedure used to select the transects for investigation in the study area; then, a brief account of the double-sampling technique; and finally, spectral reflectances and ground sampling for biophysical characteristics of sample plots' data acquisition procedures and methods employed to analyse the information are considered. 4.1 Transect Selection Procedure Topographical, rainfall, soil and vegetation maps of the Kajiado study area were examined. A hundred transects were located in areas thought to have relatively ecologically homogeneous biophysical characteristics. The vegetation component of these characteristics was, however, more emphasized. Most transects were placed in grass-land, dwarf shrubland, and open-wooded grassland vegetation cover types. No transects were located in hilly forested areas because they could not be ground-truthed satisfactorily. The one hundred selected transects were marked on 1:250,000 topographical map, which was used for navigational purposes. 4.2 The Double-Sampling Technique The method of double-sampling was used to collect information on spectral reflectances and biophysical characteristics of clipped-plot samples. This information was used to generate regression models that 27 related spectral reflectances to vegetation attributes of target sample plots. Regression estimates were also computed. A brief explanation of the double-sampling technique employed follows. If the knowledge of the population mean X or distribution of Xj^j the auxiliary variate, is lacking, population stratification based on values of x^  cannot be done (Cochran 1963; 1977). When this is the case, i t is necessary to take a large sample in which x^ alone is measured. This will provide a good estimate of X or of the frequency distribution of x^. In this study the variate x-^  was the spectral reflectance ratios. Regression estimators were to be made of a variate y^ (standing crop, gm/m^ ). i t may pay to obtain a large preliminary sample of x-^  (spectral reflectance ratios) and devote a lesser effort, in terms of man-hours/day, to sample values of y^ (standing crop, gm/m^ ). Since we do not know the distribution of x^  in advance, we cannot stratifying the population on the basis of the values of x^  (Cochran 1963, 1977). Hence, the best we could do is to obtain the regression estimate of Y, the population mean for the y-^ . The estimate of Y is y l r = y + b (x' - x) 4.1 Where, x' , x are the means of the x- in the first (n') and second 28 (n) samples and b is the least squares regression coefficient of y. on x-j^ , computed from the second sample. Suppose we assume, following Royall (1970), that the finite population is itself a random sample from an infinite superpopulation in which a linear regression model holds. Then yj_r becomes model-unbiased and exact small-sample results for its variance can be obtained. In this study, i t is assumed that the regression model in the superpopulation is y = 0( + p x + e 4.2 Where, for given x's, the e's are independent with mean 0 and variance 9 9 erg (1- p ), where oy and p are now parameters of the superpopulation. Substituting for y, Y, and b from Eqn. 4.2, we obtain y l r - Y = £ N - \ + P(x' - x ) + ( x ' " x ) " g j ( x j ~ X ) 4.3 n , -.2 I ( x i " x> By averaging over the distribution of the e's, it follows from Eqn. 4.3, that y i r is model-unbiased for fixed x's in the finite population and the two samples (i.e. the first and the second samples). We then obtain E [(;LR-5)2ixj- 4<I-P2HH> + p 2 r * ' - « 2 + c - 2 c i - ' ^ ^ 2 4 - 4 The last term in Eqn. 4.4, results from the sampling error of b and has an order of 1/n relative to the first two terms on the right. In this study, the second sample is small relative to the first sample. In particular, terms in 1/n are not negligible relative 29 to 1, but those in 1/n' are. An estimate of variance suggested for simple random samples from Eqn. 4.4, is v(y, ) = s w l r y.x 1 n (x' - x) 2 E(x - x) 2 2 2 2 s - s s v y-x _ _ J I n' N 4.5 Where, 2 y.x n - 2 n E (y, - y>2 1=1 2 - 2 - b E (x. - x) 1=1 1 4.6 2 K y i - y)' s = — :  y n - 1 4.7 and, N = Population Size. Eqn. 4.5, provides the model-unbiased estimate of the variance, V(yi r), and it can be referred to as a hybrid of the conditional variance and the average variance (Eqn. 12.57, Cochran 1977). Let c and c' be the cost of measuring and classifying each unit, in the double-sample exercise. Furthermore, let C, be a specified cost for the sampling operation, and p the population correlation coefficient. Then, -, n' c'(l - p") c 2 C = cn + c'n' and, c/c' > (1 + * j l - P 2) 2 4.8 4.9 or p2 > 4(c/c') (1+c/c')2 4.10 30 Equations (4.9) and (4.10) give the critical ranges of C/c' for given p and of P for given c/c' that make double-sampling profitable, for our kind of investigation. It is important to note that, if a l l resources are devoted instead to a single sample with no regression adjustment, this sample has size C/c and the variance of its mean is V(y) = 4.11 C N The use of the equations given in this section shall be outlined in section 4.5. 4.3 Sampling for Spectral Reflectances The digital radiometer (Tektronics J-16) was used to collect spectral radiance or reflectance estimates of vegetation canopy (Pearson ej: al., 1976a). The instrument probes were fitted under the right wing of a twin-engine aircraft (Partanavia, Plate 1). The question of the appropriate surveying altitude for this study was considered. A transect was selected and surveyed at three different altitudes, for spectral reflectances of vegetation "greenness". These altitudes were 300 (91.44 m), 800 (244 m) and 1300 ft (396.24 m). Twenty paired spectral reflectances at 0.675 .urn and 0.800 ym were obtained at each altitude. The average ratio of the spectral reflectances was computed for each altitude. The Duncan's Multiple Range Test was performed on the three ratios. There were no signifi-cant differences amongst the altitude spectral reflectance mean ratios 31 Plate 1: Aircraft fitted with digital radiometer (biometer) equipment. 3IQ 32 (Table A2.3, Appendix I I ) . As a r e s u l t , we chose to survey the study area a t 800 f t (244 m) above the ground, as i t was be l i e ved to be safe and reasonable. F l i g h t s were made at a constant speed of 150 km/hr. The one hundred s e l e c t ed t r an sec t s were surveyed f o r the s p e c t r a l r e f l e c t a n c e s . Twenty r a t i o s of r e f l e c t a n c e s (0.800JA m referenced to 0.675^Am) were c o l l e c t e d per t r a n s e c t . On each t r a n s e c t , the readings were obta ined under s i m i l a r environmental cond i t i on s ( i . e . c loud cover, s un l i gh t i n t e n s i t y , e t c . ) as much as p o s s i b l e . The survey took two working days to complete by us ing the s e r v i ce s of a s t a f f p i l o t , a l a b o r a t o r y t e c h n i c i a n , and the author . Observat ions were read o f f the d i g i t a l d i s p l a y by the author, who communicated them to the l abo ra to r y t e c h n i c i a n . The l a t t e r recorded them on the data forms immediate ly. F igures 4.1a and b, and F i gu re 4.2 show the d i g i t a l biometer set up i n a l a b o r a t o r y , and probe-view from the a i r c r a f t used i n the survey r e s p e c t i v e l y . 4.4 Sampling B i o p h y s i c a l C h a r a c t e r i s t i c s of Sample P l o t s A subset of twenty t r an sec t s be l i e ved to cover a wide spectrum of range forage l e v e l s was drawn at random from the pool of e i gh ty a e r i a l surveyed t r an sec t s a f t e r d i s c a r d i n g twenty t r an sec t s from a hundred surveyed t r an sec t s f o r con ta i n i ng e r r o r s i n the s p e c t r a l rad iance or r e f l e c t a n c e r a t i o s (RR). Ten 1-m2 v ege ta t i ve sample p l o t s were l o c a t e d and c l i p p e d along each of the s e l e c ted t r a n s e c t . The d i r e c t i o n of the ground t ransec t was made to c o i n c i de w i t h the a e r i a l f l i g h t l i n e as much as p o s s i b l e . Transport to the vege t a t i v e sample p l o t s was done by automobi le, and the s e r v i ce of two other persons was u t i l i z e d , as i n 33 Figure 4.1a laboratory set-up of the digital radiometer used as a green/brown estimation device. The instrument consists of a % digital radiometer which measures radiances from vegetative samples through two filtered probes. 34 (A) FRONT VIEW ' '(B) SIDE VIEW Cables connecting the two filter probes to the radiometer The Probe main system. (C) AERIAL VIEW Probe's overlap view. Probe 2 Probe 1 Figure 4.1b. Radiometer Filter Probe 's Projection To The Vegetative Sample Plots. Look-angle 35' the case with the aerial survey exercise. Poor or inadequate roads posed major operations constraints. At each of the vegetative sample plots, subjective estimates of some biophysical characteristics were made. These included: percent vegetation greenness (GREN), percent vegetation cover (CEST) and vegetation or foliage height (VHT), in metres. These estimates were made before clipping the plant material (if any) in the plots. The clipped material was sorted as much as i t could be done in the minimum time on site. Only obviously dead stems, dry leaves, and dry blades were separated from the predominantly green standing matter. The latter was weighed to give the biomass fresh weights (FW). Field notes were taken of 1) the overall view of the vegetation distribution along the transect, and 2) the biophysical characteristics of each clipped plot. Where possible, plant species were identified. Photographs were taken of each clipped transect (sample photographs: plates 3-5) and of selected vegetative sample plots (sample photograph: plate 2). Some of these pictures were to be used to adjust some of the visual estimates thought to be exhibiting certain obvious discrepancies. Local herdsmen, whenever encountered were interviewed about the state of the vegetation along the transect and in the area, during the early period of the peak biomass season. A view of the annual spectrum vegetation status was also sorted for. All the field notes would provide extra information vital to interpretation of the results. This sampling exercise was carried out in the months of July and August, 1980. 36 Plate 2 : Clipping of sample microplots (local-level reference) for biomass sampling. B 6 q 37 Plate 3: Shompole area - a typical overgrazed grassland range. Characteristic of erratic biometer behaviour. 37Q 38 Ngong Hills area - savanna shrubland illustrating the over-topping of grasses by shrubs. Fluctuations in biometer readings reflect different levels of range forage. 39 ) Plate 5: Ecotone between grassland and woodland where radiometer (biometer) readings are erratic. H 40 4.5 Data Analyses Procedures The clipped-plot samples obtained from the twenty local-level referenced transects were oven-dried at 50°C over a 48-hr period. These samples were then removed from the oven and re-weighed to obtain the biomass dry weights (DW) (gm/m2) data. Then, the samples were subsampled by plot and pooled to form a transect sample. Twenty such samples were prepared. Next, these pooled samples were analysed following procedures outlined byA.O.A.C. (1965).The analyses provided data on percent crude fibre (CF) , percent crude protein (CP), and percent dry matter digestibility (DGM) of the plant material in the samples. The variances of the spectral data of the local-level referenced transects were computed. From these variances, the standard deviations were generated. The latter were then named, the greenness variation index (GVI). Next, the estimated annual index of water availability (WA%) was generated from an East African map showing the distribution of this index (Woodhead, 1970). This index was generated for each of the local-level referenced transects. The value recorded represented the class-median of the corresponding index class (a total of ten classes observed with a 10% range) for each of the transects referred to above. Finally, a data matrix was compiled for the twenty transects referred to above. Two transects were discarded for having errors. The biophysical characteristics variables included in this matrix are: biomass fresh weights (FW), biomass dry weights (DW), spectral radiance or reflectance ratios (RR), percent crude fibre (CF), percent crude 41 protein (CP), percent dry matter digestibility (DGM), percent vegeta-tion greenness (GREN), percent vegetation cover (CEST), estimated annual index of water availability (WA%), the greenness variation index (GVI), and vegetation or foliage height (VHT). Transformations were performed on the data matrix to obtain additional variables of interest. These included: leaf water content (LW = FW - DW), biomass density (BD = FW/CEST), and the herbage density (HD = VHT * CEST) (Alexander et al., 1962), since double-sampling is a bivariate statistical technique. The original data matrix without transformations was then .analysed by various statistical techniques, which are outlined in subsequent paragraphs. The MIDAS (Michigan Interactive Data Analysis System) statistical package (Fox and Guire, 1976) was used to perform most of the statisti-cal analyses. Summary statistics were generated on the paired data set for the observed and derived biophyscial characteristics variables for n = 18 transects. These statistics include: minimum and maximum values, mean, and standard deviation. Coefficients of variation and standard errors of the mean were also derived. Similar statistics were computed on the spectral radiance or reflectance ratio data for the combined observations for the eighty retained aerial transects surveyed. The spectral data were grouped into three major vegetation cover types for these summaries. Histograms were also generated for each vegetation cover type using the same interval width for compari-sons. One histogram was generated' for all groups combined. 