Predicting future changes in climate and evaporation by a stepwise regression method

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1 Sustainability of Wate Resouces unde Inceasing Uncetainty (Poceedings of the Rabat Symposium S1, Apil 1997). IAHS Publ. no. 24, Pedicting futue changes in climate and evapoation by a stepwise egession method HUAXIA YAO & AKIRA TERAKAWA Hydology Division, Public Woks Reseach Institute, 1 Asahi, Tsukuba, Ibaaki 35, Japan MICHIO HASHINO Depatment of Civil Engineeing, The Univesity of Tokushima, 2-1 Minami-josanjima, Tokushima 77, Japan Abstact A stepwise egession method is used fo pedicting egional futue climate change unde global climate waming. Fist, 98 yeas of data fom five meteoological obsevatoies in Japan wee teated and pepaed. Second, statistical elationships between moving aveaged tempeatue, pecipitation, net adiation, humidity o wind speed wee sepaately analysed and tested fo those sites. The coelation of tempeatue with othe climate factos fo all months ae quite good. Thid, by using these egessions, the futue climate situation at aound 3 was pedicted unde a global waming scenaio of an incease of 2 C. Although changes in pecipitation, net adiation and wind speed ae diffeent at each of the five sites, thee is a consistent incease in evapoation. INTRODUCTION Thee ae two main methodologies fo pedicting futue climate change caused by global waming due to inceased geenhouse gases. One is to descibe the atmospheic system analytically and constuct a geneal ciculation model (GCM). Such a model has a physical basis, but equies extensive data and numeical computation and has limitations fo assessing egional impacts (Bad, 1994). A second option is to define statistical elationships between diffeent climate paametes which is elatively easy to apply although it has the disadvantage of not having a physical basis. Recently a stepwise egession method has been applied to the analysis of possible climate change (Hashino & Yuo, 1994). Based on 3 yeas of tempeatue and pecipitation data fom Japan, they coelated monthly pecipitation with mean monthly tempeatues, and the fluctuation in pecipitation was estimated with espect to thee possible scenaios of futue tempeatue. A simila study is descibed by Yao et al. (1995) whee fou climatic factos wee egessed with tempeatue and the pedicted climate change was applied to a hydologie model to estimate the coesponding changes in the wate cycle in a headwate basin. Results fom futhe eseach ae descibed in this pape, based on data fom five locations in Japan (Fukuoka, Hioshima, Tokushima, Kofu, Niigata). STEPWISE REGRESSION METHOD Intoduction Relationships between climate vaiables can be detemined fom histoical meteoological data, and these elationships can be used to estimate the sensitivities of climate

2 34 Huaxia Yao et al. vaiables to climate change scenaios. The pinciple of a stepwise egession method was descibed in detail by Enslein et al. (1977) and enables the most significant independent vaiables to be selected and coefficients of egession equations to be estimated. Six independent vaiables ae initially assumed to be epesentative of tempeatue chaacteistics. The dependent vaiable Y (ainfall, net adiation, wind speed o humidity) may be expessed by a linea function of these six independent vaiables (X x ~X 6 ) as follows: Y = b + b x X x + b 2 X 2 + b 3 X 3 + b 4 X 4 + b 5 X 5 + b 6 X 6 (1) whee b is the egession coefficient calculated by the stepwise egession method. Vaiable teatment Thee ae thee aspects elating to the analysis of the climate data. Fist it is evident that climate changes non-unifomly thoughout a yea. Theefoe, it is difficult to eceate the oiginal annual seies and in ode to analyse the long tem climate vaiability a -yea moving aveage has been used. Second, climate data usually exhibit obvious seasonality and theefoe monthly athe than annual statistical elationships ae sought fo evey unknown dependent vaiable. Thid, the independent and dependent vaiables ae tansfomed to make them non-dimensional. Supposing that thee aetv yeas of monthly data. They can be defined initially as: monthly aveage tempeatue T{i,j), pecipitation P(i,j), net adiationr(i, J), humidity H(i, J), and wind speed U(i, j), whee the numbe of yea i = 1, 2,..., N and the numbe of month/' = 1, 2,..., 12. Data of Af yeas is pocessed with a -yea moving aveage, and (N + 1) values ae poduced fo each vaiable as follows: 1 T. 2 o(/v<) = ^ilw + k-l,/) (2a) f 1 1 R aov,k) = ±LW+k-lJ) f (2c) H m2 o(jm =ie^' + *-W) 1=1 (2d) in which k is the numbe of the moving aveage (k = 1,2,..., N + 1). The tempeatue is tansfomed to a non-dimensional fom. Among seveal foms tied, the logaithm of absolute tempeatue was found to be the best and a basic vaiable is defined as:

3 Pedicting futue changes in climate and evapoation 341 X T (j,k) = In T m(j,k)+273 A (j) whee Aj(j) is the total aveage of moving aveage values fo each month, and is expessed as: A T (j) 1 7V W+1-7 E W/.*> + 1 jfc=l Futhemoe, a new seies of data T b (i,j) is ceated fom the oiginal tempeatue data fo the pupose of inceasing data volume, simply by means of aveaging the value of one month and the value of the fome month, expessed as:. nu-vnj) (5) This new data is also teated by a moving aveage: (3) (4) t (6) The moving aveage values ae also tansfomed into a non-dimensional fom, and anothe basic vaiable is poduced as: X Tb (j,k) = In T hm (j,k) +273 A Tb (j) +273 whee the total aveage is witten as: A Th (J) = N+l 1 iv + 1 " m2o(/ ' /:) Finally the six independent tempeatue vaiables ae defined as: (V) (8) A.1 Ji-j* x 3 = x T X*=X, Tb (9a) (9c) (9e) X 2 = X T X 4 ~ X 6 = Similaly the dependent vaiables (pecipitation P(i, j), net adiation R(i, j), humidity H(i, j) and wind U(i, j)) ae tansfomed into moving aveage and nondimensional foms as follows: X Tb X Tb (9b) (9d) (9f) Y P = In f m2o(/>^) Ap(j) (a) In R m(j> k ) (b) In AdJ) (c) In A R (J) _ (lod) Ait!)

4 342 Huaxia Yao et al. whee P m (j, k), R m (j, k), H m (j, k), U m (J, k) and A P (j), A R (j), A H (j), Afj) ae the moving aveage and total aveage espectively fo pecipitation, net adiation, humidity and wind speed. The total aveages ae calculated as: N~19 ^-w^ig'-<''» N~19 <1Ia) W Tè* H ->«M k=\ N-19 "^ NttS "*> (llc) <1W) REGRESSION RESULTS Data fom five meteoological obsevatoies in Japan wee used in the analysis. They ae Fukuoka in the west, Hioshima in the southwest, Tokushima in the south, Kofu in the cente, and Niigata in the noth. A total of 98 yeas of data ( ) ae available fo each station. These data ae standadized and each dependent vaiable (Y P, Y R, Y H, Y v ) egessed with the six independent vaiables (X h i = 1, 2,..., 6) using a stepwise egession method. As an example, the paametes b t and the coelation coefficient of each month fo Niigata ae listed in Table 1. The coelation coefficients ae vey high and only the independent vaiables X x and X 4 ae chosen. The estimated moving aveage and the obseved values ae plotted in Fig. 1 fo Niigata. Pecipitation, net adiation and humidity ae well pedicted in all months, but wind speed is estimated less well. These esults indicate a statistical elationship between climate vaiability and tempeatue and can be used to estimate the impact of futue climate vaiability. PREDICTING CLIMATE CHANGES Tempeatue incease Consideable eseach effot has been diected towads estimating the esponse of global and egional climate to inceased geenhouse gases. The change in tempeatue has been studied most extensively and compaative esults have been gained using GCM simulations (JM A, 199JUCHWR, 1992, 1995). Assuming the concentation of geenhouse gases in the atmosphee inceases continuously at the pesent ate, it will double by aound 3 compaed with The global aveage tempeatue fo the yea 3 is estimated to incease by C compaed with the mean tempeatue fo the past yeas.

5 Pedicting futue changes in climate and evapoation 343 Table 1 Regession paametes and coelation coefficient. Month pecipitation Net adiation (- 3 ) bx b bo * * Month humidity Wind speed *o(- 3 ) b> b 4 bo b t b In this pape, a hypothetical scenaio of an incease of 2. C is used. Tempeatues in 3 ae given by T(N + 4, j) = A^) + 2., whee Aj(j) is the total aveage of tempeatues duing N yeas ( ) and y is the month numbe. Futhemoe, it is assumed that the tempeatue ise fom 1991 to 4 would take place in a linea manne. Pedicted esults The statistical elationship of tempeatue to othe climatic factos was deived fom long tem data ecods and is assumed epesentative of the climate system of both the pesent and the futue. It may be supposed that the climate system itself will not change damatically unde the global waming condition, and that the egession elationships can be used to estimate futue conditions. Regading the yea of 3, a -yea aveage tempeatue is poduced fom the assumed tempeatue seies of 214. This value is then substituted into the egession fomula and coesponding aveage values fo monthly pecipitation, net adiation, humidity and wind speed ae calculated and pedicted espectively. These

6 344 Huaxia Yao et al. 4 obseved Jan : Feb ' : Ma : Ap May : Jun. Jul Aug Se P Oct Nov Uec ' Annual egessed (a) Pecipitation (mm) : - : - L " " Jan : Feb Ma Ap May : Jun Jul Aug Sep : Oct Nov '_ Dec - ' 1 ' 6 Annual (b) Net adiation (mm). 6 Jan Feb Ma Ap May Jun Jul Aug Sep Oct Nov Jan Feb Ma Ap May Jun Jul Aug Sep Oct Nov 6 Dec Annual (c) Humidity (%) 198 Dec 8 Annual (d) Wind speed (m/s) Fig. 1 Obseved and pedicted climate vaiables fo Niigita.

