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vi 7 Coastal Zone Information SHORELINES Center A COASTAL ZONE MANAGEMENT PROGRAM MAY 5 1976 DESCRIPTION AND ANALYSIS OF A MACRO LAND USE MODEL (MACLUSE) by K. C. Swanson R. P. Paquette MAY ae. Irm m*Y a, Irm MY am. 1975 BASIN No 3 WIN No 3 WIN -0 3 00 MILE 1.0 3 70 141LE No . 1. m1v NO 3 MAP SCALIE 3 " .0 W MCA" 3 " 10 MW LE 3 ".mIVjM @D AMID= Mft-m 'TTMSCA Ivim mv4-ED Ultz"TIALs Ou"Im-3 FIEDUML COMPIIERCIALI-08 % :S .4 % MAY im K"IN No 3 00 MILE No 4ft RW *c^L9 iS 00 4 *mmm RAPP" Commmift 1-" @UNIVERSITY OF WASHINGTON F,, Z',ZENTER for-QUANTITATIVE SCIENCE 0 in FORESTRY, FISHERIES and WILDLIFE Prepared for the /4 WASHINGTON STATE DEPARTMENT OF.ECOLOGY DESCRIPTION AND ANALYSIS OF A MACRO LAND USE MODEL (MACLUSE) SH04 by K. C.' Swanson R. P. Paquette June 1974 This is an informal report of@preliminary research results supported by University of Washington Sea Grant and the Washington State Department of Ecology. It is intended for internal use only and no distribution or reproduction should be made without permission from the project office. Project Director: -L. J. Bledsoe Center for Quantitative Science University of Washington Seattle, Washington- 98195 S. TABLE OF CONTENTS INTRODUCTION 1 I. PROGRAM ELEMENTS 2 II. DATA BASE 4 III. BASIC M06EL MECHANISMS 8 IV. MATHEMATICAL CONSTRAINTS IN THE MODEL 9 1, VERSION 1 12 2. VERSION 2 15 COMPUTER OUTPUT 22 3. VERSION 3 26 COMPUTER OUTPUT - -Example .1 27 COMPUTER OUTPUT - Example 2 32 COMPUTER OUTP17T Example 3 37 V. CONCLUSION 42 TABLES & GRAPHS .TABLE I Description of Primary System Variables .................. 3, 2 Description of Auxiliary variables, Driving Function s and Parameters .......................................... 5 3 Correlation between Snohomish County Inventory Land Use and MACLUSE Categories ............................. 6 4 Interaction Matrix ....................................... 10 5 Program Equations ........................................ 11 6 Version I Flow Chart ..................................... 14 7 Version II Flow Chart ..................................... 17 8 Version III Example 1 Input Data .......................... 27 9 Version III Example 1 Relative Dollar Values and Allowable Transfers .................. *'*** . 2.8 bl 10 Version III Example I Program Output: Value of Varia es Through Time ........................................... 28 11 Version III Example 2 Input Data .......................... 32 12 Version III Example 2 Relative Dollar Values and Allowable Transfers ......................... 33 13 Version III Example 2 Program Output: Value of I Through Time ............................................ 33 14 Version III Example 3 Input Data ......................... 37 1.5 Version III Example 3 Relative Dollar Values and Allowable Transfers ..................................... 38 16 Version III Example 3 Program Output: Value of Variables Through Time ............................................ 38 GRAPH 1 Changes in State and County Populations (Version 2) ....... 24 2 Changes in Eight Land-Use Categories (Version 2) ......... 24 3 Version III, Example 1, Projected Residential Chanqe ..... 29 4 Version III, Example 1, Projected Recreational Change .... 30 5 Version III, Example I .................................... 31 6 Version III, Example 2, Projected Residential Change ..... 34 7 Version III, Example 2, Projection Recreational Change ... 35 8 Version III, Example 2, Changes in Natural v. Conservation/Rural - ................. 36 -9 Version III, Example 3, Projected Residential Change ..... 39. 10 Version III, Example 3,.Projected Recreational Change .... 40 11 Version III, Example 3, Changes in Natural vs. Conservation/Rural ..................................... 41 Introduction Land use decisions must be made continuously by local. governments. Models have often been used to help determine the possible effects of alternative decisions. The purpose of this effort is to-create a land-use model that would meet the needs of local jurisdictions faced with a variety of specific shorelines problems. The Macro Land,Use Model (MACLUSE) was developed to achieve this objective,as quickly as possible. MACLUSE is a computerized system designed to describe the transfer of land among land-use categories through time. Eight categories were identified as basic to shorelines. Data for the model were derived from "experts" who are in a position to project the needs of a category into the future. In this study three versions.have been developed-- the initial version and two subsequent modifications. Snohomish County is the geographic area covered by the analysis. 