42 The spectral data were then analysed using the unbalanced nested-design of the analysis of variance (ANOVA) model. This analysis was completed by using the UBC GENLIN (General Least Squares Analysis of Variance) statistical package adapted by Greig and Bjerring (1980). The model employed is of the following form: Y. = "U, + V. + T + £,,..> 4.12 with l j k r 1 k ( l j ) i = 1, ..., 3 j = 1, q; q = 29, 25, 26 V^r s respectively k = 1, ..., 20 y = the effect of overall mean V^  = the i t n vegetation cover type T.,.v = the j t n transect nested in V-t • e^^^= random error, k = 1, 20, for a l l i , j . The Null-hypotheses being tested by model (4.12) are as follows: (i) HQ]^  : That the vegetation cover types do not exhibit significant differences in their spectral reflectivity characteristics. : Alternative. (ii) HQ2 : That the transects within vegetation type do not exhibit significant differences in their spectral reflectivity characteristics. H^ 2 : Alternative. The standard procedures for analysing data by using a balanced nested-design model are given in Hicks (1973). 43 The costs for sample selection and classification and data acquisition for the entire survey were compiled. Then, the double-sampling formulae given in section 4.2 were employed to derive informa-tion on: regression estimates (Eqn. 4.1), estimates of suggested sample variance (Eqns. 4.5, 4.6 and 4.7), double-sampling policy (Eqns. 4.8, 4.9 and 4.10), and single sample variance, without double sampling (Eqn. 4.11). These parameters would provide information necessary to determine the optimal sampling policy for this type of inventory problem. Attempts were also made to stratify the samples obtained by double-sampling into three or four major vegetation cover types. This proved to be meaningless due to the violation of the necessary assump-tions as given in Rao (1973) and Cochran (1977). Had this succeeded, it could be possible to generate optimal sampling procedure based on each of the major vegetation cover types, a phenomenon that could have even facilitated the choice of sampling priorities. Next, regression analyses were performed on the data matrix described earlier. Again, the MIDAS statistical package was utilized. Observations associated with two of the paired transects were dropped from these analyses as they were believed to contain a certain degree of unacceptable error. The latter might have resulted from possible mistakes made in the course of the sampling process. Only eighteen transects were included in the regression analyses. First, the general model of the multiple linear regression analysis fitted on the data set is of the following form: Y. = B A + B.X.. + 3 0X 0. + ... + g X . + e. 4.13 l 0 1 l i 2 2i p pi x 44 Where, 3Q = r e g re s s i on constant . 3 ^ t g : V±'s = 1> •••> P a r e c a l l e d the model r eg re s s i on parameters r e f e r r e d to as the p a r t i a l r eg re s s i on c o e f f i c i e n t s . £^ = random d i s turbance or e r r o r ; e ^ r v / N (0, a 2 ) . = the f t h ob se rva t i on of the dependent v a r i a b l e . x P i = the i t n ob se rva t i on of the independent v a r i a b l e , p. For ¥ 3 ^ t g = 0, where i = 2, p, the m u l t i p l e r e g re s -s i on model (4.13) , becomes a s imple l i n e a r r eg re s s i on model. The s imple l i n e a r model was used to r e l a t e the s p e c t r a l rad iance or r e f l e c t a n c e r a t i o s (RR) to va r i ou s b i o p h y s i c a l c h a r a c t e r i s t i c s v a r i a b l e s i n the data se t . Severa l other r eg re s s i on equations were generated and cons idered. Next, the polynomial r eg re s s i on model was f i t t e d on the same data se t . This model i s of the f o l l o w i n g form: Y. = 3_ + 3.X. + 3„X 2 + 3 0 X 3 + e. 4.14 l 0 l i 2 x 3 x x where 3Q = r e g r e s s i o n contant ^ i ' s : V i ' s = 1, 3 are r e f e r r e d to as the p a r t i a l r eg re s s i on c o e f f i c i e n t s . e i = random d i s turbance or e r r o r ; e-L/^N (0,a ). Y^ = t n e i * " * 1 ob se rva t i on of the dependent v a r i a b l e . X. = the i t n ob se rva t i on of the s i n g l e independent v a r i a b l e . 45 In this analysis, model (4.14), was used to determine the relationship between the spectral radiance or reflectance ratios (RR) as the dependent variable and the biomass fresh weights (FW) as the independent variable. Finally, the exponential regression model (4.15) was fitted on the data set. This model is referred to as nonintrinsically nonlinear (Draper and Smith, 1966). The model was used to determine the relationship between spectral radiance or reflectance ratios (RR) and the biomass fresh weights (FW). The model is of the following form: Y ± = exp(6 1lnX i - QQ + e ±) 4.15 Where 0 . , for V., =0,1 are the nonlinear parameters to be estimated, i s x s r lnX^ = the natural logarithm of the i ^ observation of the single independent variable. 2 = random disturbance or error, where E(e) = 0, V (e) = a . til Y = the i observation of the dependent variable. By taking natural logarithms on both sides of Eqn. (4.15), the result is given by Eqn. 4.16. The least square analysis was applied to the transformed model: In Y. = e.lnX. - 6_ + e. 4.16 x l l 0 I For the multiple linear regression analyses, the stepwise procedure was used to select only those independent variables whose coefficients of partial correlation (with the dependent variable and 46 with the other independent variables in the equation) were statistically significant. However, in some equations insignificant variables were included to help understand their marginal effect to predictions. In general, the criterion for significance was chosen on the basis of a desirable F-statistic corresponding to P <0.05 and P <0.01, where applicable. The analyses explained above employed the method of least-squares as outlined in Draper and Smith (1966), and Chatterjee and Price (1977). The analyses of residuals for the generated regression equations were also performed. The residual plots used are those in which the standardized residuals o ( o . = o , , o = y - y ) were plotted as the M i s V M i s  yl/s' M i  y±  yr  v ordinate against (i) the fitted value, y, and (ii) the independent variable X^ . However, the reproduction of the bulky residual plots is omitted from this documentation. The comparisons of the regression models generated in this investigation was based on two criteria, namely: (i) The standard error of estimate (square root residual mean squares) defined as 4.17 Where p number of parameters estimated in the model n total number of observations and Y^  are the observed and predicted values (e.g. spectral reflectance ratios). 47 (ii) The mean bias defined as Bias- = j^Y.-V/n Where n = number of observations Y^  and Y^  are the observed and predicted values (e.g. spectral reflectance ratios). In the next chapter, the results of the analyses described above are presented. 48 5.0 RESULTS In t h i s chapte r , the r e s u l t s of the analyses descr ibed i n Chapter 4 are presented: f i r s t , a s t a t i s t i c a l summary of the b i o p h y s i c a l cha rac -t e r i s t i c s of the sample p l o t s of the t r an sec t s i n the pa i red data se t , and the s p e c t r a l rad iance or r e f l e c t a n c e r a t i o s (RR) c o l l e c t e d i n the study area; next the r e s u l t s of the a n a l y s i s of va r i ance (ANOVA) of the s p e c t r a l rad iance or r e f l e c t a n c e r a t i o s (RR) f o r the e i gh ty surveyed t r a n s e c t s ; then the r eg re s s i on equations der ived from the pa i red data s e t ; and f i n a l l y the double-sampl ing parameters a s soc i a ted w i t h the study r e s u l t s . 5.1 Summary S t a t i s t i c s The s t a t i s t i c a l summary of the b i o p h y s i c a l c h a r a c t e r i s t i c s v a r i a b l e s measured i n the study area are g iven i n Table 5.1a. The l a r g e s t range of va lues occurred i n the biomass f r e s h weights (FW) (gm/m2) wh i l e the sma l le s t i s a s soc i a ted w i th the greenness v a r i a t i o n index (GVI). S i m i l a r l y , the c o e f f i c i e n t s of v a r i a t i o n (CV) and the standard e r r o r s of the mean v a r i e d g r e a t l y . The percent dry matter d i g e s t i b i l i t y (DGM) had the lowest c o e f f i c i e n t of v a r i a t i o n (CV) of 0.45%. On the other hand, the biomass f r e s h weights (FW) (gm/m2) had the h ighest CV, 68.71%. The biomass f r e s h weights (FW) (gm/m2) had the h i ge s t standard e r r o r of the mean, 41.863, wh i l e the vege ta t i on or f o l i a g e height (VHT) was a s soc ia ted w i th the smal le s t standard e r ro r of the mean, 0.0559. TABLE 5.1a: The statistical summary of the biophysical characteristics variables measured in Kajiado study area, for n = 18 transects, surveyed July - August, 1980. No. Variable n Minimum Maximum Mean Standard Coefficient Standard error deviation of variation of the mean CY) (S) (%) S.e-1. Biomass Fresh Weights (FW) 1! i 45.840 628.48 258.48 177.61 68.71 41.8631 2. Biomass Dry Weights (DW) 1 i 26.900 367.87 165.59 109.97 66.41 25.9202 3. Spectral Reflectance Ratios (RR) li i .81100 2.8270 1.2304 .48246 39.21 0.1137 4. Dry matter Digestibility (DGM) % li i 94.140 96.000 95.419 .42885 0.45 0.1011 5. Crude Protein (CP) % li i .98000 8.4200 4.2978 1.6981 39.51 0.4002 6. Crude Fibre (CF) % 1 i . 58000 7.4200 3.5422 2.0874 58.93 0.4920 7. Vegetable Cover (CEST) % li i 14.000 79.500 49.983 17.627 35.27 4.1547 8. Vegetation Greenness (GREN) % 4 J 12.300 85.100 43.506 24.539 56.40 5.7839 9. Vegetation/Foliage Height (VHT) li i .57000 -1 .98000 .40717 .23724 58.27 0.0559 10. Index of Water Availability (WA) % If i 15.000 45.000 30.556 8.5559 28.00 2.0166 11. Greenness Variation Index (GVI) 11 .30000 -1 .30800 .12856 .80006 -1 62.23 0.0189 TABLE 5.1b: The statistical summary of the spectral radiance or reflectance ratios (RR) grouped by major vegetation cover types in Kajiado study area, for n = 80 transects, surveyed in July, 1980. Variable (Y) Standard deviation (S) Coefficient of variation « ) Standard error of the mean S.e-1. Grasslands 2. Bushlands 3. Wooded Grasslands 4. All combined 580 0.5940 500 0.5840 520 0.6150 1600 0.5840 7.0000 5.7350 3.8890 7.0000 1.7826 1.3618 1.4678 1.5488 1.1841 0.672 94 0.62135 0.89844 66.43 49.42 42.33 58.01 0.0492 0.0301 0.0272 0.0225 * Total number of spectral radiance or reflectance ratios on transects (20 per transect) in vegetation cover type j . ^ 50 For the spectral radiance or reflectance ratios (RR) collected on the eighty transects surveyed, the highest CV, 66.43%, is given by readings collected in grassland areas, while the lowest, 42.33%, is associated with readings collected in wooded-grassland areas. The standard error of the mean for the spectral data did not differ greatly for a l l the three vegetation groups. For the entire spectral data set (combined), the CV is 58.01%, and the standard error of the mean, 2.25%. Full results are given in Table 5.1b above. Figs. 5.1, 5.2, 5.3 and 5.4 are histograms for the spectral radiance or reflectance ratios (RR) data for the eighty transects surveyed. The grasslands data show peaks in the distribution. The main peaks in each histogram account for 23.6%, 21.8%, 17.1%, and 18.8%, of the readings, respectively. All the histograms are positively (right) skewed. 5.2 The Analysis of Variance (ANOVA) of Spectral Reflectance Ratio  (RR) Data. The results of the analysis of variance (ANOVA) of the spectral data using model 4.12 are summarized in Table 5.2. . There were significant differences between transects within the vegetation cover types (P <0.01). Further, significant difference were found between the vegetation cover types (P <0.01). The Bartlett's Chi-square test ( x ^ c = 286.84) for 2 d.f., showed that the variances of the three vegetation cover types were significantly different (non-homogeneous) (P <0.01). HISTOGRAM .' SPECTRAL REFLECTANCE RATIO DATA BY VEGETATION COVER TYPE IN KAJIADO STUDY AREA MIDPOINT HIST% COUNT FOR 1.GRAS (EACH X= 2) 09 c PC fu pd H-<_l. CO H- r t fu O PL PL cw O p H r t P CD P B r t C O H i PL O o V ! M i-i h-1 fu fD cn H O m r t fD P tt) O • PL r t H , — \ P 3 M M tl r o t-i VO P PL H-r t P H 3 P o 3 fD cn fD o O i-i r t CO i-f fD H i H- M 3 fD O 09 r t i-t P P 3 CD O CO fD I-1 P H 3 P PL r t CD H-O 0. . 