Modeling maximum daily temperature using a varying coefficient regression model

A novel clustering method for bivariate functional data is proposed to group streams based on their water–air temperature relationship. A distance measure is developed for bivariate curves by using a time‐varying coefficient model and a weighting scheme. This distance is also adjusted by spatial correlation of streams via the variogram. Therefore, the proposed distance not only measures the difference among the streams with respect to their water–air temperature relationship but also accounts for spatial correlation among the streams. The proposed clustering method is applied to 62 streams in Southeast US that have paired air–water temperature measured over a ten‐month period. The results show that streams in the same cluster reflect common characteristics such as solar radiation, percent forest and elevation. Copyright © 2015 John Wiley & Sons, Ltd.

“…() and Li et al. (). For each site i , the estimated coefficients

{boldX}_{i} (t) = ({\overset{θ}{true}}_{0 i} (t), {\overset{θ}{true}}_{1 i} (t))

are the profiles of the bivariate curves used in the following analysis.…”

Section: Proposed Clustering Methodsmentioning

confidence: 97%

“…For site i , we describe the varying coefficient model (Li et al. ) for the air–water temperature relationship as

\begin{matrix} W_{i} (t) = θ_{0 i} (t) + A_{i} (t) θ_{1 i} (t) + ε_{i} (t), \end{matrix}

where

θ_{0 i} (t) = \sum_{j = 1}^{K} α_{ij} b_{ij} (t)

and

θ_{1 i} (t) = \sum_{j = 1}^{K} β_{ij} b_{ij} (t)

are varying intercept and slope coefficients. The ε i ( t ) is the error term in the model with E ( ε i ( t )) = 0 and var

(ε_{i} (t)) = σ_{i}^{2} (t)

.…”

Section: Proposed Clustering Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Bivariate functional data clustering: grouping streams based on a varying coefficient model of the stream water and air temperature relationship

Deng

Dolloff

et al. 2015

Missing data imputation for paired stream and air temperature sensor data

Deng

Smith

2016

Self Cite

Stream water temperature is an important factor in determining the impact of climate change on hydrologic systems. Near continuous monitoring of air and stream temperatures over large spatial scales is possible due to inexpensive temperature recorders. However, missing water temperature data commonly occur due to the failure or loss of equipment. Missing data creates difficulties in modeling relationships between air and stream water temperatures. It also imposes challenges if the objective is an analysis, for example, clustering streams in terms of the effect of changes in water temperature. In this work, we propose to use a novel spatial–temporal varying coefficient model to impute missing water temperatures. Modeling the relationship between air and water temperature over time and space increases the effectiveness of imputing the missing water temperatures. A parameter estimation method is developed, which utilizes the temporal covariation in the relationship, borrows strength from neighboring stream sites, and is useful for imputing sequences of missing data. A simulation study is conducted to examine the performance of the proposed method in comparison with several existing imputation methods. The proposed method is applied to cluster streams with missing water temperatures into groups from 156 streams with meaningful interpretations.

Regression methods for the appearances of extremes in climate data

Bláha

Kane

et al. 2022

For any given city, on any calendar day, there will be record high and low temperatures. Which record occurred earlier? If there is a trend towards warming then, intuitively, there should be a preponderance of record highs occurring more recently than the record lows for each of the 365 calendar days. We are interested in modeling the joint distribution of appearances of the extremes but not these values themselves. We develop a bivariate discrete distribution modeling the joint indices of maximum and minimum in a sequence of independent random variables sampled from different distributions. We assume these distributions share a proportional hazard rate and develop regression methods for these paired values. This approach has reasonable power to detect a small mean change over a decade. Using readily available public data, we examine the daily calendar extreme values of five US cities for the decade 2011–2020. We develop linear regression models for these data, describe models to account for calendar‐date dependence, and use diagnostic measures to detect remarkable observations.