2 I. Program Elements Table 1 describes the eight land-use categories which form the primary system variables (PSV's) of the model. The following criteria guided the selection of the eight land- use categories: a) Choose categories which roughly corresponded to those used in the various county inventories, so that the existing data base can be most easily utilizedi b) Choose categories which would be meaningful in terms of planning land-management strategies. That is, categories which are considered important or significant to the people who will ultimately use the model to plan shoreline development. c) Choose categories br,Dad enough to include all pcrssible land uses ion a county's shoreline. In modeling jargon, the -primary system variables (PSV's). are the variables of primary.interest in the system being simulated. The principle objective of the model, then, is to calculate values of the PS'V1s as a function of time, Auxiliary variables, driving functions, and parameters of the model. The auxiliary variables are functions of time and their values at -a point in time depend on the current state of the system. The driving functions, on the other hand, are Also 3 Table 1. Description of Primary System Variables. 0 o Definition Primary System Variables V1 RES miles Residential land platted.for residential use (single and multiple units). V2 REC miles Recreational - land sustaining non-private., high-d(-@@nslty, recreational use., V3 NAT miles Natural - land sustaining very low density, non@private -use whi,ch seeks to maintain .land in its natural state. V4 CONR miles Conservancy and Rural - Farmland, open space, land used for renewable resources with little non-reversible change. V5 SHDI miles Shoreline Dependent Industrial - any industry that must be located on the shoreline to function. V6 SHDC miles Shoreline Dependent Commercial - any commercial operation that depends on a shoreline location to receive trade. V7 TRANS miles Transshipment - any cargo loading, receiving or storage facility dealing with water traffic and located on the shoreline. V8 NSHD miles Non-Shoreline Dependent Development - any development (industrial or commercial) that is not dependent on a shoreline location but may be located there all the same. 4 functions of time but depend on factors extrinsic to the I system for their value at a point in time, The parameters are simply constants whose values are independent of the current state of the system. Table 2 lists the auxiliary variables, driving functions and the parameters used in the MACLUSE model. II. Data Base, A. Initial values for the eight primary system variables were obtained from the Snohomish County Inventory Summary (January 1,1973). These were considered to be the state of the system on January 1, 1973. Since the categories used in the Inventory Summary did not correspond precisely to the eight MACLUSE categories, a rough correspondence in percentages between overlapping categories was determined in an interview with Mr. John E. Galt, Snohomish County Planning Department. The results are listed in Table 3. B. Since the model was.a preliminary effort designed to acquaint the authors with certain characteristics of shoreline models, data upon which projections are based were derived from.the experts'. "mental model" approach, the authors' intuition and an interaction matrix. The interaction matrix was developed from expert opinion in a brainstorming session at the University of Washington. 5 Table 2. Description Of Auxiliary Variables, Driving Functions and Parameters 0 ly 0 ly 4@2 C" a� Definition Auxiliary Variables FLDD FLDD Dollar damageto RES, CONR, and NSHD as due to a 100 year flood. PTI PTI Propensity to industrialize. Driving Functions CPOP CPOP 1000's County population (Snohomish County). SPOP SPOP 1000's Washington State population. Parameters PTR PTR Propensity to recreate. A A $/mile Dollar per mile flood damage to CONR- B B $/mile Dollar per mile flood damage to NSHD. C C $/mile Dollar per mile flood damage to RES. NT Number of. time periods over which model,is run. .NCOM Number of primary system variables. Yl Initial time point (year). 