15000 .30000 .45000 .60000 .7 5000 .90000 1.0500 1.2000 1.3500 1.5000 1.6500 1.8Q00 1 .9500 2 . 1000 2.2500 2.4000 2.5500 2.7COO 2 .8500 3.0000 3.1500 3.300O 4 500 6000 7500 9000 0500 2000 3500 500O 6500 6000 9500 1000 2500 4 00O 5500 7000 8500 OOOO 6.1500 6.3000 4500 6000 7500 9000 0500 0. 0. 0. 0. g 9. 1 23.6 5.7 5 7 9 4 3 1 7 4 5 7 8 9 .5 1 .0 1 . 2 1.0 2.8 j.5 2.6 1 . 7 1.9 1.2 1 .0 .9 .3 . 7 .9 .5 .5 .5 0. .2 . 5 . 2 .5 . 2 . 2 0. O. o. 0 + 0 + 0 «-0 + 5 + XXX 53 +XXXXXXXXXXXXXXXXXXXXXXXXXXX 137 +XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 33 +XXXXXXXXXXXXXXXXX 33 +XXXXXXXXXXXXXXXXX 43 +XXXXXXXXXXXXXXXXXXXXXX 55 +XXXXXXXXXXXXXXXXXXXXXXXXXXXX 27 +XXXXXXXXXXXXXX 22 +XXXXXXXXXXX 1 1 +XXXXXX 3 +XX 6 +XXX 7 +XXXX 6 +XXX 16 +XXXXXXXX 32 +XXXXXXXXXXXXXXXX 15 +XXXXXXXX 10 +XXXXX 1 1 +XXXXXX 7 +XXXX 6 +XXX . 5 +XXX 2 +X 4 +XX 5 +XXX 3 +XX 3 +XX 3 +XX 0 + 2 +X 0 + 1 +X . 3 +XX 1 +X 3 +XX 1 +x 1 +x 0 + o + 0 + 1 +x +x + +x TOTAL 580 (INTERVAL WIDTH" .15000) HISTOGRAM : SPECTRAL REFLECTANCE RATIO DATA BY VEGETATION COVER TYPE IN KAJIADO STUOY AREA MIDPOINT HIST"/. COUNT FOR 2.BUSH (EACH X = 2) 00 c i-! CD N3 ,—v 5d H ' CO H- —^> r t P3 O O Co i-t rt Co CO CO S r t C O H i O O V ! h-1 H 1—1 Co (B CO o n> r t tt> CO (D O • CL r t H —\ CO Ti h-1 ho i-i CO H-r t fu n CO o 3 ro CO fi) o o H r t co i-j s - ' fi) h- 1 3 fi> o a " r t c co cn 3 3* o M fi) fo 3 n Co CO r t H-O 0. 0. 0 + .15000 0. 0 + .30000 0. 0 4-.4 5000 0. 0 + .G0000 4 2 +x .7 5000 6. 8 34 +XXXXXXXXXXXXXXXXX .90000 19. 0 95 +XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 1.0500 21 . 8 109 +XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 1.2000 14 . 0 70 +XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 1.3500 9. 8 49 +XXXXXXXXXXXXXXXXXXXXXXXXX 1.5000 6. 0 30 +XXXXXXXXXXXXXXX 1.6500 2 . 6 13 +XXXXXXX 1.8000 3. ,6 18 +XXXXXXXXX 1.9500 3. .4 17 •i-XXXXXXXXX 2.1000 3 . 2 16 +XXXXXXXX 2.2500 2 . 8 14 +XXXXXXX 2.4000 1 . 8 9 +XXXXX 2.5500 1 . .0 5 + XXX 2.7000 . 2 1 +x 2.8500 . 2 1 +x 3.0000 0. 0 + 3.1500 . 8 4 + XX 3.3000 . 4 2 + X 3. 45C0 . o 1 +x 3.6000 .6 3 +xx 3.7500 0. 0 + 3.9C00 0 0 + 4.0500 .2 1 +x 4.2000 .2 1 +x 4.3500 0. 0 + 4.5000 0 0 + 4.6500 0 0 + 4.8000 0 0 + 4.9500 .2 1 +x 5.1000 .6 3 +xx 5 .2500 0 0 + 5 .4000 0 0 + 5 .5500 0 0 + 5 .7000 .2 1 +x MISSING 80 TOTAL 580 (INTERVAL WIDTH= .15000) r o 'T3BXB Aprils OpBT-fB}! ' SpUBTSSBjS-pOOM UI (S^ DSSUBjr.} *92=U) pS^OaTXOO B}Bp (^ H) OT3BJ aouB^DaxjBa xo aouBjpBj iBaaoads JOJ UlBa§03STH H 3 Z ID u u u u u u u u u u u u u 8 u i O u i G c n o < J i O u i O t n o c n O u t O O O O O O O O O O O O O O O O O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 X • o *—* i—i - J 01 .£> C J • o i / i M O O o O U l •o -1 O U l O o o o O o o o o o o o o o O o o o o o o o o o NT RAM X M O f c Q O l C D b f c - j o y O O O O i / i TJ -1 m f o c n a i O M u o - j u i c o c o c j U l U l — co C J s« o H X I o > U l o r~ a> cn I C J 1^ CO cn • c O O CD CD IO U l ID CO CD O O O O z XI - t m + + + + + + + + + + + + + + + + + + + + + + + + + + - n xxxxxxxxxxxx X X X X X X X X X X X r -*—< X X X xxxxxxx X X X X X X X X X X o m z X X X xxxxxxx X X X X X X X X X X XI o -H x xxxxxxx X X X X X X X X X X —1 m X X X X X X X X X X X X X X X CO > X X X X X X X X X X X X X X z < X X X X X X X X X X X X X c o > X X X X X X X X X X X X X o m r~ X X X X X X X X X X X X a X X X X X X X X X X X o 73 X X X X X X X X X X X > i—i X X X X X X X X X X X -1 D X X X X X X X X X X .—, - t X X X X X X X X X X m o I X X X X X X X X X X > II X X X X X X X X X X O a X X X X X X X X X x > X X X X X X X X X —* X X X X X X X X J> U l X X X X X X X II O X X X X X X X CD O X X X X X X X -< O X X X X X X X w >—' X X X X X X < X X X X X X m X X X X X X o X X X X X X m X X X X X X —1 X X X X X X > X X X X X X -1 X X X X X X X X X X X X o X X X X X z X X X X X X X X X X O X X X X X o X X X X X < X X X X X r n X X X X X X ) X X X X X X X X X X —1 X X X X X •< X X X X •o X X X X m X X X X X X X X 1—1 X X X X z X X X X X X X X X X X X > X X X X c X X X X »—1 X X X X > X X X X O X X X X O X X X X X X X X cn X X X X -1 X X X X c X X X X a X X X X < X X X X X X X X > X X X X XI X X X X m X X X X > X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 5:4 < tSl a. o z D O u X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X x x x x x X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X xxxxxxx xxxxxxx xxxxxxx xxxxxxxx xxxxxxxx xxxxxxxxx xxxxxxxxx xxxxxxxxx xxxxxxxxxx xxxxxxxxxx xxxxxxxxxxx xxxxxxxxxxx xxxxxxxxxxx :     X X X X : x x x x .. . : x x x x x x x x x x 4 4 4 4 + + X X X X X X X X X X X X X X xxx xxxx xxxxxxxxx xxxxxxxxx 4 4 4 4 4 4 4 4 4 X X X X X X X X X X X X X X X X X X X xxxxxxxxxxxx + + 4 + + + + + + + + + X X X X X 4 4 4 4 4 X X X 4 4 4 4 4 X X 4 4 X 4 O O O O c o n - ' I O ( I l ^ f ^ o - ^ N O l l ' l I ' r » U ) 0 ^ n M ( o n U ) l l l n n n o n n ^ n ' • f -O O n r - o w M n K i n n c c - M ^ ' - M " - ' - ' " •- n M >- ' ^ — O G O — C N O C N O O O IT) •x t -Q < > a ID y-Z O o i s l O t o ^ ^ i o c n i n u n o O n i D c ' i t i n n o i c j e o i n p i o v p i r i r i CM CM — CM O O O O u to t - O t - T f o n c M C M — *- CM — — O O O O z O O O O O O O O O O O O o o o O O O O Q o O O O O O O o o O O o o o O c O o o 5 o O O o O i n O ui O IT) O m O m o IT, O i n a i n O i n O i n O O f v n i n O CO c n CM • T i n r - t o G r o •7 CP r -5 o • CM CM CN CM CN CM O C O O O O O O O O O O O O O O O O O O O O O O O O O O ~1 O m O i n O i n O i n O i n O m O i n O i n O i n O i n O i n O t o O i n O i n < O — c o ^ c o r - c n O c N r o i n i a c o c r ) ' - C N ' j i n r - - a ) 0 " - c , 5 ^ - i D r - - ( T ) 0 (-O ronrir>nnco^nn^ ^^ i^ninLniricoinu)CDiotoc£><DtDr~ t-Figure 5.4: Histogram for combined spectral radiance or reflectance data collected (n=80, transects) in a l l vegetation cover types surveyed, Kajiado study, area. 55 TABLE 5.2: The analysis of variance of the spectral radiance or reflectance ratio data for Kajiado study area (n = 80 transects, each with 20 observations). Source of variation Sum of squares Degrees of freedom Mean square F-ratio Total Transects Cover types Transects within cover types Error 1290.70 1156.307 52.607 1103.7 134.35 1599 79 2 77 1520 14.6368 26.30352 14.33383 0.08844 165.575 (1/4); 1.835 <2/3>** (3/4 )*• 162.147 *Significant at P <0.01 **Significant at P <0.25 The Bartlett Chi-square tests on homogeneity of variances in transects and vegetation cover types showed significant differences (X^ c = 883.06 and 42.006 respectively, P <0.01). Twenty-six homogeneous subsets were identified among the 1600 observations made on the eighty transects surveyed. A complete summary of these ANOVA results is given in Appendix III. 5.3 The Least Squares Regression Equations The simple (partial) linear regression equations derived by model (4.13), relating the spectral radiance or reflectance ratios (RR) to 56 the biophysical characteristics variables of the vegetative sample plots are given in Table 5.3. In the same table, are the equations showing the relationship between the spectral greenness variation index (GVI) and leaf water content (LW), and the estimated annual index of water availability (WA). All the relationships between spectral radiance or reflectance ratios (RR), and percent crude fibre (CF), herbage density (HD), vegetation or foliage height (VHT), and percent dry matter digestibility (DGM) were found to be statistically non-significant (P <0.05). Their inclusion here is vital and will be examined in Chapter 6. The simple linear regression equations showing interrelationship between some of the biophysical characteristics variables of the vegetative sample plots are given in Table 5.4. The highest correla-tion coefficient (r = 0.936) is associated with the direct relationship between biomass dry weights (DW) and biomass fresh weights (FW). The lowest correlation coefficient (r = 0.7199) is given by the relation-ship between biomass dry weights (DW) and herbage density (HD). All the regression equations reported in Table 5.4 are direct and statisti-cally significant at P <0.01 as indicated. The multiple linear regression equations in Tables 5.5 - 5.9 were generated by fitting model (4.13) on the data. These equations relate the spectral radiance or reflectance ratios (RR) to some of the biophy-sical characteristics variables of the vegetative sample plots as indicated. The regression equations reported in Tables 5.5 - 5.7 are statistically significant at 1% probability level, while those reported in TABLE 5 . 3 : A summary of the linear regression equations characterizing the relationship between the spectral radiance or reflectance ratios (RR) to biomass fresh weights (FW), vegetation or foliage height (VHT), percent vegetation greenness (GREN), percent vegetation cover (CEST), leaf water content (LW), estimated annual index of water a v a i l a b i l i t y (WA), biomass density (BD), percent crude fibre (CF), herbage density (HD), and percent dry matter d i g e s t i b i l i t y (DGM); biomass dry weights (DW) to spectral radiance or reflectance ratios (RR); and greenness variation index (GVI) to leaf water content (LW) and estimated annual index of water a v a i l a b i l i t y (WA) in Kajiado study area (July-August, 1980). Equation Regression Estimated Parameters No. n = 1 8 5 . 1 R R = 0 . 7 3 7 + 0 . 0 0 1 9 F W r a = 0 . 7 0 3 , s* = 0 . 3 5 3 , P < 0 . 0 1 s.e b(B 0) = 0 . 1 5 0 3 , s . e ^ ) = 0 . 0 0 0 4 8 3 T C(e Q) = 4 . 9 1 0 , K^) » 3 . 9 5 8 C.I. d: RR + 1 . 0 2 3 0 S 0 + 0 . 4 3 4 7 Bj + 0 . 0 0 1 4 5 . 2 DW = 2 5 . 1 4 7 + 1 1 4 . 1 4 R R r = 0 . 5 0 0 7 , s = 98.118, P < 0 . 0 5 s.e.(B0> " 6 4 . 9 4 9 , s.e.(Bj) - 4 9 . 3 2 5 T(B 0) = 0 . 3 8 7 2 , Kg^ = 2 . 3 1 4 1 C.I.: DW + 2 0 7 . 0 2 9 0 B 0 + 1 3 7 . 0 4 2 4 Bi + 1 0 4 . 0 7 5 8 5 . 3 RR = 1 . 0 3 5 4 + 0 . 4 7 9 V H T * * r - 0 . 2 3 5 5 , s = 0 . 4 8 3 3 , P < 0 . 0 5 s . e ( B 0 ) - 0 . 2 3 1 2 , s . e . ^ ) = 0 . . T ( B Q ) = 4 . 4 7 8 4 , K ^ ) - 0 . 9 6 9 4 5 . 4 R R = 0 . 7 5 1 2 + 0 . 0 1 1 0 2 G R E N r = 0 . 5 6 0 3 , s = 0 . 4 1 1 9 , P < 0 . 0 5 s.e(g Q) = 0 . 2 0 2 0 , s.e(g ) - 0 . 0 0 4 0 7 1 T ( 6 0 ) - 3 . 7 1 8 9 , KBj) » 2 . 7 0 6 0 C . I . : R R + 0 . 8 6 9 1 B0 + 0 . 4 2 6 2 Bx + 0 . 0 0 8 5 9 5 . 5 " R R = 0 . 5 7 0 4 + 0 . 0 1 3 2 I C E S T r = 0 . 4 8 2 5 , s - 0 . 4 3 5 6 , P < 0 . 0 5 8.e(B Q) - 0 . 3 1 6 7 , s . e d ^ ) ' 0 . 0 0 5 9 9 3 T ( B 0 ) - 1 . 8 0 1 2 , T ( B ) " 2 . 2 0 3 3 C . I . : RR + 0 . 9 1 9 1 B0 + 0 . 6 6 8 2 Bj + 0 . 0 1 2 6 5 5 . 6 R R = 0 . 7 8 8 7 + 0 . 0 0 4 7 5 6 L W r = 0 . 8 2 9 9 , s - 0 . 2 7 7 5 , P < 0 . 0 1 s.e(B 0) - 0 . 0 9 8 9 5 , s . e ^ ) - 0 . 0 0 0 7 9 9 4 T(B 0) = 7 . 9 7 1 2 , KBj) - 5 . 9 4 9 2 C . I . : RR + 0 . 8 0 4 2 B 0 + 0 . 2 8 6 8 Bi + 0 . 0 0 2 3 1 7 TABLE 5.3 (continued) Equation No. Regression Estimated Parameters n = 18 5.7 RR = 0.2013 + 0.03368WA 5.8 RR = 0.6102 + 0.1294BD 0.5973, s = 0.3988, P <0.05 s.e(g Q) = 0.3580, s. e ( 6 l ) = 0.01131 2. 97 91 T(6 0) 0.5622, K S j ) C.I.: RR + 0.8415 g 0 + 0.7554 Bj + 0.02386 r = 0.6165, s = 0.3915, P <0.01 5.9 RR = 1.3485 - 0.03334CF** 5.10 RR - 1.0561 + 0.007577HD** 5.11 RR » 0.05507DGM - 4.0245** 5.12 GVI = 0.0738 + 0.0005895LW 5.13 GVI - 0.00538WA - 0.0358 T(Bp) = 2.7929,'T(B) = 3.1323 C.I.: RR + 1.1346 B Q + 0.6332 B x + 0.1197 r - 0.1442, s = 0.4921, P <0.05 s.e(g Q ) - 0.2334, s .eCg^ - 0.05718 T(B 0) - 5.7778, T(Bj) = -0.5830 r - 0.3047, s ='0.4737, P <0.05 s .e(B 0) = 0.1762, s .e(Bj) = 0.005922 T(B Q) - 5.9956, T(§j) = 1.2795 r - 0.04895, s - 0.4967, P <0.05 s . e ( § 0 ) - 26.804, s.eCgj) = 0.2809 T(B 0) - -0.15014, T(BJ) - 0.19605 r - 0.6203, s - 0.06468^ P <0.01 s.e(B0> = 0.02307, s .e(Bj) = 0.0001864 T(g 0) - 3.1995, K g p - 3.1636 C.I. : GVI + 0.1874 B 0 + 0.06686 gj + 0.0005402 r - 0.575, s = 0.0675, P <0.05 s .e(B Q) - 0.0606, s.eCjjj) = 0.00191 T(B Q) = -0.5915, T<§ ) = 2.8133 C.I.: GVI + 0.1424 g 0 + 0.1279 §! + 0.004030 *: Standard error of the estimate Y at (n-1) degrees of freedom, a: Correlation c o e f f i c i e n t . b: Standard error of estimate of the p a r t i a l regression c o e f f i c i e c: T - S t a t i s t i c d: Confidence Intervals (P <0.05 or P <0.01 as shown). **: Non-significant regression (P <0.05), while the rest of the equations are sig n i f i c a n t at P <0.05 and P <0.01 as Indicated. TABLE 5.4*: The l i n e a r regression equations showing the r e l a t i o n s h i p between the biophysical c h a r a c t e r i s i t c s v a r i a b l e s : biomass fresh weights (FW), biomass dry weights (DW), percent vegetation cover (CEST), percent vegetation greenness (GREN), herbage density (HD), and estimated annual index of water a v a i l a b i l i t y (WA), leaf water content (LW), and biomass density (BD), i n Kajiado study area, July-August, 1980. Equation No. Regression Estimated Parameters n = 18 5.13 FW = 7.906CEST - 136.69 5.14 FW = 84.568 + 1.8724LW 5.15 DW = 15.85 + 0.58FW 5.16 DW = 19.87 + 3.3496GREN 5.17 DW = 71.703 + 4.0807HD 5.18 WA = 19.614 + 0.2515GREN 5.19 GREN = 6.1947 + 7.7822BD s.e (e 0) 0.7846, sa = 113.50, P <0.01 :.514, s . e ( i j ) = 1.5616 T(e Q) = -1.6566, TCgj) = 5.0626 C . I . d : FW + 328.9230 B0 + 239.1256 gx + 4.5255 r = 0.8875, s = 84.372, P <0.01 s . e ( g 0 ) = 30.086, s . e ^ ) = 0.2431 T ( B 0 ) = 2.8108, TCgj) = 7.7029 C . I . : FW + 244.5101 g 0 + 87.1892 gx + 0.7045 r » 0.936, s = 39.991, P <0.01 s.e(gQ) = 16. 