7 Pedicting futue changes in climate and evapoation Tempeatue (%) i m i F?HI. cm i.m Radiation (%) H Humidity(%) Tempeatue (%)_ il, m, jpi.il. 3! Radiation (%) - -3 hj m ^ Jl -H Humidity(%) ^ c a i " Tempeatue (%) 3 - [M.sn.-i.FI, JM -H H 1 1 (- : Radiation (%) Ta Humidity (%) BS oi ni B H n HI ma EBL Potential Evapoation (%) MAMJJ AS ON DJF (a) Fukuoka Ann ^H &a EH. M. _ca Potential Evapoation (%) MAMJJ AS ON DJF (b) Hioshima Ann _Ei_ Potential Evapoation (%) MAMJJ AS ON DJF Ann (c) Tokushima 3 - Tempeatue (%) "F~l. f~1, ~l, n,,,m ET H _+. 1 (_ Radiation (%) JIL,, H 1 1 H Humidity (%) TT - \ Tempeatue (%) ii..n.n., Radiation (%) ^ m m nn P3 _H Humidity (%) -H H 3 Potential Evapoation (%) \ potential Evapoation (%) MAM JJ AS ON DJF Ann MAM JJ AS ON DJF Ann (d) Kofu (e) Niigata Fig. 2 Estimated seasonal climate changes fo five sites. EH" pedicted values of 214 ae compaed with those of which epesent the pesent climate status climate changes (in pecentages) can be detemined, as shown in Fig. 2 fo five sites. Only seasonal changes ae shown. Usually thee ae five seasons in Japan: sping (Mach-Apil-May, MAM), ainy summe (June-July, JJ), hot summe (August-Septembe, AS), autumn (Octobe-Novembe, ON) and winte (Decembe- Januay-Febuay, DJF).

8 346 Huaxia Yao et al. Finally, the change in potential evapoation is estimated using the Penman equation, which includes tempeatue, net adiation, humidity and wind speed. Change in wind speed is not consideed because it is difficult to estimate its esponse to climate change. Change in evapoation is also estimated and plotted in Fig. 2. Thee ae two conclusive points about climate change esults fom these sites. Fist, unde the same scenaio of futue tempeatue ise, seasonal and annual climate at each site seems to change in a diffeent way. Fo example, annual pecipitation would incease in Fukuoka and Tokushima, but decease in Hioshima, Kofu and Niigata and annual net adiation would incease in Fukuoka, Kofu and Niigata, but decease in Hioshima and Tokushima. Howeve, humidity deceases in almost all seasons fo all sites, a diffeence which might be elated to the topogaphical condition of each site. It may also mean that local climate esponds to global waming but thee ae not consistent egional tends. Potential evapoation inceases seasonally and annually fo all sites, although the change in climate is diffeent. The eason fo this is that tempeatues ae estimated to become highe and humidity lowe, both of which incease evapoative demand. Theefoe, wate demand would incease, which might esult in moe sevee wate supply conditions in futue. REFERENCES Bad, B. (1994) Biospheic Aspects of the Hydological Cycle (BAHC) Focus 4: the weathe geneato poject. HABC Repot no. 4, Enslein, K., Ralston, A. & Wilf, H. S. (1977) Statistical Methods fo Digital Computes. Wiley, New Yok, USA. Hashino, M. & Yue, S. (1994) Statistical analysis of effects of monthly tempeatue on monthly pecipitation popeties. In: Poc. Second Symp. on Eath Envionment (Tokyo), JSCE. JMA (199) Climate Changes as Geenhouse Gases Incease (in Japanese). Japan Meteoological Agency, Pess of Ministy of Finance,Japan. JUCHWR (1992) Poc. Wokshop on the Effects of Global Climate Change on Hydology and Wate Resouces at the Catchment Scale. Japan-US Committee on Hydology, Wate Resouces and Global Climate Change, Tuskuba, Japan. JUCH WR ( 1995) Poc. Thid PWRI- USGS Wokshop on Hydology, Wate Resouces and Global Climate Change. Japan- US Committee on Hydology, Wate Resouces and Global Climate Change, Tuskuba, Japan. Yao, H., Hashino, M. & Yoshida, H. (1995) Pediction of futue changes in climate and wate cycle by using step-wise egession method. J. Jpn Soc. Hydol. Wat. Resou. 8,