6 Table 3. Version III, Example 1, Projected Residential Change Snohomish County 'Shoreline Inventory Length in Percentage Correspondence to Category Miles MACLUSE Categories Residential 143.36 RES (100%) Commercial 6.72 SFIDC (80%), NSHD (20%) Industrial 40.83 TRANS (10%), SHDI (20%), NSHD (70%) Service .78 NSHD (100%) Recreational 26.55 REC (100%) Circulation NSHD (iOO%) Utilities 11.33 NSHD (100%) Agriculture 176.53 CONR (100%) Comm. Forest 347.96 CONR (100%) Undeveloped 412.95 NAT (100%) 1219.23 C. Data on changes in the transshipment category over 5 years were obtained from Mr. Dennis Gregoire, a planner with the City of Everett (Enc' Department). rineering Year Piers Warehouse- 1960-1972 890 ft- 450 ft. 1973 990 ft. 450 ft. Based upon the "mental model" of a planner with the Seattle Port Commission the process used for projecting future changes is contingent upon historical trends. The implication is that future changes-in transshipment (TRANS) are equal to the average of the changes in five previous years. Therefore, .the above data was interpreted as a change of 100 ft. in five years or 20 ft. .004 mile each year. 7 D. Data on amount of, damage expected from a 100 year flood in Snohomish County were obtained from Mr. Bob Hamlin, Department of Emergency Services, Snohomish County. Total Damage to Damage to Damage to River System Damage $ Buildings (RES) Agric. (CONR) All Other (NSHD) Snohomish 16,980,000 35% 5,943,000 45% 7,641 '0001 20% 3,396,000 Stillaguamish 3,355,000 50% 1,677,500 39% 1,308,450 11% 369,050 Total 20,335,000 7.16.20,500 8,949,450 3,765,050 For Snohomish River, percentages were given as 26% Agric. and 19% - Dikes, which were combined into the 45.% figure shown. These data were used to obtain'dollar/inile 'damage coefficients for the 3 categories (Residential, Conservancy and Rural, and Non-Sboreline Dependent Development) in which flood damage is considered to occur. E. Population statistics for Snohomish County and the State of Washington were obtained from the Washington State Bureau of Vital Statistics. Data obtained are tabled below. Year 1970 1975 1990 Snohomish 265,300 285,000 409,000 County Washington 3,427,200 3,925,8 00 5,445,100 State A linear interpolation was performed to obtain population figures for intermediate years. 8 III. Basic Model Mechanisms MACLUSE is designed to calculate new values for the primary system variable of past values, selected parameters aInd the driving functions. Thus,. if Vn M = value of n th PSV at time j, then V n(j) = Vn (i-l)+AVn(j), where,AVn(j) is the change which occurred between time j-1 and time j. It was necessary as a first step to postulate which factors influence the values of the primary system variables at the current time point, as well as what factors influence the change in the primary system variables between the previous and the-current time point. The potential affecting factors include both the values of the PSV's at the previous time point and the values of the changes in PSV's between previous time points. The interaction matrix (see Table 4) is a convenient way of representing these postulations. The "affectees" are the current, values of the PSV's (states at time J) and the changes in PSV's between the previous and current time points (changes between time (J-1) and time (j)). These head the columns of the matrix. The "affectors" are the values of the PSV's at the previous time point (states -at time J-l) and the changes in PSV's over the previous 6 years. The matrix may be read as follows: for any category at the top of the matrix, look down the column beneath it. The X's indicate which factors are postulated to be those 9 "interacting with" or influencing the value of the category. Note the interaction matrix says nothing about the exact form of the relationship between the category and its influencing or "interacting" factors. This information is provided by the.equations of Table 5 for those factors influencing the changes in PSV's. The weight, to be given to each influencing factor,.as represented in the! equations, was determined from expert opinion and intuition. Returning to the general. equation of the first paragraph, Vn(j) = V n(j-l)+AVn(j), it becomes apparent that the interaction matrix describes the -s-ame pro-@cess (for example, RES (J) is influenced by RES(J-1) and ARES(J)). It furth Ier indicates which factors influence AV (j); an equation of Table 5 says n how AV (j) is affected by these factors. n IV. Mathematical Constraints in the Model The set of mathematical constraints in the model include: 1) The amount of land in any category must never become negative. 2) The sum of changes between categories in any one year (or unit time period) must be zero, i.e. total land amount should remain constant throughout. the time period over which the model.is:ruh.:, @3) A particular type of' land must not take land from itself, i.e. only transfer's among different land 10 Table 4 Interaction Matrix Changes betWeen time (J-1) and.time J States at time i affectees U E--i 2 0C@ UO C C) W W 0 := = C4 U) Cn U E-4 z C@ C@ affectors a@ C!