973, s.eCgj) = 0.0546 C . I . : DW + 115.8939 $0 + 49.1878 §i + 0.1582 r = 0.7474, s = 75.309, P <0.01 s.e(§0) = 36.929, s.eCgj) = 0.7443 T(g 0) - 0.5381, T ( g p = 4.5001 C . I . : DW + 218.2455 B 0 + 107.0202 gx + 2.1570 r = 0.7199, s = 78.679, P <0.01 s.e(§0) = 29.260, s.e(g1) = 0.9836 T(g Q) = 2.4506, T(g 1) C . I . : DW + 228.0117 Br, + 84.7955 4.1486 B l + 2.8505 r = 0.7213, s = 6.1083, P <0.01 s.e ( B 0 ) = 2.9953, s.eC^) = 0.06037 T(g Q) = 6.5483, T<| t ) = 4.1657 C . I . : WA + 17.7019 B 0 + 8.6804, 6i + 0.1750 r = 0.7292, s = 17.310, P <0.01 s.e(gQ) = 9.6585, s.eCgj) = 1.8260 C . I . : GREN + 50.1644 g 0 + 27.9903 § x + 5.2917 60 All the regression equations in Table 5.4 are statistically significant at P <0.01 Correlation coefficient. Standard error of the estimate Y at (n-1) degrees of freedom. Standard error of estimate of the partial regression coefficient g T-statistic. Confidence intervals at P <0.01 as indicated. 61 TABLE 5.5:* The multiple linear relationship between the spectral reflectance ratios (RR); the fresh biomass weights (FW) and dry biomass weights (DW), in Kajiado study area, July-August, 1980. ^ b a C Variable Partial Regression^ s.e(@.) T(J3.) Significance r coef f icient(g\) Constant - 0.825 0.1239 6.6567 0.0000 FW 0.769 0.005 0.0011 4.6591 0.0003 DW -0.628 -0.006 0.0018 -3.1229 0.0070 n = 18 Rd = 0.833 s 6 = 0.2842 P <0.01 Regression Model: RR = 3Q + 3^FW - 3 2 D W + e *: Significant at P <0.01 a: Partial regression coefficient 3^ b: Standard error of the estimate of the partial regression coefficient 3^ c: T-statistic of the partial regression coefficient 3^ d: Multiple regression coefficient e: Standard error of the estimate Y at (N-l) degrees of freedom. 62 TABLE 5.6:* The multiple linear relationship between the spectral reflectance ratios (RR); the estimated annual index of water availability (WA) and leaf water content (LW), in Kajiado study area, July-August, 1980. Variable Partial Regression s.e(g. ) T(3.) Significance r coefficient 3 ) 1 1 Constant WA LW 0.292 0.746 0.509 0.011 0.00413 0.256 1.9884 0.00936 1.18127 0.000951 4.3444 0.0653 0.2559 0.0006 n = 18 Rd = 0.846 s e = 0.2741 P <0.01 Regression Model: RR = gQ + 3jWA + 32LW + e a b c: d: e: Significant at P <0.01 Partial regression coefficient 3^ Standard error of the estimate of the partial regression coefficient 3 i T-statistic of the partial regression coefficient Multiple regression coefficient Standard error of the estimate Y at (N-1) degrees of freedom. Non-significant - included to illustrate a point in the discussion. 63 TABLE 5.7:* The multiple linear relationship between the spectral reflectance ratios (RR); and the sample plot biophysical characteristics variables: the percent cover estimate (CEST), the percent green (GREN) and the vegetation or foliage height (VHT), in Kajiado study area, July-August, 1980. Variable Partial Regression^ s.e(g.) T(§.)° Significance r coefficient^.) a 1 1 Constant — 0.456 0.2862 1.5933 0.1334 CEST . 0.428 0.013 0.007340 1.7703 0.0984 GREN 0.540 0.0126 0.005226 2.4032 0.0307 VHT -0.412 -1.03 4 9 0.6111 -1.6936 0.1125 n = 18 Rd = 0.683 s 6 = 0.3881 P <0.05 Regression Model: RR = g Q + 3]_CEST + 32GREN - 33VHT + e *: Significant at P <0.05 a: Partial regression coefficient 3JL b: Standard error of the estimate of the partial regression coefficient 3 i c: T-statistic of the partial regression coefficient 3^  d: Multiple regression coefficient e: Standard error of the estimate Y at (N-l) degrees of freedom. Note: Non-significant variables are included to investigate their marginal contribution. 64 Tables 5.8 and 5.9 are n o n - s i g n i f i c a n t , at 5% p r o b a b i l i t y l e v e l . I t i s important to note that the l a t t e r two equat ions are repor ted f o r the i l l u s t r a t i o n of a po in t pursued i n Chapter 6. In Table 5.10, the m u l t i p l e l i n e a r r eg re s s i on r e l a t i n g the greenness v a r i a t i o n index (GVI) to biomass f r e s h weights (FW) and the est imated annual index of water a v a i l a b i l i t y (WA) i s g i ven . This r e g re s s i on equat ion i s s i g n i f i c a n t (P <0.05) w i t h a m u l t i p l e c o r r e l a -t i o n c o e f f i c i e n t , R = 0.625. In these ana ly ses , conf idence i n t e r v a l s about the reg re s s i on est imates are g iven only f o r those s imple l i n e a r equat ions s i g n i f i c a n t a t P <0.05 and P <0.01, as i n d i c a t e d i n each t a b l e of r e s u l t s . The po lynomia l and exponent ia l r eg re s s i on equat ions r e l a t i n g s p e c t r a l rad iance or r e f l e c t a n c e r a t i o s (RR) to biomass f r e s h weights (FW) are g iven i n Table 5.11 and 5.12 r e s p e c t i v e l y . The former r eg re s s i on equat ion has a h igh c o r r e l a t i o n c o e f f i c i e n t ( r = 0.8723, P <0.01), wh i l e the l a t t e r has a s l i g h t l y lower one ( r = 0.6098, P <0.01). Thus, the l i n e a r r e l a t i o n s h i p between the s p e c t r a l rad iance or r e f l e c t a n c e r a t i o s (RR) and biomass f r e s h weights (FW) ( r = 0.7030, P <0.01) i s s l i g h t l y b e t t e r than t ha t g i ven by the exponent i a l r e l a t i o n s h i p . The standard e r r o r of the est imate (Eqn. 4.17) and the mean b ia s (Eqn. 4.18) of the l i n e a r and polynomia l reg res s ions are 35.3% and 0.23%, and 30.6% and 0.72% r e s p e c t i v e l y (Table 5.13). On t h i s b a s i s , the l i n e a r r e l a t i o n s h i p between s p e c t r a l rad iance or r e f l e c t a n c e r a t i o s 65 TABLE 5.8:* The multiple linear relationship between the spectral radiance or reflectance ratios (RR); biomass density (BD), herbage density (HD), dry biomass weights (DW), vegetation or foliage height (VHT), percent vegetation greenness (GREN) and the estimated annual index of water availability (WA%) in Kajiado study area, July-August, 1980. Variable Partial Regression s.e(§.) T(g.) C Significance r coefficient^.) 1 1 Constant — 0.27845 0.48595 0.57299 0.5782 BD 0.46585 0.20878 0.11957 1.7461 0.1086 HD 0.36412 0.37172 -1 0.28667 -1 1.2967 0.2213 DW -0.35921 -0.39729 -2 0.31121 -2 -1.2766 0.2280 VHT -0.34067 -2.1502 1.7892 -1.2018 0.2547 GREN -0.08208 -0.25912 -2 0.94865 -2 -0.27314 0.7898 WA 0.38426 0.24279 -1 0.17588 -1 1.3804 0.1949 n = 18 Rd = 0.741 s e = 0.4025 (P <0.05) Regression Model: RR = 3 Q + S1BD + 32HD - BgDW - 34VHT - B^ GREN + 3&WA + e *: Non-significant at P <0.05 a: Partial regression coefficient 3^ b: Standard error of the estimate of the partial regression coefficient 3^  c: T-statistic of the partial regression coefficient 3^ d: Multiple regression coefficient e: Standard error of the estimate Y at (N-l) degrees of freedom. Note: Non-significant variables are included to investigate their contribution. 66 TABLE 5.9:* The multiple linear relationship between the spectral radiance or reflectance ratios (RR); biomass fresh weights (FW), percent dry matter digestibility (DGM), percent crude protein (CP), percent crude fibre (CF), percent vegetation cover (CEST), vegetation or foliage height (VHT), percent vegetation greenness (GREN), and the estimated annual index of water availability (WA%) in Kajiado study area, July-August, 1980. Variable Partial Regression r coefficient(§ Constant _ 12.264 FW 0.44936 0.21433 -2 DGM -0.16049 -0.12574 CP 0.35446 0.77403 -1 CF -0.25383 -0.46748 -1 CEST -0.13399 -0.54877 -2 VHT 0.03578 0.89499 -1 GREN -0.11686 -0.39071 -2 WA 0.33268 0.21310 -1 n = 18 Rd = 0.806 s e = 0.3925 s.e(g.) T(B.) C Significance x x 24.535 0.49987 0.6292 0.14204 -2 1.5090 0.1656 0.25778 -0.48778 0.6374 0.68064 -1 1.1372 0.2848 0.59391 -1 -0.78729 0.4513 0.13529 -1 -0.40564 0.6945 0.83317 0.10742 0.9168 0.11068 -1 -0.35300 0.7322 0.20136 -1 1.0583 0.3175 (P <0.05) Regression Model: RR = 3 Q + 3XFW - 32DGM + 33CP - 34CF - 35CEST + 3&VHT - 3^ GREN + 3gWA + e *: Non-significant at P <0.05 a: Partial regression coefficient 3j_ b: Standard error of the estimate of the partial regression coefficient 3^  c: T-statistic of the partial regression coefficient 3^  d: Multiple regression coefficient e: Standard error of the estimate Y at (N-1) degrees of freedom. Note: Non-significant variables are included to investigate their contribution. 67 TABLE 5.10:* The multiple linear relationship between the greenness variation index ( G V I ) ; biomass fresh weights (FW) and the estimated annual index of water availability (WA%), in Kajiado study area, July-August, 1980. Variable Partial r Regression coefficient(3 )' s.e(3.) 1 T(3.) 1 Significance Constant - -0.13435 -1 0.62517 -1 -0.21490 0.8327 FW 0.29759 0.14455 -3 0.11973 -3 1.2073 0.2460 WA 0.33514 0.34242 -2 0.24855 -2 1.3777 0.1885 n = 18 Rd = 0.625 s e = 0.06651 P <0.05 Regression Model: GV I = 3iFW + 3 2WA - 3Q + e a b c: d: e: Significant at P <0.05 Partial regression coefficient 3-^  Standard error of the estimate of the partial regression coefficient 3^  T-statistic of the partial regression coefficient Multiple regression coefficient Standard error of the estimate Y at (N-l) degrees of freedom. Note: Non-significant variables are included to investigate their contribution. 68 TABLE 5.11:* The polynomial relationship between the spectral radiance or reflectance ratios (RR) and biomass fresh weights (FW) in Kajiado study area, July-August, 1980. Variable Partial Regression^ s.e(g.)b T(§.) C Significance r coefficient(§ ) 1 1 Constant - 1.1435 0.20715 5.5201 0.0001 FW -0.30361 -0.19669 -2 0.15937 -2 -1.234$' 0.2361 FW2 0.54556 0.61628 -5 0.24444 -5 2.5212 0.0235 n = 18 Rd = 0.87232 ' s e = 0.24315 P < 0 . 0 1 Regression Model: RR = g + g FW + g„FW + e *: Significant at P <0.01 a: Partial regression coefficient g^ b: Standard error of the estimate of the partial regression coefficient Bj_ c: T-statistic of the partial regression coefficient 3^ d: Multiple regression coefficient e: Standard error of the estimate Y at (N-1) degrees of freedom. f: Non-significant - included to illustrate the polynomial regression. 69 TABLE 5.12:** The exponential relationship between the spectral radiance or reflectance ratios (RR) and the biomass fresh weights (FW) in Kajiado study area, July-August, 1980. ~ b ^ c Variable Partial Regression s.e(g.) T(g.) Significance r coefficient(g ) Constant - -1.1181 0.41766 -2.6770 0.0165 LFW* 0.60981 0.24045 0.78126 -1 3.0777 0.0072 n = 18 Rd = 0.60981 s e = 0.25774 P <0.01 Regression Model: RR = exp(e^LFW or In RR = 6,LFW - e Q + e) - 9"o + e" *: LFW = natural logarithm of FW *: Significant at P <0.01 a: Partial regression coefficient g^ b: Standard error of the estimate of the partial regression coefficient g-j. c: T-statistic of the partial regression coefficient g^ d: Regression coefficient e: Standard error of the estimate Y at (N-l) degrees of freedom. TABLE 5.13: Spectral radiance or reflectance ratio (RR), biomass fresh weights (FW) equations and the mean bias. 2 2 Mean** Equations b Q ^ b 2 R or r S^* b i a g RR = bQ+ bxFW 0.737 0.0019 0.494 0.353 0.002341 RR = b Q - bxFW + b2FW2 1.1435 -0.19669-2 0.61628-5 0.645 0.30596 0.007199 *: The standard error of estimate (square root residual mean squares) computed from Equation 4.17. **: The mean bias computed from Equation 4.18. 