[R-sig-ME] Warning message with lmer function

[FMH]

Dear All,

I have a set of data which consist of 1575 groups with 11 temperature values in each group. This temperature is recorded across 11 different depths of the sea. The R script are shown below:

############################################################
#Temp : Temperature
#dp1, dp2, dp3 : covariate with respect to linear, quadratic and cubic terms
#group : 1575 groups in which there are 11 observations in each group
#sub3 : Data set 1
#set3 : Data set 2

dp1 <- rep(rev(seq(1,51, by = 5)),1575)
dp2 <- dp1^2
dp3 <- dp1^3
group <- rep(1:1575, each = 11)
set3 <- data.frame(sub3, dp1, dp2, dp3)
(lm.lme3 <- lmer(Temp ~ dp1 + dp2 + dp3 + (dp1 + dp2 + dp3|group), data = set3))
############################################################


I tried to fit a linear mixed model via lmer function, with all the fixed and random effects are included, but there is a 'Warning' message given after the output, as shown below.


##############################################
Linear mixed model fit by REML 
Formula: Temp ~ dp1 + dp2 + dp3 + (dp1 + dp2 + dp3 | group) 
   Data: set3 
   AIC   BIC logLik deviance REMLdev
 65627 65743 -32799    65539   65597
Random effects:
 Groups   Name        Variance   Std.Dev.   Corr                 
 group    (Intercept) 4.8336e-01 6.9524e-01                      
          dp1         5.2199e-04 2.2847e-02  0.000               
          dp2         3.0528e-07 5.5252e-04  0.000  0.000        
          dp3         7.8888e-11 8.8819e-06 -0.966  0.000  0.000 
 Residual             1.9939e+00 1.4120e+00                      
Number of obs: 17325, groups: group, 1575
Fixed effects:
              Estimate Std. Error t value
(Intercept)  1.363e+01  4.043e-02   337.1
dp1         -2.930e-01  6.328e-03   -46.3
dp2          3.924e-03  2.870e-04    13.7
dp3         -1.900e-05  3.628e-06    -5.2
Correlation of Fixed Effects:
    (Intr) dp1    dp2   
dp1 -0.739              
dp2  0.616 -0.959       
dp3 -0.563  0.904 -0.982

Warning message:
In mer_finalize(ans) : false convergence (8)
#############################################


Does the output given is valid? Could someone please advice on this message.

Thank you
Fir