@ u 14 W E_ ;j@ @ :@ 0 = - .:Jl<,<,< -Ili <@ < 1<j MU'LO UQ E-qjZj jr@41 J-6 to ASHDC(J-5) X I I I I I I I I 1 1 J-5 TTRANS(J-5) X 11 J-5 to A sTI-D c-Tj-- 4 ) X H J-4 TTRANS(J-4) X 11 J-4 to AS11DC (J-3) X I I J-3 ATRANS (J - 3) J-3 to AS11DC(J-2) j-2 ATRANS(J-2) J-2 ASHDC (J-1) to ATRANS(J_1) ANSI-ID(J-1) @J-l AREC (J-1) RES(J-1) REC(J-1) NAT(J-1) 41 CONR(J-1) 4J SHDI FJ-1) SHDC(J-1) TRANS(J-1) 4J NSfID(J-1) 4J U) SPOP(J-1) CPOP(i -1).. ARLS(J) I 'II A R-E C (J) ANAT(J) 4J t-3 ACONR(J) 1z AS11DI (J) 0) (D E-: AS11DC (J) rA T7r_R_A_N_S7 J) ANS11D (J) U) IrV3 Aspop(j) r -1 ACpop(j) (a Prili (J) JPTR (J) Table 5.' Equations used to describe changes in demand for 8 land-use cateqories. PSV Acronym Equation for change in PSV for interval ending at time I (IDV(I), I=1,NCOi%l) vi RES ARES(I) = 5.*'@CPOP(i)- * (NAT(I-1)+CONR(I-1)] CPOP(I-l) if ACPOP(I)>O = 0 if ACPOP(I)<O V2 REC AREC(I) = PTR* REC(I-I)*[ CPOP(I)+ACPOP(I) CPOP(I) [SPOP (I) +ASPOP (I) SPOP(I) V3 NAT ANAT(I) -(l,/3*ARES(I)+1/3*AREC(I)) V4 CONR ACONRM -(:2/3*ARES(I)+2/3*L@REC(I)+PTI) V5 SHDI ASHDI(I) = -.131*SHDI(I-1)+PTI I-1 V61 SHDC ASHDC(I) = 1/:5* E ASHDC(J) J=I-5 V7 TRANS ATRANS(I) 1,/5* E ATRANS(J) J=I-5 V8 NSHD ANSIID(I) .1*ANSHD(I-1)*[CPOP(I)+ CPOP 1 3 CPOP(I) FLDD FLDD(I) = A*C,DNR(I-1)+B*NSIID(I-1)+C*RES(I-1) PTI PTI SPOP(I)-SPOP(I-1)* ASHDI(I-1) SPOP (I-1) 12 use types are considered, not transfers within a single category. 4) Transfers of land may not occur from more expensive categories to less expensive categories. 5) If the least expensive transfer cannot satisfy the amount of land called for by the equation no further attempt is made to satisfy this demand by taking land from the next least expensive categ ory. How each successive version of the model satisfied, or did not satisfy, these constraints will be discussed in following sections. The fourth and fifth constraint were added upon evaluation of Version 2 of the model. 1. Version 1 A. Explanation of Mechanisms The first version consists of a main program and four subroutines (INPUT, SOLVE, DIFF, ADD). The program flow and transfers in and out of the various subroutines is represented in flow chart Version I is fairly straight- forward; only the standardization of the changes in the primary system variables referred to as AV(AVn ) needs elaboration. This standardization is necessary due to the constraint to keep the total number of shoreline miles constant. 13 The standardization of the DV's in subroutine DIFF works as follows: Let vn (i) = sys tem variable n at time i. DV (i+l) change in system variable n from time i to i+l n Y (not standardized) Constraint (2) can be formulated for Snohomish County as Z Vn (i) = 1219. miles at any time i n Then the standardized change is DV*(i+l), where n E (Vn (i)+DVn(i+l) Sum n SUM (V (i)+DV (i+l) = G' (i+l) 1219. n n n G (i+l) -V (i) = DV* (i+l) n n n V (i+l) = V (i)+DV*(i+'L) n n n Then we also have EV n (i+l) 1219. at time i+1 n B. Problems with Version I The standardization package used in Version 1 satisfied constraint (2) of the model, but violated constraint (1). That is, land amount in some categories was allowed to go negative when DV*(i+l) was negative and greater in absolute n value than V n(i). 14 Table 6. Flow Chart I 77 @17 7 2. Version 2 A. Explanation of Mechanisms Changes in Version 1 incorporated into Version 2 are described below and illustrated in Flow Chart II. 1) Subroutine INPUTi, which reads a vector D of dollar values for each of the eight land-use categories and a matrix F of allowable land transfers. The elements of.F are f Olif land transfer not allowed from ij= category j to category i (1 if transfer is allowed By convention, all diagonal elements are zero. This satisfies constraint (3) of the model. If i's occur on all off-diagonal elements, this implies a no-policy situation (all transfers are allowed). If O's occur on off-diagonal elements, existence of policies preventing certain transfers from occurring is implied. 2) In subroutine DIFF, the standardization package is removed. For sake of clarity, it should be noted that the DV's calculated in DIFF do not represent final changes in PSV's; these are now calculated in sub- routine DIFF2. Rather, the DV's in DIFF now represent demands for chancre in the eight categories; they indicate how much change each.cateqory would "want" to undergo between time points if there were no constraints to change. 