71 (RR) and biomass fresh weights (FW) is considered to be the best and simplest to apply. The exponential model (4.16) will not be considered for applications in this study. Considering the regression equations in an integral form may be helpful towards the determination of the factors that characterize the spectral information of vegetation "greenness". From Equations 5.15 and 5.17, the variation in the biomass dry weights (DW) is explained by biomass fresh weights (FW) and herbage density (HD) to the tune of 87.61% and 51.83% respectively. However, spectral radiance or reflec-tance ratio (RR) explains only 25.07% of the variation in biomass dry weights (DW) (Eqn. 5.2), yet biomass fresh weights (FW) explains 49.42% of the variation in the spectral radiance or reflectance ratios (RR) (Eqn. 5.1). This shows a loss of 24.35% of explanatory power of the variation in spectral radiance or reflectance ratios (RR) by drying the biomass fresh weights (FW) samples. This loss is probably higher than might have been expected. By considering results in Table 5.5, only 69.39% of the variation in spectral radiance or reflectance ratios (RR) is explained by the biomass fresh weights (FW) and biomass dry weights (DW), yet the two independent variables in the regression are highly significantly correlated (r = 0.936, P <0.01) (Eqn. 5.15). In essence, some variation in the spectral radiance or reflectance ratios (RR) is unaccounted for. The leaf water content (LW) could be considered as a function of the estimated annual index of water availability (WA) and other 72 biophysical characteristics variables of the vegetative sample plots. This is reflected in the fact that only 35.68% of the variation in spectral radiance or reflectance ratios (RR) is explained by the estimated annual index of water availability (WA) (Eqn. 5.7), while only 68.87% of the variation in the same variable is explained by the leaf water content (LW) (Eqn. 5.6). A total of 71.57% of the variation in the spectral radiance or reflectance ratios (RR) is explained by both the leaf water content (LW) and estimated annual index of water availability (WA) (Table 5.6). This shows that only 2.68% of the variation is accounted for by including the estimated annual index of water availability (WA) in the multiple regression equation. The chemical analysis variables: percent crude fibre (CF), percent crude protein (CP) and percent dry matter digestibility (DGM), do not seem to explain a significant amount of the variation in the spectral reflectance information of vegetation "greenness". For instance, only 2.08% of the variation in the spectral radiance or reflectance ratios (RR) is accounted for by the percent crude fibre (CF) content of the clipped plant material (Eqn. 5.9). Whereas only 49.42% of the variation in the spectral radiance or reflectance ratios (RR) is explained by the biomass fresh weights (FW) (Eqn. 5.1), the polynomial relationship between the two variables (Table 5.11) shows that 64.51% of the variation in the former variable is accounted for by the latter. It therefore appears that some of the biophysical characteristics variables which influence the spectral reflectivity of vegetation canopy may be having a polynomial behaviour 73 in some range of the spectral data. In a descending order, the most important biophysical characteristics variables influencing the spectral radiance or reflectivity ratios'(RR) are: the leaf water content (LW), biomass fresh weights (FW), biomass density (BD), estimated annual index of water availability (WA), and percent vegetation cover (CEST). The regression equations reported in this documentation were selected on the basis of their simplicity. On the same premise, these equations together with field notes are used to interpret those factors that may influence the behaviour of the digital radiometer used in this study. Fig. 5.5 shows the polynomial and the linear regressions relating the spectral radiance or reflectances (RR) to biomass fresh weights (FW). A complete summary of the correlation matrix for the spectral radiance or reflectance ratios (RR) and biophysical character-istics variables of vegetative sample plots is given in Table 5.14, while the paired data set used is given in Appendix IV. 5.4 The Double-Sampling Parameters The double-sampling parameters are computed by using Equations given in Section 4.2 of Chapter 4. The sampling costs are given in man-hrs/transect. The costs of fuel for the automobile and aircraft are not included in these computations, as they fluctuate a lot. Suppose that the estimated total cost of this study was C = 1,000 man-hrs, for aerial and local-level reference sampling (clipping and associated operations). Furthermore, let c' = 0.05 man-hrs/transect TABLE 5.14:* Correlation matr ix for the spectral reflectance and biophysical characteristics variables observed in Kajiado study area (July-August, 1980). Variable FW DW RR DGM CP CF GREN VHT WA GVI LW BD HD CEST FW 1.000 0.936 0.703 0.183 0.071 0.028 DW 1.000 0.501 0.185 0.220 0.071 RR 1.000 0.049 0.158 0.144 DGM 1.000 0.121 0.123 CP 1.000 0.329 CF 1.000 GREN VHT WA GVI LW BD HD CEST 0.766 0.523 0.652 0.560 0.887 0.908 0.620 0.785 0.747 0.609 0.626 0.429 0.668 0.807 0.720 0.851 0.560 0.236 0.597 0.562 0.830 0.617 0.305 0.482 0.214 0.037 0.318 0.409 0.144 0.233 0.134 0.023 0.282 0.415 0.213 0.106 0.139 0.017 0.404 0.182 0.315 0.082 0.202 0.080 0.032 0.053 0.012 0.113 1.000 0.665 0.721 0.573 0.639 0.729 0.693 0.548 1.000 0.388 0.390 0.308 0.336 0.957 0.673 1.000 0.575 0.557 0.571 0.449 0.578 1.000 0.620 0.515 0.428 0.435 1.000 0.861 0.367 0.543 1.000 0.373 0.492 1.000 0.796 1.000 * Variable names are listed on page x i i . Spectra! or Radiance Reflectance Ratio (RR) ro 76 and c = 10 man-hrs/transect. We know that the first sample is of size n' = 80, and the second sample, n = 18. Then, by Equation 4.1, the unbiased-model estimate of Y is y l r = 165.59 + 114.14 (1.5488 - 1.2304) = 206.41 gm/m2 (biomass dry weights (DW)). To compute the variance of this estimate, v(y^ r), we have n - 2 Z (y. - y) = 205593.5305 i=l 1 n - 2 y (x. - x) = 3.95698848 i-1 1 (x' - x) 2 = 0.12787776 by Equation 4.6, s 2 y . x = 9627.632724 By Equation 4.7, s 2 y = 12093.73709 Hence, by Equation 4.5, v(y 1 r) = 876.8304201, by assuming that the last term, s2v/N is negligible. Similarly, for the case of simple random sample, V(y) - 120.9373709, and n = C/c = 100. By using Equation 4.8, Figure 5.6 plots values of n1 and n for specified population correlation coefficient ( p ) , as indicated to make double-sampling a viable procedure for this type of study. Similarly, we could use Equations 4.9 and 4.10 to give the critical ranges of c/c' for given p and p for given c/c' that make double-sampling profitable. An example of such plots can be found in Cochran (1977), and that for 77 p r a c t i c a l use, the curves overest imate the gains to be achieved from double- sampl ing, because the best va lues of n and n' must e i t h e r be est imated from previous data (e .g . from F igure 5.6 f o r t h i s study) or guessed. In t h i s study, the double-sampl ing sample s i z e i s o n e - f i f t h of the suggested s imple random sample to achieve the same p r e c i s i o n . The sampling e f f o r t took three persons, 21 days working an average of 8 hrs/day. The cost of t r an sec t s e l e c t i o n and c l a s s i f i c a -t i o n amounted to 4 man-hrs at 0.05 man-hrs/t ransect . The cost of c o l l e c t i n g s p e c t r a l i n f o rmat i on amounted to 45 man-hrs. Thus, the t o t a l cost of the sampling exe r c i s e f o r t h i s study was 553 man-hrs. This gave a saving of 447 man-hrs which were spent on data r e d u c t i o n . I f a s imple random sample of n = 100, had been taken, there could be no sav ing i n cos t of the sampling e x e r c i s e . More samples cou ld have been taken i n the double-sampl ing e x e r c i s e , but automobile breakdown and o p e r a t i o n a l c o n s t r a i n t s could not permit i t . Using the Equations cons idered i n t h i s s e c t i on and F i g . 12.1 i n Cochran (1977), the r eg re s s i on e s t ima t i on of biomass f r e sh weights (FW) and biomass dry weights (DW) r e s u l t s i n p r e c i s i o n ga in to the tune of 25% and 10% at a cost r a t i o of approx imate ly 16. These va lues are based "on the double-sampl ing c o r r e l a t i o n es t imates ( i . e . T = 0.703 and ,flr= 0.5007, P <0.01 and P <0.05 f o r FW and DW, r e s p e c t i v e l y ) . Regress ion e s t i m a t i o n of l e a f water content (LW) would r e s u l t i n a 50% ga in i n p r e c i s i o n i f double-sampl ing i s adopted. Figure 5.6 The relationship between second sample (n) and first large sample (n') size for specified population correlation coefficient CP) in a double-sampling scheme. 70 60 OB 79 6.0 DISCUSSION, RECOMMENDATIONS AND CONCLUSIONS The biophysical factors that influence the radiometer estimates of spectral radiance or reflectance ratios of vegetation greenness have been examined. Leaf water content was found to be a major influencing factor (r = 0.83, P <0.01, d.f. = 18). The biomass fresh weights, biomass density, estimated index of water availability, vegetation cover estimate (%), and vegetation greenness (%) were also found to influence the spectral reflectivity of vegetation canopies. However, the influence of other factors that include, vegetation herbage density, vegetation or foliage height, crude fibre content (%), crude protein (%) and dry matter digestibility (%) was not significant (P <0.05). The multiple correlation coefficient between the spectral radiance or reflectance ratios and biomass fresh weights and biomass dry weights seemed to be somewhat lower than expected (R = 0.833, P <0.01) (Table 5.5). This observation seems to be in agreement with the influence of relative total moisture potential in the study area (Table 5.6) on the spectral performance of the vegetation canopies, found to be significant (r = 0.846, P <0.01). These phenomena could be partly attributed to the possible effect of the geographical location of transects considered across the study area that may be reflective of differential spectral performance of the vegetation cover types. It appears that the foregoing observations are in harmony with climatic patterns prevalent in the area (Chapter 3), as well as the complexity 80 and diversity of vegetation communities surveyed. Further, considera-tion of the results in Tables 5.6 and 5.10 seem to suggest that the geographical scale involved in this study is an important factor influencing these differential characteristics of spectral performance across the study area. For the purposes of characterizing, and hence predicting, spectral reflectance ratios from biomass fresh weights, three regres-sion equations have been derived. These are equation 5.1, and those reported in Tables 5.11 and 5.12. Whereas, the equation given in Table 5.11 seems to have a higher predicting power (as r = 0.803, P <0.01) than the other two, i t would be reasonable to adopt the use of equation 5.1 as i t appears to be simple and easy to understand. The regression equation in Table 5.12 did not seem to have accounted for a lot of the variation in the dependent variable compared to the others considered above. It therefore appears that consideration of exponential performance of spectral reflectance of vegetation greenness could be ignored at this stage. Although the study objective was to examine those factors that influence the biometer readings of spectral reflectance, other relationships between the biophysical variables were also considered for clarity of the existing dynamics in sample plots. The biophysical variables seem to cross influence each other at various probability levels. This activity might be stochastic. For instance, biomass fresh weights seems to be a good predictor of the biomass dry weights as they are highly correlated (r = 0.936, P <0.01). This relationship 81 (equation 5.15) seems to suggest that the biomass dry weights are highly correlated with the spectral reflectance ratios, since the latter were found to have a high correlation with biomass fresh weights (r = 0.703, P <0.01). This was somewhat surprising since the correla-tion between the two variables was found to be low but respectable (r = 0.501, P <0.05). Again the characteristics reflected by geographical variations of transect location elucidated earlier are a possible explanation. Hence, if these phenomena are considered in the context of annual plant growth stages, the stochastic dynamics of the factors considered above would be evident. It would be interesting to note that, although there exists a high correlation coefficient between the biomass dry weights and herbage density (r = 0.720, P <0.01) (equation 5.17), the latter variable, unlike the former, does not significantly influence the spectral reflectances. This result could have stemmed from a possible reduction effect that the vegetation or foliage height may have on estimated vegetation cover by not allowing for optimal exposure of total leaf area, necessary for maximizing vegetation canopy reflectivity of vegetative sample plots. Western (1977) suggested that moisture content in plant material gave a reasonable method of independently appraising percentage vegeta-tion greenness. The biophysical characteristics variables equations derived in this study seem to agree with this suggestion. In particu-lar, the relationships between estimated annual index of water availa-bility and the percent vegetation greenness (equation 5.18, r = 0.721, 82 P <0.01), and that between the latter variable and leaf water content (r = 