tag:blogger.com,1999:blog-7729093380675162051.post8452315213897850018..comments2023-06-01T16:34:22.422+10:00Comments on moyhu: TempLS V2 Math basisNick Stokeshttp://www.blogger.com/profile/06377413236983002873noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-7729093380675162051.post-38025087162496007172012-03-29T22:26:59.532+11:002012-03-29T22:26:59.532+11:00Kevin,
It has the form of a general expansion in o...Kevin,<br />It has the form of a general expansion in orthogonal functions. If J_y is linear, say, then it is effectively a spherical harmonics expansion of trend. The coefficients are fitted jointly with the station offsets. <br /><br />The way I do it by month means that really you just couple a SH series for a single month temp with the local offsets. Although fitting jointly has some theoretical advantages, I think in practice the coupling is weak, and as I said at SKS, there isn't much difference to just calculating the anomalies without space dependence and fitting the SH coefficients afterwards.<br /><br />In principle J_y could be any function of time. But because you have only one vs a whole family of space functions, it should be something fundamental. I've used just linear, so it's just fitting a spatially varying trend, and a sort of pulse function. The pulse function isn't saying that that is how the temp actually progressed. It's just saying that you weight the current month or year differently. You only look at past values to get local averages.<br /><br />The main practical advantage of the joint fitting is that you avoid the troubles of GISS etc in dealing with an anomaly base period where some stations don't have data.<br /><br />Let me try to put it another way. If you were doing a 2D fourier series on a square, say, you would make a series a_jk sin(jx) sin(ky) (plus cos terms etc). j and k would vary over a similar range. Here I'm in effect reducing one range to a single value. That is time, and the (partial) justification of the lopsidedness is that we have more data in space than in time (measured in years).Nick Stokeshttps://www.blogger.com/profile/06377413236983002873noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-4223794435810218492012-03-29T21:52:06.299+11:002012-03-29T21:52:06.299+11:00OK, I'm confused on spatial dependence. You...OK, I'm confused on spatial dependence. You're using Psk Hk to account for a geographical dependence. But that term is time-independent, so should look the same in every map. And you're scaling it by a factor which varies with year.<br />So what the model is saying is that any change over time happens according to a geographical function scaled by a time function, plus the local adjustment. Is that right?<br />I don't understand the bullet points describing J at all, I'm afraid.<br />Kevin CAnonymousnoreply@blogger.com