16 3) For a particular land type, subroutine IMATR chooses from the allowable transfers to that type the one which will in fact occur, based on economic constraints. In effect, it chooses the least expensive of these allowable transfers. To do this for the i th land type, it multiplies the i th row times the vector D of dollar values, then chooses the smallest non- zero element of the resulting vector (which is the th i row of matrix FF). This element is then assigned a new value which is either the amount of land avail- able in the chosen donor category or the amount of land desired (calculated in DIFF), whichever is smaller. All other elements in the row are converted -th to zero. Thus, the i row of FF becomes the vector of actual land transfers into the i th category. After this is done for all rows, the Fr matrix is complete except for the diagonal elements. These mustreflect the land removed from each category. This is done by simply summing along a particular column of FF and assigning the negative of this sum to the diagonal element of that column. 4) Subroutine DIFF2 adds the losses and gains for each category determined in MATR. To do this, it simply sums across the rows of FF to, get total changes for 17 Table 7. Flow Chart II Subro,,,,tine read control -ca-l c7u -1a t e c --7L " parame ters in' cf@@k CIALL 17" rioz) d V(1), DV', OV3 alculate i)Vl, Fc 1: S, e s C',L i@:! -"j 1,1 r al d d ol 1 a, r - F,711@7u la te P fI value vector D I I niatrix F of allow- ulate DVf* D able land-transfer @calc L;i.-IL ADD V (1) I=l 11,7@;,, F calcuiate i)V6 J=l D V -V, subroutine SLLVt:, CALL J=j+1 V(1),O.) ,D C 11cula ';c FL.DD ..)Ubrouine ALL output FJ V(I),I=l A im no IT ? "ubro-ut- i-ne D `2 yes ..D V(I)=V(I)i-'DV(I*', sul@,, C. Ff 1 7 J) + return 0=1, !:";L;Il no r yes. L- rcturn @J= i @11 yes Table 7 (cont.) Subroutine-JI'l"R 18 CA =@:=ia x (1) J- 1 F(IIJ) D(J) "TII(I,j) C, e.s -F( I,J]'=2. -x Y. X 110 T 7c tj - 11 CM?--- D- - - --@, E yes B=m ill U."I "es min(V(j ) @.DV (1) J=N'CC.N,? yes no j 1 + -.SUM ? @j j 1 > "C.- cs C",@ re tijrn 19 each row* These are the DV's, or final changes in PSV's between time points, In subroutine SOLVE these are added to the PSV's (V(I)ls) to get the new values for the PSV's. B. Problems with Version 2 Version 2 satisfies constraint (2) by assigning a negative value to diagonal elements of FF, equal to land loss in each category. Thus, total land amount will stay constant. It satisfies constraint (3) by making the diagonal ele- ments of F equal to zero, i.e. a category cannot take land from itself. It does not satisfy constraint (1). As land is taken from a category, the amount left in that category is not changed. Consequently, you can take more than is there, i.e. several land types ca,n take the same amount of land -from a category, driving it below zero. Furthermore, Version 2 allows the transfer of land from more axpensive to less expensive categories. This is unlikely to occur in.the real world. Hence, a fourth constraint in the model would bethat this is not, allowed to occur. Also, if the least expensive transfer cannot satisfy the land amount "wanted" by a category (i.e., for transfer from category j to category i, V(J)<DV(I)), then no furtherattempt is made-to satisfy this demand by taking land from the next 20 least expensive category, etc. This should be added as a fifth constraint in the model. C. Output from Version 2 Following is a copy of output from Version 2 for a 13-year run starting at 1.973 as the initial time point (Yl). Note (1) Input data values State population projected statistics (SPOP) and county population projected statistics (CPOP) for Snohomish County are printed forthe 13-year period. These are followed by the 1973 values for the eight primary system variables (vector V), the vector DV of tendencies to change as calculated in subroutine DIFF for 1973, and the matrix DW of changes in the five years preceding 1973 in the categories S11DC (V06) and TRA14S (V7) . Note (2) Input.values for dollar values and matrix The dollar-value vector D for the eight cate- .gories is printed. These were arrived at by an arbitrary, intuitiveranking. They are followed by the matrix F, which.indicates allowable land transfers. The columns and rows are ordered in the manner used throughout this documentation,.i.e. RES, RECO NAT, CONR, S11DI, S11DC, TRANS, NS11D. 21 Thus, a "l" in F(3,4) indicates land transfer is allowed from category 4 (CONR) to category 3 (NAT). Choices for these values were also arbitrary at this stage. Note (3) Output for 13-year run Year 1 is the initial year (1973); note these values correspond to input data values for vector V. For years 2 through 14, values for vector V of the eight primary system variables are given, as,well as a value for FLDD (dollar damage as due to a 100-year flood). Note that negative values occurred in the NAT category, and also that it gained land although it is the least expensive category. These problems were discussed in the preceding section. CALCULATION OF MILE!:! CF SHORELINE 13Y.CATEGORY 8 CATEGORI.