0.639, P <0.01, Table 5.13), have been found to be acceptable. Further, Western (1977) suggested that estimates of the canopy greenness can be confused where the distinction between the percentage of a tree in leaf cover and the percentage of trees with leaf cover is not recognized. Canopy greenness is the product of the two. At this stage, i t is not clear as to whether or not the spectral reflectance of vegetation canopy as estimated by the digital biometer would help towards elucidating this difference in order to define percent vegeta-tion greenness. The latter variable characterizes the spectral reflec-tances of vegetation canopy significantly (equation 5.4, r = 0.560, P <0.05), and could therefore be used in its place appropriately, if well defined. On a percentage basis the spectral reflectance from a canopy is considerably less than that from a single leaf because of a general attenuation of radiation by variations in illumination angle, leaf orientation, shadows, and non-foliage background surfaces such as soils (Knipling, 1970). In this study, a high spectral reflectance ratio suggests that the leaf area index of the target is sufficiently large hence exposure of the greater part of the canopy for reflectivity. The interaction(s) with the soil background become less and less as the vegetational density or biomass increases until the asymptotic spectral radiance or reflectance is reached (Tucker, 1977). Further, this seems to indicate that each transect surveyed in the present study would have unique reflectivity characteristics. Considering our results, this 83 indication seems to be reasonable. The analysis of variance (ANOVA) of the spectral data (Table 5.2) collected on eighty transects showed non-significant (P <0.05) differences between transects within the vegeta-tion cover types. Twenty-six homogeneous subsets of spectral radiance or reflectance ratios observed across the vegetation cover types were isolated. Whether these homogeneous subsets reflect similar range forage levels within each subset is not clear. In particular, i t is not clear whether, three independent vegetative sample plots in each of the cover types having the same response of spectral reflectivity as estimated by the digital biometer, would be characterized by similar i f not identical biophysical characteristics within those plots. Further, the method used in this study for grouping transects into the three vegetation cover types seems to be non-optimal. Thus, there seems to be reason to believe that spectral reflec-tance readings of bushland and wooded grassland vegetation sample plots are somewhat sub-optimal (i.e. far below the spectral asymptotic level associated with every plant community) due to the canopy architecture, associated with at least 20% vegetation cover. Hence this phenomenon requires further investigation. It is important to note that the kind of rangeland we are dealing with has a tremendous variability in rainfall effectiveness, species composition and topographical characteristics. These factors influence the canopy architecture and thus the canopy spectral reflectivity. Equally important is the non-replicability of the vegetative sample plots traced by the biometer probes (i.e. area traced by the moving 84 cone-projection by probes on the surface) in the sub-samples harvested in the local-level reference exercise. The influence of these impor-tant factors on reflectivity of the canopies need further consideration. Some difficulties were experienced while collecting spectral reflectance and local-level reference data. The digital biometer in use exhibited erratic behaviour when readings were taken on some transects, especially so, when the probes focused on transition zones between vegetated and non-vegetated ground or on ecotone vegetation cover types (Plates 3 and 5). This behaviour could have resulted in some errors in the spectral data. Fluctuations in probe readings reflect a minimum and a maximum spectral level which suggests a diver-sity in biomass distribution (Plates 3-5). The fluctuations should be well understood if spectral data is to be used for monitoring rangeland condition. The difficulty of relying on readings made over very dense vegetation canopies posed another problem. Canopy depth might have, also, enhanced this problem and hence introducing some errors through under-estimation of the actual spectral reflectance measurements of the vegetation greenness. Girard (1974) dealing with agricultural crops suggested that i f the canopy cover is at least 15%, then the crop would eliminate the spectral response of the soil beneath. Further, Poulton (1981, personal communications) commented that when dealing with thick canopies like those in bushland areas, any spectral data associated with a canopy cover of 15 - 20% would be difficult to segregate on the 85 basis of bush canopy or understory plant material contributions. However, any spectral data received on over 20% canopy cover would exclude a significant proportion of the spectral response of the understory plants. This problem seems to be prevalent in most of the transects surveyed other than those in grassland areas. It would, therefore be sub-optimal to discuss the concept of carrying capacities of those areas surveyed, especially so, in bushland and wooded grass-land vegetation cover types. Other sources of errors were probably introduced by the sorting procedure employed in obtaining biomass fresh weights data due to the impossibility of completely separating all chlorophyllous material from the remaining plant parts. Another factor to be examined is the directional trend in green flux on some transects which suggests that directional variation in plant phenological characteristics may be associated with both plant community composition and the effects of the soil catena. By averaging transect ratios to obtain a transect value, some errors might have been introduced by confounding the apparent directional dynamics. The trend phenomenon considered here, indicate that i f the inves-tigation were extended to cover all the growing seasons (spatial and temporal coverage), then a stochastic nature of the spectral reflec-tivity of canopies in various vegetation cover types, would be unveiled. Hence, as mentioned earlier such intraseasonal and inter-seasonal stochastic characteristics of spectral reflectances, i f well documented, would constitute important phenomena in ecological monitoring of the Kenyan rangelands. 86 Another factor that could have induced errors in spectral data is the possible dust cover on plant leaves on some transects. Such dust could have resulted from movements of grazing animals (e.g. livestock, wildebeests, etc.) or from wind storms across the transect, just before the spectral readings were taken. In such a case, the spectral reflectances collected would not be due to the actual biophysical characteristics of the ground truth vegetative sample plots. However, this phenomenon did not seem to affect a significant number of the ground truthed transects in our study area. In light of the foregoing analysis and a critical examination of some of the literature on the subject (Robbins 1957, Alcock ^ t al. 1967, Thomas et al. 1967, Colwell 1969, Gausman et al. 1969, Suits 1972, Sinclair ^_t jal. 1973, Gausman et al. 1973, Van Bavel 1974, Kanemasu 1974, Drake 1976, Roberts et al. 1977, Tucker 1977a,b, Kumar 1977, and Campbell 1977) reveals a tremendous amount of information concerning plant metabolic performance levels as a major influence on spectral reflectance levels. Figure 6.1, which shows a suggested relationship between spectral radiance or reflectance ratios (0.800 ym to 0.675 ym) and biomass (standing crop) (gm/m2), results from this examination. 6.1 Double-sampling and Land-use Policy Design In this study the cost of sampling the biophysical character-istics variables was not assumed to be uniform across the vegetation cover types. It was found that in some plots, more time was required to complete the sampling effort, for example in bushed plots. However, 87 Peak Biomass Spectra[ " Asymptotic level Youthful growth Stage Rapid increase in plant vigor Senile growth stage Biomass (gm/m2) Figure 6.1 General relationship (suggested) between Spectral Reflectance Ratios and Biomass over the three stages of growth. q, :a member of a family of such curves that represent different plant communit ies. a = 0.6, the average lowest value for the spectral reflectance ratios received on three non-vegetated transects in the study area. 88 for computational purpose, the average cost for sampling a transect in the study area was found to be, c = 10 man-hours. Total cost of the study was set at C = 1,000 man-hours, and the cost of selecting and classifying the aerial transects, c' = 0.05 man-hours/transect. The double-sampling procedure employed in this study indicated cost and time efficiency, and high job productivity. Without the adoption of double-sampling, n = 100 simple random samples could have been clipped, but only twenty were clipped, eighteen of which were considered in the analyses discussed in this chapter. The unbiased-model estimate of Y was found to be 206.41 gm/m^  (biomass dry weights (DW)). Considering the fact that the area under study is 40,000 km^ , the total biomass dry weight, available is 0.82565 x 10 1 0 kgs. Allowing for a 10% harvesting level of standing crop by livestock and wildlife populations, this would suggest that about 0.82564 x 10^ kgs of forage was available for ingestion during the study period i f the appropriate carrying capacity was observed. With an average of 90.09% of dry matter digestibility, this would provide about 7.44E +11 kgs of digestable forage. If the actual number of livestock and wildlife stock was available, a land-use policy could be designed for the period under study. This could be extended to the annual land-use planning. It was found that the sampling effort accounted for 553 man-hours, saving 447 man-hours. This provided sufficient time for data reduction procedures, and a sample size (n = 20), which is one-fifth of the suggested simple random sample. Further, there was 25% and 10% 89 precision gain in estimating biomass fresh weights and biomass dry weights respectively. Figure 5.6 could be used to estimate sample size options for a given inventory problem. Hence, rapid data acquisition could increase the speed of formulating a reliable land-use policy. 6.2 Recommendations Some recommendations could be made following the discussion in preceding sections: (i) With regard to the evident differential reflectivity characteristics between vegetation cover types, i t is reasonable to suggest that predictive regression equations relating range forage to spectral reflectances should be specific to individual vegetation cover types. In this case, information gained from such relationships would probably be near-optimal and reliable. In addition, i t would eliminate the possible precision trade-offs associated with a combined regression equation, as in the case of equation 5.2. However, it would seem difficult to explain the spectral reflectance differences between the vegetation cover types, exclusive of the influence of the grazing pressure of both livestock and wildlife popula-tions, other than of the natural variations in the bio-physical characteristics prevalent in the cover types. 90 (ii) Considering that some canopies may constitute understory, brush and woodland subsystems, the integration of these produce the estimated spectra. There is need to develop a simple procedure to define these subsystems in order to account for the spectral intensity of each subsystem. Separation of spectral intensities associated with each subsystem could be a very useful achievement in procedures of ecological monitoring. ( i i i ) The discussion by Robbins (1957) considered the d i f f i -culties with respect to the physiological aging in plants. It was suggested that a l l plants probably do have a physiological maximum life-span which is invariant. Further, Wright and Van Dyne (1976) suggested that the mean life-span of a species is probably not fixed but differs from the physiological maximum in response to many factors. Therefore, effects of environmental fluctuations need to be understood in order to account for possible departures from the expected physiological patterns. This would help towards a better understanding of plant community spectral reflectance characteristics over the life-span. (iv) The need to develop growth models of major plant communities in Kenyan rangelands is necessary if reliable 91 characterization of spectral reflectances is to be achieved for the purposes of ecological monitoring. If such models were in existence, the limitations facing the digital biometer would have been relatively easier to elucidate. Further, there is also great need to examine intra- and interseasonal fluctuations of the spectral reflectance at 0.675 ym and 0.800 ym, and maybe also at other wavelengths (e.g. green), as a function of growth stages of various plant communities. This might be extended to a study of plant communities under different resource use treatments. (v) If digital biometers are not available to estimate spectral reflectances for the purpose of predicting range forage, the results of this study indicate that subjective estimates of percent vegetation greenness could be used instead. Other workers, including Western (1977) and Croze (1977) found that such estimates collected at low flying levels are good indicators of the biomass distribution of large mammals, and hence by inference range forage. (vi) For the purpose of using the digital biometers (Tektronics J-16) for estimating spectral reflectances of vegetation greenness, for prediction of range forage, the results of this study indicate that such applications should probably be limited to grassland areas. However, this restriction 92 would be invalid if significant regression equations relating spectral information to biophysical characteris-tics variables in major plant communities in bushland and wooded grassland vegetation cover types, are developed successfully. Considering the cost analysis of the present study such an exercise would be slightly expensive if acceptable sampling effort is to be attained. (vii) Finally, the results of this study indicate that for opti-mality of acquisition of spectral reflectances of vegeta-tion canopies, a more efficient and reliable biometer should be developed. Such a device would be required to receive spectral reflectances at the green, red and infra-red wavelengths. This way most of the factors character-izing spectral information could be integrated into one ratio, which would then be used to predict range forage. Further, such a device could have a mechanism for adjust-ing automatically according to vegetation canopy depth. In addition, i t could be connected to an on-line mini-computer and an automatic movie camera. The former would allow real time data analysis while the latter, synchro-nized with the biometer probes' operation would provide precise location of plots inventoried from the air, hence making the local-level reference exercise meaningful. Professor Paul T. Tueller (1981, personal communications) agrees with this recommendation. 93 6.3 Conclusions This study has determined those biophysical characteristics variables that influence spectral reflectivity of vegetation canopies. The leaf water content was found to be a principal factor of influence. Spatial variation in spectral readings was found to be evident in the study area. Locally, this was connected to the soil catena character-istics and on a large geographical scale, moisture potential was an influencing factor. The need to develop specific plant community growth models and associated regression equations was identified. Further, the importance of developing an advanced and hence efficient and flexible radiometer (biometer) system was emphasized. It is believed that such a system would optimize spectral information acquisition possibly by utilizing automatic mechanism reacting to target canopy depth. The feasibility of using the present radiometer system (Tektronics J-16) is recommended for grassland areas only. Until the complex canopy structure in bushland and wooded grassland areas is well understood, the present system's spectral readings appear to remain sub-optimal. The effect of grazing pressure or wind storms could not be accounted for explicitly in the context of the observed differences in spectral reflectances across the study area. 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Norton-Griffiths, M. 1977. Aspects of Climate of Kajiado District. FAO. KEN/71526, Project Working Document No. 13. August 1977. Pasto, J.K., J.R. Allison, and J.B. Washko. 1957. Ground cover and height of sward as a means of estimating pasture production. Agron. J. 49:407-409. Payne, G.F. 1974. Cover-weight reltionships. J. Range Manage. 27:403-404. Pearson, R.L. 1973. Remote multispectral sensing of biomass. Ph.D. Thesis, Colorado State University. Pearson, R.L., and L.D. Miller. 1972. Remote mapping of standing crop biomass for estimation of the productivity of the shortgrass prairie 102 National Grasslands, Colorado. In.: Proc. 8th Int. Symp. on Remote Sensing of Environ., University of Michigan, Ann Arbor. Pearson, R.L., L.D. Miller, and C.J. Tucker. 1976rfe. A handheld spectral radiometer to estimate gramineous biomass. Applied Optics 15(2):416-418. Pearson, R.L., C.J. Tucker, and L.D. Miller. 1976a. Spectral maping of shortgrass prairie biomass. Photogrammetric Engineering and Remote Sensing 42(3):317-323. Pechanec, J.F., and G.D. Pickford. 1937. A weight estimate method for determination of range pasture production. J. Amer. Soc. Agron. 29:894-904. Peden, D.G. 1980. Analysis of green meter readings for Masai Mara Ecosystem. Mimeo. KREMU, Nairobi, Kenya. Poulton, C.E. 1981. Personal Communications. Society for Range Management Annual Meeting, February 9-13, Tulsa, Oklahoma, U.S.A. Pratt, D.J., and M.D. Gwynee. 1977. Rangeland management and ecology in East Africa. 310 pp. Pratt, D.J., P.J. Greenway, and M.D. Gwynne. 1966. A classification of East African rangeland, with an appendix on terminology. J. Appl. Ecol. 3:369-382. Rao, J.N.K. 1973. On double sampling for stratification and analytical surveys. Biometrika 60(1):125-133. Reginato, R.J., S.B. Idso, and R.D. Jackson. 1978. Estimating forage crop production: A technique adaptable to remote sensing. Remote Sensing Environ. 7:77-80. 103 Reese, G.A., R.L. Bayn, and N.E. West. 1980. Evaluation of double-sampling estimators of subalpine herbage production. J. of Range Management 33(4):300-306. Roberts, J.R., C.L. Wiegand, and V.I. Myers. 1967. Reflectance of cotton leaves and its relation to yield. Agronomy Journal 59:551-554. Robbins, W.J. 1957. Physiological aspects of aging in plants. Am. Jour. Botany 44:289-295. Rouse, J.W., R.H. Haas, J.A. Schell, and D.W. Deering. 1973. Monitoring vegetation systems in the Great Plains with ERTS. Third ERTS Symposium, NASA SP-327 1:309-317. Royall, R.M. 1970a. On finite population sampling theory under certain linear regression models. Biometrika, 57:377-387. Royall, R.M. 1970b. Finite population sampling - on labels in estimation. Ann. Math. Stat., 41:1774-1779. Sinclair, T.R., M.M. Schreiber, and R.M. Hoffer. 1973. Diffuse reflectance hypothesis for the pathway of solar radiation through leaves. Agron. Journ., 65:276-288. Suits, G.H. 1972. The calculation of the directional reflectance of a vegetative canopy. Remote Sensing of Environment. V.2, 117-125 pp. Teare, I.D. 1963. Estimating forage yield in situ. Ph.D. Thesis, Purdue University. Thomas, J.R., C.L. Wiegand, and V.I. Myers. 1967. Reflectance of cotton leaves and its relation to yield. Agronomy Journal 59:551-554. Tucker, C.J. 1977a. Asymptotic nature of grass canopy spectral reflectance. Appl. Opt. 16(5):1151-1156. 104 Tucker, C.J. 1977b. Spectral estimation of grass canopy variables. Remote Sensing of Environment 6:11-16. Tucker, C.J. 1980. A spectral method for determining the percentage of green herbage material in clipped samples. Remote Sensing of Environment 9:175-181. Tucker, C.J., L.D. Miller, and R.L. Pearson. 1975. Shortgrass prairie spectral measurements. Photogrammetric Engineering and Remote Sensing 41(9):1157-1162. Tucker, C.J., and L.D. Miller. 1977a. Soil spectra contributions to grass canopy spectral reflectance. Photogram. Engr. and Remote Sensing 43(6):721-726. Tucker, C.J., and L.D. Miller. 1977b. Extraction of the underlying soil spectra from canopy spectroreflectance measurements of the shortgrass prairie. Remote Sensing of Earth Resources. Vol. 3. (Ed. Shahrokhi,R.). Tucker, C.J. 1978. A comparison of satellite sensor bands for vegetation monitoring. Photogram. Engr. and Remote Sensing 44(11):1369-1380. Tucker, C.J. 1979. Red and photographic infrared linear combinations for monitoring vegetation. Remote Sensing of Environment. Tucker, C.J., J.H. Elgin, Jr., and J.E. McMurtrey III. 1979a. Temporal spectral measurements of corn and soybean crops. Photogram. Eng. Remote Sensing, V. XLV, pp. 643-653. Tucker, C.J., J.H. Elgin, Jr., J.E. McMurtrey III, and C.J. Fan. 1979b. Monitoring corn and soybean crop development with hand-held radiometer spectral data. Remote Sensing of Environment. 105 Tucker, C.J., J.H. Elgin, and J.E. McMurtrey. 1979c. Relationship of red and photographic infrared spectral radiances to alfalfa biomass, leaf water content, percentage moisture, percent cover, and drought stress. Remote Sensing of Environment. Tueller, P.T. 1981. Personal Communications. Society for Range Management Annual Meeting, February 9-13, Tulsa, Oklahoma, U.S.A. Van Bavel, C.H.M. 1974. Soil water potential and plant behaviour: a case modeling study with sunflowers. Decol. Plant. 9(2):89-109. Wagner, T.W., and J.E. Colwell. 1969. An investigation of grassland resources using multispectral processing and analysis techniques. Willow Run Laboratories, the Institute of Science and Technology, the University of Michigan, Report No. 34795-1-F. (Unpublished). Western, D. 1977. Aerial method of monitoring large mammals and their environment. UNDP/FAO KEN/71/526, Nairobi, Kenya. Wilm, H.G., D.F. Costello, and G.E. Klipple. 1944. Estimating forage yield by double sampling method. J. Amer. Soc. Agron. 36:194-203. Woodhead, T. 1970. A classification of East African rangeland. II. The waterbalance as a guide to site potential. J. Appl. Ecol. 7:647-752, Dec. 1970. Wright, R.G., and G.M. van Dyne. 1976. Environmental factors influencing semi-desert grassland perennial grass demography. The Southwestern Naturalist, 21(3):259-274, Nov. 10.6 APPENDIX I DEFINITIONS OF IMPORTANT TERMS Biomass Bushland Carrying capacity Community Cover, percent The sum total of living plants and/or animals above and below ground in an area at a given time. In this work the term refers to above-ground living matter unless otherwise specified. Syn., standing crop, range forage (herbage) production. An area covered primarily with shrubs. The maximum stocking rate of herbivores possible without inducing damage to vegetation or related resources. It may vary from year to year on the same area due to fluctuating forage production. Syn., grazing capacity. A group of one or more populations of plants and animals in a common spatial arrangement. In this study we refer to vegetation community. The area covered by the combined aerial parts of plants and mulch expressed as a percent of the total area. Ecotone Forage (n) Fresh weight Grassland Grazing pressure A transition area of vegetation between two communities, having some characteristics of both kinds of neighbouring vegetation as well as characteristics of its own. Varies in width depending on site and climatic factors. All browse and herbaceous foods that are available to grazing animals. It may be grazed or harvested for feeding. Syn., graze. Hence, forage production refers to the weight of forage that is produced within a designated period of time on a given area. The weight of plant material at the time of harvest. Syn., green weight. Land on which grasses are the dominant plant cover component. The actual animals-to-forage ratio at a specific time. For example, three animal-units per ton of standing forage. 107-: Oven-dry weights The weight of plant material after it has been in the oven to remove moisture content. It is not the same as air-dry weight, as the latter refers to the weight of a substance after it has been allowed to dry to equilibrium with the atmosphere. Radiometer A device specially designed to receive and record spectral reflectances of targets, e.g. vegetation canopy. The reflectances are received at specified radiation wavelengths at a fixed angular view and then digitized and displayed for recording. Syn., biometer. Range forage Forage produced on rangeland. Syn., forage, standing crop, vegetation biomass. Spectral reflectance Is the proportion of incident solar radiation received by plant canopies and reflected back"> into space. Hence, spectral ratio is such radiation energy received at one wavelength and referenced to that received at a different wavelength. Such reception may be by the digital biometer, or any such specialized equipment. 