-':.S CALGEVERY i YRS FROM YR I FOR 13 YPS 22 Q INPUT DATA VALUE.S SpOp'f-CpOp,-----vt 3.7383E+66 3.@3,'-10E+06 3e925BE+06 4*0195E+06 4.11--2E+06 SfDf' 4.2067;-:+C,6 4*3C@6E+06 4,3943E+06 4*4991E+06 4*6C44E+C6 4.'7595E+ .66 4 -, A145=+C6 4 9 19 C-;:' + .9 6 2.6350E+05 2*767 -C7+C5 2.3560E+G5 2.9330;-:+65 3.5150E+05 .3.429CE+05 3 398@E+C,5 3.131 6 5 3 6 3 J E * 0 -5 3,346CC 3*5110E+05 3. 5 9 L+ 0 9 3.677oc-+G5 143.4 26.55 413*0 527o5, B*i2p- 5.356 4 . 2 7. 160 9 0 0. -0 . I)v _00 . 940 1766 . 17 66 0 .1760 .1760 4:0u'-00E-C3 4 2" 0 C- E 0 3 4.CC.C:OE-03 4.96GOEE-C.3 4 . 0,@, 0 r E- G 3 TrAtJS r))INPUT VALUES FOR-DOLLAR VALUES AND VATRIX ice 00 1 0 0 0 10 . a C 19.00 13.0-i D r '15 0 0 a 0 j 3 o 0 0 -0 --o' 1 1. -0 C. -0 1 i 1 -0 1 1 1 -0 ni -0 C -0 C C- s,., i e- o G -0 1 Zo -0 0-YR RES R E C NAT C 0 14 R SHOI SHOC TR@i4S N 0 FLDD -14@@.4 26*5 413.0 527,5 B 0 1 5o4 4 * 1 94 3 2 287.0 27.7 268.1 527.5 all 5.4 4.2 94.4 .2572115" 3 1*10 . a 29al 143,4 5 '-' 7 s 5 8.1 5*5 4 a 94o4 3 -'-' 8 5 7 8 7 ? 4 510*6 314.1 40,7 527,5 all 5.7 4.3 94*4 38697972 5 551.3 33.3 527.5 8.1 508 4.5 94.4 41661346 6 54897 3 0 s, 7 (1' 2 =.9 5 '214 . q, 5.5 3 1 . 9 94.4 4 0885-305 7 5-61.7 30.7 2- 5 2 4 -9 5 * 5 3.4 2. 0 94.4 41635819 6 561*4 30.5 it 2 5 2 4 7' 5.3 3 o 1 1.7 94*4 41619818 9 561".6 30,5 3 -5 "? 4 7' 5*3 3.3 1-4, 9 9404 41688037 to 562.4 304 2 1.3 2 4 5.0 3.0 116 94,4. 41670854 11 563.6 3 2 5 2 4, 5.0 3.2 1.7 94*4 4 17 4 111 12 563*4 30.0 1.'-' 524o;! 4*8 209 1*5 94o4 41727231 13 564.6 0 0 2 5 2 4 62 4*8 3*0 it 6 94.4 4179919-3 23 D. Analysis of Sample Output F DV D RESI REC NAT CONR SIM SHDC TRANS NS11D in it ial RES 0 0 1 1 0 0 0 1 7.16 15.01 REC 1 0 1 1 0 1 1 .9 1110.01 NAT 0 1 0 1 0 0 0 0 1.01 .CONR 0 1 0 0 0 0 0 0 10.0 SHDI 1 0 1 1 0 1 1 1 0 1960 SHDC 1 0 .1 1 1 0 1 1 0 18.0 TRANS 1 0 1 1 1 1 1 0 20.0 NSHD 0 0 1 1 0 0 .94 3.01 =0 The policies reflected by this F-matrix and D-vector are as follows: M Industrialcategories are most favored (SHDI, SHDC, and TRANS) by both F and D (2) NAT and CONR are least favored (3) RES is more restricted than the industrial categories in the number of categories from which it is allowed to draw, but has a relatively high dollar-value rank 24 Graph 1 Changes in State &'County Populations 5.0 @4.5 spop (X106 4.0 0 .H -P m 3.5 r-4 0 04 CPOP (X105) 0 P4 3.0 2.5 ;:1973 1980 1986 Graph 2 Chanqes in Eight-Land-Use Cateqor,ies 600 5 00 CONR 400 4 0 U) 44 0 300 U) 200 NAT. 100 NSHD @Spop (x,06) REC: S H Dl 1973 1980 1986 2 5 The most drastic changes occurred in the RES and NAT categories. Note that the initial DV for RES was extremely high compared to the other categories and that the NAT category had an extremely low dollar-value ranking compared to the other categories from which RES could draw. Thus, the RES category had a very strong "pull" and would return to the NAT category each iteration to fulfill it's "desire" for land. The other category that achieved any significant increase over the 13-year period was REC (3 miles). Note that this category had an initial DV of .9, considerably less than RES. It, too, would go first to NAT to draw land, thus increasing the drain on natural land. NS11D was the only other category to increase, but only by one-tenth of a mile. It was also the only other category to have a positive initial DV (.94). It could draw from SIM and SHDC, which partially accounts for their decrease. All other categories had an initial DV of 0. Note that the industrial categories,.all highly favored by the F policy matrix and the D dollar-value vector, all showed a steady decrease. It thus appears that the DV vector (of "tendencies" to change based mainly on population changes)-is of much greater significance than,F or D (i.e. economic factors) in determining 26 what changes actually occurred. This may indicate a need for revision of the basic model mechanisms. 3. Version 3 A. Modification of Version 2 Needed modifications to the model, as indicated in the discussion of problems with Version 2, were incorporated into Version 2. These included the following: a) Land was ranked in ascending order by dollar value, and as a category made allowable land transfers to itself, it drew sequentially from these ranked categories until its "need" was satisfied; b) A category was not allowed to draw land from a category more expensive than itself; c) When.land was drawn from a category, the amount left was adjusted to reflect the loss. B. Output from Version 3 There are three examples of output produced by Version 3, each of which represents the outcome of the simulation of different land Use policies. Each output contains a listing of initial input values followed by a table of land- use change in the eight categories over a thirteen-year time span. Those are followed by three analytical graphs, the first two of which depict how a single variable changes 27 over time., The third depicts how variable 3 (natural land type) varies with variable 4 (conservatory--rural land). This graph shows the threshold nature of the relationship between the two variables. 1. The first example indicates what might happenif present policies (as controlled by the matrix of allowable transfers) are allowed to continue. The sample output and analytical graphs follow. CALCULATION OF MILES OF SHORELINE BY CATEGORY 8 CATEGORIES CALC EVERY 1 YRS FROM YR 1973 FOR 13 YRS Table 8 INPUT DATA STATE AND COUNTY POPULATIONS YEAR STATE POP COUNTY POP 1973 3738300 268500 1974 3832000 276700 1975 3925800 285000 1976 4019500 293300 1977 4113200 301500 1978 4206700 309800 1979 4300600 318100 1980 4394300 326300 1981 4499100 334600 1982 4604400 342900 1983 4709500 351100 1984 4814500 359400 1985 4919600 367700 INITIAL STATE VARIABLE VALUES V-S 143.4 26.5413.0527.5 8.1 5.4 4.1 94.3 DV-S' 7.2 .9 -0.0 -0.0 -0.0 -0.0 .9 28 Table 9 RELATIVE DOLLAR VALUES AND ALLOWABLE TRANSFERS CATEGORY RES REG NAT CONN' SHOI SHOC TRAN SHOG 15 io 1 10 ig 18 20 3 1) -0 -0 1 1 -u -0 -0 1 2) 1 -0 1 1 -0 1 1 1 4 3) -0 1 -0 1 -0 -0 -0 -0 4) .-0 -0 1 _0 _0 -0 _0 -0 5 1- 0, 1 1 u I I I 6) 1 -0 1 1 1 -0 1 1 7) -70 6) -0 -0 -0 -0 1 1 -0 -0 Table 10 THE OUTPUT GENERATED BY THIS PROGRAM CONSISTS OF A TAULE PRESENTING VARIABLE VALUES THROUGH T I -H-E. A NO ONE TO SEVERAL GRAPHS, YEAR RES RtG NAT CONR---SH01- - -SHOC-, T.RANS FLOD - 1973 14J.4 2 b.'5 413.0 527.5 8.1 5.4 4.1 94.3 2 8 7 . 0 2 7.17 - ? -.--.94 . 3__ 2 5717276 1975 410.0 29.1 143.4 527.5 8.1 5.6 4.2 94.3 32853598 lw6 510.6 31.0 40.7 527.5 8.1 508 4*3 94.3 38693657 191Z 592.4 33.3 u 527.5 8.1 5.9 4.5 50.7 41693612 1976 667.0 0.0-5.uo 4 .6 .0 43726981 1979 735.9 159013 0.0 427.5 8.1 6*2 4.7 0.0 46993820 19SU 792.4 44. 0. 0 366.1 8.1 6.3 4.8 0 . 0 49661147 1961 840.2 5U*4 0.0 31Z.2 8.1 605 4,4 0.0 51892623 19d2 8714.9 57.8 -10 . 0-264 . 9 8. 1 6.6- -5.0 0.0 537223tti 1963 912-4 67.1 0.0 222.9 8.1 6.8 5.1 0.0 55184797 1984 939*3 78.7 0.0 184.U @8.1 6.9 5.2 0.0 56360230 19d5 961.1 93.4 0.0 147.3 8.1 .7.0 5 3 0,0 57e54770 -.1 9 86-96 1 *1 11-1.0 0.0 129.5 8.1 7.2 -5: 4 0., 0-57 0 7 5 8 8 6 .29 Graph 3 Projected Changes in Residential Use 9611. 798.. 63 $4 0 X: M 4 7 CL 44 0 U) 307-- 14 31 v 1973 1976 1979 1982 1985 1988 Time 30 Graph 4 Projected Change in Recreational Use 120 95 Q) r@ 75 u) 44 45 0 20 5 1973 1976 1979 1982 1985 1988 Time 31 Graph 5 Land LoSSeS from NAT CONR between 1973 & 1.986 540 1977 1975 1973 445 !1979 355 1982 255 44 0 160 1986 65 -50 .50 150 250 350 450 Miles of Shoreline NAT 32 2. The second example is intended to represent a conservation. approach. It differs from the first in that the transfer of NAT (natural land type) and CONR (conservancy--rural land type) into any other land category is severely restricted. The key aspects of this policy are: a) NAT land is allowed to transfer into CONR, b) CONR into REC (recreational type), and c) REC into NAT. CALCULATION OF MILES CF SHCRELINE By CATEGORY 8 CATEGORIES CALC EVERY 1 YRS FROM YR 1973 FOR 13 YRS Table 11 INPUT DATA STATE AND COUNTY POPULATIONS YEAR STATE POP COUNTY POP 1973 3738300 268500 1974 3832000 276700 1975 3925800 285000 1976 4019500 293300 1977 4113200 301500 1978 4206700 309800 1979 4300600 318100 1980 4394300 326300 1981 4499100 334600 1982 4604400 342900 1983 4709500 351100 1984 4814500 359400 1985 4919600 367700 INITIAL STATE VARIABLE VALUES V-S: 143.4 26.5413.0527.5 8.1 5.4 4.1 94.3 DV-2: 7.2 .9 -0.0 -0.0 -0.0 -0.0 -0.0 .9 33 Table 12 RELATIVE DOLLAR VALUES AND ALLOWABLE TRANSFERS CATEGORY RES REC NAT CONR Shoj SHOC TRAIN SHOC 1,@ lu I lu 19 id 2u .--..-0 -, . - U 0 0 --.7 0 -- --- 2) 1 u 0 1 0 .3). ..-. 0 . - I I 1-- .0 0 -- a -- . 0 --- ---o 4) -0 -0 1 -0 -0 -0 -0 -0 5.) 1-00 .0 0 1 1 1 6) 1 0 0 u 1 0 1 1 7) 1 -0 -0 -0 1 1 0 -0 Table 13 THE OUTPUT GENERATED BY THIS PROGRAM CONSISTS OF A TABLE PRESENTING VARIAOLE VALUES THROUGH TO SEVERAL CRAPHS. YEAR RES REG NAT CONR SHOI SHOC TRANS NSHO FLOO _1973 94.3 1974 ej7.5 27*7 413*0 526.4 8.1 5.5 4*2 .0 igo6lG68 -1975 237*3 29.1 413.0 524-c 801 5.6 4.2 0.0 119034116 1976 237.0 31.0 413.0 523.1 8.1 5.8 4.,3 0.0 19000905 1977 2 j() . 