108 APPENDIX II TABLE A2.1: Analysis of variance of biometer ratios for the Mara ecosystem - May 1980 Source of variation S.S. D.F. M.S. Total 871.322 819 Transect 355.669 40 Habitat 200.833 4 Transect within Habitat 154.836 36 Error 515.653 779 0.872 8.8901 13.429 * (1/4) 50.2082 11.674 *(2/3) 4.3013 6.497 * (2/4) 0.6624 * Significant at about P < 0.05. TABLE A2.2: Duncan's multiple range test for the biometer spectral reflectance ratios in different vegetation types of Mara ecosystem - May 1980 Vegetation cover type Mean ratio Ranges of non-significance WG SG GL SL DG 3.733 3.463 2.926 2.717 2.241 A A B B 109 APPENDIX II (Cont'd) TABLE A2.3: Duncan's multiple range test for the biometer spectral reflectance ratios at three different flight altitudes over an annual grassland transect Flight altitude (ft) Mean Ranges of non-significance 300 800 1300 0.9269 0.9918 0.9320 A A A LISTING OF FILE TATU. 2 11:OOA.M. MAY 08, 1981 ID=TATU APPENDIX III 1 INPUT FILE=JOSIA FORMAT^(1X.F1.0,1X , F2.0,1X.F5.3) 2 TITLE , SPECTRAL REFLECTANCE RATIOS FOR KAJIADO 3 VARIABLES C T 1(SR) 4 MODEL,SR= 5 C+T(C) 6 LEVELS,C=3,T=29 7 OUTPUT OBSE PRED FREO HOMO TERMS' 8 C,T(C) 9 RANGE TYPE=N PR0B=0.05 SOMETIMES TERMS= 10 C,T(C) 11 COMPUTE 12 -SPECTRAL REFLECTANCE RATIOS FOR KAJIADO 13 OAnalysis for SR 14 O Analysis of variance table 15 O Sum of Mean 16 Source <;min^o= T 17 18 C 52.607 2. 26.303 297.58 0.0 RESIDUAL 19 T(C) 1 103.7 77 </t niA •-squares D F square F-ratio Probabi1ity Test term 1103°7 7 7 2' f 7 - 5 8 °-° R E S I D U * L % J^f" 1 3 4 3 5 1 5 2 ° - ' ° B 8 3 9 l E - 0 1 1 6 2 - 1 7 °'° RESIDUAL T o t a 1 1290.7 1599. 22 O ^ Overa11 23 Overall mean standard deviation 24 SR 1.5488 0.89844 25 0 26 Frequencies, means, standard deviations for C 27 1 . 2. 3. 28 29 580 500 520 30 0 MEAN 1.7825 1.3616 1.4677 31 P MEAN 1.7826 1.3618 1.4678 32 0 STDV 1.1840 0.67294 0.62131 33 S ERR M 0.12345E-01 0.13296E-01 0.13038E-01 34 O Homogeneity of variance test 35 36 B a r t l e t t b a r t l e t t Degrees Layard Size 37 Factors Chi-square Probability of freedom Chi-square Probability warn 38 C 286.84 O.OOOOO 2 67.100 0.00000 39 0 Multiple range tests 40 0 Newman-Keuls test at 5% pr o b a b i l i t y level 41 There are 3 homogeneous subsets which are l i s t e d as follows: 42 0 ( 2. ) 43 0 ( 3. ) 44 0 ( 1 . ) 45 Time for multiple range test was 0.77408E-01 seconds. Cumulative time is 18.818 seconds. 46 O 47 Frequencies, means, standard deviations for T(C) 48 1. 2. 3. 49 . 1 50 20 20 20 51 0 MEAN 3.0824 1.6992 3.2638 52 P MEAN 3.0824 1.6992 3.2638 53 0 STDV 0.60435 0.28204 0.39604 54 S ERR M 0.66480E-01 0.66480E-01 0.66480E-01 55 .2 56 20 20 20 57 0 MEAN 2.8273 2.2318 1.8387 58 P MP AM 1 o n - -P MEAN 2.8273 2.2318 1 8387 L I S T I N G OF F I L E TATU . 2 1 1 : 0 0 A M. MAY 0 8 59 0 STDV 0 . 15344 0 . 1 7 3 4 7 0 . 2 4794 6 0 S ERR M 0 . 6 6 4 8 0 E -01 0 . 6 6 4 8 0 E -01 0 . 6 6 4 8 0 E -01 61 3 62 2 0 2 0 2 0 63 0 MEAN 0 . 9 6 3 7 5 1 . 8 6 3 0 1 . 9032 64 P MEAN 0 . 9 6 3 7 5 1 . 8 6 3 0 1 . 9032 65 0 STDV 0 . 5 5 0 3 7 E -01 0 . 3 4 8 8 5 0 . 5 6 7 9 7 6 6 S ERR M 0 . 6 6 4 8 0 E -01 0 . 6 6 4 8 0 E -01 0 . 6 6 4 8 0 E -01 67 4 6 8 2 0 2 0 2 0 6 9 0 MEAN 1 . 4 1 5 3 1 . 5 9 6 3 1 . 6 3 3 5 7 0 P MEAN 1 . 4 154 1 .5963 1 . 6 3 3 5 71 0 STDV 0 . 3 4 2 6 8 0 . 2 4 4 5 4 0 . 2 6 1 8 9 72 s ERR M 0 . 6 6 4 8 0 E -01 0 . 6 6 4 8 0 E -01 0 . 6 6 4 8 0 E -01 73 5 74 2 0 2 0 2 0 75 0 MEAN 0 . 8 0 2 4 5 1 .2142 2 . 4 7 4 7 76 p MEAN 0 . 8 0 2 4 5 1 .2142 2 . 4 7 4 7 77 0 STDV 0 . 8 7 1 8 4 E -01 0 . 1 1549 0 . 3 0 2 3 3 78 s ERR M 0 . 6 6 4 8 0 E -01 0 . 6 6 4 8 0 E -01 0 . 6 6 4 8 0 E -01 79 6 -8 0 2 0 2 0 2 0 81 0 MEAN 0 . 9 8 6 2 0 1 .0324 1 .0211 82 p MEAN 0 . 9 8 6 2 0 1 .0324 1 . 0 2 1 2 83 0 STDV 0 . 1 0 5 1 4 0 . 8 3 7 4 0 E -01 0 . 1 0 1 4 8 84 s ERR M 0 . 6 6 4 8 0 E -01 0 . 6 6 4 8 0 E -01 0 . 6 6 4 8 0 E -01 85 7 8 6 2 0 2 0 2 0 87 0 MEAN 1 . 1839 0 . 9 6 2 8 0 1 .3541 88 p MEAN 1 . 1839 0 . 9 6 2 8 0 1.3541 89 0 STDV 0 . 1 8 3 7 4 0 . 1 9 6 7 6 0 . 2 3 1 0 3 9 0 s ERR M 0 . 6 6 4 8 0 E - 01 0 . 6 6 4 8 0 E -01 0 . 6 6 4 8 0 E -01 91 8 92 2 0 2 0 2 0 9 3 0 MEAN 1 .1238 0 . 9 2 9 7 5 1 . 3 9 5 8 94 p MEAN 1 . 1239 0 . 9 2 9 7 5 1 . 3958 9 5 0 STDV 0 . 4 2 1 9 2 0 . 7 6 8 7 1 E -01 0 . 3 1 6 0 9 9 6 s ERR M 0 . 6 6 4 8 0 E - 01 0 . 6 6 4 8 0 E -01 0 . 6 6 4 8 0 E -01 9 7 9 98 2 0 2 0 2 0 99 0 MEAN 1 . 5 7 8 2 1 . 0839 0 . 9 4 4 4 5 100 p MEAN 1 . 5782 1 . 0840 0 . 9 4 4 4 5 101 0 STDV 0 . 3 0 7 9 9 0 . 1431 1 0 . 9 6 1 3 1 E -01 102 s ERR M 0 . 6 6 4 8 0 E - 01 0 . 6 6 4 8 0 E -01 0 . 6 6 4 8 0 E -01 103 10 104 2 0 2 0 2 0 105 0 MEAN 4 . 0 4 9 8 1 .1265 1 . 0595 106 p MEAN 4 . 0 4 9 8 1 .1265 1 . 0596 107 0 STDV 0 . 5 1 3 9 3 0 . 1071 1 0 . 6 1 0 5 0 E -01 108 s ERR M 0 . 6 6 4 8 0 E - 01 0 . 6 6 4 8 0 E -01 0 . 6 6 4 8 0 E -01 109 1 1 1 10 2 0 2 0 2 0 1 1 1 0 MEAN 5 . 6 0 2 5 0 . 8 4 8 6 5 1 . 4 254 1 12 p MEAN 5 . 6 0 2 5 0 . 8 4 8 6 5 1 . 4 254 1 13 0 STDV 0 . 9 1 8 3 2 0 . 6 4 5 6 5 E -01 0 . 2 3 4 3 2 1 14 s ERR M 0 . 6 6 4 8 0 E -01 0 . 6 6 4 8 0 E -01 0 . 6 6 4 8 0 E -01 1 15 12 1 16 2 0 2 0 2 0 1981 ID=TATU APPENDIX III (cont'd) LISTING OF FILE TATU.2 1 17 1 18 1 19 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 MEAN MEAN STDV ERR M 13 MEAN MEAN STDV ERR M 14 0 MEAN P MEAN 0 STDV S ERR M . 15 ' 0 MEAN P MEAN 0 STDV S ERR M . 16 0 MEAN P MEAN 0 STDV S ERR M . 17 0 MEAN P MEAN 0 STDV S ERR M . 18 0 MEAN P MEAN 0 STDV S ERR M . 19 0 MEAN P MEAN 0 STDV S ERR M . 20 0 MEAN P MEAN 0 STDV S ERR M .21 0 MEAN P MEAN 0 STDV S ERR M 1 . 2293 1.2294 0.11130 0.66480E-01 20 1 . 5155 1 . 5155 0. 16222 0.66480E-01 20 2.5187 2.5187 0. 53387 0.66480E-01 20 1.4960 1.4960 0.11853 0.66480E-01 20 3.0466 3 .0466 0.24150 0.66480E-01 20 3 . 1566 3 . 1566 0.49389 0.66480E-01 20 2.6173 2.6173 0.65186 0.66480E-01 20 O.87655 0.87655 0.22982E-01 0.66480E-01 20 1.3641 1.3641 0. 1 1044 0.66480E-01 20 1 . 4960 1 . 4960 0. 1 1853 0.66480E-01 11:00 A.M. MAY 08, 1981 2.0122 0.88605 2.0122 0.88605 0.37370 0.10999 0.66480E-01 0.66480E-01 ID=TATU APPENDIX III (Cont'd) 20 1 . 3752 1 . 3752 0. 12056 20 1.0657 1.0657 0.43488E-01 0.66480E-01 0.66480E-01 20 1 . 5836 1 .5837 0.50496 0.66480E-01 20 1.3661 1.3662 0.14338 0.66480E-01 20 1.0688 1 .0689 0.47009E-01 0.66480E-01 20 1 .0820 1 .0820 0.78057E-01 0.66480E-01 20 1.1848 1.1848 0.34007 0.66480E-01 20 1.0223 1.0224 0.98717E-01 0.66480E-01 20 O.842 10 0.84210 0.29923E-01 0.66480E-01 20 0.92190 0.92190 0.74365E-01 20 1.1593 1.1593 0.97049E-01 O.66480E-01 20 2.4538 2.4538 0.61418 0.66480E-01 20 2 .0932 2 .0932 0. 37683 0.66480E-01 20 0.92445 0.92445 0.84536E-01 0.66480E-01 20 1 . 3409 1.3409 0. 12147 0. 66480E-01 20 1 .4774 1 .4775 O.11069 0.66480E-01 20 1.5766 1.5766 O.30463 0.66480E-01 20 1 . 1729 1 . 1730 0. 16229 0.G6480E-01 0.66480E-01 LISTING OF FILE TATU.2 11:00 A.M. MAY 08, 1981 ID=TATU APPENDIX III (Cont'd) 175 . 22 176 20 20 20 177 0 MEAN 0.83730 0.83805 0.88620 178 P MEAN 0.83730 0.83805 0.88620 179 0 STDV 0.28557E-01 0. 13251 0.13668 180 S ERR M 0.66480E-01 0.66480E-01 0.66480E-01 181 . 23 182 20 20 20 183 0 MEAN 0.89010 1.1935 1.3542 184 P MEAN 0.89010 1.1936 1.3542 185 0 STDV 0.30819E-01 0.12399 0.17009 186 S ERR M 0.66480E-01 0.66480E-01 0.66480E-01 187 . 24 188 20 20 20 189 0 MEAN 1.9958 3.7789 1.2075 190 P MEAN 1 .9958 3.7789 1.2075 191 0 STDV 0.53622 0.94894 0.13555 192 S ERR M 0.66480E-01 0.66480E-01 0.66480E-01 193 . 25 194 20 20 20 195 0 MEAN 1 .7162 1.1857 1.2886 196 P MEAN 1.7162 1.1858 1.2887 197 0 STDV 0.12965 0.16507 0.21138 198 S ERR M 0.66480E-01 0.66480E-01 0.66480E-01 199 . 26 200 20 0 20 201 0 MEAN 0.81135 0.0 0.96225 202 P MEAN 0. 81135 0.0 0.96225 203 0 STDV 0.74285E-01 0.0 0.19712 204 S ERR M 0.66480E-01 0.74326E-02 0.66480E-01 205 . 27 206 20 0 0 207 0 MEAN 0. 77485 0.0 0.0 208 P MEAN 0.77485 0.0 0.0 209 0 STDV 0.53995E-01 0.0 0.0 210 S ERR M 0.66480E-01 0.74326E-02 0.74326E-02 211 . 28 212 20 0 0 213 0 MEAN 0.92415 0.0 0.0 214 P MEAN 0.92415 0.0 0.0 215 0 STDV 0.60204E-01 0.0 0.0 216 S ERR M 0.66480E-01 0.74326E-02 0.74326E-02 217 . 29 218 20 0 0 219 0 MEAN 0.81320 0.0 0.0 220 P MEAN 0.81322 0.0 0.0 221 0 STDV 0. 13721 0.0 0.0 222 S ERR M 0.66480E-01 0.74326E-02 0. 74326E-02 223 0 Homogeneity of variance test 224 225 Ba r t l e t t Degrees Layard 226 Factors Chi-square Probability of freedom Chi-square Probabili 227 C,T 1820.0 0. 0 79 401.87 0.00000 228 C 42. 006 0. 00000 2 7.8845 0.01940 229 T 883 .06 0. 0 28 195.50 0.00000 230 OT i me for homogeneity of variance test was 0.89722E-02 seconds. Cumulative time 231 7 empty eel Is w i l l be ignored 232 0 Newman-Keuls test at 5% pro b a b i l i t y level Size warn 20.800 seconds. LISTING OF F 233 T 234 0 235 236 0 237 238 0 239 240 0 241 242 0 243 244 0 245 246 0 247 248 0 249 250 0 251 252 0 ( 253 254 o ( 255 256 o ( 257 258 o ( 259 o ( 260 o ( 261 0 ( 262 o ( 263 o ( 264 0 ( 265 0 ( 266 o ( 267 o ( 268 o ( 269 o ( 270 o ( 271 o ( 272 T i me LE TATU.2 11:00 A.M. MAY 08, 1981 ID=TATU APPENDIX III (Cont'd) 1 28, 3 17, 2 8, 2 8, 3 9, 3 26, 3 9, 3 26, 2 7, 13, 3 6, 1 27, 15, 1 26, 1 29. 1 22, 2 22, 2 20, 2 11, 1 19, 3 12, 3 22, 1 23, 2 21, 2 7, 13, 1 6, 3 6, 2 19, 2 6, 3 10, 3 13, 2 16, 2 17, 2 9, 1 8, 2 10 ) 1 26, 1 29, 1 22, 2 22, 2 20, 2 11, 1 19, 3 12, 3 22, 1 23, 2 21, 1 28, 3 17 1 6, 3 6, 2 19, 2 6,3 10, 3 13, 2 16, 2 17, 2 9, 1 8, 2 10, 3 14 ) 1 22, 2 22, 2 20, 2 11, 1 19, 3 12, 3 22, 1 23, 2 21, 1 28, 3 17, 2 8, 3 9, 3 26, 2 7, 13, 16 2 19, 2 6, 3 10, 3 13, 2 16, 2 17, 2 9, 1 8, 2 10, 3 14, 3 21, 1 7, 2 18, 2 25, 2 23 ) 1 19, 3 12, 3 22, 1 23, 2 21, 1 28, 3 17, 2 8, 3 9, 3 26, 2 7, 1 3, 1 6, 3 6, 2 19, 2 6 2 16, 2 17, 2 9, 1 8, 2 10, 3 14, 3 21, 1 7, 2 18, 2 25, 2 23, 3 24, 2 5, 1 12 ) 3 9,3 26, 2 7, 13, 1 6, 3 6, 2 19, 2 6, 3 10, 3 13, 2 16, 2 2 25, 2 23, 3 24, 2 5, 1 12, 3 25 ) 3 6, 2 19, 2 6, 3 10, 3 13, 2 16, 2 17, 2 9, 1 8, 2 10 1 12, 3 25, 3 18, 3 7, 3 23 ) 2 6, 3 10, 3 13, 2 16, 2 17, 2 9, 1 8, 2 10, 3 14, 3 21, 1 7, 2 18, 2 25, 2 23, 3 24, 2 5, 1 12, 3 25 3 18, 3 7,3 23, 1 20, 2 15 ) 3 10, 3 13, 2 16, 2 17, 2 9, 1 8, 2 10, 3 14, 3 21, 1 7, 2 18, 2 25, 2 23, 3 24, 2 5, 1 12, 3 25, 3 18, 3 7, 3 23, 1 20, 2 15, 2 13, 3 8 ) 2 17, 2 9, 1 8, 2 10, 3 14, 3 21, 1 7, 2 18, 2 25, 2 23, 3 24, 2 5, 1 12, 3 25, 3 18, 3 7, 3 23, 1 20, 3 10, 3 13, 12 ) 17, 2 9, 1 8, 2 10, 3 14, 3 21, 1 7, 2 18, 3 14, 3 21, 1 7, 2 18, 2 25, 2 23, 3 24, 2 5, 2 25, 2 23, 3 24, 2 5, 1 12, 3 25, 3 18, 3 7, 3 23, 1 20, 2 15, 2 13, i . 3 24, 2 5, 1 12, 3 25, 3 18, 3 7, 3 23, 1 20, 2 15, 2 13, 3 8, 1 4, 3 18, 3 7, 3 23, 1 20, 2 15, 2 13, 3 8, 1 4, 3 11, 3 19 2 1, 1 25 ) 2 15, 2 13, 3 8, 1 4 ) 1 8, 2 10, 3 14, 3 21, 1 7, 2 18, 3 8, 1 4 , 3 1 1 ) 3 14, 3 21, 1 7, 2 18, 2 25, 2 23 3 11,319, 121, 1 1 5 ) 1 7, 2 18, 2 25, 2 23, 3 24, 2 5, 1 12, 3 25, 121, 115, 1 1 3 ) 3 25, 3 18, 3 7, 3 23, 1 20, 2 15, 2 13, 3 8, 1 4, 3 11, 3 19, 1 21, 1 15, 1 13, 3 20, 1 9, 2 14, 2 4 ) 3 18, 3 7, 3 23, 1 20, 2 15, 2 13, 3 8, 1 4, 3 11, 3 19, 1 21, 1 15, 1 13, 3 20, 1 9, 2 14, 2 4, 3 4 ) 3 8 , 1 4, 3 11, 3 19, 1 21, 1 15, 1 13, 3 20, 19, 2 14, 24, 3 4 , 2 1 ) 1 4, 3 11, 3 19, 1 21, 1 15, 1 13, 3 20, 1 9, 2 14, 2 4, 3 4 3 20, 1 9, 2 14, 2 4, 3 4, 2 1, 1 25, 3 2, 2 3 ) 2 1, 1 25, 3 2, 2 3, 3 3 ) 3 2, 2 3, 3 3, 1 24, 2 12, 3 16 ) 1 24, 2 12, 3 16, 2 2 ) 3 15, 3 5, 1 14, 1 18 ) 1 2 ) 1 16, 1 1 , 1 17, 3 1 ) 2 24 ) 1 10 ) 1 11 ) Time for multiple range test was 2.7384 Execution Terminated 11:00:05 T=0.09 RC=0 $.32 seconds. Cumulative time is 23.540 seconds. Transect RR No. APPENDIX IV / TABLE A3.1: Summary: Spectral reflectance ratios and biophysical c h a r a c t e r i s t i c s variables data for Kajiado study area: J u l y - August, 1980* FW . DW „ (gra/m ) (gn/m ) LW DGM(%) CP(%) CF(%) CEST(%) GREN(%) VHT WA(%) GVI (meters) BD HD 03 05 11 17 20 36 39 44 46 65 67 69 E F N S T X 1.699 579.54 297.01 2.827 628.48 318.21 1.633 263.04 1.032 147.74 1.375 137.34 1.2.29 232.54 1.184 239.04 0.944 346.04 0.986 0.841 0.922 100.04 0.811 190.04 168.77 118.75 76.66 153.10 143.09 281.61 57.22 44.64 58.88 111.24 268.04 184.37 420.54 367.87 85.43 63.34 1.032 1.173 0.930 415.65 281.44 1.066 63.04 0.886 45.84 1.578 426.84 32.91 26.90 253.04 282.53 95.66 310.27 95.33 94.27 95.94 28.99 95.29 60.68 95.10 79.44 95.40 95.95 95.06 64.43 95.60 28.21 95.71 18.70 95.72 41.16 95.42 78.80 95.24 83.67 95.15 52.67 95.29 134.21 30.13 18.94 95.63 94.14 96.00 168.80 95.86 5.86 5.05 4.59 10.98 8.42 4.95 3.31 2.81 3.53 . 6.04 5.48 5.01 2.92 3.30 4.70 4.72 3.66 2.03 34.44 30.84 35.88 30.85 34.37 31.67 30.58 32.04 33.91 36.19 32.83 33.41 41.97 34.81 37.42 35.46 31.60 35.49 67.30 68.00 52.50 54.00 55.00 40.50 38.50 69.30 34.50 35.50 26.00 50.50 57.00 79.50 48.70 35.30 14.00 73.60 64.50 85.10 41.50 12.30 13.50 48.00 15.50 15.20 32.70 28.50 52.00 69.00 29.50 14.50 45.00 76.00 0.405 0.520 0.310 0.328 0.243 0.280 71.20 0.633 69.10 0.980 0.275 0.260 0.284 0.390 0.275 0.590 0.273 0.317 0.057 0.909 35.00 0.282 8.611 27.257 45.00 0.153 9.242 35.360 45.00 0.262 5.010 16.275 25.00 0.084 2.736 17.712 25.00 0.121 2.497 13.365 25.00 0.111 5.742 11.340 35.00 0.184 6.209 24.371 35.00 0.096 4.993 67.914 25.00 0.105 2.476 9.488 25.00 0.030 1.784 9.230 25.00 0.074 3.848 7.384 25.00 0.074 3.763 19.695 45.00 0.098 4.702 15.675 35.00 0.102 5.290 46.905 25.00 0.077 8.535 13.295 15.00 0.043 1.786 11.190 25.00 0.110 3.274 0.798 35.00 0.308 5.799 66.902 * The names of the variables i n t h i s table are l i s t e d on page X. 

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