7 33.3 413.0 520.8 8.1 5.9 4.5 0 .0 18 -j @'.) I 1@j G 6 1976 236.5 36.2 413-0 517.8 8.1 6.1 4.6 O.U 18,317d69 ---1979 236.2 39.9 413.0 514.2 8.1 6.2 4.7 0 ..0-18.8 6,7 2 4-5- 1980 2Jo.0 44.5 41-3.u 509.5 8.1 6.J 4*8 000 ld806395 1981 Z@5*8 50.4 413.0 50,3.7 8.1 6.5 4.9 0.0 18733U10 982---2 8.1 6.6 5.0 0 -.0-1 1983 235.3 67:1 1#13.0 487.0 8.1 6.8 5.L 0 .0 1853(-b87 78.7 413.0 475.3 8.1 6.9 5.2 0-.0 1 13t*O')52E 1965 234.8 93.4 413.0 460.7 8.1 7.0 5.3 0.0 18:1414 0 9 1 234 .5 1'. 0-4 1.3 .-0----443 1 8. 1 7.2 5.4 0. U 18 05322? 34 Graph 6 Projected Changes in Residential Use 285 240 195. o 150 (D 105 601 1973 1976 1979 1982 1985 1988 Time 35 Graph 7 Projected Change in Recreational Use 120 75 70 I-A 0 45 44 0 CA (D 20 5 1973. 1976 1979 1982 1988 Time 36 Graph 8 Land Losses from NAT CONR between 1973 1986 635. 540. 1973 0 Q) 445- 1986 $4 0 U) 350- 4-4 0 Z@ 255., 350 450 Miles of Shoreline NAT 37 In the third example, the policy used reflects another conservation approach. Land is allowed to transfer into residential type from CONR.indirectly: CONR into REC, REC into NAT, and NAT into RES. Again, the output and analytical graphs are presented below. CALCULATION OF MILES OF SHORELINE BY CATEGORY 8 CATEGORIES CALC EVERY 1 YRS FROM YR 1973 FOR 13 YRS Table 14 INPUT OATA STATE AND C0UNTY POPULATIONS YEAR STATE POP COUNTY POP 1973 3738300 268500 1974 3832000 276700 1975 3925800 285000 1976 4019500 293300 1977 4113200 301500 1978 4206700 309800 1979 4300600 318100 1980 4394300 326300 198l 4499100 334600 1982 4604400 342900 1983 4709500 351100 1984 4814500 359400 1985 4919600 367700 INITIAL STATE VARIABLE VALUES V-S: 143.4 26.5413.0527.5 8.1 5.4 4.1 94.3 DV-S: 7.2 .9 -0.0 -0.0 -0.0 -0.0 -0.0 .9 38 Table 15 RELATIVE DOLLAR VALUES AND ALLOWAELE TRANSFERS CATEGORY RES REC NAT CONP SH9I "s-Hoc-TR@'N-sq0C 5-i 0 0 19 18 20 3 0 0 1 21 1 0 3 1 0 1 1 1 3) 9 0 0 G I G 4) 1 3 0 0 a__@ c 9 1 1 1 r 7) 9) 3 a 0 0 1 1 Table 16 THE OUTPUT GENTRATF0 Bv THIS PROGRAM CO@ISISTS OF A TABLF PPESENTING VAPIA9_LE__VAL'_uE�_TH-ROUGH TIME, AND ONE TO SEVERAL GRAPHS. RES ___RTC__"NAT ___C_6NJR_ SPOI SHOC 1973 143.4 25.5 413.3 527.5 8*1 19.4 4*1 _94*3 1974 2117,C 27.7 269.4 5 2 7. 5"_ -9 - _C_ 5- 5 -_ -4 . 2 92*9 _256644L;@ 1975 410,2 213. 1 146.2 527.5 Rol 5: 6- - _4 . '_1 91.3 31746177 1976 511,11- 31.r, 45.2 52 7. !; 8.1 5*3 4*3 89.2 3 0 5 8 r) -j i 1@ J977 593,6 33*3 C.C 527.5 801 5"q 4*5 49*4 4171153@7 -8 6 0 4Pr)F)3277 -lq78 61-2.7 36.2 0.0 5?4. E@ n 1979 642,5 3q,q 0.0 S-2c.9 Rol 602 4*7 %,.C 42512,r3 19#30 64"',3 44 * 5 516 9-1 E@- 3 9 . C- 42451'@r3 iq 8 1 642.0 5J.4 C . 0 51r.4 8.j 6.5 o C 4C77--419 IqA2 64J.8 5 r. 03 C . 0 Sv:!. 13 A'j 6*6 C*C 4 77 8 q79 -1 1911 641.5 67.1 0 . C 4q:z. 7 got, 6. 1 __5 u.o C 421RCI?q6 19 f) 641.3 74.7 C. 8 @C-.j . I 6 5 C -4 96 9 r. c IqR5 64 1 q7 0 467.14 A o J 7.3 5 418' 1913 6 6140. A ill-0 0. a 44 @7. 1i gel 7 o C' 5.4 6.L, 4 1 Ij e, 39 Graph 9 Projected Changes in Residential Use 660 &/006.....Op 545 430 4 0 44 0 315 200 85 1973 1976 1979 1982 1985 1988 Time 40 Graph 10 Projected Change in Recreational Use 120 95 75 @4 0 45 4-4 0 W 20 1973 1;76 1979 1982 1985 1968 Time 41 Graph 11 Land Losses from NAj@ CONR between 1973 1986 635 540 1977 1975 1973 ...... . .... ...... . 445 1,986* 3-50 255 -50 50 150 250, 350 450 Miles of Shoreline NAT 42 V. Conclusion Following the construction and exercising of Version 3 of-the MACLUSE model, it was decided to temporarily cease the modeling effort and focus on a data-gathering project. It was felt at this point that detailed land-use information of a historical nature was required to continue the modeling phase of the project in a meaningful manner. This was necessary for several reasons. First, a knowledge of what land use types are actually involved in a pr ocess of change is necessary to better define the primary system variables of the model. Second, historical data is required to isolate the important causal factors. Third, such data is necessary to fit model parameters and to provide a comparison to model results, thus making possible a good evaluation of the forecasting power of the model. Toward this end, aerial photographs of the Snohomish County marine shoreline were obtained for the years 19471 1955, 1965 and 1969., The anzilysis of this raw data set is to be carried out and will be described in a future paper. It is anticipated that the modeling effort will continue, although it may not take the exact form of further refinements of MACLUSE. NOAA COASTAL SERVICES CrR LIBRARY 3 6668 14112738 3